Finite Group Databasebeta

← #32861269

Subgroups — #32861269

Order 18176.

2038 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601541C211yesmaximal, characteristic
2#22597005C212yesmaximal, complemented
3#22597003C214yesmaximal, complemented
4#22596996C214yesmaximal, complemented
5#22596994C212yesmaximal, complemented
6#22596989C211yesmaximal, characteristic, complemented
7#22596988C212yesmaximal, complemented
8#22596982C211yesmaximal, characteristic, complemented
9#22596981C212yesmaximal, complemented
10#22596978C211yesmaximal, characteristic, complemented
11#22596974C212yesmaximal, complemented
12#433×D71C212yesmaximal, complemented
13#22596905C212yesmaximal, complemented
14#22596786C212yesmaximal
15#22596765C211yesmaximal, characteristic, complemented
16C4×#14556134C211yesmaximal, characteristic, complemented
17C2×#433×C71C211yesmaximal, characteristic, complemented
18C22×#11765865C2211yescharacteristic
19C2×#14556134C2212yes—
20C2×#14556134C2212yes—
21#17986480C414yes—
22#17986479C412yes—
23#17986479C412yes—
24#17986476C412yes—
25#17986473C412yes—
26#17986472C414yes—
27C4×#11765865C2211yescharacteristic
28C4×#11765865C2211yescharacteristic
29C4×#11765865C2211yescharacteristic
30C4×#11765865C2211yescharacteristic
31#17986467C2212yes—
32#17986467C2212yes—
33C2×#14556087C2211yescharacteristic
34#117×D71C2212yes—
35#117×D71C2212yes—
36#17986061C2212yescomplemented
37#17986061C2212yescomplemented
38#17986060C2212yes—
39#17986060C2212yes—
40#17986060C2212yescomplemented
41#17986060C2212yescomplemented
42#17986059C2214yescomplemented
43#17986059C2214yescomplemented
44#17986058C2212yescomplemented
45#17986058C2212yescomplemented
46#17986057C2214yes—
47#17986057C2214yes—
48#17986055C2214yescomplemented
49#17986054C2214yescomplemented
50#17986053C2214yescomplemented
51#17986051C2214yescomplemented
52#17986050C2214yescomplemented
53#17986049C2214yescomplemented
54#17986025C2212yescomplemented
55#17986025C2212yescomplemented
56#17986024C2214yescomplemented
57#17986024C2214yescomplemented
58#17986023C2212yescomplemented
59#17986021C2214yescomplemented
60C4⋊C8×D71C2214yescomplemented
61#17985965C2212yes—
62#17985965C2212yes—
63#17985964C2214yes—
64#17985964C2214yes—
65#17985963C2212yes—
66#17985961C2214yes—
67C22⋊C8×D71C2214yes—
68#17985956C2214yescomplemented
69#17985954C2212yescomplemented
70#17985954C2212yescomplemented
71#17985953C2214yescomplemented
72C4×#11765849C2211yescharacteristic, complemented
73C4×#11765849C2211yescharacteristic, complemented
74#17985951C2212yescomplemented
75C4×#11765848C2212yescomplemented
76#97×D71C2212yescomplemented
77C4×C8×D71C2212yescomplemented
78C2×#117×C71C2211yescharacteristic
79#433×C71C2211yescharacteristic
80#433×C71C2211yescharacteristic
81#433×C71C2212yes—
82#433×C71C2211yescharacteristic, complemented
83#433×C71C2211yescharacteristic, complemented
84#433×C71C2212yescomplemented
85C2×C4⋊C8×C71C2212yescomplemented
86C2×C22⋊C8×C71C2212yes—
87C2×#97×C71C2211yescharacteristic, complemented
88C2×C4×C8×C71C2211yescharacteristic, complemented
89C2×#11765865—28no—
90C2×#11765865C2×C411yescharacteristic
91C2×#11765865C2×C411yescharacteristic
92C2×#11765865C2×C412yes—
93C2×#11765865C2312yes—
94C2×#11765865C2311yescharacteristic
95C2×#11765865C2311yescharacteristic
96C22×Dic142C2×C411yescharacteristic
97C22×D284C2×C411yescharacteristic
98C22×C22⋊D71C2×C412yes—
99C22×C4×D71C2312yes—
100#14556134—28no—
101#14556134—28no—
102C2×#11765849C2312yes—
103C2×#11765849C2312yes—
104C2×#11765848C2314yes—
105C2×#11765848C2314yes—
106C2×C8×D71C2314yes—
107C2×C8×D71C2314yes—
108C4×Dic142C2×C412yes—
109C4×Dic142C2×C412yes—
110C4×Dic142C2×C412yes—
111C4×Dic142C2×C412yes—
112#14556093C2×C414yes—
113#14556093C2×C414yes—
114C4×D284C2×C412yes—
115C4×D284C2×C412yes—
116C4×D284C2×C412yes—
117C4×D284C2×C412yes—
118#14556090C2×C414yes—
119#14556090C2×C414yes—
120C4×C22⋊D71C2×C414yes—
121C4×C22⋊D71C2×C414yes—
122C4×C22⋊D71C2×C414yes—
123C4×C22⋊D71C2×C414yes—
124(C22⋊D71)⋊C4C2×C414yes—
125(C22⋊D71)⋊C4C2×C414yes—
126(C22⋊D71)⋊C4C2×C414yes—
127(C22⋊D71)⋊C4C2×C414yes—
128#14556087C2×C412yes—
129#14556087C2×C412yes—
130#14556087C2312yes—
131#14556087C2311yescharacteristic
132#14556087C2311yescharacteristic
133#14556086C2×C414yes—
134#14556086C2×C414yes—
135#14556085C2312yes—
136#14556085C2312yes—
137#14556085C2312yes—
138#14556085C2312yes—
139#14556084C2×C414yes—
140#14556084C2×C414yes—
141C2×C4⋊Dic71C2×C412yes—
142C4⋊C4×D71C2×C414yes—
143C4⋊C4×D71C2×C414yes—
144C2×C22⋊Dic71C2×C412yes—
145C22⋊C4×D71C2×C414yes—
146C22⋊C4×D71C2×C414yes—
147C2×C4×Dic71C2312yes—
148C42×D71C2312yes—
149C42×D71C2312yes—
150C42×D71C2312yes—
151C42×D71C2312yes—
152C4⋊(C71⋊C8)C2314yes—
153C4⋊(C71⋊C8)C2314yes—
154Dic71⋊C8C2314yes—
155Dic71⋊C8C2314yes—
156Dic71⋊C8C2314yes—
157Dic71⋊C8C2314yes—
158C22⋊(C71⋊C8)C2314yes—
159C22⋊(C71⋊C8)C2314yes—
160(C2×D71)⋊C8C2314yes—
161(C2×D71)⋊C8C2314yes—
162(C2×D71)⋊C8C2314yes—
163(C2×D71)⋊C8C2314yes—
164#14556039C2312yes—
165#14556039C2312yes—
166#14556038C2314yes—
167#14556038C2314yes—
168C4×C71⋊C8C2312yes—
169C4×C71⋊C8C2312yes—
170C8×Dic71C2314yes—
171C8×Dic71C2314yes—
172C23×C4×C71C2311yescharacteristic
173C22×C8×C71C2312yes—
174C22×C8×C71C2312yes—
175#117×C71C2×C412yes—
176#117×C71C2×C412yes—
177#117×C71C2311yescharacteristic
178#117×C71C2311yescharacteristic
179#117×C71C2311yescharacteristic
180#117×C71C2311yescharacteristic
181C2×C4⋊C4×C71C2×C412yes—
182C2×C22⋊C4×C71C2×C412yes—
183C2×C42×C71C2311yescharacteristic
184C2×C42×C71C2311yescharacteristic
185C4⋊C8×C71C2312yes—
186C4⋊C8×C71C2312yes—
187C4⋊C8×C71C2312yes—
188C4⋊C8×C71C2312yes—
189C22⋊C8×C71C2312yes—
190C22⋊C8×C71C2312yes—
191C22⋊C8×C71C2312yes—
192C22⋊C8×C71C2312yes—
193#97×C71C2312yes—
194#97×C71C2311yescharacteristic
195#97×C71C2311yescharacteristic
196C4×C8×C71C2312yes—
197C4×C8×C71C2311yescharacteristic
198C4×C8×C71C2311yescharacteristic
199C23×D71C22×C412yes—
200#11765865—24no—
201#11765865—28no—
202#11765865—24no—
203#11765865—28no—
204#11765865—24no—
205#11765865#4118yes—
206C2×Dic142—24no—
207C2×Dic142C22×C412yes—
208C2×Dic142C22×C411yescharacteristic
209C2×Dic142C22×C411yescharacteristic
210C2×D284—24no—
211C2×D284C22×C412yes—
212C2×D284C22×C411yescharacteristic
213C2×D284C22×C411yescharacteristic
214C2×C22⋊D71—28no—
215C2×C22⋊D71C22×C412yes—
216C2×C22⋊D71C22×C412yes—
217C2×C22⋊D71C22×C412yes—
218C2×C22⋊D71C22×C412yes—
219C22×Dic71C22×C412yes—
220C22×Dic71C22×C414yes—
221C2×C4×D71—28no—
222C2×C4×D71C22×C412yes—
223C2×C4×D71C22×C412yes—
224C2×C4×D71C22×C414yes—
225C2×C4×D71C22×C414yes—
226C2×C4×D71C22×C414yes—
227C2×C4×D71C22×C414yes—
228C2×C4×D71C2412yes—
229C2×C4×D71C2412yes—
230#11765849—24no—
231#11765849—24no—
232#11765848—28no—
233#11765848—28no—
234C2×C71⋊C8C2414yes—
235C2×C71⋊C8C2414yes—
236C8×D71—28no—
237C8×D71—28no—
238C4⋊Dic71C22×C414yes—
239C4⋊Dic71C22×C412yes—
240C4⋊Dic71C22×C412yes—
241Dic71⋊C4C22×C414yes—
242Dic71⋊C4C22×C414yes—
243Dic71⋊C4C22×C414yes—
244Dic71⋊C4C22×C414yes—
245C22⋊Dic71C22×C414yes—
246C22⋊Dic71C22×C412yes—
247C22⋊Dic71C22×C412yes—
248(C2×D71)⋊C4C22×C414yes—
249(C2×D71)⋊C4C22×C414yes—
250(C2×D71)⋊C4C22×C414yes—
251(C2×D71)⋊C4C22×C414yes—
252C4×Dic71C22×C414yes—
253C4×Dic71C22×C414yes—
254C4×Dic71C22×C414yes—
255C4×Dic71C22×C414yes—
256C4×Dic71C22×C414yes—
257C4×Dic71C2412yes—
258C4×Dic71C2412yes—
259C24×C71C22×C411yescharacteristic
260C22×C4×C71—24no—
261C22×C4×C71C22×C411yescharacteristic
262C22×C4×C71C22×C411yescharacteristic
263C22×C4×C71C22×C411yescharacteristic
264C22×C4×C71C22×C412yes—
265C22×C4×C71C22×C412yes—
266C22×C4×C71C2411yescharacteristic
267C22×C4×C71C2411yescharacteristic
268C22×C4×C71C2411yescharacteristic
269C2×C8×C71—24no—
270C2×C8×C71—24no—
271C2×C8×C71C2412yes—
272C2×C8×C71C2412yes—
273C2×C8×C71C2412yes—
274C2×C8×C71C2412yes—
275C4⋊C4×C71C22×C412yes—
276C4⋊C4×C71C22×C412yes—
277C4⋊C4×C71C22×C412yes—
278C4⋊C4×C71C22×C412yes—
279C22⋊C4×C71C22×C412yes—
280C22⋊C4×C71C22×C412yes—
281C22⋊C4×C71C22×C412yes—
282C22⋊C4×C71C22×C412yes—
283C42×C71C22×C412yes—
284C42×C71C22×C412yes—
285C42×C71C2411yescharacteristic
286C42×C71C2411yescharacteristic
287C42×C71C2411yescharacteristic
288C42×C71C2411yescharacteristic
289C23×C71—22no—
290C23×C71—42no—
291C23×C71C23×C411yescharacteristic
292C23×C71C23×C411yescharacteristic
293C23×C71C23×C411yescharacteristic
294C22×D71—24no—
295C22×D71—44no—
296C22×D71C23×C412yes—
297C22×D71C23×C412yes—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—42no—
304C2×C4×C71—42no—
305C2×C4×C71C23×C412yes—
306C2×C4×C71C23×C412yes—
307C2×C4×C71C23×C412yes—
308C2×C4×C71C23×C412yes—
309C2×C4×C71C23×C411yescharacteristic
310C2×C4×C71C23×C411yescharacteristic
311C2×C4×C71C23×C411yescharacteristic
312C2×C4×C71C2×#4114yes—
313C2×C4×C71C2511yescharacteristic
314C22⋊D71—24no—
315C22⋊D71—24no—
316C22⋊D71—24no—
317C22⋊D71#11718yes—
318C2×Dic71—24no—
319C2×Dic71—44no—
320C2×Dic71C23×C412yes—
321C2×Dic71C23×C414yes—
322C2×Dic71C23×C414yes—
323C2×Dic71C23×C412yes—
324D284—24no—
325D284—22no—
326D284#11714yes—
327C4×D71—24no—
328C4×D71—24no—
329C4×D71—24no—
330C4×D71—44no—
331C4×D71—44no—
332C4×D71—44no—
333C4×D71—44no—
334C4×D71C2×#4118yes—
335Dic142—22no—
336Dic142—24no—
337Dic142#11714yes—
338C8×C71—22no—
339C8×C71—22no—
340C8×C71—22no—
341C8×C71—22no—
342C71⋊C8—24no—
343C71⋊C8—24no—
344C22×C71—22no—
345C22×C71—21no—
346C22×C71—21no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—82no—
350C22×C71C2×#11712yes—
351C22×C71C24×C411yescharacteristic
352C2×D71—24no—
353C2×D71—22no—
354C2×D71—24no—
355C2×D71—84no—
356C2×D71C2×#11714yes—
357C4×C71—21no—
358C4×C71—21no—
359C4×C71—22no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—22no—
363C4×C71C2×#11712yes—
364C4×C71C22×#4112yes—
365Dic71—22no—
366Dic71—24no—
367Dic71—24no—
368Dic71C2×#11714yes—
369#60129—711nomaximal, Sylow
370C2×C71—22no—
371C2×C71—41no—
372C2×C71—41no—
373C2×C71C22×#11711yescharacteristic
374C2×C71#357312yes—
375D71—24no—
376D71—42no—
377#3428—711no—
378#2925—714no—
379#2925—712no—
380#2924—714no—
381#2924—712no—
382#2923—712no—
383#2923—711no—
384#2922—712no—
385#2922—711no—
386#2921—712no—
387#2921—711no—
388C2×#433—712no—
389C2×#433D7111yescharacteristic, complemented
390#2906—712no—
391#2880—712no—
392#2875—711no—
393C4×#131—711no—
394C71#6012911yescharacteristic, complemented, Sylow
395C22×#41—711no—
396C2×#131—712no—
397C2×#131—712no—
398#520—712no—
399#520—712no—
400#520—714no—
401#519—712no—
402#518—712no—
403#518—714no—
404C4×#41—712no—
405C4×#41—712no—
406C4×#41—711no—
407C4×#41—711no—
408C4×#41—711no—
409C4×#41—711no—
410C2×#117—711no—
411C2×#117—712no—
412C2×#117—712no—
413C2×#117C2×D7111yescharacteristic
414#433—712no—
415#433—712no—
416#433—712no—
417#433—712no—
418#433—714no—
419#433—714no—
420#433—714no—
421#433—714no—
422#433—712no—
423#433—712no—
424#433—712no—
425#433—712no—
426#433C2×D7111yescharacteristic
427#433C2×D7111yescharacteristic
428#433C2×D7112yes—
429#433C2×D7111yescharacteristic, complemented
430#433C2×D7111yescharacteristic, complemented
431#433C2×D7112yescomplemented
432#432—714no—
433#432—714no—
434#432—714no—
435#431—714no—
436#431—714no—
437#431—714no—
438#424—712no—
439#424—712no—
440#424—714no—
441#424—714no—
442#423—712no—
443#423—714no—
444C2×C4⋊C8—714no—
445C2×C4⋊C8C2×D7112yescomplemented
446#408—712no—
447#408—712no—
448#408—714no—
449#408—714no—
450#407—712no—
451#407—714no—
452C2×C22⋊C8—714no—
453C2×C22⋊C8C2×D7112yes—
454#405—712no—
455#405—712no—
456#405—714no—
457#405—714no—
458C4×M16—711no—
459C4×M16—711no—
460C4×M16—712no—
461C4×M16—712no—
462C2×#97—712no—
463C2×#97C2×D7111yescharacteristic, complemented
464C2×C4×C8—712no—
465C2×C4×C8C2×D7111yescharacteristic, complemented
466C2×#41—711no—
467C2×#41—711no—
468C2×#41—712no—
469C2×#41—711no—
470C2×#41—712no—
471C2×#41—711no—
472C2×#41—1428no—
473C22×Q8—711no—
474C22×D4—712no—
475C22×D4—711no—
476C23×C4—712no—
477C23×C4C22×D7111yescharacteristic
478#131—1428no—
479#131—1428no—
480C2×M16—712no—
481C2×M16—712no—
482C2×M16—714no—
483C2×M16—714no—
484C22×C8—714no—
485C22×C8—714no—
486C22×C8C22×D7112yes—
487C22×C8C22×D7112yes—
488C4×Q8—714no—
489C4×Q8—714no—
490C4×Q8—712no—
491C4×Q8—712no—
492C4×Q8—712no—
493C4×Q8—712no—
494C4×D4—714no—
495C4×D4—714no—
496C4×D4—714no—
497C4×D4—714no—
498C4×D4—714no—
499C4×D4—714no—
500C4×D4—714no—
501C4×D4—714no—
502C4×D4—714no—
503C4×D4—714no—
504C4×D4—712no—
505C4×D4—712no—
506C4×D4—712no—
507C4×D4—712no—
508#117—712no—
509#117—712no—
510#117—712no—
511#117—711no—
512#117—711no—
513#117—714no—
514#117—714no—
515#117—714no—
516#117—714no—
517#117—712no—
518#117—712no—
519#117—712no—
520#117—712no—
521#117C4×D7112yes—
522#117C4×D7112yes—
523#117C22×D7111yescharacteristic
524#117C22×D7111yescharacteristic
525#117C22×D7111yescharacteristic
526#117C22×D7111yescharacteristic
527C2×C4⋊C4—712no—
528C2×C4⋊C4—714no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4C4×D7112yes—
531C2×C22⋊C4—712no—
532C2×C22⋊C4—714no—
533C2×C22⋊C4—714no—
534C2×C22⋊C4C4×D7112yes—
535C2×C42—712no—
536C2×C42—712no—
537C2×C42—712no—
538C2×C42—712no—
539C2×C42—712no—
540C2×C42C22×D7111yescharacteristic
541C2×C42C22×D7111yescharacteristic
542C4⋊C8—714no—
543C4⋊C8—714no—
544C4⋊C8—714no—
545C4⋊C8—714no—
546C4⋊C8—714no—
547C4⋊C8—714no—
548C4⋊C8C22×D7112yes—
549C4⋊C8C22×D7112yes—
550C4⋊C8C22×D7112yes—
551C4⋊C8C22×D7112yes—
552C22⋊C8—714no—
553C22⋊C8—714no—
554C22⋊C8—714no—
555C22⋊C8—714no—
556C22⋊C8—714no—
557C22⋊C8—714no—
558C22⋊C8C22×D7112yes—
559C22⋊C8C22×D7112yes—
560C22⋊C8C22×D7112yes—
561C22⋊C8C22×D7112yes—
562#97—714no—
563#97—714no—
564#97—712no—
565#97—712no—
566#97C22×D7111yescharacteristic
567#97C22×D7111yescharacteristic
568#97C22×D7112yes—
569C4×C8—714no—
570C4×C8—714no—
571C4×C8—712no—
572C4×C8—712no—
573C4×C8C22×D7111yescharacteristic
574C4×C8C22×D7111yescharacteristic
575C4×C8C22×D7112yes—
576C24—712no—
577C24C2×C4×D7111yescharacteristic
578#41—718no—
579#41—1428no—
580#41—1428no—
581#41—1424no—
582#41—1424no—
583#41—1424no—
584C2×Q8—711no—
585C2×Q8—712no—
586C2×Q8—711no—
587C2×Q8—1424no—
588C2×D4—712no—
589C2×D4—712no—
590C2×D4—712no—
591C2×D4—712no—
592C2×D4—711no—
593C2×D4—712no—
594C2×D4—711no—
595C2×D4—1424no—
596C2×D4—1428no—
597C22×C4—24no—
598C22×C4—714no—
599C22×C4—714no—
600C22×C4—714no—
601C22×C4—714no—
602C22×C4—714no—
603C22×C4—712no—
604C22×C4—712no—
605C22×C4—712no—
606C22×C4—712no—
607C22×C4—712no—
608C22×C4—1428no—
609C22×C4C2×C4×D7111yescharacteristic
610C22×C4C2×C4×D7111yescharacteristic
611C22×C4C2×C4×D7111yescharacteristic
612C22×C4C2×C4×D7112yes—
613C22×C4C2×C4×D7112yes—
614C22×C4C23×D7111yescharacteristic
615C22×C4C23×D7111yescharacteristic
616C22×C4C23×D7111yescharacteristic
617M16—1428no—
618M16—1428no—
619M16—1424no—
620M16—1424no—
621C2×C8—24no—
622C2×C8—24no—
623C2×C8—714no—
624C2×C8—714no—
625C2×C8—1428no—
626C2×C8—1428no—
627C2×C8C23×D7112yes—
628C2×C8C23×D7112yes—
629C2×C8C23×D7112yes—
630C2×C8C23×D7112yes—
631C4⋊C4—714no—
632C4⋊C4—714no—
633C4⋊C4—714no—
634C4⋊C4—714no—
635C4⋊C4—714no—
636C4⋊C4—712no—
637C4⋊C4—712no—
638C4⋊C4C2×C4×D7112yes—
639C4⋊C4C2×C4×D7112yes—
640C4⋊C4C2×C4×D7112yes—
641C4⋊C4C2×C4×D7112yes—
642C22⋊C4—714no—
643C22⋊C4—712no—
644C22⋊C4—712no—
645C22⋊C4—714no—
646C22⋊C4—714no—
647C22⋊C4—714no—
648C22⋊C4—714no—
649C22⋊C4C2×C4×D7112yes—
650C22⋊C4C2×C4×D7112yes—
651C22⋊C4C2×C4×D7112yes—
652C22⋊C4C2×C4×D7112yes—
653C42—714no—
654C42—714no—
655C42—714no—
656C42—714no—
657C42—714no—
658C42—712no—
659C42—712no—
660C42C2×C4×D7112yes—
661C42C2×C4×D7112yes—
662C42C23×D7111yescharacteristic
663C42C23×D7111yescharacteristic
664C42C23×D7111yescharacteristic
665C42C23×D7111yescharacteristic
666C23—22no—
667C23—42no—
668C23—2844no—
669C23—712no—
670C23—712no—
671C23—1424no—
672C23C22×C4×D7111yescharacteristic
673C23C22×C4×D7111yescharacteristic
674C23C22×C4×D7111yescharacteristic
675Q8—714no—
676Q8—1424no—
677Q8—1422no—
678D4—718no—
679D4—714no—
680D4—1424no—
681D4—1424no—
682D4—1424no—
683D4—1424no—
684D4—1422no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—2844no—
693C2×C4—2844no—
694C2×C4—2844no—
695C2×C4—2844no—
696C2×C4—2844no—
697C2×C4—712no—
698C2×C4—718no—
699C2×C4—714no—
700C2×C4—714no—
701C2×C4—712no—
702C2×C4—1424no—
703C2×C4—1424no—
704C2×C4—1424no—
705C2×C4—1424no—
706C2×C4C22×C4×D7111yescharacteristic
707C2×C4C22×C4×D7112yes—
708C2×C4C22×C4×D7112yes—
709C2×C4C22×C4×D7112yes—
710C2×C4C22×C4×D7112yes—
711C2×C4C22×C4×D7111yescharacteristic
712C2×C4C22×C4×D7111yescharacteristic
713C2×C4#41×D7114yes—
714C2×C4C24×D7111yescharacteristic
715C8—22no—
716C8—22no—
717C8—22no—
718C8—22no—
719C8—1424no—
720C8—1424no—
721C22—22no—
722C22—21no—
723C22—21no—
724C22—22no—
725C22—22no—
726C22—82no—
727C22—5684no—
728C22—714no—
729C22—1422no—
730C22—1424no—
731C22—1424no—
732C22#117×D7112yes—
733C22C23×C4×D7111yescharacteristic
734C4—21no—
735C4—21no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—714no—
741C4—1422no—
742C4—1424no—
743C4—1424no—
744C4#117×D7112yes—
745C4C2×#41×D7112yes—
746C2—22no—
747C2—41no—
748C2—41no—
749C2—2842no—
750C2—1424no—
751C2C2×#117×D7111yescharacteristic
752C2#2260305112yes—
subgroupG/H
center, FrattiniC2×C4C24×D71
commutator, socleC22×C71C24×C4
FittingC2×#433×C71C2
prime radicalC22×#11765865C22
cosocleC2×C4×C71C25
hypercenterC2×#433D71
hypocenterC71#60129
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #22597005C2semidirect
3. #22597003C2semidirect
4. #22596996C2semidirect
5. #22596994C2semidirect
6. #22596989C2semidirect
7. #22596988C2semidirect
8. #22596982C2semidirect
9. #22596981C2semidirect
10. #22596978C2semidirect
11. #22596974C2semidirect
12. #433×D71C2semidirect
13. #22596905C2semidirect
15. #22596765C2semidirect
16. C4×#14556134C2semidirect
17. C2×#433×C71C2semidirect
36. #17986061C22semidirect
37. #17986061C22semidirect
40. #17986060C22semidirect
41. #17986060C22semidirect
42. #17986059C22semidirect
43. #17986059C22semidirect
44. #17986058C22semidirect
45. #17986058C22semidirect
48. #17986055C22semidirect
49. #17986054C22semidirect
50. #17986053C22semidirect
51. #17986051C22semidirect
52. #17986050C22semidirect
53. #17986049C22semidirect
54. #17986025C22semidirect
55. #17986025C22semidirect
56. #17986024C22semidirect
57. #17986024C22semidirect
58. #17986023C22semidirect
59. #17986021C22semidirect
60. C4⋊C8×D71C22semidirect
68. #17985956C22semidirect
69. #17985954C22semidirect
70. #17985954C22semidirect
71. #17985953C22semidirect
72. C4×#11765849C22semidirect
73. C4×#11765849C22semidirect
74. #17985951C22semidirect
75. C4×#11765848C22semidirect
76. #97×D71C22semidirect
77. C4×C8×D71C22semidirect
82. #433×C71C22semidirect
83. #433×C71C22semidirect
84. #433×C71C22semidirect
85. C2×C4⋊C8×C71C22semidirect
87. C2×#97×C71C22semidirect
88. C2×C4×C8×C71C22semidirect
389. C2×#433D71semidirect
394. C71#60129semidirect
429. #433C2×D71semidirect
430. #433C2×D71semidirect
431. #433C2×D71semidirect
445. C2×C4⋊C8C2×D71semidirect
463. C2×#97C2×D71semidirect
465. C2×C4×C8C2×D71semidirect

Maximal subgroups

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

subgroupindex
#226015412
#225970052
#225970032
#225969962
#225969942
#225969892
#225969882
#225969822
#225969812
#225969782
#225969742
#433×D712
#225969052
#225967862
#225967652
C4×#145561342
C2×#433×C712
#6012971