Finite Group Databasebeta

← C71×#62162 #31883034

Subgroups — C71×#62162 #31883034

Order 18176.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C71×#3565C211yesmaximal, characteristic, complemented
2C71×#3517C211yesmaximal, characteristic, complemented
3C71×#3390C211yesmaximal, characteristic, complemented
4C71×#3388C211yesmaximal, characteristic, complemented
5C71×#3368C211yesmaximal, characteristic, complemented
6C71×#3366C211yesmaximal, characteristic, complemented
7C71×#3350C211yesmaximal, characteristic, complemented
8C71×#3347C211yesmaximal, characteristic, complemented
9C71×#3345C211yesmaximal, characteristic, complemented
10C71×#3343C211yesmaximal, characteristic, complemented
11C71×#3339C211yesmaximal, characteristic, complemented
12C71×#3337C211yesmaximal, characteristic, complemented
13C71×#3317C211yesmaximal, characteristic, complemented
14C71×#3317C211yesmaximal, characteristic, complemented
15C71×#3309C211yesmaximal, characteristic, complemented
16C71×#3309C211yesmaximal, characteristic, complemented
17C71×#3305C211yesmaximal, characteristic, complemented
18C71×#3304C211yesmaximal, characteristic, complemented
19C71×#3257C211yesmaximal, characteristic, complemented
20C71×#3257C211yesmaximal, characteristic, complemented
21C71×#3247C211yesmaximal, characteristic, complemented
22C71×#3241C211yesmaximal, characteristic, complemented
23C71×#3241C211yesmaximal, characteristic, complemented
24C71×#3235C211yesmaximal, characteristic, complemented
25C71×#3125C211yesmaximal, characteristic, complemented
26C71×#3124C211yesmaximal, characteristic, complemented
27C71×#3111C211yesmaximal, characteristic, complemented
28C71×#3084C211yesmaximal, characteristic, complemented
29C71×#3083C211yesmaximal, characteristic, complemented
30C71×#3076C211yesmaximal, characteristic, complemented
31C71×#2992C211yesmaximal, characteristic, complemented
32#563×C71—21no—
33#562×C71—21no—
34#557×C71C2211yescharacteristic
35#557×C71C2211yescharacteristic
36#556×C71—21no—
37#556×C71C2211yescharacteristic
38#555×C71C2211yescharacteristic
39#554×C71C2211yescharacteristic
40#553×C71—21no—
41#553×C71—21no—
42#553×C71C2211yescharacteristic
43#553×C71C2211yescharacteristic
44#553×C71C2211yescharacteristic
45#553×C71C2211yescharacteristic
46#552×C71—21no—
47#552×C71C2211yescharacteristic
48#552×C71C2211yescharacteristic
49#550×C71—21no—
50#550×C71C2211yescharacteristic
51#550×C71C2211yescharacteristic
52#550×C71C2211yescharacteristic
53#550×C71C2211yescharacteristic
54#547×C71—21no—
55#547×C71C2211yescharacteristic
56#544×C71C2211yescharacteristic
57#544×C71C2211yescharacteristic
58#542×C71—21no—
59#542×C71—21no—
60#542×C71C2211yescharacteristic
61#542×C71C2211yescharacteristic
62#541×C71—21no—
63#540×C71—21no—
64#540×C71—21no—
65#540×C71C2211yescharacteristic
66#540×C71C2211yescharacteristic
67#539×C71—21no—
68#533×C71C2211yescharacteristic
69#532×C71—21no—
70#532×C71C2211yescharacteristic
71#529×C71—21no—
72#529×C71C2211yescharacteristic
73#529×C71C2211yescharacteristic
74#520×C71C2211yescharacteristic
75#520×C71C2211yescharacteristic
76C4×#41×C71C2211yescharacteristic
77#501×C71C2211yescharacteristic
78#501×C71C2211yescharacteristic
79#501×C71C2211yescharacteristic
80#501×C71C2211yescharacteristic
81#499×C71C2211yescharacteristic
82#499×C71C2211yescharacteristic
83#490×C71C2211yescharacteristic
84#490×C71C2211yescharacteristic
85#490×C71C2211yescharacteristic
86#490×C71C2211yescharacteristic
87#486×C71C2211yescharacteristic
88#486×C71C2211yescharacteristic
89#485×C71C2211yescharacteristic
90#484×C71C2211yescharacteristic
91#483×C71C2211yescharacteristic
92#482×C71C2211yescharacteristic
93#482×C71C2211yescharacteristic
94#482×C71C2211yescharacteristic
95#482×C71C2211yescharacteristic
96#482×C71C2211yescharacteristic
97#482×C71C2211yescharacteristic
98#482×C71C2211yescharacteristic
99#482×C71C2211yescharacteristic
100#482×C71C2211yescharacteristic
101#481×C71C2211yescharacteristic
102#481×C71C2211yescharacteristic
103#481×C71C2211yescharacteristic
104#480×C71C2211yescharacteristic
105#480×C71C2211yescharacteristic
106#480×C71C2211yescharacteristic
107#479×C71C2211yescharacteristic
108#479×C71C2211yescharacteristic
109#479×C71C2211yescharacteristic
110#479×C71C2211yescharacteristic
111#479×C71C2211yescharacteristic
112#479×C71C2211yescharacteristic
113#479×C71C2211yescharacteristic
114#478×C71C2211yescharacteristic
115#478×C71C2211yescharacteristic
116#478×C71C2211yescharacteristic
117#478×C71C2211yescharacteristic
118#478×C71C2211yescharacteristic
119#478×C71C2211yescharacteristic
120#478×C71C2211yescharacteristic
121#478×C71C2211yescharacteristic
122#478×C71C2211yescharacteristic
123#477×C71C2211yescharacteristic
124#477×C71C2211yescharacteristic
125#477×C71C2211yescharacteristic
126#476×C71C2211yescharacteristic
127#476×C71C2211yescharacteristic
128#476×C71C2211yescharacteristic
129#476×C71C2211yescharacteristic
130#476×C71C2211yescharacteristic
131#475×C71C2211yescharacteristic
132#475×C71C2211yescharacteristic
133#474×C71C2211yescharacteristic
134#474×C71C2211yescharacteristic
135#474×C71C2211yescharacteristic
136#474×C71C2211yescharacteristic
137#469×C71C2211yescharacteristic
138#469×C71C2211yescharacteristic
139#468×C71C2211yescharacteristic
140#468×C71C2211yescharacteristic
141#466×C71C2211yescharacteristic
142#466×C71C2211yescharacteristic
143#466×C71C2211yescharacteristic
144#466×C71C2211yescharacteristic
145#465×C71C2211yescharacteristic
146#465×C71C2211yescharacteristic
147#465×C71C2211yescharacteristic
148#465×C71C2211yescharacteristic
149#464×C71C2211yescharacteristic
150#463×C71C2211yescharacteristic
151#463×C71C2211yescharacteristic
152#463×C71C2211yescharacteristic
153#460×C71C2211yescharacteristic
154#460×C71C2211yescharacteristic
155#460×C71C2211yescharacteristic
156#459×C71C2211yescharacteristic
157#459×C71C2211yescharacteristic
158#459×C71C2211yescharacteristic
159#452×C71C2211yescharacteristic
160#452×C71C2211yescharacteristic
161#452×C71C2211yescharacteristic
162#449×C71C2211yescharacteristic
163#449×C71C2211yescharacteristic
164#449×C71C2211yescharacteristic
165#446×C71C2211yescharacteristic
166#446×C71C2211yescharacteristic
167#442×C71C2211yescharacteristic
168#442×C71C2211yescharacteristic
169#441×C71C2211yescharacteristic
170#441×C71C2211yescharacteristic
171#440×C71C2211yescharacteristic
172#440×C71C2211yescharacteristic
173#440×C71C2211yescharacteristic
174#440×C71C2211yescharacteristic
175C4×Q16×C71C2211yescharacteristic
176C4×SD16×C71C2211yescharacteristic
177C4×SD16×C71C2211yescharacteristic
178C4×D8×C71C2211yescharacteristic
179#435×C71C2211yescharacteristic
180#435×C71C2211yescharacteristic
181#435×C71C2211yescharacteristic
182#435×C71C2211yescharacteristic
183C8×D4×C71C2211yescharacteristic
184C8×D4×C71C2211yescharacteristic
185#433×C71C2211yescharacteristic
186#433×C71C2211yescharacteristic
187#432×C71C2211yescharacteristic
188#428×C71C2211yescharacteristic
189#428×C71C2211yescharacteristic
190#427×C71C2211yescharacteristic
191#427×C71C2211yescharacteristic
192C2×#107×C71C2211yescharacteristic
193C2×#106×C71C2211yescharacteristic
194#424×C71C2211yescharacteristic
195#424×C71C2211yescharacteristic
196C2×C4⋊C8×C71C2211yescharacteristic
197#417×C71C2211yescharacteristic
198#417×C71C2211yescharacteristic
199#416×C71C2211yescharacteristic
200#416×C71C2211yescharacteristic
201#416×C71C2211yescharacteristic
202#416×C71C2211yescharacteristic
203C2×#41×C71—21no—
204C2×#41×C71—21no—
205C2×#41×C71—21no—
206C2×#41×C71C2311yescharacteristic
207C2×#41×C71C2311yescharacteristic
208C2×#41×C71C2311yescharacteristic
209C2×Q16×C71C2311yescharacteristic
210C2×SD16×C71C2311yescharacteristic
211C2×SD16×C71C2311yescharacteristic
212C2×SD16×C71C2311yescharacteristic
213C2×SD16×C71C2311yescharacteristic
214C2×D8×C71C2311yescharacteristic
215C2×D8×C71C2311yescharacteristic
216C2×D8×C71C2311yescharacteristic
217C2×M16×C71C2311yescharacteristic
218C2×M16×C71C2311yescharacteristic
219C22×C8×C71C2311yescharacteristic
220C22×C8×C71C2311yescharacteristic
221C22×C8×C71C2311yescharacteristic
222C22×C8×C71C2311yescharacteristic
223C4⋊Q8×C71—21no—
224C4⋊Q8×C71—21no—
225C4⋊Q8×C71—21no—
226C4⋊Q8×C71—21no—
227C4⋊Q8×C71C2311yescharacteristic
228C4⋊Q8×C71C2311yescharacteristic
229C4⋊Q8×C71C2311yescharacteristic
230C4⋊Q8×C71C2311yescharacteristic
231C4⋊Q8×C71C2311yescharacteristic
232#127×C71—21no—
233#127×C71—21no—
234#127×C71—21no—
235#127×C71C2311yescharacteristic
236#127×C71C2311yescharacteristic
237#127×C71C2311yescharacteristic
238#126×C71—21no—
239#126×C71—21no—
240#126×C71—21no—
241#126×C71—21no—
242#126×C71—21no—
243#126×C71—21no—
244#126×C71—21no—
245#126×C71—21no—
246#126×C71—21no—
247#126×C71—21no—
248#126×C71—21no—
249#126×C71D411yescharacteristic
250#126×C71D411yescharacteristic
251#125×C71—21no—
252#125×C71—21no—
253#125×C71—21no—
254#125×C71—21no—
255#125×C71—21no—
256#125×C71—21no—
257#125×C71—21no—
258#125×C71—21no—
259#125×C71D411yescharacteristic
260#125×C71C2311yescharacteristic
261#125×C71C2311yescharacteristic
262#125×C71C2311yescharacteristic
263#125×C71C2311yescharacteristic
264#125×C71C2311yescharacteristic
265#125×C71C2311yescharacteristic
266#125×C71C2311yescharacteristic
267#124×C71—21no—
268#124×C71—21no—
269#124×C71—21no—
270#124×C71—21no—
271#124×C71—21no—
272#124×C71—21no—
273#124×C71D411yescharacteristic
274#124×C71C2311yescharacteristic
275#123×C71—21no—
276#123×C71—21no—
277#123×C71—21no—
278#123×C71—21no—
279#123×C71—21no—
280#123×C71—21no—
281#123×C71—21no—
282#123×C71—21no—
283#123×C71—21no—
284#123×C71—21no—
285#123×C71—21no—
286#123×C71—21no—
287#123×C71—21no—
288#123×C71—21no—
289#123×C71—21no—
290#123×C71D411yescharacteristic
291#123×C71D411yescharacteristic
292C22⋊Q8×C71—21no—
293C22⋊Q8×C71—21no—
294C22⋊Q8×C71—21no—
295C22⋊Q8×C71—21no—
296C22⋊Q8×C71—21no—
297C22⋊Q8×C71—21no—
298C22⋊Q8×C71—21no—
299C22⋊Q8×C71—21no—
300C22⋊Q8×C71—21no—
301C22⋊Q8×C71—21no—
302C22⋊Q8×C71—21no—
303C22⋊Q8×C71—21no—
304C22⋊Q8×C71D411yescharacteristic
305C22⋊Q8×C71C2311yescharacteristic
306C22⋊Q8×C71C2311yescharacteristic
307C22⋊Q8×C71C2311yescharacteristic
308#121×C71—21no—
309#121×C71—21no—
310#121×C71—21no—
311#121×C71—21no—
312#121×C71—21no—
313#121×C71—21no—
314#121×C71—21no—
315#121×C71—21no—
316#121×C71—21no—
317#121×C71—21no—
318#121×C71—21no—
319#121×C71—21no—
320#121×C71—21no—
321#121×C71—21no—
322#121×C71—21no—
323#121×C71—21no—
324#121×C71—21no—
325#121×C71—21no—
326#121×C71—21no—
327#121×C71D411yescharacteristic
328#121×C71C2311yescharacteristic
329#121×C71C2311yescharacteristic
330#121×C71C2311yescharacteristic
331#121×C71C2311yescharacteristic
332#121×C71C2311yescharacteristic
333#121×C71C2311yescharacteristic
334#121×C71C2311yescharacteristic
335#121×C71C2311yescharacteristic
336#121×C71C2311yescharacteristic
337C4×Q8×C71—21no—
338C4×Q8×C71—21no—
339C4×Q8×C71—21no—
340C4×Q8×C71—21no—
341C4×Q8×C71—21no—
342C4×Q8×C71C2311yescharacteristic
343C4×Q8×C71C2311yescharacteristic
344C4×Q8×C71C2311yescharacteristic
345C4×Q8×C71C2311yescharacteristic
346C4×Q8×C71C2311yescharacteristic
347C4×Q8×C71C2311yescharacteristic
348C4×Q8×C71C2311yescharacteristic
349C4×Q8×C71C2311yescharacteristic
350C4×D4×C71—21no—
351C4×D4×C71—21no—
352C4×D4×C71—21no—
353C4×D4×C71—21no—
354C4×D4×C71—21no—
355C4×D4×C71—21no—
356C4×D4×C71—21no—
357C4×D4×C71—21no—
358C4×D4×C71—21no—
359C4×D4×C71—21no—
360C4×D4×C71—21no—
361C4×D4×C71—21no—
362C4×D4×C71—21no—
363C4×D4×C71—21no—
364C4×D4×C71—21no—
365C4×D4×C71C2311yescharacteristic
366C4×D4×C71C2311yescharacteristic
367C4×D4×C71C2311yescharacteristic
368C4×D4×C71C2311yescharacteristic
369C4×D4×C71C2311yescharacteristic
370C4×D4×C71C2311yescharacteristic
371C4×D4×C71C2311yescharacteristic
372C4×D4×C71C2311yescharacteristic
373C4×D4×C71C2311yescharacteristic
374C4×D4×C71C2311yescharacteristic
375C4×D4×C71C2311yescharacteristic
376C4×D4×C71C2311yescharacteristic
377#117×C71—21no—
378#117×C71—21no—
379#117×C71—21no—
380#117×C71—21no—
381#117×C71—21no—
382#117×C71—21no—
383#117×C71—21no—
384#117×C71C2311yescharacteristic
385#117×C71C2311yescharacteristic
386#117×C71C2311yescharacteristic
387#117×C71C2311yescharacteristic
388#117×C71C2311yescharacteristic
389#117×C71C2311yescharacteristic
390#117×C71C2311yescharacteristic
391C2×C4⋊C4×C71—21no—
392C2×C4⋊C4×C71—21no—
393C2×C4⋊C4×C71—21no—
394C2×C4⋊C4×C71C2311yescharacteristic
395C2×C4⋊C4×C71C2311yescharacteristic
396C2×C4⋊C4×C71C2311yescharacteristic
397C2×C4⋊C4×C71C2311yescharacteristic
398C2×C42×C71—21no—
399C2×C42×C71C2311yescharacteristic
400#107×C71C2311yescharacteristic
401#107×C71C2311yescharacteristic
402#107×C71C2311yescharacteristic
403#107×C71C2311yescharacteristic
404#107×C71C2311yescharacteristic
405#107×C71C2311yescharacteristic
406#107×C71C2311yescharacteristic
407#107×C71C2311yescharacteristic
408#107×C71C2311yescharacteristic
409#107×C71C2311yescharacteristic
410#107×C71C2311yescharacteristic
411#107×C71C2311yescharacteristic
412#106×C71C2311yescharacteristic
413#106×C71C2311yescharacteristic
414#106×C71C2311yescharacteristic
415#106×C71C2311yescharacteristic
416#106×C71C2311yescharacteristic
417#106×C71C2311yescharacteristic
418#106×C71C2311yescharacteristic
419#106×C71C2311yescharacteristic
420#106×C71C2311yescharacteristic
421#106×C71C2311yescharacteristic
422#106×C71C2311yescharacteristic
423#106×C71C2311yescharacteristic
424C4⋊C8×C71C2311yescharacteristic
425C4⋊C8×C71C2311yescharacteristic
426C4⋊C8×C71C2311yescharacteristic
427C4⋊C8×C71C2311yescharacteristic
428C4⋊C8×C71C2311yescharacteristic
429C4⋊C8×C71C2311yescharacteristic
430C4⋊C8×C71C2311yescharacteristic
431C4⋊C8×C71C2311yescharacteristic
432C4⋊C8×C71C2311yescharacteristic
433C4⋊C8×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#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
462#102×C71C2311yescharacteristic
463#102×C71C2311yescharacteristic
464#102×C71C2311yescharacteristic
465#102×C71C2311yescharacteristic
466C22⋊C8×C71C2311yescharacteristic
467C22⋊C8×C71C2311yescharacteristic
468C22⋊C8×C71C2311yescharacteristic
469C22⋊C8×C71C2311yescharacteristic
470C22⋊C8×C71C2311yescharacteristic
471C22⋊C8×C71C2311yescharacteristic
472#97×C71C2311yescharacteristic
473#97×C71C2311yescharacteristic
474#97×C71C2311yescharacteristic
475#97×C71C2311yescharacteristic
476C4×C8×C71C2311yescharacteristic
477C4×C8×C71C2311yescharacteristic
478#41×C71—22no—
479#41×C71—22no—
480#41×C71—22no—
481#41×C71—41no—
482#41×C71—41no—
483#41×C71—41no—
484#41×C71—82no—
485#41×C71—82no—
486#41×C71—82no—
487C2×Q8×C71—21no—
488C2×Q8×C71—21no—
489C2×Q8×C71—21no—
490C2×Q8×C71—21no—
491C2×Q8×C71—21no—
492C2×Q8×C71C2×D411yescharacteristic
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—21no—
513C2×D4×C71C2×D411yescharacteristic
514C2×D4×C71C2×D411yescharacteristic
515C2×D4×C71C2×D411yescharacteristic
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×C71C2×D411yescharacteristic
537C22×C4×C71C2×D411yescharacteristic
538C22×C4×C71C2411yescharacteristic
539C22×C4×C71C2411yescharacteristic
540C22×C4×C71C2411yescharacteristic
541Q16×C71—22no—
542SD16×C71—22no—
543SD16×C71—41no—
544SD16×C71—41no—
545SD16×C71—41no—
546D8×C71—41no—
547D8×C71—41no—
548D8×C71—41no—
549M16×C71—41no—
550M16×C71—41no—
551C2×C8×C71—41no—
552C2×C8×C71—41no—
553C2×C8×C71—41no—
554C2×C8×C71—41no—
555C2×C8×C71C2411yescharacteristic
556C2×C8×C71C2411yescharacteristic
557C2×C8×C71C2411yescharacteristic
558C2×C8×C71C2411yescharacteristic
559C2×C8×C71C2411yescharacteristic
560C2×C8×C71C2411yescharacteristic
561C2×C8×C71C2411yescharacteristic
562C2×C8×C71C2411yescharacteristic
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×C71—21no—
594C4⋊C4×C71—21no—
595C4⋊C4×C71—21no—
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×C71C2411yescharacteristic
607C4⋊C4×C71C2411yescharacteristic
608C4⋊C4×C71C2411yescharacteristic
609C4⋊C4×C71C2411yescharacteristic
610C4⋊C4×C71C2411yescharacteristic
611C4⋊C4×C71C2411yescharacteristic
612C4⋊C4×C71C2411yescharacteristic
613C4⋊C4×C71C2411yescharacteristic
614C4⋊C4×C71C2411yescharacteristic
615C4⋊C4×C71C2411yescharacteristic
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×C71C2×D411yescharacteristic
645C22⋊C4×C71C2×D411yescharacteristic
646C22⋊C4×C71C2×D411yescharacteristic
647C22⋊C4×C71C2×D411yescharacteristic
648C22⋊C4×C71C2×D411yescharacteristic
649C22⋊C4×C71C2×D411yescharacteristic
650C22⋊C4×C71C2×D411yescharacteristic
651C22⋊C4×C71C2×D411yescharacteristic
652C22⋊C4×C71C2×D411yescharacteristic
653C22⋊C4×C71C2×D411yescharacteristic
654C42×C71—21no—
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×C71C2×D411yescharacteristic
667C42×C71C2×D411yescharacteristic
668C42×C71C2411yescharacteristic
669C42×C71C2411yescharacteristic
670C42×C71C2411yescharacteristic
671C42×C71C2411yescharacteristic
672C23×C71—21no—
673C23×C71—21no—
674C23×C71—21no—
675C23×C71—21no—
676C23×C71C22×D411yescharacteristic
677C23×C71C22×D411yescharacteristic
678C23×C71C22×D411yescharacteristic
679Q8×C71—21no—
680Q8×C71—21no—
681Q8×C71—21no—
682Q8×C71—41no—
683Q8×C71—42no—
684Q8×C71—81no—
685Q8×C71—81no—
686Q8×C71—81no—
687Q8×C71—81no—
688Q8×C712−1+412yes—
689D4×C71—21no—
690D4×C71—21no—
691D4×C71—21no—
692D4×C71—21no—
693D4×C71—21no—
694D4×C71—21no—
695D4×C71—21no—
696D4×C71—21no—
697D4×C71—41no—
698D4×C71—41no—
699D4×C71—41no—
700D4×C71—42no—
701D4×C71—42no—
702D4×C71—42no—
703D4×C71—42no—
704D4×C71—81no—
705D4×C71—81no—
706D4×C71—81no—
707D4×C71—81no—
708D4×C71—81no—
709D4×C71—81no—
710D4×C71—81no—
711D4×C71—81no—
712D4×C71—81no—
713D4×C71—81no—
714D4×C71—81no—
715D4×C71—81no—
716D4×C71—81no—
717D4×C71—81no—
718C2×C4×C71—21no—
719C2×C4×C71—21no—
720C2×C4×C71—21no—
721C2×C4×C71—21no—
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—42no—
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×C71—81no—
750C2×C4×C71—81no—
751C2×C4×C71—81no—
752C2×C4×C71—81no—
753C2×C4×C71—81no—
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×C71C22×D411yescharacteristic
763C2×C4×C71C22×D411yescharacteristic
764C2×C4×C71C22×D411yescharacteristic
765C2×C4×C71C2511yescharacteristic
766C8×C71—21no—
767C8×C71—21no—
768C8×C71—21no—
769C8×C71—21no—
770C8×C71—21no—
771C8×C71—21no—
772C8×C71—21no—
773C8×C71—21no—
774C22×C71—21no—
775C22×C71—21no—
776C22×C71—21no—
777C22×C71—21no—
778C22×C71—21no—
779C22×C71—21no—
780C22×C71—21no—
781C22×C71—21no—
782C22×C71—21no—
783C22×C71—41no—
784C22×C71—41no—
785C22×C71—41no—
786C22×C71—41no—
787C22×C71—41no—
788C22×C71—41no—
789C22×C71—41no—
790C22×C71—41no—
791C22×C71—41no—
792C22×C71—41no—
793C22×C71—41no—
794C22×C71—41no—
795C22×C71C23×D411yescharacteristic
796C4×C71—21no—
797C4×C71—21no—
798C4×C71—21no—
799C4×C71—21no—
800C4×C71—21no—
801C4×C71—21no—
802C4×C71—21no—
803C4×C71—21no—
804C4×C71—21no—
805C4×C71—21no—
806C4×C71—21no—
807C4×C71—22no—
808C4×C71—41no—
809C4×C71—41no—
810C4×C71—41no—
811C4×C71—41no—
812C4×C71—41no—
813C4×C71—41no—
814C4×C71—41no—
815C4×C71—41no—
816C4×C71—41no—
817C4×C71—41no—
818C4×C71—41no—
819C4×C71C2×2−1+411yescharacteristic
820C4×C71#58511yescharacteristic
821#62162C7111yesmaximal, characteristic, direct product factor, Sylow
822C2×C71—41no—
823C2×C71—41no—
824C2×C71—41no—
825C2×C71—81no—
826C2×C71—81no—
827C2×C71—81no—
828C2×C71—81no—
829C2×C71#348911yescharacteristic
830C2×C71#358411yescharacteristic
831C2×C71#358511yescharacteristic
832#3565C2×C7111yescharacteristic, complemented
833#3517C2×C7111yescharacteristic, complemented
834#3390C2×C7111yescharacteristic, complemented
835#3388C2×C7111yescharacteristic, complemented
836#3368C2×C7111yescharacteristic, complemented
837#3366C2×C7111yescharacteristic, complemented
838#3350C2×C7111yescharacteristic, complemented
839#3347C2×C7111yescharacteristic, complemented
840#3345C2×C7111yescharacteristic, complemented
841#3343C2×C7111yescharacteristic, complemented
842#3339C2×C7111yescharacteristic, complemented
843#3337C2×C7111yescharacteristic, complemented
844#3317C2×C7111yescharacteristic, complemented
845#3317C2×C7111yescharacteristic, complemented
846#3309C2×C7111yescharacteristic, complemented
847#3309C2×C7111yescharacteristic, complemented
848#3305C2×C7111yescharacteristic, complemented
849#3304C2×C7111yescharacteristic, complemented
850#3257C2×C7111yescharacteristic, complemented
851#3257C2×C7111yescharacteristic, complemented
852#3247C2×C7111yescharacteristic, complemented
853#3241C2×C7111yescharacteristic, complemented
854#3241C2×C7111yescharacteristic, complemented
855#3235C2×C7111yescharacteristic, complemented
856#3125C2×C7111yescharacteristic, complemented
857#3124C2×C7111yescharacteristic, complemented
858#3111C2×C7111yescharacteristic, complemented
859#3084C2×C7111yescharacteristic, complemented
860#3083C2×C7111yescharacteristic, complemented
861#3076C2×C7111yescharacteristic, complemented
862#2992C2×C7111yescharacteristic, complemented
863C71#6216211yescharacteristic, direct product factor, Sylow
864#563—21no—
865#562—21no—
866#557C22×C7111yescharacteristic
867#557C22×C7111yescharacteristic
868#556—21no—
869#556C22×C7111yescharacteristic
870#555C22×C7111yescharacteristic
871#554C22×C7111yescharacteristic
872#553—21no—
873#553—21no—
874#553C22×C7111yescharacteristic
875#553C22×C7111yescharacteristic
876#553C22×C7111yescharacteristic
877#553C22×C7111yescharacteristic
878#552—21no—
879#552C22×C7111yescharacteristic
880#552C22×C7111yescharacteristic
881#550—21no—
882#550C22×C7111yescharacteristic
883#550C22×C7111yescharacteristic
884#550C22×C7111yescharacteristic
885#550C22×C7111yescharacteristic
886#547—21no—
887#547C22×C7111yescharacteristic
888#544C22×C7111yescharacteristic
889#544C22×C7111yescharacteristic
890#542—21no—
891#542—21no—
892#542C22×C7111yescharacteristic
893#542C22×C7111yescharacteristic
894#541—21no—
895#540—21no—
896#540—21no—
897#540C22×C7111yescharacteristic
898#540C22×C7111yescharacteristic
899#539—21no—
900#533C22×C7111yescharacteristic
901#532—21no—
902#532C22×C7111yescharacteristic
903#529—21no—
904#529C22×C7111yescharacteristic
905#529C22×C7111yescharacteristic
906#520C22×C7111yescharacteristic
907#520C22×C7111yescharacteristic
908C4×#41C22×C7111yescharacteristic
909#501C22×C7111yescharacteristic
910#501C22×C7111yescharacteristic
911#501C22×C7111yescharacteristic
912#501C22×C7111yescharacteristic
913#499C22×C7111yescharacteristic
914#499C22×C7111yescharacteristic
915#490C22×C7111yescharacteristic
916#490C22×C7111yescharacteristic
917#490C22×C7111yescharacteristic
918#490C22×C7111yescharacteristic
919#486C22×C7111yescharacteristic
920#486C22×C7111yescharacteristic
921#485C22×C7111yescharacteristic
922#484C22×C7111yescharacteristic
923#483C22×C7111yescharacteristic
924#482C22×C7111yescharacteristic
925#482C22×C7111yescharacteristic
926#482C22×C7111yescharacteristic
927#482C22×C7111yescharacteristic
928#482C22×C7111yescharacteristic
929#482C22×C7111yescharacteristic
930#482C22×C7111yescharacteristic
931#482C22×C7111yescharacteristic
932#482C22×C7111yescharacteristic
933#481C22×C7111yescharacteristic
934#481C22×C7111yescharacteristic
935#481C22×C7111yescharacteristic
936#480C22×C7111yescharacteristic
937#480C22×C7111yescharacteristic
938#480C22×C7111yescharacteristic
939#479C22×C7111yescharacteristic
940#479C22×C7111yescharacteristic
941#479C22×C7111yescharacteristic
942#479C22×C7111yescharacteristic
943#479C22×C7111yescharacteristic
944#479C22×C7111yescharacteristic
945#479C22×C7111yescharacteristic
946#478C22×C7111yescharacteristic
947#478C22×C7111yescharacteristic
948#478C22×C7111yescharacteristic
949#478C22×C7111yescharacteristic
950#478C22×C7111yescharacteristic
951#478C22×C7111yescharacteristic
952#478C22×C7111yescharacteristic
953#478C22×C7111yescharacteristic
954#478C22×C7111yescharacteristic
955#477C22×C7111yescharacteristic
956#477C22×C7111yescharacteristic
957#477C22×C7111yescharacteristic
958#476C22×C7111yescharacteristic
959#476C22×C7111yescharacteristic
960#476C22×C7111yescharacteristic
961#476C22×C7111yescharacteristic
962#476C22×C7111yescharacteristic
963#475C22×C7111yescharacteristic
964#475C22×C7111yescharacteristic
965#474C22×C7111yescharacteristic
966#474C22×C7111yescharacteristic
967#474C22×C7111yescharacteristic
968#474C22×C7111yescharacteristic
969#469C22×C7111yescharacteristic
970#469C22×C7111yescharacteristic
971#468C22×C7111yescharacteristic
972#468C22×C7111yescharacteristic
973#466C22×C7111yescharacteristic
974#466C22×C7111yescharacteristic
975#466C22×C7111yescharacteristic
976#466C22×C7111yescharacteristic
977#465C22×C7111yescharacteristic
978#465C22×C7111yescharacteristic
979#465C22×C7111yescharacteristic
980#465C22×C7111yescharacteristic
981#464C22×C7111yescharacteristic
982#463C22×C7111yescharacteristic
983#463C22×C7111yescharacteristic
984#463C22×C7111yescharacteristic
985#460C22×C7111yescharacteristic
986#460C22×C7111yescharacteristic
987#460C22×C7111yescharacteristic
988#459C22×C7111yescharacteristic
989#459C22×C7111yescharacteristic
990#459C22×C7111yescharacteristic
991#452C22×C7111yescharacteristic
992#452C22×C7111yescharacteristic
993#452C22×C7111yescharacteristic
994#449C22×C7111yescharacteristic
995#449C22×C7111yescharacteristic
996#449C22×C7111yescharacteristic
997#446C22×C7111yescharacteristic
998#446C22×C7111yescharacteristic
999#442C22×C7111yescharacteristic
1000#442C22×C7111yescharacteristic
1001#441C22×C7111yescharacteristic
1002#441C22×C7111yescharacteristic
1003#440C22×C7111yescharacteristic
1004#440C22×C7111yescharacteristic
1005#440C22×C7111yescharacteristic
1006#440C22×C7111yescharacteristic
1007C4×Q16C22×C7111yescharacteristic
1008C4×SD16C22×C7111yescharacteristic
1009C4×SD16C22×C7111yescharacteristic
1010C4×D8C22×C7111yescharacteristic
1011#435C22×C7111yescharacteristic
1012#435C22×C7111yescharacteristic
1013#435C22×C7111yescharacteristic
1014#435C22×C7111yescharacteristic
1015C8×D4C22×C7111yescharacteristic
1016C8×D4C22×C7111yescharacteristic
1017#433C22×C7111yescharacteristic
1018#433C22×C7111yescharacteristic
1019#432C22×C7111yescharacteristic
1020#428C22×C7111yescharacteristic
1021#428C22×C7111yescharacteristic
1022#427C22×C7111yescharacteristic
1023#427C22×C7111yescharacteristic
1024C2×#107C22×C7111yescharacteristic
1025C2×#106C22×C7111yescharacteristic
1026#424C22×C7111yescharacteristic
1027#424C22×C7111yescharacteristic
1028C2×C4⋊C8C22×C7111yescharacteristic
1029#417C22×C7111yescharacteristic
1030#417C22×C7111yescharacteristic
1031#416C22×C7111yescharacteristic
1032#416C22×C7111yescharacteristic
1033#416C22×C7111yescharacteristic
1034#416C22×C7111yescharacteristic
1035C2×#41—21no—
1036C2×#41—21no—
1037C2×#41—21no—
1038C2×#41C23×C7111yescharacteristic
1039C2×#41C23×C7111yescharacteristic
1040C2×#41C23×C7111yescharacteristic
1041C2×Q16C23×C7111yescharacteristic
1042C2×SD16C23×C7111yescharacteristic
1043C2×SD16C23×C7111yescharacteristic
1044C2×SD16C23×C7111yescharacteristic
1045C2×SD16C23×C7111yescharacteristic
1046C2×D8C23×C7111yescharacteristic
1047C2×D8C23×C7111yescharacteristic
1048C2×D8C23×C7111yescharacteristic
1049C2×M16C23×C7111yescharacteristic
1050C2×M16C23×C7111yescharacteristic
1051C22×C8C23×C7111yescharacteristic
1052C22×C8C23×C7111yescharacteristic
1053C22×C8C23×C7111yescharacteristic
1054C22×C8C23×C7111yescharacteristic
1055C4⋊Q8—21no—
1056C4⋊Q8—21no—
1057C4⋊Q8—21no—
1058C4⋊Q8—21no—
1059C4⋊Q8C23×C7111yescharacteristic
1060C4⋊Q8C23×C7111yescharacteristic
1061C4⋊Q8C23×C7111yescharacteristic
1062C4⋊Q8C23×C7111yescharacteristic
1063C4⋊Q8C23×C7111yescharacteristic
1064#127—21no—
1065#127—21no—
1066#127—21no—
1067#127C23×C7111yescharacteristic
1068#127C23×C7111yescharacteristic
1069#127C23×C7111yescharacteristic
1070#126—21no—
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#126D4×C7111yescharacteristic
1082#126D4×C7111yescharacteristic
1083#125—21no—
1084#125—21no—
1085#125—21no—
1086#125—21no—
1087#125—21no—
1088#125—21no—
1089#125—21no—
1090#125—21no—
1091#125D4×C7111yescharacteristic
1092#125C23×C7111yescharacteristic
1093#125C23×C7111yescharacteristic
1094#125C23×C7111yescharacteristic
1095#125C23×C7111yescharacteristic
1096#125C23×C7111yescharacteristic
1097#125C23×C7111yescharacteristic
1098#125C23×C7111yescharacteristic
1099#124—21no—
1100#124—21no—
1101#124—21no—
1102#124—21no—
1103#124—21no—
1104#124—21no—
1105#124D4×C7111yescharacteristic
1106#124C23×C7111yescharacteristic
1107#123—21no—
1108#123—21no—
1109#123—21no—
1110#123—21no—
1111#123—21no—
1112#123—21no—
1113#123—21no—
1114#123—21no—
1115#123—21no—
1116#123—21no—
1117#123—21no—
1118#123—21no—
1119#123—21no—
1120#123—21no—
1121#123—21no—
1122#123D4×C7111yescharacteristic
1123#123D4×C7111yescharacteristic
1124C22⋊Q8—21no—
1125C22⋊Q8—21no—
1126C22⋊Q8—21no—
1127C22⋊Q8—21no—
1128C22⋊Q8—21no—
1129C22⋊Q8—21no—
1130C22⋊Q8—21no—
1131C22⋊Q8—21no—
1132C22⋊Q8—21no—
1133C22⋊Q8—21no—
1134C22⋊Q8—21no—
1135C22⋊Q8—21no—
1136C22⋊Q8D4×C7111yescharacteristic
1137C22⋊Q8C23×C7111yescharacteristic
1138C22⋊Q8C23×C7111yescharacteristic
1139C22⋊Q8C23×C7111yescharacteristic
1140#121—21no—
1141#121—21no—
1142#121—21no—
1143#121—21no—
1144#121—21no—
1145#121—21no—
1146#121—21no—
1147#121—21no—
1148#121—21no—
1149#121—21no—
1150#121—21no—
1151#121—21no—
1152#121—21no—
1153#121—21no—
1154#121—21no—
1155#121—21no—
1156#121—21no—
1157#121—21no—
1158#121—21no—
1159#121D4×C7111yescharacteristic
1160#121C23×C7111yescharacteristic
1161#121C23×C7111yescharacteristic
1162#121C23×C7111yescharacteristic
1163#121C23×C7111yescharacteristic
1164#121C23×C7111yescharacteristic
1165#121C23×C7111yescharacteristic
1166#121C23×C7111yescharacteristic
1167#121C23×C7111yescharacteristic
1168#121C23×C7111yescharacteristic
1169C4×Q8—21no—
1170C4×Q8—21no—
1171C4×Q8—21no—
1172C4×Q8—21no—
1173C4×Q8—21no—
1174C4×Q8C23×C7111yescharacteristic
1175C4×Q8C23×C7111yescharacteristic
1176C4×Q8C23×C7111yescharacteristic
1177C4×Q8C23×C7111yescharacteristic
1178C4×Q8C23×C7111yescharacteristic
1179C4×Q8C23×C7111yescharacteristic
1180C4×Q8C23×C7111yescharacteristic
1181C4×Q8C23×C7111yescharacteristic
1182C4×D4—21no—
1183C4×D4—21no—
1184C4×D4—21no—
1185C4×D4—21no—
1186C4×D4—21no—
1187C4×D4—21no—
1188C4×D4—21no—
1189C4×D4—21no—
1190C4×D4—21no—
1191C4×D4—21no—
1192C4×D4—21no—
1193C4×D4—21no—
1194C4×D4—21no—
1195C4×D4—21no—
1196C4×D4—21no—
1197C4×D4C23×C7111yescharacteristic
1198C4×D4C23×C7111yescharacteristic
1199C4×D4C23×C7111yescharacteristic
1200C4×D4C23×C7111yescharacteristic
1201C4×D4C23×C7111yescharacteristic
1202C4×D4C23×C7111yescharacteristic
1203C4×D4C23×C7111yescharacteristic
1204C4×D4C23×C7111yescharacteristic
1205C4×D4C23×C7111yescharacteristic
1206C4×D4C23×C7111yescharacteristic
1207C4×D4C23×C7111yescharacteristic
1208C4×D4C23×C7111yescharacteristic
1209#117—21no—
1210#117—21no—
1211#117—21no—
1212#117—21no—
1213#117—21no—
1214#117—21no—
1215#117—21no—
1216#117C23×C7111yescharacteristic
1217#117C23×C7111yescharacteristic
1218#117C23×C7111yescharacteristic
1219#117C23×C7111yescharacteristic
1220#117C23×C7111yescharacteristic
1221#117C23×C7111yescharacteristic
1222#117C23×C7111yescharacteristic
1223C2×C4⋊C4—21no—
1224C2×C4⋊C4—21no—
1225C2×C4⋊C4—21no—
1226C2×C4⋊C4C23×C7111yescharacteristic
1227C2×C4⋊C4C23×C7111yescharacteristic
1228C2×C4⋊C4C23×C7111yescharacteristic
1229C2×C4⋊C4C23×C7111yescharacteristic
1230C2×C42—21no—
1231C2×C42C23×C7111yescharacteristic
1232#107C23×C7111yescharacteristic
1233#107C23×C7111yescharacteristic
1234#107C23×C7111yescharacteristic
1235#107C23×C7111yescharacteristic
1236#107C23×C7111yescharacteristic
1237#107C23×C7111yescharacteristic
1238#107C23×C7111yescharacteristic
1239#107C23×C7111yescharacteristic
1240#107C23×C7111yescharacteristic
1241#107C23×C7111yescharacteristic
1242#107C23×C7111yescharacteristic
1243#107C23×C7111yescharacteristic
1244#106C23×C7111yescharacteristic
1245#106C23×C7111yescharacteristic
1246#106C23×C7111yescharacteristic
1247#106C23×C7111yescharacteristic
1248#106C23×C7111yescharacteristic
1249#106C23×C7111yescharacteristic
1250#106C23×C7111yescharacteristic
1251#106C23×C7111yescharacteristic
1252#106C23×C7111yescharacteristic
1253#106C23×C7111yescharacteristic
1254#106C23×C7111yescharacteristic
1255#106C23×C7111yescharacteristic
1256C4⋊C8C23×C7111yescharacteristic
1257C4⋊C8C23×C7111yescharacteristic
1258C4⋊C8C23×C7111yescharacteristic
1259C4⋊C8C23×C7111yescharacteristic
1260C4⋊C8C23×C7111yescharacteristic
1261C4⋊C8C23×C7111yescharacteristic
1262C4⋊C8C23×C7111yescharacteristic
1263C4⋊C8C23×C7111yescharacteristic
1264C4⋊C8C23×C7111yescharacteristic
1265C4⋊C8C23×C7111yescharacteristic
1266#103C23×C7111yescharacteristic
1267#103C23×C7111yescharacteristic
1268#103C23×C7111yescharacteristic
1269#103C23×C7111yescharacteristic
1270#103C23×C7111yescharacteristic
1271#103C23×C7111yescharacteristic
1272#103C23×C7111yescharacteristic
1273#103C23×C7111yescharacteristic
1274#103C23×C7111yescharacteristic
1275#103C23×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
1286#102C23×C7111yescharacteristic
1287#102C23×C7111yescharacteristic
1288#102C23×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
1298C22⋊C8C23×C7111yescharacteristic
1299C22⋊C8C23×C7111yescharacteristic
1300C22⋊C8C23×C7111yescharacteristic
1301C22⋊C8C23×C7111yescharacteristic
1302C22⋊C8C23×C7111yescharacteristic
1303C22⋊C8C23×C7111yescharacteristic
1304#97C23×C7111yescharacteristic
1305#97C23×C7111yescharacteristic
1306#97C23×C7111yescharacteristic
1307#97C23×C7111yescharacteristic
1308C4×C8C23×C7111yescharacteristic
1309C4×C8C23×C7111yescharacteristic
1310#41—22no—
1311#41—22no—
1312#41—22no—
1313#41—41no—
1314#41—41no—
1315#41—41no—
1316#41—82no—
1317#41—82no—
1318#41—82no—
1319C2×Q8—21no—
1320C2×Q8—21no—
1321C2×Q8—21no—
1322C2×Q8—21no—
1323C2×Q8—21no—
1324C2×Q8C2×D4×C7111yescharacteristic
1325C2×Q8C24×C7111yescharacteristic
1326C2×Q8C24×C7111yescharacteristic
1327C2×D4—21no—
1328C2×D4—21no—
1329C2×D4—21no—
1330C2×D4—21no—
1331C2×D4—21no—
1332C2×D4—21no—
1333C2×D4—21no—
1334C2×D4—21no—
1335C2×D4—21no—
1336C2×D4—21no—
1337C2×D4—21no—
1338C2×D4—21no—
1339C2×D4—21no—
1340C2×D4—21no—
1341C2×D4—21no—
1342C2×D4—21no—
1343C2×D4—21no—
1344C2×D4—21no—
1345C2×D4C2×D4×C7111yescharacteristic
1346C2×D4C2×D4×C7111yescharacteristic
1347C2×D4C2×D4×C7111yescharacteristic
1348C2×D4C24×C7111yescharacteristic
1349C2×D4C24×C7111yescharacteristic
1350C2×D4C24×C7111yescharacteristic
1351C2×D4C24×C7111yescharacteristic
1352C22×C4—21no—
1353C22×C4—21no—
1354C22×C4—21no—
1355C22×C4—21no—
1356C22×C4—21no—
1357C22×C4—21no—
1358C22×C4—21no—
1359C22×C4—21no—
1360C22×C4—21no—
1361C22×C4—21no—
1362C22×C4—21no—
1363C22×C4—21no—
1364C22×C4—21no—
1365C22×C4—21no—
1366C22×C4—21no—
1367C22×C4—21no—
1368C22×C4C2×D4×C7111yescharacteristic
1369C22×C4C2×D4×C7111yescharacteristic
1370C22×C4C24×C7111yescharacteristic
1371C22×C4C24×C7111yescharacteristic
1372C22×C4C24×C7111yescharacteristic
1373Q16—22no—
1374SD16—22no—
1375SD16—41no—
1376SD16—41no—
1377SD16—41no—
1378D8—41no—
1379D8—41no—
1380D8—41no—
1381M16—41no—
1382M16—41no—
1383C2×C8—41no—
1384C2×C8—41no—
1385C2×C8—41no—
1386C2×C8—41no—
1387C2×C8C24×C7111yescharacteristic
1388C2×C8C24×C7111yescharacteristic
1389C2×C8C24×C7111yescharacteristic
1390C2×C8C24×C7111yescharacteristic
1391C2×C8C24×C7111yescharacteristic
1392C2×C8C24×C7111yescharacteristic
1393C2×C8C24×C7111yescharacteristic
1394C2×C8C24×C7111yescharacteristic
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⋊C4—21no—
1418C4⋊C4—21no—
1419C4⋊C4—21no—
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⋊C4C2×D4×C7111yescharacteristic
1429C4⋊C4C2×D4×C7111yescharacteristic
1430C4⋊C4C2×D4×C7111yescharacteristic
1431C4⋊C4C2×D4×C7111yescharacteristic
1432C4⋊C4C2×D4×C7111yescharacteristic
1433C4⋊C4C2×D4×C7111yescharacteristic
1434C4⋊C4C2×D4×C7111yescharacteristic
1435C4⋊C4C2×D4×C7111yescharacteristic
1436C4⋊C4C2×D4×C7111yescharacteristic
1437C4⋊C4C2×D4×C7111yescharacteristic
1438C4⋊C4C24×C7111yescharacteristic
1439C4⋊C4C24×C7111yescharacteristic
1440C4⋊C4C24×C7111yescharacteristic
1441C4⋊C4C24×C7111yescharacteristic
1442C4⋊C4C24×C7111yescharacteristic
1443C4⋊C4C24×C7111yescharacteristic
1444C4⋊C4C24×C7111yescharacteristic
1445C4⋊C4C24×C7111yescharacteristic
1446C4⋊C4C24×C7111yescharacteristic
1447C4⋊C4C24×C7111yescharacteristic
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⋊C4—21no—
1476C22⋊C4C2×D4×C7111yescharacteristic
1477C22⋊C4C2×D4×C7111yescharacteristic
1478C22⋊C4C2×D4×C7111yescharacteristic
1479C22⋊C4C2×D4×C7111yescharacteristic
1480C22⋊C4C2×D4×C7111yescharacteristic
1481C22⋊C4C2×D4×C7111yescharacteristic
1482C22⋊C4C2×D4×C7111yescharacteristic
1483C22⋊C4C2×D4×C7111yescharacteristic
1484C22⋊C4C2×D4×C7111yescharacteristic
1485C22⋊C4C2×D4×C7111yescharacteristic
1486C42—21no—
1487C42—21no—
1488C42—21no—
1489C42—21no—
1490C42—21no—
1491C42—21no—
1492C42—21no—
1493C42—21no—
1494C42—21no—
1495C42—21no—
1496C42—21no—
1497C42—21no—
1498C42C2×D4×C7111yescharacteristic
1499C42C2×D4×C7111yescharacteristic
1500C42C24×C7111yescharacteristic
1501C42C24×C7111yescharacteristic
1502C42C24×C7111yescharacteristic
1503C42C24×C7111yescharacteristic
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23C22×D4×C7111yescharacteristic
1509C23C22×D4×C7111yescharacteristic
1510C23C22×D4×C7111yescharacteristic
1511Q8—21no—
1512Q8—21no—
1513Q8—21no—
1514Q8—41no—
1515Q8—42no—
1516Q8—81no—
1517Q8—81no—
1518Q8—81no—
1519Q8—81no—
1520Q82−1+4×C7112yes—
1521D4—21no—
1522D4—21no—
1523D4—21no—
1524D4—21no—
1525D4—21no—
1526D4—21no—
1527D4—21no—
1528D4—21no—
1529D4—41no—
1530D4—41no—
1531D4—41no—
1532D4—42no—
1533D4—42no—
1534D4—42no—
1535D4—42no—
1536D4—81no—
1537D4—81no—
1538D4—81no—
1539D4—81no—
1540D4—81no—
1541D4—81no—
1542D4—81no—
1543D4—81no—
1544D4—81no—
1545D4—81no—
1546D4—81no—
1547D4—81no—
1548D4—81no—
1549D4—81no—
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—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—21no—
1564C2×C4—21no—
1565C2×C4—21no—
1566C2×C4—21no—
1567C2×C4—21no—
1568C2×C4—41no—
1569C2×C4—41no—
1570C2×C4—42no—
1571C2×C4—42no—
1572C2×C4—42no—
1573C2×C4—42no—
1574C2×C4—81no—
1575C2×C4—81no—
1576C2×C4—81no—
1577C2×C4—81no—
1578C2×C4—81no—
1579C2×C4—81no—
1580C2×C4—81no—
1581C2×C4—81no—
1582C2×C4—81no—
1583C2×C4—81no—
1584C2×C4—81no—
1585C2×C4—81no—
1586C2×C4C22×D4×C7111yescharacteristic
1587C2×C4C22×D4×C7111yescharacteristic
1588C2×C4C22×D4×C7111yescharacteristic
1589C2×C4C22×D4×C7111yescharacteristic
1590C2×C4C22×D4×C7111yescharacteristic
1591C2×C4C22×D4×C7111yescharacteristic
1592C2×C4C22×D4×C7111yescharacteristic
1593C2×C4C22×D4×C7111yescharacteristic
1594C2×C4C22×D4×C7111yescharacteristic
1595C2×C4C22×D4×C7111yescharacteristic
1596C2×C4C22×D4×C7111yescharacteristic
1597C2×C4C25×C7111yescharacteristic
1598C8—21no—
1599C8—21no—
1600C8—21no—
1601C8—21no—
1602C8—21no—
1603C8—21no—
1604C8—21no—
1605C8—21no—
1606C22—21no—
1607C22—21no—
1608C22—21no—
1609C22—21no—
1610C22—21no—
1611C22—21no—
1612C22—21no—
1613C22—21no—
1614C22—21no—
1615C22—41no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—41no—
1627C22C23×D4×C7111yescharacteristic
1628C4—21no—
1629C4—21no—
1630C4—21no—
1631C4—21no—
1632C4—21no—
1633C4—21no—
1634C4—21no—
1635C4—21no—
1636C4—21no—
1637C4—21no—
1638C4—21no—
1639C4—22no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4C2×2−1+4×C7111yescharacteristic
1652C4#585×C7111yescharacteristic
1653C2—41no—
1654C2—41no—
1655C2—41no—
1656C2—81no—
1657C2—81no—
1658C2—81no—
1659C2—81no—
1660C2C71×#348911yescharacteristic
1661C2C71×#358411yescharacteristic
1662C2C71×#358511yescharacteristic
subgroupG/H
center, socleC22×C71C23×D4
commutator, Frattini, cosocleC2×C4C25×C71
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C71 ◁ #529×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C71×#3565C2semidirect
2. C71×#3517C2semidirect
3. C71×#3390C2semidirect
4. C71×#3388C2semidirect
5. C71×#3368C2semidirect
6. C71×#3366C2semidirect
7. C71×#3350C2semidirect
8. C71×#3347C2semidirect
9. C71×#3345C2semidirect
10. C71×#3343C2semidirect
11. C71×#3339C2semidirect
12. C71×#3337C2semidirect
13. C71×#3317C2semidirect
14. C71×#3317C2semidirect
15. C71×#3309C2semidirect
16. C71×#3309C2semidirect
17. C71×#3305C2semidirect
18. C71×#3304C2semidirect
19. C71×#3257C2semidirect
20. C71×#3257C2semidirect
21. C71×#3247C2semidirect
22. C71×#3241C2semidirect
23. C71×#3241C2semidirect
24. C71×#3235C2semidirect
25. C71×#3125C2semidirect
26. C71×#3124C2semidirect
27. C71×#3111C2semidirect
28. C71×#3084C2semidirect
29. C71×#3083C2semidirect
30. C71×#3076C2semidirect
31. C71×#2992C2semidirect
821. #62162C71direct (N × H)
832. #3565C2×C71semidirect
833. #3517C2×C71semidirect
834. #3390C2×C71semidirect
835. #3388C2×C71semidirect
836. #3368C2×C71semidirect
837. #3366C2×C71semidirect
838. #3350C2×C71semidirect
839. #3347C2×C71semidirect
840. #3345C2×C71semidirect
841. #3343C2×C71semidirect
842. #3339C2×C71semidirect
843. #3337C2×C71semidirect
844. #3317C2×C71semidirect
845. #3317C2×C71semidirect
846. #3309C2×C71semidirect
847. #3309C2×C71semidirect
848. #3305C2×C71semidirect
849. #3304C2×C71semidirect
850. #3257C2×C71semidirect
851. #3257C2×C71semidirect
852. #3247C2×C71semidirect
853. #3241C2×C71semidirect
854. #3241C2×C71semidirect
855. #3235C2×C71semidirect
856. #3125C2×C71semidirect
857. #3124C2×C71semidirect
858. #3111C2×C71semidirect
859. #3084C2×C71semidirect
860. #3083C2×C71semidirect
861. #3076C2×C71semidirect
862. #2992C2×C71semidirect
863. C71#62162direct (N × H)

Maximal subgroups

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

subgroupindex
C71×#35652
C71×#35172
C71×#33902
C71×#33882
C71×#33682
C71×#33662
C71×#33502
C71×#33472
C71×#33452
C71×#33432
C71×#33392
C71×#33372
C71×#33172
C71×#33092
C71×#33052
C71×#33042
C71×#32572
C71×#32472
C71×#32412
C71×#32352
C71×#31252
C71×#31242
C71×#31112
C71×#30842
C71×#30832
C71×#30762
C71×#29922
#6216271