Finite Group Databasebeta

← #7717467

Subgroups — #7717467

Order 512.

6484 conjugacy classes of subgroups.

The subgroup lattice has 1453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3563C211yesmaximal, characteristic, complemented
2C2×#3559C211yesmaximal, characteristic, complemented
3#51979C212yesmaximal, complemented
4#51904C212yesmaximal, complemented
5#51754C212yesmaximal, complemented
6#51751C212yesmaximal, complemented
7#51750C212yesmaximal, complemented
8#51750C212yesmaximal, complemented
9#51548C212yesmaximal, complemented
10#51544C212yesmaximal, complemented
11#44781C214yesmaximal, complemented
12#44780C214yesmaximal, complemented
13#44663C214yesmaximal, complemented
14#44635C214yesmaximal, complemented
15#39160C214yesmaximal, complemented
16#38087C214yesmaximal, complemented
17#38087C214yesmaximal, complemented
18#36742C212yesmaximal, complemented
19#36741C212yesmaximal, complemented
20#36424C214yesmaximal, complemented
21#35326C211yesmaximal, characteristic, complemented
22#35303C211yesmaximal, characteristic, complemented
23#35158C212yesmaximal, complemented
24#35119C211yesmaximal, characteristic, complemented
25#35006C212yesmaximal, complemented
26#34637C211yesmaximal, characteristic, complemented
27C2×#2371C211yesmaximal, characteristic, complemented
28#3563—216no—
29#3559—216no—
30C2×#564C2212yes—
31C2×#563C2212yes—
32C2×#563C2212yes—
33C2×#562C2212yes—
34C2×#557C2212yes—
35C2×#554C2212yes—
36C2×#554C2212yes—
37C2×#553C2212yes—
38C2×#553C2212yes—
39C2×#552C2214yes—
40C2×#552C2212yes—
41C2×#552C2212yes—
42C2×#547C2214yes—
43C2×#547C2212yes—
44C2×#544C2212yes—
45C2×#544C2212yes—
46C2×#544C2212yes—
47C2×#541C2212yes—
48C2×#541C2214yes—
49C2×#540C2212yes—
50C2×#539C2214yes—
51C2×#539C2212yes—
52C2×#539C2212yes—
53C2×#537C2212yes—
54C2×#533C2211yescharacteristic
55C2×#532C2211yescharacteristic
56C2×#529C2211yescharacteristic
57C2×#529C2211yescharacteristic
58C22×#125C2211yescharacteristic
59#2857C2212yes—
60#2856C2212yes—
61#2854C2214yes—
62#2854C2214yes—
63#2850C2214yes—
64#2850C2212yes—
65#2850C2212yes—
66#2723C2214yes—
67#2723C2214yes—
68#2721C2214yes—
69#2720C2214yes—
70#2719C2214yes—
71#2719C2214yes—
72#2716C2214yes—
73#2716C2214yes—
74#2716C2214yes—
75#2716C2214yes—
76#2714C2214yes—
77#2714C2214yes—
78#2714C2214yes—
79#2713C2214yes—
80#2713C2214yes—
81#2713C2214yes—
82#2711C2214yes—
83#2711C2214yes—
84#2711C2214yes—
85#2711C2214yes—
86#2696C2214yes—
87#2696C2214yes—
88#2696C2214yes—
89#2696C2214yes—
90#2694C2214yes—
91#2694C2214yes—
92#2694C2214yes—
93#2692C2214yes—
94#2692C2214yes—
95#2692C2214yes—
96#2690C2214yes—
97#2690C2214yes—
98#2690C2214yes—
99#2690C2214yes—
100#2677C2214yes—
101#2676C2214yes—
102#2676C2214yes—
103#2674C2214yes—
104#2674C2214yes—
105#2673C2214yes—
106#2660C2211yescharacteristic
107#2660C2211yescharacteristic
108#2659C2211yescharacteristic
109#2658C2211yescharacteristic
110#2657C2211yescharacteristic
111#2656C2211yescharacteristic
112#2642C2211yescharacteristic
113#2642C2212yes—
114#2641C2211yescharacteristic
115#2641C2212yes—
116#2640C2211yescharacteristic
117#2640C2212yes—
118#2640C2211yescharacteristic
119#2640C2212yes—
120#2639C2211yescharacteristic
121#2639C2211yescharacteristic
122#2639C2212yes—
123#2639C2212yes—
124#2639C2214yes—
125#2639C2214yes—
126#2618C2214yes—
127#2611C2212yes—
128#2611C2212yes—
129#2611C2212yes—
130#2611C2212yes—
131#2610C2212yes—
132#2610C2212yes—
133#2610C2212yes—
134#2610C2212yes—
135#2604C2212yes—
136#2604C2212yes—
137#2604C2214yes—
138#2603C2212yes—
139#2603C2212yes—
140#2603C2214yes—
141#2564C2214yes—
142#2564C2214yes—
143#2560C2214yes—
144#2560C2214yes—
145#2560C2214yes—
146#2560C2214yes—
147#2558C2214yes—
148#2558C2214yes—
149#2558C2214yes—
150#2558C2214yes—
151#2556C2214yes—
152#2556C2214yes—
153#2554C2214yes—
154#2554C2214yes—
155#2550C2214yes—
156#2543C2214yes—
157#2543C2214yes—
158#2540C2214yes—
159#2512C2214yes—
160#2506C2214yes—
161#2498C2212yes—
162#2498C2214yes—
163#2498C2214yes—
164#2498C2212yes—
165#2492C2214yes—
166#2492C2214yes—
167#2492C2214yes—
168#2491C2214yes—
169#2491C2214yes—
170#2490C2214yes—
171#2490C2214yes—
172#2490C2214yes—
173#2489C2214yes—
174#2489C2214yes—
175#2481C2214yes—
176#2481C2214yes—
177#2481C2214yes—
178#2477C2214yes—
179#2477C2214yes—
180#2477C2214yes—
181#2475C2214yes—
182#2473C2214yes—
183#2473C2214yes—
184#2471C2214yes—
185#2471C2214yes—
186#2469C2214yes—
187#2467C2214yes—
188#2467C2214yes—
189#2465C2214yes—
190#2465C2214yes—
191#2463C2214yes—
192#2460C2214yes—
193#2460C2214yes—
194#2460C2214yes—
195#2458C2214yes—
196#2458C2214yes—
197#2458C2214yes—
198#2452C2214yes—
199#2445C2214yes—
200#2443C2214yes—
201#2430C2212yes—
202#2430C2214yes—
203#2430C2214yes—
204#2430C2212yes—
205#2417C2214yes—
206#2416C2214yes—
207#2398C2214yes—
208#2398C2214yes—
209#2371C2212yes—
210#2371C2212yes—
211#2371C2212yes—
212#2371C2212yes—
213#2371C2214yes—
214#2371C2214yes—
215#2367C2214yes—
216#2363C2214yes—
217#2360C2214yes—
218#2352C2214yes—
219#2328C2212yes—
220#2327C2212yes—
221#2326C2212yes—
222#2326C2212yes—
223#2325C2214yes—
224#2325C2214yes—
225#2311C2214yes—
226C4×#121C2214yes—
227#2297C2214yes—
228#2297C2214yes—
229C2×#387C2212yes—
230C2×#387C2212yes—
231C2×#387C2212yes—
232C2×#387C2212yes—
233C2×C4×C4⋊C4C2212yes—
234C2×C4×C4⋊C4C2212yes—
235C2×#376C2211yescharacteristic
236C2×#376C2211yescharacteristic
237C22×#41C2314yes—
238C22×#41C2312yes—
239#564—216no—
240#563—216no—
241#563—216no—
242#562—216no—
243#557—216no—
244#554—216no—
245#554—216no—
246#553—216no—
247#553—216no—
248#552—216no—
249#552—232no—
250#552—216no—
251#547—232no—
252#547—216no—
253#544—216no—
254#544—216no—
255#544—216no—
256#541—232no—
257#541—216no—
258#540—216no—
259#539—232no—
260#539—216no—
261#539—216no—
262#537—216no—
263#533—28no—
264#532—28no—
265C2×C4⋊Q8C2311yescharacteristic
266C2×C4⋊Q8C2311yescharacteristic
267C2×C4⋊Q8C2311yescharacteristic
268C2×C4⋊Q8C2312yes—
269C2×C4⋊Q8C2314yes—
270C2×C4⋊Q8C2314yes—
271C2×C4⋊Q8C2312yes—
272C2×C4⋊Q8C2314yes—
273C2×C4⋊Q8C2312yes—
274C2×#127C2311yescharacteristic
275C2×#127C2312yes—
276#529—28no—
277#529—28no—
278C2×#126C2314yes—
279C2×#126C2314yes—
280C2×#126C2314yes—
281C2×#126C2314yes—
282C2×#126C2312yes—
283C2×#126C2312yes—
284C2×#126C2314yes—
285C2×#126C2314yes—
286C2×#125D4116yescomplemented
287C2×#125C2312yes—
288C2×#125C2311yescharacteristic
289C2×#125C2311yescharacteristic
290C2×#125C2314yes—
291C2×#125C2314yes—
292C2×#125C2314yes—
293C2×#125C2314yes—
294C2×#125C2314yes—
295C2×#125C2314yes—
296C2×#125C2314yes—
297C2×#125C2312yes—
298C2×#125C2312yes—
299C2×#125C2314yes—
300C2×#125C2314yes—
301C2×#125C2312yes—
302C2×#125C2312yes—
303C2×#125C2312yes—
304C2×#125C2312yes—
305C2×#124C2312yes—
306C2×#124C2311yescharacteristic
307C2×#124C2311yescharacteristic
308C2×#124C2312yes—
309C2×#124C2312yes—
310C2×#124C2314yes—
311C2×#123C2312yes—
312C2×#123C2312yes—
313C2×#123C2314yes—
314C2×#123C2314yes—
315C2×#123C2314yes—
316C2×#123C2314yes—
317C2×#123C2314yes—
318C2×#123C2314yes—
319C2×#123C2314yes—
320C2×#123C2314yes—
321C2×C22⋊Q8C2314yes—
322C2×C22⋊Q8C2314yes—
323C2×C22⋊Q8C2314yes—
324C2×C22⋊Q8C2314yes—
325C2×C22⋊Q8C2312yes—
326C2×C22⋊Q8C2314yes—
327C2×C22⋊Q8C2311yescharacteristic
328C2×C22⋊Q8C2312yes—
329C2×C22⋊Q8C2311yescharacteristic
330C2×C22⋊Q8C2314yes—
331C2×C22⋊Q8C2314yes—
332C2×C22⋊Q8C2314yes—
333C2×C22⋊Q8C2314yes—
334C2×C22⋊Q8C2312yes—
335C2×C22⋊Q8C2312yes—
336C2×C22⋊Q8C2314yes—
337C2×C22⋊Q8C2314yes—
338C2×#121C2311yescharacteristic
339C2×#121C2312yes—
340C2×#121C2314yes—
341C2×#121C2311yescharacteristic
342C2×#121C2312yes—
343C2×#121C2314yes—
344C2×#121C2312yes—
345C2×#121C2314yes—
346C2×#121C2312yes—
347C2×#121C2314yes—
348C2×#121C2314yes—
349C2×#121C2314yes—
350C2×#121C2314yes—
351C2×#121C2314yes—
352C2×C4×Q8C2311yescharacteristic
353C2×C4×Q8C2312yes—
354C2×C4×Q8C2311yescharacteristic
355C2×C4×Q8C2312yes—
356C2×C4×Q8C2314yes—
357C2×C4×Q8C2312yes—
358C2×C4×Q8C2312yes—
359C2×C4×D4C2312yes—
360C2×C4×D4C2314yes—
361C2×C4×D4C2312yes—
362C2×C4×D4C2314yes—
363C2×C4×D4C2311yescharacteristic
364C2×C4×D4C2312yes—
365C2×C4×D4C2311yescharacteristic
366C2×C4×D4C2312yes—
367C2×C4×D4C2314yes—
368C2×C4×D4C2312yes—
369C2×C4×D4C2312yes—
370C2×C4×D4C2314yes—
371C2×#117C2314yes—
372C2×#117C2314yes—
373C2×#117C2312yes—
374C2×#117C2312yes—
375C2×#117C2312yes—
376C2×#117C2312yes—
377C2×#117C2312yes—
378C22×C4⋊C4C2314yes—
379C22×C4⋊C4C2312yes—
380C22×C4⋊C4C2312yes—
381C22×C4⋊C4C2312yes—
382C22×C4⋊C4C2312yes—
383C22×C4⋊C4C2312yes—
384C22×C4⋊C4C2312yes—
385C22×C4⋊C4C2311yescharacteristic
386C22×C4⋊C4C2311yescharacteristic
387C22×C42C2312yes—
388C22×C42C2312yes—
389C22×C42C2312yes—
390C22×C42C2312yes—
391C22×C42C2311yescharacteristic
392#400C2314yes—
393#400C2314yes—
394#400C2312yes—
395#400C2312yes—
396#400C2312yes—
397#400C2312yes—
398#400C2314yes—
399#400C2314yes—
400#400C2314yes—
401#400C2314yes—
402#400C2314yes—
403#400C2314yes—
404#400C2314yes—
405#400C2314yes—
406#399C2314yes—
407#399C2314yes—
408#399C2312yes—
409#399C2312yes—
410#399C2312yes—
411#399C2312yes—
412#399C2314yes—
413#399C2314yes—
414#398C2314yes—
415#398C2314yes—
416#398C2314yes—
417#398C2314yes—
418#398C2312yes—
419#398C2312yes—
420#398C2314yes—
421#398C2312yes—
422#398C2312yes—
423#398C2314yes—
424#398C2314yes—
425#398C2314yes—
426#397C2312yes—
427#397C2312yes—
428#397C2314yes—
429#397C2314yes—
430#397C2312yes—
431#397C2314yes—
432#397C2312yes—
433#397C2314yes—
434#397C2314yes—
435#397C2314yes—
436#397C2314yes—
437#397C2314yes—
438#397C2314yes—
439#397C2314yes—
440#396C2314yes—
441#396C2314yes—
442#396C2314yes—
443#396C2314yes—
444#396C2314yes—
445#396C2314yes—
446#396C2314yes—
447#396C2314yes—
448#395C2314yes—
449#395C2314yes—
450#395C2312yes—
451#395C2312yes—
452#395C2312yes—
453#395C2312yes—
454#395C2314yes—
455#395C2314yes—
456#394C2314yes—
457#394C2314yes—
458#394C2314yes—
459#394C2314yes—
460#394C2312yes—
461#394C2312yes—
462#394C2314yes—
463#394C2312yes—
464#394C2312yes—
465#394C2314yes—
466#394C2314yes—
467#394C2314yes—
468#394C2314yes—
469#394C2314yes—
470#394C2314yes—
471#394C2314yes—
472#394C2314yes—
473#394C2314yes—
474#393C2312yes—
475#393C2312yes—
476#393C2314yes—
477#393C2314yes—
478#393C2314yes—
479#393C2314yes—
480#393C2312yes—
481#393C2312yes—
482#393C2314yes—
483#393C2314yes—
484#393C2314yes—
485#393C2314yes—
486#393C2314yes—
487#393C2314yes—
488#392C2312yes—
489#392C2312yes—
490#392C2314yes—
491#392C2312yes—
492#392C2312yes—
493#392C2314yes—
494#392C2314yes—
495#392C2314yes—
496#391C2312yes—
497#391C2312yes—
498#391C2314yes—
499#391C2314yes—
500#391C2314yes—
501#391C2314yes—
502#391C2312yes—
503#391C2312yes—
504#391C2314yes—
505#391C2314yes—
506#391C2314yes—
507#391C2314yes—
508#390C2314yes—
509#390C2314yes—
510#390C2314yes—
511#390C2314yes—
512#390C2314yes—
513#390C2312yes—
514#390C2312yes—
515#390C2312yes—
516#390C2312yes—
517#390C2314yes—
518#390C2314yes—
519#390C2314yes—
520#390C2314yes—
521#390C2314yes—
522#390C2314yes—
523#390C2314yes—
524#390C2314yes—
525#390C2314yes—
526#390C2314yes—
527#389C2314yes—
528#389C2314yes—
529#389C2314yes—
530#389C2314yes—
531#389C2314yes—
532#389C2314yes—
533#389C2314yes—
534#389C2314yes—
535#389C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#388C2314yes—
540#388C2314yes—
541#388C2314yes—
542#388C2314yes—
543#388C2314yes—
544#388C2314yes—
545#388C2314yes—
546#388C2314yes—
547#388C2314yes—
548#388C2314yes—
549#388C2314yes—
550#388C2314yes—
551#388C2314yes—
552#388C2314yes—
553#388C2314yes—
554#388C2314yes—
555#388C2314yes—
556#388C2314yes—
557#388C2314yes—
558#388C2314yes—
559#388C2314yes—
560#388C2314yes—
561#388C2314yes—
562#388C2314yes—
563#388C2314yes—
564#388C2314yes—
565#388C2314yes—
566#388C2314yes—
567#388C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#387C2314yes—
586#387C2314yes—
587#387C2314yes—
588#387C2314yes—
589#387C2314yes—
590#387C2314yes—
591#387C2314yes—
592#387C2314yes—
593#387C2314yes—
594#387C2314yes—
595#387C2314yes—
596#387C2314yes—
597#387C2314yes—
598#386C2314yes—
599#386C2314yes—
600#386C2314yes—
601#386C2314yes—
602#386C2314yes—
603#386C2314yes—
604#386C2314yes—
605#386C2314yes—
606#386C2314yes—
607#386C2314yes—
608#386C2314yes—
609#386C2314yes—
610#386C2314yes—
611#386C2314yes—
612#386C2314yes—
613#386C2314yes—
614#386C2314yes—
615#386C2314yes—
616#386C2314yes—
617#386C2314yes—
618#386C2314yes—
619#386C2314yes—
620#386C2314yes—
621#386C2314yes—
622#385C2314yes—
623#385C2314yes—
624#385C2314yes—
625#385C2314yes—
626#385C2314yes—
627#385C2314yes—
628#385C2314yes—
629#385C2314yes—
630#385C2314yes—
631#385C2314yes—
632#385C2314yes—
633#385C2314yes—
634#385C2314yes—
635#385C2314yes—
636#384C2312yes—
637#384C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2314yes—
641#380C2314yes—
642#380C2314yes—
643#380C2314yes—
644#380C2314yes—
645#380C2314yes—
646#380C2314yes—
647#380C2314yes—
648#380C2314yes—
649#380C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2314yes—
653C4×C4⋊C4C2314yes—
654C4×C4⋊C4C2314yes—
655C4×C4⋊C4C2314yes—
656C4×C4⋊C4C2314yes—
657C4×C4⋊C4C2314yes—
658C4×C4⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2314yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2314yes—
667C4×C22⋊C4C2314yes—
668C4×C22⋊C4C2314yes—
669#376C2312yes—
670#376C2312yes—
671#376C2312yes—
672#376C2312yes—
673#376C2311yescharacteristic
674#376C2311yescharacteristic
675#376C2312yes—
676#376C2312yes—
677#376C2311yescharacteristic
678#376C2311yescharacteristic
679C2×#95C2312yes—
680C2×#95C2312yes—
681C2×#95C2312yes—
682C2×#95C2312yes—
683C2×#95C2311yescharacteristic
684C2×#95C2311yescharacteristic
685C2×#95C2311yescharacteristic
686C2×#95C2311yescharacteristic
687C2×#95C2312yes—
688C2×#95C2312yes—
689C2×#41—28no—
690C2×#41—216no—
691C2×#41—48no—
692C2×#41—48no—
693C2×#41—48no—
694C22×Q8C2412yes—
695C22×Q8C2411yescharacteristic
696C22×Q8C2414yes—
697C22×Q8C2412yes—
698C22×Q8C2411yescharacteristic
699C22×Q8C2414yes—
700C22×Q8C2412yes—
701C22×D4C2412yes—
702C22×D4C2412yes—
703C22×D4C2414yes—
704C22×D4C2412yes—
705C22×D4C2414yes—
706C22×D4C2411yescharacteristic
707C22×D4C2412yes—
708C22×D4C2414yes—
709C22×D4C2411yescharacteristic
710C22×D4C2414yes—
711C22×D4C2412yes—
712C22×D4C2414yes—
713C22×D4C2414yes—
714C23×C4C2412yes—
715C23×C4C2412yes—
716C23×C4C2411yescharacteristic
717C23×C4C2412yes—
718C23×C4C2412yes—
719C23×C4C2414yes—
720C23×C4C2414yes—
721C23×C4C2414yes—
722C23×C4C2414yes—
723C23×C4C2414yes—
724C23×C4C2412yes—
725C23×C4C2412yes—
726C23×C4C2412yes—
727C23×C4C2412yes—
728C23×C4C2411yescharacteristic
729C23×C4C2411yescharacteristic
730C4⋊Q8—216no—
731C4⋊Q8—28no—
732C4⋊Q8—216no—
733C4⋊Q8—28no—
734C4⋊Q8—216no—
735C4⋊Q8—24no—
736C4⋊Q8—24no—
737C4⋊Q8—24no—
738C4⋊Q8—44no—
739#127—24no—
740#127—44no—
741#126—216no—
742#126—216no—
743#126—216no—
744#126—216no—
745#126—216no—
746#126—216no—
747#126—28no—
748#126—28no—
749#125—216no—
750#125—216no—
751#125—216no—
752#125—216no—
753#125—216no—
754#125—216no—
755#125—216no—
756#125—28no—
757#125—216no—
758#125—216no—
759#125—28no—
760#125—24no—
761#125—24no—
762#125—28no—
763#125C2×D4116yes—
764#125C2×D4116yes—
765#125C2×D4116yes—
766#125C2×D4116yes—
767#124—24no—
768#124—24no—
769#124—28no—
770#124—48no—
771#124—44no—
772#124—44no—
773#123—28no—
774#123—28no—
775#123—216no—
776#123—216no—
777#123—216no—
778#123—216no—
779#123—216no—
780#123—216no—
781#123—216no—
782#123—216no—
783C22⋊Q8—24no—
784C22⋊Q8—24no—
785C22⋊Q8—28no—
786C22⋊Q8—28no—
787C22⋊Q8—216no—
788C22⋊Q8—216no—
789C22⋊Q8—216no—
790C22⋊Q8—216no—
791C22⋊Q8—216no—
792C22⋊Q8—216no—
793C22⋊Q8—216no—
794C22⋊Q8—28no—
795C22⋊Q8—28no—
796C22⋊Q8—216no—
797C22⋊Q8—216no—
798C22⋊Q8—216no—
799C22⋊Q8—48no—
800#121—24no—
801#121—24no—
802#121—28no—
803#121—28no—
804#121—216no—
805#121—216no—
806#121—216no—
807#121—28no—
808#121—216no—
809#121—28no—
810#121—48no—
811#121—48no—
812#121—48no—
813#121—48no—
814C4×Q8—216no—
815C4×Q8—28no—
816C4×Q8—28no—
817C4×Q8—24no—
818C4×Q8—24no—
819C4×Q8—28no—
820C4×Q8—28no—
821C4×D4—28no—
822C4×D4—28no—
823C4×D4—216no—
824C4×D4—216no—
825C4×D4—216no—
826C4×D4—28no—
827C4×D4—28no—
828C4×D4—24no—
829C4×D4—24no—
830C4×D4—28no—
831C4×D4—28no—
832C4×D4—48no—
833#117—28no—
834#117—216no—
835#117—216no—
836#117—28no—
837#117—28no—
838#117—28no—
839#117—28no—
840C2×C4⋊C4—216no—
841C2×C4⋊C4—28no—
842C2×C4⋊C4—28no—
843C2×C4⋊C4—44no—
844C2×C4⋊C4—44no—
845C2×C4⋊C4C2×D4116yes—
846C2×C4⋊C4C2×D4116yes—
847C2×C4⋊C4C2×D418yes—
848C2×C4⋊C4C2×D418yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊C4C2412yes—
851C2×C4⋊C4C2412yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2412yes—
859C2×C4⋊C4C2412yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2412yes—
863C2×C4⋊C4C2412yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2414yes—
868C2×C4⋊C4C2412yes—
869C2×C4⋊C4C2411yescharacteristic
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2411yescharacteristic
872C2×C4⋊C4C2414yes—
873C2×C4⋊C4C2412yes—
874C2×C4⋊C4C2412yes—
875C2×C4⋊C4C2411yescharacteristic
876C2×C4⋊C4C2411yescharacteristic
877C2×C4⋊C4C2414yes—
878C2×C4⋊C4C2414yes—
879C2×C4⋊C4C2414yes—
880C2×C4⋊C4C2414yes—
881C2×C4⋊C4C2412yes—
882C2×C4⋊C4C2414yes—
883C2×C4⋊C4C2414yes—
884C2×C4⋊C4C2414yes—
885C2×C4⋊C4C2414yes—
886C2×C4⋊C4C2414yes—
887C2×C4⋊C4C2414yes—
888C2×C4⋊C4C2414yes—
889C2×C4⋊C4C2414yes—
890C2×C4⋊C4C2414yes—
891C2×C4⋊C4C2414yes—
892C2×C4⋊C4C2414yes—
893C2×C4⋊C4C2414yes—
894C2×C4⋊C4C2414yes—
895C2×C4⋊C4C2412yes—
896C2×C4⋊C4C2412yes—
897C2×C4⋊C4C2412yes—
898C2×C4⋊C4C2412yes—
899C2×C4⋊C4C2414yes—
900C2×C4⋊C4C2414yes—
901C2×C4⋊C4C2414yes—
902C2×C22⋊C4C2414yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2412yes—
908C2×C22⋊C4C2412yes—
909C2×C22⋊C4C2414yes—
910C2×C22⋊C4C2412yes—
911C2×C22⋊C4C2414yes—
912C2×C22⋊C4C2412yes—
913C2×C22⋊C4C2412yes—
914C2×C22⋊C4C2414yes—
915C2×C22⋊C4C2414yes—
916C2×C22⋊C4C2414yes—
917C2×C22⋊C4C2414yes—
918C2×C22⋊C4C2414yes—
919C2×C22⋊C4C2414yes—
920C2×C22⋊C4C2414yes—
921C2×C22⋊C4C2412yes—
922C2×C22⋊C4C2412yes—
923C2×C22⋊C4C2414yes—
924C2×C22⋊C4C2414yes—
925C2×C22⋊C4C2414yes—
926C2×C22⋊C4C2414yes—
927C2×C22⋊C4C2414yes—
928C2×C22⋊C4C2414yes—
929C2×C22⋊C4C2414yes—
930C2×C22⋊C4C2414yes—
931C2×C22⋊C4C2414yes—
932C2×C22⋊C4C2414yes—
933C2×C22⋊C4C2414yes—
934C2×C22⋊C4C2414yes—
935C2×C22⋊C4C2414yes—
936C2×C22⋊C4C2414yes—
937C2×C22⋊C4C2414yes—
938C2×C22⋊C4C2414yes—
939C2×C22⋊C4C2414yes—
940C2×C22⋊C4C2414yes—
941C2×C22⋊C4C2414yes—
942C2×C22⋊C4C2414yes—
943C2×C22⋊C4C2414yes—
944C2×C22⋊C4C2414yes—
945C2×C22⋊C4C2414yes—
946C2×C22⋊C4C2414yes—
947C2×C22⋊C4C2414yes—
948C2×C22⋊C4C2414yes—
949C2×C42—44no—
950C2×C42—44no—
951C2×C42—44no—
952C2×C42—44no—
953C2×C42C2×D418yes—
954C2×C42C2414yes—
955C2×C42C2414yes—
956C2×C42C2412yes—
957C2×C42C2414yes—
958C2×C42C2412yes—
959C2×C42C2414yes—
960C2×C42C2414yes—
961C2×C42C2414yes—
962C2×C42C2412yes—
963C2×C42C2412yes—
964C2×C42C2414yes—
965C2×C42C2412yes—
966C2×C42C2414yes—
967C2×C42C2412yes—
968C2×C42C2414yes—
969C2×C42C2414yes—
970C2×C42C2414yes—
971C2×C42C2411yescharacteristic
972C2×C42C2411yescharacteristic
973C2×C42C2411yescharacteristic
974C2×C42C2411yescharacteristic
975#95C2412yes—
976#95C2411yescharacteristic
977#95C2412yes—
978#95C2411yescharacteristic
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2414yes—
984#95C2414yes—
985#95C2412yes—
986#95C2412yes—
987#95C2411yescharacteristic
988#95C2412yes—
989#95C2412yes—
990#95C2411yescharacteristic
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2414yes—
995#95C2414yes—
996#95C2414yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2414yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2414yes—
1006#95C2414yes—
1007#95C2414yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025C24C2512yes—
1026C24C2514yes—
1027C24C2512yes—
1028C24C2511yescharacteristic
1029#41—816no—
1030#41—832no—
1031C2×Q8—24no—
1032C2×Q8—22no—
1033C2×Q8—28no—
1034C2×Q8—24no—
1035C2×Q8—22no—
1036C2×Q8—28no—
1037C2×Q8—24no—
1038C2×Q8—42no—
1039C2×Q8—42no—
1040C2×Q8—44no—
1041C2×Q8—44no—
1042C2×Q8—42no—
1043C2×Q8—42no—
1044C2×Q8—42no—
1045C2×Q8—42no—
1046C2×Q8—44no—
1047C2×Q8—44no—
1048C2×Q8—44no—
1049C2×D4—24no—
1050C2×D4—24no—
1051C2×D4—28no—
1052C2×D4—28no—
1053C2×D4—28no—
1054C2×D4—28no—
1055C2×D4—28no—
1056C2×D4—24no—
1057C2×D4—28no—
1058C2×D4—22no—
1059C2×D4—24no—
1060C2×D4—22no—
1061C2×D4—28no—
1062C2×D4—24no—
1063C2×D4—28no—
1064C2×D4—42no—
1065C2×D4—42no—
1066C2×D4—44no—
1067C2×D4—44no—
1068C2×D4—44no—
1069C2×D4—42no—
1070C2×D4—42no—
1071C2×D4—42no—
1072C2×D4—42no—
1073C2×D4—44no—
1074C2×D4—44no—
1075C2×D4—44no—
1076C2×D4—44no—
1077C2×D4—44no—
1078C2×D4—44no—
1079C2×D4—44no—
1080C2×D4—44no—
1081C2×D4—44no—
1082C2×D4—44no—
1083C22×C4—24no—
1084C22×C4—24no—
1085C22×C4—24no—
1086C22×C4—24no—
1087C22×C4—24no—
1088C22×C4—24no—
1089C22×C4—24no—
1090C22×C4—24no—
1091C22×C4—24no—
1092C22×C4—24no—
1093C22×C4—28no—
1094C22×C4—28no—
1095C22×C4—28no—
1096C22×C4—28no—
1097C22×C4—28no—
1098C22×C4—42no—
1099C22×C4—42no—
1100C22×C4—42no—
1101C22×C4—42no—
1102C22×C4—42no—
1103C22×C4—41no—
1104C22×C4—41no—
1105C22×C4—42no—
1106C22×C4—42no—
1107C22×C4—42no—
1108C22×C4—42no—
1109C22×C4—42no—
1110C22×C4—42no—
1111C22×C4—42no—
1112C22×C4—44no—
1113C22×C4—44no—
1114C22×C4—44no—
1115C22×C4—44no—
1116C22×C4—42no—
1117C22×C4—42no—
1118C22×C4—44no—
1119C22×C4—44no—
1120C22×C4—44no—
1121C22×C4—44no—
1122C22×C4—44no—
1123C22×C4—44no—
1124C22×C4C22×D414yes—
1125C22×C4C22×D418yes—
1126C22×C4C22×D414yes—
1127C22×C4C22×D414yes—
1128C22×C4C22×D418yes—
1129C22×C4C2512yes—
1130C22×C4C2514yes—
1131C22×C4C2514yes—
1132C22×C4C2512yes—
1133C22×C4C2512yes—
1134C22×C4C2514yes—
1135C22×C4C2512yes—
1136C22×C4C2514yes—
1137C22×C4C2512yes—
1138C22×C4C2512yes—
1139C22×C4C2512yes—
1140C22×C4C2514yes—
1141C22×C4C2512yes—
1142C22×C4C2512yes—
1143C22×C4C2511yescharacteristic
1144C22×C4C2511yescharacteristic
1145C22×C4C2511yescharacteristic
1146C22×C4C2511yescharacteristic
1147C22×C4C2511yescharacteristic
1148C22×C4C2511yescharacteristic
1149C22×C4C2514yes—
1150C22×C4C2514yes—
1151C22×C4C2512yes—
1152C4⋊C4—24no—
1153C4⋊C4—24no—
1154C4⋊C4—24no—
1155C4⋊C4—28no—
1156C4⋊C4—28no—
1157C4⋊C4—28no—
1158C4⋊C4—28no—
1159C4⋊C4—28no—
1160C4⋊C4—24no—
1161C4⋊C4—24no—
1162C4⋊C4—28no—
1163C4⋊C4—24no—
1164C4⋊C4—28no—
1165C4⋊C4—24no—
1166C4⋊C4—24no—
1167C4⋊C4—24no—
1168C4⋊C4—24no—
1169C4⋊C4—28no—
1170C4⋊C4—24no—
1171C4⋊C4—22no—
1172C4⋊C4—28no—
1173C4⋊C4—22no—
1174C4⋊C4—24no—
1175C4⋊C4—24no—
1176C4⋊C4—22no—
1177C4⋊C4—22no—
1178C4⋊C4—28no—
1179C4⋊C4—28no—
1180C4⋊C4—28no—
1181C4⋊C4—28no—
1182C4⋊C4—24no—
1183C4⋊C4—28no—
1184C4⋊C4—28no—
1185C4⋊C4—28no—
1186C4⋊C4—44no—
1187C4⋊C4—44no—
1188C4⋊C4—44no—
1189C4⋊C4—44no—
1190C4⋊C4—44no—
1191C4⋊C4—44no—
1192C4⋊C4—44no—
1193C4⋊C4—44no—
1194C4⋊C4—44no—
1195C4⋊C4—44no—
1196C4⋊C4—44no—
1197C4⋊C4C22×D4116yes—
1198C4⋊C4C22×D418yes—
1199C4⋊C4C22×D418yes—
1200C4⋊C4C22×D418yes—
1201C4⋊C4C22×D418yes—
1202C4⋊C4C22×D4116yes—
1203C4⋊C4C22×D4116yes—
1204C4⋊C4C22×D4116yes—
1205C22⋊C4—28no—
1206C22⋊C4—24no—
1207C22⋊C4—24no—
1208C22⋊C4—24no—
1209C22⋊C4—24no—
1210C22⋊C4—28no—
1211C22⋊C4—24no—
1212C22⋊C4—24no—
1213C22⋊C4—28no—
1214C22⋊C4—24no—
1215C22⋊C4—28no—
1216C22⋊C4—24no—
1217C22⋊C4—28no—
1218C22⋊C4—28no—
1219C22⋊C4—28no—
1220C22⋊C4—28no—
1221C22⋊C4—28no—
1222C22⋊C4—28no—
1223C22⋊C4—28no—
1224C22⋊C4—24no—
1225C22⋊C4—24no—
1226C22⋊C4—28no—
1227C22⋊C4—28no—
1228C22⋊C4—44no—
1229C22⋊C4—44no—
1230C22⋊C4—44no—
1231C22⋊C4—44no—
1232C22⋊C4—44no—
1233C22⋊C4—44no—
1234C22⋊C4—44no—
1235C22⋊C4—44no—
1236C22⋊C4—44no—
1237C22⋊C4—44no—
1238C22⋊C4—44no—
1239C22⋊C4—44no—
1240C22⋊C4—44no—
1241C22⋊C4—44no—
1242C22⋊C4—44no—
1243C22⋊C4—44no—
1244C22⋊C4—44no—
1245C22⋊C4—44no—
1246C22⋊C4—44no—
1247C22⋊C4—44no—
1248C22⋊C4—44no—
1249C22⋊C4—44no—
1250C22⋊C4—44no—
1251C22⋊C4—44no—
1252C42—28no—
1253C42—28no—
1254C42—24no—
1255C42—28no—
1256C42—24no—
1257C42—28no—
1258C42—28no—
1259C42—28no—
1260C42—24no—
1261C42—24no—
1262C42—44no—
1263C42—42no—
1264C42—42no—
1265C42—44no—
1266C42—44no—
1267C42—44no—
1268C42—44no—
1269C42C22×D414yes—
1270C42C22×D414yes—
1271C42C22×D414yes—
1272C42C22×D414yes—
1273C23—22no—
1274C23—21no—
1275C23—21no—
1276C23—22no—
1277C23—24no—
1278C23—22no—
1279C23—24no—
1280C23—24no—
1281C23—24no—
1282C23—24no—
1283C23—24no—
1284C23—24no—
1285C23—24no—
1286C23—24no—
1287C23—22no—
1288C23—24no—
1289C23—24no—
1290C23—22no—
1291C23—22no—
1292C23—22no—
1293C23C23×D412yes—
1294C23#58514yes—
1295C23C2611yescharacteristic
1296Q8—48no—
1297Q8—88no—
1298Q8—82no—
1299Q8—82no—
1300Q8—84no—
1301Q8—88no—
1302Q8—84no—
1303D4—48no—
1304D4—48no—
1305D4—48no—
1306D4—416no—
1307D4—88no—
1308D4—82no—
1309D4—84no—
1310D4—82no—
1311D4—88no—
1312D4—88no—
1313D4—84no—
1314D4—164no—
1315D4—164no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—24no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—22no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—28no—
1331C2×C4—216no—
1332C2×C4—24no—
1333C2×C4—22no—
1334C2×C4—22no—
1335C2×C4—22no—
1336C2×C4—22no—
1337C2×C4—24no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—24no—
1342C2×C4—22no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—24no—
1346C2×C4—22no—
1347C2×C4—24no—
1348C2×C4—24no—
1349C2×C4—24no—
1350C2×C4—22no—
1351C2×C4—24no—
1352C2×C4—24no—
1353C2×C4—24no—
1354C2×C4—24no—
1355C2×C4—24no—
1356C2×C4—24no—
1357C2×C4—24no—
1358C2×C4—22no—
1359C2×C4—22no—
1360C2×C4—22no—
1361C2×C4—24no—
1362C2×C4—24no—
1363C2×C4—24no—
1364C2×C4—22no—
1365C2×C4—22no—
1366C2×C4—22no—
1367C2×C4—24no—
1368C2×C4—22no—
1369C2×C4—22no—
1370C2×C4—48no—
1371C2×C4—44no—
1372C2×C4—44no—
1373C2×C4—48no—
1374C2×C4—48no—
1375C2×C4—48no—
1376C2×C4—48no—
1377C2×C4—88no—
1378C2×C4—88no—
1379C2×C4—88no—
1380C2×C4—88no—
1381C2×C4—88no—
1382C2×C4—84no—
1383C2×C4—84no—
1384C2×C4C23×D412yes—
1385C2×C4C23×D412yes—
1386C2×C4C23×D412yes—
1387C2×C4C23×D418yes—
1388C2×C4C23×D418yes—
1389C2×C4C23×D412yes—
1390C2×C4C23×D412yes—
1391C2×C4C23×D412yes—
1392C2×C4#58514yes—
1393C22—22no—
1394C22—22no—
1395C22—24no—
1396C22—24no—
1397C22—44no—
1398C22—42no—
1399C22—42no—
1400C22—42no—
1401C22—44no—
1402C22—42no—
1403C22—42no—
1404C22—42no—
1405C22—44no—
1406C22—44no—
1407C22—44no—
1408C22—44no—
1409C22—44no—
1410C22—44no—
1411C22—44no—
1412C22—44no—
1413C22—44no—
1414C22#350014yes—
1415C22C24×D411yescharacteristic
1416C22C2×#58512yes—
1417C22C2×#58512yes—
1418C222−1+611yescharacteristic
1419C222−1+611yescharacteristic
1420C4—22no—
1421C4—28no—
1422C4—22no—
1423C4—28no—
1424C4—22no—
1425C4—22no—
1426C4—22no—
1427C4—22no—
1428C4—24no—
1429C4—42no—
1430C4—44no—
1431C4—42no—
1432C4—42no—
1433C4—44no—
1434C4—42no—
1435C4—42no—
1436C4—42no—
1437C4—44no—
1438C4—42no—
1439C4—44no—
1440C4—44no—
1441C4—42no—
1442C4—42no—
1443C2—24no—
1444C2—84no—
1445C2—82no—
1446C2—82no—
1447C2C2×#350011yescharacteristic
1448C2#6281211yescharacteristic
1449C2#6284811yescharacteristic
1450C2#6290912yes—
1451C2#6293412yes—
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. C2×#3563C2semidirect
2. C2×#3559C2semidirect
3. #51979C2semidirect
4. #51904C2semidirect
5. #51754C2semidirect
6. #51751C2semidirect
7. #51750C2semidirect
8. #51750C2semidirect
9. #51548C2semidirect
10. #51544C2semidirect
11. #44781C2semidirect
12. #44780C2semidirect
13. #44663C2semidirect
14. #44635C2semidirect
15. #39160C2semidirect
16. #38087C2semidirect
17. #38087C2semidirect
18. #36742C2semidirect
19. #36741C2semidirect
20. #36424C2semidirect
21. #35326C2semidirect
22. #35303C2semidirect
23. #35158C2semidirect
24. #35119C2semidirect
25. #35006C2semidirect
26. #34637C2semidirect
27. C2×#2371C2semidirect
286. C2×#125D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35632
C2×#35592
#519792
#519042
#517542
#517512
#517502
#515482
#515442
#447812
#447802
#446632
#446352
#391602
#380872
#367422
#367412
#364242
#353262
#353032
#351582
#351192
#350062
#346372
C2×#23712