Finite Group Databasebeta

← #27089324

Subgroups — #27089324

Order 12032.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256778C211yesmaximal, characteristic, complemented
2#20254853C214yesmaximal, complemented
3#20254844C214yesmaximal, complemented
4#20254814C214yesmaximal, complemented
5#20254799C214yesmaximal, complemented
6#20253197C212yesmaximal, complemented
7#20253193C211yesmaximal, characteristic, complemented
8#20253185C211yesmaximal, characteristic, complemented
9#20253014C212yesmaximal, complemented
10#20253003C212yesmaximal, complemented
11#20252878C212yesmaximal, complemented
12#20252860C211yesmaximal, characteristic, complemented
13#20252852C211yesmaximal, characteristic, complemented
14#20251952C211yesmaximal, characteristic, complemented
15C2×C47×#542C211yesmaximal, characteristic, complemented
16C2×#13094055C2212yes—
17C2×#13094050C2212yes—
18C22×#10625329C2212yes—
19#15689744C2212yescomplemented
20#15689744C2212yescomplemented
21#15689735C2212yescomplemented
22#15689728C2212yescomplemented
23#15689720—21no—
24#15689720—21no—
25#15689711—21no—
26#15689711—21no—
27#15689680C2211yescharacteristic
28#15689673C2211yescharacteristic
29#15689651—22no—
30#15689651—22no—
31#15689634C2212yes—
32C4×#10625350C2212yes—
33#15689430C2214yescomplemented
34#15689423C2214yescomplemented
35#15689418C2212yescomplemented
36#15689415C2214yescomplemented
37#15689413C2212yescomplemented
38#15689410C2214yescomplemented
39#15689408C2212yescomplemented
40#15689405C2214yescomplemented
41#15689403C2212yescomplemented
42#15689400C2214yescomplemented
43#15689379C2214yescomplemented
44#15689374C2214yes—
45#15689371C2214yescomplemented
46#15689367C2214yes—
47#15689362C2214yescomplemented
48#15689357C2214yes—
49#15689354C2214yescomplemented
50#15689350C2214yes—
51#15689345C2214yescomplemented
52#15689342C2214yescomplemented
53#15689342C2214yescomplemented
54#15689338C2214yescomplemented
55#15689335C2214yescomplemented
56#15689335C2214yescomplemented
57#15689333C2212yescomplemented
58#15689328C2212yescomplemented
59#15689323C2212yescomplemented
60#15689318C2212yescomplemented
61#15689163C2212yes—
62#15689163C2212yes—
63#15689150C2214yescomplemented
64#15689150C2214yescomplemented
65#15689147C2211yescharacteristic
66#15689147C2211yescharacteristic
67#15689147C2212yes—
68#15689132C2212yes—
69#15689128C2212yes—
70#15689122C2212yes—
71#15689122C2212yes—
72C47×#542—22no—
73C47×#542—22no—
74C47×#542C2214yes—
75C47×#542C2214yes—
76C2×C4⋊Q8×C47C2211yescharacteristic
77C2×#126×C47—21no—
78C2×#124×C47—21no—
79C2×#124×C47C2211yescharacteristic
80C2×#123×C47—21no—
81C2×C22⋊Q8×C47—21no—
82C2×C22⋊Q8×C47C2211yescharacteristic
83C2×#121×C47C2211yescharacteristic
84C2×C4×Q8×C47C2211yescharacteristic
85C2×C4×D4×C47C2211yescharacteristic
86C2×#117×C47C2211yescharacteristic
87C2×#10625350C2312yes—
88#13094055—44no—
89#13094050—44no—
90C2×#10625337C2314yes—
91C2×#10625335C2314yes—
92C2×#10625336C2314yes—
93C2×#10625334C2314yes—
94C2×#10625329—44no—
95C2×#10625329C2312yes—
96C2×#10625329C2312yes—
97C2×#10625329C2314yes—
98C22×C47⋊C8C2314yes—
99#13094024C2311yescharacteristic
100#13094024C2311yescharacteristic
101#13094024C2311yescharacteristic
102#13094021C2311yescharacteristic
103#13094019—22no—
104#13094019—22no—
105#13094017—22no—
106#13094017—22no—
107#13094016C2312yes—
108#13094014—22no—
109#13094014—22no—
110#13094012C2312yes—
111#13094010—22no—
112#13094010—22no—
113#13094009—22no—
114#13094009—22no—
115#13094007—22no—
116#13094006—22no—
117#13094006—22no—
118#13094003—21no—
119#13094003—21no—
120#13094003C2312yes—
121#13094003C2312yes—
122#13094002—22no—
123#13094002—22no—
124#13093998—21no—
125#13093998—21no—
126#13093998C2312yes—
127#13093998C2312yes—
128#13093997—22no—
129#13093997—22no—
130#13093993—22no—
131C4×Dic94—21no—
132C4×Dic94—21no—
133C4×Dic94C2312yes—
134C4×Dic94C2312yes—
135C4×D188—21no—
136C4×D188—21no—
137C4×D188C2312yes—
138C4×D188C2312yes—
139C4×C22⋊D47—22no—
140C4×C22⋊D47—22no—
141C4×C22⋊D47—22no—
142C4×C22⋊D47—22no—
143#13093983C2312yes—
144#13093981—22no—
145C42×D47—22no—
146#13093957C2314yes—
147#13093957C2314yes—
148#13093955C2314yes—
149#13093955C2314yes—
150C4⋊(C47⋊C8)C2312yes—
151C4⋊(C47⋊C8)C2312yes—
152C4⋊(C47⋊C8)C2314yes—
153C4⋊(C47⋊C8)C2314yes—
154C4⋊(C47⋊C8)C2312yes—
155C4⋊(C47⋊C8)C2312yes—
156#13093948C2314yes—
157#13093948C2314yes—
158#13093947C2314yes—
159#13093947C2314yes—
160#13093945C2314yes—
161#13093945C2314yes—
162#13093944C2314yes—
163#13093944C2314yes—
164C22×Q8×C47—21no—
165C22×Q8×C47C2311yescharacteristic
166C22×D4×C47—21no—
167C22×D4×C47C2311yescharacteristic
168C23×C4×C47—21no—
169C23×C4×C47C2311yescharacteristic
170C4⋊Q8×C47—22no—
171C4⋊Q8×C47C2314yes—
172#126×C47—24no—
173#126×C47—24no—
174#124×C47—24no—
175#124×C47—24no—
176#124×C47—22no—
177#124×C47C2314yes—
178#123×C47—24no—
179#123×C47—24no—
180C22⋊Q8×C47—22no—
181C22⋊Q8×C47—24no—
182C22⋊Q8×C47—24no—
183C22⋊Q8×C47C2314yes—
184#121×C47—22no—
185#121×C47C2314yes—
186C4×Q8×C47—21no—
187C4×Q8×C47—21no—
188C4×Q8×C47C2312yes—
189C4×Q8×C47C2312yes—
190C4×D4×C47—21no—
191C4×D4×C47—21no—
192C4×D4×C47C2312yes—
193C4×D4×C47C2312yes—
194#117×C47D412yes—
195#117×C47D412yes—
196#117×C47C2312yes—
197#117×C47C2312yes—
198C2×C4⋊C4×C47—21no—
199C2×C4⋊C4×C47—21no—
200C2×C4⋊C4×C47—21no—
201C2×C4⋊C4×C47D411yescharacteristic
202C2×C4⋊C4×C47D411yescharacteristic
203C2×C4⋊C4×C47C2311yescharacteristic
204C2×C4⋊C4×C47C2311yescharacteristic
205C2×C22⋊C4×C47—21no—
206C2×C22⋊C4×C47—21no—
207C2×C22⋊C4×C47—21no—
208C2×C22⋊C4×C47—21no—
209C2×C22⋊C4×C47—21no—
210C2×C22⋊C4×C47D411yescharacteristic
211C2×C22⋊C4×C47D411yescharacteristic
212C2×C42×C47—21no—
213C2×C42×C47C2311yescharacteristic
214C2×C42×C47C2311yescharacteristic
215C24×C47—21no—
216C24×C47C2×D411yescharacteristic
217C2×Q8×C47—21no—
218C2×Q8×C47—24no—
219C2×Q8×C47—22no—
220C2×Q8×C47—22no—
221C2×Q8×C47—82no—
222C2×Q8×C47C2412yes—
223C2×D4×C47—24no—
224C2×D4×C47—21no—
225C2×D4×C47—22no—
226C2×D4×C47—22no—
227C2×D4×C47—82no—
228C2×D4×C47C2412yes—
229C22×C4×C47—22no—
230C22×C4×C47—22no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—22no—
235C22×C4×C47—22no—
236C22×C4×C47—82no—
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D412yes—
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2412yes—
244C22×C4×C47C2411yescharacteristic
245C2×C22⋊D47—22no—
246C2×C22⋊D47—22no—
247C2×C22⋊D47—22no—
248#10625350—24no—
249#10625350—24no—
250C2×D188—21no—
251C2×D188—21no—
252C2×D188C2412yes—
253C2×C4×D47—22no—
254C2×C4×D47—22no—
255C2×C4×D47—22no—
256C2×Dic94—21no—
257C2×Dic94—21no—
258C2×Dic94C2412yes—
259C4⋊C4×C47—22no—
260C4⋊C4×C47—22no—
261C4⋊C4×C47—24no—
262C4⋊C4×C47—24no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47C2×D412yes—
266C4⋊C4×C47C2×D412yes—
267C4⋊C4×C47C2×D412yes—
268C4⋊C4×C47C2×D412yes—
269C4⋊C4×C47C2412yes—
270C4⋊C4×C47C2412yes—
271C22⋊C4×C47—24no—
272C22⋊C4×C47—22no—
273C22⋊C4×C47—22no—
274C22⋊C4×C47—24no—
275C22⋊C4×C47—24no—
276C22⋊C4×C47—24no—
277C22⋊C4×C47C2×D412yes—
278C22⋊C4×C47C2×D412yes—
279C22⋊C4×C47C2×D412yes—
280C22⋊C4×C47C2×D412yes—
281C42×C47—22no—
282C42×C47—22no—
283C42×C47C2×D411yescharacteristic
284C42×C47C2×D411yescharacteristic
285C42×C47C2×D412yes—
286C42×C47C2411yescharacteristic
287C42×C47C2411yescharacteristic
288C42×C47C2412yes—
289C22⋊Dic47—22no—
290C22⋊Dic47—22no—
291C22⋊Dic47—22no—
292#10625337—44no—
293#10625336—44no—
294#10625335—44no—
295#10625334—44no—
296(C2×D47)⋊C4—22no—
297(C2×D47)⋊C4—22no—
298(C2×D47)⋊C4—22no—
299(C2×D47)⋊C4—22no—
300(C2×D47)⋊C4—22no—
301(C2×D47)⋊C4—22no—
302C4⋊Dic47—21no—
303C4⋊Dic47—21no—
304C4⋊Dic47—21no—
305C4⋊Dic47—21no—
306C4⋊Dic47C2412yes—
307C4⋊Dic47C2412yes—
308Dic47⋊C4—22no—
309Dic47⋊C4—22no—
310Dic47⋊C4—22no—
311Dic47⋊C4—22no—
312Dic47⋊C4—22no—
313Dic47⋊C4—22no—
314C4×Dic47—22no—
315C4×Dic47—22no—
316C4×Dic47—22no—
317#10625329—24no—
318#10625329—24no—
319#10625329—44no—
320C2×C47⋊C8—44no—
321C2×C47⋊C8C2414yes—
322C2×C47⋊C8C2414yes—
323C23×C47—22no—
324C23×C47—22no—
325C23×C47—41no—
326C23×C47—41no—
327C23×C47—42no—
328C23×C47—42no—
329C23×C47—42no—
330C23×C47C22×D412yes—
331C23×C47C22×D411yescharacteristic
332C22×D47—22no—
333Q8×C47—22no—
334Q8×C47—22no—
335Q8×C47—42no—
336Q8×C47—84no—
337D4×C47—22no—
338D4×C47—22no—
339D4×C47—42no—
340D4×C47—84no—
341C2×C4×C47—22no—
342C2×C4×C47—24no—
343C2×C4×C47—22no—
344C2×C4×C47—22no—
345C2×C4×C47—22no—
346C2×C4×C47—22no—
347C2×C4×C47—22no—
348C2×C4×C47—41no—
349C2×C4×C47—41no—
350C2×C4×C47—41no—
351C2×C4×C47—41no—
352C2×C4×C47—42no—
353C2×C4×C47—42no—
354C2×C4×C47—42no—
355C2×C4×C47—82no—
356C2×C4×C47—82no—
357C2×C4×C47C22×D412yes—
358C2×C4×C47C22×D412yes—
359C2×C4×C47C22×D411yescharacteristic
360C2×C4×C47C22×D411yescharacteristic
361C2×C4×C47C22×D412yes—
362C2×C4×C47C22×D411yescharacteristic
363C2×C4×C47C22×D411yescharacteristic
364C2×C4×C47C22×D411yescharacteristic
365C2×C4×C47H(5,𝔽2)12yes—
366C2×C4×C472−1+412yes—
367C2×C4×C47C2511yescharacteristic
368C22⋊D47—44no—
369C22⋊D47—82no—
370C22⋊D47—82no—
371C2×Dic47—22no—
372C2×Dic47—22no—
373C2×Dic47—22no—
374D188—22no—
375D188—22no—
376D188—81no—
377D188—81no—
378C4×D47—44no—
379C4×D47—82no—
380C4×D47—82no—
381Dic94—22no—
382Dic94—22no—
383Dic94—81no—
384Dic94—81no—
385C47⋊C8—24no—
386C47⋊C8—24no—
387#60919—471nomaximal, Sylow
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—22no—
391C22×C47—22no—
392C22×C47—22no—
393C22×C47—42no—
394C22×C47—42no—
395C22×C47—42no—
396C22×C47—82no—
397C22×C47—84no—
398C22×C47#53712yes—
399C22×C47C23×D411yescharacteristic
400C2×D47—42no—
401C2×D47—42no—
402C2×D47—42no—
403C4×C47—21no—
404C4×C47—22no—
405C4×C47—21no—
406C4×C47—21no—
407C4×C47—22no—
408C4×C47—21no—
409C4×C47—22no—
410C4×C47—42no—
411C4×C47—42no—
412C4×C47—42no—
413C4×C47#53712yes—
414C4×C47C2×H(5,𝔽2)11yescharacteristic
415C4×C47C2×2−1+411yescharacteristic
416Dic47—42no—
417Dic47—42no—
418Dic47—42no—
419#3455—471no—
420C2×#542D4711yescharacteristic, complemented
421#3263—474no—
422#3262—474no—
423#3258—474no—
424#3257—474no—
425#3079—472no—
426#3078—471no—
427#3077—471no—
428#3056—472no—
429#3055—472no—
430#3040—472no—
431#3037—471no—
432#3036—471no—
433#2905—471no—
434C2×C47—22no—
435C2×C47—42no—
436C2×C47—82no—
437C2×C47C2×#53711yescharacteristic
438C2×C47#358511yescharacteristic
439C2×C47#358611yescharacteristic
440D47—82no—
441C2×#137—472no—
442C2×AGL(1,ℤ/8)—472no—
443C22×M16—472no—
444#542—22no—
445#542—22no—
446#542—472no—
447#542—472no—
448#542C2×D4714yes—
449#542C2×D4714yes—
450#541—472no—
451#540—472no—
452#539—941no—
453#539—941no—
454#538—941no—
455#538—941no—
456#533—471no—
457#532—471no—
458C2×C4⋊Q8C2×D4711yescharacteristic
459#529—942no—
460#529—942no—
461C2×#126—21no—
462C2×#124—21no—
463C2×#124C2×D4711yescharacteristic
464#525—472no—
465C2×#123—21no—
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8C2×D4711yescharacteristic
468C2×#121C2×D4711yescharacteristic
469C4×#41—472no—
470C2×C4×Q8C2×D4711yescharacteristic
471C2×C4×D4C2×D4711yescharacteristic
472C2×#117C2×D4711yescharacteristic
473#479—474no—
474#478—474no—
475#477—474no—
476#477—472no—
477#476—474no—
478#476—472no—
479#475—474no—
480#475—472no—
481#474—474no—
482#474—472no—
483#470—474no—
484#469—474no—
485#468—474no—
486#468—474no—
487#467—474no—
488#466—474no—
489#465—474no—
490#465—474no—
491#464—474no—
492#464—474no—
493#464—474no—
494#463—474no—
495#463—474no—
496#463—474no—
497#462—472no—
498#461—472no—
499#460—472no—
500#459—472no—
501#428—472no—
502#428—472no—
503#424—474no—
504#424—474no—
505#423—471no—
506#423—471no—
507#423—472no—
508#419—472no—
509#418—472no—
510#417—472no—
511#417—472no—
512C47#6091911yescharacteristic, complemented, Sylow
513C2×#41—472no—
514C22×Q8—21no—
515C22×Q8C22×D4711yescharacteristic
516C22×D4—21no—
517C22×D4C22×D4711yescharacteristic
518C23×C4—21no—
519C23×C4C22×D4711yescharacteristic
520#137—1884no—
521AGL(1,ℤ/8)—1884no—
522C2×Q16—474no—
523C2×SD16—474no—
524C2×SD16—474no—
525C2×D8—474no—
526C2×M16—472no—
527C2×M16—472no—
528C2×M16—474no—
529C2×M16—1884no—
530C22×C8—474no—
531C4⋊Q8—22no—
532C4⋊Q8—471no—
533C4⋊Q8—471no—
534C4⋊Q8—471no—
535C4⋊Q8C22×D4714yes—
536#127—471no—
537#126—24no—
538#126—24no—
539#126—942no—
540#126—942no—
541#126—942no—
542#126—942no—
543#125—472no—
544#125—942no—
545#125—942no—
546#124—24no—
547#124—24no—
548#124—22no—
549#124—472no—
550#124—942no—
551#124—942no—
552#124C22×D4714yes—
553#123—24no—
554#123—24no—
555#123—942no—
556#123—942no—
557#123—942no—
558#123—942no—
559#123—942no—
560C22⋊Q8—22no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563C22⋊Q8—472no—
564C22⋊Q8—472no—
565C22⋊Q8—941no—
566C22⋊Q8—941no—
567C22⋊Q8—942no—
568C22⋊Q8—942no—
569C22⋊Q8C22×D4714yes—
570#121—22no—
571#121—472no—
572#121—472no—
573#121—941no—
574#121—941no—
575#121—942no—
576#121—942no—
577#121C22×D4714yes—
578#120—942no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—472no—
582C4×Q8—472no—
583C4×Q8—941no—
584C4×Q8—941no—
585C4×Q8C22×D4712yes—
586C4×Q8C22×D4712yes—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—472no—
590C4×D4—472no—
591C4×D4—942no—
592C4×D4—942no—
593C4×D4—942no—
594C4×D4—942no—
595C4×D4—941no—
596C4×D4—941no—
597C4×D4C22×D4712yes—
598C4×D4C22×D4712yes—
599#117—472no—
600#117—942no—
601#117C22⋊D4712yes—
602#117C22⋊D4712yes—
603#117C22×D4712yes—
604#117C22×D4712yes—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4C22⋊D4711yescharacteristic
609C2×C4⋊C4C22⋊D4711yescharacteristic
610C2×C4⋊C4C22×D4711yescharacteristic
611C2×C4⋊C4C22×D4711yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4C22⋊D4711yescharacteristic
618C2×C22⋊C4C22⋊D4711yescharacteristic
619C2×C42—21no—
620C2×C42—942no—
621C2×C42C22×D4711yescharacteristic
622C2×C42C22×D4711yescharacteristic
623#107—474no—
624#107—474no—
625#106—474no—
626#106—474no—
627C4⋊C8—472no—
628C4⋊C8—472no—
629C4⋊C8—472no—
630C4⋊C8—474no—
631C4⋊C8—474no—
632C4⋊C8—472no—
633#103—474no—
634#103—474no—
635#103—474no—
636#103—474no—
637#102—474no—
638#102—474no—
639#102—474no—
640#102—474no—
641C24—21no—
642C24C2×C22⋊D4711yescharacteristic
643#41—944no—
644#41—944no—
645C2×Q8—21no—
646C2×Q8—24no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—82no—
650C2×Q8—472no—
651C2×Q8—941no—
652C2×Q8—941no—
653C2×Q8C23×D4712yes—
654C2×D4—24no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—82no—
659C2×D4—472no—
660C2×D4—942no—
661C2×D4—942no—
662C2×D4—942no—
663C2×D4—941no—
664C2×D4—941no—
665C2×D4C23×D4712yes—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—82no—
674C22×C4—942no—
675C22×C4—942no—
676C22×C4—942no—
677C22×C4C2×C22⋊D4711yescharacteristic
678C22×C4C2×C22⋊D4712yes—
679C22×C4C2×C22⋊D4711yescharacteristic
680C22×C4C2×C22⋊D4711yescharacteristic
681C22×C4C2×C22⋊D4711yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C23×D4712yes—
684C22×C4C23×D4711yescharacteristic
685Q16—1884no—
686SD16—1884no—
687SD16—1884no—
688D8—1884no—
689M16—944no—
690M16—944no—
691M16—1884no—
692C2×C8—474no—
693C2×C8—474no—
694C2×C8—1884no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—472no—
702C4⋊C4—472no—
703C4⋊C4—942no—
704C4⋊C4—942no—
705C4⋊C4—942no—
706C4⋊C4—942no—
707C4⋊C4—942no—
708C4⋊C4—942no—
709C4⋊C4—941no—
710C4⋊C4—941no—
711C4⋊C4—941no—
712C4⋊C4—941no—
713C4⋊C4C2×C22⋊D4712yes—
714C4⋊C4C2×C22⋊D4712yes—
715C4⋊C4C2×C22⋊D4712yes—
716C4⋊C4C2×C22⋊D4712yes—
717C4⋊C4C23×D4712yes—
718C4⋊C4C23×D4712yes—
719C22⋊C4—24no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—942no—
726C22⋊C4—942no—
727C22⋊C4—942no—
728C22⋊C4—942no—
729C22⋊C4—942no—
730C22⋊C4—942no—
731C22⋊C4—942no—
732C22⋊C4—942no—
733C22⋊C4—942no—
734C22⋊C4C2×C22⋊D4712yes—
735C22⋊C4C2×C22⋊D4712yes—
736C22⋊C4C2×C22⋊D4712yes—
737C22⋊C4C2×C22⋊D4712yes—
738C42—22no—
739C42—22no—
740C42—942no—
741C42—942no—
742C42—942no—
743C42C2×C22⋊D4712yes—
744C42C2×C22⋊D4711yescharacteristic
745C42C2×C22⋊D4711yescharacteristic
746C42C23×D4712yes—
747C42C23×D4711yescharacteristic
748C42C23×D4711yescharacteristic
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—942no—
757C23C22×C22⋊D4712yes—
758C23C22×C22⋊D4711yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—42no—
762Q8—84no—
763Q8—942no—
764Q8—942no—
765Q8—3761no—
766Q8—3761no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—84no—
771D4—942no—
772D4—942no—
773D4—3761no—
774D4—3761no—
775D4—3762no—
776D4—3762no—
777D4—1884no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—942no—
795C2×C4—942no—
796C2×C4—942no—
797C2×C4—3762no—
798C2×C4—3762no—
799C2×C4—1884no—
800C2×C4C22×C22⋊D4711yescharacteristic
801C2×C4C22×C22⋊D4711yescharacteristic
802C2×C4C22×C22⋊D4712yes—
803C2×C4C22×C22⋊D4712yes—
804C2×C4C22×C22⋊D4711yescharacteristic
805C2×C4C22×C22⋊D4711yescharacteristic
806C2×C4C22×C22⋊D4712yes—
807C2×C4C22×C22⋊D4711yescharacteristic
808C2×C4#1309407012yes—
809C2×C4#1309407112yes—
810C2×C4C24×D4711yescharacteristic
811C8—944no—
812C8—944no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—84no—
823C22—1882no—
824C22—1882no—
825C22—1882no—
826C22#1568970112yes—
827C22C23×C22⋊D4711yescharacteristic
828C4—21no—
829C4—21no—
830C4—22no—
831C4—22no—
832C4—21no—
833C4—21no—
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—1882no—
839C4—1882no—
840C4—1882no—
841C4#1568970112yes—
842C4C2×#1309407011yescharacteristic
843C4C2×#1309407111yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—3762no—
848C2C2×#1568970111yescharacteristic
849C2#2025816811yescharacteristic
850C2#2025817511yescharacteristic
subgroupG/H
centerC22C23×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#542C2
socleC22×C47C23×D4
hypercenterC2×#542D47
hypocenterC47#60919
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #20256778C2semidirect
2. #20254853C2semidirect
3. #20254844C2semidirect
4. #20254814C2semidirect
5. #20254799C2semidirect
6. #20253197C2semidirect
7. #20253193C2semidirect
8. #20253185C2semidirect
9. #20253014C2semidirect
10. #20253003C2semidirect
11. #20252878C2semidirect
12. #20252860C2semidirect
13. #20252852C2semidirect
14. #20251952C2semidirect
15. C2×C47×#542C2semidirect
19. #15689744C22semidirect
20. #15689744C22semidirect
21. #15689735C22semidirect
22. #15689728C22semidirect
33. #15689430C22semidirect
34. #15689423C22semidirect
35. #15689418C22semidirect
36. #15689415C22semidirect
37. #15689413C22semidirect
38. #15689410C22semidirect
39. #15689408C22semidirect
40. #15689405C22semidirect
41. #15689403C22semidirect
42. #15689400C22semidirect
43. #15689379C22semidirect
45. #15689371C22semidirect
47. #15689362C22semidirect
49. #15689354C22semidirect
51. #15689345C22semidirect
52. #15689342C22semidirect
53. #15689342C22semidirect
54. #15689338C22semidirect
55. #15689335C22semidirect
56. #15689335C22semidirect
57. #15689333C22semidirect
58. #15689328C22semidirect
59. #15689323C22semidirect
60. #15689318C22semidirect
63. #15689150C22semidirect
64. #15689150C22semidirect
420. C2×#542D47semidirect
512. C47#60919semidirect

Maximal subgroups

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

subgroupindex
#202567782
#202548532
#202548442
#202548142
#202547992
#202531972
#202531932
#202531852
#202530142
#202530032
#202528782
#202528602
#202528522
#202519522
C2×C47×#5422
#6091947