Finite Group Databasebeta

← #7712685

Subgroups — #7712685

Order 512.

4906 conjugacy classes of subgroups.

The subgroup lattice has 1437 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60021C214yesmaximal, complemented
2#60008C214yesmaximal, complemented
3#45892C214yesmaximal, complemented
4#45868C214yesmaximal, complemented
5#40461C214yesmaximal, complemented
6#40430C214yesmaximal, complemented
7#40265C214yesmaximal, complemented
8#40234C214yesmaximal, complemented
9#38217C212yesmaximal, complemented
10#38216C212yesmaximal, complemented
11#38205C212yesmaximal, complemented
12#38204C212yesmaximal, complemented
13#37519C211yesmaximal, characteristic, complemented
14#37515C211yesmaximal, characteristic, complemented
15#37382C211yesmaximal, characteristic, complemented
16#37286C211yesmaximal, characteristic, complemented
17#37272C212yesmaximal, complemented
18#36638C212yesmaximal, complemented
19#36202C212yesmaximal, complemented
20#36171C212yesmaximal, complemented
21#36141C212yesmaximal, complemented
22#36112C212yesmaximal, complemented
23#35342C212yesmaximal, complemented
24#35333C211yesmaximal, characteristic, complemented
25#35328C211yesmaximal, characteristic, complemented
26#34410C212yesmaximal, complemented
27C4×#532C211yesmaximal, characteristic, complemented
28C2×#537C2212yes—
29C2×#532C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#529C2212yes—
32C22×#125C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2866C2214yes—
36#2865C2214yes—
37#2864C2212yes—
38#2863C2212yes—
39#2861C2212yes—
40#2860C2212yes—
41#2855C2212yes—
42#2854C2212yes—
43#2853C2214yes—
44#2852C2214yes—
45#2851C2212yes—
46#2851C2212yes—
47#2851C2212yes—
48#2850C2212yes—
49#2850C2212yes—
50#2850C2212yes—
51#2827C2214yes—
52#2825C2214yes—
53#2793C2214yes—
54#2791C2214yes—
55#2787C2214yes—
56#2781C2214yes—
57#2767C2214yes—
58#2766C2214yes—
59#2757C2214yes—
60#2753C2214yes—
61#2753C2214yes—
62#2750C2214yes—
63#2749C2214yes—
64#2744C2214yes—
65#2741C2214yes—
66#2740C2214yes—
67#2740C2214yes—
68#2739C2214yes—
69#2738C2214yes—
70#2730C2214yes—
71#2729C2214yes—
72#2722C2214yes—
73#2718C2214yes—
74#2718C2214yes—
75#2714C2214yes—
76#2705C2214yes—
77#2705C2214yes—
78#2699C2214yes—
79#2693C2214yes—
80#2688C2214yes—
81#2686C2214yes—
82#2682C2214yes—
83#2673C2214yes—
84#2671C2214yes—
85#2666C2214yes—
86#2661C2214yes—
87#2653C2214yes—
88#2651C2214yes—
89#2629C2211yescharacteristic
90#2629C2211yescharacteristic
91#2629C2211yescharacteristic
92#2629C2211yescharacteristic
93#2625C2212yes—
94#2624C2212yes—
95#2621C2211yescharacteristic
96#2621C2211yescharacteristic
97#2619C2211yescharacteristic
98#2619C2211yescharacteristic
99#2616C2212yes—
100#2615C2212yes—
101#2609C2214yes—
102#2604C2214yes—
103#2603C2214yes—
104#2602C2214yes—
105#2602C2214yes—
106#2600C2214yes—
107#2600C2214yes—
108#2599C2214yes—
109#2598C2214yes—
110#2598C2214yes—
111#2595C2214yes—
112#2579C2214yes—
113#2579C2214yes—
114#2578C2214yes—
115#2575C2214yes—
116#2566C2214yes—
117#2565C2214yes—
118#2559C2214yes—
119#2558C2214yes—
120#2554C2214yes—
121#2543C2214yes—
122#2543C2214yes—
123#2536C2214yes—
124#2535C2214yes—
125#2531C2214yes—
126#2531C2214yes—
127#2530C2214yes—
128#2529C2214yes—
129#2528C2214yes—
130#2526C2214yes—
131#2525C2214yes—
132#2524C2214yes—
133#2522C2214yes—
134#2519C2214yes—
135#2518C2214yes—
136#2518C2214yes—
137#2517C2214yes—
138#2516C2214yes—
139#2512C2212yes—
140#2511C2212yes—
141#2509C2212yes—
142#2508C2212yes—
143#2507C2214yes—
144#2505C2214yes—
145#2500C2214yes—
146#2498C2214yes—
147#2495C2212yes—
148#2494C2212yes—
149#2493C2214yes—
150#2490C2212yes—
151#2489C2212yes—
152#2487C2212yes—
153#2486C2212yes—
154#2481C2214yes—
155#2476C2214yes—
156#2475C2214yes—
157#2471C2214yes—
158#2468C2214yes—
159#2467C2214yes—
160#2464C2214yes—
161#2464C2214yes—
162#2460C2214yes—
163#2457C2214yes—
164#2457C2214yes—
165#2456C2214yes—
166#2456C2214yes—
167#2454C2212yes—
168#2453C2212yes—
169#2446C2212yes—
170#2445C2212yes—
171#2443C2214yes—
172#2429C2212yes—
173#2428C2212yes—
174#2423C2212yes—
175#2422C2212yes—
176#2419C2214yes—
177#2417C2212yes—
178#2416C2212yes—
179#2415C2212yes—
180#2414C2212yes—
181#2407C2212yes—
182#2407C2212yes—
183#2377C2214yes—
184#2377C2214yes—
185#2374C2214yes—
186#2373C2214yes—
187#2364C2214yes—
188#2364C2214yes—
189#2363C2212yes—
190#2363C2214yes—
191#2362C2212yes—
192#2361C2212yes—
193#2361C2214yes—
194#2360C2212yes—
195#2359C2214yes—
196#2359C2214yes—
197#2352C2214yes—
198#2345C2212yes—
199#2344C2212yes—
200#2343C2214yes—
201#2341C2212yes—
202#2339C2212yes—
203#2333C2214yes—
204#2332C2214yes—
205#2329C2214yes—
206#2324C2212yes—
207#2324C2212yes—
208#2324C2214yes—
209#2323C2212yes—
210#2323C2212yes—
211#2317C2212yes—
212#2311C2212yes—
213#2311C2212yes—
214C4×C4⋊Q8C2212yes—
215C4×#127C2212yes—
216C4×#125C2212yes—
217C4×#126C2214yes—
218C4×#124C2212yes—
219C4×#124C2212yes—
220C4×#124C2212yes—
221C4×C22⋊Q8C2212yes—
222C4×#123C2214yes—
223C4×#121C2212yes—
224C4×#121C2212yes—
225C4×#121C2212yes—
226C4×#121C2212yes—
227C4×#121C2212yes—
228#2298C2214yes—
229#2297C2211yescharacteristic
230#2297C2211yescharacteristic
231#2295C2212yes—
232#2293C2212yes—
233#2293C2212yes—
234#2293C2212yes—
235#2290C2214yes—
236#2285C2211yescharacteristic
237#2285C2211yescharacteristic
238#2283C2212yes—
239C2×#382C2211yescharacteristic
240C42×D4C2212yes—
241C42×D4C2212yes—
242C2×C43C2211yescharacteristic
243C22×#41C2312yes—
244C22×#41C2311yescharacteristic
245C22×#41C2311yescharacteristic
246#537—216no—
247#532—28no—
248#532—44no—
249C2×C4⋊Q8C2311yescharacteristic
250C2×C4⋊Q8C2311yescharacteristic
251C2×#127C2311yescharacteristic
252C2×#127C2311yescharacteristic
253#529—48no—
254C2×#126C2314yes—
255C2×#126C2314yes—
256C2×#126C2314yes—
257C2×#125—44no—
258C2×#125C2312yes—
259C2×#125C2314yes—
260C2×#125C2311yescharacteristic
261C2×#125C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2311yescharacteristic
264C2×#124C2311yescharacteristic
265C2×#123C2314yes—
266C2×#123C2314yes—
267C2×#123C2314yes—
268C2×#123C2314yes—
269C2×#123C2314yes—
270C2×C22⋊Q8C2312yes—
271C2×C22⋊Q8C2314yes—
272C2×C22⋊Q8C2312yes—
273C2×C22⋊Q8C2312yes—
274C2×C22⋊Q8C2312yes—
275C2×#121C2314yes—
276C2×#121C2312yes—
277C2×#121C2312yes—
278C2×#121C2314yes—
279C2×#121C2314yes—
280C2×#121C2312yes—
281C2×#121C2312yes—
282C2×#121C2312yes—
283C2×#121C2312yes—
284C2×#121C2314yes—
285C2×#121C2314yes—
286C2×#121C2314yes—
287C4×#41—44no—
288C4×#41—44no—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×Q8C2312yes—
292C2×C4×Q8C2312yes—
293C2×C4×D4C2312yes—
294C2×C4×D4C2312yes—
295C2×C4×D4C2312yes—
296C2×C4×D4C2312yes—
297C2×C4×D4C2312yes—
298C2×C4×D4C2312yes—
299C2×C4×D4C2312yes—
300C2×C4×D4C2312yes—
301C2×C4×D4C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2314yes—
305C2×C4×D4C2312yes—
306C2×C4×D4C2312yes—
307C2×C4×D4C2314yes—
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×C4×D4C2314yes—
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2311yescharacteristic
314C2×#117C2311yescharacteristic
315C2×#117C2312yes—
316C2×#117C2314yes—
317C2×#117C2314yes—
318C2×#117C2314yes—
319C2×#117C2311yescharacteristic
320C22×C4⋊C4C2312yes—
321C22×C4⋊C4C2312yes—
322C22×C4⋊C4C2314yes—
323C22×C42C2311yescharacteristic
324C22×C42C2311yescharacteristic
325C22×C42C2312yes—
326C22×C42C2311yescharacteristic
327C22×C42C2311yescharacteristic
328C22×C42C2312yes—
329C22×C42C2312yes—
330C22×C42C2311yescharacteristic
331#401C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#399C2314yes—
344#399C2314yes—
345#399C2314yes—
346#399C2314yes—
347#398C2314yes—
348#398C2314yes—
349#398C2314yes—
350#398C2314yes—
351#398C2314yes—
352#398C2314yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2314yes—
359#398C2314yes—
360#398C2314yes—
361#397C2314yes—
362#397C2314yes—
363#397C2314yes—
364#397C2314yes—
365#397C2314yes—
366#397C2314yes—
367#397C2314yes—
368#397C2314yes—
369#397C2314yes—
370#397C2314yes—
371#397C2314yes—
372#397C2314yes—
373#397C2314yes—
374#396C2314yes—
375#396C2314yes—
376#396C2314yes—
377#396C2314yes—
378#396C2314yes—
379#396C2314yes—
380#396C2314yes—
381#396C2314yes—
382#396C2314yes—
383#395C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#394C2314yes—
388#394C2314yes—
389#394C2314yes—
390#394C2314yes—
391#394C2314yes—
392#394C2314yes—
393#394C2314yes—
394#394C2314yes—
395#394C2314yes—
396#394C2314yes—
397#394C2314yes—
398#394C2314yes—
399#394C2314yes—
400#394C2314yes—
401#393C2314yes—
402#392C2314yes—
403#392C2314yes—
404#392C2314yes—
405#392C2314yes—
406#392C2314yes—
407#392C2314yes—
408#392C2314yes—
409#392C2314yes—
410#392C2314yes—
411#391C2312yes—
412#391C2312yes—
413#391C2314yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#390C2312yes—
421#390C2312yes—
422#390C2312yes—
423#390C2312yes—
424#390C2312yes—
425#390C2312yes—
426#390C2314yes—
427#390C2312yes—
428#390C2312yes—
429#390C2312yes—
430#390C2314yes—
431#390C2314yes—
432#390C2314yes—
433#390C2314yes—
434#390C2314yes—
435#390C2312yes—
436#390C2312yes—
437#390C2312yes—
438#390C2314yes—
439#390C2314yes—
440#389C2312yes—
441#389C2312yes—
442#389C2312yes—
443#389C2312yes—
444#389C2312yes—
445#389C2312yes—
446#389C2312yes—
447#389C2312yes—
448#389C2312yes—
449#389C2312yes—
450#389C2314yes—
451#389C2312yes—
452#389C2314yes—
453#389C2312yes—
454#389C2314yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2312yes—
459#389C2314yes—
460#389C2314yes—
461#389C2314yes—
462#389C2314yes—
463#388C2314yes—
464#388C2314yes—
465#388C2314yes—
466#388C2314yes—
467#388C2314yes—
468#388C2314yes—
469#388C2314yes—
470#388C2314yes—
471#388C2314yes—
472#388C2314yes—
473#388C2314yes—
474#388C2314yes—
475#388C2314yes—
476#388C2314yes—
477#388C2314yes—
478#388C2314yes—
479#388C2314yes—
480#388C2314yes—
481#388C2314yes—
482#388C2314yes—
483#388C2314yes—
484#388C2314yes—
485#388C2314yes—
486#388C2314yes—
487#388C2314yes—
488#388C2314yes—
489#388C2314yes—
490#388C2314yes—
491#388C2312yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2312yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2312yes—
505#388C2312yes—
506#388C2312yes—
507#388C2312yes—
508#388C2312yes—
509#388C2312yes—
510#387C2314yes—
511#387C2314yes—
512#387C2314yes—
513#387C2314yes—
514#387C2314yes—
515#387C2314yes—
516#387C2314yes—
517#387C2314yes—
518#387C2314yes—
519#387C2314yes—
520#387C2314yes—
521#387C2314yes—
522#387C2314yes—
523#387C2314yes—
524#387C2314yes—
525#387C2314yes—
526#387C2314yes—
527#387C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2314yes—
531#387C2314yes—
532#387C2314yes—
533#387C2314yes—
534#387C2314yes—
535#387C2314yes—
536#387C2314yes—
537#387C2314yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2314yes—
544#387C2314yes—
545#387C2314yes—
546#387C2314yes—
547#386C2314yes—
548#386C2314yes—
549#386C2314yes—
550#386C2314yes—
551#386C2312yes—
552#386C2314yes—
553#386C2314yes—
554#386C2314yes—
555#386C2314yes—
556#386C2314yes—
557#386C2314yes—
558#386C2314yes—
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#386C2311yescharacteristic
572#386C2311yescharacteristic
573#386C2314yes—
574#386C2314yes—
575#386C2311yescharacteristic
576#386C2311yescharacteristic
577#386C2312yes—
578#385C2314yes—
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#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#384C2312yes—
598#384C2314yes—
599#384C2311yescharacteristic
600#384C2311yescharacteristic
601#383C2314yes—
602#383C2314yes—
603#383C2314yes—
604#382C2312yes—
605#382C2314yes—
606#382C2314yes—
607#382C2312yes—
608#382C2314yes—
609#382C2314yes—
610#382C2311yescharacteristic
611#382C2311yescharacteristic
612#382C2312yes—
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#381C2314yes—
617#381C2314yes—
618#380C2312yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2314yes—
623#380C2314yes—
624#380C2314yes—
625#380C2312yes—
626#380C2312yes—
627#380C2314yes—
628#380C2314yes—
629#380C2314yes—
630#380C2314yes—
631#380C2312yes—
632#380C2312yes—
633#380C2312yes—
634#380C2312yes—
635C4×C4⋊C4C2314yes—
636C4×C4⋊C4C2314yes—
637C4×C4⋊C4C2314yes—
638C4×C4⋊C4C2314yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2312yes—
642C4×C4⋊C4C2312yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2314yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2314yes—
649C4×C4⋊C4C2312yes—
650C4×C4⋊C4C2312yes—
651C4×C22⋊C4C2314yes—
652C4×C22⋊C4C2314yes—
653C4×C22⋊C4C2314yes—
654C4×C22⋊C4C2312yes—
655C4×C22⋊C4C2312yes—
656C4×C22⋊C4C2314yes—
657C4×C22⋊C4C2314yes—
658C4×C22⋊C4C2314yes—
659C4×C22⋊C4C2314yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2312yes—
662C4×C22⋊C4C2312yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2314yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668C4×C22⋊C4C2312yes—
669C4×C22⋊C4C2312yes—
670C4×C22⋊C4C2312yes—
671C4×C22⋊C4C2312yes—
672C4×C22⋊C4C2312yes—
673#376C2314yes—
674#376C2314yes—
675C2×#95C2314yes—
676C2×#95C2314yes—
677C43C2312yes—
678C43C2312yes—
679C43C2312yes—
680C43C2312yes—
681C2×#41—24no—
682C2×#41—28no—
683C2×#41—42no—
684C2×#41—42no—
685C2×#41—42no—
686C2×#41—42no—
687C2×#41—44no—
688C2×#41—44no—
689C2×#41#4118yes—
690C22×Q8C2412yes—
691C22×Q8C2411yescharacteristic
692C22×Q8C2411yescharacteristic
693C22×D4C2412yes—
694C22×D4C2412yes—
695C22×D4C2412yes—
696C22×D4C2412yes—
697C22×D4C2411yescharacteristic
698C22×D4C2414yes—
699C22×D4C2414yes—
700C22×D4C2414yes—
701C22×D4C2414yes—
702C22×D4C2414yes—
703C22×D4C2414yes—
704C22×D4C2411yescharacteristic
705C22×D4C2411yescharacteristic
706C22×D4C2411yescharacteristic
707C23×C4C2412yes—
708C23×C4C2411yescharacteristic
709C23×C4C2412yes—
710C23×C4C2411yescharacteristic
711C23×C4C2411yescharacteristic
712C23×C4C2411yescharacteristic
713C23×C4C2412yes—
714C23×C4C2414yes—
715C23×C4C2414yes—
716C23×C4C2412yes—
717C23×C4C2412yes—
718C23×C4C2412yes—
719C23×C4C2412yes—
720C23×C4C2414yes—
721C23×C4C2414yes—
722C23×C4C2414yes—
723C23×C4C2411yescharacteristic
724C4⋊Q8—24no—
725C4⋊Q8—42no—
726#127—24no—
727#127—42no—
728#126—48no—
729#126—48no—
730#126—48no—
731#125—28no—
732#125—42no—
733#125—42no—
734#125—48no—
735#124—24no—
736#124—24no—
737#124—28no—
738#123—48no—
739#123—48no—
740#123—48no—
741#123—48no—
742#123—48no—
743C22⋊Q8—216no—
744C22⋊Q8—28no—
745C22⋊Q8—28no—
746C22⋊Q8—44no—
747C22⋊Q8—44no—
748#121—28no—
749#121—28no—
750#121—216no—
751#121—216no—
752#121—216no—
753#121—28no—
754#121—28no—
755#121—48no—
756#121—48no—
757#121—48no—
758#121—44no—
759#121—44no—
760C4×Q8—44no—
761C4×Q8—44no—
762C4×Q8—44no—
763C4×Q8—44no—
764C4×D4—28no—
765C4×D4—28no—
766C4×D4—44no—
767C4×D4—44no—
768C4×D4—48no—
769C4×D4—48no—
770C4×D4—44no—
771C4×D4—44no—
772C4×D4—44no—
773C4×D4—44no—
774C4×D4—44no—
775C4×D4—44no—
776C4×D4—44no—
777C4×D4—44no—
778C4×D4—44no—
779C4×D4—44no—
780C4×D4—48no—
781C4×D4—48no—
782#117—48no—
783#117—44no—
784#117—42no—
785#117—42no—
786#117—42no—
787#117—42no—
788#117—48no—
789#117—48no—
790#117—44no—
791C2×C4⋊C4—28no—
792C2×C4⋊C4—48no—
793C2×C4⋊C4—44no—
794C2×C4⋊C4C2414yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2412yes—
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2414yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2414yes—
803C2×C4⋊C4C2412yes—
804C2×C4⋊C4C2412yes—
805C2×C4⋊C4C2412yes—
806C2×C4⋊C4C2412yes—
807C2×C4⋊C4C2412yes—
808C2×C4⋊C4C2414yes—
809C2×C4⋊C4C2414yes—
810C2×C4⋊C4C2414yes—
811C2×C4⋊C4C2414yes—
812C2×C4⋊C4C2414yes—
813C2×C4⋊C4C2414yes—
814C2×C4⋊C4C2414yes—
815C2×C4⋊C4C2412yes—
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2414yes—
824C2×C4⋊C4C2414yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2414yes—
829C2×C4⋊C4C2414yes—
830C2×C4⋊C4C2414yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2414yes—
834C2×C4⋊C4C2414yes—
835C2×C4⋊C4C2414yes—
836C2×C4⋊C4C2414yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2414yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2414yes—
843C2×C22⋊C4C2414yes—
844C2×C22⋊C4C2412yes—
845C2×C22⋊C4C2412yes—
846C2×C22⋊C4C2412yes—
847C2×C22⋊C4C2412yes—
848C2×C22⋊C4C2412yes—
849C2×C22⋊C4C2412yes—
850C2×C22⋊C4C2414yes—
851C2×C22⋊C4C2414yes—
852C2×C22⋊C4C2414yes—
853C2×C22⋊C4C2414yes—
854C2×C22⋊C4C2414yes—
855C2×C22⋊C4C2414yes—
856C2×C22⋊C4C2411yescharacteristic
857C2×C22⋊C4C2411yescharacteristic
858C2×C22⋊C4C2412yes—
859C2×C22⋊C4C2412yes—
860C2×C22⋊C4C2412yes—
861C2×C22⋊C4C2412yes—
862C2×C22⋊C4C2412yes—
863C2×C22⋊C4C2414yes—
864C2×C22⋊C4C2414yes—
865C2×C22⋊C4C2414yes—
866C2×C22⋊C4C2414yes—
867C2×C22⋊C4C2414yes—
868C2×C22⋊C4C2414yes—
869C2×C22⋊C4C2414yes—
870C2×C22⋊C4C2412yes—
871C2×C22⋊C4C2412yes—
872C2×C22⋊C4C2412yes—
873C2×C22⋊C4C2412yes—
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×C22⋊C4C2414yes—
883C2×C22⋊C4C2414yes—
884C2×C22⋊C4C2414yes—
885C2×C22⋊C4C2414yes—
886C2×C22⋊C4C2414yes—
887C2×C22⋊C4C2414yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C42—24no—
892C2×C42—24no—
893C2×C42—24no—
894C2×C42—28no—
895C2×C42—24no—
896C2×C42—44no—
897C2×C42—44no—
898C2×C42—42no—
899C2×C42C2411yescharacteristic
900C2×C42C2412yes—
901C2×C42C2412yes—
902C2×C42C2414yes—
903C2×C42C2411yescharacteristic
904C2×C42C2411yescharacteristic
905C2×C42C2412yes—
906C2×C42C2412yes—
907C2×C42C2412yes—
908C2×C42C2412yes—
909C2×C42C2412yes—
910C2×C42C2412yes—
911C2×C42C2412yes—
912C2×C42C2412yes—
913C2×C42C2412yes—
914C2×C42C2411yescharacteristic
915C2×C42C2412yes—
916C2×C42C2411yescharacteristic
917C2×C42C2414yes—
918C2×C42C2414yes—
919C2×C42C2414yes—
920C2×C42C2414yes—
921C2×C42C2414yes—
922C2×C42C2414yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2412yes—
927C2×C42C2412yes—
928C2×C42C2411yescharacteristic
929#95C2412yes—
930#95C2414yes—
931#95C2414yes—
932#95C2414yes—
933#95C2414yes—
934#95C2414yes—
935#95C2414yes—
936#95C2414yes—
937#95C2414yes—
938#95C2414yes—
939#95C2414yes—
940#95C2414yes—
941#95C2414yes—
942#95C2414yes—
943#95C2414yes—
944#95C2412yes—
945#95C2414yes—
946#95C2412yes—
947#95C2412yes—
948#95C2412yes—
949#95C2414yes—
950#95C2412yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2412yes—
957#95C2414yes—
958#95C2414yes—
959#95C2414yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2414yes—
969#95C2414yes—
970#95C2414yes—
971#95C2414yes—
972#95C2414yes—
973#95C2414yes—
974#95C2414yes—
975#95C2414yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983C24C2514yes—
984C24C2512yes—
985C24C2511yescharacteristic
986C24C2511yescharacteristic
987C24C2511yescharacteristic
988#41—416no—
989#41—416no—
990#41—816no—
991C2×Q8—24no—
992C2×Q8—22no—
993C2×Q8—24no—
994C2×Q8—24no—
995C2×Q8—41no—
996C2×Q8—41no—
997C2×Q8—41no—
998C2×Q8—41no—
999C2×Q8C2×#4114yes—
1000C2×D4—24no—
1001C2×D4—24no—
1002C2×D4—24no—
1003C2×D4—28no—
1004C2×D4—28no—
1005C2×D4—28no—
1006C2×D4—24no—
1007C2×D4—22no—
1008C2×D4—24no—
1009C2×D4—24no—
1010C2×D4—24no—
1011C2×D4—24no—
1012C2×D4—41no—
1013C2×D4—41no—
1014C2×D4—41no—
1015C2×D4—41no—
1016C2×D4—42no—
1017C2×D4—42no—
1018C2×D4—42no—
1019C2×D4—41no—
1020C2×D4—41no—
1021C2×D4—41no—
1022C2×D4—41no—
1023C2×D4—42no—
1024C2×D4—44no—
1025C2×D4—44no—
1026C2×D4—44no—
1027C2×D4—44no—
1028C2×D4—44no—
1029C2×D4—44no—
1030C2×D4—44no—
1031C2×D4—44no—
1032C2×D4—44no—
1033C2×D4—44no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—44no—
1037C2×D4—44no—
1038C2×D4—44no—
1039C2×D4C2×#4114yes—
1040C2×D4C2×#4114yes—
1041C2×D4C2×#4114yes—
1042C22×C4—22no—
1043C22×C4—22no—
1044C22×C4—22no—
1045C22×C4—22no—
1046C22×C4—22no—
1047C22×C4—22no—
1048C22×C4—24no—
1049C22×C4—28no—
1050C22×C4—24no—
1051C22×C4—24no—
1052C22×C4—24no—
1053C22×C4—24no—
1054C22×C4—24no—
1055C22×C4—24no—
1056C22×C4—28no—
1057C22×C4—24no—
1058C22×C4—24no—
1059C22×C4—24no—
1060C22×C4—24no—
1061C22×C4—28no—
1062C22×C4—41no—
1063C22×C4—42no—
1064C22×C4—42no—
1065C22×C4—42no—
1066C22×C4—42no—
1067C22×C4—41no—
1068C22×C4—44no—
1069C22×C4—44no—
1070C22×C4—44no—
1071C22×C4—44no—
1072C22×C4—44no—
1073C22×C4—42no—
1074C22×C4—42no—
1075C22×C4—42no—
1076C22×C4—42no—
1077C22×C4—42no—
1078C22×C4—42no—
1079C22×C4—42no—
1080C22×C4—42no—
1081C22×C4—44no—
1082C22×C4—44no—
1083C22×C4—44no—
1084C22×C4—44no—
1085C22×C4—44no—
1086C22×C4—44no—
1087C22×C4—44no—
1088C22×C4C2×#4114yes—
1089C22×C4C2×#4114yes—
1090C22×C4C2×#4114yes—
1091C22×C4C2514yes—
1092C22×C4C2514yes—
1093C22×C4C2514yes—
1094C22×C4C2512yes—
1095C22×C4C2512yes—
1096C22×C4C2512yes—
1097C22×C4C2512yes—
1098C22×C4C2514yes—
1099C22×C4C2512yes—
1100C22×C4C2514yes—
1101C22×C4C2514yes—
1102C22×C4C2514yes—
1103C22×C4C2512yes—
1104C22×C4C2512yes—
1105C22×C4C2512yes—
1106C22×C4C2511yescharacteristic
1107C22×C4C2511yescharacteristic
1108C22×C4C2511yescharacteristic
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2511yescharacteristic
1113C4⋊C4—28no—
1114C4⋊C4—24no—
1115C4⋊C4—24no—
1116C4⋊C4—24no—
1117C4⋊C4—24no—
1118C4⋊C4—28no—
1119C4⋊C4—28no—
1120C4⋊C4—28no—
1121C4⋊C4—24no—
1122C4⋊C4—28no—
1123C4⋊C4—24no—
1124C4⋊C4—24no—
1125C4⋊C4—28no—
1126C4⋊C4—24no—
1127C4⋊C4—24no—
1128C4⋊C4—24no—
1129C4⋊C4—28no—
1130C4⋊C4—28no—
1131C4⋊C4—44no—
1132C4⋊C4—44no—
1133C4⋊C4—44no—
1134C4⋊C4—44no—
1135C4⋊C4—44no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—42no—
1141C4⋊C4—42no—
1142C4⋊C4—42no—
1143C4⋊C4—44no—
1144C4⋊C4—42no—
1145C4⋊C4—42no—
1146C4⋊C4—44no—
1147C4⋊C4—44no—
1148C4⋊C4—44no—
1149C4⋊C4—44no—
1150C4⋊C4—44no—
1151C4⋊C4—44no—
1152C4⋊C4—44no—
1153C4⋊C4—44no—
1154C4⋊C4—44no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C22⋊C4—24no—
1159C22⋊C4—24no—
1160C22⋊C4—28no—
1161C22⋊C4—28no—
1162C22⋊C4—24no—
1163C22⋊C4—24no—
1164C22⋊C4—28no—
1165C22⋊C4—28no—
1166C22⋊C4—28no—
1167C22⋊C4—28no—
1168C22⋊C4—24no—
1169C22⋊C4—24no—
1170C22⋊C4—28no—
1171C22⋊C4—24no—
1172C22⋊C4—24no—
1173C22⋊C4—28no—
1174C22⋊C4—28no—
1175C22⋊C4—44no—
1176C22⋊C4—44no—
1177C22⋊C4—44no—
1178C22⋊C4—44no—
1179C22⋊C4—41no—
1180C22⋊C4—42no—
1181C22⋊C4—41no—
1182C22⋊C4—42no—
1183C22⋊C4—42no—
1184C22⋊C4—42no—
1185C22⋊C4—42no—
1186C22⋊C4—44no—
1187C22⋊C4—42no—
1188C22⋊C4—42no—
1189C22⋊C4—42no—
1190C22⋊C4—42no—
1191C22⋊C4—44no—
1192C22⋊C4—44no—
1193C22⋊C4—44no—
1194C22⋊C4—44no—
1195C22⋊C4—44no—
1196C22⋊C4—44no—
1197C22⋊C4—44no—
1198C22⋊C4—44no—
1199C22⋊C4—44no—
1200C22⋊C4—44no—
1201C22⋊C4—44no—
1202C22⋊C4—44no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—44no—
1206C22⋊C4—44no—
1207C22⋊C4—44no—
1208C22⋊C4—44no—
1209C22⋊C4—44no—
1210C42—24no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—24no—
1215C42—24no—
1216C42—22no—
1217C42—22no—
1218C42—24no—
1219C42—24no—
1220C42—24no—
1221C42—24no—
1222C42—24no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—28no—
1228C42—42no—
1229C42—42no—
1230C42—42no—
1231C42—42no—
1232C42—42no—
1233C42—44no—
1234C42—44no—
1235C42—44no—
1236C42—44no—
1237C42—44no—
1238C42—44no—
1239C42H(5,𝔽2)14yes—
1240C23—21no—
1241C23—21no—
1242C23—21no—
1243C23—22no—
1244C23—22no—
1245C23—21no—
1246C23—22no—
1247C23—22no—
1248C23—22no—
1249C23—22no—
1250C23—21no—
1251C23—21no—
1252C23—22no—
1253C23—24no—
1254C23—24no—
1255C23—22no—
1256C23—24no—
1257C23—22no—
1258C23—24no—
1259C23—24no—
1260C23—22no—
1261C23—22no—
1262C23—24no—
1263C23—22no—
1264C23—22no—
1265C23—24no—
1266C23C22×#4112yes—
1267C23C22×#4112yes—
1268C23C22×#4112yes—
1269C23C2611yescharacteristic
1270Q8—44no—
1271Q8—44no—
1272Q8—48no—
1273D4—44no—
1274D4—44no—
1275D4—44no—
1276D4—48no—
1277D4—48no—
1278D4—44no—
1279D4—48no—
1280D4—48no—
1281D4—88no—
1282D4—88no—
1283D4—88no—
1284D4—88no—
1285D4—88no—
1286D4—164no—
1287C2×C4—22no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—28no—
1300C2×C4—28no—
1301C2×C4—28no—
1302C2×C4—22no—
1303C2×C4—24no—
1304C2×C4—24no—
1305C2×C4—22no—
1306C2×C4—24no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—22no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—24no—
1316C2×C4—22no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—22no—
1321C2×C4—22no—
1322C2×C4—24no—
1323C2×C4—24no—
1324C2×C4—22no—
1325C2×C4—22no—
1326C2×C4—24no—
1327C2×C4—22no—
1328C2×C4—24no—
1329C2×C4—24no—
1330C2×C4—24no—
1331C2×C4—24no—
1332C2×C4—24no—
1333C2×C4—24no—
1334C2×C4—24no—
1335C2×C4—22no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—24no—
1340C2×C4—22no—
1341C2×C4—24no—
1342C2×C4—24no—
1343C2×C4—22no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—44no—
1348C2×C4—48no—
1349C2×C4—48no—
1350C2×C4—44no—
1351C2×C4—48no—
1352C2×C4—84no—
1353C2×C4—84no—
1354C2×C4—84no—
1355C2×C4—84no—
1356C2×C4—88no—
1357C2×C4—88no—
1358C2×C4—88no—
1359C2×C4—88no—
1360C2×C4—88no—
1361C2×C4C22×#4112yes—
1362C2×C4C22×#4112yes—
1363C2×C4C22×#4112yes—
1364C2×C4C22×#4112yes—
1365C2×C4C2×H(5,𝔽2)14yes—
1366C2×C4C2×H(5,𝔽2)12yes—
1367C2×C4#58514yes—
1368C2×C4#58514yes—
1369C2×C4#58512yes—
1370C22—22no—
1371C22—22no—
1372C22—22no—
1373C22—24no—
1374C22—24no—
1375C22—24no—
1376C22—42no—
1377C22—42no—
1378C22—42no—
1379C22—41no—
1380C22—41no—
1381C22—41no—
1382C22—41no—
1383C22—41no—
1384C22—41no—
1385C22—42no—
1386C22—44no—
1387C22—42no—
1388C22—44no—
1389C22—42no—
1390C22—44no—
1391C22—42no—
1392C22—42no—
1393C22—44no—
1394C22—44no—
1395C22—44no—
1396C22—42no—
1397C22—44no—
1398C22—42no—
1399C22C23×#4111yescharacteristic
1400C22C22×H(5,𝔽2)11yescharacteristic
1401C22C2×#58512yes—
1402C22C2×#58512yes—
1403C22C2×#58511yescharacteristic
1404C4—24no—
1405C4—22no—
1406C4—22no—
1407C4—22no—
1408C4—24no—
1409C4—24no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—44no—
1414C4—42no—
1415C4—44no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—42no—
1420C4—44no—
1421C4—44no—
1422C4—44no—
1423C4—44no—
1424C4—42no—
1425C4#350514yes—
1426C2—42no—
1427C2—42no—
1428C2—42no—
1429C2—82no—
1430C2—84no—
1431C2#6275912yes—
1432C2C2×#350511yescharacteristic
1433C2#6281012yes—
1434C2#6282911yescharacteristic
1435C2#6284011yescharacteristic
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. #60021C2semidirect
2. #60008C2semidirect
3. #45892C2semidirect
4. #45868C2semidirect
5. #40461C2semidirect
6. #40430C2semidirect
7. #40265C2semidirect
8. #40234C2semidirect
9. #38217C2semidirect
10. #38216C2semidirect
11. #38205C2semidirect
12. #38204C2semidirect
13. #37519C2semidirect
14. #37515C2semidirect
15. #37382C2semidirect
16. #37286C2semidirect
17. #37272C2semidirect
18. #36638C2semidirect
19. #36202C2semidirect
20. #36171C2semidirect
21. #36141C2semidirect
22. #36112C2semidirect
23. #35342C2semidirect
24. #35333C2semidirect
25. #35328C2semidirect
26. #34410C2semidirect
27. C4×#532C2semidirect

Maximal subgroups

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

subgroupindex
#600212
#600082
#458922
#458682
#404612
#404302
#402652
#402342
#382172
#382162
#382052
#382042
#375192
#375152
#373822
#372862
#372722
#366382
#362022
#361712
#361412
#361122
#353422
#353332
#353282
#344102
C4×#5322