Finite Group Databasebeta

← #7695552

Subgroups — #7695552

Order 512.

4852 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59857C213yesmaximal, complemented
2#59695C213yesmaximal, complemented
3#59681C213yesmaximal, complemented
4#52262C213yesmaximal
5#45397C213yesmaximal, complemented
6#45348C213yesmaximal, complemented
7#45342C213yesmaximal, complemented
8#45309C213yesmaximal, complemented
9#45262C213yesmaximal, complemented
10#45130C213yesmaximal, complemented
11#39819C213yesmaximal, complemented
12#39553C213yesmaximal, complemented
13#39283C213yesmaximal, complemented
14#39186C213yesmaximal, complemented
15#38217C213yesmaximal, complemented
16#38128C213yesmaximal, complemented
17Q8×#126C211yesmaximal, characteristic, complemented
18Q8×#121C211yesmaximal, characteristic, complemented
19#36475C211yesmaximal, characteristic, complemented
20#35883C211yesmaximal, characteristic, complemented
21#35723C211yesmaximal, characteristic, complemented
22#35723C211yesmaximal, characteristic, complemented
23#35700C211yesmaximal, characteristic, complemented
24#35700C211yesmaximal, characteristic, complemented
25#35700C211yesmaximal, characteristic, complemented
26#34311C211yesmaximal, characteristic, complemented
27#34311C211yesmaximal, characteristic, complemented
28#34311C211yesmaximal, characteristic, complemented
29#34291C211yesmaximal, characteristic, complemented
30#34262C211yesmaximal, characteristic, complemented
31#34249C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C2×#519C2211yescharacteristic
41C2×#519C2211yescharacteristic
42C2×#519C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2864C2213yes—
45#2863C2213yes—
46#2857C2213yes—
47#2803C2213yes—
48#2802C2216yes—
49#2802C2216yes—
50#2802C2213yes—
51#2801C2213yes—
52#2800C2213yes—
53#2800C2216yes—
54#2800C2213yes—
55#2797C2213yes—
56#2796C2213yes—
57#2795C2216yes—
58#2793C2216yes—
59#2787C2213yes—
60#2787C2216yes—
61#2783C2216yes—
62#2781C2216yes—
63#2779C2213yes—
64#2777C2216yes—
65#2777C2213yes—
66#2776C2216yes—
67#2772C2213yes—
68#2772C2216yes—
69#2770C2216yes—
70#2766C2216yes—
71#2757C2213yes—
72#2753C2213yes—
73#2725C2213yes—
74#2714C2211yescharacteristic
75#2711C2213yes—
76#2645C2213yes—
77#2625C2213yes—
78#2625C2213yes—
79#2621C2213yes—
80#2621C2213yes—
81#2621C2213yes—
82#2606C2216yes—
83#2597C2216yes—
84#2596C2216yes—
85#2595C2216yes—
86#2594C2216yes—
87#2594C2216yes—
88#2593C2216yes—
89#2590C2216yes—
90#2590C2216yes—
91#2590C2216yes—
92#2585C2216yes—
93#2577C2216yes—
94#2570C2216yes—
95#2570C2213yes—
96#2570C2213yes—
97#2546C2213yes—
98#2546C2213yes—
99#2546C2213yes—
100#2546C2213yes—
101#2538C2213yes—
102#2536C2213yes—
103#2536C2213yes—
104#2536C2213yes—
105#2530C2216yes—
106#2529C2216yes—
107#2529C2216yes—
108#2525C2216yes—
109#2525C2216yes—
110#2525C2216yes—
111#2514C2213yes—
112#2514C2213yes—
113#2511C2213yes—
114#2511C2213yes—
115#2511C2213yes—
116#2511C2213yes—
117#2509C2216yes—
118#2509C2213yes—
119#2508C2213yes—
120#2507C2216yes—
121#2507C2213yes—
122#2506C2213yes—
123#2499C2213yes—
124#2499C2213yes—
125#2497C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2497C2213yes—
129#2495C2213yes—
130#2494C2213yes—
131#2485C2213yes—
132#2485C2213yes—
133#2446C2213yes—
134#2446C2213yes—
135#2446C2213yes—
136#2446C2213yes—
137#2429C2213yes—
138#2429C2213yes—
139#2429C2213yes—
140#2429C2213yes—
141#2429C2213yes—
142#2429C2213yes—
143#2429C2213yes—
144#2429C2213yes—
145#2423C2213yes—
146#2423C2213yes—
147#2421C2213yes—
148#2421C2213yes—
149#2417C2213yes—
150#2417C2213yes—
151#2415C2213yes—
152#2415C2213yes—
153#2415C2213yes—
154#2415C2213yes—
155#2415C2213yes—
156#2415C2213yes—
157#2401C2213yes—
158#2395C2213yes—
159#2395C2213yes—
160#2392C2213yes—
161#2392C2213yes—
162#2392C2213yes—
163#2370C2216yes—
164#2365C2213yes—
165#2365C2213yes—
166#2365C2213yes—
167#2365C2213yes—
168#2362C2213yes—
169#2362C2213yes—
170#2362C2213yes—
171#2362C2213yes—
172#2362C2213yes—
173#2362C2213yes—
174#2362C2213yes—
175#2360C2213yes—
176#2356C2213yes—
177#2355C2213yes—
178#2354C2213yes—
179#2354C2213yes—
180#2354C2213yes—
181#2352C2213yes—
182#2351C2213yes—
183#2351C2211yescharacteristic
184#2351C2211yescharacteristic
185#2351C2213yes—
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192Q8×C4⋊C4C2213yes—
193Q8×C4⋊C4C2213yes—
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196#2347C2213yes—
197#2346C2213yes—
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206Q8×C22⋊C4C2211yescharacteristic
207Q8×C22⋊C4C2211yescharacteristic
208#2327C2213yes—
209#2323C2213yes—
210#2323C2213yes—
211#2323C2213yes—
212#2323C2213yes—
213#2323C2213yes—
214#2323C2213yes—
215#2323C2213yes—
216#2320C2213yes—
217#2317C2213yes—
218#2317C2213yes—
219#2314C2213yes—
220C4×C4⋊Q8C2213yes—
221C4×C4⋊Q8C2213yes—
222C4×C4⋊Q8C2213yes—
223C4×#125C2213yes—
224C4×#126C2213yes—
225C4×C22⋊Q8C2213yes—
226C4×#121C2213yes—
227#2298C2213yes—
228#2296C2213yes—
229#2296C2213yes—
230#2295C2213yes—
231#2293C2213yes—
232#2293C2213yes—
233#2293C2213yes—
234#2290C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C23×Q8C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242D4×Q8—28no—
243D4×Q8—28no—
244D4×Q8—28no—
245D4×Q8—28no—
246D4×Q8—44no—
247D4×Q8—44no—
248C2×C4⋊Q8C2313yes—
249C2×C4⋊Q8C2313yes—
250C2×C4⋊Q8C2313yes—
251C2×C4⋊Q8C2313yes—
252C2×C4⋊Q8C2313yes—
253C2×C4⋊Q8C2313yes—
254C2×#126C2311yescharacteristic
255C2×#125C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2313yes—
262C2×C22⋊Q8C2313yes—
263C2×C22⋊Q8C2313yes—
264C2×C22⋊Q8C2313yes—
265C2×C22⋊Q8C2313yes—
266C2×C22⋊Q8C2313yes—
267C2×C22⋊Q8C2313yes—
268C2×#121C2311yescharacteristic
269#519—28no—
270#519—28no—
271#519—44no—
272#519—44no—
273#519—44no—
274C2×C4×Q8—44no—
275C2×C4×Q8C2313yes—
276C2×C4×Q8C2313yes—
277C2×C4×Q8C2313yes—
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×Q8C2313yes—
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2311yescharacteristic
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2313yes—
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C2×#117C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C2×#117C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C42C2313yes—
316#401C2316yes—
317#401C2313yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2316yes—
323#400C2313yes—
324#400C2313yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2316yes—
329#400C2316yes—
330#400C2313yes—
331#400C2313yes—
332#399C2313yes—
333#399C2313yes—
334#398C2313yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2316yes—
341#398C2313yes—
342#398C2313yes—
343#398C2316yes—
344#398C2316yes—
345#398C2316yes—
346#398C2316yes—
347#398C2313yes—
348#398C2316yes—
349#398C2316yes—
350#398C2313yes—
351#397C2313yes—
352#397C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2316yes—
356#397C2316yes—
357#397C2316yes—
358#397C2313yes—
359#397C2313yes—
360#397C2313yes—
361#397C2313yes—
362#397C2313yes—
363#397C2313yes—
364#397C2313yes—
365#397C2311yescharacteristic
366#397C2313yes—
367#397C2313yes—
368#396C2313yes—
369#396C2316yes—
370#396C2313yes—
371#396C2313yes—
372#396C2313yes—
373#396C2313yes—
374#396C2313yes—
375#396C2313yes—
376#396C2316yes—
377#396C2316yes—
378#394C2313yes—
379#394C2313yes—
380#394C2313yes—
381#394C2313yes—
382#394C2313yes—
383#394C2313yes—
384#394C2313yes—
385#394C2313yes—
386#394C2313yes—
387#394C2313yes—
388#394C2311yescharacteristic
389#394C2311yescharacteristic
390#394C2313yes—
391#392C2311yescharacteristic
392#392C2311yescharacteristic
393#392C2311yescharacteristic
394#391C2313yes—
395#391C2313yes—
396#391C2313yes—
397#391C2313yes—
398#391C2313yes—
399#391C2313yes—
400#391C2313yes—
401#391C2313yes—
402#391C2313yes—
403#391C2313yes—
404#391C2313yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#390C2313yes—
415#390C2313yes—
416#390C2313yes—
417#390C2313yes—
418#390C2311yescharacteristic
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#389C2313yes—
422#389C2313yes—
423#389C2313yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2316yes—
428#389C2316yes—
429#389C2313yes—
430#389C2316yes—
431#389C2313yes—
432#389C2313yes—
433#389C2313yes—
434#389C2316yes—
435#389C2313yes—
436#389C2316yes—
437#389C2316yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2316yes—
449#389C2316yes—
450#389C2313yes—
451#389C2313yes—
452#389C2316yes—
453#389C2316yes—
454#389C2316yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2316yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2313yes—
472#388C2316yes—
473#388C2313yes—
474#388C2316yes—
475#388C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2313yes—
481#388C2316yes—
482#388C2316yes—
483#388C2316yes—
484#388C2316yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2316yes—
493#388C2316yes—
494#388C2316yes—
495#388C2316yes—
496#388C2313yes—
497#388C2313yes—
498#388C2313yes—
499#388C2313yes—
500#388C2313yes—
501#388C2313yes—
502#388C2313yes—
503#388C2313yes—
504#388C2313yes—
505#388C2316yes—
506#388C2313yes—
507#388C2311yescharacteristic
508#387C2313yes—
509#387C2313yes—
510#387C2313yes—
511#387C2311yescharacteristic
512#387C2313yes—
513#387C2313yes—
514#387C2313yes—
515#387C2316yes—
516#387C2316yes—
517#387C2316yes—
518#387C2316yes—
519#387C2316yes—
520#387C2316yes—
521#387C2316yes—
522#387C2313yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2316yes—
531#387C2313yes—
532#387C2316yes—
533#387C2316yes—
534#387C2313yes—
535#387C2316yes—
536#387C2316yes—
537#387C2316yes—
538#387C2316yes—
539#387C2316yes—
540#387C2316yes—
541#387C2316yes—
542#387C2316yes—
543#387C2313yes—
544#387C2313yes—
545#387C2313yes—
546#386C2313yes—
547#386C2313yes—
548#386C2313yes—
549#386C2311yescharacteristic
550#385C2313yes—
551#385C2316yes—
552#385C2313yes—
553#385C2313yes—
554#385C2313yes—
555#385C2313yes—
556#385C2311yescharacteristic
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2316yes—
561#384C2313yes—
562#384C2313yes—
563#383C2313yes—
564#383C2316yes—
565#383C2316yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2316yes—
570#382C2313yes—
571#382C2313yes—
572#382C2313yes—
573#382C2316yes—
574#380C2313yes—
575#380C2313yes—
576#380C2316yes—
577#380C2313yes—
578#380C2313yes—
579#380C2313yes—
580#380C2313yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2316yes—
595C4×C4⋊C4C2316yes—
596C4×C4⋊C4C2316yes—
597C4×C4⋊C4C2316yes—
598C4×C4⋊C4C2316yes—
599C4×C4⋊C4C2316yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2316yes—
607C4×C4⋊C4C2316yes—
608C4×C4⋊C4C2316yes—
609C4×C4⋊C4C2316yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2316yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626#376C2313yes—
627#376C2316yes—
628C43C2313yes—
629C43C2313yes—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8—24no—
637C22×Q8—24no—
638C22×Q8—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8#4118yes—
642C22×Q8C2413yes—
643C22×Q8C2413yes—
644C22×Q8C2413yes—
645C22×Q8C2413yes—
646C22×Q8C2411yescharacteristic
647C22×D4C2411yescharacteristic
648C22×D4C2411yescharacteristic
649C22×D4C2411yescharacteristic
650C22×D4C2411yescharacteristic
651C22×D4C2411yescharacteristic
652C22×D4C2411yescharacteristic
653C23×C4C2413yes—
654C23×C4C2413yes—
655C23×C4C2413yes—
656C23×C4C2413yes—
657C23×C4C2411yescharacteristic
658C23×C4C2413yes—
659C4⋊Q8—212no—
660C4⋊Q8—212no—
661C4⋊Q8—212no—
662C4⋊Q8—212no—
663C4⋊Q8—46no—
664C4⋊Q8—46no—
665#126—24no—
666#125—212no—
667C22⋊Q8—212no—
668C22⋊Q8—212no—
669C22⋊Q8—212no—
670C22⋊Q8—212no—
671C22⋊Q8—212no—
672C22⋊Q8—212no—
673C22⋊Q8—212no—
674C22⋊Q8—212no—
675C22⋊Q8—46no—
676C22⋊Q8—46no—
677C22⋊Q8—46no—
678C22⋊Q8—46no—
679#121—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—212no—
691C4×Q8—212no—
692C4×Q8—212no—
693C4×Q8—212no—
694C4×Q8—46no—
695C4×Q8—46no—
696C4×Q8—46no—
697C4×Q8—46no—
698C4×Q8—46no—
699C4×Q8—46no—
700C4×Q8—46no—
701C4×Q8—46no—
702C4×Q8#4118yes—
703C4×D4—212no—
704C4×D4—212no—
705C4×D4—212no—
706C4×D4—212no—
707C4×D4—46no—
708C4×D4—46no—
709#117—212no—
710#117—212no—
711#117—212no—
712#117—212no—
713#117—46no—
714#117—46no—
715#117—46no—
716#117—46no—
717#117—46no—
718#117—46no—
719C2×C4⋊C4—46no—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2416yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2416yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2416yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2411yescharacteristic
793C2×C22⋊C4C2411yescharacteristic
794C2×C22⋊C4C2411yescharacteristic
795C2×C22⋊C4C2411yescharacteristic
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2413yes—
798C2×C22⋊C4C2411yescharacteristic
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2413yes—
802C2×C22⋊C4C2413yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2413yes—
805C2×C22⋊C4C2413yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2411yescharacteristic
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2411yescharacteristic
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2411yescharacteristic
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C42—46no—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2416yes—
828C2×C42C2413yes—
829C2×C42C2416yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2413yes—
835C2×C42C2411yescharacteristic
836C2×C42C2416yes—
837C2×C42C2416yes—
838C2×C42C2416yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2411yescharacteristic
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2416yes—
848C2×C42C2413yes—
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2416yes—
856#95C2416yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2416yes—
867#95C2413yes—
868#95C2413yes—
869#95C2416yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2416yes—
879#95C2411yescharacteristic
880#95C2416yes—
881#95C2413yes—
882#95C2411yescharacteristic
883#95C2413yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2411yescharacteristic
887#95C2416yes—
888#95C2416yes—
889#95C2416yes—
890#95C2416yes—
891#95C2416yes—
892#95C2416yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2416yes—
898#95C2416yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2416yes—
908#95C2416yes—
909#95C2416yes—
910C24C2511yescharacteristic
911C24C2511yescharacteristic
912C24C2511yescharacteristic
913C24C2511yescharacteristic
914C2×Q8—232no—
915C2×Q8—26no—
916C2×Q8—26no—
917C2×Q8—26no—
918C2×Q8—26no—
919C2×Q8—26no—
920C2×Q8—26no—
921C2×Q8—26no—
922C2×Q8—26no—
923C2×Q8—26no—
924C2×Q8—26no—
925C2×Q8—26no—
926C2×Q8—416no—
927C2×Q8—416no—
928C2×Q8—416no—
929C2×Q8C2×#41112yes—
930C2×Q8C2×#4114yes—
931C2×Q8C2×#4114yes—
932C2×Q8H(5,𝔽2)14yes—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4—22no—
936C2×D4—22no—
937C2×D4—22no—
938C2×D4—22no—
939C2×D4—22no—
940C2×D4—41no—
941C2×D4—41no—
942C2×D4—41no—
943C2×D4—41no—
944C2×D4—41no—
945C2×D4—41no—
946C2×D4—41no—
947C2×D4—41no—
948C2×D4—41no—
949C2×D4—41no—
950C2×D4—41no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—26no—
956C22×C4—26no—
957C22×C4—26no—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—26no—
962C22×C4—22no—
963C22×C4—41no—
964C22×C4—41no—
965C22×C4—43no—
966C22×C4—43no—
967C22×C4—43no—
968C22×C4C2×#41112yes—
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2513yes—
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2513yes—
977C22×C4C2513yes—
978C22×C4C2511yescharacteristic
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2513yes—
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2513yes—
989C22×C4C2513yes—
990C22×C4C2511yescharacteristic
991C22×C4C2513yes—
992C22×C4C2511yescharacteristic
993C22×C4C2511yescharacteristic
994C22×C4C2511yescharacteristic
995C22×C4C2513yes—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—212no—
1010C4⋊C4—212no—
1011C4⋊C4—212no—
1012C4⋊C4—212no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—26no—
1019C4⋊C4—26no—
1020C4⋊C4—26no—
1021C4⋊C4—26no—
1022C4⋊C4—26no—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—46no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—46no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—43no—
1033C4⋊C4—43no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—46no—
1037C4⋊C4—46no—
1038C4⋊C4—46no—
1039C4⋊C4—43no—
1040C4⋊C4—46no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—46no—
1053C4⋊C4C2×#41112yes—
1054C4⋊C42−1+414yes—
1055C22⋊C4—26no—
1056C22⋊C4—26no—
1057C22⋊C4—26no—
1058C22⋊C4—26no—
1059C22⋊C4—26no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—26no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—26no—
1066C22⋊C4—26no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—43no—
1076C22⋊C4—41no—
1077C22⋊C4—43no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—43no—
1085C22⋊C4—43no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—43no—
1094C22⋊C4—43no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C42—212no—
1098C42—26no—
1099C42—26no—
1100C42—212no—
1101C42—26no—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—22no—
1111C42—43no—
1112C42—43no—
1113C42—43no—
1114C42—43no—
1115C42—43no—
1116C42—41no—
1117C42—43no—
1118C42—46no—
1119C42—43no—
1120C42—46no—
1121C42—46no—
1122C42—46no—
1123C42C2×#41112yes—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23C22×#4112yes—
1152C23C2611yescharacteristic
1153Q8—224no—
1154Q8—412no—
1155Q8—412no—
1156Q8—412no—
1157Q8#553116yes—
1158D4—44no—
1159D4—44no—
1160D4—44no—
1161D4—44no—
1162D4—44no—
1163D4—44no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—23no—
1167C2×C4—21no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—224no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—23no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—23no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—23no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—23no—
1221C2×C4—23no—
1222C2×C4—23no—
1223C2×C4—21no—
1224C2×C4—23no—
1225C2×C4—21no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—23no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—44no—
1238C2×C4—412no—
1239C2×C4—412no—
1240C2×C4—412no—
1241C2×C4—86no—
1242C2×C4C22×#4116yes—
1243C2×C4C22×#4112yes—
1244C2×C4C22×#4116yes—
1245C2×C4C22×#4116yes—
1246C2×C4C22×#4116yes—
1247C2×C4C2×H(5,𝔽2)16yes—
1248C2×C4C2×2−1+412yes—
1249C2×C4C2×2−1+412yes—
1250C2×C4C2×2−1+412yes—
1251C22—22no—
1252C22—22no—
1253C22—22no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22C23×#4111yescharacteristic
1280C22C23×#4111yescharacteristic
1281C22C22×H(5,𝔽2)11yescharacteristic
1282C22C22×2−1+411yescharacteristic
1283C222−1+611yescharacteristic
1284C222−1+611yescharacteristic
1285C222−1+611yescharacteristic
1286C4—22no—
1287C4—22no—
1288C4—26no—
1289C4—22no—
1290C4—22no—
1291C4—26no—
1292C4—43no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—43no—
1297C4—43no—
1298C4—43no—
1299C4—41no—
1300C4—43no—
1301C4—43no—
1302C4—43no—
1303C4—43no—
1304C4—41no—
1305C4—41no—
1306C4—43no—
1307C4—43no—
1308C4—41no—
1309C4—43no—
1310C4—43no—
1311C4—43no—
1312C4C2×#553112yes—
1313C2—42no—
1314C2—81no—
1315C2—81no—
1316C2—81no—
1317C2C22×#55311yescharacteristic
1318C2#6285011yescharacteristic
1319C2#6285011yescharacteristic
1320C2#6291311yescharacteristic
1321C2#6299811yescharacteristic
1322C2#6300111yescharacteristic
1323C2#6304411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2714C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59857C2semidirect
2. #59695C2semidirect
3. #59681C2semidirect
5. #45397C2semidirect
6. #45348C2semidirect
7. #45342C2semidirect
8. #45309C2semidirect
9. #45262C2semidirect
10. #45130C2semidirect
11. #39819C2semidirect
12. #39553C2semidirect
13. #39283C2semidirect
14. #39186C2semidirect
15. #38217C2semidirect
16. #38128C2semidirect
17. Q8×#126C2semidirect
18. Q8×#121C2semidirect
19. #36475C2semidirect
20. #35883C2semidirect
21. #35723C2semidirect
22. #35723C2semidirect
23. #35700C2semidirect
24. #35700C2semidirect
25. #35700C2semidirect
26. #34311C2semidirect
27. #34311C2semidirect
28. #34311C2semidirect
29. #34291C2semidirect
30. #34262C2semidirect
31. #34249C2semidirect

Maximal subgroups

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

subgroupindex
#598572
#596952
#596812
#522622
#453972
#453482
#453422
#453092
#452622
#451302
#398192
#395532
#392832
#391862
#382172
#381282
Q8×#1262
Q8×#1212
#364752
#358832
#357232
#357002
#343112
#342912
#342622
#342492