Finite Group Databasebeta

← #7632224

Subgroups — #7632224

Order 512.

5065 conjugacy classes of subgroups.

The subgroup lattice has 1303 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36578C211yesmaximal, characteristic, complemented
2#36577C211yesmaximal, characteristic, complemented
3#36551C213yesmaximal, complemented
4Q8×#123C211yesmaximal, characteristic, complemented
5#36488C213yesmaximal, complemented
6#36434C211yesmaximal, characteristic
7#36256C213yesmaximal, complemented
8#36255C213yesmaximal, complemented
9#35974C213yesmaximal, complemented
10#35911C213yesmaximal, complemented
11#35898C211yesmaximal, characteristic, complemented
12#35886C213yesmaximal, complemented
13#35884C213yesmaximal, complemented
14#35883C211yesmaximal, characteristic, complemented
15#35868C211yesmaximal, characteristic, complemented
16#35854C211yesmaximal, characteristic, complemented
17#35655C213yesmaximal, complemented
18#35650C213yesmaximal, complemented
19#35610C213yesmaximal, complemented
20#35587C213yesmaximal, complemented
21#35270C213yesmaximal, complemented
22#35231C213yesmaximal, complemented
23#34811C213yesmaximal, complemented
24#34788C213yesmaximal, complemented
25#34336C211yesmaximal, characteristic, complemented
26#34294C211yesmaximal, characteristic, complemented
27#34294C211yesmaximal, characteristic, complemented
28#34263C211yesmaximal, characteristic, complemented
29#34192C211yesmaximal, characteristic, complemented
30C4×D4×Q8C211yesmaximal, characteristic, complemented
31C2×#2276C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2211yescharacteristic
35C2×#548C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39C22×C4×Q8C2211yescharacteristic
40C22×C4×Q8C2211yescharacteristic
41#2857C2213yes—
42#2855C2213yes—
43#2854C2213yes—
44#2852C2216yes—
45#2851C2216yes—
46#2850C2213yes—
47#2655C2216yes—
48#2654C2216yes—
49#2647C2213yes—
50#2645C2213yes—
51#2644C2213yes—
52#2640C2213yes—
53#2595C2216yes—
54#2594C2216yes—
55#2592C2213yes—
56#2589C2216yes—
57#2589C2216yes—
58#2587C2216yes—
59#2585C2216yes—
60#2582C2213yes—
61#2577C2216yes—
62#2573C2216yes—
63#2570C2213yes—
64#2568C2213yes—
65#2563C2213yes—
66#2552C2213yes—
67#2545C2213yes—
68#2536C2213yes—
69#2533C2213yes—
70#2532C2216yes—
71#2532C2216yes—
72#2532C2213yes—
73#2531C2213yes—
74#2530C2216yes—
75#2530C2213yes—
76#2529C2216yes—
77#2529C2213yes—
78#2528C2216yes—
79#2528C2213yes—
80#2527C2213yes—
81#2527C2216yes—
82#2526C2213yes—
83#2525C2216yes—
84#2525C2216yes—
85#2524C2216yes—
86#2519C2216yes—
87#2516C2216yes—
88#2514C2213yes—
89#2514C2213yes—
90#2513C2213yes—
91#2512C2213yes—
92#2512C2213yes—
93#2511C2213yes—
94#2510C2216yes—
95#2510C2213yes—
96#2509C2213yes—
97#2509C2216yes—
98#2507C2213yes—
99#2506C2213yes—
100#2506C2213yes—
101#2505C2213yes—
102#2504C2213yes—
103#2502C2213yes—
104#2497C2213yes—
105#2497C2213yes—
106#2496C2213yes—
107#2495C2213yes—
108#2494C2213yes—
109#2494C2213yes—
110#2493C2213yes—
111#2490C2213yes—
112#2490C2213yes—
113#2489C2213yes—
114#2489C2213yes—
115#2488C2213yes—
116#2487C2213yes—
117#2487C2213yes—
118#2478C2216yes—
119#2475C2216yes—
120#2468C2216yes—
121#2454C2216yes—
122#2453C2213yes—
123#2453C2213yes—
124#2450C2216yes—
125#2450C2213yes—
126#2448C2213yes—
127#2448C2213yes—
128#2446C2213yes—
129#2446C2213yes—
130#2444C2213yes—
131#2442C2213yes—
132#2442C2213yes—
133#2429C2213yes—
134#2426C2213yes—
135#2425C2213yes—
136#2423C2213yes—
137#2423C2213yes—
138#2421C2213yes—
139#2421C2213yes—
140#2419C2216yes—
141#2419C2211yescharacteristic
142#2417C2213yes—
143#2416C2213yes—
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#2361C2213yes—
157#2361C2213yes—
158#2360C2213yes—
159#2360C2213yes—
160#2360C2213yes—
161#2360C2213yes—
162#2357C2213yes—
163#2356C2213yes—
164#2356C2213yes—
165#2355C2213yes—
166#2354C2213yes—
167#2351C2211yescharacteristic
168#2351C2211yescharacteristic
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172Q8×C4⋊C4C2211yescharacteristic
173Q8×C4⋊C4C2211yescharacteristic
174Q8×C4⋊C4C2211yescharacteristic
175Q8×C4⋊C4C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177D4×C4⋊C4C2213yes—
178D4×C4⋊C4C2213yes—
179D4×C4⋊C4C2213yes—
180#2345C2213yes—
181#2345C2213yes—
182#2345C2213yes—
183#2344C2213yes—
184#2341C2211yescharacteristic
185#2341C2211yescharacteristic
186#2341C2211yescharacteristic
187#2341C2211yescharacteristic
188Q8×C22⋊C4C2211yescharacteristic
189Q8×C22⋊C4C2211yescharacteristic
190Q8×C22⋊C4C2211yescharacteristic
191Q8×C22⋊C4C2211yescharacteristic
192Q8×C22⋊C4C2211yescharacteristic
193Q8×C22⋊C4C2211yescharacteristic
194#2331C2213yes—
195#2330C2213yes—
196#2326C2213yes—
197#2326C2213yes—
198#2323C2213yes—
199#2323C2213yes—
200#2320C2213yes—
201#2320C2213yes—
202#2319C2213yes—
203#2314C2213yes—
204C4×C4⋊Q8C2213yes—
205C4×#125C2213yes—
206C4×C22⋊Q8C2213yes—
207C4×C22⋊Q8C2213yes—
208C4×C22⋊Q8C2213yes—
209C4×#123C2213yes—
210C4×#123C2213yes—
211C4×#121C2213yes—
212C4×#121C2213yes—
213C4×#121C2216yes—
214C4×#121C2213yes—
215#2298C2213yes—
216#2295C2213yes—
217#2293C2213yes—
218#2290C2213yes—
219#2290C2213yes—
220#2290C2216yes—
221#2283C2213yes—
222#2283C2213yes—
223#2276C2213yes—
224#2276C2211yescharacteristic
225#2276C2213yes—
226#2276C2211yescharacteristic
227#2276C2211yescharacteristic
228#2276C2211yescharacteristic
229#2276C2213yes—
230#2276C2213yes—
231#2276C2211yescharacteristic
232C42×Q8C2211yescharacteristic
233C42×D4C2213yes—
234C2×C4×C4⋊C4C2213yes—
235C2×C4×C4⋊C4C2213yes—
236C2×C4×C4⋊C4C2213yes—
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×#126C2316yes—
248C2×#125C2313yes—
249C2×#125C2313yes—
250C2×#125C2316yes—
251C2×#124C2313yes—
252C2×#124C2313yes—
253C2×#123C2311yescharacteristic
254C2×#123C2313yes—
255C2×C22⋊Q8C2313yes—
256C2×C22⋊Q8C2313yes—
257C2×C22⋊Q8C2313yes—
258C2×C22⋊Q8C2313yes—
259C2×C22⋊Q8C2313yes—
260C2×#121C2313yes—
261C2×#121C2313yes—
262C2×#121C2313yes—
263#520—28no—
264C2×C4×Q8—28no—
265C2×C4×Q8—28no—
266C2×C4×Q8—28no—
267C2×C4×Q8—28no—
268C2×C4×Q8C2313yes—
269C2×C4×Q8C2313yes—
270C2×C4×Q8C2313yes—
271C2×C4×Q8C2313yes—
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×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×Q8C2313yes—
283C2×C4×Q8C2313yes—
284C2×C4×Q8C2313yes—
285C2×C4×Q8C2313yes—
286C2×C4×Q8C2313yes—
287C2×C4×Q8C2311yescharacteristic
288C2×C4×Q8C2311yescharacteristic
289C2×C4×D4C2313yes—
290C2×C4×D4C2313yes—
291C2×C4×D4C2313yes—
292C2×C4×D4C2313yes—
293C2×C4×D4C2313yes—
294C2×C4×D4C2311yescharacteristic
295C2×C4×D4C2313yes—
296C2×C4×D4C2316yes—
297C2×C4×D4C2316yes—
298C2×#117C2313yes—
299C2×#117C2316yes—
300C22×C4⋊C4C2313yes—
301C22×C4⋊C4C2313yes—
302C22×C4⋊C4C2313yes—
303C22×C4⋊C4C2313yes—
304C22×C4⋊C4C2313yes—
305C22×C42C2313yes—
306C22×C42C2313yes—
307C22×C42C2313yes—
308C22×C42C2313yes—
309C22×C42C2316yes—
310#401C2313yes—
311#401C2316yes—
312#401C2313yes—
313#400C2316yes—
314#400C2316yes—
315#400C2313yes—
316#400C2313yes—
317#400C2316yes—
318#400C2313yes—
319#400C2316yes—
320#400C2316yes—
321#400C2316yes—
322#400C2313yes—
323#400C2313yes—
324#400C2316yes—
325#400C2313yes—
326#400C2313yes—
327#400C2313yes—
328#400C2311yescharacteristic
329#400C2313yes—
330#400C2313yes—
331#400C2313yes—
332#399C2316yes—
333#399C2316yes—
334#398C2316yes—
335#398C2316yes—
336#398C2316yes—
337#398C2316yes—
338#398C2316yes—
339#398C2316yes—
340#398C2313yes—
341#398C2316yes—
342#398C2313yes—
343#398C2311yescharacteristic
344#398C2313yes—
345#397C2316yes—
346#397C2313yes—
347#397C2316yes—
348#397C2313yes—
349#397C2316yes—
350#397C2313yes—
351#397C2316yes—
352#397C2316yes—
353#397C2313yes—
354#397C2316yes—
355#397C2313yes—
356#397C2311yescharacteristic
357#397C2311yescharacteristic
358#397C2313yes—
359#396C2316yes—
360#396C2313yes—
361#396C2316yes—
362#396C2316yes—
363#396C2313yes—
364#394C2316yes—
365#394C2313yes—
366#394C2313yes—
367#393C2313yes—
368#393C2316yes—
369#393C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#391C2313yes—
374#391C2316yes—
375#391C2313yes—
376#391C2313yes—
377#391C2313yes—
378#391C2313yes—
379#391C2313yes—
380#391C2313yes—
381#391C2313yes—
382#391C2313yes—
383#391C2313yes—
384#391C2316yes—
385#391C2313yes—
386#391C2313yes—
387#390C2316yes—
388#390C2313yes—
389#390C2313yes—
390#390C2313yes—
391#390C2313yes—
392#390C2313yes—
393#390C2313yes—
394#390C2313yes—
395#390C2313yes—
396#390C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2316yes—
400#389C2316yes—
401#389C2313yes—
402#389C2313yes—
403#389C2316yes—
404#389C2313yes—
405#389C2313yes—
406#389C2313yes—
407#389C2313yes—
408#389C2313yes—
409#389C2313yes—
410#389C2316yes—
411#389C2316yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2316yes—
422#389C2313yes—
423#389C2316yes—
424#389C2313yes—
425#389C2313yes—
426#389C2313yes—
427#389C2313yes—
428#388C2316yes—
429#388C2316yes—
430#388C2313yes—
431#388C2316yes—
432#388C2313yes—
433#388C2316yes—
434#388C2316yes—
435#388C2316yes—
436#388C2316yes—
437#388C2316yes—
438#388C2316yes—
439#388C2313yes—
440#388C2313yes—
441#388C2316yes—
442#388C2313yes—
443#388C2313yes—
444#388C2316yes—
445#388C2316yes—
446#388C2316yes—
447#388C2313yes—
448#388C2316yes—
449#388C2313yes—
450#388C2316yes—
451#388C2313yes—
452#388C2313yes—
453#388C2313yes—
454#388C2313yes—
455#388C2313yes—
456#388C2313yes—
457#387C2313yes—
458#387C2316yes—
459#387C2313yes—
460#387C2316yes—
461#387C2316yes—
462#387C2316yes—
463#387C2316yes—
464#387C2316yes—
465#387C2316yes—
466#387C2316yes—
467#387C2316yes—
468#387C2316yes—
469#387C2316yes—
470#387C2313yes—
471#387C2316yes—
472#387C2313yes—
473#387C2313yes—
474#387C2313yes—
475#387C2313yes—
476#387C2316yes—
477#387C2316yes—
478#387C2316yes—
479#387C2313yes—
480#387C2313yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2316yes—
487#387C2313yes—
488#387C2311yescharacteristic
489#387C2311yescharacteristic
490#387C2313yes—
491#387C2313yes—
492#386C2313yes—
493#386C2316yes—
494#386C2313yes—
495#386C2313yes—
496#386C2316yes—
497#386C2311yescharacteristic
498#386C2313yes—
499#386C2313yes—
500#386C2313yes—
501#386C2313yes—
502#385C2316yes—
503#385C2316yes—
504#385C2316yes—
505#385C2316yes—
506#385C2313yes—
507#385C2316yes—
508#385C2313yes—
509#385C2313yes—
510#385C2316yes—
511#385C2316yes—
512#385C2313yes—
513#385C2313yes—
514#385C2311yescharacteristic
515#385C2311yescharacteristic
516#385C2313yes—
517#384C2313yes—
518#384C2313yes—
519#384C2313yes—
520#384C2313yes—
521#384C2313yes—
522#383C2313yes—
523#383C2316yes—
524#383C2313yes—
525#383C2316yes—
526#382C2313yes—
527#382C2316yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#381C2316yes—
535#381C2313yes—
536#381C2311yescharacteristic
537#381C2311yescharacteristic
538#381C2313yes—
539#380C2313yes—
540#380C2313yes—
541#380C2313yes—
542#380C2313yes—
543#380C2313yes—
544#380C2316yes—
545#380C2313yes—
546#380C2313yes—
547#380C2316yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2311yescharacteristic
555C4×C4⋊C4C2313yes—
556C4×C4⋊C4C2313yes—
557C4×C4⋊C4C2316yes—
558C4×C4⋊C4C2316yes—
559C4×C4⋊C4C2313yes—
560C4×C4⋊C4C2316yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2316yes—
566C4×C4⋊C4C2316yes—
567C4×C4⋊C4C2316yes—
568C4×C4⋊C4C2316yes—
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⋊C4C2316yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2313yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C22⋊C4C2316yes—
595C4×C22⋊C4C2316yes—
596C4×C22⋊C4C2316yes—
597C4×C22⋊C4C2313yes—
598C4×C22⋊C4C2313yes—
599C4×C22⋊C4C2313yes—
600C4×C22⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2313yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2316yes—
610C4×C22⋊C4C2313yes—
611C4×C22⋊C4C2313yes—
612#376C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2316yes—
616#376C2313yes—
617#376C2313yes—
618#376C2313yes—
619#376C2313yes—
620#376C2313yes—
621#376C2313yes—
622C2×#95C2313yes—
623C2×#95C2311yescharacteristic
624C2×#95C2313yes—
625C2×#95C2313yes—
626C43C2313yes—
627C2×#41—24no—
628C2×#41—24no—
629C2×#41—24no—
630C22×Q8—24no—
631C22×Q8—24no—
632C22×Q8—24no—
633C22×Q8—24no—
634C22×Q8—24no—
635C22×Q8#4118yes—
636C22×Q8C2413yes—
637C22×Q8C2413yes—
638C22×Q8C2413yes—
639C22×Q8C2411yescharacteristic
640C22×D4C2413yes—
641C22×D4C2413yes—
642C22×D4C2413yes—
643C22×D4C2411yescharacteristic
644C23×C4C2413yes—
645C23×C4C2413yes—
646C23×C4C2411yescharacteristic
647C23×C4C2413yes—
648C23×C4C2413yes—
649C23×C4C2411yescharacteristic
650C23×C4C2411yescharacteristic
651C23×C4C2411yescharacteristic
652C23×C4C2413yes—
653C23×C4C2413yes—
654C23×C4C2413yes—
655C23×C4C2416yes—
656C4⋊Q8—212no—
657C4⋊Q8—212no—
658#126—86no—
659#125—212no—
660#125—212no—
661#125—86no—
662#124—212no—
663#124—212no—
664#123—24no—
665#123—46no—
666C22⋊Q8—212no—
667C22⋊Q8—212no—
668C22⋊Q8—212no—
669C22⋊Q8—212no—
670C22⋊Q8—46no—
671#121—212no—
672#121—212no—
673#121—212no—
674C4×Q8—212no—
675C4×Q8—212no—
676C4×Q8—24no—
677C4×Q8—24no—
678C4×Q8—24no—
679C4×Q8—24no—
680C4×Q8—24no—
681C4×Q8—24no—
682C4×Q8—24no—
683C4×Q8—24no—
684C4×Q8—24no—
685C4×Q8—24no—
686C4×Q8—212no—
687C4×Q8—212no—
688C4×Q8—212no—
689C4×Q8—212no—
690C4×Q8—212no—
691C4×Q8—212no—
692C4×Q8—212no—
693C4×Q8#4118yes—
694C4×Q8#4118yes—
695C4×D4—24no—
696C4×D4—212no—
697C4×D4—212no—
698C4×D4—212no—
699C4×D4—212no—
700C4×D4—212no—
701C4×D4—412no—
702C4×D4—46no—
703C4×D4—86no—
704#117—212no—
705#117—86no—
706C2×C4⋊C4—212no—
707C2×C4⋊C4—212no—
708C2×C4⋊C4—212no—
709C2×C4⋊C4—212no—
710C2×C4⋊C4—212no—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2413yes—
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2416yes—
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2416yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2416yes—
722C2×C4⋊C4C2411yescharacteristic
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2413yes—
725C2×C4⋊C4C2413yes—
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2413yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2416yes—
741C2×C4⋊C4C2416yes—
742C2×C4⋊C4C2413yes—
743C2×C4⋊C4C2416yes—
744C2×C4⋊C4C2413yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C4⋊C4C2413yes—
750C2×C4⋊C4C2413yes—
751C2×C4⋊C4C2413yes—
752C2×C4⋊C4C2416yes—
753C2×C4⋊C4C2413yes—
754C2×C4⋊C4C2413yes—
755C2×C4⋊C4C2411yescharacteristic
756C2×C4⋊C4C2411yescharacteristic
757C2×C4⋊C4C2413yes—
758C2×C4⋊C4C2416yes—
759C2×C4⋊C4C2413yes—
760C2×C4⋊C4C2413yes—
761C2×C4⋊C4C2413yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2411yescharacteristic
765C2×C22⋊C4C2411yescharacteristic
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2416yes—
775C2×C22⋊C4C2416yes—
776C2×C22⋊C4C2413yes—
777C2×C22⋊C4C2413yes—
778C2×C22⋊C4C2411yescharacteristic
779C2×C22⋊C4C2411yescharacteristic
780C2×C22⋊C4C2411yescharacteristic
781C2×C22⋊C4C2413yes—
782C2×C22⋊C4C2416yes—
783C2×C22⋊C4C2413yes—
784C2×C22⋊C4C2416yes—
785C2×C22⋊C4C2413yes—
786C2×C22⋊C4C2416yes—
787C2×C22⋊C4C2413yes—
788C2×C22⋊C4C2413yes—
789C2×C22⋊C4C2413yes—
790C2×C22⋊C4C2413yes—
791C2×C22⋊C4C2411yescharacteristic
792C2×C22⋊C4C2413yes—
793C2×C22⋊C4C2413yes—
794C2×C22⋊C4C2416yes—
795C2×C22⋊C4C2413yes—
796C2×C42—212no—
797C2×C42—212no—
798C2×C42—212no—
799C2×C42—212no—
800C2×C42—86no—
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2411yescharacteristic
805C2×C42C2413yes—
806C2×C42C2413yes—
807C2×C42C2413yes—
808C2×C42C2413yes—
809C2×C42C2413yes—
810C2×C42C2413yes—
811C2×C42C2413yes—
812C2×C42C2413yes—
813C2×C42C2413yes—
814C2×C42C2413yes—
815C2×C42C2413yes—
816C2×C42C2413yes—
817C2×C42C2413yes—
818C2×C42C2413yes—
819C2×C42C2413yes—
820C2×C42C2413yes—
821C2×C42C2416yes—
822C2×C42C2413yes—
823C2×C42C2416yes—
824C2×C42C2416yes—
825C2×C42C2416yes—
826C2×C42C2416yes—
827C2×C42C2413yes—
828C2×C42C2413yes—
829C2×C42C2413yes—
830#95C2411yescharacteristic
831#95C2411yescharacteristic
832#95C2411yescharacteristic
833#95C2411yescharacteristic
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2413yes—
841#95C2413yes—
842#95C2413yes—
843#95C2413yes—
844#95C2413yes—
845#95C2413yes—
846#95C2411yescharacteristic
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2416yes—
853#95C2416yes—
854#95C2411yescharacteristic
855#95C2411yescharacteristic
856#95C2411yescharacteristic
857#95C2411yescharacteristic
858#95C2413yes—
859#95C2413yes—
860#95C2413yes—
861#95C2413yes—
862#95C2413yes—
863#95C2413yes—
864#95C2413yes—
865#95C2413yes—
866#95C2413yes—
867#95C2413yes—
868#95C2413yes—
869#95C2413yes—
870#95C2413yes—
871#95C2416yes—
872#95C2413yes—
873#95C2416yes—
874#95C2416yes—
875#95C2416yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2416yes—
880#95C2413yes—
881#95C2413yes—
882#95C2413yes—
883#95C2413yes—
884#95C2411yescharacteristic
885#95C2416yes—
886#95C2411yescharacteristic
887#95C2411yescharacteristic
888#95C2411yescharacteristic
889#95C2413yes—
890#95C2413yes—
891#95C2411yescharacteristic
892#95C2416yes—
893#95C2416yes—
894#95C2413yes—
895#95C2413yes—
896#95C2413yes—
897#95C2413yes—
898#95C2416yes—
899#95C2416yes—
900#95C2413yes—
901#95C2413yes—
902C24C2513yes—
903C24C2511yescharacteristic
904C24C2511yescharacteristic
905#41—416no—
906C2×Q8—232no—
907C2×Q8—26no—
908C2×Q8—26no—
909C2×Q8—26no—
910C2×Q8—26no—
911C2×Q8—26no—
912C2×Q8—26no—
913C2×Q8—43no—
914C2×Q8—43no—
915C2×Q8—416no—
916C2×Q8C2×#41112yes—
917C2×Q8C2×#4114yes—
918C2×Q8C2×#4114yes—
919C2×Q8C2×#4114yes—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—26no—
923C2×D4—26no—
924C2×D4—26no—
925C2×D4—26no—
926C2×D4—26no—
927C2×D4—26no—
928C2×D4—26no—
929C2×D4—26no—
930C2×D4—43no—
931C2×D42−1+414yes—
932C22×C4—26no—
933C22×C4—26no—
934C22×C4—22no—
935C22×C4—26no—
936C22×C4—22no—
937C22×C4—22no—
938C22×C4—26no—
939C22×C4—22no—
940C22×C4—26no—
941C22×C4—22no—
942C22×C4—22no—
943C22×C4—22no—
944C22×C4—22no—
945C22×C4—22no—
946C22×C4—26no—
947C22×C4—26no—
948C22×C4—26no—
949C22×C4—26no—
950C22×C4—26no—
951C22×C4—26no—
952C22×C4—26no—
953C22×C4—26no—
954C22×C4—26no—
955C22×C4—212no—
956C22×C4—43no—
957C22×C4—43no—
958C22×C4—43no—
959C22×C4—41no—
960C22×C4—41no—
961C22×C4—41no—
962C22×C4—43no—
963C22×C4—46no—
964C22×C4—43no—
965C22×C4—46no—
966C22×C4—43no—
967C22×C4C2×#41112yes—
968C22×C4C2511yescharacteristic
969C22×C4C2511yescharacteristic
970C22×C4C2511yescharacteristic
971C22×C4C2511yescharacteristic
972C22×C4C2511yescharacteristic
973C22×C4C2513yes—
974C22×C4C2513yes—
975C22×C4C2511yescharacteristic
976C22×C4C2511yescharacteristic
977C22×C4C2513yes—
978C22×C4C2513yes—
979C22×C4C2513yes—
980C22×C4C2511yescharacteristic
981C22×C4C2513yes—
982C22×C4C2513yes—
983C22×C4C2511yescharacteristic
984C22×C4C2513yes—
985C22×C4C2513yes—
986C22×C4C2511yescharacteristic
987C22×C4C2513yes—
988C22×C4C2513yes—
989C22×C4C2511yescharacteristic
990C22×C4C2511yescharacteristic
991C22×C4C2513yes—
992C22×C4C2513yes—
993C22×C4C2513yes—
994C22×C4C2511yescharacteristic
995C22×C4C2513yes—
996C4⋊C4—26no—
997C4⋊C4—26no—
998C4⋊C4—212no—
999C4⋊C4—212no—
1000C4⋊C4—212no—
1001C4⋊C4—26no—
1002C4⋊C4—26no—
1003C4⋊C4—26no—
1004C4⋊C4—26no—
1005C4⋊C4—26no—
1006C4⋊C4—212no—
1007C4⋊C4—22no—
1008C4⋊C4—26no—
1009C4⋊C4—26no—
1010C4⋊C4—26no—
1011C4⋊C4—22no—
1012C4⋊C4—26no—
1013C4⋊C4—26no—
1014C4⋊C4—26no—
1015C4⋊C4—26no—
1016C4⋊C4—26no—
1017C4⋊C4—26no—
1018C4⋊C4—212no—
1019C4⋊C4—212no—
1020C4⋊C4—22no—
1021C4⋊C4—26no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—41no—
1025C4⋊C4—43no—
1026C4⋊C4—43no—
1027C4⋊C4—46no—
1028C4⋊C4—41no—
1029C4⋊C4—43no—
1030C4⋊C4—46no—
1031C4⋊C4—43no—
1032C4⋊C4—46no—
1033C4⋊C4—46no—
1034C4⋊C4—43no—
1035C4⋊C4—43no—
1036C4⋊C4—43no—
1037C4⋊C4—43no—
1038C4⋊C4—43no—
1039C4⋊C4—43no—
1040C4⋊C4—43no—
1041C4⋊C4—43no—
1042C4⋊C4—46no—
1043C4⋊C4—43no—
1044C4⋊C4—43no—
1045C4⋊C4C2×#41112yes—
1046C4⋊C4C2×#41112yes—
1047C22⋊C4—22no—
1048C22⋊C4—26no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—26no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—26no—
1056C22⋊C4—26no—
1057C22⋊C4—26no—
1058C22⋊C4—26no—
1059C22⋊C4—22no—
1060C22⋊C4—26no—
1061C22⋊C4—26no—
1062C22⋊C4—26no—
1063C22⋊C4—212no—
1064C22⋊C4—212no—
1065C22⋊C4—26no—
1066C22⋊C4—46no—
1067C22⋊C4—43no—
1068C22⋊C4—41no—
1069C22⋊C4—43no—
1070C22⋊C4—43no—
1071C22⋊C4—43no—
1072C22⋊C4—43no—
1073C22⋊C4—46no—
1074C22⋊C4—46no—
1075C22⋊C4—43no—
1076C22⋊C4—43no—
1077C22⋊C4—46no—
1078C22⋊C4—43no—
1079C22⋊C4—43no—
1080C22⋊C4—43no—
1081C42—26no—
1082C42—26no—
1083C42—26no—
1084C42—26no—
1085C42—26no—
1086C42—26no—
1087C42—26no—
1088C42—26no—
1089C42—26no—
1090C42—26no—
1091C42—26no—
1092C42—26no—
1093C42—26no—
1094C42—26no—
1095C42—26no—
1096C42—26no—
1097C42—26no—
1098C42—26no—
1099C42—22no—
1100C42—46no—
1101C42—46no—
1102C42—46no—
1103C42—46no—
1104C42—43no—
1105C42—43no—
1106C42—43no—
1107C42—46no—
1108C42C2×#41112yes—
1109C42C2×#41112yes—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—23no—
1121C23—23no—
1122C23—23no—
1123C23—23no—
1124C23—23no—
1125C23—23no—
1126C23—23no—
1127C23C22×#4112yes—
1128C23C2×2−1+412yes—
1129C23C2×2−1+412yes—
1130C23#58512yes—
1131C23C2611yescharacteristic
1132Q8—224no—
1133Q8—412no—
1134Q8—86no—
1135Q8#529116yes—
1136D4—28no—
1137D4—412no—
1138D4—412no—
1139D4—412no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—21no—
1144C2×C4—23no—
1145C2×C4—21no—
1146C2×C4—23no—
1147C2×C4—21no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—224no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
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—23no—
1171C2×C4—23no—
1172C2×C4—23no—
1173C2×C4—23no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—23no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—23no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—23no—
1187C2×C4—23no—
1188C2×C4—23no—
1189C2×C4—23no—
1190C2×C4—23no—
1191C2×C4—23no—
1192C2×C4—23no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—23no—
1197C2×C4—23no—
1198C2×C4—23no—
1199C2×C4—23no—
1200C2×C4—21no—
1201C2×C4—23no—
1202C2×C4—21no—
1203C2×C4—23no—
1204C2×C4—23no—
1205C2×C4—21no—
1206C2×C4—23no—
1207C2×C4—23no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—23no—
1212C2×C4—23no—
1213C2×C4—21no—
1214C2×C4—23no—
1215C2×C4—21no—
1216C2×C4—44no—
1217C2×C4—44no—
1218C2×C4—412no—
1219C2×C4—44no—
1220C2×C4—412no—
1221C2×C4—412no—
1222C2×C4—44no—
1223C2×C4—412no—
1224C2×C4—412no—
1225C2×C4—86no—
1226C2×C4—812no—
1227C2×C4C22×#4112yes—
1228C2×C4C22×#4112yes—
1229C2×C4C22×#4116yes—
1230C2×C4C22×#4116yes—
1231C2×C4C22×#4116yes—
1232C2×C4C22×#4116yes—
1233C2×C4C22×#4116yes—
1234C2×C4C22×#4116yes—
1235C2×C4C2×2−1+412yes—
1236C22—22no—
1237C22—22no—
1238C22—22no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—22no—
1243C22—22no—
1244C22—22no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—41no—
1249C22—43no—
1250C22—43no—
1251C22—43no—
1252C22—43no—
1253C22—43no—
1254C22—43no—
1255C22—43no—
1256C22#351614yes—
1257C22C23×#4111yescharacteristic
1258C22C23×#4111yescharacteristic
1259C22C23×#4111yescharacteristic
1260C22C22×2−1+411yescharacteristic
1261C22C2×#58511yescharacteristic
1262C22H(7,𝔽2)11yescharacteristic
1263C222−1+611yescharacteristic
1264C4—22no—
1265C4—26no—
1266C4—22no—
1267C4—26no—
1268C4—22no—
1269C4—26no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—43no—
1276C4—41no—
1277C4—43no—
1278C4—43no—
1279C4—43no—
1280C4—43no—
1281C4—43no—
1282C4—41no—
1283C4—41no—
1284C4—43no—
1285C4—41no—
1286C4—43no—
1287C4—43no—
1288C4—43no—
1289C4—41no—
1290C4—43no—
1291C4C2×#529112yes—
1292C2—24no—
1293C2—42no—
1294C2—83no—
1295C2C22×#52911yescharacteristic
1296C2C2×#351611yescharacteristic
1297C2#6285111yescharacteristic
1298C2#6299811yescharacteristic
1299C2#6300011yescharacteristic
1300C2#6300511yescharacteristic
1301C2#6300811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#36434C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36578C2semidirect
2. #36577C2semidirect
3. #36551C2semidirect
4. Q8×#123C2semidirect
5. #36488C2semidirect
7. #36256C2semidirect
8. #36255C2semidirect
9. #35974C2semidirect
10. #35911C2semidirect
11. #35898C2semidirect
12. #35886C2semidirect
13. #35884C2semidirect
14. #35883C2semidirect
15. #35868C2semidirect
16. #35854C2semidirect
17. #35655C2semidirect
18. #35650C2semidirect
19. #35610C2semidirect
20. #35587C2semidirect
21. #35270C2semidirect
22. #35231C2semidirect
23. #34811C2semidirect
24. #34788C2semidirect
25. #34336C2semidirect
26. #34294C2semidirect
27. #34294C2semidirect
28. #34263C2semidirect
29. #34192C2semidirect
30. C4×D4×Q8C2semidirect
31. C2×#2276C2semidirect

Maximal subgroups

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

subgroupindex
#365782
#365772
#365512
Q8×#1232
#364882
#364342
#362562
#362552
#359742
#359112
#358982
#358862
#358842
#358832
#358682
#358542
#356552
#356502
#356102
#355872
#352702
#352312
#348112
#347882
#343362
#342942
#342632
#341922
C4×D4×Q82
C2×#22762