Finite Group Databasebeta

← #7714908

Subgroups — #7714908

Order 512.

6394 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3553C212yesmaximal, complemented
2#51784C214yesmaximal, complemented
3#51591C214yesmaximal, complemented
4#51588C214yesmaximal, complemented
5#51587C214yesmaximal, complemented
6#47787C214yesmaximal, complemented
7#47680C214yesmaximal, complemented
8#47677C214yesmaximal, complemented
9#47676C214yesmaximal, complemented
10#39742C212yesmaximal, complemented
11#39738C212yesmaximal, complemented
12#39614C212yesmaximal, complemented
13#39610C212yesmaximal, complemented
14#39165C214yesmaximal, complemented
15#39160C214yesmaximal, complemented
16#37620C212yesmaximal, complemented
17#37130C212yesmaximal, complemented
18#37130C212yesmaximal, complemented
19#35119C211yesmaximal, characteristic, complemented
20#35119C211yesmaximal, characteristic, complemented
21#35006C212yesmaximal, complemented
22#35004C212yesmaximal, complemented
23C2×#2330C211yesmaximal, characteristic, complemented
24#3553—232no—
25C2×#564C2212yes—
26C2×#563C2212yes—
27C2×#563C2212yes—
28C2×#562C2212yes—
29C2×#554C2214yes—
30C2×#554C2214yes—
31C2×#553C2214yes—
32C2×#553C2214yes—
33C2×#552C2214yes—
34C2×#552C2214yes—
35C2×#541C2214yes—
36C2×#541C2214yes—
37C2×#539C2214yes—
38C2×#539C2214yes—
39C2×#539C2214yes—
40C2×#539C2214yes—
41C2×#529C2212yes—
42C2×#529C2212yes—
43C22×#125C2211yescharacteristic
44#2857C2212yes—
45#2856C2212yes—
46#2854C2212yes—
47#2854C2212yes—
48#2854C2212yes—
49#2854C2212yes—
50#2850C2214yes—
51#2823C2214yes—
52#2823C2214yes—
53#2727C2212yes—
54#2727C2212yes—
55#2727C2214yes—
56#2726C2212yes—
57#2726C2212yes—
58#2726C2214yes—
59#2725C2214yes—
60#2725C2214yes—
61#2725C2214yes—
62#2725C2214yes—
63#2723C2214yes—
64#2721C2214yes—
65#2720C2214yes—
66#2719C2214yes—
67#2716C2214yes—
68#2714C2214yes—
69#2713C2214yes—
70#2711C2214yes—
71#2707C2214yes—
72#2707C2214yes—
73#2707C2214yes—
74#2707C2214yes—
75#2705C2214yes—
76#2705C2214yes—
77#2705C2214yes—
78#2705C2214yes—
79#2704C2214yes—
80#2704C2214yes—
81#2704C2214yes—
82#2704C2214yes—
83#2702C2214yes—
84#2702C2214yes—
85#2702C2214yes—
86#2702C2214yes—
87#2696C2214yes—
88#2694C2214yes—
89#2692C2214yes—
90#2690C2214yes—
91#2683C2212yes—
92#2683C2212yes—
93#2683C2214yes—
94#2682C2212yes—
95#2682C2212yes—
96#2682C2214yes—
97#2681C2214yes—
98#2681C2214yes—
99#2681C2214yes—
100#2681C2214yes—
101#2677C2214yes—
102#2676C2214yes—
103#2674C2214yes—
104#2673C2214yes—
105#2659C2211yescharacteristic
106#2659C2211yescharacteristic
107#2659C2212yes—
108#2656C2211yescharacteristic
109#2656C2211yescharacteristic
110#2656C2212yes—
111#2639C2212yes—
112#2639C2212yes—
113#2639C2214yes—
114#2629C2214yes—
115#2629C2214yes—
116#2620C2214yes—
117#2620C2214yes—
118#2618C2214yes—
119#2618C2214yes—
120#2611C2214yes—
121#2611C2214yes—
122#2610C2214yes—
123#2610C2214yes—
124#2604C2214yes—
125#2604C2214yes—
126#2603C2214yes—
127#2603C2214yes—
128#2582C2212yes—
129#2564C2214yes—
130#2564C2214yes—
131#2560C2214yes—
132#2560C2214yes—
133#2558C2214yes—
134#2558C2214yes—
135#2556C2214yes—
136#2556C2214yes—
137#2554C2214yes—
138#2554C2214yes—
139#2543C2214yes—
140#2543C2214yes—
141#2538C2212yes—
142#2538C2212yes—
143#2537C2212yes—
144#2519C2214yes—
145#2519C2214yes—
146#2512C2212yes—
147#2512C2212yes—
148#2506C2212yes—
149#2506C2212yes—
150#2481C2214yes—
151#2479C2214yes—
152#2477C2214yes—
153#2475C2214yes—
154#2473C2214yes—
155#2471C2214yes—
156#2469C2214yes—
157#2467C2214yes—
158#2465C2214yes—
159#2463C2214yes—
160#2462C2214yes—
161#2461C2214yes—
162#2461C2214yes—
163#2460C2214yes—
164#2458C2214yes—
165#2456C2214yes—
166#2454C2214yes—
167#2453C2214yes—
168#2452C2212yes—
169#2452C2214yes—
170#2452C2212yes—
171#2451C2214yes—
172#2449C2214yes—
173#2445C2212yes—
174#2445C2212yes—
175#2443C2214yes—
176#2442C2214yes—
177#2441C2214yes—
178#2440C2214yes—
179#2439C2214yes—
180#2429C2214yes—
181#2428C2214yes—
182#2427C2214yes—
183#2426C2214yes—
184#2417C2214yes—
185#2417C2214yes—
186#2417C2214yes—
187#2417C2214yes—
188#2417C2214yes—
189#2416C2214yes—
190#2416C2214yes—
191#2416C2214yes—
192#2416C2214yes—
193#2416C2214yes—
194#2415C2214yes—
195#2414C2214yes—
196#2330C2214yes—
197#2330C2214yes—
198#2330C2214yes—
199#2330C2214yes—
200#2325C2212yes—
201#2325C2212yes—
202#2325C2212yes—
203#2325C2212yes—
204#2325C2212yes—
205#2325C2212yes—
206#2325C2214yes—
207C4×#121C2212yes—
208C4×#121C2212yes—
209C4×#121C2214yes—
210C2×#389C2211yescharacteristic
211C2×#389C2211yescharacteristic
212C2×#389C2212yes—
213C2×#389C2212yes—
214C2×#387C2212yes—
215C2×#387C2212yes—
216C2×#384C2211yescharacteristic
217C2×C4×C4⋊C4C2211yescharacteristic
218C2×C4×C4⋊C4C2211yescharacteristic
219C2×#376C2211yescharacteristic
220#564—216no—
221#563—216no—
222#563—216no—
223#562—216no—
224#554—232no—
225#554—232no—
226#553—232no—
227#553—232no—
228#552—232no—
229#552—232no—
230#541—232no—
231#541—232no—
232#539—232no—
233#539—232no—
234#539—232no—
235#539—232no—
236C2×C4⋊Q8C2314yes—
237C2×C4⋊Q8C2314yes—
238C2×C4⋊Q8C2312yes—
239C2×#127C2312yes—
240#529—216no—
241#529—216no—
242C2×#126C2314yes—
243C2×#126C2314yes—
244C2×#126C2314yes—
245C2×#126C2314yes—
246C2×#126C2314yes—
247C2×#126C2314yes—
248C2×#126C2314yes—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125D4116yescomplemented
253C2×#125C2312yes—
254C2×#125C2312yes—
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#125C2314yes—
258C2×#125C2314yes—
259C2×#125C2314yes—
260C2×#125C2314yes—
261C2×#125C2314yes—
262C2×#125C2314yes—
263C2×#125C2314yes—
264C2×#125C2314yes—
265C2×#125C2314yes—
266C2×#125C2312yes—
267C2×#125C2312yes—
268C2×#124C2312yes—
269C2×#124C2312yes—
270C2×#124C2314yes—
271C2×#123C2314yes—
272C2×#123C2314yes—
273C2×#123C2314yes—
274C2×#123C2314yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×#123C2314yes—
279C2×#123C2314yes—
280C2×#123C2314yes—
281C2×C22⋊Q8C2314yes—
282C2×C22⋊Q8C2314yes—
283C2×C22⋊Q8C2314yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2314yes—
288C2×C22⋊Q8C2314yes—
289C2×C22⋊Q8C2314yes—
290C2×C22⋊Q8C2314yes—
291C2×C22⋊Q8C2314yes—
292C2×C22⋊Q8C2314yes—
293C2×C22⋊Q8C2314yes—
294C2×C22⋊Q8C2314yes—
295C2×C22⋊Q8C2314yes—
296C2×C22⋊Q8C2314yes—
297C2×C22⋊Q8C2314yes—
298C2×C22⋊Q8C2314yes—
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2314yes—
302C2×#121C2314yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#121C2314yes—
306C2×#121C2314yes—
307C2×#121C2312yes—
308C2×#121C2312yes—
309C2×#121C2314yes—
310C2×#121C2314yes—
311C2×#121C2314yes—
312C2×#121C2314yes—
313C2×#121C2314yes—
314C2×#121C2314yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2312yes—
317C2×C4×Q8C2314yes—
318C2×C4×Q8C2314yes—
319C2×C4×D4C2314yes—
320C2×C4×D4C2314yes—
321C2×C4×D4C2314yes—
322C2×C4×D4C2314yes—
323C2×C4×D4C2314yes—
324C2×C4×D4C2314yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2314yes—
328C2×C4×D4C2314yes—
329C2×C4×D4C2312yes—
330C2×C4×D4C2314yes—
331C2×C4×D4C2312yes—
332C2×#117C2314yes—
333C2×#117C2314yes—
334C2×#117C2314yes—
335C2×#117C2314yes—
336C22×C4⋊C4C2314yes—
337C22×C4⋊C4C2314yes—
338C22×C4⋊C4C2311yescharacteristic
339C22×C4⋊C4C2311yescharacteristic
340C22×C4⋊C4C2312yes—
341C22×C4⋊C4C2312yes—
342C22×C4⋊C4C2312yes—
343C22×C4⋊C4C2312yes—
344C22×C4⋊C4C2311yescharacteristic
345C22×C4⋊C4C2311yescharacteristic
346C22×C4⋊C4C2312yes—
347C22×C4⋊C4C2312yes—
348C22×C42C2311yescharacteristic
349C22×C42C2311yescharacteristic
350C22×C42C2312yes—
351C22×C42C2312yes—
352C22×C42C2311yescharacteristic
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2314yes—
360#399C2314yes—
361#399C2314yes—
362#399C2314yes—
363#399C2314yes—
364#399C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2314yes—
376#398C2314yes—
377#398C2314yes—
378#398C2314yes—
379#398C2314yes—
380#398C2314yes—
381#398C2314yes—
382#398C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#396C2314yes—
390#396C2314yes—
391#396C2314yes—
392#396C2314yes—
393#396C2314yes—
394#396C2314yes—
395#396C2314yes—
396#396C2314yes—
397#396C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#396C2314yes—
407#396C2314yes—
408#396C2314yes—
409#396C2314yes—
410#396C2314yes—
411#396C2314yes—
412#396C2314yes—
413#395C2314yes—
414#395C2314yes—
415#395C2314yes—
416#395C2314yes—
417#395C2314yes—
418#395C2314yes—
419#394C2314yes—
420#394C2314yes—
421#394C2314yes—
422#394C2314yes—
423#394C2314yes—
424#394C2314yes—
425#394C2314yes—
426#394C2314yes—
427#394C2314yes—
428#394C2314yes—
429#394C2314yes—
430#394C2314yes—
431#394C2314yes—
432#394C2314yes—
433#394C2314yes—
434#394C2314yes—
435#394C2314yes—
436#394C2314yes—
437#393C2314yes—
438#393C2314yes—
439#393C2314yes—
440#393C2314yes—
441#393C2314yes—
442#393C2314yes—
443#392C2314yes—
444#392C2314yes—
445#392C2314yes—
446#392C2314yes—
447#392C2314yes—
448#392C2314yes—
449#391C2314yes—
450#391C2314yes—
451#391C2314yes—
452#391C2314yes—
453#391C2314yes—
454#391C2314yes—
455#390C2314yes—
456#390C2314yes—
457#390C2312yes—
458#390C2312yes—
459#390C2312yes—
460#390C2312yes—
461#390C2312yes—
462#390C2312yes—
463#390C2312yes—
464#390C2312yes—
465#390C2314yes—
466#390C2312yes—
467#390C2312yes—
468#390C2314yes—
469#390C2314yes—
470#390C2314yes—
471#390C2314yes—
472#390C2314yes—
473#390C2312yes—
474#390C2312yes—
475#389C2314yes—
476#389C2314yes—
477#389C2314yes—
478#389C2314yes—
479#389C2314yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2312yes—
486#389C2312yes—
487#389C2312yes—
488#389C2312yes—
489#389C2314yes—
490#389C2314yes—
491#389C2312yes—
492#389C2312yes—
493#389C2312yes—
494#389C2312yes—
495#389C2312yes—
496#389C2312yes—
497#389C2312yes—
498#389C2312yes—
499#389C2314yes—
500#389C2312yes—
501#389C2312yes—
502#389C2314yes—
503#389C2314yes—
504#389C2314yes—
505#389C2314yes—
506#389C2314yes—
507#389C2314yes—
508#389C2314yes—
509#389C2312yes—
510#389C2312yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#388C2314yes—
529#388C2314yes—
530#388C2314yes—
531#388C2314yes—
532#388C2314yes—
533#388C2314yes—
534#388C2314yes—
535#388C2314yes—
536#388C2314yes—
537#388C2314yes—
538#388C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
557#387C2314yes—
558#387C2314yes—
559#386C2314yes—
560#386C2314yes—
561#386C2314yes—
562#386C2314yes—
563#386C2314yes—
564#386C2314yes—
565#386C2314yes—
566#386C2314yes—
567#386C2314yes—
568#386C2314yes—
569#386C2314yes—
570#386C2314yes—
571#386C2314yes—
572#386C2314yes—
573#386C2314yes—
574#386C2314yes—
575#386C2314yes—
576#386C2314yes—
577#386C2314yes—
578#386C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#385C2314yes—
590#385C2314yes—
591#384C2312yes—
592#384C2312yes—
593#384C2314yes—
594#384C2312yes—
595#384C2312yes—
596#382C2314yes—
597#380C2312yes—
598#380C2314yes—
599#380C2314yes—
600#380C2312yes—
601#380C2312yes—
602#380C2312yes—
603#380C2314yes—
604#380C2314yes—
605#380C2314yes—
606#380C2314yes—
607#380C2314yes—
608#380C2314yes—
609#380C2314yes—
610#380C2314yes—
611C4×C4⋊C4C2312yes—
612C4×C4⋊C4C2312yes—
613C4×C4⋊C4C2312yes—
614C4×C4⋊C4C2312yes—
615C4×C4⋊C4C2314yes—
616C4×C4⋊C4C2314yes—
617C4×C4⋊C4C2312yes—
618C4×C4⋊C4C2314yes—
619C4×C4⋊C4C2312yes—
620C4×C22⋊C4C2314yes—
621C4×C22⋊C4C2314yes—
622C4×C22⋊C4C2314yes—
623C4×C22⋊C4C2314yes—
624#376C2314yes—
625#376C2314yes—
626C2×#95C2312yes—
627C2×#95C2312yes—
628C2×#95C2311yescharacteristic
629C2×#95C2311yescharacteristic
630C2×#95C2312yes—
631C2×#95C2311yescharacteristic
632C2×#95C2311yescharacteristic
633C2×#95C2312yes—
634C22×Q8C2414yes—
635C22×Q8C2414yes—
636C22×Q8C2412yes—
637C22×Q8C2412yes—
638C22×D4C2414yes—
639C22×D4C2414yes—
640C22×D4C2412yes—
641C22×D4C2412yes—
642C22×D4C2414yes—
643C22×D4C2414yes—
644C22×D4C2412yes—
645C22×D4C2412yes—
646C22×D4C2414yes—
647C22×D4C2412yes—
648C22×D4C2414yes—
649C22×D4C2412yes—
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2412yes—
653C23×C4C2412yes—
654C23×C4C2414yes—
655C23×C4C2414yes—
656C23×C4C2414yes—
657C23×C4C2414yes—
658C23×C4C2414yes—
659C23×C4C2414yes—
660C23×C4C2411yescharacteristic
661C23×C4C2411yescharacteristic
662C23×C4C2412yes—
663C23×C4C2412yes—
664C23×C4C2411yescharacteristic
665C23×C4C2411yescharacteristic
666C23×C4C2411yescharacteristic
667C4⋊Q8—216no—
668C4⋊Q8—216no—
669C4⋊Q8—82no—
670#127—82no—
671#126—216no—
672#126—216no—
673#126—216no—
674#126—216no—
675#126—216no—
676#126—216no—
677#126—216no—
678#126—216no—
679#126—216no—
680#126—216no—
681#125—216no—
682#125—216no—
683#125—216no—
684#125—216no—
685#125—216no—
686#125—216no—
687#125—216no—
688#125—216no—
689#125—216no—
690#125—216no—
691#125—28no—
692#125—28no—
693#125C2×D4132yes—
694#125C2×D4116yes—
695#125C2×D4116yes—
696#124—28no—
697#124—28no—
698#124—84no—
699#123—216no—
700#123—216no—
701#123—216no—
702#123—216no—
703#123—216no—
704#123—216no—
705#123—216no—
706#123—216no—
707#123—216no—
708#123—216no—
709C22⋊Q8—28no—
710C22⋊Q8—28no—
711C22⋊Q8—216no—
712C22⋊Q8—216no—
713C22⋊Q8—216no—
714C22⋊Q8—216no—
715C22⋊Q8—216no—
716C22⋊Q8—216no—
717C22⋊Q8—216no—
718C22⋊Q8—216no—
719C22⋊Q8—216no—
720C22⋊Q8—216no—
721C22⋊Q8—216no—
722C22⋊Q8—216no—
723C22⋊Q8—84no—
724C22⋊Q8—84no—
725C22⋊Q8—84no—
726C22⋊Q8—84no—
727#121—28no—
728#121—28no—
729#121—216no—
730#121—216no—
731#121—28no—
732#121—28no—
733#121—216no—
734#121—216no—
735#121—44no—
736#121—44no—
737#121—48no—
738#121—48no—
739#121—84no—
740#121—84no—
741#121—84no—
742#121—84no—
743C4×Q8—216no—
744C4×Q8—216no—
745C4×Q8—28no—
746C4×Q8—28no—
747C4×D4—216no—
748C4×D4—216no—
749C4×D4—216no—
750C4×D4—216no—
751C4×D4—216no—
752C4×D4—216no—
753C4×D4—216no—
754C4×D4—216no—
755C4×D4—28no—
756C4×D4—28no—
757C4×D4—82no—
758C4×D4—82no—
759C4×D4—84no—
760#117—216no—
761#117—216no—
762#117—216no—
763#117—216no—
764C2×C4⋊C4—216no—
765C2×C4⋊C4—216no—
766C2×C4⋊C4—42no—
767C2×C4⋊C4—42no—
768C2×C4⋊C4—82no—
769C2×C4⋊C4—82no—
770C2×C4⋊C4—82no—
771C2×C4⋊C4—82no—
772C2×C4⋊C4C2×D418yes—
773C2×C4⋊C4C2×D418yes—
774C2×C4⋊C4C2×D4116yes—
775C2×C4⋊C4C2×D4116yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2414yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2412yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2414yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C4⋊C4C2414yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2414yes—
804C2×C4⋊C4C2414yes—
805C2×C4⋊C4C2414yes—
806C2×C4⋊C4C2414yes—
807C2×C4⋊C4C2414yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2411yescharacteristic
811C2×C4⋊C4C2412yes—
812C2×C4⋊C4C2412yes—
813C2×C4⋊C4C2412yes—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2414yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2412yes—
826C2×C4⋊C4C2414yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2411yescharacteristic
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2414yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C22⋊C4C2414yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2414yes—
857C2×C22⋊C4C2414yes—
858C2×C22⋊C4C2414yes—
859C2×C22⋊C4C2414yes—
860C2×C22⋊C4C2414yes—
861C2×C22⋊C4C2414yes—
862C2×C22⋊C4C2414yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2414yes—
871C2×C22⋊C4C2414yes—
872C2×C22⋊C4C2414yes—
873C2×C22⋊C4C2414yes—
874C2×C22⋊C4C2414yes—
875C2×C22⋊C4C2414yes—
876C2×C22⋊C4C2414yes—
877C2×C22⋊C4C2414yes—
878C2×C22⋊C4C2414yes—
879C2×C22⋊C4C2414yes—
880C2×C22⋊C4C2414yes—
881C2×C22⋊C4C2414yes—
882C2×C42—24no—
883C2×C42—42no—
884C2×C42—82no—
885C2×C42—82no—
886C2×C42C2×D418yes—
887C2×C42C2414yes—
888C2×C42C2414yes—
889C2×C42C2414yes—
890C2×C42C2414yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2412yes—
894C2×C42C2412yes—
895C2×C42C2414yes—
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2414yes—
899C2×C42C2412yes—
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2412yes—
903C2×C42C2412yes—
904C2×C42C2412yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2414yes—
912#95C2414yes—
913#95C2412yes—
914#95C2412yes—
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—
943C24C2514yes—
944C24C2514yes—
945C24C2511yescharacteristic
946C2×Q8—28no—
947C2×Q8—28no—
948C2×Q8—24no—
949C2×Q8—24no—
950C2×Q8—42no—
951C2×Q8—42no—
952C2×Q8—44no—
953C2×Q8—44no—
954C2×Q8—42no—
955C2×Q8—42no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×D4—28no—
959C2×D4—28no—
960C2×D4—28no—
961C2×D4—28no—
962C2×D4—28no—
963C2×D4—28no—
964C2×D4—28no—
965C2×D4—28no—
966C2×D4—24no—
967C2×D4—24no—
968C2×D4—24no—
969C2×D4—24no—
970C2×D4—44no—
971C2×D4—42no—
972C2×D4—42no—
973C2×D4—44no—
974C2×D4—42no—
975C2×D4—42no—
976C2×D4—44no—
977C2×D4—44no—
978C2×D4—44no—
979C2×D4—42no—
980C2×D4—42no—
981C2×D4—44no—
982C2×D4—42no—
983C2×D4—42no—
984C2×D4—44no—
985C2×D4—42no—
986C2×D4—42no—
987C2×D4—44no—
988C2×D4—42no—
989C2×D4—42no—
990C2×D4—44no—
991C2×D4—44no—
992C2×D4—42no—
993C2×D4—42no—
994C22×C4—22no—
995C22×C4—22no—
996C22×C4—22no—
997C22×C4—22no—
998C22×C4—22no—
999C22×C4—24no—
1000C22×C4—24no—
1001C22×C4—28no—
1002C22×C4—28no—
1003C22×C4—28no—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—28no—
1007C22×C4—41no—
1008C22×C4—41no—
1009C22×C4—42no—
1010C22×C4—42no—
1011C22×C4—41no—
1012C22×C4—41no—
1013C22×C4—41no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—41no—
1017C22×C4—41no—
1018C22×C4—41no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—41no—
1024C22×C4—41no—
1025C22×C4—44no—
1026C22×C4—44no—
1027C22×C4—44no—
1028C22×C4—44no—
1029C22×C4—44no—
1030C22×C4—44no—
1031C22×C4—44no—
1032C22×C4—44no—
1033C22×C4—44no—
1034C22×C4—44no—
1035C22×C4—44no—
1036C22×C4—44no—
1037C22×C4—41no—
1038C22×C4—41no—
1039C22×C4C22×D414yes—
1040C22×C4C22×D414yes—
1041C22×C4C22×D414yes—
1042C22×C4C22×D418yes—
1043C22×C4C22×D418yes—
1044C22×C42−1+414yes—
1045C22×C4C2512yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2514yes—
1050C22×C4C2514yes—
1051C22×C4C2514yes—
1052C22×C4C2512yes—
1053C22×C4C2514yes—
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2514yes—
1057C22×C4C2512yes—
1058C22×C4C2514yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2511yescharacteristic
1063C22×C4C2511yescharacteristic
1064C22×C4C2512yes—
1065C4⋊C4—28no—
1066C4⋊C4—28no—
1067C4⋊C4—28no—
1068C4⋊C4—28no—
1069C4⋊C4—28no—
1070C4⋊C4—28no—
1071C4⋊C4—28no—
1072C4⋊C4—28no—
1073C4⋊C4—28no—
1074C4⋊C4—28no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—28no—
1079C4⋊C4—28no—
1080C4⋊C4—28no—
1081C4⋊C4—28no—
1082C4⋊C4—28no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—28no—
1086C4⋊C4—28no—
1087C4⋊C4—28no—
1088C4⋊C4—28no—
1089C4⋊C4—24no—
1090C4⋊C4—24no—
1091C4⋊C4—41no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—41no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—44no—
1101C4⋊C4—44no—
1102C4⋊C4—44no—
1103C4⋊C4—44no—
1104C4⋊C4—42no—
1105C4⋊C4—42no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—44no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—44no—
1120C4⋊C4C22×D4116yes—
1121C4⋊C4C22×D4116yes—
1122C4⋊C4C22×D4116yes—
1123C4⋊C4C22×D4116yes—
1124C4⋊C4C22×D414yes—
1125C4⋊C4C22×D418yes—
1126C4⋊C4C22×D418yes—
1127C4⋊C4C22×D418yes—
1128C4⋊C4C22×D414yes—
1129C22⋊C4—28no—
1130C22⋊C4—28no—
1131C22⋊C4—28no—
1132C22⋊C4—28no—
1133C22⋊C4—28no—
1134C22⋊C4—28no—
1135C22⋊C4—28no—
1136C22⋊C4—28no—
1137C22⋊C4—28no—
1138C22⋊C4—28no—
1139C22⋊C4—28no—
1140C22⋊C4—28no—
1141C22⋊C4—28no—
1142C22⋊C4—28no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—44no—
1150C22⋊C4—44no—
1151C22⋊C4—44no—
1152C22⋊C4—44no—
1153C22⋊C4—44no—
1154C22⋊C4—44no—
1155C22⋊C4—44no—
1156C22⋊C4—44no—
1157C22⋊C4—44no—
1158C22⋊C4—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—44no—
1163C22⋊C4—44no—
1164C22⋊C4—44no—
1165C22⋊C4—44no—
1166C22⋊C4—44no—
1167C22⋊C4—44no—
1168C22⋊C4—44no—
1169C22⋊C4—44no—
1170C22⋊C4—44no—
1171C42—28no—
1172C42—28no—
1173C42—28no—
1174C42—28no—
1175C42—28no—
1176C42—28no—
1177C42—24no—
1178C42—24no—
1179C42—42no—
1180C42—42no—
1181C42—42no—
1182C42—42no—
1183C42—44no—
1184C42—44no—
1185C42—42no—
1186C42—42no—
1187C42C22×D418yes—
1188C42C22×D418yes—
1189C23—21no—
1190C23—21no—
1191C23—21no—
1192C23—21no—
1193C23—24no—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23—24no—
1201C23—24no—
1202C23—24no—
1203C23—24no—
1204C23—24no—
1205C23—24no—
1206C23—24no—
1207C23C23×D412yes—
1208C23C2×2−1+412yes—
1209C23#58512yes—
1210C23C2611yescharacteristic
1211Q8—88no—
1212Q8—84no—
1213Q8—84no—
1214Q8—88no—
1215D4—416no—
1216D4—416no—
1217D4—88no—
1218D4—88no—
1219D4—84no—
1220D4—84no—
1221D4—84no—
1222D4—84no—
1223D4—88no—
1224D4—162no—
1225D4—164no—
1226D4—162no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—24no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—28no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—24no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—24no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—24no—
1257C2×C4—24no—
1258C2×C4—24no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—24no—
1263C2×C4—22no—
1264C2×C4—24no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—24no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—24no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—24no—
1277C2×C4—24no—
1278C2×C4—24no—
1279C2×C4—24no—
1280C2×C4—48no—
1281C2×C4—48no—
1282C2×C4—44no—
1283C2×C4—44no—
1284C2×C4—44no—
1285C2×C4—44no—
1286C2×C4—88no—
1287C2×C4—88no—
1288C2×C4—88no—
1289C2×C4—88no—
1290C2×C4—88no—
1291C2×C4—88no—
1292C2×C4—84no—
1293C2×C4—84no—
1294C2×C4—82no—
1295C2×C4—82no—
1296C2×C4C23×D414yes—
1297C2×C4C23×D414yes—
1298C2×C4C23×D414yes—
1299C2×C4C23×D418yes—
1300C2×C4C23×D414yes—
1301C2×C4C23×D412yes—
1302C2×C4C23×D412yes—
1303C2×C4C2×2−1+414yes—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—44no—
1311C22—44no—
1312C22—44no—
1313C22—44no—
1314C22—44no—
1315C22—44no—
1316C22—44no—
1317C22—44no—
1318C22—44no—
1319C22—44no—
1320C22—44no—
1321C22—44no—
1322C22—44no—
1323C22—44no—
1324C22#349714yes—
1325C22C24×D411yescharacteristic
1326C22C22×2−1+411yescharacteristic
1327C22C2×#58511yescharacteristic
1328C22H(7,𝔽2)11yescharacteristic
1329C22H(7,𝔽2)11yescharacteristic
1330C222−1+611yescharacteristic
1331C222−1+611yescharacteristic
1332C4—22no—
1333C4—22no—
1334C4—24no—
1335C4—28no—
1336C4—24no—
1337C4—24no—
1338C4—24no—
1339C4—24no—
1340C4—44no—
1341C4—44no—
1342C4—44no—
1343C4—44no—
1344C4—44no—
1345C4—44no—
1346C4—42no—
1347C4—44no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C2—24no—
1353C2—84no—
1354C2—84no—
1355C2C2×#349711yescharacteristic
1356C2#6285311yescharacteristic
1357C2#6285311yescharacteristic
1358C2#6286511yescharacteristic
1359C2#6287011yescharacteristic
1360C2#6287311yescharacteristic
1361C2#6287711yescharacteristic
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×#3553C2semidirect
2. #51784C2semidirect
3. #51591C2semidirect
4. #51588C2semidirect
5. #51587C2semidirect
6. #47787C2semidirect
7. #47680C2semidirect
8. #47677C2semidirect
9. #47676C2semidirect
10. #39742C2semidirect
11. #39738C2semidirect
12. #39614C2semidirect
13. #39610C2semidirect
14. #39165C2semidirect
15. #39160C2semidirect
16. #37620C2semidirect
17. #37130C2semidirect
18. #37130C2semidirect
19. #35119C2semidirect
20. #35119C2semidirect
21. #35006C2semidirect
22. #35004C2semidirect
23. C2×#2330C2semidirect
252. C2×#125D4semidirect

Maximal subgroups

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

subgroupindex
C2×#35532
#517842
#515912
#515882
#515872
#477872
#476802
#476772
#476762
#397422
#397382
#396142
#396102
#391652
#391602
#376202
#371302
#351192
#350062
#350042
C2×#23302