Finite Group Databasebeta

← #7633065

Subgroups — #7633065

Order 512.

5168 conjugacy classes of subgroups.

The subgroup lattice has 1139 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36599C212yesmaximal, complemented
2#36481C212yesmaximal, complemented
3#36288C212yesmaximal, complemented
4#36277C214yesmaximal, complemented
5#36133C212yesmaximal, complemented
6#36129C214yesmaximal, complemented
7#35951C218yesmaximal, complemented
8#35819C214yesmaximal, complemented
9#35788C214yesmaximal, complemented
10#35602C214yesmaximal, complemented
11#35585C212yesmaximal, complemented
12#35583C214yesmaximal, complemented
13#35575C212yesmaximal
14#35279C211yesmaximal, characteristic
15#35199C212yesmaximal, complemented
16#35176C212yesmaximal, complemented
17#35167C211yesmaximal, characteristic, complemented
18#34952C211yesmaximal, characteristic
19#34951C212yesmaximal, complemented
20#34929C212yesmaximal, complemented
21C2×#2546C211yesmaximal, characteristic, complemented
22#34272C212yesmaximal, complemented
23#34253C212yesmaximal
24#34216C211yesmaximal, characteristic, complemented
25Q8×#117C211yesmaximal, characteristic, complemented
26C4×#520C211yesmaximal, characteristic
27C2×#544C2212yes—
28C2×#533C2214yes—
29C22×C4⋊Q8C2211yescharacteristic
30C22×C4⋊Q8C2212yes—
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35#2863C2214yes—
36#2862C2214yes—
37#2857C2214yes—
38#2857C2214yes—
39#2857C2212yes—
40#2857C2212yes—
41#2855C2214yes—
42#2667C2218yes—
43#2666C2218yes—
44#2659C2214yes—
45#2628C2214yes—
46#2612C2218yes—
47#2607C2218yes—
48#2606C2218yes—
49#2605C2218yes—
50#2589C2218yes—
51#2588C2218yes—
52#2585C2218yes—
53#2585C2218yes—
54#2582C2211yescharacteristic
55#2582C2211yescharacteristic
56#2581C2212yes—
57#2580C2212yes—
58#2579C2214yes—
59#2574C2218yes—
60#2569C2218yes—
61#2569C2218yes—
62#2568C2212yes—
63#2567C2212yes—
64#2564C2218yes—
65#2563C2212yes—
66#2556C2218yes—
67#2552C2212yes—
68#2552C2212yes—
69#2551C2212yes—
70#2551C2212yes—
71#2550C2214yes—
72#2550C2218yes—
73#2550C2214yes—
74#2546C2214yes—
75#2546C2212yes—
76#2546C2212yes—
77#2546C2212yes—
78#2546C2212yes—
79#2546C2214yes—
80#2542C2212yes—
81#2538C2211yescharacteristic
82#2538C2211yescharacteristic
83#2522C2218yes—
84#2522C2218yes—
85#2520C2218yes—
86#2511C2214yes—
87#2509C2214yes—
88#2509C2214yes—
89#2508C2214yes—
90#2508C2214yes—
91#2507C2214yes—
92#2507C2214yes—
93#2506C2214yes—
94#2506C2214yes—
95#2492C2218yes—
96#2492C2214yes—
97#2487C2214yes—
98#2487C2212yes—
99#2462C2218yes—
100#2454C2214yes—
101#2453C2214yes—
102#2452C2214yes—
103#2451C2218yes—
104#2451C2214yes—
105#2451C2214yes—
106#2446C2214yes—
107#2446C2214yes—
108#2442C2218yes—
109#2442C2214yes—
110#2441C2214yes—
111#2440C2214yes—
112#2439C2218yes—
113#2439C2214yes—
114#2438C2218yes—
115#2429C2214yes—
116#2429C2214yes—
117#2423C2214yes—
118#2417C2218yes—
119#2409C2212yes—
120#2409C2214yes—
121#2402C2218yes—
122#2396C2218yes—
123#2396C2214yes—
124C2×#398C2214yes—
125#2370C2214yes—
126#2370C2214yes—
127#2369C2212yes—
128#2369C2212yes—
129#2369C2214yes—
130#2368C2218yes—
131#2365C2212yes—
132#2365C2214yes—
133#2365C2212yes—
134#2360C2218yes—
135#2355C2211yescharacteristic
136#2355C2212yes—
137#2355C2212yes—
138#2355C2211yescharacteristic
139#2353C2218yes—
140#2352C2218yes—
141Q8×C4⋊C4C2211yescharacteristic
142Q8×C4⋊C4C2211yescharacteristic
143#2347C2214yes—
144#2346C2214yes—
145#2345C2214yes—
146#2345C2212yes—
147#2345C2214yes—
148#2345C2214yes—
149#2344C2214yes—
150Q8×C22⋊C4C2212yes—
151Q8×C22⋊C4C2214yes—
152#2331C2214yes—
153#2331C2214yes—
154#2330C2214yes—
155#2320C2214yes—
156#2319C2214yes—
157#2317C2212yes—
158#2316C2212yes—
159#2316C2212yes—
160#2311C2212yes—
161C4×C4⋊Q8C2214yes—
162C4×C4⋊Q8C2212yes—
163C4×C4⋊Q8C2212yes—
164C4×C4⋊Q8C2214yes—
165C4×#125C2214yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2214yes—
168C4×C22⋊Q8C2212yes—
169#2297C2212yes—
170#2296C2212yes—
171#2295C2214yes—
172#2295C2212yes—
173#2295C2214yes—
174#2295C2214yes—
175C2×#391C2212yes—
176#2293C2214yes—
177C2×#389C2212yes—
178C2×#389C2212yes—
179#2285C2212yes—
180#2285C2211yescharacteristic
181#2285C2211yescharacteristic
182#2276C2212yes—
183#2275C2212yes—
184#2275C2214yes—
185#2274C2211yescharacteristic
186#2274C2212yes—
187#2274C2212yes—
188#2274C2211yescharacteristic
189#2274C2212yes—
190C42×Q8C2212yes—
191C42×Q8C2212yes—
192C42×D4C2214yes—
193C42×D4C2212yes—
194C4×#117C2211yescharacteristic
195C4×#117C2212yes—
196C4×#117C2212yes—
197C2×C4×C4⋊C4C2212yes—
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2312yes—
202#544—216no—
203#533—416no—
204C2×C4⋊Q8—28no—
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2312yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2318yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×C22⋊Q8C2318yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2318yes—
225#520—28no—
226#520Q8116yescomplemented
227C4×#41—28no—
228C2×C4×Q8—28no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2318yes—
243C2×C4×Q8C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2314yes—
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2312yes—
252C2×#117C2312yes—
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2318yes—
259C2×#117C2311yescharacteristic
260C2×#117C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2314yes—
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2311yescharacteristic
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2314yes—
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2314yes—
282#400C2318yes—
283#399C2318yes—
284#399C2314yes—
285#399C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2314yes—
291#398C2314yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#396C2318yes—
301#396C2314yes—
302#396C2314yes—
303#396C2318yes—
304#395C2318yes—
305#395C2318yes—
306#395C2318yes—
307#395C2314yes—
308#395C2318yes—
309#393C2318yes—
310#393C2318yes—
311#393C2314yes—
312#391C2312yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2318yes—
317#391C2314yes—
318#391C2314yes—
319#391C2318yes—
320#391C2312yes—
321#391C2312yes—
322#391C2312yes—
323#391C2318yes—
324#391C2318yes—
325#391C2318yes—
326#391C2318yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2318yes—
333#391C2318yes—
334#391C2314yes—
335#390C2314yes—
336#390C2312yes—
337#390C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2312yes—
341#389C2314yes—
342#389C2314yes—
343#389C2314yes—
344#389C2318yes—
345#389C2318yes—
346#389C2314yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2318yes—
364#389C2318yes—
365#389C2314yes—
366#389C2318yes—
367#389C2318yes—
368#389C2312yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2314yes—
373#389C2312yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#389C2314yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2314yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2314yes—
399#387C2314yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2314yes—
408#387C2314yes—
409#386C2314yes—
410#386C2318yes—
411#386C2314yes—
412#385C2318yes—
413#385C2318yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2314yes—
418#385C2314yes—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2314yes—
422#384C2314yes—
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2312yes—
426#384C2312yes—
427#383C2318yes—
428#382C2314yes—
429#382C2318yes—
430#382C2318yes—
431#382C2312yes—
432#382C2312yes—
433#382C2312yes—
434#382C2312yes—
435#381C2318yes—
436#380C2314yes—
437#380C2314yes—
438#380C2314yes—
439#380C2318yes—
440#380C2314yes—
441#380C2314yes—
442#380C2318yes—
443#380C2318yes—
444#380C2318yes—
445#380C2312yes—
446#380C2312yes—
447#380C2312yes—
448#380C2314yes—
449#380C2312yes—
450#380C2312yes—
451#380C2312yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2318yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2318yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2314yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2312yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2311yescharacteristic
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2318yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2312yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2312yes—
518#376C2318yes—
519#376C2314yes—
520C2×#95C2314yes—
521C2×#95C2314yes—
522C2×#95C2314yes—
523C2×#95C2312yes—
524C43C2314yes—
525C43C2312yes—
526C43C2314yes—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41C2×Q818yes—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—28no—
533C22×Q8—42no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8C2411yescharacteristic
537C22×Q8C2414yes—
538C22×Q8C2412yes—
539C22×Q8C2411yescharacteristic
540C22×Q8C2411yescharacteristic
541C22×Q8C2418yes—
542C22×Q8C2414yes—
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2414yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2412yes—
554C23×C4C2414yes—
555C23×C4C2411yescharacteristic
556C23×C4C2412yes—
557C23×C4C2411yescharacteristic
558C4⋊Q8—216no—
559C4⋊Q8—216no—
560C4⋊Q8—216no—
561C4⋊Q8—28no—
562C4⋊Q8—28no—
563C4⋊Q8—28no—
564C4⋊Q8—28no—
565C4⋊Q8—48no—
566C4⋊Q8—48no—
567C4⋊Q8—416no—
568#125—216no—
569#125—216no—
570#125—416no—
571C22⋊Q8—28no—
572C22⋊Q8—232no—
573C22⋊Q8—416no—
574C22⋊Q8—44no—
575C22⋊Q8—48no—
576C22⋊Q8—48no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—24no—
580C4×Q8—24no—
581C4×Q8—28no—
582C4×Q8—24no—
583C4×Q8—28no—
584C4×Q8—24no—
585C4×Q8—24no—
586C4×Q8—24no—
587C4×Q8—416no—
588C4×Q8—48no—
589C4×Q8—44no—
590C4×Q8—48no—
591C4×Q8C2×Q8116yescomplemented
592C4×D4—28no—
593C4×D4—28no—
594C4×D4—216no—
595C4×D4—28no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4C2×Q8132yes—
599C4×D4C2×Q8116yescomplemented
600#117—24no—
601#117—24no—
602#117—28no—
603#117—28no—
604#117—28no—
605#117—28no—
606#117—416no—
607#117C2×Q818yes—
608#117C2×Q8116yescomplemented
609C2×C4⋊C4—28no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—28no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—28no—
614C2×C4⋊C4—48no—
615C2×C4⋊C4—48no—
616C2×C4⋊C4C2×Q818yes—
617C2×C4⋊C4C2×Q8116yescomplemented
618C2×C4⋊C4#4118yes—
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2418yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2412yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2412yes—
672C2×C4⋊C4C2414yes—
673C2×C4⋊C4C2412yes—
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2412yes—
676C2×C4⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2412yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2412yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2414yes—
692C2×C42—28no—
693C2×C42—28no—
694C2×C42—44no—
695C2×C42—48no—
696C2×C42#4118yes—
697C2×C42C2414yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2414yes—
712C2×C42C2418yes—
713C2×C42C2414yes—
714C2×C42C2414yes—
715C2×C42C2418yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#95C2412yes—
731#95C2414yes—
732#95C2418yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2412yes—
740#95C2414yes—
741#95C2414yes—
742#95C2412yes—
743#95C2412yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2418yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2418yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768#95C2418yes—
769#95C2414yes—
770#95C2414yes—
771#95C2418yes—
772#95C2414yes—
773#95C2414yes—
774C24C2512yes—
775C24C2511yescharacteristic
776#41—232no—
777C2×Q8—22no—
778C2×Q8—22no—
779C2×Q8—22no—
780C2×Q8—24no—
781C2×Q8—22no—
782C2×Q8—28no—
783C2×Q8—216no—
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—28no—
790C2×Q8—22no—
791C2×Q8—42no—
792C2×Q8—48no—
793C2×Q8—44no—
794C2×Q8—44no—
795C2×Q8—48no—
796C2×Q8—416no—
797C2×Q8—816no—
798C2×Q8C22×Q814yes—
799C2×Q8H(5,𝔽2)14yes—
800C2×D4—24no—
801C2×D4—24no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4C22×Q818yes—
805C2×D4C22×Q814yes—
806C22×C4—24no—
807C22×C4—24no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—44no—
836C22×C4C22×Q818yes—
837C22×C4C22×Q818yes—
838C22×C4C22×Q8116yes—
839C22×C4C22×Q814yes—
840C22×C4C2×#4114yes—
841C22×C4C2×#4114yes—
842C22×C4C2×#4118yes—
843C22×C4C2×#4114yes—
844C22×C4C2×#4114yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2518yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2511yescharacteristic
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2511yescharacteristic
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C4⋊C4—22no—
870C4⋊C4—28no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—28no—
882C4⋊C4—22no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—216no—
892C4⋊C4—216no—
893C4⋊C4—216no—
894C4⋊C4—216no—
895C4⋊C4—216no—
896C4⋊C4—28no—
897C4⋊C4—24no—
898C4⋊C4—28no—
899C4⋊C4—24no—
900C4⋊C4—24no—
901C4⋊C4—24no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—48no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C4⋊C4C22×Q818yes—
921C4⋊C4C22×Q818yes—
922C4⋊C4C22×Q814yes—
923C4⋊C4C22×Q8116yes—
924C4⋊C4C22×Q814yes—
925C4⋊C4C2×#4118yes—
926C4⋊C4C2×#4118yes—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—24no—
933C22⋊C4—24no—
934C22⋊C4—28no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4C22×Q818yes—
941C22⋊C4C22×Q8116yes—
942C42—24no—
943C42—24no—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—28no—
950C42—24no—
951C42—28no—
952C42—28no—
953C42—24no—
954C42—28no—
955C42—28no—
956C42—24no—
957C42—44no—
958C42—44no—
959C42—44no—
960C42—42no—
961C42—44no—
962C42—44no—
963C42—42no—
964C42—44no—
965C42—44no—
966C42—48no—
967C42—44no—
968C42—48no—
969C42C22×Q818yes—
970C42C22×Q8116yes—
971C42C2×#4114yes—
972C42C2×#4114yes—
973C42C2×#4114yes—
974C42C2×#4114yes—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23C23×Q814yes—
986C23C23×Q812yes—
987C23C22×#4112yes—
988C23C22×#4112yes—
989C23C2611yescharacteristic
990Q8—28no—
991Q8—28no—
992Q8—48no—
993Q8—44no—
994Q8—416no—
995Q8—816no—
996Q8—88no—
997D4—216no—
998D4—28no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—24no—
1004C2×C4—24no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—216no—
1018C2×C4—28no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—28no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—24no—
1035C2×C4—28no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—24no—
1039C2×C4—24no—
1040C2×C4—28no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—48no—
1056C2×C4—416no—
1057C2×C4—48no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—88no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—88no—
1065C2×C4#533116yescomplemented
1066C2×C4C23×Q814yes—
1067C2×C4C23×Q814yes—
1068C2×C4C23×Q814yes—
1069C2×C4C23×Q818yes—
1070C2×C4C23×Q812yes—
1071C2×C4C23×Q812yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4118yes—
1074C2×C4C22×#4112yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C2×H(5,𝔽2)14yes—
1082C2×C4C2×H(5,𝔽2)12yes—
1083C2×C4#58512yes—
1084C22—22no—
1085C22—22no—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22C2×#53314yes—
1098C22C24×Q811yescharacteristic
1099C22C23×#4111yescharacteristic
1100C22C23×#4111yescharacteristic
1101C22C22×H(5,𝔽2)11yescharacteristic
1102C22C2×#58511yescharacteristic
1103C222−1+611yescharacteristic
1104C222−1+611yescharacteristic
1105C4—24no—
1106C4—28no—
1107C4—28no—
1108C4—24no—
1109C4—22no—
1110C4—24no—
1111C4—22no—
1112C4—22no—
1113C4—24no—
1114C4—42no—
1115C4—44no—
1116C4—44no—
1117C4—42no—
1118C4—44no—
1119C4—44no—
1120C4—42no—
1121C4—42no—
1122C4—48no—
1123C4—42no—
1124C4—42no—
1125C4—42no—
1126C4C2×#53314yes—
1127C4C2×#53314yes—
1128C4#349414yes—
1129C2—24no—
1130C2—44no—
1131C2C22×#53311yescharacteristic
1132C2C2×#349411yescharacteristic
1133C2#6286011yescharacteristic
1134C2Q8×H(5,𝔽2)11yescharacteristic
1135C2#6298411yescharacteristic
1136C2#6300411yescharacteristic
1137C2#6300711yescharacteristic
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. #36288C2semidirect
4. #36277C2semidirect
5. #36133C2semidirect
6. #36129C2semidirect
7. #35951C2semidirect
8. #35819C2semidirect
9. #35788C2semidirect
10. #35602C2semidirect
11. #35585C2semidirect
12. #35583C2semidirect
15. #35199C2semidirect
16. #35176C2semidirect
17. #35167C2semidirect
19. #34951C2semidirect
20. #34929C2semidirect
21. C2×#2546C2semidirect
22. #34272C2semidirect
24. #34216C2semidirect
25. Q8×#117C2semidirect
226. #520Q8semidirect
591. C4×Q8C2×Q8semidirect
599. C4×D4C2×Q8semidirect
608. #117C2×Q8semidirect
617. C2×C4⋊C4C2×Q8semidirect
1065. C2×C4#533semidirect

Maximal subgroups

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

subgroupindex
#365992
#364812
#362882
#362772
#361332
#361292
#359512
#358192
#357882
#356022
#355852
#355832
#355752
#352792
#351992
#351762
#351672
#349522
#349512
#349292
C2×#25462
#342722
#342532
#342162
Q8×#1172
C4×#5202