Finite Group Databasebeta

← #7633171

Subgroups — #7633171

Order 512.

4894 conjugacy classes of subgroups.

The subgroup lattice has 1123 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36599C212yesmaximal, complemented
2#36481C212yesmaximal, complemented
3#36287C212yesmaximal, complemented
4#36278C214yesmaximal, complemented
5#36193C212yesmaximal, complemented
6#36189C214yesmaximal, complemented
7#36039C214yesmaximal, complemented
8#35951C218yesmaximal, complemented
9#35708C214yesmaximal, complemented
10#35642C214yesmaximal, complemented
11#35639C212yesmaximal
12#35612C214yesmaximal, complemented
13#35585C212yesmaximal, complemented
14#35280C211yesmaximal, characteristic
15#35208C212yesmaximal, complemented
16#35176C212yesmaximal, complemented
17#35173C211yesmaximal, characteristic, complemented
18#34951C212yesmaximal, complemented
19#34947C211yesmaximal, characteristic
20#34941C212yesmaximal, complemented
21C2×#2552C211yesmaximal, characteristic, complemented
22#34253C212yesmaximal
23#34217C212yesmaximal, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34145C211yesmaximal, characteristic, complemented
26C4×#520C211yesmaximal, characteristic
27C2×#533C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C22×#125C2212yes—
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2863C2214yes—
34#2859C2214yes—
35#2857C2214yes—
36#2857C2214yes—
37#2857C2212yes—
38#2857C2212yes—
39#2855C2214yes—
40#2667C2218yes—
41#2666C2218yes—
42#2659C2214yes—
43#2629C2214yes—
44#2612C2218yes—
45#2608C2218yes—
46#2606C2218yes—
47#2606C2218yes—
48#2590C2218yes—
49#2587C2218yes—
50#2585C2218yes—
51#2585C2218yes—
52#2584C2214yes—
53#2584C2214yes—
54#2582C2212yes—
55#2582C2212yes—
56#2579C2218yes—
57#2574C2218yes—
58#2570C2218yes—
59#2569C2218yes—
60#2569C2218yes—
61#2568C2211yescharacteristic
62#2567C2212yes—
63#2567C2212yes—
64#2567C2211yescharacteristic
65#2566C2212yes—
66#2565C2212yes—
67#2564C2214yes—
68#2563C2211yescharacteristic
69#2556C2218yes—
70#2552C2214yes—
71#2552C2212yes—
72#2552C2212yes—
73#2552C2214yes—
74#2552C2212yes—
75#2552C2212yes—
76#2546C2212yes—
77#2546C2212yes—
78#2542C2211yescharacteristic
79#2538C2212yes—
80#2538C2212yes—
81#2522C2218yes—
82#2522C2218yes—
83#2520C2218yes—
84#2511C2214yes—
85#2511C2214yes—
86#2509C2214yes—
87#2509C2214yes—
88#2508C2214yes—
89#2508C2214yes—
90#2507C2214yes—
91#2507C2214yes—
92#2507C2218yes—
93#2507C2214yes—
94#2506C2214yes—
95#2506C2214yes—
96#2497C2218yes—
97#2497C2214yes—
98#2487C2218yes—
99#2462C2218yes—
100#2454C2214yes—
101#2454C2214yes—
102#2453C2214yes—
103#2453C2214yes—
104#2446C2214yes—
105#2442C2218yes—
106#2442C2214yes—
107#2442C2214yes—
108#2441C2218yes—
109#2441C2214yes—
110#2441C2214yes—
111#2438C2218yes—
112#2429C2214yes—
113#2423C2214yes—
114#2423C2214yes—
115#2417C2212yes—
116#2417C2214yes—
117#2417C2214yes—
118#2417C2212yes—
119#2402C2218yes—
120#2396C2218yes—
121#2396C2214yes—
122C2×#398C2214yes—
123#2370C2212yes—
124#2370C2212yes—
125#2370C2214yes—
126#2370C2214yes—
127#2370C2214yes—
128#2370C2214yes—
129#2369C2211yescharacteristic
130#2369C2211yescharacteristic
131#2368C2214yes—
132#2365C2211yescharacteristic
133#2365C2211yescharacteristic
134#2360C2212yes—
135#2360C2214yes—
136#2360C2212yes—
137#2360C2214yes—
138#2355C2212yes—
139#2355C2212yes—
140#2353C2218yes—
141#2352C2218yes—
142Q8×C4⋊C4C2212yes—
143Q8×C4⋊C4C2212yes—
144#2347C2214yes—
145#2346C2214yes—
146#2345C2218yes—
147#2345C2218yes—
148#2345C2214yes—
149#2344C2214yes—
150#2330C2214yes—
151#2330C2214yes—
152#2330C2214yes—
153#2320C2214yes—
154#2319C2214yes—
155#2317C2212yes—
156#2316C2212yes—
157#2316C2212yes—
158#2316C2212yes—
159#2311C2212yes—
160C4×C4⋊Q8C2214yes—
161C4×C4⋊Q8C2212yes—
162C4×C4⋊Q8C2212yes—
163C4×#125C2214yes—
164C4×#125C2214yes—
165C4×C22⋊Q8C2212yes—
166C4×C22⋊Q8C2214yes—
167C4×C22⋊Q8C2212yes—
168#2297C2212yes—
169#2296C2212yes—
170#2295C2214yes—
171#2295C2214yes—
172#2295C2212yes—
173#2295C2214yes—
174#2293C2214yes—
175C2×#389C2212yes—
176C2×#389C2212yes—
177#2285C2212yes—
178#2285C2214yes—
179C2×#384C2212yes—
180C2×#384C2211yescharacteristic
181#2276C2212yes—
182#2275C2212yes—
183#2275C2214yes—
184#2274C2211yescharacteristic
185#2274C2212yes—
186#2274C2212yes—
187#2274C2211yescharacteristic
188#2274C2212yes—
189C42×Q8C2212yes—
190C42×Q8C2212yes—
191C42×D4C2214yes—
192C42×D4C2212yes—
193C4×#117C2211yescharacteristic
194C4×#117C2212yes—
195C4×#117C2212yes—
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200#533—28no—
201#533—28no—
202C2×C4⋊Q8C2311yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2314yes—
207C2×#125—216no—
208C2×#125C2314yes—
209C2×#125C2312yes—
210C2×#125C2312yes—
211C2×#125C2314yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#125C2318yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223#520—28no—
224#520Q8116yescomplemented
225C4×#41—28no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×Q8C2312yes—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2312yes—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2314yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2318yes—
253C2×#117C2312yes—
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2314yes—
257C22×C4⋊C4C2314yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2314yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C42C2312yes—
268C22×C42C2312yes—
269C22×C42C2314yes—
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272#400C2314yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#399C2314yes—
280#399C2318yes—
281#399C2318yes—
282#398C2314yes—
283#398C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#396C2314yes—
299#396C2314yes—
300#396C2318yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#395C2314yes—
305#395C2318yes—
306#395C2318yes—
307#393C2314yes—
308#391C2312yes—
309#391C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2312yes—
313#391C2312yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2312yes—
318#391C2314yes—
319#391C2312yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#390C2312yes—
324#390C2312yes—
325#390C2314yes—
326#389C2314yes—
327#389C2314yes—
328#389C2314yes—
329#389C2314yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2318yes—
334#389C2318yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2312yes—
340#389C2312yes—
341#389C2318yes—
342#389C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2318yes—
354#389C2318yes—
355#389C2318yes—
356#389C2318yes—
357#389C2318yes—
358#389C2314yes—
359#389C2318yes—
360#389C2312yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2312yes—
365#389C2318yes—
366#389C2314yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2312yes—
371#389C2314yes—
372#389C2314yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2314yes—
382#387C2314yes—
383#387C2314yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2314yes—
403#387C2314yes—
404#387C2314yes—
405#386C2314yes—
406#386C2314yes—
407#386C2318yes—
408#385C2314yes—
409#385C2314yes—
410#385C2314yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2314yes—
415#384C2312yes—
416#384C2314yes—
417#384C2312yes—
418#384C2312yes—
419#384C2314yes—
420#384C2318yes—
421#384C2314yes—
422#384C2312yes—
423#384C2312yes—
424#384C2314yes—
425#384C2312yes—
426#383C2318yes—
427#382C2312yes—
428#382C2312yes—
429#382C2318yes—
430#382C2318yes—
431#382C2314yes—
432#381C2318yes—
433#380C2312yes—
434#380C2312yes—
435#380C2314yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2314yes—
440#380C2318yes—
441#380C2318yes—
442#380C2318yes—
443#380C2318yes—
444#380C2318yes—
445#380C2318yes—
446#380C2314yes—
447C4×C4⋊C4C2312yes—
448C4×C4⋊C4C2312yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2318yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2318yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
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×C22⋊C4C2314yes—
499C4×C22⋊C4C2318yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514#376C2314yes—
515#376C2312yes—
516#376C2318yes—
517#376C2314yes—
518C2×#95C2312yes—
519C2×#95C2314yes—
520C2×#95C2314yes—
521C2×#95C2312yes—
522C43C2314yes—
523C43C2312yes—
524C43C2314yes—
525C2×#41—24no—
526C2×#41—24no—
527C2×#41C2×Q818yes—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×D4C2412yes—
534C22×D4C2411yescharacteristic
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2411yescharacteristic
538C23×C4C2414yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2414yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2414yes—
545C23×C4C2412yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C4⋊Q8—24no—
549C4⋊Q8—24no—
550C4⋊Q8—24no—
551C4⋊Q8—24no—
552C4⋊Q8—48no—
553#125—216no—
554#125—216no—
555#125—216no—
556#125—216no—
557#125—28no—
558#125—28no—
559#125—88no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—28no—
563C22⋊Q8—28no—
564C22⋊Q8—48no—
565C22⋊Q8—44no—
566C22⋊Q8—44no—
567C22⋊Q8—84no—
568C4×Q8—28no—
569C4×Q8—24no—
570C4×Q8—24no—
571C4×Q8—28no—
572C4×Q8—28no—
573C4×Q8—28no—
574C4×Q8—28no—
575C4×Q8—44no—
576C4×Q8—44no—
577C4×Q8—48no—
578C4×Q8—84no—
579C4×Q8C2×Q8116yes—
580C4×D4—28no—
581C4×D4—28no—
582C4×D4—216no—
583C4×D4—28no—
584C4×D4—24no—
585C4×D4—24no—
586C4×D4C2×Q8116yes—
587C4×D4C2×Q8132yes—
588#117—24no—
589#117—24no—
590#117—28no—
591#117—28no—
592#117—28no—
593#117—28no—
594#117—88no—
595#117C2×Q8116yes—
596#117C2×Q818yes—
597C2×C4⋊C4—216no—
598C2×C4⋊C4—216no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—42no—
602C2×C4⋊C4—42no—
603C2×C4⋊C4—44no—
604C2×C4⋊C4—84no—
605C2×C4⋊C4—82no—
606C2×C4⋊C4C2×Q8116yes—
607C2×C4⋊C4C2×Q818yes—
608C2×C4⋊C4#4118yes—
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C42—28no—
685C2×C42—28no—
686C2×C42—48no—
687C2×C42—44no—
688C2×C42#4118yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2414yes—
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2414yes—
703C2×C42C2414yes—
704C2×C42C2418yes—
705C2×C42C2412yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2418yes—
709C2×C42C2414yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2412yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2412yes—
717C2×C42C2414yes—
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#95C2412yes—
723#95C2414yes—
724#95C2418yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2412yes—
729#95C2412yes—
730#95C2412yes—
731#95C2412yes—
732#95C2418yes—
733#95C2412yes—
734#95C2414yes—
735#95C2412yes—
736#95C2414yes—
737#95C2412yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2418yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2418yes—
763#95C2418yes—
764#95C2418yes—
765#95C2414yes—
766C24C2512yes—
767C24C2511yescharacteristic
768#41—232no—
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8C22×Q814yes—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—22no—
787C2×D4—22no—
788C2×D4C22×Q818yes—
789C2×D4C22×Q814yes—
790C22×C4—24no—
791C22×C4—24no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—24no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—44no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—41no—
806C22×C4—42no—
807C22×C4—44no—
808C22×C4—41no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4—42no—
817C22×C4—44no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4C22×Q818yes—
821C22×C4C22×Q8116yes—
822C22×C4C22×Q818yes—
823C22×C4C22×Q814yes—
824C22×C4C2×#4114yes—
825C22×C4C2×#4114yes—
826C22×C4C2×#4118yes—
827C22×C4C2×#4114yes—
828C22×C4C2×#4114yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2512yes—
834C22×C4C2514yes—
835C22×C4C2514yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2512yes—
839C22×C4C2512yes—
840C22×C4C2518yes—
841C22×C4C2512yes—
842C22×C4C2512yes—
843C22×C4C2512yes—
844C22×C4C2512yes—
845C22×C4C2514yes—
846C22×C4C2511yescharacteristic
847C22×C4C2511yescharacteristic
848C22×C4C2514yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C22×C4C2511yescharacteristic
853C4⋊C4—22no—
854C4⋊C4—28no—
855C4⋊C4—216no—
856C4⋊C4—216no—
857C4⋊C4—216no—
858C4⋊C4—216no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—22no—
862C4⋊C4—24no—
863C4⋊C4—24no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—28no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—28no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—44no—
886C4⋊C4—48no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—48no—
905C4⋊C4—48no—
906C4⋊C4C22×Q814yes—
907C4⋊C4C22×Q818yes—
908C4⋊C4C22×Q8116yes—
909C4⋊C4C22×Q818yes—
910C4⋊C4C22×Q814yes—
911C4⋊C4C2×#4118yes—
912C4⋊C4C2×#4118yes—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—28no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—44no—
924C22⋊C4—48no—
925C22⋊C4—44no—
926C22⋊C4C22×Q8116yes—
927C22⋊C4C22×Q818yes—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—28no—
936C42—24no—
937C42—28no—
938C42—28no—
939C42—24no—
940C42—28no—
941C42—24no—
942C42—44no—
943C42—44no—
944C42—44no—
945C42—42no—
946C42—44no—
947C42—44no—
948C42—44no—
949C42—48no—
950C42—48no—
951C42—44no—
952C42—44no—
953C42—42no—
954C42—44no—
955C42C22×Q8116yes—
956C42C22×Q818yes—
957C42C2×#4114yes—
958C42C2×#4114yes—
959C42C2×#4114yes—
960C42C2×#4114yes—
961C23—21no—
962C23—21no—
963C23—21no—
964C23—21no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23C23×Q814yes—
972C23C23×Q812yes—
973C23C22×#4112yes—
974C23C22×#4112yes—
975C23C2611yescharacteristic
976Q8—28no—
977Q8—48no—
978Q8—48no—
979Q8—48no—
980Q8—84no—
981D4—216no—
982D4—28no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—24no—
994C2×C4—21no—
995C2×C4—22no—
996C2×C4—21no—
997C2×C4—24no—
998C2×C4—21no—
999C2×C4—216no—
1000C2×C4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—28no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—28no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—22no—
1031C2×C4—24no—
1032C2×C4—28no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—48no—
1041C2×C4—416no—
1042C2×C4—48no—
1043C2×C4—44no—
1044C2×C4—48no—
1045C2×C4—88no—
1046C2×C4—84no—
1047C2×C4—84no—
1048C2×C4—84no—
1049C2×C4—88no—
1050C2×C4#533116yes—
1051C2×C4C23×Q814yes—
1052C2×C4C23×Q814yes—
1053C2×C4C23×Q814yes—
1054C2×C4C23×Q818yes—
1055C2×C4C23×Q812yes—
1056C2×C4C23×Q812yes—
1057C2×C4C22×#4112yes—
1058C2×C4C22×#4118yes—
1059C2×C4C22×#4112yes—
1060C2×C4C22×#4112yes—
1061C2×C4C22×#4112yes—
1062C2×C4C22×#4112yes—
1063C2×C4C22×#4112yes—
1064C2×C4C22×#4112yes—
1065C2×C4C22×#4112yes—
1066C2×C4#58512yes—
1067C2×C4#58512yes—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22C2×#53314yes—
1082C22C24×Q811yescharacteristic
1083C22C23×#4111yescharacteristic
1084C22C23×#4111yescharacteristic
1085C22C2×#58511yescharacteristic
1086C22C2×#58511yescharacteristic
1087C22H(7,𝔽2)11yescharacteristic
1088C222−1+611yescharacteristic
1089C4—24no—
1090C4—28no—
1091C4—28no—
1092C4—24no—
1093C4—22no—
1094C4—22no—
1095C4—22no—
1096C4—24no—
1097C4—42no—
1098C4—42no—
1099C4—42no—
1100C4—42no—
1101C4—42no—
1102C4—42no—
1103C4—48no—
1104C4—42no—
1105C4—44no—
1106C4—44no—
1107C4—42no—
1108C4—44no—
1109C4—44no—
1110C4C2×#53314yes—
1111C4C2×#53314yes—
1112C4#351214yes—
1113C2—24no—
1114C2—44no—
1115C2C22×#53311yescharacteristic
1116C2C2×#351211yescharacteristic
1117C2#6285611yescharacteristic
1118C2#6298911yescharacteristic
1119C2#6299111yescharacteristic
1120C2#6300411yescharacteristic
1121C2#6300611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36599C2semidirect
2. #36481C2semidirect
3. #36287C2semidirect
4. #36278C2semidirect
5. #36193C2semidirect
6. #36189C2semidirect
7. #36039C2semidirect
8. #35951C2semidirect
9. #35708C2semidirect
10. #35642C2semidirect
12. #35612C2semidirect
13. #35585C2semidirect
15. #35208C2semidirect
16. #35176C2semidirect
17. #35173C2semidirect
18. #34951C2semidirect
20. #34941C2semidirect
21. C2×#2552C2semidirect
23. #34217C2semidirect
24. #34214C2semidirect
25. #34145C2semidirect
224. #520Q8semidirect

Maximal subgroups

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

subgroupindex
#365992
#364812
#362872
#362782
#361932
#361892
#360392
#359512
#357082
#356422
#356392
#356122
#355852
#352802
#352082
#351762
#351732
#349512
#349472
#349412
C2×#25522
#342532
#342172
#342142
#341452
C4×#5202