Finite Group Databasebeta

← C71×#61627 #31882499

Subgroups — C71×#61627 #31882499

Order 18176.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3540C211yesmaximal, characteristic, complemented
2C71×#3489C211yesmaximal, characteristic, complemented
3C71×#3329C211yesmaximal, characteristic, complemented
4C71×#3328C211yesmaximal, characteristic, complemented
5C71×#3321C211yesmaximal, characteristic, complemented
6C71×#3319C211yesmaximal, characteristic, complemented
7C71×#3313C211yesmaximal, characteristic, complemented
8C71×#3311C211yesmaximal, characteristic, complemented
9C71×#3303C211yesmaximal, characteristic, complemented
10C71×#3302C211yesmaximal, characteristic, complemented
11C71×#3285C211yesmaximal, characteristic, complemented
12C71×#3282C211yesmaximal, characteristic, complemented
13C71×#3275C211yesmaximal, characteristic, complemented
14C71×#3273C211yesmaximal, characteristic, complemented
15C71×#3270C211yesmaximal, characteristic, complemented
16C71×#3269C211yesmaximal, characteristic, complemented
17C71×#3267C211yesmaximal, characteristic, complemented
18C71×#3266C211yesmaximal, characteristic, complemented
19C71×#3225C211yesmaximal, characteristic, complemented
20C71×#3225C211yesmaximal, characteristic, complemented
21C71×#3201C211yesmaximal, characteristic, complemented
22C71×#3198C211yesmaximal, characteristic, complemented
23C71×#3196C211yesmaximal, characteristic, complemented
24C71×#3190C211yesmaximal, characteristic, complemented
25C71×#3125C211yesmaximal, characteristic, complemented
26C71×#3124C211yesmaximal, characteristic, complemented
27C71×#3011C211yesmaximal, characteristic, complemented
28C71×#3010C211yesmaximal, characteristic, complemented
29C71×#3005C211yesmaximal, characteristic, complemented
30C71×#3002C211yesmaximal, characteristic, complemented
31C71×#2976C211yesmaximal, characteristic, complemented
32C2×2−1+4×C71C2211yescharacteristic
33C22×#41×C71C2211yescharacteristic, complemented
34C2×#137×C71C2211yescharacteristic
35C2×#137×C71C2211yescharacteristic, complemented
36C2×AGL(1,ℤ/8)×C71C2211yescharacteristic
37C2×AGL(1,ℤ/8)×C71C2211yescharacteristic, complemented
38C2×#135×C71C2211yescharacteristic
39C2×#135×C71C2211yescharacteristic
40C22×Q16×C71C2211yescharacteristic, complemented
41C22×SD16×C71C2211yescharacteristic, complemented
42H(3,𝔽4)×C71—21no—
43#560×C71—21no—
44#559×C71—21no—
45#556×C71C2211yescharacteristic
46#556×C71C2211yescharacteristic, complemented
47#555×C71C2211yescharacteristic
48#555×C71C2211yescharacteristic, complemented
49#551×C71—21no—
50D4×Q8×C71C2211yescharacteristic
51D4×Q8×C71C2211yescharacteristic, complemented
52#548×C71C2211yescharacteristic
53#548×C71C2211yescharacteristic
54#548×C71C2211yescharacteristic, complemented
55#548×C71C2211yescharacteristic, complemented
56#547×C71—21no—
57#547×C71—21no—
58#547×C71C2211yescharacteristic
59#547×C71C2211yescharacteristic, complemented
60#546×C71—21no—
61#546×C71—21no—
62#546×C71C2211yescharacteristic
63#546×C71C2211yescharacteristic
64#546×C71C2211yescharacteristic, complemented
65#546×C71C2211yescharacteristic, complemented
66#542×C71—21no—
67#542×C71—21no—
68#542×C71C2211yescharacteristic, complemented
69#542×C71C2211yescharacteristic, complemented
70#538×C71—21no—
71#538×C71—21no—
72#537×C71—21no—
73#537×C71C2211yescharacteristic
74#536×C71—21no—
75#536×C71C2211yescharacteristic, complemented
76#536×C71C2211yescharacteristic, complemented
77#535×C71C2211yescharacteristic, complemented
78#525×C71—21no—
79#525×C71C2211yescharacteristic
80#525×C71C2211yescharacteristic
81#525×C71C2211yescharacteristic
82C2×C22⋊Q8×C71—21no—
83C2×C22⋊Q8×C71C2211yescharacteristic, complemented
84#520×C71C2211yescharacteristic, complemented
85#497×C71C2211yescharacteristic, complemented
86#497×C71C2211yescharacteristic, complemented
87#495×C71C2211yescharacteristic, complemented
88#495×C71C2211yescharacteristic, complemented
89#489×C71C2211yescharacteristic, complemented
90#489×C71C2211yescharacteristic, complemented
91#487×C71C2211yescharacteristic, complemented
92#487×C71C2211yescharacteristic, complemented
93#485×C71C2211yescharacteristic, complemented
94#485×C71C2211yescharacteristic, complemented
95#485×C71C2211yescharacteristic, complemented
96#485×C71C2211yescharacteristic, complemented
97#485×C71C2211yescharacteristic, complemented
98#485×C71C2211yescharacteristic, complemented
99#484×C71C2211yescharacteristic, complemented
100#483×C71C2211yescharacteristic, complemented
101#482×C71C2211yescharacteristic, complemented
102#482×C71C2211yescharacteristic, complemented
103#481×C71C2211yescharacteristic, complemented
104#480×C71C2211yescharacteristic, complemented
105#477×C71C2211yescharacteristic, complemented
106#476×C71C2211yescharacteristic, complemented
107#475×C71C2211yescharacteristic, complemented
108#474×C71C2211yescharacteristic, complemented
109#470×C71C2211yescharacteristic, complemented
110#470×C71C2211yescharacteristic, complemented
111#470×C71C2211yescharacteristic, complemented
112#469×C71C2211yescharacteristic, complemented
113#468×C71C2211yescharacteristic
114#468×C71C2211yescharacteristic
115#468×C71C2211yescharacteristic, complemented
116#468×C71C2211yescharacteristic, complemented
117#467×C71C2211yescharacteristic, complemented
118#467×C71C2211yescharacteristic, complemented
119#467×C71C2211yescharacteristic, complemented
120#466×C71C2211yescharacteristic, complemented
121#465×C71C2211yescharacteristic, complemented
122#465×C71C2211yescharacteristic, complemented
123#465×C71C2211yescharacteristic, complemented
124#465×C71C2211yescharacteristic, complemented
125#464×C71C2211yescharacteristic, complemented
126#464×C71C2211yescharacteristic, complemented
127#464×C71C2211yescharacteristic, complemented
128#464×C71C2211yescharacteristic, complemented
129#463×C71C2211yescharacteristic, complemented
130#463×C71C2211yescharacteristic, complemented
131#463×C71C2211yescharacteristic, complemented
132#463×C71C2211yescharacteristic, complemented
133#462×C71C2211yescharacteristic, complemented
134#462×C71C2211yescharacteristic, complemented
135#461×C71C2211yescharacteristic, complemented
136#461×C71C2211yescharacteristic, complemented
137#452×C71C2211yescharacteristic
138#452×C71C2211yescharacteristic
139#452×C71C2211yescharacteristic, complemented
140#452×C71C2211yescharacteristic, complemented
141#452×C71C2211yescharacteristic, complemented
142#452×C71C2211yescharacteristic, complemented
143#452×C71C2211yescharacteristic, complemented
144#452×C71C2211yescharacteristic, complemented
145#452×C71C2211yescharacteristic, complemented
146#452×C71C2211yescharacteristic, complemented
147#452×C71C2211yescharacteristic, complemented
148#452×C71C2211yescharacteristic, complemented
149#451×C71C2211yescharacteristic, complemented
150#451×C71C2211yescharacteristic, complemented
151#451×C71C2211yescharacteristic, complemented
152#451×C71C2211yescharacteristic, complemented
153#451×C71C2211yescharacteristic, complemented
154#451×C71C2211yescharacteristic, complemented
155#450×C71C2211yescharacteristic, complemented
156#450×C71C2211yescharacteristic, complemented
157#449×C71C2211yescharacteristic
158#449×C71C2211yescharacteristic
159#449×C71C2211yescharacteristic
160#449×C71C2211yescharacteristic
161#449×C71C2211yescharacteristic
162#449×C71C2211yescharacteristic
163#449×C71C2211yescharacteristic, complemented
164#449×C71C2211yescharacteristic, complemented
165#448×C71C2211yescharacteristic
166#448×C71C2211yescharacteristic, complemented
167#448×C71C2211yescharacteristic, complemented
168#448×C71C2211yescharacteristic, complemented
169#448×C71C2211yescharacteristic, complemented
170#448×C71C2211yescharacteristic, complemented
171#447×C71C2211yescharacteristic
172#447×C71C2211yescharacteristic, complemented
173#442×C71C2211yescharacteristic, complemented
174#441×C71C2211yescharacteristic, complemented
175#440×C71C2211yescharacteristic, complemented
176#440×C71C2211yescharacteristic, complemented
177C4×Q16×C71C2211yescharacteristic, complemented
178C4×SD16×C71C2211yescharacteristic, complemented
179C4×SD16×C71C2211yescharacteristic, complemented
180C4×D8×C71C2211yescharacteristic, complemented
181#436×C71C2211yescharacteristic
182#436×C71C2211yescharacteristic, complemented
183#435×C71C2211yescharacteristic
184#435×C71C2211yescharacteristic, complemented
185#435×C71C2211yescharacteristic, complemented
186#435×C71C2211yescharacteristic, complemented
187C8×D4×C71C2211yescharacteristic, complemented
188C8×D4×C71C2211yescharacteristic, complemented
189#433×C71C2211yescharacteristic, complemented
190#433×C71C2211yescharacteristic, complemented
191#419×C71C2211yescharacteristic, complemented
192#419×C71C2211yescharacteristic, complemented
193#419×C71C2211yescharacteristic, complemented
194#418×C71C2211yescharacteristic, complemented
195#416×C71C2211yescharacteristic, complemented
196#416×C71C2211yescharacteristic, complemented
197#416×C71C2211yescharacteristic, complemented
198#416×C71C2211yescharacteristic, complemented
199#408×C71C2211yescharacteristic, complemented
200#408×C71C2211yescharacteristic, complemented
201#407×C71C2211yescharacteristic, complemented
202C2×C22⋊C8×C71C2211yescharacteristic, complemented
2032−1+4×C71—42no—
2042−1+4×C71—42no—
205C2×#41×C71—21no—
206C2×#41×C71—21no—
207C2×#41×C71—21no—
208C2×#41×C71—21no—
209C2×#41×C71—21no—
210C2×#41×C71—42no—
211C2×#41×C71—42no—
212C2×#41×C71C2311yescharacteristic
213C2×#41×C71C2311yescharacteristic
214C2×#41×C71C2311yescharacteristic
215C2×#41×C71C2311yescharacteristic
216C2×#41×C71C2311yescharacteristic
217C2×#41×C71C2311yescharacteristic
218C2×#41×C71C2311yescharacteristic
219C2×#41×C71C2311yescharacteristic
220C2×#41×C71C2311yescharacteristic
221C22×Q8×C71—21no—
222C22×Q8×C71C2311yescharacteristic
223C22×Q8×C71C2311yescharacteristic
224C22×Q8×C71C2311yescharacteristic
225C22×Q8×C71C2311yescharacteristic
226C22×Q8×C71C2311yescharacteristic
227C22×D4×C71—21no—
228C22×D4×C71C2311yescharacteristic
229C22×D4×C71C2311yescharacteristic
230C23×C4×C71—21no—
231C23×C4×C71C2311yescharacteristic
232#137×C71—42no—
233#137×C71—42no—
234AGL(1,ℤ/8)×C71—42no—
235AGL(1,ℤ/8)×C71—42no—
236#135×C71—42no—
237#135×C71—42no—
238C2×Q16×C71—42no—
239C2×Q16×C71C2311yescharacteristic
240C2×Q16×C71C2311yescharacteristic
241C2×Q16×C71C2311yescharacteristic
242C2×Q16×C71C2311yescharacteristic
243C2×Q16×C71C2311yescharacteristic
244C2×Q16×C71C2311yescharacteristic
245C2×Q16×C71C2311yescharacteristic
246C2×Q16×C71C2311yescharacteristic
247C2×SD16×C71—42no—
248C2×SD16×C71C2311yescharacteristic
249C2×SD16×C71C2311yescharacteristic
250C2×SD16×C71C2311yescharacteristic
251C2×SD16×C71C2311yescharacteristic
252C2×SD16×C71C2311yescharacteristic
253C2×SD16×C71C2311yescharacteristic
254C2×SD16×C71C2311yescharacteristic
255C2×SD16×C71C2311yescharacteristic
256C2×SD16×C71C2311yescharacteristic
257C2×SD16×C71C2311yescharacteristic
258C2×SD16×C71C2311yescharacteristic
259C2×SD16×C71C2311yescharacteristic
260C2×D8×C71C2311yescharacteristic
261C2×D8×C71C2311yescharacteristic
262C2×D8×C71C2311yescharacteristic
263C2×D8×C71C2311yescharacteristic
264C2×M16×C71C2311yescharacteristic
265C2×M16×C71C2311yescharacteristic
266C2×M16×C71C2311yescharacteristic
267C2×M16×C71C2311yescharacteristic
268C22×C8×C71C2311yescharacteristic
269C22×C8×C71C2311yescharacteristic
270C22×C8×C71C2311yescharacteristic
271C22×C8×C71C2311yescharacteristic
272C4⋊Q8×C71—21no—
273C4⋊Q8×C71—21no—
274C4⋊Q8×C71—21no—
275C4⋊Q8×C71C2311yescharacteristic
276C4⋊Q8×C71C2311yescharacteristic
277C4⋊Q8×C71C2311yescharacteristic
278C4⋊Q8×C71C2311yescharacteristic
279#127×C71—21no—
280#126×C71—21no—
281#126×C71—21no—
282#126×C71—21no—
283#126×C71—21no—
284#126×C71—21no—
285#126×C71—21no—
286#124×C71—21no—
287#124×C71—21no—
288#124×C71—21no—
289#124×C71—21no—
290#124×C71—21no—
291#124×C71—21no—
292#124×C71—21no—
293#124×C71—21no—
294#124×C71—21no—
295#124×C71—21no—
296#124×C71—21no—
297#124×C71—21no—
298#124×C71—21no—
299#124×C71—21no—
300#124×C71C2311yescharacteristic
301#124×C71C2311yescharacteristic
302#124×C71C2311yescharacteristic
303#124×C71C2311yescharacteristic
304#123×C71—21no—
305#123×C71—21no—
306#123×C71—21no—
307#123×C71—21no—
308#123×C71—21no—
309#123×C71—21no—
310#123×C71—21no—
311#123×C71—21no—
312#123×C71—21no—
313#123×C71—21no—
314#123×C71—21no—
315#123×C71—21no—
316#123×C71—21no—
317#123×C71—21no—
318#123×C71—21no—
319#123×C71—21no—
320#123×C71D411yescharacteristic
321#123×C71D411yescharacteristic
322C22⋊Q8×C71—21no—
323C22⋊Q8×C71—21no—
324C22⋊Q8×C71—21no—
325C22⋊Q8×C71—21no—
326C22⋊Q8×C71—21no—
327C22⋊Q8×C71—21no—
328C22⋊Q8×C71—21no—
329C22⋊Q8×C71—21no—
330C22⋊Q8×C71—21no—
331C22⋊Q8×C71—21no—
332C22⋊Q8×C71—21no—
333C22⋊Q8×C71—21no—
334C22⋊Q8×C71—21no—
335C22⋊Q8×C71—21no—
336C22⋊Q8×C71—21no—
337C22⋊Q8×C71D411yescharacteristic
338C22⋊Q8×C71D411yescharacteristic
339C22⋊Q8×C71C2311yescharacteristic
340C22⋊Q8×C71C2311yescharacteristic
341C22⋊Q8×C71C2311yescharacteristic
342C22⋊Q8×C71C2311yescharacteristic
343C22⋊Q8×C71C2311yescharacteristic
344C22⋊Q8×C71C2311yescharacteristic
345C22⋊Q8×C71C2311yescharacteristic
346C22⋊Q8×C71C2311yescharacteristic
347C22⋊Q8×C71C2311yescharacteristic
348C22⋊Q8×C71C2311yescharacteristic
349C22⋊Q8×C71C2311yescharacteristic
350C22⋊Q8×C71C2311yescharacteristic
351#121×C71—21no—
352#121×C71—21no—
353#121×C71—21no—
354#121×C71—21no—
355#121×C71—21no—
356#121×C71—21no—
357#121×C71—21no—
358#121×C71—21no—
359#121×C71—21no—
360#121×C71—21no—
361#121×C71—21no—
362#121×C71—21no—
363#121×C71—21no—
364#121×C71—21no—
365#121×C71—21no—
366#121×C71D411yescharacteristic
367#121×C71D411yescharacteristic
368#121×C71C2311yescharacteristic
369#121×C71C2311yescharacteristic
370#121×C71C2311yescharacteristic
371#121×C71C2311yescharacteristic
372#121×C71C2311yescharacteristic
373#121×C71C2311yescharacteristic
374#121×C71C2311yescharacteristic
375#121×C71C2311yescharacteristic
376#120×C71—21no—
377#120×C71—21no—
378#120×C71—21no—
379#120×C71—21no—
380#120×C71—21no—
381#120×C71—21no—
382#120×C71—21no—
383#120×C71—21no—
384#120×C71D411yescharacteristic
385#120×C71D411yescharacteristic
386C4×Q8×C71—21no—
387C4×Q8×C71—21no—
388C4×Q8×C71C2311yescharacteristic
389C4×Q8×C71C2311yescharacteristic
390C4×Q8×C71C2311yescharacteristic
391C4×Q8×C71C2311yescharacteristic
392C4×D4×C71—21no—
393C4×D4×C71—21no—
394C4×D4×C71—21no—
395C4×D4×C71—21no—
396C4×D4×C71—21no—
397C4×D4×C71—21no—
398C4×D4×C71—21no—
399C4×D4×C71—21no—
400C4×D4×C71—21no—
401C4×D4×C71—21no—
402C4×D4×C71—21no—
403C4×D4×C71—21no—
404C4×D4×C71C2311yescharacteristic
405C4×D4×C71C2311yescharacteristic
406C4×D4×C71C2311yescharacteristic
407C4×D4×C71C2311yescharacteristic
408C4×D4×C71C2311yescharacteristic
409C4×D4×C71C2311yescharacteristic
410C4×D4×C71C2311yescharacteristic
411C4×D4×C71C2311yescharacteristic
412#117×C71—21no—
413#117×C71—21no—
414#117×C71—21no—
415#117×C71C2311yescharacteristic
416#117×C71C2311yescharacteristic
417#117×C71C2311yescharacteristic
418#117×C71C2311yescharacteristic
419#117×C71C2311yescharacteristic
420C2×C4⋊C4×C71—21no—
421C2×C4⋊C4×C71—21no—
422C2×C4⋊C4×C71—21no—
423C2×C4⋊C4×C71—21no—
424C2×C4⋊C4×C71C2311yescharacteristic
425C2×C22⋊C4×C71—21no—
426C2×C22⋊C4×C71—21no—
427C2×C22⋊C4×C71—21no—
428C2×C22⋊C4×C71—21no—
429C2×C22⋊C4×C71—21no—
430#107×C71C2311yescharacteristic
431#107×C71C2311yescharacteristic
432#107×C71C2311yescharacteristic
433#107×C71C2311yescharacteristic
434#106×C71C2311yescharacteristic
435#106×C71C2311yescharacteristic
436#106×C71C2311yescharacteristic
437#106×C71C2311yescharacteristic
438C4⋊C8×C71C2311yescharacteristic
439C4⋊C8×C71C2311yescharacteristic
440C4⋊C8×C71C2311yescharacteristic
441C4⋊C8×C71C2311yescharacteristic
442#103×C71C2311yescharacteristic
443#103×C71C2311yescharacteristic
444#103×C71C2311yescharacteristic
445#103×C71C2311yescharacteristic
446#103×C71C2311yescharacteristic
447#103×C71C2311yescharacteristic
448#103×C71C2311yescharacteristic
449#103×C71C2311yescharacteristic
450#103×C71C2311yescharacteristic
451#103×C71C2311yescharacteristic
452#103×C71C2311yescharacteristic
453#103×C71C2311yescharacteristic
454#103×C71C2311yescharacteristic
455#103×C71C2311yescharacteristic
456#103×C71C2311yescharacteristic
457#103×C71C2311yescharacteristic
458#103×C71C2311yescharacteristic
459#103×C71C2311yescharacteristic
460#103×C71C2311yescharacteristic
461#103×C71C2311yescharacteristic
462#102×C71C2311yescharacteristic
463#102×C71C2311yescharacteristic
464#102×C71C2311yescharacteristic
465#102×C71C2311yescharacteristic
466#102×C71C2311yescharacteristic
467#102×C71C2311yescharacteristic
468#102×C71C2311yescharacteristic
469#102×C71C2311yescharacteristic
470#102×C71C2311yescharacteristic
471#102×C71C2311yescharacteristic
472#102×C71C2311yescharacteristic
473#102×C71C2311yescharacteristic
474C22⋊C8×C71C2311yescharacteristic
475C22⋊C8×C71C2311yescharacteristic
476C22⋊C8×C71C2311yescharacteristic
477C22⋊C8×C71C2311yescharacteristic
478C22⋊C8×C71C2311yescharacteristic
479C22⋊C8×C71C2311yescharacteristic
480C22⋊C8×C71C2311yescharacteristic
481C22⋊C8×C71C2311yescharacteristic
482C22⋊C8×C71C2311yescharacteristic
483C22⋊C8×C71C2311yescharacteristic
484C22⋊C8×C71C2311yescharacteristic
485C22⋊C8×C71C2311yescharacteristic
486#97×C71C2311yescharacteristic
487#97×C71C2311yescharacteristic
488C4×C8×C71C2311yescharacteristic
489C4×C8×C71C2311yescharacteristic
490C24×C71—21no—
491C24×C71—21no—
492C24×C71C2×D411yescharacteristic
493#41×C71—22no—
494#41×C71—22no—
495#41×C71—22no—
496#41×C71—22no—
497#41×C71—22no—
498#41×C71—22no—
499#41×C71—41no—
500#41×C71—41no—
501#41×C71—41no—
502#41×C71—41no—
503#41×C71—41no—
504#41×C71—41no—
505#41×C71—41no—
506#41×C71—41no—
507#41×C71—44no—
508#41×C71—44no—
509#41×C71—41no—
510#41×C71—41no—
511#41×C71—41no—
512#41×C71—41no—
513#41×C71—44no—
514#41×C71—44no—
515#41×C71—44no—
516C2×Q8×C71—21no—
517C2×Q8×C71—21no—
518C2×Q8×C71—21no—
519C2×Q8×C71—21no—
520C2×Q8×C71—21no—
521C2×Q8×C71—21no—
522C2×Q8×C71—21no—
523C2×Q8×C71—22no—
524C2×Q8×C71—22no—
525C2×Q8×C71—22no—
526C2×Q8×C71—41no—
527C2×Q8×C71—41no—
528C2×Q8×C71—41no—
529C2×Q8×C71—41no—
530C2×Q8×C71—41no—
531C2×Q8×C71—44no—
532C2×Q8×C71—41no—
533C2×Q8×C71—41no—
534C2×Q8×C71C2×D411yescharacteristic
535C2×Q8×C71C2411yescharacteristic
536C2×Q8×C71C2411yescharacteristic
537C2×Q8×C71C2411yescharacteristic
538C2×Q8×C71C2411yescharacteristic
539C2×Q8×C71C2411yescharacteristic
540C2×Q8×C71C2411yescharacteristic
541C2×D4×C71—21no—
542C2×D4×C71—22no—
543C2×D4×C71—21no—
544C2×D4×C71—21no—
545C2×D4×C71—21no—
546C2×D4×C71—21no—
547C2×D4×C71—21no—
548C2×D4×C71—21no—
549C2×D4×C71—21no—
550C2×D4×C71—21no—
551C2×D4×C71—21no—
552C2×D4×C71—21no—
553C2×D4×C71—21no—
554C2×D4×C71—21no—
555C2×D4×C71—21no—
556C2×D4×C71—21no—
557C2×D4×C71—21no—
558C2×D4×C71—21no—
559C2×D4×C71—21no—
560C2×D4×C71—41no—
561C2×D4×C71—41no—
562C2×D4×C71—41no—
563C2×D4×C71—44no—
564C2×D4×C71C2×D411yescharacteristic
565C2×D4×C71C2×D411yescharacteristic
566C2×D4×C71C2×D411yescharacteristic
567C2×D4×C71C2×D411yescharacteristic
568C2×D4×C71C2×D411yescharacteristic
569C2×D4×C71C2×D411yescharacteristic
570C2×D4×C71C2×D411yescharacteristic
571C2×D4×C71C2411yescharacteristic
572C2×D4×C71C2411yescharacteristic
573C2×D4×C71C2411yescharacteristic
574C2×D4×C71C2411yescharacteristic
575C22×C4×C71—21no—
576C22×C4×C71—21no—
577C22×C4×C71—21no—
578C22×C4×C71—21no—
579C22×C4×C71—21no—
580C22×C4×C71—21no—
581C22×C4×C71—21no—
582C22×C4×C71—21no—
583C22×C4×C71—21no—
584C22×C4×C71—21no—
585C22×C4×C71—21no—
586C22×C4×C71—21no—
587C22×C4×C71—21no—
588C22×C4×C71—21no—
589C22×C4×C71—21no—
590C22×C4×C71—21no—
591C22×C4×C71—21no—
592C22×C4×C71—21no—
593C22×C4×C71—41no—
594C22×C4×C71—41no—
595C22×C4×C71—44no—
596C22×C4×C71C2×D411yescharacteristic
597C22×C4×C71C2×D411yescharacteristic
598C22×C4×C71C2×D411yescharacteristic
599C22×C4×C71C2411yescharacteristic
600C22×C4×C71C2411yescharacteristic
601C22×C4×C71C2411yescharacteristic
602C22×C4×C71C2411yescharacteristic
603C22×C4×C71C2411yescharacteristic
604Q16×C71—22no—
605Q16×C71—22no—
606Q16×C71—41no—
607Q16×C71—41no—
608Q16×C71—41no—
609Q16×C71—41no—
610Q16×C71—41no—
611Q16×C71—41no—
612SD16×C71—22no—
613SD16×C71—22no—
614SD16×C71—22no—
615SD16×C71—22no—
616SD16×C71—41no—
617SD16×C71—41no—
618SD16×C71—41no—
619SD16×C71—41no—
620SD16×C71—41no—
621SD16×C71—41no—
622SD16×C71—41no—
623SD16×C71—41no—
624D8×C71—22no—
625D8×C71—22no—
626D8×C71—41no—
627D8×C71—41no—
628M16×C71—41no—
629M16×C71—41no—
630M16×C71—41no—
631M16×C71—41no—
632C2×C8×C71—41no—
633C2×C8×C71—41no—
634C2×C8×C71—41no—
635C2×C8×C71—41no—
636C2×C8×C71C2411yescharacteristic
637C2×C8×C71C2411yescharacteristic
638C2×C8×C71C2411yescharacteristic
639C2×C8×C71C2411yescharacteristic
640C2×C8×C71C2411yescharacteristic
641C2×C8×C71C2411yescharacteristic
642C2×C8×C71C2411yescharacteristic
643C2×C8×C71C2411yescharacteristic
644C4⋊C4×C71—21no—
645C4⋊C4×C71—21no—
646C4⋊C4×C71—21no—
647C4⋊C4×C71—21no—
648C4⋊C4×C71—21no—
649C4⋊C4×C71—21no—
650C4⋊C4×C71—21no—
651C4⋊C4×C71—21no—
652C4⋊C4×C71—21no—
653C4⋊C4×C71—21no—
654C4⋊C4×C71—21no—
655C4⋊C4×C71—21no—
656C4⋊C4×C71—21no—
657C4⋊C4×C71—21no—
658C4⋊C4×C71—21no—
659C4⋊C4×C71—21no—
660C4⋊C4×C71—21no—
661C4⋊C4×C71—21no—
662C4⋊C4×C71—21no—
663C4⋊C4×C71—21no—
664C4⋊C4×C71—21no—
665C4⋊C4×C71—21no—
666C4⋊C4×C71—21no—
667C4⋊C4×C71C2×D411yescharacteristic
668C4⋊C4×C71C2×D411yescharacteristic
669C4⋊C4×C71C2×D411yescharacteristic
670C4⋊C4×C71C2×D411yescharacteristic
671C4⋊C4×C71C2×D411yescharacteristic
672C4⋊C4×C71C2×D411yescharacteristic
673C4⋊C4×C71C2411yescharacteristic
674C4⋊C4×C71C2411yescharacteristic
675C4⋊C4×C71C2411yescharacteristic
676C4⋊C4×C71C2411yescharacteristic
677C4⋊C4×C71C2411yescharacteristic
678C4⋊C4×C71C2411yescharacteristic
679C22⋊C4×C71—21no—
680C22⋊C4×C71—21no—
681C22⋊C4×C71—21no—
682C22⋊C4×C71—21no—
683C22⋊C4×C71—21no—
684C22⋊C4×C71—21no—
685C22⋊C4×C71—21no—
686C22⋊C4×C71—21no—
687C22⋊C4×C71—21no—
688C22⋊C4×C71—21no—
689C22⋊C4×C71—21no—
690C22⋊C4×C71—21no—
691C22⋊C4×C71—21no—
692C22⋊C4×C71—21no—
693C22⋊C4×C71—21no—
694C22⋊C4×C71—21no—
695C22⋊C4×C71—21no—
696C22⋊C4×C71—21no—
697C22⋊C4×C71—21no—
698C22⋊C4×C71—21no—
699C22⋊C4×C71—21no—
700C22⋊C4×C71—21no—
701C22⋊C4×C71—21no—
702C22⋊C4×C71—21no—
703C22⋊C4×C71—21no—
704C22⋊C4×C71—21no—
705C22⋊C4×C71—21no—
706C22⋊C4×C71—21no—
707C22⋊C4×C71—21no—
708C22⋊C4×C71—21no—
709C22⋊C4×C71—21no—
710C22⋊C4×C71—21no—
711C22⋊C4×C71—21no—
712C22⋊C4×C71—21no—
713C22⋊C4×C71—21no—
714C22⋊C4×C71—21no—
715C22⋊C4×C71C2×D411yescharacteristic
716C22⋊C4×C71C2×D411yescharacteristic
717C22⋊C4×C71C2×D411yescharacteristic
718C22⋊C4×C71C2×D411yescharacteristic
719C22⋊C4×C71C2×D411yescharacteristic
720C22⋊C4×C71C2×D411yescharacteristic
721C22⋊C4×C71C2×D411yescharacteristic
722C22⋊C4×C71C2×D411yescharacteristic
723C22⋊C4×C71C2×D411yescharacteristic
724C22⋊C4×C71C2×D411yescharacteristic
725C42×C71—21no—
726C42×C71—21no—
727C42×C71—21no—
728C42×C71—21no—
729C42×C71—21no—
730C42×C71—21no—
731C42×C71—21no—
732C42×C71—21no—
733C42×C71C2411yescharacteristic
734C42×C71C2411yescharacteristic
735C23×C71—21no—
736C23×C71—21no—
737C23×C71—21no—
738C23×C71—21no—
739C23×C71—41no—
740C23×C71—41no—
741C23×C71—41no—
742C23×C71—42no—
743C23×C71—42no—
744C23×C71—81no—
745C23×C71—81no—
746C23×C71—81no—
747C23×C71—81no—
748C23×C71C22×D411yescharacteristic
749C23×C71C22×D411yescharacteristic
750C23×C71C22×D411yescharacteristic
751C23×C71C22×D411yescharacteristic
752C23×C71C22×D411yescharacteristic
753Q8×C71—21no—
754Q8×C71—21no—
755Q8×C71—21no—
756Q8×C71—21no—
757Q8×C71—21no—
758Q8×C71—21no—
759Q8×C71—21no—
760Q8×C71—21no—
761Q8×C71—21no—
762Q8×C71—21no—
763Q8×C71—21no—
764Q8×C71—41no—
765Q8×C71—42no—
766Q8×C71—42no—
767Q8×C71—42no—
768Q8×C71—42no—
769Q8×C71—81no—
770Q8×C71—81no—
771Q8×C71—81no—
772Q8×C71H(5,𝔽2)12yes—
773D4×C71—24no—
774D4×C71—21no—
775D4×C71—21no—
776D4×C71—21no—
777D4×C71—21no—
778D4×C71—21no—
779D4×C71—21no—
780D4×C71—21no—
781D4×C71—41no—
782D4×C71—41no—
783D4×C71—41no—
784D4×C71—41no—
785D4×C71—41no—
786D4×C71—41no—
787D4×C71—41no—
788D4×C71—42no—
789D4×C71—42no—
790D4×C71—42no—
791D4×C71—42no—
792D4×C71—42no—
793D4×C71—42no—
794D4×C71—81no—
795D4×C71—81no—
796D4×C71—81no—
797D4×C71—81no—
798D4×C71—81no—
799D4×C71—81no—
800D4×C71—81no—
801D4×C71—81no—
802D4×C71—81no—
803D4×C71—81no—
804D4×C71—81no—
805D4×C71H(5,𝔽2)12yes—
806C2×C4×C71—24no—
807C2×C4×C71—21no—
808C2×C4×C71—21no—
809C2×C4×C71—21no—
810C2×C4×C71—21no—
811C2×C4×C71—21no—
812C2×C4×C71—21no—
813C2×C4×C71—21no—
814C2×C4×C71—21no—
815C2×C4×C71—21no—
816C2×C4×C71—21no—
817C2×C4×C71—21no—
818C2×C4×C71—21no—
819C2×C4×C71—21no—
820C2×C4×C71—21no—
821C2×C4×C71—21no—
822C2×C4×C71—21no—
823C2×C4×C71—21no—
824C2×C4×C71—21no—
825C2×C4×C71—21no—
826C2×C4×C71—21no—
827C2×C4×C71—21no—
828C2×C4×C71—21no—
829C2×C4×C71—41no—
830C2×C4×C71—41no—
831C2×C4×C71—41no—
832C2×C4×C71—42no—
833C2×C4×C71—42no—
834C2×C4×C71—42no—
835C2×C4×C71—42no—
836C2×C4×C71—42no—
837C2×C4×C71—42no—
838C2×C4×C71—42no—
839C2×C4×C71—42no—
840C2×C4×C71—42no—
841C2×C4×C71—81no—
842C2×C4×C71—81no—
843C2×C4×C71—81no—
844C2×C4×C71—81no—
845C2×C4×C71—81no—
846C2×C4×C71—81no—
847C2×C4×C71—81no—
848C2×C4×C71—81no—
849C2×C4×C71C22×D411yescharacteristic
850C2×C4×C71C22×D411yescharacteristic
851C2×C4×C71C22×D411yescharacteristic
852C2×C4×C71C22×D411yescharacteristic
853C2×C4×C71C22×D411yescharacteristic
854C2×C4×C71C22×D411yescharacteristic
855C2×C4×C71C22×D411yescharacteristic
856C2×C4×C71C22×D411yescharacteristic
857C2×C4×C71C22×D411yescharacteristic
858C2×C4×C71C2511yescharacteristic
859C8×C71—21no—
860C8×C71—21no—
861C8×C71—21no—
862C8×C71—21no—
863C8×C71—21no—
864C8×C71—21no—
865C8×C71—21no—
866C8×C71—21no—
867C22×C71—21no—
868C22×C71—21no—
869C22×C71—21no—
870C22×C71—21no—
871C22×C71—21no—
872C22×C71—21no—
873C22×C71—21no—
874C22×C71—21no—
875C22×C71—21no—
876C22×C71—21no—
877C22×C71—21no—
878C22×C71—22no—
879C22×C71—21no—
880C22×C71—21no—
881C22×C71—21no—
882C22×C71—21no—
883C22×C71—41no—
884C22×C71—41no—
885C22×C71—41no—
886C22×C71—41no—
887C22×C71—41no—
888C22×C71—41no—
889C22×C71—41no—
890C22×C71—41no—
891C22×C71—41no—
892C22×C71—41no—
893C22×C71—41no—
894C22×C71—82no—
895C22×C71—84no—
896C22×C71—162no—
897C22×C71C23×D411yescharacteristic
898C4×C71—21no—
899C4×C71—21no—
900C4×C71—21no—
901C4×C71—21no—
902C4×C71—21no—
903C4×C71—22no—
904C4×C71—21no—
905C4×C71—21no—
906C4×C71—21no—
907C4×C71—21no—
908C4×C71—41no—
909C4×C71—41no—
910C4×C71—41no—
911C4×C71—41no—
912C4×C71—41no—
913C4×C71—41no—
914C4×C71—41no—
915C4×C71—41no—
916C4×C71—41no—
917C4×C71—41no—
918C4×C71—41no—
919C4×C71C2×H(5,𝔽2)11yescharacteristic
920C4×C71C2×H(5,𝔽2)11yescharacteristic
921#61627C7111yesmaximal, characteristic, direct product factor, Sylow
922C2×C71—41no—
923C2×C71—41no—
924C2×C71—41no—
925C2×C71—41no—
926C2×C71—41no—
927C2×C71—42no—
928C2×C71—81no—
929C2×C71—81no—
930C2×C71—81no—
931C2×C71#348411yescharacteristic
932C2×C71#358411yescharacteristic
933C2×C71#358611yescharacteristic
934#3540C2×C7111yescharacteristic, complemented
935#3489C2×C7111yescharacteristic, complemented
936#3329C2×C7111yescharacteristic, complemented
937#3328C2×C7111yescharacteristic, complemented
938#3321C2×C7111yescharacteristic, complemented
939#3319C2×C7111yescharacteristic, complemented
940#3313C2×C7111yescharacteristic, complemented
941#3311C2×C7111yescharacteristic, complemented
942#3303C2×C7111yescharacteristic, complemented
943#3302C2×C7111yescharacteristic, complemented
944#3285C2×C7111yescharacteristic, complemented
945#3282C2×C7111yescharacteristic, complemented
946#3275C2×C7111yescharacteristic, complemented
947#3273C2×C7111yescharacteristic, complemented
948#3270C2×C7111yescharacteristic, complemented
949#3269C2×C7111yescharacteristic, complemented
950#3267C2×C7111yescharacteristic, complemented
951#3266C2×C7111yescharacteristic, complemented
952#3225C2×C7111yescharacteristic, complemented
953#3225C2×C7111yescharacteristic, complemented
954#3201C2×C7111yescharacteristic, complemented
955#3198C2×C7111yescharacteristic, complemented
956#3196C2×C7111yescharacteristic, complemented
957#3190C2×C7111yescharacteristic, complemented
958#3125C2×C7111yescharacteristic, complemented
959#3124C2×C7111yescharacteristic, complemented
960#3011C2×C7111yescharacteristic, complemented
961#3010C2×C7111yescharacteristic, complemented
962#3005C2×C7111yescharacteristic, complemented
963#3002C2×C7111yescharacteristic, complemented
964#2976C2×C7111yescharacteristic, complemented
965C71#6162711yescharacteristic, direct product factor, Sylow
966C2×2−1+4C22×C7111yescharacteristic
967C22×#41C22×C7111yescharacteristic, complemented
968C2×#137C22×C7111yescharacteristic
969C2×#137C22×C7111yescharacteristic, complemented
970C2×AGL(1,ℤ/8)C22×C7111yescharacteristic
971C2×AGL(1,ℤ/8)C22×C7111yescharacteristic, complemented
972C2×#135C22×C7111yescharacteristic
973C2×#135C22×C7111yescharacteristic
974C22×Q16C22×C7111yescharacteristic, complemented
975C22×SD16C22×C7111yescharacteristic, complemented
976H(3,𝔽4)—21no—
977#560—21no—
978#559—21no—
979#556C22×C7111yescharacteristic
980#556C22×C7111yescharacteristic, complemented
981#555C22×C7111yescharacteristic
982#555C22×C7111yescharacteristic, complemented
983#551—21no—
984D4×Q8C22×C7111yescharacteristic
985D4×Q8C22×C7111yescharacteristic, complemented
986#548C22×C7111yescharacteristic
987#548C22×C7111yescharacteristic
988#548C22×C7111yescharacteristic, complemented
989#548C22×C7111yescharacteristic, complemented
990#547—21no—
991#547—21no—
992#547C22×C7111yescharacteristic
993#547C22×C7111yescharacteristic, complemented
994#546—21no—
995#546—21no—
996#546C22×C7111yescharacteristic
997#546C22×C7111yescharacteristic
998#546C22×C7111yescharacteristic, complemented
999#546C22×C7111yescharacteristic, complemented
1000#542—21no—
1001#542—21no—
1002#542C22×C7111yescharacteristic, complemented
1003#542C22×C7111yescharacteristic, complemented
1004#538—21no—
1005#538—21no—
1006#537—21no—
1007#537C22×C7111yescharacteristic
1008#536—21no—
1009#536C22×C7111yescharacteristic, complemented
1010#536C22×C7111yescharacteristic, complemented
1011#535C22×C7111yescharacteristic, complemented
1012#525—21no—
1013#525C22×C7111yescharacteristic
1014#525C22×C7111yescharacteristic
1015#525C22×C7111yescharacteristic
1016C2×C22⋊Q8—21no—
1017C2×C22⋊Q8C22×C7111yescharacteristic, complemented
1018#520C22×C7111yescharacteristic, complemented
1019#497C22×C7111yescharacteristic, complemented
1020#497C22×C7111yescharacteristic, complemented
1021#495C22×C7111yescharacteristic, complemented
1022#495C22×C7111yescharacteristic, complemented
1023#489C22×C7111yescharacteristic, complemented
1024#489C22×C7111yescharacteristic, complemented
1025#487C22×C7111yescharacteristic, complemented
1026#487C22×C7111yescharacteristic, complemented
1027#485C22×C7111yescharacteristic, complemented
1028#485C22×C7111yescharacteristic, complemented
1029#485C22×C7111yescharacteristic, complemented
1030#485C22×C7111yescharacteristic, complemented
1031#485C22×C7111yescharacteristic, complemented
1032#485C22×C7111yescharacteristic, complemented
1033#484C22×C7111yescharacteristic, complemented
1034#483C22×C7111yescharacteristic, complemented
1035#482C22×C7111yescharacteristic, complemented
1036#482C22×C7111yescharacteristic, complemented
1037#481C22×C7111yescharacteristic, complemented
1038#480C22×C7111yescharacteristic, complemented
1039#477C22×C7111yescharacteristic, complemented
1040#476C22×C7111yescharacteristic, complemented
1041#475C22×C7111yescharacteristic, complemented
1042#474C22×C7111yescharacteristic, complemented
1043#470C22×C7111yescharacteristic, complemented
1044#470C22×C7111yescharacteristic, complemented
1045#470C22×C7111yescharacteristic, complemented
1046#469C22×C7111yescharacteristic, complemented
1047#468C22×C7111yescharacteristic
1048#468C22×C7111yescharacteristic
1049#468C22×C7111yescharacteristic, complemented
1050#468C22×C7111yescharacteristic, complemented
1051#467C22×C7111yescharacteristic, complemented
1052#467C22×C7111yescharacteristic, complemented
1053#467C22×C7111yescharacteristic, complemented
1054#466C22×C7111yescharacteristic, complemented
1055#465C22×C7111yescharacteristic, complemented
1056#465C22×C7111yescharacteristic, complemented
1057#465C22×C7111yescharacteristic, complemented
1058#465C22×C7111yescharacteristic, complemented
1059#464C22×C7111yescharacteristic, complemented
1060#464C22×C7111yescharacteristic, complemented
1061#464C22×C7111yescharacteristic, complemented
1062#464C22×C7111yescharacteristic, complemented
1063#463C22×C7111yescharacteristic, complemented
1064#463C22×C7111yescharacteristic, complemented
1065#463C22×C7111yescharacteristic, complemented
1066#463C22×C7111yescharacteristic, complemented
1067#462C22×C7111yescharacteristic, complemented
1068#462C22×C7111yescharacteristic, complemented
1069#461C22×C7111yescharacteristic, complemented
1070#461C22×C7111yescharacteristic, complemented
1071#452C22×C7111yescharacteristic
1072#452C22×C7111yescharacteristic
1073#452C22×C7111yescharacteristic, complemented
1074#452C22×C7111yescharacteristic, complemented
1075#452C22×C7111yescharacteristic, complemented
1076#452C22×C7111yescharacteristic, complemented
1077#452C22×C7111yescharacteristic, complemented
1078#452C22×C7111yescharacteristic, complemented
1079#452C22×C7111yescharacteristic, complemented
1080#452C22×C7111yescharacteristic, complemented
1081#452C22×C7111yescharacteristic, complemented
1082#452C22×C7111yescharacteristic, complemented
1083#451C22×C7111yescharacteristic, complemented
1084#451C22×C7111yescharacteristic, complemented
1085#451C22×C7111yescharacteristic, complemented
1086#451C22×C7111yescharacteristic, complemented
1087#451C22×C7111yescharacteristic, complemented
1088#451C22×C7111yescharacteristic, complemented
1089#450C22×C7111yescharacteristic, complemented
1090#450C22×C7111yescharacteristic, complemented
1091#449C22×C7111yescharacteristic
1092#449C22×C7111yescharacteristic
1093#449C22×C7111yescharacteristic
1094#449C22×C7111yescharacteristic
1095#449C22×C7111yescharacteristic
1096#449C22×C7111yescharacteristic
1097#449C22×C7111yescharacteristic, complemented
1098#449C22×C7111yescharacteristic, complemented
1099#448C22×C7111yescharacteristic
1100#448C22×C7111yescharacteristic, complemented
1101#448C22×C7111yescharacteristic, complemented
1102#448C22×C7111yescharacteristic, complemented
1103#448C22×C7111yescharacteristic, complemented
1104#448C22×C7111yescharacteristic, complemented
1105#447C22×C7111yescharacteristic
1106#447C22×C7111yescharacteristic, complemented
1107#442C22×C7111yescharacteristic, complemented
1108#441C22×C7111yescharacteristic, complemented
1109#440C22×C7111yescharacteristic, complemented
1110#440C22×C7111yescharacteristic, complemented
1111C4×Q16C22×C7111yescharacteristic, complemented
1112C4×SD16C22×C7111yescharacteristic, complemented
1113C4×SD16C22×C7111yescharacteristic, complemented
1114C4×D8C22×C7111yescharacteristic, complemented
1115#436C22×C7111yescharacteristic
1116#436C22×C7111yescharacteristic, complemented
1117#435C22×C7111yescharacteristic
1118#435C22×C7111yescharacteristic, complemented
1119#435C22×C7111yescharacteristic, complemented
1120#435C22×C7111yescharacteristic, complemented
1121C8×D4C22×C7111yescharacteristic, complemented
1122C8×D4C22×C7111yescharacteristic, complemented
1123#433C22×C7111yescharacteristic, complemented
1124#433C22×C7111yescharacteristic, complemented
1125#419C22×C7111yescharacteristic, complemented
1126#419C22×C7111yescharacteristic, complemented
1127#419C22×C7111yescharacteristic, complemented
1128#418C22×C7111yescharacteristic, complemented
1129#416C22×C7111yescharacteristic, complemented
1130#416C22×C7111yescharacteristic, complemented
1131#416C22×C7111yescharacteristic, complemented
1132#416C22×C7111yescharacteristic, complemented
1133#408C22×C7111yescharacteristic, complemented
1134#408C22×C7111yescharacteristic, complemented
1135#407C22×C7111yescharacteristic, complemented
1136C2×C22⋊C8C22×C7111yescharacteristic, complemented
11372−1+4—42no—
11382−1+4—42no—
1139C2×#41—21no—
1140C2×#41—21no—
1141C2×#41—21no—
1142C2×#41—21no—
1143C2×#41—21no—
1144C2×#41—42no—
1145C2×#41—42no—
1146C2×#41C23×C7111yescharacteristic
1147C2×#41C23×C7111yescharacteristic
1148C2×#41C23×C7111yescharacteristic
1149C2×#41C23×C7111yescharacteristic
1150C2×#41C23×C7111yescharacteristic
1151C2×#41C23×C7111yescharacteristic
1152C2×#41C23×C7111yescharacteristic
1153C2×#41C23×C7111yescharacteristic
1154C2×#41C23×C7111yescharacteristic
1155C22×Q8—21no—
1156C22×Q8C23×C7111yescharacteristic
1157C22×Q8C23×C7111yescharacteristic
1158C22×Q8C23×C7111yescharacteristic
1159C22×Q8C23×C7111yescharacteristic
1160C22×Q8C23×C7111yescharacteristic
1161C22×D4—21no—
1162C22×D4C23×C7111yescharacteristic
1163C22×D4C23×C7111yescharacteristic
1164C23×C4—21no—
1165C23×C4C23×C7111yescharacteristic
1166#137—42no—
1167#137—42no—
1168AGL(1,ℤ/8)—42no—
1169AGL(1,ℤ/8)—42no—
1170#135—42no—
1171#135—42no—
1172C2×Q16—42no—
1173C2×Q16C23×C7111yescharacteristic
1174C2×Q16C23×C7111yescharacteristic
1175C2×Q16C23×C7111yescharacteristic
1176C2×Q16C23×C7111yescharacteristic
1177C2×Q16C23×C7111yescharacteristic
1178C2×Q16C23×C7111yescharacteristic
1179C2×Q16C23×C7111yescharacteristic
1180C2×Q16C23×C7111yescharacteristic
1181C2×SD16—42no—
1182C2×SD16C23×C7111yescharacteristic
1183C2×SD16C23×C7111yescharacteristic
1184C2×SD16C23×C7111yescharacteristic
1185C2×SD16C23×C7111yescharacteristic
1186C2×SD16C23×C7111yescharacteristic
1187C2×SD16C23×C7111yescharacteristic
1188C2×SD16C23×C7111yescharacteristic
1189C2×SD16C23×C7111yescharacteristic
1190C2×SD16C23×C7111yescharacteristic
1191C2×SD16C23×C7111yescharacteristic
1192C2×SD16C23×C7111yescharacteristic
1193C2×SD16C23×C7111yescharacteristic
1194C2×D8C23×C7111yescharacteristic
1195C2×D8C23×C7111yescharacteristic
1196C2×D8C23×C7111yescharacteristic
1197C2×D8C23×C7111yescharacteristic
1198C2×M16C23×C7111yescharacteristic
1199C2×M16C23×C7111yescharacteristic
1200C2×M16C23×C7111yescharacteristic
1201C2×M16C23×C7111yescharacteristic
1202C22×C8C23×C7111yescharacteristic
1203C22×C8C23×C7111yescharacteristic
1204C22×C8C23×C7111yescharacteristic
1205C22×C8C23×C7111yescharacteristic
1206C4⋊Q8—21no—
1207C4⋊Q8—21no—
1208C4⋊Q8—21no—
1209C4⋊Q8C23×C7111yescharacteristic
1210C4⋊Q8C23×C7111yescharacteristic
1211C4⋊Q8C23×C7111yescharacteristic
1212C4⋊Q8C23×C7111yescharacteristic
1213#127—21no—
1214#126—21no—
1215#126—21no—
1216#126—21no—
1217#126—21no—
1218#126—21no—
1219#126—21no—
1220#124—21no—
1221#124—21no—
1222#124—21no—
1223#124—21no—
1224#124—21no—
1225#124—21no—
1226#124—21no—
1227#124—21no—
1228#124—21no—
1229#124—21no—
1230#124—21no—
1231#124—21no—
1232#124—21no—
1233#124—21no—
1234#124C23×C7111yescharacteristic
1235#124C23×C7111yescharacteristic
1236#124C23×C7111yescharacteristic
1237#124C23×C7111yescharacteristic
1238#123—21no—
1239#123—21no—
1240#123—21no—
1241#123—21no—
1242#123—21no—
1243#123—21no—
1244#123—21no—
1245#123—21no—
1246#123—21no—
1247#123—21no—
1248#123—21no—
1249#123—21no—
1250#123—21no—
1251#123—21no—
1252#123—21no—
1253#123—21no—
1254#123D4×C7111yescharacteristic
1255#123D4×C7111yescharacteristic
1256C22⋊Q8—21no—
1257C22⋊Q8—21no—
1258C22⋊Q8—21no—
1259C22⋊Q8—21no—
1260C22⋊Q8—21no—
1261C22⋊Q8—21no—
1262C22⋊Q8—21no—
1263C22⋊Q8—21no—
1264C22⋊Q8—21no—
1265C22⋊Q8—21no—
1266C22⋊Q8—21no—
1267C22⋊Q8—21no—
1268C22⋊Q8—21no—
1269C22⋊Q8—21no—
1270C22⋊Q8—21no—
1271C22⋊Q8D4×C7111yescharacteristic
1272C22⋊Q8D4×C7111yescharacteristic
1273C22⋊Q8C23×C7111yescharacteristic
1274C22⋊Q8C23×C7111yescharacteristic
1275C22⋊Q8C23×C7111yescharacteristic
1276C22⋊Q8C23×C7111yescharacteristic
1277C22⋊Q8C23×C7111yescharacteristic
1278C22⋊Q8C23×C7111yescharacteristic
1279C22⋊Q8C23×C7111yescharacteristic
1280C22⋊Q8C23×C7111yescharacteristic
1281C22⋊Q8C23×C7111yescharacteristic
1282C22⋊Q8C23×C7111yescharacteristic
1283C22⋊Q8C23×C7111yescharacteristic
1284C22⋊Q8C23×C7111yescharacteristic
1285#121—21no—
1286#121—21no—
1287#121—21no—
1288#121—21no—
1289#121—21no—
1290#121—21no—
1291#121—21no—
1292#121—21no—
1293#121—21no—
1294#121—21no—
1295#121—21no—
1296#121—21no—
1297#121—21no—
1298#121—21no—
1299#121—21no—
1300#121D4×C7111yescharacteristic
1301#121D4×C7111yescharacteristic
1302#121C23×C7111yescharacteristic
1303#121C23×C7111yescharacteristic
1304#121C23×C7111yescharacteristic
1305#121C23×C7111yescharacteristic
1306#121C23×C7111yescharacteristic
1307#121C23×C7111yescharacteristic
1308#121C23×C7111yescharacteristic
1309#121C23×C7111yescharacteristic
1310#120—21no—
1311#120—21no—
1312#120—21no—
1313#120—21no—
1314#120—21no—
1315#120—21no—
1316#120—21no—
1317#120—21no—
1318#120D4×C7111yescharacteristic
1319#120D4×C7111yescharacteristic
1320C4×Q8—21no—
1321C4×Q8—21no—
1322C4×Q8C23×C7111yescharacteristic
1323C4×Q8C23×C7111yescharacteristic
1324C4×Q8C23×C7111yescharacteristic
1325C4×Q8C23×C7111yescharacteristic
1326C4×D4—21no—
1327C4×D4—21no—
1328C4×D4—21no—
1329C4×D4—21no—
1330C4×D4—21no—
1331C4×D4—21no—
1332C4×D4—21no—
1333C4×D4—21no—
1334C4×D4—21no—
1335C4×D4—21no—
1336C4×D4—21no—
1337C4×D4—21no—
1338C4×D4C23×C7111yescharacteristic
1339C4×D4C23×C7111yescharacteristic
1340C4×D4C23×C7111yescharacteristic
1341C4×D4C23×C7111yescharacteristic
1342C4×D4C23×C7111yescharacteristic
1343C4×D4C23×C7111yescharacteristic
1344C4×D4C23×C7111yescharacteristic
1345C4×D4C23×C7111yescharacteristic
1346#117—21no—
1347#117—21no—
1348#117—21no—
1349#117C23×C7111yescharacteristic
1350#117C23×C7111yescharacteristic
1351#117C23×C7111yescharacteristic
1352#117C23×C7111yescharacteristic
1353#117C23×C7111yescharacteristic
1354C2×C4⋊C4—21no—
1355C2×C4⋊C4—21no—
1356C2×C4⋊C4—21no—
1357C2×C4⋊C4—21no—
1358C2×C4⋊C4C23×C7111yescharacteristic
1359C2×C22⋊C4—21no—
1360C2×C22⋊C4—21no—
1361C2×C22⋊C4—21no—
1362C2×C22⋊C4—21no—
1363C2×C22⋊C4—21no—
1364#107C23×C7111yescharacteristic
1365#107C23×C7111yescharacteristic
1366#107C23×C7111yescharacteristic
1367#107C23×C7111yescharacteristic
1368#106C23×C7111yescharacteristic
1369#106C23×C7111yescharacteristic
1370#106C23×C7111yescharacteristic
1371#106C23×C7111yescharacteristic
1372C4⋊C8C23×C7111yescharacteristic
1373C4⋊C8C23×C7111yescharacteristic
1374C4⋊C8C23×C7111yescharacteristic
1375C4⋊C8C23×C7111yescharacteristic
1376#103C23×C7111yescharacteristic
1377#103C23×C7111yescharacteristic
1378#103C23×C7111yescharacteristic
1379#103C23×C7111yescharacteristic
1380#103C23×C7111yescharacteristic
1381#103C23×C7111yescharacteristic
1382#103C23×C7111yescharacteristic
1383#103C23×C7111yescharacteristic
1384#103C23×C7111yescharacteristic
1385#103C23×C7111yescharacteristic
1386#103C23×C7111yescharacteristic
1387#103C23×C7111yescharacteristic
1388#103C23×C7111yescharacteristic
1389#103C23×C7111yescharacteristic
1390#103C23×C7111yescharacteristic
1391#103C23×C7111yescharacteristic
1392#103C23×C7111yescharacteristic
1393#103C23×C7111yescharacteristic
1394#103C23×C7111yescharacteristic
1395#103C23×C7111yescharacteristic
1396#102C23×C7111yescharacteristic
1397#102C23×C7111yescharacteristic
1398#102C23×C7111yescharacteristic
1399#102C23×C7111yescharacteristic
1400#102C23×C7111yescharacteristic
1401#102C23×C7111yescharacteristic
1402#102C23×C7111yescharacteristic
1403#102C23×C7111yescharacteristic
1404#102C23×C7111yescharacteristic
1405#102C23×C7111yescharacteristic
1406#102C23×C7111yescharacteristic
1407#102C23×C7111yescharacteristic
1408C22⋊C8C23×C7111yescharacteristic
1409C22⋊C8C23×C7111yescharacteristic
1410C22⋊C8C23×C7111yescharacteristic
1411C22⋊C8C23×C7111yescharacteristic
1412C22⋊C8C23×C7111yescharacteristic
1413C22⋊C8C23×C7111yescharacteristic
1414C22⋊C8C23×C7111yescharacteristic
1415C22⋊C8C23×C7111yescharacteristic
1416C22⋊C8C23×C7111yescharacteristic
1417C22⋊C8C23×C7111yescharacteristic
1418C22⋊C8C23×C7111yescharacteristic
1419C22⋊C8C23×C7111yescharacteristic
1420#97C23×C7111yescharacteristic
1421#97C23×C7111yescharacteristic
1422C4×C8C23×C7111yescharacteristic
1423C4×C8C23×C7111yescharacteristic
1424C24—21no—
1425C24—21no—
1426C24C2×D4×C7111yescharacteristic
1427#41—22no—
1428#41—22no—
1429#41—22no—
1430#41—22no—
1431#41—22no—
1432#41—22no—
1433#41—41no—
1434#41—41no—
1435#41—41no—
1436#41—41no—
1437#41—41no—
1438#41—41no—
1439#41—41no—
1440#41—41no—
1441#41—44no—
1442#41—44no—
1443#41—41no—
1444#41—41no—
1445#41—41no—
1446#41—41no—
1447#41—44no—
1448#41—44no—
1449#41—44no—
1450C2×Q8—21no—
1451C2×Q8—21no—
1452C2×Q8—21no—
1453C2×Q8—21no—
1454C2×Q8—21no—
1455C2×Q8—21no—
1456C2×Q8—21no—
1457C2×Q8—22no—
1458C2×Q8—22no—
1459C2×Q8—22no—
1460C2×Q8—41no—
1461C2×Q8—41no—
1462C2×Q8—41no—
1463C2×Q8—41no—
1464C2×Q8—41no—
1465C2×Q8—44no—
1466C2×Q8—41no—
1467C2×Q8—41no—
1468C2×Q8C2×D4×C7111yescharacteristic
1469C2×Q8C24×C7111yescharacteristic
1470C2×Q8C24×C7111yescharacteristic
1471C2×Q8C24×C7111yescharacteristic
1472C2×Q8C24×C7111yescharacteristic
1473C2×Q8C24×C7111yescharacteristic
1474C2×Q8C24×C7111yescharacteristic
1475C2×D4—21no—
1476C2×D4—22no—
1477C2×D4—21no—
1478C2×D4—21no—
1479C2×D4—21no—
1480C2×D4—21no—
1481C2×D4—21no—
1482C2×D4—21no—
1483C2×D4—21no—
1484C2×D4—21no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—21no—
1492C2×D4—21no—
1493C2×D4—21no—
1494C2×D4—41no—
1495C2×D4—41no—
1496C2×D4—41no—
1497C2×D4—44no—
1498C2×D4C2×D4×C7111yescharacteristic
1499C2×D4C2×D4×C7111yescharacteristic
1500C2×D4C2×D4×C7111yescharacteristic
1501C2×D4C2×D4×C7111yescharacteristic
1502C2×D4C2×D4×C7111yescharacteristic
1503C2×D4C2×D4×C7111yescharacteristic
1504C2×D4C2×D4×C7111yescharacteristic
1505C2×D4C24×C7111yescharacteristic
1506C2×D4C24×C7111yescharacteristic
1507C2×D4C24×C7111yescharacteristic
1508C2×D4C24×C7111yescharacteristic
1509C22×C4—21no—
1510C22×C4—21no—
1511C22×C4—21no—
1512C22×C4—21no—
1513C22×C4—21no—
1514C22×C4—21no—
1515C22×C4—21no—
1516C22×C4—21no—
1517C22×C4—21no—
1518C22×C4—21no—
1519C22×C4—21no—
1520C22×C4—21no—
1521C22×C4—21no—
1522C22×C4—21no—
1523C22×C4—21no—
1524C22×C4—21no—
1525C22×C4—21no—
1526C22×C4—21no—
1527C22×C4—41no—
1528C22×C4—41no—
1529C22×C4—44no—
1530C22×C4C2×D4×C7111yescharacteristic
1531C22×C4C2×D4×C7111yescharacteristic
1532C22×C4C2×D4×C7111yescharacteristic
1533C22×C4C24×C7111yescharacteristic
1534C22×C4C24×C7111yescharacteristic
1535C22×C4C24×C7111yescharacteristic
1536C22×C4C24×C7111yescharacteristic
1537C22×C4C24×C7111yescharacteristic
1538Q16—22no—
1539Q16—22no—
1540Q16—41no—
1541Q16—41no—
1542Q16—41no—
1543Q16—41no—
1544Q16—41no—
1545Q16—41no—
1546SD16—22no—
1547SD16—22no—
1548SD16—22no—
1549SD16—22no—
1550SD16—41no—
1551SD16—41no—
1552SD16—41no—
1553SD16—41no—
1554SD16—41no—
1555SD16—41no—
1556SD16—41no—
1557SD16—41no—
1558D8—22no—
1559D8—22no—
1560D8—41no—
1561D8—41no—
1562M16—41no—
1563M16—41no—
1564M16—41no—
1565M16—41no—
1566C2×C8—41no—
1567C2×C8—41no—
1568C2×C8—41no—
1569C2×C8—41no—
1570C2×C8C24×C7111yescharacteristic
1571C2×C8C24×C7111yescharacteristic
1572C2×C8C24×C7111yescharacteristic
1573C2×C8C24×C7111yescharacteristic
1574C2×C8C24×C7111yescharacteristic
1575C2×C8C24×C7111yescharacteristic
1576C2×C8C24×C7111yescharacteristic
1577C2×C8C24×C7111yescharacteristic
1578C4⋊C4—21no—
1579C4⋊C4—21no—
1580C4⋊C4—21no—
1581C4⋊C4—21no—
1582C4⋊C4—21no—
1583C4⋊C4—21no—
1584C4⋊C4—21no—
1585C4⋊C4—21no—
1586C4⋊C4—21no—
1587C4⋊C4—21no—
1588C4⋊C4—21no—
1589C4⋊C4—21no—
1590C4⋊C4—21no—
1591C4⋊C4—21no—
1592C4⋊C4—21no—
1593C4⋊C4—21no—
1594C4⋊C4—21no—
1595C4⋊C4—21no—
1596C4⋊C4—21no—
1597C4⋊C4—21no—
1598C4⋊C4—21no—
1599C4⋊C4—21no—
1600C4⋊C4—21no—
1601C4⋊C4C2×D4×C7111yescharacteristic
1602C4⋊C4C2×D4×C7111yescharacteristic
1603C4⋊C4C2×D4×C7111yescharacteristic
1604C4⋊C4C2×D4×C7111yescharacteristic
1605C4⋊C4C2×D4×C7111yescharacteristic
1606C4⋊C4C2×D4×C7111yescharacteristic
1607C4⋊C4C24×C7111yescharacteristic
1608C4⋊C4C24×C7111yescharacteristic
1609C4⋊C4C24×C7111yescharacteristic
1610C4⋊C4C24×C7111yescharacteristic
1611C4⋊C4C24×C7111yescharacteristic
1612C4⋊C4C24×C7111yescharacteristic
1613C22⋊C4—21no—
1614C22⋊C4—21no—
1615C22⋊C4—21no—
1616C22⋊C4—21no—
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—21no—
1624C22⋊C4—21no—
1625C22⋊C4—21no—
1626C22⋊C4—21no—
1627C22⋊C4—21no—
1628C22⋊C4—21no—
1629C22⋊C4—21no—
1630C22⋊C4—21no—
1631C22⋊C4—21no—
1632C22⋊C4—21no—
1633C22⋊C4—21no—
1634C22⋊C4—21no—
1635C22⋊C4—21no—
1636C22⋊C4—21no—
1637C22⋊C4—21no—
1638C22⋊C4—21no—
1639C22⋊C4—21no—
1640C22⋊C4—21no—
1641C22⋊C4—21no—
1642C22⋊C4—21no—
1643C22⋊C4—21no—
1644C22⋊C4—21no—
1645C22⋊C4—21no—
1646C22⋊C4—21no—
1647C22⋊C4—21no—
1648C22⋊C4—21no—
1649C22⋊C4C2×D4×C7111yescharacteristic
1650C22⋊C4C2×D4×C7111yescharacteristic
1651C22⋊C4C2×D4×C7111yescharacteristic
1652C22⋊C4C2×D4×C7111yescharacteristic
1653C22⋊C4C2×D4×C7111yescharacteristic
1654C22⋊C4C2×D4×C7111yescharacteristic
1655C22⋊C4C2×D4×C7111yescharacteristic
1656C22⋊C4C2×D4×C7111yescharacteristic
1657C22⋊C4C2×D4×C7111yescharacteristic
1658C22⋊C4C2×D4×C7111yescharacteristic
1659C42—21no—
1660C42—21no—
1661C42—21no—
1662C42—21no—
1663C42—21no—
1664C42—21no—
1665C42—21no—
1666C42—21no—
1667C42C24×C7111yescharacteristic
1668C42C24×C7111yescharacteristic
1669C23—21no—
1670C23—21no—
1671C23—21no—
1672C23—21no—
1673C23—41no—
1674C23—41no—
1675C23—41no—
1676C23—42no—
1677C23—42no—
1678C23—81no—
1679C23—81no—
1680C23—81no—
1681C23—81no—
1682C23C22×D4×C7111yescharacteristic
1683C23C22×D4×C7111yescharacteristic
1684C23C22×D4×C7111yescharacteristic
1685C23C22×D4×C7111yescharacteristic
1686C23C22×D4×C7111yescharacteristic
1687Q8—21no—
1688Q8—21no—
1689Q8—21no—
1690Q8—21no—
1691Q8—21no—
1692Q8—21no—
1693Q8—21no—
1694Q8—21no—
1695Q8—21no—
1696Q8—21no—
1697Q8—21no—
1698Q8—41no—
1699Q8—42no—
1700Q8—42no—
1701Q8—42no—
1702Q8—42no—
1703Q8—81no—
1704Q8—81no—
1705Q8—81no—
1706Q8H(5,𝔽2)×C7112yes—
1707D4—24no—
1708D4—21no—
1709D4—21no—
1710D4—21no—
1711D4—21no—
1712D4—21no—
1713D4—21no—
1714D4—21no—
1715D4—41no—
1716D4—41no—
1717D4—41no—
1718D4—41no—
1719D4—41no—
1720D4—41no—
1721D4—41no—
1722D4—42no—
1723D4—42no—
1724D4—42no—
1725D4—42no—
1726D4—42no—
1727D4—42no—
1728D4—81no—
1729D4—81no—
1730D4—81no—
1731D4—81no—
1732D4—81no—
1733D4—81no—
1734D4—81no—
1735D4—81no—
1736D4—81no—
1737D4—81no—
1738D4—81no—
1739D4H(5,𝔽2)×C7112yes—
1740C2×C4—24no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—21no—
1750C2×C4—21no—
1751C2×C4—21no—
1752C2×C4—21no—
1753C2×C4—21no—
1754C2×C4—21no—
1755C2×C4—21no—
1756C2×C4—21no—
1757C2×C4—21no—
1758C2×C4—21no—
1759C2×C4—21no—
1760C2×C4—21no—
1761C2×C4—21no—
1762C2×C4—21no—
1763C2×C4—41no—
1764C2×C4—41no—
1765C2×C4—41no—
1766C2×C4—42no—
1767C2×C4—42no—
1768C2×C4—42no—
1769C2×C4—42no—
1770C2×C4—42no—
1771C2×C4—42no—
1772C2×C4—42no—
1773C2×C4—42no—
1774C2×C4—42no—
1775C2×C4—81no—
1776C2×C4—81no—
1777C2×C4—81no—
1778C2×C4—81no—
1779C2×C4—81no—
1780C2×C4—81no—
1781C2×C4—81no—
1782C2×C4—81no—
1783C2×C4C22×D4×C7111yescharacteristic
1784C2×C4C22×D4×C7111yescharacteristic
1785C2×C4C22×D4×C7111yescharacteristic
1786C2×C4C22×D4×C7111yescharacteristic
1787C2×C4C22×D4×C7111yescharacteristic
1788C2×C4C22×D4×C7111yescharacteristic
1789C2×C4C22×D4×C7111yescharacteristic
1790C2×C4C22×D4×C7111yescharacteristic
1791C2×C4C22×D4×C7111yescharacteristic
1792C2×C4C25×C7111yescharacteristic
1793C8—21no—
1794C8—21no—
1795C8—21no—
1796C8—21no—
1797C8—21no—
1798C8—21no—
1799C8—21no—
1800C8—21no—
1801C22—21no—
1802C22—21no—
1803C22—21no—
1804C22—21no—
1805C22—21no—
1806C22—21no—
1807C22—21no—
1808C22—21no—
1809C22—21no—
1810C22—21no—
1811C22—21no—
1812C22—22no—
1813C22—21no—
1814C22—21no—
1815C22—21no—
1816C22—21no—
1817C22—41no—
1818C22—41no—
1819C22—41no—
1820C22—41no—
1821C22—41no—
1822C22—41no—
1823C22—41no—
1824C22—41no—
1825C22—41no—
1826C22—41no—
1827C22—41no—
1828C22—82no—
1829C22—84no—
1830C22—162no—
1831C22C23×D4×C7111yescharacteristic
1832C4—21no—
1833C4—21no—
1834C4—21no—
1835C4—21no—
1836C4—21no—
1837C4—22no—
1838C4—21no—
1839C4—21no—
1840C4—21no—
1841C4—21no—
1842C4—41no—
1843C4—41no—
1844C4—41no—
1845C4—41no—
1846C4—41no—
1847C4—41no—
1848C4—41no—
1849C4—41no—
1850C4—41no—
1851C4—41no—
1852C4—41no—
1853C4C2×H(5,𝔽2)×C7111yescharacteristic
1854C4C2×H(5,𝔽2)×C7111yescharacteristic
1855C2—41no—
1856C2—41no—
1857C2—41no—
1858C2—41no—
1859C2—41no—
1860C2—42no—
1861C2—81no—
1862C2—81no—
1863C2—81no—
1864C2C71×#348411yescharacteristic
1865C2C71×#358411yescharacteristic
1866C2C71×#358611yescharacteristic
subgroupG/H
center, socleC22×C71C23×D4
commutator, Frattini, cosocleC2×C4C25×C71
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C71 ◁ #525×C71 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C71×#3540C2semidirect
2. C71×#3489C2semidirect
3. C71×#3329C2semidirect
4. C71×#3328C2semidirect
5. C71×#3321C2semidirect
6. C71×#3319C2semidirect
7. C71×#3313C2semidirect
8. C71×#3311C2semidirect
9. C71×#3303C2semidirect
10. C71×#3302C2semidirect
11. C71×#3285C2semidirect
12. C71×#3282C2semidirect
13. C71×#3275C2semidirect
14. C71×#3273C2semidirect
15. C71×#3270C2semidirect
16. C71×#3269C2semidirect
17. C71×#3267C2semidirect
18. C71×#3266C2semidirect
19. C71×#3225C2semidirect
20. C71×#3225C2semidirect
21. C71×#3201C2semidirect
22. C71×#3198C2semidirect
23. C71×#3196C2semidirect
24. C71×#3190C2semidirect
25. C71×#3125C2semidirect
26. C71×#3124C2semidirect
27. C71×#3011C2semidirect
28. C71×#3010C2semidirect
29. C71×#3005C2semidirect
30. C71×#3002C2semidirect
31. C71×#2976C2semidirect
33. C22×#41×C71C22semidirect
35. C2×#137×C71C22semidirect
37. C2×AGL(1,ℤ/8)×C71C22semidirect
40. C22×Q16×C71C22semidirect
41. C22×SD16×C71C22semidirect
46. #556×C71C22semidirect
48. #555×C71C22semidirect
51. D4×Q8×C71C22semidirect
54. #548×C71C22semidirect
55. #548×C71C22semidirect
59. #547×C71C22semidirect
64. #546×C71C22semidirect
65. #546×C71C22semidirect
68. #542×C71C22semidirect
69. #542×C71C22semidirect
75. #536×C71C22semidirect
76. #536×C71C22semidirect
77. #535×C71C22semidirect
83. C2×C22⋊Q8×C71C22semidirect
84. #520×C71C22semidirect
85. #497×C71C22semidirect
86. #497×C71C22semidirect
87. #495×C71C22semidirect
88. #495×C71C22semidirect
89. #489×C71C22semidirect
90. #489×C71C22semidirect
91. #487×C71C22semidirect
92. #487×C71C22semidirect
93. #485×C71C22semidirect
94. #485×C71C22semidirect
95. #485×C71C22semidirect
96. #485×C71C22semidirect
97. #485×C71C22semidirect
98. #485×C71C22semidirect
99. #484×C71C22semidirect
100. #483×C71C22semidirect
101. #482×C71C22semidirect
102. #482×C71C22semidirect
103. #481×C71C22semidirect
104. #480×C71C22semidirect
105. #477×C71C22semidirect
106. #476×C71C22semidirect
107. #475×C71C22semidirect
108. #474×C71C22semidirect
109. #470×C71C22semidirect
110. #470×C71C22semidirect
111. #470×C71C22semidirect
112. #469×C71C22semidirect
115. #468×C71C22semidirect
116. #468×C71C22semidirect
117. #467×C71C22semidirect
118. #467×C71C22semidirect
119. #467×C71C22semidirect
120. #466×C71C22semidirect
121. #465×C71C22semidirect
122. #465×C71C22semidirect
123. #465×C71C22semidirect
124. #465×C71C22semidirect
125. #464×C71C22semidirect
126. #464×C71C22semidirect
127. #464×C71C22semidirect
128. #464×C71C22semidirect
129. #463×C71C22semidirect
130. #463×C71C22semidirect
131. #463×C71C22semidirect
132. #463×C71C22semidirect
133. #462×C71C22semidirect
134. #462×C71C22semidirect
135. #461×C71C22semidirect
136. #461×C71C22semidirect
139. #452×C71C22semidirect
140. #452×C71C22semidirect
141. #452×C71C22semidirect
142. #452×C71C22semidirect
143. #452×C71C22semidirect
144. #452×C71C22semidirect
145. #452×C71C22semidirect
146. #452×C71C22semidirect
147. #452×C71C22semidirect
148. #452×C71C22semidirect
149. #451×C71C22semidirect
150. #451×C71C22semidirect
151. #451×C71C22semidirect
152. #451×C71C22semidirect
153. #451×C71C22semidirect
154. #451×C71C22semidirect
155. #450×C71C22semidirect
156. #450×C71C22semidirect
163. #449×C71C22semidirect
164. #449×C71C22semidirect
166. #448×C71C22semidirect
167. #448×C71C22semidirect
168. #448×C71C22semidirect
169. #448×C71C22semidirect
170. #448×C71C22semidirect
172. #447×C71C22semidirect
173. #442×C71C22semidirect
174. #441×C71C22semidirect
175. #440×C71C22semidirect
176. #440×C71C22semidirect
177. C4×Q16×C71C22semidirect
178. C4×SD16×C71C22semidirect
179. C4×SD16×C71C22semidirect
180. C4×D8×C71C22semidirect
182. #436×C71C22semidirect
184. #435×C71C22semidirect
185. #435×C71C22semidirect
186. #435×C71C22semidirect
187. C8×D4×C71C22semidirect
188. C8×D4×C71C22semidirect
189. #433×C71C22semidirect
190. #433×C71C22semidirect
191. #419×C71C22semidirect
192. #419×C71C22semidirect
193. #419×C71C22semidirect
194. #418×C71C22semidirect
195. #416×C71C22semidirect
196. #416×C71C22semidirect
197. #416×C71C22semidirect
198. #416×C71C22semidirect
199. #408×C71C22semidirect
200. #408×C71C22semidirect
201. #407×C71C22semidirect
202. C2×C22⋊C8×C71C22semidirect
921. #61627C71direct (N × H)
934. #3540C2×C71semidirect
935. #3489C2×C71semidirect
936. #3329C2×C71semidirect
937. #3328C2×C71semidirect
938. #3321C2×C71semidirect
939. #3319C2×C71semidirect
940. #3313C2×C71semidirect
941. #3311C2×C71semidirect
942. #3303C2×C71semidirect
943. #3302C2×C71semidirect
944. #3285C2×C71semidirect
945. #3282C2×C71semidirect
946. #3275C2×C71semidirect
947. #3273C2×C71semidirect
948. #3270C2×C71semidirect
949. #3269C2×C71semidirect
950. #3267C2×C71semidirect
951. #3266C2×C71semidirect
952. #3225C2×C71semidirect
953. #3225C2×C71semidirect
954. #3201C2×C71semidirect
955. #3198C2×C71semidirect
956. #3196C2×C71semidirect
957. #3190C2×C71semidirect
958. #3125C2×C71semidirect
959. #3124C2×C71semidirect
960. #3011C2×C71semidirect
961. #3010C2×C71semidirect
962. #3005C2×C71semidirect
963. #3002C2×C71semidirect
964. #2976C2×C71semidirect
965. C71#61627direct (N × H)
967. C22×#41C22×C71semidirect
969. C2×#137C22×C71semidirect
971. C2×AGL(1,ℤ/8)C22×C71semidirect
974. C22×Q16C22×C71semidirect
975. C22×SD16C22×C71semidirect
980. #556C22×C71semidirect
982. #555C22×C71semidirect
985. D4×Q8C22×C71semidirect
988. #548C22×C71semidirect
989. #548C22×C71semidirect
993. #547C22×C71semidirect
998. #546C22×C71semidirect
999. #546C22×C71semidirect
1002. #542C22×C71semidirect
1003. #542C22×C71semidirect
1009. #536C22×C71semidirect
1010. #536C22×C71semidirect
1011. #535C22×C71semidirect
1017. C2×C22⋊Q8C22×C71semidirect
1018. #520C22×C71semidirect
1019. #497C22×C71semidirect
1020. #497C22×C71semidirect
1021. #495C22×C71semidirect
1022. #495C22×C71semidirect
1023. #489C22×C71semidirect
1024. #489C22×C71semidirect
1025. #487C22×C71semidirect
1026. #487C22×C71semidirect
1027. #485C22×C71semidirect
1028. #485C22×C71semidirect
1029. #485C22×C71semidirect
1030. #485C22×C71semidirect
1031. #485C22×C71semidirect
1032. #485C22×C71semidirect
1033. #484C22×C71semidirect
1034. #483C22×C71semidirect
1035. #482C22×C71semidirect
1036. #482C22×C71semidirect
1037. #481C22×C71semidirect
1038. #480C22×C71semidirect
1039. #477C22×C71semidirect
1040. #476C22×C71semidirect
1041. #475C22×C71semidirect
1042. #474C22×C71semidirect
1043. #470C22×C71semidirect
1044. #470C22×C71semidirect
1045. #470C22×C71semidirect
1046. #469C22×C71semidirect
1049. #468C22×C71semidirect
1050. #468C22×C71semidirect
1051. #467C22×C71semidirect
1052. #467C22×C71semidirect
1053. #467C22×C71semidirect
1054. #466C22×C71semidirect
1055. #465C22×C71semidirect
1056. #465C22×C71semidirect
1057. #465C22×C71semidirect
1058. #465C22×C71semidirect
1059. #464C22×C71semidirect
1060. #464C22×C71semidirect
1061. #464C22×C71semidirect
1062. #464C22×C71semidirect
1063. #463C22×C71semidirect
1064. #463C22×C71semidirect
1065. #463C22×C71semidirect
1066. #463C22×C71semidirect
1067. #462C22×C71semidirect
1068. #462C22×C71semidirect
1069. #461C22×C71semidirect
1070. #461C22×C71semidirect
1073. #452C22×C71semidirect
1074. #452C22×C71semidirect
1075. #452C22×C71semidirect
1076. #452C22×C71semidirect
1077. #452C22×C71semidirect
1078. #452C22×C71semidirect
1079. #452C22×C71semidirect
1080. #452C22×C71semidirect
1081. #452C22×C71semidirect
1082. #452C22×C71semidirect
1083. #451C22×C71semidirect
1084. #451C22×C71semidirect
1085. #451C22×C71semidirect
1086. #451C22×C71semidirect
1087. #451C22×C71semidirect
1088. #451C22×C71semidirect
1089. #450C22×C71semidirect
1090. #450C22×C71semidirect
1097. #449C22×C71semidirect
1098. #449C22×C71semidirect
1100. #448C22×C71semidirect
1101. #448C22×C71semidirect
1102. #448C22×C71semidirect
1103. #448C22×C71semidirect
1104. #448C22×C71semidirect
1106. #447C22×C71semidirect
1107. #442C22×C71semidirect
1108. #441C22×C71semidirect
1109. #440C22×C71semidirect
1110. #440C22×C71semidirect
1111. C4×Q16C22×C71semidirect
1112. C4×SD16C22×C71semidirect
1113. C4×SD16C22×C71semidirect
1114. C4×D8C22×C71semidirect
1116. #436C22×C71semidirect
1118. #435C22×C71semidirect
1119. #435C22×C71semidirect
1120. #435C22×C71semidirect
1121. C8×D4C22×C71semidirect
1122. C8×D4C22×C71semidirect
1123. #433C22×C71semidirect
1124. #433C22×C71semidirect
1125. #419C22×C71semidirect
1126. #419C22×C71semidirect
1127. #419C22×C71semidirect
1128. #418C22×C71semidirect
1129. #416C22×C71semidirect
1130. #416C22×C71semidirect
1131. #416C22×C71semidirect
1132. #416C22×C71semidirect
1133. #408C22×C71semidirect
1134. #408C22×C71semidirect
1135. #407C22×C71semidirect
1136. C2×C22⋊C8C22×C71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C71×#35402
C71×#34892
C71×#33292
C71×#33282
C71×#33212
C71×#33192
C71×#33132
C71×#33112
C71×#33032
C71×#33022
C71×#32852
C71×#32822
C71×#32752
C71×#32732
C71×#32702
C71×#32692
C71×#32672
C71×#32662
C71×#32252
C71×#32012
C71×#31982
C71×#31962
C71×#31902
C71×#31252
C71×#31242
C71×#30112
C71×#30102
C71×#30052
C71×#30022
C71×#29762
#6162771