Finite Group Databasebeta

← #7677572

Subgroups — #7677572

Order 512.

4768 conjugacy classes of subgroups.

The subgroup lattice has 1149 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59329C212yesmaximal, complemented
2#59302C212yesmaximal, complemented
3#59257C212yesmaximal, complemented
4#59256C212yesmaximal, complemented
5#59249C212yesmaximal, complemented
6#59242C212yesmaximal, complemented
7#59235C212yesmaximal, complemented
8#59227C212yesmaximal, complemented
9#45254C214yesmaximal, complemented
10#45132C214yesmaximal, complemented
11#45123C214yesmaximal, complemented
12#45119C214yesmaximal, complemented
13#38974C214yesmaximal, complemented
14#38222C218yesmaximal, complemented
15#36254C214yesmaximal, complemented
16#35627C212yesmaximal, complemented
17#35618C212yesmaximal
18#35181C211yesmaximal, characteristic, complemented
19#35160C212yesmaximal, complemented
20#34952C211yesmaximal, characteristic, complemented
21#34952C211yesmaximal, characteristic, complemented
22#34252C212yesmaximal, complemented
23#34188C211yesmaximal, characteristic, complemented
24#34183C211yesmaximal, characteristic, complemented
25C2×#2355C211yesmaximal, characteristic, complemented
26C4×#537C211yesmaximal, characteristic
27C2×#537C2211yescharacteristic
28C2×#520C2212yes—
29C2×C4×#41C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32#2852C2218yes—
33#2851C2214yes—
34#2794C2218yes—
35#2793C2218yes—
36#2787C2218yes—
37#2781C2218yes—
38#2775C2218yes—
39#2774C2218yes—
40#2770C2218yes—
41#2767C2218yes—
42#2751C2218yes—
43#2750C2218yes—
44#2745C2218yes—
45#2744C2218yes—
46#2646C2214yes—
47#2643C2218yes—
48#2609C2218yes—
49#2596C2218yes—
50#2582C2211yescharacteristic
51#2582C2211yescharacteristic
52#2582C2211yescharacteristic
53#2582C2211yescharacteristic
54#2581C2212yes—
55#2581C2212yes—
56#2580C2212yes—
57#2580C2212yes—
58#2579C2214yes—
59#2579C2214yes—
60#2575C2218yes—
61#2573C2218yes—
62#2571C2214yes—
63#2571C2214yes—
64#2571C2212yes—
65#2571C2212yes—
66#2570C2214yes—
67#2570C2214yes—
68#2570C2214yes—
69#2570C2214yes—
70#2570C2214yes—
71#2562C2214yes—
72#2552C2212yes—
73#2552C2212yes—
74#2538C2211yescharacteristic
75#2538C2211yescharacteristic
76#2538C2211yescharacteristic
77#2538C2211yescharacteristic
78#2533C2218yes—
79#2529C2218yes—
80#2528C2218yes—
81#2524C2218yes—
82#2514C2214yes—
83#2514C2214yes—
84#2513C2214yes—
85#2512C2214yes—
86#2511C2214yes—
87#2511C2214yes—
88#2509C2214yes—
89#2509C2214yes—
90#2508C2214yes—
91#2508C2214yes—
92#2505C2218yes—
93#2505C2218yes—
94#2504C2214yes—
95#2503C2214yes—
96#2503C2214yes—
97#2500C2214yes—
98#2499C2214yes—
99#2499C2214yes—
100#2497C2214yes—
101#2496C2214yes—
102#2496C2214yes—
103#2495C2214yes—
104#2495C2214yes—
105#2494C2214yes—
106#2489C2214yes—
107#2489C2214yes—
108#2487C2212yes—
109#2487C2212yes—
110#2484C2218yes—
111#2481C2218yes—
112#2479C2218yes—
113#2478C2218yes—
114#2444C2218yes—
115#2444C2218yes—
116#2421C2214yes—
117#2421C2214yes—
118#2420C2214yes—
119#2420C2214yes—
120#2417C2214yes—
121#2415C2214yes—
122#2409C2212yes—
123#2409C2212yes—
124#2396C2214yes—
125#2396C2214yes—
126#2370C2214yes—
127#2357C2214yes—
128#2356C2214yes—
129#2355C2212yes—
130#2355C2214yes—
131#2355C2214yes—
132#2355C2214yes—
133#2355C2212yes—
134#2355C2212yes—
135#2355C2212yes—
136#2355C2212yes—
137#2355C2212yes—
138#2354C2214yes—
139#2354C2212yes—
140#2354C2212yes—
141#2352C2214yes—
142#2352C2214yes—
143#2352C2214yes—
144Q8×C4⋊C4C2212yes—
145Q8×C4⋊C4C2212yes—
146D4×C4⋊C4C2214yes—
147D4×C4⋊C4C2212yes—
148D4×C4⋊C4C2214yes—
149D4×C4⋊C4C2212yes—
150#2347C2214yes—
151#2346C2214yes—
152#2346C2214yes—
153#2345C2214yes—
154#2344C2214yes—
155#2344C2214yes—
156#2325C2214yes—
157#2324C2212yes—
158#2324C2212yes—
159#2323C2212yes—
160#2323C2212yes—
161#2318C2218yes—
162#2317C2212yes—
163#2317C2212yes—
164#2317C2214yes—
165#2317C2212yes—
166#2316C2211yescharacteristic
167#2314C2214yes—
168#2311C2212yes—
169#2311C2211yescharacteristic
170#2311C2211yescharacteristic
171C4×C22⋊Q8C2212yes—
172C4×C22⋊Q8C2212yes—
173C4×C22⋊Q8C2212yes—
174C4×C22⋊Q8C2212yes—
175C4×C22⋊Q8C2212yes—
176C4×C22⋊Q8C2212yes—
177C4×#121C2214yes—
178C4×#121C2212yes—
179C4×#121C2212yes—
180#2297C2212yes—
181#2297C2212yes—
182#2296C2212yes—
183#2296C2212yes—
184C2×#391C2212yes—
185#2290C2218yes—
186C2×#387C2214yes—
187#2285C2212yes—
188#2285C2212yes—
189#2285C2211yescharacteristic
190#2285C2211yescharacteristic
191#2285C2212yes—
192C2×#384C2211yescharacteristic
193C2×#384C2212yes—
194C2×#382C2212yes—
195#2274C2212yes—
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202#537—28no—
203C2×#126C2318yes—
204C2×#125C2314yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2312yes—
207C2×C22⋊Q8C2312yes—
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2312yes—
210C2×C22⋊Q8C2312yes—
211C2×#121C2312yes—
212C2×#121C2312yes—
213C2×#121C2314yes—
214#520—216no—
215C4×#41—28no—
216C4×#41—28no—
217C2×C4×Q8—28no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2312yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2314yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2314yes—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2312yes—
243C2×#117C2312yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2314yes—
247C2×#117C2314yes—
248C2×#117C2318yes—
249C2×#117C2314yes—
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2312yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2314yes—
260C22×C42C2312yes—
261C22×C42C2312yes—
262C22×C42C2312yes—
263C22×C42C2312yes—
264C22×C42C2314yes—
265C22×C42C2311yescharacteristic
266#401C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2314yes—
278#400C2314yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#399C2314yes—
283#399C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#396C2314yes—
300#396C2314yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#395C2314yes—
305#395C2314yes—
306#394C2318yes—
307#394C2318yes—
308#393C2314yes—
309#393C2314yes—
310#391C2312yes—
311#391C2312yes—
312#391C2314yes—
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2318yes—
324#390C2312yes—
325#390C2312yes—
326#390C2314yes—
327#390C2314yes—
328#390C2312yes—
329#390C2312yes—
330#390C2312yes—
331#390C2312yes—
332#389C2312yes—
333#389C2312yes—
334#389C2312yes—
335#389C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2314yes—
339#389C2314yes—
340#389C2314yes—
341#389C2314yes—
342#389C2312yes—
343#389C2312yes—
344#389C2318yes—
345#389C2314yes—
346#389C2314yes—
347#389C2318yes—
348#389C2312yes—
349#389C2312yes—
350#389C2318yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2312yes—
356#389C2312yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2314yes—
366#388C2318yes—
367#388C2318yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2314yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#386C2314yes—
404#386C2314yes—
405#386C2318yes—
406#386C2314yes—
407#386C2314yes—
408#386C2314yes—
409#386C2314yes—
410#386C2314yes—
411#386C2314yes—
412#386C2318yes—
413#386C2318yes—
414#385C2318yes—
415#385C2318yes—
416#385C2318yes—
417#385C2318yes—
418#385C2318yes—
419#385C2314yes—
420#385C2314yes—
421#385C2314yes—
422#385C2314yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2314yes—
429#384C2312yes—
430#384C2314yes—
431#384C2314yes—
432#384C2314yes—
433#384C2314yes—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2312yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2312yes—
440#384C2314yes—
441#384C2312yes—
442#383C2318yes—
443#383C2318yes—
444#382C2312yes—
445#382C2314yes—
446#382C2312yes—
447#382C2314yes—
448#382C2314yes—
449#382C2314yes—
450#382C2314yes—
451#382C2314yes—
452#382C2314yes—
453#382C2318yes—
454#382C2318yes—
455#382C2318yes—
456#382C2314yes—
457#382C2314yes—
458#382C2314yes—
459#381C2318yes—
460#381C2318yes—
461#381C2318yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2314yes—
473#380C2318yes—
474#380C2312yes—
475#380C2312yes—
476#380C2312yes—
477#380C2312yes—
478#380C2314yes—
479#380C2312yes—
480#380C2312yes—
481#380C2314yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2318yes—
500C4×C4⋊C4C2318yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2314yes—
507C4×C4⋊C4C2314yes—
508C4×C4⋊C4C2314yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2314yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2318yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519#376C2318yes—
520C2×#95C2314yes—
521C2×#95C2312yes—
522C2×#95C2314yes—
523C2×#95C2314yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41#4118yes—
530C22×Q8—24no—
531C22×Q8—42no—
532C22×Q8—42no—
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2411yescharacteristic
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×D4C2412yes—
539C22×D4C2411yescharacteristic
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C22×D4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2411yescharacteristic
547C23×C4C2412yes—
548C23×C4C2418yes—
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558#126—88no—
559#125—48no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—44no—
563C22⋊Q8—44no—
564C22⋊Q8—44no—
565C22⋊Q8—44no—
566#121—28no—
567#121—216no—
568#121—28no—
569C4×Q8—216no—
570C4×Q8—24no—
571C4×Q8—24no—
572C4×Q8—24no—
573C4×Q8—24no—
574C4×Q8—28no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—24no—
579C4×Q8—24no—
580C4×D4—232no—
581C4×D4—216no—
582C4×D4—28no—
583C4×D4—28no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—24no—
589C4×D4—24no—
590C4×D4—48no—
591#117—24no—
592#117—24no—
593#117—216no—
594#117—28no—
595#117—28no—
596#117—28no—
597#117—28no—
598#117—48no—
599#117—88no—
600#117—84no—
601C2×C4⋊C4—24no—
602C2×C4⋊C4—28no—
603C2×C4⋊C4—216no—
604C2×C4⋊C4—28no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—48no—
609C2×C4⋊C4—82no—
610C2×C4⋊C4—84no—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2414yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2418yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2418yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C42—28no—
692C2×C42—28no—
693C2×C42—28no—
694C2×C42—44no—
695C2×C42—84no—
696C2×C42#4118yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2418yes—
712C2×C42C2418yes—
713C2×C42C2418yes—
714C2×C42C2418yes—
715C2×C42C2414yes—
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#95C2418yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724#95C2414yes—
725#95C2414yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2418yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
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#95C2418yes—
764C24C2512yes—
765C24C2512yes—
766C24C2511yescharacteristic
767#41—232no—
768#41—416no—
769C2×Q8—22no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—22no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—416no—
784C2×Q8C2×#4114yes—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4C2×#4118yes—
799C2×D4C2×#4114yes—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—216no—
808C22×C4—28no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—41no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—41no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—42no—
839C22×C4C2×#4114yes—
840C22×C4C2×#4118yes—
841C22×C4C2×#4114yes—
842C22×C4C2×#4114yes—
843C22×C4C2×#4114yes—
844C22×C42−1+414yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2512yes—
855C22×C4C2518yes—
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C4⋊C4—28no—
869C4⋊C4—24no—
870C4⋊C4—216no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—28no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—24no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—42no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—44no—
912C4⋊C4—42no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—44no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—48no—
922C4⋊C4—44no—
923C22⋊C4—216no—
924C22⋊C4—28no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—24no—
932C22⋊C4—24no—
933C22⋊C4—28no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—216no—
959C42—28no—
960C42—28no—
961C42—28no—
962C42—44no—
963C42—48no—
964C42—48no—
965C42—48no—
966C42—48no—
967C42C2×#4114yes—
968C42C2×#4114yes—
969C42C2×#4114yes—
970C42C2×#4114yes—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23C22×#4114yes—
989C23C22×#4112yes—
990C23C22×#4112yes—
991C23C2×2−1+412yes—
992C23C2611yescharacteristic
993Q8—28no—
994Q8—48no—
995Q8—44no—
996Q8—44no—
997Q8—44no—
998D4—216no—
999D4—28no—
1000D4—48no—
1001D4—44no—
1002D4—88no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—216no—
1012C2×C4—28no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—28no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—28no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—24no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—48no—
1066C2×C4—48no—
1067C2×C4—48no—
1068C2×C4—48no—
1069C2×C4—48no—
1070C2×C4—84no—
1071C2×C4—88no—
1072C2×C4—816no—
1073C2×C4#552116yes—
1074C2×C4C22×#4114yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C22×#4112yes—
1082C2×C4C22×#4112yes—
1083C2×C4C2×2−1+412yes—
1084C2×C4C2×2−1+412yes—
1085C2×C4#58512yes—
1086C2×C4#58512yes—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—22no—
1093C22—24no—
1094C22—24no—
1095C22—24no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22C2×#55214yes—
1108C22C23×#4111yescharacteristic
1109C22C23×#4111yescharacteristic
1110C22C22×2−1+411yescharacteristic
1111C22C2×#58511yescharacteristic
1112C22C2×#58511yescharacteristic
1113C22H(7,𝔽2)11yescharacteristic
1114C222−1+611yescharacteristic
1115C4—22no—
1116C4—22no—
1117C4—22no—
1118C4—24no—
1119C4—44no—
1120C4—44no—
1121C4—48no—
1122C4—44no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—42no—
1129C4—42no—
1130C4—42no—
1131C4—44no—
1132C4—44no—
1133C4—44no—
1134C4—42no—
1135C4C2×#55214yes—
1136C4C2×#55214yes—
1137C4#349314yes—
1138C2—24no—
1139C2—44no—
1140C2—82no—
1141C2C22×#55211yescharacteristic
1142C2C2×#349311yescharacteristic
1143C2#6284511yescharacteristic
1144C2#6292611yescharacteristic
1145C2#6295611yescharacteristic
1146C2#6299511yescharacteristic
1147C2#6301011yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#537C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59329C2semidirect
2. #59302C2semidirect
3. #59257C2semidirect
4. #59256C2semidirect
5. #59249C2semidirect
6. #59242C2semidirect
7. #59235C2semidirect
8. #59227C2semidirect
9. #45254C2semidirect
10. #45132C2semidirect
11. #45123C2semidirect
12. #45119C2semidirect
13. #38974C2semidirect
14. #38222C2semidirect
15. #36254C2semidirect
16. #35627C2semidirect
18. #35181C2semidirect
19. #35160C2semidirect
20. #34952C2semidirect
21. #34952C2semidirect
22. #34252C2semidirect
23. #34188C2semidirect
24. #34183C2semidirect
25. C2×#2355C2semidirect

Maximal subgroups

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

subgroupindex
#593292
#593022
#592572
#592562
#592492
#592422
#592352
#592272
#452542
#451322
#451232
#451192
#389742
#382222
#362542
#356272
#356182
#351812
#351602
#349522
#342522
#341882
#341832
C2×#23552
C4×#5372