Finite Group Databasebeta

← #7645794

Subgroups — #7645794

Order 512.

4316 conjugacy classes of subgroups.

The subgroup lattice has 1432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42328C214yesmaximal, complemented
2#42195C214yesmaximal, complemented
3#42192C214yesmaximal, complemented
4#42160C214yesmaximal, complemented
5#39758C211yesmaximal, characteristic, complemented
6#39757C211yesmaximal, characteristic, complemented
7#39731C212yesmaximal, complemented
8#39502C211yesmaximal, characteristic, complemented
9#39501C211yesmaximal, characteristic, complemented
10#39475C212yesmaximal, complemented
11#39187C211yesmaximal, characteristic, complemented
12#39186C211yesmaximal, characteristic, complemented
13#39153C212yesmaximal, complemented
14#38971C211yesmaximal, characteristic, complemented
15#38970C211yesmaximal, characteristic, complemented
16#38937C212yesmaximal, complemented
17#37495C212yesmaximal, complemented
18#37494C212yesmaximal, complemented
19#36998C214yesmaximal, complemented
20#36997C214yesmaximal, complemented
21#35460C214yesmaximal, complemented
22#35229C212yesmaximal, complemented
23#35228C212yesmaximal, complemented
24#35132C211yesmaximal, characteristic, complemented
25#35130C211yesmaximal, characteristic
26#35099C214yesmaximal, complemented
27#34972C211yesmaximal, characteristic, complemented
28#34971C211yesmaximal, characteristic, complemented
29#34224C211yesmaximal, characteristic, complemented
30C2×#2356C211yesmaximal, characteristic, complemented
31#34060C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2864C2211yescharacteristic
36#2864C2211yescharacteristic
37#2862C2211yescharacteristic
38#2859C2211yescharacteristic
39#2855C2214yes—
40#2854C2214yes—
41#2853C2214yes—
42#2853C2214yes—
43#2851C2212yes—
44#2850C2212yes—
45#2833C2214yes—
46#2832C2214yes—
47#2831C2214yes—
48#2831C2214yes—
49#2810C2214yes—
50#2809C2214yes—
51#2808C2214yes—
52#2805C2214yes—
53#2803C2214yes—
54#2802C2214yes—
55#2800C2214yes—
56#2798C2214yes—
57#2797C2214yes—
58#2794C2214yes—
59#2793C2214yes—
60#2791C2214yes—
61#2790C2214yes—
62#2789C2214yes—
63#2788C2214yes—
64#2787C2214yes—
65#2787C2214yes—
66#2787C2214yes—
67#2786C2214yes—
68#2784C2214yes—
69#2783C2214yes—
70#2781C2214yes—
71#2776C2214yes—
72#2775C2214yes—
73#2774C2214yes—
74#2771C2214yes—
75#2770C2214yes—
76#2767C2214yes—
77#2759C2214yes—
78#2750C2214yes—
79#2745C2214yes—
80#2744C2214yes—
81#2666C2214yes—
82#2666C2214yes—
83#2665C2214yes—
84#2655C2214yes—
85#2654C2214yes—
86#2653C2214yes—
87#2651C2214yes—
88#2650C2214yes—
89#2650C2214yes—
90#2646C2214yes—
91#2645C2212yes—
92#2645C2212yes—
93#2643C2214yes—
94#2643C2214yes—
95#2642C2212yes—
96#2640C2212yes—
97#2639C2214yes—
98#2637C2212yes—
99#2636C2212yes—
100#2625C2212yes—
101#2625C2212yes—
102#2621C2212yes—
103#2620C2212yes—
104#2612C2214yes—
105#2609C2214yes—
106#2604C2214yes—
107#2599C2214yes—
108#2581C2211yescharacteristic
109#2581C2211yescharacteristic
110#2581C2211yescharacteristic
111#2580C2211yescharacteristic
112#2578C2214yes—
113#2577C2214yes—
114#2573C2214yes—
115#2572C2214yes—
116#2570C2212yes—
117#2565C2211yescharacteristic
118#2565C2211yescharacteristic
119#2550C2212yes—
120#2545C2211yescharacteristic
121#2545C2211yescharacteristic
122#2536C2211yescharacteristic
123#2536C2211yescharacteristic
124#2536C2211yescharacteristic
125#2535C2211yescharacteristic
126#2533C2214yes—
127#2533C2214yes—
128#2533C2214yes—
129#2532C2214yes—
130#2532C2214yes—
131#2532C2214yes—
132#2531C2214yes—
133#2531C2214yes—
134#2530C2214yes—
135#2530C2214yes—
136#2529C2214yes—
137#2529C2214yes—
138#2528C2214yes—
139#2528C2214yes—
140#2527C2214yes—
141#2527C2214yes—
142#2526C2214yes—
143#2526C2214yes—
144#2525C2214yes—
145#2525C2214yes—
146#2524C2214yes—
147#2524C2214yes—
148#2523C2214yes—
149#2522C2214yes—
150#2520C2214yes—
151#2518C2214yes—
152#2516C2214yes—
153#2515C2214yes—
154#2514C2212yes—
155#2514C2214yes—
156#2513C2212yes—
157#2511C2212yes—
158#2511C2212yes—
159#2510C2214yes—
160#2510C2214yes—
161#2509C2212yes—
162#2507C2212yes—
163#2505C2214yes—
164#2503C2211yescharacteristic
165#2501C2211yescharacteristic
166#2498C2212yes—
167#2497C2212yes—
168#2495C2214yes—
169#2494C2212yes—
170#2493C2214yes—
171#2493C2214yes—
172#2492C2212yes—
173#2492C2212yes—
174#2490C2212yes—
175#2489C2212yes—
176#2488C2214yes—
177#2486C2212yes—
178#2484C2212yes—
179#2450C2214yes—
180#2447C2212yes—
181#2446C2212yes—
182#2444C2214yes—
183#2442C2212yes—
184#2440C2212yes—
185#2438C2214yes—
186#2436C2211yescharacteristic
187#2434C2211yescharacteristic
188#2430C2212yes—
189#2429C2212yes—
190#2427C2212yes—
191#2425C2214yes—
192#2419C2214yes—
193#2417C2212yes—
194#2416C2212yes—
195#2413C2214yes—
196#2409C2212yes—
197#2406C2212yes—
198#2399C2212yes—
199#2398C2212yes—
200#2396C2214yes—
201#2373C2214yes—
202#2370C2212yes—
203#2367C2212yes—
204#2357C2211yescharacteristic
205#2356C2211yescharacteristic
206#2356C2211yescharacteristic
207#2356C2212yes—
208#2356C2212yes—
209#2356C2211yescharacteristic
210#2356C2211yescharacteristic
211#2356C2214yes—
212#2356C2212yes—
213#2356C2212yes—
214#2356C2211yescharacteristic
215#2351C2211yescharacteristic
216#2349C2211yescharacteristic
217#2347C2212yes—
218#2343C2212yes—
219#2331C2212yes—
220#2330C2212yes—
221#2329C2214yes—
222#2325C2214yes—
223#2324C2212yes—
224#2323C2212yes—
225#2322C2214yes—
226#2320C2212yes—
227#2320C2212yes—
228#2319C2212yes—
229#2319C2212yes—
230#2318C2212yes—
231#2318C2212yes—
232#2318C2212yes—
233#2317C2212yes—
234#2314C2212yes—
235#2314C2212yes—
236#2314C2212yes—
237#2314C2212yes—
238#2311C2212yes—
239C4×C4⋊Q8C2211yescharacteristic
240C4×C4⋊Q8C2211yescharacteristic
241C4×#124C2211yescharacteristic
242C4×#124C2211yescharacteristic
243C4×C22⋊Q8C2212yes—
244C4×C22⋊Q8C2212yes—
245C4×C22⋊Q8C2212yes—
246C4×#123C2214yes—
247C4×#123C2214yes—
248C4×#121C2212yes—
249#2295C2211yescharacteristic
250#2295C2211yescharacteristic
251C2×#391C2212yes—
252#2293C2211yescharacteristic
253#2293C2211yescharacteristic
254#2290C2212yes—
255#2290C2212yes—
256C2×#387C2214yes—
257#2285C2212yes—
258#2283C2212yes—
259#2283C2211yescharacteristic
260C2×#383C2212yes—
261C2×#382C2211yescharacteristic
262#2275C2212yes—
263C4×#117C2211yescharacteristic
264C2×C4×C4⋊C4C2211yescharacteristic
265C2×C4×C4⋊C4C2212yes—
266C2×#376C2212yes—
267C22×#41C2311yescharacteristic
268C23×Q8C2311yescharacteristic
269C2×C4⋊Q8C2311yescharacteristic
270C2×C4⋊Q8C2311yescharacteristic
271C2×C4⋊Q8C2312yes—
272#529—28no—
273C2×#126C2312yes—
274C2×#125C2311yescharacteristic
275C2×#125C2312yes—
276C2×#124C2311yescharacteristic
277C2×#124C2311yescharacteristic
278C2×#124C2311yescharacteristic
279C2×#123C2312yes—
280C2×#123C2314yes—
281C2×#123C2314yes—
282C2×C22⋊Q8C2311yescharacteristic
283C2×C22⋊Q8C2312yes—
284C2×C22⋊Q8C2314yes—
285C2×C22⋊Q8C2312yes—
286C2×C22⋊Q8C2312yes—
287C2×#121C2311yescharacteristic
288C2×#121C2312yes—
289C2×#121C2314yes—
290C4×#41—28no—
291C2×C4×Q8—28no—
292C2×C4×Q8C2311yescharacteristic
293C2×C4×Q8C2311yescharacteristic
294C2×C4×Q8C2311yescharacteristic
295C2×C4×Q8C2311yescharacteristic
296C2×C4×Q8C2311yescharacteristic
297C2×C4×Q8C2311yescharacteristic
298C2×C4×Q8C2311yescharacteristic
299C2×C4×Q8C2312yes—
300C2×C4×Q8C2312yes—
301C2×C4×Q8C2312yes—
302C2×C4×D4C2312yes—
303C2×C4×D4C2312yes—
304C2×C4×D4C2311yescharacteristic
305C2×C4×D4C2311yescharacteristic
306C2×C4×D4C2312yes—
307C2×C4×D4C2311yescharacteristic
308C2×C4×D4C2312yes—
309C2×C4×D4C2314yes—
310C2×#117C2312yes—
311C2×#117C2311yescharacteristic
312C2×#117C2312yes—
313C2×#117C2312yes—
314C2×#117C2312yes—
315C2×#117C2312yes—
316C22×C4⋊C4C2312yes—
317C22×C4⋊C4C2311yescharacteristic
318C22×C4⋊C4C2312yes—
319C22×C4⋊C4C2312yes—
320C22×C42C2312yes—
321C22×C42C2312yes—
322C22×C42C2314yes—
323C22×C42C2312yes—
324C22×C42C2311yescharacteristic
325#401C2314yes—
326#401C2314yes—
327#401C2314yes—
328#401C2314yes—
329#400C2314yes—
330#400C2314yes—
331#400C2314yes—
332#400C2314yes—
333#400C2314yes—
334#400C2314yes—
335#400C2314yes—
336#400C2314yes—
337#400C2314yes—
338#400C2314yes—
339#400C2314yes—
340#400C2314yes—
341#400C2314yes—
342#400C2314yes—
343#400C2314yes—
344#400C2314yes—
345#400C2312yes—
346#400C2312yes—
347#400C2312yes—
348#400C2314yes—
349#400C2314yes—
350#400C2314yes—
351#400C2314yes—
352#400C2314yes—
353#400C2314yes—
354#400C2314yes—
355#400C2314yes—
356#400C2314yes—
357#400C2314yes—
358#400C2314yes—
359#399C2312yes—
360#399C2314yes—
361#398C2314yes—
362#398C2314yes—
363#398C2314yes—
364#398C2314yes—
365#398C2314yes—
366#398C2314yes—
367#398C2314yes—
368#398C2314yes—
369#398C2314yes—
370#398C2314yes—
371#398C2314yes—
372#398C2314yes—
373#398C2314yes—
374#398C2314yes—
375#398C2312yes—
376#398C2314yes—
377#398C2312yes—
378#398C2312yes—
379#398C2314yes—
380#397C2314yes—
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#397C2312yes—
395#397C2314yes—
396#397C2314yes—
397#397C2314yes—
398#396C2314yes—
399#396C2314yes—
400#396C2314yes—
401#396C2314yes—
402#396C2314yes—
403#396C2314yes—
404#396C2314yes—
405#396C2314yes—
406#395C2314yes—
407#395C2314yes—
408#395C2314yes—
409#395C2312yes—
410#395C2312yes—
411#395C2312yes—
412#395C2314yes—
413#394C2314yes—
414#394C2314yes—
415#394C2314yes—
416#394C2314yes—
417#394C2314yes—
418#394C2312yes—
419#394C2312yes—
420#394C2312yes—
421#393C2314yes—
422#393C2314yes—
423#393C2314yes—
424#393C2314yes—
425#393C2314yes—
426#393C2312yes—
427#393C2314yes—
428#392C2312yes—
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2312yes—
436#391C2312yes—
437#391C2314yes—
438#391C2314yes—
439#391C2314yes—
440#391C2312yes—
441#391C2312yes—
442#391C2312yes—
443#391C2314yes—
444#391C2314yes—
445#391C2314yes—
446#391C2314yes—
447#391C2314yes—
448#391C2312yes—
449#391C2312yes—
450#391C2312yes—
451#391C2312yes—
452#391C2312yes—
453#391C2314yes—
454#390C2312yes—
455#390C2312yes—
456#390C2311yescharacteristic
457#390C2312yes—
458#390C2311yescharacteristic
459#390C2314yes—
460#390C2314yes—
461#390C2312yes—
462#389C2314yes—
463#389C2314yes—
464#389C2312yes—
465#389C2312yes—
466#389C2312yes—
467#389C2312yes—
468#389C2312yes—
469#389C2312yes—
470#389C2314yes—
471#389C2312yes—
472#389C2312yes—
473#389C2312yes—
474#389C2314yes—
475#389C2314yes—
476#389C2314yes—
477#389C2312yes—
478#389C2312yes—
479#389C2312yes—
480#389C2314yes—
481#389C2314yes—
482#389C2314yes—
483#389C2314yes—
484#389C2314yes—
485#389C2314yes—
486#389C2312yes—
487#389C2312yes—
488#389C2314yes—
489#388C2312yes—
490#388C2312yes—
491#388C2312yes—
492#388C2312yes—
493#388C2312yes—
494#388C2312yes—
495#388C2312yes—
496#388C2312yes—
497#388C2314yes—
498#388C2314yes—
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#388C2314yes—
518#388C2314yes—
519#388C2314yes—
520#388C2314yes—
521#388C2314yes—
522#388C2314yes—
523#388C2314yes—
524#388C2314yes—
525#388C2314yes—
526#388C2314yes—
527#388C2314yes—
528#387C2314yes—
529#387C2314yes—
530#387C2312yes—
531#387C2312yes—
532#387C2312yes—
533#387C2312yes—
534#387C2312yes—
535#387C2312yes—
536#387C2312yes—
537#387C2312yes—
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#387C2314yes—
558#387C2314yes—
559#387C2314yes—
560#387C2314yes—
561#387C2314yes—
562#387C2314yes—
563#387C2314yes—
564#387C2314yes—
565#387C2314yes—
566#387C2314yes—
567#387C2314yes—
568#387C2314yes—
569#387C2314yes—
570#387C2314yes—
571#387C2314yes—
572#387C2314yes—
573#387C2314yes—
574#387C2314yes—
575#387C2314yes—
576#387C2314yes—
577#387C2314yes—
578#387C2314yes—
579#387C2314yes—
580#387C2314yes—
581#387C2314yes—
582#387C2314yes—
583#387C2314yes—
584#387C2314yes—
585#386C2312yes—
586#386C2312yes—
587#386C2312yes—
588#386C2312yes—
589#386C2314yes—
590#386C2314yes—
591#386C2314yes—
592#386C2314yes—
593#386C2314yes—
594#386C2314yes—
595#386C2314yes—
596#386C2314yes—
597#386C2314yes—
598#386C2314yes—
599#385C2312yes—
600#385C2312yes—
601#385C2312yes—
602#385C2312yes—
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#384C2311yescharacteristic
618#384C2311yescharacteristic
619#384C2312yes—
620#384C2312yes—
621#384C2312yes—
622#383C2314yes—
623#383C2314yes—
624#383C2314yes—
625#383C2312yes—
626#383C2312yes—
627#383C2312yes—
628#383C2312yes—
629#383C2312yes—
630#383C2312yes—
631#383C2312yes—
632#383C2312yes—
633#383C2314yes—
634#382C2311yescharacteristic
635#382C2311yescharacteristic
636#382C2312yes—
637#382C2312yes—
638#382C2312yes—
639#382C2312yes—
640#382C2312yes—
641#382C2312yes—
642#382C2312yes—
643#382C2314yes—
644#382C2311yescharacteristic
645#382C2311yescharacteristic
646#382C2311yescharacteristic
647#382C2311yescharacteristic
648#382C2312yes—
649#382C2312yes—
650#382C2314yes—
651#381C2312yes—
652#381C2314yes—
653#381C2312yes—
654#381C2312yes—
655#381C2312yes—
656#381C2314yes—
657#381C2314yes—
658#381C2314yes—
659#380C2312yes—
660#380C2312yes—
661#380C2312yes—
662#380C2312yes—
663#380C2312yes—
664#380C2312yes—
665#380C2312yes—
666#380C2312yes—
667#380C2312yes—
668#380C2312yes—
669#380C2314yes—
670#380C2312yes—
671#380C2314yes—
672#380C2314yes—
673#380C2312yes—
674#380C2314yes—
675C4×C4⋊C4C2314yes—
676C4×C4⋊C4C2314yes—
677C4×C4⋊C4C2311yescharacteristic
678C4×C4⋊C4C2311yescharacteristic
679C4×C4⋊C4C2311yescharacteristic
680C4×C4⋊C4C2311yescharacteristic
681C4×C4⋊C4C2312yes—
682C4×C4⋊C4C2312yes—
683C4×C4⋊C4C2312yes—
684C4×C4⋊C4C2312yes—
685C4×C4⋊C4C2312yes—
686C4×C4⋊C4C2312yes—
687C4×C4⋊C4C2314yes—
688C4×C4⋊C4C2312yes—
689C4×C4⋊C4C2312yes—
690C4×C4⋊C4C2312yes—
691C4×C4⋊C4C2312yes—
692C4×C4⋊C4C2314yes—
693C4×C4⋊C4C2311yescharacteristic
694C4×C4⋊C4C2311yescharacteristic
695C4×C4⋊C4C2312yes—
696C4×C4⋊C4C2314yes—
697C4×C4⋊C4C2314yes—
698C4×C4⋊C4C2314yes—
699C4×C4⋊C4C2314yes—
700C4×C4⋊C4C2312yes—
701C4×C4⋊C4C2312yes—
702C4×C22⋊C4C2314yes—
703C4×C22⋊C4C2314yes—
704C4×C22⋊C4C2314yes—
705C4×C22⋊C4C2312yes—
706C4×C22⋊C4C2312yes—
707C4×C22⋊C4C2314yes—
708C4×C22⋊C4C2314yes—
709C4×C22⋊C4C2312yes—
710C4×C22⋊C4C2314yes—
711C4×C22⋊C4C2314yes—
712C4×C22⋊C4C2312yes—
713C4×C22⋊C4C2312yes—
714C4×C22⋊C4C2311yescharacteristic
715C4×C22⋊C4C2311yescharacteristic
716#376C2312yes—
717#376C2312yes—
718#376C2312yes—
719#376C2312yes—
720#376C2312yes—
721#376C2314yes—
722#376C2312yes—
723#376C2314yes—
724#376C2312yes—
725#376C2312yes—
726#376C2312yes—
727C2×#95C2311yescharacteristic
728C2×#95C2311yescharacteristic
729C2×#95C2312yes—
730C2×#95C2312yes—
731C2×#95C2314yes—
732C2×#95C2314yes—
733C2×#95C2312yes—
734C2×#95C2314yes—
735C43C2311yescharacteristic
736C43C2311yescharacteristic
737C2×#41—24no—
738C2×#41—44no—
739C22×Q8—24no—
740C22×Q8—42no—
741C22×Q8—42no—
742C22×Q8C2411yescharacteristic
743C22×Q8C2411yescharacteristic
744C22×Q8C2411yescharacteristic
745C22×Q8C2412yes—
746C22×Q8C2411yescharacteristic
747C22×Q8C2414yes—
748C22×D4C2412yes—
749C22×D4C2411yescharacteristic
750C22×D4C2412yes—
751C22×D4C2411yescharacteristic
752C22×D4C2414yes—
753C23×C4C2412yes—
754C23×C4C2412yes—
755C23×C4C2411yescharacteristic
756C23×C4C2411yescharacteristic
757C23×C4C2412yes—
758C23×C4C2414yes—
759C23×C4C2412yes—
760C23×C4C2412yes—
761C23×C4C2412yes—
762C23×C4C2412yes—
763C23×C4C2412yes—
764C23×C4C2414yes—
765C23×C4C2411yescharacteristic
766C4⋊Q8—44no—
767C4⋊Q8—42no—
768C4⋊Q8—42no—
769#126—28no—
770#125—24no—
771#125—44no—
772#124—24no—
773#124—42no—
774#124—42no—
775#123—28no—
776#123—48no—
777#123—48no—
778C22⋊Q8—24no—
779C22⋊Q8—48no—
780C22⋊Q8—44no—
781C22⋊Q8—44no—
782C22⋊Q8—44no—
783#121—24no—
784#121—44no—
785#121—48no—
786C4×Q8—24no—
787C4×Q8—24no—
788C4×Q8—28no—
789C4×Q8—24no—
790C4×Q8—24no—
791C4×Q8—28no—
792C4×Q8—24no—
793C4×Q8—24no—
794C4×Q8—24no—
795C4×Q8—44no—
796C4×D4—28no—
797C4×D4—28no—
798C4×D4—28no—
799C4×D4—24no—
800C4×D4—24no—
801C4×D4—24no—
802C4×D4—44no—
803C4×D4—48no—
804#117—24no—
805#117—28no—
806#117—28no—
807#117—44no—
808#117—44no—
809#117—44no—
810C2×C4⋊C4—24no—
811C2×C4⋊C4—28no—
812C2×C4⋊C4—44no—
813C2×C4⋊C4—44no—
814C2×C4⋊C4C2411yescharacteristic
815C2×C4⋊C4C2411yescharacteristic
816C2×C4⋊C4C2412yes—
817C2×C4⋊C4C2412yes—
818C2×C4⋊C4C2412yes—
819C2×C4⋊C4C2412yes—
820C2×C4⋊C4C2412yes—
821C2×C4⋊C4C2412yes—
822C2×C4⋊C4C2412yes—
823C2×C4⋊C4C2412yes—
824C2×C4⋊C4C2412yes—
825C2×C4⋊C4C2411yescharacteristic
826C2×C4⋊C4C2411yescharacteristic
827C2×C4⋊C4C2412yes—
828C2×C4⋊C4C2412yes—
829C2×C4⋊C4C2412yes—
830C2×C4⋊C4C2411yescharacteristic
831C2×C4⋊C4C2412yes—
832C2×C4⋊C4C2411yescharacteristic
833C2×C4⋊C4C2412yes—
834C2×C4⋊C4C2412yes—
835C2×C4⋊C4C2412yes—
836C2×C4⋊C4C2412yes—
837C2×C4⋊C4C2414yes—
838C2×C4⋊C4C2412yes—
839C2×C4⋊C4C2412yes—
840C2×C4⋊C4C2412yes—
841C2×C4⋊C4C2412yes—
842C2×C4⋊C4C2412yes—
843C2×C4⋊C4C2412yes—
844C2×C4⋊C4C2412yes—
845C2×C4⋊C4C2412yes—
846C2×C4⋊C4C2414yes—
847C2×C4⋊C4C2414yes—
848C2×C4⋊C4C2414yes—
849C2×C4⋊C4C2414yes—
850C2×C4⋊C4C2414yes—
851C2×C4⋊C4C2414yes—
852C2×C4⋊C4C2414yes—
853C2×C4⋊C4C2414yes—
854C2×C4⋊C4C2414yes—
855C2×C4⋊C4C2414yes—
856C2×C4⋊C4C2414yes—
857C2×C4⋊C4C2414yes—
858C2×C4⋊C4C2414yes—
859C2×C4⋊C4C2414yes—
860C2×C4⋊C4C2414yes—
861C2×C4⋊C4C2414yes—
862C2×C4⋊C4C2414yes—
863C2×C4⋊C4C2414yes—
864C2×C4⋊C4C2412yes—
865C2×C4⋊C4C2412yes—
866C2×C4⋊C4C2412yes—
867C2×C4⋊C4C2412yes—
868C2×C4⋊C4C2414yes—
869C2×C4⋊C4C2414yes—
870C2×C4⋊C4C2414yes—
871C2×C4⋊C4C2414yes—
872C2×C4⋊C4C2414yes—
873C2×C22⋊C4C2412yes—
874C2×C22⋊C4C2412yes—
875C2×C22⋊C4C2412yes—
876C2×C22⋊C4C2412yes—
877C2×C22⋊C4C2412yes—
878C2×C22⋊C4C2412yes—
879C2×C22⋊C4C2412yes—
880C2×C22⋊C4C2412yes—
881C2×C22⋊C4C2414yes—
882C2×C22⋊C4C2412yes—
883C2×C22⋊C4C2412yes—
884C2×C22⋊C4C2412yes—
885C2×C22⋊C4C2412yes—
886C2×C22⋊C4C2412yes—
887C2×C22⋊C4C2412yes—
888C2×C22⋊C4C2414yes—
889C2×C22⋊C4C2414yes—
890C2×C22⋊C4C2414yes—
891C2×C22⋊C4C2414yes—
892C2×C22⋊C4C2414yes—
893C2×C22⋊C4C2414yes—
894C2×C22⋊C4C2414yes—
895C2×C22⋊C4C2414yes—
896C2×C22⋊C4C2414yes—
897C2×C22⋊C4C2414yes—
898C2×C22⋊C4C2414yes—
899C2×C22⋊C4C2414yes—
900C2×C22⋊C4C2414yes—
901C2×C22⋊C4C2414yes—
902C2×C22⋊C4C2412yes—
903C2×C22⋊C4C2412yes—
904C2×C22⋊C4C2412yes—
905C2×C22⋊C4C2412yes—
906C2×C22⋊C4C2414yes—
907C2×C22⋊C4C2414yes—
908C2×C22⋊C4C2414yes—
909C2×C42—28no—
910C2×C42—28no—
911C2×C42—44no—
912C2×C42—48no—
913C2×C42#4118yes—
914C2×C42C2411yescharacteristic
915C2×C42C2411yescharacteristic
916C2×C42C2412yes—
917C2×C42C2412yes—
918C2×C42C2412yes—
919C2×C42C2412yes—
920C2×C42C2412yes—
921C2×C42C2412yes—
922C2×C42C2412yes—
923C2×C42C2412yes—
924C2×C42C2412yes—
925C2×C42C2412yes—
926C2×C42C2411yescharacteristic
927C2×C42C2411yescharacteristic
928C2×C42C2412yes—
929C2×C42C2412yes—
930C2×C42C2414yes—
931C2×C42C2414yes—
932C2×C42C2412yes—
933C2×C42C2412yes—
934C2×C42C2414yes—
935C2×C42C2414yes—
936C2×C42C2414yes—
937C2×C42C2414yes—
938C2×C42C2414yes—
939C2×C42C2412yes—
940C2×C42C2414yes—
941C2×C42C2412yes—
942C2×C42C2411yescharacteristic
943C2×C42C2411yescharacteristic
944C2×C42C2411yescharacteristic
945C2×C42C2411yescharacteristic
946#95C2411yescharacteristic
947#95C2411yescharacteristic
948#95C2412yes—
949#95C2411yescharacteristic
950#95C2412yes—
951#95C2414yes—
952#95C2412yes—
953#95C2414yes—
954#95C2414yes—
955#95C2414yes—
956#95C2414yes—
957#95C2412yes—
958#95C2411yescharacteristic
959#95C2412yes—
960#95C2414yes—
961#95C2414yes—
962#95C2414yes—
963#95C2414yes—
964#95C2414yes—
965#95C2414yes—
966#95C2414yes—
967#95C2414yes—
968#95C2412yes—
969#95C2412yes—
970#95C2414yes—
971#95C2414yes—
972#95C2412yes—
973#95C2414yes—
974#95C2412yes—
975#95C2414yes—
976#95C2412yes—
977#95C2412yes—
978#95C2412yes—
979#95C2412yes—
980#95C2412yes—
981#95C2412yes—
982#95C2412yes—
983#95C2412yes—
984#95C2412yes—
985#95C2412yes—
986#95C2412yes—
987#95C2412yes—
988#95C2412yes—
989#95C2412yes—
990#95C2414yes—
991#95C2414yes—
992#95C2414yes—
993#95C2414yes—
994#95C2412yes—
995#95C2412yes—
996#95C2412yes—
997#95C2414yes—
998#95C2414yes—
999#95C2414yes—
1000#95C2414yes—
1001#95C2414yes—
1002#95C2412yes—
1003#95C2414yes—
1004#95C2414yes—
1005#95C2412yes—
1006#95C2412yes—
1007#95C2412yes—
1008#95C2414yes—
1009#95C2414yes—
1010#95C2414yes—
1011#95C2414yes—
1012#95C2414yes—
1013#95C2414yes—
1014#95C2414yes—
1015#95C2414yes—
1016#95C2414yes—
1017#95C2414yes—
1018#95C2414yes—
1019#95C2414yes—
1020#95C2414yes—
1021#95C2414yes—
1022#95C2414yes—
1023#95C2414yes—
1024#95C2414yes—
1025#95C2414yes—
1026#95C2414yes—
1027#95C2414yes—
1028#95C2414yes—
1029#95C2414yes—
1030C24C2512yes—
1031C24C2512yes—
1032C24C2511yescharacteristic
1033#41—416no—
1034C2×Q8—24no—
1035C2×Q8—22no—
1036C2×Q8—22no—
1037C2×Q8—22no—
1038C2×Q8—22no—
1039C2×Q8—22no—
1040C2×Q8—22no—
1041C2×Q8—22no—
1042C2×Q8—22no—
1043C2×Q8—22no—
1044C2×Q8—22no—
1045C2×Q8—42no—
1046C2×Q8—42no—
1047C2×Q8—42no—
1048C2×Q8—44no—
1049C2×Q8—44no—
1050C2×Q8—44no—
1051C2×Q8—416no—
1052C2×D4—24no—
1053C2×D4—24no—
1054C2×D4—28no—
1055C2×D4—24no—
1056C2×D4—24no—
1057C2×D4—22no—
1058C2×D4—22no—
1059C2×D4—22no—
1060C2×D4—22no—
1061C2×D4—42no—
1062C2×D4—44no—
1063C2×D4—44no—
1064C2×D4—44no—
1065C22×C4—24no—
1066C22×C4—22no—
1067C22×C4—22no—
1068C22×C4—24no—
1069C22×C4—24no—
1070C22×C4—24no—
1071C22×C4—28no—
1072C22×C4—28no—
1073C22×C4—24no—
1074C22×C4—24no—
1075C22×C4—24no—
1076C22×C4—24no—
1077C22×C4—24no—
1078C22×C4—24no—
1079C22×C4—24no—
1080C22×C4—42no—
1081C22×C4—42no—
1082C22×C4—42no—
1083C22×C4—42no—
1084C22×C4—42no—
1085C22×C4—42no—
1086C22×C4—42no—
1087C22×C4—42no—
1088C22×C4—44no—
1089C22×C4—44no—
1090C22×C4—42no—
1091C22×C4—42no—
1092C22×C4—42no—
1093C22×C4—44no—
1094C22×C4—44no—
1095C22×C4—44no—
1096C22×C4—44no—
1097C22×C4C2×#4114yes—
1098C22×C4C2×#4114yes—
1099C22×C4C2×#4114yes—
1100C22×C4C2512yes—
1101C22×C4C2512yes—
1102C22×C4C2512yes—
1103C22×C4C2512yes—
1104C22×C4C2514yes—
1105C22×C4C2512yes—
1106C22×C4C2512yes—
1107C22×C4C2514yes—
1108C22×C4C2512yes—
1109C22×C4C2512yes—
1110C22×C4C2512yes—
1111C22×C4C2512yes—
1112C22×C4C2514yes—
1113C22×C4C2514yes—
1114C22×C4C2512yes—
1115C22×C4C2512yes—
1116C22×C4C2512yes—
1117C22×C4C2512yes—
1118C22×C4C2512yes—
1119C22×C4C2512yes—
1120C22×C4C2512yes—
1121C22×C4C2512yes—
1122C22×C4C2511yescharacteristic
1123C22×C4C2511yescharacteristic
1124C22×C4C2511yescharacteristic
1125C22×C4C2511yescharacteristic
1126C22×C4C2511yescharacteristic
1127C22×C4C2511yescharacteristic
1128C4⋊C4—24no—
1129C4⋊C4—22no—
1130C4⋊C4—22no—
1131C4⋊C4—24no—
1132C4⋊C4—24no—
1133C4⋊C4—24no—
1134C4⋊C4—24no—
1135C4⋊C4—22no—
1136C4⋊C4—22no—
1137C4⋊C4—24no—
1138C4⋊C4—24no—
1139C4⋊C4—24no—
1140C4⋊C4—24no—
1141C4⋊C4—22no—
1142C4⋊C4—24no—
1143C4⋊C4—22no—
1144C4⋊C4—24no—
1145C4⋊C4—24no—
1146C4⋊C4—24no—
1147C4⋊C4—24no—
1148C4⋊C4—24no—
1149C4⋊C4—42no—
1150C4⋊C4—42no—
1151C4⋊C4—42no—
1152C4⋊C4—42no—
1153C4⋊C4—44no—
1154C4⋊C4—42no—
1155C4⋊C4—44no—
1156C4⋊C4—44no—
1157C4⋊C4—44no—
1158C4⋊C4—44no—
1159C4⋊C4—44no—
1160C4⋊C4—42no—
1161C4⋊C4—42no—
1162C4⋊C4—42no—
1163C4⋊C4—42no—
1164C4⋊C4—42no—
1165C4⋊C4—42no—
1166C4⋊C4—42no—
1167C4⋊C4—42no—
1168C4⋊C4—42no—
1169C4⋊C4—44no—
1170C4⋊C4—44no—
1171C4⋊C4—44no—
1172C4⋊C4—44no—
1173C4⋊C4—44no—
1174C4⋊C4—44no—
1175C4⋊C4—44no—
1176C4⋊C4—44no—
1177C4⋊C4—44no—
1178C4⋊C4—44no—
1179C4⋊C4—44no—
1180C4⋊C4—44no—
1181C4⋊C4—44no—
1182C4⋊C4—44no—
1183C4⋊C4—44no—
1184C4⋊C4—44no—
1185C4⋊C4—44no—
1186C4⋊C4—44no—
1187C22⋊C4—24no—
1188C22⋊C4—24no—
1189C22⋊C4—24no—
1190C22⋊C4—24no—
1191C22⋊C4—28no—
1192C22⋊C4—24no—
1193C22⋊C4—24no—
1194C22⋊C4—24no—
1195C22⋊C4—24no—
1196C22⋊C4—24no—
1197C22⋊C4—24no—
1198C22⋊C4—42no—
1199C22⋊C4—44no—
1200C22⋊C4—42no—
1201C22⋊C4—42no—
1202C22⋊C4—42no—
1203C22⋊C4—44no—
1204C22⋊C4—44no—
1205C22⋊C4—42no—
1206C22⋊C4—42no—
1207C22⋊C4—42no—
1208C22⋊C4—42no—
1209C22⋊C4—44no—
1210C22⋊C4—44no—
1211C22⋊C4—44no—
1212C22⋊C4—44no—
1213C22⋊C4—44no—
1214C22⋊C4—44no—
1215C22⋊C4—44no—
1216C22⋊C4—44no—
1217C22⋊C4—44no—
1218C22⋊C4—44no—
1219C22⋊C4—44no—
1220C22⋊C4—44no—
1221C22⋊C4—44no—
1222C22⋊C4—44no—
1223C42—24no—
1224C42—24no—
1225C42—24no—
1226C42—24no—
1227C42—24no—
1228C42—24no—
1229C42—24no—
1230C42—24no—
1231C42—24no—
1232C42—24no—
1233C42—22no—
1234C42—22no—
1235C42—22no—
1236C42—22no—
1237C42—42no—
1238C42—42no—
1239C42—44no—
1240C42—44no—
1241C42—44no—
1242C42—44no—
1243C42—44no—
1244C42—42no—
1245C42—42no—
1246C42—44no—
1247C42—42no—
1248C42—42no—
1249C42—44no—
1250C42—44no—
1251C42C2×#4114yes—
1252C42C2×#4114yes—
1253C42C2×#4114yes—
1254C42C2×#4114yes—
1255C23—21no—
1256C23—21no—
1257C23—22no—
1258C23—22no—
1259C23—22no—
1260C23—22no—
1261C23—22no—
1262C23—22no—
1263C23—24no—
1264C23—22no—
1265C23—22no—
1266C23—22no—
1267C23—22no—
1268C23—24no—
1269C23—22no—
1270C23C22×#4112yes—
1271C23#58514yes—
1272C23C2611yescharacteristic
1273Q8—48no—
1274Q8—44no—
1275Q8—44no—
1276Q8—44no—
1277Q8—44no—
1278Q8—164no—
1279D4—44no—
1280D4—48no—
1281D4—48no—
1282D4—44no—
1283D4—164no—
1284C2×C4—21no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—21no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—28no—
1291C2×C4—28no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—22no—
1311C2×C4—22no—
1312C2×C4—24no—
1313C2×C4—24no—
1314C2×C4—24no—
1315C2×C4—22no—
1316C2×C4—24no—
1317C2×C4—22no—
1318C2×C4—22no—
1319C2×C4—22no—
1320C2×C4—24no—
1321C2×C4—22no—
1322C2×C4—22no—
1323C2×C4—24no—
1324C2×C4—24no—
1325C2×C4—24no—
1326C2×C4—22no—
1327C2×C4—22no—
1328C2×C4—22no—
1329C2×C4—22no—
1330C2×C4—22no—
1331C2×C4—22no—
1332C2×C4—22no—
1333C2×C4—22no—
1334C2×C4—24no—
1335C2×C4—24no—
1336C2×C4—24no—
1337C2×C4—22no—
1338C2×C4—22no—
1339C2×C4—22no—
1340C2×C4—24no—
1341C2×C4—22no—
1342C2×C4—22no—
1343C2×C4—24no—
1344C2×C4—22no—
1345C2×C4—22no—
1346C2×C4—24no—
1347C2×C4—22no—
1348C2×C4—22no—
1349C2×C4—22no—
1350C2×C4—24no—
1351C2×C4—24no—
1352C2×C4—22no—
1353C2×C4—22no—
1354C2×C4—44no—
1355C2×C4—48no—
1356C2×C4—48no—
1357C2×C4—48no—
1358C2×C4—48no—
1359C2×C4—48no—
1360C2×C4—84no—
1361C2×C4—84no—
1362C2×C4—84no—
1363C2×C4—88no—
1364C2×C4—164no—
1365C2×C4C22×#4112yes—
1366C2×C4C22×#4112yes—
1367C2×C4C22×#4112yes—
1368C2×C4C22×#4112yes—
1369C2×C4C22×#4112yes—
1370C2×C4C22×#4112yes—
1371C2×C4#58512yes—
1372C2×C4#58512yes—
1373C22—22no—
1374C22—22no—
1375C22—24no—
1376C22—24no—
1377C22—42no—
1378C22—42no—
1379C22—42no—
1380C22—42no—
1381C22—44no—
1382C22—42no—
1383C22—42no—
1384C22—42no—
1385C22—42no—
1386C22—42no—
1387C22—44no—
1388C22—42no—
1389C22#345514yes—
1390C22C23×#4111yescharacteristic
1391C22C2×#58511yescharacteristic
1392C22C2×#58511yescharacteristic
1393C22C2×#58512yes—
1394C222−1+612yes—
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—22no—
1399C4—22no—
1400C4—42no—
1401C4—42no—
1402C4—42no—
1403C4—42no—
1404C4—42no—
1405C4—42no—
1406C4—42no—
1407C4—42no—
1408C4—42no—
1409C4—42no—
1410C4—42no—
1411C4—42no—
1412C4—44no—
1413C4—42no—
1414C4—42no—
1415C4—42no—
1416C4—42no—
1417C4—42no—
1418C4—44no—
1419C4—44no—
1420C4—44no—
1421C4—42no—
1422C4#349314yes—
1423C2—24no—
1424C2—82no—
1425C2—82no—
1426C2C2×#345511yescharacteristic
1427C2C2×#349311yescharacteristic
1428C2#6286011yescharacteristic
1429C2#6293412yes—
1430C2#6296412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35130C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42328C2semidirect
2. #42195C2semidirect
3. #42192C2semidirect
4. #42160C2semidirect
5. #39758C2semidirect
6. #39757C2semidirect
7. #39731C2semidirect
8. #39502C2semidirect
9. #39501C2semidirect
10. #39475C2semidirect
11. #39187C2semidirect
12. #39186C2semidirect
13. #39153C2semidirect
14. #38971C2semidirect
15. #38970C2semidirect
16. #38937C2semidirect
17. #37495C2semidirect
18. #37494C2semidirect
19. #36998C2semidirect
20. #36997C2semidirect
21. #35460C2semidirect
22. #35229C2semidirect
23. #35228C2semidirect
24. #35132C2semidirect
26. #35099C2semidirect
27. #34972C2semidirect
28. #34971C2semidirect
29. #34224C2semidirect
30. C2×#2356C2semidirect
31. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#423282
#421952
#421922
#421602
#397582
#397572
#397312
#395022
#395012
#394752
#391872
#391862
#391532
#389712
#389702
#389372
#374952
#374942
#369982
#369972
#354602
#352292
#352282
#351322
#351302
#350992
#349722
#349712
#342242
C2×#23562
#340602