Finite Group Databasebeta

← #7630742

Subgroups — #7630742

Order 512.

5070 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36047C214yesmaximal, complemented
2#35975C214yesmaximal, complemented
3#35969C214yesmaximal, complemented
4#35946C214yesmaximal, complemented
5#35908C214yesmaximal, complemented
6#35866C214yesmaximal, complemented
7#35864C214yesmaximal, complemented
8#35852C214yesmaximal, complemented
9#35118C212yesmaximal, complemented
10#35093C212yesmaximal, complemented
11#35035C212yesmaximal, complemented
12#35035C212yesmaximal, complemented
13#35024C212yesmaximal, complemented
14#35023C212yesmaximal, complemented
15#35013C211yesmaximal, characteristic, complemented
16#35012C211yesmaximal, characteristic, complemented
17#35004C211yesmaximal, characteristic, complemented
18#35003C211yesmaximal, characteristic
19#34989C212yesmaximal, complemented
20#34595C211yesmaximal, characteristic, complemented
21#34594C211yesmaximal, characteristic, complemented
22#34584C212yesmaximal, complemented
23#34570C212yesmaximal, complemented
24#34278C212yesmaximal, complemented
25#34277C212yesmaximal, complemented
26#34224C212yesmaximal, complemented
27C2×#2274C211yesmaximal, characteristic, complemented
28C2×#539C2212yes—
29C2×#538C2212yes—
30C2×#529C2212yes—
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34#2855C2212yes—
35#2854C2212yes—
36#2853C2214yes—
37#2851C2212yes—
38#2851C2212yes—
39#2850C2212yes—
40#2850C2212yes—
41#2849C2214yes—
42#2848C2212yes—
43#2847C2212yes—
44#2666C2214yescomplemented
45#2666C2214yescomplemented
46#2664C2214yescomplemented
47#2662C2214yescomplemented
48#2659C2211yescharacteristic
49#2659C2211yescharacteristic
50#2659C2211yescharacteristic
51#2656C2211yescharacteristic
52#2655C2214yescomplemented
53#2654C2214yescomplemented
54#2653C2214yes—
55#2652C2214yes—
56#2651C2214yescomplemented
57#2650C2214yescomplemented
58#2649C2214yes—
59#2648C2214yes—
60#2646C2212yes—
61#2643C2214yes—
62#2643C2214yes—
63#2639C2212yes—
64#2627C2212yes—
65#2627C2212yes—
66#2627C2212yes—
67#2626C2212yes—
68#2623C2214yes—
69#2622C2214yes—
70#2618C2212yes—
71#2618C2212yes—
72#2618C2212yes—
73#2617C2212yes—
74#2611C2214yes—
75#2610C2214yes—
76#2609C2214yes—
77#2609C2214yes—
78#2601C2214yes—
79#2601C2214yes—
80#2599C2214yes—
81#2598C2214yes—
82#2597C2214yes—
83#2596C2214yescomplemented
84#2595C2214yes—
85#2595C2214yescomplemented
86#2595C2214yescomplemented
87#2594C2214yescomplemented
88#2594C2214yescomplemented
89#2594C2214yescomplemented
90#2588C2214yescomplemented
91#2588C2214yescomplemented
92#2587C2214yescomplemented
93#2587C2214yescomplemented
94#2586C2214yescomplemented
95#2585C2214yescomplemented
96#2578C2214yes—
97#2577C2214yescomplemented
98#2576C2214yes—
99#2575C2214yescomplemented
100#2574C2214yes—
101#2556C2214yes—
102#2556C2214yescomplemented
103#2555C2214yes—
104#2554C2214yescomplemented
105#2553C2214yes—
106#2529C2214yescomplemented
107#2529C2214yescomplemented
108#2528C2214yescomplemented
109#2528C2214yescomplemented
110#2522C2214yes—
111#2521C2214yes—
112#2520C2214yescomplemented
113#2519C2214yescomplemented
114#2514C2212yescomplemented
115#2513C2212yescomplemented
116#2509C2212yescomplemented
117#2508C2212yescomplemented
118#2495C2212yes—
119#2494C2212yes—
120#2490C2212yes—
121#2489C2212yes—
122#2481C2214yes—
123#2481C2214yes—
124#2478C2214yes—
125#2478C2214yes—
126#2476C2214yes—
127#2476C2214yes—
128#2475C2214yescomplemented
129#2475C2214yescomplemented
130#2474C2214yes—
131#2474C2214yes—
132#2474C2214yescomplemented
133#2474C2214yescomplemented
134#2473C2214yes—
135#2473C2214yes—
136#2470C2214yes—
137#2470C2214yes—
138#2465C2214yes—
139#2464C2214yes—
140#2462C2214yescomplemented
141#2461C2214yescomplemented
142#2454C2212yescomplemented
143#2453C2212yescomplemented
144#2449C2214yes—
145#2449C2214yes—
146#2448C2212yescomplemented
147#2447C2212yescomplemented
148#2443C2214yes—
149#2443C2214yes—
150#2427C2212yes—
151#2426C2212yes—
152#2421C2212yes—
153#2420C2212yes—
154#2402C2214yescomplemented
155#2402C2214yescomplemented
156#2401C2214yes—
157#2401C2214yescomplemented
158#2399C2214yescomplemented
159#2398C2214yes—
160#2396C2214yescomplemented
161#2396C2214yescomplemented
162#2395C2214yes—
163#2395C2214yescomplemented
164#2392C2214yes—
165#2392C2214yescomplemented
166#2374C2214yes—
167#2374C2214yescomplemented
168#2373C2214yes—
169#2373C2214yes—
170#2373C2214yescomplemented
171#2373C2214yescomplemented
172#2373C2214yescomplemented
173#2373C2214yescomplemented
174#2372C2214yes—
175#2371C2214yescomplemented
176#2370C2212yescomplemented
177#2370C2214yescomplemented
178#2370C2212yescomplemented
179#2368C2214yescomplemented
180#2367C2214yes—
181#2367C2212yescomplemented
182#2367C2212yescomplemented
183#2364C2214yes—
184#2363C2214yes—
185#2362C2214yescomplemented
186#2359C2214yes—
187#2359C2214yescomplemented
188#2357C2212yescomplemented
189#2356C2212yescomplemented
190#2351C2212yescomplemented
191#2349C2212yescomplemented
192#2347C2214yescomplemented
193#2343C2214yescomplemented
194#2329C2212yes—
195#2329C2212yes—
196#2325C2212yes—
197#2325C2212yes—
198#2322C2214yes—
199#2322C2214yes—
200#2322C2214yes—
201#2321C2214yes—
202#2318C2214yes—
203#2313C2212yes—
204#2312C2212yes—
205C4×C22⋊Q8C2212yes—
206C4×C22⋊Q8C2212yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×#123C2214yes—
210C4×#121C2212yes—
211C4×#121C2212yes—
212C4×#121C2212yes—
213C4×#121C2212yes—
214C4×#120C2214yes—
215#2290C2214yes—
216#2290C2214yes—
217#2283C2212yes—
218#2275C2214yes—
219#2274C2214yes—
220#2274C2214yes—
221#2274C2214yes—
222#2274C2214yes—
223C2×C4×C4⋊C4C2211yescharacteristic
224C2×C4×C4⋊C4C2211yescharacteristic
225C2×C4×C4⋊C4C2211yescharacteristic
226C2×C4×C4⋊C4C2211yescharacteristic
227C2×C4×C4⋊C4C2211yescharacteristic
228C2×C4×C4⋊C4C2211yescharacteristic
229C2×C4×C4⋊C4C2211yescharacteristic
230C2×C4×C4⋊C4C2211yescharacteristic
231C2×C4×C22⋊C4C2211yescharacteristic
232C2×C4×C22⋊C4C2211yescharacteristic
233C2×C4×C22⋊C4C2211yescharacteristic
234C2×C4×C22⋊C4C2211yescharacteristic
235C24×C4C2311yescharacteristic
236C24×C4C2311yescharacteristic
237C24×C4C2311yescharacteristic
238#539—216no—
239#538—216no—
240#529—216no—
241C2×#126C2314yes—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#125C2312yes—
245C2×#125C2314yes—
246C2×#125C2312yes—
247C2×#125C2312yes—
248C2×#124C2312yes—
249C2×#124C2314yes—
250C2×#124C2312yes—
251C2×#124C2312yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×C22⋊Q8C2312yes—
257C2×C22⋊Q8C2312yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×#121C2312yes—
263C2×#121C2312yes—
264C2×#121C2312yes—
265C2×#121C2314yes—
266C2×#121C2312yes—
267C2×#121C2312yes—
268C2×#120C2314yes—
269C2×C4×Q8C2312yes—
270C2×C4×Q8C2312yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2314yes—
281C2×C4×D4C2312yes—
282C2×C4×D4C2312yes—
283C2×C4×D4C2314yes—
284C2×#117—28no—
285C2×#117—28no—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C2×#117C2314yes—
292C2×#117C2314yes—
293C22×C4⋊C4—28no—
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2311yescharacteristic
299C22×C4⋊C4C2311yescharacteristic
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2314yes—
302C22×C4⋊C4C2314yes—
303C22×C4⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C22⋊C4C2311yescharacteristic
307C22×C22⋊C4C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318C22×C42C2311yescharacteristic
319C22×C42C2311yescharacteristic
320#401C2314yes—
321#401C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
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#398C2314yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#396C2314yes—
371#396C2314yes—
372#396C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#395C2314yes—
381#395C2314yes—
382#395C2314yes—
383#395C2314yes—
384#395C2314yes—
385#395C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#393C2314yes—
397#393C2314yes—
398#392C2314yes—
399#392C2314yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#390C2314yes—
411#390C2314yes—
412#390C2312yes—
413#390C2312yes—
414#390C2312yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#389C2314yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2312yes—
432#389C2312yes—
433#389C2312yes—
434#389C2312yes—
435#389C2312yes—
436#389C2312yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#388C2314yes—
445#388C2314yes—
446#388C2314yes—
447#388C2314yes—
448#388C2314yes—
449#388C2314yes—
450#388C2314yes—
451#388C2314yes—
452#388C2314yes—
453#388C2314yes—
454#388C2314yes—
455#388C2314yes—
456#388C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#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#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2314yes—
531#386C2314yes—
532#386C2314yes—
533#386C2314yes—
534#386C2314yes—
535#386C2314yes—
536#386C2314yes—
537#386C2314yes—
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#385C2314yes—
555#385C2314yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#383C2314yes—
561#383C2314yes—
562#382C2314yes—
563#382C2312yes—
564#382C2312yes—
565#382C2312yes—
566#382C2312yes—
567#382C2312yes—
568#382C2312yes—
569#381C2314yes—
570#381C2314yes—
571#381C2314yes—
572#380C2312yes—
573#380C2312yes—
574#380C2312yes—
575#380C2312yes—
576#380C2314yes—
577#380C2312yes—
578#380C2312yes—
579#380C2312yes—
580#380C2312yes—
581#380C2312yes—
582#380C2312yes—
583#379C2314yes—
584C4×C4⋊C4C2314yes—
585C4×C4⋊C4C2312yes—
586C4×C4⋊C4C2312yes—
587C4×C4⋊C4C2314yes—
588C4×C4⋊C4C2314yes—
589C4×C4⋊C4C2314yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2314yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2312yes—
599C4×C4⋊C4C2312yes—
600C4×C4⋊C4C2312yes—
601C4×C4⋊C4C2312yes—
602C4×C4⋊C4C2312yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2312yes—
605C4×C4⋊C4C2312yes—
606C4×C4⋊C4C2312yes—
607C4×C4⋊C4C2312yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2314yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2314yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2312yes—
619C4×C4⋊C4C2312yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2314yes—
622C4×C4⋊C4C2314yes—
623C4×C4⋊C4C2314yes—
624C4×C4⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2312yes—
631C4×C22⋊C4C2314yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2312yes—
636C4×C22⋊C4C2312yes—
637C4×C22⋊C4C2314yes—
638C4×C22⋊C4C2314yes—
639C4×C22⋊C4C2314yes—
640C4×C22⋊C4C2314yes—
641C4×C22⋊C4C2314yes—
642C4×C22⋊C4C2314yes—
643C4×C22⋊C4C2314yes—
644C4×C22⋊C4C2314yes—
645C4×C22⋊C4C2314yes—
646C4×C22⋊C4C2314yes—
647C4×C22⋊C4C2314yes—
648C4×C22⋊C4C2314yes—
649C4×C22⋊C4C2314yes—
650C4×C22⋊C4C2314yes—
651#376C2314yes—
652#376C2314yes—
653#376C2314yes—
654#376C2314yes—
655C2×#95C2311yescharacteristic
656C2×#95C2311yescharacteristic
657C2×#95C2311yescharacteristic
658C2×#95C2314yes—
659C2×#95C2311yescharacteristic
660C2×#95C2311yescharacteristic
661C2×#95C2311yescharacteristic
662C2×#95C2311yescharacteristic
663C2×#95C2311yescharacteristic
664C25C2411yescharacteristic
665C22×Q8C2412yes—
666C22×Q8C2412yes—
667C22×Q8C2412yes—
668C22×D4C2414yes—
669C22×D4C2412yes—
670C22×D4C2414yes—
671C22×D4C2414yes—
672C22×D4C2412yes—
673C22×D4C2412yes—
674C23×C4—24no—
675C23×C4—24no—
676C23×C4—24no—
677C23×C4—24no—
678C23×C4—24no—
679C23×C4—81no—
680C23×C4—81no—
681C23×C4—81no—
682C23×C4—81no—
683C23×C4C2414yes—
684C23×C4C2411yescharacteristic
685C23×C4C2411yescharacteristic
686C23×C4C2411yescharacteristic
687C23×C4C2411yescharacteristic
688C23×C4C2411yescharacteristic
689C23×C4C2411yescharacteristic
690C23×C4C2414yes—
691C23×C4C2412yes—
692C23×C4C2412yes—
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C23×C4C2414yes—
696C23×C4C2414yes—
697C23×C4C2414yes—
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704#126—216no—
705#126—216no—
706#126—216no—
707#125—216no—
708#125—28no—
709#125—82no—
710#125—82no—
711#124—216no—
712#124—28no—
713#124—82no—
714#124—82no—
715#123—216no—
716#123—216no—
717#123—216no—
718#123—216no—
719C22⋊Q8—28no—
720C22⋊Q8—28no—
721C22⋊Q8—28no—
722C22⋊Q8—216no—
723C22⋊Q8—82no—
724C22⋊Q8—82no—
725#121—28no—
726#121—28no—
727#121—28no—
728#121—216no—
729#121—82no—
730#121—82no—
731#120—216no—
732C4×Q8—28no—
733C4×Q8—82no—
734C4×Q8—82no—
735C4×Q8—82no—
736C4×Q8—82no—
737C4×D4—216no—
738C4×D4—216no—
739C4×D4—216no—
740C4×D4—28no—
741C4×D4—82no—
742C4×D4—82no—
743C4×D4—82no—
744C4×D4—82no—
745C4×D4—84no—
746C4×D4—84no—
747#117—216no—
748#117—216no—
749#117—216no—
750#117—216no—
751#117—216no—
752#117—84no—
753#117—84no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—24no—
756C2×C4⋊C4—24no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—24no—
759C2×C4⋊C4—24no—
760C2×C4⋊C4—24no—
761C2×C4⋊C4—216no—
762C2×C4⋊C4—216no—
763C2×C4⋊C4#4118yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2412yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C22⋊C4—24no—
817C2×C22⋊C4—24no—
818C2×C22⋊C4—24no—
819C2×C22⋊C4#4118yes—
820C2×C22⋊C4C2412yes—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2414yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C42—24no—
858C2×C42—24no—
859C2×C42—24no—
860C2×C42—81no—
861C2×C42—81no—
862C2×C42—81no—
863C2×C42—81no—
864C2×C42—81no—
865C2×C42—81no—
866C2×C42—81no—
867C2×C42—81no—
868C2×C42#4118yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2412yes—
891C2×C42C2412yes—
892C2×C42C2412yes—
893C2×C42C2412yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2411yescharacteristic
901#95C2411yescharacteristic
902#95C2414yes—
903#95C2414yes—
904#95C2411yescharacteristic
905#95C2411yescharacteristic
906#95C2414yes—
907#95C2414yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2414yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956C24—22no—
957C24—22no—
958C24—41no—
959C24—41no—
960C24—41no—
961C24—41no—
962C24C2×#4114yes—
963C24C2514yes—
964C24C2512yes—
965C24C2511yescharacteristic
966C2×Q8—24no—
967C2×Q8—24no—
968C2×Q8—24no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×Q8—42no—
974C2×Q8—42no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—28no—
978C2×D4—28no—
979C2×D4—28no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—42no—
984C2×D4—42no—
985C2×D4—42no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—44no—
992C2×D4—44no—
993C22×C4—232no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—28no—
999C22×C4—28no—
1000C22×C4—28no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—22no—
1006C22×C4—22no—
1007C22×C4—28no—
1008C22×C4—24no—
1009C22×C4—24no—
1010C22×C4—28no—
1011C22×C4—28no—
1012C22×C4—28no—
1013C22×C4—41no—
1014C22×C4—41no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—41no—
1021C22×C4—41no—
1022C22×C4—41no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—41no—
1026C22×C4—41no—
1027C22×C4—41no—
1028C22×C4—41no—
1029C22×C4—41no—
1030C22×C4—41no—
1031C22×C4—41no—
1032C22×C4—41no—
1033C22×C4—41no—
1034C22×C4—41no—
1035C22×C4—41no—
1036C22×C4—41no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—44no—
1042C22×C4—44no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—42no—
1046C22×C4—42no—
1047C22×C4—44no—
1048C22×C4—44no—
1049C22×C4—88no—
1050C22×C4—88no—
1051C22×C4C2×#4114yes—
1052C22×C4C2×#4114yes—
1053C22×C4C2×#4114yes—
1054C22×C4C2×#4114yes—
1055C22×C4C2×#4114yes—
1056C22×C4C2×#4114yes—
1057C22×C4C2×#4114yes—
1058C22×C4C2×#4114yes—
1059C22×C4C2514yes—
1060C22×C4C2514yes—
1061C22×C4C2514yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2514yes—
1072C22×C4C2514yes—
1073C22×C4C2514yes—
1074C22×C4C2511yescharacteristic
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2512yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2511yescharacteristic
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—28no—
1092C4⋊C4—24no—
1093C4⋊C4—28no—
1094C4⋊C4—28no—
1095C4⋊C4—28no—
1096C4⋊C4—28no—
1097C4⋊C4—24no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—24no—
1101C4⋊C4—28no—
1102C4⋊C4—28no—
1103C4⋊C4—24no—
1104C4⋊C4—24no—
1105C4⋊C4—24no—
1106C4⋊C4—28no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—28no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—44no—
1134C4⋊C4C2×#41116yes—
1135C22⋊C4—24no—
1136C22⋊C4—24no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—24no—
1143C22⋊C4—24no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
1154C22⋊C4—28no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4C2×#41116yes—
1172C42—28no—
1173C42—24no—
1174C42—24no—
1175C42—28no—
1176C42—28no—
1177C42—28no—
1178C42—28no—
1179C42—44no—
1180C42—44no—
1181C42—42no—
1182C42—42no—
1183C42—42no—
1184C42—42no—
1185C42—42no—
1186C42—42no—
1187C42—42no—
1188C42—42no—
1189C42—42no—
1190C42—42no—
1191C42—42no—
1192C42—42no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C42C2×#4118yes—
1200C42C2×#4118yes—
1201C23—21no—
1202C23—21no—
1203C23—21no—
1204C23—21no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—22no—
1210C23—22no—
1211C23—28no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—24no—
1218C23—24no—
1219C23—44no—
1220C23—44no—
1221C23—44no—
1222C23—44no—
1223C23—44no—
1224C23—44no—
1225C23C22×#4114yes—
1226C23C22×#4112yes—
1227C23C22×#4112yes—
1228C23C22×#4112yes—
1229C23C2611yescharacteristic
1230Q8—48no—
1231Q8—84no—
1232Q8—84no—
1233D4—48no—
1234D4—416no—
1235D4—84no—
1236D4—84no—
1237D4—88no—
1238D4—88no—
1239C2×C4—232no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—28no—
1259C2×C4—28no—
1260C2×C4—22no—
1261C2×C4—21no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—22no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—24no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—24no—
1303C2×C4—21no—
1304C2×C4—24no—
1305C2×C4—44no—
1306C2×C4—44no—
1307C2×C4—44no—
1308C2×C4—44no—
1309C2×C4—44no—
1310C2×C4—44no—
1311C2×C4—44no—
1312C2×C4—44no—
1313C2×C4—44no—
1314C2×C4—44no—
1315C2×C4—44no—
1316C2×C4—44no—
1317C2×C4—88no—
1318C2×C4—88no—
1319C2×C4—88no—
1320C2×C4—88no—
1321C2×C4—84no—
1322C2×C4—84no—
1323C2×C4C22×#4112yes—
1324C2×C4C22×#4114yes—
1325C2×C4C22×#4114yes—
1326C2×C4C22×#4114yes—
1327C2×C4C22×#4114yes—
1328C2×C4C22×#4112yes—
1329C2×C4C22×#4114yes—
1330C2×C4C22×#4114yes—
1331C2×C4C22×#4114yes—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—22no—
1337C22—22no—
1338C22—24no—
1339C22—24no—
1340C22—24no—
1341C22—416no—
1342C22—42no—
1343C22—42no—
1344C22—42no—
1345C22—42no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22—44no—
1352C22—44no—
1353C22#344414yes—
1354C22C23×#4111yescharacteristic
1355C22C23×#4111yescharacteristic
1356C22C23×#4111yescharacteristic
1357C22H(7,𝔽2)11yescharacteristic
1358C22H(7,𝔽2)11yescharacteristic
1359C222−1+611yescharacteristic
1360C222−1+611yescharacteristic
1361C4—24no—
1362C4—24no—
1363C4—24no—
1364C4—24no—
1365C4—24no—
1366C4—22no—
1367C4—22no—
1368C4—24no—
1369C4—24no—
1370C4—42no—
1371C4—44no—
1372C4—41no—
1373C4—41no—
1374C4—42no—
1375C4—44no—
1376C4—41no—
1377C4—42no—
1378C4—41no—
1379C4—44no—
1380C4—44no—
1381C4—44no—
1382C4—42no—
1383C4—44no—
1384C4—44no—
1385C2—24no—
1386C2—44no—
1387C2—84no—
1388C2C2×#344411yescharacteristic
1389C2#6284511yescharacteristic
1390C2#6284611yescharacteristic
1391C2#6284711yescharacteristic
1392C2#6284711yescharacteristic
1393C2#6285011yescharacteristic
1394C2#6285611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35003C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36047C2semidirect
2. #35975C2semidirect
3. #35969C2semidirect
4. #35946C2semidirect
5. #35908C2semidirect
6. #35866C2semidirect
7. #35864C2semidirect
8. #35852C2semidirect
9. #35118C2semidirect
10. #35093C2semidirect
11. #35035C2semidirect
12. #35035C2semidirect
13. #35024C2semidirect
14. #35023C2semidirect
15. #35013C2semidirect
16. #35012C2semidirect
17. #35004C2semidirect
19. #34989C2semidirect
20. #34595C2semidirect
21. #34594C2semidirect
22. #34584C2semidirect
23. #34570C2semidirect
24. #34278C2semidirect
25. #34277C2semidirect
26. #34224C2semidirect
27. C2×#2274C2semidirect
44. #2666C22semidirect
45. #2666C22semidirect
46. #2664C22semidirect
47. #2662C22semidirect
52. #2655C22semidirect
53. #2654C22semidirect
56. #2651C22semidirect
57. #2650C22semidirect
83. #2596C22semidirect
85. #2595C22semidirect
86. #2595C22semidirect
87. #2594C22semidirect
88. #2594C22semidirect
89. #2594C22semidirect
90. #2588C22semidirect
91. #2588C22semidirect
92. #2587C22semidirect
93. #2587C22semidirect
94. #2586C22semidirect
95. #2585C22semidirect
97. #2577C22semidirect
99. #2575C22semidirect
102. #2556C22semidirect
104. #2554C22semidirect
106. #2529C22semidirect
107. #2529C22semidirect
108. #2528C22semidirect
109. #2528C22semidirect
112. #2520C22semidirect
113. #2519C22semidirect
114. #2514C22semidirect
115. #2513C22semidirect
116. #2509C22semidirect
117. #2508C22semidirect
128. #2475C22semidirect
129. #2475C22semidirect
132. #2474C22semidirect
133. #2474C22semidirect
140. #2462C22semidirect
141. #2461C22semidirect
142. #2454C22semidirect
143. #2453C22semidirect
146. #2448C22semidirect
147. #2447C22semidirect
154. #2402C22semidirect
155. #2402C22semidirect
157. #2401C22semidirect
158. #2399C22semidirect
160. #2396C22semidirect
161. #2396C22semidirect
163. #2395C22semidirect
165. #2392C22semidirect
167. #2374C22semidirect
170. #2373C22semidirect
171. #2373C22semidirect
172. #2373C22semidirect
173. #2373C22semidirect
175. #2371C22semidirect
176. #2370C22semidirect
177. #2370C22semidirect
178. #2370C22semidirect
179. #2368C22semidirect
181. #2367C22semidirect
182. #2367C22semidirect
185. #2362C22semidirect
187. #2359C22semidirect
188. #2357C22semidirect
189. #2356C22semidirect
190. #2351C22semidirect
191. #2349C22semidirect
192. #2347C22semidirect
193. #2343C22semidirect

Maximal subgroups

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

subgroupindex
#360472
#359752
#359692
#359462
#359082
#358662
#358642
#358522
#351182
#350932
#350352
#350242
#350232
#350132
#350122
#350042
#350032
#349892
#345952
#345942
#345842
#345702
#342782
#342772
#342242
C2×#22742