Finite Group Databasebeta

← #7697204

Subgroups — #7697204

Order 512.

4803 conjugacy classes of subgroups.

The subgroup lattice has 1449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59873C212yesmaximal, complemented
2#59821C211yesmaximal, characteristic, complemented
3#59542C214yesmaximal, complemented
4#59487C212yesmaximal, complemented
5#52280C212yesmaximal, complemented
6#52272C211yesmaximal, characteristic, complemented
7#45269C212yesmaximal, complemented
8#45123C212yesmaximal, complemented
9#44998C212yesmaximal, complemented
10#44130C214yesmaximal, complemented
11#44016C214yesmaximal, complemented
12#43972C214yesmaximal, complemented
13#39629C211yesmaximal, characteristic, complemented
14#39582C212yesmaximal, complemented
15#39500C211yesmaximal, characteristic, complemented
16#39287C212yesmaximal, complemented
17#38736C214yesmaximal, complemented
18#38467C212yesmaximal, complemented
19#38226C212yesmaximal, complemented
20#38192C214yesmaximal, complemented
21#36490C212yesmaximal, complemented
22#36476C211yesmaximal, characteristic, complemented
23#35905C212yesmaximal, complemented
24#35880C212yesmaximal, complemented
25#35704C212yesmaximal, complemented
26#34330C211yesmaximal, characteristic, complemented
27#34326C212yesmaximal, complemented
28#34308C211yesmaximal, characteristic, complemented
29#34263C212yesmaximal, complemented
30C2×#556C2212yes—
31C2×#550C2211yescharacteristic
32C2×#547C2211yescharacteristic
33C2×#520C2212yes—
34#2866C2214yes—
35#2862C2211yescharacteristic
36#2860C2212yes—
37#2855C2212yes—
38#2810C2211yescharacteristic
39#2808C2212yes—
40#2808C2211yescharacteristic
41#2808C2212yes—
42#2806C2212yes—
43#2806C2212yes—
44#2805C2211yescharacteristic
45#2805C2212yes—
46#2805C2212yes—
47#2803C2214yes—
48#2800C2212yes—
49#2800C2214yes—
50#2798C2212yes—
51#2794C2214yes—
52#2793C2212yes—
53#2793C2214yes—
54#2781C2214yes—
55#2779C2214yes—
56#2776C2212yes—
57#2775C2214yes—
58#2774C2214yes—
59#2761C2214yes—
60#2759C2212yes—
61#2756C2214yes—
62#2753C2214yes—
63#2752C2214yes—
64#2746C2214yes—
65#2743C2214yes—
66#2737C2214yes—
67#2733C2212yes—
68#2733C2212yes—
69#2730C2214yes—
70#2727C2211yescharacteristic
71#2727C2212yes—
72#2727C2212yes—
73#2716C2212yes—
74#2714C2214yes—
75#2714C2214yes—
76#2706C2214yes—
77#2696C2214yes—
78#2696C2214yes—
79#2687C2214yes—
80#2652C2214yes—
81#2650C2214yes—
82#2647C2212yes—
83#2644C2212yes—
84#2635C2214yes—
85#2619C2212yes—
86#2610C2214yes—
87#2607C2214yes—
88#2602C2214yes—
89#2597C2214yes—
90#2597C2214yes—
91#2596C2214yes—
92#2596C2214yes—
93#2591C2214yes—
94#2589C2214yes—
95#2589C2214yes—
96#2587C2214yes—
97#2581C2212yes—
98#2580C2212yes—
99#2578C2214yes—
100#2573C2214yes—
101#2572C2214yes—
102#2570C2212yes—
103#2564C2214yes—
104#2563C2211yescharacteristic
105#2557C2214yes—
106#2554C2214yes—
107#2553C2214yes—
108#2548C2212yes—
109#2542C2211yescharacteristic
110#2542C2212yes—
111#2538C2212yes—
112#2535C2212yes—
113#2533C2214yes—
114#2529C2214yes—
115#2527C2214yes—
116#2526C2214yes—
117#2524C2214yes—
118#2521C2214yes—
119#2520C2214yes—
120#2520C2214yes—
121#2516C2214yes—
122#2515C2214yes—
123#2512C2214yes—
124#2509C2212yes—
125#2508C2212yes—
126#2498C2214yes—
127#2497C2212yes—
128#2495C2212yes—
129#2492C2212yes—
130#2491C2212yes—
131#2491C2212yes—
132#2488C2214yes—
133#2481C2214yes—
134#2481C2214yes—
135#2481C2214yes—
136#2477C2214yes—
137#2477C2214yes—
138#2476C2214yes—
139#2476C2214yes—
140#2474C2214yes—
141#2471C2214yes—
142#2471C2214yes—
143#2469C2214yes—
144#2468C2214yes—
145#2467C2214yes—
146#2466C2214yes—
147#2461C2214yes—
148#2459C2214yes—
149#2459C2214yes—
150#2457C2214yes—
151#2456C2214yes—
152#2456C2214yes—
153#2451C2212yes—
154#2451C2212yes—
155#2450C2214yes—
156#2448C2212yes—
157#2448C2212yes—
158#2447C2214yes—
159#2445C2212yes—
160#2445C2212yes—
161#2431C2212yes—
162#2431C2212yes—
163#2426C2212yes—
164#2426C2212yes—
165#2423C2212yes—
166#2422C2212yes—
167#2421C2212yes—
168#2421C2212yes—
169#2420C2212yes—
170#2419C2214yes—
171#2415C2214yes—
172#2413C2214yes—
173#2406C2214yes—
174#2401C2212yes—
175#2398C2212yes—
176#2396C2212yes—
177#2395C2214yes—
178#2392C2214yes—
179#2388C2214yes—
180#2373C2214yes—
181#2373C2214yes—
182#2369C2211yescharacteristic
183#2368C2214yes—
184#2367C2212yes—
185#2367C2212yes—
186#2366C2212yes—
187#2366C2211yescharacteristic
188#2365C2211yescharacteristic
189#2365C2211yescharacteristic
190#2364C2214yes—
191#2363C2212yes—
192#2361C2212yes—
193#2361C2212yes—
194#2361C2212yes—
195#2360C2212yes—
196#2359C2214yes—
197#2357C2212yes—
198#2357C2212yes—
199#2357C2214yes—
200#2357C2212yes—
201#2356C2212yes—
202#2355C2212yes—
203#2355C2212yes—
204#2355C2211yescharacteristic
205#2354C2211yescharacteristic
206#2354C2214yes—
207#2354C2212yes—
208#2353C2214yes—
209#2351C2212yes—
210Q8×C4⋊C4C2212yes—
211D4×C4⋊C4C2211yescharacteristic
212D4×C4⋊C4C2211yescharacteristic
213#2345C2212yes—
214#2345C2214yes—
215#2344C2212yes—
216#2344C2212yes—
217#2344C2214yes—
218#2343C2214yes—
219#2341C2212yes—
220#2341C2212yes—
221#2339C2212yes—
222#2339C2212yes—
223#2334C2214yes—
224#2333C2214yes—
225#2332C2214yes—
226#2328C2212yes—
227#2327C2212yes—
228#2326C2212yes—
229#2323C2212yes—
230#2322C2214yes—
231#2319C2212yes—
232#2319C2214yes—
233#2314C2214yes—
234#2314C2212yes—
235C4×C4⋊Q8C2211yescharacteristic
236C4×C4⋊Q8C2211yescharacteristic
237C4×#127C2211yescharacteristic
238C4×#126C2214yes—
239C4×#126C2212yes—
240C4×#124C2212yes—
241C4×#124C2214yes—
242C4×C22⋊Q8C2212yes—
243C4×#121C2212yes—
244C4×#121C2212yes—
245#2298C2214yes—
246#2298C2214yes—
247#2298C2212yes—
248#2297C2212yes—
249#2295C2212yes—
250#2295C2211yescharacteristic
251#2293C2211yescharacteristic
252#2293C2214yes—
253#2293C2212yes—
254C2×#389C2212yes—
255#2276C2212yes—
256#2275C2212yes—
257C42×Q8C2212yes—
258C42×D4C2211yescharacteristic
259C22×#41C2312yes—
260C22×#41C2312yes—
261#556—216no—
262#550—28no—
263#547—28no—
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×#127C2311yescharacteristic
269C2×#127C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#124C2312yes—
275C2×#124C2312yes—
276C2×#124C2314yes—
277C2×#124C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2312yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2312yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2314yes—
287C2×#121C2314yes—
288C2×#121C2312yes—
289C2×#121C2312yes—
290C2×#121C2312yes—
291C2×#121C2312yes—
292#520—216no—
293C2×C4×Q8C2312yes—
294C2×C4×Q8C2312yes—
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2312yes—
297C2×C4×Q8C2312yes—
298C2×C4×Q8C2312yes—
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2314yes—
304C2×C4×D4C2312yes—
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2311yescharacteristic
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2312yes—
310C2×C4×D4C2311yescharacteristic
311C2×C4×D4C2314yes—
312C2×C4×D4C2312yes—
313C2×C4×D4C2312yes—
314C2×C4×D4C2312yes—
315C2×C4×D4C2312yes—
316C2×C4×D4C2314yes—
317C2×C4×D4C2314yes—
318C2×C4×D4C2311yescharacteristic
319C2×#117C2312yes—
320C2×#117C2314yes—
321C2×#117C2314yes—
322C2×#117C2312yes—
323C2×#117C2314yes—
324C2×#117C2314yes—
325C22×C4⋊C4C2314yes—
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2312yes—
328C22×C4⋊C4C2312yes—
329C22×C42C2312yes—
330#401C2312yes—
331#400C2312yes—
332#400C2314yes—
333#400C2314yes—
334#400C2312yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2312yes—
339#400C2314yes—
340#400C2312yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2314yes—
346#400C2312yes—
347#400C2314yes—
348#399C2314yes—
349#399C2314yes—
350#399C2314yes—
351#399C2314yes—
352#399C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2312yes—
360#398C2314yes—
361#397C2314yes—
362#397C2312yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2312yes—
373#397C2314yes—
374#397C2312yes—
375#397C2312yes—
376#397C2312yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2312yes—
382#396C2312yes—
383#396C2314yes—
384#396C2312yes—
385#396C2314yes—
386#395C2314yes—
387#395C2314yes—
388#395C2314yes—
389#395C2312yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#394C2312yes—
402#394C2314yes—
403#394C2314yes—
404#394C2314yes—
405#394C2312yes—
406#393C2314yes—
407#393C2314yes—
408#393C2314yes—
409#393C2314yes—
410#393C2312yes—
411#393C2312yes—
412#393C2312yes—
413#392C2314yes—
414#392C2314yes—
415#392C2314yes—
416#392C2314yes—
417#392C2314yes—
418#392C2314yes—
419#392C2314yes—
420#391C2312yes—
421#391C2312yes—
422#391C2314yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2314yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2311yescharacteristic
433#391C2312yes—
434#391C2312yes—
435#391C2312yes—
436#391C2312yes—
437#391C2312yes—
438#391C2311yescharacteristic
439#390C2312yes—
440#390C2312yes—
441#390C2312yes—
442#390C2312yes—
443#390C2312yes—
444#390C2312yes—
445#390C2314yes—
446#390C2314yes—
447#390C2312yes—
448#390C2312yes—
449#390C2314yes—
450#390C2314yes—
451#390C2314yes—
452#390C2314yes—
453#390C2314yes—
454#390C2314yes—
455#390C2312yes—
456#390C2314yes—
457#390C2312yes—
458#390C2311yescharacteristic
459#390C2312yes—
460#390C2312yes—
461#390C2311yescharacteristic
462#389C2312yes—
463#389C2312yes—
464#389C2311yescharacteristic
465#389C2312yes—
466#389C2311yescharacteristic
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2314yes—
473#389C2312yes—
474#389C2314yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2312yes—
479#389C2314yes—
480#389C2314yes—
481#389C2312yes—
482#389C2312yes—
483#389C2311yescharacteristic
484#389C2312yes—
485#389C2314yes—
486#389C2314yes—
487#389C2312yes—
488#389C2311yescharacteristic
489#389C2312yes—
490#389C2311yescharacteristic
491#389C2311yescharacteristic
492#388C2314yes—
493#388C2312yes—
494#388C2314yes—
495#388C2312yes—
496#388C2314yes—
497#388C2312yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2312yes—
508#388C2314yes—
509#388C2312yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2312yes—
533#388C2314yes—
534#388C2312yes—
535#388C2312yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2312yes—
541#387C2312yes—
542#387C2314yes—
543#387C2312yes—
544#387C2312yes—
545#387C2312yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2312yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#387C2314yes—
582#387C2312yes—
583#387C2312yes—
584#387C2312yes—
585#387C2312yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#384C2311yescharacteristic
621#384C2314yes—
622#384C2312yes—
623#383C2312yes—
624#383C2314yes—
625#383C2314yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2312yes—
630#382C2312yes—
631#382C2314yes—
632#382C2314yes—
633#381C2314yes—
634#381C2314yes—
635#381C2314yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#380C2312yes—
641#380C2312yes—
642#380C2314yes—
643#380C2314yes—
644#380C2312yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2314yes—
649#380C2314yes—
650#380C2312yes—
651#380C2312yes—
652C4×C4⋊C4C2311yescharacteristic
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2312yes—
657C4×C4⋊C4C2312yes—
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2314yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2311yescharacteristic
666C4×C4⋊C4C2314yes—
667C4×C4⋊C4C2314yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2314yes—
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2311yescharacteristic
684C4×C22⋊C4C2314yes—
685C4×C22⋊C4C2312yes—
686C4×C22⋊C4C2312yes—
687C4×C22⋊C4C2314yes—
688C4×C22⋊C4C2312yes—
689C4×C22⋊C4C2314yes—
690C4×C22⋊C4C2314yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2312yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2314yes—
706C4×C22⋊C4C2312yes—
707#376C2312yes—
708#376C2314yes—
709#376C2312yes—
710#376C2314yes—
711C2×#95C2314yes—
712C2×#95C2314yes—
713C43C2312yes—
714C43C2314yes—
715C43C2311yescharacteristic
716C2×#41—28no—
717C2×#41—28no—
718C2×#41—28no—
719C2×#41—44no—
720C2×#41—82no—
721C2×#41—82no—
722C22×Q8C2412yes—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2411yescharacteristic
730C22×D4C2411yescharacteristic
731C22×D4C2412yes—
732C22×D4C2414yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C22×D4C2414yes—
737C23×C4C2412yes—
738C23×C4C2414yes—
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2414yes—
743C23×C4C2414yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C4⋊Q8—42no—
748C4⋊Q8—42no—
749C4⋊Q8—42no—
750C4⋊Q8#4118yescomplemented
751#127—28no—
752#127—24no—
753#126—216no—
754#126—216no—
755#126—44no—
756#126—84no—
757#124—28no—
758#124—28no—
759#124—48no—
760#124—84no—
761#123—216no—
762#123—84no—
763#123—84no—
764#123—84no—
765C22⋊Q8—28no—
766C22⋊Q8—216no—
767C22⋊Q8—44no—
768C22⋊Q8—84no—
769C22⋊Q8—82no—
770#121—28no—
771#121—28no—
772#121—216no—
773#121—44no—
774#121—44no—
775C4×Q8—28no—
776C4×Q8—28no—
777C4×Q8—28no—
778C4×Q8—28no—
779C4×Q8—24no—
780C4×Q8—28no—
781C4×Q8—44no—
782C4×Q8—44no—
783C4×Q8—82no—
784C4×D4—28no—
785C4×D4—216no—
786C4×D4—28no—
787C4×D4—216no—
788C4×D4—24no—
789C4×D4—24no—
790C4×D4—28no—
791C4×D4—44no—
792C4×D4—44no—
793C4×D4—42no—
794C4×D4—48no—
795C4×D4—82no—
796C4×D4—82no—
797C4×D4—84no—
798C4×D4—82no—
799C4×D4—84no—
800C4×D4#4118yes—
801#117—216no—
802#117—216no—
803#117—28no—
804#117—82no—
805#117—84no—
806#117—84no—
807C2×C4⋊C4—216no—
808C2×C4⋊C4—28no—
809C2×C4⋊C4—28no—
810C2×C4⋊C4—82no—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2411yescharacteristic
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2411yescharacteristic
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2411yescharacteristic
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2411yescharacteristic
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2411yescharacteristic
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2412yes—
861C2×C4⋊C4C2411yescharacteristic
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2411yescharacteristic
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2412yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2412yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2414yes—
906C2×C22⋊C4C2412yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2412yes—
917C2×C42—82no—
918C2×C42C2414yes—
919C2×C42C2412yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2411yescharacteristic
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2412yes—
928C2×C42C2412yes—
929C2×C42C2414yes—
930C2×C42C2412yes—
931C2×C42C2414yes—
932C2×C42C2414yes—
933C2×C42C2411yescharacteristic
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2414yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2414yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2412yes—
945C2×C42C2411yescharacteristic
946C2×C42C2411yescharacteristic
947C2×C42C2411yescharacteristic
948C2×C42C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2414yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2412yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2414yes—
980#95C2414yes—
981#95C2412yes—
982#95C2414yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2412yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2412yes—
994#95C2412yes—
995#95C2414yes—
996#95C2412yes—
997#95C2412yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2412yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2412yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2414yes—
1012#95C2412yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016C24C2514yes—
1017C24C2512yes—
1018C24C2512yes—
1019#41—432no—
1020#41—816no—
1021C2×Q8—24no—
1022C2×Q8—22no—
1023C2×Q8—24no—
1024C2×Q8—24no—
1025C2×Q8—24no—
1026C2×Q8—41no—
1027C2×Q8—41no—
1028C2×Q8—42no—
1029C2×Q8—42no—
1030C2×Q8—42no—
1031C2×Q8—42no—
1032C2×Q8—42no—
1033C2×Q8—42no—
1034C2×Q8—42no—
1035C2×Q8C2×#4118yes—
1036C2×D4—28no—
1037C2×D4—28no—
1038C2×D4—28no—
1039C2×D4—22no—
1040C2×D4—22no—
1041C2×D4—24no—
1042C2×D4—24no—
1043C2×D4—28no—
1044C2×D4—24no—
1045C2×D4—24no—
1046C2×D4—22no—
1047C2×D4—24no—
1048C2×D4—41no—
1049C2×D4—42no—
1050C2×D4—42no—
1051C2×D4—41no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—44no—
1056C2×D4—44no—
1057C2×D4—44no—
1058C2×D4—44no—
1059C2×D4—44no—
1060C2×D4—44no—
1061C2×D4—44no—
1062C2×D4—42no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4C2×#4114yes—
1066C22×C4—28no—
1067C22×C4—28no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—24no—
1072C22×C4—24no—
1073C22×C4—28no—
1074C22×C4—28no—
1075C22×C4—28no—
1076C22×C4—24no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—42no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—42no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—44no—
1091C22×C4—44no—
1092C22×C4—44no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4C2×#4118yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2514yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2512yes—
1108C22×C4C2514yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2512yes—
1113C22×C4C2514yes—
1114C22×C4C2511yescharacteristic
1115C22×C4C2512yes—
1116C22×C4C2511yescharacteristic
1117C22×C4C2514yes—
1118C22×C4C2511yescharacteristic
1119C22×C4C2511yescharacteristic
1120C22×C4C2511yescharacteristic
1121C22×C4C2511yescharacteristic
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—22no—
1125C4⋊C4—28no—
1126C4⋊C4—28no—
1127C4⋊C4—24no—
1128C4⋊C4—28no—
1129C4⋊C4—24no—
1130C4⋊C4—24no—
1131C4⋊C4—24no—
1132C4⋊C4—22no—
1133C4⋊C4—22no—
1134C4⋊C4—24no—
1135C4⋊C4—28no—
1136C4⋊C4—28no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—22no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—22no—
1144C4⋊C4—22no—
1145C4⋊C4—41no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—42no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—41no—
1154C4⋊C4—44no—
1155C4⋊C4—42no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—42no—
1159C4⋊C4—41no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—41no—
1165C4⋊C4—44no—
1166C4⋊C4—44no—
1167C4⋊C4—41no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—42no—
1171C4⋊C4—42no—
1172C4⋊C4—44no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—42no—
1176C4⋊C4—42no—
1177C4⋊C4C2×#4114yes—
1178C4⋊C4C2×#4118yes—
1179C4⋊C4C2×#4118yes—
1180C22⋊C4—28no—
1181C22⋊C4—24no—
1182C22⋊C4—24no—
1183C22⋊C4—28no—
1184C22⋊C4—28no—
1185C22⋊C4—28no—
1186C22⋊C4—24no—
1187C22⋊C4—24no—
1188C22⋊C4—28no—
1189C22⋊C4—28no—
1190C22⋊C4—28no—
1191C22⋊C4—28no—
1192C22⋊C4—28no—
1193C22⋊C4—24no—
1194C22⋊C4—42no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—42no—
1199C22⋊C4—42no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—42no—
1205C22⋊C4—44no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—42no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—42no—
1226C22⋊C4—42no—
1227C22⋊C4C2×#4118yes—
1228C42—28no—
1229C42—28no—
1230C42—24no—
1231C42—28no—
1232C42—28no—
1233C42—24no—
1234C42—24no—
1235C42—24no—
1236C42—22no—
1237C42—24no—
1238C42—22no—
1239C42—41no—
1240C42—42no—
1241C42—42no—
1242C42—42no—
1243C42—41no—
1244C42—42no—
1245C42—44no—
1246C42—42no—
1247C42—44no—
1248C42—44no—
1249C42—44no—
1250C42—41no—
1251C42—44no—
1252C42—44no—
1253C42—44no—
1254C42—44no—
1255C42—42no—
1256C42—42no—
1257C42C2×#4114yes—
1258C42C2×#4114yes—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23—22no—
1267C23—22no—
1268C23—24no—
1269C23—22no—
1270C23—24no—
1271C23—24no—
1272C23—22no—
1273C23—22no—
1274C23—24no—
1275C23—22no—
1276C23—24no—
1277C23—24no—
1278C23—22no—
1279C23C22×#4114yes—
1280C23C2611yescharacteristic
1281Q8—216no—
1282Q8—44no—
1283Q8—84no—
1284Q8—84no—
1285Q8—162no—
1286D4—28no—
1287D4—416no—
1288D4—44no—
1289D4—48no—
1290D4—48no—
1291D4—84no—
1292D4—88no—
1293D4—88no—
1294D4—88no—
1295D4—88no—
1296C2×C4—24no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—24no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—22no—
1317C2×C4—24no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—22no—
1324C2×C4—22no—
1325C2×C4—21no—
1326C2×C4—22no—
1327C2×C4—24no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—24no—
1332C2×C4—22no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—21no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—22no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—21no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—48no—
1365C2×C4—416no—
1366C2×C4—48no—
1367C2×C4—48no—
1368C2×C4—88no—
1369C2×C4—88no—
1370C2×C4—84no—
1371C2×C4—88no—
1372C2×C4—88no—
1373C2×C4—164no—
1374C2×C4C22×#4112yes—
1375C2×C4C22×#4118yes—
1376C2×C4C22×#4114yes—
1377C2×C4C22×#4112yes—
1378C2×C4C22×#4112yes—
1379C2×C4C22×#4112yes—
1380C2×C4C22×#4112yes—
1381C2×C4C22×#4112yes—
1382C2×C4#58512yes—
1383C2×C4#58512yes—
1384C22—24no—
1385C22—24no—
1386C22—24no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22—44no—
1392C22—42no—
1393C22—44no—
1394C22—42no—
1395C22—42no—
1396C22—44no—
1397C22—42no—
1398C22—44no—
1399C22—42no—
1400C22—44no—
1401C22—42no—
1402C22—44no—
1403C22—44no—
1404C22—42no—
1405C22C23×#4111yescharacteristic
1406C22C23×#4111yescharacteristic
1407C22C2×#58511yescharacteristic
1408C22C2×#58511yescharacteristic
1409C22H(7,𝔽2)11yescharacteristic
1410C22H(7,𝔽2)11yescharacteristic
1411C222−1+611yescharacteristic
1412C4—22no—
1413C4—22no—
1414C4—22no—
1415C4—24no—
1416C4—22no—
1417C4—28no—
1418C4—22no—
1419C4—42no—
1420C4—42no—
1421C4—44no—
1422C4—42no—
1423C4—42no—
1424C4—42no—
1425C4—44no—
1426C4—41no—
1427C4—42no—
1428C4—44no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—42no—
1433C4—42no—
1434C4—42no—
1435C4—42no—
1436C4—44no—
1437C4#347514yes—
1438C2—44no—
1439C2—84no—
1440C2—82no—
1441C2C2×#347511yescharacteristic
1442C2#6284611yescharacteristic
1443C2#6285111yescharacteristic
1444C2#6296511yescharacteristic
1445C2#6299511yescharacteristic
1446C2#6300611yescharacteristic
1447C2#6305611yescharacteristic
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. #59873C2semidirect
2. #59821C2semidirect
3. #59542C2semidirect
4. #59487C2semidirect
5. #52280C2semidirect
6. #52272C2semidirect
7. #45269C2semidirect
8. #45123C2semidirect
9. #44998C2semidirect
10. #44130C2semidirect
11. #44016C2semidirect
12. #43972C2semidirect
13. #39629C2semidirect
14. #39582C2semidirect
15. #39500C2semidirect
16. #39287C2semidirect
17. #38736C2semidirect
18. #38467C2semidirect
19. #38226C2semidirect
20. #38192C2semidirect
21. #36490C2semidirect
22. #36476C2semidirect
23. #35905C2semidirect
24. #35880C2semidirect
25. #35704C2semidirect
26. #34330C2semidirect
27. #34326C2semidirect
28. #34308C2semidirect
29. #34263C2semidirect
750. C4⋊Q8#41semidirect

Maximal subgroups

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

subgroupindex
#598732
#598212
#595422
#594872
#522802
#522722
#452692
#451232
#449982
#441302
#440162
#439722
#396292
#395822
#395002
#392872
#387362
#384672
#382262
#381922
#364902
#364762
#359052
#358802
#357042
#343302
#343262
#343082
#342632