Finite Group Databasebeta

← #7659294

Subgroups — #7659294

Order 512.

4855 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52276C213yesmaximal, complemented
2#42750C213yesmaximal, complemented
3#42551C213yesmaximal, complemented
4#42548C213yesmaximal, complemented
5#42543C213yesmaximal, complemented
6#42453C213yesmaximal, complemented
7#42452C213yesmaximal, complemented
8#40165C213yesmaximal, complemented
9#40152C213yesmaximal, complemented
10#40149C213yesmaximal, complemented
11#40052C213yesmaximal, complemented
12#39631C213yesmaximal, complemented
13#39199C213yesmaximal, complemented
14#37410C213yesmaximal, complemented
15#37330C213yesmaximal, complemented
16#37326C213yesmaximal, complemented
17#36578C211yesmaximal, characteristic, complemented
18Q8×#126C211yesmaximal, characteristic, complemented
19Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
20#36475C211yesmaximal, characteristic, complemented
21#36456C211yesmaximal, characteristic, complemented
22#36430C211yesmaximal, characteristic
23#36005C211yesmaximal, characteristic, complemented
24#35983C211yesmaximal, characteristic, complemented
25#35983C211yesmaximal, characteristic, complemented
26#35971C211yesmaximal, characteristic, complemented
27#35898C211yesmaximal, characteristic, complemented
28#35748C211yesmaximal, characteristic, complemented
29#34313C211yesmaximal, characteristic, complemented
30#34294C211yesmaximal, characteristic, complemented
31#34250C211yesmaximal, characteristic, complemented
32C2×Q82C2211yescharacteristic
33C2×#550C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×#520C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2864C2213yes—
42#2863C2213yes—
43#2857C2213yes—
44#2857C2213yes—
45#2854C2213yes—
46#2850C2213yes—
47#2835C2216yes—
48#2827C2216yes—
49#2807C2216yes—
50#2807C2213yes—
51#2805C2216yes—
52#2802C2213yes—
53#2798C2213yes—
54#2798C2216yes—
55#2796C2213yes—
56#2796C2213yes—
57#2786C2216yes—
58#2783C2213yes—
59#2782C2213yes—
60#2776C2213yes—
61#2773C2216yes—
62#2771C2216yes—
63#2757C2213yes—
64#2750C2216yes—
65#2747C2213yes—
66#2746C2213yes—
67#2745C2216yes—
68#2744C2216yes—
69#2740C2216yes—
70#2737C2216yes—
71#2732C2216yes—
72#2728C2216yes—
73#2723C2216yes—
74#2707C2216yes—
75#2696C2216yes—
76#2694C2213yes—
77#2693C2216yes—
78#2691C2213yes—
79#2690C2213yes—
80#2689C2211yescharacteristic
81#2689C2216yes—
82#2687C2216yes—
83#2681C2213yes—
84#2652C2216yes—
85#2647C2213yes—
86#2646C2216yes—
87#2644C2213yes—
88#2638C2216yes—
89#2638C2216yes—
90#2636C2216yes—
91#2628C2213yes—
92#2625C2213yes—
93#2625C2213yes—
94#2624C2213yes—
95#2623C2216yes—
96#2582C2213yes—
97#2580C2213yes—
98#2571C2213yes—
99#2570C2213yes—
100#2570C2213yes—
101#2570C2213yes—
102#2567C2213yes—
103#2563C2213yes—
104#2544C2213yes—
105#2542C2213yes—
106#2538C2213yes—
107#2535C2213yes—
108#2513C2213yes—
109#2512C2213yes—
110#2512C2213yes—
111#2511C2213yes—
112#2511C2213yes—
113#2511C2213yes—
114#2509C2213yes—
115#2509C2213yes—
116#2508C2213yes—
117#2508C2213yes—
118#2508C2213yes—
119#2507C2213yes—
120#2507C2213yes—
121#2506C2213yes—
122#2504C2213yes—
123#2503C2213yes—
124#2503C2213yes—
125#2501C2213yes—
126#2497C2213yes—
127#2497C2213yes—
128#2497C2213yes—
129#2497C2213yes—
130#2496C2213yes—
131#2494C2213yes—
132#2488C2216yes—
133#2487C2213yes—
134#2487C2213yes—
135#2487C2213yes—
136#2487C2213yes—
137#2466C2216yes—
138#2463C2216yes—
139#2452C2213yes—
140#2452C2213yes—
141#2452C2213yes—
142#2452C2213yes—
143#2451C2213yes—
144#2451C2213yes—
145#2449C2216yes—
146#2449C2216yes—
147#2448C2213yes—
148#2448C2213yes—
149#2447C2213yes—
150#2447C2213yes—
151#2447C2213yes—
152#2447C2213yes—
153#2445C2213yes—
154#2445C2213yes—
155#2440C2213yes—
156#2440C2213yes—
157#2440C2213yes—
158#2440C2213yes—
159#2439C2213yes—
160#2439C2213yes—
161#2428C2213yes—
162#2427C2213yes—
163#2422C2213yes—
164#2422C2213yes—
165#2421C2213yes—
166#2421C2213yes—
167#2420C2213yes—
168#2420C2213yes—
169#2420C2213yes—
170#2420C2213yes—
171#2419C2216yes—
172#2415C2213yes—
173#2414C2213yes—
174#2402C2213yes—
175#2401C2213yes—
176#2396C2213yes—
177#2395C2213yes—
178#2395C2213yes—
179#2395C2213yes—
180#2367C2213yes—
181#2366C2213yes—
182#2361C2213yes—
183#2361C2213yes—
184#2361C2213yes—
185#2360C2213yes—
186#2351C2211yescharacteristic
187#2351C2211yescharacteristic
188#2351C2211yescharacteristic
189#2351C2211yescharacteristic
190#2351C2211yescharacteristic
191#2351C2211yescharacteristic
192#2351C2211yescharacteristic
193Q8×C4⋊C4C2211yescharacteristic
194Q8×C4⋊C4C2211yescharacteristic
195Q8×C4⋊C4C2211yescharacteristic
196Q8×C4⋊C4C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200#2349C2213yes—
201#2349C2213yes—
202D4×C4⋊C4C2213yes—
203D4×C4⋊C4C2213yes—
204D4×C4⋊C4C2213yes—
205D4×C4⋊C4C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2326C2213yes—
217#2325C2216yes—
218#2324C2213yes—
219#2324C2213yes—
220#2323C2213yes—
221#2322C2216yes—
222#2317C2213yes—
223#2316C2213yes—
224C4×#127C2213yes—
225C4×#125C2213yes—
226C4×#126C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×C22⋊Q8C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2296C2213yes—
233#2293C2213yes—
234C2×#389C2213yes—
235#2290C2213yes—
236#2276C2211yescharacteristic
237C42×Q8C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241Q82—44no—
242#550—28no—
243#548—28no—
244#548—44no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×C4⋊Q8C2313yes—
248C2×#127C2313yes—
249C2×#126C2311yescharacteristic
250C2×#126C2316yes—
251C2×#125C2313yes—
252C2×#124C2313yes—
253C2×#124C2313yes—
254C2×#123C2316yes—
255C2×#123C2313yes—
256C2×#123C2316yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2313yes—
260C2×C22⋊Q8C2313yes—
261C2×C22⋊Q8C2316yes—
262C2×C22⋊Q8C2316yes—
263C2×C22⋊Q8C2316yes—
264C2×C22⋊Q8C2316yes—
265C2×#121C2313yes—
266C2×#121C2313yes—
267C2×#121C2313yes—
268C2×#121C2313yes—
269C2×#121C2313yes—
270#520—28no—
271#520—44no—
272#520—44no—
273C4×#41—44no—
274C2×C4×Q8—44no—
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2313yes—
288C2×C4×Q8C2313yes—
289C2×C4×Q8C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×C4×D4C2313yes—
296C2×C4×D4C2313yes—
297C2×C4×D4C2313yes—
298C2×C4×D4C2313yes—
299C2×C4×D4C2313yes—
300C2×C4×D4C2313yes—
301C2×C4×D4C2316yes—
302C2×C4×D4C2316yes—
303C2×C4×D4C2316yes—
304C2×#117C2313yes—
305C2×#117C2313yes—
306C2×#117C2313yes—
307C2×#117C2313yes—
308C22×C4⋊C4C2313yes—
309C22×C4⋊C4C2313yes—
310C22×C4⋊C4C2313yes—
311C22×C4⋊C4C2313yes—
312C22×C4⋊C4C2316yes—
313C22×C42C2313yes—
314C22×C42C2313yes—
315#401C2313yes—
316#400C2316yes—
317#400C2316yes—
318#400C2316yes—
319#400C2313yes—
320#400C2313yes—
321#400C2316yes—
322#400C2313yes—
323#400C2313yes—
324#400C2316yes—
325#400C2316yes—
326#400C2316yes—
327#400C2316yes—
328#400C2313yes—
329#400C2313yes—
330#400C2316yes—
331#400C2316yes—
332#400C2313yes—
333#400C2313yes—
334#400C2311yescharacteristic
335#400C2311yescharacteristic
336#400C2313yes—
337#399C2313yes—
338#399C2316yes—
339#399C2316yes—
340#399C2316yes—
341#399C2313yes—
342#399C2313yes—
343#399C2313yes—
344#398C2313yes—
345#398C2316yes—
346#398C2316yes—
347#398C2316yes—
348#398C2316yes—
349#398C2313yes—
350#398C2313yes—
351#398C2316yes—
352#398C2313yes—
353#398C2313yes—
354#398C2311yescharacteristic
355#398C2313yes—
356#398C2313yes—
357#398C2313yes—
358#397C2313yes—
359#397C2316yes—
360#397C2316yes—
361#397C2313yes—
362#397C2316yes—
363#397C2316yes—
364#397C2313yes—
365#397C2316yes—
366#397C2313yes—
367#397C2316yes—
368#397C2316yes—
369#397C2313yes—
370#397C2313yes—
371#397C2316yes—
372#397C2313yes—
373#397C2316yes—
374#397C2311yescharacteristic
375#397C2311yescharacteristic
376#397C2313yes—
377#397C2313yes—
378#397C2313yes—
379#396C2316yes—
380#396C2316yes—
381#396C2316yes—
382#396C2313yes—
383#396C2313yes—
384#396C2316yes—
385#396C2313yes—
386#395C2316yes—
387#395C2316yes—
388#395C2316yes—
389#395C2311yescharacteristic
390#394C2316yes—
391#394C2316yes—
392#394C2316yes—
393#394C2313yes—
394#394C2313yes—
395#394C2313yes—
396#394C2316yes—
397#394C2313yes—
398#394C2313yes—
399#394C2313yes—
400#393C2316yes—
401#393C2316yes—
402#393C2313yes—
403#393C2316yes—
404#392C2316yes—
405#391C2313yes—
406#391C2313yes—
407#391C2313yes—
408#391C2313yes—
409#391C2313yes—
410#391C2313yes—
411#391C2313yes—
412#391C2313yes—
413#391C2313yes—
414#391C2316yes—
415#391C2316yes—
416#391C2311yescharacteristic
417#390C2313yes—
418#390C2313yes—
419#390C2316yes—
420#390C2313yes—
421#390C2313yes—
422#390C2313yes—
423#390C2313yes—
424#390C2313yes—
425#390C2313yes—
426#390C2313yes—
427#390C2313yes—
428#390C2313yes—
429#390C2313yes—
430#390C2313yes—
431#390C2313yes—
432#390C2313yes—
433#389C2313yes—
434#389C2313yes—
435#389C2313yes—
436#389C2316yes—
437#389C2313yes—
438#389C2313yes—
439#389C2313yes—
440#389C2313yes—
441#389C2313yes—
442#389C2313yes—
443#389C2316yes—
444#389C2313yes—
445#389C2313yes—
446#389C2313yes—
447#389C2316yes—
448#389C2313yes—
449#389C2313yes—
450#389C2313yes—
451#389C2313yes—
452#389C2313yes—
453#389C2316yes—
454#389C2313yes—
455#389C2313yes—
456#389C2313yes—
457#389C2313yes—
458#389C2313yes—
459#389C2313yes—
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2313yes—
467#389C2313yes—
468#389C2313yes—
469#389C2313yes—
470#389C2313yes—
471#389C2313yes—
472#389C2313yes—
473#389C2311yescharacteristic
474#389C2311yescharacteristic
475#389C2313yes—
476#388C2313yes—
477#388C2313yes—
478#388C2313yes—
479#388C2313yes—
480#388C2316yes—
481#388C2316yes—
482#388C2316yes—
483#388C2313yes—
484#388C2313yes—
485#388C2316yes—
486#388C2313yes—
487#388C2313yes—
488#388C2316yes—
489#388C2316yes—
490#388C2316yes—
491#388C2313yes—
492#388C2313yes—
493#388C2313yes—
494#388C2311yescharacteristic
495#388C2313yes—
496#387C2313yes—
497#387C2313yes—
498#387C2313yes—
499#387C2311yescharacteristic
500#387C2313yes—
501#387C2313yes—
502#387C2313yes—
503#387C2316yes—
504#387C2316yes—
505#387C2316yes—
506#387C2316yes—
507#387C2313yes—
508#387C2316yes—
509#387C2316yes—
510#387C2316yes—
511#387C2316yes—
512#387C2313yes—
513#387C2313yes—
514#387C2316yes—
515#387C2313yes—
516#387C2313yes—
517#387C2313yes—
518#387C2313yes—
519#387C2313yes—
520#386C2316yes—
521#386C2316yes—
522#386C2316yes—
523#386C2316yes—
524#386C2316yes—
525#386C2316yes—
526#386C2316yes—
527#386C2316yes—
528#386C2313yes—
529#386C2313yes—
530#386C2313yes—
531#386C2313yes—
532#386C2313yes—
533#385C2316yes—
534#385C2316yes—
535#385C2316yes—
536#385C2313yes—
537#385C2316yes—
538#385C2316yes—
539#385C2316yes—
540#385C2316yes—
541#385C2316yes—
542#385C2316yes—
543#385C2313yes—
544#385C2313yes—
545#385C2313yes—
546#385C2313yes—
547#385C2313yes—
548#385C2313yes—
549#385C2313yes—
550#385C2313yes—
551#385C2316yes—
552#385C2316yes—
553#385C2311yescharacteristic
554#385C2313yes—
555#384C2313yes—
556#384C2313yes—
557#384C2313yes—
558#384C2313yes—
559#384C2313yes—
560#384C2313yes—
561#384C2313yes—
562#383C2313yes—
563#382C2313yes—
564#382C2313yes—
565#382C2313yes—
566#382C2313yes—
567#382C2313yes—
568#382C2313yes—
569#382C2313yes—
570#382C2313yes—
571#382C2316yes—
572#381C2316yes—
573#381C2316yes—
574#381C2316yes—
575#381C2316yes—
576#381C2311yescharacteristic
577#380C2313yes—
578#380C2316yes—
579#380C2316yes—
580#380C2316yes—
581#380C2313yes—
582#380C2313yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593C4×C4⋊C4C2313yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2313yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C22⋊C4C2313yes—
614C4×C22⋊C4C2313yes—
615C4×C22⋊C4C2313yes—
616C4×C22⋊C4C2316yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624#376C2313yes—
625C2×#95C2316yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C2×#41—24no—
631C2×#41—24no—
632C2×#41#4118yes—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2411yescharacteristic
638C22×Q8C2416yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2413yes—
644C22×D4C2413yes—
645C22×D4C2416yes—
646C23×C4C2413yes—
647C23×C4C2413yes—
648C23×C4C2411yescharacteristic
649C23×C4C2413yes—
650C23×C4C2416yes—
651C23×C4C2413yes—
652C23×C4C2416yes—
653C23×C4C2413yes—
654C23×C4C2413yes—
655C23×C4C2416yes—
656C4⋊Q8—46no—
657C4⋊Q8—46no—
658C4⋊Q8—46no—
659#127—212no—
660#126—24no—
661#126—86no—
662#125—46no—
663#124—212no—
664#124—46no—
665#123—412no—
666#123—46no—
667#123—86no—
668C22⋊Q8—212no—
669C22⋊Q8—24no—
670C22⋊Q8—46no—
671C22⋊Q8—46no—
672C22⋊Q8—86no—
673C22⋊Q8—86no—
674C22⋊Q8—86no—
675C22⋊Q8—86no—
676#121—212no—
677#121—212no—
678#121—212no—
679#121—212no—
680#121—46no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—24no—
687C4×Q8—24no—
688C4×Q8—24no—
689C4×Q8—24no—
690C4×Q8—24no—
691C4×Q8—24no—
692C4×Q8—24no—
693C4×Q8—46no—
694C4×Q8—46no—
695C4×Q8—46no—
696C4×D4—212no—
697C4×D4—212no—
698C4×D4—212no—
699C4×D4—212no—
700C4×D4—46no—
701C4×D4—46no—
702C4×D4—46no—
703C4×D4—46no—
704C4×D4—46no—
705C4×D4—46no—
706C4×D4—46no—
707C4×D4—86no—
708C4×D4—86no—
709C4×D4—86no—
710#117—212no—
711#117—46no—
712#117—46no—
713#117—46no—
714C2×C4⋊C4—212no—
715C2×C4⋊C4—46no—
716C2×C4⋊C4—46no—
717C2×C4⋊C4—46no—
718C2×C4⋊C4—86no—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2413yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2411yescharacteristic
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2416yes—
750C2×C4⋊C4C2416yes—
751C2×C4⋊C4C2416yes—
752C2×C4⋊C4C2411yescharacteristic
753C2×C4⋊C4C2411yescharacteristic
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2413yes—
756C2×C4⋊C4C2416yes—
757C2×C4⋊C4C2416yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2416yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2413yes—
772C2×C4⋊C4C2413yes—
773C2×C4⋊C4C2416yes—
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2413yes—
776C2×C4⋊C4C2413yes—
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2413yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2413yes—
785C2×C22⋊C4C2416yes—
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2411yescharacteristic
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2411yescharacteristic
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2413yes—
796C2×C22⋊C4C2413yes—
797C2×C22⋊C4C2411yescharacteristic
798C2×C22⋊C4C2413yes—
799C2×C22⋊C4C2413yes—
800C2×C22⋊C4C2413yes—
801C2×C22⋊C4C2416yes—
802C2×C22⋊C4C2416yes—
803C2×C22⋊C4C2413yes—
804C2×C22⋊C4C2416yes—
805C2×C22⋊C4C2416yes—
806C2×C22⋊C4C2413yes—
807C2×C22⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2416yes—
811C2×C22⋊C4C2416yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2413yes—
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2411yescharacteristic
820C2×C42—46no—
821C2×C42—46no—
822C2×C42C2413yes—
823C2×C42C2413yes—
824C2×C42C2413yes—
825C2×C42C2413yes—
826C2×C42C2413yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830C2×C42C2413yes—
831C2×C42C2413yes—
832C2×C42C2413yes—
833C2×C42C2413yes—
834C2×C42C2411yescharacteristic
835C2×C42C2413yes—
836C2×C42C2413yes—
837C2×C42C2413yes—
838C2×C42C2416yes—
839C2×C42C2413yes—
840C2×C42C2413yes—
841C2×C42C2413yes—
842C2×C42C2411yescharacteristic
843#95C2413yes—
844#95C2413yes—
845#95C2416yes—
846#95C2416yes—
847#95C2411yescharacteristic
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2411yescharacteristic
852#95C2411yescharacteristic
853#95C2411yescharacteristic
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2416yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2411yescharacteristic
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2416yes—
878#95C2411yescharacteristic
879#95C2411yescharacteristic
880#95C2411yescharacteristic
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2413yes—
885#95C2413yes—
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2416yes—
900#95C2416yes—
901#95C2416yes—
902#95C2416yes—
903#95C2416yes—
904#95C2416yes—
905#95C2416yes—
906#95C2416yes—
907C24C2513yes—
908C24C2513yes—
909C24C2511yescharacteristic
910#41—232no—
911#41—416no—
912C2×Q8—26no—
913C2×Q8—26no—
914C2×Q8—22no—
915C2×Q8—26no—
916C2×Q8—22no—
917C2×Q8—41no—
918C2×Q8—46no—
919C2×Q8—46no—
920C2×Q8—46no—
921C2×Q8—416no—
922C2×Q8C2×#4114yes—
923C2×Q8H(5,𝔽2)14yes—
924C2×Q82−1+414yes—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—212no—
929C2×D4—26no—
930C2×D4—26no—
931C2×D4—26no—
932C2×D4—26no—
933C2×D4—26no—
934C2×D4—26no—
935C2×D4—26no—
936C2×D4—43no—
937C2×D4—43no—
938C2×D4—43no—
939C2×D4—46no—
940C2×D4—46no—
941C2×D4—43no—
942C2×D4C2×#41112yes—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—22no—
946C22×C4—212no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—22no—
954C22×C4—26no—
955C22×C4—41no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4—46no—
961C22×C4—43no—
962C22×C4—43no—
963C22×C4—43no—
964C22×C4—43no—
965C22×C4—46no—
966C22×C4—46no—
967C22×C4—46no—
968C22×C4—46no—
969C22×C4—46no—
970C22×C4—46no—
971C22×C4—46no—
972C22×C4C2×#41112yes—
973C22×C4C2511yescharacteristic
974C22×C4C2511yescharacteristic
975C22×C4C2513yes—
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2511yescharacteristic
980C22×C4C2511yescharacteristic
981C22×C4C2511yescharacteristic
982C22×C4C2513yes—
983C22×C4C2513yes—
984C22×C4C2511yescharacteristic
985C22×C4C2513yes—
986C22×C4C2513yes—
987C22×C4C2513yes—
988C22×C4C2511yescharacteristic
989C22×C4C2513yes—
990C22×C4C2513yes—
991C22×C4C2511yescharacteristic
992C22×C4C2513yes—
993C22×C4C2511yescharacteristic
994C22×C4C2513yes—
995C22×C4C2513yes—
996C22×C4C2511yescharacteristic
997C22×C4C2511yescharacteristic
998C22×C4C2511yescharacteristic
999C22×C4C2511yescharacteristic
1000C22×C4C2513yes—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—26no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
1020C4⋊C4—22no—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—26no—
1025C4⋊C4—26no—
1026C4⋊C4—22no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—46no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—46no—
1034C4⋊C4—41no—
1035C4⋊C4—41no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—46no—
1039C4⋊C4—46no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—43no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4—43no—
1046C4⋊C4—43no—
1047C4⋊C4—43no—
1048C4⋊C4—43no—
1049C4⋊C4—43no—
1050C4⋊C4—43no—
1051C4⋊C4—46no—
1052C4⋊C4—46no—
1053C4⋊C4—46no—
1054C4⋊C4—43no—
1055C4⋊C4—43no—
1056C4⋊C4—43no—
1057C4⋊C4—43no—
1058C4⋊C4—43no—
1059C4⋊C4—43no—
1060C4⋊C4—43no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—26no—
1064C22⋊C4—26no—
1065C22⋊C4—212no—
1066C22⋊C4—22no—
1067C22⋊C4—22no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—26no—
1071C22⋊C4—26no—
1072C22⋊C4—26no—
1073C22⋊C4—26no—
1074C22⋊C4—43no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—43no—
1078C22⋊C4—46no—
1079C22⋊C4—41no—
1080C22⋊C4—43no—
1081C22⋊C4—43no—
1082C22⋊C4—43no—
1083C22⋊C4—43no—
1084C22⋊C4—46no—
1085C22⋊C4—46no—
1086C22⋊C4—46no—
1087C22⋊C4—46no—
1088C22⋊C4—43no—
1089C22⋊C4—43no—
1090C22⋊C4—43no—
1091C22⋊C4—43no—
1092C22⋊C4—43no—
1093C22⋊C4—46no—
1094C22⋊C4—46no—
1095C22⋊C4—43no—
1096C22⋊C4—43no—
1097C22⋊C4—46no—
1098C22⋊C4—43no—
1099C22⋊C4—43no—
1100C22⋊C4—43no—
1101C22⋊C42−1+414yes—
1102C42—26no—
1103C42—26no—
1104C42—26no—
1105C42—26no—
1106C42—26no—
1107C42—26no—
1108C42—26no—
1109C42—26no—
1110C42—26no—
1111C42—26no—
1112C42—26no—
1113C42—26no—
1114C42—22no—
1115C42—41no—
1116C42—43no—
1117C42—43no—
1118C42—43no—
1119C42—43no—
1120C42—43no—
1121C42—46no—
1122C42—43no—
1123C23—21no—
1124C23—23no—
1125C23—21no—
1126C23—21no—
1127C23—23no—
1128C23—23no—
1129C23—23no—
1130C23—21no—
1131C23—21no—
1132C23—23no—
1133C23—21no—
1134C23—23no—
1135C23—23no—
1136C23—23no—
1137C23—23no—
1138C23—23no—
1139C23—23no—
1140C23—23no—
1141C23—23no—
1142C23C22×#4116yes—
1143C23C2×2−1+412yes—
1144C23C2611yescharacteristic
1145Q8—44no—
1146Q8—412no—
1147Q8—166no—
1148Q8#539116yes—
1149D4—224no—
1150D4—412no—
1151D4—412no—
1152D4—412no—
1153D4—812no—
1154D4—86no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—224no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—23no—
1171C2×C4—21no—
1172C2×C4—23no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—23no—
1181C2×C4—23no—
1182C2×C4—23no—
1183C2×C4—23no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—21no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—23no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—23no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—23no—
1214C2×C4—23no—
1215C2×C4—23no—
1216C2×C4—23no—
1217C2×C4—23no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—23no—
1223C2×C4—23no—
1224C2×C4—23no—
1225C2×C4—23no—
1226C2×C4—23no—
1227C2×C4—23no—
1228C2×C4—23no—
1229C2×C4—23no—
1230C2×C4—23no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—44no—
1234C2×C4—412no—
1235C2×C4—412no—
1236C2×C4—86no—
1237C2×C4—812no—
1238C2×C4—86no—
1239C2×C4—86no—
1240C2×C4—166no—
1241C2×C4—166no—
1242C2×C4C22×#4112yes—
1243C2×C4C22×#4116yes—
1244C2×C4C2×H(5,𝔽2)16yes—
1245C2×C4C2×2−1+412yes—
1246C2×C4C2×2−1+412yes—
1247C2×C4C2×2−1+416yes—
1248C2×C4#58512yes—
1249C22—22no—
1250C22—26no—
1251C22—26no—
1252C22—22no—
1253C22—26no—
1254C22—22no—
1255C22—41no—
1256C22—43no—
1257C22—41no—
1258C22—43no—
1259C22—41no—
1260C22—43no—
1261C22—41no—
1262C22—43no—
1263C22—43no—
1264C22—43no—
1265C22—43no—
1266C22—43no—
1267C22—43no—
1268C22—43no—
1269C22—43no—
1270C22C23×#4111yescharacteristic
1271C22C22×H(5,𝔽2)11yescharacteristic
1272C22C22×2−1+411yescharacteristic
1273C22C22×2−1+411yescharacteristic
1274C22C2×#58511yescharacteristic
1275C22H(7,𝔽2)11yescharacteristic
1276C22H(7,𝔽2)11yescharacteristic
1277C4—22no—
1278C4—22no—
1279C4—22no—
1280C4—22no—
1281C4—41no—
1282C4—41no—
1283C4—43no—
1284C4—41no—
1285C4—43no—
1286C4—43no—
1287C4—43no—
1288C4—41no—
1289C4—41no—
1290C4—43no—
1291C4—41no—
1292C4—41no—
1293C4—43no—
1294C4—43no—
1295C4—43no—
1296C4—43no—
1297C4—43no—
1298C4—41no—
1299C4—43no—
1300C4—41no—
1301C4—41no—
1302C4—43no—
1303C4—43no—
1304C4C2×#539112yes—
1305C2—42no—
1306C2—46no—
1307C2—83no—
1308C2C22×#53911yescharacteristic
1309C2#6294311yescharacteristic
1310C2#6295211yescharacteristic
1311C2#6300011yescharacteristic
1312C2#6301011yescharacteristic
1313C2#6301511yescharacteristic
1314C2#6306611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36430C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52276C2semidirect
2. #42750C2semidirect
3. #42551C2semidirect
4. #42548C2semidirect
5. #42543C2semidirect
6. #42453C2semidirect
7. #42452C2semidirect
8. #40165C2semidirect
9. #40152C2semidirect
10. #40149C2semidirect
11. #40052C2semidirect
12. #39631C2semidirect
13. #39199C2semidirect
14. #37410C2semidirect
15. #37330C2semidirect
16. #37326C2semidirect
17. #36578C2semidirect
18. Q8×#126C2semidirect
19. Q8×C22⋊Q8C2semidirect
20. #36475C2semidirect
21. #36456C2semidirect
23. #36005C2semidirect
24. #35983C2semidirect
25. #35983C2semidirect
26. #35971C2semidirect
27. #35898C2semidirect
28. #35748C2semidirect
29. #34313C2semidirect
30. #34294C2semidirect
31. #34250C2semidirect

Maximal subgroups

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

subgroupindex
#522762
#427502
#425512
#425482
#425432
#424532
#424522
#401652
#401522
#401492
#400522
#396312
#391992
#374102
#373302
#373262
#365782
Q8×#1262
Q8×C22⋊Q82
#364752
#364562
#364302
#360052
#359832
#359712
#358982
#357482
#343132
#342942
#342502