Finite Group Databasebeta

← #27080485

Subgroups — #27080485

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×#15689923C211yesmaximal, characteristic
2#20256589C211yesmaximal, characteristic, complemented
3C2×#15689604C211yesmaximal, characteristic, complemented
4#20252271C214yesmaximal, complemented
5#20252262C214yesmaximal, complemented
6#20252229C214yesmaximal, complemented
7#20252218C214yesmaximal, complemented
8#20252206C214yesmaximal, complemented
9#20252195C214yesmaximal, complemented
10#20251905C211yesmaximal, characteristic, complemented
11C2×#15689122C211yesmaximal, characteristic, complemented
12#20251806C211yesmaximal, characteristic, complemented
13C2×C47×#428C211yesmaximal, characteristic, complemented
14C22×#10625350C2211yescharacteristic
15C22×#10625350C2211yescharacteristic
16#15689923C4116yescomplemented
17C2×#13094057C2212yes—
18C2×#13094057C2212yes—
19C2×#13094052C2212yes—
20C2×#13094052C2212yes—
21C2×#13094046C2214yes—
22C22×#10625329C2211yescharacteristic
23#15689604—22no—
24#15689604—22no—
25#15689604C2214yes—
26#15689604C2214yescomplemented
27#15689604C2212yescomplemented
28#15689604C2212yescomplemented
29#15689603—21no—
30#15689603—21no—
31#15689600C2212yescomplemented
32#15689597C2212yescomplemented
33#15689596—22no—
34C4×#10625350—22no—
35#15689591C2214yes—
36C2×#13093989C2212yescomplemented
37C2×#13093986C2212yescomplemented
38C2×C4×C22⋊D47—22no—
39C2×#13093983C2211yescharacteristic
40C2×#13093982—21no—
41#117×D47—22no—
42C2×C4⋊C4×D47—21no—
43#15689234C2218yescomplemented
44#15689229C2218yescomplemented
45#15689222C2218yescomplemented
46#15689222C2218yescomplemented
47#15689217C2218yescomplemented
48#15689210C2218yescomplemented
49#15689210C2218yescomplemented
50#15689205C2218yescomplemented
51#15689131C2212yescomplemented
52#15689127C2212yescomplemented
53#15689122C2214yes—
54#15689122C2212yescomplemented
55#15689122C2212yescomplemented
56#15689122C2214yescomplemented
57#15689117C2214yes—
58C2×#13093947C2212yescomplemented
59C2×#13093944C2212yescomplemented
60#15689081C2214yescomplemented
61#15689078C2214yescomplemented
62M16×Dic47C2214yescomplemented
63C22×M16×C47C2211yescharacteristic
64C2×#117×C47C2211yescharacteristic
65C22×C4⋊C4×C47C2211yescharacteristic
66C47×#428C2214yescomplemented
67C47×#428C2214yescomplemented
68C2×#107×C47C2212yescomplemented
69C2×#106×C47C2212yescomplemented
70C2×#10625350—21no—
71C2×#10625350—21no—
72C2×#10625350—21no—
73C2×#10625350—21no—
74C2×#10625350—24no—
75C2×#10625350—24no—
76C2×#10625350C2×C418yescomplemented
77C2×#10625350C2×C418yescomplemented
78C2×#10625350C2312yes—
79C2×#10625350C2312yes—
80C2×#10625350C2312yes—
81C2×#10625350C2312yes—
82C22×Dic94C2311yescharacteristic
83C22×Dic94C2311yescharacteristic
84C22×D188C2311yescharacteristic
85C22×D188C2311yescharacteristic
86C22×C22⋊D47—21no—
87C22×C22⋊D47—21no—
88C22×C4×D47—21no—
89C22×C4×D47—21no—
90C22×C4×D47—22no—
91#13094057C2×C4116yescomplemented
92#13094057C2×C4116yescomplemented
93#13094052C2×C4116yescomplemented
94#13094052C2×C4116yescomplemented
95#13094046C2×C4132yescomplemented
96C2×Dic188C2314yes—
97C2×#10625325C2314yes—
98C2×#10625325C2314yes—
99C2×D376C2314yes—
100C2×#10625329—24no—
101C2×#10625329C2312yes—
102C2×#10625329C2312yes—
103C22×C47⋊C8C2312yes—
104C4×Dic94—22no—
105C4×Dic94—22no—
106#13093989—24no—
107#13093989C2314yes—
108#13093989C2318yes—
109#13093989C2314yes—
110C4×D188—22no—
111C4×D188—22no—
112#13093986—24no—
113#13093986C2314yes—
114#13093986C2318yes—
115#13093986C2314yes—
116C4×C22⋊D47—28no—
117C4×C22⋊D47—28no—
118C4×C22⋊D47—24no—
119C4×C22⋊D47—24no—
120(C22⋊D47)⋊C4—24no—
121(C22⋊D47)⋊C4—24no—
122#13093983D412yes—
123#13093983D412yes—
124#13093983C2312yes—
125#13093983C2312yes—
126#13093982—22no—
127#13093982—22no—
128#13093982—24no—
129#13093982—24no—
130#13093981—24no—
131#13093980—24no—
132C2×C4⋊Dic47D411yescharacteristic
133C2×C4⋊Dic47D411yescharacteristic
134C2×Dic47⋊C4—22no—
135C4⋊C4×D47—24no—
136C4⋊C4×D47—24no—
137C4⋊C4×D47—22no—
138C4⋊C4×D47—22no—
139C2×C22⋊Dic47D412yes—
140C2×(C2×D47)⋊C4—22no—
141C22⋊C4×D47—24no—
142C2×C4×Dic47—22no—
143C2×C4×Dic47C2312yes—
144C42×D47—24no—
145#13093947C2314yes—
146#13093947C2318yes—
147#13093947C2314yes—
148#13093944C2314yes—
149#13093944C2318yes—
150#13093944C2314yes—
151#13093934C2318yes—
152C8×Dic47C2318yes—
153C23×C4×C47—21no—
154C23×C4×C47C2311yescharacteristic
155C2×M16×C47C2×C418yescomplemented
156C2×M16×C47C2312yes—
157C2×M16×C47C2312yes—
158C22×C8×C47C2312yes—
159#117×C47—21no—
160#117×C47—21no—
161#117×C47C2312yes—
162#117×C47C2312yes—
163C2×C4⋊C4×C47—21no—
164C2×C4⋊C4×C47—21no—
165C2×C4⋊C4×C47—21no—
166C2×C4⋊C4×C47C2312yes—
167C2×C4⋊C4×C47C2312yes—
168C2×C4⋊C4×C47C2312yes—
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C42×C47—21no—
173#107×C47C2318yes—
174#106×C47C2318yes—
175C24×C47C2×D411yescharacteristic
176C23×D47—21no—
177C23×D47—21no—
178C22×C4×C47—22no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—82no—
184C22×C4×C47C22×C414yes—
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47#4114yes—
189C22×C4×C47C2411yescharacteristic
190C22×C4×C47C2411yescharacteristic
191C22×C4×C47C2411yescharacteristic
192C2×C22⋊D47—28no—
193C2×C22⋊D47—28no—
194C2×C22⋊D47—22no—
195C2×C22⋊D47—22no—
196C2×C22⋊D47—22no—
197C2×C22⋊D47—22no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47C2×D412yes—
201C22×Dic47C2×D412yes—
202#10625350—28no—
203#10625350—28no—
204#10625350—28no—
205#10625350—28no—
206#10625350—24no—
207#10625350—24no—
208#10625350—24no—
209#10625350—24no—
210#10625350C22×C418yes—
211#10625350C22×C418yes—
212#10625350C22×C418yes—
213#10625350C22×C418yescomplemented
214C2×D188—21no—
215C2×D188—21no—
216C2×D188—22no—
217C2×D188—22no—
218C2×D188C22×C414yes—
219C2×D188C22×C414yescomplemented
220C2×D188C2412yes—
221C2×D188C2412yes—
222C2×C4×D47—28no—
223C2×C4×D47—28no—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—24no—
229C2×C4×D47—24no—
230C2×C4×D47—28no—
231C2×C4×D47—84no—
232C2×Dic94—21no—
233C2×Dic94—21no—
234C2×Dic94—22no—
235C2×Dic94—22no—
236C2×Dic94C22×C414yes—
237C2×Dic94C22×C414yescomplemented
238C2×Dic94C2412yes—
239C2×Dic94C2412yes—
240M16×C47C22×C418yes—
241M16×C47C22×C418yescomplemented
242C2×C8×C47C22×C418yescomplemented
243C2×C8×C47C2414yes—
244C4⋊C4×C47—22no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—22no—
247C4⋊C4×C47—21no—
248C4⋊C4×C47—21no—
249C4⋊C4×C47C2412yes—
250C4⋊C4×C47C2414yes—
251C4⋊C4×C47C2412yes—
252C22⋊C4×C47—22no—
253C22⋊C4×C47—22no—
254C42×C47—22no—
255C42×C47—22no—
256C22⋊Dic47C2×D414yes—
257C22⋊Dic47C2×D414yes—
258(C2×D47)⋊C4—24no—
259(C2×D47)⋊C4—24no—
260(C2×D47)⋊C4—28no—
261C4⋊Dic47C2×D412yes—
262C4⋊Dic47C2×D412yes—
263C4⋊Dic47C2×D412yes—
264C4⋊Dic47C2×D412yes—
265Dic47⋊C4—28no—
266Dic47⋊C4—24no—
267Dic47⋊C4—24no—
268C4×Dic47—24no—
269C4×Dic47—24no—
270C4×Dic47—28no—
271C4×Dic47C2×D414yes—
272C4×Dic47C2414yes—
273#10625329—24no—
274#10625329—24no—
275C2×C47⋊C8—24no—
276C2×C47⋊C8C2414yes—
277Dic188C22×C4116yescomplemented
278D376C22×C4116yescomplemented
279#10625325C22×C4116yescomplemented
280#10625325C22×C4116yescomplemented
281C23×C47—41no—
282C23×C47—41no—
283C23×C47C4×D414yes—
284C23×C47C22×D411yescharacteristic
285C23×C47C22×D411yescharacteristic
286C23×C47C22×D411yescharacteristic
287C22×D47—24no—
288C22×D47—22no—
289C22×D47—22no—
290C22×D47—24no—
291C22×D47—42no—
292C22×D47—42no—
293C22×D47—81no—
294C22×D47—81no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—24no—
298C2×C4×C47—44no—
299C2×C4×C47—81no—
300C2×C4×C47—81no—
301C2×C4×C47—82no—
302C2×C4×C47—82no—
303C2×C4×C47C4×D414yes—
304C2×C4×C47C4×D414yes—
305C2×C4×C47C4×D414yes—
306C2×C4×C47C23×C412yes—
307C2×C4×C47C23×C412yes—
308C2×C4×C47C23×C412yes—
309C2×C4×C47C22×D411yescharacteristic
310C2×C4×C47C22×D411yescharacteristic
311C2×C4×C47C22×D411yescharacteristic
312C2×C4×C47C2×#4112yes—
313C2×C4×C47C2×#4112yes—
314C2×C4×C47C2×#4112yes—
315C2×C4×C47C2511yescharacteristic
316C22⋊D47—28no—
317C22⋊D47—28no—
318C22⋊D47—28no—
319C22⋊D47—28no—
320C2×Dic47—24no—
321C2×Dic47—24no—
322C2×Dic47—22no—
323C2×Dic47—22no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47C22×D414yes—
327C2×Dic47C22×D414yes—
328D188—24no—
329D188—24no—
330D188—22no—
331D188—22no—
332D188C23×C414yes—
333D188C23×C414yes—
334C4×D47—28no—
335C4×D47—28no—
336C4×D47—28no—
337C4×D47—28no—
338C4×D47—84no—
339C4×D47—84no—
340C4×D47—88no—
341Dic94—24no—
342Dic94—24no—
343Dic94—22no—
344Dic94—22no—
345Dic94C23×C414yes—
346Dic94C23×C414yes—
347C8×C47C23×C418yes—
348C47⋊C8—24no—
349#60170—471nomaximal, Sylow
350C22×C47—21no—
351C22×C47—21no—
352C22×C47—21no—
353C22×C47—21no—
354C22×C47—21no—
355C22×C47—21no—
356C22×C47—44no—
357C22×C47C2×C4×D412yes—
358C22×C47C2×C4×D412yes—
359C22×C47C2×C4×D412yes—
360C22×C47C23×D411yescharacteristic
361C2×D47—24no—
362C2×D47—24no—
363C2×D47—48no—
364C2×D47—42no—
365C2×D47—42no—
366C2×D47—42no—
367C2×D47—42no—
368C2×D47—84no—
369C4×C47—44no—
370C4×C47—42no—
371C4×C47—42no—
372C4×C47C2×C4×D412yes—
373C4×C47C2×C4×D412yes—
374C4×C47C2×C4×D412yes—
375C4×C47C24×C411yescharacteristic
376C4×C47C22×#4111yescharacteristic
377Dic47—24no—
378Dic47—24no—
379Dic47—24no—
380Dic47—24no—
381C2×#575—471no—
382#3428—471no—
383C2×#520—471no—
384#2952—474no—
385#2951—474no—
386#2947—474no—
387#2946—474no—
388C4×#137—474no—
389C4×AGL(1,ℤ/8)—474no—
390C2×#428D4711yescharacteristic, complemented
391#2896—471no—
392C2×#417—471no—
393#2873—471no—
394C2×C47—22no—
395C2×C47—22no—
396C2×C47—22no—
397C2×C47C22×C4×D411yescharacteristic
398C2×C47#358511yescharacteristic
399C2×C47#358611yescharacteristic
400D47—44no—
401D47—44no—
402C22×#41—471no—
403C22×#41—471no—
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×M16C2×D4711yescharacteristic
412#520—474no—
413#520—474no—
414#520—472no—
415#520—472no—
416#520—942no—
417#520—942no—
418#520—941no—
419#520—941no—
420#519—472no—
421#518—472no—
422#518—942no—
423C4×#41—474no—
424C4×#41—942no—
425C2×C4×Q8—472no—
426C2×C4×D4—472no—
427C2×C4×D4—942no—
428C2×#117—471no—
429C2×#117—941no—
430C2×#117—942no—
431C2×#117C2×D4711yescharacteristic
432C22×C4⋊C4—941no—
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#428C2×D4714yescomplemented
443#428C2×D4714yescomplemented
444C2×#107C2×D4712yescomplemented
445C2×#106C2×D4712yescomplemented
446#419—472no—
447#418—472no—
448#417—474no—
449#417—474no—
450#417—472no—
451#417—472no—
452#416—474no—
453C2×#103—472no—
454C2×#102—472no—
455#405—474no—
456#405—474no—
457C4×M16—474no—
458C47#6017011yescharacteristic, complemented, Sylow
459C2×#41—478no—
460C2×#41—478no—
461C2×#41—472no—
462C2×#41—472no—
463C2×#41—472no—
464C2×#41—472no—
465C2×#41—941no—
466C2×#41—941no—
467C2×#41—941no—
468C2×#41—941no—
469C2×#41—944no—
470C2×#41—944no—
471C22×Q8—471no—
472C22×Q8—471no—
473C22×D4—471no—
474C22×D4—471no—
475C22×D4—941no—
476C22×D4—941no—
477C23×C4—21no—
478C23×C4—942no—
479C23×C4—941no—
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—472no—
492C2×M16—472no—
493C2×M16—944no—
494C2×M16C4×D4718yescomplemented
495C2×M16C22×D4712yes—
496C2×M16C22×D4712yes—
497C22×C8—472no—
498C22×C8C22×D4712yes—
499C4×Q8—478no—
500C4×Q8—474no—
501C4×Q8—474no—
502C4×Q8—942no—
503C4×Q8—942no—
504C4×Q8—944no—
505C4×D4—478no—
506C4×D4—474no—
507C4×D4—474no—
508C4×D4—942no—
509C4×D4—942no—
510C4×D4—944no—
511C4×D4—944no—
512C4×D4—944no—
513C4×D4—948no—
514C4×D4—948no—
515C4×D4—944no—
516C4×D4—944no—
517#117—21no—
518#117—21no—
519#117—472no—
520#117—472no—
521#117—472no—
522#117—472no—
523#117—944no—
524#117—944no—
525#117—944no—
526#117—944no—
527#117—942no—
528#117—942no—
529#117C22×D4712yes—
530#117C22×D4712yes—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—471no—
535C2×C4⋊C4—471no—
536C2×C4⋊C4—944no—
537C2×C4⋊C4—944no—
538C2×C4⋊C4—942no—
539C2×C4⋊C4—942no—
540C2×C4⋊C4—942no—
541C2×C4⋊C4C22×D4712yes—
542C2×C4⋊C4C22×D4712yes—
543C2×C4⋊C4C22×D4712yes—
544C2×C4⋊C4C22×D4711yescharacteristic
545C2×C4⋊C4C22×D4711yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—472no—
548C2×C22⋊C4—944no—
549C2×C22⋊C4—942no—
550C2×C42—21no—
551C2×C42—472no—
552C2×C42—944no—
553C2×C42—942no—
554#107C22×D4718yes—
555#106C22×D4718yes—
556#103—478no—
557#103—474no—
558#103—474no—
559#102—478no—
560#102—474no—
561#102—474no—
562#97—478no—
563C4×C8—478no—
564C24—941no—
565C24—941no—
566C24D4×D4711yescharacteristic
567#41—478no—
568#41—478no—
569#41—478no—
570#41—478no—
571#41—948no—
572#41—948no—
573#41—948no—
574#41—948no—
575#41—944no—
576#41—944no—
577#41—944no—
578#41—944no—
579C2×Q8—474no—
580C2×Q8—474no—
581C2×Q8—472no—
582C2×Q8—472no—
583C2×Q8—941no—
584C2×Q8—941no—
585C2×Q8—942no—
586C2×Q8—942no—
587C2×D4—474no—
588C2×D4—474no—
589C2×D4—472no—
590C2×D4—472no—
591C2×D4—948no—
592C2×D4—948no—
593C2×D4—942no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—941no—
598C2×D4—941no—
599C2×D4—942no—
600C2×D4—942no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—82no—
607C22×C4—472no—
608C22×C4—472no—
609C22×C4—944no—
610C22×C4—944no—
611C22×C4—948no—
612C22×C4—941no—
613C22×C4—941no—
614C22×C4—948no—
615C22×C4—948no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—3764no—
621C22×C4C2×C4×D4714yes—
622C22×C4D4×D4711yescharacteristic
623C22×C4D4×D4711yescharacteristic
624C22×C4D4×D4711yescharacteristic
625C22×C4#1062535414yes—
626C22×C4C23×D4711yescharacteristic
627C22×C4C23×D4711yescharacteristic
628C22×C4C23×D4711yescharacteristic
629Q16—4716no—
630SD16—4716no—
631SD16—4716no—
632D8—4716no—
633M16—944no—
634M16—944no—
635M16C2×C4×D4718yes—
636M16C2×C4×D4718yescomplemented
637C2×C8—474no—
638C2×C8—944no—
639C2×C8C2×C4×D4718yescomplemented
640C2×C8C23×D4714yes—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—472no—
647C4⋊C4—472no—
648C4⋊C4—472no—
649C4⋊C4—472no—
650C4⋊C4—948no—
651C4⋊C4—944no—
652C4⋊C4—944no—
653C4⋊C4C23×D4712yes—
654C4⋊C4C23×D4714yes—
655C4⋊C4C23×D4712yes—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—474no—
659C22⋊C4—474no—
660C22⋊C4—944no—
661C22⋊C4—944no—
662C22⋊C4—948no—
663C42—22no—
664C42—22no—
665C42—474no—
666C42—474no—
667C42—944no—
668C42—944no—
669C42—948no—
670C23—41no—
671C23—41no—
672C23—944no—
673C23—944no—
674C23—942no—
675C23—942no—
676C23—3761no—
677C23—3761no—
678C23—1882no—
679C23—1882no—
680C23#1309398614yes—
681C23C2×D4×D4711yescharacteristic
682C23C2×D4×D4711yescharacteristic
683C23C2×D4×D4711yescharacteristic
684Q8—474no—
685Q8—474no—
686Q8—944no—
687Q8—944no—
688Q8—942no—
689Q8—942no—
690D4—474no—
691D4—474no—
692D4—948no—
693D4—948no—
694D4—948no—
695D4—948no—
696D4—944no—
697D4—944no—
698D4—942no—
699D4—942no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—44no—
704C2×C4—81no—
705C2×C4—81no—
706C2×C4—82no—
707C2×C4—82no—
708C2×C4—474no—
709C2×C4—474no—
710C2×C4—944no—
711C2×C4—944no—
712C2×C4—942no—
713C2×C4—942no—
714C2×C4—948no—
715C2×C4—948no—
716C2×C4—948no—
717C2×C4—948no—
718C2×C4—3764no—
719C2×C4—3764no—
720C2×C4—3768no—
721C2×C4—1882no—
722C2×C4—1882no—
723C2×C4#1309398614yes—
724C2×C4#1309398614yes—
725C2×C4#1309398614yes—
726C2×C4C22×C4×D4712yes—
727C2×C4C22×C4×D4712yes—
728C2×C4C22×C4×D4712yes—
729C2×C4C2×D4×D4711yescharacteristic
730C2×C4C2×D4×D4711yescharacteristic
731C2×C4C2×D4×D4711yescharacteristic
732C2×C4C2×#1062535412yes—
733C2×C4C2×#1062535412yes—
734C2×C4C2×#1062535412yes—
735C2×C4C24×D4711yescharacteristic
736C8—944no—
737C8C22×C4×D4718yes—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—944no—
746C22—944no—
747C22—3764no—
748C22—1888no—
749C22—1882no—
750C22—1882no—
751C22—1882no—
752C22—1882no—
753C22C2×#1309398612yes—
754C22C2×#1309398612yes—
755C22C2×#1309398612yes—
756C22C22×D4×D4711yescharacteristic
757C4—44no—
758C4—42no—
759C4—42no—
760C4—944no—
761C4—944no—
762C4—944no—
763C4—944no—
764C4C2×#1309398612yes—
765C4C2×#1309398612yes—
766C4C2×#1309398612yes—
767C4C23×C4×D4711yescharacteristic
768C4C22×#1062535411yescharacteristic
769C2—22no—
770C2—22no—
771C2—22no—
772C2—1884no—
773C2—1884no—
774C2C22×#1309398611yescharacteristic
775C2#2025816411yescharacteristic
776C2#2025817111yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC2×C47×#428C2
socleC22×C47C23×D4
prime radicalC2×#15689923C2
cosocleC2×C4×C47C25
hypercenterC2×#428D47
hypocenterC47#60170
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
2. #20256589C2semidirect
3. C2×#15689604C2semidirect
4. #20252271C2semidirect
5. #20252262C2semidirect
6. #20252229C2semidirect
7. #20252218C2semidirect
8. #20252206C2semidirect
9. #20252195C2semidirect
10. #20251905C2semidirect
11. C2×#15689122C2semidirect
12. #20251806C2semidirect
13. C2×C47×#428C2semidirect
16. #15689923C4semidirect
26. #15689604C22semidirect
27. #15689604C22semidirect
28. #15689604C22semidirect
31. #15689600C22semidirect
32. #15689597C22semidirect
36. C2×#13093989C22semidirect
37. C2×#13093986C22semidirect
43. #15689234C22semidirect
44. #15689229C22semidirect
45. #15689222C22semidirect
46. #15689222C22semidirect
47. #15689217C22semidirect
48. #15689210C22semidirect
49. #15689210C22semidirect
50. #15689205C22semidirect
51. #15689131C22semidirect
52. #15689127C22semidirect
54. #15689122C22semidirect
55. #15689122C22semidirect
56. #15689122C22semidirect
58. C2×#13093947C22semidirect
59. C2×#13093944C22semidirect
60. #15689081C22semidirect
61. #15689078C22semidirect
62. M16×Dic47C22semidirect
66. C47×#428C22semidirect
67. C47×#428C22semidirect
68. C2×#107×C47C22semidirect
69. C2×#106×C47C22semidirect
76. C2×#10625350C2×C4semidirect
77. C2×#10625350C2×C4semidirect
91. #13094057C2×C4semidirect
92. #13094057C2×C4semidirect
93. #13094052C2×C4semidirect
94. #13094052C2×C4semidirect
95. #13094046C2×C4semidirect
155. C2×M16×C47C2×C4semidirect
213. #10625350C22×C4semidirect
219. C2×D188C22×C4semidirect
237. C2×Dic94C22×C4semidirect
241. M16×C47C22×C4semidirect
242. C2×C8×C47C22×C4semidirect
277. Dic188C22×C4semidirect
278. D376C22×C4semidirect
279. #10625325C22×C4semidirect
280. #10625325C22×C4semidirect
390. C2×#428D47semidirect
442. #428C2×D47semidirect
443. #428C2×D47semidirect
444. C2×#107C2×D47semidirect
445. C2×#106C2×D47semidirect
458. C47#60170semidirect
494. C2×M16C4×D47semidirect
636. M16C2×C4×D47semidirect
639. C2×C8C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156899232
#202565892
C2×#156896042
#202522712
#202522622
#202522292
#202522182
#202522062
#202521952
#202519052
C2×#156891222
#202518062
C2×C47×#4282
#6017047