Finite Group Databasebeta

← #27084756

Subgroups — #27084756

Order 12032.

2218 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256780C211yesmaximal, characteristic, complemented
2C2×#15689595C211yesmaximal, characteristic, complemented
3#20253642C214yesmaximal, complemented
4#20253633C214yesmaximal, complemented
5#20253579C214yesmaximal, complemented
6#20253577C214yesmaximal, complemented
7#20253322C212yesmaximal, complemented
8#20253181C211yesmaximal, characteristic, complemented
9#20252854C211yesmaximal, characteristic, complemented
10#20252852C211yesmaximal, characteristic, complemented
11#20252617C212yesmaximal, complemented
12#20252195C212yesmaximal, complemented
13#20252192C212yesmaximal, complemented
14#20252025C211yesmaximal, characteristic, complemented
15C47×#3077C211yesmaximal, characteristic, complemented
16C22×D4×D47C2211yescharacteristic
17C2×#13094052C2212yes—
18C2×#13094050C2212yes—
19#15689747C2212yescomplemented
20#15689747C2212yescomplemented
21#15689736C2212yescomplemented
22#15689729C2212yescomplemented
23#15689722—21no—
24#15689722—21no—
25#15689713—21no—
26#15689713—21no—
27#15689673C2211yescharacteristic, complemented
28#15689660—22no—
29#15689660—22no—
30#15689635C2212yes—
31#15689595—22no—
32#15689595—22no—
33#15689595C2214yes—
34#15689595C2214yes—
35#15689591C2212yescomplemented
36C2×C4×D188C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×#13093986C2211yescharacteristic
39C2×C4×C22⋊D47—21no—
40C2×(C22⋊D47)⋊C4—21no—
41C2×#13093982C2211yescharacteristic
42C2×#13093981C2211yescharacteristic
43C22×(C2×D47)⋊C4—21no—
44C2×C22⋊C4×D47—21no—
45#15689467C2214yescomplemented
46#15689466C2214yescomplemented
47#15689450C2214yescomplemented
48#15689449C2214yescomplemented
49#15689420C2214yescomplemented
50#15689410C2212yescomplemented
51#15689400C2212yescomplemented
52#15689339C2214yescomplemented
53#15689338C2214yescomplemented
54#15689329C2212yescomplemented
55#15689328C2212yescomplemented
56#15689319C2212yescomplemented
57#15689318C2212yescomplemented
58#15689275C2214yes—
59#15689275C2214yes—
60#15689258C2214yes—
61#15689258C2214yes—
62#15689234C2214yescomplemented
63#15689232C2214yescomplemented
64#15689222C2214yescomplemented
65#15689220C2214yescomplemented
66#15689214C2214yescomplemented
67#15689210C2214yescomplemented
68#15689205C2214yescomplemented
69#15689203C2214yescomplemented
70#15689183C2214yescomplemented
71#15689183C2214yescomplemented
72#15689166C2212yescomplemented
73#15689147C2211yescharacteristic, complemented
74#15689127C2212yes—
75#15689125C2212yescomplemented
76#15689122C2212yescomplemented
77#15689086C2212yes—
78M16×Dic47C2212yescomplemented
79C47×#533C2211yescharacteristic, complemented
80C2×C4×D4×C47C2211yescharacteristic
81C47×#478C2214yescomplemented
82C47×#476C2212yescomplemented
83C47×#474C2212yescomplemented
84C47×#428C2212yescomplemented
85C47×#423C2211yescharacteristic, complemented
86C47×#418C2212yes—
87C24×D47—21no—
88C2×#10625350C2312yes—
89C22×D188C2311yescharacteristic
90C22×C22⋊D47—21no—
91C2×D4×D47—24no—
92C2×D4×D47—24no—
93C2×D4×D47—22no—
94C2×D4×D47C2314yes—
95C23×Dic47—21no—
96C22×C4×D47—21no—
97C22×C4×D47—21no—
98C22×C4×D47C2311yescharacteristic
99#13094052—28no—
100#13094050—28no—
101C2×#10625325C2314yes—
102C2×#10625335C2314yes—
103C2×D376C2314yes—
104C2×#10625334C2314yes—
105C2×#10625329C2312yes—
106#13094024C2311yescharacteristic, complemented
107#13094021C2311yescharacteristic, complemented
108#13094019—22no—
109#13094019—22no—
110#13094019—22no—
111#13094019—22no—
112#13094015—22no—
113#13094015—22no—
114#13094013—22no—
115#13094013—22no—
116#13094012C2312yescomplemented
117#13094009—22no—
118#13094009—22no—
119#13094009—22no—
120#13094009—22no—
121#13094008—22no—
122#13094004C2312yes—
123#13094004C2312yes—
124#13094000—22no—
125#13094000—22no—
126#13093999—22no—
127#13093999—22no—
128#13093999C2312yes—
129#13093999C2312yes—
130#13093998—21no—
131#13093998—21no—
132#13093994—22no—
133#13093989C2312yescomplemented
134#13093989C2312yescomplemented
135C4×D188—22no—
136C4×D188—22no—
137C4×D188—21no—
138C4×D188—21no—
139C4×D188—21no—
140C4×D188—21no—
141C4×D188C2312yes—
142C4×D188C2312yes—
143D4×Dic47—22no—
144D4×Dic47C2314yes—
145#13093986—22no—
146#13093986C2314yes—
147#13093986C2312yescomplemented
148#13093986C2312yescomplemented
149C4×C22⋊D47—24no—
150C4×C22⋊D47—24no—
151(C22⋊D47)⋊C4—22no—
152(C22⋊D47)⋊C4—22no—
153(C22⋊D47)⋊C4—24no—
154(C22⋊D47)⋊C4—24no—
155#13093982—22no—
156#13093982C2314yes—
157#13093981—22no—
158#13093981D412yes—
159#13093981D412yes—
160#13093981C2312yes—
161#13093981C2312yes—
162C2×C4⋊Dic47C2311yescharacteristic
163C2×Dic47⋊C4D411yescharacteristic
164C2×Dic47⋊C4D411yescharacteristic
165C2×C22⋊Dic47—21no—
166C2×(C2×D47)⋊C4—21no—
167C2×(C2×D47)⋊C4—21no—
168C2×(C2×D47)⋊C4—21no—
169C2×(C2×D47)⋊C4—24no—
170C2×(C2×D47)⋊C4—24no—
171C2×(C2×D47)⋊C4D411yescharacteristic
172C2×(C2×D47)⋊C4D411yescharacteristic
173C22⋊C4×D47—24no—
174C22⋊C4×D47—24no—
175C2×C4×Dic47—21no—
176C2×C4×Dic47C2311yescharacteristic
177C42×D47—22no—
178#13093957C2314yescomplemented
179#13093955C2314yescomplemented
180C4⋊(C47⋊C8)C2312yescomplemented
181C4⋊(C47⋊C8)C2312yescomplemented
182#13093949C2314yescomplemented
183#13093947C2314yescomplemented
184#13093946C2314yescomplemented
185#13093944C2314yes—
186#13093944C2314yes—
187#13093944C2314yescomplemented
188(C2×D47)⋊C8C2314yes—
189(C2×D47)⋊C8C2314yes—
190#13093934C2314yescomplemented
191C8×Dic47C2314yescomplemented
192C22×D4×C47C2311yescharacteristic
193C23×C4×C47—21no—
194C2×M16×C47C2312yes—
195C4⋊Q8×C47C2311yescharacteristic, complemented
196C4⋊Q8×C47C2311yescharacteristic, complemented
197#125×C47C2312yescomplemented
198C22⋊Q8×C47—21no—
199C22⋊Q8×C47—21no—
200C4×Q8×C47—21no—
201C4×Q8×C47—21no—
202C4×D4×C47—21no—
203C4×D4×C47—21no—
204C4×D4×C47C2312yes—
205C4×D4×C47C2312yes—
206#117×C47C2312yes—
207C2×C4⋊C4×C47C2311yescharacteristic
208C2×C22⋊C4×C47—21no—
209C2×C42×C47C2311yescharacteristic
210#107×C47C2314yescomplemented
211#106×C47C2314yescomplemented
212C4⋊C8×C47C2312yescomplemented
213C4⋊C8×C47C2312yescomplemented
214#102×C47C2314yes—
215#102×C47C2314yes—
216C24×C47—21no—
217C23×D47—21no—
218C23×D47—28no—
219C23×D47—24no—
220C23×D47—82no—
221C23×D47—82no—
222C23×D47C2×D411yescharacteristic
223C2×Q8×C47—21no—
224C2×Q8×C47—21no—
225C2×D4×C47—21no—
226C2×D4×C47—22no—
227C2×D4×C47#4114yes—
228C2×D4×C47C2412yes—
229C22×C4×C47—21no—
230C22×C4×C47—22no—
231C22×C4×C47—22no—
232C22×C4×C47—82no—
233C22×C4×C47C2×D411yescharacteristic
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2411yescharacteristic
236C2×C22⋊D47—28no—
237C2×C22⋊D47—22no—
238C2×C22⋊D47—24no—
239C22×Dic47—21no—
240C22×Dic47—24no—
241C22×Dic47—82no—
242C22×Dic47C2×D411yescharacteristic
243C22×Dic47C2×D411yescharacteristic
244C22×Dic47C2×D411yescharacteristic
245D4×D47—216no—
246D4×D47—28no—
247D4×D47—28no—
248#10625350—24no—
249#10625350—24no—
250C2×D188—21no—
251C2×D188—22no—
252C2×D188—22no—
253C2×D188—22no—
254C2×D188—21no—
255C2×D188—21no—
256C2×D188#4114yes—
257C2×D188C2412yes—
258C2×D188C2412yes—
259C2×C4×D47—22no—
260C2×C4×D47—22no—
261C2×C4×D47—22no—
262C2×C4×D47—22no—
263C2×C4×D47—22no—
264C2×C4×D47—22no—
265C2×C4×D47—22no—
266C2×C4×D47—24no—
267C2×C4×D47—82no—
268C2×C4×D47—82no—
269C2×C4×D47C2×D412yes—
270C2×C4×D47C2412yes—
271C2×Dic94C2412yes—
272M16×C47—24no—
273C2×C8×C47C2414yes—
274C4⋊C4×C47—21no—
275C4⋊C4×C47—22no—
276C4⋊C4×C47—22no—
277C4⋊C4×C47—21no—
278C4⋊C4×C47—21no—
279C4⋊C4×C47C2412yes—
280C4⋊C4×C47C2412yes—
281C4⋊C4×C47C2412yes—
282C22⋊C4×C47—22no—
283C22⋊C4×C47—22no—
284C22⋊C4×C47—22no—
285C42×C47—22no—
286C42×C47C2×D411yescharacteristic
287C42×C47C2×D411yescharacteristic
288C42×C47C2411yescharacteristic
289C42×C47C2411yescharacteristic
290C22⋊Dic47—24no—
291#10625335—28no—
292#10625334—28no—
293(C2×D47)⋊C4—24no—
294(C2×D47)⋊C4—22no—
295(C2×D47)⋊C4—22no—
296(C2×D47)⋊C4—22no—
297(C2×D47)⋊C4—22no—
298(C2×D47)⋊C4—22no—
299(C2×D47)⋊C4—22no—
300(C2×D47)⋊C4—24no—
301(C2×D47)⋊C4—22no—
302(C2×D47)⋊C4—22no—
303(C2×D47)⋊C4—22no—
304(C2×D47)⋊C4—22no—
305(C2×D47)⋊C4C2×D412yes—
306(C2×D47)⋊C4C2×D412yes—
307(C2×D47)⋊C4C2×D412yes—
308(C2×D47)⋊C4C2×D412yes—
309C4⋊Dic47—21no—
310C4⋊Dic47—21no—
311C4⋊Dic47—21no—
312C4⋊Dic47—22no—
313C4⋊Dic47—22no—
314C4⋊Dic47C2412yes—
315Dic47⋊C4—22no—
316Dic47⋊C4—22no—
317Dic47⋊C4C2×D412yes—
318Dic47⋊C4C2×D412yes—
319Dic47⋊C4C2×D412yes—
320Dic47⋊C4C2×D412yes—
321C4×Dic47—22no—
322C4×Dic47—22no—
323C4×Dic47—24no—
324C4×Dic47C2×D412yes—
325C4×Dic47C2412yes—
326#10625329—24no—
327C2×C47⋊C8C2414yes—
328D376—28no—
329#10625325—28no—
330C23×C47—24no—
331C23×C47—22no—
332C23×C47—42no—
333C23×C47—42no—
334C23×C47C22×D411yescharacteristic
335C22×D47—22no—
336C22×D47—24no—
337C22×D47—22no—
338C22×D47—216no—
339C22×D47—22no—
340C22×D47—41no—
341C22×D47—41no—
342C22×D47—42no—
343C22×D47—42no—
344C22×D47—84no—
345C22×D47—84no—
346C22×D47—816no—
347C22×D47C22×D412yes—
348Q8×C47—81no—
349Q8×C47—81no—
350D4×C47—24no—
351D4×C47—22no—
352D4×C47C2×#4114yes—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—41no—
357C2×C4×C47—41no—
358C2×C4×C47—42no—
359C2×C4×C47—82no—
360C2×C4×C47—82no—
361C2×C4×C47C22×D411yescharacteristic
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47C22×D411yescharacteristic
366C2×C4×C47C2×#4112yes—
367C2×C4×C47C2×#4112yes—
368C2×C4×C47C2511yescharacteristic
369C22⋊D47—216no—
370C22⋊D47—44no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374C2×Dic47—41no—
375C2×Dic47—41no—
376C2×Dic47—42no—
377C2×Dic47—84no—
378C2×Dic47C22×D412yes—
379C2×Dic47C22×D412yes—
380C2×Dic47C22×D412yes—
381D188—24no—
382D188—22no—
383D188—22no—
384D188—22no—
385D188—81no—
386D188—81no—
387D188—82no—
388D188—82no—
389D188C2×#4114yes—
390C4×D47—24no—
391C4×D47—22no—
392C4×D47—22no—
393C4×D47—44no—
394C4×D47—82no—
395C4×D47—82no—
396C4×D47—84no—
397C4×D47—82no—
398C4×D47—82no—
399Dic94—22no—
400Dic94—22no—
401C8×C47—24no—
402C47⋊C8—24no—
403#60564—471nomaximal, Sylow
404C22×C47—21no—
405C22×C47—21no—
406C22×C47—24no—
407C22×C47—48no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47#52512yes—
411C22×C47C23×D411yescharacteristic
412C2×D47—22no—
413C2×D47—22no—
414C2×D47—22no—
415C2×D47—24no—
416C2×D47—48no—
417C2×D47—44no—
418C2×D47—42no—
419C2×D47—42no—
420C2×D47—42no—
421C2×D47—42no—
422C2×D47—42no—
423C2×D47—816no—
424C4×C47—21no—
425C4×C47—21no—
426C4×C47—21no—
427C4×C47—21no—
428C4×C47—42no—
429C4×C47—42no—
430C4×C47—42no—
431C4×C47#52512yes—
432C4×C47C22×#4111yescharacteristic
433C4×C47C22×#4111yescharacteristic
434Dic47—22no—
435Dic47—22no—
436Dic47—22no—
437Dic47—42no—
438Dic47—42no—
439#3455—471no—
440C2×#518—471no—
441#3123—474no—
442#3122—474no—
443#3118—474no—
444#3118—474no—
445#3093—472no—
446#3077—471no—
447#3077D4711yescharacteristic, complemented
448#3036—471no—
449#3036—471no—
450#3003—472no—
451C4×AGL(1,ℤ/8)—472no—
452C4×AGL(1,ℤ/8)—472no—
453#2921—471no—
454C2×C47—22no—
455C2×C47—44no—
456C2×C47C2×#52511yescharacteristic
457C2×C47#358511yescharacteristic
458C2×C47#358511yescharacteristic
459D47—42no—
460D47—44no—
461D47—82no—
462C23×D4—471no—
463C2×AGL(1,ℤ/8)—472no—
464C2×AGL(1,ℤ/8)—472no—
465#542—472no—
466#542—472no—
467#541—472no—
468#540—472no—
469#539—941no—
470#539—941no—
471#538—941no—
472#538—941no—
473#533C2×D4711yescharacteristic, complemented
474#532—471no—
475#529—942no—
476#529—942no—
477#525—472no—
478#518—474no—
479#518—474no—
480#518—942no—
481#518—942no—
482C4×#41—472no—
483C2×C4×D4—471no—
484C2×C4×D4—471no—
485C2×C4×D4—471no—
486C2×C4×D4—941no—
487C2×C4×D4—941no—
488C2×C4×D4C2×D4711yescharacteristic
489C2×#117—471no—
490C2×#117—471no—
491C22×C22⋊C4—941no—
492C22×C22⋊C4—941no—
493#485—474no—
494#485—474no—
495#482—474no—
496#482—474no—
497#478—474no—
498#478C2×D4714yescomplemented
499#476—472no—
500#476C2×D4712yescomplemented
501#474—472no—
502#474C2×D4712yescomplemented
503#463—474no—
504#463—474no—
505#461—472no—
506#461—472no—
507#459—472no—
508#459—472no—
509#450—474no—
510#450—474no—
511#447—474no—
512#447—474no—
513#442—474no—
514#442—474no—
515#440—474no—
516#440—474no—
517C4×SD16—474no—
518C4×SD16—474no—
519C4×D8—474no—
520C4×D8—474no—
521#433—474no—
522#433—474no—
523#428—472no—
524#428C2×D4712yescomplemented
525#423—471no—
526#423C2×D4711yescharacteristic, complemented
527#418—472no—
528#418C2×D4712yes—
529#417—472no—
530#417—472no—
531#407—472no—
532C4×M16—472no—
533C47#6056411yescharacteristic, complemented, Sylow
534C25—941no—
535C2×#41—472no—
536C22×D4—474no—
537C22×D4—471no—
538C22×D4—942no—
539C22×D4—941no—
540C22×D4—944no—
541C22×D4—944no—
542C22×D4C22×D4711yescharacteristic
543C23×C4—21no—
544C23×C4—471no—
545C23×C4—941no—
546C23×C4—941no—
547C23×C4—941no—
548AGL(1,ℤ/8)—948no—
549AGL(1,ℤ/8)—948no—
550C2×SD16—474no—
551C2×SD16—474no—
552C2×D8—474no—
553C2×D8—474no—
554C2×M16—472no—
555C2×M16C22×D4712yes—
556C4⋊Q8—471no—
557C4⋊Q8C22×D4711yescharacteristic, complemented
558C4⋊Q8C22×D4711yescharacteristic, complemented
559#127—471no—
560#126—942no—
561#126—942no—
562#126—942no—
563#126—942no—
564#125—942no—
565#125—942no—
566#125C22×D4712yescomplemented
567#124—472no—
568#124—942no—
569#124—942no—
570#123—942no—
571#123—942no—
572#123—942no—
573#123—942no—
574#123—942no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—472no—
578C22⋊Q8—472no—
579C22⋊Q8—942no—
580C22⋊Q8—942no—
581#121—472no—
582#121—472no—
583#121—942no—
584#121—942no—
585#121—941no—
586#121—941no—
587#120—942no—
588C4×Q8—21no—
589C4×Q8—21no—
590C4×Q8—472no—
591C4×Q8—472no—
592C4×D4—21no—
593C4×D4—21no—
594C4×D4—474no—
595C4×D4—474no—
596C4×D4—472no—
597C4×D4—472no—
598C4×D4—472no—
599C4×D4—472no—
600C4×D4—942no—
601C4×D4—942no—
602C4×D4—942no—
603C4×D4—942no—
604C4×D4—944no—
605C4×D4—944no—
606C4×D4—942no—
607C4×D4—942no—
608C4×D4—944no—
609C4×D4—944no—
610C4×D4—941no—
611C4×D4—941no—
612C4×D4—941no—
613C4×D4—941no—
614C4×D4C22×D4712yes—
615C4×D4C22×D4712yes—
616#117—472no—
617#117—472no—
618#117—472no—
619#117—472no—
620#117—474no—
621#117—942no—
622#117—942no—
623#117C22×D4712yes—
624C2×C4⋊C4—471no—
625C2×C4⋊C4—471no—
626C2×C4⋊C4—471no—
627C2×C4⋊C4C22×D4711yescharacteristic
628C2×C22⋊C4—21no—
629C2×C22⋊C4—471no—
630C2×C22⋊C4—471no—
631C2×C22⋊C4—944no—
632C2×C22⋊C4—944no—
633C2×C22⋊C4—944no—
634C2×C22⋊C4—944no—
635C2×C22⋊C4—941no—
636C2×C22⋊C4—941no—
637C2×C22⋊C4—941no—
638C2×C22⋊C4—941no—
639C2×C42—471no—
640C2×C42—942no—
641C2×C42—941no—
642C2×C42C22×D4711yescharacteristic
643#107—474no—
644#107C22×D4714yescomplemented
645#106—474no—
646#106C22×D4714yescomplemented
647C4⋊C8—472no—
648C4⋊C8—472no—
649C4⋊C8C22×D4712yescomplemented
650C4⋊C8C22×D4712yescomplemented
651#103—474no—
652#103—474no—
653#102—474no—
654#102—474no—
655#102—474no—
656#102—474no—
657#102C22×D4714yes—
658#102C22×D4714yes—
659C22⋊C8—474no—
660C22⋊C8—474no—
661#97—474no—
662C4×C8—474no—
663C24—21no—
664C24—471no—
665C24—944no—
666C24—948no—
667C24—941no—
668C24—3762no—
669C24—3762no—
670#41—944no—
671#41—944no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8—472no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—474no—
678C2×D4—472no—
679C2×D4—472no—
680C2×D4—942no—
681C2×D4—942no—
682C2×D4—944no—
683C2×D4—948no—
684C2×D4—9416no—
685C2×D4—948no—
686C2×D4—948no—
687C2×D4—942no—
688C2×D4—941no—
689C2×D4—941no—
690C2×D4—941no—
691C2×D4—942no—
692C2×D4#1062535414yes—
693C2×D4C23×D4712yes—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—82no—
698C22×C4—471no—
699C22×C4—471no—
700C22×C4—471no—
701C22×C4—472no—
702C22×C4—472no—
703C22×C4—942no—
704C22×C4—942no—
705C22×C4—944no—
706C22×C4—944no—
707C22×C4—942no—
708C22×C4—942no—
709C22×C4—941no—
710C22×C4—942no—
711C22×C4—942no—
712C22×C4—942no—
713C22×C4—3762no—
714C22×C4—3762no—
715C22×C4—3762no—
716C22×C4D4×D4711yescharacteristic
717C22×C4D4×D4711yescharacteristic
718C22×C4C23×D4711yescharacteristic
719SD16—948no—
720SD16—948no—
721D8—948no—
722D8—948no—
723M16—24no—
724M16—944no—
725C2×C8—474no—
726C2×C8C23×D4714yes—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—472no—
733C4⋊C4—472no—
734C4⋊C4—472no—
735C4⋊C4—472no—
736C4⋊C4—472no—
737C4⋊C4—942no—
738C4⋊C4—942no—
739C4⋊C4—942no—
740C4⋊C4—942no—
741C4⋊C4—941no—
742C4⋊C4—941no—
743C4⋊C4—941no—
744C4⋊C4C23×D4712yes—
745C4⋊C4C23×D4712yes—
746C4⋊C4C23×D4712yes—
747C22⋊C4—22no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—472no—
751C22⋊C4—472no—
752C22⋊C4—472no—
753C22⋊C4—472no—
754C22⋊C4—944no—
755C22⋊C4—942no—
756C22⋊C4—942no—
757C22⋊C4—942no—
758C22⋊C4—942no—
759C22⋊C4—944no—
760C22⋊C4—942no—
761C22⋊C4—942no—
762C22⋊C4—944no—
763C22⋊C4—942no—
764C22⋊C4—942no—
765C22⋊C4—942no—
766C22⋊C4—942no—
767C42—22no—
768C42—472no—
769C42—472no—
770C42—944no—
771C42—942no—
772C42—942no—
773C42D4×D4711yescharacteristic
774C42D4×D4711yescharacteristic
775C42C23×D4711yescharacteristic
776C42C23×D4711yescharacteristic
777C23—24no—
778C23—22no—
779C23—42no—
780C23—42no—
781C23—472no—
782C23—9416no—
783C23—942no—
784C23—944no—
785C23—942no—
786C23—942no—
787C23—3764no—
788C23—3764no—
789C23—37616no—
790C23—1881no—
791C23—1881no—
792C23—1882no—
793C23—1882no—
794C23C2×D4×D4711yescharacteristic
795Q8—81no—
796Q8—81no—
797Q8—942no—
798Q8—942no—
799D4—24no—
800D4—22no—
801D4—474no—
802D4—9416no—
803D4—944no—
804D4—942no—
805D4—942no—
806D4—942no—
807D4—3761no—
808D4—3761no—
809D4—3762no—
810D4—3762no—
811D4—1884no—
812D4C2×#1062535414yes—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—42no—
819C2×C4—82no—
820C2×C4—82no—
821C2×C4—472no—
822C2×C4—472no—
823C2×C4—472no—
824C2×C4—942no—
825C2×C4—944no—
826C2×C4—942no—
827C2×C4—942no—
828C2×C4—942no—
829C2×C4—942no—
830C2×C4—3762no—
831C2×C4—3762no—
832C2×C4—3762no—
833C2×C4—3762no—
834C2×C4—3764no—
835C2×C4—3764no—
836C2×C4—1881no—
837C2×C4—1881no—
838C2×C4—1882no—
839C2×C4—1884no—
840C2×C4C2×D4×D4711yescharacteristic
841C2×C4C2×D4×D4711yescharacteristic
842C2×C4C2×D4×D4711yescharacteristic
843C2×C4C2×D4×D4711yescharacteristic
844C2×C4C2×D4×D4711yescharacteristic
845C2×C4#41×D4712yes—
846C2×C4C2×#1062535412yes—
847C2×C4C24×D4711yescharacteristic
848C8—24no—
849C8—944no—
850C22—21no—
851C22—21no—
852C22—24no—
853C22—48no—
854C22—42no—
855C22—42no—
856C22—942no—
857C22—942no—
858C22—942no—
859C22—944no—
860C22—37616no—
861C22—1884no—
862C22—1888no—
863C22—1882no—
864C22—1882no—
865C22—1882no—
866C22—1882no—
867C22—1882no—
868C22#1568963612yes—
869C22C22×D4×D4711yescharacteristic
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—42no—
875C4—42no—
876C4—42no—
877C4—942no—
878C4—942no—
879C4—942no—
880C4—1882no—
881C4—1882no—
882C4#1568963612yes—
883C4C2×#41×D4711yescharacteristic
884C4C22×#1062535411yescharacteristic
885C2—22no—
886C2—44no—
887C2—3762no—
888C2—1882no—
889C2—1884no—
890C2C2×#1568963611yescharacteristic
891C2#2025816411yescharacteristic
892C2#2025816511yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3077C2
socleC22×C47C23×D4
hypercenter#3077D47
hypocenterC47#60564
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #20256780C2semidirect
2. C2×#15689595C2semidirect
3. #20253642C2semidirect
4. #20253633C2semidirect
5. #20253579C2semidirect
6. #20253577C2semidirect
7. #20253322C2semidirect
8. #20253181C2semidirect
9. #20252854C2semidirect
10. #20252852C2semidirect
11. #20252617C2semidirect
12. #20252195C2semidirect
13. #20252192C2semidirect
14. #20252025C2semidirect
15. C47×#3077C2semidirect
19. #15689747C22semidirect
20. #15689747C22semidirect
21. #15689736C22semidirect
22. #15689729C22semidirect
27. #15689673C22semidirect
35. #15689591C22semidirect
45. #15689467C22semidirect
46. #15689466C22semidirect
47. #15689450C22semidirect
48. #15689449C22semidirect
49. #15689420C22semidirect
50. #15689410C22semidirect
51. #15689400C22semidirect
52. #15689339C22semidirect
53. #15689338C22semidirect
54. #15689329C22semidirect
55. #15689328C22semidirect
56. #15689319C22semidirect
57. #15689318C22semidirect
62. #15689234C22semidirect
63. #15689232C22semidirect
64. #15689222C22semidirect
65. #15689220C22semidirect
66. #15689214C22semidirect
67. #15689210C22semidirect
68. #15689205C22semidirect
69. #15689203C22semidirect
70. #15689183C22semidirect
71. #15689183C22semidirect
72. #15689166C22semidirect
73. #15689147C22semidirect
75. #15689125C22semidirect
76. #15689122C22semidirect
78. M16×Dic47C22semidirect
79. C47×#533C22semidirect
81. C47×#478C22semidirect
82. C47×#476C22semidirect
83. C47×#474C22semidirect
84. C47×#428C22semidirect
85. C47×#423C22semidirect
106. #13094024C23semidirect
107. #13094021C23semidirect
116. #13094012C23semidirect
133. #13093989C23semidirect
134. #13093989C23semidirect
147. #13093986C23semidirect
148. #13093986C23semidirect
178. #13093957C23semidirect
179. #13093955C23semidirect
180. C4⋊(C47⋊C8)C23semidirect
181. C4⋊(C47⋊C8)C23semidirect
182. #13093949C23semidirect
183. #13093947C23semidirect
184. #13093946C23semidirect
187. #13093944C23semidirect
190. #13093934C23semidirect
191. C8×Dic47C23semidirect
195. C4⋊Q8×C47C23semidirect
196. C4⋊Q8×C47C23semidirect
197. #125×C47C23semidirect
210. #107×C47C23semidirect
211. #106×C47C23semidirect
212. C4⋊C8×C47C23semidirect
213. C4⋊C8×C47C23semidirect
447. #3077D47semidirect
473. #533C2×D47semidirect
498. #478C2×D47semidirect
500. #476C2×D47semidirect
502. #474C2×D47semidirect
524. #428C2×D47semidirect
526. #423C2×D47semidirect
533. C47#60564semidirect
557. C4⋊Q8C22×D47semidirect
558. C4⋊Q8C22×D47semidirect
566. #125C22×D47semidirect
644. #107C22×D47semidirect
646. #106C22×D47semidirect
649. C4⋊C8C22×D47semidirect
650. C4⋊C8C22×D47semidirect

Maximal subgroups

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

subgroupindex
#202567802
C2×#156895952
#202536422
#202536332
#202535792
#202535772
#202533222
#202531812
#202528542
#202528522
#202526172
#202521952
#202521922
#202520252
C47×#30772
#6056447