Finite Group Databasebeta

← #7656006

Subgroups — #7656006

Order 512.

4744 conjugacy classes of subgroups.

The subgroup lattice has 1473 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42694C212yesmaximal, complemented
2#42667C212yesmaximal, complemented
3#42509C212yesmaximal, complemented
4#42467C212yesmaximal, complemented
5#41752C214yesmaximal, complemented
6#41652C214yesmaximal, complemented
7#41139C214yesmaximal, complemented
8#40995C214yesmaximal, complemented
9#39732C212yesmaximal, complemented
10#39061C214yesmaximal, complemented
11#38939C212yesmaximal, complemented
12#37779C214yesmaximal, complemented
13#37561C211yesmaximal, characteristic, complemented
14#37554C211yesmaximal, characteristic
15#37465C212yesmaximal, complemented
16#37464C212yesmaximal, complemented
17#36488C212yesmaximal, complemented
18#36118C212yesmaximal, complemented
19#35952C212yesmaximal, complemented
20#35905C212yesmaximal, complemented
21#35788C212yesmaximal, complemented
22#35785C212yesmaximal, complemented
23#35178C211yesmaximal, characteristic, complemented
24#35021C212yesmaximal, complemented
25#34602C211yesmaximal, characteristic, complemented
26#34594C212yesmaximal, complemented
27#34243C211yesmaximal, characteristic, complemented
28#34236C211yesmaximal, characteristic, complemented
29C2×#2355C211yesmaximal, characteristic, complemented
30C2×#536C2212yes—
31C2×#532C2211yescharacteristic
32C2×#529C2211yescharacteristic
33C2×#529C2214yes—
34C22×C4×Q8C2211yescharacteristic
35#2854C2212yes—
36#2854C2212yes—
37#2853C2214yes—
38#2852C2214yes—
39#2845C2212yes—
40#2844C2212yes—
41#2839C2214yes—
42#2836C2214yes—
43#2830C2214yes—
44#2829C2214yes—
45#2820C2212yes—
46#2819C2212yes—
47#2795C2214yes—
48#2793C2214yes—
49#2790C2214yes—
50#2785C2214yes—
51#2781C2214yes—
52#2775C2214yes—
53#2758C2214yes—
54#2754C2214yes—
55#2751C2214yes—
56#2744C2214yes—
57#2741C2214yes—
58#2739C2214yes—
59#2737C2214yes—
60#2722C2214yes—
61#2718C2214yes—
62#2716C2214yes—
63#2715C2214yes—
64#2713C2214yes—
65#2712C2214yes—
66#2705C2214yes—
67#2704C2214yes—
68#2702C2214yes—
69#2700C2214yes—
70#2698C2214yes—
71#2667C2214yes—
72#2666C2214yes—
73#2665C2214yes—
74#2664C2214yes—
75#2664C2214yes—
76#2662C2214yes—
77#2662C2214yes—
78#2660C2212yes—
79#2659C2212yes—
80#2656C2212yes—
81#2654C2214yes—
82#2652C2214yes—
83#2650C2214yes—
84#2648C2214yes—
85#2647C2212yes—
86#2646C2212yes—
87#2639C2214yes—
88#2639C2212yes—
89#2637C2214yes—
90#2637C2212yes—
91#2637C2212yes—
92#2636C2214yes—
93#2634C2212yes—
94#2632C2212yes—
95#2630C2214yes—
96#2628C2212yes—
97#2627C2211yescharacteristic
98#2627C2211yescharacteristic
99#2623C2212yes—
100#2619C2212yes—
101#2618C2211yescharacteristic
102#2618C2214yes—
103#2618C2212yes—
104#2618C2211yescharacteristic
105#2618C2212yes—
106#2614C2212yes—
107#2607C2214yes—
108#2595C2214yes—
109#2595C2214yes—
110#2593C2214yes—
111#2588C2214yes—
112#2587C2214yes—
113#2585C2214yes—
114#2580C2212yes—
115#2578C2214yes—
116#2574C2214yes—
117#2574C2214yes—
118#2573C2214yes—
119#2571C2212yes—
120#2570C2212yes—
121#2570C2212yes—
122#2569C2214yes—
123#2566C2212yes—
124#2563C2212yes—
125#2550C2212yes—
126#2548C2212yes—
127#2546C2212yes—
128#2545C2214yes—
129#2538C2212yes—
130#2538C2212yes—
131#2536C2214yes—
132#2535C2212yes—
133#2525C2214yes—
134#2525C2214yes—
135#2524C2214yes—
136#2522C2214yes—
137#2520C2214yes—
138#2513C2212yes—
139#2512C2212yes—
140#2512C2212yes—
141#2512C2212yes—
142#2508C2212yes—
143#2507C2212yes—
144#2507C2212yes—
145#2506C2212yes—
146#2500C2212yes—
147#2500C2212yes—
148#2497C2212yes—
149#2496C2212yes—
150#2495C2212yes—
151#2495C2212yes—
152#2491C2212yes—
153#2490C2212yes—
154#2488C2214yes—
155#2481C2214yes—
156#2477C2214yes—
157#2475C2214yes—
158#2474C2214yes—
159#2474C2214yes—
160#2469C2214yes—
161#2469C2214yes—
162#2468C2214yes—
163#2468C2214yes—
164#2468C2214yes—
165#2468C2214yes—
166#2467C2214yes—
167#2465C2214yes—
168#2459C2214yes—
169#2457C2214yes—
170#2451C2214yes—
171#2450C2214yes—
172#2450C2214yes—
173#2444C2214yes—
174#2443C2214yes—
175#2442C2212yes—
176#2441C2212yes—
177#2440C2212yes—
178#2439C2212yes—
179#2439C2214yes—
180#2438C2214yes—
181#2438C2214yes—
182#2430C2214yes—
183#2425C2214yes—
184#2425C2214yes—
185#2422C2212yes—
186#2420C2212yes—
187#2419C2214yes—
188#2419C2214yes—
189#2416C2212yes—
190#2416C2212yes—
191#2399C2212yes—
192#2398C2212yes—
193#2396C2214yes—
194#2396C2214yes—
195#2396C2212yes—
196#2396C2212yes—
197#2392C2214yes—
198#2392C2214yes—
199#2370C2212yes—
200#2370C2212yes—
201#2369C2211yescharacteristic
202#2369C2211yescharacteristic
203#2367C2212yes—
204#2366C2211yescharacteristic
205#2366C2211yescharacteristic
206#2365C2212yes—
207#2361C2212yes—
208#2361C2212yes—
209#2361C2212yes—
210#2361C2212yes—
211#2359C2214yes—
212#2357C2212yes—
213#2357C2212yes—
214#2355C2212yes—
215#2355C2214yes—
216#2355C2214yes—
217#2355C2212yes—
218#2355C2212yes—
219#2355C2212yes—
220#2355C2211yescharacteristic
221#2354C2212yes—
222#2354C2211yescharacteristic
223#2352C2212yes—
224Q8×C4⋊C4C2211yescharacteristic
225#2349C2212yes—
226D4×C4⋊C4C2212yes—
227D4×C4⋊C4C2211yescharacteristic
228#2345C2212yes—
229#2344C2212yes—
230#2339C2214yes—
231#2337C2214yes—
232#2334C2214yes—
233#2322C2214yes—
234#2319C2212yes—
235#2318C2214yes—
236#2314C2212yes—
237#2311C2212yes—
238C4×C22⋊Q8C2212yes—
239C4×#123C2212yes—
240C4×#123C2212yes—
241C4×#121C2212yes—
242C4×#121C2212yes—
243C4×#121C2214yes—
244C4×#121C2212yes—
245C2×#391C2212yes—
246C2×#387C2212yes—
247C2×#387C2212yes—
248#2285C2211yescharacteristic
249C2×#384C2211yescharacteristic
250#2283C2211yescharacteristic
251C2×#382C2211yescharacteristic
252C2×#382C2211yescharacteristic
253#2275C2212yes—
254#2274C2212yes—
255C2×C4×C4⋊C4C2211yescharacteristic
256C2×C4×C4⋊C4C2212yes—
257C2×C4×C4⋊C4C2211yescharacteristic
258C2×C4×C4⋊C4C2211yescharacteristic
259C22×#41C2312yes—
260C23×Q8C2311yescharacteristic
261#536—48no—
262#532—28no—
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2314yes—
266C2×#127C2311yescharacteristic
267#529—28no—
268#529—416no—
269C2×#126C2312yes—
270C2×#126C2314yes—
271C2×#126C2314yes—
272C2×#126C2314yes—
273C2×#126C2314yes—
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#125C2314yes—
277C2×#124C2311yescharacteristic
278C2×#124C2312yes—
279C2×#124C2314yes—
280C2×#124C2314yes—
281C2×#123C2314yes—
282C2×#123C2312yes—
283C2×#123C2312yes—
284C2×#123C2314yes—
285C2×#123C2312yes—
286C2×#123C2314yes—
287C2×C22⋊Q8C2311yescharacteristic
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×#121C2312yes—
292C2×#121C2312yes—
293C2×#121C2311yescharacteristic
294C2×#121C2312yes—
295C2×#121C2312yes—
296C2×#121C2314yes—
297C2×#121C2314yes—
298C2×C4×Q8—28no—
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×Q8C2312yes—
303C2×C4×Q8C2312yes—
304C2×C4×Q8C2314yes—
305C2×C4×Q8C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2312yes—
308C2×C4×D4C2311yescharacteristic
309C2×C4×D4C2312yes—
310C2×C4×D4C2312yes—
311C2×C4×D4C2312yes—
312C2×C4×D4C2314yes—
313C2×C4×D4C2314yes—
314C2×C4×D4C2314yes—
315C2×C4×D4C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2314yes—
320C2×#117C2312yes—
321C2×#117C2312yes—
322C2×#117C2314yes—
323C2×#117C2312yes—
324C2×#117C2314yes—
325C22×C4⋊C4C2311yescharacteristic
326C22×C4⋊C4C2312yes—
327C22×C4⋊C4C2311yescharacteristic
328C22×C4⋊C4C2311yescharacteristic
329C22×C4⋊C4C2311yescharacteristic
330C22×C4⋊C4C2312yes—
331C22×C4⋊C4C2311yescharacteristic
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2311yescharacteristic
334C22×C4⋊C4C2312yes—
335C22×C42C2312yes—
336C22×C42C2311yescharacteristic
337C22×C42C2311yescharacteristic
338C22×C42C2312yes—
339C22×C42C2312yes—
340C22×C42C2311yescharacteristic
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2314yes—
347#400C2314yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2312yes—
355#400C2314yes—
356#400C2314yes—
357#400C2312yes—
358#400C2312yes—
359#399C2314yes—
360#399C2314yes—
361#399C2312yes—
362#399C2312yes—
363#399C2314yes—
364#398C2312yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2312yes—
370#398C2312yes—
371#398C2312yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2312yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#398C2314yes—
384#398C2314yes—
385#398C2312yes—
386#398C2312yes—
387#398C2314yes—
388#398C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2312yes—
397#397C2314yes—
398#397C2314yes—
399#397C2314yes—
400#397C2314yes—
401#397C2312yes—
402#397C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#396C2314yes—
414#396C2312yes—
415#396C2312yes—
416#396C2312yes—
417#396C2312yes—
418#396C2314yes—
419#396C2314yes—
420#396C2314yes—
421#395C2314yes—
422#395C2312yes—
423#395C2314yes—
424#395C2314yes—
425#395C2314yes—
426#395C2312yes—
427#395C2312yes—
428#395C2312yes—
429#395C2312yes—
430#395C2312yes—
431#395C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2312yes—
436#394C2314yes—
437#394C2314yes—
438#394C2314yes—
439#394C2314yes—
440#394C2314yes—
441#394C2314yes—
442#394C2314yes—
443#394C2314yes—
444#394C2312yes—
445#394C2314yes—
446#394C2314yes—
447#394C2314yes—
448#393C2314yes—
449#393C2314yes—
450#393C2314yes—
451#393C2314yes—
452#393C2314yes—
453#393C2314yes—
454#393C2312yes—
455#393C2312yes—
456#393C2312yes—
457#393C2312yes—
458#392C2314yes—
459#392C2314yes—
460#392C2314yes—
461#391C2314yes—
462#391C2312yes—
463#391C2314yes—
464#391C2314yes—
465#391C2314yes—
466#391C2314yes—
467#391C2314yes—
468#391C2314yes—
469#391C2314yes—
470#391C2314yes—
471#391C2314yes—
472#390C2312yes—
473#390C2312yes—
474#390C2312yes—
475#390C2312yes—
476#390C2314yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2314yes—
483#390C2312yes—
484#390C2312yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2314yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2314yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2314yes—
501#389C2314yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2312yes—
506#389C2312yes—
507#389C2312yes—
508#389C2312yes—
509#388C2314yes—
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#388C2312yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2312yes—
538#388C2312yes—
539#388C2312yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
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#387C2312yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2312yes—
579#387C2312yes—
580#387C2312yes—
581#386C2314yes—
582#386C2314yes—
583#386C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2312yes—
594#386C2312yes—
595#386C2314yes—
596#386C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2312yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2312yes—
613#384C2312yes—
614#384C2312yes—
615#384C2312yes—
616#384C2311yescharacteristic
617#384C2311yescharacteristic
618#384C2312yes—
619#384C2314yes—
620#383C2314yes—
621#383C2312yes—
622#383C2314yes—
623#382C2312yes—
624#382C2312yes—
625#382C2312yes—
626#382C2312yes—
627#382C2312yes—
628#382C2314yes—
629#382C2312yes—
630#382C2311yescharacteristic
631#382C2312yes—
632#382C2312yes—
633#382C2311yescharacteristic
634#382C2312yes—
635#382C2314yes—
636#382C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2312yes—
640#381C2312yes—
641#381C2314yes—
642#381C2314yes—
643#381C2312yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2312yes—
650#380C2312yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2311yescharacteristic
658#380C2311yescharacteristic
659#380C2314yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2311yescharacteristic
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2314yes—
669C4×C4⋊C4C2314yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2314yes—
672C4×C4⋊C4C2314yes—
673C4×C4⋊C4C2314yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2311yescharacteristic
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2312yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708#376C2312yes—
709C2×#95C2314yes—
710C2×#95C2312yes—
711C2×#95C2312yes—
712C2×#95C2312yes—
713C2×#95C2312yes—
714C2×#95C2312yes—
715C2×#95C2312yes—
716C2×#95C2312yes—
717C2×#41—28no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8—24no—
721C22×Q8—24no—
722C22×Q8—42no—
723C22×Q8C2412yes—
724C22×Q8C2412yes—
725C22×Q8C2411yescharacteristic
726C22×Q8C2412yes—
727C22×Q8C2414yes—
728C22×D4C2412yes—
729C22×D4C2412yes—
730C22×D4C2414yes—
731C22×D4C2411yescharacteristic
732C22×D4C2412yes—
733C22×D4C2412yes—
734C22×D4C2414yes—
735C22×D4C2414yes—
736C23×C4C2412yes—
737C23×C4C2411yescharacteristic
738C23×C4C2412yes—
739C23×C4C2411yescharacteristic
740C23×C4C2411yescharacteristic
741C23×C4C2411yescharacteristic
742C23×C4C2411yescharacteristic
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2411yescharacteristic
746C23×C4C2414yes—
747C23×C4C2412yes—
748C23×C4C2414yes—
749C23×C4C2414yes—
750C23×C4C2414yes—
751C23×C4C2411yescharacteristic
752C4⋊Q8—24no—
753C4⋊Q8—44no—
754C4⋊Q8—48no—
755#127—24no—
756#126—28no—
757#126—48no—
758#126—48no—
759#126—84no—
760#126—84no—
761#125—24no—
762#125—44no—
763#125—48no—
764#124—24no—
765#124—28no—
766#124—48no—
767#124—48no—
768#123—28no—
769#123—28no—
770#123—216no—
771#123—44no—
772#123—48no—
773#123—84no—
774C22⋊Q8—24no—
775C22⋊Q8—48no—
776C22⋊Q8—48no—
777C22⋊Q8—48no—
778#121—24no—
779#121—28no—
780#121—28no—
781#121—44no—
782#121—44no—
783#121—48no—
784#121—48no—
785C4×Q8—28no—
786C4×Q8—28no—
787C4×Q8—28no—
788C4×Q8—28no—
789C4×Q8—24no—
790C4×Q8—48no—
791C4×Q8—82no—
792C4×D4—28no—
793C4×D4—28no—
794C4×D4—24no—
795C4×D4—28no—
796C4×D4—28no—
797C4×D4—48no—
798C4×D4—44no—
799C4×D4—48no—
800C4×D4—48no—
801C4×D4—48no—
802C4×D4—84no—
803C4×D4—82no—
804C4×D4—82no—
805C4×D4—82no—
806#117—28no—
807#117—48no—
808#117—48no—
809#117—44no—
810#117—44no—
811C2×C4⋊C4—24no—
812C2×C4⋊C4—24no—
813C2×C4⋊C4—24no—
814C2×C4⋊C4—24no—
815C2×C4⋊C4—28no—
816C2×C4⋊C4—42no—
817C2×C4⋊C4—42no—
818C2×C4⋊C4—42no—
819C2×C4⋊C4—44no—
820C2×C4⋊C4—82no—
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2411yescharacteristic
832C2×C4⋊C4C2412yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2412yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2412yes—
856C2×C4⋊C4C2412yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2411yescharacteristic
860C2×C4⋊C4C2411yescharacteristic
861C2×C4⋊C4C2412yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2414yes—
876C2×C4⋊C4C2414yes—
877C2×C4⋊C4C2412yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2412yes—
883C2×C4⋊C4C2412yes—
884C2×C4⋊C4C2412yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2411yescharacteristic
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2412yes—
893C2×C22⋊C4C2412yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2414yes—
904C2×C22⋊C4C2414yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2412yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2412yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2412yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C42—24no—
931C2×C42—24no—
932C2×C42—28no—
933C2×C42—82no—
934C2×C42—82no—
935C2×C42#4118yes—
936C2×C42C2414yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2412yes—
940C2×C42C2412yes—
941C2×C42C2412yes—
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2414yes—
945C2×C42C2414yes—
946C2×C42C2414yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2412yes—
950C2×C42C2412yes—
951C2×C42C2414yes—
952C2×C42C2414yes—
953C2×C42C2412yes—
954C2×C42C2414yes—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2411yescharacteristic
958C2×C42C2411yescharacteristic
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961#95C2412yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2412yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2412yes—
998#95C2412yes—
999#95C2412yes—
1000#95C2412yes—
1001#95C2412yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2414yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2414yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2412yes—
1016#95C2412yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027C24C2512yes—
1028C24C2514yes—
1029C24C2511yescharacteristic
1030#41—816no—
1031C2×Q8—24no—
1032C2×Q8—24no—
1033C2×Q8—22no—
1034C2×Q8—24no—
1035C2×Q8—24no—
1036C2×Q8—24no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—41no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—44no—
1044C2×Q8—44no—
1045C2×Q8—42no—
1046C2×Q8—416no—
1047C2×D4—24no—
1048C2×D4—28no—
1049C2×D4—24no—
1050C2×D4—28no—
1051C2×D4—28no—
1052C2×D4—24no—
1053C2×D4—22no—
1054C2×D4—24no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—24no—
1058C2×D4—24no—
1059C2×D4—42no—
1060C2×D4—41no—
1061C2×D4—42no—
1062C2×D4—41no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C2×D4—44no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—42no—
1069C2×D4—44no—
1070C2×D4—42no—
1071C22×C4—22no—
1072C22×C4—22no—
1073C22×C4—22no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—22no—
1079C22×C4—22no—
1080C22×C4—24no—
1081C22×C4—22no—
1082C22×C4—22no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—28no—
1091C22×C4—28no—
1092C22×C4—28no—
1093C22×C4—41no—
1094C22×C4—42no—
1095C22×C4—41no—
1096C22×C4—41no—
1097C22×C4—41no—
1098C22×C4—41no—
1099C22×C4—41no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—42no—
1104C22×C4—42no—
1105C22×C4—44no—
1106C22×C4—44no—
1107C22×C4—44no—
1108C22×C4—44no—
1109C22×C4—44no—
1110C22×C4—42no—
1111C22×C4—44no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4C2×#4114yes—
1116C22×C4C2×#4114yes—
1117C22×C4C2×#4114yes—
1118C22×C4H(5,𝔽2)14yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2514yes—
1123C22×C4C2512yes—
1124C22×C4C2512yes—
1125C22×C4C2512yes—
1126C22×C4C2512yes—
1127C22×C4C2512yes—
1128C22×C4C2514yes—
1129C22×C4C2514yes—
1130C22×C4C2512yes—
1131C22×C4C2512yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2514yes—
1136C22×C4C2512yes—
1137C22×C4C2511yescharacteristic
1138C22×C4C2511yescharacteristic
1139C22×C4C2511yescharacteristic
1140C22×C4C2511yescharacteristic
1141C22×C4C2511yescharacteristic
1142C22×C4C2512yes—
1143C22×C4C2512yes—
1144C22×C4C2511yescharacteristic
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—24no—
1150C4⋊C4—24no—
1151C4⋊C4—24no—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—22no—
1156C4⋊C4—24no—
1157C4⋊C4—22no—
1158C4⋊C4—24no—
1159C4⋊C4—24no—
1160C4⋊C4—28no—
1161C4⋊C4—24no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—22no—
1166C4⋊C4—24no—
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—24no—
1170C4⋊C4—24no—
1171C4⋊C4—24no—
1172C4⋊C4—42no—
1173C4⋊C4—42no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—41no—
1180C4⋊C4—41no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4—42no—
1186C4⋊C4—42no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—42no—
1196C4⋊C4—44no—
1197C4⋊C4—44no—
1198C4⋊C4—44no—
1199C4⋊C4—44no—
1200C4⋊C4—44no—
1201C4⋊C4—44no—
1202C4⋊C4—42no—
1203C4⋊C4—42no—
1204C4⋊C4—44no—
1205C4⋊C4—44no—
1206C4⋊C4—44no—
1207C4⋊C4—42no—
1208C4⋊C4—42no—
1209C4⋊C4—44no—
1210C4⋊C42−1+414yes—
1211C22⋊C4—24no—
1212C22⋊C4—28no—
1213C22⋊C4—24no—
1214C22⋊C4—24no—
1215C22⋊C4—24no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—24no—
1220C22⋊C4—24no—
1221C22⋊C4—24no—
1222C22⋊C4—28no—
1223C22⋊C4—24no—
1224C22⋊C4—28no—
1225C22⋊C4—28no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—42no—
1229C22⋊C4—42no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—42no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—42no—
1250C22⋊C4—42no—
1251C22⋊C4—42no—
1252C22⋊C4—44no—
1253C22⋊C4—44no—
1254C42—24no—
1255C42—24no—
1256C42—24no—
1257C42—24no—
1258C42—24no—
1259C42—28no—
1260C42—28no—
1261C42—24no—
1262C42—24no—
1263C42—42no—
1264C42—42no—
1265C42—42no—
1266C42—44no—
1267C42—42no—
1268C42—44no—
1269C42—44no—
1270C42—44no—
1271C42—44no—
1272C42—44no—
1273C42—44no—
1274C42—44no—
1275C42C2×#4114yes—
1276C42C2×#4114yes—
1277C42C2×#4114yes—
1278C42C2×#4114yes—
1279C23—21no—
1280C23—21no—
1281C23—21no—
1282C23—21no—
1283C23—22no—
1284C23—24no—
1285C23—24no—
1286C23—22no—
1287C23—24no—
1288C23—22no—
1289C23—22no—
1290C23—24no—
1291C23—22no—
1292C23—24no—
1293C23—24no—
1294C23—22no—
1295C23—24no—
1296C23—22no—
1297C23C22×#4112yes—
1298C23C2×H(5,𝔽2)12yes—
1299C23#58512yes—
1300C23C2611yescharacteristic
1301Q8—48no—
1302Q8—48no—
1303Q8—44no—
1304Q8—84no—
1305Q8—88no—
1306D4—48no—
1307D4—44no—
1308D4—48no—
1309D4—416no—
1310D4—48no—
1311D4—84no—
1312D4—88no—
1313D4—88no—
1314C2×C4—22no—
1315C2×C4—22no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—22no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—28no—
1329C2×C4—28no—
1330C2×C4—28no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—22no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—24no—
1359C2×C4—24no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—22no—
1363C2×C4—22no—
1364C2×C4—24no—
1365C2×C4—22no—
1366C2×C4—24no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—22no—
1371C2×C4—22no—
1372C2×C4—22no—
1373C2×C4—24no—
1374C2×C4—24no—
1375C2×C4—22no—
1376C2×C4—22no—
1377C2×C4—22no—
1378C2×C4—22no—
1379C2×C4—22no—
1380C2×C4—22no—
1381C2×C4—24no—
1382C2×C4—22no—
1383C2×C4—22no—
1384C2×C4—24no—
1385C2×C4—44no—
1386C2×C4—48no—
1387C2×C4—44no—
1388C2×C4—44no—
1389C2×C4—44no—
1390C2×C4—48no—
1391C2×C4—88no—
1392C2×C4—88no—
1393C2×C4—88no—
1394C2×C4—84no—
1395C2×C4—84no—
1396C2×C4—84no—
1397C2×C4—164no—
1398C2×C4C22×#4112yes—
1399C2×C4C22×#4112yes—
1400C2×C4C22×#4112yes—
1401C2×C4C22×#4112yes—
1402C2×C4C22×#4112yes—
1403C2×C4C22×#4112yes—
1404C2×C4C2×H(5,𝔽2)14yes—
1405C2×C4C2×2−1+414yes—
1406C2×C4C2×2−1+412yes—
1407C2×C4#58512yes—
1408C22—22no—
1409C22—22no—
1410C22—22no—
1411C22—22no—
1412C22—22no—
1413C22—22no—
1414C22—44no—
1415C22—42no—
1416C22—42no—
1417C22—44no—
1418C22—42no—
1419C22—44no—
1420C22—42no—
1421C22—44no—
1422C22—44no—
1423C22—42no—
1424C22—42no—
1425C22—44no—
1426C22—44no—
1427C22—42no—
1428C22#349414yes—
1429C22C23×#4111yescharacteristic
1430C22C22×H(5,𝔽2)11yescharacteristic
1431C22C22×2−1+411yescharacteristic
1432C22C2×#58511yescharacteristic
1433C22C2×#58511yescharacteristic
1434C22H(7,𝔽2)11yescharacteristic
1435C222−1+611yescharacteristic
1436C4—22no—
1437C4—22no—
1438C4—24no—
1439C4—22no—
1440C4—22no—
1441C4—22no—
1442C4—24no—
1443C4—42no—
1444C4—44no—
1445C4—42no—
1446C4—42no—
1447C4—42no—
1448C4—42no—
1449C4—42no—
1450C4—42no—
1451C4—44no—
1452C4—42no—
1453C4—42no—
1454C4—44no—
1455C4—44no—
1456C4—42no—
1457C4—42no—
1458C4—42no—
1459C4—44no—
1460C4—42no—
1461C4#346114yes—
1462C2—24no—
1463C2—84no—
1464C2—82no—
1465C2C2×#346111yescharacteristic
1466C2C2×#349411yescharacteristic
1467C2#6284511yescharacteristic
1468C2#6294411yescharacteristic
1469C2#6294911yescharacteristic
1470C2#6296011yescharacteristic
1471C2#6296511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37554C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42694C2semidirect
2. #42667C2semidirect
3. #42509C2semidirect
4. #42467C2semidirect
5. #41752C2semidirect
6. #41652C2semidirect
7. #41139C2semidirect
8. #40995C2semidirect
9. #39732C2semidirect
10. #39061C2semidirect
11. #38939C2semidirect
12. #37779C2semidirect
13. #37561C2semidirect
15. #37465C2semidirect
16. #37464C2semidirect
17. #36488C2semidirect
18. #36118C2semidirect
19. #35952C2semidirect
20. #35905C2semidirect
21. #35788C2semidirect
22. #35785C2semidirect
23. #35178C2semidirect
24. #35021C2semidirect
25. #34602C2semidirect
26. #34594C2semidirect
27. #34243C2semidirect
28. #34236C2semidirect
29. C2×#2355C2semidirect

Maximal subgroups

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

subgroupindex
#426942
#426672
#425092
#424672
#417522
#416522
#411392
#409952
#397322
#390612
#389392
#377792
#375612
#375542
#374652
#374642
#364882
#361182
#359522
#359052
#357882
#357852
#351782
#350212
#346022
#345942
#342432
#342362
C2×#23552