Finite Group Databasebeta

← #7642208

Subgroups — #7642208

Order 512.

4338 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37435C212yesmaximal, complemented
2#37382C211yesmaximal, characteristic, complemented
3#37380C211yesmaximal, characteristic, complemented
4#37329C212yesmaximal, complemented
5#37328C212yesmaximal, complemented
6#37327C212yesmaximal, complemented
7#37287C212yesmaximal, complemented
8#37286C211yesmaximal, characteristic, complemented
9#37283C211yesmaximal, characteristic
10#37282C212yesmaximal, complemented
11#37032C214yesmaximal, complemented
12#37029C214yesmaximal, complemented
13#36990C214yesmaximal, complemented
14#36989C214yesmaximal, complemented
15#36838C214yesmaximal, complemented
16#36835C214yesmaximal, complemented
17#36784C214yesmaximal, complemented
18#36783C214yesmaximal, complemented
19#35343C211yesmaximal, characteristic, complemented
20#35302C212yesmaximal, complemented
21#35294C211yesmaximal, characteristic, complemented
22#35217C212yesmaximal, complemented
23#35216C212yesmaximal, complemented
24#35203C212yesmaximal, complemented
25#35193C212yesmaximal, complemented
26#34084C212yesmaximal, complemented
27#34048C211yesmaximal, characteristic, complemented
28C2×#529C2212yes—
29C22×#117C2211yescharacteristic
30#2868C2211yescharacteristic, complemented
31#2866C2214yes—
32#2866C2214yescomplemented
33#2863C2214yescomplemented
34#2861C2212yescomplemented
35#2860C2214yes—
36#2859C2211yescharacteristic, complemented
37#2859C2211yescharacteristic, complemented
38#2859C2212yescomplemented
39#2858C2211yescharacteristic, complemented
40#2855C2212yes—
41#2854C2212yes—
42#2853C2214yes—
43#2853C2214yescomplemented
44#2851C2214yescomplemented
45#2850C2214yes—
46#2848C2212yes—
47#2847C2212yes—
48#2803C2214yes—
49#2802C2214yescomplemented
50#2801C2214yes—
51#2800C2214yes—
52#2800C2214yescomplemented
53#2795C2214yes—
54#2793C2214yescomplemented
55#2793C2214yescomplemented
56#2791C2214yescomplemented
57#2790C2214yescomplemented
58#2787C2214yes—
59#2784C2214yes—
60#2783C2214yes—
61#2781C2214yescomplemented
62#2780C2214yescomplemented
63#2779C2214yes—
64#2779C2214yes—
65#2777C2214yescomplemented
66#2776C2214yescomplemented
67#2775C2214yescomplemented
68#2772C2214yes—
69#2772C2214yescomplemented
70#2768C2214yes—
71#2767C2214yescomplemented
72#2766C2214yescomplemented
73#2765C2214yes—
74#2765C2214yescomplemented
75#2765C2214yescomplemented
76#2761C2214yescomplemented
77#2757C2214yes—
78#2756C2214yes—
79#2753C2214yes—
80#2751C2214yes—
81#2750C2214yes—
82#2749C2214yes—
83#2746C2214yes—
84#2744C2214yes—
85#2743C2214yes—
86#2739C2214yes—
87#2739C2214yescomplemented
88#2737C2214yes—
89#2735C2214yes—
90#2731C2214yes—
91#2729C2214yescomplemented
92#2725C2214yes—
93#2725C2214yes—
94#2720C2214yescomplemented
95#2719C2214yescomplemented
96#2718C2214yes—
97#2718C2214yescomplemented
98#2716C2214yescomplemented
99#2715C2214yes—
100#2711C2214yes—
101#2708C2214yes—
102#2707C2214yescomplemented
103#2705C2214yes—
104#2701C2214yes—
105#2694C2214yes—
106#2693C2214yes—
107#2687C2214yes—
108#2685C2214yes—
109#2684C2214yes—
110#2678C2214yes—
111#2674C2214yes—
112#2655C2214yescomplemented
113#2654C2214yescomplemented
114#2653C2214yescomplemented
115#2652C2214yescomplemented
116#2651C2214yes—
117#2650C2214yes—
118#2649C2214yes—
119#2648C2214yes—
120#2629C2211yescharacteristic
121#2629C2211yescharacteristic
122#2629C2212yes—
123#2629C2212yes—
124#2628C2212yes—
125#2621C2211yescharacteristic
126#2620C2212yes—
127#2620C2212yes—
128#2620C2212yes—
129#2619C2211yescharacteristic
130#2609C2214yes—
131#2609C2214yes—
132#2602C2214yes—
133#2602C2214yes—
134#2601C2214yes—
135#2601C2214yes—
136#2601C2214yescomplemented
137#2601C2214yescomplemented
138#2595C2214yes—
139#2594C2214yes—
140#2588C2214yescomplemented
141#2587C2214yescomplemented
142#2579C2214yes—
143#2576C2214yescomplemented
144#2575C2214yescomplemented
145#2570C2214yescomplemented
146#2558C2214yes—
147#2557C2214yes—
148#2550C2214yescomplemented
149#2534C2214yes—
150#2533C2214yescomplemented
151#2532C2214yes—
152#2531C2214yes—
153#2530C2214yescomplemented
154#2514C2212yescomplemented
155#2513C2212yescomplemented
156#2512C2212yescomplemented
157#2511C2212yescomplemented
158#2509C2212yescomplemented
159#2508C2212yescomplemented
160#2507C2212yescomplemented
161#2506C2212yescomplemented
162#2497C2212yes—
163#2496C2212yes—
164#2495C2212yes—
165#2494C2212yes—
166#2492C2212yes—
167#2491C2212yes—
168#2490C2212yes—
169#2489C2212yes—
170#2479C2214yes—
171#2478C2214yescomplemented
172#2477C2214yescomplemented
173#2476C2214yes—
174#2454C2212yescomplemented
175#2453C2212yescomplemented
176#2452C2212yescomplemented
177#2451C2212yescomplemented
178#2448C2212yescomplemented
179#2447C2212yescomplemented
180#2446C2212yescomplemented
181#2445C2212yescomplemented
182#2441C2214yes—
183#2439C2214yes—
184#2429C2212yes—
185#2428C2212yes—
186#2427C2212yes—
187#2426C2212yes—
188#2423C2212yes—
189#2422C2212yes—
190#2421C2212yes—
191#2420C2212yes—
192#2413C2214yes—
193#2411C2214yes—
194#2335C2214yes—
195#2335C2214yes—
196#2334C2214yescomplemented
197#2334C2214yescomplemented
198#2331C2212yescomplemented
199#2330C2212yescomplemented
200#2330C2212yescomplemented
201#2330C2211yescharacteristic, complemented
202#2330C2211yescharacteristic, complemented
203#2328C2211yescharacteristic, complemented
204#2327C2211yescharacteristic, complemented
205#2326C2212yescomplemented
206#2326C2212yescomplemented
207#2326C2212yescomplemented
208#2324C2212yes—
209#2324C2212yes—
210#2324C2212yes—
211#2324C2212yes—
212#2323C2212yes—
213#2323C2212yes—
214#2323C2212yes—
215#2323C2212yes—
216#2314C2212yes—
217#2314C2212yes—
218#2314C2212yes—
219#2314C2212yes—
220#2313C2212yes—
221#2313C2212yes—
222#2312C2212yes—
223#2312C2212yes—
224#2298C2212yes—
225#2298C2212yes—
226#2298C2212yes—
227#2298C2212yes—
228#2298C2214yescomplemented
229#2296C2214yescomplemented
230#2295C2212yescomplemented
231#2293C2214yes—
232#2293C2212yescomplemented
233#2290C2214yes—
234#2285C2211yescharacteristic
235#2285C2211yescharacteristic
236#2285C2212yes—
237#2280C2211yescharacteristic
238#2280C2211yescharacteristic
239C42×Q8C2212yescomplemented
240C42×D4C2212yescomplemented
241C4×#117C2211yescharacteristic
242C4×#117C2211yescharacteristic
243C24×C4C2311yescharacteristic
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2312yes—
246C2×C4⋊Q8C2314yes—
247C2×#127C2311yescharacteristic
248#529—216no—
249C2×#126C2314yes—
250C2×#126C2314yes—
251C2×#126C2314yes—
252C2×#125C2312yes—
253C2×#125C2311yescharacteristic
254C2×#125C2311yescharacteristic
255C2×#125C2314yes—
256C2×#125C2314yes—
257C2×#124C2312yes—
258C2×#124C2312yes—
259C2×#124C2314yes—
260C2×#123C2314yes—
261C2×#123C2314yes—
262C2×#123C2314yes—
263C2×#123C2314yes—
264C2×C22⋊Q8C2312yes—
265C2×C22⋊Q8C2312yes—
266C2×C22⋊Q8C2312yes—
267C2×C22⋊Q8C2314yes—
268C2×#121C2312yes—
269C2×#121C2312yes—
270C2×#121C2312yes—
271C2×#121C2314yes—
272C2×#120C2314yes—
273C2×C4×Q8C2312yes—
274C2×C4×Q8C2312yes—
275C2×C4×Q8C2312yes—
276C2×C4×D4C2314yes—
277C2×C4×D4C2312yes—
278C2×C4×D4C2312yes—
279C2×C4×D4C2312yes—
280C2×#117—28no—
281C2×#117C2312yes—
282C2×#117C2312yes—
283C2×#117C2312yes—
284C2×#117C2314yes—
285C2×#117C2312yes—
286C2×#117C2311yescharacteristic
287C2×#117C2311yescharacteristic
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2314yes—
291C2×#117C2314yes—
292C22×C4⋊C4C2312yes—
293C22×C22⋊C4C2312yes—
294C22×C42C2311yescharacteristic
295C22×C42C2314yes—
296C22×C42C2311yescharacteristic
297#401C2314yes—
298#401C2314yes—
299#400C2314yes—
300#400C2314yes—
301#400C2314yes—
302#400C2314yes—
303#400C2314yes—
304#400C2314yes—
305#400C2314yes—
306#400C2314yes—
307#400C2314yes—
308#400C2314yes—
309#400C2314yes—
310#400C2314yes—
311#400C2314yes—
312#400C2314yes—
313#400C2314yes—
314#400C2314yes—
315#399C2314yes—
316#399C2314yes—
317#399C2314yes—
318#399C2314yes—
319#398C2314yes—
320#398C2314yes—
321#398C2314yes—
322#398C2314yes—
323#398C2314yes—
324#398C2314yes—
325#398C2314yes—
326#398C2314yes—
327#398C2314yes—
328#398C2314yes—
329#398C2314yes—
330#398C2314yes—
331#398C2314yes—
332#398C2314yes—
333#398C2314yes—
334#398C2314yes—
335#397C2314yes—
336#397C2314yes—
337#397C2314yes—
338#397C2314yes—
339#397C2314yes—
340#397C2314yes—
341#397C2314yes—
342#397C2314yes—
343#397C2314yes—
344#397C2314yes—
345#397C2314yes—
346#397C2314yes—
347#397C2314yes—
348#397C2314yes—
349#397C2314yes—
350#397C2314yes—
351#396C2314yes—
352#396C2314yes—
353#396C2314yes—
354#396C2314yes—
355#396C2314yes—
356#396C2314yes—
357#396C2314yes—
358#396C2314yes—
359#396C2314yes—
360#396C2314yes—
361#396C2314yes—
362#396C2314yes—
363#396C2314yes—
364#396C2314yes—
365#396C2314yes—
366#396C2314yes—
367#396C2314yes—
368#396C2314yes—
369#395C2314yes—
370#395C2314yes—
371#394C2314yes—
372#394C2314yes—
373#394C2314yes—
374#394C2314yes—
375#394C2314yes—
376#394C2314yes—
377#394C2314yes—
378#394C2314yes—
379#394C2314yes—
380#394C2314yes—
381#394C2314yes—
382#394C2314yes—
383#394C2314yes—
384#394C2314yes—
385#394C2314yes—
386#394C2314yes—
387#393C2314yes—
388#393C2314yes—
389#393C2314yes—
390#393C2314yes—
391#392C2314yes—
392#392C2314yes—
393#391C2312yes—
394#391C2312yes—
395#391C2312yes—
396#391C2312yes—
397#391C2312yes—
398#391C2312yes—
399#391C2314yes—
400#391C2314yes—
401#391C2314yes—
402#391C2314yes—
403#390C2312yes—
404#390C2312yes—
405#390C2314yes—
406#390C2314yes—
407#390C2314yes—
408#390C2312yes—
409#390C2312yes—
410#390C2314yes—
411#390C2312yes—
412#390C2312yes—
413#390C2314yes—
414#390C2314yes—
415#390C2314yes—
416#390C2314yes—
417#389C2314yes—
418#389C2314yes—
419#389C2312yes—
420#389C2312yes—
421#389C2314yes—
422#389C2314yes—
423#389C2314yes—
424#389C2314yes—
425#389C2312yes—
426#389C2312yes—
427#389C2312yes—
428#389C2312yes—
429#389C2312yes—
430#389C2312yes—
431#389C2314yes—
432#389C2314yes—
433#389C2314yes—
434#389C2314yes—
435#389C2314yes—
436#389C2314yes—
437#389C2312yes—
438#389C2312yes—
439#389C2312yes—
440#389C2312yes—
441#389C2314yes—
442#389C2314yes—
443#389C2314yes—
444#389C2314yes—
445#389C2314yes—
446#389C2314yes—
447#389C2314yes—
448#389C2314yes—
449#388C2312yes—
450#388C2312yes—
451#388C2312yes—
452#388C2312yes—
453#388C2312yes—
454#388C2312yes—
455#388C2312yes—
456#388C2312yes—
457#388C2312yes—
458#388C2312yes—
459#388C2312yes—
460#388C2312yes—
461#388C2312yes—
462#388C2312yes—
463#388C2312yes—
464#388C2312yes—
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#388C2314yes—
492#388C2314yes—
493#388C2314yes—
494#388C2314yes—
495#388C2314yes—
496#388C2314yes—
497#388C2314yes—
498#388C2314yes—
499#388C2314yes—
500#388C2314yes—
501#388C2314yes—
502#388C2314yes—
503#388C2314yes—
504#388C2314yes—
505#388C2314yes—
506#388C2314yes—
507#387C2312yes—
508#387C2312yes—
509#387C2312yes—
510#387C2312yes—
511#387C2312yes—
512#387C2312yes—
513#387C2312yes—
514#387C2312yes—
515#387C2312yes—
516#387C2312yes—
517#387C2312yes—
518#387C2312yes—
519#387C2312yes—
520#387C2312yes—
521#387C2312yes—
522#387C2312yes—
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#387C2314yes—
548#387C2314yes—
549#387C2314yes—
550#387C2314yes—
551#387C2314yes—
552#387C2314yes—
553#387C2314yes—
554#387C2314yes—
555#387C2314yes—
556#387C2314yes—
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#385C2314yes—
572#385C2314yes—
573#385C2314yes—
574#385C2314yes—
575#385C2314yes—
576#385C2314yes—
577#385C2314yes—
578#385C2314yes—
579#385C2314yes—
580#385C2314yes—
581#385C2314yes—
582#385C2314yes—
583#385C2314yes—
584#385C2314yes—
585#385C2314yes—
586#385C2314yes—
587#385C2314yes—
588#385C2314yes—
589#384C2312yes—
590#384C2311yescharacteristic
591#384C2311yescharacteristic
592#384C2314yes—
593#384C2312yes—
594#384C2312yes—
595#384C2312yes—
596#384C2311yescharacteristic
597#384C2311yescharacteristic
598#383C2314yes—
599#383C2314yes—
600#382C2311yescharacteristic
601#382C2312yes—
602#382C2311yescharacteristic
603#382C2314yes—
604#382C2314yes—
605#382C2314yes—
606#382C2314yes—
607#382C2311yescharacteristic
608#382C2311yescharacteristic
609#382C2312yes—
610#381C2311yescharacteristic
611#381C2312yes—
612#381C2311yescharacteristic
613#381C2314yes—
614#381C2314yes—
615#381C2314yes—
616#380C2312yes—
617#380C2312yes—
618#380C2312yes—
619#380C2312yes—
620#380C2312yes—
621#380C2312yes—
622#380C2312yes—
623#380C2312yes—
624#380C2312yes—
625#380C2312yes—
626#380C2312yes—
627#380C2312yes—
628#380C2314yes—
629#380C2312yes—
630#380C2312yes—
631#380C2314yes—
632#380C2314yes—
633#379C2312yes—
634#379C2311yescharacteristic
635#379C2311yescharacteristic
636#379C2314yes—
637C4×C4⋊C4C2312yes—
638C4×C4⋊C4C2312yes—
639C4×C4⋊C4C2312yes—
640C4×C4⋊C4C2312yes—
641C4×C4⋊C4C2314yes—
642C4×C4⋊C4C2314yes—
643C4×C4⋊C4C2312yes—
644C4×C4⋊C4C2312yes—
645C4×C4⋊C4C2312yes—
646C4×C4⋊C4C2312yes—
647C4×C4⋊C4C2312yes—
648C4×C4⋊C4C2312yes—
649C4×C4⋊C4C2314yes—
650C4×C4⋊C4C2314yes—
651C4×C4⋊C4C2314yes—
652C4×C4⋊C4C2312yes—
653C4×C4⋊C4C2312yes—
654C4×C4⋊C4C2312yes—
655C4×C4⋊C4C2312yes—
656C4×C22⋊C4C2312yes—
657C4×C22⋊C4C2312yes—
658C4×C22⋊C4C2312yes—
659C4×C22⋊C4C2312yes—
660C4×C22⋊C4C2314yes—
661C4×C22⋊C4C2314yes—
662C4×C22⋊C4C2314yes—
663C4×C22⋊C4C2314yes—
664C4×C22⋊C4C2312yes—
665C4×C22⋊C4C2312yes—
666C4×C22⋊C4C2312yes—
667C4×C22⋊C4C2312yes—
668#376C2312yes—
669#376C2311yescharacteristic
670#376C2311yescharacteristic
671#376C2314yes—
672C43C2311yescharacteristic
673C43C2311yescharacteristic
674C43C2314yes—
675C43C2312yes—
676C25C2411yescharacteristic
677C22×Q8C2412yes—
678C22×Q8C2414yes—
679C22×D4C2412yes—
680C22×D4C2414yes—
681C22×D4C2414yes—
682C22×D4C2414yes—
683C22×D4C2414yes—
684C23×C4—24no—
685C23×C4—42no—
686C23×C4—42no—
687C23×C4C2412yes—
688C23×C4C2411yescharacteristic
689C23×C4C2412yes—
690C23×C4C2411yescharacteristic
691C23×C4C2414yes—
692C23×C4C2412yes—
693C23×C4C2414yes—
694C23×C4C2414yes—
695C23×C4C2412yes—
696C4⋊Q8—44no—
697C4⋊Q8—42no—
698C4⋊Q8—84no—
699#127—42no—
700#126—216no—
701#126—84no—
702#126—84no—
703#125—28no—
704#125—42no—
705#125—42no—
706#125—84no—
707#125—84no—
708#124—28no—
709#124—44no—
710#124—84no—
711#123—216no—
712#123—84no—
713#123—84no—
714#123—84no—
715C22⋊Q8—28no—
716C22⋊Q8—44no—
717C22⋊Q8—44no—
718C22⋊Q8—84no—
719#121—28no—
720#121—44no—
721#121—44no—
722#121—84no—
723#120—84no—
724C4×Q8—28no—
725C4×Q8—44no—
726C4×Q8—44no—
727C4×D4—216no—
728C4×D4—28no—
729C4×D4—44no—
730C4×D4—44no—
731#117—28no—
732#117—28no—
733#117—28no—
734#117—28no—
735#117—216no—
736#117—42no—
737#117—42no—
738#117—42no—
739#117—42no—
740#117—84no—
741#117—84no—
742C2×C4⋊C4—28no—
743C2×C4⋊C4C2412yes—
744C2×C4⋊C4C2412yes—
745C2×C4⋊C4C2412yes—
746C2×C4⋊C4C2412yes—
747C2×C4⋊C4C2414yes—
748C2×C4⋊C4C2414yes—
749C2×C4⋊C4C2412yes—
750C2×C4⋊C4C2412yes—
751C2×C4⋊C4C2412yes—
752C2×C4⋊C4C2414yes—
753C2×C4⋊C4C2412yes—
754C2×C4⋊C4C2412yes—
755C2×C4⋊C4C2412yes—
756C2×C4⋊C4C2414yes—
757C2×C4⋊C4C2414yes—
758C2×C4⋊C4C2414yes—
759C2×C4⋊C4C2414yes—
760C2×C4⋊C4C2414yes—
761C2×C4⋊C4C2411yescharacteristic
762C2×C4⋊C4C2412yes—
763C2×C4⋊C4C2411yescharacteristic
764C2×C4⋊C4C2412yes—
765C2×C4⋊C4C2411yescharacteristic
766C2×C4⋊C4C2411yescharacteristic
767C2×C4⋊C4C2414yes—
768C2×C4⋊C4C2414yes—
769C2×C4⋊C4C2414yes—
770C2×C4⋊C4C2412yes—
771C2×C4⋊C4C2414yes—
772C2×C4⋊C4C2414yes—
773C2×C4⋊C4C2414yes—
774C2×C4⋊C4C2412yes—
775C2×C4⋊C4C2414yes—
776C2×C4⋊C4C2414yes—
777C2×C4⋊C4C2414yes—
778C2×C4⋊C4C2414yes—
779C2×C4⋊C4C2414yes—
780C2×C4⋊C4C2412yes—
781C2×C4⋊C4C2414yes—
782C2×C4⋊C4C2414yes—
783C2×C4⋊C4C2414yes—
784C2×C4⋊C4C2414yes—
785C2×C4⋊C4C2414yes—
786C2×C4⋊C4C2414yes—
787C2×C4⋊C4C2412yes—
788C2×C4⋊C4C2414yes—
789C2×C4⋊C4C2414yes—
790C2×C4⋊C4C2414yes—
791C2×C4⋊C4C2412yes—
792C2×C4⋊C4C2414yes—
793C2×C4⋊C4C2412yes—
794C2×C4⋊C4C2412yes—
795C2×C4⋊C4C2412yes—
796C2×C4⋊C4C2414yes—
797C2×C4⋊C4C2414yes—
798C2×C4⋊C4C2414yes—
799C2×C22⋊C4—28no—
800C2×C22⋊C4C2412yes—
801C2×C22⋊C4C2412yes—
802C2×C22⋊C4C2412yes—
803C2×C22⋊C4C2412yes—
804C2×C22⋊C4C2414yes—
805C2×C22⋊C4C2414yes—
806C2×C22⋊C4C2414yes—
807C2×C22⋊C4C2414yes—
808C2×C22⋊C4C2414yes—
809C2×C22⋊C4C2414yes—
810C2×C22⋊C4C2414yes—
811C2×C22⋊C4C2414yes—
812C2×C22⋊C4C2414yes—
813C2×C22⋊C4C2411yescharacteristic
814C2×C22⋊C4C2412yes—
815C2×C22⋊C4C2411yescharacteristic
816C2×C22⋊C4C2412yes—
817C2×C22⋊C4C2411yescharacteristic
818C2×C22⋊C4C2411yescharacteristic
819C2×C22⋊C4C2414yes—
820C2×C22⋊C4C2414yes—
821C2×C22⋊C4C2414yes—
822C2×C22⋊C4C2414yes—
823C2×C22⋊C4C2412yes—
824C2×C22⋊C4C2414yes—
825C2×C22⋊C4C2414yes—
826C2×C22⋊C4C2414yes—
827C2×C22⋊C4C2414yes—
828C2×C22⋊C4C2414yes—
829C2×C22⋊C4C2414yes—
830C2×C22⋊C4C2412yes—
831C2×C22⋊C4C2414yes—
832C2×C22⋊C4C2414yes—
833C2×C22⋊C4C2414yes—
834C2×C22⋊C4C2414yes—
835C2×C22⋊C4C2412yes—
836C2×C22⋊C4C2414yes—
837C2×C22⋊C4C2414yes—
838C2×C22⋊C4C2414yes—
839C2×C22⋊C4C2412yes—
840C2×C22⋊C4C2412yes—
841C2×C22⋊C4C2412yes—
842C2×C22⋊C4C2412yes—
843C2×C22⋊C4C2412yes—
844C2×C22⋊C4C2414yes—
845C2×C22⋊C4C2414yes—
846C2×C22⋊C4C2414yes—
847C2×C22⋊C4C2414yes—
848C2×C22⋊C4C2414yes—
849C2×C42—24no—
850C2×C42—84no—
851C2×C42#4118yes—
852C2×C42C2412yes—
853C2×C42C2411yescharacteristic
854C2×C42C2411yescharacteristic
855C2×C42C2412yes—
856C2×C42C2412yes—
857C2×C42C2414yes—
858C2×C42C2411yescharacteristic
859C2×C42C2411yescharacteristic
860C2×C42C2411yescharacteristic
861C2×C42C2411yescharacteristic
862C2×C42C2412yes—
863C2×C42C2414yes—
864C2×C42C2414yes—
865C2×C42C2414yes—
866C2×C42C2414yes—
867C2×C42C2414yes—
868C2×C42C2412yes—
869C2×C42C2414yes—
870C2×C42C2414yes—
871C2×C42C2412yes—
872C2×C42C2412yes—
873C2×C42C2412yes—
874C2×C42C2412yes—
875C2×C42C2412yes—
876C2×C42C2412yes—
877C2×C42C2414yes—
878C2×C42C2412yes—
879C2×C42C2411yescharacteristic
880C2×C42C2411yescharacteristic
881#95C2412yes—
882#95C2412yes—
883#95C2412yes—
884#95C2412yes—
885#95C2412yes—
886#95C2412yes—
887#95C2412yes—
888#95C2412yes—
889#95C2414yes—
890#95C2414yes—
891#95C2414yes—
892#95C2414yes—
893#95C2414yes—
894#95C2414yes—
895#95C2414yes—
896#95C2412yes—
897#95C2412yes—
898#95C2412yes—
899#95C2412yes—
900#95C2412yes—
901#95C2412yes—
902#95C2412yes—
903#95C2412yes—
904#95C2414yes—
905#95C2414yes—
906#95C2414yes—
907#95C2414yes—
908#95C2414yes—
909#95C2412yes—
910#95C2412yes—
911#95C2412yes—
912#95C2412yes—
913#95C2414yes—
914#95C2412yes—
915#95C2414yes—
916#95C2412yes—
917#95C2412yes—
918#95C2412yes—
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—
943#95C2414yes—
944#95C2414yes—
945C24—22no—
946C24—41no—
947C24—41no—
948C24—42no—
949C24—42no—
950C24C2512yes—
951C24C2514yes—
952C24C2511yescharacteristic
953C2×Q8—24no—
954C2×Q8—24no—
955C2×Q8—24no—
956C2×Q8—44no—
957C2×Q8—44no—
958C2×Q8—44no—
959C2×D4—28no—
960C2×D4—24no—
961C2×D4—24no—
962C2×D4—24no—
963C2×D4—44no—
964C2×D4—44no—
965C2×D4—44no—
966C2×D4—44no—
967C2×D4—44no—
968C2×D4—44no—
969C2×D4—44no—
970C2×D4—44no—
971C2×D4—44no—
972C2×D4—44no—
973C2×D4—44no—
974C22×C4—22no—
975C22×C4—22no—
976C22×C4—22no—
977C22×C4—24no—
978C22×C4—24no—
979C22×C4—24no—
980C22×C4—28no—
981C22×C4—24no—
982C22×C4—24no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—41no—
988C22×C4—41no—
989C22×C4—42no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—42no—
997C22×C4—44no—
998C22×C4—42no—
999C22×C4—416no—
1000C22×C4C2×#4114yes—
1001C22×C4C2×#4118yes—
1002C22×C4C2512yes—
1003C22×C4C2512yes—
1004C22×C4C2512yes—
1005C22×C4C2511yescharacteristic
1006C22×C4C2511yescharacteristic
1007C22×C4C2511yescharacteristic
1008C22×C4C2512yes—
1009C22×C4C2514yes—
1010C22×C4C2514yes—
1011C22×C4C2514yes—
1012C22×C4C2512yes—
1013C22×C4C2512yes—
1014C22×C4C2514yes—
1015C22×C4C2514yes—
1016C22×C4C2514yes—
1017C22×C4C2512yes—
1018C22×C4C2512yes—
1019C22×C4C2512yes—
1020C22×C4C2514yes—
1021C22×C4C2511yescharacteristic
1022C22×C4C2512yes—
1023C22×C4C2511yescharacteristic
1024C22×C4C2512yes—
1025C22×C4C2511yescharacteristic
1026C4⋊C4—24no—
1027C4⋊C4—24no—
1028C4⋊C4—24no—
1029C4⋊C4—24no—
1030C4⋊C4—28no—
1031C4⋊C4—28no—
1032C4⋊C4—24no—
1033C4⋊C4—28no—
1034C4⋊C4—24no—
1035C4⋊C4—28no—
1036C4⋊C4—24no—
1037C4⋊C4—24no—
1038C4⋊C4—24no—
1039C4⋊C4—24no—
1040C4⋊C4—44no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—44no—
1045C4⋊C4—44no—
1046C4⋊C4—42no—
1047C4⋊C4—44no—
1048C4⋊C4—41no—
1049C4⋊C4—42no—
1050C4⋊C4—41no—
1051C4⋊C4—41no—
1052C4⋊C4—42no—
1053C4⋊C4—41no—
1054C4⋊C4—44no—
1055C4⋊C4—44no—
1056C4⋊C4—44no—
1057C4⋊C4—44no—
1058C4⋊C4—44no—
1059C4⋊C4—44no—
1060C4⋊C4—44no—
1061C4⋊C4—44no—
1062C4⋊C4—44no—
1063C4⋊C4—42no—
1064C4⋊C4—44no—
1065C4⋊C4—42no—
1066C4⋊C4—44no—
1067C4⋊C4—44no—
1068C4⋊C4—44no—
1069C4⋊C4—44no—
1070C4⋊C4—44no—
1071C4⋊C4—44no—
1072C4⋊C4—44no—
1073C4⋊C4—42no—
1074C4⋊C4—44no—
1075C4⋊C4—44no—
1076C4⋊C4—44no—
1077C4⋊C4—44no—
1078C4⋊C4—42no—
1079C4⋊C4—44no—
1080C4⋊C4—44no—
1081C4⋊C4—44no—
1082C22⋊C4—28no—
1083C22⋊C4—24no—
1084C22⋊C4—24no—
1085C22⋊C4—24no—
1086C22⋊C4—24no—
1087C22⋊C4—28no—
1088C22⋊C4—28no—
1089C22⋊C4—28no—
1090C22⋊C4—28no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—44no—
1097C22⋊C4—42no—
1098C22⋊C4—44no—
1099C22⋊C4—44no—
1100C22⋊C4—41no—
1101C22⋊C4—42no—
1102C22⋊C4—41no—
1103C22⋊C4—41no—
1104C22⋊C4—42no—
1105C22⋊C4—41no—
1106C22⋊C4—44no—
1107C22⋊C4—44no—
1108C22⋊C4—44no—
1109C22⋊C4—44no—
1110C22⋊C4—44no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—44no—
1114C22⋊C4—44no—
1115C22⋊C4—44no—
1116C22⋊C4—42no—
1117C22⋊C4—44no—
1118C22⋊C4—44no—
1119C22⋊C4—44no—
1120C22⋊C4—44no—
1121C22⋊C4—42no—
1122C22⋊C4—44no—
1123C22⋊C4—44no—
1124C22⋊C4—44no—
1125C22⋊C4—44no—
1126C22⋊C4—44no—
1127C22⋊C4—44no—
1128C22⋊C4—42no—
1129C22⋊C4—44no—
1130C22⋊C4—42no—
1131C42—22no—
1132C42—22no—
1133C42—24no—
1134C42—28no—
1135C42—24no—
1136C42—24no—
1137C42—22no—
1138C42—22no—
1139C42—22no—
1140C42—22no—
1141C42—42no—
1142C42—44no—
1143C42—44no—
1144C42—44no—
1145C42—42no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—44no—
1150C42—42no—
1151C42—44no—
1152C42—44no—
1153C42—44no—
1154C42—42no—
1155C42—44no—
1156C42—42no—
1157C42C2×#4118yes—
1158C42C2×#4114yes—
1159C42C2×#4114yes—
1160C23—21no—
1161C23—21no—
1162C23—22no—
1163C23—22no—
1164C23—22no—
1165C23—24no—
1166C23—24no—
1167C23—22no—
1168C23—22no—
1169C23—24no—
1170C23—22no—
1171C23—24no—
1172C23—24no—
1173C23—22no—
1174C23—22no—
1175C23—24no—
1176C23—24no—
1177C23—22no—
1178C23—44no—
1179C23—84no—
1180C23—84no—
1181C23—82no—
1182C23—82no—
1183C23C22×#4112yes—
1184C23C2611yescharacteristic
1185Q8—48no—
1186Q8—164no—
1187D4—48no—
1188D4—88no—
1189D4—164no—
1190D4—164no—
1191D4—164no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—28no—
1199C2×C4—22no—
1200C2×C4—22no—
1201C2×C4—24no—
1202C2×C4—24no—
1203C2×C4—24no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—21no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—24no—
1219C2×C4—24no—
1220C2×C4—24no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—24no—
1227C2×C4—24no—
1228C2×C4—24no—
1229C2×C4—22no—
1230C2×C4—24no—
1231C2×C4—24no—
1232C2×C4—24no—
1233C2×C4—24no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—24no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—24no—
1248C2×C4—24no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—48no—
1256C2×C4—416no—
1257C2×C4—48no—
1258C2×C4—44no—
1259C2×C4—48no—
1260C2×C4—84no—
1261C2×C4—88no—
1262C2×C4—88no—
1263C2×C4C22×#4114yes—
1264C2×C4C22×#4112yes—
1265C2×C4C22×#4114yes—
1266C2×C4C22×#4112yes—
1267C2×C4#58512yes—
1268C2×C4#58512yes—
1269C22—24no—
1270C22—22no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—44no—
1275C22—44no—
1276C22—42no—
1277C22—42no—
1278C22—44no—
1279C22—44no—
1280C22—42no—
1281C22—42no—
1282C22—44no—
1283C22—42no—
1284C22—44no—
1285C22—42no—
1286C22—42no—
1287C22—44no—
1288C22—88no—
1289C22C23×#4111yescharacteristic
1290C22C2×#58511yescharacteristic
1291C22C2×#58511yescharacteristic
1292C22H(7,𝔽2)12yes—
1293C222−1+612yes—
1294C4—24no—
1295C4—24no—
1296C4—22no—
1297C4—44no—
1298C4—42no—
1299C4—42no—
1300C4—44no—
1301C4—42no—
1302C4—42no—
1303C4—44no—
1304C4—42no—
1305C4—44no—
1306C4—42no—
1307C4—41no—
1308C4—42no—
1309C4—44no—
1310C4—44no—
1311C4—41no—
1312C4—42no—
1313C4—41no—
1314C4—41no—
1315C4—42no—
1316C4—44no—
1317C4#345514yes—
1318C2—42no—
1319C2—84no—
1320C2—82no—
1321C2C2×#345511yescharacteristic
1322C2#6285612yes—
1323C2#6288212yes—
1324C2#6288311yescharacteristic
1325C2#6289011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#37283C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37435C2semidirect
2. #37382C2semidirect
3. #37380C2semidirect
4. #37329C2semidirect
5. #37328C2semidirect
6. #37327C2semidirect
7. #37287C2semidirect
8. #37286C2semidirect
10. #37282C2semidirect
11. #37032C2semidirect
12. #37029C2semidirect
13. #36990C2semidirect
14. #36989C2semidirect
15. #36838C2semidirect
16. #36835C2semidirect
17. #36784C2semidirect
18. #36783C2semidirect
19. #35343C2semidirect
20. #35302C2semidirect
21. #35294C2semidirect
22. #35217C2semidirect
23. #35216C2semidirect
24. #35203C2semidirect
25. #35193C2semidirect
26. #34084C2semidirect
27. #34048C2semidirect
30. #2868C22semidirect
32. #2866C22semidirect
33. #2863C22semidirect
34. #2861C22semidirect
36. #2859C22semidirect
37. #2859C22semidirect
38. #2859C22semidirect
39. #2858C22semidirect
43. #2853C22semidirect
44. #2851C22semidirect
49. #2802C22semidirect
52. #2800C22semidirect
54. #2793C22semidirect
55. #2793C22semidirect
56. #2791C22semidirect
57. #2790C22semidirect
61. #2781C22semidirect
62. #2780C22semidirect
65. #2777C22semidirect
66. #2776C22semidirect
67. #2775C22semidirect
69. #2772C22semidirect
71. #2767C22semidirect
72. #2766C22semidirect
74. #2765C22semidirect
75. #2765C22semidirect
76. #2761C22semidirect
87. #2739C22semidirect
91. #2729C22semidirect
94. #2720C22semidirect
95. #2719C22semidirect
97. #2718C22semidirect
98. #2716C22semidirect
102. #2707C22semidirect
112. #2655C22semidirect
113. #2654C22semidirect
114. #2653C22semidirect
115. #2652C22semidirect
136. #2601C22semidirect
137. #2601C22semidirect
140. #2588C22semidirect
141. #2587C22semidirect
143. #2576C22semidirect
144. #2575C22semidirect
145. #2570C22semidirect
148. #2550C22semidirect
150. #2533C22semidirect
153. #2530C22semidirect
154. #2514C22semidirect
155. #2513C22semidirect
156. #2512C22semidirect
157. #2511C22semidirect
158. #2509C22semidirect
159. #2508C22semidirect
160. #2507C22semidirect
161. #2506C22semidirect
171. #2478C22semidirect
172. #2477C22semidirect
174. #2454C22semidirect
175. #2453C22semidirect
176. #2452C22semidirect
177. #2451C22semidirect
178. #2448C22semidirect
179. #2447C22semidirect
180. #2446C22semidirect
181. #2445C22semidirect
196. #2334C22semidirect
197. #2334C22semidirect
198. #2331C22semidirect
199. #2330C22semidirect
200. #2330C22semidirect
201. #2330C22semidirect
202. #2330C22semidirect
203. #2328C22semidirect
204. #2327C22semidirect
205. #2326C22semidirect
206. #2326C22semidirect
207. #2326C22semidirect
228. #2298C22semidirect
229. #2296C22semidirect
230. #2295C22semidirect
232. #2293C22semidirect
239. C42×Q8C22semidirect
240. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#374352
#373822
#373802
#373292
#373282
#373272
#372872
#372862
#372832
#372822
#370322
#370292
#369902
#369892
#368382
#368352
#367842
#367832
#353432
#353022
#352942
#352172
#352162
#352032
#351932
#340842
#340482