Finite Group Databasebeta

← #7746766

Subgroups — #7746766

Order 512.

4786 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45381C214yesmaximal, complemented
2#45318C212yesmaximal, complemented
3#45302C214yesmaximal, complemented
4#45270C212yesmaximal, complemented
5#45260C214yesmaximal, complemented
6#45090C214yesmaximal, complemented
7#44993C214yesmaximal, complemented
8#42899C214yesmaximal, complemented
9#42632C214yesmaximal, complemented
10#42557C214yesmaximal, complemented
11#36609C211yesmaximal, characteristic, complemented
12#36560C211yesmaximal, characteristic, complemented
13#36189C212yesmaximal, complemented
14#36187C211yesmaximal, characteristic, complemented
15#36151C211yesmaximal, characteristic, complemented
16#36150C212yesmaximal, complemented
17#36040C212yesmaximal, complemented
18#36011C212yesmaximal, complemented
19#35895C214yesmaximal, complemented
20#35884C214yesmaximal, complemented
21#35288C212yesmaximal, complemented
22#35283C211yesmaximal, characteristic, complemented
23#34551C211yesmaximal, characteristic, complemented
24#34225C212yesmaximal, complemented
25#34207C211yesmaximal, characteristic, complemented
26C2×#557C2212yes—
27C2×#555C2212yes—
28C2×#533C2212yes—
29C2×#532C2211yescharacteristic
30C2×#520C2212yes—
31#2868C2211yescharacteristic
32#2862C2211yescharacteristic
33#2859C2212yes—
34#2858C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2856C2212yes—
38#2837C2218yes—
39#2797C2218yes—
40#2796C2218yes—
41#2781C2218yes—
42#2771C2218yes—
43#2756C2218yes—
44#2754C2218yes—
45#2747C2218yes—
46#2744C2218yes—
47#2741C2218yes—
48#2738C2218yes—
49#2731C2218yes—
50#2711C2218yes—
51#2654C2218yes—
52#2651C2218yes—
53#2647C2212yes—
54#2644C2214yes—
55#2635C2214yes—
56#2628C2214yes—
57#2628C2212yes—
58#2624C2214yes—
59#2595C2218yes—
60#2594C2218yes—
61#2592C2214yes—
62#2591C2214yes—
63#2580C2212yes—
64#2580C2214yes—
65#2577C2218yes—
66#2570C2214yes—
67#2568C2212yes—
68#2565C2214yes—
69#2563C2212yes—
70#2563C2214yes—
71#2546C2214yes—
72#2540C2214yes—
73#2537C2214yes—
74#2536C2212yes—
75#2532C2218yes—
76#2531C2218yes—
77#2531C2218yes—
78#2530C2218yes—
79#2513C2214yes—
80#2513C2214yes—
81#2511C2214yes—
82#2511C2214yes—
83#2507C2214yes—
84#2506C2214yes—
85#2506C2214yes—
86#2500C2214yes—
87#2497C2214yes—
88#2492C2214yes—
89#2491C2214yes—
90#2491C2214yes—
91#2490C2214yes—
92#2490C2214yes—
93#2489C2214yes—
94#2487C2214yes—
95#2484C2214yes—
96#2475C2218yes—
97#2474C2218yes—
98#2459C2218yes—
99#2454C2218yes—
100#2454C2214yes—
101#2454C2214yes—
102#2453C2214yes—
103#2451C2214yes—
104#2448C2214yes—
105#2448C2214yes—
106#2448C2214yes—
107#2448C2218yes—
108#2447C2214yes—
109#2447C2214yes—
110#2442C2218yes—
111#2442C2214yes—
112#2441C2214yes—
113#2427C2214yes—
114#2427C2214yes—
115#2426C2214yes—
116#2426C2214yes—
117#2426C2214yes—
118#2423C2214yes—
119#2423C2214yes—
120#2421C2214yes—
121#2420C2214yes—
122#2417C2214yes—
123#2415C2214yes—
124#2414C2214yes—
125#2407C2214yes—
126#2402C2211yescharacteristic
127#2402C2212yes—
128#2401C2212yes—
129#2401C2212yes—
130#2401C2212yes—
131#2398C2212yes—
132#2398C2211yescharacteristic
133#2396C2214yes—
134#2396C2212yes—
135#2396C2211yescharacteristic
136#2395C2212yes—
137#2395C2214yes—
138#2395C2212yes—
139#2395C2212yes—
140#2392C2212yes—
141#2392C2211yescharacteristic
142#2370C2214yes—
143#2370C2214yes—
144#2367C2214yes—
145#2367C2214yes—
146#2365C2214yes—
147#2363C2214yes—
148#2362C2214yes—
149#2362C2214yes—
150#2362C2214yes—
151#2361C2214yes—
152#2361C2214yes—
153#2360C2214yes—
154#2357C2212yes—
155#2356C2214yes—
156#2354C2214yes—
157#2354C2214yes—
158#2352C2214yes—
159#2351C2212yes—
160#2351C2214yes—
161D4×C4⋊C4C2214yes—
162#2347C2214yes—
163#2346C2214yes—
164#2345C2214yes—
165#2341C2214yes—
166#2331C2212yes—
167#2326C2212yes—
168#2326C2212yes—
169#2324C2214yes—
170#2323C2214yes—
171#2323C2214yes—
172#2320C2214yes—
173#2319C2214yes—
174#2314C2212yes—
175#2311C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2212yes—
178C4×C4⋊Q8C2211yescharacteristic
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2212yes—
181C4×#127C2211yescharacteristic
182C4×#127C2211yescharacteristic
183#2285C2212yes—
184C2×#384C2211yescharacteristic
185#2276C2214yes—
186C42×Q8C2211yescharacteristic
187C42×D4C2212yes—
188C42×D4C2211yescharacteristic
189C4×#117C2211yescharacteristic
190C4×#117C2212yes—
191C22×#41C2312yes—
192#557—48no—
193#555—48no—
194#533—216no—
195#532—28no—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2314yes—
199C2×C4⋊Q8C2314yes—
200C2×C4⋊Q8C2311yescharacteristic
201C2×#127C2311yescharacteristic
202C2×#125C2314yes—
203C2×#125C2314yes—
204C2×#125C2318yes—
205C2×#124C2312yes—
206C2×#124C2314yes—
207C2×#124C2314yes—
208C2×#124C2318yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2314yes—
216C2×#121C2314yes—
217C2×#121C2314yes—
218#520—48no—
219C2×C4×Q8C2312yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2312yes—
229C2×C4×D4C2312yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2314yes—
234C2×C4×D4C2312yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2312yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×#117C2311yescharacteristic
242C2×#117C2314yes—
243C2×#117C2311yescharacteristic
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2314yes—
247C2×#117C2314yes—
248C2×#117C2314yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2314yes—
251C22×C4⋊C4C2314yes—
252C22×C42C2312yes—
253C22×C42C2311yescharacteristic
254#401C2312yes—
255#400C2314yes—
256#400C2314yes—
257#400C2318yes—
258#400C2312yes—
259#400C2314yes—
260#400C2318yes—
261#400C2318yes—
262#400C2318yes—
263#400C2312yes—
264#400C2312yes—
265#400C2311yescharacteristic
266#400C2312yes—
267#400C2312yes—
268#400C2312yes—
269#400C2312yes—
270#399C2311yescharacteristic
271#399C2314yes—
272#399C2318yes—
273#399C2318yes—
274#399C2314yes—
275#399C2312yes—
276#399C2318yes—
277#398C2318yes—
278#398C2318yes—
279#398C2318yes—
280#398C2318yes—
281#398C2318yes—
282#398C2312yes—
283#398C2311yescharacteristic
284#398C2312yes—
285#398C2312yes—
286#398C2312yes—
287#398C2314yes—
288#397C2318yes—
289#397C2318yes—
290#397C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2312yes—
294#397C2318yes—
295#397C2318yes—
296#397C2311yescharacteristic
297#397C2312yes—
298#397C2312yes—
299#397C2312yes—
300#397C2312yes—
301#397C2312yes—
302#397C2312yes—
303#397C2318yes—
304#396C2312yes—
305#396C2318yes—
306#396C2318yes—
307#396C2312yes—
308#396C2312yes—
309#396C2318yes—
310#395C2311yescharacteristic
311#395C2314yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2311yescharacteristic
316#394C2314yes—
317#394C2318yes—
318#394C2318yes—
319#394C2312yes—
320#394C2312yes—
321#394C2312yes—
322#394C2312yes—
323#394C2318yes—
324#393C2311yescharacteristic
325#393C2314yes—
326#393C2314yes—
327#393C2314yes—
328#393C2314yes—
329#393C2312yes—
330#392C2311yescharacteristic
331#392C2318yes—
332#391C2312yes—
333#391C2314yes—
334#391C2312yes—
335#391C2314yes—
336#391C2314yes—
337#391C2318yes—
338#391C2318yes—
339#391C2314yes—
340#391C2314yes—
341#391C2314yes—
342#391C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2314yes—
346#390C2314yes—
347#390C2314yes—
348#390C2318yes—
349#390C2314yes—
350#390C2314yes—
351#390C2314yes—
352#390C2318yes—
353#390C2318yes—
354#390C2314yes—
355#390C2314yes—
356#390C2314yes—
357#390C2318yes—
358#389C2314yes—
359#389C2314yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2314yes—
368#389C2314yes—
369#389C2314yes—
370#389C2318yes—
371#389C2318yes—
372#389C2314yes—
373#389C2318yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#386C2318yes—
413#386C2318yes—
414#386C2318yes—
415#386C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2314yes—
428#384C2314yes—
429#383C2318yes—
430#382C2314yes—
431#382C2318yes—
432#382C2314yes—
433#382C2312yes—
434#382C2312yes—
435#382C2314yes—
436#381C2318yes—
437#381C2314yes—
438#380C2318yes—
439#380C2318yes—
440#380C2318yes—
441#380C2318yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2318yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2318yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C22⋊C4C2318yes—
480C4×C22⋊C4C2314yes—
481C4×C22⋊C4C2318yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2312yes—
486C4×C22⋊C4C2312yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497#376C2312yes—
498#376C2311yescharacteristic
499#376C2311yescharacteristic
500#376C2318yes—
501#376C2312yes—
502C43C2311yescharacteristic
503C43C2311yescharacteristic
504C43C2312yes—
505C2×#41—28no—
506C2×#41—28no—
507C2×#41—44no—
508C22×Q8C2414yes—
509C22×Q8C2412yes—
510C22×Q8C2411yescharacteristic
511C22×Q8C2414yes—
512C22×D4C2414yes—
513C22×D4C2412yes—
514C22×D4C2414yes—
515C22×D4C2411yescharacteristic
516C22×D4C2412yes—
517C22×D4C2418yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2412yes—
521C23×C4C2412yes—
522C23×C4C2414yes—
523C23×C4C2411yescharacteristic
524C23×C4C2414yes—
525C23×C4C2414yes—
526C23×C4C2414yes—
527C4⋊Q8—28no—
528C4⋊Q8—28no—
529C4⋊Q8—48no—
530C4⋊Q8—48no—
531C4⋊Q8#4118yes—
532#127—24no—
533#125—216no—
534#125—48no—
535#125—416no—
536#124—28no—
537#124—48no—
538#124—48no—
539#124—416no—
540C22⋊Q8—216no—
541C22⋊Q8—216no—
542C22⋊Q8—48no—
543C22⋊Q8—48no—
544#121—216no—
545#121—48no—
546#121—48no—
547#121—48no—
548#121—48no—
549C4×Q8—216no—
550C4×Q8—216no—
551C4×Q8—28no—
552C4×Q8—24no—
553C4×Q8—44no—
554C4×Q8—48no—
555C4×Q8—48no—
556C4×Q8—44no—
557C4×Q8—48no—
558C4×Q8—48no—
559C4×D4—28no—
560C4×D4—216no—
561C4×D4—28no—
562C4×D4—24no—
563C4×D4—48no—
564C4×D4—48no—
565C4×D4—48no—
566C4×D4—44no—
567C4×D4—44no—
568C4×D4—44no—
569C4×D4—44no—
570C4×D4—48no—
571#117—24no—
572#117—216no—
573#117—24no—
574#117—44no—
575#117—44no—
576#117—48no—
577#117—48no—
578#117—48no—
579C2×C4⋊C4—48no—
580C2×C4⋊C4—48no—
581C2×C4⋊C4—44no—
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2412yes—
584C2×C4⋊C4C2412yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2414yes—
587C2×C4⋊C4C2414yes—
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2414yes—
593C2×C4⋊C4C2412yes—
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2418yes—
598C2×C4⋊C4C2418yes—
599C2×C4⋊C4C2414yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2414yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2418yes—
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2412yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2412yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2414yes—
624C2×C22⋊C4C2411yescharacteristic
625C2×C22⋊C4C2411yescharacteristic
626C2×C22⋊C4C2414yes—
627C2×C22⋊C4C2418yes—
628C2×C22⋊C4C2412yes—
629C2×C22⋊C4C2418yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2418yes—
635C2×C22⋊C4C2418yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2412yes—
640C2×C22⋊C4C2412yes—
641C2×C22⋊C4C2412yes—
642C2×C22⋊C4C2412yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2412yes—
645C2×C22⋊C4C2412yes—
646C2×C22⋊C4C2418yes—
647C2×C22⋊C4C2418yes—
648C2×C22⋊C4C2418yes—
649C2×C22⋊C4C2418yes—
650C2×C22⋊C4C2418yes—
651C2×C22⋊C4C2418yes—
652C2×C22⋊C4C2418yes—
653C2×C22⋊C4C2418yes—
654C2×C22⋊C4C2418yes—
655C2×C22⋊C4C2418yes—
656C2×C42—24no—
657C2×C42—28no—
658C2×C42C2411yescharacteristic
659C2×C42C2412yes—
660C2×C42C2414yes—
661C2×C42C2412yes—
662C2×C42C2412yes—
663C2×C42C2412yes—
664C2×C42C2418yes—
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2412yes—
668C2×C42C2412yes—
669C2×C42C2412yes—
670C2×C42C2412yes—
671C2×C42C2412yes—
672C2×C42C2412yes—
673C2×C42C2412yes—
674C2×C42C2412yes—
675C2×C42C2412yes—
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2418yes—
679C2×C42C2414yes—
680C2×C42C2418yes—
681C2×C42C2418yes—
682C2×C42C2418yes—
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#95C2412yes—
686#95C2412yes—
687#95C2412yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2412yes—
695#95C2412yes—
696#95C2412yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2412yes—
701#95C2411yescharacteristic
702#95C2411yescharacteristic
703#95C2412yes—
704#95C2411yescharacteristic
705#95C2412yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2412yes—
710#95C2412yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2418yes—
715#95C2411yescharacteristic
716#95C2412yes—
717#95C2412yes—
718#95C2418yes—
719#95C2418yes—
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2414yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730C24C2512yes—
731C24C2514yes—
732C24C2511yescharacteristic
733#41—432no—
734C2×Q8—28no—
735C2×Q8—24no—
736C2×Q8—22no—
737C2×Q8—28no—
738C2×Q8—24no—
739C2×Q8—28no—
740C2×Q8—28no—
741C2×Q8—42no—
742C2×Q8—48no—
743C2×Q8C2×#4118yes—
744C2×D4—24no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—28no—
748C2×D4—24no—
749C2×D4—24no—
750C2×D4—22no—
751C2×D4—24no—
752C2×D4—28no—
753C2×D4—28no—
754C2×D4—44no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—24no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—28no—
768C22×C4—24no—
769C22×C4—24no—
770C22×C4—28no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—28no—
778C22×C4—44no—
779C22×C4—48no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—48no—
783C22×C4—48no—
784C22×C42−1+414yes—
785C22×C4C2512yes—
786C22×C4C2512yes—
787C22×C4C2512yes—
788C22×C4C2512yes—
789C22×C4C2511yescharacteristic
790C22×C4C2512yes—
791C22×C4C2512yes—
792C22×C4C2518yes—
793C22×C4C2512yes—
794C22×C4C2512yes—
795C22×C4C2514yes—
796C22×C4C2518yes—
797C22×C4C2514yes—
798C22×C4C2512yes—
799C22×C4C2511yescharacteristic
800C22×C4C2512yes—
801C22×C4C2514yes—
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C22×C4C2511yescharacteristic
805C22×C4C2511yescharacteristic
806C22×C4C2512yes—
807C4⋊C4—28no—
808C4⋊C4—216no—
809C4⋊C4—216no—
810C4⋊C4—28no—
811C4⋊C4—22no—
812C4⋊C4—24no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—22no—
816C4⋊C4—22no—
817C4⋊C4—28no—
818C4⋊C4—28no—
819C4⋊C4—22no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—24no—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—28no—
827C4⋊C4—44no—
828C4⋊C4—48no—
829C4⋊C4—44no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4—42no—
833C4⋊C4—42no—
834C4⋊C4—42no—
835C4⋊C4—42no—
836C4⋊C4—42no—
837C4⋊C4—42no—
838C4⋊C4—42no—
839C4⋊C4—42no—
840C4⋊C4—48no—
841C4⋊C4—48no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—48no—
845C4⋊C4—48no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4C2×#41116yes—
849C22⋊C4—24no—
850C22⋊C4—24no—
851C22⋊C4—216no—
852C22⋊C4—216no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—28no—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—42no—
859C22⋊C4—42no—
860C22⋊C4—42no—
861C22⋊C4—42no—
862C22⋊C4—44no—
863C22⋊C4—48no—
864C22⋊C4—48no—
865C22⋊C4—48no—
866C22⋊C4—42no—
867C22⋊C4—42no—
868C22⋊C4—42no—
869C22⋊C4—42no—
870C22⋊C4—48no—
871C22⋊C4—42no—
872C22⋊C4—42no—
873C22⋊C4—48no—
874C22⋊C4—48no—
875C22⋊C4—48no—
876C22⋊C4—48no—
877C22⋊C4—48no—
878C22⋊C4—48no—
879C22⋊C4—48no—
880C22⋊C4—48no—
881C42—24no—
882C42—24no—
883C42—24no—
884C42—22no—
885C42—24no—
886C42—216no—
887C42—22no—
888C42—28no—
889C42—24no—
890C42—22no—
891C42—22no—
892C42—24no—
893C42—24no—
894C42—24no—
895C42—24no—
896C42—24no—
897C42—24no—
898C42—24no—
899C42—24no—
900C42—24no—
901C42—48no—
902C42—44no—
903C42—48no—
904C42—48no—
905C42—48no—
906C42C2×#4114yes—
907C42H(5,𝔽2)14yes—
908C23—21no—
909C23—21no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—24no—
914C23—22no—
915C23—24no—
916C23—22no—
917C23—24no—
918C23—22no—
919C23—22no—
920C23—28no—
921C23—28no—
922C23—22no—
923C23—22no—
924C23C2×2−1+412yes—
925C23C2611yescharacteristic
926Q8—216no—
927Q8—44no—
928Q8—416no—
929Q8—88no—
930D4—416no—
931D4—44no—
932D4—48no—
933D4—48no—
934D4—416no—
935D4—168no—
936C2×C4—21no—
937C2×C4—24no—
938C2×C4—21no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—28no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—28no—
948C2×C4—21no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—28no—
976C2×C4—28no—
977C2×C4—28no—
978C2×C4—28no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—28no—
982C2×C4—28no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—416no—
988C2×C4—48no—
989C2×C4—48no—
990C2×C4—48no—
991C2×C4—48no—
992C2×C4—88no—
993C2×C4—164no—
994C2×C4—164no—
995C2×C4C22×#4118yes—
996C2×C4C22×#4112yes—
997C2×C4C22×#4114yes—
998C2×C4C2×H(5,𝔽2)12yes—
999C2×C4C2×H(5,𝔽2)12yes—
1000C2×C4C2×H(5,𝔽2)12yes—
1001C2×C4C2×2−1+412yes—
1002C2×C4C2×2−1+412yes—
1003C2×C4#58514yes—
1004C2×C4#58514yes—
1005C22—22no—
1006C22—24no—
1007C22—42no—
1008C22—41no—
1009C22—41no—
1010C22—44no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—48no—
1015C22—44no—
1016C22—42no—
1017C22—42no—
1018C22—44no—
1019C22—42no—
1020C22—42no—
1021C22—48no—
1022C22C23×#4111yescharacteristic
1023C22C22×H(5,𝔽2)11yescharacteristic
1024C22C22×2−1+411yescharacteristic
1025C22C2×#58512yes—
1026C22C2×#58512yes—
1027C4—22no—
1028C4—28no—
1029C4—22no—
1030C4—22no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—48no—
1036C4—41no—
1037C4—42no—
1038C4—44no—
1039C4—44no—
1040C4—41no—
1041C4—48no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4#352014yes—
1048C4#352418yes—
1049C2—42no—
1050C2—84no—
1051C2—82no—
1052C2C2×#352011yescharacteristic
1053C2C2×#352412yes—
1054C2#6283611yescharacteristic
1055C2#6283611yescharacteristic
1056C2#6283812yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45381C2semidirect
2. #45318C2semidirect
3. #45302C2semidirect
4. #45270C2semidirect
5. #45260C2semidirect
6. #45090C2semidirect
7. #44993C2semidirect
8. #42899C2semidirect
9. #42632C2semidirect
10. #42557C2semidirect
11. #36609C2semidirect
12. #36560C2semidirect
13. #36189C2semidirect
14. #36187C2semidirect
15. #36151C2semidirect
16. #36150C2semidirect
17. #36040C2semidirect
18. #36011C2semidirect
19. #35895C2semidirect
20. #35884C2semidirect
21. #35288C2semidirect
22. #35283C2semidirect
23. #34551C2semidirect
24. #34225C2semidirect
25. #34207C2semidirect

Maximal subgroups

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

subgroupindex
#453812
#453182
#453022
#452702
#452602
#450902
#449932
#428992
#426322
#425572
#366092
#365602
#361892
#361872
#361512
#361502
#360402
#360112
#358952
#358842
#352882
#352832
#345512
#342252
#342072