Finite Group Databasebeta

← #7656625

Subgroups — #7656625

Order 512.

5153 conjugacy classes of subgroups.

The subgroup lattice has 1407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42705C213yesmaximal, complemented
2#42669C213yesmaximal, complemented
3#42641C213yesmaximal, complemented
4#42633C213yesmaximal, complemented
5#42570C213yesmaximal, complemented
6#42565C213yesmaximal, complemented
7#42508C213yesmaximal, complemented
8#42460C213yesmaximal, complemented
9#40217C213yesmaximal, complemented
10#40198C213yesmaximal, complemented
11#39785C213yesmaximal, complemented
12#39664C213yesmaximal, complemented
13#37627C213yesmaximal, complemented
14#37594C213yesmaximal, complemented
15#36576C211yesmaximal, characteristic, complemented
16Q8×#123C211yesmaximal, characteristic, complemented
17#36483C211yesmaximal, characteristic, complemented
18#36434C211yesmaximal, characteristic, complemented
19#35983C211yesmaximal, characteristic, complemented
20#35927C211yesmaximal, characteristic, complemented
21#35868C211yesmaximal, characteristic, complemented
22#35831C211yesmaximal, characteristic, complemented
23#35831C211yesmaximal, characteristic, complemented
24#35771C211yesmaximal, characteristic, complemented
25#35737C211yesmaximal, characteristic, complemented
26#35723C211yesmaximal, characteristic, complemented
27#35109C213yesmaximal, complemented
28#34597C213yesmaximal, complemented
29#34312C211yesmaximal, characteristic, complemented
30#34263C211yesmaximal, characteristic, complemented
31C4×D4×Q8C211yesmaximal, 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×#520C2211yescharacteristic
44C2×#519C2211yescharacteristic
45C22×C4×Q8C2211yescharacteristic
46C22×C4×Q8C2211yescharacteristic
47#2856C2213yes—
48#2855C2213yes—
49#2854C2213yes—
50#2850C2213yes—
51#2837C2216yes—
52#2837C2216yes—
53#2837C2216yes—
54#2836C2216yes—
55#2793C2216yes—
56#2791C2216yes—
57#2780C2216yes—
58#2752C2216yes—
59#2748C2216yes—
60#2748C2216yes—
61#2743C2216yes—
62#2743C2216yes—
63#2741C2216yes—
64#2740C2216yes—
65#2740C2216yes—
66#2711C2216yes—
67#2707C2216yes—
68#2701C2216yes—
69#2688C2216yes—
70#2671C2216yes—
71#2667C2213yes—
72#2667C2213yes—
73#2667C2216yes—
74#2661C2213yes—
75#2661C2213yes—
76#2658C2213yes—
77#2654C2213yes—
78#2654C2213yes—
79#2651C2213yes—
80#2651C2213yes—
81#2651C2216yes—
82#2649C2216yes—
83#2649C2213yes—
84#2649C2213yes—
85#2648C2213yes—
86#2648C2213yes—
87#2647C2213yes—
88#2635C2213yes—
89#2635C2213yes—
90#2630C2211yescharacteristic
91#2630C2213yes—
92#2629C2216yes—
93#2625C2213yes—
94#2625C2213yes—
95#2624C2216yes—
96#2621C2213yes—
97#2620C2213yes—
98#2620C2213yes—
99#2620C2213yes—
100#2570C2213yes—
101#2552C2213yes—
102#2548C2213yes—
103#2547C2213yes—
104#2545C2213yes—
105#2545C2213yes—
106#2544C2213yes—
107#2544C2213yes—
108#2542C2213yes—
109#2542C2213yes—
110#2542C2213yes—
111#2540C2213yes—
112#2540C2213yes—
113#2540C2213yes—
114#2538C2213yes—
115#2538C2213yes—
116#2537C2213yes—
117#2537C2213yes—
118#2536C2213yes—
119#2535C2213yes—
120#2522C2216yes—
121#2516C2216yes—
122#2516C2216yes—
123#2509C2213yes—
124#2507C2213yes—
125#2506C2213yes—
126#2506C2213yes—
127#2503C2213yes—
128#2502C2213yes—
129#2501C2213yes—
130#2499C2213yes—
131#2497C2216yes—
132#2490C2216yes—
133#2487C2213yes—
134#2487C2213yes—
135#2486C2213yes—
136#2485C2213yes—
137#2476C2216yes—
138#2471C2216yes—
139#2464C2216yes—
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#2421C2213yes—
166#2420C2213yes—
167#2420C2213yes—
168#2417C2213yes—
169#2417C2213yes—
170#2417C2213yes—
171#2417C2213yes—
172#2417C2213yes—
173#2416C2213yes—
174#2416C2213yes—
175#2416C2213yes—
176#2416C2213yes—
177#2416C2213yes—
178#2415C2213yes—
179#2414C2213yes—
180#2402C2213yes—
181#2397C2213yes—
182#2395C2213yes—
183#2395C2213yes—
184#2392C2213yes—
185#2392C2213yes—
186#2392C2213yes—
187#2392C2213yes—
188#2367C2213yes—
189#2365C2213yes—
190#2363C2213yes—
191#2360C2213yes—
192#2360C2213yes—
193#2360C2213yes—
194#2357C2213yes—
195#2354C2213yes—
196#2352C2213yes—
197#2351C2211yescharacteristic
198#2351C2211yescharacteristic
199#2351C2211yescharacteristic
200Q8×C4⋊C4C2211yescharacteristic
201Q8×C4⋊C4C2211yescharacteristic
202Q8×C4⋊C4C2211yescharacteristic
203Q8×C4⋊C4C2211yescharacteristic
204Q8×C4⋊C4C2211yescharacteristic
205D4×C4⋊C4C2213yes—
206#2345C2213yes—
207#2344C2213yes—
208#2341C2211yescharacteristic
209#2341C2211yescharacteristic
210#2341C2211yescharacteristic
211#2341C2211yescharacteristic
212Q8×C22⋊C4C2211yescharacteristic
213Q8×C22⋊C4C2211yescharacteristic
214Q8×C22⋊C4C2211yescharacteristic
215Q8×C22⋊C4C2211yescharacteristic
216Q8×C22⋊C4C2211yescharacteristic
217Q8×C22⋊C4C2211yescharacteristic
218#2333C2216yes—
219#2333C2216yes—
220#2324C2213yes—
221#2323C2213yes—
222#2319C2213yes—
223#2314C2213yes—
224C4×C4⋊Q8C2213yes—
225C4×#124C2213yes—
226C4×C22⋊Q8C2213yes—
227C4×C22⋊Q8C2213yes—
228C4×#123C2213yes—
229C4×#123C2213yes—
230C4×#121C2213yes—
231C4×#121C2213yes—
232#2298C2213yes—
233#2293C2213yes—
234#2293C2213yes—
235#2276C2211yescharacteristic
236C42×Q8C2211yescharacteristic
237C42×D4C2213yes—
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×#123C2313yes—
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×#121C2316yes—
282C2×#121C2313yes—
283C2×#121C2313yes—
284C2×#121C2313yes—
285C2×#121C2313yes—
286C2×#121C2313yes—
287C2×#121C2313yes—
288C2×#121C2313yes—
289C2×#121C2313yes—
290C2×#121C2316yes—
291C2×#121C2316yes—
292#520—28no—
293#520—44no—
294#519—44no—
295C2×C4×Q8—44no—
296C2×C4×Q8—44no—
297C2×C4×Q8C2311yescharacteristic
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×Q8C2313yes—
307C2×C4×Q8C2313yes—
308C2×C4×Q8C2313yes—
309C2×C4×Q8C2313yes—
310C2×C4×Q8C2313yes—
311C2×C4×Q8C2313yes—
312C2×C4×Q8C2311yescharacteristic
313C2×C4×D4C2313yes—
314C2×C4×D4C2313yes—
315C2×C4×D4C2313yes—
316C2×C4×D4C2313yes—
317C2×C4×D4C2311yescharacteristic
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×D4C2313yes—
329C2×#117C2313yes—
330C2×#117C2313yes—
331C2×#117C2313yes—
332C2×#117C2313yes—
333C2×#117C2316yes—
334C22×C4⋊C4C2313yes—
335C22×C4⋊C4C2313yes—
336C22×C4⋊C4C2313yes—
337C22×C4⋊C4C2313yes—
338C22×C42C2313yes—
339C22×C42C2313yes—
340#400C2313yes—
341#400C2316yes—
342#400C2316yes—
343#400C2313yes—
344#400C2316yes—
345#400C2316yes—
346#400C2313yes—
347#400C2313yes—
348#400C2313yes—
349#400C2313yes—
350#399C2316yes—
351#399C2313yes—
352#399C2316yes—
353#399C2316yes—
354#399C2316yes—
355#399C2316yes—
356#399C2316yes—
357#399C2313yes—
358#399C2313yes—
359#399C2313yes—
360#399C2313yes—
361#399C2313yes—
362#398C2316yes—
363#398C2313yes—
364#398C2316yes—
365#398C2316yes—
366#398C2316yes—
367#398C2313yes—
368#398C2316yes—
369#398C2316yes—
370#398C2316yes—
371#398C2316yes—
372#398C2313yes—
373#398C2313yes—
374#398C2311yescharacteristic
375#398C2313yes—
376#398C2313yes—
377#398C2313yes—
378#398C2313yes—
379#398C2313yes—
380#397C2313yes—
381#397C2316yes—
382#397C2316yes—
383#397C2313yes—
384#397C2313yes—
385#397C2316yes—
386#397C2316yes—
387#397C2316yes—
388#397C2316yes—
389#397C2313yes—
390#397C2311yescharacteristic
391#397C2313yes—
392#397C2313yes—
393#397C2313yes—
394#397C2313yes—
395#397C2313yes—
396#396C2316yes—
397#396C2316yes—
398#396C2316yes—
399#396C2316yes—
400#396C2316yes—
401#396C2316yes—
402#396C2316yes—
403#396C2316yes—
404#396C2313yes—
405#396C2313yes—
406#396C2311yescharacteristic
407#396C2311yescharacteristic
408#396C2313yes—
409#396C2313yes—
410#396C2313yes—
411#396C2313yes—
412#394C2313yes—
413#394C2316yes—
414#394C2316yes—
415#394C2316yes—
416#394C2316yes—
417#394C2316yes—
418#394C2316yes—
419#394C2316yes—
420#394C2316yes—
421#394C2313yes—
422#394C2311yescharacteristic
423#394C2311yescharacteristic
424#394C2313yes—
425#394C2311yescharacteristic
426#394C2313yes—
427#394C2313yes—
428#394C2313yes—
429#394C2313yes—
430#394C2313yes—
431#394C2313yes—
432#394C2313yes—
433#394C2313yes—
434#394C2313yes—
435#394C2313yes—
436#392C2311yescharacteristic
437#392C2313yes—
438#392C2313yes—
439#392C2313yes—
440#392C2313yes—
441#392C2313yes—
442#392C2313yes—
443#392C2313yes—
444#391C2313yes—
445#391C2313yes—
446#391C2313yes—
447#391C2313yes—
448#391C2313yes—
449#391C2313yes—
450#391C2313yes—
451#391C2313yes—
452#391C2313yes—
453#391C2313yes—
454#391C2313yes—
455#391C2313yes—
456#390C2313yes—
457#390C2313yes—
458#390C2313yes—
459#390C2313yes—
460#390C2316yes—
461#390C2316yes—
462#390C2316yes—
463#390C2316yes—
464#390C2313yes—
465#390C2313yes—
466#390C2313yes—
467#390C2313yes—
468#390C2313yes—
469#390C2316yes—
470#390C2313yes—
471#390C2316yes—
472#390C2313yes—
473#390C2313yes—
474#389C2316yes—
475#389C2316yes—
476#389C2313yes—
477#389C2313yes—
478#389C2313yes—
479#389C2313yes—
480#389C2313yes—
481#389C2313yes—
482#389C2313yes—
483#389C2313yes—
484#389C2313yes—
485#389C2313yes—
486#389C2313yes—
487#389C2313yes—
488#389C2313yes—
489#389C2313yes—
490#389C2313yes—
491#389C2313yes—
492#389C2313yes—
493#389C2313yes—
494#389C2316yes—
495#389C2313yes—
496#389C2313yes—
497#389C2316yes—
498#388C2316yes—
499#388C2316yes—
500#388C2313yes—
501#388C2316yes—
502#388C2316yes—
503#388C2313yes—
504#388C2313yes—
505#388C2313yes—
506#388C2316yes—
507#388C2316yes—
508#388C2316yes—
509#388C2316yes—
510#388C2316yes—
511#388C2316yes—
512#388C2313yes—
513#388C2311yescharacteristic
514#388C2313yes—
515#388C2313yes—
516#388C2313yes—
517#388C2313yes—
518#388C2313yes—
519#388C2313yes—
520#388C2313yes—
521#388C2313yes—
522#388C2316yes—
523#388C2313yes—
524#388C2313yes—
525#387C2313yes—
526#387C2316yes—
527#387C2316yes—
528#387C2316yes—
529#387C2316yes—
530#387C2313yes—
531#387C2316yes—
532#387C2316yes—
533#387C2316yes—
534#387C2313yes—
535#387C2316yes—
536#387C2316yes—
537#387C2311yescharacteristic
538#387C2313yes—
539#387C2313yes—
540#387C2316yes—
541#387C2313yes—
542#387C2313yes—
543#387C2316yes—
544#386C2316yes—
545#386C2313yes—
546#386C2313yes—
547#386C2316yes—
548#386C2316yes—
549#386C2316yes—
550#386C2316yes—
551#386C2316yes—
552#386C2316yes—
553#386C2316yes—
554#386C2311yescharacteristic
555#386C2313yes—
556#386C2313yes—
557#386C2313yes—
558#386C2316yes—
559#385C2316yes—
560#385C2316yes—
561#385C2316yes—
562#385C2316yes—
563#385C2311yescharacteristic
564#385C2313yes—
565#385C2316yes—
566#384C2313yes—
567#384C2313yes—
568#384C2313yes—
569#384C2313yes—
570#384C2313yes—
571#384C2316yes—
572#382C2313yes—
573#382C2313yes—
574#382C2313yes—
575#381C2316yes—
576#381C2313yes—
577#381C2316yes—
578#381C2313yes—
579#381C2316yes—
580#380C2313yes—
581#380C2313yes—
582#380C2316yes—
583#380C2313yes—
584#380C2313yes—
585#380C2313yes—
586#380C2313yes—
587#380C2313yes—
588#380C2313yes—
589#380C2313yes—
590#380C2313yes—
591#380C2316yes—
592#380C2316yes—
593#380C2316yes—
594#380C2311yescharacteristic
595#380C2313yes—
596#380C2316yes—
597C4×C4⋊C4C2313yes—
598C4×C4⋊C4C2316yes—
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C4⋊C4C2313yes—
602C4×C4⋊C4C2313yes—
603C4×C4⋊C4C2313yes—
604C4×C4⋊C4C2313yes—
605C4×C4⋊C4C2313yes—
606C4×C4⋊C4C2313yes—
607C4×C4⋊C4C2313yes—
608C4×C4⋊C4C2313yes—
609C4×C4⋊C4C2313yes—
610C4×C4⋊C4C2313yes—
611C4×C4⋊C4C2313yes—
612C4×C4⋊C4C2313yes—
613C4×C4⋊C4C2313yes—
614C4×C22⋊C4C2316yes—
615C4×C22⋊C4C2316yes—
616C4×C22⋊C4C2313yes—
617C4×C22⋊C4C2313yes—
618C4×C22⋊C4C2313yes—
619C4×C22⋊C4C2313yes—
620C4×C22⋊C4C2313yes—
621C4×C22⋊C4C2313yes—
622C4×C22⋊C4C2313yes—
623C4×C22⋊C4C2313yes—
624C4×C22⋊C4C2313yes—
625C4×C22⋊C4C2313yes—
626C4×C22⋊C4C2313yes—
627C4×C22⋊C4C2313yes—
628C4×C22⋊C4C2316yes—
629C4×C22⋊C4C2313yes—
630C4×C22⋊C4C2313yes—
631#376C2313yes—
632C43C2313yes—
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×D4C2411yescharacteristic
653C22×D4C2413yes—
654C22×D4C2413yes—
655C22×D4C2411yescharacteristic
656C22×D4C2411yescharacteristic
657C22×D4C2413yes—
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×C4C2416yes—
672C23×C4C2411yescharacteristic
673C23×C4C2413yes—
674C23×C4C2416yes—
675C23×C4C2411yescharacteristic
676C4⋊Q8—212no—
677C4⋊Q8—46no—
678C4⋊Q8—46no—
679#127—46no—
680#125—86no—
681#124—212no—
682#124—46no—
683#124—46no—
684#124—46no—
685#124—46no—
686#124—46no—
687#123—24no—
688#123—46no—
689#123—86no—
690C22⋊Q8—212no—
691C22⋊Q8—212no—
692C22⋊Q8—212no—
693C22⋊Q8—46no—
694C22⋊Q8—46no—
695C22⋊Q8—46no—
696C22⋊Q8—46no—
697C22⋊Q8—46no—
698C22⋊Q8—46no—
699C22⋊Q8—46no—
700C22⋊Q8—46no—
701C22⋊Q8—46no—
702#121—212no—
703#121—212no—
704#121—412no—
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—86no—
714#121—86no—
715C4×Q8—24no—
716C4×Q8—24no—
717C4×Q8—24no—
718C4×Q8—24no—
719C4×Q8—24no—
720C4×Q8—24no—
721C4×Q8—24no—
722C4×Q8—24no—
723C4×Q8—24no—
724C4×Q8—46no—
725C4×Q8—46no—
726C4×Q8—46no—
727C4×Q8—46no—
728C4×Q8—46no—
729C4×Q8—46no—
730C4×Q8#4118yes—
731C4×D4—24no—
732C4×D4—212no—
733C4×D4—212no—
734C4×D4—212no—
735C4×D4—212no—
736C4×D4—46no—
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—
747#117—212no—
748#117—46no—
749#117—46no—
750#117—46no—
751#117—86no—
752C2×C4⋊C4—212no—
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⋊C4C2411yescharacteristic
764C2×C4⋊C4C2413yes—
765C2×C4⋊C4C2413yes—
766C2×C4⋊C4C2413yes—
767C2×C4⋊C4C2411yescharacteristic
768C2×C4⋊C4C2413yes—
769C2×C4⋊C4C2413yes—
770C2×C4⋊C4C2413yes—
771C2×C4⋊C4C2416yes—
772C2×C4⋊C4C2411yescharacteristic
773C2×C4⋊C4C2411yescharacteristic
774C2×C4⋊C4C2413yes—
775C2×C4⋊C4C2416yes—
776C2×C4⋊C4C2416yes—
777C2×C4⋊C4C2411yescharacteristic
778C2×C4⋊C4C2413yes—
779C2×C4⋊C4C2413yes—
780C2×C4⋊C4C2413yes—
781C2×C4⋊C4C2416yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2413yes—
784C2×C4⋊C4C2413yes—
785C2×C4⋊C4C2413yes—
786C2×C4⋊C4C2413yes—
787C2×C4⋊C4C2413yes—
788C2×C4⋊C4C2413yes—
789C2×C4⋊C4C2413yes—
790C2×C4⋊C4C2413yes—
791C2×C4⋊C4C2416yes—
792C2×C4⋊C4C2416yes—
793C2×C4⋊C4C2413yes—
794C2×C4⋊C4C2416yes—
795C2×C4⋊C4C2416yes—
796C2×C4⋊C4C2416yes—
797C2×C4⋊C4C2416yes—
798C2×C4⋊C4C2413yes—
799C2×C4⋊C4C2413yes—
800C2×C4⋊C4C2413yes—
801C2×C4⋊C4C2413yes—
802C2×C4⋊C4C2413yes—
803C2×C4⋊C4C2411yescharacteristic
804C2×C4⋊C4C2411yescharacteristic
805C2×C4⋊C4C2413yes—
806C2×C4⋊C4C2413yes—
807C2×C4⋊C4C2413yes—
808C2×C22⋊C4C2413yes—
809C2×C22⋊C4C2413yes—
810C2×C22⋊C4C2411yescharacteristic
811C2×C22⋊C4C2413yes—
812C2×C22⋊C4C2413yes—
813C2×C22⋊C4C2413yes—
814C2×C22⋊C4C2413yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2411yescharacteristic
817C2×C22⋊C4C2416yes—
818C2×C22⋊C4C2413yes—
819C2×C22⋊C4C2413yes—
820C2×C22⋊C4C2411yescharacteristic
821C2×C22⋊C4C2411yescharacteristic
822C2×C22⋊C4C2411yescharacteristic
823C2×C22⋊C4C2411yescharacteristic
824C2×C22⋊C4C2413yes—
825C2×C22⋊C4C2411yescharacteristic
826C2×C22⋊C4C2413yes—
827C2×C22⋊C4C2413yes—
828C2×C22⋊C4C2413yes—
829C2×C22⋊C4C2416yes—
830C2×C22⋊C4C2411yescharacteristic
831C2×C22⋊C4C2411yescharacteristic
832C2×C22⋊C4C2411yescharacteristic
833C2×C22⋊C4C2411yescharacteristic
834C2×C22⋊C4C2411yescharacteristic
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⋊C4C2413yes—
846C2×C22⋊C4C2413yes—
847C2×C22⋊C4C2413yes—
848C2×C22⋊C4C2416yes—
849C2×C22⋊C4C2416yes—
850C2×C22⋊C4C2416yes—
851C2×C22⋊C4C2416yes—
852C2×C22⋊C4C2416yes—
853C2×C22⋊C4C2416yes—
854C2×C22⋊C4C2416yes—
855C2×C22⋊C4C2413yes—
856C2×C22⋊C4C2416yes—
857C2×C22⋊C4C2413yes—
858C2×C22⋊C4C2413yes—
859C2×C22⋊C4C2413yes—
860C2×C22⋊C4C2413yes—
861C2×C22⋊C4C2413yes—
862C2×C22⋊C4C2413yes—
863C2×C22⋊C4C2413yes—
864C2×C42—46no—
865C2×C42—46no—
866C2×C42C2413yes—
867C2×C42C2413yes—
868C2×C42C2413yes—
869C2×C42C2413yes—
870C2×C42C2413yes—
871C2×C42C2413yes—
872C2×C42C2413yes—
873C2×C42C2413yes—
874C2×C42C2411yescharacteristic
875C2×C42C2413yes—
876C2×C42C2413yes—
877C2×C42C2416yes—
878C2×C42C2416yes—
879C2×C42C2413yes—
880C2×C42C2413yes—
881C2×C42C2413yes—
882C2×C42C2413yes—
883C2×C42C2413yes—
884C2×C42C2413yes—
885C2×C42C2413yes—
886#95C2411yescharacteristic
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2411yescharacteristic
891#95C2411yescharacteristic
892#95C2413yes—
893#95C2411yescharacteristic
894#95C2411yescharacteristic
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2413yes—
899#95C2413yes—
900#95C2413yes—
901#95C2413yes—
902#95C2413yes—
903#95C2413yes—
904#95C2413yes—
905#95C2413yes—
906#95C2413yes—
907#95C2413yes—
908#95C2413yes—
909#95C2416yes—
910#95C2413yes—
911#95C2416yes—
912#95C2413yes—
913#95C2413yes—
914#95C2416yes—
915#95C2413yes—
916#95C2413yes—
917#95C2416yes—
918#95C2411yescharacteristic
919#95C2411yescharacteristic
920#95C2411yescharacteristic
921#95C2416yes—
922#95C2416yes—
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—
936C24C2513yes—
937C24C2513yes—
938C24C2511yescharacteristic
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—22no—
959C2×D4—22no—
960C2×D4—22no—
961C2×D4—22no—
962C2×D4—26no—
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—41no—
978C2×D4—41no—
979C2×D4—43no—
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—26no—
998C22×C4—26no—
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—22no—
1014C22×C4—212no—
1015C22×C4—41no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—43no—
1020C22×C4—43no—
1021C22×C4—46no—
1022C22×C4—43no—
1023C22×C4—43no—
1024C22×C4—43no—
1025C22×C4—46no—
1026C22×C4—46no—
1027C22×C4—46no—
1028C22×C4—46no—
1029C22×C42−1+414yes—
1030C22×C4C2511yescharacteristic
1031C22×C4C2511yescharacteristic
1032C22×C4C2511yescharacteristic
1033C22×C4C2513yes—
1034C22×C4C2513yes—
1035C22×C4C2513yes—
1036C22×C4C2511yescharacteristic
1037C22×C4C2513yes—
1038C22×C4C2513yes—
1039C22×C4C2513yes—
1040C22×C4C2511yescharacteristic
1041C22×C4C2513yes—
1042C22×C4C2511yescharacteristic
1043C22×C4C2511yescharacteristic
1044C22×C4C2513yes—
1045C22×C4C2513yes—
1046C22×C4C2513yes—
1047C22×C4C2513yes—
1048C22×C4C2511yescharacteristic
1049C22×C4C2511yescharacteristic
1050C22×C4C2513yes—
1051C22×C4C2511yescharacteristic
1052C22×C4C2513yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2511yescharacteristic
1055C22×C4C2513yes—
1056C4⋊C4—26no—
1057C4⋊C4—26no—
1058C4⋊C4—22no—
1059C4⋊C4—26no—
1060C4⋊C4—26no—
1061C4⋊C4—212no—
1062C4⋊C4—26no—
1063C4⋊C4—26no—
1064C4⋊C4—26no—
1065C4⋊C4—26no—
1066C4⋊C4—26no—
1067C4⋊C4—26no—
1068C4⋊C4—26no—
1069C4⋊C4—26no—
1070C4⋊C4—22no—
1071C4⋊C4—26no—
1072C4⋊C4—22no—
1073C4⋊C4—22no—
1074C4⋊C4—43no—
1075C4⋊C4—46no—
1076C4⋊C4—46no—
1077C4⋊C4—43no—
1078C4⋊C4—41no—
1079C4⋊C4—43no—
1080C4⋊C4—41no—
1081C4⋊C4—41no—
1082C4⋊C4—43no—
1083C4⋊C4—43no—
1084C4⋊C4—43no—
1085C4⋊C4—46no—
1086C4⋊C4—43no—
1087C4⋊C4—41no—
1088C4⋊C4—43no—
1089C4⋊C4—43no—
1090C4⋊C4—43no—
1091C4⋊C4—43no—
1092C4⋊C4—43no—
1093C4⋊C4—43no—
1094C4⋊C4—43no—
1095C4⋊C4—46no—
1096C4⋊C4—43no—
1097C4⋊C4—46no—
1098C4⋊C4—46no—
1099C4⋊C4—46no—
1100C4⋊C4—46no—
1101C4⋊C4—43no—
1102C4⋊C4—43no—
1103C4⋊C4—46no—
1104C4⋊C4—43no—
1105C4⋊C4—43no—
1106C4⋊C4—43no—
1107C4⋊C4C2×#41112yes—
1108C22⋊C4—22no—
1109C22⋊C4—22no—
1110C22⋊C4—26no—
1111C22⋊C4—22no—
1112C22⋊C4—26no—
1113C22⋊C4—26no—
1114C22⋊C4—22no—
1115C22⋊C4—26no—
1116C22⋊C4—26no—
1117C22⋊C4—26no—
1118C22⋊C4—212no—
1119C22⋊C4—22no—
1120C22⋊C4—26no—
1121C22⋊C4—26no—
1122C22⋊C4—22no—
1123C22⋊C4—22no—
1124C22⋊C4—43no—
1125C22⋊C4—43no—
1126C22⋊C4—43no—
1127C22⋊C4—41no—
1128C22⋊C4—43no—
1129C22⋊C4—43no—
1130C22⋊C4—43no—
1131C22⋊C4—43no—
1132C22⋊C4—46no—
1133C22⋊C4—43no—
1134C22⋊C4—41no—
1135C22⋊C4—41no—
1136C22⋊C4—41no—
1137C22⋊C4—41no—
1138C22⋊C4—41no—
1139C22⋊C4—43no—
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—46no—
1151C22⋊C4—43no—
1152C22⋊C4—43no—
1153C22⋊C4—46no—
1154C22⋊C4—46no—
1155C22⋊C4—46no—
1156C22⋊C4—46no—
1157C22⋊C4—46no—
1158C22⋊C4—43no—
1159C22⋊C4—46no—
1160C22⋊C4—46no—
1161C22⋊C4—43no—
1162C22⋊C4—43no—
1163C22⋊C4—43no—
1164C42—26no—
1165C42—26no—
1166C42—26no—
1167C42—26no—
1168C42—26no—
1169C42—26no—
1170C42—26no—
1171C42—26no—
1172C42—26no—
1173C42—22no—
1174C42—43no—
1175C42—43no—
1176C42—43no—
1177C42—43no—
1178C42—43no—
1179C42—46no—
1180C42—43no—
1181C42—46no—
1182C42—43no—
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—23no—
1197C23—23no—
1198C23—21no—
1199C23—21no—
1200C23—23no—
1201C23—23no—
1202C23—21no—
1203C23—23no—
1204C23—23no—
1205C23—21no—
1206C23—23no—
1207C23—23no—
1208C23—21no—
1209C23—23no—
1210C23—23no—
1211C23—23no—
1212C23—23no—
1213C23—21no—
1214C23—23no—
1215C23—23no—
1216C23—21no—
1217C23C2×2−1+412yes—
1218C23#58512yes—
1219C23C2611yescharacteristic
1220Q8—412no—
1221Q8—412no—
1222Q8—412no—
1223Q8#540116yes—
1224D4—28no—
1225D4—44no—
1226D4—44no—
1227D4—412no—
1228D4—412no—
1229D4—86no—
1230D4—86no—
1231D4—86no—
1232D4—86no—
1233D4—86no—
1234D4—86no—
1235D4—86no—
1236D4—166no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—23no—
1242C2×C4—21no—
1243C2×C4—23no—
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—23no—
1282C2×C4—21no—
1283C2×C4—23no—
1284C2×C4—23no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—23no—
1288C2×C4—21no—
1289C2×C4—23no—
1290C2×C4—23no—
1291C2×C4—23no—
1292C2×C4—21no—
1293C2×C4—23no—
1294C2×C4—23no—
1295C2×C4—23no—
1296C2×C4—23no—
1297C2×C4—23no—
1298C2×C4—23no—
1299C2×C4—23no—
1300C2×C4—21no—
1301C2×C4—23no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—23no—
1305C2×C4—23no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—44no—
1309C2×C4—44no—
1310C2×C4—412no—
1311C2×C4—412no—
1312C2×C4—412no—
1313C2×C4—412no—
1314C2×C4—412no—
1315C2×C4—812no—
1316C2×C4—86no—
1317C2×C4—86no—
1318C2×C4—166no—
1319C2×C4C22×#4112yes—
1320C2×C4C22×#4116yes—
1321C2×C4C22×#4116yes—
1322C2×C4C2×H(5,𝔽2)16yes—
1323C2×C4C2×H(5,𝔽2)16yes—
1324C2×C4C2×2−1+412yes—
1325C2×C4C2×2−1+412yes—
1326C22—22no—
1327C22—22no—
1328C22—22no—
1329C22—22no—
1330C22—22no—
1331C22—22no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—43no—
1341C22—43no—
1342C22—41no—
1343C22—43no—
1344C22—41no—
1345C22—43no—
1346C22—41no—
1347C22—43no—
1348C22—43no—
1349C22—41no—
1350C22—43no—
1351C22—43no—
1352C22—43no—
1353C22—43no—
1354C22—41no—
1355C22—43no—
1356C22—41no—
1357C22—43no—
1358C22—41no—
1359C22—43no—
1360C22—43no—
1361C22C23×#4111yescharacteristic
1362C22C22×H(5,𝔽2)11yescharacteristic
1363C22C22×H(5,𝔽2)11yescharacteristic
1364C22C22×2−1+411yescharacteristic
1365C22C2×#58511yescharacteristic
1366C22H(7,𝔽2)11yescharacteristic
1367C222−1+611yescharacteristic
1368C4—22no—
1369C4—26no—
1370C4—22no—
1371C4—22no—
1372C4—41no—
1373C4—43no—
1374C4—41no—
1375C4—41no—
1376C4—43no—
1377C4—43no—
1378C4—43no—
1379C4—43no—
1380C4—41no—
1381C4—41no—
1382C4—43no—
1383C4—43no—
1384C4—41no—
1385C4—43no—
1386C4—43no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—43no—
1391C4—43no—
1392C4—43no—
1393C4C2×#540112yes—
1394C2—42no—
1395C2—42no—
1396C2—83no—
1397C2—81no—
1398C2—83no—
1399C2C22×#54011yescharacteristic
1400C2#6278811yescharacteristic
1401C2#6285711yescharacteristic
1402C2#6289311yescharacteristic
1403C2#6289911yescharacteristic
1404C2#6291711yescharacteristic
1405C2#6291911yescharacteristic
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. #42705C2semidirect
2. #42669C2semidirect
3. #42641C2semidirect
4. #42633C2semidirect
5. #42570C2semidirect
6. #42565C2semidirect
7. #42508C2semidirect
8. #42460C2semidirect
9. #40217C2semidirect
10. #40198C2semidirect
11. #39785C2semidirect
12. #39664C2semidirect
13. #37627C2semidirect
14. #37594C2semidirect
15. #36576C2semidirect
16. Q8×#123C2semidirect
17. #36483C2semidirect
18. #36434C2semidirect
19. #35983C2semidirect
20. #35927C2semidirect
21. #35868C2semidirect
22. #35831C2semidirect
23. #35831C2semidirect
24. #35771C2semidirect
25. #35737C2semidirect
26. #35723C2semidirect
27. #35109C2semidirect
28. #34597C2semidirect
29. #34312C2semidirect
30. #34263C2semidirect
31. C4×D4×Q8C2semidirect

Maximal subgroups

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

subgroupindex
#427052
#426692
#426412
#426332
#425702
#425652
#425082
#424602
#402172
#401982
#397852
#396642
#376272
#375942
#365762
Q8×#1232
#364832
#364342
#359832
#359272
#358682
#358312
#357712
#357372
#357232
#351092
#345972
#343122
#342632
C4×D4×Q82