Finite Group Databasebeta

← #7785247

Subgroups — #7785247

Order 512.

5088 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59886C212yesmaximal, complemented
2#59314C212yesmaximal, complemented
3#48859C214yesmaximal, complemented
4#47987C214yesmaximal, complemented
5#47963C214yesmaximal, complemented
6#47962C214yesmaximal, complemented
7#43565C214yesmaximal, complemented
8#43494C214yesmaximal, complemented
9#43138C214yesmaximal, complemented
10#43127C214yesmaximal, complemented
11#43121C214yesmaximal, complemented
12#39670C212yesmaximal, complemented
13#39669C212yesmaximal, complemented
14#39610C212yesmaximal, complemented
15#37872C212yesmaximal, complemented
16#37684C212yesmaximal, complemented
17#36749C212yesmaximal, complemented
18#36544C212yesmaximal, complemented
19#35836C214yesmaximal, complemented
20#35012C211yesmaximal, characteristic, complemented
21C2×#2423C211yesmaximal, characteristic, complemented
22#34437C212yesmaximal
23#34273C211yesmaximal, characteristic
24C2×#554C2214yescomplemented
25C2×#554C2212yescomplemented
26C2×#543C2212yescomplemented
27C2×#534C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29C2×#518C2212yes—
30C22×C4×Q8C2211yescharacteristic, complemented
31#2857C2212yescomplemented
32#2851C2212yescomplemented
33#2851C2212yescomplemented
34#2848C2212yes—
35#2807C2214yescomplemented
36#2806C2212yescomplemented
37#2805C2212yescomplemented
38#2804C2212yescomplemented
39#2792C2214yescomplemented
40#2792C2214yescomplemented
41#2791C2214yescomplemented
42#2790C2214yescomplemented
43#2790C2214yescomplemented
44#2790C2214yescomplemented
45#2788C2214yescomplemented
46#2788C2214yescomplemented
47#2784C2214yes—
48#2780C2214yes—
49#2780C2214yescomplemented
50#2774C2214yescomplemented
51#2768C2214yescomplemented
52#2768C2214yescomplemented
53#2768C2214yescomplemented
54#2748C2214yes—
55#2748C2214yescomplemented
56#2748C2214yescomplemented
57#2742C2214yescomplemented
58#2742C2214yescomplemented
59#2732C2214yes—
60#2732C2212yescomplemented
61#2729C2214yescomplemented
62#2729C2214yescomplemented
63#2720C2214yescomplemented
64#2720C2214yescomplemented
65#2720C2214yescomplemented
66#2720C2214yescomplemented
67#2720C2214yescomplemented
68#2713C2214yescomplemented
69#2692C2214yes—
70#2692C2214yes—
71#2692C2214yes—
72#2692C2214yescomplemented
73#2692C2214yescomplemented
74#2683C2214yes—
75#2677C2214yescomplemented
76#2677C2214yescomplemented
77#2659C2212yescomplemented
78#2659C2212yescomplemented
79#2659C2211yescharacteristic, complemented
80#2659C2211yescharacteristic, complemented
81#2659C2212yescomplemented
82#2646C2212yescomplemented
83#2628C2214yescomplemented
84#2626C2212yes—
85#2626C2212yescomplemented
86#2626C2214yescomplemented
87#2626C2212yescomplemented
88#2590C2214yescomplemented
89#2590C2214yescomplemented
90#2589C2214yescomplemented
91#2587C2214yescomplemented
92#2586C2214yescomplemented
93#2585C2214yescomplemented
94#2584C2212yescomplemented
95#2584C2212yescomplemented
96#2583C2214yescomplemented
97#2580C2214yes—
98#2580C2212yescomplemented
99#2580C2212yescomplemented
100#2579C2214yescomplemented
101#2579C2214yescomplemented
102#2574C2214yescomplemented
103#2574C2214yescomplemented
104#2569C2214yescomplemented
105#2569C2214yescomplemented
106#2567C2212yescomplemented
107#2564C2214yes—
108#2564C2214yescomplemented
109#2564C2214yescomplemented
110#2564C2214yescomplemented
111#2556C2214yescomplemented
112#2556C2214yescomplemented
113#2551C2212yescomplemented
114#2549C2214yescomplemented
115#2542C2214yes—
116#2542C2214yescomplemented
117#2538C2212yescomplemented
118#2538C2212yescomplemented
119#2522C2214yescomplemented
120#2522C2214yescomplemented
121#2522C2214yescomplemented
122#2520C2214yescomplemented
123#2506C2214yescomplemented
124#2505C2214yescomplemented
125#2502C2214yescomplemented
126#2487C2214yes—
127#2487C2214yescomplemented
128#2473C2214yescomplemented
129#2465C2214yescomplemented
130#2465C2214yescomplemented
131#2465C2214yescomplemented
132#2465C2214yescomplemented
133#2465C2214yescomplemented
134#2462C2214yescomplemented
135#2454C2214yes—
136#2454C2214yes—
137#2450C2214yescomplemented
138#2450C2214yescomplemented
139#2449C2214yes—
140#2449C2214yes—
141#2449C2214yescomplemented
142#2449C2214yescomplemented
143#2449C2214yescomplemented
144#2449C2214yescomplemented
145#2449C2214yescomplemented
146#2449C2214yescomplemented
147#2449C2214yescomplemented
148#2449C2214yescomplemented
149#2441C2214yescomplemented
150#2441C2214yescomplemented
151#2440C2214yescomplemented
152#2440C2214yescomplemented
153#2440C2214yescomplemented
154#2437C2214yes—
155#2437C2214yes—
156#2437C2214yescomplemented
157#2437C2214yescomplemented
158#2437C2214yescomplemented
159#2437C2214yescomplemented
160#2423C2214yescomplemented
161#2423C2214yescomplemented
162#2423C2214yescomplemented
163#2423C2214yescomplemented
164#2423C2214yescomplemented
165#2423C2214yescomplemented
166#2417C2214yescomplemented
167#2409C2214yescomplemented
168#2396C2214yescomplemented
169C2×#399C2212yes—
170C2×#399C2214yescomplemented
171C2×#398C2212yescomplemented
172#2376C2214yes—
173#2375C2214yes—
174#2374C2214yes—
175#2368C2214yescomplemented
176#2364C2214yes—
177#2361C2214yes—
178#2360C2214yescomplemented
179#2359C2214yes—
180#2359C2214yes—
181#2358C2214yes—
182#2358C2214yes—
183#2358C2214yes—
184#2355C2212yescomplemented
185Q8×C4⋊C4C2212yescomplemented
186#2349C2214yescomplemented
187D4×C4⋊C4C2212yescomplemented
188D4×C4⋊C4C2214yescomplemented
189D4×C4⋊C4C2214yescomplemented
190D4×C22⋊C4C2214yes—
191D4×C22⋊C4C2214yes—
192#2335C2214yes—
193#2335C2214yes—
194#2329C2212yescomplemented
195#2329C2212yescomplemented
196#2329C2212yescomplemented
197#2325C2212yes—
198#2325C2212yes—
199#2325C2212yes—
200#2325C2212yes—
201#2321C2214yes—
202#2321C2214yes—
203#2315C2211yescharacteristic
204#2315C2212yescomplemented
205#2312C2212yes—
206C4×C22⋊Q8C2212yescomplemented
207C4×#121C2212yes—
208C4×#121C2212yes—
209C4×#121C2212yes—
210C4×#121C2212yes—
211C2×#391C2211yescharacteristic, complemented
212C2×#389C2211yescharacteristic, complemented
213C2×#388C2212yes—
214C2×#387C2212yescomplemented
215C2×#386C2212yes—
216C2×#384C2211yescharacteristic, complemented
217C2×#380C2211yescharacteristic
218C2×C4×C22⋊C4C2211yescharacteristic
219C23×Q8C2311yescharacteristic
220C23×D4C2312yes—
221C24×C4C2311yescharacteristic
222#554—416no—
223#554—48no—
224#543—48no—
225#534Q8116yescomplemented
226C2×C4⋊Q8C2312yes—
227C2×C4⋊Q8C2314yes—
228C2×C4⋊Q8C2314yes—
229C2×#125C2312yes—
230C2×#125C2312yes—
231C2×#125C2314yes—
232C2×#125C2314yes—
233C2×#123C2314yes—
234C2×C22⋊Q8—44no—
235C2×C22⋊Q8C2312yes—
236C2×C22⋊Q8C2312yes—
237C2×C22⋊Q8C2314yes—
238C2×C22⋊Q8C2314yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2314yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2312yes—
243C2×C22⋊Q8C2312yes—
244C2×C22⋊Q8C2314yes—
245C2×C22⋊Q8C2312yes—
246C2×C22⋊Q8C2314yes—
247C2×C22⋊Q8C2314yes—
248C2×C22⋊Q8C2314yes—
249C2×C22⋊Q8C2314yes—
250C2×C22⋊Q8C2314yes—
251C2×C22⋊Q8C2314yes—
252C2×C22⋊Q8C2314yes—
253C2×C22⋊Q8C2314yes—
254C2×C22⋊Q8C2314yes—
255C2×C22⋊Q8C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×#121C2312yes—
258C2×#121C2312yes—
259C2×#120C2314yes—
260#518—48no—
261C2×C4×Q8—44no—
262C2×C4×Q8C2312yes—
263C2×C4×Q8C2312yes—
264C2×C4×Q8C2314yes—
265C2×C4×Q8C2312yes—
266C2×C4×Q8C2312yes—
267C2×C4×Q8C2312yes—
268C2×C4×D4C2314yes—
269C2×C4×D4C2314yes—
270C2×C4×D4C2312yes—
271C2×C4×D4C2314yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2312yes—
275C2×C4×D4C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2314yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×#117C2314yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2311yescharacteristic
284C22×C4⋊C4C2312yes—
285C22×C4⋊C4C2314yes—
286C22×C4⋊C4C2314yes—
287C22×C4⋊C4C2312yes—
288C22×C4⋊C4C2311yescharacteristic
289C22×C4⋊C4C2311yescharacteristic
290C22×C4⋊C4C2314yes—
291C22×C4⋊C4C2312yes—
292C22×C4⋊C4C2312yes—
293C22×C22⋊C4C2311yescharacteristic
294C22×C22⋊C4C2312yes—
295C22×C22⋊C4C2312yes—
296C22×C22⋊C4C2314yes—
297C22×C22⋊C4C2312yes—
298C22×C22⋊C4C2314yes—
299C22×C22⋊C4C2312yes—
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2311yescharacteristic
303C22×C42C2311yescharacteristic
304C22×C42C2312yes—
305C22×C42C2311yescharacteristic
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#399C2314yes—
320#399C2314yes—
321#399C2314yes—
322#399C2314yes—
323#399C2314yes—
324#399C2314yes—
325#399C2314yes—
326#399C2314yes—
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#398C2314yes—
336#398C2314yes—
337#398C2314yes—
338#398C2314yes—
339#398C2314yes—
340#398C2314yes—
341#398C2314yes—
342#398C2314yes—
343#398C2314yes—
344#398C2314yes—
345#398C2314yes—
346#398C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#396C2314yes—
370#396C2314yes—
371#395C2314yes—
372#395C2314yes—
373#395C2314yes—
374#395C2314yes—
375#395C2314yes—
376#395C2314yes—
377#395C2314yes—
378#395C2314yes—
379#395C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#393C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#393C2314yes—
392#393C2314yes—
393#393C2314yes—
394#391C2314yes—
395#391C2312yes—
396#391C2312yes—
397#391C2314yes—
398#391C2314yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#390C2312yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
408#390C2314yes—
409#390C2312yes—
410#390C2312yes—
411#390C2314yes—
412#390C2312yes—
413#389C2312yes—
414#389C2312yes—
415#389C2312yes—
416#389C2312yes—
417#389C2314yes—
418#389C2314yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2312yes—
425#389C2314yes—
426#389C2314yes—
427#389C2312yes—
428#389C2312yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2314yes—
438#389C2314yes—
439#389C2314yes—
440#389C2314yes—
441#389C2314yes—
442#389C2312yes—
443#389C2312yes—
444#389C2314yes—
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#387C2314yes—
466#387C2314yes—
467#387C2314yes—
468#387C2314yes—
469#387C2314yes—
470#387C2314yes—
471#387C2314yes—
472#387C2314yes—
473#387C2314yes—
474#387C2314yes—
475#387C2314yes—
476#387C2314yes—
477#387C2314yes—
478#387C2314yes—
479#387C2314yes—
480#387C2314yes—
481#387C2314yes—
482#387C2314yes—
483#387C2314yes—
484#387C2314yes—
485#387C2314yes—
486#387C2314yes—
487#387C2314yes—
488#387C2314yes—
489#387C2314yes—
490#387C2314yes—
491#387C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#386C2314yes—
499#386C2314yes—
500#386C2314yes—
501#386C2314yes—
502#386C2314yes—
503#386C2314yes—
504#386C2314yes—
505#386C2314yes—
506#386C2314yes—
507#386C2314yes—
508#386C2314yes—
509#386C2314yes—
510#386C2314yes—
511#386C2314yes—
512#386C2314yes—
513#386C2314yes—
514#386C2314yes—
515#386C2314yes—
516#385C2314yes—
517#385C2314yes—
518#385C2314yes—
519#385C2314yes—
520#385C2314yes—
521#385C2314yes—
522#385C2314yes—
523#385C2314yes—
524#385C2314yes—
525#385C2314yes—
526#385C2314yes—
527#385C2314yes—
528#385C2314yes—
529#385C2314yes—
530#385C2314yes—
531#385C2314yes—
532#385C2314yes—
533#385C2314yes—
534#385C2314yes—
535#385C2314yes—
536#385C2314yes—
537#385C2314yes—
538#385C2314yes—
539#385C2314yes—
540#385C2314yes—
541#385C2314yes—
542#385C2314yes—
543#385C2314yes—
544#385C2314yes—
545#385C2314yes—
546#385C2314yes—
547#385C2314yes—
548#385C2314yes—
549#385C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#384C2314yes—
555#384C2312yes—
556#384C2312yes—
557#384C2314yes—
558#384C2314yes—
559#384C2314yes—
560#384C2312yes—
561#382C2312yes—
562#382C2314yes—
563#382C2312yes—
564#380C2314yes—
565#380C2314yes—
566#380C2314yes—
567#380C2312yes—
568#380C2314yes—
569#380C2314yes—
570#380C2314yes—
571#380C2312yes—
572#380C2312yes—
573#380C2312yes—
574#380C2314yes—
575#380C2314yes—
576#380C2314yes—
577#380C2312yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2314yes—
582#380C2314yes—
583#380C2314yes—
584#380C2314yes—
585#380C2312yes—
586#380C2312yes—
587#380C2314yes—
588#379C2314yes—
589#379C2314yes—
590#379C2314yes—
591C4×C4⋊C4C2312yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2312yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2314yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2312yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2312yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2314yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2314yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C2×#95C2314yes—
613C2×#95C2312yes—
614C2×#95C2312yes—
615C2×#95C2312yes—
616C2×#95C2312yes—
617C2×#95C2311yescharacteristic
618C2×#95C2312yes—
619C2×#95C2311yescharacteristic
620C2×#95C2312yes—
621C25C2411yescharacteristic
622C25C2412yes—
623C22×Q8—24no—
624C22×Q8—42no—
625C22×Q8—42no—
626C22×Q8C2412yes—
627C22×Q8C2412yes—
628C22×Q8C2411yescharacteristic
629C22×Q8C2414yes—
630C22×Q8C2414yes—
631C22×Q8C2412yes—
632C22×Q8C2411yescharacteristic
633C22×D4—44no—
634C22×D4—44no—
635C22×D4C2×Q8116yes—
636C22×D4C2414yes—
637C22×D4C2412yes—
638C22×D4C2412yes—
639C22×D4C2414yes—
640C23×C4—42no—
641C23×C4—42no—
642C23×C4—42no—
643C23×C4C2411yescharacteristic
644C23×C4C2412yes—
645C23×C4C2412yes—
646C23×C4C2411yescharacteristic
647C23×C4C2412yes—
648C23×C4C2412yes—
649C23×C4C2414yes—
650C23×C4C2414yes—
651C23×C4C2412yes—
652C23×C4C2412yes—
653C23×C4C2411yescharacteristic
654C23×C4C2412yes—
655C23×C4C2412yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2411yescharacteristic
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2411yescharacteristic
664C4⋊Q8—44no—
665C4⋊Q8—48no—
666C4⋊Q8—84no—
667#125—44no—
668#125—44no—
669#125—48no—
670#125—48no—
671#123C2×Q8132yescomplemented
672C22⋊Q8—28no—
673C22⋊Q8—216no—
674C22⋊Q8—28no—
675C22⋊Q8—44no—
676C22⋊Q8—48no—
677C22⋊Q8—48no—
678C22⋊Q8—48no—
679C22⋊Q8—48no—
680C22⋊Q8—48no—
681C22⋊Q8—48no—
682C22⋊Q8—48no—
683C22⋊Q8—48no—
684C22⋊Q8—48no—
685C22⋊Q8—48no—
686C22⋊Q8—48no—
687C22⋊Q8—44no—
688C22⋊Q8—48no—
689C22⋊Q8—44no—
690C22⋊Q8—44no—
691C22⋊Q8—48no—
692C22⋊Q8—84no—
693C22⋊Q8—84no—
694#121C2×Q8116yes—
695#121C2×Q8116yes—
696#120C2×Q8132yescomplemented
697C4×Q8—28no—
698C4×Q8—44no—
699C4×Q8—44no—
700C4×Q8—44no—
701C4×Q8—44no—
702C4×Q8—48no—
703C4×D4—216no—
704C4×D4—44no—
705C4×D4—48no—
706C4×D4—44no—
707C4×D4—44no—
708C4×D4—44no—
709C4×D4—48no—
710C4×D4—48no—
711C4×D4—48no—
712C4×D4—48no—
713C4×D4—48no—
714C4×D4—48no—
715C4×D4—84no—
716#117—48no—
717C2×C4⋊C4—28no—
718C2×C4⋊C4—44no—
719C2×C4⋊C4—42no—
720C2×C4⋊C4—42no—
721C2×C4⋊C4—44no—
722C2×C4⋊C4—48no—
723C2×C4⋊C4—48no—
724C2×C4⋊C4—42no—
725C2×C4⋊C4—82no—
726C2×C4⋊C4—84no—
727C2×C4⋊C4—82no—
728C2×C4⋊C4C2412yes—
729C2×C4⋊C4C2414yes—
730C2×C4⋊C4C2412yes—
731C2×C4⋊C4C2412yes—
732C2×C4⋊C4C2412yes—
733C2×C4⋊C4C2412yes—
734C2×C4⋊C4C2414yes—
735C2×C4⋊C4C2414yes—
736C2×C4⋊C4C2414yes—
737C2×C4⋊C4C2414yes—
738C2×C4⋊C4C2414yes—
739C2×C4⋊C4C2414yes—
740C2×C4⋊C4C2414yes—
741C2×C4⋊C4C2414yes—
742C2×C4⋊C4C2414yes—
743C2×C4⋊C4C2414yes—
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2412yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2414yes—
751C2×C4⋊C4C2414yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2414yes—
754C2×C4⋊C4C2414yes—
755C2×C4⋊C4C2414yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2414yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C22⋊C4—24no—
794C2×C22⋊C4—44no—
795C2×C22⋊C4—48no—
796C2×C22⋊C4—44no—
797C2×C22⋊C4—48no—
798C2×C22⋊C4—44no—
799C2×C22⋊C4—44no—
800C2×C22⋊C4—82no—
801C2×C22⋊C4—84no—
802C2×C22⋊C4C2×Q818yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
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×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C42—42no—
838C2×C42—44no—
839C2×C42—42no—
840C2×C42C2414yes—
841C2×C42C2412yes—
842C2×C42C2412yes—
843C2×C42C2412yes—
844C2×C42C2412yes—
845C2×C42C2414yes—
846C2×C42C2414yes—
847C2×C42C2414yes—
848C2×C42C2414yes—
849C2×C42C2414yes—
850C2×C42C2414yes—
851C2×C42C2412yes—
852C2×C42C2412yes—
853C2×C42C2412yes—
854C2×C42C2414yes—
855C2×C42C2412yes—
856#95C2414yes—
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#95C2414yes—
873#95C2414yes—
874#95C2414yes—
875#95C2414yes—
876#95C2414yes—
877#95C2414yes—
878#95C2414yes—
879#95C2414yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
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—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902C24—22no—
903C24—22no—
904C24—41no—
905C24—41no—
906C24—41no—
907C24—41no—
908C24—42no—
909C24—42no—
910C24—42no—
911C24—42no—
912C24—42no—
913C24—42no—
914C24C22×Q814yes—
915C24C22×Q818yes—
916C24C2512yes—
917C24C2514yes—
918C24C2511yescharacteristic
919C2×Q8—24no—
920C2×Q8—24no—
921C2×Q8—22no—
922C2×Q8—24no—
923C2×Q8—42no—
924C2×Q8—41no—
925C2×Q8—42no—
926C2×Q8—41no—
927C2×Q8—41no—
928C2×Q8—41no—
929C2×Q8—42no—
930C2×Q8—44no—
931C2×Q8—42no—
932C2×Q8—44no—
933C2×Q8—44no—
934C2×Q8—44no—
935C2×Q8—42no—
936C2×Q8—42no—
937C2×Q8—44no—
938C2×Q8—44no—
939C2×Q8—416no—
940C2×Q8H(5,𝔽2)14yes—
941C2×D4—28no—
942C2×D4—28no—
943C2×D4—42no—
944C2×D4—44no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—44no—
948C2×D4—42no—
949C2×D4—432no—
950C2×D4C22×Q8116yes—
951C2×D4C22×Q818yes—
952C2×D4C22×Q818yes—
953C2×D4C22×Q8116yes—
954C22×C4—22no—
955C22×C4—22no—
956C22×C4—22no—
957C22×C4—24no—
958C22×C4—22no—
959C22×C4—24no—
960C22×C4—24no—
961C22×C4—24no—
962C22×C4—22no—
963C22×C4—24no—
964C22×C4—28no—
965C22×C4—28no—
966C22×C4—24no—
967C22×C4—24no—
968C22×C4—41no—
969C22×C4—41no—
970C22×C4—41no—
971C22×C4—41no—
972C22×C4—42no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—41no—
979C22×C4—42no—
980C22×C4—44no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—41no—
984C22×C4—42no—
985C22×C4—41no—
986C22×C4—44no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—41no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—42no—
998C22×C4—42no—
999C22×C4—44no—
1000C22×C4—42no—
1001C22×C4—44no—
1002C22×C4—42no—
1003C22×C4—42no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4—44no—
1009C22×C4—44no—
1010C22×C4—44no—
1011C22×C4—42no—
1012C22×C4—42no—
1013C22×C4—88no—
1014C22×C4C22×Q814yes—
1015C22×C4C22×Q814yes—
1016C22×C4C22×Q818yes—
1017C22×C4H(5,𝔽2)14yes—
1018C22×C4C2514yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2512yes—
1022C22×C4C2514yes—
1023C22×C4C2514yes—
1024C22×C4C2514yes—
1025C22×C4C2514yes—
1026C22×C4C2514yes—
1027C22×C4C2512yes—
1028C22×C4C2512yes—
1029C22×C4C2512yes—
1030C22×C4C2514yes—
1031C22×C4C2512yes—
1032C22×C4C2512yes—
1033C22×C4C2514yes—
1034C22×C4C2512yes—
1035C22×C4C2511yescharacteristic
1036C22×C4C2512yes—
1037C22×C4C2511yescharacteristic
1038C4⋊C4—28no—
1039C4⋊C4—28no—
1040C4⋊C4—24no—
1041C4⋊C4—24no—
1042C4⋊C4—24no—
1043C4⋊C4—24no—
1044C4⋊C4—24no—
1045C4⋊C4—28no—
1046C4⋊C4—28no—
1047C4⋊C4—28no—
1048C4⋊C4—28no—
1049C4⋊C4—28no—
1050C4⋊C4—28no—
1051C4⋊C4—28no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—44no—
1064C4⋊C4—44no—
1065C4⋊C4—44no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—42no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—42no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—42no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4C22×Q818yes—
1102C4⋊C4C22×Q818yes—
1103C22⋊C4—28no—
1104C22⋊C4—28no—
1105C22⋊C4—28no—
1106C22⋊C4—28no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—44no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—44no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—44no—
1131C22⋊C4—44no—
1132C22⋊C4—44no—
1133C22⋊C4—44no—
1134C22⋊C4C22×Q8116yes—
1135C22⋊C4C22×Q8116yes—
1136C22⋊C4C22×Q8116yes—
1137C42—24no—
1138C42—24no—
1139C42—24no—
1140C42—28no—
1141C42—24no—
1142C42—42no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—44no—
1147C42—44no—
1148C42—44no—
1149C42—44no—
1150C42—44no—
1151C42—44no—
1152C42—44no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—22no—
1158C23—24no—
1159C23—22no—
1160C23—24no—
1161C23—24no—
1162C23—22no—
1163C23—24no—
1164C23—22no—
1165C23—22no—
1166C23—24no—
1167C23—22no—
1168C23—24no—
1169C23—28no—
1170C23—44no—
1171C23—44no—
1172C23—48no—
1173C23—48no—
1174C23—48no—
1175C23—82no—
1176C23—82no—
1177C23—82no—
1178C23—82no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23—162no—
1183C23C23×Q814yes—
1184C23C23×Q818yes—
1185C23C23×Q812yes—
1186C23C2×H(5,𝔽2)12yes—
1187C23#58512yes—
1188C23C2611yescharacteristic
1189Q8—44no—
1190Q8—48no—
1191Q8—48no—
1192Q8—44no—
1193Q8—162no—
1194Q8—164no—
1195Q8—164no—
1196D4—232no—
1197D4—416no—
1198D4—48no—
1199D4—48no—
1200C2×C4—28no—
1201C2×C4—22no—
1202C2×C4—24no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—24no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—24no—
1219C2×C4—22no—
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—22no—
1231C2×C4—22no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—24no—
1235C2×C4—24no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—22no—
1249C2×C4—24no—
1250C2×C4—24no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—44no—
1255C2×C4—44no—
1256C2×C4—48no—
1257C2×C4—44no—
1258C2×C4—48no—
1259C2×C4—88no—
1260C2×C4—88no—
1261C2×C4—84no—
1262C2×C4—84no—
1263C2×C4—84no—
1264C2×C4—82no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—82no—
1268C2×C4—88no—
1269C2×C4—162no—
1270C2×C4—164no—
1271C2×C4—164no—
1272C2×C4—164no—
1273C2×C4—162no—
1274C2×C4C23×Q814yes—
1275C2×C4C23×Q814yes—
1276C2×C4C23×Q818yes—
1277C2×C4C2×H(5,𝔽2)14yes—
1278C2×C4C2×H(5,𝔽2)12yes—
1279C2×C4C2×H(5,𝔽2)14yes—
1280C2×C4#58512yes—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—28no—
1288C22—24no—
1289C22—28no—
1290C22—24no—
1291C22—24no—
1292C22—28no—
1293C22—42no—
1294C22—44no—
1295C22—44no—
1296C22—42no—
1297C22—44no—
1298C22—42no—
1299C22—44no—
1300C22—42no—
1301C22—88no—
1302C22—168no—
1303C22#350114yes—
1304C22C24×Q811yescharacteristic
1305C22C22×H(5,𝔽2)11yescharacteristic
1306C22C22×H(5,𝔽2)11yescharacteristic
1307C22C2×#58511yescharacteristic
1308C22C2×#58511yescharacteristic
1309C22H(7,𝔽2)11yescharacteristic
1310C222−1+611yescharacteristic
1311C4—24no—
1312C4—24no—
1313C4—28no—
1314C4—22no—
1315C4—22no—
1316C4—24no—
1317C4—24no—
1318C4—42no—
1319C4—42no—
1320C4—44no—
1321C4—44no—
1322C4—44no—
1323C4—44no—
1324C4—44no—
1325C4—42no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—44no—
1330C4—44no—
1331C2—24no—
1332C2—44no—
1333C2—48no—
1334C2C2×#350111yescharacteristic
1335C2#6282011yescharacteristic
1336C2#6286911yescharacteristic
1337C2#6290111yescharacteristic
1338C2#6291611yescharacteristic
1339C2Q8×H(5,𝔽2)11yescharacteristic
1340C2#6298911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#534C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59886C2semidirect
2. #59314C2semidirect
3. #48859C2semidirect
4. #47987C2semidirect
5. #47963C2semidirect
6. #47962C2semidirect
7. #43565C2semidirect
8. #43494C2semidirect
9. #43138C2semidirect
10. #43127C2semidirect
11. #43121C2semidirect
12. #39670C2semidirect
13. #39669C2semidirect
14. #39610C2semidirect
15. #37872C2semidirect
16. #37684C2semidirect
17. #36749C2semidirect
18. #36544C2semidirect
19. #35836C2semidirect
20. #35012C2semidirect
21. C2×#2423C2semidirect
24. C2×#554C22semidirect
25. C2×#554C22semidirect
26. C2×#543C22semidirect
30. C22×C4×Q8C22semidirect
31. #2857C22semidirect
32. #2851C22semidirect
33. #2851C22semidirect
35. #2807C22semidirect
36. #2806C22semidirect
37. #2805C22semidirect
38. #2804C22semidirect
39. #2792C22semidirect
40. #2792C22semidirect
41. #2791C22semidirect
42. #2790C22semidirect
43. #2790C22semidirect
44. #2790C22semidirect
45. #2788C22semidirect
46. #2788C22semidirect
49. #2780C22semidirect
50. #2774C22semidirect
51. #2768C22semidirect
52. #2768C22semidirect
53. #2768C22semidirect
55. #2748C22semidirect
56. #2748C22semidirect
57. #2742C22semidirect
58. #2742C22semidirect
60. #2732C22semidirect
61. #2729C22semidirect
62. #2729C22semidirect
63. #2720C22semidirect
64. #2720C22semidirect
65. #2720C22semidirect
66. #2720C22semidirect
67. #2720C22semidirect
68. #2713C22semidirect
72. #2692C22semidirect
73. #2692C22semidirect
75. #2677C22semidirect
76. #2677C22semidirect
77. #2659C22semidirect
78. #2659C22semidirect
79. #2659C22semidirect
80. #2659C22semidirect
81. #2659C22semidirect
82. #2646C22semidirect
83. #2628C22semidirect
85. #2626C22semidirect
86. #2626C22semidirect
87. #2626C22semidirect
88. #2590C22semidirect
89. #2590C22semidirect
90. #2589C22semidirect
91. #2587C22semidirect
92. #2586C22semidirect
93. #2585C22semidirect
94. #2584C22semidirect
95. #2584C22semidirect
96. #2583C22semidirect
98. #2580C22semidirect
99. #2580C22semidirect
100. #2579C22semidirect
101. #2579C22semidirect
102. #2574C22semidirect
103. #2574C22semidirect
104. #2569C22semidirect
105. #2569C22semidirect
106. #2567C22semidirect
108. #2564C22semidirect
109. #2564C22semidirect
110. #2564C22semidirect
111. #2556C22semidirect
112. #2556C22semidirect
113. #2551C22semidirect
114. #2549C22semidirect
116. #2542C22semidirect
117. #2538C22semidirect
118. #2538C22semidirect
119. #2522C22semidirect
120. #2522C22semidirect
121. #2522C22semidirect
122. #2520C22semidirect
123. #2506C22semidirect
124. #2505C22semidirect
125. #2502C22semidirect
127. #2487C22semidirect
128. #2473C22semidirect
129. #2465C22semidirect
130. #2465C22semidirect
131. #2465C22semidirect
132. #2465C22semidirect
133. #2465C22semidirect
134. #2462C22semidirect
137. #2450C22semidirect
138. #2450C22semidirect
141. #2449C22semidirect
142. #2449C22semidirect
143. #2449C22semidirect
144. #2449C22semidirect
145. #2449C22semidirect
146. #2449C22semidirect
147. #2449C22semidirect
148. #2449C22semidirect
149. #2441C22semidirect
150. #2441C22semidirect
151. #2440C22semidirect
152. #2440C22semidirect
153. #2440C22semidirect
156. #2437C22semidirect
157. #2437C22semidirect
158. #2437C22semidirect
159. #2437C22semidirect
160. #2423C22semidirect
161. #2423C22semidirect
162. #2423C22semidirect
163. #2423C22semidirect
164. #2423C22semidirect
165. #2423C22semidirect
166. #2417C22semidirect
167. #2409C22semidirect
168. #2396C22semidirect
170. C2×#399C22semidirect
171. C2×#398C22semidirect
175. #2368C22semidirect
178. #2360C22semidirect
184. #2355C22semidirect
185. Q8×C4⋊C4C22semidirect
186. #2349C22semidirect
187. D4×C4⋊C4C22semidirect
188. D4×C4⋊C4C22semidirect
189. D4×C4⋊C4C22semidirect
194. #2329C22semidirect
195. #2329C22semidirect
196. #2329C22semidirect
204. #2315C22semidirect
206. C4×C22⋊Q8C22semidirect
211. C2×#391C22semidirect
212. C2×#389C22semidirect
214. C2×#387C22semidirect
216. C2×#384C22semidirect
225. #534Q8semidirect
671. #123C2×Q8semidirect
696. #120C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#598862
#593142
#488592
#479872
#479632
#479622
#435652
#434942
#431382
#431272
#431212
#396702
#396692
#396102
#378722
#376842
#367492
#365442
#358362
#350122
C2×#24232
#344372
#342732