Finite Group Databasebeta

← #7630921

Subgroups — #7630921

Order 512.

4848 conjugacy classes of subgroups.

The subgroup lattice has 1422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36052C212yesmaximal, complemented
2#36047C214yesmaximal, complemented
3#36046C212yesmaximal, complemented
4#35975C214yesmaximal, complemented
5#35967C214yesmaximal, complemented
6#35946C214yesmaximal, complemented
7#35872C214yesmaximal, complemented
8#35864C214yesmaximal, complemented
9#35857C212yesmaximal, complemented
10#35851C212yesmaximal, complemented
11#35340C212yesmaximal, complemented
12#35325C211yesmaximal, characteristic, complemented
13#35324C212yesmaximal, complemented
14#35318C212yesmaximal, complemented
15#35310C212yesmaximal, complemented
16#35302C211yesmaximal, characteristic
17#35300C212yesmaximal, complemented
18#35291C212yesmaximal, complemented
19#35282C212yesmaximal, complemented
20#35260C212yesmaximal
21#34631C211yesmaximal, characteristic, complemented
22#34629C212yesmaximal, complemented
23#34625C211yesmaximal, characteristic, complemented
24#34619C212yesmaximal, complemented
25#34281C212yesmaximal, complemented
26#34279C212yesmaximal, complemented
27#34227C211yesmaximal, characteristic, complemented
28#34225C211yesmaximal, characteristic, complemented
29#33996C211yesmaximal, characteristic, complemented
30C2×#542C2212yes—
31C2×#541C2212yes—
32C2×#533C2211yescharacteristic
33C2×#529C2211yescharacteristic
34C22×#117C2212yes—
35C22×#117C2211yescharacteristic
36#2864C2212yescomplemented
37#2862C2212yescomplemented
38#2861C2212yescomplemented
39#2859C2212yescomplemented
40#2857C2212yes—
41#2857C2212yes—
42#2855C2212yes—
43#2855C2211yescharacteristic
44#2854C2211yescharacteristic
45#2851C2212yes—
46#2850C2212yes—
47#2848C2212yes—
48#2848C2211yescharacteristic
49#2847C2211yescharacteristic
50#2667C2212yes—
51#2666C2214yescomplemented
52#2665C2212yes—
53#2664C2212yescomplemented
54#2664C2212yescomplemented
55#2663C2214yes—
56#2660C2212yescomplemented
57#2660C2211yescharacteristic, complemented
58#2658C2211yescharacteristic, complemented
59#2655C2214yescomplemented
60#2655C2214yescomplemented
61#2654C2214yescomplemented
62#2653C2214yes—
63#2652C2214yes—
64#2652C2214yes—
65#2650C2214yescomplemented
66#2649C2214yes—
67#2647C2212yescomplemented
68#2645C2212yescomplemented
69#2645C2212yescomplemented
70#2645C2212yescomplemented
71#2644C2212yescomplemented
72#2642C2211yescharacteristic, complemented
73#2640C2211yescharacteristic, complemented
74#2629C2212yes—
75#2629C2212yes—
76#2628C2212yes—
77#2628C2212yes—
78#2625C2212yes—
79#2625C2212yes—
80#2625C2212yes—
81#2624C2212yes—
82#2621C2212yes—
83#2621C2212yes—
84#2620C2212yes—
85#2620C2212yes—
86#2611C2214yes—
87#2609C2214yes—
88#2601C2214yes—
89#2599C2214yes—
90#2597C2214yes—
91#2596C2214yescomplemented
92#2595C2214yes—
93#2594C2214yescomplemented
94#2594C2214yescomplemented
95#2588C2214yescomplemented
96#2588C2214yescomplemented
97#2587C2214yescomplemented
98#2586C2214yescomplemented
99#2585C2214yescomplemented
100#2583C2212yes—
101#2579C2212yes—
102#2578C2214yes—
103#2577C2214yescomplemented
104#2576C2214yes—
105#2576C2214yes—
106#2575C2214yes—
107#2575C2214yes—
108#2575C2214yescomplemented
109#2574C2214yes—
110#2561C2212yes—
111#2558C2214yes—
112#2556C2214yes—
113#2556C2214yescomplemented
114#2556C2214yescomplemented
115#2553C2214yes—
116#2553C2214yes—
117#2534C2212yes—
118#2529C2214yescomplemented
119#2528C2214yescomplemented
120#2528C2214yescomplemented
121#2527C2214yes—
122#2527C2214yes—
123#2526C2214yes—
124#2522C2214yes—
125#2521C2214yes—
126#2521C2214yes—
127#2520C2214yescomplemented
128#2519C2214yescomplemented
129#2519C2214yescomplemented
130#2514C2214yescomplemented
131#2509C2214yescomplemented
132#2508C2214yescomplemented
133#2495C2214yes—
134#2494C2214yes—
135#2489C2214yes—
136#2484C2212yes—
137#2482C2212yes—
138#2481C2214yes—
139#2480C2214yes—
140#2480C2214yes—
141#2479C2214yes—
142#2478C2214yes—
143#2478C2214yes—
144#2477C2214yes—
145#2475C2214yes—
146#2475C2214yes—
147#2475C2214yescomplemented
148#2474C2214yes—
149#2473C2214yes—
150#2473C2214yes—
151#2472C2214yes—
152#2470C2214yes—
153#2470C2214yes—
154#2465C2214yes—
155#2462C2214yescomplemented
156#2453C2214yescomplemented
157#2449C2214yes—
158#2421C2214yes—
159#2418C2214yes—
160#2413C2212yes—
161#2411C2212yes—
162#2402C2214yescomplemented
163#2402C2214yescomplemented
164#2402C2212yescomplemented
165#2401C2214yes—
166#2401C2214yes—
167#2401C2214yescomplemented
168#2399C2212yescomplemented
169#2398C2214yes—
170#2396C2214yes—
171#2396C2214yescomplemented
172#2396C2214yescomplemented
173#2395C2214yes—
174#2395C2212yes—
175#2395C2212yes—
176#2374C2214yes—
177#2374C2214yes—
178#2373C2214yes—
179#2373C2214yes—
180#2373C2214yes—
181#2373C2214yes—
182#2373C2214yescomplemented
183#2373C2214yescomplemented
184#2373C2214yescomplemented
185#2372C2214yes—
186#2371C2214yescomplemented
187#2371C2214yescomplemented
188#2370C2214yescomplemented
189#2370C2214yescomplemented
190#2370C2214yescomplemented
191#2368C2214yescomplemented
192#2367C2214yes—
193#2362C2214yes—
194#2362C2214yescomplemented
195#2359C2214yes—
196#2357C2212yes—
197#2356C2212yescomplemented
198#2353C2212yes—
199#2351C2212yescomplemented
200#2347C2212yes—
201#2347C2212yescomplemented
202#2346C2212yes—
203#2343C2212yescomplemented
204#2331C2212yescomplemented
205#2330C2212yescomplemented
206#2327C2212yescomplemented
207#2326C2212yescomplemented
208#2324C2212yes—
209#2324C2212yes—
210#2323C2212yes—
211#2323C2212yes—
212#2323C2212yes—
213#2323C2212yes—
214#2323C2212yes—
215#2323C2212yes—
216#2320C2212yescomplemented
217#2320C2211yescharacteristic, complemented
218#2319C2211yescharacteristic, complemented
219#2314C2212yes—
220#2314C2212yes—
221C4×C4⋊Q8C2212yescomplemented
222C4×C4⋊Q8C2212yescomplemented
223C4×C4⋊Q8C2212yescomplemented
224C4×C4⋊Q8C2212yescomplemented
225C4×#125C2212yescomplemented
226C4×#125C2212yescomplemented
227C4×#124C2212yescomplemented
228C4×#124C2212yescomplemented
229C4×C22⋊Q8C2212yes—
230C4×C22⋊Q8C2212yes—
231C4×C22⋊Q8C2212yes—
232C4×#121C2212yes—
233#2295C2212yescomplemented
234#2295C2212yescomplemented
235#2295C2212yescomplemented
236#2293C2212yescomplemented
237#2285C2211yescharacteristic
238#2283C2211yescharacteristic
239#2276C2212yescomplemented
240#2276C2211yescharacteristic, complemented
241#2275C2211yescharacteristic, complemented
242#2274C2211yescharacteristic
243#2274C2212yes—
244#2274C2212yes—
245#2274C2212yes—
246#2274C2212yes—
247#2274C2212yes—
248#2274C2211yescharacteristic
249#2273C2211yescharacteristic
250#2273C2212yes—
251#2273C2211yescharacteristic
252C4×#117C2212yes—
253C4×#117C2212yes—
254C4×#117C2211yescharacteristic
255C4×#117C2211yescharacteristic
256C4×#117C2212yes—
257C4×#117C2212yes—
258C4×#117C2212yes—
259C24×C4C2311yescharacteristic
260#542—216no—
261#541—216no—
262#533—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267#529—28no—
268C2×#126C2312yes—
269C2×#126C2314yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#125C2311yescharacteristic
273C2×#125C2312yes—
274C2×#125C2312yes—
275C2×#125C2314yes—
276C2×#125C2314yes—
277C2×#125C2314yes—
278C2×#124C2312yes—
279C2×#124C2311yescharacteristic
280C2×#124C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2311yescharacteristic
287C2×C22⋊Q8C2312yes—
288C2×C22⋊Q8C2312yes—
289C2×C22⋊Q8C2312yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×#121C2311yescharacteristic
293C2×#121C2312yes—
294C2×#120C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2314yes—
302C2×C4×Q8C2314yes—
303C2×C4×D4C2311yescharacteristic
304C2×C4×D4C2312yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2314yes—
307C2×#117—216no—
308C2×#117—28no—
309C2×#117C2312yes—
310C2×#117C2312yes—
311C2×#117C2312yes—
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C2×#117C2312yes—
317C2×#117C2312yes—
318C2×#117C2312yes—
319C2×#117C2312yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2312yes—
324C2×#117C2312yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2311yescharacteristic
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C22⋊C4C2311yescharacteristic
330C22×C22⋊C4C2312yes—
331C22×C22⋊C4C2312yes—
332C22×C22⋊C4C2311yescharacteristic
333C22×C42C2312yes—
334C22×C42C2311yescharacteristic
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337#401C2314yes—
338#401C2314yes—
339#401C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2314yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2312yes—
352#400C2312yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2312yes—
363#399C2312yes—
364#399C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2312yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#393C2314yes—
419#393C2314yes—
420#393C2314yes—
421#391C2314yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2314yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2312yes—
431#391C2314yes—
432#391C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2314yes—
440#390C2314yes—
441#390C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2312yes—
453#389C2312yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#389C2314yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2314yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2314yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2314yes—
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#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#386C2312yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2312yes—
557#386C2314yes—
558#386C2314yes—
559#385C2314yes—
560#385C2312yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2312yes—
566#385C2314yes—
567#385C2314yes—
568#385C2314yes—
569#385C2314yes—
570#385C2314yes—
571#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#384C2312yes—
576#384C2312yes—
577#384C2312yes—
578#383C2314yes—
579#383C2312yes—
580#383C2312yes—
581#382C2312yes—
582#382C2312yes—
583#382C2312yes—
584#382C2314yes—
585#382C2314yes—
586#382C2314yes—
587#382C2314yes—
588#382C2312yes—
589#382C2312yes—
590#381C2314yes—
591#381C2312yes—
592#381C2312yes—
593#381C2312yes—
594#380C2312yes—
595#380C2312yes—
596#380C2312yes—
597#380C2312yes—
598#380C2314yes—
599#380C2312yes—
600#380C2311yescharacteristic
601#380C2311yescharacteristic
602#380C2312yes—
603#380C2312yes—
604#380C2314yes—
605#380C2314yes—
606#379C2314yes—
607#379C2312yes—
608C4×C4⋊C4C2311yescharacteristic
609C4×C4⋊C4C2312yes—
610C4×C4⋊C4C2312yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2314yes—
613C4×C4⋊C4C2314yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2311yescharacteristic
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C4⋊C4C2314yes—
626C4×C4⋊C4C2314yes—
627C4×C4⋊C4C2312yes—
628C4×C4⋊C4C2312yes—
629C4×C4⋊C4C2312yes—
630C4×C4⋊C4C2312yes—
631C4×C4⋊C4C2312yes—
632C4×C4⋊C4C2312yes—
633C4×C4⋊C4C2312yes—
634C4×C4⋊C4C2312yes—
635C4×C4⋊C4C2312yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2311yescharacteristic
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2314yes—
641C4×C4⋊C4C2311yescharacteristic
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2314yes—
644C4×C4⋊C4C2314yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2314yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2311yescharacteristic
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2311yescharacteristic
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C22⋊C4C2312yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2314yes—
671C4×C22⋊C4C2314yes—
672C4×C22⋊C4C2312yes—
673C4×C22⋊C4C2312yes—
674C4×C22⋊C4C2312yes—
675C4×C22⋊C4C2314yes—
676C4×C22⋊C4C2311yescharacteristic
677C4×C22⋊C4C2311yescharacteristic
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2314yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682C4×C22⋊C4C2314yes—
683C4×C22⋊C4C2312yes—
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2314yes—
687C4×C22⋊C4C2312yes—
688C4×C22⋊C4C2314yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2312yes—
691C4×C22⋊C4C2312yes—
692C4×C22⋊C4C2311yescharacteristic
693C4×C22⋊C4C2311yescharacteristic
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2312yes—
696C4×C22⋊C4C2312yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2312yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2312yes—
701#376C2311yescharacteristic
702#376C2312yes—
703#376C2312yes—
704#376C2314yes—
705#376C2312yes—
706#376C2314yes—
707#376C2314yes—
708#376C2314yes—
709#376C2311yescharacteristic
710#376C2312yes—
711#376C2311yescharacteristic
712#376C2311yescharacteristic
713C2×#95C2312yes—
714C43C2312yes—
715C43C2312yes—
716C43C2312yes—
717C43C2312yes—
718C25C2411yescharacteristic
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×Q8C2412yes—
722C22×Q8C2414yes—
723C22×D4C2411yescharacteristic
724C22×D4C2412yes—
725C22×D4C2414yes—
726C23×C4—24no—
727C23×C4—28no—
728C23×C4C2411yescharacteristic
729C23×C4C2412yes—
730C23×C4C2412yes—
731C23×C4C2411yescharacteristic
732C23×C4C2412yes—
733C23×C4C2412yes—
734C23×C4C2411yescharacteristic
735C23×C4C2412yes—
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C23×C4C2414yes—
739C23×C4C2412yes—
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C4⋊Q8—24no—
743C4⋊Q8—24no—
744C4⋊Q8—28no—
745C4⋊Q8—28no—
746#126—216no—
747#126—216no—
748#126—216no—
749#126—28no—
750#125—216no—
751#125—216no—
752#125—24no—
753#125—28no—
754#125—28no—
755#125—84no—
756#124—216no—
757#124—24no—
758#124—28no—
759#123—28no—
760#123—216no—
761#123—82no—
762C22⋊Q8—24no—
763C22⋊Q8—28no—
764C22⋊Q8—28no—
765C22⋊Q8—28no—
766C22⋊Q8—28no—
767C22⋊Q8—28no—
768C22⋊Q8—216no—
769C22⋊Q8—84no—
770#121—24no—
771#121—28no—
772#120—82no—
773C4×Q8—24no—
774C4×Q8—28no—
775C4×Q8—28no—
776C4×Q8—28no—
777C4×Q8—28no—
778C4×Q8—28no—
779C4×Q8—84no—
780C4×Q8—84no—
781C4×D4—28no—
782C4×D4—24no—
783C4×D4—28no—
784C4×D4—84no—
785#117—28no—
786#117—28no—
787#117—28no—
788#117—28no—
789#117—28no—
790#117—28no—
791#117—28no—
792#117—28no—
793#117—28no—
794#117—28no—
795#117—28no—
796#117—28no—
797#117—28no—
798#117—84no—
799#117—82no—
800#117#41116yes—
801C2×C4⋊C4—24no—
802C2×C4⋊C4—24no—
803C2×C4⋊C4—28no—
804C2×C4⋊C4—28no—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2412yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2414yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2412yes—
862C2×C22⋊C4—24no—
863C2×C22⋊C4—24no—
864C2×C22⋊C4—28no—
865C2×C22⋊C4—28no—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C42—24no—
905C2×C42—28no—
906C2×C42—28no—
907C2×C42#4118yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2412yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2414yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2411yescharacteristic
947C2×C42C2412yes—
948C2×C42C2411yescharacteristic
949C2×C42C2411yescharacteristic
950#95C2411yescharacteristic
951#95C2412yes—
952#95C2414yes—
953#95C2411yescharacteristic
954#95C2412yes—
955#95C2411yescharacteristic
956#95C2411yescharacteristic
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2411yescharacteristic
965#95C2412yes—
966#95C2411yescharacteristic
967#95C2411yescharacteristic
968#95C2412yes—
969#95C2412yes—
970#95C2412yes—
971#95C2411yescharacteristic
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2412yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2412yes—
1004#95C2412yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020C24—22no—
1021C24—24no—
1022C24—41no—
1023C24—42no—
1024C24—41no—
1025C24C2512yes—
1026C24C2511yescharacteristic
1027C24C2512yes—
1028C2×Q8—22no—
1029C2×Q8—24no—
1030C2×Q8—24no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—24no—
1034C2×Q8—28no—
1035C2×Q8—42no—
1036C2×Q8—42no—
1037C2×Q8—44no—
1038C2×Q8—44no—
1039C2×D4—24no—
1040C2×D4—28no—
1041C2×D4—22no—
1042C2×D4—24no—
1043C2×D4—44no—
1044C2×D4—42no—
1045C2×D4—42no—
1046C2×D4—44no—
1047C22×C4—232no—
1048C22×C4—22no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—22no—
1057C22×C4—22no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—24no—
1062C22×C4—24no—
1063C22×C4—28no—
1064C22×C4—41no—
1065C22×C4—41no—
1066C22×C4—42no—
1067C22×C4—44no—
1068C22×C4—42no—
1069C22×C4—42no—
1070C22×C4—41no—
1071C22×C4—42no—
1072C22×C4—42no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—44no—
1077C22×C4—44no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—41no—
1081C22×C4C2×#4114yes—
1082C22×C4C2×#4118yes—
1083C22×C4C2×#4114yes—
1084C22×C4C2×#4114yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2512yes—
1088C22×C4C2512yes—
1089C22×C4C2514yes—
1090C22×C4C2514yes—
1091C22×C4C2514yes—
1092C22×C4C2512yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2514yes—
1096C22×C4C2512yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2514yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2511yescharacteristic
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2512yes—
1108C22×C4C2511yescharacteristic
1109C22×C4C2511yescharacteristic
1110C22×C4C2511yescharacteristic
1111C4⋊C4—24no—
1112C4⋊C4—24no—
1113C4⋊C4—24no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—24no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—22no—
1129C4⋊C4—24no—
1130C4⋊C4—28no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—28no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—28no—
1140C4⋊C4—28no—
1141C4⋊C4—28no—
1142C4⋊C4—28no—
1143C4⋊C4—28no—
1144C4⋊C4—28no—
1145C4⋊C4—28no—
1146C4⋊C4—28no—
1147C4⋊C4—28no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—44no—
1166C4⋊C4C2×#4118yes—
1167C4⋊C4C2×#4118yes—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—28no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—24no—
1176C22⋊C4—24no—
1177C22⋊C4—24no—
1178C22⋊C4—24no—
1179C22⋊C4—24no—
1180C22⋊C4—24no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—24no—
1184C22⋊C4—24no—
1185C22⋊C4—24no—
1186C22⋊C4—24no—
1187C22⋊C4—28no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—42no—
1200C22⋊C4—42no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4C2×#4118yes—
1205C22⋊C4C2×#4118yes—
1206C42—24no—
1207C42—24no—
1208C42—24no—
1209C42—24no—
1210C42—24no—
1211C42—24no—
1212C42—24no—
1213C42—24no—
1214C42—24no—
1215C42—28no—
1216C42—28no—
1217C42—28no—
1218C42—28no—
1219C42—42no—
1220C42—42no—
1221C42—42no—
1222C42—42no—
1223C42—44no—
1224C42—42no—
1225C42—42no—
1226C42—44no—
1227C42—42no—
1228C42—42no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—42no—
1234C42—42no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—42no—
1239C42—42no—
1240C42—42no—
1241C42—42no—
1242C42C2×#4118yes—
1243C42C2×#4118yes—
1244C42C2×#4114yes—
1245C42C2×#4114yes—
1246C42C2×#4114yes—
1247C42C2×#4114yes—
1248C23—28no—
1249C23—22no—
1250C23—22no—
1251C23—22no—
1252C23—21no—
1253C23—22no—
1254C23—22no—
1255C23—22no—
1256C23—22no—
1257C23—21no—
1258C23—22no—
1259C23—22no—
1260C23—24no—
1261C23—22no—
1262C23—22no—
1263C23—24no—
1264C23—82no—
1265C23—84no—
1266C23—82no—
1267C23—84no—
1268C23C22×#4114yes—
1269C23C22×#4112yes—
1270C23C2611yescharacteristic
1271Q8—48no—
1272Q8—44no—
1273Q8—48no—
1274Q8—88no—
1275D4—44no—
1276D4—84no—
1277D4—88no—
1278C2×C4—28no—
1279C2×C4—216no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—22no—
1285C2×C4—21no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—21no—
1296C2×C4—22no—
1297C2×C4—216no—
1298C2×C4—28no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—22no—
1310C2×C4—24no—
1311C2×C4—24no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—24no—
1338C2×C4—24no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—44no—
1343C2×C4—44no—
1344C2×C4—84no—
1345C2×C4—88no—
1346C2×C4—84no—
1347C2×C4—84no—
1348C2×C4—84no—
1349C2×C4—84no—
1350C2×C4—82no—
1351C2×C4—82no—
1352C2×C4C22×#4112yes—
1353C2×C4C22×#4114yes—
1354C2×C4C22×#4114yes—
1355C2×C4C22×#4112yes—
1356C2×C4C22×#4114yes—
1357C2×C4C22×#4114yes—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4114yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4114yes—
1364C22—22no—
1365C22—24no—
1366C22—22no—
1367C22—24no—
1368C22—22no—
1369C22—24no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—44no—
1378C22—42no—
1379C22—44no—
1380C22—42no—
1381C22—88no—
1382C22C23×#4111yescharacteristic
1383C22C23×#4112yes—
1384C22H(7,𝔽2)11yescharacteristic
1385C222−1+611yescharacteristic
1386C222−1+612yes—
1387C4—22no—
1388C4—22no—
1389C4—24no—
1390C4—24no—
1391C4—22no—
1392C4—22no—
1393C4—24no—
1394C4—24no—
1395C4—24no—
1396C4—22no—
1397C4—42no—
1398C4—42no—
1399C4—44no—
1400C4—44no—
1401C4—42no—
1402C4—42no—
1403C4—44no—
1404C4—44no—
1405C4—42no—
1406C4—42no—
1407C4—44no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—44no—
1412C4#344414yes—
1413C2—42no—
1414C2—44no—
1415C2—82no—
1416C2C2×#344411yescharacteristic
1417C2#6285611yescharacteristic
1418C2#6285712yes—
1419C2#6286011yescharacteristic
1420C2#6286112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2847C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36052C2semidirect
2. #36047C2semidirect
3. #36046C2semidirect
4. #35975C2semidirect
5. #35967C2semidirect
6. #35946C2semidirect
7. #35872C2semidirect
8. #35864C2semidirect
9. #35857C2semidirect
10. #35851C2semidirect
11. #35340C2semidirect
12. #35325C2semidirect
13. #35324C2semidirect
14. #35318C2semidirect
15. #35310C2semidirect
17. #35300C2semidirect
18. #35291C2semidirect
19. #35282C2semidirect
21. #34631C2semidirect
22. #34629C2semidirect
23. #34625C2semidirect
24. #34619C2semidirect
25. #34281C2semidirect
26. #34279C2semidirect
27. #34227C2semidirect
28. #34225C2semidirect
29. #33996C2semidirect
36. #2864C22semidirect
37. #2862C22semidirect
38. #2861C22semidirect
39. #2859C22semidirect
51. #2666C22semidirect
53. #2664C22semidirect
54. #2664C22semidirect
56. #2660C22semidirect
57. #2660C22semidirect
58. #2658C22semidirect
59. #2655C22semidirect
60. #2655C22semidirect
61. #2654C22semidirect
65. #2650C22semidirect
67. #2647C22semidirect
68. #2645C22semidirect
69. #2645C22semidirect
70. #2645C22semidirect
71. #2644C22semidirect
72. #2642C22semidirect
73. #2640C22semidirect
91. #2596C22semidirect
93. #2594C22semidirect
94. #2594C22semidirect
95. #2588C22semidirect
96. #2588C22semidirect
97. #2587C22semidirect
98. #2586C22semidirect
99. #2585C22semidirect
103. #2577C22semidirect
108. #2575C22semidirect
113. #2556C22semidirect
114. #2556C22semidirect
118. #2529C22semidirect
119. #2528C22semidirect
120. #2528C22semidirect
127. #2520C22semidirect
128. #2519C22semidirect
129. #2519C22semidirect
130. #2514C22semidirect
131. #2509C22semidirect
132. #2508C22semidirect
147. #2475C22semidirect
155. #2462C22semidirect
156. #2453C22semidirect
162. #2402C22semidirect
163. #2402C22semidirect
164. #2402C22semidirect
167. #2401C22semidirect
168. #2399C22semidirect
171. #2396C22semidirect
172. #2396C22semidirect
182. #2373C22semidirect
183. #2373C22semidirect
184. #2373C22semidirect
186. #2371C22semidirect
187. #2371C22semidirect
188. #2370C22semidirect
189. #2370C22semidirect
190. #2370C22semidirect
191. #2368C22semidirect
194. #2362C22semidirect
197. #2356C22semidirect
199. #2351C22semidirect
201. #2347C22semidirect
203. #2343C22semidirect
204. #2331C22semidirect
205. #2330C22semidirect
206. #2327C22semidirect
207. #2326C22semidirect
216. #2320C22semidirect
217. #2320C22semidirect
218. #2319C22semidirect
221. C4×C4⋊Q8C22semidirect
222. C4×C4⋊Q8C22semidirect
223. C4×C4⋊Q8C22semidirect
224. C4×C4⋊Q8C22semidirect
225. C4×#125C22semidirect
226. C4×#125C22semidirect
227. C4×#124C22semidirect
228. C4×#124C22semidirect
233. #2295C22semidirect
234. #2295C22semidirect
235. #2295C22semidirect
236. #2293C22semidirect
239. #2276C22semidirect
240. #2276C22semidirect
241. #2275C22semidirect

Maximal subgroups

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

subgroupindex
#360522
#360472
#360462
#359752
#359672
#359462
#358722
#358642
#358572
#358512
#353402
#353252
#353242
#353182
#353102
#353022
#353002
#352912
#352822
#352602
#346312
#346292
#346252
#346192
#342812
#342792
#342272
#342252
#339962