Finite Group Databasebeta

← #7743520

Subgroups — #7743520

Order 512.

4424 conjugacy classes of subgroups.

The subgroup lattice has 1431 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#51195C212yesmaximal, complemented
2#51055C212yesmaximal, complemented
3#50880C212yesmaximal, complemented
4#50675C212yesmaximal, complemented
5#50190C214yesmaximal, complemented
6#48883C214yesmaximal, complemented
7#48877C214yesmaximal, complemented
8#48802C214yesmaximal, complemented
9#45459C214yesmaximal, complemented
10#45459C214yesmaximal, complemented
11#39566C212yesmaximal, complemented
12#39546C212yesmaximal, complemented
13#39081C212yesmaximal, complemented
14#39041C212yesmaximal, complemented
15#38260C212yesmaximal, complemented
16#38204C212yesmaximal, complemented
17#37970C212yesmaximal, complemented
18#37937C212yesmaximal, complemented
19#37481C211yesmaximal, characteristic, complemented
20#37445C211yesmaximal, characteristic
21#37370C212yesmaximal, complemented
22#37369C212yesmaximal, complemented
23#35614C212yesmaximal, complemented
24#35613C212yesmaximal, complemented
25#35227C211yesmaximal, characteristic, complemented
26#35227C211yesmaximal, characteristic, complemented
27#34391C211yesmaximal, characteristic, complemented
28#34342C211yesmaximal, characteristic, complemented
29#34178C211yesmaximal, characteristic, complemented
30C2×#525C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C23×C4⋊C4C2211yescharacteristic
33#2863C2212yescomplemented
34#2859C2212yescomplemented
35#2854C2212yescomplemented
36#2851C2212yescomplemented
37#2849C2214yes—
38#2849C2212yes—
39#2849C2212yes—
40#2842C2212yes—
41#2842C2212yes—
42#2812C2214yes—
43#2802C2214yescomplemented
44#2796C2214yescomplemented
45#2796C2214yescomplemented
46#2794C2214yescomplemented
47#2789C2214yescomplemented
48#2787C2214yescomplemented
49#2783C2214yescomplemented
50#2783C2214yescomplemented
51#2777C2214yescomplemented
52#2777C2214yescomplemented
53#2773C2214yescomplemented
54#2768C2214yescomplemented
55#2767C2214yescomplemented
56#2767C2214yescomplemented
57#2766C2214yescomplemented
58#2765C2214yes—
59#2765C2214yes—
60#2761C2214yes—
61#2761C2214yes—
62#2754C2214yescomplemented
63#2750C2214yes—
64#2750C2214yes—
65#2749C2214yes—
66#2749C2214yes—
67#2748C2214yescomplemented
68#2747C2214yescomplemented
69#2746C2214yes—
70#2746C2214yes—
71#2744C2214yes—
72#2744C2214yes—
73#2740C2214yes—
74#2740C2214yes—
75#2740C2214yescomplemented
76#2738C2214yes—
77#2738C2214yes—
78#2738C2214yescomplemented
79#2726C2214yescomplemented
80#2724C2214yescomplemented
81#2721C2214yescomplemented
82#2707C2214yes—
83#2707C2214yes—
84#2706C2214yes—
85#2706C2214yes—
86#2705C2214yescomplemented
87#2694C2214yes—
88#2694C2214yes—
89#2693C2214yes—
90#2693C2214yes—
91#2667C2214yes—
92#2667C2212yes—
93#2667C2212yes—
94#2663C2212yes—
95#2661C2212yes—
96#2647C2212yescomplemented
97#2644C2212yescomplemented
98#2638C2212yes—
99#2635C2212yes—
100#2629C2212yes—
101#2629C2212yes—
102#2629C2212yescomplemented
103#2625C2211yescharacteristic
104#2625C2212yescomplemented
105#2624C2211yescharacteristic
106#2623C2214yes—
107#2623C2214yes—
108#2616C2211yescharacteristic
109#2615C2211yescharacteristic
110#2611C2214yescomplemented
111#2609C2214yes—
112#2609C2214yes—
113#2608C2214yes—
114#2602C2214yes—
115#2601C2214yes—
116#2601C2214yes—
117#2597C2214yescomplemented
118#2595C2214yescomplemented
119#2594C2214yescomplemented
120#2590C2214yescomplemented
121#2590C2214yescomplemented
122#2589C2214yescomplemented
123#2588C2214yescomplemented
124#2577C2214yescomplemented
125#2577C2214yescomplemented
126#2576C2214yes—
127#2576C2214yes—
128#2575C2214yes—
129#2575C2214yes—
130#2570C2214yescomplemented
131#2554C2214yes—
132#2554C2214yes—
133#2553C2214yes—
134#2553C2214yes—
135#2553C2214yescomplemented
136#2528C2214yescomplemented
137#2524C2214yescomplemented
138#2519C2214yescomplemented
139#2517C2214yescomplemented
140#2516C2214yes—
141#2516C2214yes—
142#2515C2214yes—
143#2515C2214yes—
144#2513C2214yescomplemented
145#2512C2212yescomplemented
146#2511C2212yescomplemented
147#2508C2214yescomplemented
148#2508C2212yescomplemented
149#2508C2212yescomplemented
150#2507C2212yescomplemented
151#2506C2212yescomplemented
152#2505C2214yescomplemented
153#2504C2211yescharacteristic
154#2504C2212yes—
155#2504C2211yescharacteristic
156#2503C2212yes—
157#2503C2212yes—
158#2502C2211yescharacteristic
159#2502C2212yes—
160#2502C2211yescharacteristic
161#2501C2212yes—
162#2501C2212yes—
163#2498C2214yescomplemented
164#2497C2212yescomplemented
165#2496C2212yescomplemented
166#2494C2212yescomplemented
167#2494C2212yescomplemented
168#2490C2212yescomplemented
169#2489C2212yescomplemented
170#2487C2212yes—
171#2487C2212yes—
172#2487C2212yes—
173#2487C2212yes—
174#2486C2214yes—
175#2486C2212yes—
176#2486C2212yes—
177#2485C2212yes—
178#2478C2214yescomplemented
179#2478C2214yescomplemented
180#2475C2214yes—
181#2475C2214yes—
182#2471C2214yes—
183#2471C2214yes—
184#2471C2214yes—
185#2471C2214yes—
186#2471C2214yescomplemented
187#2470C2214yes—
188#2470C2214yes—
189#2454C2212yescomplemented
190#2453C2212yescomplemented
191#2441C2212yes—
192#2441C2212yes—
193#2441C2212yes—
194#2441C2212yes—
195#2441C2214yescomplemented
196#2423C2212yescomplemented
197#2422C2212yescomplemented
198#2415C2212yes—
199#2414C2212yes—
200#2407C2212yes—
201#2378C2211yescharacteristic
202#2378C2212yes—
203#2378C2211yescharacteristic
204#2377C2211yescharacteristic
205#2377C2212yes—
206#2377C2211yescharacteristic
207#2376C2212yes—
208#2376C2212yes—
209#2375C2212yes—
210#2375C2212yes—
211#2375C2214yes—
212#2363C2212yes—
213#2362C2212yes—
214#2357C2212yes—
215#2353C2212yes—
216#2347C2211yescharacteristic
217#2346C2211yescharacteristic
218#2345C2212yes—
219#2345C2212yes—
220#2345C2212yes—
221#2345C2212yes—
222#2344C2212yes—
223#2344C2212yes—
224#2344C2214yes—
225#2341C2211yescharacteristic
226#2339C2211yescharacteristic
227#2335C2214yes—
228#2330C2212yescomplemented
229#2324C2212yes—
230#2324C2212yescomplemented
231#2323C2212yes—
232#2320C2212yescomplemented
233#2319C2212yes—
234#2318C2212yes—
235#2317C2212yes—
236#2317C2212yes—
237#2316C2212yes—
238#2314C2212yescomplemented
239#2313C2212yes—
240#2313C2212yes—
241#2311C2212yes—
242#2311C2212yes—
243C4×#125C2212yescomplemented
244C4×C22⋊Q8C2212yescomplemented
245#2298C2212yes—
246#2297C2212yes—
247#2293C2212yes—
248#2293C2212yes—
249#2293C2212yescomplemented
250#2290C2212yes—
251#2290C2212yes—
252#2285C2212yescomplemented
253#2280C2211yescharacteristic
254#2280C2211yescharacteristic
255#2280C2211yescharacteristic
256#2280C2211yescharacteristic
257#2280C2214yes—
258#2274C2212yes—
259C22×#41C2311yescharacteristic
260C22×#41C2311yescharacteristic
261C24×C4C2312yes—
262C24×C4C2311yescharacteristic
263C2×#126C2314yes—
264C2×#126C2314yes—
265C2×#125C2312yes—
266C2×#125C2312yes—
267C2×#125C2314yes—
268C2×#125C2314yes—
269#525—28no—
270#525—28no—
271C2×#123C2312yes—
272C2×#123C2312yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2311yescharacteristic
281C2×C22⋊Q8C2311yescharacteristic
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2312yes—
284C2×#121C2311yescharacteristic
285C2×#121C2311yescharacteristic
286C2×#121C2311yescharacteristic
287C2×#121C2311yescharacteristic
288C2×#121C2312yes—
289C2×#120C2312yes—
290C2×#120C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×D4C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×#117C2311yescharacteristic
298C2×#117C2311yescharacteristic
299C2×#117C2312yes—
300C2×#117C2312yes—
301C2×#117C2312yes—
302C2×#117C2312yes—
303C2×#117C2312yes—
304C2×#117C2314yes—
305C2×#117C2314yes—
306C2×#117C2314yes—
307C2×#117C2314yes—
308C22×C4⋊C4—28no—
309C22×C4⋊C4C2312yes—
310C22×C4⋊C4C2312yes—
311C22×C4⋊C4C2312yes—
312C22×C4⋊C4C2311yescharacteristic
313C22×C4⋊C4C2312yes—
314C22×C4⋊C4C2312yes—
315C22×C4⋊C4C2311yescharacteristic
316C22×C42C2312yes—
317#401C2314yes—
318#401C2314yes—
319#400C2312yes—
320#400C2314yes—
321#400C2314yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#399C2314yes—
337#399C2314yes—
338#399C2314yes—
339#399C2314yes—
340#399C2314yes—
341#399C2314yes—
342#399C2314yes—
343#399C2314yes—
344#399C2312yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
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#397C2312yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#395C2312yes—
403#394C2314yes—
404#394C2314yes—
405#394C2312yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
411#394C2314yes—
412#393C2312yes—
413#392C2314yes—
414#392C2312yes—
415#392C2314yes—
416#392C2314yes—
417#391C2312yes—
418#391C2314yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#390C2312yes—
425#390C2314yes—
426#390C2312yes—
427#390C2314yes—
428#390C2312yes—
429#390C2314yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2312yes—
434#390C2312yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2312yes—
439#390C2312yes—
440#390C2314yes—
441#389C2312yes—
442#389C2312yes—
443#389C2314yes—
444#389C2314yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2314yes—
450#389C2314yes—
451#389C2312yes—
452#389C2314yes—
453#389C2312yes—
454#389C2312yes—
455#389C2314yes—
456#389C2314yes—
457#389C2312yes—
458#389C2312yes—
459#389C2312yes—
460#389C2312yes—
461#389C2314yes—
462#389C2312yes—
463#389C2314yes—
464#389C2314yes—
465#389C2312yes—
466#389C2314yes—
467#389C2314yes—
468#389C2312yes—
469#389C2314yes—
470#389C2314yes—
471#389C2314yes—
472#389C2312yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2312yes—
483#388C2312yes—
484#388C2314yes—
485#388C2312yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2312yes—
503#388C2312yes—
504#388C2314yes—
505#388C2312yes—
506#388C2314yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#388C2312yes—
511#388C2312yes—
512#388C2312yes—
513#388C2312yes—
514#388C2312yes—
515#388C2312yes—
516#388C2312yes—
517#388C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2312yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2312yes—
563#387C2312yes—
564#387C2312yes—
565#387C2312yes—
566#387C2312yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2312yes—
573#386C2312yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#386C2312yes—
580#386C2312yes—
581#386C2312yes—
582#386C2312yes—
583#386C2314yes—
584#386C2314yes—
585#386C2312yes—
586#386C2312yes—
587#386C2312yes—
588#386C2312yes—
589#386C2312yes—
590#386C2312yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2312yes—
597#385C2314yes—
598#385C2314yes—
599#385C2312yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2312yes—
605#385C2312yes—
606#385C2312yes—
607#385C2314yes—
608#385C2312yes—
609#385C2312yes—
610#385C2312yes—
611#385C2314yes—
612#385C2314yes—
613#384C2312yes—
614#384C2314yes—
615#384C2312yes—
616#384C2312yes—
617#384C2312yes—
618#383C2312yes—
619#383C2314yes—
620#383C2314yes—
621#382C2312yes—
622#382C2314yes—
623#382C2314yes—
624#382C2312yes—
625#382C2314yes—
626#382C2312yes—
627#382C2314yes—
628#382C2314yes—
629#382C2314yes—
630#382C2314yes—
631#381C2311yescharacteristic
632#381C2311yescharacteristic
633#381C2312yes—
634#381C2312yes—
635#381C2312yes—
636#381C2314yes—
637#381C2314yes—
638#381C2314yes—
639#381C2314yes—
640#381C2314yes—
641#381C2314yes—
642#381C2312yes—
643#380C2312yes—
644#380C2314yes—
645#380C2312yes—
646#380C2312yes—
647#380C2312yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2312yes—
652#380C2311yescharacteristic
653#380C2311yescharacteristic
654#380C2312yes—
655#380C2314yes—
656#380C2312yes—
657#380C2312yes—
658#380C2311yescharacteristic
659#380C2311yescharacteristic
660#380C2312yes—
661#380C2311yescharacteristic
662#380C2311yescharacteristic
663#380C2314yes—
664#380C2314yes—
665#380C2312yes—
666#380C2312yes—
667#380C2311yescharacteristic
668#380C2311yescharacteristic
669#380C2314yes—
670#379C2311yescharacteristic
671#379C2311yescharacteristic
672#379C2312yes—
673#379C2312yes—
674#379C2312yes—
675C4×C4⋊C4C2312yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2314yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2314yes—
685C4×C4⋊C4C2314yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2312yes—
688C4×C4⋊C4C2314yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C22⋊C4C2314yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2312yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2312yes—
700C4×C22⋊C4C2311yescharacteristic
701C4×C22⋊C4C2311yescharacteristic
702C4×C22⋊C4C2312yes—
703C4×C22⋊C4C2312yes—
704C4×C22⋊C4C2312yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2312yes—
708C4×C22⋊C4C2312yes—
709C4×C22⋊C4C2311yescharacteristic
710C4×C22⋊C4C2311yescharacteristic
711#376C2312yes—
712#376C2312yes—
713C2×#95C2312yes—
714C43C2312yes—
715C25C2411yescharacteristic
716C2×#41—24no—
717C2×#41—24no—
718C2×#41—44no—
719C2×#41—44no—
720C22×Q8C2411yescharacteristic
721C22×Q8C2411yescharacteristic
722C22×D4C2411yescharacteristic
723C22×D4C2412yes—
724C22×D4C2412yes—
725C22×D4C2412yes—
726C22×D4C2412yes—
727C22×D4C2412yes—
728C22×D4C2412yes—
729C22×D4C2411yescharacteristic
730C22×D4C2414yes—
731C23×C4—28no—
732C23×C4—44no—
733C23×C4—84no—
734C23×C4#4118yes—
735C23×C4C2412yes—
736C23×C4C2411yescharacteristic
737C23×C4C2411yescharacteristic
738C23×C4C2411yescharacteristic
739C23×C4C2414yes—
740C23×C4C2412yes—
741C23×C4C2414yes—
742C23×C4C2412yes—
743C23×C4C2412yes—
744C23×C4C2412yes—
745C23×C4C2414yes—
746C23×C4C2412yes—
747C23×C4C2411yescharacteristic
748C23×C4C2411yescharacteristic
749C23×C4C2411yescharacteristic
750#126—84no—
751#126—84no—
752#125—44no—
753#125—44no—
754#125—84no—
755#125—84no—
756#123—28no—
757#123—28no—
758#123—84no—
759#123—84no—
760#123—84no—
761#123—84no—
762#123—84no—
763#123—84no—
764C22⋊Q8—24no—
765C22⋊Q8—24no—
766C22⋊Q8—24no—
767C22⋊Q8—24no—
768C22⋊Q8—44no—
769#121—24no—
770#121—24no—
771#121—24no—
772#121—24no—
773#121—44no—
774#120—28no—
775#120—28no—
776C4×Q8—44no—
777C4×D4—28no—
778C4×D4—28no—
779C4×D4—28no—
780C4×D4—28no—
781C4×D4—44no—
782#117—24no—
783#117—24no—
784#117—44no—
785#117—44no—
786#117—44no—
787#117—44no—
788#117—44no—
789#117—84no—
790#117—84no—
791#117—84no—
792#117—84no—
793C2×C4⋊C4—28no—
794C2×C4⋊C4—28no—
795C2×C4⋊C4—28no—
796C2×C4⋊C4—24no—
797C2×C4⋊C4—24no—
798C2×C4⋊C4—28no—
799C2×C4⋊C4—28no—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2411yescharacteristic
809C2×C4⋊C4C2411yescharacteristic
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2411yescharacteristic
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C4⋊C4C2414yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2414yes—
843C2×C4⋊C4C2414yes—
844C2×C4⋊C4C2414yes—
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2412yes—
854C2×C4⋊C4C2412yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2412yes—
866C2×C22⋊C4C2412yes—
867C2×C22⋊C4C2412yes—
868C2×C22⋊C4C2412yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2412yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2412yes—
889C2×C22⋊C4C2412yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2412yes—
898C2×C22⋊C4C2412yes—
899C2×C22⋊C4C2412yes—
900C2×C22⋊C4C2412yes—
901C2×C22⋊C4C2412yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2411yescharacteristic
904C2×C22⋊C4C2411yescharacteristic
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2411yescharacteristic
907C2×C22⋊C4C2411yescharacteristic
908C2×C22⋊C4C2414yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2412yes—
912C2×C22⋊C4C2414yes—
913C2×C42—44no—
914C2×C42C2412yes—
915C2×C42C2412yes—
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2414yes—
924C2×C42C2414yes—
925C2×C42C2414yes—
926C2×C42C2414yes—
927C2×C42C2414yes—
928C2×C42C2414yes—
929C2×C42C2412yes—
930C2×C42C2412yes—
931C2×C42C2412yes—
932C2×C42C2414yes—
933C2×C42C2412yes—
934C2×C42C2412yes—
935#95C2411yescharacteristic
936#95C2412yes—
937#95C2414yes—
938#95C2411yescharacteristic
939#95C2412yes—
940#95C2414yes—
941#95C2412yes—
942#95C2412yes—
943#95C2412yes—
944#95C2411yescharacteristic
945#95C2412yes—
946#95C2412yes—
947#95C2414yes—
948#95C2411yescharacteristic
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2414yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2412yes—
964#95C2412yes—
965#95C2412yes—
966#95C2414yes—
967#95C2412yes—
968#95C2414yes—
969#95C2412yes—
970#95C2412yes—
971#95C2412yes—
972#95C2414yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2412yes—
985#95C2412yes—
986#95C2414yes—
987#95C2414yes—
988#95C2412yes—
989#95C2414yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003C24—42no—
1004C24—42no—
1005C24—41no—
1006C24—41no—
1007C24C2×#4114yes—
1008C24C2512yes—
1009C24C2512yes—
1010C24C2511yescharacteristic
1011C24C2511yescharacteristic
1012C24C2511yescharacteristic
1013#41—88no—
1014#41—88no—
1015C2×Q8—22no—
1016C2×Q8—22no—
1017C2×Q8—24no—
1018C2×Q8—42no—
1019C2×D4—24no—
1020C2×D4—24no—
1021C2×D4—24no—
1022C2×D4—24no—
1023C2×D4—24no—
1024C2×D4—24no—
1025C2×D4—22no—
1026C2×D4—22no—
1027C2×D4—24no—
1028C2×D4—42no—
1029C2×D4—44no—
1030C2×D4—42no—
1031C2×D4—42no—
1032C2×D4—42no—
1033C2×D4—42no—
1034C2×D4—42no—
1035C2×D4—42no—
1036C2×D4—42no—
1037C2×D4—44no—
1038C2×D4—42no—
1039C2×D4—44no—
1040C2×D4—44no—
1041C2×D4—44no—
1042C22×C4—24no—
1043C22×C4—24no—
1044C22×C4—24no—
1045C22×C4—28no—
1046C22×C4—24no—
1047C22×C4—28no—
1048C22×C4—24no—
1049C22×C4—24no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—416no—
1054C22×C4—42no—
1055C22×C4—42no—
1056C22×C4—44no—
1057C22×C4—44no—
1058C22×C4—42no—
1059C22×C4—42no—
1060C22×C4—42no—
1061C22×C4—42no—
1062C22×C4—42no—
1063C22×C4—44no—
1064C22×C4—44no—
1065C22×C4—42no—
1066C22×C4—44no—
1067C22×C4—44no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—42no—
1072C22×C4—44no—
1073C22×C4—816no—
1074C22×C4C2×#4114yes—
1075C22×C4C2×#4114yes—
1076C22×C4C2×#4114yes—
1077C22×C4C2×#4114yes—
1078C22×C4C2×#4114yes—
1079C22×C4C2×#4114yes—
1080C22×C4C2512yes—
1081C22×C4C2512yes—
1082C22×C4C2512yes—
1083C22×C4C2512yes—
1084C22×C4C2512yes—
1085C22×C4C2512yes—
1086C22×C4C2512yes—
1087C22×C4C2514yes—
1088C22×C4C2514yes—
1089C22×C4C2512yes—
1090C22×C4C2512yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2512yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2514yes—
1097C22×C4C2514yes—
1098C22×C4C2512yes—
1099C22×C4C2512yes—
1100C22×C4C2511yescharacteristic
1101C22×C4C2511yescharacteristic
1102C22×C4C2511yescharacteristic
1103C22×C4C2511yescharacteristic
1104C4⋊C4—28no—
1105C4⋊C4—24no—
1106C4⋊C4—24no—
1107C4⋊C4—28no—
1108C4⋊C4—24no—
1109C4⋊C4—24no—
1110C4⋊C4—22no—
1111C4⋊C4—22no—
1112C4⋊C4—22no—
1113C4⋊C4—22no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—24no—
1119C4⋊C4—24no—
1120C4⋊C4—24no—
1121C4⋊C4—24no—
1122C4⋊C4—42no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—44no—
1126C4⋊C4—42no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—44no—
1130C4⋊C4—42no—
1131C4⋊C4—42no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—44no—
1138C4⋊C4—44no—
1139C4⋊C4—44no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—44no—
1143C4⋊C4—44no—
1144C4⋊C4—44no—
1145C4⋊C4—44no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—42no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—44no—
1161C4⋊C4—42no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—24no—
1165C22⋊C4—24no—
1166C22⋊C4—24no—
1167C22⋊C4—24no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—24no—
1171C22⋊C4—24no—
1172C22⋊C4—42no—
1173C22⋊C4—44no—
1174C22⋊C4—41no—
1175C22⋊C4—42no—
1176C22⋊C4—41no—
1177C22⋊C4—44no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—42no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—41no—
1185C22⋊C4—41no—
1186C22⋊C4—42no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—42no—
1192C22⋊C4—42no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—42no—
1196C22⋊C4—42no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
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—42no—
1217C42—24no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—42no—
1224C42—42no—
1225C42—44no—
1226C42—42no—
1227C42—42no—
1228C42—44no—
1229C42—44no—
1230C42—44no—
1231C42—44no—
1232C42—42no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—42no—
1238C23—22no—
1239C23—22no—
1240C23—22no—
1241C23—22no—
1242C23—22no—
1243C23—22no—
1244C23—21no—
1245C23—21no—
1246C23—21no—
1247C23—21no—
1248C23—21no—
1249C23—21no—
1250C23—22no—
1251C23—22no—
1252C23—22no—
1253C23—24no—
1254C23—22no—
1255C23—22no—
1256C23—24no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—44no—
1263C23—44no—
1264C23—44no—
1265C23—48no—
1266C23—48no—
1267C23C22×#4112yes—
1268C23C22×#4112yes—
1269C23C22×#4112yes—
1270C23C2611yescharacteristic
1271Q8—44no—
1272Q8—82no—
1273D4—44no—
1274D4—82no—
1275D4—84no—
1276D4—84no—
1277D4—84no—
1278D4—84no—
1279D4—84no—
1280D4—84no—
1281D4—164no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—28no—
1286C2×C4—28no—
1287C2×C4—28no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—24no—
1295C2×C4—24no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—24no—
1306C2×C4—24no—
1307C2×C4—24no—
1308C2×C4—24no—
1309C2×C4—24no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—22no—
1314C2×C4—22no—
1315C2×C4—24no—
1316C2×C4—24no—
1317C2×C4—24no—
1318C2×C4—24no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—22no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—24no—
1345C2×C4—22no—
1346C2×C4—44no—
1347C2×C4—44no—
1348C2×C4—44no—
1349C2×C4—416no—
1350C2×C4—48no—
1351C2×C4—48no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—88no—
1355C2×C4—84no—
1356C2×C4—84no—
1357C2×C4—88no—
1358C2×C4C22×#4112yes—
1359C2×C4C22×#4112yes—
1360C2×C4C22×#4112yes—
1361C2×C4C22×#4112yes—
1362C2×C4#58514yes—
1363C22—22no—
1364C22—22no—
1365C22—22no—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—22no—
1370C22—22no—
1371C22—22no—
1372C22—416no—
1373C22—42no—
1374C22—42no—
1375C22—42no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—42no—
1382C22—44no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—44no—
1387C22—42no—
1388C22—42no—
1389C22—42no—
1390C22—42no—
1391C22C23×#4111yescharacteristic
1392C22C2×#58512yes—
1393C22H(7,𝔽2)12yes—
1394C222−1+611yescharacteristic
1395C222−1+611yescharacteristic
1396C4—22no—
1397C4—22no—
1398C4—22no—
1399C4—42no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—44no—
1405C4—42no—
1406C4—44no—
1407C4—42no—
1408C4—42no—
1409C4—44no—
1410C4—44no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—44no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—42no—
1419C4#349114yes—
1420C2—42no—
1421C2—42no—
1422C2—42no—
1423C2—82no—
1424C2—82no—
1425C2C2×#349111yescharacteristic
1426C2#6285511yescharacteristic
1427C2#6286011yescharacteristic
1428C2#6304312yes—
1429C2#6304712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37445C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #51195C2semidirect
2. #51055C2semidirect
3. #50880C2semidirect
4. #50675C2semidirect
5. #50190C2semidirect
6. #48883C2semidirect
7. #48877C2semidirect
8. #48802C2semidirect
9. #45459C2semidirect
10. #45459C2semidirect
11. #39566C2semidirect
12. #39546C2semidirect
13. #39081C2semidirect
14. #39041C2semidirect
15. #38260C2semidirect
16. #38204C2semidirect
17. #37970C2semidirect
18. #37937C2semidirect
19. #37481C2semidirect
21. #37370C2semidirect
22. #37369C2semidirect
23. #35614C2semidirect
24. #35613C2semidirect
25. #35227C2semidirect
26. #35227C2semidirect
27. #34391C2semidirect
28. #34342C2semidirect
29. #34178C2semidirect
33. #2863C22semidirect
34. #2859C22semidirect
35. #2854C22semidirect
36. #2851C22semidirect
43. #2802C22semidirect
44. #2796C22semidirect
45. #2796C22semidirect
46. #2794C22semidirect
47. #2789C22semidirect
48. #2787C22semidirect
49. #2783C22semidirect
50. #2783C22semidirect
51. #2777C22semidirect
52. #2777C22semidirect
53. #2773C22semidirect
54. #2768C22semidirect
55. #2767C22semidirect
56. #2767C22semidirect
57. #2766C22semidirect
62. #2754C22semidirect
67. #2748C22semidirect
68. #2747C22semidirect
75. #2740C22semidirect
78. #2738C22semidirect
79. #2726C22semidirect
80. #2724C22semidirect
81. #2721C22semidirect
86. #2705C22semidirect
96. #2647C22semidirect
97. #2644C22semidirect
102. #2629C22semidirect
104. #2625C22semidirect
110. #2611C22semidirect
117. #2597C22semidirect
118. #2595C22semidirect
119. #2594C22semidirect
120. #2590C22semidirect
121. #2590C22semidirect
122. #2589C22semidirect
123. #2588C22semidirect
124. #2577C22semidirect
125. #2577C22semidirect
130. #2570C22semidirect
135. #2553C22semidirect
136. #2528C22semidirect
137. #2524C22semidirect
138. #2519C22semidirect
139. #2517C22semidirect
144. #2513C22semidirect
145. #2512C22semidirect
146. #2511C22semidirect
147. #2508C22semidirect
148. #2508C22semidirect
149. #2508C22semidirect
150. #2507C22semidirect
151. #2506C22semidirect
152. #2505C22semidirect
163. #2498C22semidirect
164. #2497C22semidirect
165. #2496C22semidirect
166. #2494C22semidirect
167. #2494C22semidirect
168. #2490C22semidirect
169. #2489C22semidirect
178. #2478C22semidirect
179. #2478C22semidirect
186. #2471C22semidirect
189. #2454C22semidirect
190. #2453C22semidirect
195. #2441C22semidirect
196. #2423C22semidirect
197. #2422C22semidirect
228. #2330C22semidirect
230. #2324C22semidirect
232. #2320C22semidirect
238. #2314C22semidirect
243. C4×#125C22semidirect
244. C4×C22⋊Q8C22semidirect
249. #2293C22semidirect
252. #2285C22semidirect

Maximal subgroups

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

subgroupindex
#511952
#510552
#508802
#506752
#501902
#488832
#488772
#488022
#454592
#395662
#395462
#390812
#390412
#382602
#382042
#379702
#379372
#374812
#374452
#373702
#373692
#356142
#356132
#352272
#343912
#343422
#341782