Finite Group Databasebeta

← #7632489

Subgroups — #7632489

Order 512.

4979 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36506C213yesmaximal, complemented
2#36450C213yesmaximal, complemented
3#36444C211yesmaximal, characteristic
4#36432C211yesmaximal, characteristic, complemented
5#36432C211yesmaximal, characteristic, complemented
6#36431C211yesmaximal, characteristic, complemented
7#36417C213yesmaximal, complemented
8#36409C213yesmaximal, complemented
9#35973C213yesmaximal, complemented
10#35910C211yesmaximal, characteristic, complemented
11#35900C213yesmaximal, complemented
12#35883C211yesmaximal, characteristic, complemented
13#35883C211yesmaximal, characteristic, complemented
14#35875C213yesmaximal, complemented
15#35868C211yesmaximal, characteristic, complemented
16#35849C213yesmaximal, complemented
17#35632C213yesmaximal, complemented
18#35631C213yesmaximal, complemented
19#35551C213yesmaximal, complemented
20#35547C213yesmaximal, complemented
21#35315C213yesmaximal, complemented
22#35162C213yesmaximal, complemented
23#34811C213yesmaximal, complemented
24#34793C213yesmaximal, complemented
25#34336C211yesmaximal, characteristic, complemented
26#34293C211yesmaximal, characteristic, complemented
27#34291C211yesmaximal, characteristic, complemented
28#34262C211yesmaximal, characteristic, complemented
29#34196C211yesmaximal, characteristic, complemented
30C4×#548C211yesmaximal, characteristic, complemented
31#33999C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39C2×C4×#41C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2865C2216yes—
42#2863C2216yes—
43#2857C2213yes—
44#2855C2213yes—
45#2855C2213yes—
46#2851C2213yes—
47#2653C2216yes—
48#2652C2216yes—
49#2647C2213yes—
50#2645C2213yes—
51#2645C2213yes—
52#2642C2213yes—
53#2597C2216yes—
54#2580C2213yes—
55#2577C2216yes—
56#2577C2216yes—
57#2576C2216yes—
58#2575C2216yes—
59#2573C2216yes—
60#2572C2216yes—
61#2570C2213yes—
62#2568C2213yes—
63#2566C2213yes—
64#2562C2213yes—
65#2558C2216yes—
66#2552C2213yes—
67#2547C2213yes—
68#2537C2213yes—
69#2533C2216yes—
70#2533C2213yes—
71#2532C2213yes—
72#2531C2211yescharacteristic
73#2530C2216yes—
74#2530C2213yes—
75#2529C2213yes—
76#2528C2216yes—
77#2528C2216yes—
78#2528C2213yes—
79#2527C2216yes—
80#2527C2213yes—
81#2526C2213yes—
82#2523C2216yes—
83#2518C2216yes—
84#2517C2216yes—
85#2516C2216yes—
86#2515C2216yes—
87#2514C2213yes—
88#2514C2213yes—
89#2514C2213yes—
90#2514C2213yes—
91#2511C2213yes—
92#2511C2213yes—
93#2510C2213yes—
94#2509C2213yes—
95#2507C2213yes—
96#2506C2213yes—
97#2506C2213yes—
98#2505C2216yes—
99#2505C2216yes—
100#2505C2213yes—
101#2499C2213yes—
102#2499C2213yes—
103#2497C2213yes—
104#2497C2213yes—
105#2495C2213yes—
106#2495C2213yes—
107#2494C2213yes—
108#2494C2216yes—
109#2494C2213yes—
110#2493C2216yes—
111#2493C2216yes—
112#2493C2213yes—
113#2492C2213yes—
114#2492C2213yes—
115#2489C2213yes—
116#2489C2213yes—
117#2489C2216yes—
118#2488C2213yes—
119#2485C2213yes—
120#2485C2213yes—
121#2476C2216yes—
122#2470C2216yes—
123#2460C2216yes—
124#2454C2213yes—
125#2452C2213yes—
126#2450C2213yes—
127#2447C2213yes—
128#2447C2213yes—
129#2447C2213yes—
130#2447C2213yes—
131#2444C2213yes—
132#2441C2213yes—
133#2439C2213yes—
134#2427C2213yes—
135#2427C2213yes—
136#2425C2213yes—
137#2422C2213yes—
138#2422C2213yes—
139#2420C2213yes—
140#2420C2213yes—
141#2419C2213yes—
142#2415C2213yes—
143#2415C2213yes—
144#2402C2213yes—
145#2401C2213yes—
146#2401C2213yes—
147#2401C2216yes—
148#2398C2213yes—
149#2395C2216yes—
150#2370C2213yes—
151#2370C2213yes—
152#2369C2213yes—
153#2367C2213yes—
154#2367C2213yes—
155#2365C2213yes—
156#2363C2213yes—
157#2362C2213yes—
158#2362C2213yes—
159#2362C2213yes—
160#2361C2213yes—
161#2360C2213yes—
162#2356C2213yes—
163#2355C2213yes—
164#2355C2213yes—
165#2355C2213yes—
166#2355C2213yes—
167#2354C2213yes—
168#2352C2213yes—
169#2352C2213yes—
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180#2347C2213yes—
181#2346C2213yes—
182#2344C2213yes—
183#2344C2213yes—
184#2341C2211yescharacteristic
185#2341C2211yescharacteristic
186Q8×C22⋊C4C2211yescharacteristic
187Q8×C22⋊C4C2211yescharacteristic
188Q8×C22⋊C4C2211yescharacteristic
189Q8×C22⋊C4C2211yescharacteristic
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192Q8×C22⋊C4C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194#2331C2213yes—
195#2330C2213yes—
196#2327C2213yes—
197#2326C2213yes—
198#2324C2213yes—
199#2323C2213yes—
200#2320C2213yes—
201#2320C2213yes—
202#2320C2213yes—
203#2314C2213yes—
204C4×#125C2213yes—
205C4×#125C2216yes—
206C4×#124C2213yes—
207C4×C22⋊Q8C2213yes—
208C4×C22⋊Q8C2213yes—
209C4×C22⋊Q8C2213yes—
210C4×C22⋊Q8C2213yes—
211C4×#123C2213yes—
212C4×#123C2213yes—
213C4×#121C2213yes—
214C4×#121C2213yes—
215#2298C2213yes—
216#2298C2216yes—
217#2295C2213yes—
218#2295C2213yes—
219#2290C2213yes—
220#2290C2213yes—
221#2285C2213yes—
222#2283C2213yes—
223#2276C2211yescharacteristic
224#2276C2211yescharacteristic
225#2276C2211yescharacteristic
226#2276C2211yescharacteristic
227#2276C2211yescharacteristic
228#2275C2213yes—
229#2275C2213yes—
230#2275C2213yes—
231#2275C2213yes—
232C42×Q8C2211yescharacteristic
233C42×D4C2213yes—
234C4×#117C2213yes—
235C4×#117C2213yes—
236C4×#117C2213yes—
237C2×#376C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240C23×Q8C2311yescharacteristic
241#557—28no—
242D4×Q8—28no—
243#548—28no—
244#548—28no—
245C2×C4⋊Q8C2313yes—
246C2×C4⋊Q8C2313yes—
247C2×#125C2313yes—
248C2×#125C2313yes—
249C2×#125C2316yes—
250C2×#124C2313yes—
251C2×#124C2313yes—
252C2×#123C2313yes—
253C2×#123C2313yes—
254C2×C22⋊Q8C2313yes—
255C2×C22⋊Q8C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×#121C2313yes—
260C2×#121C2313yes—
261C2×#121C2313yes—
262#519—28no—
263C4×#41—28no—
264C4×#41—28no—
265C4×#41—28no—
266C2×C4×Q8—28no—
267C2×C4×Q8C2313yes—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×Q8C2311yescharacteristic
279C2×C4×Q8C2311yescharacteristic
280C2×C4×Q8C2313yes—
281C2×C4×Q8C2313yes—
282C2×C4×Q8C2311yescharacteristic
283C2×C4×Q8C2311yescharacteristic
284C2×C4×D4C2313yes—
285C2×C4×D4C2313yes—
286C2×C4×D4C2313yes—
287C2×C4×D4C2313yes—
288C2×C4×D4C2313yes—
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2313yes—
295C2×#117C2313yes—
296C2×#117C2313yes—
297C2×#117C2313yes—
298C2×#117C2313yes—
299C2×#117C2313yes—
300C2×#117C2316yes—
301C22×C4⋊C4C2313yes—
302C22×C42C2313yes—
303C22×C42C2313yes—
304C22×C42C2313yes—
305C22×C42C2313yes—
306#401C2316yes—
307#401C2316yes—
308#401C2313yes—
309#401C2313yes—
310#400C2316yes—
311#400C2313yes—
312#400C2313yes—
313#400C2316yes—
314#400C2313yes—
315#400C2316yes—
316#400C2313yes—
317#400C2316yes—
318#400C2316yes—
319#400C2313yes—
320#400C2316yes—
321#400C2313yes—
322#400C2313yes—
323#400C2316yes—
324#400C2316yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2313yes—
329#400C2313yes—
330#399C2316yes—
331#398C2316yes—
332#398C2313yes—
333#398C2316yes—
334#398C2313yes—
335#398C2311yescharacteristic
336#398C2313yes—
337#397C2316yes—
338#397C2316yes—
339#397C2316yes—
340#397C2316yes—
341#397C2316yes—
342#397C2316yes—
343#397C2316yes—
344#397C2313yes—
345#397C2316yes—
346#397C2313yes—
347#397C2313yes—
348#397C2313yes—
349#397C2313yes—
350#397C2311yescharacteristic
351#397C2311yescharacteristic
352#397C2313yes—
353#396C2316yes—
354#396C2316yes—
355#396C2313yes—
356#396C2313yes—
357#394C2313yes—
358#394C2316yes—
359#394C2316yes—
360#394C2316yes—
361#394C2316yes—
362#394C2311yescharacteristic
363#393C2313yes—
364#393C2316yes—
365#393C2313yes—
366#391C2313yes—
367#391C2313yes—
368#391C2313yes—
369#391C2313yes—
370#391C2316yes—
371#391C2316yes—
372#391C2313yes—
373#391C2313yes—
374#391C2313yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2313yes—
385#391C2313yes—
386#391C2313yes—
387#390C2313yes—
388#390C2313yes—
389#390C2316yes—
390#390C2313yes—
391#390C2313yes—
392#390C2311yescharacteristic
393#389C2313yes—
394#389C2316yes—
395#389C2313yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2316yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2313yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2316yes—
420#389C2313yes—
421#388C2316yes—
422#388C2316yes—
423#388C2313yes—
424#388C2316yes—
425#388C2316yes—
426#388C2316yes—
427#388C2316yes—
428#388C2316yes—
429#388C2316yes—
430#388C2316yes—
431#388C2316yes—
432#388C2313yes—
433#388C2316yes—
434#388C2313yes—
435#388C2313yes—
436#388C2313yes—
437#388C2313yes—
438#388C2313yes—
439#388C2316yes—
440#388C2313yes—
441#388C2313yes—
442#388C2313yes—
443#388C2311yescharacteristic
444#388C2311yescharacteristic
445#388C2311yescharacteristic
446#388C2311yescharacteristic
447#387C2313yes—
448#387C2313yes—
449#387C2316yes—
450#387C2316yes—
451#387C2316yes—
452#387C2316yes—
453#387C2316yes—
454#387C2316yes—
455#387C2316yes—
456#387C2316yes—
457#387C2313yes—
458#387C2316yes—
459#387C2316yes—
460#387C2313yes—
461#387C2316yes—
462#387C2316yes—
463#387C2313yes—
464#387C2316yes—
465#387C2316yes—
466#387C2316yes—
467#387C2313yes—
468#387C2313yes—
469#387C2316yes—
470#387C2316yes—
471#387C2316yes—
472#387C2313yes—
473#387C2313yes—
474#387C2316yes—
475#387C2313yes—
476#387C2313yes—
477#387C2316yes—
478#387C2313yes—
479#387C2313yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2311yescharacteristic
484#387C2313yes—
485#387C2311yescharacteristic
486#387C2313yes—
487#386C2313yes—
488#386C2316yes—
489#386C2313yes—
490#386C2313yes—
491#386C2313yes—
492#386C2313yes—
493#386C2313yes—
494#386C2313yes—
495#386C2311yescharacteristic
496#385C2313yes—
497#385C2316yes—
498#385C2313yes—
499#385C2316yes—
500#385C2316yes—
501#385C2313yes—
502#385C2316yes—
503#385C2313yes—
504#385C2316yes—
505#385C2313yes—
506#385C2316yes—
507#385C2313yes—
508#385C2313yes—
509#385C2313yes—
510#384C2313yes—
511#384C2313yes—
512#384C2313yes—
513#384C2313yes—
514#384C2313yes—
515#383C2316yes—
516#383C2316yes—
517#383C2316yes—
518#383C2313yes—
519#383C2313yes—
520#382C2316yes—
521#382C2313yes—
522#382C2313yes—
523#382C2313yes—
524#382C2313yes—
525#382C2316yes—
526#382C2316yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#381C2313yes—
531#381C2316yes—
532#381C2313yes—
533#381C2313yes—
534#381C2316yes—
535#381C2313yes—
536#380C2313yes—
537#380C2313yes—
538#380C2313yes—
539#380C2313yes—
540#380C2313yes—
541#380C2316yes—
542#380C2313yes—
543#380C2313yes—
544#380C2313yes—
545#380C2313yes—
546#380C2313yes—
547#380C2316yes—
548#380C2313yes—
549#380C2313yes—
550#380C2311yescharacteristic
551#380C2313yes—
552C4×C4⋊C4C2316yes—
553C4×C4⋊C4C2313yes—
554C4×C4⋊C4C2316yes—
555C4×C4⋊C4C2316yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2316yes—
558C4×C4⋊C4C2313yes—
559C4×C4⋊C4C2316yes—
560C4×C4⋊C4C2316yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2313yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2313yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C22⋊C4C2316yes—
589C4×C22⋊C4C2316yes—
590C4×C22⋊C4C2316yes—
591C4×C22⋊C4C2316yes—
592C4×C22⋊C4C2316yes—
593C4×C22⋊C4C2313yes—
594C4×C22⋊C4C2313yes—
595C4×C22⋊C4C2313yes—
596C4×C22⋊C4C2313yes—
597C4×C22⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2316yes—
607C4×C22⋊C4C2316yes—
608C4×C22⋊C4C2316yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2311yescharacteristic
611#376C2313yes—
612#376C2313yes—
613#376C2313yes—
614#376C2316yes—
615#376C2313yes—
616#376C2313yes—
617#376C2311yescharacteristic
618#376C2313yes—
619#376C2313yes—
620#376C2313yes—
621C2×#95C2313yes—
622C2×#95C2313yes—
623C2×#95C2313yes—
624C2×#95C2313yes—
625C43C2316yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41#4118yes—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8—24no—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2411yescharacteristic
642C22×D4C2413yes—
643C22×D4C2413yes—
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2413yes—
647C23×C4C2411yescharacteristic
648C23×C4C2413yes—
649C23×C4C2413yes—
650C23×C4C2413yes—
651C23×C4C2413yes—
652C23×C4C2413yes—
653C23×C4C2413yes—
654C23×C4C2413yes—
655C4⋊Q8—212no—
656C4⋊Q8—212no—
657#125—212no—
658#125—212no—
659#125—412no—
660#124—212no—
661#124—212no—
662#123—46no—
663#123—46no—
664C22⋊Q8—212no—
665C22⋊Q8—212no—
666C22⋊Q8—212no—
667C22⋊Q8—212no—
668C22⋊Q8—46no—
669#121—212no—
670#121—212no—
671#121—46no—
672C4×Q8—24no—
673C4×Q8—24no—
674C4×Q8—24no—
675C4×Q8—24no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—212no—
683C4×Q8—212no—
684C4×Q8—212no—
685C4×Q8—212no—
686C4×Q8—212no—
687C4×Q8#4118yes—
688C4×Q8#4118yes—
689C4×D4—212no—
690C4×D4—212no—
691C4×D4—212no—
692C4×D4—212no—
693C4×D4—212no—
694C4×D4—212no—
695C4×D4—212no—
696C4×D4—212no—
697C4×D4—212no—
698C4×D4—46no—
699C4×D4—46no—
700#117—212no—
701#117—212no—
702#117—212no—
703#117—212no—
704#117—212no—
705#117—412no—
706C2×C4⋊C4—212no—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2416yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2413yes—
718C2×C4⋊C4C2413yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2411yescharacteristic
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2413yes—
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2416yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2416yes—
732C2×C4⋊C4C2416yes—
733C2×C4⋊C4C2416yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2413yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2413yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2416yes—
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2413yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C22⋊C4C2411yescharacteristic
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2413yes—
758C2×C22⋊C4C2413yes—
759C2×C22⋊C4C2416yes—
760C2×C22⋊C4C2416yes—
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2411yescharacteristic
763C2×C22⋊C4C2411yescharacteristic
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2413yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2416yes—
771C2×C22⋊C4C2416yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2413yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2413yes—
779C2×C22⋊C4C2413yes—
780C2×C22⋊C4C2413yes—
781C2×C22⋊C4C2411yescharacteristic
782C2×C22⋊C4C2411yescharacteristic
783C2×C22⋊C4C2411yescharacteristic
784C2×C22⋊C4C2411yescharacteristic
785C2×C22⋊C4C2411yescharacteristic
786C2×C22⋊C4C2413yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2416yes—
789C2×C22⋊C4C2416yes—
790C2×C42—212no—
791C2×C42—212no—
792C2×C42—212no—
793C2×C42—212no—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2416yes—
798C2×C42C2413yes—
799C2×C42C2413yes—
800C2×C42C2413yes—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2413yes—
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2411yescharacteristic
811C2×C42C2411yescharacteristic
812C2×C42C2411yescharacteristic
813C2×C42C2416yes—
814C2×C42C2416yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2416yes—
818C2×C42C2411yescharacteristic
819C2×C42C2413yes—
820C2×C42C2416yes—
821C2×C42C2416yes—
822C2×C42C2413yes—
823C2×C42C2413yes—
824#95C2411yescharacteristic
825#95C2411yescharacteristic
826#95C2411yescharacteristic
827#95C2411yescharacteristic
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2411yescharacteristic
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2416yes—
847#95C2416yes—
848#95C2411yescharacteristic
849#95C2411yescharacteristic
850#95C2413yes—
851#95C2411yescharacteristic
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2413yes—
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2416yes—
863#95C2413yes—
864#95C2416yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2416yes—
871#95C2416yes—
872#95C2413yes—
873#95C2413yes—
874#95C2411yescharacteristic
875#95C2411yescharacteristic
876#95C2411yescharacteristic
877#95C2413yes—
878#95C2416yes—
879#95C2411yescharacteristic
880#95C2413yes—
881#95C2416yes—
882#95C2416yes—
883#95C2413yes—
884#95C2416yes—
885#95C2416yes—
886#95C2416yes—
887#95C2413yes—
888#95C2413yes—
889#95C2413yes—
890#95C2416yes—
891#95C2416yes—
892#95C2413yes—
893#95C2413yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898C24C2511yescharacteristic
899C24C2513yes—
900C24C2511yescharacteristic
901#41—232no—
902C2×Q8—26no—
903C2×Q8—26no—
904C2×Q8—26no—
905C2×Q8—26no—
906C2×Q8—26no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—43no—
910C2×Q8—43no—
911C2×Q8—416no—
912C2×Q8—416no—
913C2×Q8C2×#4114yes—
914C2×Q8C2×#4114yes—
915C2×Q8C2×#4114yes—
916C2×D4—26no—
917C2×D4—26no—
918C2×D4—22no—
919C2×D4—26no—
920C2×D4—26no—
921C2×D4—26no—
922C2×D4—22no—
923C2×D4—43no—
924C2×D4—41no—
925C2×D4—43no—
926C2×D4—43no—
927C2×D4C2×#41112yes—
928C22×C4—26no—
929C22×C4—26no—
930C22×C4—26no—
931C22×C4—26no—
932C22×C4—26no—
933C22×C4—22no—
934C22×C4—26no—
935C22×C4—26no—
936C22×C4—26no—
937C22×C4—26no—
938C22×C4—26no—
939C22×C4—26no—
940C22×C4—26no—
941C22×C4—22no—
942C22×C4—26no—
943C22×C4—26no—
944C22×C4—26no—
945C22×C4—26no—
946C22×C4—43no—
947C22×C4—41no—
948C22×C4—43no—
949C22×C4—43no—
950C22×C4—43no—
951C22×C4—43no—
952C22×C4—43no—
953C22×C4—43no—
954C22×C4—43no—
955C22×C4—43no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—43no—
960C22×C4C2×#41112yes—
961C22×C4C2511yescharacteristic
962C22×C4C2511yescharacteristic
963C22×C4C2511yescharacteristic
964C22×C4C2511yescharacteristic
965C22×C4C2513yes—
966C22×C4C2511yescharacteristic
967C22×C4C2513yes—
968C22×C4C2513yes—
969C22×C4C2511yescharacteristic
970C22×C4C2513yes—
971C22×C4C2513yes—
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2511yescharacteristic
976C22×C4C2513yes—
977C22×C4C2511yescharacteristic
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2513yes—
981C22×C4C2513yes—
982C22×C4C2511yescharacteristic
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2511yescharacteristic
986C22×C4C2513yes—
987C22×C4C2511yescharacteristic
988C22×C4C2513yes—
989C4⋊C4—26no—
990C4⋊C4—212no—
991C4⋊C4—26no—
992C4⋊C4—26no—
993C4⋊C4—26no—
994C4⋊C4—26no—
995C4⋊C4—26no—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—26no—
999C4⋊C4—26no—
1000C4⋊C4—26no—
1001C4⋊C4—22no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—26no—
1007C4⋊C4—26no—
1008C4⋊C4—212no—
1009C4⋊C4—212no—
1010C4⋊C4—26no—
1011C4⋊C4—22no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—43no—
1020C4⋊C4—43no—
1021C4⋊C4—43no—
1022C4⋊C4—43no—
1023C4⋊C4—41no—
1024C4⋊C4—46no—
1025C4⋊C4—46no—
1026C4⋊C4—43no—
1027C4⋊C4—43no—
1028C4⋊C4—43no—
1029C4⋊C4—43no—
1030C4⋊C4—43no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—46no—
1034C4⋊C4—46no—
1035C4⋊C4C2×#41112yes—
1036C4⋊C4C2×#41112yes—
1037C22⋊C4—212no—
1038C22⋊C4—26no—
1039C22⋊C4—26no—
1040C22⋊C4—212no—
1041C22⋊C4—212no—
1042C22⋊C4—26no—
1043C22⋊C4—26no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—26no—
1048C22⋊C4—212no—
1049C22⋊C4—212no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—26no—
1053C22⋊C4—26no—
1054C22⋊C4—26no—
1055C22⋊C4—22no—
1056C22⋊C4—41no—
1057C22⋊C4—43no—
1058C22⋊C4—43no—
1059C22⋊C4—43no—
1060C22⋊C4—46no—
1061C22⋊C4—41no—
1062C22⋊C4—46no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—43no—
1067C22⋊C4—43no—
1068C22⋊C4—43no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C42—22no—
1073C42—22no—
1074C42—22no—
1075C42—26no—
1076C42—26no—
1077C42—26no—
1078C42—26no—
1079C42—26no—
1080C42—26no—
1081C42—26no—
1082C42—26no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—212no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—46no—
1092C42—43no—
1093C42—41no—
1094C42—46no—
1095C42—46no—
1096C42—46no—
1097C42—43no—
1098C42—43no—
1099C42—46no—
1100C42C2×#41112yes—
1101C42C2×#41112yes—
1102C23—21no—
1103C23—23no—
1104C23—23no—
1105C23—21no—
1106C23—21no—
1107C23—23no—
1108C23—21no—
1109C23—23no—
1110C23—21no—
1111C23—21no—
1112C23—23no—
1113C23—23no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23C22×#4116yes—
1122C23#58512yes—
1123C23C2611yescharacteristic
1124Q8—412no—
1125Q8—412no—
1126Q8—86no—
1127Q8#529116yes—
1128D4—224no—
1129D4—44no—
1130D4—412no—
1131D4—86no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—23no—
1136C2×C4—21no—
1137C2×C4—23no—
1138C2×C4—21no—
1139C2×C4—23no—
1140C2×C4—23no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—224no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—23no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—23no—
1156C2×C4—23no—
1157C2×C4—23no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—23no—
1161C2×C4—23no—
1162C2×C4—23no—
1163C2×C4—23no—
1164C2×C4—23no—
1165C2×C4—23no—
1166C2×C4—23no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—23no—
1175C2×C4—23no—
1176C2×C4—23no—
1177C2×C4—23no—
1178C2×C4—23no—
1179C2×C4—23no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—23no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—23no—
1194C2×C4—23no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—44no—
1209C2×C4—412no—
1210C2×C4—412no—
1211C2×C4—412no—
1212C2×C4—86no—
1213C2×C4—86no—
1214C2×C4—86no—
1215C2×C4—86no—
1216C2×C4—86no—
1217C2×C4—86no—
1218C2×C4C22×#4112yes—
1219C2×C4C22×#4116yes—
1220C2×C4C22×#4112yes—
1221C2×C4C22×#4112yes—
1222C2×C4C22×#4116yes—
1223C2×C4C22×#4116yes—
1224C2×C4C22×#4116yes—
1225C2×C4C22×#4116yes—
1226C2×C4#58512yes—
1227C22—22no—
1228C22—22no—
1229C22—26no—
1230C22—22no—
1231C22—26no—
1232C22—26no—
1233C22—43no—
1234C22—41no—
1235C22—43no—
1236C22—43no—
1237C22—43no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22C23×#4111yescharacteristic
1249C22C23×#4111yescharacteristic
1250C22C23×#4111yescharacteristic
1251C22C2×#58511yescharacteristic
1252C22C2×#58511yescharacteristic
1253C222−1+611yescharacteristic
1254C222−1+611yescharacteristic
1255C4—26no—
1256C4—22no—
1257C4—22no—
1258C4—22no—
1259C4—26no—
1260C4—22no—
1261C4—41no—
1262C4—43no—
1263C4—41no—
1264C4—43no—
1265C4—41no—
1266C4—43no—
1267C4—43no—
1268C4—43no—
1269C4—41no—
1270C4—43no—
1271C4—41no—
1272C4—43no—
1273C4—41no—
1274C4—43no—
1275C4—43no—
1276C4—41no—
1277C4—41no—
1278C4—43no—
1279C4—41no—
1280C4—43no—
1281C4—43no—
1282C4C2×#529112yes—
1283C2—42no—
1284C2—46no—
1285C2—81no—
1286C2C22×#52911yescharacteristic
1287C2#6281611yescharacteristic
1288C2#6286111yescharacteristic
1289C2#6299311yescharacteristic
1290C2#6300511yescharacteristic
1291C2#6300511yescharacteristic
1292C2#6300911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36444C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36506C2semidirect
2. #36450C2semidirect
4. #36432C2semidirect
5. #36432C2semidirect
6. #36431C2semidirect
7. #36417C2semidirect
8. #36409C2semidirect
9. #35973C2semidirect
10. #35910C2semidirect
11. #35900C2semidirect
12. #35883C2semidirect
13. #35883C2semidirect
14. #35875C2semidirect
15. #35868C2semidirect
16. #35849C2semidirect
17. #35632C2semidirect
18. #35631C2semidirect
19. #35551C2semidirect
20. #35547C2semidirect
21. #35315C2semidirect
22. #35162C2semidirect
23. #34811C2semidirect
24. #34793C2semidirect
25. #34336C2semidirect
26. #34293C2semidirect
27. #34291C2semidirect
28. #34262C2semidirect
29. #34196C2semidirect
30. C4×#548C2semidirect
31. #33999C2semidirect

Maximal subgroups

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

subgroupindex
#365062
#364502
#364442
#364322
#364312
#364172
#364092
#359732
#359102
#359002
#358832
#358752
#358682
#358492
#356322
#356312
#355512
#355472
#353152
#351622
#348112
#347932
#343362
#342932
#342912
#342622
#341962
C4×#5482
#339992