Finite Group Databasebeta

← C71×#61919 #31882791

Subgroups — C71×#61919 #31882791

Order 18176.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3557C211yesmaximal, characteristic, complemented
2C71×#3506C211yesmaximal, characteristic, complemented
3C71×#3403C211yesmaximal, characteristic, complemented
4C71×#3402C211yesmaximal, characteristic, complemented
5C71×#3401C211yesmaximal, characteristic, complemented
6C71×#3401C211yesmaximal, characteristic, complemented
7C71×#3399C211yesmaximal, characteristic, complemented
8C71×#3397C211yesmaximal, characteristic, complemented
9C71×#3396C211yesmaximal, characteristic, complemented
10C71×#3394C211yesmaximal, characteristic, complemented
11C71×#3377C211yesmaximal, characteristic, complemented
12C71×#3376C211yesmaximal, characteristic, complemented
13C71×#3371C211yesmaximal, characteristic, complemented
14C71×#3370C211yesmaximal, characteristic, complemented
15C71×#3368C211yesmaximal, characteristic, complemented
16C71×#3366C211yesmaximal, characteristic, complemented
17C71×#3365C211yesmaximal, characteristic, complemented
18C71×#3361C211yesmaximal, characteristic, complemented
19C71×#3224C211yesmaximal, characteristic, complemented
20C71×#3224C211yesmaximal, characteristic, complemented
21C71×#3222C211yesmaximal, characteristic, complemented
22C71×#3220C211yesmaximal, characteristic, complemented
23C71×#3219C211yesmaximal, characteristic, complemented
24C71×#3212C211yesmaximal, characteristic, complemented
25C71×#3125C211yesmaximal, characteristic, complemented
26C71×#3124C211yesmaximal, characteristic, complemented
27C71×#3120C211yesmaximal, characteristic, complemented
28C71×#3119C211yesmaximal, characteristic, complemented
29C71×#3114C211yesmaximal, characteristic, complemented
30C71×#3105C211yesmaximal, 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
38#559×C71C2211yescharacteristic, complemented
39#559×C71C2211yescharacteristic, complemented
40#557×C71C2211yescharacteristic, complemented
41#557×C71C2211yescharacteristic, complemented
42#556×C71C2211yescharacteristic
43#556×C71C2211yescharacteristic
44#556×C71C2211yescharacteristic, complemented
45#556×C71C2211yescharacteristic, complemented
46#555×C71—21no—
47#554×C71C2211yescharacteristic, complemented
48#554×C71C2211yescharacteristic, complemented
49#553×C71—21no—
50#553×C71—21no—
51#552×C71—21no—
52#552×C71—21no—
53#550×C71C2211yescharacteristic
54#550×C71C2211yescharacteristic
55#547×C71—21no—
56#542×C71—21no—
57#542×C71—21no—
58#542×C71C2211yescharacteristic
59#542×C71C2211yescharacteristic
60#541×C71C2211yescharacteristic
61#540×C71C2211yescharacteristic
62#539×C71—21no—
63#539×C71—21no—
64#538×C71—21no—
65#538×C71—21no—
66#535×C71C2211yescharacteristic
67#535×C71C2211yescharacteristic
68#533×C71C2211yescharacteristic
69#532×C71C2211yescharacteristic
70#529×C71C2211yescharacteristic
71#529×C71C2211yescharacteristic
72#525×C71—21no—
73#525×C71—21no—
74#520×C71C2211yescharacteristic
75#520×C71C2211yescharacteristic
76C2×C4×D4×C71C2211yescharacteristic
77#497×C71C2211yescharacteristic
78#497×C71C2211yescharacteristic, complemented
79#496×C71C2211yescharacteristic
80#496×C71C2211yescharacteristic
81#496×C71C2211yescharacteristic
82#496×C71C2211yescharacteristic, complemented
83#495×C71C2211yescharacteristic
84#495×C71C2211yescharacteristic
85#495×C71C2211yescharacteristic, complemented
86#495×C71C2211yescharacteristic, complemented
87#493×C71C2211yescharacteristic
88#492×C71C2211yescharacteristic
89#491×C71C2211yescharacteristic, complemented
90#490×C71C2211yescharacteristic
91#490×C71C2211yescharacteristic
92#490×C71C2211yescharacteristic, complemented
93#489×C71C2211yescharacteristic
94#489×C71C2211yescharacteristic
95#488×C71C2211yescharacteristic
96#488×C71C2211yescharacteristic
97#488×C71C2211yescharacteristic, complemented
98#488×C71C2211yescharacteristic, complemented
99#486×C71C2211yescharacteristic
100#486×C71C2211yescharacteristic
101#484×C71C2211yescharacteristic
102#483×C71C2211yescharacteristic
103#481×C71C2211yescharacteristic
104#480×C71C2211yescharacteristic
105#479×C71C2211yescharacteristic, complemented
106#479×C71C2211yescharacteristic, complemented
107#478×C71C2211yescharacteristic
108#478×C71C2211yescharacteristic
109#478×C71C2211yescharacteristic
110#478×C71C2211yescharacteristic
111#478×C71C2211yescharacteristic, complemented
112#478×C71C2211yescharacteristic, complemented
113#477×C71C2211yescharacteristic, complemented
114#476×C71C2211yescharacteristic, complemented
115#475×C71C2211yescharacteristic, complemented
116#474×C71C2211yescharacteristic, complemented
117#464×C71C2211yescharacteristic
118#464×C71C2211yescharacteristic
119#464×C71C2211yescharacteristic
120#464×C71C2211yescharacteristic
121#464×C71C2211yescharacteristic, complemented
122#464×C71C2211yescharacteristic, complemented
123#464×C71C2211yescharacteristic, complemented
124#464×C71C2211yescharacteristic, complemented
125#463×C71C2211yescharacteristic
126#463×C71C2211yescharacteristic
127#463×C71C2211yescharacteristic
128#463×C71C2211yescharacteristic
129#463×C71C2211yescharacteristic
130#463×C71C2211yescharacteristic
131#463×C71C2211yescharacteristic
132#463×C71C2211yescharacteristic
133#463×C71C2211yescharacteristic, complemented
134#463×C71C2211yescharacteristic, complemented
135#463×C71C2211yescharacteristic, complemented
136#463×C71C2211yescharacteristic, complemented
137#462×C71C2211yescharacteristic, complemented
138#462×C71C2211yescharacteristic, complemented
139#461×C71C2211yescharacteristic, complemented
140#461×C71C2211yescharacteristic, complemented
141#460×C71C2211yescharacteristic
142#460×C71C2211yescharacteristic
143#460×C71C2211yescharacteristic
144#460×C71C2211yescharacteristic
145#460×C71C2211yescharacteristic, complemented
146#460×C71C2211yescharacteristic, complemented
147#459×C71C2211yescharacteristic
148#459×C71C2211yescharacteristic
149#459×C71C2211yescharacteristic
150#459×C71C2211yescharacteristic
151#459×C71C2211yescharacteristic, complemented
152#459×C71C2211yescharacteristic, complemented
153#452×C71C2211yescharacteristic
154#452×C71C2211yescharacteristic
155#452×C71C2211yescharacteristic
156#452×C71C2211yescharacteristic
157#450×C71C2211yescharacteristic
158#450×C71C2211yescharacteristic
159#449×C71C2211yescharacteristic
160#449×C71C2211yescharacteristic
161#449×C71C2211yescharacteristic
162#449×C71C2211yescharacteristic
163#447×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
175#442×C71C2211yescharacteristic, complemented
176#442×C71C2211yescharacteristic, complemented
177#441×C71C2211yescharacteristic, complemented
178#441×C71C2211yescharacteristic, complemented
179#440×C71C2211yescharacteristic
180#440×C71C2211yescharacteristic
181#440×C71C2211yescharacteristic, complemented
182#440×C71C2211yescharacteristic, complemented
183#440×C71C2211yescharacteristic, complemented
184#440×C71C2211yescharacteristic, complemented
185C4×Q16×C71C2211yescharacteristic, complemented
186C4×Q16×C71C2211yescharacteristic, complemented
187C4×SD16×C71C2211yescharacteristic
188C4×SD16×C71C2211yescharacteristic
189C4×SD16×C71C2211yescharacteristic, complemented
190C4×SD16×C71C2211yescharacteristic, complemented
191C4×SD16×C71C2211yescharacteristic, complemented
192C4×SD16×C71C2211yescharacteristic, complemented
193C4×D8×C71C2211yescharacteristic
194C4×D8×C71C2211yescharacteristic
195C4×D8×C71C2211yescharacteristic, complemented
196C4×D8×C71C2211yescharacteristic, complemented
197#433×C71C2211yescharacteristic
198#433×C71C2211yescharacteristic
199#433×C71C2211yescharacteristic
200#433×C71C2211yescharacteristic
201#432×C71C2211yescharacteristic
202#431×C71C2211yescharacteristic
203C2×#41×C71—21no—
204C2×#41×C71—21no—
205C2×#41×C71C2311yescharacteristic
206C2×#41×C71C2311yescharacteristic
207C22×D4×C71C2311yescharacteristic
208C23×C4×C71—21no—
209C2×Q16×C71C2311yescharacteristic
210C2×Q16×C71C2311yescharacteristic
211C2×Q16×C71C2311yescharacteristic
212C2×Q16×C71C2311yescharacteristic
213C2×SD16×C71C2311yescharacteristic
214C2×SD16×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×D8×C71C2311yescharacteristic
226C2×D8×C71C2311yescharacteristic
227C2×D8×C71C2311yescharacteristic
228C2×D8×C71C2311yescharacteristic
229C2×D8×C71C2311yescharacteristic
230C2×D8×C71C2311yescharacteristic
231C2×D8×C71C2311yescharacteristic
232C2×D8×C71C2311yescharacteristic
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
241#127×C71C2311yescharacteristic
242#127×C71C2311yescharacteristic
243#127×C71C2311yescharacteristic
244#127×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#125×C71—21no—
262#125×C71—21no—
263#125×C71—21no—
264#125×C71—21no—
265#125×C71—21no—
266#125×C71—21no—
267#125×C71D411yescharacteristic
268#125×C71D411yescharacteristic
269#125×C71C2311yescharacteristic
270#125×C71C2311yescharacteristic
271#125×C71C2311yescharacteristic
272#125×C71C2311yescharacteristic
273#124×C71—21no—
274#124×C71—21no—
275#124×C71—21no—
276#124×C71—21no—
277#124×C71—21no—
278#124×C71—21no—
279#124×C71—21no—
280#124×C71—21no—
281#124×C71C2311yescharacteristic
282#124×C71C2311yescharacteristic
283#124×C71C2311yescharacteristic
284#124×C71C2311yescharacteristic
285#124×C71C2311yescharacteristic
286#124×C71C2311yescharacteristic
287#124×C71C2311yescharacteristic
288#124×C71C2311yescharacteristic
289#124×C71C2311yescharacteristic
290#124×C71C2311yescharacteristic
291#123×C71—21no—
292#123×C71—21no—
293#123×C71—21no—
294#123×C71—21no—
295#123×C71—21no—
296#123×C71—21no—
297#123×C71—21no—
298#123×C71—21no—
299#123×C71—21no—
300#123×C71—21no—
301#123×C71—21no—
302#123×C71—21no—
303#123×C71—21no—
304#123×C71—21no—
305#123×C71—21no—
306#123×C71—21no—
307#123×C71—21no—
308#123×C71—21no—
309C22⋊Q8×C71—21no—
310C22⋊Q8×C71—21no—
311C22⋊Q8×C71—21no—
312C22⋊Q8×C71—21no—
313C22⋊Q8×C71—21no—
314C22⋊Q8×C71—21no—
315C22⋊Q8×C71—21no—
316C22⋊Q8×C71—21no—
317C22⋊Q8×C71—21no—
318C22⋊Q8×C71—21no—
319C22⋊Q8×C71—21no—
320C22⋊Q8×C71—21no—
321C22⋊Q8×C71D411yescharacteristic
322C22⋊Q8×C71D411yescharacteristic
323C22⋊Q8×C71D411yescharacteristic
324C22⋊Q8×C71D411yescharacteristic
325C22⋊Q8×C71C2311yescharacteristic
326C22⋊Q8×C71C2311yescharacteristic
327#121×C71—21no—
328#121×C71—21no—
329#121×C71—21no—
330#121×C71—21no—
331#121×C71—21no—
332#121×C71—21no—
333#121×C71—21no—
334#121×C71—21no—
335#121×C71—21no—
336#121×C71—21no—
337#121×C71—21no—
338#121×C71—21no—
339#121×C71—21no—
340#121×C71—21no—
341#121×C71C2311yescharacteristic
342#121×C71C2311yescharacteristic
343#120×C71—21no—
344#120×C71—21no—
345#120×C71—21no—
346#120×C71—21no—
347C4×Q8×C71—21no—
348C4×Q8×C71—21no—
349C4×Q8×C71C2311yescharacteristic
350C4×Q8×C71C2311yescharacteristic
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×D4×C71—21no—
364C4×D4×C71—21no—
365C4×D4×C71—21no—
366C4×D4×C71—21no—
367C4×D4×C71—21no—
368C4×D4×C71—21no—
369C4×D4×C71—21no—
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
388C4×D4×C71C2311yescharacteristic
389C4×D4×C71C2311yescharacteristic
390C4×D4×C71C2311yescharacteristic
391C4×D4×C71C2311yescharacteristic
392C4×D4×C71C2311yescharacteristic
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×C71—21no—
401#117×C71C2311yescharacteristic
402#117×C71C2311yescharacteristic
403C2×C4⋊C4×C71—21no—
404C2×C4⋊C4×C71—21no—
405C2×C4⋊C4×C71—21no—
406C2×C4⋊C4×C71—21no—
407C2×C4⋊C4×C71C2311yescharacteristic
408C2×C22⋊C4×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#102×C71C2311yescharacteristic
443#102×C71C2311yescharacteristic
444#102×C71C2311yescharacteristic
445#102×C71C2311yescharacteristic
446#102×C71C2311yescharacteristic
447#102×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—
481#41×C71—41no—
482#41×C71—41no—
483#41×C71—82no—
484#41×C71—82no—
485C2×Q8×C71—21no—
486C2×Q8×C71—21no—
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×D4×C71—21no—
496C2×D4×C71—21no—
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—21no—
505C2×D4×C71—21no—
506C2×D4×C71—21no—
507C2×D4×C71—21no—
508C2×D4×C71—21no—
509C2×D4×C71—21no—
510C2×D4×C71—21no—
511C2×D4×C71—21no—
512C2×D4×C71—41no—
513C2×D4×C71—41no—
514C2×D4×C71C2411yescharacteristic
515C2×D4×C71C2411yescharacteristic
516C2×D4×C71C2411yescharacteristic
517C2×D4×C71C2411yescharacteristic
518C2×D4×C71C2411yescharacteristic
519C2×D4×C71C2411yescharacteristic
520C22×C4×C71—21no—
521C22×C4×C71—21no—
522C22×C4×C71—21no—
523C22×C4×C71—21no—
524C22×C4×C71—21no—
525C22×C4×C71—21no—
526C22×C4×C71—21no—
527C22×C4×C71—21no—
528C22×C4×C71—21no—
529C22×C4×C71—21no—
530C22×C4×C71—21no—
531C22×C4×C71—21no—
532C22×C4×C71—21no—
533C22×C4×C71—21no—
534C22×C4×C71—21no—
535C22×C4×C71—21no—
536C22×C4×C71—21no—
537C22×C4×C71—82no—
538C22×C4×C71C2×D411yescharacteristic
539C22×C4×C71C2×D411yescharacteristic
540C22×C4×C71C2411yescharacteristic
541Q16×C71—41no—
542Q16×C71—41no—
543Q16×C71—41no—
544Q16×C71—41no—
545SD16×C71—41no—
546SD16×C71—41no—
547SD16×C71—41no—
548SD16×C71—41no—
549SD16×C71—41no—
550SD16×C71—41no—
551SD16×C71—41no—
552SD16×C71—41no—
553SD16×C71—41no—
554SD16×C71—41no—
555SD16×C71—41no—
556SD16×C71—41no—
557D8×C71—41no—
558D8×C71—41no—
559D8×C71—41no—
560D8×C71—41no—
561D8×C71—41no—
562D8×C71—41no—
563D8×C71—41no—
564D8×C71—41no—
565C2×C8×C71C2411yescharacteristic
566C2×C8×C71C2411yescharacteristic
567C2×C8×C71C2411yescharacteristic
568C2×C8×C71C2411yescharacteristic
569C2×C8×C71C2411yescharacteristic
570C2×C8×C71C2411yescharacteristic
571C2×C8×C71C2411yescharacteristic
572C2×C8×C71C2411yescharacteristic
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×C71—21no—
594C4⋊C4×C71—21no—
595C4⋊C4×C71—21no—
596C4⋊C4×C71—21no—
597C4⋊C4×C71—21no—
598C4⋊C4×C71—21no—
599C4⋊C4×C71—21no—
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×C71C2×D411yescharacteristic
610C4⋊C4×C71C2×D411yescharacteristic
611C4⋊C4×C71C2×D411yescharacteristic
612C4⋊C4×C71C2×D411yescharacteristic
613C4⋊C4×C71C2×D411yescharacteristic
614C4⋊C4×C71C2×D411yescharacteristic
615C4⋊C4×C71C2×D411yescharacteristic
616C4⋊C4×C71C2411yescharacteristic
617C4⋊C4×C71C2411yescharacteristic
618C4⋊C4×C71C2411yescharacteristic
619C4⋊C4×C71C2411yescharacteristic
620C4⋊C4×C71C2411yescharacteristic
621C4⋊C4×C71C2411yescharacteristic
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×C71—21no—
652C22⋊C4×C71—21no—
653C22⋊C4×C71—21no—
654C22⋊C4×C71—21no—
655C22⋊C4×C71—21no—
656C22⋊C4×C71—21no—
657C22⋊C4×C71—21no—
658C22⋊C4×C71—21no—
659C22⋊C4×C71—21no—
660C22⋊C4×C71C2×D411yescharacteristic
661C22⋊C4×C71C2×D411yescharacteristic
662C22⋊C4×C71C2×D411yescharacteristic
663C22⋊C4×C71C2×D411yescharacteristic
664C42×C71—21no—
665C42×C71—21no—
666C42×C71—21no—
667C42×C71—21no—
668C42×C71—21no—
669C42×C71—21no—
670C42×C71—21no—
671C42×C71—21no—
672C42×C71—21no—
673C42×C71—21no—
674C42×C71C2×D411yescharacteristic
675C42×C71C2×D411yescharacteristic
676C42×C71C2411yescharacteristic
677C42×C71C2411yescharacteristic
678C42×C71C2411yescharacteristic
679C42×C71C2411yescharacteristic
680C42×C71C2411yescharacteristic
681C42×C71C2411yescharacteristic
682C23×C71—21no—
683C23×C71—21no—
684C23×C71—21no—
685C23×C71—21no—
686C23×C71—21no—
687C23×C71—21no—
688C23×C71—42no—
689C23×C71—81no—
690C23×C71—81no—
691C23×C71C22×D411yescharacteristic
692Q8×C71—21no—
693Q8×C71—21no—
694Q8×C71—21no—
695Q8×C71—21no—
696Q8×C71—21no—
697Q8×C71—21no—
698Q8×C71—21no—
699Q8×C71—21no—
700Q8×C71—41no—
701Q8×C71—41no—
702Q8×C71—41no—
703Q8×C71—41no—
704Q8×C71—81no—
705Q8×C71—81no—
706D4×C71—21no—
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—21no—
716D4×C71—21no—
717D4×C71—21no—
718D4×C71—42no—
719D4×C71—42no—
720D4×C71—42no—
721D4×C71—42no—
722D4×C71—81no—
723D4×C71—81no—
724D4×C71—81no—
725D4×C71—81no—
726D4×C71—81no—
727D4×C71—81no—
728D4×C71—81no—
729D4×C71—81no—
730D4×C71—81no—
731D4×C71—81no—
732D4×C71—81no—
733D4×C71—81no—
734D4×C71—81no—
735C2×C4×C71—21no—
736C2×C4×C71—21no—
737C2×C4×C71—21no—
738C2×C4×C71—21no—
739C2×C4×C71—21no—
740C2×C4×C71—21no—
741C2×C4×C71—21no—
742C2×C4×C71—21no—
743C2×C4×C71—21no—
744C2×C4×C71—21no—
745C2×C4×C71—21no—
746C2×C4×C71—21no—
747C2×C4×C71—41no—
748C2×C4×C71—41no—
749C2×C4×C71—42no—
750C2×C4×C71—42no—
751C2×C4×C71—42no—
752C2×C4×C71—42no—
753C2×C4×C71—81no—
754C2×C4×C71—81no—
755C2×C4×C71—81no—
756C2×C4×C71—81no—
757C2×C4×C71—81no—
758C2×C4×C71—81no—
759C2×C4×C71—81no—
760C2×C4×C71—81no—
761C2×C4×C71—81no—
762C2×C4×C71—81no—
763C2×C4×C71—81no—
764C2×C4×C71—81no—
765C2×C4×C71—81no—
766C2×C4×C71C22×D411yescharacteristic
767C2×C4×C71C22×D411yescharacteristic
768C2×C4×C71C22×D411yescharacteristic
769C2×C4×C71C22×D411yescharacteristic
770C2×C4×C71C22×D411yescharacteristic
771C2×C4×C71C22×D411yescharacteristic
772C2×C4×C71C22×D411yescharacteristic
773C2×C4×C71C22×D411yescharacteristic
774C2×C4×C71C22×D411yescharacteristic
775C2×C4×C71C22×D411yescharacteristic
776C2×C4×C71C22×D411yescharacteristic
777C2×C4×C71C22×D411yescharacteristic
778C2×C4×C71C22×D411yescharacteristic
779C2×C4×C71C2511yescharacteristic
780C8×C71—21no—
781C8×C71—21no—
782C8×C71—21no—
783C8×C71—21no—
784C8×C71—21no—
785C8×C71—21no—
786C8×C71—21no—
787C8×C71—21no—
788C22×C71—21no—
789C22×C71—21no—
790C22×C71—21no—
791C22×C71—41no—
792C22×C71—41no—
793C22×C71—41no—
794C22×C71—41no—
795C22×C71—41no—
796C22×C71—41no—
797C22×C71—41no—
798C22×C71—41no—
799C22×C71—41no—
800C22×C71—41no—
801C22×C71—41no—
802C22×C71—41no—
803C22×C71—41no—
804C22×C71—41no—
805C22×C71—41no—
806C22×C71—41no—
807C22×C71—41no—
808C22×C71—41no—
809C22×C71—84no—
810C22×C71C23×D411yescharacteristic
811C4×C71—21no—
812C4×C71—21no—
813C4×C71—21no—
814C4×C71—21no—
815C4×C71—21no—
816C4×C71—21no—
817C4×C71—21no—
818C4×C71—21no—
819C4×C71—21no—
820C4×C71—21no—
821C4×C71—21no—
822C4×C71—21no—
823C4×C71—21no—
824C4×C71—41no—
825C4×C71—41no—
826C4×C71—41no—
827C4×C71—41no—
828C4×C71—41no—
829C4×C71—41no—
830C4×C71—41no—
831C4×C71—41no—
832C4×C71—41no—
833C4×C71—41no—
834C4×C71#58511yescharacteristic
835C4×C71#58511yescharacteristic
836#61919C7111yesmaximal, characteristic, direct product factor, Sylow
837C2×C71—41no—
838C2×C71—81no—
839C2×C71—81no—
840C2×C71—81no—
841C2×C71—81no—
842C2×C71—81no—
843C2×C71—81no—
844C2×C71#348711yescharacteristic
845C2×C71#358411yescharacteristic
846C2×C71#358511yescharacteristic
847#3557C2×C7111yescharacteristic, complemented
848#3506C2×C7111yescharacteristic, complemented
849#3403C2×C7111yescharacteristic, complemented
850#3402C2×C7111yescharacteristic, complemented
851#3401C2×C7111yescharacteristic, complemented
852#3401C2×C7111yescharacteristic, complemented
853#3399C2×C7111yescharacteristic, complemented
854#3397C2×C7111yescharacteristic, complemented
855#3396C2×C7111yescharacteristic, complemented
856#3394C2×C7111yescharacteristic, complemented
857#3377C2×C7111yescharacteristic, complemented
858#3376C2×C7111yescharacteristic, complemented
859#3371C2×C7111yescharacteristic, complemented
860#3370C2×C7111yescharacteristic, complemented
861#3368C2×C7111yescharacteristic, complemented
862#3366C2×C7111yescharacteristic, complemented
863#3365C2×C7111yescharacteristic, complemented
864#3361C2×C7111yescharacteristic, complemented
865#3224C2×C7111yescharacteristic, complemented
866#3224C2×C7111yescharacteristic, complemented
867#3222C2×C7111yescharacteristic, complemented
868#3220C2×C7111yescharacteristic, complemented
869#3219C2×C7111yescharacteristic, complemented
870#3212C2×C7111yescharacteristic, complemented
871#3125C2×C7111yescharacteristic, complemented
872#3124C2×C7111yescharacteristic, complemented
873#3120C2×C7111yescharacteristic, complemented
874#3119C2×C7111yescharacteristic, complemented
875#3114C2×C7111yescharacteristic, complemented
876#3105C2×C7111yescharacteristic, complemented
877#2985C2×C7111yescharacteristic, complemented
878C71#6191911yescharacteristic, direct product factor, Sylow
879#563—21no—
880#563—21no—
881#559C22×C7111yescharacteristic
882#559C22×C7111yescharacteristic
883#559C22×C7111yescharacteristic
884#559C22×C7111yescharacteristic
885#559C22×C7111yescharacteristic, complemented
886#559C22×C7111yescharacteristic, complemented
887#557C22×C7111yescharacteristic, complemented
888#557C22×C7111yescharacteristic, complemented
889#556C22×C7111yescharacteristic
890#556C22×C7111yescharacteristic
891#556C22×C7111yescharacteristic, complemented
892#556C22×C7111yescharacteristic, complemented
893#555—21no—
894#554C22×C7111yescharacteristic, complemented
895#554C22×C7111yescharacteristic, complemented
896#553—21no—
897#553—21no—
898#552—21no—
899#552—21no—
900#550C22×C7111yescharacteristic
901#550C22×C7111yescharacteristic
902#547—21no—
903#542—21no—
904#542—21no—
905#542C22×C7111yescharacteristic
906#542C22×C7111yescharacteristic
907#541C22×C7111yescharacteristic
908#540C22×C7111yescharacteristic
909#539—21no—
910#539—21no—
911#538—21no—
912#538—21no—
913#535C22×C7111yescharacteristic
914#535C22×C7111yescharacteristic
915#533C22×C7111yescharacteristic
916#532C22×C7111yescharacteristic
917#529C22×C7111yescharacteristic
918#529C22×C7111yescharacteristic
919#525—21no—
920#525—21no—
921#520C22×C7111yescharacteristic
922#520C22×C7111yescharacteristic
923C2×C4×D4C22×C7111yescharacteristic
924#497C22×C7111yescharacteristic
925#497C22×C7111yescharacteristic, complemented
926#496C22×C7111yescharacteristic
927#496C22×C7111yescharacteristic
928#496C22×C7111yescharacteristic
929#496C22×C7111yescharacteristic, complemented
930#495C22×C7111yescharacteristic
931#495C22×C7111yescharacteristic
932#495C22×C7111yescharacteristic, complemented
933#495C22×C7111yescharacteristic, complemented
934#493C22×C7111yescharacteristic
935#492C22×C7111yescharacteristic
936#491C22×C7111yescharacteristic, complemented
937#490C22×C7111yescharacteristic
938#490C22×C7111yescharacteristic
939#490C22×C7111yescharacteristic, complemented
940#489C22×C7111yescharacteristic
941#489C22×C7111yescharacteristic
942#488C22×C7111yescharacteristic
943#488C22×C7111yescharacteristic
944#488C22×C7111yescharacteristic, complemented
945#488C22×C7111yescharacteristic, complemented
946#486C22×C7111yescharacteristic
947#486C22×C7111yescharacteristic
948#484C22×C7111yescharacteristic
949#483C22×C7111yescharacteristic
950#481C22×C7111yescharacteristic
951#480C22×C7111yescharacteristic
952#479C22×C7111yescharacteristic, complemented
953#479C22×C7111yescharacteristic, complemented
954#478C22×C7111yescharacteristic
955#478C22×C7111yescharacteristic
956#478C22×C7111yescharacteristic
957#478C22×C7111yescharacteristic
958#478C22×C7111yescharacteristic, complemented
959#478C22×C7111yescharacteristic, complemented
960#477C22×C7111yescharacteristic, complemented
961#476C22×C7111yescharacteristic, complemented
962#475C22×C7111yescharacteristic, complemented
963#474C22×C7111yescharacteristic, complemented
964#464C22×C7111yescharacteristic
965#464C22×C7111yescharacteristic
966#464C22×C7111yescharacteristic
967#464C22×C7111yescharacteristic
968#464C22×C7111yescharacteristic, complemented
969#464C22×C7111yescharacteristic, complemented
970#464C22×C7111yescharacteristic, complemented
971#464C22×C7111yescharacteristic, complemented
972#463C22×C7111yescharacteristic
973#463C22×C7111yescharacteristic
974#463C22×C7111yescharacteristic
975#463C22×C7111yescharacteristic
976#463C22×C7111yescharacteristic
977#463C22×C7111yescharacteristic
978#463C22×C7111yescharacteristic
979#463C22×C7111yescharacteristic
980#463C22×C7111yescharacteristic, complemented
981#463C22×C7111yescharacteristic, complemented
982#463C22×C7111yescharacteristic, complemented
983#463C22×C7111yescharacteristic, complemented
984#462C22×C7111yescharacteristic, complemented
985#462C22×C7111yescharacteristic, complemented
986#461C22×C7111yescharacteristic, complemented
987#461C22×C7111yescharacteristic, complemented
988#460C22×C7111yescharacteristic
989#460C22×C7111yescharacteristic
990#460C22×C7111yescharacteristic
991#460C22×C7111yescharacteristic
992#460C22×C7111yescharacteristic, complemented
993#460C22×C7111yescharacteristic, complemented
994#459C22×C7111yescharacteristic
995#459C22×C7111yescharacteristic
996#459C22×C7111yescharacteristic
997#459C22×C7111yescharacteristic
998#459C22×C7111yescharacteristic, complemented
999#459C22×C7111yescharacteristic, complemented
1000#452C22×C7111yescharacteristic
1001#452C22×C7111yescharacteristic
1002#452C22×C7111yescharacteristic
1003#452C22×C7111yescharacteristic
1004#450C22×C7111yescharacteristic
1005#450C22×C7111yescharacteristic
1006#449C22×C7111yescharacteristic
1007#449C22×C7111yescharacteristic
1008#449C22×C7111yescharacteristic
1009#449C22×C7111yescharacteristic
1010#447C22×C7111yescharacteristic
1011#447C22×C7111yescharacteristic
1012#446C22×C7111yescharacteristic, complemented
1013#446C22×C7111yescharacteristic, complemented
1014#446C22×C7111yescharacteristic, complemented
1015#446C22×C7111yescharacteristic, complemented
1016#446C22×C7111yescharacteristic, complemented
1017#446C22×C7111yescharacteristic, complemented
1018C8×Q8C22×C7111yescharacteristic, complemented
1019C8×Q8C22×C7111yescharacteristic, complemented
1020#442C22×C7111yescharacteristic
1021#442C22×C7111yescharacteristic
1022#442C22×C7111yescharacteristic, complemented
1023#442C22×C7111yescharacteristic, complemented
1024#441C22×C7111yescharacteristic, complemented
1025#441C22×C7111yescharacteristic, complemented
1026#440C22×C7111yescharacteristic
1027#440C22×C7111yescharacteristic
1028#440C22×C7111yescharacteristic, complemented
1029#440C22×C7111yescharacteristic, complemented
1030#440C22×C7111yescharacteristic, complemented
1031#440C22×C7111yescharacteristic, complemented
1032C4×Q16C22×C7111yescharacteristic, complemented
1033C4×Q16C22×C7111yescharacteristic, complemented
1034C4×SD16C22×C7111yescharacteristic
1035C4×SD16C22×C7111yescharacteristic
1036C4×SD16C22×C7111yescharacteristic, complemented
1037C4×SD16C22×C7111yescharacteristic, complemented
1038C4×SD16C22×C7111yescharacteristic, complemented
1039C4×SD16C22×C7111yescharacteristic, complemented
1040C4×D8C22×C7111yescharacteristic
1041C4×D8C22×C7111yescharacteristic
1042C4×D8C22×C7111yescharacteristic, complemented
1043C4×D8C22×C7111yescharacteristic, complemented
1044#433C22×C7111yescharacteristic
1045#433C22×C7111yescharacteristic
1046#433C22×C7111yescharacteristic
1047#433C22×C7111yescharacteristic
1048#432C22×C7111yescharacteristic
1049#431C22×C7111yescharacteristic
1050C2×#41—21no—
1051C2×#41—21no—
1052C2×#41C23×C7111yescharacteristic
1053C2×#41C23×C7111yescharacteristic
1054C22×D4C23×C7111yescharacteristic
1055C23×C4—21no—
1056C2×Q16C23×C7111yescharacteristic
1057C2×Q16C23×C7111yescharacteristic
1058C2×Q16C23×C7111yescharacteristic
1059C2×Q16C23×C7111yescharacteristic
1060C2×SD16C23×C7111yescharacteristic
1061C2×SD16C23×C7111yescharacteristic
1062C2×SD16C23×C7111yescharacteristic
1063C2×SD16C23×C7111yescharacteristic
1064C2×SD16C23×C7111yescharacteristic
1065C2×SD16C23×C7111yescharacteristic
1066C2×SD16C23×C7111yescharacteristic
1067C2×SD16C23×C7111yescharacteristic
1068C2×SD16C23×C7111yescharacteristic
1069C2×SD16C23×C7111yescharacteristic
1070C2×SD16C23×C7111yescharacteristic
1071C2×SD16C23×C7111yescharacteristic
1072C2×D8C23×C7111yescharacteristic
1073C2×D8C23×C7111yescharacteristic
1074C2×D8C23×C7111yescharacteristic
1075C2×D8C23×C7111yescharacteristic
1076C2×D8C23×C7111yescharacteristic
1077C2×D8C23×C7111yescharacteristic
1078C2×D8C23×C7111yescharacteristic
1079C2×D8C23×C7111yescharacteristic
1080C4⋊Q8—21no—
1081C4⋊Q8—21no—
1082C4⋊Q8D4×C7111yescharacteristic
1083C4⋊Q8D4×C7111yescharacteristic
1084C4⋊Q8C23×C7111yescharacteristic
1085C4⋊Q8C23×C7111yescharacteristic
1086C4⋊Q8C23×C7111yescharacteristic
1087C4⋊Q8C23×C7111yescharacteristic
1088#127C23×C7111yescharacteristic
1089#127C23×C7111yescharacteristic
1090#127C23×C7111yescharacteristic
1091#127C23×C7111yescharacteristic
1092#127C23×C7111yescharacteristic
1093#127C23×C7111yescharacteristic
1094#126—21no—
1095#126—21no—
1096#126—21no—
1097#126—21no—
1098#126—21no—
1099#126—21no—
1100#126—21no—
1101#126—21no—
1102#126—21no—
1103#126—21no—
1104#126—21no—
1105#126—21no—
1106#126—21no—
1107#126—21no—
1108#125—21no—
1109#125—21no—
1110#125—21no—
1111#125—21no—
1112#125—21no—
1113#125—21no—
1114#125D4×C7111yescharacteristic
1115#125D4×C7111yescharacteristic
1116#125C23×C7111yescharacteristic
1117#125C23×C7111yescharacteristic
1118#125C23×C7111yescharacteristic
1119#125C23×C7111yescharacteristic
1120#124—21no—
1121#124—21no—
1122#124—21no—
1123#124—21no—
1124#124—21no—
1125#124—21no—
1126#124—21no—
1127#124—21no—
1128#124C23×C7111yescharacteristic
1129#124C23×C7111yescharacteristic
1130#124C23×C7111yescharacteristic
1131#124C23×C7111yescharacteristic
1132#124C23×C7111yescharacteristic
1133#124C23×C7111yescharacteristic
1134#124C23×C7111yescharacteristic
1135#124C23×C7111yescharacteristic
1136#124C23×C7111yescharacteristic
1137#124C23×C7111yescharacteristic
1138#123—21no—
1139#123—21no—
1140#123—21no—
1141#123—21no—
1142#123—21no—
1143#123—21no—
1144#123—21no—
1145#123—21no—
1146#123—21no—
1147#123—21no—
1148#123—21no—
1149#123—21no—
1150#123—21no—
1151#123—21no—
1152#123—21no—
1153#123—21no—
1154#123—21no—
1155#123—21no—
1156C22⋊Q8—21no—
1157C22⋊Q8—21no—
1158C22⋊Q8—21no—
1159C22⋊Q8—21no—
1160C22⋊Q8—21no—
1161C22⋊Q8—21no—
1162C22⋊Q8—21no—
1163C22⋊Q8—21no—
1164C22⋊Q8—21no—
1165C22⋊Q8—21no—
1166C22⋊Q8—21no—
1167C22⋊Q8—21no—
1168C22⋊Q8D4×C7111yescharacteristic
1169C22⋊Q8D4×C7111yescharacteristic
1170C22⋊Q8D4×C7111yescharacteristic
1171C22⋊Q8D4×C7111yescharacteristic
1172C22⋊Q8C23×C7111yescharacteristic
1173C22⋊Q8C23×C7111yescharacteristic
1174#121—21no—
1175#121—21no—
1176#121—21no—
1177#121—21no—
1178#121—21no—
1179#121—21no—
1180#121—21no—
1181#121—21no—
1182#121—21no—
1183#121—21no—
1184#121—21no—
1185#121—21no—
1186#121—21no—
1187#121—21no—
1188#121C23×C7111yescharacteristic
1189#121C23×C7111yescharacteristic
1190#120—21no—
1191#120—21no—
1192#120—21no—
1193#120—21no—
1194C4×Q8—21no—
1195C4×Q8—21no—
1196C4×Q8C23×C7111yescharacteristic
1197C4×Q8C23×C7111yescharacteristic
1198C4×Q8C23×C7111yescharacteristic
1199C4×Q8C23×C7111yescharacteristic
1200C4×Q8C23×C7111yescharacteristic
1201C4×Q8C23×C7111yescharacteristic
1202C4×Q8C23×C7111yescharacteristic
1203C4×Q8C23×C7111yescharacteristic
1204C4×Q8C23×C7111yescharacteristic
1205C4×Q8C23×C7111yescharacteristic
1206C4×Q8C23×C7111yescharacteristic
1207C4×Q8C23×C7111yescharacteristic
1208C4×Q8C23×C7111yescharacteristic
1209C4×Q8C23×C7111yescharacteristic
1210C4×D4—21no—
1211C4×D4—21no—
1212C4×D4—21no—
1213C4×D4—21no—
1214C4×D4—21no—
1215C4×D4—21no—
1216C4×D4—21no—
1217C4×D4—21no—
1218C4×D4—21no—
1219C4×D4—21no—
1220C4×D4—21no—
1221C4×D4—21no—
1222C4×D4—21no—
1223C4×D4—21no—
1224C4×D4—21no—
1225C4×D4—21no—
1226C4×D4C23×C7111yescharacteristic
1227C4×D4C23×C7111yescharacteristic
1228C4×D4C23×C7111yescharacteristic
1229C4×D4C23×C7111yescharacteristic
1230C4×D4C23×C7111yescharacteristic
1231C4×D4C23×C7111yescharacteristic
1232C4×D4C23×C7111yescharacteristic
1233C4×D4C23×C7111yescharacteristic
1234C4×D4C23×C7111yescharacteristic
1235C4×D4C23×C7111yescharacteristic
1236C4×D4C23×C7111yescharacteristic
1237C4×D4C23×C7111yescharacteristic
1238C4×D4C23×C7111yescharacteristic
1239C4×D4C23×C7111yescharacteristic
1240#117—21no—
1241#117—21no—
1242#117—21no—
1243#117—21no—
1244#117—21no—
1245#117—21no—
1246#117—21no—
1247#117—21no—
1248#117C23×C7111yescharacteristic
1249#117C23×C7111yescharacteristic
1250C2×C4⋊C4—21no—
1251C2×C4⋊C4—21no—
1252C2×C4⋊C4—21no—
1253C2×C4⋊C4—21no—
1254C2×C4⋊C4C23×C7111yescharacteristic
1255C2×C22⋊C4—21no—
1256C2×C42C23×C7111yescharacteristic
1257#107C23×C7111yescharacteristic
1258#107C23×C7111yescharacteristic
1259#107C23×C7111yescharacteristic
1260#107C23×C7111yescharacteristic
1261#106C23×C7111yescharacteristic
1262#106C23×C7111yescharacteristic
1263#106C23×C7111yescharacteristic
1264#106C23×C7111yescharacteristic
1265C4⋊C8C23×C7111yescharacteristic
1266C4⋊C8C23×C7111yescharacteristic
1267C4⋊C8C23×C7111yescharacteristic
1268C4⋊C8C23×C7111yescharacteristic
1269C4⋊C8C23×C7111yescharacteristic
1270C4⋊C8C23×C7111yescharacteristic
1271C4⋊C8C23×C7111yescharacteristic
1272C4⋊C8C23×C7111yescharacteristic
1273C4⋊C8C23×C7111yescharacteristic
1274C4⋊C8C23×C7111yescharacteristic
1275C4⋊C8C23×C7111yescharacteristic
1276C4⋊C8C23×C7111yescharacteristic
1277#103C23×C7111yescharacteristic
1278#103C23×C7111yescharacteristic
1279#103C23×C7111yescharacteristic
1280#103C23×C7111yescharacteristic
1281#103C23×C7111yescharacteristic
1282#103C23×C7111yescharacteristic
1283#103C23×C7111yescharacteristic
1284#103C23×C7111yescharacteristic
1285#103C23×C7111yescharacteristic
1286#103C23×C7111yescharacteristic
1287#103C23×C7111yescharacteristic
1288#103C23×C7111yescharacteristic
1289#102C23×C7111yescharacteristic
1290#102C23×C7111yescharacteristic
1291#102C23×C7111yescharacteristic
1292#102C23×C7111yescharacteristic
1293#102C23×C7111yescharacteristic
1294#102C23×C7111yescharacteristic
1295#102C23×C7111yescharacteristic
1296#102C23×C7111yescharacteristic
1297#102C23×C7111yescharacteristic
1298#102C23×C7111yescharacteristic
1299#102C23×C7111yescharacteristic
1300#102C23×C7111yescharacteristic
1301#102C23×C7111yescharacteristic
1302#102C23×C7111yescharacteristic
1303#102C23×C7111yescharacteristic
1304#102C23×C7111yescharacteristic
1305#102C23×C7111yescharacteristic
1306#102C23×C7111yescharacteristic
1307#102C23×C7111yescharacteristic
1308#102C23×C7111yescharacteristic
1309C22⋊C8C23×C7111yescharacteristic
1310C22⋊C8C23×C7111yescharacteristic
1311C22⋊C8C23×C7111yescharacteristic
1312C22⋊C8C23×C7111yescharacteristic
1313#97C23×C7111yescharacteristic
1314#97C23×C7111yescharacteristic
1315#97C23×C7111yescharacteristic
1316#97C23×C7111yescharacteristic
1317#97C23×C7111yescharacteristic
1318#97C23×C7111yescharacteristic
1319C4×C8C23×C7111yescharacteristic
1320C4×C8C23×C7111yescharacteristic
1321C4×C8C23×C7111yescharacteristic
1322C4×C8C23×C7111yescharacteristic
1323C4×C8C23×C7111yescharacteristic
1324C4×C8C23×C7111yescharacteristic
1325C24—21no—
1326#41—41no—
1327#41—41no—
1328#41—41no—
1329#41—41no—
1330#41—82no—
1331#41—82no—
1332C2×Q8—21no—
1333C2×Q8—21no—
1334C2×Q8C2×D4×C7111yescharacteristic
1335C2×Q8C2×D4×C7111yescharacteristic
1336C2×Q8C2×D4×C7111yescharacteristic
1337C2×Q8C2×D4×C7111yescharacteristic
1338C2×Q8C24×C7111yescharacteristic
1339C2×Q8C24×C7111yescharacteristic
1340C2×Q8C24×C7111yescharacteristic
1341C2×Q8C24×C7111yescharacteristic
1342C2×D4—21no—
1343C2×D4—21no—
1344C2×D4—21no—
1345C2×D4—21no—
1346C2×D4—21no—
1347C2×D4—21no—
1348C2×D4—21no—
1349C2×D4—21no—
1350C2×D4—21no—
1351C2×D4—21no—
1352C2×D4—21no—
1353C2×D4—21no—
1354C2×D4—21no—
1355C2×D4—21no—
1356C2×D4—21no—
1357C2×D4—21no—
1358C2×D4—21no—
1359C2×D4—41no—
1360C2×D4—41no—
1361C2×D4C24×C7111yescharacteristic
1362C2×D4C24×C7111yescharacteristic
1363C2×D4C24×C7111yescharacteristic
1364C2×D4C24×C7111yescharacteristic
1365C2×D4C24×C7111yescharacteristic
1366C2×D4C24×C7111yescharacteristic
1367C22×C4—21no—
1368C22×C4—21no—
1369C22×C4—21no—
1370C22×C4—21no—
1371C22×C4—21no—
1372C22×C4—21no—
1373C22×C4—21no—
1374C22×C4—21no—
1375C22×C4—21no—
1376C22×C4—21no—
1377C22×C4—21no—
1378C22×C4—21no—
1379C22×C4—21no—
1380C22×C4—21no—
1381C22×C4—21no—
1382C22×C4—21no—
1383C22×C4—21no—
1384C22×C4—82no—
1385C22×C4C2×D4×C7111yescharacteristic
1386C22×C4C2×D4×C7111yescharacteristic
1387C22×C4C24×C7111yescharacteristic
1388Q16—41no—
1389Q16—41no—
1390Q16—41no—
1391Q16—41no—
1392SD16—41no—
1393SD16—41no—
1394SD16—41no—
1395SD16—41no—
1396SD16—41no—
1397SD16—41no—
1398SD16—41no—
1399SD16—41no—
1400SD16—41no—
1401SD16—41no—
1402SD16—41no—
1403SD16—41no—
1404D8—41no—
1405D8—41no—
1406D8—41no—
1407D8—41no—
1408D8—41no—
1409D8—41no—
1410D8—41no—
1411D8—41no—
1412C2×C8C24×C7111yescharacteristic
1413C2×C8C24×C7111yescharacteristic
1414C2×C8C24×C7111yescharacteristic
1415C2×C8C24×C7111yescharacteristic
1416C2×C8C24×C7111yescharacteristic
1417C2×C8C24×C7111yescharacteristic
1418C2×C8C24×C7111yescharacteristic
1419C2×C8C24×C7111yescharacteristic
1420C4⋊C4—21no—
1421C4⋊C4—21no—
1422C4⋊C4—21no—
1423C4⋊C4—21no—
1424C4⋊C4—21no—
1425C4⋊C4—21no—
1426C4⋊C4—21no—
1427C4⋊C4—21no—
1428C4⋊C4—21no—
1429C4⋊C4—21no—
1430C4⋊C4—21no—
1431C4⋊C4—21no—
1432C4⋊C4—21no—
1433C4⋊C4—21no—
1434C4⋊C4—21no—
1435C4⋊C4—21no—
1436C4⋊C4—21no—
1437C4⋊C4—21no—
1438C4⋊C4—21no—
1439C4⋊C4—21no—
1440C4⋊C4—21no—
1441C4⋊C4—21no—
1442C4⋊C4—21no—
1443C4⋊C4—21no—
1444C4⋊C4—21no—
1445C4⋊C4—21no—
1446C4⋊C4—21no—
1447C4⋊C4C2×D4×C7111yescharacteristic
1448C4⋊C4C2×D4×C7111yescharacteristic
1449C4⋊C4C2×D4×C7111yescharacteristic
1450C4⋊C4C2×D4×C7111yescharacteristic
1451C4⋊C4C2×D4×C7111yescharacteristic
1452C4⋊C4C2×D4×C7111yescharacteristic
1453C4⋊C4C2×D4×C7111yescharacteristic
1454C4⋊C4C2×D4×C7111yescharacteristic
1455C4⋊C4C2×D4×C7111yescharacteristic
1456C4⋊C4C2×D4×C7111yescharacteristic
1457C4⋊C4C2×D4×C7111yescharacteristic
1458C4⋊C4C2×D4×C7111yescharacteristic
1459C4⋊C4C2×D4×C7111yescharacteristic
1460C4⋊C4C2×D4×C7111yescharacteristic
1461C4⋊C4C2×D4×C7111yescharacteristic
1462C4⋊C4C2×D4×C7111yescharacteristic
1463C4⋊C4C24×C7111yescharacteristic
1464C4⋊C4C24×C7111yescharacteristic
1465C4⋊C4C24×C7111yescharacteristic
1466C4⋊C4C24×C7111yescharacteristic
1467C4⋊C4C24×C7111yescharacteristic
1468C4⋊C4C24×C7111yescharacteristic
1469C22⋊C4—21no—
1470C22⋊C4—21no—
1471C22⋊C4—21no—
1472C22⋊C4—21no—
1473C22⋊C4—21no—
1474C22⋊C4—21no—
1475C22⋊C4—21no—
1476C22⋊C4—21no—
1477C22⋊C4—21no—
1478C22⋊C4—21no—
1479C22⋊C4—21no—
1480C22⋊C4—21no—
1481C22⋊C4—21no—
1482C22⋊C4—21no—
1483C22⋊C4—21no—
1484C22⋊C4—21no—
1485C22⋊C4—21no—
1486C22⋊C4—21no—
1487C22⋊C4—21no—
1488C22⋊C4—21no—
1489C22⋊C4—21no—
1490C22⋊C4—21no—
1491C22⋊C4—21no—
1492C22⋊C4—21no—
1493C22⋊C4—21no—
1494C22⋊C4—21no—
1495C22⋊C4—21no—
1496C22⋊C4—21no—
1497C22⋊C4—21no—
1498C22⋊C4—21no—
1499C22⋊C4—21no—
1500C22⋊C4—21no—
1501C22⋊C4—21no—
1502C22⋊C4—21no—
1503C22⋊C4—21no—
1504C22⋊C4—21no—
1505C22⋊C4—21no—
1506C22⋊C4—21no—
1507C22⋊C4C2×D4×C7111yescharacteristic
1508C22⋊C4C2×D4×C7111yescharacteristic
1509C22⋊C4C2×D4×C7111yescharacteristic
1510C22⋊C4C2×D4×C7111yescharacteristic
1511C42—21no—
1512C42—21no—
1513C42—21no—
1514C42—21no—
1515C42—21no—
1516C42—21no—
1517C42—21no—
1518C42—21no—
1519C42—21no—
1520C42—21no—
1521C42C2×D4×C7111yescharacteristic
1522C42C2×D4×C7111yescharacteristic
1523C42C24×C7111yescharacteristic
1524C42C24×C7111yescharacteristic
1525C42C24×C7111yescharacteristic
1526C42C24×C7111yescharacteristic
1527C42C24×C7111yescharacteristic
1528C42C24×C7111yescharacteristic
1529C23—21no—
1530C23—21no—
1531C23—21no—
1532C23—21no—
1533C23—21no—
1534C23—21no—
1535C23—42no—
1536C23—81no—
1537C23—81no—
1538C23C22×D4×C7111yescharacteristic
1539Q8—21no—
1540Q8—21no—
1541Q8—21no—
1542Q8—21no—
1543Q8—21no—
1544Q8—21no—
1545Q8—21no—
1546Q8—21no—
1547Q8—41no—
1548Q8—41no—
1549Q8—41no—
1550Q8—41no—
1551Q8—81no—
1552Q8—81no—
1553D4—21no—
1554D4—21no—
1555D4—21no—
1556D4—21no—
1557D4—21no—
1558D4—21no—
1559D4—21no—
1560D4—21no—
1561D4—21no—
1562D4—21no—
1563D4—21no—
1564D4—21no—
1565D4—42no—
1566D4—42no—
1567D4—42no—
1568D4—42no—
1569D4—81no—
1570D4—81no—
1571D4—81no—
1572D4—81no—
1573D4—81no—
1574D4—81no—
1575D4—81no—
1576D4—81no—
1577D4—81no—
1578D4—81no—
1579D4—81no—
1580D4—81no—
1581D4—81no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—41no—
1595C2×C4—41no—
1596C2×C4—42no—
1597C2×C4—42no—
1598C2×C4—42no—
1599C2×C4—42no—
1600C2×C4—81no—
1601C2×C4—81no—
1602C2×C4—81no—
1603C2×C4—81no—
1604C2×C4—81no—
1605C2×C4—81no—
1606C2×C4—81no—
1607C2×C4—81no—
1608C2×C4—81no—
1609C2×C4—81no—
1610C2×C4—81no—
1611C2×C4—81no—
1612C2×C4—81no—
1613C2×C4C22×D4×C7111yescharacteristic
1614C2×C4C22×D4×C7111yescharacteristic
1615C2×C4C22×D4×C7111yescharacteristic
1616C2×C4C22×D4×C7111yescharacteristic
1617C2×C4C22×D4×C7111yescharacteristic
1618C2×C4C22×D4×C7111yescharacteristic
1619C2×C4C22×D4×C7111yescharacteristic
1620C2×C4C22×D4×C7111yescharacteristic
1621C2×C4C22×D4×C7111yescharacteristic
1622C2×C4C22×D4×C7111yescharacteristic
1623C2×C4C22×D4×C7111yescharacteristic
1624C2×C4C22×D4×C7111yescharacteristic
1625C2×C4C22×D4×C7111yescharacteristic
1626C2×C4C25×C7111yescharacteristic
1627C8—21no—
1628C8—21no—
1629C8—21no—
1630C8—21no—
1631C8—21no—
1632C8—21no—
1633C8—21no—
1634C8—21no—
1635C22—21no—
1636C22—21no—
1637C22—21no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—41no—
1654C22—41no—
1655C22—41no—
1656C22—84no—
1657C22C23×D4×C7111yescharacteristic
1658C4—21no—
1659C4—21no—
1660C4—21no—
1661C4—21no—
1662C4—21no—
1663C4—21no—
1664C4—21no—
1665C4—21no—
1666C4—21no—
1667C4—21no—
1668C4—21no—
1669C4—21no—
1670C4—21no—
1671C4—41no—
1672C4—41no—
1673C4—41no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—41no—
1680C4—41no—
1681C4#585×C7111yescharacteristic
1682C4#585×C7111yescharacteristic
1683C2—41no—
1684C2—81no—
1685C2—81no—
1686C2—81no—
1687C2—81no—
1688C2—81no—
1689C2—81no—
1690C2C71×#348711yescharacteristic
1691C2C71×#358411yescharacteristic
1692C2C71×#358511yescharacteristic
subgroupG/H
center, socleC22×C71C23×D4
commutator, Frattini, cosocleC2×C4C25×C71
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×#3557C2semidirect
2. C71×#3506C2semidirect
3. C71×#3403C2semidirect
4. C71×#3402C2semidirect
5. C71×#3401C2semidirect
6. C71×#3401C2semidirect
7. C71×#3399C2semidirect
8. C71×#3397C2semidirect
9. C71×#3396C2semidirect
10. C71×#3394C2semidirect
11. C71×#3377C2semidirect
12. C71×#3376C2semidirect
13. C71×#3371C2semidirect
14. C71×#3370C2semidirect
15. C71×#3368C2semidirect
16. C71×#3366C2semidirect
17. C71×#3365C2semidirect
18. C71×#3361C2semidirect
19. C71×#3224C2semidirect
20. C71×#3224C2semidirect
21. C71×#3222C2semidirect
22. C71×#3220C2semidirect
23. C71×#3219C2semidirect
24. C71×#3212C2semidirect
25. C71×#3125C2semidirect
26. C71×#3124C2semidirect
27. C71×#3120C2semidirect
28. C71×#3119C2semidirect
29. C71×#3114C2semidirect
30. C71×#3105C2semidirect
31. C71×#2985C2semidirect
38. #559×C71C22semidirect
39. #559×C71C22semidirect
40. #557×C71C22semidirect
41. #557×C71C22semidirect
44. #556×C71C22semidirect
45. #556×C71C22semidirect
47. #554×C71C22semidirect
48. #554×C71C22semidirect
78. #497×C71C22semidirect
82. #496×C71C22semidirect
85. #495×C71C22semidirect
86. #495×C71C22semidirect
89. #491×C71C22semidirect
92. #490×C71C22semidirect
97. #488×C71C22semidirect
98. #488×C71C22semidirect
105. #479×C71C22semidirect
106. #479×C71C22semidirect
111. #478×C71C22semidirect
112. #478×C71C22semidirect
113. #477×C71C22semidirect
114. #476×C71C22semidirect
115. #475×C71C22semidirect
116. #474×C71C22semidirect
121. #464×C71C22semidirect
122. #464×C71C22semidirect
123. #464×C71C22semidirect
124. #464×C71C22semidirect
133. #463×C71C22semidirect
134. #463×C71C22semidirect
135. #463×C71C22semidirect
136. #463×C71C22semidirect
137. #462×C71C22semidirect
138. #462×C71C22semidirect
139. #461×C71C22semidirect
140. #461×C71C22semidirect
145. #460×C71C22semidirect
146. #460×C71C22semidirect
151. #459×C71C22semidirect
152. #459×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
175. #442×C71C22semidirect
176. #442×C71C22semidirect
177. #441×C71C22semidirect
178. #441×C71C22semidirect
181. #440×C71C22semidirect
182. #440×C71C22semidirect
183. #440×C71C22semidirect
184. #440×C71C22semidirect
185. C4×Q16×C71C22semidirect
186. C4×Q16×C71C22semidirect
189. C4×SD16×C71C22semidirect
190. C4×SD16×C71C22semidirect
191. C4×SD16×C71C22semidirect
192. C4×SD16×C71C22semidirect
195. C4×D8×C71C22semidirect
196. C4×D8×C71C22semidirect
836. #61919C71direct (N × H)
847. #3557C2×C71semidirect
848. #3506C2×C71semidirect
849. #3403C2×C71semidirect
850. #3402C2×C71semidirect
851. #3401C2×C71semidirect
852. #3401C2×C71semidirect
853. #3399C2×C71semidirect
854. #3397C2×C71semidirect
855. #3396C2×C71semidirect
856. #3394C2×C71semidirect
857. #3377C2×C71semidirect
858. #3376C2×C71semidirect
859. #3371C2×C71semidirect
860. #3370C2×C71semidirect
861. #3368C2×C71semidirect
862. #3366C2×C71semidirect
863. #3365C2×C71semidirect
864. #3361C2×C71semidirect
865. #3224C2×C71semidirect
866. #3224C2×C71semidirect
867. #3222C2×C71semidirect
868. #3220C2×C71semidirect
869. #3219C2×C71semidirect
870. #3212C2×C71semidirect
871. #3125C2×C71semidirect
872. #3124C2×C71semidirect
873. #3120C2×C71semidirect
874. #3119C2×C71semidirect
875. #3114C2×C71semidirect
876. #3105C2×C71semidirect
877. #2985C2×C71semidirect
878. C71#61919direct (N × H)
885. #559C22×C71semidirect
886. #559C22×C71semidirect
887. #557C22×C71semidirect
888. #557C22×C71semidirect
891. #556C22×C71semidirect
892. #556C22×C71semidirect
894. #554C22×C71semidirect
895. #554C22×C71semidirect
925. #497C22×C71semidirect
929. #496C22×C71semidirect
932. #495C22×C71semidirect
933. #495C22×C71semidirect
936. #491C22×C71semidirect
939. #490C22×C71semidirect
944. #488C22×C71semidirect
945. #488C22×C71semidirect
952. #479C22×C71semidirect
953. #479C22×C71semidirect
958. #478C22×C71semidirect
959. #478C22×C71semidirect
960. #477C22×C71semidirect
961. #476C22×C71semidirect
962. #475C22×C71semidirect
963. #474C22×C71semidirect
968. #464C22×C71semidirect
969. #464C22×C71semidirect
970. #464C22×C71semidirect
971. #464C22×C71semidirect
980. #463C22×C71semidirect
981. #463C22×C71semidirect
982. #463C22×C71semidirect
983. #463C22×C71semidirect
984. #462C22×C71semidirect
985. #462C22×C71semidirect
986. #461C22×C71semidirect
987. #461C22×C71semidirect
992. #460C22×C71semidirect
993. #460C22×C71semidirect
998. #459C22×C71semidirect
999. #459C22×C71semidirect
1012. #446C22×C71semidirect
1013. #446C22×C71semidirect
1014. #446C22×C71semidirect
1015. #446C22×C71semidirect
1016. #446C22×C71semidirect
1017. #446C22×C71semidirect
1018. C8×Q8C22×C71semidirect
1019. C8×Q8C22×C71semidirect
1022. #442C22×C71semidirect
1023. #442C22×C71semidirect
1024. #441C22×C71semidirect
1025. #441C22×C71semidirect
1028. #440C22×C71semidirect
1029. #440C22×C71semidirect
1030. #440C22×C71semidirect
1031. #440C22×C71semidirect
1032. C4×Q16C22×C71semidirect
1033. C4×Q16C22×C71semidirect
1036. C4×SD16C22×C71semidirect
1037. C4×SD16C22×C71semidirect
1038. C4×SD16C22×C71semidirect
1039. C4×SD16C22×C71semidirect
1042. C4×D8C22×C71semidirect
1043. C4×D8C22×C71semidirect

Maximal subgroups

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

subgroupindex
C71×#35572
C71×#35062
C71×#34032
C71×#34022
C71×#34012
C71×#33992
C71×#33972
C71×#33962
C71×#33942
C71×#33772
C71×#33762
C71×#33712
C71×#33702
C71×#33682
C71×#33662
C71×#33652
C71×#33612
C71×#32242
C71×#32222
C71×#32202
C71×#32192
C71×#32122
C71×#31252
C71×#31242
C71×#31202
C71×#31192
C71×#31142
C71×#31052
C71×#29852
#6191971