Finite Group Databasebeta

← #7659862

Subgroups — #7659862

Order 512.

5161 conjugacy classes of subgroups.

The subgroup lattice has 1408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52249C213yesmaximal, complemented
2#42714C213yesmaximal, complemented
3#42705C213yesmaximal, complemented
4#42641C213yesmaximal, complemented
5#42641C213yesmaximal, complemented
6#42557C213yesmaximal, complemented
7#42508C213yesmaximal, complemented
8#40223C213yesmaximal, complemented
9#40170C213yesmaximal, complemented
10#40054C213yesmaximal, complemented
11#39900C213yesmaximal, complemented
12#39606C213yesmaximal, complemented
13#39220C213yesmaximal, complemented
14#37409C213yesmaximal, complemented
15#37384C213yesmaximal, complemented
16#37348C213yesmaximal, complemented
17#36576C211yesmaximal, characteristic, complemented
18Q8×#123C211yesmaximal, characteristic, complemented
19Q8×#123C211yesmaximal, characteristic, complemented
20#36444C211yesmaximal, characteristic, complemented
21#36434C211yesmaximal, characteristic, complemented
22#36430C211yesmaximal, characteristic, complemented
23#35996C211yesmaximal, characteristic, complemented
24#35927C211yesmaximal, characteristic, complemented
25#35868C211yesmaximal, characteristic, complemented
26#35831C211yesmaximal, characteristic, complemented
27#35801C211yesmaximal, characteristic, complemented
28#35771C211yesmaximal, characteristic, complemented
29#34294C211yesmaximal, characteristic, complemented
30#34291C211yesmaximal, characteristic, complemented
31#34193C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×D4×Q8C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#548C2211yescharacteristic
38C2×#548C2211yescharacteristic
39C2×#548C2211yescharacteristic
40C2×#548C2211yescharacteristic
41C2×#548C2211yescharacteristic
42C2×#520C2211yescharacteristic
43C2×#519C2211yescharacteristic
44C2×C4×#41C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47#2857C2213yes—
48#2856C2213yes—
49#2855C2213yes—
50#2855C2213yes—
51#2850C2213yes—
52#2850C2213yes—
53#2837C2216yes—
54#2837C2216yes—
55#2803C2216yes—
56#2797C2216yes—
57#2793C2216yes—
58#2793C2216yes—
59#2777C2216yes—
60#2777C2213yes—
61#2773C2213yes—
62#2768C2216yes—
63#2768C2213yes—
64#2756C2213yes—
65#2753C2213yes—
66#2752C2216yes—
67#2749C2213yes—
68#2748C2216yes—
69#2748C2216yes—
70#2748C2213yes—
71#2748C2216yes—
72#2743C2216yes—
73#2743C2213yes—
74#2741C2216yes—
75#2741C2213yes—
76#2741C2216yes—
77#2740C2216yes—
78#2740C2213yes—
79#2738C2216yes—
80#2738C2213yes—
81#2711C2216yes—
82#2711C2216yes—
83#2706C2211yescharacteristic
84#2703C2213yes—
85#2701C2216yes—
86#2699C2213yes—
87#2688C2213yes—
88#2671C2216yes—
89#2671C2213yes—
90#2658C2213yes—
91#2651C2216yes—
92#2651C2216yes—
93#2649C2216yes—
94#2649C2216yes—
95#2647C2213yes—
96#2635C2216yes—
97#2629C2216yes—
98#2625C2213yes—
99#2624C2213yes—
100#2620C2213yes—
101#2620C2213yes—
102#2570C2213yes—
103#2552C2213yes—
104#2548C2213yes—
105#2547C2213yes—
106#2545C2213yes—
107#2545C2213yes—
108#2544C2213yes—
109#2544C2213yes—
110#2542C2213yes—
111#2542C2213yes—
112#2542C2213yes—
113#2540C2213yes—
114#2540C2213yes—
115#2540C2213yes—
116#2538C2213yes—
117#2538C2213yes—
118#2537C2213yes—
119#2537C2213yes—
120#2536C2213yes—
121#2535C2213yes—
122#2516C2216yes—
123#2509C2213yes—
124#2507C2213yes—
125#2507C2216yes—
126#2506C2213yes—
127#2506C2213yes—
128#2502C2213yes—
129#2502C2213yes—
130#2502C2213yes—
131#2500C2213yes—
132#2487C2213yes—
133#2487C2213yes—
134#2486C2213yes—
135#2485C2213yes—
136#2476C2216yes—
137#2476C2216yes—
138#2464C2216yes—
139#2454C2216yes—
140#2448C2213yes—
141#2448C2213yes—
142#2447C2213yes—
143#2447C2213yes—
144#2446C2213yes—
145#2446C2213yes—
146#2446C2213yes—
147#2446C2213yes—
148#2429C2213yes—
149#2429C2213yes—
150#2428C2213yes—
151#2428C2213yes—
152#2427C2213yes—
153#2427C2213yes—
154#2427C2213yes—
155#2427C2213yes—
156#2426C2213yes—
157#2426C2213yes—
158#2426C2213yes—
159#2426C2213yes—
160#2423C2213yes—
161#2423C2213yes—
162#2423C2213yes—
163#2423C2213yes—
164#2423C2213yes—
165#2422C2213yes—
166#2422C2213yes—
167#2421C2213yes—
168#2417C2213yes—
169#2417C2213yes—
170#2416C2213yes—
171#2416C2213yes—
172#2416C2213yes—
173#2416C2213yes—
174#2415C2213yes—
175#2415C2213yes—
176#2415C2213yes—
177#2415C2213yes—
178#2414C2213yes—
179#2414C2213yes—
180#2402C2213yes—
181#2397C2213yes—
182#2395C2213yes—
183#2395C2213yes—
184#2392C2213yes—
185#2392C2213yes—
186#2367C2213yes—
187#2365C2213yes—
188#2362C2213yes—
189#2361C2213yes—
190#2360C2213yes—
191#2360C2213yes—
192#2354C2213yes—
193#2354C2213yes—
194#2352C2213yes—
195#2351C2211yescharacteristic
196#2351C2211yescharacteristic
197Q8×C4⋊C4C2211yescharacteristic
198Q8×C4⋊C4C2211yescharacteristic
199Q8×C4⋊C4C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203D4×C4⋊C4C2213yes—
204#2347C2213yes—
205#2347C2213yes—
206#2341C2211yescharacteristic
207#2341C2211yescharacteristic
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210Q8×C22⋊C4C2211yescharacteristic
211Q8×C22⋊C4C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216#2335C2216yes—
217#2327C2213yes—
218#2326C2213yes—
219#2324C2216yes—
220#2323C2213yes—
221#2323C2213yes—
222#2319C2213yes—
223#2319C2213yes—
224C4×C22⋊Q8C2213yes—
225C4×#123C2213yes—
226C4×#123C2213yes—
227C4×#121C2213yes—
228C4×#121C2213yes—
229C4×#121C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2290C2213yes—
233#2290C2213yes—
234#2285C2213yes—
235#2283C2213yes—
236#2276C2211yescharacteristic
237#2276C2211yescharacteristic
238C22×#41C2311yescharacteristic
239C22×#41C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241C23×Q8C2311yescharacteristic
242C23×Q8C2311yescharacteristic
243#550—44no—
244D4×Q8—28no—
245D4×Q8—44no—
246D4×Q8—44no—
247#548—28no—
248#548—44no—
249#548—44no—
250#548—44no—
251#548—44no—
252#548—44no—
253C2×C4⋊Q8C2313yes—
254C2×C4⋊Q8C2313yes—
255C2×C4⋊Q8C2313yes—
256C2×#127C2313yes—
257C2×#125C2316yes—
258C2×#124C2313yes—
259C2×#124C2313yes—
260C2×#124C2313yes—
261C2×#124C2313yes—
262C2×#124C2313yes—
263C2×#124C2313yes—
264C2×#123C2311yescharacteristic
265C2×#123C2311yescharacteristic
266C2×#123C2316yes—
267C2×C22⋊Q8C2313yes—
268C2×C22⋊Q8C2313yes—
269C2×C22⋊Q8C2313yes—
270C2×C22⋊Q8C2313yes—
271C2×C22⋊Q8C2313yes—
272C2×C22⋊Q8C2313yes—
273C2×C22⋊Q8C2313yes—
274C2×C22⋊Q8C2313yes—
275C2×C22⋊Q8C2313yes—
276C2×C22⋊Q8C2313yes—
277C2×C22⋊Q8C2313yes—
278C2×C22⋊Q8C2313yes—
279C2×#121C2313yes—
280C2×#121C2313yes—
281C2×#121C2313yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2313yes—
291C2×#121C2316yes—
292C2×#121C2316yes—
293#520—44no—
294#519—44no—
295C4×#41—28no—
296C2×C4×Q8—44no—
297C2×C4×Q8—44no—
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2311yescharacteristic
300C2×C4×Q8C2311yescharacteristic
301C2×C4×Q8C2311yescharacteristic
302C2×C4×Q8C2311yescharacteristic
303C2×C4×Q8C2311yescharacteristic
304C2×C4×Q8C2311yescharacteristic
305C2×C4×Q8C2311yescharacteristic
306C2×C4×Q8C2311yescharacteristic
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2313yes—
311C2×C4×Q8C2313yes—
312C2×C4×Q8C2313yes—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2313yes—
318C2×C4×D4C2313yes—
319C2×C4×D4C2313yes—
320C2×C4×D4C2313yes—
321C2×C4×D4C2313yes—
322C2×C4×D4C2313yes—
323C2×C4×D4C2313yes—
324C2×C4×D4C2313yes—
325C2×C4×D4C2313yes—
326C2×C4×D4C2313yes—
327C2×C4×D4C2313yes—
328C2×C4×D4C2316yes—
329C2×#117C2313yes—
330C2×#117C2313yes—
331C2×#117C2313yes—
332C2×#117C2313yes—
333C2×#117C2316yes—
334C22×C4⋊C4C2313yes—
335C22×C4⋊C4C2313yes—
336C22×C4⋊C4C2313yes—
337C22×C42C2313yes—
338C22×C42C2313yes—
339C22×C42C2313yes—
340#400C2313yes—
341#400C2316yes—
342#400C2316yes—
343#400C2313yes—
344#400C2316yes—
345#400C2313yes—
346#400C2313yes—
347#400C2313yes—
348#400C2313yes—
349#399C2313yes—
350#399C2316yes—
351#399C2316yes—
352#399C2316yes—
353#399C2316yes—
354#399C2313yes—
355#399C2316yes—
356#399C2311yescharacteristic
357#399C2313yes—
358#399C2313yes—
359#399C2313yes—
360#399C2316yes—
361#398C2316yes—
362#398C2313yes—
363#398C2316yes—
364#398C2316yes—
365#398C2316yes—
366#398C2313yes—
367#398C2313yes—
368#398C2316yes—
369#398C2316yes—
370#398C2313yes—
371#398C2313yes—
372#398C2313yes—
373#398C2316yes—
374#398C2316yes—
375#398C2311yescharacteristic
376#398C2313yes—
377#397C2313yes—
378#397C2313yes—
379#397C2316yes—
380#397C2316yes—
381#397C2316yes—
382#397C2316yes—
383#397C2316yes—
384#397C2313yes—
385#397C2313yes—
386#397C2313yes—
387#397C2313yes—
388#397C2316yes—
389#397C2311yescharacteristic
390#397C2313yes—
391#396C2313yes—
392#396C2316yes—
393#396C2316yes—
394#396C2316yes—
395#396C2313yes—
396#396C2316yes—
397#396C2316yes—
398#396C2316yes—
399#396C2311yescharacteristic
400#396C2313yes—
401#396C2316yes—
402#394C2313yes—
403#394C2316yes—
404#394C2316yes—
405#394C2316yes—
406#394C2316yes—
407#394C2316yes—
408#394C2313yes—
409#394C2316yes—
410#394C2313yes—
411#394C2316yes—
412#394C2311yescharacteristic
413#394C2313yes—
414#394C2313yes—
415#394C2313yes—
416#394C2316yes—
417#394C2316yes—
418#394C2316yes—
419#394C2313yes—
420#394C2313yes—
421#394C2313yes—
422#394C2316yes—
423#392C2313yes—
424#392C2313yes—
425#392C2316yes—
426#392C2313yes—
427#392C2311yescharacteristic
428#392C2313yes—
429#392C2313yes—
430#391C2313yes—
431#391C2313yes—
432#391C2313yes—
433#391C2313yes—
434#391C2313yes—
435#391C2313yes—
436#391C2313yes—
437#391C2313yes—
438#391C2313yes—
439#391C2313yes—
440#391C2313yes—
441#391C2313yes—
442#390C2313yes—
443#390C2313yes—
444#390C2313yes—
445#390C2313yes—
446#390C2316yes—
447#390C2316yes—
448#390C2316yes—
449#390C2313yes—
450#390C2316yes—
451#390C2313yes—
452#390C2313yes—
453#390C2313yes—
454#390C2316yes—
455#390C2316yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2311yescharacteristic
460#389C2313yes—
461#389C2313yes—
462#389C2313yes—
463#389C2313yes—
464#389C2313yes—
465#389C2313yes—
466#389C2316yes—
467#389C2316yes—
468#389C2313yes—
469#389C2313yes—
470#389C2316yes—
471#389C2316yes—
472#389C2313yes—
473#389C2313yes—
474#389C2316yes—
475#389C2313yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#388C2316yes—
486#388C2316yes—
487#388C2316yes—
488#388C2316yes—
489#388C2313yes—
490#388C2316yes—
491#388C2316yes—
492#388C2316yes—
493#388C2313yes—
494#388C2316yes—
495#388C2313yes—
496#388C2313yes—
497#388C2313yes—
498#388C2316yes—
499#388C2316yes—
500#388C2313yes—
501#388C2316yes—
502#388C2316yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2316yes—
507#388C2313yes—
508#388C2316yes—
509#388C2316yes—
510#388C2313yes—
511#388C2313yes—
512#388C2313yes—
513#388C2313yes—
514#388C2313yes—
515#388C2311yescharacteristic
516#387C2316yes—
517#387C2316yes—
518#387C2313yes—
519#387C2316yes—
520#387C2313yes—
521#387C2316yes—
522#387C2316yes—
523#387C2316yes—
524#387C2316yes—
525#387C2316yes—
526#387C2316yes—
527#387C2313yes—
528#387C2313yes—
529#387C2316yes—
530#387C2313yes—
531#387C2313yes—
532#387C2313yes—
533#387C2313yes—
534#386C2316yes—
535#386C2316yes—
536#386C2313yes—
537#386C2313yes—
538#386C2316yes—
539#386C2316yes—
540#386C2313yes—
541#386C2313yes—
542#386C2313yes—
543#386C2313yes—
544#386C2316yes—
545#386C2313yes—
546#386C2313yes—
547#386C2313yes—
548#386C2313yes—
549#386C2311yescharacteristic
550#386C2313yes—
551#386C2313yes—
552#386C2311yescharacteristic
553#385C2313yes—
554#385C2316yes—
555#385C2316yes—
556#385C2316yes—
557#385C2316yes—
558#385C2316yes—
559#385C2313yes—
560#385C2313yes—
561#385C2316yes—
562#385C2313yes—
563#385C2311yescharacteristic
564#385C2313yes—
565#384C2313yes—
566#384C2313yes—
567#384C2313yes—
568#384C2313yes—
569#384C2313yes—
570#384C2313yes—
571#384C2316yes—
572#383C2313yes—
573#383C2313yes—
574#382C2313yes—
575#382C2313yes—
576#382C2311yescharacteristic
577#382C2313yes—
578#381C2313yes—
579#381C2313yes—
580#381C2313yes—
581#381C2313yes—
582#381C2316yes—
583#380C2316yes—
584#380C2313yes—
585#380C2313yes—
586#380C2316yes—
587#380C2316yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2313yes—
592#380C2313yes—
593#380C2313yes—
594#380C2313yes—
595#380C2313yes—
596#380C2316yes—
597#380C2313yes—
598#380C2313yes—
599#380C2313yes—
600#380C2313yes—
601#380C2311yescharacteristic
602#380C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2316yes—
609C4×C4⋊C4C2316yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C4⋊C4C2313yes—
615C4×C4⋊C4C2313yes—
616C4×C4⋊C4C2313yes—
617C4×C4⋊C4C2313yes—
618C4×C4⋊C4C2313yes—
619C4×C22⋊C4C2316yes—
620C4×C22⋊C4C2316yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2313yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631#376C2313yes—
632#376C2313yes—
633C2×#41—24no—
634C2×#41—24no—
635C2×#41—24no—
636C2×#41—24no—
637C2×#41—24no—
638C2×#41—24no—
639C22×Q8—24no—
640C22×Q8—24no—
641C22×Q8—24no—
642C22×Q8—24no—
643C22×Q8—24no—
644C22×Q8—24no—
645C22×Q8—24no—
646C22×Q8—24no—
647C22×Q8—24no—
648C22×Q8C2413yes—
649C22×Q8C2413yes—
650C22×Q8C2413yes—
651C22×Q8C2411yescharacteristic
652C22×D4C2413yes—
653C22×D4C2413yes—
654C22×D4C2411yescharacteristic
655C22×D4C2411yescharacteristic
656C22×D4C2413yes—
657C22×D4C2411yescharacteristic
658C22×D4C2413yes—
659C22×D4C2413yes—
660C22×D4C2413yes—
661C22×D4C2413yes—
662C22×D4C2413yes—
663C22×D4C2413yes—
664C22×D4C2416yes—
665C23×C4C2413yes—
666C23×C4C2413yes—
667C23×C4C2413yes—
668C23×C4C2413yes—
669C23×C4C2413yes—
670C23×C4C2413yes—
671C23×C4C2411yescharacteristic
672C23×C4C2413yes—
673C23×C4C2411yescharacteristic
674C23×C4C2413yes—
675C23×C4C2413yes—
676C23×C4C2416yes—
677C4⋊Q8—212no—
678C4⋊Q8—46no—
679C4⋊Q8—46no—
680#127—46no—
681#125—86no—
682#124—212no—
683#124—46no—
684#124—46no—
685#124—46no—
686#124—46no—
687#124—46no—
688#123—24no—
689#123—24no—
690#123—412no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—212no—
694C22⋊Q8—46no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697C22⋊Q8—46no—
698C22⋊Q8—46no—
699C22⋊Q8—46no—
700C22⋊Q8—46no—
701C22⋊Q8—46no—
702C22⋊Q8—46no—
703#121—212no—
704#121—212no—
705#121—46no—
706#121—46no—
707#121—46no—
708#121—46no—
709#121—46no—
710#121—46no—
711#121—46no—
712#121—46no—
713#121—46no—
714#121—46no—
715#121—86no—
716#121—86no—
717C4×Q8—24no—
718C4×Q8—24no—
719C4×Q8—24no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—24no—
725C4×Q8—24no—
726C4×Q8—46no—
727C4×Q8—46no—
728C4×Q8—46no—
729C4×Q8—46no—
730C4×Q8—46no—
731C4×Q8—46no—
732C4×Q8#4118yes—
733C4×D4—212no—
734C4×D4—212no—
735C4×D4—212no—
736C4×D4—212no—
737C4×D4—46no—
738C4×D4—46no—
739C4×D4—46no—
740C4×D4—46no—
741C4×D4—46no—
742C4×D4—46no—
743C4×D4—46no—
744C4×D4—46no—
745C4×D4—46no—
746C4×D4—46no—
747C4×D4—86no—
748#117—212no—
749#117—46no—
750#117—46no—
751#117—46no—
752#117—86no—
753C2×C4⋊C4—46no—
754C2×C4⋊C4—46no—
755C2×C4⋊C4—46no—
756C2×C4⋊C4C2413yes—
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2413yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C4⋊C4C2413yes—
763C2×C4⋊C4C2413yes—
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2413yes—
768C2×C4⋊C4C2416yes—
769C2×C4⋊C4C2411yescharacteristic
770C2×C4⋊C4C2411yescharacteristic
771C2×C4⋊C4C2411yescharacteristic
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2413yes—
774C2×C4⋊C4C2416yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2411yescharacteristic
777C2×C4⋊C4C2413yes—
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2411yescharacteristic
782C2×C4⋊C4C2413yes—
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2416yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2416yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2413yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2413yes—
795C2×C4⋊C4C2416yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2416yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2411yescharacteristic
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2416yes—
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C22⋊C4C2416yes—
808C2×C22⋊C4C2411yescharacteristic
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2413yes—
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2416yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2413yes—
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2411yescharacteristic
820C2×C22⋊C4C2413yes—
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2413yes—
823C2×C22⋊C4C2413yes—
824C2×C22⋊C4C2416yes—
825C2×C22⋊C4C2416yes—
826C2×C22⋊C4C2411yescharacteristic
827C2×C22⋊C4C2411yescharacteristic
828C2×C22⋊C4C2411yescharacteristic
829C2×C22⋊C4C2411yescharacteristic
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2413yes—
832C2×C22⋊C4C2413yes—
833C2×C22⋊C4C2413yes—
834C2×C22⋊C4C2416yes—
835C2×C22⋊C4C2413yes—
836C2×C22⋊C4C2413yes—
837C2×C22⋊C4C2413yes—
838C2×C22⋊C4C2413yes—
839C2×C22⋊C4C2413yes—
840C2×C22⋊C4C2413yes—
841C2×C22⋊C4C2413yes—
842C2×C22⋊C4C2413yes—
843C2×C22⋊C4C2413yes—
844C2×C22⋊C4C2413yes—
845C2×C22⋊C4C2416yes—
846C2×C22⋊C4C2416yes—
847C2×C22⋊C4C2416yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2416yes—
850C2×C22⋊C4C2413yes—
851C2×C22⋊C4C2413yes—
852C2×C22⋊C4C2413yes—
853C2×C22⋊C4C2413yes—
854C2×C22⋊C4C2416yes—
855C2×C22⋊C4C2411yescharacteristic
856C2×C22⋊C4C2413yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2411yescharacteristic
862C2×C42—212no—
863C2×C42—46no—
864C2×C42—46no—
865C2×C42C2413yes—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2413yes—
875C2×C42C2411yescharacteristic
876C2×C42C2416yes—
877C2×C42C2416yes—
878C2×C42C2416yes—
879C2×C42C2413yes—
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884#95C2411yescharacteristic
885#95C2411yescharacteristic
886#95C2413yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2413yes—
891#95C2413yes—
892#95C2411yescharacteristic
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2411yescharacteristic
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2416yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2416yes—
907#95C2413yes—
908#95C2413yes—
909#95C2413yes—
910#95C2413yes—
911#95C2413yes—
912#95C2413yes—
913#95C2416yes—
914#95C2413yes—
915#95C2413yes—
916#95C2411yescharacteristic
917#95C2411yescharacteristic
918#95C2416yes—
919#95C2413yes—
920#95C2413yes—
921#95C2413yes—
922#95C2413yes—
923#95C2413yes—
924#95C2413yes—
925#95C2413yes—
926#95C2413yes—
927#95C2413yes—
928#95C2413yes—
929#95C2413yes—
930#95C2413yes—
931#95C2413yes—
932#95C2416yes—
933#95C2416yes—
934#95C2416yes—
935#95C2416yes—
936C24C2511yescharacteristic
937C24C2513yes—
938C24C2513yes—
939C24C2511yescharacteristic
940C24C2511yescharacteristic
941#41—416no—
942#41—416no—
943C2×Q8—26no—
944C2×Q8—26no—
945C2×Q8—26no—
946C2×Q8—26no—
947C2×Q8—26no—
948C2×Q8—26no—
949C2×Q8—26no—
950C2×Q8—26no—
951C2×Q8—26no—
952C2×Q8—416no—
953C2×Q8—416no—
954C2×Q8—416no—
955C2×Q8C2×#4114yes—
956C2×Q8H(5,𝔽2)14yes—
957C2×Q8H(5,𝔽2)14yes—
958C2×D4—26no—
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—22no—
963C2×D4—26no—
964C2×D4—26no—
965C2×D4—26no—
966C2×D4—22no—
967C2×D4—26no—
968C2×D4—26no—
969C2×D4—26no—
970C2×D4—26no—
971C2×D4—26no—
972C2×D4—26no—
973C2×D4—26no—
974C2×D4—26no—
975C2×D4—41no—
976C2×D4—41no—
977C2×D4—43no—
978C2×D4—41no—
979C2×D4—41no—
980C2×D4—43no—
981C2×D4—43no—
982C2×D4—43no—
983C2×D4—43no—
984C2×D4—43no—
985C2×D4—43no—
986C2×D4—43no—
987C2×D4—43no—
988C2×D4—43no—
989C2×D4—43no—
990C2×D4—43no—
991C2×D4—43no—
992C2×D4—43no—
993C2×D4—43no—
994C2×D4—46no—
995C2×D4—46no—
996C2×D4—46no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—26no—
1000C22×C4—26no—
1001C22×C4—26no—
1002C22×C4—26no—
1003C22×C4—26no—
1004C22×C4—26no—
1005C22×C4—26no—
1006C22×C4—26no—
1007C22×C4—26no—
1008C22×C4—26no—
1009C22×C4—26no—
1010C22×C4—26no—
1011C22×C4—26no—
1012C22×C4—26no—
1013C22×C4—26no—
1014C22×C4—26no—
1015C22×C4—26no—
1016C22×C4—22no—
1017C22×C4—26no—
1018C22×C4—41no—
1019C22×C4—41no—
1020C22×C4—43no—
1021C22×C4—41no—
1022C22×C4—43no—
1023C22×C4—43no—
1024C22×C4—43no—
1025C22×C4—43no—
1026C22×C4—43no—
1027C22×C4—43no—
1028C22×C4—43no—
1029C22×C4—43no—
1030C22×C4—46no—
1031C22×C4—46no—
1032C22×C4—46no—
1033C22×C4C2511yescharacteristic
1034C22×C4C2511yescharacteristic
1035C22×C4C2511yescharacteristic
1036C22×C4C2513yes—
1037C22×C4C2511yescharacteristic
1038C22×C4C2511yescharacteristic
1039C22×C4C2511yescharacteristic
1040C22×C4C2513yes—
1041C22×C4C2513yes—
1042C22×C4C2513yes—
1043C22×C4C2513yes—
1044C22×C4C2513yes—
1045C22×C4C2511yescharacteristic
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2513yes—
1049C22×C4C2513yes—
1050C22×C4C2513yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2511yescharacteristic
1053C22×C4C2513yes—
1054C22×C4C2511yescharacteristic
1055C22×C4C2513yes—
1056C22×C4C2511yescharacteristic
1057C22×C4C2511yescharacteristic
1058C22×C4C2513yes—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—26no—
1062C4⋊C4—212no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—26no—
1071C4⋊C4—26no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—22no—
1075C4⋊C4—22no—
1076C4⋊C4—43no—
1077C4⋊C4—46no—
1078C4⋊C4—46no—
1079C4⋊C4—41no—
1080C4⋊C4—41no—
1081C4⋊C4—46no—
1082C4⋊C4—43no—
1083C4⋊C4—41no—
1084C4⋊C4—43no—
1085C4⋊C4—43no—
1086C4⋊C4—43no—
1087C4⋊C4—43no—
1088C4⋊C4—41no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—43no—
1096C4⋊C4—46no—
1097C4⋊C4—43no—
1098C4⋊C4—43no—
1099C4⋊C4—43no—
1100C4⋊C4—46no—
1101C4⋊C4—46no—
1102C4⋊C4—46no—
1103C4⋊C4—46no—
1104C4⋊C4—46no—
1105C4⋊C4—46no—
1106C4⋊C4—43no—
1107C4⋊C4—43no—
1108C4⋊C4—43no—
1109C4⋊C4C2×#41112yes—
1110C22⋊C4—22no—
1111C22⋊C4—26no—
1112C22⋊C4—26no—
1113C22⋊C4—212no—
1114C22⋊C4—22no—
1115C22⋊C4—26no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—212no—
1119C22⋊C4—26no—
1120C22⋊C4—22no—
1121C22⋊C4—22no—
1122C22⋊C4—22no—
1123C22⋊C4—41no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—43no—
1128C22⋊C4—43no—
1129C22⋊C4—41no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—43no—
1133C22⋊C4—46no—
1134C22⋊C4—46no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—41no—
1138C22⋊C4—41no—
1139C22⋊C4—41no—
1140C22⋊C4—43no—
1141C22⋊C4—43no—
1142C22⋊C4—43no—
1143C22⋊C4—43no—
1144C22⋊C4—43no—
1145C22⋊C4—43no—
1146C22⋊C4—43no—
1147C22⋊C4—43no—
1148C22⋊C4—43no—
1149C22⋊C4—43no—
1150C22⋊C4—43no—
1151C22⋊C4—43no—
1152C22⋊C4—46no—
1153C22⋊C4—43no—
1154C22⋊C4—43no—
1155C22⋊C4—43no—
1156C22⋊C4—43no—
1157C22⋊C4—46no—
1158C22⋊C4—46no—
1159C22⋊C4—46no—
1160C22⋊C4—46no—
1161C22⋊C4—46no—
1162C22⋊C4—43no—
1163C22⋊C4—46no—
1164C22⋊C42−1+414yes—
1165C42—22no—
1166C42—26no—
1167C42—26no—
1168C42—26no—
1169C42—26no—
1170C42—26no—
1171C42—26no—
1172C42—26no—
1173C42—26no—
1174C42—26no—
1175C42—26no—
1176C42—43no—
1177C42—43no—
1178C42—43no—
1179C42—43no—
1180C42—46no—
1181C42—46no—
1182C42—46no—
1183C42C2×#41112yes—
1184C23—21no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—21no—
1194C23—21no—
1195C23—21no—
1196C23—21no—
1197C23—23no—
1198C23—23no—
1199C23—23no—
1200C23—21no—
1201C23—23no—
1202C23—21no—
1203C23—23no—
1204C23—23no—
1205C23—21no—
1206C23—23no—
1207C23—23no—
1208C23—23no—
1209C23—21no—
1210C23—23no—
1211C23—23no—
1212C23—21no—
1213C23—23no—
1214C23—23no—
1215C23—23no—
1216C23—21no—
1217C23C2×2−1+412yes—
1218C23#58512yes—
1219C23C2611yescharacteristic
1220Q8—412no—
1221Q8—412no—
1222Q8—412no—
1223Q8#540116yes—
1224D4—412no—
1225D4—44no—
1226D4—44no—
1227D4—44no—
1228D4—412no—
1229D4—412no—
1230D4—86no—
1231D4—86no—
1232D4—86no—
1233D4—86no—
1234D4—86no—
1235D4—86no—
1236D4—166no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—23no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—23no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—23no—
1247C2×C4—23no—
1248C2×C4—21no—
1249C2×C4—23no—
1250C2×C4—23no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—23no—
1259C2×C4—23no—
1260C2×C4—23no—
1261C2×C4—23no—
1262C2×C4—23no—
1263C2×C4—23no—
1264C2×C4—23no—
1265C2×C4—23no—
1266C2×C4—23no—
1267C2×C4—23no—
1268C2×C4—23no—
1269C2×C4—23no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—23no—
1273C2×C4—23no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—23no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—23no—
1286C2×C4—23no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—23no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—23no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—23no—
1307C2×C4—21no—
1308C2×C4—412no—
1309C2×C4—44no—
1310C2×C4—44no—
1311C2×C4—412no—
1312C2×C4—412no—
1313C2×C4—412no—
1314C2×C4—412no—
1315C2×C4—412no—
1316C2×C4—86no—
1317C2×C4—86no—
1318C2×C4—86no—
1319C2×C4—166no—
1320C2×C4C22×#4112yes—
1321C2×C4C22×#4116yes—
1322C2×C4C22×#4116yes—
1323C2×C4C2×H(5,𝔽2)16yes—
1324C2×C4C2×H(5,𝔽2)16yes—
1325C2×C4C2×2−1+412yes—
1326C2×C4C2×2−1+412yes—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—22no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—43no—
1342C22—43no—
1343C22—41no—
1344C22—43no—
1345C22—41no—
1346C22—43no—
1347C22—43no—
1348C22—43no—
1349C22—41no—
1350C22—41no—
1351C22—43no—
1352C22—43no—
1353C22—43no—
1354C22—41no—
1355C22—43no—
1356C22—41no—
1357C22—43no—
1358C22—43no—
1359C22—41no—
1360C22—43no—
1361C22—43no—
1362C22C23×#4111yescharacteristic
1363C22C22×H(5,𝔽2)11yescharacteristic
1364C22C22×H(5,𝔽2)11yescharacteristic
1365C22C22×2−1+411yescharacteristic
1366C22C2×#58511yescharacteristic
1367C22H(7,𝔽2)11yescharacteristic
1368C222−1+611yescharacteristic
1369C4—22no—
1370C4—26no—
1371C4—22no—
1372C4—22no—
1373C4—43no—
1374C4—41no—
1375C4—41no—
1376C4—43no—
1377C4—41no—
1378C4—43no—
1379C4—43no—
1380C4—43no—
1381C4—43no—
1382C4—43no—
1383C4—43no—
1384C4—43no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—43no—
1392C4—43no—
1393C4—43no—
1394C4C2×#540112yes—
1395C2—42no—
1396C2—42no—
1397C2—83no—
1398C2—83no—
1399C2—81no—
1400C2C22×#54011yescharacteristic
1401C2#6289911yescharacteristic
1402C2#6291311yescharacteristic
1403C2#6300011yescharacteristic
1404C2#6300511yescharacteristic
1405C2#6301511yescharacteristic
1406C2#6305211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52249C2semidirect
2. #42714C2semidirect
3. #42705C2semidirect
4. #42641C2semidirect
5. #42641C2semidirect
6. #42557C2semidirect
7. #42508C2semidirect
8. #40223C2semidirect
9. #40170C2semidirect
10. #40054C2semidirect
11. #39900C2semidirect
12. #39606C2semidirect
13. #39220C2semidirect
14. #37409C2semidirect
15. #37384C2semidirect
16. #37348C2semidirect
17. #36576C2semidirect
18. Q8×#123C2semidirect
19. Q8×#123C2semidirect
20. #36444C2semidirect
21. #36434C2semidirect
22. #36430C2semidirect
23. #35996C2semidirect
24. #35927C2semidirect
25. #35868C2semidirect
26. #35831C2semidirect
27. #35801C2semidirect
28. #35771C2semidirect
29. #34294C2semidirect
30. #34291C2semidirect
31. #34193C2semidirect

Maximal subgroups

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

subgroupindex
#522492
#427142
#427052
#426412
#425572
#425082
#402232
#401702
#400542
#399002
#396062
#392202
#374092
#373842
#373482
#365762
Q8×#1232
#364442
#364342
#364302
#359962
#359272
#358682
#358312
#358012
#357712
#342942
#342912
#341932