Finite Group Databasebeta

← #25132947

Subgroups — #25132947

Order 11008.

960 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144396C211yesmaximal, characteristic, complemented
2C4×#13063355C211yesmaximal, characteristic
3#19139787C211yesmaximal, characteristic, complemented
4#19135942C211yesmaximal, characteristic, complemented
5#19135937C211yesmaximal, characteristic, complemented
6#19135753C211yesmaximal, characteristic, complemented
7#19135753C211yesmaximal, characteristic, complemented
8#19135589C211yesmaximal, characteristic, complemented
9#19135540C211yesmaximal, characteristic, complemented
10#19134964C211yesmaximal, characteristic
11#19134964C211yesmaximal, characteristic
12#19134828C211yesmaximal, characteristic
13#19134821C211yesmaximal, characteristic
14#19134615C211yesmaximal, characteristic
15C43×#3504C211yesmaximal, characteristic
16C2×#13063355C2211yescharacteristic
17C2×C4×Dic86C2211yescharacteristic
18#14583203—21no—
19#14583203—21no—
20#14583191—21no—
21#14583181—21no—
22#14583004—21no—
23#14582999—21no—
24C4×#10621885—21no—
25C4×#10621883—21no—
26#14582942C2211yescharacteristic
27#14582942C2211yescharacteristic
28#14582942C2211yescharacteristic
29#14582923C2211yescharacteristic
30C2×#13063252C2211yescharacteristic
31C2×#13063252C2211yescharacteristic
32#14582907C2211yescharacteristic
33#14582907C2211yescharacteristic
34#14582907C2211yescharacteristic
35#14582900C2211yescharacteristic
36C4×#10621877C2211yescharacteristic
37#14582832—22no—
38#14582804C2211yescharacteristic
39#14582804C2211yescharacteristic
40#14582780—22no—
41#14582768C2211yescharacteristic
42#14582764C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582668C2211yescharacteristic
45#14582668C2211yescharacteristic
46#14582668C2211yescharacteristic
47#14582668C2211yescharacteristic
48#14582658C2211yescharacteristic
49#14582658C2211yescharacteristic
50#14582658C2211yescharacteristic
51#14582658C2211yescharacteristic
52#14582658C2211yescharacteristic
53#14582658C2211yescharacteristic
54C43×#557—21no—
55C43×#557—21no—
56C43×#554—21no—
57C43×#554—21no—
58C43×#554—22no—
59C43×#554—22no—
60C43×#544—21no—
61C43×#544—21no—
62C43×#544C2211yescharacteristic
63C43×#544C2211yescharacteristic
64C43×#533—21no—
65C43×#533C2211yescharacteristic
66C2×#125×C43—21no—
67C2×#125×C43C2211yescharacteristic
68C43×#520C2211yescharacteristic
69C43×#520C2211yescharacteristic
70C4×#41×C43C2211yescharacteristic
71C22×Dic86C2311yescharacteristic
72#13063355—22no—
73#13063355Q814yescomplemented
74C2×#10621885—21no—
75C2×#10621883—21no—
76C2×#10621877C2311yescharacteristic
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C2×C4⋊Dic43—21no—
85C2×C4⋊Dic43C2311yescharacteristic
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—22no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—21no—
92#13063258—21no—
93#13063258—21no—
94#13063256—21no—
95#13063256—21no—
96#13063256—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)—21no—
99#13063252—22no—
100#13063252—22no—
101#13063249—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063246—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C43⋊#95—22no—
112C43⋊#95—22no—
113C43⋊#95—22no—
114C43⋊#95—21no—
115C2×#41×C43C2311yescharacteristic
116C4⋊Q8×C43—22no—
117C4⋊Q8×C43—22no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—21no—
121C4⋊Q8×C43—21no—
122C4⋊Q8×C43D411yescharacteristic
123C4⋊Q8×C43D411yescharacteristic
124#125×C43—22no—
125#125×C43—22no—
126#125×C43—22no—
127#125×C43—22no—
128#125×C43—21no—
129#125×C43—21no—
130#125×C43—21no—
131#125×C43—21no—
132#125×C43—21no—
133#125×C43—21no—
134#125×C43—21no—
135#125×C43—21no—
136#125×C43D411yescharacteristic
137#125×C43D411yescharacteristic
138C22⋊Q8×C43—22no—
139C22⋊Q8×C43—22no—
140C22⋊Q8×C43—22no—
141C22⋊Q8×C43—22no—
142C22⋊Q8×C43—22no—
143C22⋊Q8×C43—22no—
144C22⋊Q8×C43—21no—
145C22⋊Q8×C43—21no—
146C22⋊Q8×C43—22no—
147C22⋊Q8×C43—22no—
148C4×Q8×C43—22no—
149C4×Q8×C43—22no—
150C4×Q8×C43—21no—
151C4×Q8×C43—21no—
152C4×Q8×C43—21no—
153C4×Q8×C43—21no—
154C4×Q8×C43D411yescharacteristic
155C4×Q8×C43D411yescharacteristic
156C4×D4×C43—21no—
157C4×D4×C43—21no—
158C4×D4×C43—21no—
159C4×D4×C43—21no—
160C4×D4×C43—22no—
161C4×D4×C43—22no—
162C4×D4×C43D411yescharacteristic
163C4×D4×C43D411yescharacteristic
164#117×C43—21no—
165#117×C43—21no—
166#117×C43—21no—
167#117×C43C2311yescharacteristic
168#117×C43C2311yescharacteristic
169#117×C43C2311yescharacteristic
170C2×C4⋊C4×C43—22no—
171C2×C4⋊C4×C43—22no—
172C2×C4⋊C4×C43—21no—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43D412yes—
175C2×C4⋊C4×C43D412yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C42×C43—21no—
179C2×C42×C43C2311yescharacteristic
180#41×C43—21no—
181#41×C43—21no—
182#41×C43C2×Q812yes—
183#41×C43#4112yes—
184C2×Q8×C43—22no—
185C2×Q8×C43—22no—
186C2×Q8×C43—21no—
187C2×Q8×C43—21no—
188C2×Q8×C43C2×D411yescharacteristic
189C2×D4×C43—21no—
190C2×D4×C43C2×D411yescharacteristic
191C22×C4×C43—21no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—21no—
195C22×C4×C43—21no—
196C22×C4×C43C2×D412yes—
197C22×C4×C43C2×D412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43C2×D411yescharacteristic
200C22×C4×C43C2411yescharacteristic
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—21no—
204C22×Dic43—21no—
205C2×Dic86—21no—
206C2×Dic86—21no—
207C2×Dic86—21no—
208C2×Dic86—21no—
209C2×Dic86—21no—
210C2×Dic86C2×Q812yes—
211C4⋊C4×C43—22no—
212C4⋊C4×C43—22no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—22no—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43—22no—
222C4⋊C4×C43—22no—
223C4⋊C4×C43—22no—
224C4⋊C4×C43—22no—
225C4⋊C4×C43—21no—
226C4⋊C4×C43—21no—
227C4⋊C4×C43—21no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43—21no—
235C4⋊C4×C43C2×D411yescharacteristic
236C4⋊C4×C43C2×D411yescharacteristic
237C4⋊C4×C43C2×D411yescharacteristic
238C4⋊C4×C43C2×D411yescharacteristic
239C4⋊C4×C43C2×D411yescharacteristic
240C4⋊C4×C43C2×D411yescharacteristic
241C22⋊C4×C43—22no—
242C22⋊C4×C43—22no—
243C22⋊C4×C43—21no—
244C22⋊C4×C43—21no—
245C22⋊C4×C43—21no—
246C22⋊C4×C43—21no—
247C22⋊C4×C43—21no—
248C42×C43—22no—
249C42×C43—22no—
250C42×C43—21no—
251C42×C43—21no—
252C42×C43—21no—
253C42×C43—21no—
254C42×C43—21no—
255C42×C43C2×D411yescharacteristic
256C42×C43C2×D411yescharacteristic
257C42×C43C2×D411yescharacteristic
258C42×C43C2×D411yescharacteristic
259#10621885—24no—
260#10621883—24no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—42no—
264Dic43⋊C4—44no—
265Dic43⋊C4—41no—
266Dic43⋊C4—41no—
267C4×Dic43—21no—
268C4×Dic43—21no—
269C4×Dic43—21no—
270C4×Dic43—21no—
271C4×Dic43—41no—
272C4×Dic43—41no—
273#10621877—21no—
274#10621877—21no—
275#10621877—21no—
276#10621877—21no—
277#10621877—21no—
278#10621877—21no—
279#10621877—21no—
280#10621877C2×Q812yes—
281C2×C43⋊C8—21no—
282C2×C43⋊C8—21no—
283C2×C43⋊C8—21no—
284C2×C43⋊C8—21no—
285C23×C43—21no—
286C23×C43C22×D411yescharacteristic
287Q8×C43—21no—
288Q8×C43—81no—
289Q8×C43—81no—
290Q8×C43—82no—
291Q8×C43—82no—
292Q8×C43C22⋊Q812yes—
293D4×C43—22no—
294D4×C43—22no—
295D4×C43—21no—
296D4×C43C22⋊Q812yes—
297C2×C4×C43—21no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—21no—
301C2×C4×C43—21no—
302C2×C4×C43—21no—
303C2×C4×C43—21no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—21no—
307C2×C4×C43—21no—
308C2×C4×C43—41no—
309C2×C4×C43—41no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—81no—
313C2×C4×C43—81no—
314C2×C4×C43—82no—
315C2×C4×C43—82no—
316C2×C4×C43#12011yescharacteristic
317C2×C4×C43#12011yescharacteristic
318C2×C4×C43#12011yescharacteristic
319C2×C4×C43#12011yescharacteristic
320C2×C4×C43C22×D411yescharacteristic
321C2×C4×C43C22×D411yescharacteristic
322C2×C4×C43C22×Q811yescharacteristic
323C2×C4×C43C2×#4111yescharacteristic
324C2×C4×C432−1+411yescharacteristic
325C2×C4×C432−1+411yescharacteristic
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—41no—
329C2×Dic43—41no—
330C2×Dic43—41no—
331C2×Dic43—41no—
332C2×Dic43—42no—
333C2×Dic43—41no—
334C2×Dic43—41no—
335C2×Dic43—41no—
336C2×Dic43—41no—
337Dic86—22no—
338Dic86—22no—
339Dic86—41no—
340Dic86—41no—
341C43⋊C8—22no—
342C43⋊C8—41no—
343C43⋊C8—41no—
344C43⋊C8—41no—
345#24325—431nomaximal, Sylow
346C22×C43—21no—
347C22×C43—21no—
348C22×C43—22no—
349C22×C43—41no—
350C22×C43—41no—
351C22×C43C2×#12011yescharacteristic
352C22×C43#54811yescharacteristic
353C22×C43D4×Q811yescharacteristic
354C4×C43—22no—
355C4×C43—21no—
356C4×C43—21no—
357C4×C43—21no—
358C4×C43—21no—
359C4×C43—42no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43—41no—
363C4×C43—42no—
364C4×C43—41no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43C2×C22⋊Q811yescharacteristic
368C4×C43#53611yescharacteristic
369C4×C43#54811yescharacteristic
370C4×C43D4×Q811yescharacteristic
371Dic43—42no—
372Dic43—42no—
373Dic43—81no—
374Dic43—81no—
375#3504D4311yescharacteristic
376#3078—431no—
377C4×#137—431no—
378#2565—431no—
379#2061—431no—
380#2060—431no—
381#2028—431no—
382#2028—431no—
383#1998—431no—
384#1986—431no—
385#1882—431no—
386#1882—431no—
387#1860—431no—
388#1859—431no—
389#1806—431no—
390C2×C43—21no—
391C2×C43—21no—
392C2×C43—42no—
393C2×C43#240911yescharacteristic
394C2×C43#301811yescharacteristic
395C2×C43#302211yescharacteristic
396C2×#137—431no—
397#557—21no—
398#557—21no—
399#554—21no—
400#554—21no—
401#554—22no—
402#554—22no—
403#544—21no—
404#544—21no—
405#544C2×D4311yescharacteristic
406#544C2×D4311yescharacteristic
407#533—21no—
408#533C2×D4311yescharacteristic
409C2×#125—21no—
410C2×#125C2×D4311yescharacteristic
411#520C2×D4311yescharacteristic
412#520C2×D4311yescharacteristic
413C4×#41C2×D4311yescharacteristic
414C2×C4×Q8—431no—
415#479—861no—
416#479—861no—
417#477—861no—
418#475—861no—
419#441—861no—
420#440—861no—
421C4×Q16—861no—
422C4×SD16—861no—
423#428—431no—
424#428—431no—
425#428—431no—
426#423—431no—
427C2×#104—431no—
428C2×#104—431no—
429#419—431no—
430#419—431no—
431#419—431no—
432#417—431no—
433C4×M16—431no—
434#398—862no—
435#391—431no—
436#391—431no—
437#387—862no—
438#384—431no—
439#382—431no—
440C4×C4⋊C4—431no—
441#343—431no—
442#343—431no—
443#343—431no—
444#343—431no—
445#339—431no—
446#339—431no—
447#339—431no—
448#339—431no—
449#339—431no—
450#339—431no—
451C43#2432511yescharacteristic, complemented, Sylow
452C2×#41C22×D4311yescharacteristic
453C22×Q8—431no—
454#137—434no—
455#137—862no—
456C2×Q16—861no—
457C2×SD16—861no—
458C2×M16—431no—
459C2×M16—431no—
460C2×M16—431no—
461C2×M16—431no—
462C4⋊Q8—22no—
463C4⋊Q8—22no—
464C4⋊Q8—21no—
465C4⋊Q8—21no—
466C4⋊Q8—21no—
467C4⋊Q8—21no—
468C4⋊Q8C22⋊D4311yescharacteristic
469C4⋊Q8C22⋊D4311yescharacteristic
470#125—22no—
471#125—22no—
472#125—22no—
473#125—22no—
474#125—21no—
475#125—21no—
476#125—21no—
477#125—21no—
478#125—21no—
479#125—21no—
480#125—21no—
481#125—21no—
482#125C22⋊D4311yescharacteristic
483#125C22⋊D4311yescharacteristic
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—22no—
489C22⋊Q8—22no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8—21no—
500C4×Q8—861no—
501C4×Q8—861no—
502C4×Q8—861no—
503C4×Q8—861no—
504C4×Q8C22⋊D4311yescharacteristic
505C4×Q8C22⋊D4311yescharacteristic
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4C22⋊D4311yescharacteristic
513C4×D4C22⋊D4311yescharacteristic
514#117—21no—
515#117—21no—
516#117—21no—
517#117C22×D4311yescharacteristic
518#117C22×D4311yescharacteristic
519#117C22×D4311yescharacteristic
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—431no—
525C2×C4⋊C4—861no—
526C2×C4⋊C4—862no—
527C2×C4⋊C4—861no—
528C2×C4⋊C4C22⋊D4312yes—
529C2×C4⋊C4C22⋊D4312yes—
530C2×C4⋊C4C22×D4311yescharacteristic
531C2×C4⋊C4C22×D4311yescharacteristic
532C2×C42—21no—
533C2×C42—431no—
534C2×C42—431no—
535C2×C42—861no—
536C2×C42C22×D4311yescharacteristic
537#107—861no—
538#107—861no—
539#107—861no—
540#106—861no—
541#106—861no—
542#106—861no—
543C4⋊C8—861no—
544C4⋊C8—861no—
545#104—862no—
546#104—862no—
547#103—861no—
548#103—861no—
549#103—861no—
550#103—861no—
551#103—861no—
552#103—861no—
553#103—861no—
554#102—861no—
555#97—861no—
556C4×C8—861no—
557#95—861no—
558#95—862no—
559#95—862no—
560#95—862no—
561#41—21no—
562#41—21no—
563#41Q8×D4312yes—
564#41#1062190212yes—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—432no—
570C2×Q8—861no—
571C2×Q8—861no—
572C2×Q8—861no—
573C2×Q8—861no—
574C2×Q8—861no—
575C2×Q8C2×C22⋊D4311yescharacteristic
576C2×D4—21no—
577C2×D4C2×C22⋊D4311yescharacteristic
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4C2×C22⋊D4312yes—
588C22×C4C2×C22⋊D4312yes—
589C22×C4C2×C22⋊D4311yescharacteristic
590C22×C4C2×C22⋊D4311yescharacteristic
591C22×C4C23×D4311yescharacteristic
592Q16—864no—
593SD16—864no—
594M16—432no—
595M16—861no—
596M16—861no—
597M16—861no—
598M16—861no—
599M16—861no—
600M16—861no—
601M16—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8—861no—
606C4⋊C4—22no—
607C4⋊C4—22no—
608C4⋊C4—22no—
609C4⋊C4—22no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—22no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—861no—
631C4⋊C4—861no—
632C4⋊C4—1724no—
633C4⋊C4—1722no—
634C4⋊C4—1721no—
635C4⋊C4—1721no—
636C4⋊C4C2×C22⋊D4311yescharacteristic
637C4⋊C4C2×C22⋊D4311yescharacteristic
638C4⋊C4C2×C22⋊D4311yescharacteristic
639C4⋊C4C2×C22⋊D4311yescharacteristic
640C4⋊C4C2×C22⋊D4311yescharacteristic
641C4⋊C4C2×C22⋊D4311yescharacteristic
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C42—22no—
650C42—22no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—861no—
657C42—861no—
658C42—861no—
659C42—861no—
660C42—1721no—
661C42—1721no—
662C42C2×C22⋊D4311yescharacteristic
663C42C2×C22⋊D4311yescharacteristic
664C42C2×C22⋊D4311yescharacteristic
665C42C2×C22⋊D4311yescharacteristic
666C23—21no—
667C23C22×C22⋊D4311yescharacteristic
668Q8—21no—
669Q8—81no—
670Q8—81no—
671Q8—82no—
672Q8—82no—
673Q8—862no—
674Q8—862no—
675Q8—1721no—
676Q8—1721no—
677Q8#1306330112yes—
678D4—22no—
679D4—22no—
680D4—21no—
681D4#1306330112yes—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—81no—
698C2×C4—81no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4—862no—
702C2×C4—862no—
703C2×C4—1721no—
704C2×C4—1722no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4#1306329411yescharacteristic
713C2×C4#1306329411yescharacteristic
714C2×C4#1306329411yescharacteristic
715C2×C4#1306329411yescharacteristic
716C2×C4C22×C22⋊D4311yescharacteristic
717C2×C4C22×C22⋊D4311yescharacteristic
718C2×C4C2×Q8×D4311yescharacteristic
719C2×C4C2×#1062190211yescharacteristic
720C2×C4#1306337311yescharacteristic
721C2×C4#1306337311yescharacteristic
722C8—862no—
723C8—1721no—
724C8—1721no—
725C8—1721no—
726C22—21no—
727C22—21no—
728C22—22no—
729C22—41no—
730C22—41no—
731C22C2×#1306329411yescharacteristic
732C22#1458356011yescharacteristic
733C22Q8×C22⋊D4311yescharacteristic
734C4—21no—
735C4—21no—
736C4—21no—
737C4—21no—
738C4—22no—
739C4—42no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—42no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—3441no—
748C4—3441no—
749C4—1722no—
750C4—1722no—
751C4C2×#1306330111yescharacteristic
752C4#1458347311yescharacteristic
753C4#1458356011yescharacteristic
754C4Q8×C22⋊D4311yescharacteristic
755C2—21no—
756C2—21no—
757C2—42no—
758C2#1913795411yescharacteristic
759C2#1914394411yescharacteristic
760C2#1914397411yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3504C2
socleC22×C43C2×#120
prime radicalC2×#41×C43C23
hypercenter#3504D43
hypocenterC43#24325
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #19144396C2semidirect
3. #19139787C2semidirect
4. #19135942C2semidirect
5. #19135937C2semidirect
6. #19135753C2semidirect
7. #19135753C2semidirect
8. #19135589C2semidirect
9. #19135540C2semidirect
73. #13063355Q8semidirect
451. C43#24325semidirect

Maximal subgroups

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

subgroupindex
#191443962
C4×#130633552
#191397872
#191359422
#191359372
#191357532
#191355892
#191355402
#191349642
#191348282
#191348212
#191346152
C43×#35042
#2432543