Finite Group Databasebeta

← #7630740

Subgroups — #7630740

Order 512.

5062 conjugacy classes of subgroups.

The subgroup lattice has 1394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36056C214yesmaximal, complemented
2#35917C214yesmaximal, complemented
3#35902C214yesmaximal, complemented
4#35896C214yesmaximal, complemented
5#35893C214yesmaximal, complemented
6#35887C214yesmaximal, complemented
7#35881C214yesmaximal, complemented
8#35878C214yesmaximal, complemented
9#35094C212yesmaximal, complemented
10#35093C212yesmaximal, complemented
11#35042C212yesmaximal, complemented
12#35042C212yesmaximal, complemented
13#35034C212yesmaximal, complemented
14#35015C211yesmaximal, characteristic, complemented
15#35015C211yesmaximal, characteristic, complemented
16#35014C211yesmaximal, characteristic, complemented
17#35006C211yesmaximal, characteristic, complemented
18#35006C211yesmaximal, characteristic, complemented
19#35005C211yesmaximal, characteristic
20#34989C212yesmaximal, complemented
21#34584C212yesmaximal, complemented
22#34584C212yesmaximal, complemented
23#34570C212yesmaximal, complemented
24#34278C212yesmaximal, complemented
25#34278C212yesmaximal, complemented
26#34277C212yesmaximal, complemented
27C2×#2274C211yesmaximal, characteristic, complemented
28C2×#539C2212yes—
29C2×#539C2212yes—
30C2×#538C2212yes—
31C22×#117C2211yescharacteristic
32C22×#117C2211yescharacteristic
33C23×C4⋊C4C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2856C2211yescharacteristic
38#2855C2212yes—
39#2855C2212yes—
40#2854C2212yes—
41#2854C2212yes—
42#2852C2214yes—
43#2849C2214yes—
44#2848C2212yes—
45#2847C2212yes—
46#2655C2214yescomplemented
47#2655C2214yescomplemented
48#2654C2214yescomplemented
49#2654C2214yescomplemented
50#2653C2214yes—
51#2652C2214yes—
52#2651C2214yescomplemented
53#2651C2214yescomplemented
54#2650C2214yescomplemented
55#2650C2214yescomplemented
56#2649C2214yes—
57#2648C2214yes—
58#2646C2212yes—
59#2646C2212yes—
60#2646C2212yes—
61#2643C2214yes—
62#2639C2212yes—
63#2639C2212yes—
64#2639C2212yes—
65#2627C2212yes—
66#2627C2212yes—
67#2626C2212yes—
68#2623C2214yes—
69#2623C2214yes—
70#2622C2214yes—
71#2618C2212yes—
72#2618C2212yes—
73#2617C2212yes—
74#2597C2214yescomplemented
75#2597C2214yescomplemented
76#2596C2214yescomplemented
77#2596C2214yescomplemented
78#2590C2214yescomplemented
79#2590C2214yescomplemented
80#2590C2214yescomplemented
81#2590C2214yescomplemented
82#2589C2214yes—
83#2589C2214yescomplemented
84#2589C2214yescomplemented
85#2588C2214yescomplemented
86#2588C2214yescomplemented
87#2587C2214yes—
88#2578C2214yes—
89#2577C2214yes—
90#2560C2214yes—
91#2560C2214yescomplemented
92#2560C2214yescomplemented
93#2559C2214yes—
94#2559C2214yes—
95#2558C2214yescomplemented
96#2558C2214yescomplemented
97#2557C2214yes—
98#2533C2214yescomplemented
99#2533C2214yescomplemented
100#2532C2214yescomplemented
101#2532C2214yescomplemented
102#2531C2214yes—
103#2530C2214yes—
104#2512C2212yescomplemented
105#2512C2212yescomplemented
106#2511C2212yescomplemented
107#2511C2212yescomplemented
108#2507C2212yescomplemented
109#2507C2212yescomplemented
110#2506C2212yescomplemented
111#2506C2212yescomplemented
112#2497C2212yes—
113#2496C2212yes—
114#2492C2212yes—
115#2491C2212yes—
116#2481C2214yes—
117#2481C2214yes—
118#2479C2214yes—
119#2479C2214yes—
120#2479C2214yescomplemented
121#2479C2214yescomplemented
122#2478C2214yes—
123#2478C2214yes—
124#2478C2214yescomplemented
125#2478C2214yescomplemented
126#2477C2214yes—
127#2477C2214yes—
128#2477C2214yes—
129#2476C2214yes—
130#2476C2214yes—
131#2476C2214yes—
132#2475C2214yes—
133#2475C2214yes—
134#2474C2214yes—
135#2474C2214yes—
136#2473C2214yes—
137#2473C2214yes—
138#2471C2214yes—
139#2471C2214yes—
140#2470C2214yes—
141#2470C2214yes—
142#2452C2212yescomplemented
143#2452C2212yescomplemented
144#2451C2212yescomplemented
145#2451C2212yescomplemented
146#2449C2214yes—
147#2449C2214yes—
148#2446C2212yescomplemented
149#2446C2212yescomplemented
150#2445C2212yescomplemented
151#2445C2212yescomplemented
152#2443C2214yes—
153#2443C2214yes—
154#2429C2212yes—
155#2428C2212yes—
156#2423C2212yes—
157#2422C2212yes—
158#2402C2214yescomplemented
159#2402C2214yescomplemented
160#2401C2214yes—
161#2401C2214yescomplemented
162#2401C2214yescomplemented
163#2398C2214yes—
164#2396C2214yescomplemented
165#2396C2214yescomplemented
166#2395C2214yes—
167#2395C2214yescomplemented
168#2395C2214yescomplemented
169#2392C2214yes—
170#2374C2214yes—
171#2374C2214yescomplemented
172#2374C2214yescomplemented
173#2373C2214yes—
174#2373C2214yes—
175#2373C2214yescomplemented
176#2373C2214yescomplemented
177#2373C2214yescomplemented
178#2373C2214yescomplemented
179#2372C2214yes—
180#2371C2214yescomplemented
181#2371C2214yescomplemented
182#2370C2214yescomplemented
183#2370C2214yescomplemented
184#2368C2214yescomplemented
185#2368C2214yescomplemented
186#2367C2214yes—
187#2364C2214yes—
188#2363C2214yes—
189#2362C2214yescomplemented
190#2362C2214yescomplemented
191#2359C2214yes—
192#2359C2214yescomplemented
193#2359C2214yescomplemented
194#2329C2212yes—
195#2329C2212yes—
196#2329C2212yes—
197#2325C2212yes—
198#2325C2212yes—
199#2325C2212yes—
200#2322C2214yes—
201#2322C2214yes—
202#2321C2214yes—
203#2313C2212yes—
204#2313C2212yes—
205#2312C2212yes—
206C4×C22⋊Q8C2212yes—
207C4×C22⋊Q8C2212yes—
208C4×C22⋊Q8C2212yes—
209C4×#123C2214yes—
210C4×#123C2214yes—
211C4×#121C2212yes—
212C4×#121C2212yes—
213C4×#121C2212yes—
214C4×#120C2214yes—
215#2290C2214yes—
216#2290C2214yes—
217#2290C2214yes—
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#539—216no—
240#538—216no—
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×#127C2311yescharacteristic
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#125C2314yes—
250C2×#125C2314yes—
251C2×#124C2314yes—
252C2×#123C2314yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×#123C2314yes—
257C2×C22⋊Q8C2314yes—
258C2×C22⋊Q8C2314yes—
259C2×C22⋊Q8C2312yes—
260C2×C22⋊Q8C2312yes—
261C2×C22⋊Q8C2312yes—
262C2×C22⋊Q8C2312yes—
263C2×C22⋊Q8C2312yes—
264C2×#121C2312yes—
265C2×#121C2312yes—
266C2×#121C2312yes—
267C2×#121C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#120C2314yes—
271C2×C4×Q8C2312yes—
272C2×C4×Q8C2312yes—
273C2×C4×Q8C2312yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2314yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2314yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×C4×D4C2312yes—
281C2×C4×D4C2314yes—
282C2×#117—28no—
283C2×#117—28no—
284C2×#117C2314yes—
285C2×#117C2314yes—
286C2×#117C2314yes—
287C2×#117C2314yes—
288C2×#117C2314yes—
289C2×#117C2314yes—
290C2×#117C2314yes—
291C22×C4⋊C4—28no—
292C22×C4⋊C4C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2311yescharacteristic
298C22×C4⋊C4C2314yes—
299C22×C4⋊C4C2314yes—
300C22×C4⋊C4C2311yescharacteristic
301C22×C4⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2311yescharacteristic
306C22×C42C2311yescharacteristic
307C22×C42C2311yescharacteristic
308C22×C42C2311yescharacteristic
309C22×C42C2311yescharacteristic
310C22×C42C2311yescharacteristic
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313C22×C42C2311yescharacteristic
314C22×C42C2311yescharacteristic
315C22×C42C2311yescharacteristic
316C22×C42C2311yescharacteristic
317C22×C42C2311yescharacteristic
318#401C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2314yes—
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#400C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
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#398C2314yes—
357#398C2314yes—
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#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#396C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#395C2314yes—
381#395C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#393C2314yes—
394#393C2314yes—
395#393C2314yes—
396#393C2314yes—
397#392C2314yes—
398#391C2314yes—
399#391C2312yes—
400#391C2312yes—
401#391C2314yes—
402#391C2314yes—
403#391C2312yes—
404#391C2312yes—
405#391C2312yes—
406#391C2312yes—
407#391C2312yes—
408#391C2312yes—
409#391C2312yes—
410#391C2312yes—
411#390C2314yes—
412#390C2312yes—
413#390C2312yes—
414#390C2314yes—
415#390C2312yes—
416#390C2312yes—
417#390C2312yes—
418#390C2312yes—
419#390C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#389C2314yes—
424#389C2314yes—
425#389C2314yes—
426#389C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
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#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
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#388C2314yes—
483#388C2314yes—
484#388C2314yes—
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#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
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#386C2314yes—
539#386C2314yes—
540#386C2314yes—
541#386C2314yes—
542#386C2314yes—
543#386C2314yes—
544#386C2314yes—
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#385C2314yes—
561#385C2314yes—
562#385C2314yes—
563#385C2314yes—
564#385C2314yes—
565#385C2314yes—
566#384C2311yescharacteristic
567#384C2311yescharacteristic
568#384C2311yescharacteristic
569#384C2311yescharacteristic
570#383C2314yes—
571#381C2314yes—
572#381C2314yes—
573#380C2312yes—
574#380C2312yes—
575#380C2312yes—
576#380C2312yes—
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⋊C4C2312yes—
589C4×C4⋊C4C2312yes—
590C4×C4⋊C4C2314yes—
591C4×C4⋊C4C2314yes—
592C4×C4⋊C4C2314yes—
593C4×C4⋊C4C2314yes—
594C4×C4⋊C4C2312yes—
595C4×C4⋊C4C2312yes—
596C4×C4⋊C4C2314yes—
597C4×C4⋊C4C2314yes—
598C4×C4⋊C4C2314yes—
599C4×C4⋊C4C2314yes—
600C4×C4⋊C4C2314yes—
601C4×C4⋊C4C2314yes—
602C4×C4⋊C4C2314yes—
603C4×C4⋊C4C2314yes—
604C4×C4⋊C4C2314yes—
605C4×C4⋊C4C2314yes—
606C4×C4⋊C4C2314yes—
607C4×C4⋊C4C2314yes—
608C4×C4⋊C4C2314yes—
609C4×C4⋊C4C2314yes—
610C4×C4⋊C4C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2312yes—
616C4×C4⋊C4C2312yes—
617C4×C4⋊C4C2314yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2314yes—
620C4×C4⋊C4C2314yes—
621C4×C4⋊C4C2312yes—
622C4×C4⋊C4C2312yes—
623C4×C22⋊C4C2314yes—
624C4×C22⋊C4C2314yes—
625C4×C22⋊C4C2314yes—
626C4×C22⋊C4C2314yes—
627C4×C22⋊C4C2314yes—
628C4×C22⋊C4C2314yes—
629C4×C22⋊C4C2314yes—
630C4×C22⋊C4C2314yes—
631C4×C22⋊C4C2312yes—
632C4×C22⋊C4C2312yes—
633C4×C22⋊C4C2314yes—
634C4×C22⋊C4C2314yes—
635C4×C22⋊C4C2314yes—
636C4×C22⋊C4C2314yes—
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⋊C4C2312yes—
650C4×C22⋊C4C2312yes—
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×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2412yes—
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
704C4⋊Q8—81no—
705C4⋊Q8—81no—
706C4⋊Q8—81no—
707#127—81no—
708#126—216no—
709#126—216no—
710#126—216no—
711#126—84no—
712#125—216no—
713#125—216no—
714#124—216no—
715#123—216no—
716#123—216no—
717#123—216no—
718#123—216no—
719#123—216no—
720C22⋊Q8—28no—
721C22⋊Q8—28no—
722C22⋊Q8—28no—
723C22⋊Q8—216no—
724C22⋊Q8—216no—
725C22⋊Q8—82no—
726C22⋊Q8—82no—
727#121—28no—
728#121—28no—
729#121—28no—
730#121—216no—
731#121—82no—
732#121—82no—
733#120—216no—
734C4×Q8—82no—
735C4×Q8—82no—
736C4×Q8—82no—
737C4×D4—216no—
738C4×D4—216no—
739C4×D4—216no—
740C4×D4—82no—
741C4×D4—82no—
742C4×D4—82no—
743C4×D4—84no—
744C4×D4—84no—
745#117—216no—
746#117—216no—
747#117—216no—
748#117—216no—
749#117—84no—
750#117—84no—
751#117—84no—
752C2×C4⋊C4—24no—
753C2×C4⋊C4—24no—
754C2×C4⋊C4—24no—
755C2×C4⋊C4—24no—
756C2×C4⋊C4—24no—
757C2×C4⋊C4—24no—
758C2×C4⋊C4—216no—
759C2×C4⋊C4—216no—
760C2×C4⋊C4#4118yes—
761C2×C4⋊C4#4118yes—
762C2×C4⋊C4C2414yes—
763C2×C4⋊C4C2412yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2412yes—
776C2×C4⋊C4C2412yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2412yes—
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C22⋊C4—24no—
815C2×C22⋊C4—24no—
816C2×C22⋊C4—24no—
817C2×C22⋊C4#4118yes—
818C2×C22⋊C4C2414yes—
819C2×C22⋊C4C2412yes—
820C2×C22⋊C4C2412yes—
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×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⋊C4C2412yes—
854C2×C22⋊C4C2412yes—
855C2×C42—24no—
856C2×C42—24no—
857C2×C42—24no—
858C2×C42—24no—
859C2×C42—81no—
860C2×C42—81no—
861C2×C42—81no—
862C2×C42—81no—
863C2×C42—81no—
864C2×C42—81no—
865C2×C42—81no—
866C2×C42—81no—
867C2×C42C2414yes—
868C2×C42C2414yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2414yes—
874C2×C42C2414yes—
875C2×C42C2414yes—
876C2×C42C2414yes—
877C2×C42C2414yes—
878C2×C42C2414yes—
879C2×C42C2414yes—
880C2×C42C2414yes—
881C2×C42C2414yes—
882C2×C42C2414yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2412yes—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2411yescharacteristic
891C2×C42C2411yescharacteristic
892C2×C42C2411yescharacteristic
893C2×C42C2411yescharacteristic
894C2×C42C2414yes—
895C2×C42C2414yes—
896#95C2414yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
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—
954C24—22no—
955C24—22no—
956C24—41no—
957C24—41no—
958C24—41no—
959C24—41no—
960C24C2×#4114yes—
961C24C2514yes—
962C24C2512yes—
963C24C2511yescharacteristic
964C2×Q8—24no—
965C2×Q8—24no—
966C2×Q8—24no—
967C2×Q8—42no—
968C2×Q8—42no—
969C2×Q8—42no—
970C2×Q8—42no—
971C2×Q8—42no—
972C2×Q8—42no—
973C2×D4—28no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—28no—
977C2×D4—28no—
978C2×D4—24no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—42no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—42no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—42no—
988C2×D4—42no—
989C2×D4—44no—
990C2×D4—44no—
991C22×C4—232no—
992C22×C4—22no—
993C22×C4—22no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—28no—
997C22×C4—28no—
998C22×C4—28no—
999C22×C4—22no—
1000C22×C4—22no—
1001C22×C4—22no—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—28no—
1006C22×C4—24no—
1007C22×C4—24no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—28no—
1011C22×C4—41no—
1012C22×C4—41no—
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—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—88no—
1048C22×C4—88no—
1049C22×C4C2×#4114yes—
1050C22×C4C2×#4114yes—
1051C22×C4C2×#4114yes—
1052C22×C4C2×#4114yes—
1053C22×C4C2×#4114yes—
1054C22×C4C2×#4114yes—
1055C22×C4C2×#4114yes—
1056C22×C4C2×#4114yes—
1057C22×C4C2514yes—
1058C22×C4C2514yes—
1059C22×C4C2514yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2512yes—
1064C22×C4C2512yes—
1065C22×C4C2512yes—
1066C22×C4C2512yes—
1067C22×C4C2514yes—
1068C22×C4C2514yes—
1069C22×C4C2514yes—
1070C22×C4C2512yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2511yescharacteristic
1074C22×C4C2511yescharacteristic
1075C22×C4C2511yescharacteristic
1076C22×C4C2511yescharacteristic
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C22×C4C2511yescharacteristic
1080C22×C4C2511yescharacteristic
1081C4⋊C4—28no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—28no—
1085C4⋊C4—28no—
1086C4⋊C4—24no—
1087C4⋊C4—24no—
1088C4⋊C4—28no—
1089C4⋊C4—28no—
1090C4⋊C4—28no—
1091C4⋊C4—28no—
1092C4⋊C4—28no—
1093C4⋊C4—24no—
1094C4⋊C4—24no—
1095C4⋊C4—24no—
1096C4⋊C4—24no—
1097C4⋊C4—28no—
1098C4⋊C4—28no—
1099C4⋊C4—28no—
1100C4⋊C4—28no—
1101C4⋊C4—24no—
1102C4⋊C4—24no—
1103C4⋊C4—28no—
1104C4⋊C4—28no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—42no—
1129C4⋊C4C2×#4118yes—
1130C4⋊C4C2×#4118yes—
1131C4⋊C4C2×#4118yes—
1132C4⋊C4C2×#4118yes—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—24no—
1141C22⋊C4—24no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
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—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
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⋊C4C2×#4118yes—
1169C22⋊C4C2×#4118yes—
1170C42—28no—
1171C42—28no—
1172C42—24no—
1173C42—24no—
1174C42—24no—
1175C42—24no—
1176C42—28no—
1177C42—28no—
1178C42—28no—
1179C42—44no—
1180C42—44no—
1181C42—44no—
1182C42—42no—
1183C42—42no—
1184C42—42no—
1185C42—42no—
1186C42—42no—
1187C42—42no—
1188C42—44no—
1189C42—41no—
1190C42—41no—
1191C42—41no—
1192C42—41no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C42—44no—
1197C42—44no—
1198C42—44no—
1199C23—21no—
1200C23—21no—
1201C23—21no—
1202C23—21no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—28no—
1210C23—24no—
1211C23—24no—
1212C23—24no—
1213C23—24no—
1214C23—24no—
1215C23—24no—
1216C23—24no—
1217C23—44no—
1218C23—44no—
1219C23—44no—
1220C23—44no—
1221C23—44no—
1222C23—44no—
1223C23C22×#4114yes—
1224C23C22×#4112yes—
1225C23C22×#4112yes—
1226C23C22×#4112yes—
1227C23C2611yescharacteristic
1228Q8—84no—
1229Q8—84no—
1230Q8—84no—
1231D4—416no—
1232D4—84no—
1233D4—84no—
1234D4—84no—
1235D4—88no—
1236D4—88no—
1237C2×C4—232no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—28no—
1261C2×C4—28no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
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—24no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—24no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—24no—
1293C2×C4—24no—
1294C2×C4—24no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—44no—
1302C2×C4—44no—
1303C2×C4—44no—
1304C2×C4—44no—
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—88no—
1314C2×C4—88no—
1315C2×C4—88no—
1316C2×C4—88no—
1317C2×C4—84no—
1318C2×C4—84no—
1319C2×C4C22×#4114yes—
1320C2×C4C22×#4114yes—
1321C2×C4C22×#4112yes—
1322C2×C4C22×#4112yes—
1323C2×C4C22×#4112yes—
1324C2×C4C22×#4114yes—
1325C2×C4C22×#4112yes—
1326C2×C4C22×#4114yes—
1327C2×C4C22×#4114yes—
1328C2×C4C22×#4112yes—
1329C2×C4C22×#4112yes—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—24no—
1337C22—24no—
1338C22—24no—
1339C22—416no—
1340C22—42no—
1341C22—42no—
1342C22—42no—
1343C22—42no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—44no—
1348C22—44no—
1349C22—44no—
1350C22—44no—
1351C22#344414yes—
1352C22C23×#4111yescharacteristic
1353C22C23×#4111yescharacteristic
1354C22C23×#4111yescharacteristic
1355C22H(7,𝔽2)11yescharacteristic
1356C22H(7,𝔽2)11yescharacteristic
1357C222−1+611yescharacteristic
1358C222−1+611yescharacteristic
1359C4—24no—
1360C4—22no—
1361C4—22no—
1362C4—24no—
1363C4—24no—
1364C4—22no—
1365C4—22no—
1366C4—22no—
1367C4—22no—
1368C4—24no—
1369C4—24no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—44no—
1376C4—44no—
1377C4—44no—
1378C4—44no—
1379C4—44no—
1380C4—42no—
1381C4—42no—
1382C4—44no—
1383C2—24no—
1384C2—44no—
1385C2—84no—
1386C2C2×#344411yescharacteristic
1387C2#6284611yescharacteristic
1388C2#6284711yescharacteristic
1389C2#6284711yescharacteristic
1390C2#6284711yescharacteristic
1391C2#6285011yescharacteristic
1392C2#6285111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35005C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36056C2semidirect
2. #35917C2semidirect
3. #35902C2semidirect
4. #35896C2semidirect
5. #35893C2semidirect
6. #35887C2semidirect
7. #35881C2semidirect
8. #35878C2semidirect
9. #35094C2semidirect
10. #35093C2semidirect
11. #35042C2semidirect
12. #35042C2semidirect
13. #35034C2semidirect
14. #35015C2semidirect
15. #35015C2semidirect
16. #35014C2semidirect
17. #35006C2semidirect
18. #35006C2semidirect
20. #34989C2semidirect
21. #34584C2semidirect
22. #34584C2semidirect
23. #34570C2semidirect
24. #34278C2semidirect
25. #34278C2semidirect
26. #34277C2semidirect
27. C2×#2274C2semidirect
46. #2655C22semidirect
47. #2655C22semidirect
48. #2654C22semidirect
49. #2654C22semidirect
52. #2651C22semidirect
53. #2651C22semidirect
54. #2650C22semidirect
55. #2650C22semidirect
74. #2597C22semidirect
75. #2597C22semidirect
76. #2596C22semidirect
77. #2596C22semidirect
78. #2590C22semidirect
79. #2590C22semidirect
80. #2590C22semidirect
81. #2590C22semidirect
83. #2589C22semidirect
84. #2589C22semidirect
85. #2588C22semidirect
86. #2588C22semidirect
91. #2560C22semidirect
92. #2560C22semidirect
95. #2558C22semidirect
96. #2558C22semidirect
98. #2533C22semidirect
99. #2533C22semidirect
100. #2532C22semidirect
101. #2532C22semidirect
104. #2512C22semidirect
105. #2512C22semidirect
106. #2511C22semidirect
107. #2511C22semidirect
108. #2507C22semidirect
109. #2507C22semidirect
110. #2506C22semidirect
111. #2506C22semidirect
120. #2479C22semidirect
121. #2479C22semidirect
124. #2478C22semidirect
125. #2478C22semidirect
142. #2452C22semidirect
143. #2452C22semidirect
144. #2451C22semidirect
145. #2451C22semidirect
148. #2446C22semidirect
149. #2446C22semidirect
150. #2445C22semidirect
151. #2445C22semidirect
158. #2402C22semidirect
159. #2402C22semidirect
161. #2401C22semidirect
162. #2401C22semidirect
164. #2396C22semidirect
165. #2396C22semidirect
167. #2395C22semidirect
168. #2395C22semidirect
171. #2374C22semidirect
172. #2374C22semidirect
175. #2373C22semidirect
176. #2373C22semidirect
177. #2373C22semidirect
178. #2373C22semidirect
180. #2371C22semidirect
181. #2371C22semidirect
182. #2370C22semidirect
183. #2370C22semidirect
184. #2368C22semidirect
185. #2368C22semidirect
189. #2362C22semidirect
190. #2362C22semidirect
192. #2359C22semidirect
193. #2359C22semidirect

Maximal subgroups

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

subgroupindex
#360562
#359172
#359022
#358962
#358932
#358872
#358812
#358782
#350942
#350932
#350422
#350342
#350152
#350142
#350062
#350052
#349892
#345842
#345702
#342782
#342772
C2×#22742