Finite Group Databasebeta

← #8429504

Subgroups — #8429504

Order 512.

4735 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59863C212yesmaximal, complemented
2#59827C211yesmaximal, characteristic, complemented
3#59259C212yesmaximal, complemented
4#59050C212yesmaximal, complemented
5#55541C218yesmaximal, complemented
6#53108C214yesmaximal, complemented
7#53101C214yesmaximal, complemented
8#53049C214yesmaximal, complemented
9#42935C214yesmaximal, complemented
10#42769C214yesmaximal, complemented
11#42594C214yesmaximal, complemented
12#39726C212yesmaximal, complemented
13#39608C212yesmaximal, complemented
14#39191C212yesmaximal, complemented
15#39137C212yesmaximal, complemented
16#38965C212yesmaximal, complemented
17#38922C212yesmaximal, complemented
18#37633C212yesmaximal, complemented
19#37627C212yesmaximal, complemented
20#37622C212yesmaximal, complemented
21#36563C211yesmaximal, characteristic, complemented
22#36187C211yesmaximal, characteristic, complemented
23#36134C211yesmaximal, characteristic, complemented
24#34934C211yesmaximal, characteristic, complemented
25#34932C211yesmaximal, characteristic, complemented
26#34929C211yesmaximal, characteristic, complemented
27C2×#559C2212yes—
28C2×#555C2212yes—
29C2×#533C2212yes—
30C2×#533C2212yes—
31C2×#529C2212yes—
32C2×#529C2212yes—
33#2868C2211yescharacteristic
34#2859C2212yes—
35#2857C2212yes—
36#2856C2212yes—
37#2837C2218yes—
38#2837C2218yes—
39#2830C2218yes—
40#2829C2218yes—
41#2816C2218yes—
42#2814C2218yes—
43#2814C2218yes—
44#2808C2218yes—
45#2768C2218yes—
46#2768C2218yes—
47#2763C2218yes—
48#2761C2218yes—
49#2753C2218yes—
50#2740C2218yes—
51#2739C2218yes—
52#2730C2218yes—
53#2724C2214yes—
54#2715C2218yes—
55#2711C2218yes—
56#2707C2218yes—
57#2705C2218yes—
58#2704C2218yes—
59#2692C2218yes—
60#2682C2218yes—
61#2681C2218yes—
62#2672C2218yes—
63#2664C2218yes—
64#2654C2218yes—
65#2651C2218yes—
66#2637C2218yes—
67#2629C2214yes—
68#2629C2214yes—
69#2628C2214yes—
70#2625C2214yes—
71#2624C2214yes—
72#2624C2214yes—
73#2621C2214yes—
74#2620C2214yes—
75#2620C2214yes—
76#2592C2214yes—
77#2592C2214yes—
78#2585C2218yes—
79#2584C2214yes—
80#2582C2212yes—
81#2582C2212yes—
82#2567C2212yes—
83#2565C2214yes—
84#2563C2212yes—
85#2563C2214yes—
86#2556C2214yes—
87#2554C2214yes—
88#2553C2214yes—
89#2552C2212yes—
90#2552C2211yescharacteristic
91#2552C2212yes—
92#2552C2211yescharacteristic
93#2551C2211yescharacteristic
94#2550C2214yes—
95#2548C2211yescharacteristic
96#2548C2214yes—
97#2547C2212yes—
98#2547C2211yescharacteristic
99#2547C2212yes—
100#2546C2211yescharacteristic
101#2545C2214yes—
102#2542C2212yes—
103#2542C2211yescharacteristic
104#2542C2211yescharacteristic
105#2541C2211yescharacteristic
106#2540C2214yes—
107#2538C2211yescharacteristic
108#2538C2212yes—
109#2538C2214yes—
110#2538C2211yescharacteristic
111#2537C2214yes—
112#2537C2211yescharacteristic
113#2537C2212yes—
114#2537C2212yes—
115#2513C2218yes—
116#2512C2212yes—
117#2508C2214yes—
118#2507C2214yes—
119#2507C2214yes—
120#2506C2212yes—
121#2500C2214yes—
122#2497C2214yes—
123#2497C2214yes—
124#2496C2212yes—
125#2492C2212yes—
126#2491C2214yes—
127#2491C2214yes—
128#2490C2212yes—
129#2490C2214yes—
130#2489C2212yes—
131#2487C2214yes—
132#2486C2214yes—
133#2485C2214yes—
134#2485C2214yes—
135#2485C2214yes—
136#2454C2214yes—
137#2452C2214yes—
138#2452C2212yes—
139#2451C2214yes—
140#2448C2218yes—
141#2447C2214yes—
142#2447C2214yes—
143#2445C2212yes—
144#2441C2214yes—
145#2441C2214yes—
146#2441C2214yes—
147#2440C2214yes—
148#2429C2212yes—
149#2429C2214yes—
150#2428C2214yes—
151#2427C2214yes—
152#2427C2212yes—
153#2426C2212yes—
154#2426C2214yes—
155#2426C2214yes—
156#2423C2214yes—
157#2423C2214yes—
158#2422C2212yes—
159#2416C2214yes—
160#2415C2214yes—
161#2415C2214yes—
162#2414C2214yes—
163#2396C2214yes—
164#2395C2214yes—
165#2392C2214yes—
166#2369C2212yes—
167#2365C2212yes—
168#2362C2214yes—
169#2355C2212yes—
170#2355C2214yes—
171#2354C2212yes—
172#2354C2212yes—
173#2354C2212yes—
174#2354C2214yes—
175Q8×C4⋊C4C2212yes—
176Q8×C4⋊C4C2212yes—
177D4×C4⋊C4C2212yes—
178D4×C4⋊C4C2212yes—
179#2324C2214yes—
180#2324C2214yes—
181#2316C2214yes—
182C4×C4⋊Q8C2211yescharacteristic
183C4×C4⋊Q8C2212yes—
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—
195#2285C2212yes—
196C42×Q8C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C42×D4C2211yescharacteristic
199#559—48no—
200#555—48no—
201#533—48no—
202#533—48no—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×#127C2311yescharacteristic
212C2×#127C2312yes—
213#529—48no—
214#529—48no—
215C2×#126C2314yes—
216C2×#126C2314yes—
217C2×#125C2312yes—
218C2×#125C2312yes—
219C2×#125C2314yes—
220C2×#125C2314yes—
221C2×#125C2314yes—
222C2×#124C2312yes—
223C2×#124C2314yes—
224C2×#124C2314yes—
225C2×#124C2312yes—
226C2×#124C2318yes—
227C2×#123C2314yes—
228C2×#123C2314yes—
229C2×#123C2318yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2312yes—
232C2×C22⋊Q8C2314yes—
233C2×C22⋊Q8C2312yes—
234C2×C22⋊Q8C2312yes—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2318yes—
240C2×C22⋊Q8C2314yes—
241C2×#121C2312yes—
242C2×#121C2314yes—
243C2×#121C2314yes—
244C2×#121C2312yes—
245C2×#121C2312yes—
246C2×#121C2314yes—
247C2×#121C2312yes—
248C2×#121C2318yes—
249C2×#121C2314yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2312yes—
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2312yes—
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×C4×D4C2311yescharacteristic
265C2×C4×D4C2314yes—
266C2×C4×D4C2312yes—
267C2×C4×D4C2314yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2314yes—
271C2×C4×D4C2311yescharacteristic
272C2×C4×D4C2311yescharacteristic
273C2×#117C2314yes—
274C2×#117C2314yes—
275C2×#117C2314yes—
276C2×#117C2314yes—
277C2×#117C2314yes—
278C2×#117C2314yes—
279C22×C4⋊C4C2314yes—
280C22×C42C2312yes—
281C22×C42C2312yes—
282#400C2314yes—
283#400C2318yes—
284#400C2318yes—
285#400C2314yes—
286#399C2318yes—
287#399C2318yes—
288#399C2314yes—
289#399C2318yes—
290#399C2314yes—
291#399C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2314yes—
301#398C2318yes—
302#398C2314yes—
303#398C2314yes—
304#398C2314yes—
305#397C2318yes—
306#397C2318yes—
307#397C2314yes—
308#397C2314yes—
309#397C2318yes—
310#397C2314yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2314yes—
317#396C2314yes—
318#396C2318yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2314yes—
326#396C2314yes—
327#396C2314yes—
328#396C2318yes—
329#395C2318yes—
330#395C2318yes—
331#395C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2318yes—
335#394C2318yes—
336#394C2318yes—
337#394C2318yes—
338#394C2314yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2318yes—
344#394C2318yes—
345#394C2314yes—
346#394C2314yes—
347#393C2314yes—
348#393C2318yes—
349#393C2318yes—
350#393C2318yes—
351#392C2318yes—
352#392C2314yes—
353#391C2314yes—
354#391C2312yes—
355#391C2312yes—
356#391C2314yes—
357#391C2312yes—
358#391C2314yes—
359#391C2314yes—
360#391C2314yes—
361#391C2312yes—
362#391C2314yes—
363#391C2318yes—
364#390C2312yes—
365#390C2312yes—
366#390C2312yes—
367#390C2314yes—
368#390C2312yes—
369#390C2314yes—
370#390C2312yes—
371#390C2318yes—
372#390C2314yes—
373#390C2318yes—
374#390C2314yes—
375#390C2314yes—
376#390C2314yes—
377#390C2318yes—
378#390C2312yes—
379#390C2312yes—
380#390C2312yes—
381#390C2318yes—
382#390C2312yes—
383#390C2312yes—
384#390C2312yes—
385#389C2314yes—
386#389C2312yes—
387#389C2314yes—
388#389C2312yes—
389#389C2312yes—
390#389C2312yes—
391#389C2314yes—
392#389C2312yes—
393#389C2312yes—
394#389C2314yes—
395#389C2312yes—
396#389C2318yes—
397#389C2318yes—
398#389C2314yes—
399#389C2312yes—
400#389C2314yes—
401#389C2314yes—
402#389C2314yes—
403#389C2314yes—
404#389C2312yes—
405#389C2314yes—
406#389C2318yes—
407#389C2318yes—
408#389C2318yes—
409#389C2314yes—
410#389C2314yes—
411#389C2314yes—
412#389C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#388C2318yes—
418#388C2318yes—
419#388C2318yes—
420#388C2314yes—
421#388C2314yes—
422#388C2318yes—
423#388C2318yes—
424#388C2318yes—
425#388C2318yes—
426#388C2318yes—
427#388C2318yes—
428#388C2318yes—
429#388C2318yes—
430#388C2314yes—
431#388C2314yes—
432#388C2314yes—
433#388C2314yes—
434#387C2318yes—
435#387C2318yes—
436#387C2318yes—
437#387C2318yes—
438#387C2314yes—
439#387C2314yes—
440#387C2318yes—
441#387C2318yes—
442#387C2318yes—
443#386C2318yes—
444#386C2318yes—
445#386C2314yes—
446#386C2314yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2314yes—
452#385C2314yes—
453#384C2311yescharacteristic
454#384C2312yes—
455#384C2311yescharacteristic
456#384C2311yescharacteristic
457#384C2312yes—
458#384C2312yes—
459#384C2314yes—
460#384C2312yes—
461#384C2314yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#384C2312yes—
466#382C2314yes—
467#382C2318yes—
468#382C2314yes—
469#382C2314yes—
470#381C2318yes—
471#380C2314yes—
472#380C2312yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2318yes—
477#380C2318yes—
478#380C2312yes—
479#380C2314yes—
480#380C2314yes—
481#380C2312yes—
482#380C2314yes—
483#380C2314yes—
484#380C2312yes—
485#380C2314yes—
486#380C2312yes—
487#380C2312yes—
488#380C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2311yescharacteristic
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2318yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C4⋊C4C2311yescharacteristic
507C4×C4⋊C4C2311yescharacteristic
508C4×C4⋊C4C2311yescharacteristic
509C4×C4⋊C4C2312yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2311yescharacteristic
512C4×C4⋊C4C2311yescharacteristic
513C4×C4⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2312yes—
519C4×C22⋊C4C2312yes—
520C4×C22⋊C4C2314yes—
521C4×C22⋊C4C2312yes—
522C4×C22⋊C4C2312yes—
523C43C2312yes—
524C43C2311yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2412yes—
527C22×Q8C2412yes—
528C22×Q8C2414yes—
529C22×Q8C2414yes—
530C22×D4C2411yescharacteristic
531C22×D4C2412yes—
532C22×D4C2411yescharacteristic
533C22×D4C2412yes—
534C22×D4C2412yes—
535C22×D4C2414yes—
536C22×D4C2414yes—
537C22×D4C2414yes—
538C22×D4C2418yes—
539C23×C4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2418yes—
547C4⋊Q8—24no—
548C4⋊Q8—28no—
549C4⋊Q8—24no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552C4⋊Q8—44no—
553C4⋊Q8—44no—
554C4⋊Q8—82no—
555#127—24no—
556#127—44no—
557#126—48no—
558#126—48no—
559#125—44no—
560#125—44no—
561#125—48no—
562#125—48no—
563#125—84no—
564#124—44no—
565#124—44no—
566#124—48no—
567#124—48no—
568#124—416no—
569#123—48no—
570#123—48no—
571#123—416no—
572C22⋊Q8—28no—
573C22⋊Q8—48no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—44no—
577C22⋊Q8—48no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—48no—
581C22⋊Q8—84no—
582C22⋊Q8—88no—
583#121—28no—
584#121—44no—
585#121—48no—
586#121—44no—
587#121—44no—
588#121—48no—
589#121—48no—
590#121—88no—
591#121—84no—
592C4×Q8—24no—
593C4×Q8—24no—
594C4×Q8—28no—
595C4×Q8—24no—
596C4×Q8—28no—
597C4×Q8—48no—
598C4×Q8—48no—
599C4×Q8—48no—
600C4×Q8—48no—
601C4×D4—24no—
602C4×D4—28no—
603C4×D4—24no—
604C4×D4—28no—
605C4×D4—24no—
606C4×D4—24no—
607C4×D4—42no—
608C4×D4—42no—
609C4×D4—48no—
610C4×D4—48no—
611C4×D4—44no—
612C4×D4—48no—
613C4×D4—48no—
614C4×D4—48no—
615#117—48no—
616#117—48no—
617#117—48no—
618#117—48no—
619#117—48no—
620#117—48no—
621C2×C4⋊C4—48no—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2412yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2411yescharacteristic
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2418yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2418yes—
698C2×C22⋊C4C2418yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2412yes—
702C2×C22⋊C4C2412yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2418yes—
708C2×C22⋊C4C2418yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2418yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C42—28no—
715C2×C42—28no—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2414yes—
722C2×C42C2411yescharacteristic
723C2×C42C2412yes—
724C2×C42C2411yescharacteristic
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2418yes—
733C2×C42C2418yes—
734C2×C42C2418yes—
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2412yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2412yes—
753#95C2412yes—
754#95C2412yes—
755#95C2414yes—
756#95C2418yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2414yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774C24C2512yes—
775C24C2514yes—
776C24C2512yes—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—24no—
780C2×Q8—24no—
781C2×Q8—24no—
782C2×Q8—28no—
783C2×Q8—22no—
784C2×Q8—24no—
785C2×Q8—24no—
786C2×Q8—24no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×Q8—44no—
792C2×D4—22no—
793C2×D4—24no—
794C2×D4—22no—
795C2×D4—24no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—22no—
799C2×D4—24no—
800C2×D4—22no—
801C2×D4—24no—
802C2×D4—28no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—24no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—44no—
811C2×D4—42no—
812C2×D4—44no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—48no—
817C2×D4—48no—
818C2×D4—48no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—28no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4C2511yescharacteristic
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2512yes—
847C22×C4C2514yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2518yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2511yescharacteristic
860C22×C4C2511yescharacteristic
861C22×C4C2512yes—
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C4⋊C4—22no—
867C4⋊C4—24no—
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—22no—
877C4⋊C4—28no—
878C4⋊C4—28no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—22no—
891C4⋊C4—22no—
892C4⋊C4—28no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—42no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—42no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—42no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C42−1+414yes—
922C22⋊C4—24no—
923C22⋊C4—28no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—42no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—42no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—48no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—48no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—24no—
963C42—24no—
964C42—24no—
965C42—24no—
966C42—28no—
967C42—28no—
968C42—22no—
969C42—24no—
970C42—22no—
971C42—24no—
972C42—22no—
973C42—24no—
974C42—48no—
975C42—48no—
976C42—48no—
977C42—42no—
978C42—41no—
979C42H(5,𝔽2)14yes—
980C42H(5,𝔽2)14yes—
981C422−1+414yes—
982C23—22no—
983C23—24no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—22no—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—24no—
1002C23—22no—
1003C23C2611yescharacteristic
1004Q8—48no—
1005Q8—44no—
1006Q8—48no—
1007Q8—88no—
1008Q8—88no—
1009D4—44no—
1010D4—48no—
1011D4—48no—
1012D4—44no—
1013D4—88no—
1014D4—84no—
1015D4—88no—
1016D4—88no—
1017D4—168no—
1018C2×C4—21no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—28no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—28no—
1073C2×C4—24no—
1074C2×C4—48no—
1075C2×C4—48no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—416no—
1079C2×C4—84no—
1080C2×C4—84no—
1081C2×C4—168no—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×H(5,𝔽2)12yes—
1085C2×C4C2×H(5,𝔽2)12yes—
1086C2×C4C2×H(5,𝔽2)12yes—
1087C2×C4C2×H(5,𝔽2)12yes—
1088C2×C4C2×2−1+414yes—
1089C2×C4C2×2−1+412yes—
1090C2×C4C2×2−1+412yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4#58512yes—
1094C2×C4#58512yes—
1095C22—44no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—44no—
1101C22—42no—
1102C22—42no—
1103C22—44no—
1104C22—42no—
1105C22—44no—
1106C22—42no—
1107C22—42no—
1108C22—44no—
1109C22—42no—
1110C22—42no—
1111C22—44no—
1112C22—42no—
1113C22—42no—
1114C22—44no—
1115C22—42no—
1116C22C22×H(5,𝔽2)11yescharacteristic
1117C22C22×H(5,𝔽2)11yescharacteristic
1118C22C22×2−1+411yescharacteristic
1119C22C22×2−1+411yescharacteristic
1120C22C2×#58511yescharacteristic
1121C22C2×#58511yescharacteristic
1122C22H(7,𝔽2)11yescharacteristic
1123C4—24no—
1124C4—22no—
1125C4—22no—
1126C4—22no—
1127C4—42no—
1128C4—44no—
1129C4—42no—
1130C4—44no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—44no—
1135C4—41no—
1136C4—42no—
1137C4—44no—
1138C4—44no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—48no—
1143C4#354714yes—
1144C4#354814yes—
1145C4#355414yes—
1146C2—82no—
1147C2—84no—
1148C2—82no—
1149C2C2×#355411yescharacteristic
1150C2C2×#354711yescharacteristic
1151C2C2×#354811yescharacteristic
1152C2#6293011yescharacteristic
1153C2#6294311yescharacteristic
1154C2#6295511yescharacteristic
1155C2#6302511yescharacteristic
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. #59863C2semidirect
2. #59827C2semidirect
3. #59259C2semidirect
4. #59050C2semidirect
5. #55541C2semidirect
6. #53108C2semidirect
7. #53101C2semidirect
8. #53049C2semidirect
9. #42935C2semidirect
10. #42769C2semidirect
11. #42594C2semidirect
12. #39726C2semidirect
13. #39608C2semidirect
14. #39191C2semidirect
15. #39137C2semidirect
16. #38965C2semidirect
17. #38922C2semidirect
18. #37633C2semidirect
19. #37627C2semidirect
20. #37622C2semidirect
21. #36563C2semidirect
22. #36187C2semidirect
23. #36134C2semidirect
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
#598632
#598272
#592592
#590502
#555412
#531082
#531012
#530492
#429352
#427692
#425942
#397262
#396082
#391912
#391372
#389652
#389222
#376332
#376272
#376222
#365632
#361872
#361342
#349342
#349322
#349292