Finite Group Databasebeta

← #7688048

Subgroups — #7688048

Order 512.

5023 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59855C213yesmaximal, complemented
2#59695C213yesmaximal, complemented
3#59441C213yesmaximal, complemented
4#59402C213yesmaximal, complemented
5#59309C213yesmaximal, complemented
6#45344C213yesmaximal, complemented
7#45310C213yesmaximal, complemented
8#45309C213yesmaximal, complemented
9#45184C213yesmaximal, complemented
10#39283C213yesmaximal, complemented
11#39263C213yesmaximal, complemented
12#38122C213yesmaximal, complemented
13#37894C213yesmaximal, complemented
14#36599C213yesmaximal, complemented
15Q8×#121C211yesmaximal, characteristic, complemented
16Q8×#121C211yesmaximal, characteristic, complemented
17Q8×#121C211yesmaximal, characteristic, complemented
18#36482C211yesmaximal, characteristic, complemented
19#36448C211yesmaximal, characteristic, complemented
20#36278C213yesmaximal, complemented
21#35883C211yesmaximal, characteristic, complemented
22#35868C211yesmaximal, characteristic, complemented
23#35723C211yesmaximal, characteristic, complemented
24#35700C211yesmaximal, characteristic, complemented
25#34856C213yesmaximal
26#34291C211yesmaximal, characteristic, complemented
27#34291C211yesmaximal, characteristic, complemented
28#34291C211yesmaximal, characteristic, complemented
29#34262C211yesmaximal, characteristic, complemented
30C4×D4×Q8C211yesmaximal, characteristic, complemented
31C2×#2351C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×D4×Q8C2211yescharacteristic
38C2×#519C2211yescharacteristic
39C2×#519C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41C22×C4×Q8C2211yescharacteristic
42C22×C4×Q8C2211yescharacteristic
43C22×C4×Q8C2211yescharacteristic
44#2863C2213yes—
45#2857C2213yes—
46#2857C2213yes—
47#2857C2213yes—
48#2855C2213yes—
49#2802C2216yes—
50#2800C2216yes—
51#2783C2216yes—
52#2777C2216yes—
53#2776C2216yes—
54#2776C2216yes—
55#2772C2216yes—
56#2772C2216yes—
57#2766C2216yes—
58#2766C2216yes—
59#2766C2216yes—
60#2765C2216yes—
61#2761C2216yes—
62#2725C2216yes—
63#2647C2213yes—
64#2645C2213yes—
65#2625C2213yes—
66#2621C2213yes—
67#2608C2216yes—
68#2606C2216yes—
69#2606C2216yes—
70#2597C2213yes—
71#2596C2213yes—
72#2595C2213yes—
73#2594C2216yes—
74#2594C2213yes—
75#2593C2213yes—
76#2591C2213yes—
77#2590C2216yes—
78#2587C2216yes—
79#2585C2213yes—
80#2585C2216yes—
81#2585C2216yes—
82#2579C2213yes—
83#2573C2213yes—
84#2570C2213yes—
85#2569C2216yes—
86#2569C2216yes—
87#2569C2213yes—
88#2558C2216yes—
89#2554C2213yes—
90#2552C2213yes—
91#2546C2213yes—
92#2546C2213yes—
93#2546C2213yes—
94#2546C2213yes—
95#2543C2211yescharacteristic
96#2538C2213yes—
97#2538C2213yes—
98#2538C2213yes—
99#2536C2213yes—
100#2529C2216yes—
101#2525C2216yes—
102#2515C2216yes—
103#2514C2213yes—
104#2514C2213yes—
105#2514C2213yes—
106#2514C2213yes—
107#2511C2213yes—
108#2511C2213yes—
109#2510C2213yes—
110#2510C2216yes—
111#2510C2216yes—
112#2509C2213yes—
113#2509C2216yes—
114#2507C2213yes—
115#2506C2213yes—
116#2506C2213yes—
117#2503C2213yes—
118#2499C2213yes—
119#2497C2213yes—
120#2496C2213yes—
121#2495C2213yes—
122#2495C2213yes—
123#2494C2213yes—
124#2494C2213yes—
125#2486C2213yes—
126#2485C2213yes—
127#2481C2213yes—
128#2446C2213yes—
129#2446C2213yes—
130#2446C2213yes—
131#2446C2213yes—
132#2444C2213yes—
133#2443C2213yes—
134#2442C2216yes—
135#2429C2213yes—
136#2429C2213yes—
137#2429C2213yes—
138#2429C2213yes—
139#2429C2213yes—
140#2429C2213yes—
141#2429C2213yes—
142#2429C2213yes—
143#2423C2213yes—
144#2421C2213yes—
145#2421C2213yes—
146#2421C2213yes—
147#2417C2213yes—
148#2417C2213yes—
149#2417C2213yes—
150#2417C2213yes—
151#2417C2213yes—
152#2417C2213yes—
153#2415C2213yes—
154#2415C2213yes—
155#2402C2213yes—
156#2401C2213yes—
157#2395C2213yes—
158#2392C2213yes—
159#2370C2216yes—
160#2365C2213yes—
161#2365C2213yes—
162#2365C2213yes—
163#2365C2213yes—
164#2362C2213yes—
165#2362C2213yes—
166#2362C2213yes—
167#2360C2213yes—
168#2360C2213yes—
169#2360C2213yes—
170#2360C2213yes—
171#2360C2213yes—
172#2356C2213yes—
173#2355C2213yes—
174#2353C2216yes—
175#2352C2213yes—
176#2352C2213yes—
177#2352C2213yes—
178#2351C2213yes—
179#2351C2211yescharacteristic
180#2351C2211yescharacteristic
181#2351C2213yes—
182#2351C2211yescharacteristic
183#2351C2211yescharacteristic
184#2351C2213yes—
185#2351C2211yescharacteristic
186#2351C2213yes—
187#2351C2211yescharacteristic
188Q8×C4⋊C4C2211yescharacteristic
189Q8×C4⋊C4C2211yescharacteristic
190Q8×C4⋊C4C2211yescharacteristic
191Q8×C4⋊C4C2211yescharacteristic
192D4×C4⋊C4C2213yes—
193#2347C2213yes—
194#2346C2213yes—
195#2345C2216yes—
196Q8×C22⋊C4C2211yescharacteristic
197Q8×C22⋊C4C2211yescharacteristic
198Q8×C22⋊C4C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204Q8×C22⋊C4C2211yescharacteristic
205Q8×C22⋊C4C2211yescharacteristic
206#2327C2213yes—
207#2327C2213yes—
208#2327C2213yes—
209#2323C2213yes—
210#2323C2213yes—
211#2323C2213yes—
212#2320C2213yes—
213#2314C2213yes—
214C4×C4⋊Q8C2213yes—
215C4×#126C2213yes—
216C4×C22⋊Q8C2213yes—
217C4×C22⋊Q8C2213yes—
218C4×C22⋊Q8C2213yes—
219C4×C22⋊Q8C2213yes—
220C4×C22⋊Q8C2213yes—
221C4×#123C2213yes—
222C4×#121C2213yes—
223C4×#121C2213yes—
224C4×#121C2213yes—
225#2298C2213yes—
226#2295C2213yes—
227C2×#389C2213yes—
228C2×#389C2213yes—
229#2290C2213yes—
230#2290C2213yes—
231#2290C2213yes—
232C2×#382C2213yes—
233#2276C2211yescharacteristic
234#2276C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C42×D4C2213yes—
237C2×C4×C4⋊C4C2213yes—
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×#126C2313yes—
255C2×#125C2316yes—
256C2×#123C2313yes—
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×C22⋊Q8C2313yes—
269C2×#121C2311yescharacteristic
270C2×#121C2311yescharacteristic
271C2×#121C2311yescharacteristic
272#519—28no—
273#519—44no—
274C2×C4×Q8—28no—
275C2×C4×Q8—44no—
276C2×C4×Q8—44no—
277C2×C4×Q8—44no—
278C2×C4×Q8C2313yes—
279C2×C4×Q8C2313yes—
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×Q8C2311yescharacteristic
290C2×C4×Q8C2311yescharacteristic
291C2×C4×Q8C2313yes—
292C2×C4×Q8C2313yes—
293C2×C4×Q8C2313yes—
294C2×C4×Q8C2313yes—
295C2×C4×Q8C2313yes—
296C2×C4×Q8C2313yes—
297C2×C4×Q8C2313yes—
298C2×C4×Q8C2313yes—
299C2×C4×Q8C2313yes—
300C2×C4×Q8C2311yescharacteristic
301C2×C4×D4C2311yescharacteristic
302C2×C4×D4C2313yes—
303C2×C4×D4C2313yes—
304C2×C4×D4C2313yes—
305C2×C4×D4C2313yes—
306C2×C4×D4C2313yes—
307C2×C4×D4C2313yes—
308C2×C4×D4C2313yes—
309C2×#117C2313yes—
310C2×#117C2313yes—
311C2×#117C2313yes—
312C2×#117C2313yes—
313C22×C4⋊C4C2313yes—
314C22×C4⋊C4C2313yes—
315C22×C4⋊C4C2313yes—
316C22×C4⋊C4C2313yes—
317C22×C4⋊C4C2313yes—
318C22×C4⋊C4C2313yes—
319C22×C42C2313yes—
320C22×C42C2313yes—
321C22×C42C2313yes—
322C22×C42C2313yes—
323#401C2316yes—
324#401C2313yes—
325#401C2316yes—
326#400C2313yes—
327#400C2316yes—
328#400C2316yes—
329#400C2313yes—
330#400C2316yes—
331#400C2316yes—
332#400C2313yes—
333#400C2313yes—
334#400C2313yes—
335#400C2316yes—
336#400C2316yes—
337#400C2313yes—
338#400C2313yes—
339#400C2313yes—
340#400C2316yes—
341#400C2316yes—
342#399C2313yes—
343#398C2316yes—
344#398C2313yes—
345#398C2313yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2313yes—
351#398C2311yescharacteristic
352#398C2316yes—
353#398C2316yes—
354#398C2316yes—
355#398C2316yes—
356#398C2313yes—
357#398C2316yes—
358#398C2316yes—
359#398C2316yes—
360#398C2316yes—
361#397C2311yescharacteristic
362#397C2316yes—
363#397C2313yes—
364#397C2313yes—
365#397C2313yes—
366#397C2313yes—
367#397C2313yes—
368#397C2313yes—
369#397C2316yes—
370#397C2316yes—
371#397C2316yes—
372#396C2313yes—
373#396C2313yes—
374#396C2316yes—
375#396C2316yes—
376#396C2313yes—
377#396C2316yes—
378#396C2316yes—
379#396C2316yes—
380#396C2316yes—
381#394C2313yes—
382#394C2313yes—
383#394C2311yescharacteristic
384#394C2313yes—
385#394C2313yes—
386#392C2311yescharacteristic
387#391C2313yes—
388#391C2313yes—
389#391C2313yes—
390#391C2313yes—
391#391C2313yes—
392#391C2313yes—
393#391C2313yes—
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#390C2313yes—
408#390C2313yes—
409#390C2313yes—
410#389C2316yes—
411#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2316yes—
418#389C2316yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2316yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2316yes—
427#389C2316yes—
428#389C2316yes—
429#389C2316yes—
430#389C2313yes—
431#389C2316yes—
432#389C2316yes—
433#389C2316yes—
434#389C2313yes—
435#389C2313yes—
436#389C2313yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2316yes—
441#389C2316yes—
442#389C2316yes—
443#389C2313yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2313yes—
448#389C2316yes—
449#389C2313yes—
450#389C2313yes—
451#388C2311yescharacteristic
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2316yes—
456#388C2313yes—
457#388C2313yes—
458#388C2313yes—
459#388C2313yes—
460#388C2313yes—
461#388C2316yes—
462#388C2316yes—
463#388C2316yes—
464#388C2316yes—
465#388C2316yes—
466#388C2313yes—
467#388C2313yes—
468#388C2313yes—
469#388C2313yes—
470#388C2313yes—
471#388C2313yes—
472#388C2313yes—
473#388C2313yes—
474#388C2313yes—
475#388C2313yes—
476#388C2313yes—
477#388C2316yes—
478#388C2311yescharacteristic
479#388C2316yes—
480#387C2313yes—
481#387C2313yes—
482#387C2313yes—
483#387C2316yes—
484#387C2316yes—
485#387C2316yes—
486#387C2316yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2316yes—
491#387C2316yes—
492#387C2316yes—
493#387C2316yes—
494#387C2316yes—
495#387C2316yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2316yes—
500#387C2316yes—
501#387C2313yes—
502#387C2313yes—
503#387C2313yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2316yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2313yes—
512#387C2316yes—
513#387C2316yes—
514#387C2313yes—
515#387C2316yes—
516#387C2313yes—
517#387C2316yes—
518#387C2316yes—
519#386C2313yes—
520#386C2313yes—
521#386C2313yes—
522#386C2313yes—
523#386C2313yes—
524#386C2313yes—
525#386C2311yescharacteristic
526#386C2311yescharacteristic
527#386C2313yes—
528#386C2313yes—
529#386C2313yes—
530#386C2311yescharacteristic
531#386C2311yescharacteristic
532#385C2313yes—
533#385C2313yes—
534#385C2313yes—
535#385C2316yes—
536#385C2313yes—
537#385C2313yes—
538#385C2313yes—
539#385C2313yes—
540#385C2316yes—
541#384C2313yes—
542#384C2313yes—
543#384C2313yes—
544#384C2313yes—
545#383C2313yes—
546#383C2316yes—
547#383C2316yes—
548#383C2316yes—
549#382C2313yes—
550#382C2313yes—
551#382C2313yes—
552#382C2316yes—
553#382C2313yes—
554#382C2313yes—
555#382C2313yes—
556#382C2316yes—
557#382C2316yes—
558#381C2313yes—
559#381C2316yes—
560#380C2313yes—
561#380C2316yes—
562#380C2316yes—
563#380C2313yes—
564#380C2316yes—
565#380C2313yes—
566#380C2313yes—
567#380C2313yes—
568#380C2313yes—
569#380C2313yes—
570#380C2313yes—
571#380C2313yes—
572#380C2313yes—
573#380C2313yes—
574#380C2313yes—
575#380C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2316yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
592C4×C4⋊C4C2316yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2316yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2316yes—
612C4×C22⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2316yes—
622C4×C22⋊C4C2316yes—
623#376C2313yes—
624#376C2313yes—
625#376C2316yes—
626C2×#95C2311yescharacteristic
627C2×#95C2313yes—
628C2×#95C2316yes—
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×C4C2411yescharacteristic
659C23×C4C2413yes—
660C23×C4C2413yes—
661C23×C4C2413yes—
662C23×C4C2413yes—
663C23×C4C2411yescharacteristic
664C23×C4C2411yescharacteristic
665C4⋊Q8—212no—
666C4⋊Q8—212no—
667C4⋊Q8—212no—
668C4⋊Q8—212no—
669C4⋊Q8—46no—
670C4⋊Q8—46no—
671#126—46no—
672#125—412no—
673#123—46no—
674C22⋊Q8—212no—
675C22⋊Q8—212no—
676C22⋊Q8—212no—
677C22⋊Q8—212no—
678C22⋊Q8—212no—
679C22⋊Q8—212no—
680C22⋊Q8—212no—
681C22⋊Q8—212no—
682C22⋊Q8—46no—
683C22⋊Q8—46no—
684C22⋊Q8—46no—
685C22⋊Q8—46no—
686#121—24no—
687#121—24no—
688#121—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—24no—
694C4×Q8—24no—
695C4×Q8—24no—
696C4×Q8—24no—
697C4×Q8—24no—
698C4×Q8—24no—
699C4×Q8—212no—
700C4×Q8—212no—
701C4×Q8—212no—
702C4×Q8—212no—
703C4×Q8—46no—
704C4×Q8—46no—
705C4×Q8—46no—
706C4×Q8—46no—
707C4×Q8—46no—
708C4×Q8—46no—
709C4×Q8—46no—
710C4×Q8—46no—
711C4×Q8#4118yes—
712C4×D4—212no—
713C4×D4—212no—
714C4×D4—212no—
715C4×D4—212no—
716C4×D4—24no—
717C4×D4—212no—
718C4×D4—46no—
719C4×D4—46no—
720#117—212no—
721#117—212no—
722#117—46no—
723#117—46no—
724C2×C4⋊C4—212no—
725C2×C4⋊C4—212no—
726C2×C4⋊C4—46no—
727C2×C4⋊C4—46no—
728C2×C4⋊C4—46no—
729C2×C4⋊C4—46no—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2416yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2413yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2411yescharacteristic
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2411yescharacteristic
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2416yes—
760C2×C4⋊C4C2416yes—
761C2×C4⋊C4C2416yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2416yes—
765C2×C4⋊C4C2416yes—
766C2×C4⋊C4C2416yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2416yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2413yes—
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2416yes—
784C2×C4⋊C4C2413yes—
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2413yes—
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2413yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2411yescharacteristic
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2411yescharacteristic
800C2×C22⋊C4C2411yescharacteristic
801C2×C22⋊C4C2411yescharacteristic
802C2×C22⋊C4C2411yescharacteristic
803C2×C22⋊C4C2411yescharacteristic
804C2×C22⋊C4C2411yescharacteristic
805C2×C22⋊C4C2411yescharacteristic
806C2×C22⋊C4C2411yescharacteristic
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2413yes—
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2413yes—
821C2×C42—212no—
822C2×C42—46no—
823C2×C42—46no—
824C2×C42—46no—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2416yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2411yescharacteristic
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2413yes—
839C2×C42C2413yes—
840C2×C42C2416yes—
841C2×C42C2413yes—
842C2×C42C2413yes—
843C2×C42C2413yes—
844C2×C42C2413yes—
845C2×C42C2413yes—
846C2×C42C2413yes—
847C2×C42C2416yes—
848C2×C42C2413yes—
849C2×C42C2413yes—
850C2×C42C2416yes—
851C2×C42C2413yes—
852#95C2416yes—
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2416yes—
862#95C2416yes—
863#95C2416yes—
864#95C2411yescharacteristic
865#95C2411yescharacteristic
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2416yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2416yes—
886#95C2416yes—
887#95C2413yes—
888#95C2416yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2416yes—
893#95C2413yes—
894#95C2416yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2416yes—
902#95C2416yes—
903#95C2411yescharacteristic
904#95C2411yescharacteristic
905#95C2416yes—
906#95C2416yes—
907#95C2416yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2413yes—
914#95C2413yes—
915#95C2416yes—
916#95C2416yes—
917C24C2511yescharacteristic
918C24C2511yescharacteristic
919C24C2511yescharacteristic
920C24C2511yescharacteristic
921C2×Q8—232no—
922C2×Q8—26no—
923C2×Q8—26no—
924C2×Q8—26no—
925C2×Q8—26no—
926C2×Q8—26no—
927C2×Q8—26no—
928C2×Q8—26no—
929C2×Q8—26no—
930C2×Q8—26no—
931C2×Q8—26no—
932C2×Q8—26no—
933C2×Q8—416no—
934C2×Q8—416no—
935C2×Q8—416no—
936C2×Q8C2×#41112yes—
937C2×Q8C2×#4114yes—
938C2×Q8C2×#4114yes—
939C2×Q8H(5,𝔽2)14yes—
940C2×D4—22no—
941C2×D4—22no—
942C2×D4—22no—
943C2×D4—22no—
944C2×D4—22no—
945C2×D4—22no—
946C2×D4—22no—
947C2×D4—22no—
948C2×D4—22no—
949C2×D4—22no—
950C2×D4—22no—
951C2×D4—22no—
952C2×D4—22no—
953C2×D4—41no—
954C2×D4—41no—
955C2×D4—41no—
956C2×D4—41no—
957C2×D42−1+414yes—
958C22×C4—26no—
959C22×C4—26no—
960C22×C4—26no—
961C22×C4—22no—
962C22×C4—22no—
963C22×C4—26no—
964C22×C4—26no—
965C22×C4—26no—
966C22×C4—22no—
967C22×C4—26no—
968C22×C4—26no—
969C22×C4—26no—
970C22×C4—26no—
971C22×C4—26no—
972C22×C4—26no—
973C22×C4—26no—
974C22×C4—26no—
975C22×C4—26no—
976C22×C4—26no—
977C22×C4—22no—
978C22×C4—22no—
979C22×C4—41no—
980C22×C4—41no—
981C22×C4—41no—
982C22×C4—43no—
983C22×C4—41no—
984C22×C4—41no—
985C22×C4—41no—
986C22×C4—43no—
987C22×C4—43no—
988C22×C4—43no—
989C22×C4—43no—
990C22×C4—43no—
991C22×C4—43no—
992C22×C4C2×#41112yes—
993C22×C42−1+414yes—
994C22×C4C2511yescharacteristic
995C22×C4C2511yescharacteristic
996C22×C4C2511yescharacteristic
997C22×C4C2513yes—
998C22×C4C2513yes—
999C22×C4C2511yescharacteristic
1000C22×C4C2511yescharacteristic
1001C22×C4C2513yes—
1002C22×C4C2513yes—
1003C22×C4C2513yes—
1004C22×C4C2511yescharacteristic
1005C22×C4C2513yes—
1006C22×C4C2513yes—
1007C22×C4C2513yes—
1008C22×C4C2513yes—
1009C22×C4C2513yes—
1010C22×C4C2513yes—
1011C22×C4C2513yes—
1012C22×C4C2513yes—
1013C22×C4C2511yescharacteristic
1014C22×C4C2513yes—
1015C22×C4C2513yes—
1016C22×C4C2511yescharacteristic
1017C22×C4C2511yescharacteristic
1018C22×C4C2511yescharacteristic
1019C22×C4C2511yescharacteristic
1020C22×C4C2513yes—
1021C4⋊C4—212no—
1022C4⋊C4—26no—
1023C4⋊C4—26no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—26no—
1027C4⋊C4—26no—
1028C4⋊C4—26no—
1029C4⋊C4—26no—
1030C4⋊C4—26no—
1031C4⋊C4—26no—
1032C4⋊C4—26no—
1033C4⋊C4—212no—
1034C4⋊C4—212no—
1035C4⋊C4—212no—
1036C4⋊C4—212no—
1037C4⋊C4—26no—
1038C4⋊C4—26no—
1039C4⋊C4—26no—
1040C4⋊C4—26no—
1041C4⋊C4—26no—
1042C4⋊C4—26no—
1043C4⋊C4—26no—
1044C4⋊C4—26no—
1045C4⋊C4—26no—
1046C4⋊C4—22no—
1047C4⋊C4—26no—
1048C4⋊C4—22no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—26no—
1052C4⋊C4—26no—
1053C4⋊C4—26no—
1054C4⋊C4—26no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—46no—
1058C4⋊C4—46no—
1059C4⋊C4—46no—
1060C4⋊C4—43no—
1061C4⋊C4—43no—
1062C4⋊C4—43no—
1063C4⋊C4—43no—
1064C4⋊C4—46no—
1065C4⋊C4—43no—
1066C4⋊C4—43no—
1067C4⋊C4—43no—
1068C4⋊C4—43no—
1069C4⋊C4—46no—
1070C4⋊C4—46no—
1071C4⋊C4—46no—
1072C4⋊C4—46no—
1073C4⋊C4—46no—
1074C4⋊C4—43no—
1075C4⋊C4C2×#41112yes—
1076C22⋊C4—26no—
1077C22⋊C4—26no—
1078C22⋊C4—26no—
1079C22⋊C4—26no—
1080C22⋊C4—26no—
1081C22⋊C4—22no—
1082C22⋊C4—22no—
1083C22⋊C4—22no—
1084C22⋊C4—22no—
1085C22⋊C4—26no—
1086C22⋊C4—26no—
1087C22⋊C4—26no—
1088C22⋊C4—26no—
1089C22⋊C4—26no—
1090C22⋊C4—26no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—22no—
1094C22⋊C4—22no—
1095C22⋊C4—22no—
1096C22⋊C4—22no—
1097C22⋊C4—43no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—41no—
1101C22⋊C4—41no—
1102C22⋊C4—43no—
1103C22⋊C4—43no—
1104C22⋊C4—43no—
1105C22⋊C4—43no—
1106C22⋊C4—43no—
1107C22⋊C4—43no—
1108C22⋊C4—43no—
1109C22⋊C4—43no—
1110C22⋊C4—43no—
1111C22⋊C4—43no—
1112C42—26no—
1113C42—26no—
1114C42—26no—
1115C42—26no—
1116C42—212no—
1117C42—26no—
1118C42—26no—
1119C42—26no—
1120C42—26no—
1121C42—26no—
1122C42—26no—
1123C42—26no—
1124C42—26no—
1125C42—22no—
1126C42—26no—
1127C42—43no—
1128C42—43no—
1129C42—43no—
1130C42—43no—
1131C42—43no—
1132C42—43no—
1133C42—43no—
1134C42—46no—
1135C42—46no—
1136C42—46no—
1137C42—43no—
1138C42C2×#41112yes—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23C22×#4112yes—
1164C23C2×2−1+412yes—
1165C23C2×2−1+412yes—
1166C23C2×2−1+412yes—
1167C23C2611yescharacteristic
1168Q8—224no—
1169Q8—412no—
1170Q8—412no—
1171Q8—412no—
1172Q8#553116yes—
1173D4—28no—
1174D4—44no—
1175D4—44no—
1176D4—44no—
1177D4—44no—
1178D4—44no—
1179C2×C4—21no—
1180C2×C4—23no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—23no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—23no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—224no—
1194C2×C4—21no—
1195C2×C4—23no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—23no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—23no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—23no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—23no—
1219C2×C4—23no—
1220C2×C4—21no—
1221C2×C4—23no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—23no—
1232C2×C4—23no—
1233C2×C4—23no—
1234C2×C4—21no—
1235C2×C4—23no—
1236C2×C4—23no—
1237C2×C4—23no—
1238C2×C4—23no—
1239C2×C4—23no—
1240C2×C4—23no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—23no—
1244C2×C4—23no—
1245C2×C4—23no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—23no—
1251C2×C4—44no—
1252C2×C4—44no—
1253C2×C4—44no—
1254C2×C4—412no—
1255C2×C4—44no—
1256C2×C4—412no—
1257C2×C4—412no—
1258C2×C4—412no—
1259C2×C4—86no—
1260C2×C4—86no—
1261C2×C4—86no—
1262C2×C4C22×#4112yes—
1263C2×C4C22×#4116yes—
1264C2×C4C22×#4116yes—
1265C2×C4C22×#4116yes—
1266C2×C4C22×#4116yes—
1267C2×C4C2×H(5,𝔽2)16yes—
1268C2×C4C2×2−1+412yes—
1269C2×C4C2×2−1+412yes—
1270C2×C4C2×2−1+412yes—
1271C2×C4#58512yes—
1272C22—22no—
1273C22—22no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22#352314yes—
1300C22C23×#4111yescharacteristic
1301C22C23×#4111yescharacteristic
1302C22C22×H(5,𝔽2)11yescharacteristic
1303C22C22×2−1+411yescharacteristic
1304C22C22×2−1+411yescharacteristic
1305C22C2×#58511yescharacteristic
1306C222−1+611yescharacteristic
1307C4—22no—
1308C4—22no—
1309C4—22no—
1310C4—26no—
1311C4—22no—
1312C4—22no—
1313C4—26no—
1314C4—43no—
1315C4—41no—
1316C4—43no—
1317C4—43no—
1318C4—43no—
1319C4—41no—
1320C4—43no—
1321C4—43no—
1322C4—43no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—43no—
1327C4—41no—
1328C4—43no—
1329C4—43no—
1330C4—43no—
1331C4—43no—
1332C4—43no—
1333C4C2×#553112yes—
1334C2—24no—
1335C2—42no—
1336C2—81no—
1337C2—81no—
1338C2C22×#55311yescharacteristic
1339C2C2×#352311yescharacteristic
1340C2#6280511yescharacteristic
1341C2#6289311yescharacteristic
1342C2#6299811yescharacteristic
1343C2#6300711yescharacteristic
1344C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#2543C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59855C2semidirect
2. #59695C2semidirect
3. #59441C2semidirect
4. #59402C2semidirect
5. #59309C2semidirect
6. #45344C2semidirect
7. #45310C2semidirect
8. #45309C2semidirect
9. #45184C2semidirect
10. #39283C2semidirect
11. #39263C2semidirect
12. #38122C2semidirect
13. #37894C2semidirect
14. #36599C2semidirect
15. Q8×#121C2semidirect
16. Q8×#121C2semidirect
17. Q8×#121C2semidirect
18. #36482C2semidirect
19. #36448C2semidirect
20. #36278C2semidirect
21. #35883C2semidirect
22. #35868C2semidirect
23. #35723C2semidirect
24. #35700C2semidirect
26. #34291C2semidirect
27. #34291C2semidirect
28. #34291C2semidirect
29. #34262C2semidirect
30. C4×D4×Q8C2semidirect
31. C2×#2351C2semidirect

Maximal subgroups

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

subgroupindex
#598552
#596952
#594412
#594022
#593092
#453442
#453102
#453092
#451842
#392832
#392632
#381222
#378942
#365992
Q8×#1212
#364822
#364482
#362782
#358832
#358682
#357232
#357002
#348562
#342912
#342622
C4×D4×Q82
C2×#23512