Finite Group Databasebeta

← #7630792

Subgroups — #7630792

Order 512.

5524 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36074C212yesmaximal, complemented
2#35992C212yesmaximal, complemented
3#35977C214yesmaximal, complemented
4#35784C214yesmaximal, complemented
5#35769C214yesmaximal, complemented
6#35754C212yesmaximal, complemented
7#35706C212yesmaximal, complemented
8#35705C212yesmaximal, complemented
9#35695C212yesmaximal, complemented
10#35694C212yesmaximal, complemented
11#35684C212yesmaximal, complemented
12#35681C214yesmaximal, complemented
13#35146C211yesmaximal, characteristic, complemented
14#35133C214yesmaximal, complemented
15#35131C211yesmaximal, characteristic, complemented
16#35048C214yesmaximal, complemented
17#35044C214yesmaximal, complemented
18#34998C214yesmaximal, complemented
19#34593C211yesmaximal, characteristic, complemented
20#34589C214yesmaximal, complemented
21C2×#2631C211yesmaximal, characteristic, complemented
22#34302C214yesmaximal, complemented
23#34240C211yesmaximal, characteristic, complemented
24#34234C211yesmaximal, characteristic, complemented
25C4×#518C211yesmaximal, characteristic, complemented
26C2×#546C2214yes—
27C2×#529C2211yescharacteristic
28C22×#124C2211yescharacteristic
29C2×#518C2212yes—
30C22×C4×D4C2211yescharacteristic
31#2863C2214yescomplemented
32#2861C2212yescomplemented
33#2858C2212yescomplemented
34#2854C2214yescomplemented
35#2853C2214yescomplemented
36#2852C2214yescomplemented
37#2850C2214yescomplemented
38#2666C2214yescomplemented
39#2665C2214yescomplemented
40#2662C2214yescomplemented
41#2661C2214yescomplemented
42#2653C2214yescomplemented
43#2653C2214yescomplemented
44#2651C2214yescomplemented
45#2650C2214yescomplemented
46#2649C2214yescomplemented
47#2648C2214yescomplemented
48#2648C2214yescomplemented
49#2648C2214yescomplemented
50#2636C2212yescomplemented
51#2636C2212yescomplemented
52#2635C2214yescomplemented
53#2633C2212yescomplemented
54#2631C2212yes—
55#2631C2212yes—
56#2631C2212yes—
57#2631C2212yes—
58#2631C2212yes—
59#2631C2212yes—
60#2631C2214yes—
61#2631C2212yescomplemented
62#2630C2214yescomplemented
63#2626C2212yes—
64#2623C2212yes—
65#2617C2212yes—
66#2613C2212yes—
67#2610C2214yescomplemented
68#2607C2214yescomplemented
69#2606C2212yescomplemented
70#2606C2212yescomplemented
71#2605C2212yescomplemented
72#2605C2212yescomplemented
73#2602C2214yescomplemented
74#2602C2214yescomplemented
75#2600C2214yescomplemented
76#2597C2214yescomplemented
77#2597C2214yescomplemented
78#2594C2214yescomplemented
79#2589C2214yescomplemented
80#2577C2214yescomplemented
81#2574C2214yescomplemented
82#2572C2214yescomplemented
83#2569C2212yes—
84#2557C2214yescomplemented
85#2557C2214yescomplemented
86#2557C2214yescomplemented
87#2555C2214yescomplemented
88#2554C2214yescomplemented
89#2549C2212yes—
90#2545C2212yescomplemented
91#2544C2212yescomplemented
92#2532C2214yescomplemented
93#2527C2214yescomplemented
94#2525C2214yescomplemented
95#2523C2214yescomplemented
96#2521C2214yescomplemented
97#2518C2214yescomplemented
98#2518C2214yescomplemented
99#2516C2214yescomplemented
100#2515C2214yescomplemented
101#2513C2214yescomplemented
102#2510C2214yes—
103#2510C2214yescomplemented
104#2505C2214yes—
105#2492C2214yescomplemented
106#2488C2214yescomplemented
107#2480C2214yes—
108#2478C2214yescomplemented
109#2472C2214yes—
110#2471C2214yescomplemented
111#2467C2214yescomplemented
112#2467C2214yescomplemented
113#2465C2214yescomplemented
114#2464C2214yescomplemented
115#2464C2214yescomplemented
116#2464C2214yescomplemented
117#2461C2214yescomplemented
118#2459C2214yescomplemented
119#2459C2214yescomplemented
120#2459C2214yescomplemented
121#2459C2214yescomplemented
122#2458C2214yescomplemented
123#2457C2214yescomplemented
124#2457C2214yescomplemented
125#2456C2214yescomplemented
126#2456C2214yescomplemented
127#2455C2214yescomplemented
128#2447C2214yescomplemented
129#2444C2214yescomplemented
130#2439C2214yescomplemented
131#2438C2214yes—
132#2437C2214yes—
133#2436C2211yescharacteristic
134#2435C2211yescharacteristic
135#2434C2211yescharacteristic
136#2433C2211yescharacteristic
137#2431C2214yescomplemented
138#2428C2214yescomplemented
139#2425C2214yescomplemented
140#2414C2214yescomplemented
141#2412C2214yes—
142#2411C2214yes—
143#2410C2214yes—
144#2407C2214yescomplemented
145#2405C2214yes—
146#2401C2214yescomplemented
147#2398C2214yescomplemented
148#2398C2211yescharacteristic, complemented
149#2398C2211yescharacteristic, complemented
150#2397C2211yescharacteristic, complemented
151#2397C2211yescharacteristic, complemented
152#2396C2214yescomplemented
153#2395C2214yescomplemented
154#2392C2214yescomplemented
155#2392C2214yescomplemented
156#2392C2214yescomplemented
157C2×#397C2212yes—
158#2388C2214yescomplemented
159#2388C2214yescomplemented
160C2×#393C2212yes—
161C2×#392C2212yes—
162C2×#392C2212yes—
163#2374C2214yescomplemented
164#2372C2212yescomplemented
165#2372C2212yescomplemented
166#2372C2214yescomplemented
167#2368C2212yes—
168#2368C2214yes—
169#2367C2214yescomplemented
170#2364C2212yes—
171#2364C2214yescomplemented
172#2364C2214yescomplemented
173#2363C2214yescomplemented
174#2359C2214yes—
175#2359C2214yescomplemented
176#2358C2214yes—
177#2358C2214yes—
178#2356C2212yescomplemented
179#2353C2214yes—
180#2353C2212yescomplemented
181#2353C2214yescomplemented
182#2347C2212yescomplemented
183#2343C2212yescomplemented
184#2342C2214yes—
185#2342C2214yes—
186#2342C2214yes—
187Q8×C22⋊C4C2212yes—
188#2339C2214yescomplemented
189D4×C22⋊C4C2214yes—
190D4×C22⋊C4C2212yes—
191#2337C2214yescomplemented
192#2337C2212yescomplemented
193#2337C2214yescomplemented
194#2336C2212yescomplemented
195#2335C2214yescomplemented
196#2333C2214yescomplemented
197#2333C2214yescomplemented
198#2329C2214yes—
199#2321C2214yes—
200#2318C2212yes—
201#2312C2212yes—
202C4×#126C2214yescomplemented
203C4×#124C2214yescomplemented
204C4×#123C2214yescomplemented
205C4×#121C2214yescomplemented
206C4×#120C2214yes—
207#2297C2214yescomplemented
208#2290C2214yescomplemented
209C2×#386C2214yes—
210#2283C2211yescharacteristic
211C2×#383C2211yescharacteristic
212#2275C2212yes—
213#2275C2212yescomplemented
214#2275C2212yescomplemented
215#2275C2214yescomplemented
216#2274C2212yes—
217#2273C2212yes—
218#2273C2212yes—
219#2273C2212yes—
220C42×D4C2212yescomplemented
221C42×D4C2212yescomplemented
222C42×D4C2214yescomplemented
223C4×#117C2211yescharacteristic
224C4×#117C2211yescharacteristic
225C2×C4×C22⋊C4C2212yes—
226C2×C4×C22⋊C4C2212yes—
227C22×#41C2314yes—
228C23×Q8C2311yescharacteristic
229C23×D4C2311yescharacteristic
230C23×D4C2311yescharacteristic
231C23×D4C2314yes—
232C24×C4C2312yes—
233#546—232no—
234C2×C4⋊Q8C2312yes—
235C2×#127C2312yes—
236#529—28no—
237C2×#126C2312yes—
238C2×#126C2314yes—
239C2×#125C2311yescharacteristic
240C2×#124—28no—
241C2×#124C2311yescharacteristic
242C2×#124C2312yes—
243C2×#124C2314yes—
244C2×#124C2312yes—
245C2×#124C2312yes—
246C2×#124C2312yes—
247C2×#124C2314yes—
248C2×#124C2312yes—
249C2×#124C2312yes—
250C2×#123C2314yes—
251C2×#123C2314yes—
252C2×#123C2312yes—
253C2×#123C2314yes—
254C2×#123C2314yes—
255C2×#123C2314yes—
256C2×C22⋊Q8C2314yes—
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2314yes—
259C2×#121C2314yes—
260C2×#121C2314yes—
261C2×#121C2311yescharacteristic
262C2×#121C2314yes—
263C2×#121C2314yes—
264C2×#121C2314yes—
265C2×#120C2314yes—
266C2×#120C2314yes—
267#518—216no—
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2314yes—
270C2×C4×D4—28no—
271C2×C4×D4C2312yes—
272C2×C4×D4C2314yes—
273C2×C4×D4C2314yes—
274C2×C4×D4C2314yes—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×C4×D4C2312yes—
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2314yes—
284C2×C4×D4C2314yes—
285C2×C4×D4C2314yes—
286C2×C4×D4C2314yes—
287C2×C4×D4C2314yes—
288C2×C4×D4C2314yes—
289C2×C4×D4C2314yes—
290C2×C4×D4C2314yes—
291C2×C4×D4C2314yes—
292C2×#117C2312yes—
293C2×#117C2312yes—
294C2×#117C2312yes—
295C2×#117C2314yes—
296C2×#117C2314yes—
297C22×C4⋊C4C2311yescharacteristic
298C22×C22⋊C4C2312yes—
299C22×C22⋊C4C2314yes—
300C22×C22⋊C4C2312yes—
301C22×C22⋊C4C2312yes—
302C22×C22⋊C4C2312yes—
303C22×C22⋊C4C2312yes—
304C22×C22⋊C4C2312yes—
305C22×C22⋊C4C2314yes—
306C22×C22⋊C4C2314yes—
307C22×C22⋊C4C2312yes—
308C22×C42C2314yes—
309C22×C42C2314yes—
310C22×C42C2311yescharacteristic
311#401C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2312yes—
319#400C2312yes—
320#399C2312yes—
321#399C2312yes—
322#399C2314yes—
323#399C2312yes—
324#399C2312yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#397C2314yes—
332#397C2314yes—
333#397C2314yes—
334#397C2314yes—
335#397C2314yes—
336#397C2312yes—
337#397C2314yes—
338#397C2312yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#396C2314yes—
347#396C2314yes—
348#396C2314yes—
349#396C2314yes—
350#396C2314yes—
351#396C2314yes—
352#396C2314yes—
353#395C2314yes—
354#395C2314yes—
355#395C2314yes—
356#394C2314yes—
357#394C2314yes—
358#394C2314yes—
359#394C2314yes—
360#394C2314yes—
361#394C2314yes—
362#394C2314yes—
363#394C2314yes—
364#394C2314yes—
365#394C2312yes—
366#394C2312yes—
367#394C2314yes—
368#394C2314yes—
369#394C2314yes—
370#394C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#393C2312yes—
375#393C2314yes—
376#393C2312yes—
377#393C2314yes—
378#393C2314yes—
379#393C2314yes—
380#393C2312yes—
381#393C2312yes—
382#393C2312yes—
383#393C2312yes—
384#393C2314yes—
385#392C2314yes—
386#392C2314yes—
387#392C2314yes—
388#392C2314yes—
389#392C2314yes—
390#392C2312yes—
391#392C2312yes—
392#392C2312yes—
393#392C2312yes—
394#392C2314yes—
395#392C2312yes—
396#392C2312yes—
397#392C2314yes—
398#392C2312yes—
399#392C2314yes—
400#392C2312yes—
401#392C2314yes—
402#392C2314yes—
403#391C2314yes—
404#391C2314yes—
405#391C2314yes—
406#391C2312yes—
407#391C2314yes—
408#391C2314yes—
409#391C2314yes—
410#391C2314yes—
411#391C2314yes—
412#391C2314yes—
413#391C2312yes—
414#391C2314yes—
415#390C2314yes—
416#390C2314yes—
417#390C2314yes—
418#390C2314yes—
419#390C2314yes—
420#390C2314yes—
421#390C2314yes—
422#390C2314yes—
423#390C2314yes—
424#390C2312yes—
425#390C2312yes—
426#390C2314yes—
427#389C2314yes—
428#389C2314yes—
429#389C2314yes—
430#389C2314yes—
431#389C2314yes—
432#389C2314yes—
433#388C2314yes—
434#388C2314yes—
435#388C2314yes—
436#388C2314yes—
437#388C2314yes—
438#388C2314yes—
439#388C2314yes—
440#388C2314yes—
441#388C2314yes—
442#388C2314yes—
443#388C2314yes—
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#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#386C2314yes—
496#386C2314yes—
497#386C2314yes—
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#386C2314yes—
517#386C2314yes—
518#386C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
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#383C2312yes—
542#383C2314yes—
543#383C2314yes—
544#383C2312yes—
545#383C2312yes—
546#383C2312yes—
547#383C2311yescharacteristic
548#383C2311yescharacteristic
549#383C2312yes—
550#382C2312yes—
551#382C2314yes—
552#382C2312yes—
553#381C2314yes—
554#381C2314yes—
555#381C2312yes—
556#381C2314yes—
557#381C2314yes—
558#381C2312yes—
559#380C2314yes—
560#380C2314yes—
561#380C2312yes—
562#380C2312yes—
563#380C2314yes—
564#380C2314yes—
565#380C2314yes—
566#379C2314yes—
567#379C2314yes—
568#379C2314yes—
569C4×C4⋊C4C2314yes—
570C4×C4⋊C4C2314yes—
571C4×C4⋊C4C2314yes—
572C4×C4⋊C4C2314yes—
573C4×C4⋊C4C2314yes—
574C4×C4⋊C4C2312yes—
575C4×C4⋊C4C2314yes—
576C4×C4⋊C4C2312yes—
577C4×C4⋊C4C2312yes—
578C4×C4⋊C4C2312yes—
579C4×C4⋊C4C2312yes—
580C4×C4⋊C4C2314yes—
581C4×C4⋊C4C2314yes—
582C4×C4⋊C4C2312yes—
583C4×C4⋊C4C2314yes—
584C4×C22⋊C4C2314yes—
585C4×C22⋊C4C2314yes—
586C4×C22⋊C4C2314yes—
587C4×C22⋊C4C2311yescharacteristic
588C4×C22⋊C4C2312yes—
589C4×C22⋊C4C2311yescharacteristic
590C4×C22⋊C4C2314yes—
591C4×C22⋊C4C2314yes—
592C4×C22⋊C4C2312yes—
593C4×C22⋊C4C2314yes—
594C4×C22⋊C4C2314yes—
595C4×C22⋊C4C2314yes—
596C4×C22⋊C4C2314yes—
597C4×C22⋊C4C2314yes—
598C4×C22⋊C4C2312yes—
599C4×C22⋊C4C2314yes—
600C4×C22⋊C4C2314yes—
601C4×C22⋊C4C2314yes—
602C4×C22⋊C4C2314yes—
603C4×C22⋊C4C2314yes—
604C4×C22⋊C4C2312yes—
605C4×C22⋊C4C2314yes—
606C4×C22⋊C4C2314yes—
607C4×C22⋊C4C2314yes—
608C4×C22⋊C4C2314yes—
609C4×C22⋊C4C2312yes—
610C4×C22⋊C4C2314yes—
611C4×C22⋊C4C2314yes—
612C4×C22⋊C4C2314yes—
613C4×C22⋊C4C2312yes—
614C4×C22⋊C4C2314yes—
615C4×C22⋊C4C2314yes—
616C4×C22⋊C4C2314yes—
617C4×C22⋊C4C2314yes—
618C4×C22⋊C4C2314yes—
619C4×C22⋊C4C2311yescharacteristic
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2312yes—
624C4×C22⋊C4C2312yes—
625C4×C22⋊C4C2311yescharacteristic
626#376C2312yes—
627#376C2311yescharacteristic
628#376C2312yes—
629#376C2311yescharacteristic
630#376C2314yes—
631#376C2312yes—
632C2×#95C2312yes—
633C2×#95C2312yes—
634C2×#95C2312yes—
635C2×#95C2314yes—
636C2×#95C2314yes—
637C2×#95C2312yes—
638C2×#95C2314yes—
639C43C2312yes—
640C43C2312yes—
641C25C2412yes—
642C25C2412yes—
643C2×#41—216no—
644C2×#41—84no—
645C2×#41—84no—
646C22×Q8—24no—
647C22×Q8—82no—
648C22×Q8C2412yes—
649C22×Q8C2411yescharacteristic
650C22×Q8C2414yes—
651C22×Q8C2412yes—
652C22×D4—28no—
653C22×D4—216no—
654C22×D4—24no—
655C22×D4—24no—
656C22×D4—82no—
657C22×D4—84no—
658C22×D4—84no—
659C22×D4C2412yes—
660C22×D4C2411yescharacteristic
661C22×D4C2411yescharacteristic
662C22×D4C2412yes—
663C22×D4C2414yes—
664C22×D4C2414yes—
665C22×D4C2412yes—
666C22×D4C2414yes—
667C22×D4C2414yes—
668C22×D4C2411yescharacteristic
669C22×D4C2414yes—
670C22×D4C2414yes—
671C22×D4C2414yes—
672C22×D4C2414yes—
673C22×D4C2412yes—
674C23×C4—28no—
675C23×C4—84no—
676C23×C4C2411yescharacteristic
677C23×C4C2412yes—
678C23×C4C2412yes—
679C23×C4C2414yes—
680C23×C4C2414yes—
681C23×C4C2414yes—
682C23×C4C2414yes—
683C23×C4C2414yes—
684C23×C4C2414yes—
685C23×C4C2412yes—
686C23×C4C2412yes—
687C23×C4C2412yes—
688C23×C4C2414yes—
689C23×C4C2412yes—
690C23×C4C2412yes—
691C23×C4C2411yescharacteristic
692C23×C4C2411yescharacteristic
693C23×C4C2414yes—
694C4⋊Q8—82no—
695#127—82no—
696#126—28no—
697#126—84no—
698#125—24no—
699#124—216no—
700#124—28no—
701#124—28no—
702#124—28no—
703#124—28no—
704#124—24no—
705#124—84no—
706#124—82no—
707#124—82no—
708#123—28no—
709#123—216no—
710#123—216no—
711#123—84no—
712#123—84no—
713#123—84no—
714C22⋊Q8—24no—
715C22⋊Q8—216no—
716C22⋊Q8—84no—
717#121—24no—
718#121—216no—
719#121—216no—
720#121—216no—
721#121—84no—
722#121—84no—
723#120—216no—
724#120—216no—
725C4×Q8—24no—
726C4×Q8—84no—
727C4×D4—216no—
728C4×D4—216no—
729C4×D4—28no—
730C4×D4—216no—
731C4×D4—216no—
732C4×D4—216no—
733C4×D4—216no—
734C4×D4—28no—
735C4×D4—24no—
736C4×D4—24no—
737C4×D4—28no—
738C4×D4—24no—
739C4×D4—24no—
740C4×D4—24no—
741C4×D4—84no—
742C4×D4—84no—
743C4×D4—84no—
744C4×D4—84no—
745C4×D4—84no—
746C4×D4—84no—
747C4×D4—84no—
748#117—28no—
749#117—28no—
750#117—28no—
751#117—84no—
752#117—84no—
753C2×C4⋊C4—24no—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2412yes—
760C2×C4⋊C4C2412yes—
761C2×C4⋊C4C2414yes—
762C2×C4⋊C4C2411yescharacteristic
763C2×C4⋊C4C2414yes—
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C22⋊C4—28no—
785C2×C22⋊C4—28no—
786C2×C22⋊C4—28no—
787C2×C22⋊C4—28no—
788C2×C22⋊C4—28no—
789C2×C22⋊C4—28no—
790C2×C22⋊C4—216no—
791C2×C22⋊C4—84no—
792C2×C22⋊C4—84no—
793C2×C22⋊C4#41116yescomplemented
794C2×C22⋊C4C2412yes—
795C2×C22⋊C4C2412yes—
796C2×C22⋊C4C2414yes—
797C2×C22⋊C4C2412yes—
798C2×C22⋊C4C2412yes—
799C2×C22⋊C4C2412yes—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2414yes—
802C2×C22⋊C4C2414yes—
803C2×C22⋊C4C2414yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2412yes—
811C2×C22⋊C4C2412yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2414yes—
814C2×C22⋊C4C2414yes—
815C2×C22⋊C4C2412yes—
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2412yes—
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×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⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2414yes—
849C2×C42—84no—
850C2×C42—84no—
851C2×C42#4118yescomplemented
852C2×C42C2414yes—
853C2×C42C2414yes—
854C2×C42C2412yes—
855C2×C42C2414yes—
856C2×C42C2414yes—
857C2×C42C2414yes—
858C2×C42C2414yes—
859C2×C42C2414yes—
860C2×C42C2412yes—
861C2×C42C2412yes—
862C2×C42C2414yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2412yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2412yes—
870C2×C42C2412yes—
871C2×C42C2414yes—
872C2×C42C2411yescharacteristic
873C2×C42C2411yescharacteristic
874C2×C42C2411yescharacteristic
875C2×C42C2411yescharacteristic
876#95C2412yes—
877#95C2412yes—
878#95C2414yes—
879#95C2412yes—
880#95C2414yes—
881#95C2414yes—
882#95C2414yes—
883#95C2414yes—
884#95C2414yes—
885#95C2412yes—
886#95C2414yes—
887#95C2412yes—
888#95C2414yes—
889#95C2414yes—
890#95C2412yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2412yes—
895#95C2414yes—
896#95C2412yes—
897#95C2414yes—
898#95C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2412yes—
902#95C2412yes—
903#95C2414yes—
904#95C2414yes—
905#95C2412yes—
906#95C2412yes—
907#95C2414yes—
908#95C2414yes—
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—
929C24—24no—
930C24—24no—
931C24—24no—
932C24—28no—
933C24—44no—
934C24—44no—
935C24—42no—
936C24—44no—
937C24—42no—
938C24C2×#4118yes—
939C24C2514yes—
940C24C2512yes—
941C24C2512yes—
942C24C2512yes—
943C24C2511yescharacteristic
944#41—832no—
945C2×Q8—24no—
946C2×Q8—22no—
947C2×Q8—28no—
948C2×Q8—24no—
949C2×Q8—44no—
950C2×Q8—44no—
951C2×Q8—42no—
952C2×Q8—42no—
953C2×Q8—44no—
954C2×Q8—42no—
955C2×Q8—88no—
956C2×D4—232no—
957C2×D4—24no—
958C2×D4—24no—
959C2×D4—24no—
960C2×D4—24no—
961C2×D4—28no—
962C2×D4—24no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—28no—
967C2×D4—28no—
968C2×D4—28no—
969C2×D4—24no—
970C2×D4—22no—
971C2×D4—22no—
972C2×D4—24no—
973C2×D4—22no—
974C2×D4—28no—
975C2×D4—28no—
976C2×D4—24no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—44no—
980C2×D4—44no—
981C2×D4—44no—
982C2×D4—44no—
983C2×D4—44no—
984C2×D4—44no—
985C2×D4—44no—
986C2×D4—44no—
987C2×D4—44no—
988C2×D4—44no—
989C2×D4—44no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—44no—
993C2×D4—42no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—44no—
997C2×D4—88no—
998C2×D4—832no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—24no—
1002C22×C4—28no—
1003C22×C4—28no—
1004C22×C4—24no—
1005C22×C4—24no—
1006C22×C4—28no—
1007C22×C4—28no—
1008C22×C4—28no—
1009C22×C4—28no—
1010C22×C4—24no—
1011C22×C4—24no—
1012C22×C4—24no—
1013C22×C4—28no—
1014C22×C4—44no—
1015C22×C4—44no—
1016C22×C4—44no—
1017C22×C4—44no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C4—44no—
1039C22×C4—816no—
1040C22×C4C2×#4114yes—
1041C22×C4C2×#4114yes—
1042C22×C4C2×#4114yes—
1043C22×C4C2×#41116yes—
1044C22×C4C2514yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2514yes—
1053C22×C4C2514yes—
1054C22×C4C2512yes—
1055C22×C4C2512yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2514yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C22×C4C2514yes—
1064C4⋊C4—24no—
1065C4⋊C4—22no—
1066C4⋊C4—22no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—24no—
1070C4⋊C4—24no—
1071C4⋊C4—28no—
1072C4⋊C4—22no—
1073C4⋊C4—28no—
1074C4⋊C4—24no—
1075C4⋊C4—22no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—44no—
1093C4⋊C4—44no—
1094C22⋊C4—24no—
1095C22⋊C4—24no—
1096C22⋊C4—28no—
1097C22⋊C4—28no—
1098C22⋊C4—28no—
1099C22⋊C4—24no—
1100C22⋊C4—28no—
1101C22⋊C4—28no—
1102C22⋊C4—28no—
1103C22⋊C4—24no—
1104C22⋊C4—24no—
1105C22⋊C4—24no—
1106C22⋊C4—24no—
1107C22⋊C4—28no—
1108C22⋊C4—28no—
1109C22⋊C4—28no—
1110C22⋊C4—28no—
1111C22⋊C4—28no—
1112C22⋊C4—28no—
1113C22⋊C4—24no—
1114C22⋊C4—24no—
1115C22⋊C4—28no—
1116C22⋊C4—28no—
1117C22⋊C4—24no—
1118C22⋊C4—24no—
1119C22⋊C4—28no—
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⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4C2×#4118yes—
1147C22⋊C4C2×#4118yes—
1148C22⋊C4C2×#41116yes—
1149C42—28no—
1150C42—28no—
1151C42—24no—
1152C42—28no—
1153C42—42no—
1154C42—44no—
1155C42—42no—
1156C42—44no—
1157C42—44no—
1158C42—44no—
1159C42—44no—
1160C42—44no—
1161C42—44no—
1162C42—44no—
1163C42—42no—
1164C42—42no—
1165C42—44no—
1166C42—44no—
1167C42—42no—
1168C42—42no—
1169C42C2×#4114yes—
1170C42C2×#4114yes—
1171C42C2×#4114yes—
1172C42C2×#4114yes—
1173C23—22no—
1174C23—22no—
1175C23—22no—
1176C23—22no—
1177C23—22no—
1178C23—22no—
1179C23—24no—
1180C23—24no—
1181C23—24no—
1182C23—24no—
1183C23—216no—
1184C23—22no—
1185C23—24no—
1186C23—24no—
1187C23—24no—
1188C23—24no—
1189C23—24no—
1190C23—22no—
1191C23—24no—
1192C23—24no—
1193C23—22no—
1194C23—24no—
1195C23—24no—
1196C23—416no—
1197C23—48no—
1198C23—84no—
1199C23—88no—
1200C23—84no—
1201C23—88no—
1202C23—84no—
1203C23—88no—
1204C23—84no—
1205C23C22×#4114yes—
1206C23C22×#4114yes—
1207C23C22×#4114yes—
1208C23C22×#4112yes—
1209C23C2611yescharacteristic
1210Q8—48no—
1211Q8—82no—
1212Q8—84no—
1213Q8—88no—
1214D4—28no—
1215D4—216no—
1216D4—28no—
1217D4—48no—
1218D4—416no—
1219D4—416no—
1220D4—416no—
1221D4—48no—
1222D4—88no—
1223D4—82no—
1224D4—84no—
1225D4—88no—
1226D4—88no—
1227D4—88no—
1228D4—88no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—22no—
1234C2×C4—24no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—24no—
1239C2×C4—28no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—24no—
1243C2×C4—24no—
1244C2×C4—22no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—24no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—24no—
1260C2×C4—24no—
1261C2×C4—24no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—24no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—44no—
1273C2×C4—44no—
1274C2×C4—416no—
1275C2×C4—48no—
1276C2×C4—48no—
1277C2×C4—88no—
1278C2×C4—88no—
1279C2×C4—88no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—88no—
1284C2×C4—88no—
1285C2×C4—88no—
1286C2×C4—84no—
1287C2×C4—88no—
1288C2×C4—84no—
1289C2×C4C22×#4112yes—
1290C2×C4C22×#4118yes—
1291C2×C4C22×#4118yes—
1292C2×C4C22×#4112yes—
1293C2×C4C22×#4112yes—
1294C2×C4C22×#4112yes—
1295C2×C4C22×#4112yes—
1296C2×C4C22×#4112yes—
1297C22—28no—
1298C22—22no—
1299C22—22no—
1300C22—28no—
1301C22—28no—
1302C22—24no—
1303C22—24no—
1304C22—44no—
1305C22—44no—
1306C22—42no—
1307C22—42no—
1308C22—42no—
1309C22—42no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—42no—
1317C22—44no—
1318C22—42no—
1319C22—44no—
1320C22—42no—
1321C22—44no—
1322C22—816no—
1323C22—168no—
1324C22#344414yes—
1325C22C23×#4112yes—
1326C22C23×#4111yescharacteristic
1327C22H(7,𝔽2)12yes—
1328C22H(7,𝔽2)12yes—
1329C4—28no—
1330C4—28no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—22no—
1336C4—22no—
1337C4—44no—
1338C4—44no—
1339C4—44no—
1340C4—44no—
1341C4—44no—
1342C4—44no—
1343C4—42no—
1344C4—42no—
1345C4—42no—
1346C4—44no—
1347C4—42no—
1348C4—42no—
1349C2—24no—
1350C2—44no—
1351C2—44no—
1352C2—82no—
1353C2—84no—
1354C2C2×#344411yescharacteristic
1355C2#6284614yes—
1356C2#6285511yescharacteristic
1357C2#6285511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36074C2semidirect
2. #35992C2semidirect
3. #35977C2semidirect
4. #35784C2semidirect
5. #35769C2semidirect
6. #35754C2semidirect
7. #35706C2semidirect
8. #35705C2semidirect
9. #35695C2semidirect
10. #35694C2semidirect
11. #35684C2semidirect
12. #35681C2semidirect
13. #35146C2semidirect
14. #35133C2semidirect
15. #35131C2semidirect
16. #35048C2semidirect
17. #35044C2semidirect
18. #34998C2semidirect
19. #34593C2semidirect
20. #34589C2semidirect
21. C2×#2631C2semidirect
22. #34302C2semidirect
23. #34240C2semidirect
24. #34234C2semidirect
25. C4×#518C2semidirect
31. #2863C22semidirect
32. #2861C22semidirect
33. #2858C22semidirect
34. #2854C22semidirect
35. #2853C22semidirect
36. #2852C22semidirect
37. #2850C22semidirect
38. #2666C22semidirect
39. #2665C22semidirect
40. #2662C22semidirect
41. #2661C22semidirect
42. #2653C22semidirect
43. #2653C22semidirect
44. #2651C22semidirect
45. #2650C22semidirect
46. #2649C22semidirect
47. #2648C22semidirect
48. #2648C22semidirect
49. #2648C22semidirect
50. #2636C22semidirect
51. #2636C22semidirect
52. #2635C22semidirect
53. #2633C22semidirect
61. #2631C22semidirect
62. #2630C22semidirect
67. #2610C22semidirect
68. #2607C22semidirect
69. #2606C22semidirect
70. #2606C22semidirect
71. #2605C22semidirect
72. #2605C22semidirect
73. #2602C22semidirect
74. #2602C22semidirect
75. #2600C22semidirect
76. #2597C22semidirect
77. #2597C22semidirect
78. #2594C22semidirect
79. #2589C22semidirect
80. #2577C22semidirect
81. #2574C22semidirect
82. #2572C22semidirect
84. #2557C22semidirect
85. #2557C22semidirect
86. #2557C22semidirect
87. #2555C22semidirect
88. #2554C22semidirect
90. #2545C22semidirect
91. #2544C22semidirect
92. #2532C22semidirect
93. #2527C22semidirect
94. #2525C22semidirect
95. #2523C22semidirect
96. #2521C22semidirect
97. #2518C22semidirect
98. #2518C22semidirect
99. #2516C22semidirect
100. #2515C22semidirect
101. #2513C22semidirect
103. #2510C22semidirect
105. #2492C22semidirect
106. #2488C22semidirect
108. #2478C22semidirect
110. #2471C22semidirect
111. #2467C22semidirect
112. #2467C22semidirect
113. #2465C22semidirect
114. #2464C22semidirect
115. #2464C22semidirect
116. #2464C22semidirect
117. #2461C22semidirect
118. #2459C22semidirect
119. #2459C22semidirect
120. #2459C22semidirect
121. #2459C22semidirect
122. #2458C22semidirect
123. #2457C22semidirect
124. #2457C22semidirect
125. #2456C22semidirect
126. #2456C22semidirect
127. #2455C22semidirect
128. #2447C22semidirect
129. #2444C22semidirect
130. #2439C22semidirect
137. #2431C22semidirect
138. #2428C22semidirect
139. #2425C22semidirect
140. #2414C22semidirect
144. #2407C22semidirect
146. #2401C22semidirect
147. #2398C22semidirect
148. #2398C22semidirect
149. #2398C22semidirect
150. #2397C22semidirect
151. #2397C22semidirect
152. #2396C22semidirect
153. #2395C22semidirect
154. #2392C22semidirect
155. #2392C22semidirect
156. #2392C22semidirect
158. #2388C22semidirect
159. #2388C22semidirect
163. #2374C22semidirect
164. #2372C22semidirect
165. #2372C22semidirect
166. #2372C22semidirect
169. #2367C22semidirect
171. #2364C22semidirect
172. #2364C22semidirect
173. #2363C22semidirect
175. #2359C22semidirect
178. #2356C22semidirect
180. #2353C22semidirect
181. #2353C22semidirect
182. #2347C22semidirect
183. #2343C22semidirect
188. #2339C22semidirect
191. #2337C22semidirect
192. #2337C22semidirect
193. #2337C22semidirect
194. #2336C22semidirect
195. #2335C22semidirect
196. #2333C22semidirect
197. #2333C22semidirect
202. C4×#126C22semidirect
203. C4×#124C22semidirect
204. C4×#123C22semidirect
205. C4×#121C22semidirect
207. #2297C22semidirect
208. #2290C22semidirect
213. #2275C22semidirect
214. #2275C22semidirect
215. #2275C22semidirect
220. C42×D4C22semidirect
221. C42×D4C22semidirect
222. C42×D4C22semidirect
793. C2×C22⋊C4#41semidirect
851. C2×C42#41semidirect

Maximal subgroups

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

subgroupindex
#360742
#359922
#359772
#357842
#357692
#357542
#357062
#357052
#356952
#356942
#356842
#356812
#351462
#351332
#351312
#350482
#350442
#349982
#345932
#345892
C2×#26312
#343022
#342402
#342342
C4×#5182