Finite Group Databasebeta

← #32861990

Subgroups — #32861990

Order 18176.

1962 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601632C211yesmaximal, characteristic
2#22597350C214yesmaximal, complemented
3#22597348C214yesmaximal, complemented
4#22597335C214yesmaximal, complemented
5#22597328C214yesmaximal, complemented
6#22597279C211yesmaximal, characteristic, complemented
7#22597278C211yesmaximal, characteristic, complemented
8#22597056C211yesmaximal, characteristic, complemented
9#22597055C211yesmaximal, characteristic, complemented
10#22597035C211yesmaximal, characteristic, complemented
11#22597034C211yesmaximal, characteristic, complemented
12#22597030C211yesmaximal, characteristic, complemented
13#22596990C211yesmaximal, characteristic, complemented
14#22596987C211yesmaximal, characteristic, complemented
15#22596969C211yesmaximal, characteristic, complemented
16#22596767C211yesmaximal, characteristic, complemented
17#22596766C211yesmaximal, characteristic, complemented
18C22×#14556038C211yesmaximal, characteristic, complemented
19C71×#2929C211yesmaximal, characteristic, complemented
20C2×#14556136C2211yescharacteristic
21C2×#14556135C2211yescharacteristic
22C2×#14556134C2211yescharacteristic
23C23×C71⋊C8C2211yescharacteristic
24#17986552C2211yescharacteristic
25#17986551C412yes—
26#17986545C2211yescharacteristic
27#17986544C412yes—
28#17986535C412yes—
29#17986530C412yes—
30#17986529C2214yes—
31#17986526C414yes—
32#17986510C2211yescharacteristic
33#17986505C414yes—
34#41×Dic71C2211yescharacteristic
35#17986467C2211yescharacteristic
36C4×#11765864C2214yes—
37C22×C4×Dic71C2211yescharacteristic
38#17986129C2214yescomplemented
39#17986128C2214yescomplemented
40#17986127C2214yescomplemented
41#17986126C2214yescomplemented
42#17986073C2214yescomplemented
43#17986071C2214yes—
44#17986070C2214yes—
45#17986070C2214yescomplemented
46#17986068C2214yescomplemented
47#17986067C2214yes—
48#17986067C2214yescomplemented
49D4×C71⋊C8C2214yes—
50C8×C22⋊D71C2214yes—
51(C22⋊D71)⋊C8C2214yes—
52#17986059C2214yescomplemented
53#17986057C2214yescomplemented
54#17986055C2214yescomplemented
55#17986053C2214yes—
56#17986053C2214yescomplemented
57#17986049C2214yes—
58#17986027C2211yescharacteristic
59#17986026C2211yescharacteristic
60#17986025C2211yescharacteristic
61#17986022C2211yescharacteristic
62#17986022C2211yescharacteristic
63#17985967C2211yescharacteristic
64#17985966C2211yescharacteristic
65#17985965C2211yescharacteristic
66#17985963C2211yescharacteristic
67#17985957C2211yescharacteristic
68#17985957C2212yescomplemented
69#17985956C2212yescomplemented
70#17985955C2211yescharacteristic
71#17985954C2211yescharacteristic
72#17985954C2212yescomplemented
73#17985953C2212yescomplemented
74M16×Dic71C2211yescharacteristic
75M16×Dic71C2211yescharacteristic
76M16×Dic71C2212yescomplemented
77C4×#11765848C2212yescomplemented
78C2×#14556038C2211yescharacteristic
79C2×#14556038C2211yescharacteristic
80C2×#14556038C2211yescharacteristic
81C2×#14556038C2211yescharacteristic
82C2×#14556038C2212yes—
83C2×#14556038C2212yes—
84C2×#14556038C2212yes—
85C2×#14556038C2212yes—
86C2×#14556038C2212yescomplemented
87#97×D71C2212yescomplemented
88C2×#131×C71C2211yescharacteristic
89C23×C8×C71C2211yescharacteristic
90#525×C71C2211yescharacteristic
91#435×C71C2214yes—
92C8×D4×C71C2214yes—
93#424×C71C2211yescharacteristic
94#408×C71C2211yescharacteristic
95#407×C71C2211yescharacteristic
96#405×C71C2211yescharacteristic
97C2×#11765865C2311yescharacteristic
98C2×#11765864C2×C414yes—
99C23×Dic71C2×C412yes—
100#14556136—24no—
101#14556135—24no—
102#14556134—24no—
103C2×#11765849C2312yes—
104C2×#11765849C2311yescharacteristic
105C2×#11765849C2311yescharacteristic
106C2×#11765848C2312yes—
107C2×#11765848C2312yes—
108C22×C71⋊C8—24no—
109C22×C71⋊C8C2312yes—
110C22×C71⋊C8C2312yes—
111C22×C71⋊C8C2312yes—
112C22×C71⋊C8C2311yescharacteristic
113C22×C71⋊C8C2311yescharacteristic
114C2×C8×D71C2312yes—
115C2×C8×D71C2312yes—
116#14556127C2×C412yes—
117#14556126C2×C411yescharacteristic
118#14556124C2×C411yescharacteristic
119#14556123C2×C414yes—
120#14556121C2×C414yes—
121#14556119C2×C412yes—
122#14556118C2×C414yes—
123#14556117C2×C411yescharacteristic
124#14556115C2×C411yescharacteristic
125#14556114C2×C414yes—
126#14556112C2×C414yes—
127#14556111C2×C412yes—
128#14556109C2×C414yes—
129#14556107C2×C412yes—
130#14556105C2×C414yes—
131#14556105C2×C414yes—
132#14556102C2×C412yes—
133#14556100C2×C414yes—
134#14556100C2×C414yes—
135#14556097C2×C412yes—
136Q8×Dic71C2×C412yes—
137C4×Dic142C2314yes—
138#14556093C2×C414yes—
139#14556093C2×C412yes—
140D4×Dic71C2×C414yes—
141D4×Dic71C2×C414yes—
142D4×Dic71C2×C412yes—
143#14556090C2×C412yes—
144C4×C22⋊D71C2314yes—
145C4×C22⋊D71C2314yes—
146(C22⋊D71)⋊C4C2×C414yes—
147(C22⋊D71)⋊C4C2×C414yes—
148(C22⋊D71)⋊C4C2×C414yes—
149#14556087C2312yes—
150#14556087C2311yescharacteristic
151#14556086C2×C414yes—
152#14556085C2312yes—
153#14556084C2×C414yes—
154#14556084C2×C414yes—
155C2×C4×Dic71C2×C412yes—
156C2×C4×Dic71C2×C412yes—
157C2×C4×Dic71C2×C412yes—
158C2×C4×Dic71C2312yes—
159C2×C4×Dic71C2312yes—
160C2×C4×Dic71C2312yes—
161C2×C4×Dic71C2311yescharacteristic
162C2×C4×Dic71C2311yescharacteristic
163C42×D71C2312yes—
164C4⋊(C71⋊C8)C2314yes—
165Dic71⋊C8C2314yes—
166Dic71⋊C8C2314yes—
167Dic71⋊C8C2314yes—
168Dic71⋊C8C2314yes—
169C22⋊(C71⋊C8)C2314yes—
170C22⋊(C71⋊C8)C2314yes—
171(C2×D71)⋊C8C2314yes—
172(C2×D71)⋊C8C2314yes—
173#14556039C2312yes—
174#14556038C2312yes—
175#14556038C2312yes—
176#14556038C2312yes—
177#14556038C2312yes—
178#14556038C2312yes—
179#14556038C2312yes—
180#14556038C2312yes—
181#14556038C2312yes—
182#14556038C2312yes—
183#14556038C2312yes—
184#14556038C2311yescharacteristic
185#14556038C2311yescharacteristic
186#14556038C2311yescharacteristic
187#14556038C2311yescharacteristic
188C4×C71⋊C8C2312yes—
189C8×Dic71C2312yes—
190C8×Dic71C2312yes—
191C8×Dic71C2312yes—
192C8×Dic71C2312yes—
193C2×#41×C71C2311yescharacteristic
194C23×C4×C71C2311yescharacteristic
195#131×C71—24no—
196C2×M16×C71C2311yescharacteristic
197C2×M16×C71C2311yescharacteristic
198C2×M16×C71C2312yes—
199C22×C8×C71—24no—
200C22×C8×C71C2311yescharacteristic
201C22×C8×C71C2312yes—
202C22×C8×C71C2312yes—
203C22×C8×C71C2312yes—
204C22×C8×C71C2311yescharacteristic
205#123×C71C2×C412yes—
206C22⋊Q8×C71C2×C412yes—
207#121×C71C2×C412yes—
208#120×C71C2×C412yes—
209C4×D4×C71C2314yes—
210#117×C71C2311yescharacteristic
211C4⋊C8×C71C2314yes—
212C22⋊C8×C71C2314yes—
213C22⋊C8×C71C2314yes—
214#97×C71C2312yes—
215C4×C8×C71C2312yes—
216#11765865—22no—
217#11765865—22no—
218#11765864—48no—
219C2×Dic142C22×C411yescharacteristic
220C2×Dic142C22×C414yes—
221C2×D284C22×C411yescharacteristic
222C2×C22⋊D71C22×C414yes—
223C2×C22⋊D71C22×C412yes—
224C2×C22⋊D71C22×C414yes—
225C22×Dic71—44no—
226C22×Dic71C22×C412yes—
227C22×Dic71C22×C412yes—
228C22×Dic71C22×C412yes—
229C22×Dic71C22×C412yes—
230C22×Dic71C22×C412yes—
231C22×Dic71C22×C412yes—
232C22×Dic71C22×C414yes—
233C2×C4×D71C22×C414yes—
234C2×C4×D71C2412yes—
235#11765849—22no—
236#11765849—22no—
237#11765849—24no—
238#11765848—24no—
239#11765848—24no—
240C2×C71⋊C8—22no—
241C2×C71⋊C8—24no—
242C2×C71⋊C8—24no—
243C2×C71⋊C8—24no—
244C2×C71⋊C8#4114yescomplemented
245C2×C71⋊C8C2412yes—
246C2×C71⋊C8C2412yes—
247C2×C71⋊C8C2412yes—
248C2×C71⋊C8C2411yescharacteristic
249C2×C71⋊C8C2411yescharacteristic
250C8×D71—24no—
251C8×D71—24no—
252C4⋊Dic71C22×C414yes—
253C4⋊Dic71C22×C412yes—
254C4⋊Dic71C22×C414yes—
255Dic71⋊C4C22×C414yes—
256Dic71⋊C4C22×C414yes—
257Dic71⋊C4C22×C414yes—
258Dic71⋊C4C22×C414yes—
259Dic71⋊C4C22×C414yes—
260C22⋊Dic71C22×C414yes—
261C22⋊Dic71C22×C414yes—
262C22⋊Dic71C22×C412yes—
263C22⋊Dic71C22×C414yes—
264(C2×D71)⋊C4C22×C414yes—
265(C2×D71)⋊C4C22×C414yes—
266(C2×D71)⋊C4C22×C414yes—
267C4×Dic71C22×C414yes—
268C4×Dic71C22×C412yes—
269C4×Dic71C22×C412yes—
270C4×Dic71C22×C412yes—
271C4×Dic71C22×C412yes—
272C4×Dic71C22×C411yescharacteristic
273C4×Dic71C22×C412yes—
274C4×Dic71C22×C411yescharacteristic
275C4×Dic71C22×C414yes—
276C4×Dic71C2411yescharacteristic
277C4×Dic71C2412yes—
278C4×Dic71C2411yescharacteristic
279C4×Dic71C2412yes—
280C24×C71C22×C411yescharacteristic
281#41×C71—22no—
282#41×C71—22no—
283C2×Q8×C71C22×C411yescharacteristic
284C2×D4×C71C22×C414yes—
285C2×D4×C71C22×C412yes—
286C2×D4×C71C22×C411yescharacteristic
287C22×C4×C71—22no—
288C22×C4×C71—22no—
289C22×C4×C71C22×C412yes—
290C22×C4×C71C22×C411yescharacteristic
291C22×C4×C71C2412yes—
292C22×C4×C71C2412yes—
293C22×C4×C71C2411yescharacteristic
294M16×C71—22no—
295M16×C71—22no—
296M16×C71—24no—
297C2×C8×C71—22no—
298C2×C8×C71—24no—
299C2×C8×C71—24no—
300C2×C8×C71—24no—
301C2×C8×C71#4114yescomplemented
302C2×C8×C71C2412yes—
303C2×C8×C71C2412yes—
304C2×C8×C71C2412yes—
305C2×C8×C71C2411yescharacteristic
306C2×C8×C71C2411yescharacteristic
307C4⋊C4×C71C22×C412yes—
308C4⋊C4×C71C22×C414yes—
309C22⋊C4×C71C22×C412yes—
310C22⋊C4×C71C22×C414yes—
311C22⋊C4×C71C22×C414yes—
312C42×C71C2412yes—
313C23×C71—22no—
314C23×C71—24no—
315C23×C71C23×C412yes—
316C23×C71C23×C411yescharacteristic
317C23×C71C23×C412yes—
318C22×D71C23×C412yes—
319Q8×C71—22no—
320D4×C71—24no—
321D4×C71—28no—
322D4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—24no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71C23×C414yes—
330C2×C4×C71C23×C412yes—
331C2×C4×C71C23×C412yes—
332C2×C4×C71C23×C411yescharacteristic
333C2×C4×C71C2×#4112yes—
334C2×C4×C71C2×#4112yes—
335C2×C4×C71C2511yescharacteristic
336C22⋊D71—24no—
337C22⋊D71—28no—
338C22⋊D71—44no—
339C2×Dic71—24no—
340C2×Dic71—24no—
341C2×Dic71—42no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71—42no—
345C2×Dic71—44no—
346C2×Dic71C23×C412yes—
347C2×Dic71C23×C412yes—
348C2×Dic71C23×C412yes—
349C2×Dic71C23×C412yes—
350C2×Dic71C23×C412yes—
351C2×Dic71C23×C414yes—
352D284—22no—
353C4×D71—22no—
354C4×D71—22no—
355C4×D71—44no—
356Dic142—22no—
357Dic142—44no—
358C8×C71—22no—
359C8×C71—22no—
360C8×C71—22no—
361C8×C71C2×#4112yes—
362C8×C71C2×#4112yes—
363C71⋊C8—22no—
364C71⋊C8—22no—
365C71⋊C8—22no—
366C71⋊C8C2×#4112yes—
367C71⋊C8C2×#4112yes—
368C22×C71—28no—
369C22×C71—22no—
370C22×C71—22no—
371C22×C71—22no—
372C22×C71—22no—
373C22×C71—24no—
374C22×C71C4×#4112yes—
375C22×C71#56814yes—
376C22×C71C24×C411yescharacteristic
377C2×D71—22no—
378C2×D71—24no—
379C4×C71—22no—
380C4×C71—22no—
381C4×C71—24no—
382C4×C71C4×#4112yes—
383C4×C71C22×#4111yescharacteristic
384C4×C71C22×#4111yescharacteristic
385Dic71—22no—
386Dic71—22no—
387Dic71—24no—
388Dic71—22no—
389Dic71—22no—
390Dic71—22no—
391#60207—711nomaximal, Sylow
392C2×C71—22no—
393C2×C71—24no—
394C2×C71—42no—
395C2×C71C2×C4×#4111yescharacteristic
396C2×C71C2×#56812yes—
397D71—42no—
398#3444—711no—
399#2970—714no—
400#2970—714no—
401#2968—714no—
402#2968—714no—
403#2961—711no—
404#2961—711no—
405#2932—711no—
406#2932—711no—
407#2929—711no—
408#2929—711no—
409#2929—711no—
410#2929D7111yescharacteristic, complemented
411#2923—711no—
412#2923—711no—
413#2920—711no—
414#2875—711no—
415#2875—711no—
416C22×#97—711no—
417C71#6020711yescharacteristic, complemented, Sylow
418C2×#131—711no—
419C2×#131—711no—
420C2×#131—711no—
421C2×#131C2×D7111yescharacteristic
422C23×C8—711no—
423C23×C8C2×D7111yescharacteristic
424#533—712no—
425#533—711no—
426#532—711no—
427#532—712no—
428#529—714no—
429#529—712no—
430#529—712no—
431#529—714no—
432#525—711no—
433#525—714no—
434#525C2×D7111yescharacteristic
435C4×#41—711no—
436C4×#41—714no—
437C4×#41—711no—
438C22×C42—711no—
439#446—714no—
440#446—714no—
441#446—714no—
442#446—714no—
443#435—714no—
444#435—714no—
445#435—714no—
446#435—714no—
447#435—714no—
448#435—714no—
449#435—714no—
450#435C2×D7114yes—
451C8×D4—714no—
452C8×D4—714no—
453C8×D4—714no—
454C8×D4C2×D7114yes—
455#433—714no—
456#433—714no—
457#432—714no—
458#432—714no—
459#432—714no—
460#431—714no—
461#424—711no—
462#424—711no—
463#424—711no—
464#424C2×D7111yescharacteristic
465#423—711no—
466#423—711no—
467#408—711no—
468#408—711no—
469#408—711no—
470#408C2×D7111yescharacteristic
471#407—711no—
472#407C2×D7111yescharacteristic
473#405—711no—
474#405—712no—
475#405—711no—
476#405—712no—
477#405—711no—
478#405—712no—
479#405—712no—
480#405C2×D7111yescharacteristic
481C4×M16—711no—
482C4×M16—711no—
483C4×M16—712no—
484C4×M16—712no—
485C2×#97—711no—
486C2×#97—711no—
487C2×#97—711no—
488C2×#97—711no—
489C2×#97—712no—
490C2×#97—712no—
491C2×#97—712no—
492C2×#97—712no—
493C2×#97—712no—
494C2×#97—712no—
495C2×#41—714no—
496C2×#41—711no—
497C2×#41C22×D7111yescharacteristic
498C23×C4—712no—
499C23×C4C22×D7111yescharacteristic
500#131—24no—
501#131—1424no—
502#131—1424no—
503#131—1424no—
504C2×M16—711no—
505C2×M16—711no—
506C2×M16—712no—
507C2×M16—712no—
508C2×M16—712no—
509C2×M16C22×D7111yescharacteristic
510C2×M16C22×D7111yescharacteristic
511C2×M16C22×D7112yes—
512C22×C8—24no—
513C22×C8—711no—
514C22×C8—711no—
515C22×C8—712no—
516C22×C8—712no—
517C22×C8—712no—
518C22×C8—712no—
519C22×C8—712no—
520C22×C8—1424no—
521C22×C8C22×D7111yescharacteristic
522C22×C8C22×D7112yes—
523C22×C8C22×D7112yes—
524C22×C8C22×D7112yes—
525C22×C8C22×D7111yescharacteristic
526C4⋊Q8—711no—
527C4⋊Q8—712no—
528#127—711no—
529#126—714no—
530#126—714no—
531#125—714no—
532#125—712no—
533#124—711no—
534#124—711no—
535#124—714no—
536#123—714no—
537#123—712no—
538#123—714no—
539#123C4×D7112yes—
540C22⋊Q8—712no—
541C22⋊Q8—714no—
542C22⋊Q8—714no—
543C22⋊Q8C4×D7112yes—
544#121—714no—
545#121—714no—
546#121—712no—
547#121C4×D7112yes—
548#120—712no—
549#120C4×D7112yes—
550C4×Q8—712no—
551C4×Q8—714no—
552C4×Q8—712no—
553C4×Q8—714no—
554C4×D4—714no—
555C4×D4—714no—
556C4×D4—712no—
557C4×D4—714no—
558C4×D4—714no—
559C4×D4—712no—
560C4×D4—714no—
561C4×D4—714no—
562C4×D4—714no—
563C4×D4C22×D7114yes—
564#117—711no—
565#117—712no—
566#117—714no—
567#117—714no—
568#117—714no—
569#117—712no—
570#117C22×D7111yescharacteristic
571C2×C42—712no—
572C2×C42—712no—
573C2×C42—712no—
574C2×C42—712no—
575C2×C42—711no—
576C2×C42—712no—
577C2×C42—712no—
578C2×C42—711no—
579C2×C42—712no—
580C4⋊C8—714no—
581C4⋊C8—714no—
582C4⋊C8—714no—
583C4⋊C8—714no—
584C4⋊C8—714no—
585C4⋊C8C22×D7114yes—
586C22⋊C8—714no—
587C22⋊C8—714no—
588C22⋊C8—714no—
589C22⋊C8—714no—
590C22⋊C8C22×D7114yes—
591C22⋊C8C22×D7114yes—
592#97—711no—
593#97—711no—
594#97—711no—
595#97—711no—
596#97—712no—
597#97—712no—
598#97—712no—
599#97—712no—
600#97—712no—
601#97—712no—
602#97—712no—
603#97—712no—
604#97—712no—
605#97—712no—
606#97—712no—
607#97C22×D7112yes—
608C4×C8—712no—
609C4×C8—712no—
610C4×C8—712no—
611C4×C8—712no—
612C4×C8—712no—
613C4×C8C22×D7112yes—
614C24C2×C4×D7111yescharacteristic
615#41—22no—
616#41—22no—
617#41—2848no—
618#41—1422no—
619#41—1422no—
620C2×Q8—714no—
621C2×Q8—711no—
622C2×Q8C2×C4×D7111yescharacteristic
623C2×D4—714no—
624C2×D4—712no—
625C2×D4—714no—
626C2×D4—711no—
627C2×D4C2×C4×D7112yes—
628C2×D4C2×C4×D7111yescharacteristic
629C2×D4C2×C4×D7114yes—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—2844no—
633C22×C4—712no—
634C22×C4—712no—
635C22×C4—712no—
636C22×C4—712no—
637C22×C4—714no—
638C22×C4—714no—
639C22×C4—712no—
640C22×C4—712no—
641C22×C4—712no—
642C22×C4C2×C4×D7112yes—
643C22×C4C2×C4×D7111yescharacteristic
644C22×C4C23×D7112yes—
645C22×C4C23×D7112yes—
646C22×C4C23×D7111yescharacteristic
647M16—22no—
648M16—22no—
649M16—24no—
650M16—1424no—
651M16—1424no—
652M16—1422no—
653M16—1422no—
654M16—1424no—
655C2×C8—22no—
656C2×C8—24no—
657C2×C8—24no—
658C2×C8—24no—
659C2×C8—714no—
660C2×C8—711no—
661C2×C8—711no—
662C2×C8—712no—
663C2×C8—712no—
664C2×C8—712no—
665C2×C8—1424no—
666C2×C8—1424no—
667C2×C8—1424no—
668C2×C8—1424no—
669C2×C8—1422no—
670C2×C8—1424no—
671C2×C8#1176586414yescomplemented
672C2×C8C23×D7112yes—
673C2×C8C23×D7112yes—
674C2×C8C23×D7112yes—
675C2×C8C23×D7111yescharacteristic
676C2×C8C23×D7111yescharacteristic
677C4⋊C4—714no—
678C4⋊C4—714no—
679C4⋊C4—714no—
680C4⋊C4—714no—
681C4⋊C4—714no—
682C4⋊C4—712no—
683C4⋊C4—714no—
684C4⋊C4—714no—
685C4⋊C4C2×C4×D7114yes—
686C4⋊C4C2×C4×D7112yes—
687C22⋊C4—712no—
688C22⋊C4—714no—
689C22⋊C4—714no—
690C22⋊C4—714no—
691C22⋊C4—714no—
692C22⋊C4—714no—
693C22⋊C4—714no—
694C22⋊C4C2×C4×D7114yes—
695C22⋊C4C2×C4×D7114yes—
696C22⋊C4C2×C4×D7112yes—
697C42—712no—
698C42—712no—
699C42—712no—
700C42—711no—
701C42—712no—
702C42—712no—
703C42—711no—
704C42—714no—
705C42—714no—
706C42—711no—
707C42—712no—
708C42—711no—
709C42—712no—
710C42C23×D7112yes—
711C23—22no—
712C23—24no—
713C23—712no—
714C23C22×C4×D7112yes—
715C23C22×C4×D7111yescharacteristic
716C23C22×C4×D7112yes—
717Q8—22no—
718Q8—2844no—
719Q8—1422no—
720D4—24no—
721D4—28no—
722D4—22no—
723D4—2844no—
724D4—1424no—
725D4—1428no—
726D4—1422no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—24no—
733C2×C4—2844no—
734C2×C4—2842no—
735C2×C4—2842no—
736C2×C4—2842no—
737C2×C4—2842no—
738C2×C4—2844no—
739C2×C4—712no—
740C2×C4—712no—
741C2×C4—712no—
742C2×C4—712no—
743C2×C4—714no—
744C2×C4—712no—
745C2×C4—1424no—
746C2×C4—1424no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4C22×C4×D7112yes—
750C2×C4C22×C4×D7112yes—
751C2×C4C22×C4×D7114yes—
752C2×C4C22×C4×D7111yescharacteristic
753C2×C4#41×D7112yes—
754C2×C4C2×#1176586412yes—
755C2×C4C24×D7111yescharacteristic
756C8—22no—
757C8—22no—
758C8—22no—
759C8—712no—
760C8—712no—
761C8—1422no—
762C8—1422no—
763C8—1422no—
764C8C2×#1176586412yes—
765C8C2×#1176586412yes—
766C22—28no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—1424no—
773C22—1422no—
774C22C4×#1176586412yes—
775C22#1798676414yes—
776C22C23×C4×D7111yescharacteristic
777C4—24no—
778C4—22no—
779C4—22no—
780C4—1422no—
781C4—1422no—
782C4—1422no—
783C4—1422no—
784C4—1424no—
785C4—1422no—
786C4C4×#1176586412yes—
787C4C2×#41×D7111yescharacteristic
788C4C22×#1176586411yescharacteristic
789C2—22no—
790C2—24no—
791C2—42no—
792C2—2842no—
793C2C2×C4×#1176586411yescharacteristic
794C2C2×#1798676412yes—
subgroupG/H
center, FrattiniC2×C4C24×D71
commutator, socleC22×C71C24×C4
FittingC71×#2929C2
prime radical#22601632C2
cosocleC2×C4×C71C25
hypercenter#2929D71
hypocenterC71#60207
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #22597350C2semidirect
3. #22597348C2semidirect
4. #22597335C2semidirect
5. #22597328C2semidirect
6. #22597279C2semidirect
7. #22597278C2semidirect
8. #22597056C2semidirect
9. #22597055C2semidirect
10. #22597035C2semidirect
11. #22597034C2semidirect
12. #22597030C2semidirect
13. #22596990C2semidirect
14. #22596987C2semidirect
15. #22596969C2semidirect
16. #22596767C2semidirect
17. #22596766C2semidirect
18. C22×#14556038C2semidirect
19. C71×#2929C2semidirect
38. #17986129C22semidirect
39. #17986128C22semidirect
40. #17986127C22semidirect
41. #17986126C22semidirect
42. #17986073C22semidirect
45. #17986070C22semidirect
46. #17986068C22semidirect
48. #17986067C22semidirect
52. #17986059C22semidirect
53. #17986057C22semidirect
54. #17986055C22semidirect
56. #17986053C22semidirect
68. #17985957C22semidirect
69. #17985956C22semidirect
72. #17985954C22semidirect
73. #17985953C22semidirect
76. M16×Dic71C22semidirect
77. C4×#11765848C22semidirect
86. C2×#14556038C22semidirect
87. #97×D71C22semidirect
244. C2×C71⋊C8#41semidirect
301. C2×C8×C71#41semidirect
410. #2929D71semidirect
417. C71#60207semidirect
671. C2×C8#11765864semidirect

Maximal subgroups

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

subgroupindex
#226016322
#225973502
#225973482
#225973352
#225973282
#225972792
#225972782
#225970562
#225970552
#225970352
#225970342
#225970302
#225969902
#225969872
#225969692
#225967672
#225967662
C22×#145560382
C71×#29292
#6020771