Finite Group Databasebeta

← C71×#61925 #31882797

Subgroups — C71×#61925 #31882797

Order 18176.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3555C211yesmaximal, characteristic, complemented
2C71×#3510C211yesmaximal, characteristic, complemented
3C71×#3402C211yesmaximal, characteristic, complemented
4C71×#3402C211yesmaximal, characteristic, complemented
5C71×#3401C211yesmaximal, characteristic, complemented
6C71×#3401C211yesmaximal, characteristic, complemented
7C71×#3400C211yesmaximal, characteristic, complemented
8C71×#3398C211yesmaximal, characteristic, complemented
9C71×#3394C211yesmaximal, characteristic, complemented
10C71×#3393C211yesmaximal, characteristic, complemented
11C71×#3377C211yesmaximal, characteristic, complemented
12C71×#3376C211yesmaximal, characteristic, complemented
13C71×#3375C211yesmaximal, characteristic, complemented
14C71×#3371C211yesmaximal, characteristic, complemented
15C71×#3370C211yesmaximal, characteristic, complemented
16C71×#3369C211yesmaximal, characteristic, complemented
17C71×#3365C211yesmaximal, characteristic, complemented
18C71×#3364C211yesmaximal, characteristic, complemented
19C71×#3225C211yesmaximal, characteristic, complemented
20C71×#3224C211yesmaximal, characteristic
21C71×#3223C211yesmaximal, characteristic, complemented
22C71×#3222C211yesmaximal, characteristic, complemented
23C71×#3215C211yesmaximal, characteristic, complemented
24C71×#3211C211yesmaximal, characteristic, complemented
25C71×#3127C211yesmaximal, characteristic, complemented
26C71×#3123C211yesmaximal, characteristic, complemented
27C71×#3121C211yesmaximal, characteristic, complemented
28C71×#3118C211yesmaximal, characteristic, complemented
29C71×#3111C211yesmaximal, characteristic, complemented
30C71×#3107C211yesmaximal, characteristic, complemented
31C71×#2985C211yesmaximal, characteristic, complemented
32#563×C71—21no—
33#563×C71—21no—
34#559×C71C2211yescharacteristic
35#559×C71C2211yescharacteristic
36#559×C71C2211yescharacteristic
37#559×C71C2211yescharacteristic
38Q82×C71C2211yescharacteristic, complemented
39#557×C71C2211yescharacteristic, complemented
40#557×C71C2211yescharacteristic, complemented
41#557×C71C2211yescharacteristic, complemented
42#556×C71—21no—
43#556×C71C2211yescharacteristic
44#556×C71C2211yescharacteristic
45#556×C71C2211yescharacteristic
46#556×C71C2211yescharacteristic
47#556×C71C2211yescharacteristic, complemented
48#556×C71C2211yescharacteristic, complemented
49#556×C71C2211yescharacteristic, complemented
50#554×C71C2211yescharacteristic, complemented
51#552×C71—21no—
52#551×C71—21no—
53#551×C71—21no—
54#551×C71—21no—
55#551×C71—21no—
56#544×C71—21no—
57#542×C71—21no—
58#542×C71—21no—
59#542×C71C2211yescharacteristic
60#542×C71C2211yescharacteristic
61#541×C71—21no—
62#541×C71—21no—
63#541×C71—21no—
64#541×C71C2211yescharacteristic
65#541×C71C2211yescharacteristic
66#536×C71C2211yescharacteristic
67#535×C71C2211yescharacteristic
68#533×C71C2211yescharacteristic
69#533×C71C2211yescharacteristic
70#529×C71—21no—
71#529×C71—21no—
72#529×C71C2211yescharacteristic
73C2×#124×C71C2211yescharacteristic
74#519×C71C2211yescharacteristic
75#518×C71C2211yescharacteristic
76C4×#41×C71C2211yescharacteristic
77#497×C71C2211yescharacteristic
78#497×C71C2211yescharacteristic
79#497×C71C2211yescharacteristic
80#497×C71C2211yescharacteristic, complemented
81#497×C71C2211yescharacteristic, complemented
82#496×C71C2211yescharacteristic
83#495×C71C2211yescharacteristic
84#495×C71C2211yescharacteristic
85#495×C71C2211yescharacteristic
86#495×C71C2211yescharacteristic, complemented
87#494×C71C2211yescharacteristic, complemented
88#492×C71C2211yescharacteristic
89#491×C71C2211yescharacteristic, complemented
90#490×C71C2211yescharacteristic
91#489×C71C2211yescharacteristic
92#489×C71C2211yescharacteristic
93#489×C71C2211yescharacteristic
94#489×C71C2211yescharacteristic, complemented
95#488×C71C2211yescharacteristic
96#488×C71C2211yescharacteristic
97#488×C71C2211yescharacteristic
98#488×C71C2211yescharacteristic, complemented
99#487×C71C2211yescharacteristic, complemented
100#486×C71C2211yescharacteristic
101#485×C71C2211yescharacteristic
102#485×C71C2211yescharacteristic
103#485×C71C2211yescharacteristic
104#482×C71C2211yescharacteristic
105#479×C71C2211yescharacteristic, complemented
106#479×C71C2211yescharacteristic, complemented
107#479×C71C2211yescharacteristic, complemented
108#478×C71C2211yescharacteristic
109#478×C71C2211yescharacteristic
110#478×C71C2211yescharacteristic, complemented
111#477×C71C2211yescharacteristic, complemented
112#476×C71C2211yescharacteristic
113#475×C71C2211yescharacteristic, complemented
114#475×C71C2211yescharacteristic, complemented
115#474×C71C2211yescharacteristic
116#474×C71C2211yescharacteristic, complemented
117#464×C71C2211yescharacteristic
118#464×C71C2211yescharacteristic
119#464×C71C2211yescharacteristic
120#464×C71C2211yescharacteristic
121#464×C71C2211yescharacteristic
122#464×C71C2211yescharacteristic
123#464×C71C2211yescharacteristic
124#464×C71C2211yescharacteristic
125#464×C71C2211yescharacteristic
126#464×C71C2211yescharacteristic, complemented
127#464×C71C2211yescharacteristic, complemented
128#464×C71C2211yescharacteristic, complemented
129#464×C71C2211yescharacteristic, complemented
130#464×C71C2211yescharacteristic, complemented
131#464×C71C2211yescharacteristic, complemented
132#463×C71C2211yescharacteristic
133#463×C71C2211yescharacteristic
134#463×C71C2211yescharacteristic
135#463×C71C2211yescharacteristic
136#463×C71C2211yescharacteristic
137#463×C71C2211yescharacteristic, complemented
138#463×C71C2211yescharacteristic, complemented
139#462×C71C2211yescharacteristic, complemented
140#462×C71C2211yescharacteristic, complemented
141#462×C71C2211yescharacteristic, complemented
142#462×C71C2211yescharacteristic, complemented
143#462×C71C2211yescharacteristic, complemented
144#462×C71C2211yescharacteristic, complemented
145#461×C71C2211yescharacteristic
146#461×C71C2211yescharacteristic
147#461×C71C2211yescharacteristic, complemented
148#461×C71C2211yescharacteristic, complemented
149#460×C71C2211yescharacteristic
150#460×C71C2211yescharacteristic
151#460×C71C2211yescharacteristic
152#459×C71C2211yescharacteristic
153#452×C71C2211yescharacteristic
154#452×C71C2211yescharacteristic
155#452×C71C2211yescharacteristic
156#451×C71C2211yescharacteristic
157#451×C71C2211yescharacteristic
158#451×C71C2211yescharacteristic
159#450×C71C2211yescharacteristic
160#450×C71C2211yescharacteristic
161#450×C71C2211yescharacteristic
162#449×C71C2211yescharacteristic
163#448×C71C2211yescharacteristic
164#447×C71C2211yescharacteristic
165#446×C71C2211yescharacteristic, complemented
166#446×C71C2211yescharacteristic, complemented
167#446×C71C2211yescharacteristic, complemented
168#446×C71C2211yescharacteristic, complemented
169#446×C71C2211yescharacteristic, complemented
170#446×C71C2211yescharacteristic, complemented
171C8×Q8×C71C2211yescharacteristic, complemented
172C8×Q8×C71C2211yescharacteristic, complemented
173#442×C71C2211yescharacteristic
174#442×C71C2211yescharacteristic, complemented
175#441×C71C2211yescharacteristic, complemented
176#441×C71C2211yescharacteristic, complemented
177#441×C71C2211yescharacteristic, complemented
178#441×C71C2211yescharacteristic, complemented
179#440×C71C2211yescharacteristic
180#440×C71C2211yescharacteristic
181#440×C71C2211yescharacteristic
182#440×C71C2211yescharacteristic, complemented
183#440×C71C2211yescharacteristic, complemented
184#440×C71C2211yescharacteristic, complemented
185C4×Q16×C71C2211yescharacteristic, complemented
186C4×Q16×C71C2211yescharacteristic, complemented
187C4×Q16×C71C2211yescharacteristic, complemented
188C4×Q16×C71C2211yescharacteristic, complemented
189C4×Q16×C71C2211yescharacteristic, complemented
190C4×SD16×C71C2211yescharacteristic
191C4×SD16×C71C2211yescharacteristic
192C4×SD16×C71C2211yescharacteristic
193C4×SD16×C71C2211yescharacteristic, complemented
194C4×SD16×C71C2211yescharacteristic, complemented
195C4×SD16×C71C2211yescharacteristic, complemented
196C4×D8×C71C2211yescharacteristic
197#433×C71C2211yescharacteristic
198#433×C71C2211yescharacteristic
199#433×C71C2211yescharacteristic
200#433×C71C2211yescharacteristic
201#432×C71C2211yescharacteristic
202#431×C71C2211yescharacteristic
203C2×#41×C71C2311yescharacteristic
204C22×Q8×C71C2311yescharacteristic
205C22×D4×C71C2311yescharacteristic
206C2×Q16×C71C2311yescharacteristic
207C2×Q16×C71C2311yescharacteristic
208C2×Q16×C71C2311yescharacteristic
209C2×Q16×C71C2311yescharacteristic
210C2×Q16×C71C2311yescharacteristic
211C2×Q16×C71C2311yescharacteristic
212C2×Q16×C71C2311yescharacteristic
213C2×Q16×C71C2311yescharacteristic
214C2×Q16×C71C2311yescharacteristic
215C2×SD16×C71C2311yescharacteristic
216C2×SD16×C71C2311yescharacteristic
217C2×SD16×C71C2311yescharacteristic
218C2×SD16×C71C2311yescharacteristic
219C2×SD16×C71C2311yescharacteristic
220C2×SD16×C71C2311yescharacteristic
221C2×SD16×C71C2311yescharacteristic
222C2×SD16×C71C2311yescharacteristic
223C2×SD16×C71C2311yescharacteristic
224C2×SD16×C71C2311yescharacteristic
225C2×SD16×C71C2311yescharacteristic
226C2×SD16×C71C2311yescharacteristic
227C2×D8×C71C2311yescharacteristic
228C2×D8×C71C2311yescharacteristic
229C2×D8×C71C2311yescharacteristic
230C4⋊Q8×C71—21no—
231C4⋊Q8×C71—21no—
232C4⋊Q8×C71—21no—
233C4⋊Q8×C71—21no—
234C4⋊Q8×C71—21no—
235C4⋊Q8×C71D411yescharacteristic
236C4⋊Q8×C71D411yescharacteristic
237C4⋊Q8×C71C2311yescharacteristic
238C4⋊Q8×C71C2311yescharacteristic
239C4⋊Q8×C71C2311yescharacteristic
240C4⋊Q8×C71C2311yescharacteristic
241C4⋊Q8×C71C2311yescharacteristic
242C4⋊Q8×C71C2311yescharacteristic
243C4⋊Q8×C71C2311yescharacteristic
244C4⋊Q8×C71C2311yescharacteristic
245#127×C71C2311yescharacteristic
246#127×C71C2311yescharacteristic
247#126×C71—21no—
248#126×C71—21no—
249#126×C71—21no—
250#126×C71—21no—
251#126×C71—21no—
252#126×C71—21no—
253#126×C71—21no—
254#126×C71—21no—
255#126×C71—21no—
256#126×C71—21no—
257#126×C71—21no—
258#126×C71—21no—
259#126×C71—21no—
260#126×C71—21no—
261#126×C71—21no—
262#126×C71—21no—
263#126×C71—21no—
264#126×C71—21no—
265#126×C71—21no—
266#126×C71—21no—
267#126×C71—21no—
268#125×C71—21no—
269#125×C71—21no—
270#125×C71—21no—
271#125×C71—21no—
272#125×C71—21no—
273#125×C71—21no—
274#125×C71—21no—
275#125×C71—21no—
276#125×C71—21no—
277#125×C71—21no—
278#125×C71—21no—
279#125×C71—21no—
280#125×C71D411yescharacteristic
281#125×C71D411yescharacteristic
282#125×C71C2311yescharacteristic
283#125×C71C2311yescharacteristic
284#125×C71C2311yescharacteristic
285#124×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×C71C2311yescharacteristic
294#124×C71C2311yescharacteristic
295#124×C71C2311yescharacteristic
296#124×C71C2311yescharacteristic
297#124×C71C2311yescharacteristic
298#124×C71C2311yescharacteristic
299#124×C71C2311yescharacteristic
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—
317C22⋊Q8×C71—21no—
318C22⋊Q8×C71—21no—
319C22⋊Q8×C71—21no—
320C22⋊Q8×C71—21no—
321C22⋊Q8×C71—21no—
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×C71D411yescharacteristic
333C22⋊Q8×C71D411yescharacteristic
334C22⋊Q8×C71D411yescharacteristic
335C22⋊Q8×C71D411yescharacteristic
336C22⋊Q8×C71C2311yescharacteristic
337C22⋊Q8×C71C2311yescharacteristic
338C22⋊Q8×C71C2311yescharacteristic
339#121×C71—21no—
340#121×C71—21no—
341#121×C71C2311yescharacteristic
342#120×C71—21no—
343#120×C71—21no—
344C4×Q8×C71—21no—
345C4×Q8×C71—21no—
346C4×Q8×C71—21no—
347C4×Q8×C71—21no—
348C4×Q8×C71—21no—
349C4×Q8×C71—21no—
350C4×Q8×C71—21no—
351C4×Q8×C71C2311yescharacteristic
352C4×Q8×C71C2311yescharacteristic
353C4×Q8×C71C2311yescharacteristic
354C4×Q8×C71C2311yescharacteristic
355C4×Q8×C71C2311yescharacteristic
356C4×Q8×C71C2311yescharacteristic
357C4×Q8×C71C2311yescharacteristic
358C4×Q8×C71C2311yescharacteristic
359C4×Q8×C71C2311yescharacteristic
360C4×Q8×C71C2311yescharacteristic
361C4×Q8×C71C2311yescharacteristic
362C4×Q8×C71C2311yescharacteristic
363C4×Q8×C71C2311yescharacteristic
364C4×Q8×C71C2311yescharacteristic
365C4×Q8×C71C2311yescharacteristic
366C4×Q8×C71C2311yescharacteristic
367C4×Q8×C71C2311yescharacteristic
368C4×Q8×C71C2311yescharacteristic
369C4×Q8×C71C2311yescharacteristic
370C4×D4×C71—21no—
371C4×D4×C71—21no—
372C4×D4×C71—21no—
373C4×D4×C71—21no—
374C4×D4×C71—21no—
375C4×D4×C71—21no—
376C4×D4×C71—21no—
377C4×D4×C71—21no—
378C4×D4×C71—21no—
379C4×D4×C71C2311yescharacteristic
380C4×D4×C71C2311yescharacteristic
381C4×D4×C71C2311yescharacteristic
382C4×D4×C71C2311yescharacteristic
383C4×D4×C71C2311yescharacteristic
384C4×D4×C71C2311yescharacteristic
385C4×D4×C71C2311yescharacteristic
386C4×D4×C71C2311yescharacteristic
387C4×D4×C71C2311yescharacteristic
388#117×C71—21no—
389#117×C71—21no—
390#117×C71—21no—
391#117×C71—21no—
392#117×C71—21no—
393#117×C71—21no—
394#117×C71—21no—
395#117×C71—21no—
396#117×C71—21no—
397#117×C71—21no—
398#117×C71—21no—
399#117×C71—21no—
400#117×C71C2311yescharacteristic
401#117×C71C2311yescharacteristic
402#117×C71C2311yescharacteristic
403C2×C4⋊C4×C71—21no—
404C2×C22⋊C4×C71—21no—
405C2×C22⋊C4×C71—21no—
406C2×C22⋊C4×C71—21no—
407C2×C22⋊C4×C71—21no—
408C2×C42×C71—21no—
409C2×C42×C71C2311yescharacteristic
410#107×C71C2311yescharacteristic
411#107×C71C2311yescharacteristic
412#107×C71C2311yescharacteristic
413#107×C71C2311yescharacteristic
414#106×C71C2311yescharacteristic
415#106×C71C2311yescharacteristic
416#106×C71C2311yescharacteristic
417#106×C71C2311yescharacteristic
418C4⋊C8×C71C2311yescharacteristic
419C4⋊C8×C71C2311yescharacteristic
420C4⋊C8×C71C2311yescharacteristic
421C4⋊C8×C71C2311yescharacteristic
422C4⋊C8×C71C2311yescharacteristic
423C4⋊C8×C71C2311yescharacteristic
424C4⋊C8×C71C2311yescharacteristic
425C4⋊C8×C71C2311yescharacteristic
426C4⋊C8×C71C2311yescharacteristic
427C4⋊C8×C71C2311yescharacteristic
428C4⋊C8×C71C2311yescharacteristic
429C4⋊C8×C71C2311yescharacteristic
430#103×C71C2311yescharacteristic
431#103×C71C2311yescharacteristic
432#103×C71C2311yescharacteristic
433#103×C71C2311yescharacteristic
434#103×C71C2311yescharacteristic
435#103×C71C2311yescharacteristic
436#103×C71C2311yescharacteristic
437#103×C71C2311yescharacteristic
438#103×C71C2311yescharacteristic
439#103×C71C2311yescharacteristic
440#103×C71C2311yescharacteristic
441#103×C71C2311yescharacteristic
442#103×C71C2311yescharacteristic
443#103×C71C2311yescharacteristic
444#103×C71C2311yescharacteristic
445#103×C71C2311yescharacteristic
446#103×C71C2311yescharacteristic
447#103×C71C2311yescharacteristic
448#102×C71C2311yescharacteristic
449#102×C71C2311yescharacteristic
450#102×C71C2311yescharacteristic
451#102×C71C2311yescharacteristic
452#102×C71C2311yescharacteristic
453#102×C71C2311yescharacteristic
454#102×C71C2311yescharacteristic
455#102×C71C2311yescharacteristic
456#102×C71C2311yescharacteristic
457#102×C71C2311yescharacteristic
458#102×C71C2311yescharacteristic
459#102×C71C2311yescharacteristic
460#102×C71C2311yescharacteristic
461#102×C71C2311yescharacteristic
462C22⋊C8×C71C2311yescharacteristic
463C22⋊C8×C71C2311yescharacteristic
464C22⋊C8×C71C2311yescharacteristic
465C22⋊C8×C71C2311yescharacteristic
466#97×C71C2311yescharacteristic
467#97×C71C2311yescharacteristic
468#97×C71C2311yescharacteristic
469#97×C71C2311yescharacteristic
470#97×C71C2311yescharacteristic
471#97×C71C2311yescharacteristic
472C4×C8×C71C2311yescharacteristic
473C4×C8×C71C2311yescharacteristic
474C4×C8×C71C2311yescharacteristic
475C4×C8×C71C2311yescharacteristic
476C4×C8×C71C2311yescharacteristic
477C4×C8×C71C2311yescharacteristic
478C24×C71—21no—
479#41×C71—41no—
480#41×C71—41no—
481C2×Q8×C71—21no—
482C2×Q8×C71—21no—
483C2×Q8×C71—21no—
484C2×Q8×C71—21no—
485C2×Q8×C71—41no—
486C2×Q8×C71—41no—
487C2×Q8×C71C2×D411yescharacteristic
488C2×Q8×C71C2×D411yescharacteristic
489C2×Q8×C71C2×D411yescharacteristic
490C2×Q8×C71C2×D411yescharacteristic
491C2×Q8×C71C2411yescharacteristic
492C2×Q8×C71C2411yescharacteristic
493C2×Q8×C71C2411yescharacteristic
494C2×Q8×C71C2411yescharacteristic
495C2×Q8×C71C2411yescharacteristic
496C2×Q8×C71C2411yescharacteristic
497C2×D4×C71—21no—
498C2×D4×C71—21no—
499C2×D4×C71—21no—
500C2×D4×C71—21no—
501C2×D4×C71—21no—
502C2×D4×C71—21no—
503C2×D4×C71—21no—
504C2×D4×C71—41no—
505C2×D4×C71—41no—
506C2×D4×C71C2411yescharacteristic
507C2×D4×C71C2411yescharacteristic
508C2×D4×C71C2411yescharacteristic
509C2×D4×C71C2411yescharacteristic
510C22×C4×C71—21no—
511C22×C4×C71—21no—
512C22×C4×C71—21no—
513C22×C4×C71—21no—
514C22×C4×C71—21no—
515C22×C4×C71—21no—
516C22×C4×C71—21no—
517C22×C4×C71—21no—
518C22×C4×C71—21no—
519C22×C4×C71—21no—
520C22×C4×C71—21no—
521C22×C4×C71C2×D411yescharacteristic
522C22×C4×C71C2×D411yescharacteristic
523C22×C4×C71C2411yescharacteristic
524Q16×C71—41no—
525Q16×C71—41no—
526Q16×C71—41no—
527Q16×C71—41no—
528Q16×C71—41no—
529Q16×C71—41no—
530Q16×C71—41no—
531Q16×C71—41no—
532Q16×C71—41no—
533SD16×C71—41no—
534SD16×C71—41no—
535SD16×C71—41no—
536SD16×C71—41no—
537SD16×C71—41no—
538SD16×C71—41no—
539SD16×C71—41no—
540SD16×C71—41no—
541SD16×C71—41no—
542SD16×C71—41no—
543SD16×C71—41no—
544SD16×C71—41no—
545D8×C71—41no—
546D8×C71—41no—
547D8×C71—41no—
548C2×C8×C71C2411yescharacteristic
549C2×C8×C71C2411yescharacteristic
550C2×C8×C71C2411yescharacteristic
551C2×C8×C71C2411yescharacteristic
552C2×C8×C71C2411yescharacteristic
553C2×C8×C71C2411yescharacteristic
554C2×C8×C71C2411yescharacteristic
555C2×C8×C71C2411yescharacteristic
556C4⋊C4×C71—21no—
557C4⋊C4×C71—21no—
558C4⋊C4×C71—21no—
559C4⋊C4×C71—21no—
560C4⋊C4×C71—21no—
561C4⋊C4×C71—21no—
562C4⋊C4×C71—21no—
563C4⋊C4×C71—21no—
564C4⋊C4×C71—21no—
565C4⋊C4×C71—21no—
566C4⋊C4×C71—21no—
567C4⋊C4×C71—21no—
568C4⋊C4×C71—21no—
569C4⋊C4×C71—21no—
570C4⋊C4×C71—21no—
571C4⋊C4×C71—21no—
572C4⋊C4×C71—21no—
573C4⋊C4×C71—21no—
574C4⋊C4×C71—21no—
575C4⋊C4×C71—21no—
576C4⋊C4×C71—21no—
577C4⋊C4×C71—21no—
578C4⋊C4×C71—21no—
579C4⋊C4×C71—21no—
580C4⋊C4×C71—21no—
581C4⋊C4×C71—21no—
582C4⋊C4×C71—21no—
583C4⋊C4×C71—21no—
584C4⋊C4×C71—21no—
585C4⋊C4×C71—21no—
586C4⋊C4×C71—21no—
587C4⋊C4×C71—21no—
588C4⋊C4×C71—21no—
589C4⋊C4×C71—21no—
590C4⋊C4×C71—21no—
591C4⋊C4×C71—21no—
592C4⋊C4×C71—21no—
593C4⋊C4×C71C2×D411yescharacteristic
594C4⋊C4×C71C2×D411yescharacteristic
595C4⋊C4×C71C2×D411yescharacteristic
596C4⋊C4×C71C2×D411yescharacteristic
597C4⋊C4×C71C2×D411yescharacteristic
598C4⋊C4×C71C2×D411yescharacteristic
599C4⋊C4×C71C2×D411yescharacteristic
600C4⋊C4×C71C2×D411yescharacteristic
601C4⋊C4×C71C2×D411yescharacteristic
602C4⋊C4×C71C2×D411yescharacteristic
603C4⋊C4×C71C2×D411yescharacteristic
604C4⋊C4×C71C2×D411yescharacteristic
605C4⋊C4×C71C2×D411yescharacteristic
606C4⋊C4×C71C2×D411yescharacteristic
607C4⋊C4×C71C2×D411yescharacteristic
608C4⋊C4×C71C2×D411yescharacteristic
609C4⋊C4×C71C2411yescharacteristic
610C4⋊C4×C71C2411yescharacteristic
611C4⋊C4×C71C2411yescharacteristic
612C4⋊C4×C71C2411yescharacteristic
613C4⋊C4×C71C2411yescharacteristic
614C4⋊C4×C71C2411yescharacteristic
615C22⋊C4×C71—21no—
616C22⋊C4×C71—21no—
617C22⋊C4×C71—21no—
618C22⋊C4×C71—21no—
619C22⋊C4×C71—21no—
620C22⋊C4×C71—21no—
621C22⋊C4×C71—21no—
622C22⋊C4×C71—21no—
623C22⋊C4×C71—21no—
624C22⋊C4×C71—21no—
625C22⋊C4×C71—21no—
626C22⋊C4×C71—21no—
627C22⋊C4×C71—21no—
628C22⋊C4×C71—21no—
629C22⋊C4×C71—21no—
630C22⋊C4×C71—21no—
631C22⋊C4×C71—21no—
632C22⋊C4×C71—21no—
633C22⋊C4×C71—21no—
634C22⋊C4×C71—21no—
635C22⋊C4×C71—21no—
636C22⋊C4×C71—21no—
637C22⋊C4×C71—21no—
638C22⋊C4×C71—21no—
639C22⋊C4×C71—21no—
640C22⋊C4×C71—21no—
641C22⋊C4×C71—21no—
642C22⋊C4×C71—21no—
643C22⋊C4×C71—21no—
644C22⋊C4×C71—21no—
645C22⋊C4×C71—21no—
646C22⋊C4×C71—21no—
647C22⋊C4×C71—21no—
648C22⋊C4×C71—21no—
649C22⋊C4×C71—21no—
650C22⋊C4×C71—21no—
651C22⋊C4×C71C2×D411yescharacteristic
652C22⋊C4×C71C2×D411yescharacteristic
653C22⋊C4×C71C2×D411yescharacteristic
654C22⋊C4×C71C2×D411yescharacteristic
655C42×C71—21no—
656C42×C71—21no—
657C42×C71—21no—
658C42×C71—21no—
659C42×C71—21no—
660C42×C71—21no—
661C42×C71—21no—
662C42×C71—21no—
663C42×C71—21no—
664C42×C71—21no—
665C42×C71—21no—
666C42×C71—21no—
667C42×C71—21no—
668C42×C71—21no—
669C42×C71—21no—
670C42×C71—21no—
671C42×C71C2×D411yescharacteristic
672C42×C71C2×D411yescharacteristic
673C42×C71C2411yescharacteristic
674C42×C71C2411yescharacteristic
675C42×C71C2411yescharacteristic
676C42×C71C2411yescharacteristic
677C42×C71C2411yescharacteristic
678C42×C71C2411yescharacteristic
679C23×C71—21no—
680C23×C71—21no—
681C23×C71—21no—
682C23×C71—21no—
683C23×C71—42no—
684C23×C71—81no—
685C23×C71—81no—
686C23×C71C22×D411yescharacteristic
687Q8×C71—21no—
688Q8×C71—21no—
689Q8×C71—21no—
690Q8×C71—21no—
691Q8×C71—21no—
692Q8×C71—21no—
693Q8×C71—21no—
694Q8×C71—21no—
695Q8×C71—21no—
696Q8×C71—21no—
697Q8×C71—21no—
698Q8×C71—21no—
699Q8×C71—41no—
700Q8×C71—41no—
701Q8×C71—41no—
702Q8×C71—41no—
703Q8×C71—42no—
704Q8×C71—81no—
705Q8×C71—81no—
706Q8×C71—81no—
707D4×C71—21no—
708D4×C71—21no—
709D4×C71—21no—
710D4×C71—21no—
711D4×C71—21no—
712D4×C71—21no—
713D4×C71—21no—
714D4×C71—21no—
715D4×C71—42no—
716D4×C71—42no—
717D4×C71—81no—
718D4×C71—81no—
719D4×C71—81no—
720D4×C71—81no—
721D4×C71—81no—
722C2×C4×C71—21no—
723C2×C4×C71—21no—
724C2×C4×C71—21no—
725C2×C4×C71—21no—
726C2×C4×C71—21no—
727C2×C4×C71—21no—
728C2×C4×C71—21no—
729C2×C4×C71—21no—
730C2×C4×C71—21no—
731C2×C4×C71—21no—
732C2×C4×C71—21no—
733C2×C4×C71—21no—
734C2×C4×C71—21no—
735C2×C4×C71—21no—
736C2×C4×C71—41no—
737C2×C4×C71—41no—
738C2×C4×C71—42no—
739C2×C4×C71—42no—
740C2×C4×C71—42no—
741C2×C4×C71—81no—
742C2×C4×C71—81no—
743C2×C4×C71—81no—
744C2×C4×C71—81no—
745C2×C4×C71—81no—
746C2×C4×C71—81no—
747C2×C4×C71—81no—
748C2×C4×C71—81no—
749C2×C4×C71C22×D411yescharacteristic
750C2×C4×C71C22×D411yescharacteristic
751C2×C4×C71C22×D411yescharacteristic
752C2×C4×C71C22×D411yescharacteristic
753C2×C4×C71C22×D411yescharacteristic
754C2×C4×C71C22×D411yescharacteristic
755C2×C4×C71C22×D411yescharacteristic
756C2×C4×C71C22×D411yescharacteristic
757C2×C4×C71C22×D411yescharacteristic
758C2×C4×C71C22×D411yescharacteristic
759C2×C4×C71C22×D411yescharacteristic
760C2×C4×C71C22×D411yescharacteristic
761C2×C4×C71C22×D411yescharacteristic
762C2×C4×C71C2511yescharacteristic
763C8×C71—21no—
764C8×C71—21no—
765C8×C71—21no—
766C8×C71—21no—
767C8×C71—21no—
768C8×C71—21no—
769C8×C71—21no—
770C8×C71—21no—
771C22×C71—21no—
772C22×C71—21no—
773C22×C71—21no—
774C22×C71—41no—
775C22×C71—41no—
776C22×C71—41no—
777C22×C71—41no—
778C22×C71—41no—
779C22×C71—41no—
780C22×C71—41no—
781C22×C71—41no—
782C22×C71—41no—
783C22×C71—41no—
784C22×C71—41no—
785C22×C71—41no—
786C22×C71—162no—
787C22×C71C23×D411yescharacteristic
788C4×C71—21no—
789C4×C71—21no—
790C4×C71—21no—
791C4×C71—21no—
792C4×C71—21no—
793C4×C71—21no—
794C4×C71—21no—
795C4×C71—21no—
796C4×C71—21no—
797C4×C71—21no—
798C4×C71—21no—
799C4×C71—21no—
800C4×C71—21no—
801C4×C71—41no—
802C4×C71—41no—
803C4×C71—41no—
804C4×C71—41no—
805C4×C71—41no—
806C4×C71—41no—
807C4×C71—41no—
808C4×C71—41no—
809C4×C71—41no—
810C4×C71—41no—
811C4×C71—41no—
812C4×C71—41no—
813C4×C71#58511yescharacteristic
814C4×C71#58511yescharacteristic
815#61925C7111yesmaximal, characteristic, direct product factor, Sylow
816C2×C71—41no—
817C2×C71—81no—
818C2×C71—81no—
819C2×C71—81no—
820C2×C71—81no—
821C2×C71#348711yescharacteristic
822C2×C71#358411yescharacteristic
823C2×C71#358611yescharacteristic
824#3555C2×C7111yescharacteristic, complemented
825#3510C2×C7111yescharacteristic, complemented
826#3402C2×C7111yescharacteristic, complemented
827#3402C2×C7111yescharacteristic, complemented
828#3401C2×C7111yescharacteristic, complemented
829#3401C2×C7111yescharacteristic, complemented
830#3400C2×C7111yescharacteristic, complemented
831#3398C2×C7111yescharacteristic, complemented
832#3394C2×C7111yescharacteristic, complemented
833#3393C2×C7111yescharacteristic, complemented
834#3377C2×C7111yescharacteristic, complemented
835#3376C2×C7111yescharacteristic, complemented
836#3375C2×C7111yescharacteristic, complemented
837#3371C2×C7111yescharacteristic, complemented
838#3370C2×C7111yescharacteristic, complemented
839#3369C2×C7111yescharacteristic, complemented
840#3365C2×C7111yescharacteristic, complemented
841#3364C2×C7111yescharacteristic, complemented
842#3225C2×C7111yescharacteristic, complemented
843#3224C2×C7111yescharacteristic
844#3223C2×C7111yescharacteristic, complemented
845#3222C2×C7111yescharacteristic, complemented
846#3215C2×C7111yescharacteristic, complemented
847#3211C2×C7111yescharacteristic, complemented
848#3127C2×C7111yescharacteristic, complemented
849#3123C2×C7111yescharacteristic, complemented
850#3121C2×C7111yescharacteristic, complemented
851#3118C2×C7111yescharacteristic, complemented
852#3111C2×C7111yescharacteristic, complemented
853#3107C2×C7111yescharacteristic, complemented
854#2985C2×C7111yescharacteristic, complemented
855C71#6192511yescharacteristic, direct product factor, Sylow
856#563—21no—
857#563—21no—
858#559C22×C7111yescharacteristic
859#559C22×C7111yescharacteristic
860#559C22×C7111yescharacteristic
861#559C22×C7111yescharacteristic
862Q82C22×C7111yescharacteristic, complemented
863#557C22×C7111yescharacteristic, complemented
864#557C22×C7111yescharacteristic, complemented
865#557C22×C7111yescharacteristic, complemented
866#556—21no—
867#556C22×C7111yescharacteristic
868#556C22×C7111yescharacteristic
869#556C22×C7111yescharacteristic
870#556C22×C7111yescharacteristic
871#556C22×C7111yescharacteristic, complemented
872#556C22×C7111yescharacteristic, complemented
873#556C22×C7111yescharacteristic, complemented
874#554C22×C7111yescharacteristic, complemented
875#552—21no—
876#551—21no—
877#551—21no—
878#551—21no—
879#551—21no—
880#544—21no—
881#542—21no—
882#542—21no—
883#542C22×C7111yescharacteristic
884#542C22×C7111yescharacteristic
885#541—21no—
886#541—21no—
887#541—21no—
888#541C22×C7111yescharacteristic
889#541C22×C7111yescharacteristic
890#536C22×C7111yescharacteristic
891#535C22×C7111yescharacteristic
892#533C22×C7111yescharacteristic
893#533C22×C7111yescharacteristic
894#529—21no—
895#529—21no—
896#529C22×C7111yescharacteristic
897C2×#124C22×C7111yescharacteristic
898#519C22×C7111yescharacteristic
899#518C22×C7111yescharacteristic
900C4×#41C22×C7111yescharacteristic
901#497C22×C7111yescharacteristic
902#497C22×C7111yescharacteristic
903#497C22×C7111yescharacteristic
904#497C22×C7111yescharacteristic, complemented
905#497C22×C7111yescharacteristic, complemented
906#496C22×C7111yescharacteristic
907#495C22×C7111yescharacteristic
908#495C22×C7111yescharacteristic
909#495C22×C7111yescharacteristic
910#495C22×C7111yescharacteristic, complemented
911#494C22×C7111yescharacteristic, complemented
912#492C22×C7111yescharacteristic
913#491C22×C7111yescharacteristic, complemented
914#490C22×C7111yescharacteristic
915#489C22×C7111yescharacteristic
916#489C22×C7111yescharacteristic
917#489C22×C7111yescharacteristic
918#489C22×C7111yescharacteristic, complemented
919#488C22×C7111yescharacteristic
920#488C22×C7111yescharacteristic
921#488C22×C7111yescharacteristic
922#488C22×C7111yescharacteristic, complemented
923#487C22×C7111yescharacteristic, complemented
924#486C22×C7111yescharacteristic
925#485C22×C7111yescharacteristic
926#485C22×C7111yescharacteristic
927#485C22×C7111yescharacteristic
928#482C22×C7111yescharacteristic
929#479C22×C7111yescharacteristic, complemented
930#479C22×C7111yescharacteristic, complemented
931#479C22×C7111yescharacteristic, complemented
932#478C22×C7111yescharacteristic
933#478C22×C7111yescharacteristic
934#478C22×C7111yescharacteristic, complemented
935#477C22×C7111yescharacteristic, complemented
936#476C22×C7111yescharacteristic
937#475C22×C7111yescharacteristic, complemented
938#475C22×C7111yescharacteristic, complemented
939#474C22×C7111yescharacteristic
940#474C22×C7111yescharacteristic, complemented
941#464C22×C7111yescharacteristic
942#464C22×C7111yescharacteristic
943#464C22×C7111yescharacteristic
944#464C22×C7111yescharacteristic
945#464C22×C7111yescharacteristic
946#464C22×C7111yescharacteristic
947#464C22×C7111yescharacteristic
948#464C22×C7111yescharacteristic
949#464C22×C7111yescharacteristic
950#464C22×C7111yescharacteristic, complemented
951#464C22×C7111yescharacteristic, complemented
952#464C22×C7111yescharacteristic, complemented
953#464C22×C7111yescharacteristic, complemented
954#464C22×C7111yescharacteristic, complemented
955#464C22×C7111yescharacteristic, complemented
956#463C22×C7111yescharacteristic
957#463C22×C7111yescharacteristic
958#463C22×C7111yescharacteristic
959#463C22×C7111yescharacteristic
960#463C22×C7111yescharacteristic
961#463C22×C7111yescharacteristic, complemented
962#463C22×C7111yescharacteristic, complemented
963#462C22×C7111yescharacteristic, complemented
964#462C22×C7111yescharacteristic, complemented
965#462C22×C7111yescharacteristic, complemented
966#462C22×C7111yescharacteristic, complemented
967#462C22×C7111yescharacteristic, complemented
968#462C22×C7111yescharacteristic, complemented
969#461C22×C7111yescharacteristic
970#461C22×C7111yescharacteristic
971#461C22×C7111yescharacteristic, complemented
972#461C22×C7111yescharacteristic, complemented
973#460C22×C7111yescharacteristic
974#460C22×C7111yescharacteristic
975#460C22×C7111yescharacteristic
976#459C22×C7111yescharacteristic
977#452C22×C7111yescharacteristic
978#452C22×C7111yescharacteristic
979#452C22×C7111yescharacteristic
980#451C22×C7111yescharacteristic
981#451C22×C7111yescharacteristic
982#451C22×C7111yescharacteristic
983#450C22×C7111yescharacteristic
984#450C22×C7111yescharacteristic
985#450C22×C7111yescharacteristic
986#449C22×C7111yescharacteristic
987#448C22×C7111yescharacteristic
988#447C22×C7111yescharacteristic
989#446C22×C7111yescharacteristic, complemented
990#446C22×C7111yescharacteristic, complemented
991#446C22×C7111yescharacteristic, complemented
992#446C22×C7111yescharacteristic, complemented
993#446C22×C7111yescharacteristic, complemented
994#446C22×C7111yescharacteristic, complemented
995C8×Q8C22×C7111yescharacteristic, complemented
996C8×Q8C22×C7111yescharacteristic, complemented
997#442C22×C7111yescharacteristic
998#442C22×C7111yescharacteristic, complemented
999#441C22×C7111yescharacteristic, complemented
1000#441C22×C7111yescharacteristic, complemented
1001#441C22×C7111yescharacteristic, complemented
1002#441C22×C7111yescharacteristic, complemented
1003#440C22×C7111yescharacteristic
1004#440C22×C7111yescharacteristic
1005#440C22×C7111yescharacteristic
1006#440C22×C7111yescharacteristic, complemented
1007#440C22×C7111yescharacteristic, complemented
1008#440C22×C7111yescharacteristic, complemented
1009C4×Q16C22×C7111yescharacteristic, complemented
1010C4×Q16C22×C7111yescharacteristic, complemented
1011C4×Q16C22×C7111yescharacteristic, complemented
1012C4×Q16C22×C7111yescharacteristic, complemented
1013C4×Q16C22×C7111yescharacteristic, complemented
1014C4×SD16C22×C7111yescharacteristic
1015C4×SD16C22×C7111yescharacteristic
1016C4×SD16C22×C7111yescharacteristic
1017C4×SD16C22×C7111yescharacteristic, complemented
1018C4×SD16C22×C7111yescharacteristic, complemented
1019C4×SD16C22×C7111yescharacteristic, complemented
1020C4×D8C22×C7111yescharacteristic
1021#433C22×C7111yescharacteristic
1022#433C22×C7111yescharacteristic
1023#433C22×C7111yescharacteristic
1024#433C22×C7111yescharacteristic
1025#432C22×C7111yescharacteristic
1026#431C22×C7111yescharacteristic
1027C2×#41C23×C7111yescharacteristic
1028C22×Q8C23×C7111yescharacteristic
1029C22×D4C23×C7111yescharacteristic
1030C2×Q16C23×C7111yescharacteristic
1031C2×Q16C23×C7111yescharacteristic
1032C2×Q16C23×C7111yescharacteristic
1033C2×Q16C23×C7111yescharacteristic
1034C2×Q16C23×C7111yescharacteristic
1035C2×Q16C23×C7111yescharacteristic
1036C2×Q16C23×C7111yescharacteristic
1037C2×Q16C23×C7111yescharacteristic
1038C2×Q16C23×C7111yescharacteristic
1039C2×SD16C23×C7111yescharacteristic
1040C2×SD16C23×C7111yescharacteristic
1041C2×SD16C23×C7111yescharacteristic
1042C2×SD16C23×C7111yescharacteristic
1043C2×SD16C23×C7111yescharacteristic
1044C2×SD16C23×C7111yescharacteristic
1045C2×SD16C23×C7111yescharacteristic
1046C2×SD16C23×C7111yescharacteristic
1047C2×SD16C23×C7111yescharacteristic
1048C2×SD16C23×C7111yescharacteristic
1049C2×SD16C23×C7111yescharacteristic
1050C2×SD16C23×C7111yescharacteristic
1051C2×D8C23×C7111yescharacteristic
1052C2×D8C23×C7111yescharacteristic
1053C2×D8C23×C7111yescharacteristic
1054C4⋊Q8—21no—
1055C4⋊Q8—21no—
1056C4⋊Q8—21no—
1057C4⋊Q8—21no—
1058C4⋊Q8—21no—
1059C4⋊Q8D4×C7111yescharacteristic
1060C4⋊Q8D4×C7111yescharacteristic
1061C4⋊Q8C23×C7111yescharacteristic
1062C4⋊Q8C23×C7111yescharacteristic
1063C4⋊Q8C23×C7111yescharacteristic
1064C4⋊Q8C23×C7111yescharacteristic
1065C4⋊Q8C23×C7111yescharacteristic
1066C4⋊Q8C23×C7111yescharacteristic
1067C4⋊Q8C23×C7111yescharacteristic
1068C4⋊Q8C23×C7111yescharacteristic
1069#127C23×C7111yescharacteristic
1070#127C23×C7111yescharacteristic
1071#126—21no—
1072#126—21no—
1073#126—21no—
1074#126—21no—
1075#126—21no—
1076#126—21no—
1077#126—21no—
1078#126—21no—
1079#126—21no—
1080#126—21no—
1081#126—21no—
1082#126—21no—
1083#126—21no—
1084#126—21no—
1085#126—21no—
1086#126—21no—
1087#126—21no—
1088#126—21no—
1089#126—21no—
1090#126—21no—
1091#126—21no—
1092#125—21no—
1093#125—21no—
1094#125—21no—
1095#125—21no—
1096#125—21no—
1097#125—21no—
1098#125—21no—
1099#125—21no—
1100#125—21no—
1101#125—21no—
1102#125—21no—
1103#125—21no—
1104#125D4×C7111yescharacteristic
1105#125D4×C7111yescharacteristic
1106#125C23×C7111yescharacteristic
1107#125C23×C7111yescharacteristic
1108#125C23×C7111yescharacteristic
1109#124—21no—
1110#124—21no—
1111#124—21no—
1112#124—21no—
1113#124—21no—
1114#124—21no—
1115#124—21no—
1116#124—21no—
1117#124C23×C7111yescharacteristic
1118#124C23×C7111yescharacteristic
1119#124C23×C7111yescharacteristic
1120#124C23×C7111yescharacteristic
1121#124C23×C7111yescharacteristic
1122#124C23×C7111yescharacteristic
1123#124C23×C7111yescharacteristic
1124#124C23×C7111yescharacteristic
1125#124C23×C7111yescharacteristic
1126#124C23×C7111yescharacteristic
1127#124C23×C7111yescharacteristic
1128#123—21no—
1129#123—21no—
1130#123—21no—
1131#123—21no—
1132#123—21no—
1133#123—21no—
1134#123—21no—
1135#123—21no—
1136#123—21no—
1137#123—21no—
1138#123—21no—
1139#123—21no—
1140#123—21no—
1141C22⋊Q8—21no—
1142C22⋊Q8—21no—
1143C22⋊Q8—21no—
1144C22⋊Q8—21no—
1145C22⋊Q8—21no—
1146C22⋊Q8—21no—
1147C22⋊Q8—21no—
1148C22⋊Q8—21no—
1149C22⋊Q8—21no—
1150C22⋊Q8—21no—
1151C22⋊Q8—21no—
1152C22⋊Q8—21no—
1153C22⋊Q8—21no—
1154C22⋊Q8—21no—
1155C22⋊Q8—21no—
1156C22⋊Q8D4×C7111yescharacteristic
1157C22⋊Q8D4×C7111yescharacteristic
1158C22⋊Q8D4×C7111yescharacteristic
1159C22⋊Q8D4×C7111yescharacteristic
1160C22⋊Q8C23×C7111yescharacteristic
1161C22⋊Q8C23×C7111yescharacteristic
1162C22⋊Q8C23×C7111yescharacteristic
1163#121—21no—
1164#121—21no—
1165#121C23×C7111yescharacteristic
1166#120—21no—
1167#120—21no—
1168C4×Q8—21no—
1169C4×Q8—21no—
1170C4×Q8—21no—
1171C4×Q8—21no—
1172C4×Q8—21no—
1173C4×Q8—21no—
1174C4×Q8—21no—
1175C4×Q8C23×C7111yescharacteristic
1176C4×Q8C23×C7111yescharacteristic
1177C4×Q8C23×C7111yescharacteristic
1178C4×Q8C23×C7111yescharacteristic
1179C4×Q8C23×C7111yescharacteristic
1180C4×Q8C23×C7111yescharacteristic
1181C4×Q8C23×C7111yescharacteristic
1182C4×Q8C23×C7111yescharacteristic
1183C4×Q8C23×C7111yescharacteristic
1184C4×Q8C23×C7111yescharacteristic
1185C4×Q8C23×C7111yescharacteristic
1186C4×Q8C23×C7111yescharacteristic
1187C4×Q8C23×C7111yescharacteristic
1188C4×Q8C23×C7111yescharacteristic
1189C4×Q8C23×C7111yescharacteristic
1190C4×Q8C23×C7111yescharacteristic
1191C4×Q8C23×C7111yescharacteristic
1192C4×Q8C23×C7111yescharacteristic
1193C4×Q8C23×C7111yescharacteristic
1194C4×D4—21no—
1195C4×D4—21no—
1196C4×D4—21no—
1197C4×D4—21no—
1198C4×D4—21no—
1199C4×D4—21no—
1200C4×D4—21no—
1201C4×D4—21no—
1202C4×D4—21no—
1203C4×D4C23×C7111yescharacteristic
1204C4×D4C23×C7111yescharacteristic
1205C4×D4C23×C7111yescharacteristic
1206C4×D4C23×C7111yescharacteristic
1207C4×D4C23×C7111yescharacteristic
1208C4×D4C23×C7111yescharacteristic
1209C4×D4C23×C7111yescharacteristic
1210C4×D4C23×C7111yescharacteristic
1211C4×D4C23×C7111yescharacteristic
1212#117—21no—
1213#117—21no—
1214#117—21no—
1215#117—21no—
1216#117—21no—
1217#117—21no—
1218#117—21no—
1219#117—21no—
1220#117—21no—
1221#117—21no—
1222#117—21no—
1223#117—21no—
1224#117C23×C7111yescharacteristic
1225#117C23×C7111yescharacteristic
1226#117C23×C7111yescharacteristic
1227C2×C4⋊C4—21no—
1228C2×C22⋊C4—21no—
1229C2×C22⋊C4—21no—
1230C2×C22⋊C4—21no—
1231C2×C22⋊C4—21no—
1232C2×C42—21no—
1233C2×C42C23×C7111yescharacteristic
1234#107C23×C7111yescharacteristic
1235#107C23×C7111yescharacteristic
1236#107C23×C7111yescharacteristic
1237#107C23×C7111yescharacteristic
1238#106C23×C7111yescharacteristic
1239#106C23×C7111yescharacteristic
1240#106C23×C7111yescharacteristic
1241#106C23×C7111yescharacteristic
1242C4⋊C8C23×C7111yescharacteristic
1243C4⋊C8C23×C7111yescharacteristic
1244C4⋊C8C23×C7111yescharacteristic
1245C4⋊C8C23×C7111yescharacteristic
1246C4⋊C8C23×C7111yescharacteristic
1247C4⋊C8C23×C7111yescharacteristic
1248C4⋊C8C23×C7111yescharacteristic
1249C4⋊C8C23×C7111yescharacteristic
1250C4⋊C8C23×C7111yescharacteristic
1251C4⋊C8C23×C7111yescharacteristic
1252C4⋊C8C23×C7111yescharacteristic
1253C4⋊C8C23×C7111yescharacteristic
1254#103C23×C7111yescharacteristic
1255#103C23×C7111yescharacteristic
1256#103C23×C7111yescharacteristic
1257#103C23×C7111yescharacteristic
1258#103C23×C7111yescharacteristic
1259#103C23×C7111yescharacteristic
1260#103C23×C7111yescharacteristic
1261#103C23×C7111yescharacteristic
1262#103C23×C7111yescharacteristic
1263#103C23×C7111yescharacteristic
1264#103C23×C7111yescharacteristic
1265#103C23×C7111yescharacteristic
1266#103C23×C7111yescharacteristic
1267#103C23×C7111yescharacteristic
1268#103C23×C7111yescharacteristic
1269#103C23×C7111yescharacteristic
1270#103C23×C7111yescharacteristic
1271#103C23×C7111yescharacteristic
1272#102C23×C7111yescharacteristic
1273#102C23×C7111yescharacteristic
1274#102C23×C7111yescharacteristic
1275#102C23×C7111yescharacteristic
1276#102C23×C7111yescharacteristic
1277#102C23×C7111yescharacteristic
1278#102C23×C7111yescharacteristic
1279#102C23×C7111yescharacteristic
1280#102C23×C7111yescharacteristic
1281#102C23×C7111yescharacteristic
1282#102C23×C7111yescharacteristic
1283#102C23×C7111yescharacteristic
1284#102C23×C7111yescharacteristic
1285#102C23×C7111yescharacteristic
1286C22⋊C8C23×C7111yescharacteristic
1287C22⋊C8C23×C7111yescharacteristic
1288C22⋊C8C23×C7111yescharacteristic
1289C22⋊C8C23×C7111yescharacteristic
1290#97C23×C7111yescharacteristic
1291#97C23×C7111yescharacteristic
1292#97C23×C7111yescharacteristic
1293#97C23×C7111yescharacteristic
1294#97C23×C7111yescharacteristic
1295#97C23×C7111yescharacteristic
1296C4×C8C23×C7111yescharacteristic
1297C4×C8C23×C7111yescharacteristic
1298C4×C8C23×C7111yescharacteristic
1299C4×C8C23×C7111yescharacteristic
1300C4×C8C23×C7111yescharacteristic
1301C4×C8C23×C7111yescharacteristic
1302C24—21no—
1303#41—41no—
1304#41—41no—
1305C2×Q8—21no—
1306C2×Q8—21no—
1307C2×Q8—21no—
1308C2×Q8—21no—
1309C2×Q8—41no—
1310C2×Q8—41no—
1311C2×Q8C2×D4×C7111yescharacteristic
1312C2×Q8C2×D4×C7111yescharacteristic
1313C2×Q8C2×D4×C7111yescharacteristic
1314C2×Q8C2×D4×C7111yescharacteristic
1315C2×Q8C24×C7111yescharacteristic
1316C2×Q8C24×C7111yescharacteristic
1317C2×Q8C24×C7111yescharacteristic
1318C2×Q8C24×C7111yescharacteristic
1319C2×Q8C24×C7111yescharacteristic
1320C2×Q8C24×C7111yescharacteristic
1321C2×D4—21no—
1322C2×D4—21no—
1323C2×D4—21no—
1324C2×D4—21no—
1325C2×D4—21no—
1326C2×D4—21no—
1327C2×D4—21no—
1328C2×D4—41no—
1329C2×D4—41no—
1330C2×D4C24×C7111yescharacteristic
1331C2×D4C24×C7111yescharacteristic
1332C2×D4C24×C7111yescharacteristic
1333C2×D4C24×C7111yescharacteristic
1334C22×C4—21no—
1335C22×C4—21no—
1336C22×C4—21no—
1337C22×C4—21no—
1338C22×C4—21no—
1339C22×C4—21no—
1340C22×C4—21no—
1341C22×C4—21no—
1342C22×C4—21no—
1343C22×C4—21no—
1344C22×C4—21no—
1345C22×C4C2×D4×C7111yescharacteristic
1346C22×C4C2×D4×C7111yescharacteristic
1347C22×C4C24×C7111yescharacteristic
1348Q16—41no—
1349Q16—41no—
1350Q16—41no—
1351Q16—41no—
1352Q16—41no—
1353Q16—41no—
1354Q16—41no—
1355Q16—41no—
1356Q16—41no—
1357SD16—41no—
1358SD16—41no—
1359SD16—41no—
1360SD16—41no—
1361SD16—41no—
1362SD16—41no—
1363SD16—41no—
1364SD16—41no—
1365SD16—41no—
1366SD16—41no—
1367SD16—41no—
1368SD16—41no—
1369D8—41no—
1370D8—41no—
1371D8—41no—
1372C2×C8C24×C7111yescharacteristic
1373C2×C8C24×C7111yescharacteristic
1374C2×C8C24×C7111yescharacteristic
1375C2×C8C24×C7111yescharacteristic
1376C2×C8C24×C7111yescharacteristic
1377C2×C8C24×C7111yescharacteristic
1378C2×C8C24×C7111yescharacteristic
1379C2×C8C24×C7111yescharacteristic
1380C4⋊C4—21no—
1381C4⋊C4—21no—
1382C4⋊C4—21no—
1383C4⋊C4—21no—
1384C4⋊C4—21no—
1385C4⋊C4—21no—
1386C4⋊C4—21no—
1387C4⋊C4—21no—
1388C4⋊C4—21no—
1389C4⋊C4—21no—
1390C4⋊C4—21no—
1391C4⋊C4—21no—
1392C4⋊C4—21no—
1393C4⋊C4—21no—
1394C4⋊C4—21no—
1395C4⋊C4—21no—
1396C4⋊C4—21no—
1397C4⋊C4—21no—
1398C4⋊C4—21no—
1399C4⋊C4—21no—
1400C4⋊C4—21no—
1401C4⋊C4—21no—
1402C4⋊C4—21no—
1403C4⋊C4—21no—
1404C4⋊C4—21no—
1405C4⋊C4—21no—
1406C4⋊C4—21no—
1407C4⋊C4—21no—
1408C4⋊C4—21no—
1409C4⋊C4—21no—
1410C4⋊C4—21no—
1411C4⋊C4—21no—
1412C4⋊C4—21no—
1413C4⋊C4—21no—
1414C4⋊C4—21no—
1415C4⋊C4—21no—
1416C4⋊C4—21no—
1417C4⋊C4C2×D4×C7111yescharacteristic
1418C4⋊C4C2×D4×C7111yescharacteristic
1419C4⋊C4C2×D4×C7111yescharacteristic
1420C4⋊C4C2×D4×C7111yescharacteristic
1421C4⋊C4C2×D4×C7111yescharacteristic
1422C4⋊C4C2×D4×C7111yescharacteristic
1423C4⋊C4C2×D4×C7111yescharacteristic
1424C4⋊C4C2×D4×C7111yescharacteristic
1425C4⋊C4C2×D4×C7111yescharacteristic
1426C4⋊C4C2×D4×C7111yescharacteristic
1427C4⋊C4C2×D4×C7111yescharacteristic
1428C4⋊C4C2×D4×C7111yescharacteristic
1429C4⋊C4C2×D4×C7111yescharacteristic
1430C4⋊C4C2×D4×C7111yescharacteristic
1431C4⋊C4C2×D4×C7111yescharacteristic
1432C4⋊C4C2×D4×C7111yescharacteristic
1433C4⋊C4C24×C7111yescharacteristic
1434C4⋊C4C24×C7111yescharacteristic
1435C4⋊C4C24×C7111yescharacteristic
1436C4⋊C4C24×C7111yescharacteristic
1437C4⋊C4C24×C7111yescharacteristic
1438C4⋊C4C24×C7111yescharacteristic
1439C22⋊C4—21no—
1440C22⋊C4—21no—
1441C22⋊C4—21no—
1442C22⋊C4—21no—
1443C22⋊C4—21no—
1444C22⋊C4—21no—
1445C22⋊C4—21no—
1446C22⋊C4—21no—
1447C22⋊C4—21no—
1448C22⋊C4—21no—
1449C22⋊C4—21no—
1450C22⋊C4—21no—
1451C22⋊C4—21no—
1452C22⋊C4—21no—
1453C22⋊C4—21no—
1454C22⋊C4—21no—
1455C22⋊C4—21no—
1456C22⋊C4—21no—
1457C22⋊C4—21no—
1458C22⋊C4—21no—
1459C22⋊C4—21no—
1460C22⋊C4—21no—
1461C22⋊C4—21no—
1462C22⋊C4—21no—
1463C22⋊C4—21no—
1464C22⋊C4—21no—
1465C22⋊C4—21no—
1466C22⋊C4—21no—
1467C22⋊C4—21no—
1468C22⋊C4—21no—
1469C22⋊C4—21no—
1470C22⋊C4—21no—
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4C2×D4×C7111yescharacteristic
1476C22⋊C4C2×D4×C7111yescharacteristic
1477C22⋊C4C2×D4×C7111yescharacteristic
1478C22⋊C4C2×D4×C7111yescharacteristic
1479C42—21no—
1480C42—21no—
1481C42—21no—
1482C42—21no—
1483C42—21no—
1484C42—21no—
1485C42—21no—
1486C42—21no—
1487C42—21no—
1488C42—21no—
1489C42—21no—
1490C42—21no—
1491C42—21no—
1492C42—21no—
1493C42—21no—
1494C42—21no—
1495C42C2×D4×C7111yescharacteristic
1496C42C2×D4×C7111yescharacteristic
1497C42C24×C7111yescharacteristic
1498C42C24×C7111yescharacteristic
1499C42C24×C7111yescharacteristic
1500C42C24×C7111yescharacteristic
1501C42C24×C7111yescharacteristic
1502C42C24×C7111yescharacteristic
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—42no—
1508C23—81no—
1509C23—81no—
1510C23C22×D4×C7111yescharacteristic
1511Q8—21no—
1512Q8—21no—
1513Q8—21no—
1514Q8—21no—
1515Q8—21no—
1516Q8—21no—
1517Q8—21no—
1518Q8—21no—
1519Q8—21no—
1520Q8—21no—
1521Q8—21no—
1522Q8—21no—
1523Q8—41no—
1524Q8—41no—
1525Q8—41no—
1526Q8—41no—
1527Q8—42no—
1528Q8—81no—
1529Q8—81no—
1530Q8—81no—
1531D4—21no—
1532D4—21no—
1533D4—21no—
1534D4—21no—
1535D4—21no—
1536D4—21no—
1537D4—21no—
1538D4—21no—
1539D4—42no—
1540D4—42no—
1541D4—81no—
1542D4—81no—
1543D4—81no—
1544D4—81no—
1545D4—81no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—41no—
1561C2×C4—41no—
1562C2×C4—42no—
1563C2×C4—42no—
1564C2×C4—42no—
1565C2×C4—81no—
1566C2×C4—81no—
1567C2×C4—81no—
1568C2×C4—81no—
1569C2×C4—81no—
1570C2×C4—81no—
1571C2×C4—81no—
1572C2×C4—81no—
1573C2×C4C22×D4×C7111yescharacteristic
1574C2×C4C22×D4×C7111yescharacteristic
1575C2×C4C22×D4×C7111yescharacteristic
1576C2×C4C22×D4×C7111yescharacteristic
1577C2×C4C22×D4×C7111yescharacteristic
1578C2×C4C22×D4×C7111yescharacteristic
1579C2×C4C22×D4×C7111yescharacteristic
1580C2×C4C22×D4×C7111yescharacteristic
1581C2×C4C22×D4×C7111yescharacteristic
1582C2×C4C22×D4×C7111yescharacteristic
1583C2×C4C22×D4×C7111yescharacteristic
1584C2×C4C22×D4×C7111yescharacteristic
1585C2×C4C22×D4×C7111yescharacteristic
1586C2×C4C25×C7111yescharacteristic
1587C8—21no—
1588C8—21no—
1589C8—21no—
1590C8—21no—
1591C8—21no—
1592C8—21no—
1593C8—21no—
1594C8—21no—
1595C22—21no—
1596C22—21no—
1597C22—21no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—162no—
1611C22C23×D4×C7111yescharacteristic
1612C4—21no—
1613C4—21no—
1614C4—21no—
1615C4—21no—
1616C4—21no—
1617C4—21no—
1618C4—21no—
1619C4—21no—
1620C4—21no—
1621C4—21no—
1622C4—21no—
1623C4—21no—
1624C4—21no—
1625C4—41no—
1626C4—41no—
1627C4—41no—
1628C4—41no—
1629C4—41no—
1630C4—41no—
1631C4—41no—
1632C4—41no—
1633C4—41no—
1634C4—41no—
1635C4—41no—
1636C4—41no—
1637C4#585×C7111yescharacteristic
1638C4#585×C7111yescharacteristic
1639C2—41no—
1640C2—81no—
1641C2—81no—
1642C2—81no—
1643C2—81no—
1644C2C71×#348711yescharacteristic
1645C2C71×#358411yescharacteristic
1646C2C71×#358611yescharacteristic
subgroupG/H
center, socleC22×C71C23×D4
commutator, Frattini, cosocleC2×C4C25×C71
prime radicalC71×#3224C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C71 ◁ #533×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C71×#3555C2semidirect
2. C71×#3510C2semidirect
3. C71×#3402C2semidirect
4. C71×#3402C2semidirect
5. C71×#3401C2semidirect
6. C71×#3401C2semidirect
7. C71×#3400C2semidirect
8. C71×#3398C2semidirect
9. C71×#3394C2semidirect
10. C71×#3393C2semidirect
11. C71×#3377C2semidirect
12. C71×#3376C2semidirect
13. C71×#3375C2semidirect
14. C71×#3371C2semidirect
15. C71×#3370C2semidirect
16. C71×#3369C2semidirect
17. C71×#3365C2semidirect
18. C71×#3364C2semidirect
19. C71×#3225C2semidirect
21. C71×#3223C2semidirect
22. C71×#3222C2semidirect
23. C71×#3215C2semidirect
24. C71×#3211C2semidirect
25. C71×#3127C2semidirect
26. C71×#3123C2semidirect
27. C71×#3121C2semidirect
28. C71×#3118C2semidirect
29. C71×#3111C2semidirect
30. C71×#3107C2semidirect
31. C71×#2985C2semidirect
38. Q82×C71C22semidirect
39. #557×C71C22semidirect
40. #557×C71C22semidirect
41. #557×C71C22semidirect
47. #556×C71C22semidirect
48. #556×C71C22semidirect
49. #556×C71C22semidirect
50. #554×C71C22semidirect
80. #497×C71C22semidirect
81. #497×C71C22semidirect
86. #495×C71C22semidirect
87. #494×C71C22semidirect
89. #491×C71C22semidirect
94. #489×C71C22semidirect
98. #488×C71C22semidirect
99. #487×C71C22semidirect
105. #479×C71C22semidirect
106. #479×C71C22semidirect
107. #479×C71C22semidirect
110. #478×C71C22semidirect
111. #477×C71C22semidirect
113. #475×C71C22semidirect
114. #475×C71C22semidirect
116. #474×C71C22semidirect
126. #464×C71C22semidirect
127. #464×C71C22semidirect
128. #464×C71C22semidirect
129. #464×C71C22semidirect
130. #464×C71C22semidirect
131. #464×C71C22semidirect
137. #463×C71C22semidirect
138. #463×C71C22semidirect
139. #462×C71C22semidirect
140. #462×C71C22semidirect
141. #462×C71C22semidirect
142. #462×C71C22semidirect
143. #462×C71C22semidirect
144. #462×C71C22semidirect
147. #461×C71C22semidirect
148. #461×C71C22semidirect
165. #446×C71C22semidirect
166. #446×C71C22semidirect
167. #446×C71C22semidirect
168. #446×C71C22semidirect
169. #446×C71C22semidirect
170. #446×C71C22semidirect
171. C8×Q8×C71C22semidirect
172. C8×Q8×C71C22semidirect
174. #442×C71C22semidirect
175. #441×C71C22semidirect
176. #441×C71C22semidirect
177. #441×C71C22semidirect
178. #441×C71C22semidirect
182. #440×C71C22semidirect
183. #440×C71C22semidirect
184. #440×C71C22semidirect
185. C4×Q16×C71C22semidirect
186. C4×Q16×C71C22semidirect
187. C4×Q16×C71C22semidirect
188. C4×Q16×C71C22semidirect
189. C4×Q16×C71C22semidirect
193. C4×SD16×C71C22semidirect
194. C4×SD16×C71C22semidirect
195. C4×SD16×C71C22semidirect
815. #61925C71direct (N × H)
824. #3555C2×C71semidirect
825. #3510C2×C71semidirect
826. #3402C2×C71semidirect
827. #3402C2×C71semidirect
828. #3401C2×C71semidirect
829. #3401C2×C71semidirect
830. #3400C2×C71semidirect
831. #3398C2×C71semidirect
832. #3394C2×C71semidirect
833. #3393C2×C71semidirect
834. #3377C2×C71semidirect
835. #3376C2×C71semidirect
836. #3375C2×C71semidirect
837. #3371C2×C71semidirect
838. #3370C2×C71semidirect
839. #3369C2×C71semidirect
840. #3365C2×C71semidirect
841. #3364C2×C71semidirect
842. #3225C2×C71semidirect
844. #3223C2×C71semidirect
845. #3222C2×C71semidirect
846. #3215C2×C71semidirect
847. #3211C2×C71semidirect
848. #3127C2×C71semidirect
849. #3123C2×C71semidirect
850. #3121C2×C71semidirect
851. #3118C2×C71semidirect
852. #3111C2×C71semidirect
853. #3107C2×C71semidirect
854. #2985C2×C71semidirect
855. C71#61925direct (N × H)
862. Q82C22×C71semidirect
863. #557C22×C71semidirect
864. #557C22×C71semidirect
865. #557C22×C71semidirect
871. #556C22×C71semidirect
872. #556C22×C71semidirect
873. #556C22×C71semidirect
874. #554C22×C71semidirect
904. #497C22×C71semidirect
905. #497C22×C71semidirect
910. #495C22×C71semidirect
911. #494C22×C71semidirect
913. #491C22×C71semidirect
918. #489C22×C71semidirect
922. #488C22×C71semidirect
923. #487C22×C71semidirect
929. #479C22×C71semidirect
930. #479C22×C71semidirect
931. #479C22×C71semidirect
934. #478C22×C71semidirect
935. #477C22×C71semidirect
937. #475C22×C71semidirect
938. #475C22×C71semidirect
940. #474C22×C71semidirect
950. #464C22×C71semidirect
951. #464C22×C71semidirect
952. #464C22×C71semidirect
953. #464C22×C71semidirect
954. #464C22×C71semidirect
955. #464C22×C71semidirect
961. #463C22×C71semidirect
962. #463C22×C71semidirect
963. #462C22×C71semidirect
964. #462C22×C71semidirect
965. #462C22×C71semidirect
966. #462C22×C71semidirect
967. #462C22×C71semidirect
968. #462C22×C71semidirect
971. #461C22×C71semidirect
972. #461C22×C71semidirect
989. #446C22×C71semidirect
990. #446C22×C71semidirect
991. #446C22×C71semidirect
992. #446C22×C71semidirect
993. #446C22×C71semidirect
994. #446C22×C71semidirect
995. C8×Q8C22×C71semidirect
996. C8×Q8C22×C71semidirect
998. #442C22×C71semidirect
999. #441C22×C71semidirect
1000. #441C22×C71semidirect
1001. #441C22×C71semidirect
1002. #441C22×C71semidirect
1006. #440C22×C71semidirect
1007. #440C22×C71semidirect
1008. #440C22×C71semidirect
1009. C4×Q16C22×C71semidirect
1010. C4×Q16C22×C71semidirect
1011. C4×Q16C22×C71semidirect
1012. C4×Q16C22×C71semidirect
1013. C4×Q16C22×C71semidirect
1017. C4×SD16C22×C71semidirect
1018. C4×SD16C22×C71semidirect
1019. C4×SD16C22×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#35552
C71×#35102
C71×#34022
C71×#34012
C71×#34002
C71×#33982
C71×#33942
C71×#33932
C71×#33772
C71×#33762
C71×#33752
C71×#33712
C71×#33702
C71×#33692
C71×#33652
C71×#33642
C71×#32252
C71×#32242
C71×#32232
C71×#32222
C71×#32152
C71×#32112
C71×#31272
C71×#31232
C71×#31212
C71×#31182
C71×#31112
C71×#31072
C71×#29852
#6192571