Finite Group Databasebeta

← #32861981

Subgroups — #32861981

Order 18176.

1878 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601725C211yesmaximal, characteristic
2#22597325C214yesmaximal, complemented
3#22597321C214yesmaximal, complemented
4#22597315C214yesmaximal, complemented
5#22597311C214yesmaximal, complemented
6#22597278C211yesmaximal, characteristic, complemented
7#22597272C211yesmaximal, characteristic, complemented
8#22597056C211yesmaximal, characteristic, complemented
9#22597050C211yesmaximal, characteristic, complemented
10#22597045C211yesmaximal, characteristic, complemented
11#22597041C211yesmaximal, characteristic, complemented
12#22597036C211yesmaximal, characteristic, complemented
13#22597032C211yesmaximal, characteristic, complemented
14#22596992C211yesmaximal, characteristic, complemented
15#22596991C211yesmaximal, characteristic, complemented
16#22596976C211yesmaximal, characteristic, complemented
17C4×#14556134C211yesmaximal, characteristic, complemented
18C2×#17985953C211yesmaximal, characteristic, complemented
19C4×#131×C71C211yesmaximal, characteristic, complemented
20C2×#14556134C2211yescharacteristic
21C2×#14556134C2211yescharacteristic
22C22×#11765848C2211yescharacteristic
23C22×C8×D71C2211yescharacteristic
24#17986621C412yes—
25#17986614C412yes—
26#17986607C412yes—
27#17986600C412yes—
28#17986591C414yes—
29#17986582C414yes—
30#17986552C2211yescharacteristic
31#17986545C2211yescharacteristic
32#17986533C2214yes—
33#17986527C2214yes—
34#17986511C2211yescharacteristic
35#17986506C2211yescharacteristic
36C4×#11765865C2211yescharacteristic
37C2×#14556085C2211yescharacteristic
38#17986129C2214yescomplemented
39#17986127C2214yescomplemented
40#17986127C2214yescomplemented
41C8×Dic142C2214yescomplemented
42#17986078C2214yes—
43#17986075C2214yes—
44#17986075C2214yescomplemented
45#17986072C2214yes—
46#17986072C2214yes—
47#17986070C2214yes—
48#17986070C2214yescomplemented
49#17986068C2214yes—
50#17986068C2214yescomplemented
51C8×D284C2214yes—
52C8×C22⋊D71C2214yes—
53C8×C22⋊D71C2214yescomplemented
54#17986061C2214yes—
55#17986060C2214yescomplemented
56#17986058C2214yes—
57#17986058C2214yescomplemented
58#17986056C2214yescomplemented
59#17986054C2214yescomplemented
60#17986027C2211yescharacteristic
61#17986027C2211yescharacteristic
62#17986026C2211yescharacteristic
63#17986026C2211yescharacteristic
64#17986022C2211yescharacteristic
65#17986022C2211yescharacteristic
66#17985967C2211yescharacteristic
67#17985967C2211yescharacteristic
68#17985966C2211yescharacteristic
69#17985966C2211yescharacteristic
70#17985962C2211yescharacteristic
71#17985962C2211yescharacteristic
72#17985954C2211yescharacteristic
73#17985954C2211yescharacteristic
74#17985953C2212yes—
75#17985953C2212yes—
76#17985953C2212yes—
77#17985953C2212yes—
78#17985953C2212yescomplemented
79#17985953C2212yescomplemented
80C4×#11765849C2211yescharacteristic
81C4×#11765848C2212yescomplemented
82C2×#14556039C2211yescharacteristic
83C2×#14556038C2211yescharacteristic
84C2×C8×Dic71C2211yescharacteristic
85C4×C8×D71C2212yescomplemented
86C2×#131×C71C2211yescharacteristic
87C2×#131×C71C2211yescharacteristic
88C4×#41×C71C2211yescharacteristic
89#405×C71C2211yescharacteristic
90#405×C71C2211yescharacteristic
91#405×C71C2212yescomplemented
92#405×C71C2212yescomplemented
93C4×M16×C71C2211yescharacteristic
94C4×M16×C71C2212yescomplemented
95C2×C4×C8×C71C2211yescharacteristic
96C2×C4×C8×C71C2212yescomplemented
97C2×#11765865C2311yescharacteristic
98C22×C4×D71C2311yescharacteristic
99#14556134—24no—
100#14556134—24no—
101C2×#11765849C2311yescharacteristic
102C2×#11765849C2311yescharacteristic
103C2×#11765848—24no—
104C2×#11765848C2312yes—
105C2×#11765848C2312yes—
106C2×#11765848C2312yes—
107C2×#11765848C2312yes—
108C22×C71⋊C8C2311yescharacteristic
109C22×C71⋊C8C2311yescharacteristic
110C2×C8×D71—24no—
111C2×C8×D71C2312yes—
112C2×C8×D71C2312yes—
113C2×C8×D71C2312yes—
114C2×C8×D71C2312yes—
115#14556127C2×C412yes—
116#14556126C2×C411yescharacteristic
117#14556124C2×C411yescharacteristic
118#14556123C2×C414yes—
119#14556122C2×C414yes—
120#14556122C2×C414yes—
121#14556121C2×C414yes—
122#14556120C2×C414yes—
123#14556119C2×C412yes—
124#14556118C2×C414yes—
125#14556117C2×C411yescharacteristic
126#14556116C2×C414yes—
127#14556115C2×C411yescharacteristic
128#14556114C2×C414yes—
129#14556113C2×C414yes—
130#14556112C2×C412yes—
131#14556111C2×C414yes—
132#14556111C2×C414yes—
133#14556110C2×C414yes—
134#14556109C2×C412yes—
135#14556108C2×C412yes—
136#14556107C2×C414yes—
137#14556106C2×C414yes—
138#14556105C2×C414yes—
139#14556104C2×C412yes—
140#14556103C2×C412yes—
141#14556102C2×C414yes—
142#14556101C2×C414yes—
143#14556100C2×C414yes—
144#14556099C2×C412yes—
145#14556098C2×C412yes—
146#14556096C2×C412yes—
147C4×Dic142C2×C412yes—
148C4×Dic142C2314yes—
149C4×D284C2×C412yes—
150C4×D284C2314yes—
151C4×C22⋊D71C2×C414yes—
152C4×C22⋊D71C2314yes—
153C4×C22⋊D71C2314yes—
154#14556087C2311yescharacteristic
155#14556085C2×C412yes—
156#14556085C2×C412yes—
157#14556085C2312yes—
158#14556085C2312yes—
159#14556085C2312yes—
160C2×Dic71⋊C4C2×C412yes—
161C2×(C2×D71)⋊C4C2×C412yes—
162C2×C4×Dic71C2311yescharacteristic
163C42×D71C2312yes—
164C4⋊(C71⋊C8)C2314yes—
165C4⋊(C71⋊C8)C2314yes—
166Dic71⋊C8C2314yes—
167Dic71⋊C8C2314yes—
168Dic71⋊C8C2314yes—
169Dic71⋊C8C2314yes—
170C22⋊(C71⋊C8)C2314yes—
171C22⋊(C71⋊C8)C2314yes—
172(C2×D71)⋊C8C2314yes—
173(C2×D71)⋊C8C2314yes—
174(C2×D71)⋊C8C2314yes—
175(C2×D71)⋊C8C2314yes—
176#14556039C2312yes—
177#14556039C2312yes—
178#14556039C2312yes—
179#14556038C2312yes—
180#14556038C2312yes—
181#14556038C2312yes—
182#14556038C2312yes—
183C4×C71⋊C8C2312yes—
184C8×Dic71C2312yes—
185C8×Dic71C2312yes—
186C8×Dic71C2312yes—
187C8×Dic71C2312yes—
188C2×#41×C71C2311yescharacteristic
189#131×C71—24no—
190#131×C71—24no—
191C2×M16×C71C2311yescharacteristic
192C2×M16×C71C2311yescharacteristic
193C2×M16×C71C2312yes—
194C2×M16×C71C2312yes—
195C22×C8×C71C2312yes—
196C22×C8×C71C2312yes—
197C22×C8×C71C2311yescharacteristic
198C22×C8×C71C2311yescharacteristic
199C4×Q8×C71C2×C412yes—
200C4×D4×C71C2×C414yes—
201C4×D4×C71C2×C412yes—
202#117×C71C2311yescharacteristic
203#117×C71C2312yes—
204C2×C42×C71C2312yes—
205C2×C42×C71C2311yescharacteristic
206#97×C71C2312yes—
207#97×C71C2312yes—
208#97×C71C2312yes—
209C4×C8×C71C2312yes—
210C4×C8×C71C2312yes—
211C4×C8×C71C2311yescharacteristic
212C4×C8×C71C2311yescharacteristic
213C4×C8×C71C2312yes—
214C4×C8×C71C2311yescharacteristic
215C4×C8×C71C2311yescharacteristic
216C23×D71C22×C411yescharacteristic
217#11765865—22no—
218#11765865—22no—
219C2×Dic142C22×C411yescharacteristic
220C2×Dic142C22×C414yes—
221C2×D284C22×C411yescharacteristic
222C2×D284C22×C414yes—
223C2×C22⋊D71C22×C412yes—
224C2×C22⋊D71C22×C414yes—
225C2×C22⋊D71C22×C414yes—
226C22×Dic71C22×C411yescharacteristic
227C22×Dic71C22×C412yes—
228C2×C4×D71—22no—
229C2×C4×D71—22no—
230C2×C4×D71C22×C412yes—
231C2×C4×D71C22×C414yes—
232C2×C4×D71C2412yes—
233C2×C4×D71C2412yes—
234#11765849—22no—
235#11765849—22no—
236#11765848—24no—
237#11765848—24no—
238#11765848—24no—
239#11765848—24no—
240C2×C71⋊C8—22no—
241C2×C71⋊C8—22no—
242C2×C71⋊C8C2412yes—
243C2×C71⋊C8C2412yes—
244C2×C71⋊C8C2412yes—
245C2×C71⋊C8C2412yes—
246C8×D71—24no—
247C8×D71—24no—
248C8×D71—24no—
249C8×D71—24no—
250C4⋊Dic71C22×C412yes—
251C4⋊Dic71C22×C414yes—
252C4⋊Dic71C22×C414yes—
253Dic71⋊C4C22×C412yes—
254Dic71⋊C4C22×C412yes—
255Dic71⋊C4C22×C412yes—
256Dic71⋊C4C22×C412yes—
257Dic71⋊C4C22×C414yes—
258Dic71⋊C4C22×C414yes—
259Dic71⋊C4C22×C414yes—
260Dic71⋊C4C22×C414yes—
261Dic71⋊C4C22×C414yes—
262C22⋊Dic71C22×C412yes—
263C22⋊Dic71C22×C414yes—
264C22⋊Dic71C22×C414yes—
265(C2×D71)⋊C4C22×C412yes—
266(C2×D71)⋊C4C22×C412yes—
267(C2×D71)⋊C4C22×C412yes—
268(C2×D71)⋊C4C22×C412yes—
269(C2×D71)⋊C4C22×C414yes—
270(C2×D71)⋊C4C22×C414yes—
271(C2×D71)⋊C4C22×C414yes—
272(C2×D71)⋊C4C22×C414yes—
273(C2×D71)⋊C4C22×C414yes—
274C4×Dic71C22×C414yes—
275C4×Dic71C22×C411yescharacteristic
276C4×Dic71C22×C411yescharacteristic
277C4×Dic71C2412yes—
278C4×Dic71C2412yes—
279#41×C71—22no—
280#41×C71—22no—
281C2×Q8×C71C22×C411yescharacteristic
282C2×D4×C71C22×C412yes—
283C2×D4×C71C22×C411yescharacteristic
284C22×C4×C71C22×C412yes—
285C22×C4×C71C22×C414yes—
286C22×C4×C71C2412yes—
287C22×C4×C71C2411yescharacteristic
288M16×C71—22no—
289M16×C71—22no—
290M16×C71—24no—
291M16×C71—24no—
292C2×C8×C71—24no—
293C2×C8×C71—24no—
294C2×C8×C71#4114yes—
295C2×C8×C71#4114yes—
296C2×C8×C71C2412yes—
297C2×C8×C71C2412yes—
298C2×C8×C71C2411yescharacteristic
299C2×C8×C71C2411yescharacteristic
300C2×C8×C71C2411yescharacteristic
301C2×C8×C71C2411yescharacteristic
302C4⋊C4×C71C22×C412yes—
303C4⋊C4×C71C22×C414yes—
304C22⋊C4×C71C22×C412yes—
305C22⋊C4×C71C22×C414yes—
306C42×C71C22×C412yes—
307C42×C71C22×C414yes—
308C42×C71C2411yescharacteristic
309C42×C71C2411yescharacteristic
310C42×C71C2412yes—
311C23×C71C23×C412yes—
312C23×C71C23×C411yescharacteristic
313C22×D71—22no—
314C22×D71—42no—
315C22×D71C23×C412yes—
316C22×D71C23×C412yes—
317Q8×C71—22no—
318D4×C71—24no—
319D4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—44no—
323C2×C4×C71—42no—
324C2×C4×C71C23×C412yes—
325C2×C4×C71C23×C412yes—
326C2×C4×C71C23×C412yes—
327C2×C4×C71C23×C414yes—
328C2×C4×C71C23×C411yescharacteristic
329C2×C4×C71C2×#4112yes—
330C2×C4×C71C2×#4112yes—
331C2×C4×C71C2511yescharacteristic
332C22⋊D71—24no—
333C22⋊D71—44no—
334C22⋊D71—44no—
335C2×Dic71—22no—
336C2×Dic71—42no—
337C2×Dic71C23×C412yes—
338C2×Dic71C23×C412yes—
339C2×Dic71C23×C414yes—
340C2×Dic71C23×C412yes—
341C2×Dic71C23×C412yes—
342D284—22no—
343D284—44no—
344C4×D71—24no—
345C4×D71—22no—
346C4×D71—22no—
347C4×D71—22no—
348C4×D71—22no—
349C4×D71—44no—
350Dic142—22no—
351Dic142—44no—
352C8×C71—22no—
353C8×C71—22no—
354C8×C71C2×#4112yes—
355C8×C71C2×#4112yes—
356C8×C71C2×#4112yes—
357C8×C71C2×#4112yes—
358C71⋊C8—22no—
359C71⋊C8—22no—
360C71⋊C8—22no—
361C71⋊C8—22no—
362C22×C71—22no—
363C22×C71—22no—
364C22×C71—24no—
365C22×C71C4×#4112yes—
366C22×C71C24×C411yescharacteristic
367C2×D71—22no—
368C2×D71—22no—
369C2×D71—24no—
370C2×D71—22no—
371C2×D71—22no—
372C2×D71—44no—
373C4×C71—22no—
374C4×C71—24no—
375C4×C71—22no—
376C4×C71—22no—
377C4×C71C4×#4112yes—
378C4×C71C22×#4111yescharacteristic
379C4×C71C22×#4111yescharacteristic
380Dic71—22no—
381Dic71—22no—
382Dic71—22no—
383Dic71—24no—
384Dic71—22no—
385#60206—711nomaximal, Sylow
386C2×C71—22no—
387C2×C71—42no—
388C2×C71C2×C4×#4111yescharacteristic
389C2×C71#357312yes—
390D71—42no—
391D71—42no—
392#3455—711no—
393#2967—714no—
394#2967—714no—
395#2966—714no—
396#2966—714no—
397#2961—711no—
398#2960—711no—
399#2932—711no—
400#2931—711no—
401#2930—711no—
402#2930—711no—
403#2929—711no—
404#2929—711no—
405#2923—711no—
406#2923—711no—
407#2921—711no—
408C4×#131—711no—
409C4×#131D7111yescharacteristic, complemented
410C2×#405—711no—
411C71#6020611yescharacteristic, complemented, Sylow
412C2×#131—711no—
413C2×#131—711no—
414C2×#131C2×D7111yescharacteristic
415C2×#131C2×D7111yescharacteristic
416C22×M16—711no—
417C23×C8—711no—
418#542—712no—
419#542—712no—
420#541—712no—
421#540—712no—
422#539—714no—
423#538—714no—
424#533—711no—
425#532—711no—
426#529—714no—
427#529—714no—
428#525—711no—
429#525—711no—
430C4×#41—711no—
431C4×#41C2×D7111yescharacteristic
432C2×#117—711no—
433#446—714no—
434#446—714no—
435#446—714no—
436C8×Q8—714no—
437#436—714no—
438#436—714no—
439#436—714no—
440#435—714no—
441#435—714no—
442#435—714no—
443#435—714no—
444#435—714no—
445#435—714no—
446C8×D4—714no—
447C8×D4—714no—
448C8×D4—714no—
449#433—714no—
450#433—714no—
451#433—714no—
452#433—714no—
453#432—714no—
454#432—714no—
455#424—711no—
456#424—711no—
457#424—711no—
458#424—711no—
459#423—711no—
460#423—711no—
461#408—711no—
462#408—711no—
463#408—711no—
464#408—711no—
465#407—711no—
466#407—711no—
467#405—711no—
468#405—711no—
469#405—712no—
470#405—712no—
471#405—712no—
472#405—712no—
473#405—712no—
474#405—712no—
475#405C2×D7111yescharacteristic
476#405C2×D7111yescharacteristic
477#405C2×D7112yescomplemented
478#405C2×D7112yescomplemented
479C4×M16—711no—
480C4×M16—712no—
481C4×M16C2×D7111yescharacteristic
482C4×M16C2×D7112yescomplemented
483C2×#97—711no—
484C2×#97—711no—
485C2×C4×C8—711no—
486C2×C4×C8—712no—
487C2×C4×C8C2×D7111yescharacteristic
488C2×C4×C8C2×D7112yescomplemented
489C2×#41—711no—
490C2×#41C22×D7111yescharacteristic
491C23×C4—711no—
492#131—24no—
493#131—24no—
494#131—1424no—
495#131—1424no—
496C2×M16—711no—
497C2×M16—711no—
498C2×M16—712no—
499C2×M16—712no—
500C2×M16—712no—
501C2×M16—712no—
502C2×M16—1424no—
503C2×M16C22×D7111yescharacteristic
504C2×M16C22×D7111yescharacteristic
505C2×M16C22×D7112yes—
506C2×M16C22×D7112yes—
507C22×C8—711no—
508C22×C8—711no—
509C22×C8—712no—
510C22×C8—712no—
511C22×C8—712no—
512C22×C8—712no—
513C22×C8—1424no—
514C22×C8C22×D7112yes—
515C22×C8C22×D7112yes—
516C22×C8C22×D7111yescharacteristic
517C22×C8C22×D7111yescharacteristic
518C4⋊Q8—711no—
519C4⋊Q8—712no—
520#127—711no—
521#126—714no—
522#126—714no—
523#126—714no—
524#126—714no—
525#125—714no—
526#125—712no—
527#125—714no—
528#124—711no—
529#124—711no—
530#124—714no—
531#124—714no—
532#123—712no—
533#123—714no—
534#123—714no—
535#123—714no—
536#123—712no—
537#123—714no—
538C22⋊Q8—712no—
539C22⋊Q8—714no—
540C22⋊Q8—712no—
541C22⋊Q8—714no—
542C22⋊Q8—714no—
543#121—712no—
544#121—714no—
545#121—714no—
546#121—712no—
547#121—714no—
548#120—712no—
549#120—712no—
550C4×Q8—712no—
551C4×Q8—714no—
552C4×Q8C4×D7112yes—
553C4×D4—714no—
554C4×D4—714no—
555C4×D4—714no—
556C4×D4—712no—
557C4×D4—714no—
558C4×D4C4×D7114yes—
559C4×D4C4×D7112yes—
560#117—711no—
561#117—712no—
562#117—712no—
563#117—712no—
564#117—712no—
565#117—712no—
566#117C22×D7111yescharacteristic
567#117C22×D7112yes—
568C2×C4⋊C4—712no—
569C2×C22⋊C4—712no—
570C2×C42—711no—
571C2×C42—712no—
572C2×C42C22×D7111yescharacteristic
573C2×C42C22×D7112yes—
574C4⋊C8—714no—
575C4⋊C8—714no—
576C4⋊C8—714no—
577C4⋊C8—714no—
578C4⋊C8—714no—
579C4⋊C8—714no—
580C22⋊C8—714no—
581C22⋊C8—714no—
582C22⋊C8—714no—
583C22⋊C8—714no—
584C22⋊C8—714no—
585C22⋊C8—714no—
586#97—712no—
587#97—712no—
588#97—712no—
589#97—712no—
590#97—712no—
591#97—712no—
592#97—712no—
593#97C22×D7112yes—
594#97C22×D7112yes—
595#97C22×D7112yes—
596C4×C8—712no—
597C4×C8—712no—
598C4×C8—712no—
599C4×C8—712no—
600C4×C8—712no—
601C4×C8C22×D7111yescharacteristic
602C4×C8C22×D7111yescharacteristic
603C4×C8C22×D7112yes—
604C4×C8C22×D7112yes—
605C4×C8C22×D7111yescharacteristic
606C4×C8C22×D7111yescharacteristic
607C4×C8C22×D7112yes—
608C24—711no—
609#41—22no—
610#41—22no—
611#41—1422no—
612#41—1422no—
613C2×Q8—714no—
614C2×Q8—711no—
615C2×Q8C2×C4×D7111yescharacteristic
616C2×D4—714no—
617C2×D4—714no—
618C2×D4—712no—
619C2×D4—714no—
620C2×D4—711no—
621C2×D4C2×C4×D7112yes—
622C2×D4C2×C4×D7111yescharacteristic
623C22×C4—712no—
624C22×C4—714no—
625C22×C4—711no—
626C22×C4—712no—
627C22×C4—712no—
628C22×C4—712no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4C2×C4×D7112yes—
632C22×C4C2×C4×D7114yes—
633C22×C4C23×D7112yes—
634C22×C4C23×D7111yescharacteristic
635M16—22no—
636M16—22no—
637M16—24no—
638M16—24no—
639M16—1422no—
640M16—1422no—
641M16—1424no—
642M16—1424no—
643M16—1424no—
644M16—1424no—
645C2×C8—24no—
646C2×C8—24no—
647C2×C8—712no—
648C2×C8—712no—
649C2×C8—712no—
650C2×C8—712no—
651C2×C8—1422no—
652C2×C8—1422no—
653C2×C8—1424no—
654C2×C8—1424no—
655C2×C8—1424no—
656C2×C8—1424no—
657C2×C8#1176586514yes—
658C2×C8#1176586514yes—
659C2×C8C23×D7112yes—
660C2×C8C23×D7112yes—
661C2×C8C23×D7111yescharacteristic
662C2×C8C23×D7111yescharacteristic
663C2×C8C23×D7111yescharacteristic
664C2×C8C23×D7111yescharacteristic
665C4⋊C4—712no—
666C4⋊C4—712no—
667C4⋊C4—712no—
668C4⋊C4—712no—
669C4⋊C4—714no—
670C4⋊C4—714no—
671C4⋊C4—714no—
672C4⋊C4—714no—
673C4⋊C4—714no—
674C4⋊C4—712no—
675C4⋊C4—714no—
676C4⋊C4—714no—
677C4⋊C4C2×C4×D7112yes—
678C4⋊C4C2×C4×D7114yes—
679C22⋊C4—712no—
680C22⋊C4—714no—
681C22⋊C4—714no—
682C22⋊C4—712no—
683C22⋊C4—712no—
684C22⋊C4—712no—
685C22⋊C4—712no—
686C22⋊C4—714no—
687C22⋊C4—714no—
688C22⋊C4—714no—
689C22⋊C4—714no—
690C22⋊C4—714no—
691C22⋊C4C2×C4×D7112yes—
692C22⋊C4C2×C4×D7114yes—
693C42—711no—
694C42—711no—
695C42—714no—
696C42—712no—
697C42—712no—
698C42C2×C4×D7112yes—
699C42C2×C4×D7114yes—
700C42C23×D7111yescharacteristic
701C42C23×D7111yescharacteristic
702C42C23×D7112yes—
703C23—2842no—
704C23—712no—
705C23—712no—
706C23—1422no—
707C23C22×C4×D7112yes—
708C23C22×C4×D7111yescharacteristic
709Q8—22no—
710Q8—2844no—
711Q8—1422no—
712D4—24no—
713D4—22no—
714D4—2844no—
715D4—2844no—
716D4—2844no—
717D4—1424no—
718D4—1422no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—42no—
722C2×C4—44no—
723C2×C4—2844no—
724C2×C4—2842no—
725C2×C4—712no—
726C2×C4—714no—
727C2×C4—712no—
728C2×C4—712no—
729C2×C4—712no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1424no—
736C2×C4C22×C4×D7112yes—
737C2×C4C22×C4×D7112yes—
738C2×C4C22×C4×D7112yes—
739C2×C4C22×C4×D7114yes—
740C2×C4C22×C4×D7111yescharacteristic
741C2×C4C2×#1176586512yes—
742C2×C4C2×#1176586512yes—
743C2×C4C24×D7111yescharacteristic
744C8—22no—
745C8—22no—
746C8—1422no—
747C8—1422no—
748C8—1422no—
749C8—1422no—
750C8C2×#1176586512yes—
751C8C2×#1176586512yes—
752C8C2×#1176586512yes—
753C8C2×#1176586512yes—
754C22—22no—
755C22—24no—
756C22—22no—
757C22—2844no—
758C22—1424no—
759C22—1422no—
760C22—1422no—
761C22—1422no—
762C22—1422no—
763C22C4×#1176586512yes—
764C22C23×C4×D7111yescharacteristic
765C4—22no—
766C4—22no—
767C4—24no—
768C4—22no—
769C4—1422no—
770C4—1424no—
771C4—1422no—
772C4—1422no—
773C4—1422no—
774C4C4×#1176586512yes—
775C4C22×#1176586511yescharacteristic
776C4C22×#1176586511yescharacteristic
777C2—22no—
778C2—42no—
779C2—2842no—
780C2—2842no—
781C2C2×C4×#1176586511yescharacteristic
782C2#2260305112yes—
subgroupG/H
centerC2×C8C23×D71
commutator, socleC22×C71C24×C4
FrattiniC2×C4C24×D71
FittingC4×#131×C71C2
prime radical#22601725C2
cosocleC2×C4×C71C25
hypercenterC4×#131D71
hypocenterC71#60206
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C8 ◁ C4×#131

Complements

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

NH ≅ G/Ntype
2. #22597325C2semidirect
3. #22597321C2semidirect
4. #22597315C2semidirect
5. #22597311C2semidirect
6. #22597278C2semidirect
7. #22597272C2semidirect
8. #22597056C2semidirect
9. #22597050C2semidirect
10. #22597045C2semidirect
11. #22597041C2semidirect
12. #22597036C2semidirect
13. #22597032C2semidirect
14. #22596992C2semidirect
15. #22596991C2semidirect
16. #22596976C2semidirect
17. C4×#14556134C2semidirect
18. C2×#17985953C2semidirect
19. C4×#131×C71C2semidirect
38. #17986129C22semidirect
39. #17986127C22semidirect
40. #17986127C22semidirect
41. C8×Dic142C22semidirect
44. #17986075C22semidirect
48. #17986070C22semidirect
50. #17986068C22semidirect
53. C8×C22⋊D71C22semidirect
55. #17986060C22semidirect
57. #17986058C22semidirect
58. #17986056C22semidirect
59. #17986054C22semidirect
78. #17985953C22semidirect
79. #17985953C22semidirect
81. C4×#11765848C22semidirect
85. C4×C8×D71C22semidirect
91. #405×C71C22semidirect
92. #405×C71C22semidirect
94. C4×M16×C71C22semidirect
96. C2×C4×C8×C71C22semidirect
409. C4×#131D71semidirect
411. C71#60206semidirect
477. #405C2×D71semidirect
478. #405C2×D71semidirect
482. C4×M16C2×D71semidirect
488. C2×C4×C8C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226017252
#225973252
#225973212
#225973152
#225973112
#225972782
#225972722
#225970562
#225970502
#225970452
#225970412
#225970362
#225970322
#225969922
#225969912
#225969762
C4×#145561342
C2×#179859532
C4×#131×C712
#6020671