Finite Group Databasebeta

← #7660766

Subgroups — #7660766

Order 512.

4764 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52281C211yesmaximal, characteristic, complemented
2#52162C212yesmaximal, complemented
3#42758C212yesmaximal, complemented
4#42585C212yesmaximal, complemented
5#42423C212yesmaximal, complemented
6#42106C214yesmaximal, complemented
7#41053C214yesmaximal, complemented
8#40958C214yesmaximal, complemented
9#40167C212yesmaximal, complemented
10#39661C212yesmaximal, complemented
11#39623C211yesmaximal, characteristic, complemented
12#39359C211yesmaximal, characteristic
13#38829C212yesmaximal, complemented
14#38771C212yesmaximal, complemented
15#38677C214yesmaximal, complemented
16#37781C214yesmaximal, complemented
17#37350C212yesmaximal, complemented
18#37315C211yesmaximal, characteristic, complemented
19#37251C212yesmaximal, complemented
20#36895C214yesmaximal, complemented
21#36315C211yesmaximal, characteristic, complemented
22#36302C211yesmaximal, characteristic, complemented
23#36251C212yesmaximal, complemented
24#36132C212yesmaximal, complemented
25#36000C212yesmaximal, complemented
26#36000C212yesmaximal, complemented
27#35815C212yesmaximal, complemented
28#34316C212yesmaximal, complemented
29#34272C211yesmaximal, characteristic, complemented
30C2×#547C2212yes—
31C2×#544C2211yescharacteristic
32C2×#537C2212yes—
33C2×#533C2214yes—
34#2861C2212yes—
35#2861C2212yes—
36#2860C2212yes—
37#2859C2212yes—
38#2857C2211yescharacteristic
39#2856C2211yescharacteristic
40#2854C2214yes—
41#2851C2214yes—
42#2832C2214yes—
43#2830C2214yes—
44#2814C2214yes—
45#2808C2211yescharacteristic
46#2808C2212yes—
47#2806C2212yes—
48#2805C2211yescharacteristic
49#2802C2214yes—
50#2796C2214yes—
51#2792C2214yes—
52#2786C2212yes—
53#2785C2214yes—
54#2783C2214yes—
55#2782C2214yes—
56#2777C2212yes—
57#2773C2212yes—
58#2770C2212yes—
59#2754C2214yes—
60#2734C2212yes—
61#2732C2212yes—
62#2729C2214yes—
63#2727C2211yescharacteristic
64#2727C2212yes—
65#2726C2211yescharacteristic
66#2725C2214yes—
67#2724C2212yes—
68#2723C2212yes—
69#2723C2214yes—
70#2722C2214yes—
71#2720C2214yes—
72#2718C2214yes—
73#2718C2214yes—
74#2717C2214yes—
75#2713C2214yes—
76#2712C2214yes—
77#2711C2214yes—
78#2711C2212yes—
79#2704C2214yes—
80#2704C2214yes—
81#2704C2214yes—
82#2694C2214yes—
83#2692C2214yes—
84#2691C2214yes—
85#2690C2214yes—
86#2683C2212yes—
87#2682C2212yes—
88#2681C2214yes—
89#2681C2214yes—
90#2681C2214yes—
91#2677C2214yes—
92#2674C2214yes—
93#2672C2214yes—
94#2672C2214yes—
95#2666C2214yes—
96#2666C2214yes—
97#2663C2214yes—
98#2662C2214yes—
99#2659C2212yes—
100#2651C2214yes—
101#2651C2214yes—
102#2650C2214yes—
103#2649C2214yes—
104#2637C2214yes—
105#2628C2212yes—
106#2624C2212yes—
107#2624C2212yes—
108#2620C2214yes—
109#2618C2212yes—
110#2616C2214yes—
111#2605C2214yes—
112#2589C2214yes—
113#2578C2214yes—
114#2578C2214yes—
115#2574C2214yes—
116#2570C2214yes—
117#2567C2212yes—
118#2560C2214yes—
119#2560C2214yes—
120#2554C2214yes—
121#2553C2214yes—
122#2552C2211yescharacteristic
123#2552C2211yescharacteristic
124#2551C2212yes—
125#2551C2212yes—
126#2550C2212yes—
127#2548C2211yescharacteristic
128#2547C2211yescharacteristic
129#2531C2214yes—
130#2531C2214yes—
131#2531C2214yes—
132#2529C2214yes—
133#2525C2214yes—
134#2525C2214yes—
135#2521C2214yes—
136#2521C2214yes—
137#2519C2214yes—
138#2518C2214yes—
139#2513C2212yes—
140#2512C2212yes—
141#2512C2212yes—
142#2508C2212yes—
143#2507C2212yes—
144#2507C2212yes—
145#2507C2212yes—
146#2507C2212yes—
147#2500C2212yes—
148#2497C2212yes—
149#2497C2212yes—
150#2497C2212yes—
151#2491C2212yes—
152#2491C2214yes—
153#2491C2212yes—
154#2490C2212yes—
155#2490C2212yes—
156#2489C2212yes—
157#2485C2212yes—
158#2478C2214yes—
159#2476C2214yes—
160#2476C2214yes—
161#2476C2214yes—
162#2476C2214yes—
163#2474C2214yes—
164#2467C2214yes—
165#2465C2214yes—
166#2465C2214yes—
167#2465C2214yes—
168#2465C2214yes—
169#2465C2214yes—
170#2462C2214yes—
171#2454C2212yes—
172#2452C2212yes—
173#2452C2212yes—
174#2452C2212yes—
175#2452C2212yes—
176#2445C2212yes—
177#2442C2212yes—
178#2440C2214yes—
179#2440C2212yes—
180#2440C2212yes—
181#2440C2212yes—
182#2439C2214yes—
183#2439C2214yes—
184#2432C2214yes—
185#2430C2214yes—
186#2429C2214yes—
187#2428C2212yes—
188#2427C2212yes—
189#2426C2214yes—
190#2426C2214yes—
191#2426C2212yes—
192#2423C2214yes—
193#2422C2212yes—
194#2416C2212yes—
195#2416C2212yes—
196#2399C2214yes—
197#2396C2212yes—
198#2396C2214yes—
199#2396C2214yes—
200#2395C2212yes—
201#2395C2212yes—
202#2374C2214yes—
203#2374C2214yes—
204#2370C2212yes—
205#2370C2212yes—
206#2369C2212yes—
207#2368C2214yes—
208#2366C2211yescharacteristic
209#2365C2212yes—
210#2365C2211yescharacteristic
211#2365C2212yes—
212#2365C2212yes—
213#2363C2212yes—
214#2363C2212yes—
215#2363C2212yes—
216#2362C2214yes—
217#2360C2214yes—
218#2355C2211yescharacteristic
219#2354C2212yes—
220#2354C2212yes—
221#2354C2212yes—
222#2354C2212yes—
223#2354C2211yescharacteristic
224#2347C2212yes—
225#2346C2212yes—
226#2345C2212yes—
227#2345C2212yes—
228#2341C2214yes—
229#2335C2214yes—
230#2335C2214yes—
231#2334C2214yes—
232#2331C2212yes—
233#2330C2212yes—
234#2329C2212yes—
235#2324C2212yes—
236#2324C2212yes—
237#2323C2214yes—
238#2317C2211yescharacteristic
239C4×C4⋊Q8C2212yes—
240C4×C4⋊Q8C2212yes—
241C4×#125C2212yes—
242C4×#125C2212yes—
243C4×#126C2212yes—
244C4×C22⋊Q8C2214yes—
245C4×C22⋊Q8C2211yescharacteristic
246C4×#121C2211yescharacteristic
247#2297C2214yes—
248#2296C2211yescharacteristic
249#2295C2212yes—
250#2293C2212yes—
251#2293C2212yes—
252C2×#389C2211yescharacteristic
253#2290C2214yes—
254#2274C2211yescharacteristic
255#2274C2212yes—
256#2274C2211yescharacteristic
257C42×D4C2212yes—
258C4×#117C2211yescharacteristic
259C22×#41C2314yes—
260#547—216no—
261#544—28no—
262#537—48no—
263#533—416no—
264C2×C4⋊Q8C2312yes—
265C2×C4⋊Q8C2312yes—
266C2×C4⋊Q8C2312yes—
267C2×C4⋊Q8C2312yes—
268C2×C4⋊Q8C2311yescharacteristic
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×#127C2311yescharacteristic
272C2×#126C2312yes—
273C2×#126C2314yes—
274C2×#126C2314yes—
275C2×#126C2314yes—
276C2×#125C2312yes—
277C2×#125C2312yes—
278C2×#125C2312yes—
279C2×#125C2314yes—
280C2×#125C2312yes—
281C2×#125C2312yes—
282C2×#124C2312yes—
283C2×#124C2312yes—
284C2×#124C2314yes—
285C2×#124C2314yes—
286C2×#123C2314yes—
287C2×#123C2314yes—
288C2×#123C2314yes—
289C2×#123C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2311yescharacteristic
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×C22⋊Q8C2314yes—
300C2×C22⋊Q8C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#121C2311yescharacteristic
304C2×#121C2314yes—
305C2×#121C2312yes—
306C2×#121C2312yes—
307C2×#121C2314yes—
308C2×#121C2314yes—
309C2×#121C2312yes—
310C2×C4×Q8C2312yes—
311C2×C4×Q8C2314yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×Q8C2314yes—
314C2×C4×Q8C2314yes—
315C2×C4×Q8C2314yes—
316C2×C4×D4C2312yes—
317C2×C4×D4C2312yes—
318C2×C4×D4C2312yes—
319C2×C4×D4C2312yes—
320C2×C4×D4C2312yes—
321C2×C4×D4C2311yescharacteristic
322C2×#117C2311yescharacteristic
323C2×#117C2312yes—
324C2×#117C2311yescharacteristic
325C2×#117C2311yescharacteristic
326C2×#117C2311yescharacteristic
327C2×#117C2312yes—
328C2×#117C2314yes—
329C2×#117C2314yes—
330C2×#117C2314yes—
331C22×C4⋊C4C2312yes—
332C22×C4⋊C4C2311yescharacteristic
333C22×C4⋊C4C2312yes—
334C22×C4⋊C4C2311yescharacteristic
335C22×C42C2314yes—
336C22×C42C2311yescharacteristic
337#400C2312yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2312yes—
345#400C2312yes—
346#399C2314yes—
347#399C2314yes—
348#399C2314yes—
349#399C2312yes—
350#399C2312yes—
351#399C2312yes—
352#399C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2312yes—
361#398C2312yes—
362#398C2314yes—
363#398C2314yes—
364#398C2312yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#397C2312yes—
374#397C2312yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2312yes—
381#397C2312yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2312yes—
387#397C2312yes—
388#397C2314yes—
389#396C2312yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2314yes—
408#395C2314yes—
409#395C2314yes—
410#395C2314yes—
411#395C2314yes—
412#395C2314yes—
413#395C2314yes—
414#395C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2312yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2312yes—
431#394C2312yes—
432#394C2312yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#393C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2312yes—
442#393C2314yes—
443#393C2314yes—
444#392C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2312yes—
453#391C2312yes—
454#391C2314yes—
455#391C2311yescharacteristic
456#391C2312yes—
457#391C2312yes—
458#390C2314yes—
459#390C2314yes—
460#390C2314yes—
461#390C2314yes—
462#390C2312yes—
463#390C2312yes—
464#390C2314yes—
465#390C2312yes—
466#390C2314yes—
467#390C2314yes—
468#390C2312yes—
469#390C2312yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2311yescharacteristic
474#390C2312yes—
475#390C2312yes—
476#390C2312yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#389C2311yescharacteristic
482#389C2312yes—
483#389C2312yes—
484#389C2312yes—
485#389C2311yescharacteristic
486#389C2314yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2312yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2314yes—
495#389C2314yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2314yes—
501#389C2312yes—
502#389C2314yes—
503#389C2311yescharacteristic
504#389C2312yes—
505#389C2314yes—
506#389C2314yes—
507#389C2311yescharacteristic
508#389C2312yes—
509#389C2314yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2312yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2312yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2311yescharacteristic
523#389C2312yes—
524#389C2311yescharacteristic
525#388C2312yes—
526#388C2312yes—
527#388C2312yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2312yes—
550#388C2312yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2312yes—
562#388C2312yes—
563#388C2314yes—
564#388C2314yes—
565#388C2312yes—
566#388C2314yes—
567#387C2312yes—
568#387C2312yes—
569#387C2312yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2312yes—
574#387C2314yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#387C2314yes—
599#387C2312yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2312yes—
610#386C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#385C2314yes—
622#385C2312yes—
623#385C2312yes—
624#385C2314yes—
625#385C2314yes—
626#385C2312yes—
627#384C2312yes—
628#384C2312yes—
629#384C2314yes—
630#384C2311yescharacteristic
631#384C2311yescharacteristic
632#384C2312yes—
633#384C2312yes—
634#383C2312yes—
635#383C2314yes—
636#382C2312yes—
637#382C2312yes—
638#382C2314yes—
639#382C2314yes—
640#382C2314yes—
641#382C2312yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2312yes—
647#380C2312yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#380C2312yes—
655#380C2311yescharacteristic
656#380C2311yescharacteristic
657C4×C4⋊C4C2311yescharacteristic
658C4×C4⋊C4C2312yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2314yes—
661C4×C4⋊C4C2311yescharacteristic
662C4×C4⋊C4C2314yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2314yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2312yes—
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2312yes—
677C4×C4⋊C4C2314yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2314yes—
680C4×C4⋊C4C2312yes—
681C4×C4⋊C4C2311yescharacteristic
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2311yescharacteristic
686C4×C4⋊C4C2314yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2311yescharacteristic
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2311yescharacteristic
692C4×C22⋊C4C2312yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2312yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701C4×C22⋊C4C2314yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711#376C2312yes—
712#376C2314yes—
713C2×#95C2312yes—
714C43C2312yes—
715C43C2312yes—
716C2×#41—216no—
717C2×#41—48no—
718C2×#41—84no—
719C22×Q8C2414yes—
720C22×Q8C2412yes—
721C22×Q8C2414yes—
722C22×Q8C2411yescharacteristic
723C22×Q8C2414yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2411yescharacteristic
727C22×D4C2412yes—
728C22×D4C2414yes—
729C22×D4C2414yes—
730C22×D4C2414yes—
731C22×D4C2412yes—
732C23×C4C2412yes—
733C23×C4C2414yes—
734C23×C4C2414yes—
735C23×C4C2411yescharacteristic
736C23×C4C2411yescharacteristic
737C23×C4C2414yes—
738C23×C4C2411yescharacteristic
739C23×C4C2412yes—
740C23×C4C2414yes—
741C23×C4C2412yes—
742C4⋊Q8—28no—
743C4⋊Q8—28no—
744C4⋊Q8—28no—
745C4⋊Q8—42no—
746C4⋊Q8—44no—
747C4⋊Q8—48no—
748C4⋊Q8—48no—
749#127—42no—
750#126—28no—
751#126—84no—
752#126—84no—
753#126—84no—
754#125—28no—
755#125—28no—
756#125—28no—
757#125—48no—
758#125—82no—
759#125—82no—
760#124—84no—
761#124—82no—
762#124—82no—
763#124—84no—
764#123—216no—
765#123—216no—
766#123—84no—
767#123—84no—
768C22⋊Q8—216no—
769C22⋊Q8—216no—
770C22⋊Q8—216no—
771C22⋊Q8—24no—
772C22⋊Q8—48no—
773C22⋊Q8—48no—
774C22⋊Q8—48no—
775C22⋊Q8—48no—
776C22⋊Q8—82no—
777C22⋊Q8—84no—
778C22⋊Q8—84no—
779#121—28no—
780#121—28no—
781#121—24no—
782#121—44no—
783#121—48no—
784#121—48no—
785#121—48no—
786#121—44no—
787#121—82no—
788C4×Q8—28no—
789C4×Q8—42no—
790C4×Q8—48no—
791C4×Q8—48no—
792C4×Q8—48no—
793C4×Q8—84no—
794C4×D4—28no—
795C4×D4—28no—
796C4×D4—28no—
797C4×D4—28no—
798C4×D4—44no—
799C4×D4—42no—
800#117—24no—
801#117—24no—
802#117—24no—
803#117—28no—
804#117—42no—
805#117—44no—
806#117—48no—
807#117—48no—
808#117—84no—
809C2×C4⋊C4—28no—
810C2×C4⋊C4—42no—
811C2×C4⋊C4—44no—
812C2×C4⋊C4#4118yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2411yescharacteristic
820C2×C4⋊C4C2411yescharacteristic
821C2×C4⋊C4C2411yescharacteristic
822C2×C4⋊C4C2411yescharacteristic
823C2×C4⋊C4C2411yescharacteristic
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2411yescharacteristic
846C2×C4⋊C4C2411yescharacteristic
847C2×C4⋊C4C2412yes—
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2411yescharacteristic
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2411yescharacteristic
857C2×C4⋊C4C2412yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2414yes—
865C2×C4⋊C4C2414yes—
866C2×C4⋊C4C2414yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2411yescharacteristic
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2412yes—
876C2×C4⋊C4C2412yes—
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2412yes—
879C2×C4⋊C4C2412yes—
880C2×C4⋊C4C2411yescharacteristic
881C2×C4⋊C4C2411yescharacteristic
882C2×C4⋊C4C2411yescharacteristic
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2412yes—
891C2×C22⋊C4C2412yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2412yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
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⋊C4C2412yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2412yes—
910C2×C22⋊C4C2414yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2414yes—
913C2×C22⋊C4C2414yes—
914C2×C22⋊C4C2412yes—
915C2×C22⋊C4C2412yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2412yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2414yes—
922C2×C22⋊C4C2414yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2412yes—
925C2×C22⋊C4C2412yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C42—48no—
931C2×C42—42no—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2412yes—
936C2×C42C2412yes—
937C2×C42C2412yes—
938C2×C42C2412yes—
939C2×C42C2414yes—
940C2×C42C2412yes—
941C2×C42C2411yescharacteristic
942C2×C42C2412yes—
943C2×C42C2412yes—
944C2×C42C2411yescharacteristic
945C2×C42C2412yes—
946C2×C42C2412yes—
947C2×C42C2414yes—
948C2×C42C2414yes—
949C2×C42C2414yes—
950C2×C42C2414yes—
951C2×C42C2412yes—
952C2×C42C2414yes—
953C2×C42C2414yes—
954C2×C42C2412yes—
955C2×C42C2412yes—
956C2×C42C2414yes—
957C2×C42C2412yes—
958C2×C42C2414yes—
959C2×C42C2411yescharacteristic
960C2×C42C2411yescharacteristic
961#95C2414yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2412yes—
967#95C2412yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2414yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2412yes—
993#95C2412yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2412yes—
1009#95C2412yes—
1010#95C2412yes—
1011#95C2412yes—
1012#95C2412yes—
1013#95C2412yes—
1014#95C2412yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021C24C2514yes—
1022C24C2512yes—
1023C24C2511yescharacteristic
1024#41—832no—
1025C2×Q8—28no—
1026C2×Q8—28no—
1027C2×Q8—28no—
1028C2×Q8—24no—
1029C2×Q8—22no—
1030C2×Q8—44no—
1031C2×Q8—44no—
1032C2×Q8—44no—
1033C2×Q8—41no—
1034C2×Q8—42no—
1035C2×Q8—44no—
1036C2×Q8—44no—
1037C2×Q8—41no—
1038C2×Q8—42no—
1039C2×Q8—44no—
1040C2×D4—24no—
1041C2×D4—28no—
1042C2×D4—24no—
1043C2×D4—28no—
1044C2×D4—24no—
1045C2×D4—22no—
1046C2×D4—24no—
1047C2×D4—24no—
1048C2×D4—24no—
1049C2×D4—42no—
1050C2×D4—41no—
1051C2×D4—44no—
1052C2×D4—44no—
1053C2×D4—42no—
1054C2×D4—44no—
1055C2×D4—41no—
1056C2×D4—44no—
1057C2×D4—42no—
1058C2×D4—44no—
1059C2×D4—42no—
1060C2×D4—44no—
1061C2×D4—42no—
1062C2×D4—44no—
1063C2×D4—42no—
1064C22×C4—22no—
1065C22×C4—22no—
1066C22×C4—24no—
1067C22×C4—28no—
1068C22×C4—28no—
1069C22×C4—24no—
1070C22×C4—28no—
1071C22×C4—28no—
1072C22×C4—24no—
1073C22×C4—28no—
1074C22×C4—22no—
1075C22×C4—22no—
1076C22×C4—44no—
1077C22×C4—42no—
1078C22×C4—44no—
1079C22×C4—42no—
1080C22×C4—44no—
1081C22×C4—41no—
1082C22×C4—41no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—41no—
1086C22×C4—41no—
1087C22×C4—44no—
1088C22×C4—44no—
1089C22×C4—42no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4C2×#4114yes—
1093C22×C4C2×#4118yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2511yescharacteristic
1097C22×C4C2512yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2514yes—
1104C22×C4C2514yes—
1105C22×C4C2514yes—
1106C22×C4C2514yes—
1107C22×C4C2511yescharacteristic
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2511yescharacteristic
1116C22×C4C2511yescharacteristic
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2511yescharacteristic
1120C4⋊C4—24no—
1121C4⋊C4—28no—
1122C4⋊C4—22no—
1123C4⋊C4—22no—
1124C4⋊C4—22no—
1125C4⋊C4—22no—
1126C4⋊C4—24no—
1127C4⋊C4—28no—
1128C4⋊C4—28no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—28no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—28no—
1135C4⋊C4—24no—
1136C4⋊C4—24no—
1137C4⋊C4—24no—
1138C4⋊C4—28no—
1139C4⋊C4—22no—
1140C4⋊C4—24no—
1141C4⋊C4—24no—
1142C4⋊C4—24no—
1143C4⋊C4—24no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—42no—
1147C4⋊C4—44no—
1148C4⋊C4—41no—
1149C4⋊C4—41no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—41no—
1157C4⋊C4—41no—
1158C4⋊C4—42no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—44no—
1162C4⋊C4—44no—
1163C4⋊C4—44no—
1164C4⋊C4—44no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—44no—
1168C4⋊C4—44no—
1169C4⋊C4—42no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—42no—
1175C4⋊C4—44no—
1176C4⋊C4—41no—
1177C4⋊C4—41no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—42no—
1181C4⋊C4—42no—
1182C4⋊C4—42no—
1183C4⋊C4—42no—
1184C4⋊C4—44no—
1185C4⋊C4C2×#4118yes—
1186C4⋊C4C2×#4118yes—
1187C4⋊C4H(5,𝔽2)14yes—
1188C4⋊C42−1+414yes—
1189C4⋊C42−1+414yes—
1190C22⋊C4—24no—
1191C22⋊C4—24no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—28no—
1195C22⋊C4—28no—
1196C22⋊C4—28no—
1197C22⋊C4—28no—
1198C22⋊C4—28no—
1199C22⋊C4—24no—
1200C22⋊C4—24no—
1201C22⋊C4—28no—
1202C22⋊C4—28no—
1203C22⋊C4—28no—
1204C22⋊C4—24no—
1205C22⋊C4—24no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—42no—
1209C22⋊C4—42no—
1210C22⋊C4—42no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—42no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—42no—
1221C22⋊C4—42no—
1222C22⋊C4—44no—
1223C22⋊C4—44no—
1224C22⋊C4—42no—
1225C22⋊C4—44no—
1226C22⋊C4—44no—
1227C22⋊C4—44no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—42no—
1232C22⋊C4—44no—
1233C22⋊C4—42no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C42—24no—
1238C42—24no—
1239C42—24no—
1240C42—24no—
1241C42—28no—
1242C42—24no—
1243C42—24no—
1244C42—28no—
1245C42—24no—
1246C42—24no—
1247C42—24no—
1248C42—22no—
1249C42—22no—
1250C42—24no—
1251C42—24no—
1252C42—41no—
1253C42—41no—
1254C42—44no—
1255C42—44no—
1256C42—44no—
1257C42—44no—
1258C42—44no—
1259C42—44no—
1260C42—42no—
1261C42—44no—
1262C42—42no—
1263C42—42no—
1264C42—44no—
1265C42—42no—
1266C23—21no—
1267C23—21no—
1268C23—21no—
1269C23—21no—
1270C23—21no—
1271C23—21no—
1272C23—24no—
1273C23—22no—
1274C23—24no—
1275C23—22no—
1276C23—22no—
1277C23—22no—
1278C23—24no—
1279C23—24no—
1280C23—22no—
1281C23—24no—
1282C23—24no—
1283C23—22no—
1284C23—24no—
1285C23—22no—
1286C23C22×#4112yes—
1287C23C2611yescharacteristic
1288Q8—416no—
1289Q8—88no—
1290Q8—82no—
1291Q8—84no—
1292Q8—88no—
1293D4—48no—
1294D4—48no—
1295D4—84no—
1296D4—82no—
1297D4—88no—
1298D4—88no—
1299D4—162no—
1300D4—164no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—24no—
1305C2×C4—21no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—24no—
1314C2×C4—22no—
1315C2×C4—28no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—22no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—21no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—22no—
1347C2×C4—22no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—22no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—22no—
1355C2×C4—24no—
1356C2×C4—22no—
1357C2×C4—22no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—22no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—21no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—24no—
1369C2×C4—21no—
1370C2×C4—48no—
1371C2×C4—416no—
1372C2×C4—416no—
1373C2×C4—48no—
1374C2×C4—82no—
1375C2×C4—82no—
1376C2×C4—88no—
1377C2×C4—88no—
1378C2×C4—162no—
1379C2×C4C22×#4112yes—
1380C2×C4C22×#4118yes—
1381C2×C4C22×#4112yes—
1382C2×C4C2×H(5,𝔽2)14yes—
1383C2×C4C2×H(5,𝔽2)12yes—
1384C2×C4C2×2−1+414yes—
1385C2×C4C2×2−1+412yes—
1386C2×C4C2×2−1+414yes—
1387C2×C4C2×2−1+412yes—
1388C2×C4#58512yes—
1389C22—22no—
1390C22—22no—
1391C22—22no—
1392C22—41no—
1393C22—41no—
1394C22—41no—
1395C22—41no—
1396C22—44no—
1397C22—42no—
1398C22—44no—
1399C22—42no—
1400C22—44no—
1401C22—42no—
1402C22—42no—
1403C22—44no—
1404C22—44no—
1405C22—42no—
1406C22—44no—
1407C22—42no—
1408C22—42no—
1409C22—44no—
1410C22C23×#4111yescharacteristic
1411C22C22×H(5,𝔽2)11yescharacteristic
1412C22C22×2−1+411yescharacteristic
1413C22C22×2−1+411yescharacteristic
1414C22C2×#58511yescharacteristic
1415C22H(7,𝔽2)11yescharacteristic
1416C22H(7,𝔽2)11yescharacteristic
1417C4—28no—
1418C4—24no—
1419C4—24no—
1420C4—24no—
1421C4—22no—
1422C4—22no—
1423C4—22no—
1424C4—44no—
1425C4—42no—
1426C4—42no—
1427C4—42no—
1428C4—42no—
1429C4—42no—
1430C4—42no—
1431C4—42no—
1432C4—44no—
1433C4—42no—
1434C4—41no—
1435C4—42no—
1436C4—42no—
1437C4—41no—
1438C4—44no—
1439C4—44no—
1440C4—42no—
1441C4—42no—
1442C4#346114yes—
1443C2—42no—
1444C2—84no—
1445C2—82no—
1446C2C2×#346111yescharacteristic
1447C2#6292911yescharacteristic
1448C2#6293011yescharacteristic
1449C2#6298311yescharacteristic
1450C2#6299911yescharacteristic
1451C2#6301611yescharacteristic
1452C2#6307011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#39359C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52281C2semidirect
2. #52162C2semidirect
3. #42758C2semidirect
4. #42585C2semidirect
5. #42423C2semidirect
6. #42106C2semidirect
7. #41053C2semidirect
8. #40958C2semidirect
9. #40167C2semidirect
10. #39661C2semidirect
11. #39623C2semidirect
13. #38829C2semidirect
14. #38771C2semidirect
15. #38677C2semidirect
16. #37781C2semidirect
17. #37350C2semidirect
18. #37315C2semidirect
19. #37251C2semidirect
20. #36895C2semidirect
21. #36315C2semidirect
22. #36302C2semidirect
23. #36251C2semidirect
24. #36132C2semidirect
25. #36000C2semidirect
26. #36000C2semidirect
27. #35815C2semidirect
28. #34316C2semidirect
29. #34272C2semidirect

Maximal subgroups

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

subgroupindex
#522812
#521622
#427582
#425852
#424232
#421062
#410532
#409582
#401672
#396612
#396232
#393592
#388292
#387712
#386772
#377812
#373502
#373152
#372512
#368952
#363152
#363022
#362512
#361322
#360002
#358152
#343162
#342722