Finite Group Databasebeta

← #7683482

Subgroups — #7683482

Order 512.

5282 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60016C214yesmaximal, complemented
2#59964C214yesmaximal, complemented
3#59952C214yesmaximal, complemented
4#59947C212yesmaximal, complemented
5#59819C212yesmaximal, complemented
6#59701C214yesmaximal, complemented
7#59339C212yesmaximal, complemented
8#59322C211yesmaximal, characteristic, complemented
9#59303C211yesmaximal, characteristic, complemented
10#43938C214yesmaximal, complemented
11#43913C214yesmaximal, complemented
12#43882C212yesmaximal, complemented
13#43842C214yesmaximal, complemented
14#43823C212yesmaximal, complemented
15#43481C212yesmaximal, complemented
16#43444C214yesmaximal, complemented
17#43389C212yesmaximal, complemented
18#35465C214yesmaximal, complemented
19#35395C212yesmaximal, complemented
20#34877C212yesmaximal, complemented
21C2×#2500C211yesmaximal, characteristic, complemented
22#34303C214yesmaximal, complemented
23#34277C212yesmaximal, complemented
24C2×#551C2214yes—
25C2×#538C2212yes—
26C2×#538C2212yes—
27C2×#529C2212yes—
28C22×#121C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2803C2214yescomplemented
31#2803C2214yescomplemented
32#2803C2214yescomplemented
33#2795C2212yescomplemented
34#2795C2214yescomplemented
35#2795C2212yescomplemented
36#2792C2212yescomplemented
37#2792C2212yescomplemented
38#2785C2214yescomplemented
39#2785C2212yescomplemented
40#2784C2212yescomplemented
41#2783C2214yescomplemented
42#2781C2214yescomplemented
43#2769C2212yescomplemented
44#2756C2214yescomplemented
45#2733C2212yescomplemented
46#2733C2214yescomplemented
47#2732C2212yescomplemented
48#2731C2214yescomplemented
49#2730C2214yescomplemented
50#2727C2214yescomplemented
51#2727C2212yescomplemented
52#2714C2214yescomplemented
53#2705C2214yescomplemented
54#2705C2214yescomplemented
55#2699C2212yescomplemented
56#2686C2214yescomplemented
57#2682C2214yescomplemented
58#2682C2212yescomplemented
59#2673C2214yescomplemented
60#2612C2212yescomplemented
61#2611C2212yescomplemented
62#2611C2212yescomplemented
63#2610C2214yescomplemented
64#2610C2212yescomplemented
65#2610C2214yescomplemented
66#2610C2214yescomplemented
67#2610C2212yescomplemented
68#2609C2212yescomplemented
69#2604C2214yescomplemented
70#2602C2214yescomplemented
71#2601C2214yescomplemented
72#2601C2214yescomplemented
73#2601C2214yescomplemented
74#2593C2212yescomplemented
75#2593C2214yescomplemented
76#2591C2212yes—
77#2591C2212yes—
78#2583C2212yes—
79#2583C2212yes—
80#2582C2211yescharacteristic, complemented
81#2574C2214yescomplemented
82#2571C2211yescharacteristic, complemented
83#2567C2214yescomplemented
84#2561C2212yes—
85#2559C2214yes—
86#2559C2214yes—
87#2559C2214yescomplemented
88#2558C2214yescomplemented
89#2555C2214yes—
90#2555C2214yes—
91#2555C2212yescomplemented
92#2555C2214yescomplemented
93#2554C2214yescomplemented
94#2554C2214yescomplemented
95#2554C2214yescomplemented
96#2554C2214yescomplemented
97#2551C2211yescharacteristic, complemented
98#2548C2214yescomplemented
99#2545C2214yescomplemented
100#2543C2214yescomplemented
101#2539C2212yes—
102#2539C2214yes—
103#2537C2211yescharacteristic, complemented
104#2534C2214yes—
105#2529C2214yescomplemented
106#2526C2214yescomplemented
107#2526C2214yescomplemented
108#2521C2214yescomplemented
109#2519C2214yescomplemented
110#2518C2214yescomplemented
111#2518C2214yescomplemented
112#2512C2214yescomplemented
113#2508C2214yescomplemented
114#2507C2214yescomplemented
115#2500C2212yes—
116#2500C2214yes—
117#2500C2212yes—
118#2500C2212yes—
119#2500C2214yes—
120#2500C2212yes—
121#2500C2214yescomplemented
122#2500C2214yescomplemented
123#2500C2214yescomplemented
124#2498C2214yescomplemented
125#2497C2214yescomplemented
126#2491C2214yescomplemented
127#2491C2214yescomplemented
128#2488C2214yes—
129#2479C2214yescomplemented
130#2479C2214yescomplemented
131#2476C2214yescomplemented
132#2476C2214yescomplemented
133#2474C2214yescomplemented
134#2472C2214yes—
135#2467C2214yescomplemented
136#2464C2214yes—
137#2464C2214yes—
138#2456C2214yescomplemented
139#2445C2214yescomplemented
140#2440C2214yes—
141#2435C2212yes—
142#2433C2212yes—
143#2428C2214yes—
144#2428C2214yes—
145#2428C2214yescomplemented
146#2426C2214yescomplemented
147#2426C2214yescomplemented
148#2425C2214yes—
149#2424C2214yes—
150#2416C2214yes—
151#2414C2214yescomplemented
152#2414C2214yescomplemented
153#2413C2214yes—
154#2411C2214yes—
155#2410C2214yes—
156#2410C2214yes—
157#2396C2212yescomplemented
158#2396C2212yescomplemented
159#2392C2212yescomplemented
160#2392C2212yescomplemented
161C2×#394C2214yes—
162#2374C2214yescomplemented
163#2374C2214yescomplemented
164#2373C2214yescomplemented
165#2373C2214yescomplemented
166#2373C2214yescomplemented
167#2373C2214yescomplemented
168#2372C2214yescomplemented
169#2372C2214yescomplemented
170#2367C2214yescomplemented
171#2364C2214yescomplemented
172#2363C2214yescomplemented
173#2363C2214yescomplemented
174#2363C2214yescomplemented
175#2362C2214yescomplemented
176#2360C2214yes—
177#2359C2214yes—
178#2359C2214yescomplemented
179#2359C2214yescomplemented
180#2358C2214yes—
181#2354C2212yescomplemented
182#2353C2214yescomplemented
183#2352C2214yes—
184Q8×C4⋊C4C2212yescomplemented
185#2346C2214yescomplemented
186#2346C2214yescomplemented
187#2343C2214yes—
188#2342C2214yes—
189#2342C2214yes—
190#2335C2214yescomplemented
191#2335C2214yescomplemented
192#2334C2214yescomplemented
193#2332C2214yescomplemented
194#2329C2212yes—
195#2325C2212yes—
196#2321C2214yes—
197#2321C2214yes—
198#2312C2212yes—
199C4×#126C2214yescomplemented
200C4×#124C2214yescomplemented
201C4×C22⋊Q8C2212yes—
202C4×#123C2214yes—
203C4×#121C2212yes—
204C4×#120C2214yes—
205#2298C2214yescomplemented
206#2293C2214yescomplemented
207#2293C2214yescomplemented
208#2293C2214yescomplemented
209C2×#390C2211yescharacteristic
210C2×#390C2211yescharacteristic
211#2290C2214yes—
212C2×#388C2214yes—
213C2×#384C2211yescharacteristic
214C2×#382C2211yescharacteristic
215#2275C2214yes—
216#2273C2212yes—
217C4×#117C2212yes—
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×D4C2311yescharacteristic
220C23×D4C2312yes—
221C24×C4C2311yescharacteristic
222#551—232no—
223#538—216no—
224#538—48no—
225C2×C4⋊Q8C2314yes—
226C2×#127C2314yes—
227#529—48no—
228C2×#126C2314yes—
229C2×#126C2314yes—
230C2×#126C2314yes—
231C2×#126C2314yes—
232C2×#126C2314yes—
233C2×#125C2312yes—
234C2×#124C2314yes—
235C2×#124C2314yes—
236C2×#124C2312yes—
237C2×#124C2314yes—
238C2×#124C2314yes—
239C2×#124C2314yes—
240C2×#123C2314yes—
241C2×#123C2314yes—
242C2×#123C2314yes—
243C2×#123C2314yes—
244C2×#123C2314yes—
245C2×#123C2314yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2312yes—
248C2×C22⋊Q8C2312yes—
249C2×C22⋊Q8C2312yes—
250C2×#121—44no—
251C2×#121C2312yes—
252C2×#121C2314yes—
253C2×#121C2312yes—
254C2×#121C2312yes—
255C2×#121C2314yes—
256C2×#121C2314yes—
257C2×#121C2312yes—
258C2×#121C2314yes—
259C2×#121C2312yes—
260C2×#121C2314yes—
261C2×#121C2314yes—
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267C2×#120C2314yes—
268C2×C4×Q8C2312yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2314yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2312yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2314yes—
280C2×#117—44no—
281C2×#117C2314yes—
282C2×#117C2314yes—
283C2×#117C2312yes—
284C2×#117C2312yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2312yes—
288C2×#117C2312yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2314yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2312yes—
297C22×C22⋊C4C2314yes—
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C42C2312yes—
302C22×C42C2311yescharacteristic
303C22×C42C2311yescharacteristic
304#400C2312yes—
305#400C2312yes—
306#400C2312yes—
307#400C2312yes—
308#400C2314yes—
309#400C2314yes—
310#399C2314yes—
311#399C2312yes—
312#399C2312yes—
313#399C2314yes—
314#398C2314yes—
315#398C2312yes—
316#398C2312yes—
317#398C2312yes—
318#398C2312yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#397C2312yes—
324#397C2312yes—
325#397C2314yes—
326#397C2314yes—
327#397C2314yes—
328#396C2314yes—
329#396C2314yes—
330#396C2314yes—
331#396C2314yes—
332#396C2314yes—
333#396C2314yes—
334#396C2314yes—
335#396C2314yes—
336#396C2314yes—
337#396C2314yes—
338#395C2312yes—
339#395C2312yes—
340#395C2314yes—
341#395C2314yes—
342#395C2312yes—
343#395C2312yes—
344#394C2312yes—
345#394C2312yes—
346#394C2312yes—
347#394C2312yes—
348#394C2314yes—
349#394C2314yes—
350#394C2314yes—
351#394C2314yes—
352#394C2314yes—
353#394C2314yes—
354#394C2314yes—
355#394C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2314yes—
366#394C2314yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#393C2312yes—
374#393C2312yes—
375#393C2314yes—
376#393C2314yes—
377#392C2314yes—
378#392C2312yes—
379#392C2312yes—
380#392C2314yes—
381#392C2314yes—
382#392C2314yes—
383#392C2314yes—
384#392C2314yes—
385#392C2314yes—
386#392C2314yes—
387#392C2314yes—
388#391C2312yes—
389#391C2314yes—
390#391C2314yes—
391#391C2314yes—
392#390C2314yes—
393#390C2314yes—
394#390C2314yes—
395#390C2314yes—
396#390C2314yes—
397#390C2312yes—
398#390C2314yes—
399#390C2314yes—
400#390C2314yes—
401#390C2314yes—
402#390C2314yes—
403#390C2314yes—
404#390C2314yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
408#390C2314yes—
409#390C2312yes—
410#390C2312yes—
411#390C2312yes—
412#390C2314yes—
413#390C2312yes—
414#390C2314yes—
415#390C2314yes—
416#390C2312yes—
417#390C2312yes—
418#389C2314yes—
419#389C2314yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2312yes—
434#389C2312yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#384C2314yes—
544#384C2314yes—
545#384C2311yescharacteristic
546#384C2311yescharacteristic
547#384C2311yescharacteristic
548#384C2311yescharacteristic
549#383C2314yes—
550#382C2314yes—
551#382C2312yes—
552#382C2314yes—
553#382C2312yes—
554#382C2314yes—
555#382C2312yes—
556#382C2312yes—
557#381C2314yes—
558#381C2314yes—
559#380C2312yes—
560#380C2312yes—
561#380C2314yes—
562#380C2314yes—
563#380C2314yes—
564#380C2314yes—
565#379C2314yes—
566#379C2314yes—
567C4×C4⋊C4C2314yes—
568C4×C4⋊C4C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2312yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2312yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2314yes—
577C4×C4⋊C4C2314yes—
578C4×C4⋊C4C2314yes—
579C4×C4⋊C4C2314yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2312yes—
582C4×C4⋊C4C2314yes—
583C4×C22⋊C4C2314yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2312yes—
587C4×C22⋊C4C2314yes—
588C4×C22⋊C4C2314yes—
589C4×C22⋊C4C2314yes—
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2312yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2312yes—
608C4×C22⋊C4C2312yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611#376C2314yes—
612#376C2312yes—
613#376C2314yes—
614#376C2314yes—
615#376C2312yes—
616C2×#95C2312yes—
617C2×#95C2314yes—
618C2×#95C2314yes—
619C43C2314yes—
620C25C2412yes—
621C25C2411yescharacteristic
622C22×Q8C2412yes—
623C22×Q8C2412yes—
624C22×Q8C2412yes—
625C22×D4—42no—
626C22×D4—42no—
627C22×D4—42no—
628C22×D4—44no—
629C22×D4—84no—
630C22×D4C2414yes—
631C22×D4C2414yes—
632C22×D4C2414yes—
633C22×D4C2414yes—
634C22×D4C2414yes—
635C22×D4C2412yes—
636C22×D4C2412yes—
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C22×D4C2414yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C23×C4—24no—
645C23×C4—42no—
646C23×C4—42no—
647C23×C4C2412yes—
648C23×C4C2411yescharacteristic
649C23×C4C2412yes—
650C23×C4C2412yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2412yes—
660C23×C4C2411yescharacteristic
661C4⋊Q8—84no—
662#127—84no—
663#126—216no—
664#126—216no—
665#126—216no—
666#126—48no—
667#126—48no—
668#125—44no—
669#124—216no—
670#124—216no—
671#124—44no—
672#124—48no—
673#124—84no—
674#124—84no—
675#123—216no—
676#123—216no—
677#123—216no—
678#123—216no—
679#123—48no—
680#123—48no—
681C22⋊Q8—216no—
682C22⋊Q8—44no—
683C22⋊Q8—44no—
684C22⋊Q8#41116yes—
685#121—28no—
686#121—216no—
687#121—44no—
688#121—48no—
689#121—44no—
690#121—48no—
691#121—48no—
692#121—48no—
693#121—44no—
694#121—44no—
695#121—84no—
696#121—84no—
697#121—84no—
698#121—84no—
699#120—216no—
700#120—216no—
701#120—48no—
702C4×Q8—44no—
703C4×Q8—44no—
704C4×Q8—84no—
705C4×D4—216no—
706C4×D4—216no—
707C4×D4—216no—
708C4×D4—216no—
709C4×D4—44no—
710C4×D4—44no—
711C4×D4—48no—
712C4×D4—48no—
713C4×D4—84no—
714#117—216no—
715#117—216no—
716#117—44no—
717#117—44no—
718#117—44no—
719#117—44no—
720#117—48no—
721#117—48no—
722#117—84no—
723#117—84no—
724C2×C4⋊C4—42no—
725C2×C4⋊C4—42no—
726C2×C4⋊C4—42no—
727C2×C4⋊C4—84no—
728C2×C4⋊C4C2414yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2414yes—
731C2×C4⋊C4C2414yes—
732C2×C4⋊C4C2414yes—
733C2×C4⋊C4C2414yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2412yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2412yes—
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2412yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2414yes—
745C2×C4⋊C4C2414yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2414yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2412yes—
758C2×C4⋊C4C2412yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C22⋊C4—28no—
772C2×C22⋊C4—216no—
773C2×C22⋊C4—28no—
774C2×C22⋊C4—216no—
775C2×C22⋊C4—44no—
776C2×C22⋊C4—84no—
777C2×C22⋊C4C2414yes—
778C2×C22⋊C4C2414yes—
779C2×C22⋊C4C2414yes—
780C2×C22⋊C4C2414yes—
781C2×C22⋊C4C2414yes—
782C2×C22⋊C4C2414yes—
783C2×C22⋊C4C2414yes—
784C2×C22⋊C4C2414yes—
785C2×C22⋊C4C2414yes—
786C2×C22⋊C4C2414yes—
787C2×C22⋊C4C2414yes—
788C2×C22⋊C4C2414yes—
789C2×C22⋊C4C2414yes—
790C2×C22⋊C4C2414yes—
791C2×C22⋊C4C2414yes—
792C2×C22⋊C4C2414yes—
793C2×C22⋊C4C2414yes—
794C2×C22⋊C4C2414yes—
795C2×C22⋊C4C2414yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2414yes—
798C2×C22⋊C4C2414yes—
799C2×C22⋊C4C2414yes—
800C2×C22⋊C4C2414yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2412yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2414yes—
816C2×C22⋊C4C2414yes—
817C2×C22⋊C4C2414yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2414yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C42—28no—
831C2×C42—42no—
832C2×C42—42no—
833C2×C42C2412yes—
834C2×C42C2412yes—
835C2×C42C2412yes—
836C2×C42C2414yes—
837C2×C42C2412yes—
838C2×C42C2412yes—
839C2×C42C2414yes—
840C2×C42C2414yes—
841C2×C42C2414yes—
842C2×C42C2411yescharacteristic
843C2×C42C2414yes—
844C2×C42C2411yescharacteristic
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2414yes—
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856C2×C42C2412yes—
857#95C2414yes—
858#95C2414yes—
859#95C2414yes—
860#95C2414yes—
861#95C2414yes—
862#95C2414yes—
863#95C2414yes—
864#95C2414yes—
865#95C2414yes—
866#95C2414yes—
867#95C2414yes—
868#95C2414yes—
869#95C2414yes—
870#95C2414yes—
871#95C2414yes—
872#95C2412yes—
873#95C2412yes—
874#95C2412yes—
875#95C2414yes—
876#95C2412yes—
877#95C2414yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2412yes—
882#95C2414yes—
883#95C2412yes—
884#95C2412yes—
885#95C2414yes—
886#95C2414yes—
887#95C2414yes—
888#95C2414yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2414yes—
897#95C2414yes—
898#95C2414yes—
899C24—22no—
900C24—28no—
901C24—24no—
902C24—24no—
903C24—41no—
904C24—41no—
905C24—42no—
906C24—44no—
907C24—42no—
908C24—42no—
909C24C2514yes—
910C24C2512yes—
911C24C2514yes—
912C24C2511yescharacteristic
913C2×Q8—42no—
914C2×Q8—42no—
915C2×Q8—42no—
916C2×Q8—44no—
917C2×Q8—42no—
918C2×Q8—44no—
919C2×Q8C2×#4118yes—
920C2×D4—28no—
921C2×D4—28no—
922C2×D4—28no—
923C2×D4—28no—
924C2×D4—28no—
925C2×D4—28no—
926C2×D4—28no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—24no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—44no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—44no—
938C2×D4—44no—
939C2×D4—44no—
940C2×D4—44no—
941C2×D4—42no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—44no—
946C2×D4—44no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—44no—
950C2×D4—42no—
951C2×D4—42no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—42no—
955C2×D4—44no—
956C2×D4—44no—
957C2×D4—44no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—88no—
961C2×D4—816no—
962C22×C4—22no—
963C22×C4—22no—
964C22×C4—22no—
965C22×C4—28no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—24no—
969C22×C4—24no—
970C22×C4—24no—
971C22×C4—24no—
972C22×C4—24no—
973C22×C4—24no—
974C22×C4—28no—
975C22×C4—28no—
976C22×C4—28no—
977C22×C4—28no—
978C22×C4—28no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—41no—
982C22×C4—41no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—416no—
1000C22×C4C2×#4118yes—
1001C22×C4H(5,𝔽2)14yes—
1002C22×C4C2514yes—
1003C22×C4C2514yes—
1004C22×C4C2514yes—
1005C22×C4C2514yes—
1006C22×C4C2512yes—
1007C22×C4C2512yes—
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2512yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2512yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2511yescharacteristic
1020C22×C4C2511yescharacteristic
1021C4⋊C4—28no—
1022C4⋊C4—28no—
1023C4⋊C4—28no—
1024C4⋊C4—28no—
1025C4⋊C4—28no—
1026C4⋊C4—24no—
1027C4⋊C4—28no—
1028C4⋊C4—28no—
1029C4⋊C4—28no—
1030C4⋊C4—28no—
1031C4⋊C4—41no—
1032C4⋊C4—42no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—42no—
1039C4⋊C4—41no—
1040C4⋊C4—44no—
1041C4⋊C4—44no—
1042C4⋊C4—44no—
1043C4⋊C4—44no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—44no—
1047C4⋊C4—42no—
1048C4⋊C4—44no—
1049C4⋊C4—44no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—42no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4C2×#41116yes—
1063C4⋊C4C2×#4118yes—
1064C22⋊C4—28no—
1065C22⋊C4—28no—
1066C22⋊C4—28no—
1067C22⋊C4—28no—
1068C22⋊C4—28no—
1069C22⋊C4—28no—
1070C22⋊C4—28no—
1071C22⋊C4—28no—
1072C22⋊C4—28no—
1073C22⋊C4—28no—
1074C22⋊C4—28no—
1075C22⋊C4—28no—
1076C22⋊C4—28no—
1077C22⋊C4—28no—
1078C22⋊C4—28no—
1079C22⋊C4—28no—
1080C22⋊C4—28no—
1081C22⋊C4—28no—
1082C22⋊C4—28no—
1083C22⋊C4—28no—
1084C22⋊C4—28no—
1085C22⋊C4—28no—
1086C22⋊C4—28no—
1087C22⋊C4—28no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—44no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—44no—
1102C22⋊C4—44no—
1103C22⋊C4—44no—
1104C22⋊C4—44no—
1105C22⋊C4—44no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4C2×#41116yes—
1117C42—28no—
1118C42—28no—
1119C42—28no—
1120C42—28no—
1121C42—24no—
1122C42—24no—
1123C42—24no—
1124C42—24no—
1125C42—28no—
1126C42—24no—
1127C42—22no—
1128C42—22no—
1129C42—42no—
1130C42—42no—
1131C42—44no—
1132C42—44no—
1133C42—44no—
1134C42—44no—
1135C42—44no—
1136C42—44no—
1137C42—44no—
1138C42—44no—
1139C42—44no—
1140C42—44no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—24no—
1145C23—24no—
1146C23—24no—
1147C23—24no—
1148C23—24no—
1149C23—24no—
1150C23—24no—
1151C23—22no—
1152C23—24no—
1153C23—24no—
1154C23—22no—
1155C23—22no—
1156C23—24no—
1157C23—24no—
1158C23—24no—
1159C23—24no—
1160C23—24no—
1161C23—24no—
1162C23—24no—
1163C23—44no—
1164C23—44no—
1165C23—44no—
1166C23—48no—
1167C23—84no—
1168C23—84no—
1169C23—84no—
1170C23—84no—
1171C23—88no—
1172C23—88no—
1173C23C22×#4114yes—
1174C23C2×H(5,𝔽2)12yes—
1175C23C2611yescharacteristic
1176Q8—48no—
1177Q8—84no—
1178Q8—162no—
1179D4—416no—
1180D4—84no—
1181D4—88no—
1182D4—88no—
1183D4—88no—
1184D4—88no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—88no—
1189D4—88no—
1190D4—164no—
1191D4—162no—
1192D4—164no—
1193C2×C4—28no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—24no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—24no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—24no—
1212C2×C4—24no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—24no—
1224C2×C4—24no—
1225C2×C4—24no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—24no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—44no—
1239C2×C4—48no—
1240C2×C4—48no—
1241C2×C4—48no—
1242C2×C4—48no—
1243C2×C4—88no—
1244C2×C4—88no—
1245C2×C4—88no—
1246C2×C4—88no—
1247C2×C4—88no—
1248C2×C4—84no—
1249C2×C4—84no—
1250C2×C4—84no—
1251C2×C4C22×#4114yes—
1252C2×C4C22×#4118yes—
1253C2×C4C22×#4118yes—
1254C2×C4C22×#4114yes—
1255C2×C4C2×H(5,𝔽2)14yes—
1256C2×C4#58512yes—
1257C2×C4#58512yes—
1258C22—24no—
1259C22—24no—
1260C22—22no—
1261C22—22no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—42no—
1273C22—44no—
1274C22—44no—
1275C22—42no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—42no—
1280C22—44no—
1281C22—88no—
1282C22—168no—
1283C22#348314yes—
1284C22C23×#4112yes—
1285C22C22×H(5,𝔽2)11yescharacteristic
1286C22C2×#58511yescharacteristic
1287C22C2×#58511yescharacteristic
1288C22H(7,𝔽2)12yes—
1289C4—24no—
1290C4—24no—
1291C4—28no—
1292C4—28no—
1293C4—22no—
1294C4—22no—
1295C4—24no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—44no—
1300C4—42no—
1301C4—42no—
1302C4—42no—
1303C4—42no—
1304C4—44no—
1305C4—42no—
1306C4—42no—
1307C4—44no—
1308C2—24no—
1309C2—84no—
1310C2—82no—
1311C2—84no—
1312C2C2×#348311yescharacteristic
1313C2#6282011yescharacteristic
1314C2#6287411yescharacteristic
1315C2#6299212yes—
1316C2#6299412yes—
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. #60016C2semidirect
2. #59964C2semidirect
3. #59952C2semidirect
4. #59947C2semidirect
5. #59819C2semidirect
6. #59701C2semidirect
7. #59339C2semidirect
8. #59322C2semidirect
9. #59303C2semidirect
10. #43938C2semidirect
11. #43913C2semidirect
12. #43882C2semidirect
13. #43842C2semidirect
14. #43823C2semidirect
15. #43481C2semidirect
16. #43444C2semidirect
17. #43389C2semidirect
18. #35465C2semidirect
19. #35395C2semidirect
20. #34877C2semidirect
21. C2×#2500C2semidirect
22. #34303C2semidirect
23. #34277C2semidirect
30. #2803C22semidirect
31. #2803C22semidirect
32. #2803C22semidirect
33. #2795C22semidirect
34. #2795C22semidirect
35. #2795C22semidirect
36. #2792C22semidirect
37. #2792C22semidirect
38. #2785C22semidirect
39. #2785C22semidirect
40. #2784C22semidirect
41. #2783C22semidirect
42. #2781C22semidirect
43. #2769C22semidirect
44. #2756C22semidirect
45. #2733C22semidirect
46. #2733C22semidirect
47. #2732C22semidirect
48. #2731C22semidirect
49. #2730C22semidirect
50. #2727C22semidirect
51. #2727C22semidirect
52. #2714C22semidirect
53. #2705C22semidirect
54. #2705C22semidirect
55. #2699C22semidirect
56. #2686C22semidirect
57. #2682C22semidirect
58. #2682C22semidirect
59. #2673C22semidirect
60. #2612C22semidirect
61. #2611C22semidirect
62. #2611C22semidirect
63. #2610C22semidirect
64. #2610C22semidirect
65. #2610C22semidirect
66. #2610C22semidirect
67. #2610C22semidirect
68. #2609C22semidirect
69. #2604C22semidirect
70. #2602C22semidirect
71. #2601C22semidirect
72. #2601C22semidirect
73. #2601C22semidirect
74. #2593C22semidirect
75. #2593C22semidirect
80. #2582C22semidirect
81. #2574C22semidirect
82. #2571C22semidirect
83. #2567C22semidirect
87. #2559C22semidirect
88. #2558C22semidirect
91. #2555C22semidirect
92. #2555C22semidirect
93. #2554C22semidirect
94. #2554C22semidirect
95. #2554C22semidirect
96. #2554C22semidirect
97. #2551C22semidirect
98. #2548C22semidirect
99. #2545C22semidirect
100. #2543C22semidirect
103. #2537C22semidirect
105. #2529C22semidirect
106. #2526C22semidirect
107. #2526C22semidirect
108. #2521C22semidirect
109. #2519C22semidirect
110. #2518C22semidirect
111. #2518C22semidirect
112. #2512C22semidirect
113. #2508C22semidirect
114. #2507C22semidirect
121. #2500C22semidirect
122. #2500C22semidirect
123. #2500C22semidirect
124. #2498C22semidirect
125. #2497C22semidirect
126. #2491C22semidirect
127. #2491C22semidirect
129. #2479C22semidirect
130. #2479C22semidirect
131. #2476C22semidirect
132. #2476C22semidirect
133. #2474C22semidirect
135. #2467C22semidirect
138. #2456C22semidirect
139. #2445C22semidirect
145. #2428C22semidirect
146. #2426C22semidirect
147. #2426C22semidirect
151. #2414C22semidirect
152. #2414C22semidirect
157. #2396C22semidirect
158. #2396C22semidirect
159. #2392C22semidirect
160. #2392C22semidirect
162. #2374C22semidirect
163. #2374C22semidirect
164. #2373C22semidirect
165. #2373C22semidirect
166. #2373C22semidirect
167. #2373C22semidirect
168. #2372C22semidirect
169. #2372C22semidirect
170. #2367C22semidirect
171. #2364C22semidirect
172. #2363C22semidirect
173. #2363C22semidirect
174. #2363C22semidirect
175. #2362C22semidirect
178. #2359C22semidirect
179. #2359C22semidirect
181. #2354C22semidirect
182. #2353C22semidirect
184. Q8×C4⋊C4C22semidirect
185. #2346C22semidirect
186. #2346C22semidirect
190. #2335C22semidirect
191. #2335C22semidirect
192. #2334C22semidirect
193. #2332C22semidirect
199. C4×#126C22semidirect
200. C4×#124C22semidirect
205. #2298C22semidirect
206. #2293C22semidirect
207. #2293C22semidirect
208. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#600162
#599642
#599522
#599472
#598192
#597012
#593392
#593222
#593032
#439382
#439132
#438822
#438422
#438232
#434812
#434442
#433892
#354652
#353952
#348772
C2×#25002
#343032
#342772