Finite Group Databasebeta

← #8927124

Subgroups — #8927124

Order 512.

4496 conjugacy classes of subgroups.

The subgroup lattice has 1392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#58386C214yesmaximal, complemented
2#57614C214yesmaximal, complemented
3#55674C214yesmaximal, complemented
4#54748C214yesmaximal, complemented
5#53404C214yesmaximal, complemented
6#53400C214yesmaximal, complemented
7#49488C214yesmaximal, complemented
8#48547C214yesmaximal, complemented
9#48119C214yesmaximal, complemented
10#46999C211yesmaximal, characteristic, complemented
11#46838C211yesmaximal, characteristic, complemented
12#46388C211yesmaximal, characteristic, complemented
13#46388C211yesmaximal, characteristic, complemented
14#46388C211yesmaximal, characteristic, complemented
15#46386C211yesmaximal, characteristic, complemented
16#46186C214yesmaximal, complemented
17#46110C214yesmaximal, complemented
18#45561C214yesmaximal, complemented
19#37119C211yesmaximal, characteristic, complemented
20#37117C211yesmaximal, characteristic
21#36970C211yesmaximal, characteristic, complemented
22#36969C211yesmaximal, characteristic, complemented
23#36966C211yesmaximal, characteristic, complemented
24#36718C211yesmaximal, characteristic, complemented
25#35452C211yesmaximal, characteristic, complemented
26#35451C211yesmaximal, characteristic, complemented
27#35351C211yesmaximal, characteristic, complemented
28C2×#543C2211yescharacteristic
29C2×#534C2211yescharacteristic
30C22×#126C2211yescharacteristic
31C22×#124C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C2×#518C2211yescharacteristic
34#2855C2212yescomplemented
35#2855C2212yescomplemented
36#2854C2212yescomplemented
37#2853C2212yescomplemented
38#2849C2212yes—
39#2848C2212yescomplemented
40#2842C2211yescharacteristic
41#2842C2211yescharacteristic
42#2838C2214yescomplemented
43#2837C2214yescomplemented
44#2836C2214yescomplemented
45#2835C2214yescomplemented
46#2833C2214yescomplemented
47#2833C2214yescomplemented
48#2831C2214yescomplemented
49#2827C2214yescomplemented
50#2797C2214yescomplemented
51#2792C2214yescomplemented
52#2788C2214yescomplemented
53#2787C2214yescomplemented
54#2784C2214yescomplemented
55#2781C2214yescomplemented
56#2774C2214yescomplemented
57#2773C2214yescomplemented
58#2772C2214yescomplemented
59#2771C2214yescomplemented
60#2767C2214yescomplemented
61#2765C2214yescomplemented
62#2765C2214yescomplemented
63#2765C2214yescomplemented
64#2755C2214yescomplemented
65#2753C2214yescomplemented
66#2750C2214yescomplemented
67#2748C2214yescomplemented
68#2746C2214yescomplemented
69#2746C2214yescomplemented
70#2746C2214yescomplemented
71#2744C2214yescomplemented
72#2744C2214yescomplemented
73#2743C2214yes—
74#2743C2214yescomplemented
75#2743C2214yescomplemented
76#2743C2214yescomplemented
77#2742C2214yescomplemented
78#2741C2214yescomplemented
79#2739C2214yescomplemented
80#2738C2214yescomplemented
81#2738C2214yescomplemented
82#2737C2214yescomplemented
83#2729C2214yescomplemented
84#2727C2214yescomplemented
85#2723C2214yescomplemented
86#2723C2214yescomplemented
87#2718C2214yes—
88#2718C2214yescomplemented
89#2717C2214yes—
90#2716C2214yescomplemented
91#2708C2214yes—
92#2708C2214yescomplemented
93#2700C2214yes—
94#2700C2214yescomplemented
95#2698C2214yescomplemented
96#2698C2214yescomplemented
97#2695C2214yes—
98#2695C2214yescomplemented
99#2695C2214yescomplemented
100#2695C2214yescomplemented
101#2693C2214yescomplemented
102#2691C2214yescomplemented
103#2689C2214yescomplemented
104#2689C2214yescomplemented
105#2688C2214yes—
106#2686C2214yescomplemented
107#2686C2214yescomplemented
108#2686C2214yescomplemented
109#2685C2214yes—
110#2685C2214yescomplemented
111#2684C2214yes—
112#2681C2214yes—
113#2681C2214yescomplemented
114#2674C2214yes—
115#2674C2214yescomplemented
116#2672C2214yes—
117#2672C2214yescomplemented
118#2671C2214yes—
119#2668C2214yes—
120#2667C2214yescomplemented
121#2654C2214yescomplemented
122#2653C2214yescomplemented
123#2653C2214yescomplemented
124#2636C2214yescomplemented
125#2628C2214yescomplemented
126#2627C2212yescomplemented
127#2626C2212yescomplemented
128#2626C2212yescomplemented
129#2623C2212yes—
130#2618C2212yescomplemented
131#2614C2212yescomplemented
132#2601C2214yescomplemented
133#2596C2214yescomplemented
134#2591C2212yescomplemented
135#2588C2214yescomplemented
136#2583C2214yescomplemented
137#2583C2212yescomplemented
138#2583C2212yescomplemented
139#2579C2212yescomplemented
140#2576C2214yes—
141#2576C2214yescomplemented
142#2576C2214yescomplemented
143#2576C2214yescomplemented
144#2575C2214yescomplemented
145#2573C2214yescomplemented
146#2570C2214yescomplemented
147#2569C2214yescomplemented
148#2561C2212yescomplemented
149#2557C2214yescomplemented
150#2553C2214yescomplemented
151#2553C2214yescomplemented
152#2553C2214yescomplemented
153#2534C2214yescomplemented
154#2534C2212yescomplemented
155#2522C2214yescomplemented
156#2521C2214yescomplemented
157#2515C2214yescomplemented
158#2510C2214yescomplemented
159#2505C2214yescomplemented
160#2503C2212yescomplemented
161#2501C2212yescomplemented
162#2494C2214yescomplemented
163#2487C2214yescomplemented
164#2486C2212yescomplemented
165#2484C2212yescomplemented
166#2483C2211yescharacteristic
167#2483C2211yescharacteristic
168#2483C2211yescharacteristic
169#2483C2211yescharacteristic
170#2483C2211yescharacteristic
171#2483C2211yescharacteristic
172#2483C2211yescharacteristic
173#2482C2212yescomplemented
174#2482C2214yescomplemented
175#2481C2214yescomplemented
176#2480C2214yescomplemented
177#2480C2214yescomplemented
178#2480C2214yescomplemented
179#2480C2214yescomplemented
180#2478C2214yescomplemented
181#2477C2214yescomplemented
182#2474C2214yes—
183#2472C2214yes—
184#2470C2214yescomplemented
185#2470C2214yescomplemented
186#2468C2214yescomplemented
187#2466C2214yescomplemented
188#2461C2214yescomplemented
189#2459C2214yescomplemented
190#2457C2214yescomplemented
191#2450C2214yescomplemented
192#2444C2214yes—
193#2444C2214yescomplemented
194#2443C2214yes—
195#2443C2214yescomplemented
196#2440C2214yescomplemented
197#2435C2212yescomplemented
198#2434C2212yescomplemented
199#2418C2214yes—
200#2412C2212yes—
201#2412C2212yescomplemented
202#2412C2212yescomplemented
203#2410C2212yes—
204#2409C2212yescomplemented
205#2405C2211yescharacteristic
206#2405C2211yescharacteristic
207#2405C2211yescharacteristic
208#2405C2211yescharacteristic
209#2405C2211yescharacteristic
210#2405C2211yescharacteristic
211#2405C2211yescharacteristic
212#2405C2211yescharacteristic
213#2405C2211yescharacteristic
214#2405C2211yescharacteristic
215#2403C2211yescharacteristic
216#2383C2214yescomplemented
217#2379C2214yescomplemented
218#2376C2214yescomplemented
219#2363C2214yescomplemented
220#2322C2212yescomplemented
221#2321C2212yescomplemented
222#2312C2211yescharacteristic
223#2312C2211yescharacteristic
224#2312C2211yescharacteristic
225#2312C2211yescharacteristic
226#2312C2211yescharacteristic
227#2312C2211yescharacteristic
228#2308C2211yescharacteristic
229#2308C2211yescharacteristic
230#2308C2211yescharacteristic
231#2308C2212yescomplemented
232C4×#123C2212yescomplemented
233C4×#123C2212yescomplemented
234C2×#385C2212yescomplemented
235C23×Q8C2311yescharacteristic
236C23×D4C2311yescharacteristic
237C23×D4C2311yescharacteristic
238C23×D4C2311yescharacteristic
239C23×D4C2311yescharacteristic
240C24×C4C2311yescharacteristic
241#543—44no—
242#534—44no—
243C2×C4⋊Q8C2314yes—
244C2×#126—44no—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#124—44no—
251C2×#124C2314yes—
252C2×#124C2314yes—
253C2×#124C2314yes—
254C2×#123C2312yes—
255C2×#123C2312yes—
256C2×#123C2312yes—
257C2×#123C2314yes—
258C2×#123C2312yes—
259C2×#123C2312yes—
260C2×#123C2312yes—
261C2×#123C2312yes—
262C2×#123C2312yes—
263C2×#123C2312yes—
264C2×#123C2312yes—
265C2×#123C2312yes—
266C2×#123C2312yes—
267C2×C22⋊Q8C2312yes—
268C2×C22⋊Q8C2312yes—
269C2×C22⋊Q8C2312yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2312yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2314yes—
274C2×C22⋊Q8C2314yes—
275C2×#121—44no—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2314yes—
281C2×#120C2312yes—
282C2×#120C2312yes—
283C2×#120C2312yes—
284C2×#120C2312yes—
285#518—44no—
286C2×C4×D4C2312yes—
287C2×C4×D4C2312yes—
288C2×C4×D4C2312yes—
289C2×C4×D4C2312yes—
290C2×C4×D4C2314yes—
291C2×#117C2312yes—
292C2×#117C2314yes—
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C4⋊C4C2311yescharacteristic
297C22×C4⋊C4C2314yes—
298C22×C22⋊C4C2311yescharacteristic
299C22×C22⋊C4C2311yescharacteristic
300C22×C22⋊C4C2311yescharacteristic
301C22×C22⋊C4C2311yescharacteristic
302C22×C22⋊C4C2311yescharacteristic
303C22×C22⋊C4C2311yescharacteristic
304C22×C22⋊C4C2311yescharacteristic
305C22×C22⋊C4C2312yes—
306C22×C22⋊C4C2312yes—
307C22×C22⋊C4C2311yescharacteristic
308C22×C22⋊C4C2311yescharacteristic
309C22×C22⋊C4C2312yes—
310C22×C22⋊C4C2312yes—
311C22×C42C2311yescharacteristic
312C22×C42C2311yescharacteristic
313#401C2314yes—
314#401C2314yes—
315#401C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
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#399C2314yes—
345#398C2314yes—
346#398C2314yes—
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#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#397C2314yes—
383#397C2314yes—
384#396C2314yes—
385#396C2314yes—
386#396C2314yes—
387#396C2314yes—
388#396C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#395C2314yes—
398#395C2314yes—
399#395C2314yes—
400#395C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#394C2314yes—
406#394C2314yes—
407#394C2314yes—
408#394C2314yes—
409#394C2314yes—
410#394C2314yes—
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#393C2314yes—
426#393C2314yes—
427#393C2314yes—
428#393C2314yes—
429#393C2314yes—
430#393C2314yes—
431#392C2314yes—
432#392C2314yes—
433#391C2314yes—
434#391C2314yes—
435#391C2314yes—
436#391C2314yes—
437#391C2314yes—
438#390C2314yes—
439#390C2314yes—
440#390C2314yes—
441#390C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#389C2314yes—
450#389C2314yes—
451#389C2314yes—
452#389C2314yes—
453#389C2314yes—
454#389C2314yes—
455#389C2314yes—
456#389C2314yes—
457#388C2314yes—
458#388C2314yes—
459#388C2314yes—
460#388C2314yes—
461#388C2314yes—
462#388C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2314yes—
492#387C2314yes—
493#387C2314yes—
494#387C2314yes—
495#387C2314yes—
496#387C2314yes—
497#387C2314yes—
498#387C2314yes—
499#387C2314yes—
500#387C2314yes—
501#387C2314yes—
502#387C2314yes—
503#387C2314yes—
504#387C2314yes—
505#387C2314yes—
506#387C2314yes—
507#387C2314yes—
508#387C2314yes—
509#387C2314yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#386C2314yes—
520#386C2314yes—
521#386C2314yes—
522#386C2314yes—
523#386C2314yes—
524#386C2314yes—
525#386C2314yes—
526#386C2314yes—
527#386C2314yes—
528#386C2314yes—
529#386C2314yes—
530#386C2312yes—
531#386C2312yes—
532#386C2312yes—
533#386C2314yes—
534#386C2314yes—
535#386C2312yes—
536#386C2312yes—
537#386C2312yes—
538#386C2312yes—
539#386C2312yes—
540#386C2312yes—
541#386C2314yes—
542#386C2312yes—
543#386C2314yes—
544#386C2314yes—
545#386C2312yes—
546#386C2314yes—
547#386C2312yes—
548#386C2314yes—
549#386C2314yes—
550#385C2314yes—
551#385C2314yes—
552#385C2314yes—
553#385C2314yes—
554#385C2312yes—
555#385C2312yes—
556#385C2314yes—
557#385C2314yes—
558#385C2314yes—
559#385C2314yes—
560#385C2312yes—
561#385C2312yes—
562#385C2314yes—
563#385C2312yes—
564#385C2314yes—
565#385C2312yes—
566#385C2312yes—
567#385C2314yes—
568#385C2312yes—
569#385C2312yes—
570#385C2312yes—
571#385C2312yes—
572#385C2312yes—
573#385C2312yes—
574#385C2312yes—
575#385C2312yes—
576#385C2312yes—
577#385C2312yes—
578#385C2312yes—
579#385C2312yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2312yes—
585#385C2312yes—
586#385C2312yes—
587#385C2312yes—
588#385C2314yes—
589#385C2312yes—
590#385C2314yes—
591#384C2314yes—
592#383C2314yes—
593#382C2314yes—
594#382C2314yes—
595#382C2314yes—
596#382C2314yes—
597#382C2314yes—
598#381C2312yes—
599#381C2312yes—
600#381C2312yes—
601#381C2312yes—
602#381C2312yes—
603#381C2312yes—
604#381C2312yes—
605#381C2312yes—
606#381C2312yes—
607#381C2314yes—
608#381C2312yes—
609#381C2312yes—
610#381C2312yes—
611#381C2312yes—
612#381C2312yes—
613#381C2312yes—
614#381C2314yes—
615#381C2312yes—
616#381C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2314yes—
624#380C2314yes—
625#380C2314yes—
626#380C2314yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2314yes—
632#380C2314yes—
633#379C2312yes—
634#379C2312yes—
635#379C2311yescharacteristic
636#379C2311yescharacteristic
637#379C2311yescharacteristic
638#379C2311yescharacteristic
639#379C2311yescharacteristic
640#379C2312yes—
641#379C2312yes—
642#379C2311yescharacteristic
643#379C2312yes—
644#379C2312yes—
645#379C2312yes—
646#379C2312yes—
647#379C2312yes—
648#379C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C22⋊C4C2312yes—
653C4×C22⋊C4C2312yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C2×#95C2314yes—
664C25C2411yescharacteristic
665C25C2411yescharacteristic
666C25C2411yescharacteristic
667C25C2411yescharacteristic
668C22×Q8—42no—
669C22×Q8—82no—
670C22×Q8C2412yes—
671C22×Q8C2412yes—
672C22×Q8C2414yes—
673C22×D4—24no—
674C22×D4—24no—
675C22×D4—24no—
676C22×D4—42no—
677C22×D4—44no—
678C22×D4—44no—
679C22×D4—82no—
680C22×D4—82no—
681C22×D4C2412yes—
682C22×D4C2412yes—
683C22×D4C2414yes—
684C22×D4C2412yes—
685C22×D4C2412yes—
686C22×D4C2412yes—
687C22×D4C2414yes—
688C22×D4C2412yes—
689C22×D4C2412yes—
690C22×D4C2412yes—
691C23×C4—42no—
692C23×C4—82no—
693C23×C4C2411yescharacteristic
694C23×C4C2411yescharacteristic
695C23×C4C2411yescharacteristic
696C23×C4C2411yescharacteristic
697C23×C4C2411yescharacteristic
698C23×C4C2411yescharacteristic
699C23×C4C2411yescharacteristic
700C23×C4C2411yescharacteristic
701C23×C4C2411yescharacteristic
702C23×C4C2411yescharacteristic
703C23×C4C2411yescharacteristic
704C23×C4C2411yescharacteristic
705C23×C4C2411yescharacteristic
706C23×C4C2411yescharacteristic
707C23×C4C2411yescharacteristic
708C23×C4C2412yes—
709C23×C4C2414yes—
710C23×C4C2414yes—
711C23×C4C2412yes—
712C23×C4C2414yes—
713C23×C4C2414yes—
714C4⋊Q8—84no—
715#126—48no—
716#126—48no—
717#126—48no—
718#126—84no—
719#126—84no—
720#124—48no—
721#124—48no—
722#124—48no—
723#123—48no—
724#123—44no—
725#123—44no—
726#123—44no—
727#123—44no—
728#123—44no—
729#123—82no—
730#123—82no—
731#123—82no—
732#123—82no—
733#123—82no—
734#123—82no—
735#123—82no—
736C22⋊Q8—44no—
737C22⋊Q8—44no—
738C22⋊Q8—44no—
739C22⋊Q8—44no—
740C22⋊Q8—44no—
741C22⋊Q8—44no—
742C22⋊Q8—84no—
743C22⋊Q8—84no—
744#121—48no—
745#121—48no—
746#121—48no—
747#121—44no—
748#121—44no—
749#120—44no—
750#120—44no—
751#120—44no—
752#120—82no—
753C4×D4—44no—
754C4×D4—44no—
755C4×D4—44no—
756C4×D4—44no—
757C4×D4—84no—
758#117—44no—
759#117—84no—
760C2×C4⋊C4—42no—
761C2×C4⋊C4—42no—
762C2×C4⋊C4—42no—
763C2×C4⋊C4—42no—
764C2×C4⋊C4—84no—
765C2×C4⋊C4C2414yes—
766C2×C4⋊C4C2414yes—
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2414yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2412yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2412yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2412yes—
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2414yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
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⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C22⋊C4—24no—
809C2×C22⋊C4—24no—
810C2×C22⋊C4—24no—
811C2×C22⋊C4—24no—
812C2×C22⋊C4—24no—
813C2×C22⋊C4—24no—
814C2×C22⋊C4—44no—
815C2×C22⋊C4—44no—
816C2×C22⋊C4—42no—
817C2×C22⋊C4—42no—
818C2×C22⋊C4—42no—
819C2×C22⋊C4—82no—
820C2×C22⋊C4—82no—
821C2×C22⋊C4C2412yes—
822C2×C22⋊C4C2412yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2412yes—
825C2×C22⋊C4C2412yes—
826C2×C22⋊C4C2412yes—
827C2×C22⋊C4C2412yes—
828C2×C22⋊C4C2412yes—
829C2×C22⋊C4C2412yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2412yes—
832C2×C22⋊C4C2412yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2414yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2412yes—
838C2×C22⋊C4C2412yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2412yes—
855C2×C22⋊C4C2412yes—
856C2×C22⋊C4C2412yes—
857C2×C22⋊C4C2412yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2412yes—
864C2×C22⋊C4C2412yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2412yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C42—42no—
886C2×C42—42no—
887C2×C42C2412yes—
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2414yes—
895C2×C42C2414yes—
896C2×C42C2414yes—
897#95C2414yes—
898#95C2414yes—
899#95C2414yes—
900#95C2414yes—
901#95C2414yes—
902#95C2414yes—
903#95C2414yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2414yes—
923#95C2414yes—
924#95C2414yes—
925#95C2414yes—
926#95C2414yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949C24—22no—
950C24—24no—
951C24—22no—
952C24—22no—
953C24—42no—
954C24—42no—
955C24—42no—
956C24—42no—
957C24—42no—
958C24—42no—
959C24—42no—
960C24—42no—
961C24—42no—
962C24—42no—
963C24—42no—
964C24H(5,𝔽2)14yes—
965C24C2512yes—
966C24C2512yes—
967C24C2511yescharacteristic
968C24C2511yescharacteristic
969C24C2511yescharacteristic
970C24C2512yes—
971C2×Q8—44no—
972C2×Q8—44no—
973C2×Q8—44no—
974C2×Q8—42no—
975C2×Q8—42no—
976C2×Q8—44no—
977C2×Q8—44no—
978C2×Q8—88no—
979C2×D4—24no—
980C2×D4—24no—
981C2×D4—24no—
982C2×D4—24no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—24no—
986C2×D4—24no—
987C2×D4—28no—
988C2×D4—28no—
989C2×D4—42no—
990C2×D4—42no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—44no—
994C2×D4—42no—
995C2×D4—42no—
996C2×D4—42no—
997C2×D4—42no—
998C2×D4—42no—
999C2×D4—42no—
1000C2×D4—42no—
1001C2×D4—44no—
1002C2×D4—44no—
1003C2×D4—42no—
1004C2×D4—42no—
1005C2×D4—44no—
1006C2×D4—44no—
1007C2×D4—416no—
1008C2×D4—88no—
1009C2×D4—88no—
1010C2×D4—88no—
1011C22×C4—22no—
1012C22×C4—22no—
1013C22×C4—22no—
1014C22×C4—22no—
1015C22×C4—22no—
1016C22×C4—22no—
1017C22×C4—22no—
1018C22×C4—22no—
1019C22×C4—22no—
1020C22×C4—22no—
1021C22×C4—22no—
1022C22×C4—22no—
1023C22×C4—22no—
1024C22×C4—22no—
1025C22×C4—22no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—42no—
1039C22×C4—42no—
1040C22×C4—42no—
1041C22×C4—42no—
1042C22×C4—42no—
1043C22×C4—42no—
1044C22×C4—42no—
1045C22×C4—44no—
1046C22×C4—44no—
1047C22×C4—42no—
1048C22×C4—42no—
1049C22×C4—42no—
1050C22×C4—42no—
1051C22×C4—42no—
1052C22×C4—44no—
1053C22×C4—44no—
1054C22×C4—44no—
1055C22×C4—44no—
1056C22×C4—44no—
1057C22×C4—88no—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2514yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2514yes—
1064C22×C4C2514yes—
1065C22×C4C2514yes—
1066C22×C4C2514yes—
1067C22×C4C2512yes—
1068C22×C4C2512yes—
1069C22×C4C2512yes—
1070C22×C4C2514yes—
1071C22×C4C2512yes—
1072C22×C4C2512yes—
1073C22×C4C2512yes—
1074C22×C4C2512yes—
1075C22×C4C2512yes—
1076C22×C4C2512yes—
1077C22×C4C2512yes—
1078C22×C4C2512yes—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C4⋊C4—44no—
1083C4⋊C4—44no—
1084C4⋊C4—44no—
1085C4⋊C4—44no—
1086C4⋊C4—44no—
1087C4⋊C4—44no—
1088C4⋊C4—44no—
1089C4⋊C4—44no—
1090C4⋊C4—44no—
1091C4⋊C4—44no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—44no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—42no—
1098C4⋊C4—42no—
1099C4⋊C4—42no—
1100C4⋊C4—42no—
1101C4⋊C4—42no—
1102C4⋊C4—42no—
1103C4⋊C4—42no—
1104C4⋊C4—42no—
1105C4⋊C4—44no—
1106C4⋊C4—44no—
1107C4⋊C4—44no—
1108C4⋊C4—44no—
1109C4⋊C4—44no—
1110C4⋊C4—44no—
1111C4⋊C4—44no—
1112C4⋊C4—44no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—44no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—44no—
1120C4⋊C4—44no—
1121C4⋊C4—44no—
1122C22⋊C4—24no—
1123C22⋊C4—24no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—24no—
1127C22⋊C4—24no—
1128C22⋊C4—24no—
1129C22⋊C4—24no—
1130C22⋊C4—24no—
1131C22⋊C4—24no—
1132C22⋊C4—24no—
1133C22⋊C4—24no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
1142C22⋊C4—44no—
1143C22⋊C4—44no—
1144C22⋊C4—44no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—42no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—42no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—42no—
1160C22⋊C4—42no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—42no—
1166C22⋊C4—44no—
1167C22⋊C4—42no—
1168C22⋊C4—42no—
1169C22⋊C4—42no—
1170C22⋊C4—42no—
1171C22⋊C4—44no—
1172C22⋊C4—44no—
1173C22⋊C4—44no—
1174C22⋊C4—42no—
1175C22⋊C4—42no—
1176C22⋊C4—44no—
1177C22⋊C4—42no—
1178C22⋊C4—42no—
1179C22⋊C4—42no—
1180C22⋊C4—44no—
1181C22⋊C4—44no—
1182C22⋊C4—44no—
1183C22⋊C4—44no—
1184C22⋊C4—44no—
1185C22⋊C4—44no—
1186C42—44no—
1187C42—44no—
1188C42—44no—
1189C42—42no—
1190C42—42no—
1191C42—44no—
1192C42—44no—
1193C42—44no—
1194C42—44no—
1195C42—44no—
1196C23—28no—
1197C23—22no—
1198C23—22no—
1199C23—22no—
1200C23—22no—
1201C23—22no—
1202C23—24no—
1203C23—22no—
1204C23—22no—
1205C23—22no—
1206C23—22no—
1207C23—22no—
1208C23—22no—
1209C23—24no—
1210C23—22no—
1211C23—22no—
1212C23—24no—
1213C23—24no—
1214C23—22no—
1215C23—22no—
1216C23—22no—
1217C23—22no—
1218C23—24no—
1219C23—24no—
1220C23—44no—
1221C23—44no—
1222C23—44no—
1223C23—44no—
1224C23—44no—
1225C23—82no—
1226C23—88no—
1227C23—82no—
1228C23—82no—
1229C23—82no—
1230C23—82no—
1231C23—82no—
1232C23—164no—
1233C23—164no—
1234C23—164no—
1235C23C2×H(5,𝔽2)12yes—
1236C23C2×H(5,𝔽2)12yes—
1237C23C2×H(5,𝔽2)12yes—
1238C23#58514yes—
1239C23C2611yescharacteristic
1240Q8—88no—
1241Q8—162no—
1242Q8—162no—
1243D4—48no—
1244D4—48no—
1245D4—88no—
1246D4—88no—
1247D4—84no—
1248D4—84no—
1249D4—84no—
1250D4—84no—
1251D4—162no—
1252D4—162no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—24no—
1270C2×C4—24no—
1271C2×C4—24no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—24no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—24no—
1281C2×C4—24no—
1282C2×C4—24no—
1283C2×C4—24no—
1284C2×C4—24no—
1285C2×C4—24no—
1286C2×C4—24no—
1287C2×C4—24no—
1288C2×C4—24no—
1289C2×C4—22no—
1290C2×C4—24no—
1291C2×C4—24no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—24no—
1296C2×C4—24no—
1297C2×C4—24no—
1298C2×C4—24no—
1299C2×C4—24no—
1300C2×C4—24no—
1301C2×C4—24no—
1302C2×C4—24no—
1303C2×C4—24no—
1304C2×C4—44no—
1305C2×C4—44no—
1306C2×C4—44no—
1307C2×C4—82no—
1308C2×C4—82no—
1309C2×C4—82no—
1310C2×C4—82no—
1311C2×C4—82no—
1312C2×C4—82no—
1313C2×C4—82no—
1314C2×C4—82no—
1315C2×C4—82no—
1316C2×C4—82no—
1317C2×C4—82no—
1318C2×C4—82no—
1319C2×C4—88no—
1320C2×C4—88no—
1321C2×C4—88no—
1322C2×C4—164no—
1323C2×C4—162no—
1324C2×C4—162no—
1325C22—28no—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—24no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—22no—
1335C22—22no—
1336C22—44no—
1337C22—44no—
1338C22—44no—
1339C22—44no—
1340C22—42no—
1341C22—42no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—42no—
1347C22—42no—
1348C22—42no—
1349C22—42no—
1350C22—42no—
1351C22—42no—
1352C22—88no—
1353C22—164no—
1354C22—164no—
1355C22—164no—
1356C22C22×H(5,𝔽2)11yescharacteristic
1357C22C2×#58512yes—
1358C22H(7,𝔽2)12yes—
1359C222−1+612yes—
1360C4—44no—
1361C4—44no—
1362C4—44no—
1363C4—44no—
1364C4—44no—
1365C4—44no—
1366C4—42no—
1367C4—42no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—42no—
1373C4—42no—
1374C4—42no—
1375C4—42no—
1376C4—42no—
1377C4—42no—
1378C4—42no—
1379C4—42no—
1380C4—42no—
1381C2—44no—
1382C2—42no—
1383C2—42no—
1384C2—42no—
1385C2—82no—
1386C2—82no—
1387C2#6282011yescharacteristic
1388C2#6286211yescharacteristic
1389C2#6287111yescharacteristic
1390C2#6305914yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37117C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #58386C2semidirect
2. #57614C2semidirect
3. #55674C2semidirect
4. #54748C2semidirect
5. #53404C2semidirect
6. #53400C2semidirect
7. #49488C2semidirect
8. #48547C2semidirect
9. #48119C2semidirect
10. #46999C2semidirect
11. #46838C2semidirect
12. #46388C2semidirect
13. #46388C2semidirect
14. #46388C2semidirect
15. #46386C2semidirect
16. #46186C2semidirect
17. #46110C2semidirect
18. #45561C2semidirect
19. #37119C2semidirect
21. #36970C2semidirect
22. #36969C2semidirect
23. #36966C2semidirect
24. #36718C2semidirect
25. #35452C2semidirect
26. #35451C2semidirect
27. #35351C2semidirect
34. #2855C22semidirect
35. #2855C22semidirect
36. #2854C22semidirect
37. #2853C22semidirect
39. #2848C22semidirect
42. #2838C22semidirect
43. #2837C22semidirect
44. #2836C22semidirect
45. #2835C22semidirect
46. #2833C22semidirect
47. #2833C22semidirect
48. #2831C22semidirect
49. #2827C22semidirect
50. #2797C22semidirect
51. #2792C22semidirect
52. #2788C22semidirect
53. #2787C22semidirect
54. #2784C22semidirect
55. #2781C22semidirect
56. #2774C22semidirect
57. #2773C22semidirect
58. #2772C22semidirect
59. #2771C22semidirect
60. #2767C22semidirect
61. #2765C22semidirect
62. #2765C22semidirect
63. #2765C22semidirect
64. #2755C22semidirect
65. #2753C22semidirect
66. #2750C22semidirect
67. #2748C22semidirect
68. #2746C22semidirect
69. #2746C22semidirect
70. #2746C22semidirect
71. #2744C22semidirect
72. #2744C22semidirect
74. #2743C22semidirect
75. #2743C22semidirect
76. #2743C22semidirect
77. #2742C22semidirect
78. #2741C22semidirect
79. #2739C22semidirect
80. #2738C22semidirect
81. #2738C22semidirect
82. #2737C22semidirect
83. #2729C22semidirect
84. #2727C22semidirect
85. #2723C22semidirect
86. #2723C22semidirect
88. #2718C22semidirect
90. #2716C22semidirect
92. #2708C22semidirect
94. #2700C22semidirect
95. #2698C22semidirect
96. #2698C22semidirect
98. #2695C22semidirect
99. #2695C22semidirect
100. #2695C22semidirect
101. #2693C22semidirect
102. #2691C22semidirect
103. #2689C22semidirect
104. #2689C22semidirect
106. #2686C22semidirect
107. #2686C22semidirect
108. #2686C22semidirect
110. #2685C22semidirect
113. #2681C22semidirect
115. #2674C22semidirect
117. #2672C22semidirect
120. #2667C22semidirect
121. #2654C22semidirect
122. #2653C22semidirect
123. #2653C22semidirect
124. #2636C22semidirect
125. #2628C22semidirect
126. #2627C22semidirect
127. #2626C22semidirect
128. #2626C22semidirect
130. #2618C22semidirect
131. #2614C22semidirect
132. #2601C22semidirect
133. #2596C22semidirect
134. #2591C22semidirect
135. #2588C22semidirect
136. #2583C22semidirect
137. #2583C22semidirect
138. #2583C22semidirect
139. #2579C22semidirect
141. #2576C22semidirect
142. #2576C22semidirect
143. #2576C22semidirect
144. #2575C22semidirect
145. #2573C22semidirect
146. #2570C22semidirect
147. #2569C22semidirect
148. #2561C22semidirect
149. #2557C22semidirect
150. #2553C22semidirect
151. #2553C22semidirect
152. #2553C22semidirect
153. #2534C22semidirect
154. #2534C22semidirect
155. #2522C22semidirect
156. #2521C22semidirect
157. #2515C22semidirect
158. #2510C22semidirect
159. #2505C22semidirect
160. #2503C22semidirect
161. #2501C22semidirect
162. #2494C22semidirect
163. #2487C22semidirect
164. #2486C22semidirect
165. #2484C22semidirect
173. #2482C22semidirect
174. #2482C22semidirect
175. #2481C22semidirect
176. #2480C22semidirect
177. #2480C22semidirect
178. #2480C22semidirect
179. #2480C22semidirect
180. #2478C22semidirect
181. #2477C22semidirect
184. #2470C22semidirect
185. #2470C22semidirect
186. #2468C22semidirect
187. #2466C22semidirect
188. #2461C22semidirect
189. #2459C22semidirect
190. #2457C22semidirect
191. #2450C22semidirect
193. #2444C22semidirect
195. #2443C22semidirect
196. #2440C22semidirect
197. #2435C22semidirect
198. #2434C22semidirect
201. #2412C22semidirect
202. #2412C22semidirect
204. #2409C22semidirect
216. #2383C22semidirect
217. #2379C22semidirect
218. #2376C22semidirect
219. #2363C22semidirect
220. #2322C22semidirect
221. #2321C22semidirect
231. #2308C22semidirect
232. C4×#123C22semidirect
233. C4×#123C22semidirect
234. C2×#385C22semidirect

Maximal subgroups

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

subgroupindex
#583862
#576142
#556742
#547482
#534042
#534002
#494882
#485472
#481192
#469992
#468382
#463882
#463862
#461862
#461102
#455612
#371192
#371172
#369702
#369692
#369662
#367182
#354522
#354512
#353512