Finite Group Databasebeta

← #27080486

Subgroups — #27080486

Order 12032.

2742 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2#20256589C211yesmaximal, characteristic, complemented
3#20252269C214yesmaximal, complemented
4#20252261C214yesmaximal, complemented
5#20252227C214yesmaximal, complemented
6#20252216C214yesmaximal, complemented
7C4×#13094055C214yesmaximal, complemented
8C4×#13094050C214yesmaximal, complemented
9C2×#15689163C211yesmaximal, characteristic, complemented
10#20251907C211yesmaximal, characteristic, complemented
11C2×#15689122C211yesmaximal, characteristic, complemented
12#20251807C211yesmaximal, characteristic, complemented
13C2×C47×#520C211yesmaximal, characteristic, complemented
14C22×#10625350C2211yescharacteristic
15#15689921C4116yescomplemented
16C2×#13094055C2212yes—
17C2×#13094054C2212yes—
18C2×#13094050C2212yes—
19C2×#13094049C2212yes—
20C2×#13094044C2214yes—
21C22×#10625329C2211yescharacteristic
22C22×#10625329C2211yescharacteristic
23#15689604—21no—
24#15689604—21no—
25#15689603C2212yescomplemented
26#15689603C2212yescomplemented
27#15689600C2212yescomplemented
28#15689597C2212yescomplemented
29#15689596—22no—
30C4×#10625350C2214yes—
31#15689591—22no—
32C2×#13093983C2211yescharacteristic
33#117×D47—22no—
34#15689233C2218yescomplemented
35#15689228C2218yescomplemented
36#15689223C2218yescomplemented
37#15689221C2218yescomplemented
38C4×#10625337C2218yescomplemented
39C4×#10625336C2218yescomplemented
40C4×#10625335C2218yescomplemented
41C4×#10625334C2218yescomplemented
42#15689163C2214yescomplemented
43#15689163C2214yescomplemented
44C2×#13093957C2212yescomplemented
45C2×#13093955C2212yescomplemented
46#15689132C2212yescomplemented
47#15689128C2212yescomplemented
48#15689124C2212yescomplemented
49#15689124C2212yescomplemented
50#15689122C2214yes—
51#15689122C2214yescomplemented
52#15689119C2214yes—
53C2×#13093947C2212yescomplemented
54C2×#13093944C2212yescomplemented
55#15689079C2214yescomplemented
56#15689079C2214yescomplemented
57C4×#10625329C2214yescomplemented
58C22×#41×C47C2211yescharacteristic
59C47×#520—22no—
60C47×#520—22no—
61C47×#520C2214yes—
62C47×#520C2214yescomplemented
63C2×C4×Q8×C47C2212yescomplemented
64C2×C4×D4×C47—22no—
65C2×C4×D4×C47C2212yescomplemented
66C2×#117×C47—21no—
67C2×#117×C47C2211yescharacteristic
68C22×C4⋊C4×C47—21no—
69C22×C4⋊C4×C47C2211yescharacteristic
70C2×#10625350—21no—
71C2×#10625350—21no—
72C2×#10625350—24no—
73C2×#10625350C2×C418yescomplemented
74C2×#10625350C2312yes—
75C2×#10625350C2312yes—
76C22×Dic94C2311yescharacteristic
77C22×D188C2311yescharacteristic
78C22×C22⋊D47—21no—
79C22×C4×D47—21no—
80#13094055C2×C4116yescomplemented
81#13094054C2×C4116yescomplemented
82#13094050C2×C4116yescomplemented
83#13094049C2×C4116yescomplemented
84#13094044C2×C4132yescomplemented
85C2×#10625337C2314yes—
86C2×#10625335C2314yes—
87C2×#10625336C2314yes—
88C2×#10625334C2314yes—
89C2×#10625329—24no—
90C2×#10625329C2×C418yescomplemented
91C2×#10625329C2312yes—
92C2×#10625329C2312yes—
93C2×#10625329C2312yes—
94C2×#10625329C2312yes—
95C22×C47⋊C8C2312yes—
96C22×C47⋊C8C2312yes—
97C4×Dic94C2314yes—
98C4×Dic94C2314yes—
99#13093989—22no—
100#13093989—22no—
101C4×D188C2314yes—
102C4×D188C2314yes—
103#13093986—22no—
104#13093986—22no—
105C4×C22⋊D47—24no—
106C4×C22⋊D47—24no—
107(C22⋊D47)⋊C4—24no—
108(C22⋊D47)⋊C4—24no—
109#13093983—21no—
110#13093983—21no—
111#13093983C2312yes—
112#13093983C2312yes—
113#13093982—22no—
114#13093982—22no—
115#13093981—24no—
116#13093980—24no—
117C2×C4⋊Dic47C2311yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C4⋊C4×D47—22no—
120C4⋊C4×D47—22no—
121C2×C22⋊Dic47—21no—
122C22⋊C4×D47—24no—
123C2×C4×Dic47—21no—
124C42×D47—24no—
125#13093957C2318yes—
126#13093955C2318yes—
127#13093948C2314yes—
128#13093948C2314yes—
129#13093947C2318yes—
130#13093945C2314yes—
131#13093945C2314yes—
132#13093944C2318yes—
133#13093935C2318yes—
134C4×C47⋊C8C2318yes—
135C2×#41×C47—21no—
136C2×#41×C47—21no—
137C2×#41×C47—24no—
138C2×#41×C47C2×C418yescomplemented
139C2×#41×C47C2312yes—
140C2×#41×C47C2312yes—
141C22×Q8×C47C2311yescharacteristic
142C22×D4×C47—21no—
143C22×D4×C47C2311yescharacteristic
144C23×C4×C47—21no—
145C23×C4×C47—21no—
146C23×C4×C47—22no—
147C23×C4×C47C2311yescharacteristic
148C4×Q8×C47—24no—
149C4×Q8×C47C2318yes—
150C4×D4×C47—28no—
151C4×D4×C47—28no—
152C4×D4×C47—24no—
153C4×D4×C47C2318yes—
154#117×C47—24no—
155#117×C47—24no—
156#117×C47D412yes—
157#117×C47D412yes—
158#117×C47C2312yes—
159#117×C47C2312yes—
160C2×C4⋊C4×C47—21no—
161C2×C4⋊C4×C47—22no—
162C2×C4⋊C4×C47—21no—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47—24no—
165C2×C4⋊C4×C47—24no—
166C2×C4⋊C4×C47D411yescharacteristic
167C2×C4⋊C4×C47D411yescharacteristic
168C2×C4⋊C4×C47C2312yes—
169C2×C4⋊C4×C47C2312yes—
170C2×C4⋊C4×C47C2312yes—
171C2×C22⋊C4×C47—22no—
172C2×C22⋊C4×C47D412yes—
173C2×C42×C47—22no—
174C2×C42×C47C2312yes—
175C24×C47—21no—
176C24×C47C2×D411yescharacteristic
177C23×D47—21no—
178#41×C47—28no—
179#41×C47—28no—
180#41×C47—24no—
181#41×C47—24no—
182#41×C47C22×C418yes—
183#41×C47C22×C418yes—
184C2×Q8×C47—21no—
185C2×Q8×C47—22no—
186C2×Q8×C47C22×C414yes—
187C2×Q8×C47C2412yes—
188C2×D4×C47—28no—
189C2×D4×C47—22no—
190C2×D4×C47—22no—
191C2×D4×C47—21no—
192C2×D4×C47—22no—
193C2×D4×C47C22×C414yes—
194C2×D4×C47C2412yes—
195C22×C4×C47—21no—
196C22×C4×C47—28no—
197C22×C4×C47—22no—
198C22×C4×C47—22no—
199C22×C4×C47—22no—
200C22×C4×C47—22no—
201C22×C4×C47—22no—
202C22×C4×C47—28no—
203C22×C4×C47—84no—
204C22×C4×C47—82no—
205C22×C4×C47C22×C414yes—
206C22×C4×C47C2×D412yes—
207C22×C4×C47C2×D412yes—
208C22×C4×C47C2×D411yescharacteristic
209C22×C4×C47C2×D411yescharacteristic
210C22×C4×C47C2×D411yescharacteristic
211C22×C4×C47#4114yes—
212C22×C4×C47C2411yescharacteristic
213C22×C4×C47C2411yescharacteristic
214C22×C4×C47C2411yescharacteristic
215C2×C22⋊D47—28no—
216C2×C22⋊D47—22no—
217C2×C22⋊D47—22no—
218C22×Dic47—21no—
219C22×Dic47—21no—
220C22×Dic47—21no—
221#10625350—28no—
222#10625350—28no—
223#10625350—24no—
224#10625350—24no—
225#10625350C22×C418yes—
226#10625350C22×C418yescomplemented
227C2×D188—21no—
228C2×D188—22no—
229C2×D188C22×C414yescomplemented
230C2×D188C2412yes—
231C2×C4×D47—28no—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—24no—
235C2×C4×D47—24no—
236C2×Dic94—21no—
237C2×Dic94—22no—
238C2×Dic94C22×C414yescomplemented
239C2×Dic94C2412yes—
240C4⋊C4×C47—22no—
241C4⋊C4×C47—22no—
242C4⋊C4×C47—28no—
243C4⋊C4×C47—22no—
244C4⋊C4×C47C2×D412yes—
245C4⋊C4×C47C2×D412yes—
246C4⋊C4×C47C2×D412yes—
247C4⋊C4×C47C2×D412yes—
248C4⋊C4×C47C2414yes—
249C22⋊C4×C47—28no—
250C22⋊C4×C47C2×D414yes—
251C22⋊C4×C47C2×D414yes—
252C42×C47—28no—
253C42×C47C2×D414yes—
254C42×C47C2414yes—
255C22⋊Dic47—22no—
256C22⋊Dic47—22no—
257#10625337C22×C4116yescomplemented
258#10625336C22×C4116yescomplemented
259#10625335C22×C4116yescomplemented
260#10625334C22×C4116yescomplemented
261(C2×D47)⋊C4—24no—
262(C2×D47)⋊C4—24no—
263C4⋊Dic47—21no—
264C4⋊Dic47—21no—
265C4⋊Dic47C2412yes—
266C4⋊Dic47C2412yes—
267Dic47⋊C4—24no—
268Dic47⋊C4—24no—
269C4×Dic47—22no—
270C4×Dic47—24no—
271C4×Dic47—24no—
272C4×Dic47—22no—
273#10625329—24no—
274#10625329—24no—
275#10625329C22×C418yes—
276#10625329C22×C418yescomplemented
277C2×C47⋊C8—24no—
278C2×C47⋊C8C22×C418yescomplemented
279C2×C47⋊C8C2414yes—
280C2×C47⋊C8C2414yes—
281C23×C47—24no—
282C23×C47—22no—
283C23×C47—41no—
284C23×C47—41no—
285C23×C47—42no—
286C23×C47—42no—
287C23×C47C4×D414yes—
288C23×C47C22×D411yescharacteristic
289C23×C47C22×D411yescharacteristic
290C23×C47C22×D411yescharacteristic
291C22×D47—22no—
292C22×D47—24no—
293C22×D47—81no—
294C22×D47—81no—
295Q8×C47—24no—
296Q8×C47—22no—
297Q8×C47C23×C414yes—
298D4×C47—28no—
299D4×C47—28no—
300D4×C47—24no—
301D4×C47—22no—
302D4×C47C23×C414yes—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—28no—
306C2×C4×C47—28no—
307C2×C4×C47—24no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—44no—
311C2×C4×C47—88no—
312C2×C4×C47—82no—
313C2×C4×C47—82no—
314C2×C4×C47C4×D414yes—
315C2×C4×C47C4×D414yes—
316C2×C4×C47C4×D414yes—
317C2×C4×C47C23×C412yes—
318C2×C4×C47C23×C412yes—
319C2×C4×C47C23×C412yes—
320C2×C4×C47C22×D414yes—
321C2×C4×C47C22×D414yes—
322C2×C4×C47C22×D411yescharacteristic
323C2×C4×C47C22×D411yescharacteristic
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C2×#4112yes—
326C2×C4×C47C2×#4112yes—
327C2×C4×C47C2×#4112yes—
328C2×C4×C47C2511yescharacteristic
329C22⋊D47—28no—
330C22⋊D47—28no—
331C2×Dic47—24no—
332C2×Dic47—22no—
333C2×Dic47—22no—
334C2×Dic47—22no—
335C2×Dic47—81no—
336C2×Dic47—81no—
337D188—24no—
338D188—22no—
339D188C23×C414yes—
340C4×D47—28no—
341C4×D47—28no—
342C4×D47—84no—
343C4×D47—84no—
344Dic94—24no—
345Dic94—22no—
346Dic94C23×C414yes—
347C47⋊C8—24no—
348C47⋊C8C23×C418yes—
349#60170—471nomaximal, Sylow
350C22×C47—21no—
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—24no—
357C22×C47—44no—
358C22×C47—48no—
359C22×C47—42no—
360C22×C47—42no—
361C22×C47C2×C4×D412yes—
362C22×C47C2×C4×D412yes—
363C22×C47C2×C4×D412yes—
364C22×C47C23×D411yescharacteristic
365C2×D47—24no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—84no—
369C4×C47—24no—
370C4×C47—24no—
371C4×C47—24no—
372C4×C47—44no—
373C4×C47C2×C4×D412yes—
374C4×C47C2×C4×D412yes—
375C4×C47C2×C4×D412yes—
376C4×C47C24×C411yescharacteristic
377C4×C47C22×#4111yescharacteristic
378Dic47—24no—
379Dic47—42no—
380Dic47—42no—
381C2×#575—471no—
382#3428—471no—
383C2×#520D4711yescharacteristic, complemented
384#2952—474no—
385#2951—474no—
386#2947—474no—
387#2946—474no—
388C4×#137—474no—
389C4×AGL(1,ℤ/8)—474no—
390C2×#428—471no—
391#2896—471no—
392C2×#417—471no—
393#2873—471no—
394C2×C47—22no—
395C2×C47—22no—
396C2×C47—22no—
397C2×C47—44no—
398C2×C47C22×C4×D411yescharacteristic
399C2×C47#358511yescharacteristic
400C2×C47#358611yescharacteristic
401D47—44no—
402C22×#41—471no—
403C22×#41C2×D4711yescharacteristic
404#575—4716no—
405C2×#137—472no—
406C2×#137—472no—
407C2×AGL(1,ℤ/8)—472no—
408C2×AGL(1,ℤ/8)—472no—
409C2×#135—474no—
410C22×M16—471no—
411C22×M16—471no—
412#520—22no—
413#520—22no—
414#520—472no—
415#520—472no—
416#520—941no—
417#520—941no—
418#520C2×D4714yes—
419#520C2×D4714yescomplemented
420#519—472no—
421#518—472no—
422#518—942no—
423C4×#41—474no—
424C4×#41—942no—
425C2×C4×Q8C2×D4712yescomplemented
426C2×C4×D4—22no—
427C2×C4×D4C2×D4712yescomplemented
428C2×#117—21no—
429C2×#117—471no—
430C2×#117—942no—
431C2×#117C2×D4711yescharacteristic
432C22×C4⋊C4—21no—
433C22×C4⋊C4C2×D4711yescharacteristic
434#442—478no—
435#441—478no—
436#440—478no—
437#440—478no—
438C4×Q16—478no—
439C4×SD16—478no—
440C4×SD16—478no—
441C4×D8—478no—
442#428—474no—
443#428—474no—
444C2×#107—472no—
445C2×#106—472no—
446#419—472no—
447#418—472no—
448#417—472no—
449#417—472no—
450#417—474no—
451#417—474no—
452#416—474no—
453C2×#103—472no—
454C2×#102—472no—
455#405—474no—
456#405—474no—
457C4×M16—474no—
458C47#6017011yescharacteristic, complemented, Sylow
459C2×#41—24no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—478no—
463C2×#41—472no—
464C2×#41—472no—
465C2×#41—944no—
466C2×#41—941no—
467C2×#41—941no—
468C2×#41C4×D4718yescomplemented
469C2×#41C22×D4712yes—
470C2×#41C22×D4712yes—
471C22×Q8—471no—
472C22×Q8C22×D4711yescharacteristic
473C22×D4—21no—
474C22×D4—471no—
475C22×D4—941no—
476C22×D4C22×D4711yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—22no—
480C23×C4—941no—
481C23×C4C22×D4711yescharacteristic
482#137—4716no—
483#137—4716no—
484AGL(1,ℤ/8)—4716no—
485AGL(1,ℤ/8)—4716no—
486#135—4732no—
487C2×Q16—474no—
488C2×SD16—474no—
489C2×SD16—474no—
490C2×D8—474no—
491C2×M16—478no—
492C2×M16—472no—
493C2×M16—472no—
494C2×M16—472no—
495C2×M16—472no—
496C2×M16—944no—
497C22×C8—472no—
498C22×C8—472no—
499C4×Q8—24no—
500C4×Q8—474no—
501C4×Q8—474no—
502C4×Q8—942no—
503C4×Q8—942no—
504C4×Q8C22×D4718yes—
505C4×D4—28no—
506C4×D4—28no—
507C4×D4—24no—
508C4×D4—474no—
509C4×D4—474no—
510C4×D4—944no—
511C4×D4—944no—
512C4×D4—942no—
513C4×D4—942no—
514C4×D4—944no—
515C4×D4—944no—
516C4×D4C22×D4718yes—
517#117—24no—
518#117—24no—
519#117—472no—
520#117—472no—
521#117—941no—
522#117—941no—
523#117—942no—
524#117—942no—
525#117—944no—
526#117—944no—
527#117C22⋊D4712yes—
528#117C22⋊D4712yes—
529#117C22×D4712yes—
530#117C22×D4712yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—24no—
536C2×C4⋊C4—24no—
537C2×C4⋊C4—471no—
538C2×C4⋊C4—471no—
539C2×C4⋊C4—942no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4C22⋊D4711yescharacteristic
542C2×C4⋊C4C22⋊D4711yescharacteristic
543C2×C4⋊C4C22×D4712yes—
544C2×C4⋊C4C22×D4712yes—
545C2×C4⋊C4C22×D4712yes—
546C2×C22⋊C4—22no—
547C2×C22⋊C4—941no—
548C2×C22⋊C4—944no—
549C2×C22⋊C4C22⋊D4712yes—
550C2×C42—22no—
551C2×C42—941no—
552C2×C42—944no—
553C2×C42C22×D4712yes—
554#107—478no—
555#106—478no—
556#103—474no—
557#103—474no—
558#103—478no—
559#102—474no—
560#102—474no—
561#102—478no—
562#97—478no—
563C4×C8—478no—
564C24—21no—
565C24—941no—
566C24C2×C22⋊D4711yescharacteristic
567#41—28no—
568#41—28no—
569#41—24no—
570#41—24no—
571#41—478no—
572#41—478no—
573#41—948no—
574#41—948no—
575#41—944no—
576#41—944no—
577#41C2×C4×D4718yes—
578#41C2×C4×D4718yes—
579C2×Q8—21no—
580C2×Q8—22no—
581C2×Q8—474no—
582C2×Q8—472no—
583C2×Q8—941no—
584C2×Q8—942no—
585C2×Q8C2×C4×D4714yes—
586C2×Q8C23×D4712yes—
587C2×D4—28no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—474no—
593C2×D4—472no—
594C2×D4—948no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—941no—
598C2×D4—942no—
599C2×D4C2×C4×D4714yes—
600C2×D4C23×D4712yes—
601C22×C4—21no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—28no—
609C22×C4—84no—
610C22×C4—82no—
611C22×C4—941no—
612C22×C4—948no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—941no—
616C22×C4—941no—
617C22×C4—944no—
618C22×C4—944no—
619C22×C4C2×C4×D4714yes—
620C22×C4#1062535014yes—
621C22×C4C2×C22⋊D4712yes—
622C22×C4C2×C22⋊D4712yes—
623C22×C4C2×C22⋊D4711yescharacteristic
624C22×C4C2×C22⋊D4711yescharacteristic
625C22×C4C2×C22⋊D4711yescharacteristic
626C22×C4C23×D4711yescharacteristic
627C22×C4C23×D4711yescharacteristic
628C22×C4C23×D4711yescharacteristic
629Q16—4716no—
630SD16—4716no—
631SD16—4716no—
632D8—4716no—
633M16—478no—
634M16—478no—
635M16—944no—
636M16—944no—
637C2×C8—478no—
638C2×C8—474no—
639C2×C8—474no—
640C2×C8—944no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—28no—
644C4⋊C4—22no—
645C4⋊C4—472no—
646C4⋊C4—472no—
647C4⋊C4—944no—
648C4⋊C4—944no—
649C4⋊C4—941no—
650C4⋊C4—941no—
651C4⋊C4C2×C22⋊D4712yes—
652C4⋊C4C2×C22⋊D4712yes—
653C4⋊C4C2×C22⋊D4712yes—
654C4⋊C4C2×C22⋊D4712yes—
655C4⋊C4C23×D4714yes—
656C22⋊C4—28no—
657C22⋊C4—942no—
658C22⋊C4—942no—
659C22⋊C4—944no—
660C22⋊C4—944no—
661C22⋊C4C2×C22⋊D4714yes—
662C22⋊C4C2×C22⋊D4714yes—
663C42—28no—
664C42—942no—
665C42—942no—
666C42—944no—
667C42—944no—
668C42C2×C22⋊D4714yes—
669C42C23×D4714yes—
670C23—24no—
671C23—22no—
672C23—41no—
673C23—41no—
674C23—42no—
675C23—42no—
676C23—944no—
677C23—942no—
678C23—3761no—
679C23—3761no—
680C23C4×C22⋊D4714yes—
681C23C22×C22⋊D4711yescharacteristic
682C23C22×C22⋊D4711yescharacteristic
683C23C22×C22⋊D4711yescharacteristic
684Q8—24no—
685Q8—22no—
686Q8—474no—
687Q8—944no—
688Q8—942no—
689Q8C22×C4×D4714yes—
690D4—28no—
691D4—28no—
692D4—24no—
693D4—22no—
694D4—474no—
695D4—948no—
696D4—948no—
697D4—944no—
698D4—942no—
699D4C22×C4×D4714yes—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—24no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—88no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—944no—
712C2×C4—942no—
713C2×C4—948no—
714C2×C4—948no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—3764no—
718C2×C4—3764no—
719C2×C4—3761no—
720C2×C4—3761no—
721C2×C4C4×C22⋊D4714yes—
722C2×C4C4×C22⋊D4714yes—
723C2×C4C4×C22⋊D4714yes—
724C2×C4C22×C4×D4712yes—
725C2×C4C22×C4×D4712yes—
726C2×C4C22×C4×D4712yes—
727C2×C4C22×C22⋊D4714yes—
728C2×C4C22×C22⋊D4714yes—
729C2×C4C22×C22⋊D4711yescharacteristic
730C2×C4C22×C22⋊D4711yescharacteristic
731C2×C4C22×C22⋊D4711yescharacteristic
732C2×C4C2×#1062535012yes—
733C2×C4C2×#1062535012yes—
734C2×C4C2×#1062535012yes—
735C2×C4C24×D4711yescharacteristic
736C8—478no—
737C8—944no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—24no—
745C22—44no—
746C22—48no—
747C22—42no—
748C22—42no—
749C22—944no—
750C22—3764no—
751C22—1882no—
752C22—1882no—
753C22C2×C4×C22⋊D4712yes—
754C22C2×C4×C22⋊D4712yes—
755C22C2×C4×C22⋊D4712yes—
756C22C23×C22⋊D4711yescharacteristic
757C4—24no—
758C4—24no—
759C4—24no—
760C4—44no—
761C4—944no—
762C4—1882no—
763C4—1882no—
764C4C2×C4×C22⋊D4712yes—
765C4C2×C4×C22⋊D4712yes—
766C4C2×C4×C22⋊D4712yes—
767C4C23×C4×D4711yescharacteristic
768C4C22×#1062535011yescharacteristic
769C2—22no—
770C2—22no—
771C2—22no—
772C2—44no—
773C2—1884no—
774C2C22×C4×C22⋊D4711yescharacteristic
775C2#2025816811yescharacteristic
776C2#2025817511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#520C2
socleC22×C47C23×D4
prime radicalC2×#15689921C2
cosocleC2×C4×C47C25
hypercenterC2×#520D47
hypocenterC47#60170
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
2. #20256589C2semidirect
3. #20252269C2semidirect
4. #20252261C2semidirect
5. #20252227C2semidirect
6. #20252216C2semidirect
7. C4×#13094055C2semidirect
8. C4×#13094050C2semidirect
9. C2×#15689163C2semidirect
10. #20251907C2semidirect
11. C2×#15689122C2semidirect
12. #20251807C2semidirect
13. C2×C47×#520C2semidirect
15. #15689921C4semidirect
25. #15689603C22semidirect
26. #15689603C22semidirect
27. #15689600C22semidirect
28. #15689597C22semidirect
34. #15689233C22semidirect
35. #15689228C22semidirect
36. #15689223C22semidirect
37. #15689221C22semidirect
38. C4×#10625337C22semidirect
39. C4×#10625336C22semidirect
40. C4×#10625335C22semidirect
41. C4×#10625334C22semidirect
42. #15689163C22semidirect
43. #15689163C22semidirect
44. C2×#13093957C22semidirect
45. C2×#13093955C22semidirect
46. #15689132C22semidirect
47. #15689128C22semidirect
48. #15689124C22semidirect
49. #15689124C22semidirect
51. #15689122C22semidirect
53. C2×#13093947C22semidirect
54. C2×#13093944C22semidirect
55. #15689079C22semidirect
56. #15689079C22semidirect
57. C4×#10625329C22semidirect
62. C47×#520C22semidirect
63. C2×C4×Q8×C47C22semidirect
65. C2×C4×D4×C47C22semidirect
73. C2×#10625350C2×C4semidirect
80. #13094055C2×C4semidirect
81. #13094054C2×C4semidirect
82. #13094050C2×C4semidirect
83. #13094049C2×C4semidirect
84. #13094044C2×C4semidirect
90. C2×#10625329C2×C4semidirect
138. C2×#41×C47C2×C4semidirect
226. #10625350C22×C4semidirect
229. C2×D188C22×C4semidirect
238. C2×Dic94C22×C4semidirect
257. #10625337C22×C4semidirect
258. #10625336C22×C4semidirect
259. #10625335C22×C4semidirect
260. #10625334C22×C4semidirect
276. #10625329C22×C4semidirect
278. C2×C47⋊C8C22×C4semidirect
383. C2×#520D47semidirect
419. #520C2×D47semidirect
425. C2×C4×Q8C2×D47semidirect
427. C2×C4×D4C2×D47semidirect
458. C47#60170semidirect
468. C2×#41C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
#202565892
#202522692
#202522612
#202522272
#202522162
C4×#130940552
C4×#130940502
C2×#156891632
#202519072
C2×#156891222
#202518072
C2×C47×#5202
#6017047