Finite Group Databasebeta

← #7670354

Subgroups — #7670354

Order 512.

5122 conjugacy classes of subgroups.

The subgroup lattice has 1169 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59868C214yesmaximal, complemented
2#59867C214yesmaximal, complemented
3#59866C214yesmaximal, complemented
4#59321C212yesmaximal, complemented
5#59144C212yesmaximal, complemented
6#39752C212yesmaximal, complemented
7#39751C212yesmaximal, complemented
8#39748C214yesmaximal, complemented
9#39640C212yesmaximal, complemented
10#39639C212yesmaximal, complemented
11#39636C214yesmaximal, complemented
12C2×#2857C211yesmaximal, characteristic
13#36599C212yesmaximal, complemented
14#36599C214yesmaximal, complemented
15#36577C212yesmaximal, complemented
16#36571C214yesmaximal, complemented
17#36552C212yesmaximal, complemented
18#36545C212yesmaximal, complemented
19#35368C214yesmaximal
20#35020C212yesmaximal
21#35011C212yesmaximal
22#34212C212yesmaximal
23#34212C212yesmaximal
24C2×C4×C22⋊Q8C211yesmaximal, characteristic
25C2×C4×C22⋊Q8C211yesmaximal, characteristic
26C2×#557C2212yescomplemented
27C22×C4⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C22×C4×Q8C2211yescharacteristic
32C22×C4×Q8C2211yescharacteristic
33C23×C42C2211yescharacteristic
34#2857C2212yes—
35#2857C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2857C2212yes—
41#2857C2212yes—
42#2857C2214yes—
43#2857C2214yes—
44#2851C2214yes—
45#2851C2214yes—
46#2809C2214yescomplemented
47#2806C2214yescomplemented
48#2805C2214yescomplemented
49#2802C2218yescomplemented
50#2799C2218yescomplemented
51#2791C2218yescomplemented
52#2774C2218yescomplemented
53#2755C2218yescomplemented
54#2726C2214yescomplemented
55#2713C2218yescomplemented
56#2659C2214yes—
57#2659C2214yes—
58#2646C2214yes—
59#2646C2214yes—
60#2590C2218yescomplemented
61#2588C2218yescomplemented
62#2585C2218yescomplemented
63#2585C2218yescomplemented
64#2585C2218yescomplemented
65#2584C2214yescomplemented
66#2583C2218yes—
67#2583C2218yes—
68#2582C2212yescomplemented
69#2582C2214yescomplemented
70#2581C2214yescomplemented
71#2569C2218yes—
72#2569C2218yes—
73#2569C2218yes—
74#2569C2218yes—
75#2568C2212yescomplemented
76#2568C2214yescomplemented
77#2565C2214yescomplemented
78#2552C2212yescomplemented
79#2552C2214yescomplemented
80#2550C2214yescomplemented
81#2546C2212yescomplemented
82#2546C2214yescomplemented
83#2520C2218yescomplemented
84#2511C2214yescomplemented
85#2511C2214yescomplemented
86#2511C2214yescomplemented
87#2509C2218yescomplemented
88#2509C2214yescomplemented
89#2508C2214yescomplemented
90#2506C2214yescomplemented
91#2505C2218yes—
92#2505C2218yes—
93#2505C2218yes—
94#2505C2218yes—
95#2502C2214yes—
96#2502C2214yes—
97#2473C2218yes—
98#2473C2218yes—
99#2473C2218yes—
100#2473C2218yes—
101#2462C2218yescomplemented
102#2453C2214yescomplemented
103#2453C2218yescomplemented
104#2453C2214yescomplemented
105#2451C2214yescomplemented
106#2446C2214yescomplemented
107#2446C2214yescomplemented
108#2446C2214yescomplemented
109#2442C2214yes—
110#2442C2218yes—
111#2442C2218yes—
112#2442C2214yes—
113#2442C2214yes—
114#2442C2214yes—
115#2434C2214yes—
116#2434C2214yes—
117#2370C2218yescomplemented
118#2370C2214yescomplemented
119#2368C2218yes—
120#2368C2218yes—
121#2365C2212yescomplemented
122#2365C2214yescomplemented
123#2360C2214yes—
124#2360C2214yes—
125#2360C2214yes—
126#2360C2214yes—
127#2355C2212yescomplemented
128#2355C2214yescomplemented
129#2351C2214yescomplemented
130Q8×C4⋊C4C2212yescomplemented
131#2345C2218yes—
132#2345C2214yes—
133#2345C2214yes—
134#2345C2218yes—
135Q8×C22⋊C4C2214yes—
136Q8×C22⋊C4C2214yes—
137#2329C2214yes—
138#2329C2214yes—
139#2329C2214yes—
140#2329C2214yes—
141#2315C2214yes—
142#2315C2214yes—
143#2315C2214yes—
144C4×C22⋊Q8C2212yes—
145C4×C22⋊Q8C2212yes—
146C4×C22⋊Q8C2212yes—
147C4×C22⋊Q8C2212yes—
148C4×C22⋊Q8C2214yes—
149C4×C22⋊Q8C2214yes—
150C4×C22⋊Q8C2214yes—
151C4×C22⋊Q8C2214yes—
152C4×C22⋊Q8C2212yes—
153C4×C22⋊Q8C2212yes—
154C4×C22⋊Q8C2212yes—
155C4×C22⋊Q8C2212yes—
156C4×C22⋊Q8C2212yes—
157C4×C22⋊Q8C2212yes—
158C4×C22⋊Q8C2212yes—
159C4×C22⋊Q8C2212yes—
160C4×C22⋊Q8C2212yes—
161C4×C22⋊Q8C2212yes—
162C4×C22⋊Q8C2212yes—
163C4×C22⋊Q8C2212yes—
164C2×#391C2212yes—
165C2×#391C2211yescharacteristic
166C2×#391C2211yescharacteristic
167C2×#389C2212yes—
168C2×#389C2212yes—
169C2×#389C2211yescharacteristic
170C2×#389C2211yescharacteristic
171C2×#387C2212yes—
172C2×#387C2212yes—
173C2×#385C2212yes—
174C2×#385C2212yes—
175C2×#384C2211yescharacteristic
176C2×#380C2212yes—
177C2×#380C2212yes—
178C2×#380C2211yescharacteristic
179C2×#380C2211yescharacteristic
180#2273C2214yes—
181C2×C4×C4⋊C4C2211yescharacteristic
182C2×C4×C4⋊C4C2212yes—
183C2×C4×C4⋊C4C2211yescharacteristic
184C2×C4×C4⋊C4C2212yes—
185C2×C4×C22⋊C4C2212yes—
186C2×C4×C22⋊C4C2212yes—
187C23×Q8C2312yes—
188C23×Q8C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2311yescharacteristic
192C24×C4C2311yescharacteristic
193#557—48no—
194C2×C4⋊Q8—44no—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2314yes—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2314yes—
201C2×#125C2314yes—
202C2×#125C2314yes—
203C2×#125C2318yes—
204C2×#125C2318yes—
205C2×C22⋊Q8—28no—
206C2×C22⋊Q8—216no—
207C2×C22⋊Q8Q8116yescomplemented
208C2×C22⋊Q8C2312yes—
209C2×C22⋊Q8C2314yes—
210C2×C22⋊Q8C2314yes—
211C2×C22⋊Q8C2314yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2312yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×C4×Q8—44no—
221C2×C4×Q8—44no—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2314yes—
228C2×C4×Q8C2314yes—
229C2×C4×Q8C2314yes—
230C2×C4×Q8C2312yes—
231C2×C4×Q8C2312yes—
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2312yes—
234C22×C4⋊C4C2312yes—
235C22×C4⋊C4C2314yes—
236C22×C4⋊C4C2312yes—
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2312yes—
241C22×C4⋊C4C2312yes—
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2312yes—
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2312yes—
248C22×C4⋊C4C2312yes—
249C22×C4⋊C4C2312yes—
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4C2312yes—
253C22×C22⋊C4C2312yes—
254C22×C22⋊C4C2314yes—
255C22×C22⋊C4C2312yes—
256C22×C22⋊C4C2312yes—
257C22×C42—44no—
258C22×C42C2311yescharacteristic
259C22×C42C2311yescharacteristic
260C22×C42C2311yescharacteristic
261C22×C42C2312yes—
262C22×C42C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267C22×C42C2311yescharacteristic
268C22×C42C2311yescharacteristic
269C22×C42C2312yes—
270C22×C42C2312yes—
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
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#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#395C2318yes—
303#395C2318yes—
304#395C2318yes—
305#395C2318yes—
306#391C2312yes—
307#391C2314yes—
308#391C2314yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2318yes—
314#391C2314yes—
315#391C2312yes—
316#391C2318yes—
317#391C2318yes—
318#391C2318yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2312yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2312yes—
334#389C2314yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C2312yes—
341#389C2318yes—
342#389C2314yes—
343#389C2318yes—
344#389C2318yes—
345#389C2318yes—
346#389C2318yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#387C2318yes—
370#387C2318yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2314yes—
388#387C2314yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2314yes—
393#387C2314yes—
394#387C2314yes—
395#387C2314yes—
396#387C2314yes—
397#387C2314yes—
398#385C2318yes—
399#385C2314yes—
400#385C2314yes—
401#385C2318yes—
402#385C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#385C2318yes—
410#385C2318yes—
411#385C2318yes—
412#385C2314yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#385C2314yes—
417#385C2314yes—
418#384C2312yes—
419#384C2312yes—
420#384C2314yes—
421#384C2312yes—
422#384C2312yes—
423#384C2314yes—
424#382C2314yes—
425#382C2314yes—
426#382C2318yes—
427#382C2318yes—
428#380C2312yes—
429#380C2318yes—
430#380C2314yes—
431#380C2314yes—
432#380C2314yes—
433#380C2318yes—
434#380C2318yes—
435#380C2318yes—
436#380C2318yes—
437#380C2318yes—
438#380C2312yes—
439#380C2314yes—
440#380C2312yes—
441#380C2314yes—
442#380C2312yes—
443#380C2314yes—
444#380C2312yes—
445#380C2314yes—
446#380C2314yes—
447#380C2312yes—
448#380C2312yes—
449#380C2312yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2312yes—
453C4×C4⋊C4C2314yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2318yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2318yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2318yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2314yes—
466C4×C4⋊C4C2314yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2312yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2312yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2314yes—
479C4×C22⋊C4C2314yes—
480C4×C22⋊C4C2318yes—
481C4×C22⋊C4C2318yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C2×#95C2312yes—
489C2×#95C2312yes—
490C2×#95C2312yes—
491C2×#95C2314yes—
492C2×#95C2312yes—
493C2×#95C2312yes—
494C2×#95C2312yes—
495C2×#95C2312yes—
496C2×#95C2312yes—
497C2×#95C2312yes—
498C2×#95C2312yes—
499C2×#95C2314yes—
500C25C2411yescharacteristic
501C22×Q8—24no—
502C22×Q8—28no—
503C22×Q8—42no—
504C22×Q8—42no—
505C22×Q8—42no—
506C22×Q8—42no—
507C22×Q8—44no—
508C22×Q8—44no—
509C22×Q8C2×Q818yescomplemented
510C22×Q8C2412yes—
511C22×Q8C2414yes—
512C22×Q8C2412yes—
513C22×Q8C2412yes—
514C22×Q8C2414yes—
515C22×Q8C2412yes—
516C23×C4—24no—
517C23×C4—42no—
518C23×C4—42no—
519C23×C4—42no—
520C23×C4—42no—
521C23×C4—42no—
522C23×C4—42no—
523C23×C4C2×Q818yes—
524C23×C4#4118yes—
525C23×C4C2411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2414yes—
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2411yescharacteristic
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C4⋊Q8—28no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556C4⋊Q8—44no—
557C4⋊Q8—48no—
558C4⋊Q8—48no—
559#125—48no—
560#125—48no—
561#125—416no—
562#125—416no—
563C22⋊Q8—28no—
564C22⋊Q8—216no—
565C22⋊Q8—28no—
566C22⋊Q8—216no—
567C22⋊Q8—28no—
568C22⋊Q8—216no—
569C22⋊Q8—28no—
570C22⋊Q8—216no—
571C22⋊Q8C2×Q8116yescomplemented
572C22⋊Q8C2×Q8116yescomplemented
573C22⋊Q8C2×Q8116yescomplemented
574C22⋊Q8C2×Q8116yescomplemented
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—44no—
578C4×Q8—44no—
579C4×Q8—44no—
580C4×Q8—44no—
581C4×Q8—44no—
582C4×Q8—44no—
583C4×Q8—48no—
584C4×Q8—48no—
585C4×Q8—48no—
586C4×Q8—48no—
587C2×C4⋊C4—24no—
588C2×C4⋊C4—28no—
589C2×C4⋊C4—28no—
590C2×C4⋊C4—216no—
591C2×C4⋊C4—42no—
592C2×C4⋊C4—44no—
593C2×C4⋊C4—44no—
594C2×C4⋊C4—42no—
595C2×C4⋊C4—44no—
596C2×C4⋊C4—44no—
597C2×C4⋊C4—42no—
598C2×C4⋊C4—42no—
599C2×C4⋊C4—44no—
600C2×C4⋊C4—44no—
601C2×C4⋊C4—44no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4C2×Q818yescomplemented
604C2×C4⋊C4C2×Q8116yescomplemented
605C2×C4⋊C4C2412yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2414yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2414yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2418yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2414yes—
653C2×C22⋊C4—28no—
654C2×C22⋊C4—216no—
655C2×C22⋊C4—28no—
656C2×C22⋊C4—28no—
657C2×C22⋊C4C2×Q8116yes—
658C2×C22⋊C4C2414yes—
659C2×C22⋊C4C2418yes—
660C2×C22⋊C4C2418yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2414yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C42—24no—
669C2×C42—24no—
670C2×C42—24no—
671C2×C42—44no—
672C2×C42—44no—
673C2×C42—42no—
674C2×C42—42no—
675C2×C42—42no—
676C2×C42—42no—
677C2×C42—42no—
678C2×C42—42no—
679C2×C42—42no—
680C2×C42—42no—
681C2×C42—42no—
682C2×C42—44no—
683C2×C42—44no—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2414yes—
693C2×C42C2414yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2418yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2418yes—
701C2×C42C2418yes—
702C2×C42C2418yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#95C2414yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2414yes—
718#95C2414yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2418yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2418yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752C24—41no—
753C24—41no—
754C24—41no—
755C24—41no—
756C24C22×Q814yes—
757C24C2×#4114yes—
758C242−1+414yes—
759C24C2511yescharacteristic
760C24C2511yescharacteristic
761C24C2511yescharacteristic
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—28no—
765C2×Q8—28no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—28no—
769C2×Q8—24no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—44no—
777C2×Q8—44no—
778C2×Q8—416no—
779C2×Q8—416no—
780C2×Q8—816no—
781C2×Q8C22×Q818yes—
782C2×Q8C22×Q818yes—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—28no—
806C22×C4—28no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—416no—
816C22×C4—416no—
817C22×C4—41no—
818C22×C4—41no—
819C22×C4—41no—
820C22×C4—41no—
821C22×C4—41no—
822C22×C4—41no—
823C22×C4—41no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—41no—
838C22×C4—41no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—44no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—44no—
855C22×C4—416no—
856C22×C4C22×Q814yes—
857C22×C4C22×Q814yes—
858C22×C4C22×Q814yes—
859C22×C4C22×Q818yes—
860C22×C4C22×Q818yes—
861C22×C4C22×Q814yes—
862C22×C4C22×Q814yes—
863C22×C4C22×Q814yes—
864C22×C4C2×#4114yes—
865C22×C4C2×#4114yes—
866C22×C4C2×#4114yes—
867C22×C4C2×#4114yes—
868C22×C4C2×#4114yes—
869C22×C4C2×#4114yes—
870C22×C4C2514yes—
871C22×C4C2511yescharacteristic
872C22×C4C2511yescharacteristic
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2518yes—
877C22×C4C2514yes—
878C22×C4C2514yes—
879C22×C4C2518yes—
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2511yescharacteristic
885C22×C4C2511yescharacteristic
886C22×C4C2511yescharacteristic
887C22×C4C2511yescharacteristic
888C22×C4C2511yescharacteristic
889C22×C4C2511yescharacteristic
890C22×C4C2511yescharacteristic
891C22×C4C2511yescharacteristic
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—24no—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—216no—
898C4⋊C4—216no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—28no—
902C4⋊C4—28no—
903C4⋊C4—24no—
904C4⋊C4—28no—
905C4⋊C4—28no—
906C4⋊C4—24no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—24no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—44no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—48no—
932C4⋊C4—48no—
933C4⋊C4—48no—
934C4⋊C4—48no—
935C4⋊C4—48no—
936C4⋊C4C22×Q818yes—
937C4⋊C4C22×Q818yes—
938C4⋊C4C22×Q8116yes—
939C4⋊C4C22×Q8116yes—
940C22⋊C4—28no—
941C22⋊C4—216no—
942C22⋊C4—216no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4C22×Q8116yes—
949C22⋊C4C22×Q8116yes—
950C42—22no—
951C42—22no—
952C42—22no—
953C42—22no—
954C42—22no—
955C42—22no—
956C42—22no—
957C42—22no—
958C42—22no—
959C42—28no—
960C42—28no—
961C42—28no—
962C42—28no—
963C42—41no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—41no—
969C42—44no—
970C42—44no—
971C42—44no—
972C42—44no—
973C42—48no—
974C42—48no—
975C42—48no—
976C42—48no—
977C42H(5,𝔽2)14yes—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—44no—
991C23—44no—
992C23—44no—
993C23—44no—
994C23—44no—
995C23—44no—
996C23#557116yescomplemented
997C23C23×Q812yes—
998C23C23×Q812yes—
999C23C23×Q812yes—
1000C23C22×#4112yes—
1001C23C22×#4112yes—
1002C23C22×#4112yes—
1003C23C2×2−1+412yes—
1004C23C2×2−1+412yes—
1005C23C2×2−1+412yes—
1006C23C2611yescharacteristic
1007Q8—216no—
1008Q8—48no—
1009Q8—48no—
1010Q8—48no—
1011Q8—416no—
1012Q8—88no—
1013C2×C4—28no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—24no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—24no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—28no—
1035C2×C4—28no—
1036C2×C4—28no—
1037C2×C4—28no—
1038C2×C4—28no—
1039C2×C4—28no—
1040C2×C4—24no—
1041C2×C4—28no—
1042C2×C4—24no—
1043C2×C4—28no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—24no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—28no—
1062C2×C4—28no—
1063C2×C4—28no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—24no—
1070C2×C4—44no—
1071C2×C4—44no—
1072C2×C4—44no—
1073C2×C4—44no—
1074C2×C4—44no—
1075C2×C4—44no—
1076C2×C4—48no—
1077C2×C4—48no—
1078C2×C4—44no—
1079C2×C4—44no—
1080C2×C4—44no—
1081C2×C4—44no—
1082C2×C4—48no—
1083C2×C4—44no—
1084C2×C4—48no—
1085C2×C4—88no—
1086C2×C4—84no—
1087C2×C4—84no—
1088C2×C4—84no—
1089C2×C4—84no—
1090C2×C4—88no—
1091C2×C4C23×Q818yes—
1092C2×C4C23×Q818yes—
1093C2×C4C23×Q812yes—
1094C2×C4C23×Q812yes—
1095C2×C4C23×Q812yes—
1096C2×C4C23×Q812yes—
1097C2×C4C22×#4112yes—
1098C2×C4C22×#4112yes—
1099C2×C4C22×#4112yes—
1100C2×C4C22×#4112yes—
1101C2×C4C2×H(5,𝔽2)12yes—
1102C2×C4C2×H(5,𝔽2)12yes—
1103C2×C4C2×H(5,𝔽2)12yes—
1104C2×C4#58512yes—
1105C2×C4#58512yes—
1106C2×C4#58512yes—
1107C22—22no—
1108C22—22no—
1109C22—22no—
1110C22—22no—
1111C22—22no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—22no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—22no—
1124C22—22no—
1125C22—416no—
1126C22C2×#55714yes—
1127C22C2×#55714yes—
1128C22C2×#55714yes—
1129C22C24×Q811yescharacteristic
1130C22C23×#4111yescharacteristic
1131C22C22×H(5,𝔽2)11yescharacteristic
1132C22C22×2−1+411yescharacteristic
1133C22C2×#58511yescharacteristic
1134C22C2×#58511yescharacteristic
1135C22C2×#58511yescharacteristic
1136C4—22no—
1137C4—22no—
1138C4—22no—
1139C4—28no—
1140C4—22no—
1141C4—22no—
1142C4—22no—
1143C4—28no—
1144C4—22no—
1145C4—22no—
1146C4—44no—
1147C4—48no—
1148C4—44no—
1149C4—48no—
1150C4—41no—
1151C4—41no—
1152C4—44no—
1153C4—44no—
1154C4—44no—
1155C4—44no—
1156C4#350114yes—
1157C4#350514yes—
1158C2—24no—
1159C2—24no—
1160C2—24no—
1161C2C22×#55711yescharacteristic
1162C2C2×#350111yescharacteristic
1163C2C2×#350511yescharacteristic
1164C2#6281311yescharacteristic
1165C2#6281511yescharacteristic
1166C2#6281911yescharacteristic
1167C2#6282311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59868C2semidirect
2. #59867C2semidirect
3. #59866C2semidirect
4. #59321C2semidirect
5. #59144C2semidirect
6. #39752C2semidirect
7. #39751C2semidirect
8. #39748C2semidirect
9. #39640C2semidirect
10. #39639C2semidirect
11. #39636C2semidirect
13. #36599C2semidirect
14. #36599C2semidirect
15. #36577C2semidirect
16. #36571C2semidirect
17. #36552C2semidirect
18. #36545C2semidirect
26. C2×#557C22semidirect
46. #2809C22semidirect
47. #2806C22semidirect
48. #2805C22semidirect
49. #2802C22semidirect
50. #2799C22semidirect
51. #2791C22semidirect
52. #2774C22semidirect
53. #2755C22semidirect
54. #2726C22semidirect
55. #2713C22semidirect
60. #2590C22semidirect
61. #2588C22semidirect
62. #2585C22semidirect
63. #2585C22semidirect
64. #2585C22semidirect
65. #2584C22semidirect
68. #2582C22semidirect
69. #2582C22semidirect
70. #2581C22semidirect
75. #2568C22semidirect
76. #2568C22semidirect
77. #2565C22semidirect
78. #2552C22semidirect
79. #2552C22semidirect
80. #2550C22semidirect
81. #2546C22semidirect
82. #2546C22semidirect
83. #2520C22semidirect
84. #2511C22semidirect
85. #2511C22semidirect
86. #2511C22semidirect
87. #2509C22semidirect
88. #2509C22semidirect
89. #2508C22semidirect
90. #2506C22semidirect
101. #2462C22semidirect
102. #2453C22semidirect
103. #2453C22semidirect
104. #2453C22semidirect
105. #2451C22semidirect
106. #2446C22semidirect
107. #2446C22semidirect
108. #2446C22semidirect
117. #2370C22semidirect
118. #2370C22semidirect
121. #2365C22semidirect
122. #2365C22semidirect
127. #2355C22semidirect
128. #2355C22semidirect
129. #2351C22semidirect
130. Q8×C4⋊C4C22semidirect
207. C2×C22⋊Q8Q8semidirect
509. C22×Q8C2×Q8semidirect
571. C22⋊Q8C2×Q8semidirect
572. C22⋊Q8C2×Q8semidirect
573. C22⋊Q8C2×Q8semidirect
574. C22⋊Q8C2×Q8semidirect
603. C2×C4⋊C4C2×Q8semidirect
604. C2×C4⋊C4C2×Q8semidirect
996. C23#557semidirect

Maximal subgroups

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

subgroupindex
#598682
#598672
#598662
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