Finite Group Databasebeta

← #7901067

Subgroups — #7901067

Order 512.

4221 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59827C211yesmaximal, characteristic
2#59565C212yesmaximal, complemented
3#52274C211yesmaximal, characteristic, complemented
4#49468C214yesmaximal, complemented
5#49131C214yesmaximal, complemented
6#48587C214yesmaximal, complemented
7#47261C214yesmaximal, complemented
8#45946C212yesmaximal, complemented
9#45383C212yesmaximal, complemented
10#45221C212yesmaximal, complemented
11#45137C212yesmaximal
12#43223C214yesmaximal, complemented
13#42639C212yesmaximal, complemented
14#42511C212yesmaximal, complemented
15#41554C214yesmaximal, complemented
16#40080C212yesmaximal, complemented
17#39629C211yesmaximal, characteristic, complemented
18#39628C211yesmaximal, characteristic
19#38788C212yesmaximal, complemented
20#38472C212yesmaximal, complemented
21#38230C212yesmaximal, complemented
22#38229C212yesmaximal, complemented
23#37162C212yesmaximal, complemented
24#36286C211yesmaximal, characteristic, complemented
25#35961C212yesmaximal, complemented
26#35632C212yesmaximal, complemented
27#35187C211yesmaximal, characteristic, complemented
28#34500C212yesmaximal
29#34331C211yesmaximal, characteristic
30C2×#559C2211yescharacteristic
31C2×#559C2212yes—
32#2864C2212yes—
33#2863C2212yes—
34#2863C2212yes—
35#2863C2212yes—
36#2862C2211yescharacteristic
37#2839C2214yes—
38#2835C2214yes—
39#2809C2211yescharacteristic
40#2806C2211yescharacteristic
41#2806C2212yes—
42#2806C2212yes—
43#2805C2211yescharacteristic
44#2805C2212yes—
45#2805C2212yes—
46#2804C2212yes—
47#2804C2212yes—
48#2802C2212yes—
49#2799C2212yes—
50#2791C2212yes—
51#2787C2214yes—
52#2787C2214yes—
53#2787C2214yes—
54#2776C2214yes—
55#2774C2212yes—
56#2770C2214yes—
57#2770C2214yes—
58#2770C2214yes—
59#2770C2214yes—
60#2770C2214yes—
61#2769C2214yes—
62#2767C2214yes—
63#2767C2214yes—
64#2764C2214yes—
65#2764C2214yes—
66#2762C2214yes—
67#2758C2214yes—
68#2755C2214yes—
69#2755C2212yes—
70#2747C2214yes—
71#2747C2214yes—
72#2745C2214yes—
73#2745C2214yes—
74#2745C2214yes—
75#2744C2214yes—
76#2744C2214yes—
77#2739C2214yes—
78#2739C2214yes—
79#2738C2214yes—
80#2732C2212yes—
81#2732C2212yes—
82#2726C2211yescharacteristic
83#2724C2212yes—
84#2724C2212yes—
85#2719C2214yes—
86#2717C2214yes—
87#2717C2214yes—
88#2717C2214yes—
89#2717C2214yes—
90#2713C2212yes—
91#2690C2214yes—
92#2690C2214yes—
93#2655C2214yes—
94#2655C2214yes—
95#2652C2214yes—
96#2652C2214yes—
97#2647C2212yes—
98#2647C2212yes—
99#2646C2214yes—
100#2645C2212yes—
101#2634C2214yes—
102#2627C2214yes—
103#2611C2214yes—
104#2605C2214yes—
105#2599C2214yes—
106#2588C2214yes—
107#2585C2214yes—
108#2582C2212yes—
109#2582C2211yescharacteristic
110#2581C2212yes—
111#2581C2212yes—
112#2580C2212yes—
113#2577C2214yes—
114#2575C2214yes—
115#2571C2211yescharacteristic
116#2570C2212yes—
117#2569C2214yes—
118#2569C2214yes—
119#2569C2214yes—
120#2568C2211yescharacteristic
121#2568C2211yescharacteristic
122#2567C2211yescharacteristic
123#2547C2212yes—
124#2547C2212yes—
125#2547C2212yes—
126#2547C2212yes—
127#2546C2211yescharacteristic
128#2533C2214yes—
129#2530C2214yes—
130#2530C2214yes—
131#2530C2214yes—
132#2528C2214yes—
133#2527C2214yes—
134#2527C2214yes—
135#2527C2214yes—
136#2524C2214yes—
137#2523C2214yes—
138#2523C2214yes—
139#2520C2214yes—
140#2520C2214yes—
141#2520C2214yes—
142#2517C2214yes—
143#2514C2212yes—
144#2514C2212yes—
145#2514C2212yes—
146#2511C2212yes—
147#2511C2212yes—
148#2511C2212yes—
149#2511C2212yes—
150#2509C2212yes—
151#2509C2212yes—
152#2508C2212yes—
153#2508C2212yes—
154#2507C2212yes—
155#2506C2212yes—
156#2506C2212yes—
157#2505C2214yes—
158#2505C2214yes—
159#2505C2214yes—
160#2505C2214yes—
161#2493C2214yes—
162#2493C2214yes—
163#2493C2214yes—
164#2489C2214yes—
165#2486C2214yes—
166#2484C2214yes—
167#2475C2214yes—
168#2475C2214yes—
169#2473C2214yes—
170#2473C2214yes—
171#2473C2214yes—
172#2462C2214yes—
173#2452C2212yes—
174#2452C2212yes—
175#2451C2212yes—
176#2451C2212yes—
177#2451C2212yes—
178#2450C2214yes—
179#2450C2214yes—
180#2447C2212yes—
181#2447C2212yes—
182#2447C2214yes—
183#2447C2212yes—
184#2447C2212yes—
185#2447C2212yes—
186#2447C2212yes—
187#2446C2212yes—
188#2446C2212yes—
189#2446C2212yes—
190#2442C2214yes—
191#2438C2214yes—
192#2438C2214yes—
193#2421C2214yes—
194#2419C2214yes—
195#2419C2214yes—
196#2419C2214yes—
197#2419C2214yes—
198#2402C2212yes—
199#2402C2212yes—
200#2399C2212yes—
201C2×#400C2214yes—
202#2379C2214yes—
203#2376C2214yes—
204#2369C2211yescharacteristic
205#2367C2212yes—
206#2367C2212yes—
207#2367C2212yes—
208#2367C2212yes—
209#2366C2211yescharacteristic
210#2365C2211yescharacteristic
211#2359C2214yes—
212#2359C2214yes—
213#2356C2212yes—
214#2355C2212yes—
215#2355C2211yescharacteristic
216#2354C2212yes—
217#2352C2214yes—
218#2351C2212yes—
219Q8×C4⋊C4C2211yescharacteristic
220#2349C2212yes—
221#2349C2212yes—
222#2349C2212yes—
223#2349C2212yes—
224#2349C2212yes—
225D4×C4⋊C4C2212yes—
226D4×C4⋊C4C2212yes—
227D4×C4⋊C4C2212yes—
228#2343C2214yes—
229#2337C2214yes—
230#2335C2214yes—
231#2335C2214yes—
232#2329C2214yes—
233#2328C2212yes—
234#2327C2212yes—
235#2327C2212yes—
236#2326C2212yes—
237#2326C2212yes—
238#2322C2214yes—
239#2320C2212yes—
240#2320C2212yes—
241#2319C2212yes—
242#2318C2214yes—
243C4×C4⋊Q8C2211yescharacteristic
244C4×C4⋊Q8C2211yescharacteristic
245C4×#127C2211yescharacteristic
246C4×#125C2212yes—
247C4×#124C2212yes—
248C4×#124C2212yes—
249#2295C2211yescharacteristic
250#2295C2212yes—
251#2295C2212yes—
252#2295C2212yes—
253#2295C2211yescharacteristic
254#2295C2212yes—
255#2293C2212yes—
256#2293C2212yes—
257#2275C2212yes—
258C42×Q8C2211yescharacteristic
259#559—28no—
260#559—216no—
261C2×C4⋊Q8C2311yescharacteristic
262C2×C4⋊Q8C2311yescharacteristic
263C2×C4⋊Q8C2311yescharacteristic
264C2×C4⋊Q8C2311yescharacteristic
265C2×C4⋊Q8C2312yes—
266C2×#127C2311yescharacteristic
267C2×#125C2312yes—
268C2×#125C2314yes—
269C2×#125C2314yes—
270C2×#124C2312yes—
271C2×#124C2312yes—
272C2×#124C2314yes—
273C2×#124C2312yes—
274C2×#124C2312yes—
275C2×#123C2314yes—
276C2×#123C2314yes—
277C2×#123C2314yes—
278C2×C22⋊Q8C2314yes—
279C2×C22⋊Q8C2314yes—
280C2×C4×Q8C2312yes—
281C2×C4×Q8C2312yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×Q8C2311yescharacteristic
285C2×C4×Q8C2311yescharacteristic
286C2×C4×Q8C2311yescharacteristic
287C2×C4×Q8C2312yes—
288C2×C4×Q8C2312yes—
289C2×C4×Q8C2312yes—
290C2×C4×Q8C2312yes—
291C2×C4×D4C2312yes—
292C2×C4×D4C2314yes—
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×#117C2314yes—
304C2×#117C2314yes—
305C22×C4⋊C4C2314yes—
306C22×C4⋊C4C2314yes—
307#401C2314yes—
308#401C2314yes—
309#401C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2312yes—
313#400C2314yes—
314#400C2314yes—
315#400C2314yes—
316#400C2314yes—
317#400C2314yes—
318#400C2314yes—
319#400C2314yes—
320#400C2314yes—
321#400C2312yes—
322#400C2314yes—
323#400C2314yes—
324#400C2314yes—
325#400C2314yes—
326#400C2314yes—
327#400C2314yes—
328#400C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2312yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2312yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2312yes—
349#399C2314yes—
350#398C2312yes—
351#398C2314yes—
352#398C2312yes—
353#398C2314yes—
354#398C2314yes—
355#398C2314yes—
356#398C2314yes—
357#398C2314yes—
358#398C2312yes—
359#398C2314yes—
360#398C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2312yes—
364#398C2314yes—
365#398C2312yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2312yes—
374#398C2312yes—
375#398C2312yes—
376#398C2312yes—
377#398C2312yes—
378#398C2312yes—
379#398C2312yes—
380#398C2314yes—
381#397C2314yes—
382#397C2314yes—
383#397C2314yes—
384#397C2314yes—
385#397C2314yes—
386#397C2314yes—
387#397C2314yes—
388#397C2314yes—
389#397C2314yes—
390#397C2314yes—
391#397C2314yes—
392#397C2314yes—
393#397C2314yes—
394#397C2314yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#397C2314yes—
399#396C2314yes—
400#396C2314yes—
401#395C2314yes—
402#395C2314yes—
403#395C2314yes—
404#395C2314yes—
405#395C2314yes—
406#395C2312yes—
407#395C2312yes—
408#395C2312yes—
409#395C2312yes—
410#393C2314yes—
411#393C2314yes—
412#393C2314yes—
413#391C2312yes—
414#391C2312yes—
415#391C2312yes—
416#391C2312yes—
417#391C2312yes—
418#391C2312yes—
419#391C2312yes—
420#391C2312yes—
421#391C2312yes—
422#391C2312yes—
423#391C2312yes—
424#391C2312yes—
425#391C2312yes—
426#391C2312yes—
427#391C2312yes—
428#391C2312yes—
429#391C2312yes—
430#391C2314yes—
431#391C2314yes—
432#391C2312yes—
433#391C2314yes—
434#391C2312yes—
435#391C2314yes—
436#391C2312yes—
437#391C2312yes—
438#391C2312yes—
439#391C2311yescharacteristic
440#391C2312yes—
441#391C2311yescharacteristic
442#391C2312yes—
443#391C2314yes—
444#391C2312yes—
445#391C2311yescharacteristic
446#391C2312yes—
447#391C2311yescharacteristic
448#390C2312yes—
449#390C2312yes—
450#390C2312yes—
451#390C2312yes—
452#390C2312yes—
453#390C2312yes—
454#390C2312yes—
455#389C2312yes—
456#389C2312yes—
457#389C2312yes—
458#389C2311yescharacteristic
459#389C2312yes—
460#389C2312yes—
461#389C2311yescharacteristic
462#389C2312yes—
463#389C2312yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2312yes—
471#389C2312yes—
472#389C2314yes—
473#389C2312yes—
474#389C2312yes—
475#389C2312yes—
476#389C2312yes—
477#389C2312yes—
478#389C2314yes—
479#389C2312yes—
480#389C2312yes—
481#389C2314yes—
482#389C2312yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2311yescharacteristic
488#389C2312yes—
489#389C2312yes—
490#389C2312yes—
491#389C2312yes—
492#389C2311yescharacteristic
493#389C2312yes—
494#389C2314yes—
495#389C2312yes—
496#389C2311yescharacteristic
497#389C2312yes—
498#389C2311yescharacteristic
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#388C2314yes—
508#388C2314yes—
509#388C2314yes—
510#388C2314yes—
511#388C2314yes—
512#388C2314yes—
513#388C2314yes—
514#388C2314yes—
515#388C2314yes—
516#388C2314yes—
517#387C2312yes—
518#387C2312yes—
519#387C2312yes—
520#387C2312yes—
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#387C2312yes—
536#387C2314yes—
537#387C2312yes—
538#387C2314yes—
539#387C2314yes—
540#387C2314yes—
541#387C2314yes—
542#387C2314yes—
543#387C2312yes—
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#387C2314yes—
560#387C2314yes—
561#387C2312yes—
562#387C2312yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2312yes—
571#387C2314yes—
572#387C2312yes—
573#387C2312yes—
574#387C2312yes—
575#387C2314yes—
576#387C2314yes—
577#387C2312yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2312yes—
582#387C2312yes—
583#387C2314yes—
584#386C2314yes—
585#386C2314yes—
586#386C2314yes—
587#386C2314yes—
588#386C2314yes—
589#385C2314yes—
590#385C2314yes—
591#385C2314yes—
592#385C2314yes—
593#385C2314yes—
594#385C2314yes—
595#385C2314yes—
596#385C2314yes—
597#385C2314yes—
598#385C2314yes—
599#385C2314yes—
600#385C2314yes—
601#385C2314yes—
602#385C2314yes—
603#385C2314yes—
604#385C2314yes—
605#385C2314yes—
606#385C2314yes—
607#385C2314yes—
608#385C2314yes—
609#385C2314yes—
610#385C2314yes—
611#385C2314yes—
612#385C2314yes—
613#385C2314yes—
614#385C2314yes—
615#385C2314yes—
616#385C2314yes—
617#385C2314yes—
618#384C2311yescharacteristic
619#384C2311yescharacteristic
620#384C2311yescharacteristic
621#384C2312yes—
622#384C2312yes—
623#383C2314yes—
624#383C2314yes—
625#383C2314yes—
626#383C2314yes—
627#383C2314yes—
628#383C2314yes—
629#382C2312yes—
630#382C2312yes—
631#382C2312yes—
632#382C2312yes—
633#382C2312yes—
634#382C2312yes—
635#382C2314yes—
636#382C2314yes—
637#382C2314yes—
638#382C2312yes—
639#382C2314yes—
640#382C2312yes—
641#381C2314yes—
642#381C2314yes—
643#381C2314yes—
644#381C2314yes—
645#381C2314yes—
646#381C2314yes—
647#381C2314yes—
648#380C2314yes—
649#380C2314yes—
650#380C2314yes—
651#380C2314yes—
652#380C2314yes—
653#380C2314yes—
654#380C2314yes—
655#380C2314yes—
656#380C2314yes—
657#380C2314yes—
658#380C2314yes—
659#380C2314yes—
660#380C2314yes—
661#380C2314yes—
662C4×C4⋊C4C2311yescharacteristic
663C4×C4⋊C4C2312yes—
664C4×C4⋊C4C2312yes—
665C4×C4⋊C4C2312yes—
666C4×C4⋊C4C2312yes—
667C4×C4⋊C4C2312yes—
668C4×C4⋊C4C2311yescharacteristic
669C4×C4⋊C4C2312yes—
670C4×C4⋊C4C2312yes—
671C4×C4⋊C4C2312yes—
672C4×C4⋊C4C2311yescharacteristic
673C4×C4⋊C4C2311yescharacteristic
674C4×C4⋊C4C2312yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2311yescharacteristic
677C4×C4⋊C4C2312yes—
678C4×C4⋊C4C2312yes—
679C4×C4⋊C4C2312yes—
680C4×C4⋊C4C2314yes—
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2314yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2311yescharacteristic
688C4×C4⋊C4C2311yescharacteristic
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C22⋊C4C2314yes—
693C4×C22⋊C4C2314yes—
694C4×C22⋊C4C2314yes—
695C4×C22⋊C4C2314yes—
696C4×C22⋊C4C2314yes—
697C4×C22⋊C4C2314yes—
698C4×C22⋊C4C2314yes—
699C4×C22⋊C4C2314yes—
700C4×C22⋊C4C2314yes—
701#376C2312yes—
702#376C2312yes—
703#376C2312yes—
704#376C2314yes—
705#376C2314yes—
706C2×#95C2314yes—
707C2×#95C2314yes—
708C2×#95C2314yes—
709C2×#95C2314yes—
710C2×#95C2314yes—
711C43C2312yes—
712C43C2311yescharacteristic
713C43C2312yes—
714C22×Q8C2411yescharacteristic
715C22×Q8C2412yes—
716C22×Q8C2411yescharacteristic
717C22×Q8C2412yes—
718C22×Q8C2412yes—
719C22×Q8C2411yescharacteristic
720C22×Q8C2412yes—
721C22×D4C2412yes—
722C22×D4C2412yes—
723C22×D4C2412yes—
724C23×C4C2414yes—
725C23×C4C2414yes—
726C23×C4C2414yes—
727C23×C4C2414yes—
728C23×C4C2414yes—
729C23×C4C2414yes—
730C23×C4C2414yes—
731C4⋊Q8—24no—
732C4⋊Q8—42no—
733C4⋊Q8—42no—
734C4⋊Q8—42no—
735C4⋊Q8—44no—
736#127#4118yes—
737#125—44no—
738#125—84no—
739#125—84no—
740#124—28no—
741#124—28no—
742#124—28no—
743#124—216no—
744#124—28no—
745#123—216no—
746#123—216no—
747#123—216no—
748C22⋊Q8—48no—
749C22⋊Q8—84no—
750C4×Q8—28no—
751C4×Q8—24no—
752C4×Q8—24no—
753C4×Q8—28no—
754C4×Q8—24no—
755C4×Q8—24no—
756C4×Q8—44no—
757C4×Q8—44no—
758C4×Q8—44no—
759C4×Q8—42no—
760C4×Q8—82no—
761C4×D4—28no—
762C4×D4—28no—
763C4×D4—28no—
764C4×D4—216no—
765C4×D4—28no—
766C4×D4—28no—
767C4×D4—44no—
768C4×D4—44no—
769C4×D4—44no—
770C4×D4—44no—
771C4×D4—82no—
772C4×D4—82no—
773#117—48no—
774#117—84no—
775C2×C4⋊C4—84no—
776C2×C4⋊C4—84no—
777C2×C4⋊C4C2412yes—
778C2×C4⋊C4C2411yescharacteristic
779C2×C4⋊C4C2411yescharacteristic
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2412yes—
782C2×C4⋊C4C2411yescharacteristic
783C2×C4⋊C4C2412yes—
784C2×C4⋊C4C2412yes—
785C2×C4⋊C4C2412yes—
786C2×C4⋊C4C2411yescharacteristic
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2412yes—
789C2×C4⋊C4C2412yes—
790C2×C4⋊C4C2412yes—
791C2×C4⋊C4C2414yes—
792C2×C4⋊C4C2411yescharacteristic
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2411yescharacteristic
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2412yes—
797C2×C4⋊C4C2411yescharacteristic
798C2×C4⋊C4C2412yes—
799C2×C4⋊C4C2412yes—
800C2×C4⋊C4C2412yes—
801C2×C4⋊C4C2412yes—
802C2×C4⋊C4C2412yes—
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⋊C4C2414yes—
814C2×C4⋊C4C2412yes—
815C2×C4⋊C4C2414yes—
816C2×C4⋊C4C2414yes—
817C2×C4⋊C4C2414yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2414yes—
820C2×C4⋊C4C2414yes—
821C2×C4⋊C4C2414yes—
822C2×C4⋊C4C2414yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2414yes—
826C2×C4⋊C4C2412yes—
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2412yes—
831C2×C4⋊C4C2414yes—
832C2×C4⋊C4C2414yes—
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2411yescharacteristic
835C2×C4⋊C4C2411yescharacteristic
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2412yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2414yes—
841C2×C4⋊C4C2414yes—
842C2×C4⋊C4C2411yescharacteristic
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2411yescharacteristic
845C2×C4⋊C4C2414yes—
846C2×C4⋊C4C2412yes—
847C2×C4⋊C4C2411yescharacteristic
848C2×C4⋊C4C2412yes—
849C2×C4⋊C4C2412yes—
850C2×C4⋊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×C42C2412yes—
873C2×C42C2411yescharacteristic
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2412yes—
878C2×C42C2412yes—
879C2×C42C2412yes—
880C2×C42C2414yes—
881C2×C42C2411yescharacteristic
882C2×C42C2412yes—
883C2×C42C2412yes—
884C2×C42C2412yes—
885C2×C42C2414yes—
886C2×C42C2414yes—
887C2×C42C2411yescharacteristic
888C2×C42C2412yes—
889C2×C42C2414yes—
890C2×C42C2412yes—
891C2×C42C2414yes—
892C2×C42C2414yes—
893C2×C42C2414yes—
894C2×C42C2412yes—
895C2×C42C2411yescharacteristic
896C2×C42C2412yes—
897C2×C42C2412yes—
898C2×C42C2412yes—
899C2×C42C2411yescharacteristic
900C2×C42C2411yescharacteristic
901C2×C42C2411yescharacteristic
902#95C2412yes—
903#95C2412yes—
904#95C2412yes—
905#95C2412yes—
906#95C2412yes—
907#95C2412yes—
908#95C2414yes—
909#95C2414yes—
910#95C2414yes—
911#95C2414yes—
912#95C2414yes—
913#95C2414yes—
914#95C2414yes—
915#95C2414yes—
916#95C2414yes—
917#95C2414yes—
918#95C2414yes—
919#95C2414yes—
920#95C2414yes—
921#95C2414yes—
922#95C2412yes—
923#95C2412yes—
924#95C2412yes—
925#95C2412yes—
926#95C2412yes—
927#95C2414yes—
928#95C2414yes—
929#95C2414yes—
930#95C2412yes—
931#95C2414yes—
932#95C2412yes—
933#95C2412yes—
934#95C2414yes—
935#95C2412yes—
936#95C2414yes—
937#95C2412yes—
938#95C2412yes—
939#95C2412yes—
940#95C2412yes—
941#95C2412yes—
942#95C2412yes—
943#95C2414yes—
944#95C2414yes—
945#95C2414yes—
946#95C2414yes—
947#95C2414yes—
948#95C2414yes—
949#95C2414yes—
950#95C2414yes—
951#95C2412yes—
952#95C2412yes—
953#95C2412yes—
954#95C2412yes—
955#95C2412yes—
956#95C2414yes—
957#95C2414yes—
958#95C2412yes—
959#95C2412yes—
960#95C2412yes—
961#95C2412yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2412yes—
967#95C2412yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2412yes—
974#95C2414yes—
975#95C2412yes—
976#95C2414yes—
977#95C2414yes—
978#95C2414yes—
979#95C2414yes—
980#95C2414yes—
981#95C2414yes—
982#95C2414yes—
983#95C2414yes—
984#95C2414yes—
985#95C2414yes—
986#95C2414yes—
987#95C2414yes—
988#95C2414yes—
989C24C2514yes—
990C2×Q8—22no—
991C2×Q8—22no—
992C2×Q8—24no—
993C2×Q8—24no—
994C2×Q8—22no—
995C2×Q8—24no—
996C2×Q8—22no—
997C2×Q8—24no—
998C2×Q8—22no—
999C2×Q8—24no—
1000C2×Q8—41no—
1001C2×Q8—41no—
1002C2×Q8—42no—
1003C2×Q8—42no—
1004C2×Q8—41no—
1005C2×Q8—41no—
1006C2×Q8—42no—
1007C2×Q8—42no—
1008C2×Q8—42no—
1009C2×Q8—42no—
1010C2×Q8—42no—
1011C2×D4—24no—
1012C2×D4—24no—
1013C2×D4—42no—
1014C2×D4—42no—
1015C2×D4—42no—
1016C2×D4—42no—
1017C2×D4C2×#4118yes—
1018C2×D4C2×#4118yes—
1019C2×D4C2×#4118yes—
1020C22×C4—28no—
1021C22×C4—28no—
1022C22×C4—28no—
1023C22×C4—28no—
1024C22×C4—44no—
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—44no—
1038C22×C4—44no—
1039C22×C4—44no—
1040C22×C4—44no—
1041C22×C4C2512yes—
1042C22×C4C2512yes—
1043C22×C4C2512yes—
1044C22×C4C2514yes—
1045C22×C4C2514yes—
1046C22×C4C2512yes—
1047C22×C4C2512yes—
1048C22×C4C2512yes—
1049C22×C4C2512yes—
1050C22×C4C2512yes—
1051C22×C4C2512yes—
1052C22×C4C2512yes—
1053C22×C4C2511yescharacteristic
1054C22×C4C2514yes—
1055C22×C4C2514yes—
1056C22×C4C2512yes—
1057C22×C4C2514yes—
1058C22×C4C2512yes—
1059C22×C4C2512yes—
1060C22×C4C2512yes—
1061C22×C4C2512yes—
1062C22×C4C2512yes—
1063C22×C4C2511yescharacteristic
1064C22×C4C2511yescharacteristic
1065C22×C4C2511yescharacteristic
1066C22×C4C2511yescharacteristic
1067C22×C4C2511yescharacteristic
1068C22×C4C2511yescharacteristic
1069C4⋊C4—24no—
1070C4⋊C4—22no—
1071C4⋊C4—22no—
1072C4⋊C4—24no—
1073C4⋊C4—24no—
1074C4⋊C4—24no—
1075C4⋊C4—24no—
1076C4⋊C4—24no—
1077C4⋊C4—28no—
1078C4⋊C4—24no—
1079C4⋊C4—22no—
1080C4⋊C4—22no—
1081C4⋊C4—24no—
1082C4⋊C4—24no—
1083C4⋊C4—24no—
1084C4⋊C4—24no—
1085C4⋊C4—24no—
1086C4⋊C4—22no—
1087C4⋊C4—24no—
1088C4⋊C4—24no—
1089C4⋊C4—22no—
1090C4⋊C4—24no—
1091C4⋊C4—22no—
1092C4⋊C4—42no—
1093C4⋊C4—42no—
1094C4⋊C4—42no—
1095C4⋊C4—44no—
1096C4⋊C4—44no—
1097C4⋊C4—44no—
1098C4⋊C4—44no—
1099C4⋊C4—44no—
1100C4⋊C4—41no—
1101C4⋊C4—41no—
1102C4⋊C4—42no—
1103C4⋊C4—41no—
1104C4⋊C4—41no—
1105C4⋊C4—41no—
1106C4⋊C4—42no—
1107C4⋊C4—42no—
1108C4⋊C4—44no—
1109C4⋊C4—42no—
1110C4⋊C4—44no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—44no—
1114C4⋊C4—42no—
1115C4⋊C4—44no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—44no—
1119C4⋊C4—42no—
1120C4⋊C4—41no—
1121C4⋊C4—42no—
1122C4⋊C4—44no—
1123C4⋊C4—44no—
1124C4⋊C4—44no—
1125C4⋊C4—42no—
1126C4⋊C4—44no—
1127C4⋊C4—44no—
1128C4⋊C4—44no—
1129C4⋊C4—42no—
1130C4⋊C4—44no—
1131C4⋊C4—44no—
1132C4⋊C4—42no—
1133C4⋊C4—42no—
1134C4⋊C4—42no—
1135C4⋊C4—42no—
1136C4⋊C4—44no—
1137C4⋊C4—42no—
1138C4⋊C4—42no—
1139C4⋊C4—42no—
1140C4⋊C4—44no—
1141C4⋊C4—44no—
1142C4⋊C4—42no—
1143C22⋊C4—28no—
1144C22⋊C4—28no—
1145C22⋊C4—28no—
1146C22⋊C4—28no—
1147C22⋊C4—28no—
1148C22⋊C4—28no—
1149C22⋊C4—28no—
1150C22⋊C4—28no—
1151C22⋊C4—28no—
1152C22⋊C4—28no—
1153C22⋊C4—28no—
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—
1164C42—28no—
1165C42—24no—
1166C42—24no—
1167C42—24no—
1168C42—24no—
1169C42—24no—
1170C42—24no—
1171C42—24no—
1172C42—22no—
1173C42—24no—
1174C42—24no—
1175C42—22no—
1176C42—41no—
1177C42—42no—
1178C42—41no—
1179C42—42no—
1180C42—42no—
1181C42—44no—
1182C42—42no—
1183C42—44no—
1184C42—41no—
1185C42—42no—
1186C42—42no—
1187C42—44no—
1188C42—44no—
1189C42—44no—
1190C42—44no—
1191C42—42no—
1192C42C2×#4114yes—
1193C422−1+414yes—
1194C23—24no—
1195C23—24no—
1196C23—24no—
1197C23—24no—
1198C23—24no—
1199C23—24no—
1200C23C22×#4118yes—
1201C23C2611yescharacteristic
1202Q8—44no—
1203Q8—44no—
1204Q8—48no—
1205Q8—84no—
1206Q8—82no—
1207Q8—84no—
1208Q8—162no—
1209D4—216no—
1210D4—48no—
1211D4—48no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—24no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—24no—
1237C2×C4—24no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—21no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—24no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—21no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—24no—
1266C2×C4—24no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—24no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
1278C2×C4—21no—
1279C2×C4—24no—
1280C2×C4—24no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—24no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—88no—
1289C2×C4—88no—
1290C2×C4—88no—
1291C2×C4—88no—
1292C2×C4—164no—
1293C2×C4—164no—
1294C2×C4—164no—
1295C2×C4C22×#4112yes—
1296C2×C4C22×#4112yes—
1297C2×C4C22×#4112yes—
1298C2×C4C2×2−1+412yes—
1299C2×C4C2×2−1+412yes—
1300C2×C4C2×2−1+412yes—
1301C2×C4#58512yes—
1302C2×C4#58512yes—
1303C22—28no—
1304C22—28no—
1305C22—28no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22C23×#4111yescharacteristic
1311C22C22×2−1+411yescharacteristic
1312C22C2×#58511yescharacteristic
1313C22C2×#58511yescharacteristic
1314C22H(7,𝔽2)11yescharacteristic
1315C222−1+611yescharacteristic
1316C222−1+611yescharacteristic
1317C4—22no—
1318C4—22no—
1319C4—22no—
1320C4—22no—
1321C4—22no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—44no—
1328C4—42no—
1329C4—42no—
1330C4—42no—
1331C4—44no—
1332C4—41no—
1333C4—42no—
1334C4—42no—
1335C4—44no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—44no—
1341C4—42no—
1342C4—42no—
1343C4—44no—
1344C4#351514yes—
1345C2—48no—
1346C2C2×#351511yescharacteristic
1347C2#6284711yescharacteristic
1348C2#6288911yescharacteristic
1349C2#6296211yescharacteristic
1350C2#6296411yescharacteristic
1351C2#6299111yescharacteristic
1352C2#6306911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#127C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59565C2semidirect
3. #52274C2semidirect
4. #49468C2semidirect
5. #49131C2semidirect
6. #48587C2semidirect
7. #47261C2semidirect
8. #45946C2semidirect
9. #45383C2semidirect
10. #45221C2semidirect
12. #43223C2semidirect
13. #42639C2semidirect
14. #42511C2semidirect
15. #41554C2semidirect
16. #40080C2semidirect
17. #39629C2semidirect
19. #38788C2semidirect
20. #38472C2semidirect
21. #38230C2semidirect
22. #38229C2semidirect
23. #37162C2semidirect
24. #36286C2semidirect
25. #35961C2semidirect
26. #35632C2semidirect
27. #35187C2semidirect

Maximal subgroups

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

subgroupindex
#598272
#595652
#522742
#494682
#491312
#485872
#472612
#459462
#453832
#452212
#451372
#432232
#426392
#425112
#415542
#400802
#396292
#396282
#387882
#384722
#382302
#382292
#371622
#362862
#359612
#356322
#351872
#345002
#343312