Finite Group Databasebeta

← #8115579

Subgroups — #8115579

Order 512.

4216 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58875C214yesmaximal, complemented
2#58872C214yesmaximal, complemented
3#58147C214yesmaximal, complemented
4#57877C214yesmaximal, complemented
5#57719C214yesmaximal, complemented
6#55738C214yesmaximal, complemented
7#54354C214yesmaximal, complemented
8#53924C214yesmaximal, complemented
9#53112C212yesmaximal, complemented
10#52989C212yesmaximal, complemented
11#44959C212yesmaximal, complemented
12#44945C212yesmaximal, complemented
13#42981C211yesmaximal, characteristic, complemented
14#42977C211yesmaximal, characteristic
15#42612C212yesmaximal, complemented
16#42569C212yesmaximal, complemented
17#42522C211yesmaximal, characteristic, complemented
18#42487C211yesmaximal, characteristic, complemented
19#38238C212yesmaximal, complemented
20#38228C212yesmaximal, complemented
21#38074C212yesmaximal, complemented
22#38056C212yesmaximal, complemented
23#37358C212yesmaximal, complemented
24#37336C212yesmaximal, complemented
25#35296C211yesmaximal, characteristic, complemented
26#35266C211yesmaximal, characteristic, complemented
27#34644C211yesmaximal, characteristic, complemented
28#2864C2211yescharacteristic, complemented
29#2860C2212yes—
30#2860C2212yes—
31#2858C2211yescharacteristic, complemented
32#2854C2212yes—
33#2844C2212yescomplemented
34#2840C2212yes—
35#2837C2214yescomplemented
36#2836C2214yescomplemented
37#2832C2214yescomplemented
38#2830C2214yescomplemented
39#2828C2212yes—
40#2827C2214yescomplemented
41#2827C2214yescomplemented
42#2827C2214yescomplemented
43#2826C2212yes—
44#2824C2214yescomplemented
45#2820C2214yescomplemented
46#2814C2214yescomplemented
47#2808C2214yescomplemented
48#2807C2212yes—
49#2804C2212yes—
50#2800C2214yescomplemented
51#2798C2214yescomplemented
52#2795C2212yescomplemented
53#2788C2214yes—
54#2786C2214yescomplemented
55#2784C2212yes—
56#2783C2214yescomplemented
57#2781C2214yescomplemented
58#2780C2214yes—
59#2768C2214yescomplemented
60#2756C2214yes—
61#2754C2214yescomplemented
62#2754C2214yescomplemented
63#2753C2214yes—
64#2753C2214yes—
65#2751C2214yes—
66#2750C2214yes—
67#2750C2214yescomplemented
68#2749C2214yes—
69#2748C2214yes—
70#2747C2214yescomplemented
71#2747C2214yescomplemented
72#2744C2214yescomplemented
73#2742C2212yes—
74#2741C2214yescomplemented
75#2739C2214yescomplemented
76#2730C2214yescomplemented
77#2729C2214yescomplemented
78#2728C2214yescomplemented
79#2724C2214yescomplemented
80#2723C2214yescomplemented
81#2722C2214yescomplemented
82#2717C2214yescomplemented
83#2716C2214yescomplemented
84#2716C2214yescomplemented
85#2712C2214yescomplemented
86#2710C2214yescomplemented
87#2708C2214yescomplemented
88#2707C2214yes—
89#2707C2214yescomplemented
90#2706C2214yes—
91#2706C2214yes—
92#2705C2214yescomplemented
93#2702C2214yescomplemented
94#2701C2214yescomplemented
95#2700C2214yescomplemented
96#2696C2214yescomplemented
97#2695C2214yescomplemented
98#2695C2214yescomplemented
99#2693C2214yescomplemented
100#2692C2214yes—
101#2691C2214yescomplemented
102#2690C2214yescomplemented
103#2687C2214yes—
104#2686C2214yescomplemented
105#2685C2214yes—
106#2684C2214yes—
107#2681C2214yescomplemented
108#2680C2212yescomplemented
109#2678C2214yes—
110#2674C2214yescomplemented
111#2674C2214yescomplemented
112#2672C2214yescomplemented
113#2670C2212yes—
114#2668C2212yes—
115#2667C2212yes—
116#2667C2212yes—
117#2666C2212yescomplemented
118#2666C2212yescomplemented
119#2666C2212yescomplemented
120#2666C2212yescomplemented
121#2665C2212yes—
122#2665C2212yes—
123#2661C2214yes—
124#2650C2214yescomplemented
125#2647C2214yescomplemented
126#2647C2212yescomplemented
127#2644C2212yes—
128#2644C2212yes—
129#2644C2212yes—
130#2644C2212yescomplemented
131#2644C2212yescomplemented
132#2641C2212yes—
133#2639C2214yescomplemented
134#2630C2214yes—
135#2630C2214yescomplemented
136#2628C2211yescharacteristic
137#2626C2214yes—
138#2625C2214yescomplemented
139#2619C2211yescharacteristic
140#2612C2212yescomplemented
141#2610C2214yes—
142#2609C2214yescomplemented
143#2603C2214yes—
144#2595C2214yescomplemented
145#2589C2214yescomplemented
146#2584C2212yescomplemented
147#2580C2212yes—
148#2580C2212yes—
149#2580C2212yescomplemented
150#2570C2212yescomplemented
151#2563C2214yes—
152#2563C2212yes—
153#2560C2214yescomplemented
154#2557C2214yes—
155#2555C2212yes—
156#2550C2212yescomplemented
157#2548C2212yes—
158#2548C2212yes—
159#2546C2212yescomplemented
160#2541C2212yes—
161#2538C2212yescomplemented
162#2534C2214yes—
163#2532C2214yescomplemented
164#2529C2214yescomplemented
165#2515C2214yescomplemented
166#2513C2212yes—
167#2513C2212yes—
168#2513C2212yes—
169#2513C2214yes—
170#2513C2212yescomplemented
171#2513C2212yescomplemented
172#2512C2214yes—
173#2512C2212yes—
174#2509C2212yescomplemented
175#2509C2212yescomplemented
176#2509C2212yescomplemented
177#2508C2212yescomplemented
178#2508C2212yescomplemented
179#2506C2212yescomplemented
180#2505C2214yescomplemented
181#2500C2212yes—
182#2498C2214yescomplemented
183#2489C2214yescomplemented
184#2488C2214yescomplemented
185#2480C2214yes—
186#2480C2214yes—
187#2475C2214yescomplemented
188#2474C2214yescomplemented
189#2474C2214yescomplemented
190#2471C2214yes—
191#2470C2214yescomplemented
192#2466C2214yescomplemented
193#2463C2212yes—
194#2454C2212yes—
195#2454C2212yescomplemented
196#2452C2212yes—
197#2452C2212yes—
198#2452C2212yescomplemented
199#2452C2212yescomplemented
200#2450C2214yes—
201#2445C2212yes—
202#2445C2212yes—
203#2445C2212yes—
204#2445C2212yes—
205#2445C2212yes—
206#2445C2212yescomplemented
207#2442C2212yes—
208#2439C2212yes—
209#2437C2212yes—
210#2433C2212yes—
211#2425C2214yescomplemented
212#2418C2214yes—
213#2418C2214yes—
214#2415C2214yescomplemented
215#2412C2214yes—
216#2412C2214yes—
217#2411C2214yes—
218#2402C2212yescomplemented
219#2399C2211yescharacteristic, complemented
220#2399C2211yescharacteristic, complemented
221#2396C2211yescharacteristic
222#2396C2212yes—
223#2396C2211yescharacteristic
224#2370C2212yescomplemented
225#2366C2212yes—
226#2363C2212yes—
227#2361C2212yes—
228#2354C2212yes—
229#2349C2212yescomplemented
230#2346C2212yes—
231D4×C22⋊C4C2212yes—
232#2331C2211yescharacteristic, complemented
233#2331C2212yescomplemented
234#2328C2212yes—
235#2328C2211yescharacteristic, complemented
236#2324C2212yes—
237#2319C2212yes—
238#2319C2212yescomplemented
239#2317C2211yescharacteristic
240#2316C2211yescharacteristic
241#2309C2211yescharacteristic
242#2309C2211yescharacteristic
243#2296C2211yescharacteristic
244#2295C2211yescharacteristic, complemented
245#2295C2211yescharacteristic, complemented
246#2295C2212yescomplemented
247#2293C2212yescomplemented
248C2×#390C2211yescharacteristic
249#2283C2212yes—
250C4×#117C2211yescharacteristic
251C23×D4C2311yescharacteristic
252C2×C4⋊Q8C2312yes—
253C2×C4⋊Q8C2311yescharacteristic
254C2×C4⋊Q8C2314yes—
255C2×#127C2312yes—
256C2×#127C2311yescharacteristic
257C2×#127C2312yes—
258C2×#126C2314yes—
259C2×#126C2314yes—
260C2×#126C2314yes—
261C2×#125C2312yes—
262C2×#125C2314yes—
263C2×#124C2314yes—
264C2×#124C2314yes—
265C2×#124C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×#123C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×C22⋊Q8C2314yes—
276C2×C22⋊Q8C2314yes—
277C2×C22⋊Q8C2314yes—
278C2×#121C2312yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#120C2314yes—
282C2×#120C2314yes—
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2312yes—
285C2×C4×Q8C2311yescharacteristic
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2312yes—
291C2×C4×D4C2314yes—
292C2×C4×D4C2314yes—
293C2×#117C2311yescharacteristic
294C2×#117C2311yescharacteristic
295C2×#117C2311yescharacteristic
296C2×#117C2311yescharacteristic
297C2×#117C2314yes—
298C2×#117C2314yes—
299C22×C4⋊C4C2311yescharacteristic
300C22×C22⋊C4C2314yes—
301C22×C22⋊C4C2314yes—
302C22×C42C2311yescharacteristic
303#400C2312yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2311yescharacteristic
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2312yes—
317#400C2312yes—
318#400C2314yes—
319#400C2314yes—
320#400C2312yes—
321#400C2311yescharacteristic
322#400C2312yes—
323#400C2312yes—
324#399C2314yes—
325#399C2314yes—
326#399C2311yescharacteristic
327#399C2314yes—
328#399C2314yes—
329#399C2314yes—
330#399C2312yes—
331#399C2311yescharacteristic
332#399C2312yes—
333#398C2314yes—
334#398C2314yes—
335#398C2312yes—
336#398C2312yes—
337#398C2312yes—
338#398C2314yes—
339#398C2314yes—
340#398C2312yes—
341#398C2314yes—
342#398C2314yes—
343#398C2312yes—
344#398C2314yes—
345#398C2312yes—
346#398C2312yes—
347#398C2314yes—
348#398C2314yes—
349#398C2312yes—
350#398C2314yes—
351#398C2312yes—
352#398C2314yes—
353#398C2312yes—
354#398C2312yes—
355#398C2312yes—
356#397C2314yes—
357#397C2314yes—
358#397C2314yes—
359#397C2314yes—
360#397C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#397C2314yes—
375#397C2314yes—
376#397C2314yes—
377#397C2314yes—
378#397C2314yes—
379#397C2314yes—
380#397C2314yes—
381#397C2314yes—
382#396C2314yes—
383#396C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2312yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2312yes—
399#396C2312yes—
400#396C2312yes—
401#395C2312yes—
402#395C2314yes—
403#395C2312yes—
404#395C2312yes—
405#395C2311yescharacteristic
406#395C2312yes—
407#395C2314yes—
408#395C2312yes—
409#395C2311yescharacteristic
410#395C2312yes—
411#394C2314yes—
412#394C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2312yes—
427#394C2314yes—
428#394C2314yes—
429#394C2312yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#393C2314yes—
436#393C2312yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#393C2314yes—
444#393C2314yes—
445#393C2311yescharacteristic
446#393C2312yes—
447#393C2314yes—
448#393C2311yescharacteristic
449#392C2314yes—
450#392C2312yes—
451#392C2314yes—
452#392C2314yes—
453#392C2312yes—
454#392C2314yes—
455#391C2314yes—
456#391C2314yes—
457#391C2314yes—
458#391C2314yes—
459#391C2314yes—
460#391C2314yes—
461#391C2312yes—
462#391C2312yes—
463#391C2312yes—
464#391C2312yes—
465#390C2314yes—
466#390C2312yes—
467#390C2314yes—
468#390C2312yes—
469#390C2314yes—
470#390C2312yes—
471#390C2312yes—
472#390C2312yes—
473#390C2314yes—
474#390C2312yes—
475#390C2312yes—
476#390C2314yes—
477#390C2312yes—
478#390C2312yes—
479#390C2312yes—
480#390C2312yes—
481#390C2312yes—
482#390C2312yes—
483#390C2312yes—
484#390C2312yes—
485#390C2312yes—
486#390C2314yes—
487#390C2314yes—
488#390C2312yes—
489#390C2312yes—
490#390C2312yes—
491#390C2312yes—
492#390C2314yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2314yes—
497#389C2312yes—
498#389C2312yes—
499#389C2312yes—
500#389C2312yes—
501#389C2312yes—
502#389C2312yes—
503#389C2312yes—
504#389C2312yes—
505#389C2312yes—
506#389C2312yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2314yes—
511#389C2312yes—
512#389C2312yes—
513#389C2312yes—
514#389C2314yes—
515#389C2312yes—
516#389C2314yes—
517#389C2314yes—
518#389C2314yes—
519#389C2312yes—
520#389C2312yes—
521#389C2312yes—
522#389C2312yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
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#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#387C2312yes—
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#387C2312yes—
575#387C2312yes—
576#387C2312yes—
577#387C2312yes—
578#387C2312yes—
579#387C2312yes—
580#387C2314yes—
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#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#385C2314yes—
602#385C2312yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2312yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#385C2314yes—
619#385C2314yes—
620#385C2314yes—
621#384C2312yes—
622#384C2312yes—
623#383C2312yes—
624#383C2312yes—
625#382C2311yescharacteristic
626#382C2314yes—
627#382C2312yes—
628#382C2314yes—
629#382C2311yescharacteristic
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2314yes—
634#382C2312yes—
635#382C2312yes—
636#381C2314yes—
637#381C2314yes—
638#381C2312yes—
639#381C2312yes—
640#380C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2312yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2312yes—
653#380C2312yes—
654#379C2312yes—
655#379C2312yes—
656#379C2314yes—
657#379C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C4⋊C4C2312yes—
660C4×C4⋊C4C2312yes—
661C4×C4⋊C4C2312yes—
662C4×C4⋊C4C2312yes—
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2311yescharacteristic
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2312yes—
673C4×C4⋊C4C2312yes—
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C22⋊C4C2314yes—
677C4×C22⋊C4C2314yes—
678C4×C22⋊C4C2312yes—
679C4×C22⋊C4C2312yes—
680C4×C22⋊C4C2312yes—
681C4×C22⋊C4C2312yes—
682#376C2312yes—
683#376C2312yes—
684#376C2311yescharacteristic
685#376C2314yes—
686#376C2311yescharacteristic
687C2×#95C2314yes—
688C43C2311yescharacteristic
689C43C2311yescharacteristic
690C25C2412yes—
691C22×Q8C2411yescharacteristic
692C22×Q8C2411yescharacteristic
693C22×Q8C2412yes—
694C22×Q8C2414yes—
695C22×Q8C2412yes—
696C22×D4—24no—
697C22×D4—42no—
698C22×D4—42no—
699C22×D4C2412yes—
700C22×D4C2412yes—
701C22×D4C2414yes—
702C22×D4C2412yes—
703C22×D4C2414yes—
704C22×D4C2414yes—
705C22×D4C2414yes—
706C22×D4C2414yes—
707C22×D4C2412yes—
708C22×D4C2412yes—
709C23×C4C2411yescharacteristic
710C23×C4C2412yes—
711C23×C4C2412yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C23×C4C2414yes—
715C23×C4C2414yes—
716C23×C4C2414yes—
717C4⋊Q8—42no—
718C4⋊Q8—44no—
719C4⋊Q8—84no—
720#127—42no—
721#127—44no—
722#127—44no—
723#126—84no—
724#126—84no—
725#126—84no—
726#125—44no—
727#125—84no—
728#124—84no—
729#124—84no—
730#124—84no—
731#123—84no—
732#123—84no—
733#123—84no—
734#123—84no—
735#123—84no—
736#123—84no—
737#123—84no—
738C22⋊Q8—84no—
739C22⋊Q8—84no—
740C22⋊Q8—84no—
741C22⋊Q8—84no—
742C22⋊Q8—84no—
743#121—28no—
744#121—84no—
745#121—84no—
746#120—84no—
747#120—84no—
748C4×Q8—42no—
749C4×Q8—44no—
750C4×Q8—42no—
751C4×D4—44no—
752C4×D4—44no—
753C4×D4—44no—
754C4×D4—44no—
755C4×D4—44no—
756C4×D4—84no—
757C4×D4—84no—
758#117—24no—
759#117—42no—
760#117—42no—
761#117—42no—
762#117—84no—
763#117—84no—
764C2×C4⋊C4—42no—
765C2×C4⋊C4C2412yes—
766C2×C4⋊C4C2412yes—
767C2×C4⋊C4C2412yes—
768C2×C4⋊C4C2412yes—
769C2×C4⋊C4C2412yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2412yes—
772C2×C4⋊C4C2412yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2414yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2412yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2411yescharacteristic
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2411yescharacteristic
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2412yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2414yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2414yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2412yes—
822C2×C22⋊C4—84no—
823C2×C22⋊C4—84no—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2414yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2411yescharacteristic
840C2×C22⋊C4C2411yescharacteristic
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2412yes—
852C2×C22⋊C4C2412yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C42—24no—
877C2×C42C2411yescharacteristic
878C2×C42C2411yescharacteristic
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881C2×C42C2412yes—
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2412yes—
886C2×C42C2411yescharacteristic
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2412yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2412yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2412yes—
896C2×C42C2414yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899#95C2412yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2412yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
915#95C2412yes—
916#95C2412yes—
917#95C2414yes—
918#95C2414yes—
919#95C2412yes—
920#95C2414yes—
921#95C2412yes—
922#95C2412yes—
923#95C2414yes—
924#95C2414yes—
925#95C2412yes—
926#95C2414yes—
927#95C2412yes—
928#95C2412yes—
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2412yes—
935#95C2414yes—
936#95C2414yes—
937#95C2411yescharacteristic
938#95C2412yes—
939#95C2412yes—
940#95C2414yes—
941#95C2414yes—
942#95C2411yescharacteristic
943#95C2412yes—
944#95C2412yes—
945#95C2414yes—
946#95C2411yescharacteristic
947#95C2412yes—
948#95C2411yescharacteristic
949#95C2412yes—
950#95C2412yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2412yes—
963#95C2412yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967C24—24no—
968C24—42no—
969C24—44no—
970C24—44no—
971C24—42no—
972C24C2514yes—
973C24C2514yes—
974C24C2511yescharacteristic
975C2×Q8—41no—
976C2×Q8—42no—
977C2×Q8—41no—
978C2×Q8—42no—
979C2×Q8—42no—
980C2×Q8—42no—
981C2×Q8—42no—
982C2×Q8—44no—
983C2×Q8—44no—
984C2×Q8—44no—
985C2×Q8—44no—
986C2×Q8—42no—
987C2×D4—28no—
988C2×D4—24no—
989C2×D4—24no—
990C2×D4—24no—
991C2×D4—24no—
992C2×D4—24no—
993C2×D4—24no—
994C2×D4—24no—
995C2×D4—44no—
996C2×D4—44no—
997C2×D4—44no—
998C2×D4—44no—
999C2×D4—44no—
1000C2×D4—42no—
1001C2×D4—42no—
1002C2×D4—44no—
1003C2×D4—44no—
1004C2×D4—44no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—44no—
1008C2×D4—44no—
1009C2×D4—44no—
1010C2×D4—44no—
1011C2×D4—42no—
1012C2×D4—42no—
1013C2×D4—44no—
1014C2×D4—44no—
1015C2×D4—88no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—24no—
1019C22×C4—42no—
1020C22×C4—44no—
1021C22×C4—44no—
1022C22×C4—44no—
1023C22×C4—44no—
1024C22×C4—44no—
1025C22×C4—44no—
1026C22×C4—42no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—42no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—44no—
1038C22×C42−1+414yes—
1039C22×C4C2511yescharacteristic
1040C22×C4C2512yes—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2514yes—
1044C22×C4C2512yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2514yes—
1049C22×C4C2512yes—
1050C22×C4C2514yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2512yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2511yescharacteristic
1060C22×C4C2511yescharacteristic
1061C22×C4C2511yescharacteristic
1062C22×C4C2511yescharacteristic
1063C4⋊C4—24no—
1064C4⋊C4—24no—
1065C4⋊C4—24no—
1066C4⋊C4—24no—
1067C4⋊C4—24no—
1068C4⋊C4—24no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—41no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—41no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—44no—
1089C4⋊C4—42no—
1090C4⋊C4—42no—
1091C4⋊C4—42no—
1092C4⋊C4—42no—
1093C4⋊C4—44no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—42no—
1114C4⋊C4—44no—
1115C4⋊C4—42no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C22⋊C4—24no—
1121C22⋊C4—28no—
1122C22⋊C4—42no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—44no—
1129C22⋊C4—44no—
1130C22⋊C4—42no—
1131C22⋊C4—41no—
1132C22⋊C4—41no—
1133C22⋊C4—42no—
1134C22⋊C4—44no—
1135C22⋊C4—44no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—44no—
1143C22⋊C4—42no—
1144C22⋊C4—44no—
1145C22⋊C4—44no—
1146C22⋊C4—44no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C22⋊C4—44no—
1172C42—24no—
1173C42—22no—
1174C42—22no—
1175C42—24no—
1176C42—22no—
1177C42—22no—
1178C42—22no—
1179C42—22no—
1180C42—24no—
1181C42—24no—
1182C42—24no—
1183C42—24no—
1184C42—42no—
1185C42—42no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—42no—
1191C42—44no—
1192C42—42no—
1193C42—42no—
1194C23—21no—
1195C23—21no—
1196C23—22no—
1197C23—22no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23—24no—
1208C23—24no—
1209C23—24no—
1210C23—24no—
1211C23—24no—
1212C23—84no—
1213C23—88no—
1214C23—88no—
1215C23—162no—
1216C23—162no—
1217C23C2×2−1+412yes—
1218C23C2611yescharacteristic
1219Q8—82no—
1220Q8—82no—
1221Q8—84no—
1222Q8—164no—
1223Q8—162no—
1224D4—48no—
1225D4—48no—
1226D4—84no—
1227D4—88no—
1228D4—88no—
1229D4—164no—
1230D4—162no—
1231D4—164no—
1232D4—164no—
1233D4—162no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—28no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—24no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—24no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—24no—
1289C2×C4—24no—
1290C2×C4—24no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—84no—
1300C2×C4—88no—
1301C2×C4—88no—
1302C2×C4—164no—
1303C2×C4—162no—
1304C2×C4—164no—
1305C2×C4—164no—
1306C2×C4C2×2−1+412yes—
1307C2×C4C2×2−1+412yes—
1308C2×C4#58512yes—
1309C2×C4#58512yes—
1310C22—22no—
1311C22—24no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—44no—
1324C22—44no—
1325C22—44no—
1326C22—44no—
1327C22—44no—
1328C22—44no—
1329C22—168no—
1330C22C22×2−1+411yescharacteristic
1331C22C2×#58511yescharacteristic
1332C22C2×#58511yescharacteristic
1333C22H(7,𝔽2)12yes—
1334C22H(7,𝔽2)12yes—
1335C4—22no—
1336C4—44no—
1337C4—42no—
1338C4—42no—
1339C4—44no—
1340C4—42no—
1341C4—42no—
1342C4—44no—
1343C4—44no—
1344C4—42no—
1345C4—44no—
1346C4—42no—
1347C4—42no—
1348C4—44no—
1349C4—42no—
1350C4—41no—
1351C4—42no—
1352C4—42no—
1353C4—41no—
1354C4—42no—
1355C4—41no—
1356C4—41no—
1357C4—42no—
1358C4#356414yes—
1359C2—42no—
1360C2—84no—
1361C2—84no—
1362C2C2×#356411yescharacteristic
1363C2#6288112yes—
1364C2#6288511yescharacteristic
1365C2#6288512yes—
1366C2#6288511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#42977C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58875C2semidirect
2. #58872C2semidirect
3. #58147C2semidirect
4. #57877C2semidirect
5. #57719C2semidirect
6. #55738C2semidirect
7. #54354C2semidirect
8. #53924C2semidirect
9. #53112C2semidirect
10. #52989C2semidirect
11. #44959C2semidirect
12. #44945C2semidirect
13. #42981C2semidirect
15. #42612C2semidirect
16. #42569C2semidirect
17. #42522C2semidirect
18. #42487C2semidirect
19. #38238C2semidirect
20. #38228C2semidirect
21. #38074C2semidirect
22. #38056C2semidirect
23. #37358C2semidirect
24. #37336C2semidirect
25. #35296C2semidirect
26. #35266C2semidirect
27. #34644C2semidirect
28. #2864C22semidirect
31. #2858C22semidirect
33. #2844C22semidirect
35. #2837C22semidirect
36. #2836C22semidirect
37. #2832C22semidirect
38. #2830C22semidirect
40. #2827C22semidirect
41. #2827C22semidirect
42. #2827C22semidirect
44. #2824C22semidirect
45. #2820C22semidirect
46. #2814C22semidirect
47. #2808C22semidirect
50. #2800C22semidirect
51. #2798C22semidirect
52. #2795C22semidirect
54. #2786C22semidirect
56. #2783C22semidirect
57. #2781C22semidirect
59. #2768C22semidirect
61. #2754C22semidirect
62. #2754C22semidirect
67. #2750C22semidirect
70. #2747C22semidirect
71. #2747C22semidirect
72. #2744C22semidirect
74. #2741C22semidirect
75. #2739C22semidirect
76. #2730C22semidirect
77. #2729C22semidirect
78. #2728C22semidirect
79. #2724C22semidirect
80. #2723C22semidirect
81. #2722C22semidirect
82. #2717C22semidirect
83. #2716C22semidirect
84. #2716C22semidirect
85. #2712C22semidirect
86. #2710C22semidirect
87. #2708C22semidirect
89. #2707C22semidirect
92. #2705C22semidirect
93. #2702C22semidirect
94. #2701C22semidirect
95. #2700C22semidirect
96. #2696C22semidirect
97. #2695C22semidirect
98. #2695C22semidirect
99. #2693C22semidirect
101. #2691C22semidirect
102. #2690C22semidirect
104. #2686C22semidirect
107. #2681C22semidirect
108. #2680C22semidirect
110. #2674C22semidirect
111. #2674C22semidirect
112. #2672C22semidirect
117. #2666C22semidirect
118. #2666C22semidirect
119. #2666C22semidirect
120. #2666C22semidirect
124. #2650C22semidirect
125. #2647C22semidirect
126. #2647C22semidirect
130. #2644C22semidirect
131. #2644C22semidirect
133. #2639C22semidirect
135. #2630C22semidirect
138. #2625C22semidirect
140. #2612C22semidirect
142. #2609C22semidirect
144. #2595C22semidirect
145. #2589C22semidirect
146. #2584C22semidirect
149. #2580C22semidirect
150. #2570C22semidirect
153. #2560C22semidirect
156. #2550C22semidirect
159. #2546C22semidirect
161. #2538C22semidirect
163. #2532C22semidirect
164. #2529C22semidirect
165. #2515C22semidirect
170. #2513C22semidirect
171. #2513C22semidirect
174. #2509C22semidirect
175. #2509C22semidirect
176. #2509C22semidirect
177. #2508C22semidirect
178. #2508C22semidirect
179. #2506C22semidirect
180. #2505C22semidirect
182. #2498C22semidirect
183. #2489C22semidirect
184. #2488C22semidirect
187. #2475C22semidirect
188. #2474C22semidirect
189. #2474C22semidirect
191. #2470C22semidirect
192. #2466C22semidirect
195. #2454C22semidirect
198. #2452C22semidirect
199. #2452C22semidirect
206. #2445C22semidirect
211. #2425C22semidirect
214. #2415C22semidirect
218. #2402C22semidirect
219. #2399C22semidirect
220. #2399C22semidirect
224. #2370C22semidirect
229. #2349C22semidirect
232. #2331C22semidirect
233. #2331C22semidirect
235. #2328C22semidirect
238. #2319C22semidirect
244. #2295C22semidirect
245. #2295C22semidirect
246. #2295C22semidirect
247. #2293C22semidirect

Maximal subgroups

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

subgroupindex
#588752
#588722
#581472
#578772
#577192
#557382
#543542
#539242
#531122
#529892
#449592
#449452
#429812
#429772
#426122
#425692
#425222
#424872
#382382
#382282
#380742
#380562
#373582
#373362
#352962
#352662
#346442