Finite Group Databasebeta

← #7712508

Subgroups — #7712508

Order 512.

4928 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59896C214yesmaximal, complemented
2#59894C214yesmaximal, complemented
3#46333C214yesmaximal, complemented
4#46332C214yesmaximal, complemented
5#39795C214yesmaximal, complemented
6#39793C214yesmaximal, complemented
7#39539C214yesmaximal, complemented
8#39537C214yesmaximal, complemented
9#39197C214yesmaximal, complemented
10#39188C212yesmaximal, complemented
11#39187C212yesmaximal, complemented
12#37550C212yesmaximal, complemented
13#37431C214yesmaximal, complemented
14#36635C211yesmaximal, characteristic, complemented
15#36631C211yesmaximal, characteristic, complemented
16#36211C211yesmaximal, characteristic, complemented
17#36210C212yesmaximal, complemented
18#36209C211yesmaximal, characteristic, complemented
19#36151C211yesmaximal, characteristic, complemented
20#36150C212yesmaximal, complemented
21#36149C211yesmaximal, characteristic, complemented
22#35297C212yesmaximal, complemented
23#35292C212yesmaximal, complemented
24#34397C212yesmaximal, complemented
25C4×#532C211yesmaximal, characteristic, complemented
26C2×#533C2212yes—
27C2×#532C2211yescharacteristic
28C2×#532C2212yes—
29C2×#529C2212yes—
30C2×C4×#41C2212yes—
31#2864C2212yes—
32#2863C2214yes—
33#2862C2211yescharacteristic
34#2861C2212yes—
35#2860C2214yes—
36#2859C2211yescharacteristic
37#2859C2211yescharacteristic
38#2858C2211yescharacteristic
39#2857C2211yescharacteristic
40#2857C2212yes—
41#2857C2212yes—
42#2857C2212yes—
43#2857C2212yes—
44#2856C2211yescharacteristic
45#2856C2212yes—
46#2855C2214yes—
47#2854C2214yes—
48#2851C2212yes—
49#2850C2212yes—
50#2821C2214yes—
51#2818C2214yes—
52#2803C2218yes—
53#2803C2218yes—
54#2803C2218yes—
55#2797C2218yes—
56#2797C2218yes—
57#2797C2218yes—
58#2797C2218yes—
59#2787C2218yes—
60#2778C2218yes—
61#2777C2218yes—
62#2775C2218yes—
63#2773C2218yes—
64#2771C2218yes—
65#2753C2218yes—
66#2749C2218yes—
67#2745C2218yes—
68#2661C2214yes—
69#2661C2214yes—
70#2635C2218yes—
71#2625C2214yes—
72#2624C2214yes—
73#2616C2214yes—
74#2615C2214yes—
75#2610C2218yes—
76#2597C2218yes—
77#2593C2218yes—
78#2592C2214yes—
79#2584C2214yes—
80#2581C2214yes—
81#2580C2214yes—
82#2562C2214yes—
83#2562C2214yes—
84#2540C2214yes—
85#2540C2214yes—
86#2536C2212yes—
87#2536C2212yes—
88#2536C2214yes—
89#2535C2212yes—
90#2535C2212yes—
91#2535C2214yes—
92#2531C2218yes—
93#2518C2218yes—
94#2516C2218yes—
95#2516C2218yes—
96#2514C2214yes—
97#2513C2218yes—
98#2513C2214yes—
99#2510C2218yes—
100#2509C2214yes—
101#2508C2214yes—
102#2495C2214yes—
103#2495C2214yes—
104#2494C2214yes—
105#2494C2214yes—
106#2490C2214yes—
107#2490C2214yes—
108#2489C2214yes—
109#2489C2214yes—
110#2485C2214yes—
111#2485C2214yes—
112#2485C2214yes—
113#2485C2214yes—
114#2454C2214yes—
115#2453C2214yes—
116#2448C2214yes—
117#2447C2214yes—
118#2427C2214yes—
119#2427C2214yes—
120#2426C2214yes—
121#2426C2214yes—
122#2421C2214yes—
123#2421C2214yes—
124#2420C2214yes—
125#2420C2214yes—
126#2415C2214yes—
127#2415C2214yes—
128#2415C2214yes—
129#2415C2214yes—
130#2414C2214yes—
131#2414C2214yes—
132#2414C2214yes—
133#2414C2214yes—
134#2407C2214yes—
135#2407C2214yes—
136#2407C2214yes—
137#2407C2214yes—
138#2383C2218yes—
139#2370C2214yes—
140#2367C2214yes—
141#2363C2214yes—
142#2363C2214yes—
143#2362C2214yes—
144#2362C2214yes—
145#2357C2212yes—
146#2356C2212yes—
147#2351C2212yes—
148#2349C2212yes—
149#2347C2214yes—
150#2346C2214yes—
151#2346C2214yes—
152#2343C2214yes—
153#2341C2214yes—
154#2339C2214yes—
155#2335C2218yes—
156#2324C2214yes—
157#2324C2214yes—
158#2323C2214yes—
159#2323C2214yes—
160#2319C2214yes—
161#2318C2214yes—
162C4×C4⋊Q8C2211yescharacteristic
163C4×C4⋊Q8C2212yes—
164C4×C4⋊Q8C2212yes—
165C4×#127C2211yescharacteristic
166C4×#127C2212yes—
167C4×#125C2212yes—
168C4×#124C2212yes—
169C4×#124C2212yes—
170C4×#124C2212yes—
171C4×C22⋊Q8C2214yes—
172C4×#121C2214yes—
173C4×#121C2212yes—
174C4×#121C2212yes—
175C4×#121C2212yes—
176C4×#121C2212yes—
177#2297C2212yes—
178#2295C2214yes—
179#2293C2211yescharacteristic
180#2293C2211yescharacteristic
181#2293C2214yes—
182#2293C2212yes—
183#2285C2211yescharacteristic
184#2285C2212yes—
185#2285C2212yes—
186#2283C2212yes—
187C42×D4C2211yescharacteristic
188C42×D4C2212yes—
189C42×D4C2211yescharacteristic
190C2×C43C2211yescharacteristic
191C22×#41C2312yes—
192C22×#41C2314yes—
193#533—48no—
194#532—28no—
195#532—48no—
196C2×C4⋊Q8C2311yescharacteristic
197C2×C4⋊Q8C2311yescharacteristic
198C2×C4⋊Q8C2312yes—
199C2×#127C2311yescharacteristic
200C2×#127C2311yescharacteristic
201#529—216no—
202C2×#126C2314yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2314yes—
206C2×#124C2312yes—
207C2×#124C2312yes—
208C2×#124C2314yes—
209C2×#124C2312yes—
210C2×#123C2314yes—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2314yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2314yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×#121C2312yes—
219C2×#121C2312yes—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#121C2314yes—
225C2×#121C2314yes—
226C2×#121C2314yes—
227C2×#121C2314yes—
228C4×#41—48no—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2312yes—
251C2×C4×D4C2312yes—
252C2×C4×D4C2312yes—
253C2×#117C2314yes—
254C2×#117C2312yes—
255C2×#117C2312yes—
256C2×#117C2312yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C22×C42C2311yescharacteristic
261C22×C42C2312yes—
262C22×C42C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2312yes—
265C22×C42C2312yes—
266C22×C42C2311yescharacteristic
267#401C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#399C2318yes—
274#399C2318yes—
275#398C2314yes—
276#398C2314yes—
277#398C2318yes—
278#397C2314yes—
279#397C2314yes—
280#397C2318yes—
281#397C2318yes—
282#397C2318yes—
283#397C2318yes—
284#397C2318yes—
285#397C2318yes—
286#397C2318yes—
287#397C2318yes—
288#397C2318yes—
289#397C2318yes—
290#396C2318yes—
291#395C2318yes—
292#394C2318yes—
293#394C2318yes—
294#394C2318yes—
295#394C2314yes—
296#394C2314yes—
297#394C2318yes—
298#394C2318yes—
299#394C2318yes—
300#394C2318yes—
301#394C2318yes—
302#394C2318yes—
303#394C2318yes—
304#393C2318yes—
305#392C2318yes—
306#392C2318yes—
307#392C2314yes—
308#392C2314yes—
309#392C2318yes—
310#392C2318yes—
311#391C2312yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#390C2312yes—
323#390C2314yes—
324#390C2312yes—
325#390C2312yes—
326#390C2312yes—
327#390C2312yes—
328#390C2312yes—
329#390C2312yes—
330#390C2318yes—
331#390C2312yes—
332#390C2314yes—
333#390C2318yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2318yes—
338#390C2314yes—
339#390C2318yes—
340#390C2314yes—
341#390C2318yes—
342#390C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2318yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#388C2318yes—
368#388C2318yes—
369#388C2318yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2312yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2312yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2312yes—
393#388C2312yes—
394#388C2312yes—
395#388C2312yes—
396#388C2312yes—
397#388C2312yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#386C2318yes—
410#386C2318yes—
411#386C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#386C2312yes—
417#386C2312yes—
418#386C2312yes—
419#386C2312yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#384C2312yes—
426#384C2311yescharacteristic
427#384C2312yes—
428#384C2311yescharacteristic
429#383C2314yes—
430#383C2314yes—
431#383C2318yes—
432#382C2312yes—
433#382C2314yes—
434#382C2314yes—
435#382C2314yes—
436#382C2312yes—
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2318yes—
440#382C2312yes—
441#382C2312yes—
442#381C2314yes—
443#381C2314yes—
444#381C2318yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2314yes—
451#380C2314yes—
452#380C2314yes—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2314yes—
456#380C2314yes—
457#380C2312yes—
458#380C2318yes—
459#380C2314yes—
460#380C2314yes—
461#380C2314yes—
462#380C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2312yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2318yes—
496#376C2314yes—
497#376C2314yes—
498C2×#95C2314yes—
499C43C2311yescharacteristic
500C43C2311yescharacteristic
501C43C2312yes—
502C43C2311yescharacteristic
503C43C2311yescharacteristic
504C43C2312yes—
505C2×#41—28no—
506C2×#41—44no—
507C2×#41—44no—
508C2×#41—48no—
509C2×#41—48no—
510C2×#41—48no—
511C22×Q8C2412yes—
512C22×Q8C2414yes—
513C22×Q8C2412yes—
514C22×D4C2412yes—
515C22×D4C2414yes—
516C22×D4C2412yes—
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2412yes—
520C22×D4C2412yes—
521C22×D4C2412yes—
522C22×D4C2414yes—
523C22×D4C2418yes—
524C22×D4C2418yes—
525C23×C4C2412yes—
526C23×C4C2412yes—
527C23×C4C2412yes—
528C23×C4C2412yes—
529C23×C4C2412yes—
530C23×C4C2412yes—
531C23×C4C2412yes—
532C23×C4C2411yescharacteristic
533C23×C4C2414yes—
534C23×C4C2418yes—
535C23×C4C2412yes—
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C4⋊Q8—24no—
539C4⋊Q8—28no—
540C4⋊Q8—24no—
541#127—24no—
542#127—24no—
543#126—216no—
544#125—28no—
545#125—44no—
546#125—48no—
547#124—28no—
548#124—28no—
549#124—44no—
550#124—48no—
551#123—216no—
552C22⋊Q8—28no—
553C22⋊Q8—48no—
554C22⋊Q8—48no—
555C22⋊Q8—48no—
556C22⋊Q8—48no—
557C22⋊Q8—48no—
558C22⋊Q8—48no—
559#121—28no—
560#121—28no—
561#121—24no—
562#121—24no—
563#121—48no—
564#121—48no—
565#121—48no—
566#121—48no—
567#121—48no—
568#121—48no—
569C4×Q8—28no—
570C4×Q8—44no—
571C4×Q8—44no—
572C4×Q8—48no—
573C4×Q8—48no—
574C4×Q8—48no—
575C4×D4—216no—
576C4×D4—28no—
577C4×D4—24no—
578C4×D4—24no—
579C4×D4—28no—
580C4×D4—48no—
581C4×D4—48no—
582C4×D4—48no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—44no—
586C4×D4—44no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—44no—
592C4×D4—44no—
593#117—216no—
594#117—44no—
595#117—44no—
596#117—44no—
597#117—48no—
598#117—48no—
599#117—48no—
600C2×C4⋊C4C2414yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2412yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2418yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2418yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2418yes—
635C2×C22⋊C4C2414yes—
636C2×C22⋊C4C2414yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2414yes—
642C2×C22⋊C4C2414yes—
643C2×C22⋊C4C2414yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2412yes—
647C2×C22⋊C4C2412yes—
648C2×C22⋊C4C2412yes—
649C2×C22⋊C4C2412yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2418yes—
664C2×C22⋊C4C2418yes—
665C2×C22⋊C4C2418yes—
666C2×C22⋊C4C2418yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2418yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2418yes—
673C2×C42—24no—
674C2×C42—28no—
675C2×C42—28no—
676C2×C42—44no—
677C2×C42—44no—
678C2×C42—42no—
679C2×C42#4118yescomplemented
680C2×C42C2411yescharacteristic
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2414yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2412yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2418yes—
696C2×C42C2418yes—
697C2×C42C2418yes—
698C2×C42C2418yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#95C2411yescharacteristic
710#95C2414yes—
711#95C2418yes—
712#95C2411yescharacteristic
713#95C2414yes—
714#95C2418yes—
715#95C2418yes—
716#95C2411yescharacteristic
717#95C2412yes—
718#95C2411yescharacteristic
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2412yes—
727#95C2412yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745C24C2514yes—
746C24C2512yes—
747C24C2512yes—
748C24C2511yescharacteristic
749#41—432no—
750#41—832no—
751C2×Q8—24no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—28no—
755C2×Q8—28no—
756C2×Q8—24no—
757C2×Q8—28no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×D4—24no—
761C2×D4—24no—
762C2×D4—28no—
763C2×D4—24no—
764C2×D4—22no—
765C2×D4—22no—
766C2×D4—24no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—28no—
770C2×D4—28no—
771C2×D4—24no—
772C2×D4—28no—
773C2×D4—42no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—24no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—28no—
814C22×C4—42no—
815C22×C4—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4C2×#4114yes—
824C22×C4C2×#4114yes—
825C22×C4C2×#4114yes—
826C22×C4C2512yes—
827C22×C4C2512yes—
828C22×C4C2512yes—
829C22×C4C2514yes—
830C22×C4C2518yes—
831C22×C4C2514yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2518yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2512yes—
838C22×C4C2512yes—
839C22×C4C2514yes—
840C22×C4C2511yescharacteristic
841C22×C4C2511yescharacteristic
842C22×C4C2511yescharacteristic
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2511yescharacteristic
846C22×C4C2512yes—
847C4⋊C4—28no—
848C4⋊C4—28no—
849C4⋊C4—22no—
850C4⋊C4—22no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—28no—
858C4⋊C4—28no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—42no—
865C4⋊C4—42no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—48no—
875C4⋊C4—48no—
876C4⋊C4—48no—
877C4⋊C4—48no—
878C4⋊C4—48no—
879C4⋊C4—48no—
880C4⋊C4—48no—
881C4⋊C4—48no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—28no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—24no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—48no—
892C22⋊C4—48no—
893C22⋊C4—42no—
894C22⋊C4—42no—
895C22⋊C4—42no—
896C22⋊C4—42no—
897C22⋊C4—42no—
898C22⋊C4—42no—
899C22⋊C4—48no—
900C22⋊C4—42no—
901C22⋊C4—42no—
902C22⋊C4—48no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—48no—
910C22⋊C4—48no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C42—28no—
921C42—22no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—22no—
934C42—22no—
935C42—42no—
936C42—42no—
937C42—42no—
938C42—42no—
939C42—42no—
940C42—48no—
941C42—48no—
942C42—48no—
943C42—48no—
944C42C2×#4114yes—
945C42C2×#4114yes—
946C42C2×#4114yes—
947C42C2×#4114yes—
948C42H(5,𝔽2)14yes—
949C23—21no—
950C23—22no—
951C23—21no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—28no—
966C23—28no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23C22×#4112yes—
973C23C2611yescharacteristic
974Q8—48no—
975Q8—48no—
976Q8—416no—
977D4—48no—
978D4—44no—
979D4—44no—
980D4—48no—
981D4—48no—
982D4—48no—
983D4—48no—
984D4—416no—
985D4—88no—
986D4—816no—
987D4—168no—
988C2×C4—21no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—21no—
994C2×C4—28no—
995C2×C4—24no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—28no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—28no—
1019C2×C4—22no—
1020C2×C4—28no—
1021C2×C4—28no—
1022C2×C4—28no—
1023C2×C4—28no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—44no—
1036C2×C4—44no—
1037C2×C4—48no—
1038C2×C4—48no—
1039C2×C4—48no—
1040C2×C4—48no—
1041C2×C4—48no—
1042C2×C4—48no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—88no—
1046C2×C4—816no—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4112yes—
1049C2×C4C22×#4112yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C2×H(5,𝔽2)12yes—
1054C2×C4C2×H(5,𝔽2)14yes—
1055C2×C4#58512yes—
1056C2×C4#58514yes—
1057C2×C4#58514yes—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—48no—
1068C22—42no—
1069C22—42no—
1070C22—44no—
1071C22—44no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—44no—
1077C22—42no—
1078C22—48no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22C23×#4111yescharacteristic
1083C22C22×H(5,𝔽2)11yescharacteristic
1084C22C2×#58512yes—
1085C22C2×#58512yes—
1086C22C2×#58511yescharacteristic
1087C4—22no—
1088C4—22no—
1089C4—22no—
1090C4—22no—
1091C4—22no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—42no—
1096C4—42no—
1097C4—48no—
1098C4—42no—
1099C4—42no—
1100C4—44no—
1101C4—44no—
1102C4—44no—
1103C4—42no—
1104C4—42no—
1105C4—48no—
1106C4#350614yes—
1107C4#355118yes—
1108C2—42no—
1109C2—82no—
1110C2—82no—
1111C2—84no—
1112C2C2×#355112yes—
1113C2C2×#350611yescharacteristic
1114C2#6281511yescharacteristic
1115C2#6281511yescharacteristic
1116C2#6283912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59896C2semidirect
2. #59894C2semidirect
3. #46333C2semidirect
4. #46332C2semidirect
5. #39795C2semidirect
6. #39793C2semidirect
7. #39539C2semidirect
8. #39537C2semidirect
9. #39197C2semidirect
10. #39188C2semidirect
11. #39187C2semidirect
12. #37550C2semidirect
13. #37431C2semidirect
14. #36635C2semidirect
15. #36631C2semidirect
16. #36211C2semidirect
17. #36210C2semidirect
18. #36209C2semidirect
19. #36151C2semidirect
20. #36150C2semidirect
21. #36149C2semidirect
22. #35297C2semidirect
23. #35292C2semidirect
24. #34397C2semidirect
25. C4×#532C2semidirect
679. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#598962
#598942
#463332
#463322
#397952
#397932
#395392
#395372
#391972
#391882
#391872
#375502
#374312
#366352
#366312
#362112
#362102
#362092
#361512
#361502
#361492
#352972
#352922
#343972
C4×#5322