Finite Group Databasebeta

← #8429475

Subgroups — #8429475

Order 512.

5085 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59823C212yesmaximal, complemented
2#59821C211yesmaximal, characteristic, complemented
3#59314C212yesmaximal, complemented
4#59057C212yesmaximal, complemented
5#55122C218yesmaximal, complemented
6#53123C214yesmaximal, complemented
7#53122C214yesmaximal, complemented
8#52959C214yesmaximal, complemented
9#42556C214yesmaximal, complemented
10#42550C214yesmaximal, complemented
11#42477C214yesmaximal, complemented
12#39607C212yesmaximal, complemented
13#39598C212yesmaximal, complemented
14#39191C212yesmaximal, complemented
15#39136C212yesmaximal, complemented
16#38965C212yesmaximal, complemented
17#38923C212yesmaximal, complemented
18#37640C212yesmaximal, complemented
19#37627C212yesmaximal, complemented
20#37620C212yesmaximal, complemented
21#36563C211yesmaximal, characteristic, complemented
22#36180C211yesmaximal, characteristic, complemented
23#36127C211yesmaximal, characteristic, complemented
24#34934C211yesmaximal, characteristic, complemented
25#34932C211yesmaximal, characteristic, complemented
26#34929C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×#554C2212yes—
29C2×#554C2214yes—
30C2×#547C2212yes—
31C2×#533C2212yes—
32C2×#532C2212yes—
33C2×#529C2212yes—
34C2×#529C2212yes—
35#2868C2211yescharacteristic
36#2859C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2837C2218yes—
40#2836C2218yes—
41#2836C2218yes—
42#2827C2218yes—
43#2823C2218yes—
44#2820C2218yes—
45#2814C2218yes—
46#2786C2218yes—
47#2768C2218yes—
48#2755C2218yes—
49#2753C2218yes—
50#2732C2218yes—
51#2730C2218yes—
52#2727C2214yes—
53#2727C2218yes—
54#2722C2218yes—
55#2720C2218yes—
56#2711C2218yes—
57#2707C2218yes—
58#2705C2218yes—
59#2704C2218yes—
60#2704C2218yes—
61#2704C2218yes—
62#2695C2218yes—
63#2683C2218yes—
64#2681C2218yes—
65#2651C2218yes—
66#2630C2218yes—
67#2629C2214yes—
68#2629C2214yes—
69#2629C2214yes—
70#2625C2214yes—
71#2624C2214yes—
72#2624C2214yes—
73#2620C2214yes—
74#2620C2214yes—
75#2620C2214yes—
76#2618C2218yes—
77#2616C2218yes—
78#2584C2214yes—
79#2582C2212yes—
80#2567C2212yes—
81#2567C2212yes—
82#2556C2214yes—
83#2554C2214yes—
84#2553C2214yes—
85#2552C2211yescharacteristic
86#2552C2212yes—
87#2552C2212yes—
88#2552C2211yescharacteristic
89#2552C2214yes—
90#2552C2212yes—
91#2551C2211yescharacteristic
92#2550C2214yes—
93#2548C2211yescharacteristic
94#2548C2212yes—
95#2547C2214yes—
96#2547C2212yes—
97#2547C2211yescharacteristic
98#2546C2211yescharacteristic
99#2542C2214yes—
100#2542C2211yescharacteristic
101#2542C2211yescharacteristic
102#2542C2212yes—
103#2541C2211yescharacteristic
104#2540C2214yes—
105#2538C2214yes—
106#2538C2214yes—
107#2538C2214yes—
108#2538C2211yescharacteristic
109#2538C2211yescharacteristic
110#2538C2214yes—
111#2538C2212yes—
112#2538C2214yes—
113#2537C2211yescharacteristic
114#2537C2212yes—
115#2537C2212yes—
116#2512C2214yes—
117#2512C2212yes—
118#2507C2214yes—
119#2507C2214yes—
120#2506C2214yes—
121#2506C2212yes—
122#2502C2214yes—
123#2497C2214yes—
124#2497C2214yes—
125#2496C2212yes—
126#2492C2212yes—
127#2490C2212yes—
128#2490C2214yes—
129#2489C2212yes—
130#2487C2214yes—
131#2485C2214yes—
132#2454C2214yes—
133#2454C2218yes—
134#2453C2214yes—
135#2452C2212yes—
136#2451C2214yes—
137#2449C2218yes—
138#2448C2214yes—
139#2445C2212yes—
140#2441C2214yes—
141#2440C2214yes—
142#2440C2214yes—
143#2440C2214yes—
144#2440C2214yes—
145#2432C2214yes—
146#2429C2214yes—
147#2429C2212yes—
148#2428C2214yes—
149#2427C2214yes—
150#2427C2212yes—
151#2426C2212yes—
152#2426C2214yes—
153#2423C2214yes—
154#2422C2214yes—
155#2422C2214yes—
156#2422C2212yes—
157#2417C2214yes—
158#2417C2214yes—
159#2417C2214yes—
160#2416C2214yes—
161#2416C2214yes—
162#2415C2214yes—
163#2414C2214yes—
164#2407C2218yes—
165#2396C2214yes—
166#2395C2214yes—
167#2392C2214yes—
168#2369C2212yes—
169#2366C2214yes—
170#2361C2214yes—
171#2355C2212yes—
172#2354C2212yes—
173Q8×C4⋊C4C2212yes—
174Q8×C4⋊C4C2212yes—
175D4×C4⋊C4C2212yes—
176D4×C4⋊C4C2212yes—
177D4×C4⋊C4C2212yes—
178D4×C4⋊C4C2212yes—
179#2324C2214yes—
180#2323C2214yes—
181#2316C2214yes—
182C4×C4⋊Q8C2212yes—
183C4×C4⋊Q8C2211yescharacteristic
184C4×C4⋊Q8C2211yescharacteristic
185C4×C4⋊Q8C2212yes—
186C4×#127C2212yes—
187C4×#127C2211yescharacteristic
188C4×C22⋊Q8C2212yes—
189C4×C22⋊Q8C2212yes—
190C4×#121C2212yes—
191C4×#121C2212yes—
192#2293C2212yes—
193#2293C2212yes—
194#2285C2212yes—
195C2×#384C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199C22×#41C2314yes—
200#556—48no—
201#554—416no—
202#554—48no—
203#547—48no—
204#533—48no—
205#532—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×#127C2312yes—
215C2×#127C2311yescharacteristic
216#529—48no—
217#529—48no—
218C2×#126C2314yes—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#125C2314yes—
222C2×#125C2314yes—
223C2×#125C2312yes—
224C2×#125C2312yes—
225C2×#125C2318yes—
226C2×#125C2314yes—
227C2×#124C2314yes—
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#124C2314yes—
231C2×#123C2314yes—
232C2×#123C2314yes—
233C2×#123C2318yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×C22⋊Q8C2314yes—
244C2×C22⋊Q8C2318yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2312yes—
247C2×C22⋊Q8C2318yes—
248C2×C22⋊Q8C2318yes—
249C2×#121C2312yes—
250C2×#121C2312yes—
251C2×#121C2314yes—
252C2×#121C2314yes—
253C2×#121C2314yes—
254C2×#121C2312yes—
255C2×#121C2312yes—
256C2×#121C2318yes—
257C2×C4×Q8C2312yes—
258C2×C4×Q8C2312yes—
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2314yes—
263C2×C4×Q8C2314yes—
264C2×C4×Q8C2314yes—
265C2×C4×D4C2311yescharacteristic
266C2×C4×D4C2312yes—
267C2×C4×D4C2312yes—
268C2×C4×D4C2311yescharacteristic
269C2×C4×D4C2311yescharacteristic
270C2×C4×D4C2311yescharacteristic
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2318yes—
280C2×C4×D4C2314yes—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C2×#117C2314yes—
284C2×#117C2314yes—
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2314yes—
288C22×C4⋊C4C2314yes—
289C22×C42C2312yes—
290C22×C42C2312yes—
291#400C2314yes—
292#400C2318yes—
293#400C2314yes—
294#400C2318yes—
295#399C2318yes—
296#399C2318yes—
297#399C2318yes—
298#399C2318yes—
299#399C2314yes—
300#399C2314yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2314yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2318yes—
311#398C2318yes—
312#398C2314yes—
313#398C2314yes—
314#398C2314yes—
315#398C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2314yes—
319#397C2318yes—
320#397C2318yes—
321#397C2314yes—
322#397C2318yes—
323#397C2314yes—
324#397C2314yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2314yes—
330#396C2318yes—
331#396C2318yes—
332#396C2318yes—
333#396C2318yes—
334#396C2318yes—
335#396C2314yes—
336#396C2318yes—
337#396C2318yes—
338#396C2314yes—
339#396C2318yes—
340#396C2314yes—
341#395C2318yes—
342#395C2318yes—
343#395C2318yes—
344#395C2314yes—
345#394C2314yes—
346#394C2318yes—
347#394C2318yes—
348#394C2318yes—
349#394C2318yes—
350#394C2314yes—
351#394C2318yes—
352#394C2318yes—
353#394C2318yes—
354#394C2318yes—
355#394C2318yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#393C2314yes—
360#392C2318yes—
361#392C2314yes—
362#391C2314yes—
363#391C2312yes—
364#391C2312yes—
365#391C2314yes—
366#391C2314yes—
367#391C2314yes—
368#391C2314yes—
369#391C2318yes—
370#391C2312yes—
371#391C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2312yes—
376#390C2314yes—
377#390C2312yes—
378#390C2314yes—
379#390C2318yes—
380#390C2314yes—
381#390C2314yes—
382#390C2312yes—
383#390C2312yes—
384#390C2312yes—
385#390C2314yes—
386#390C2318yes—
387#390C2312yes—
388#390C2318yes—
389#390C2312yes—
390#390C2312yes—
391#389C2314yes—
392#389C2312yes—
393#389C2314yes—
394#389C2312yes—
395#389C2312yes—
396#389C2312yes—
397#389C2314yes—
398#389C2312yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2312yes—
404#389C2314yes—
405#389C2318yes—
406#389C2314yes—
407#389C2318yes—
408#389C2312yes—
409#389C2318yes—
410#389C2318yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2314yes—
415#389C2314yes—
416#389C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2314yes—
420#389C2318yes—
421#389C2318yes—
422#389C2312yes—
423#389C2312yes—
424#389C2312yes—
425#389C2312yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2318yes—
431#388C2314yes—
432#388C2314yes—
433#388C2318yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#387C2318yes—
439#387C2318yes—
440#387C2318yes—
441#387C2318yes—
442#387C2314yes—
443#387C2314yes—
444#386C2318yes—
445#386C2318yes—
446#386C2318yes—
447#386C2318yes—
448#386C2314yes—
449#386C2314yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2318yes—
455#385C2318yes—
456#385C2314yes—
457#385C2314yes—
458#384C2311yescharacteristic
459#384C2312yes—
460#384C2311yescharacteristic
461#384C2312yes—
462#384C2312yes—
463#384C2311yescharacteristic
464#384C2314yes—
465#384C2314yes—
466#384C2314yes—
467#384C2312yes—
468#384C2312yes—
469#384C2314yes—
470#384C2312yes—
471#384C2314yes—
472#384C2312yes—
473#384C2312yes—
474#382C2314yes—
475#382C2314yes—
476#380C2318yes—
477#380C2318yes—
478#380C2314yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2314yes—
483#380C2314yes—
484#380C2314yes—
485#380C2314yes—
486#380C2318yes—
487#380C2318yes—
488#380C2312yes—
489#380C2312yes—
490#380C2312yes—
491#380C2312yes—
492#380C2312yes—
493#380C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C4⋊C4C2311yescharacteristic
514C4×C4⋊C4C2311yescharacteristic
515C4×C4⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2312yes—
524C4×C22⋊C4C2312yes—
525C43C2312yes—
526C43C2311yescharacteristic
527C2×#41—48no—
528C2×#41—48no—
529C2×#41—84no—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2411yescharacteristic
533C22×Q8C2414yes—
534C22×Q8C2414yes—
535C22×D4C2411yescharacteristic
536C22×D4C2412yes—
537C22×D4C2412yes—
538C22×D4C2414yes—
539C22×D4C2411yescharacteristic
540C22×D4C2414yes—
541C22×D4C2414yes—
542C22×D4C2412yes—
543C22×D4C2418yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2414yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2418yes—
552C23×C4C2418yes—
553C4⋊Q8—28no—
554C4⋊Q8—28no—
555C4⋊Q8—24no—
556C4⋊Q8—24no—
557C4⋊Q8—44no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560C4⋊Q8—82no—
561#127—28no—
562#127—24no—
563#126—48no—
564#126—48no—
565#126—416no—
566#125—44no—
567#125—44no—
568#125—48no—
569#125—48no—
570#125—416no—
571#125—84no—
572#124—44no—
573#124—44no—
574#124—48no—
575#124—48no—
576#123—48no—
577#123—48no—
578#123—416no—
579C22⋊Q8—28no—
580C22⋊Q8—28no—
581C22⋊Q8—416no—
582C22⋊Q8—416no—
583C22⋊Q8—48no—
584C22⋊Q8—48no—
585C22⋊Q8—44no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—48no—
590C22⋊Q8—48no—
591C22⋊Q8—416no—
592C22⋊Q8—48no—
593C22⋊Q8—88no—
594#121—28no—
595#121—28no—
596#121—44no—
597#121—44no—
598#121—48no—
599#121—48no—
600#121—48no—
601#121—88no—
602C4×Q8—24no—
603C4×Q8—24no—
604C4×Q8—28no—
605C4×Q8—24no—
606C4×Q8—28no—
607C4×Q8—48no—
608C4×Q8—48no—
609C4×Q8—48no—
610C4×D4—24no—
611C4×D4—24no—
612C4×D4—24no—
613C4×D4—28no—
614C4×D4—24no—
615C4×D4—24no—
616C4×D4—28no—
617C4×D4—24no—
618C4×D4—48no—
619C4×D4—48no—
620C4×D4—48no—
621C4×D4—48no—
622C4×D4—48no—
623C4×D4—44no—
624C4×D4—48no—
625C4×D4—416no—
626#117—48no—
627#117—48no—
628#117—48no—
629#117—48no—
630C2×C4⋊C4—216no—
631C2×C4⋊C4—48no—
632C2×C4⋊C4—48no—
633C2×C4⋊C4—84no—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2414yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2414yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2418yes—
682C2×C4⋊C4C2414yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2414yes—
687C2×C4⋊C4C2418yes—
688C2×C4⋊C4C2414yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2412yes—
699C2×C22⋊C4C2412yes—
700C2×C22⋊C4C2412yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2418yes—
712C2×C22⋊C4C2418yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2414yes—
716C2×C22⋊C4C2418yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2414yes—
719C2×C22⋊C4C2414yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2414yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2418yes—
725C2×C22⋊C4C2418yes—
726C2×C22⋊C4C2414yes—
727C2×C22⋊C4C2418yes—
728C2×C42—28no—
729C2×C42—28no—
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2414yes—
735C2×C42C2414yes—
736C2×C42C2411yescharacteristic
737C2×C42C2412yes—
738C2×C42C2412yes—
739C2×C42C2412yes—
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2412yes—
743C2×C42C2412yes—
744C2×C42C2412yes—
745C2×C42C2412yes—
746C2×C42C2418yes—
747C2×C42C2418yes—
748C2×C42C2412yes—
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753#95C2412yes—
754#95C2412yes—
755#95C2412yes—
756#95C2412yes—
757#95C2412yes—
758#95C2412yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2412yes—
766#95C2412yes—
767#95C2412yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777#95C2414yes—
778#95C2418yes—
779#95C2414yes—
780#95C2418yes—
781#95C2418yes—
782#95C2418yes—
783#95C2418yes—
784#95C2418yes—
785C24C2514yes—
786C24C2512yes—
787C24C2512yes—
788#41—832no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—22no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—28no—
796C2×Q8—28no—
797C2×Q8—22no—
798C2×Q8—24no—
799C2×Q8—24no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×D4—28no—
805C2×D4—28no—
806C2×D4—28no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—24no—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—22no—
815C2×D4—22no—
816C2×D4—24no—
817C2×D4—28no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—44no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—44no—
824C2×D4—44no—
825C2×D4—48no—
826C2×D4—48no—
827C2×D4—44no—
828C2×D4—44no—
829C2×D4—48no—
830C2×D42−1+414yes—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—28no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—28no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—28no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—216no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4C2512yes—
859C22×C4C2511yescharacteristic
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2514yes—
865C22×C4C2514yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2514yes—
870C22×C4C2518yes—
871C22×C4C2514yes—
872C22×C4C2512yes—
873C22×C4C2511yescharacteristic
874C22×C4C2512yes—
875C22×C4C2511yescharacteristic
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C4⋊C4—28no—
882C4⋊C4—216no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—22no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—22no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—22no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—42no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—42no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—48no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—48no—
929C4⋊C4—44no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—44no—
934C4⋊C4—48no—
935C4⋊C4—44no—
936C4⋊C4—42no—
937C4⋊C4—44no—
938C4⋊C4H(5,𝔽2)14yes—
939C4⋊C42−1+414yes—
940C22⋊C4—24no—
941C22⋊C4—28no—
942C22⋊C4—24no—
943C22⋊C4—24no—
944C22⋊C4—24no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—24no—
948C22⋊C4—24no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C22⋊C4—44no—
970C22⋊C4—48no—
971C22⋊C4—44no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—44no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—24no—
981C42—24no—
982C42—24no—
983C42—28no—
984C42—28no—
985C42—22no—
986C42—24no—
987C42—22no—
988C42—22no—
989C42—24no—
990C42—24no—
991C42—48no—
992C42—48no—
993C42—42no—
994C42—41no—
995C42H(5,𝔽2)14yes—
996C42H(5,𝔽2)14yes—
997C422−1+414yes—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—24no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—24no—
1009C23—24no—
1010C23—22no—
1011C23—22no—
1012C23—24no—
1013C23—24no—
1014C23—22no—
1015C23—24no—
1016C23—24no—
1017C23—22no—
1018C23C2×2−1+414yes—
1019C23C2611yescharacteristic
1020Q8—48no—
1021Q8—48no—
1022Q8—44no—
1023Q8—88no—
1024Q8—88no—
1025D4—28no—
1026D4—416no—
1027D4—48no—
1028D4—44no—
1029D4—48no—
1030D4—48no—
1031D4—88no—
1032D4—88no—
1033D4—816no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—28no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—24no—
1088C2×C4—28no—
1089C2×C4—48no—
1090C2×C4—48no—
1091C2×C4—48no—
1092C2×C4—416no—
1093C2×C4—48no—
1094C2×C4—48no—
1095C2×C4—48no—
1096C2×C4—816no—
1097C2×C4—168no—
1098C2×C4C2×H(5,𝔽2)12yes—
1099C2×C4C2×H(5,𝔽2)12yes—
1100C2×C4C2×H(5,𝔽2)14yes—
1101C2×C4C2×H(5,𝔽2)12yes—
1102C2×C4C2×H(5,𝔽2)12yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4C2×H(5,𝔽2)12yes—
1105C2×C4C2×H(5,𝔽2)12yes—
1106C2×C4C2×2−1+414yes—
1107C2×C4C2×2−1+412yes—
1108C2×C4C2×2−1+412yes—
1109C2×C4C2×2−1+412yes—
1110C2×C4C2×2−1+412yes—
1111C2×C4C2×2−1+412yes—
1112C22—24no—
1113C22—24no—
1114C22—24no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—44no—
1121C22—44no—
1122C22—42no—
1123C22—44no—
1124C22—42no—
1125C22—44no—
1126C22—42no—
1127C22—42no—
1128C22—44no—
1129C22—42no—
1130C22—44no—
1131C22—42no—
1132C22—44no—
1133C22C22×H(5,𝔽2)11yescharacteristic
1134C22C22×H(5,𝔽2)11yescharacteristic
1135C22C22×H(5,𝔽2)11yescharacteristic
1136C22C22×2−1+411yescharacteristic
1137C22C22×2−1+411yescharacteristic
1138C22C22×2−1+411yescharacteristic
1139C22H(7,𝔽2)11yescharacteristic
1140C4—24no—
1141C4—22no—
1142C4—24no—
1143C4—22no—
1144C4—22no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—44no—
1150C4—42no—
1151C4—44no—
1152C4—44no—
1153C4—41no—
1154C4—48no—
1155C4—44no—
1156C4—42no—
1157C4—42no—
1158C4—44no—
1159C4—42no—
1160C4#354814yes—
1161C4#354814yes—
1162C4#355214yes—
1163C2—44no—
1164C2—82no—
1165C2—84no—
1166C2C2×#355211yescharacteristic
1167C2C2×#354811yescharacteristic
1168C2C2×#354811yescharacteristic
1169C2#6291211yescharacteristic
1170C2#6294311yescharacteristic
1171C2#6294411yescharacteristic
1172C2#6301611yescharacteristic
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. #59823C2semidirect
2. #59821C2semidirect
3. #59314C2semidirect
4. #59057C2semidirect
5. #55122C2semidirect
6. #53123C2semidirect
7. #53122C2semidirect
8. #52959C2semidirect
9. #42556C2semidirect
10. #42550C2semidirect
11. #42477C2semidirect
12. #39607C2semidirect
13. #39598C2semidirect
14. #39191C2semidirect
15. #39136C2semidirect
16. #38965C2semidirect
17. #38923C2semidirect
18. #37640C2semidirect
19. #37627C2semidirect
20. #37620C2semidirect
21. #36563C2semidirect
22. #36180C2semidirect
23. #36127C2semidirect
24. #34934C2semidirect
25. #34932C2semidirect
26. #34929C2semidirect

Maximal subgroups

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

subgroupindex
#598232
#598212
#593142
#590572
#551222
#531232
#531222
#529592
#425562
#425502
#424772
#396072
#395982
#391912
#391362
#389652
#389232
#376402
#376272
#376202
#365632
#361802
#361272
#349342
#349322
#349292