Finite Group Databasebeta

← #7646389

Subgroups — #7646389

Order 512.

4784 conjugacy classes of subgroups.

The subgroup lattice has 1157 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42693C214yesmaximal, complemented
2#42691C214yesmaximal, complemented
3#42661C214yesmaximal, complemented
4#42659C214yesmaximal, complemented
5#39761C212yesmaximal, complemented
6#39736C212yesmaximal, complemented
7#39505C212yesmaximal, complemented
8#39478C212yesmaximal, complemented
9#39193C212yesmaximal, complemented
10#39159C212yesmaximal, complemented
11#38977C212yesmaximal, complemented
12#38941C212yesmaximal, complemented
13#37494C214yesmaximal, complemented
14#36781C218yesmaximal, complemented
15#35620C212yesmaximal, complemented
16#35618C212yesmaximal, complemented
17#35275C211yesmaximal, characteristic, complemented
18#35273C211yesmaximal, characteristic
19#35230C214yesmaximal, complemented
20#35160C212yesmaximal, complemented
21#35158C212yesmaximal, complemented
22#34955C211yesmaximal, characteristic, complemented
23#34952C211yesmaximal, characteristic, complemented
24#34206C211yesmaximal, characteristic, complemented
25C2×#2355C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic, complemented
27C2×#544C2212yes—
28C2×#537C2212yes—
29C2×#532C2211yescharacteristic
30C2×#520C2212yes—
31C2×C4×#41C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33#2868C2212yes—
34#2859C2212yes—
35#2857C2212yes—
36#2856C2212yes—
37#2852C2218yes—
38#2850C2218yes—
39#2832C2218yes—
40#2831C2218yes—
41#2795C2218yes—
42#2793C2218yes—
43#2779C2218yes—
44#2767C2218yes—
45#2765C2218yes—
46#2761C2218yes—
47#2758C2218yes—
48#2757C2218yes—
49#2747C2218yes—
50#2745C2218yes—
51#2739C2218yes—
52#2737C2218yes—
53#2731C2218yes—
54#2716C2218yes—
55#2691C2218yes—
56#2686C2218yes—
57#2665C2218yes—
58#2660C2214yes—
59#2653C2218yes—
60#2651C2218yes—
61#2650C2218yes—
62#2645C2214yes—
63#2643C2218yes—
64#2640C2214yes—
65#2639C2218yes—
66#2625C2214yes—
67#2620C2214yes—
68#2620C2214yes—
69#2592C2212yes—
70#2592C2212yes—
71#2591C2214yes—
72#2582C2211yescharacteristic
73#2582C2211yescharacteristic
74#2581C2212yes—
75#2580C2212yes—
76#2579C2214yes—
77#2568C2214yes—
78#2568C2211yescharacteristic
79#2568C2211yescharacteristic
80#2566C2214yes—
81#2565C2214yes—
82#2563C2214yes—
83#2552C2212yes—
84#2552C2212yes—
85#2551C2212yes—
86#2551C2212yes—
87#2548C2211yescharacteristic
88#2548C2211yescharacteristic
89#2538C2211yescharacteristic
90#2538C2212yes—
91#2538C2211yescharacteristic
92#2538C2212yes—
93#2537C2212yes—
94#2537C2212yes—
95#2521C2218yes—
96#2515C2218yes—
97#2514C2214yes—
98#2513C2214yes—
99#2512C2214yes—
100#2512C2214yes—
101#2511C2214yes—
102#2511C2214yes—
103#2508C2214yes—
104#2504C2214yes—
105#2504C2212yes—
106#2503C2214yes—
107#2500C2214yes—
108#2499C2214yes—
109#2497C2214yes—
110#2496C2214yes—
111#2495C2214yes—
112#2495C2214yes—
113#2494C2214yes—
114#2492C2214yes—
115#2492C2214yes—
116#2492C2214yes—
117#2491C2214yes—
118#2491C2214yes—
119#2491C2214yes—
120#2490C2214yes—
121#2490C2214yes—
122#2489C2214yes—
123#2489C2214yes—
124#2487C2212yes—
125#2450C2218yes—
126#2450C2218yes—
127#2447C2214yes—
128#2444C2218yes—
129#2444C2218yes—
130#2442C2214yes—
131#2442C2214yes—
132#2440C2214yes—
133#2440C2214yes—
134#2439C2214yes—
135#2439C2214yes—
136#2436C2212yes—
137#2427C2214yes—
138#2421C2214yes—
139#2421C2214yes—
140#2420C2214yes—
141#2420C2214yes—
142#2416C2214yes—
143#2416C2214yes—
144#2409C2212yes—
145#2398C2214yes—
146#2396C2214yes—
147#2367C2214yes—
148#2366C2212yes—
149#2365C2212yes—
150#2355C2212yes—
151#2355C2212yes—
152#2355C2212yes—
153#2355C2212yes—
154#2355C2214yes—
155#2355C2214yes—
156#2354C2212yes—
157#2352C2214yes—
158D4×C4⋊C4C2212yes—
159#2331C2214yes—
160#2325C2214yes—
161#2324C2214yes—
162#2320C2212yes—
163#2319C2212yes—
164#2319C2214yes—
165#2318C2214yes—
166#2317C2211yescharacteristic
167#2317C2211yescharacteristic
168#2317C2212yes—
169#2314C2212yes—
170#2314C2212yes—
171#2314C2214yes—
172#2311C2211yescharacteristic
173#2311C2211yescharacteristic
174#2311C2212yes—
175#2311C2212yes—
176C4×#124C2212yes—
177C4×#124C2212yes—
178C4×C22⋊Q8C2212yes—
179C4×C22⋊Q8C2212yes—
180C4×#121C2214yes—
181#2297C2212yes—
182#2297C2212yes—
183#2297C2212yes—
184#2296C2212yes—
185#2295C2212yes—
186C2×#391C2212yes—
187#2293C2212yes—
188#2290C2214yes—
189C2×#387C2214yes—
190#2285C2212yes—
191#2285C2211yescharacteristic
192C2×#384C2211yescharacteristic
193#2283C2212yes—
194C2×#382C2212yes—
195C4×#117C2211yescharacteristic
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2312yes—
201C23×Q8C2311yescharacteristic
202#544—48no—
203#537—48no—
204#532—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×#127C2311yescharacteristic
211C2×#126C2318yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#124C2312yes—
217C2×#124C2318yes—
218C2×C22⋊Q8C2318yes—
219C2×C22⋊Q8C2314yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×#121C2312yes—
224C2×#121C2312yes—
225C2×#121C2314yes—
226C2×#121C2318yes—
227C2×#121C2314yes—
228C2×#121C2314yes—
229C2×#121C2314yes—
230#520—48no—
231C4×#41—28no—
232C2×C4×Q8—28no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2312yes—
245C2×C4×D4C2312yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2318yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2311yescharacteristic
255C2×#117C2312yes—
256C2×#117C2314yes—
257C2×#117C2314yes—
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2314yes—
264C22×C4⋊C4C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C42C2312yes—
267C22×C42C2312yes—
268C22×C42C2312yes—
269C22×C42C2314yes—
270C22×C42C2311yescharacteristic
271#401C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2314yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2314yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#399C2314yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2318yes—
291#397C2318yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2314yes—
297#397C2314yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2314yes—
306#396C2314yes—
307#396C2318yes—
308#396C2318yes—
309#395C2314yes—
310#395C2318yes—
311#395C2318yes—
312#394C2318yes—
313#394C2318yes—
314#394C2318yes—
315#394C2314yes—
316#394C2314yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#393C2318yes—
321#393C2318yes—
322#393C2314yes—
323#393C2314yes—
324#393C2314yes—
325#393C2318yes—
326#393C2318yes—
327#391C2312yes—
328#391C2314yes—
329#391C2312yes—
330#391C2312yes—
331#391C2314yes—
332#391C2312yes—
333#391C2318yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#391C2318yes—
339#391C2318yes—
340#391C2312yes—
341#391C2312yes—
342#391C2312yes—
343#391C2312yes—
344#391C2318yes—
345#391C2314yes—
346#391C2314yes—
347#390C2312yes—
348#390C2314yes—
349#390C2312yes—
350#390C2312yes—
351#390C2312yes—
352#390C2314yes—
353#390C2312yes—
354#390C2314yes—
355#390C2312yes—
356#390C2318yes—
357#390C2312yes—
358#390C2312yes—
359#390C2312yes—
360#390C2312yes—
361#390C2314yes—
362#390C2314yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2314yes—
368#389C2314yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2312yes—
373#389C2312yes—
374#389C2312yes—
375#389C2312yes—
376#389C2312yes—
377#389C2314yes—
378#389C2314yes—
379#389C2314yes—
380#389C2314yes—
381#389C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2314yes—
394#388C2314yes—
395#388C2314yes—
396#388C2314yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#386C2314yes—
420#386C2314yes—
421#386C2318yes—
422#386C2318yes—
423#386C2314yes—
424#386C2314yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2314yes—
431#386C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2314yes—
435#385C2314yes—
436#385C2318yes—
437#385C2314yes—
438#385C2314yes—
439#385C2314yes—
440#385C2314yes—
441#385C2318yes—
442#384C2312yes—
443#384C2312yes—
444#384C2314yes—
445#384C2314yes—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2312yes—
449#384C2312yes—
450#384C2312yes—
451#384C2312yes—
452#384C2314yes—
453#383C2314yes—
454#383C2318yes—
455#382C2312yes—
456#382C2314yes—
457#382C2314yes—
458#382C2312yes—
459#382C2312yes—
460#382C2312yes—
461#382C2314yes—
462#382C2314yes—
463#382C2312yes—
464#382C2318yes—
465#382C2314yes—
466#382C2314yes—
467#381C2314yes—
468#381C2318yes—
469#381C2318yes—
470#380C2318yes—
471#380C2318yes—
472#380C2312yes—
473#380C2312yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2312yes—
481#380C2314yes—
482#380C2314yes—
483#380C2312yes—
484#380C2312yes—
485#380C2314yes—
486#380C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2312yes—
507C4×C4⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2312yes—
518#376C2312yes—
519#376C2314yes—
520C2×#95C2312yes—
521C2×#95C2314yes—
522C2×#95C2314yes—
523C2×#95C2314yes—
524C43C2312yes—
525C2×#41—24no—
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—24no—
529C2×#41—24no—
530C2×#41—28no—
531C22×Q8—24no—
532C22×Q8—42no—
533C22×Q8—42no—
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2418yes—
540C22×D4C2412yes—
541C22×D4C2412yes—
542C22×D4C2414yes—
543C22×D4C2411yescharacteristic
544C22×D4C2412yes—
545C22×D4C2412yes—
546C22×D4C2418yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2411yescharacteristic
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2418yes—
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C4⋊Q8—24no—
561C4⋊Q8—48no—
562C4⋊Q8—48no—
563C4⋊Q8—48no—
564C4⋊Q8—84no—
565#127—24no—
566#126—88no—
567#125—48no—
568#125—48no—
569#124—28no—
570#124—44no—
571#124—44no—
572#124—88no—
573C22⋊Q8—416no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578#121—28no—
579#121—28no—
580#121—48no—
581#121—48no—
582#121—48no—
583#121—416no—
584#121—84no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—28no—
588C4×Q8—28no—
589C4×Q8—24no—
590C4×Q8—24no—
591C4×Q8—24no—
592C4×Q8—24no—
593C4×Q8—48no—
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—28no—
599C4×D4—28no—
600C4×D4—48no—
601C4×D4—48no—
602C4×D4—416no—
603#117—24no—
604#117—28no—
605#117—24no—
606#117—24no—
607#117—28no—
608#117—48no—
609#117—48no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—28no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—82no—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2418yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C42—28no—
698C2×C42—28no—
699C2×C42—44no—
700C2×C42—84no—
701C2×C42#4118yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2418yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2414yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#95C2418yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2412yes—
734#95C2412yes—
735#95C2412yes—
736#95C2412yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2418yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769C24C2512yes—
770C24C2514yes—
771C24C2511yescharacteristic
772#41—416no—
773#41—432no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—22no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—48no—
790C2×Q8—48no—
791C2×Q8—48no—
792C2×Q8—416no—
793C2×D4—24no—
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—24no—
797C2×D4—24no—
798C2×D4—28no—
799C2×D4—22no—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—24no—
807C2×D4—24no—
808C2×D4—24no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—48no—
812C2×D4—48no—
813C2×D4—48no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—28no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4C2×#4114yes—
849C22×C4C2×#4114yes—
850C22×C4C2×#4114yes—
851C22×C4H(5,𝔽2)14yes—
852C22×C42−1+414yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2514yes—
860C22×C4C2512yes—
861C22×C4C2512yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2518yes—
868C22×C4C2512yes—
869C22×C4C2514yes—
870C22×C4C2511yescharacteristic
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2511yescharacteristic
874C22×C4C2511yescharacteristic
875C22×C4C2511yescharacteristic
876C4⋊C4—24no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—24no—
886C4⋊C4—24no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—28no—
892C4⋊C4—28no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—22no—
900C4⋊C4—22no—
901C4⋊C4—28no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—48no—
922C4⋊C4—48no—
923C4⋊C4—42no—
924C22⋊C4—24no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—44no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—24no—
962C42—28no—
963C42—24no—
964C42—24no—
965C42—28no—
966C42—24no—
967C42—24no—
968C42—44no—
969C42—48no—
970C42—48no—
971C42—42no—
972C42—48no—
973C42—42no—
974C42C2×#4114yes—
975C42C2×#4114yes—
976C42C2×#4114yes—
977C42C2×#4114yes—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—22no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23C22×#4112yes—
997C23C2×H(5,𝔽2)12yes—
998C23C2×2−1+412yes—
999C23C2611yescharacteristic
1000Q8—48no—
1001Q8—44no—
1002Q8—48no—
1003Q8—44no—
1004Q8—44no—
1005Q8—168no—
1006D4—48no—
1007D4—416no—
1008D4—44no—
1009D4—48no—
1010D4—48no—
1011D4—84no—
1012D4—168no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—28no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—28no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—28no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—22no—
1071C2×C4—44no—
1072C2×C4—48no—
1073C2×C4—48no—
1074C2×C4—48no—
1075C2×C4—416no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—84no—
1079C2×C4—84no—
1080C2×C4—88no—
1081C2×C4—168no—
1082C2×C4#542116yes—
1083C2×C4C22×#4112yes—
1084C2×C4C22×#4112yes—
1085C2×C4C22×#4112yes—
1086C2×C4C22×#4112yes—
1087C2×C4C22×#4112yes—
1088C2×C4C22×#4112yes—
1089C2×C4C2×H(5,𝔽2)12yes—
1090C2×C4C2×H(5,𝔽2)12yes—
1091C2×C4C2×2−1+412yes—
1092C2×C4C2×2−1+412yes—
1093C2×C4#58512yes—
1094C2×C4#58512yes—
1095C22—22no—
1096C22—22no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—42no—
1102C22—44no—
1103C22—42no—
1104C22—44no—
1105C22—42no—
1106C22—44no—
1107C22—44no—
1108C22—42no—
1109C22—42no—
1110C22—44no—
1111C22—44no—
1112C22—42no—
1113C22—42no—
1114C22—44no—
1115C22C2×#54214yes—
1116C22C23×#4111yescharacteristic
1117C22C22×H(5,𝔽2)11yescharacteristic
1118C22C22×2−1+411yescharacteristic
1119C22C2×#58511yescharacteristic
1120C22C2×#58511yescharacteristic
1121C22H(7,𝔽2)11yescharacteristic
1122C222−1+611yescharacteristic
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—42no—
1132C4—42no—
1133C4—44no—
1134C4—42no—
1135C4—44no—
1136C4—44no—
1137C4—42no—
1138C4—44no—
1139C4—42no—
1140C4—48no—
1141C4—44no—
1142C4—42no—
1143C4C2×#54214yes—
1144C4C2×#54214yes—
1145C4#349314yes—
1146C2—24no—
1147C2—82no—
1148C2—84no—
1149C2C22×#54211yescharacteristic
1150C2C2×#349311yescharacteristic
1151C2#6285611yescharacteristic
1152C2#6292611yescharacteristic
1153C2#6293111yescharacteristic
1154C2#6295611yescharacteristic
1155C2#6296111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35273C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42693C2semidirect
2. #42691C2semidirect
3. #42661C2semidirect
4. #42659C2semidirect
5. #39761C2semidirect
6. #39736C2semidirect
7. #39505C2semidirect
8. #39478C2semidirect
9. #39193C2semidirect
10. #39159C2semidirect
11. #38977C2semidirect
12. #38941C2semidirect
13. #37494C2semidirect
14. #36781C2semidirect
15. #35620C2semidirect
16. #35618C2semidirect
17. #35275C2semidirect
19. #35230C2semidirect
20. #35160C2semidirect
21. #35158C2semidirect
22. #34955C2semidirect
23. #34952C2semidirect
24. #34206C2semidirect
25. C2×#2355C2semidirect
26. #34060C2semidirect

Maximal subgroups

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

subgroupindex
#426932
#426912
#426612
#426592
#397612
#397362
#395052
#394782
#391932
#391592
#389772
#389412
#374942
#367812
#356202
#356182
#352752
#352732
#352302
#351602
#351582
#349552
#349522
#342062
C2×#23552
#340602