Finite Group Databasebeta

← #7672153

Subgroups — #7672153

Order 512.

5100 conjugacy classes of subgroups.

The subgroup lattice has 1217 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59325C214yesmaximal, complemented
2#59324C214yesmaximal, complemented
3#59322C212yesmaximal, complemented
4#59321C212yesmaximal, complemented
5#59259C212yesmaximal, complemented
6#59245C212yesmaximal, complemented
7#39609C212yesmaximal, complemented
8#39607C212yesmaximal, complemented
9#39603C214yesmaximal, complemented
10#37877C214yesmaximal, complemented
11#37873C214yesmaximal
12#36625C211yesmaximal, characteristic
13#36571C214yesmaximal, complemented
14#36564C212yesmaximal, complemented
15#36552C212yesmaximal, complemented
16#36193C214yesmaximal, complemented
17#36190C214yesmaximal
18#35668C212yesmaximal, complemented
19#35585C212yesmaximal, complemented
20#35253C212yesmaximal
21#35179C211yesmaximal, characteristic, complemented
22#35167C211yesmaximal, characteristic, complemented
23#34213C211yesmaximal, characteristic, complemented
24#34203C212yesmaximal
25#34182C211yesmaximal, characteristic, complemented
26C2×C4×C22⋊Q8C211yesmaximal, characteristic
27C2×#2285C211yesmaximal, characteristic
28C2×#544C2212yes—
29C2×#533C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C2×#519C2212yes—
32C22×C4×Q8C2211yescharacteristic
33C22×#117C2212yes—
34C23×C42C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2857C2211yescharacteristic
39#2857C2214yes—
40#2857C2214yes—
41#2855C2212yes—
42#2855C2212yes—
43#2855C2214yes—
44#2851C2212yes—
45#2851C2212yes—
46#2851C2214yes—
47#2848C2212yes—
48#2848C2212yes—
49#2792C2218yescomplemented
50#2791C2218yescomplemented
51#2788C2218yes—
52#2774C2218yescomplemented
53#2768C2218yes—
54#2755C2218yescomplemented
55#2742C2218yes—
56#2704C2218yes—
57#2659C2214yes—
58#2629C2214yes—
59#2628C2214yes—
60#2627C2214yes—
61#2590C2218yescomplemented
62#2588C2218yescomplemented
63#2586C2218yescomplemented
64#2585C2218yescomplemented
65#2583C2218yes—
66#2582C2212yescomplemented
67#2582C2212yescomplemented
68#2581C2214yescomplemented
69#2574C2218yes—
70#2569C2218yes—
71#2568C2214yescomplemented
72#2568C2212yescomplemented
73#2567C2214yescomplemented
74#2567C2214yescomplemented
75#2567C2212yescomplemented
76#2565C2214yescomplemented
77#2565C2214yescomplemented
78#2565C2214yescomplemented
79#2552C2212yescomplemented
80#2552C2212yescomplemented
81#2552C2214yescomplemented
82#2551C2212yescomplemented
83#2551C2212yescomplemented
84#2550C2214yescomplemented
85#2550C2214yescomplemented
86#2549C2218yes—
87#2522C2218yes—
88#2520C2218yescomplemented
89#2520C2218yescomplemented
90#2511C2214yescomplemented
91#2511C2214yescomplemented
92#2509C2214yescomplemented
93#2509C2214yescomplemented
94#2508C2214yescomplemented
95#2508C2214yescomplemented
96#2508C2218yescomplemented
97#2507C2214yescomplemented
98#2507C2214yescomplemented
99#2507C2214yescomplemented
100#2507C2214yescomplemented
101#2506C2214yescomplemented
102#2506C2214yescomplemented
103#2505C2218yes—
104#2505C2218yes—
105#2502C2214yes—
106#2497C2214yes—
107#2497C2214yes—
108#2492C2214yes—
109#2473C2218yes—
110#2453C2214yescomplemented
111#2453C2214yescomplemented
112#2451C2214yescomplemented
113#2451C2214yescomplemented
114#2442C2218yes—
115#2442C2214yes—
116#2441C2214yes—
117#2440C2214yes—
118#2440C2214yes—
119#2439C2214yes—
120#2438C2218yes—
121#2438C2218yes—
122#2438C2218yes—
123#2437C2218yes—
124#2423C2214yes—
125#2370C2218yescomplemented
126#2370C2214yescomplemented
127#2369C2214yescomplemented
128#2369C2212yescomplemented
129#2368C2218yes—
130#2365C2212yescomplemented
131#2362C2214yes—
132#2362C2214yes—
133#2360C2214yes—
134#2360C2214yes—
135#2360C2214yes—
136#2355C2214yescomplemented
137#2355C2212yescomplemented
138#2355C2214yescomplemented
139#2351C2214yescomplemented
140#2351C2214yescomplemented
141Q8×C4⋊C4C2212yescomplemented
142Q8×C4⋊C4C2212yescomplemented
143Q8×C4⋊C4C2212yescomplemented
144Q8×C4⋊C4C2212yescomplemented
145Q8×C4⋊C4C2212yescomplemented
146#2345C2214yes—
147#2344C2218yes—
148#2342C2218yes—
149#2329C2214yes—
150#2323C2214yes—
151#2323C2214yes—
152#2317C2212yes—
153#2317C2212yes—
154#2316C2212yes—
155#2316C2212yes—
156#2316C2214yes—
157#2310C2212yes—
158C4×C22⋊Q8C2212yes—
159C4×C22⋊Q8C2212yes—
160C4×C22⋊Q8C2212yes—
161C4×C22⋊Q8C2212yes—
162C4×C22⋊Q8C2214yes—
163C4×C22⋊Q8C2212yes—
164C4×C22⋊Q8C2214yes—
165C4×C22⋊Q8C2214yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2212yes—
169C4×C22⋊Q8C2212yes—
170C4×C22⋊Q8C2212yes—
171C4×C22⋊Q8C2212yes—
172C4×C22⋊Q8C2212yes—
173#2296C2212yes—
174C2×#391C2211yescharacteristic
175C2×#389C2211yescharacteristic
176C2×#387C2212yes—
177C2×#385C2212yes—
178#2285C2212yes—
179#2285C2211yescharacteristic
180#2285C2214yes—
181#2285C2211yescharacteristic
182#2285C2212yes—
183#2285C2211yescharacteristic
184#2285C2211yescharacteristic
185#2285C2211yescharacteristic
186#2285C2212yes—
187#2285C2212yes—
188#2285C2212yes—
189#2285C2212yes—
190C2×#384C2211yescharacteristic
191C2×#384C2211yescharacteristic
192C2×#382C2212yes—
193#2280C2212yes—
194C2×#380C2212yes—
195C2×#380C2211yescharacteristic
196C2×#380C2212yes—
197#2274C2212yes—
198C2×C4×C4⋊C4C2211yescharacteristic
199C2×C4×C4⋊C4C2212yes—
200C2×C4×C4⋊C4C2212yes—
201C2×C4×C4⋊C4C2212yes—
202C2×C4×C22⋊C4C2212yes—
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C24×C4C2311yescharacteristic
207#544—48no—
208#533—28no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×#125C2312yes—
215C2×#125C2314yes—
216C2×#125C2314yes—
217C2×#125C2318yes—
218C2×C22⋊Q8Q8116yescomplemented
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2318yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231#519—48no—
232C2×C4×Q8—28no—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2314yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2314yes—
244C2×#117—48no—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2318yes—
250C2×#117C2314yes—
251C2×#117C2314yes—
252C2×#117C2312yes—
253C2×#117C2312yes—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2311yescharacteristic
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2312yes—
266C22×C22⋊C4C2314yes—
267C22×C22⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C42—28no—
270C22×C42C2311yescharacteristic
271C22×C42C2311yescharacteristic
272C22×C42C2311yescharacteristic
273C22×C42C2311yescharacteristic
274C22×C42C2312yes—
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2311yescharacteristic
281C22×C42C2311yescharacteristic
282C22×C42C2314yes—
283C22×C42C2312yes—
284C22×C42C2311yescharacteristic
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#400C2318yes—
290#400C2318yes—
291#400C2318yes—
292#400C2318yes—
293#399C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#395C2318yes—
315#395C2318yes—
316#393C2318yes—
317#391C2314yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2318yes—
327#391C2318yes—
328#391C2318yes—
329#391C2318yes—
330#391C2312yes—
331#391C2318yes—
332#391C2312yes—
333#391C2312yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#389C2318yes—
338#389C2314yes—
339#389C2314yes—
340#389C2318yes—
341#389C2318yes—
342#389C2318yes—
343#389C2314yes—
344#389C2314yes—
345#389C2318yes—
346#389C2318yes—
347#389C2318yes—
348#389C2318yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2318yes—
360#389C2318yes—
361#389C2318yes—
362#389C2312yes—
363#389C2312yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#389C2312yes—
368#389C2312yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2318yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#389C2312yes—
379#388C2318yes—
380#388C2318yes—
381#388C2318yes—
382#388C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2314yes—
398#387C2314yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2314yes—
409#387C2314yes—
410#385C2314yes—
411#385C2318yes—
412#385C2318yes—
413#385C2314yes—
414#385C2314yes—
415#385C2314yes—
416#385C2318yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#385C2314yes—
425#385C2314yes—
426#384C2312yes—
427#384C2314yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#384C2314yes—
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2314yes—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2314yes—
440#384C2312yes—
441#384C2312yes—
442#384C2312yes—
443#382C2312yes—
444#382C2314yes—
445#382C2314yes—
446#382C2312yes—
447#382C2318yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2318yes—
452#382C2314yes—
453#382C2314yes—
454#381C2318yes—
455#381C2314yes—
456#380C2314yes—
457#380C2318yes—
458#380C2318yes—
459#380C2312yes—
460#380C2312yes—
461#380C2314yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2318yes—
474#380C2312yes—
475#380C2312yes—
476#380C2312yes—
477#380C2314yes—
478#380C2312yes—
479#380C2312yes—
480#380C2314yes—
481#380C2312yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#379C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2312yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2318yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2312yes—
495C4×C4⋊C4C2318yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2318yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2312yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2314yes—
505C4×C4⋊C4C2312yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C4⋊C4C2312yes—
511C4×C4⋊C4C2312yes—
512C4×C4⋊C4C2314yes—
513C4×C4⋊C4C2312yes—
514C4×C4⋊C4C2312yes—
515C4×C4⋊C4C2314yes—
516C4×C4⋊C4C2314yes—
517C4×C4⋊C4C2312yes—
518C4×C4⋊C4C2314yes—
519C4×C4⋊C4C2314yes—
520C4×C4⋊C4C2314yes—
521C4×C22⋊C4C2318yes—
522C4×C22⋊C4C2314yes—
523C4×C22⋊C4C2318yes—
524C4×C22⋊C4C2318yes—
525C4×C22⋊C4C2314yes—
526C4×C22⋊C4C2314yes—
527C4×C22⋊C4C2314yes—
528C4×C22⋊C4C2314yes—
529C4×C22⋊C4C2314yes—
530C2×#95C2312yes—
531C2×#95C2312yes—
532C2×#95C2314yes—
533C2×#95C2312yes—
534C2×#95C2312yes—
535C2×#95C2312yes—
536C2×#95C2314yes—
537C25C2411yescharacteristic
538C22×Q8—24no—
539C22×Q8—24no—
540C22×Q8C2×Q818yes—
541C22×Q8C2412yes—
542C22×Q8C2412yes—
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C22×Q8C2418yes—
546C23×C4—24no—
547C23×C4—24no—
548C23×C4—24no—
549C23×C4—24no—
550C23×C4—24no—
551C23×C4—42no—
552C23×C4—42no—
553C23×C4—42no—
554C23×C4C2×Q818yes—
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562C23×C4C2411yescharacteristic
563C23×C4C2412yes—
564C23×C4C2411yescharacteristic
565C23×C4C2411yescharacteristic
566C23×C4C2411yescharacteristic
567C23×C4C2411yescharacteristic
568C23×C4C2411yescharacteristic
569C23×C4C2411yescharacteristic
570C23×C4C2411yescharacteristic
571C23×C4C2414yes—
572C23×C4C2414yes—
573C23×C4C2412yes—
574C23×C4C2412yes—
575C23×C4C2411yescharacteristic
576C23×C4C2412yes—
577C23×C4C2411yescharacteristic
578C23×C4C2411yescharacteristic
579C4⋊Q8—24no—
580C4⋊Q8—24no—
581C4⋊Q8—48no—
582C4⋊Q8—48no—
583C4⋊Q8—48no—
584#125—28no—
585#125—48no—
586#125—48no—
587#125—416no—
588C22⋊Q8—28no—
589C22⋊Q8—28no—
590C22⋊Q8—28no—
591C22⋊Q8—416no—
592C22⋊Q8—44no—
593C22⋊Q8—416no—
594C22⋊Q8—44no—
595C22⋊Q8—44no—
596C22⋊Q8C2×Q8116yes—
597C22⋊Q8C2×Q8116yes—
598C22⋊Q8C2×Q8116yes—
599C22⋊Q8C2×Q8116yes—
600C4×Q8—28no—
601C4×Q8—28no—
602C4×Q8—28no—
603C4×Q8—28no—
604C4×Q8—28no—
605C4×Q8—28no—
606C4×Q8—48no—
607C4×Q8—48no—
608C4×Q8—48no—
609C4×Q8—48no—
610C4×Q8—48no—
611#117—28no—
612#117—28no—
613#117—28no—
614#117—28no—
615#117—48no—
616#117—48no—
617#117—416no—
618#117—44no—
619#117—44no—
620C2×C4⋊C4—28no—
621C2×C4⋊C4—24no—
622C2×C4⋊C4—24no—
623C2×C4⋊C4—28no—
624C2×C4⋊C4—44no—
625C2×C4⋊C4—44no—
626C2×C4⋊C4—44no—
627C2×C4⋊C4—44no—
628C2×C4⋊C4—44no—
629C2×C4⋊C4—44no—
630C2×C4⋊C4C2×Q8116yes—
631C2×C4⋊C4C2×Q818yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2412yes—
666C2×C4⋊C4C2414yes—
667C2×C4⋊C4C2412yes—
668C2×C4⋊C4C2412yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2418yes—
675C2×C4⋊C4C2418yes—
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2418yes—
679C2×C4⋊C4C2418yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2418yes—
686C2×C4⋊C4C2418yes—
687C2×C4⋊C4C2414yes—
688C2×C4⋊C4C2412yes—
689C2×C4⋊C4C2412yes—
690C2×C4⋊C4C2414yes—
691C2×C22⋊C4—44no—
692C2×C22⋊C4—48no—
693C2×C22⋊C4C2×Q8116yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C42—28no—
709C2×C42—24no—
710C2×C42—24no—
711C2×C42—24no—
712C2×C42—24no—
713C2×C42—24no—
714C2×C42—24no—
715C2×C42—24no—
716C2×C42—24no—
717C2×C42—24no—
718C2×C42—24no—
719C2×C42—24no—
720C2×C42—48no—
721C2×C42—44no—
722C2×C42#4118yes—
723C2×C42C2414yes—
724C2×C42C2414yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2414yes—
728C2×C42C2414yes—
729C2×C42C2414yes—
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2418yes—
745C2×C42C2418yes—
746C2×C42C2418yes—
747C2×C42C2418yes—
748C2×C42C2414yes—
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751C2×C42C2411yescharacteristic
752C2×C42C2411yescharacteristic
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2414yes—
767#95C2414yes—
768#95C2414yes—
769#95C2414yes—
770#95C2414yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2414yes—
776#95C2414yes—
777#95C2418yes—
778#95C2418yes—
779#95C2418yes—
780#95C2418yes—
781#95C2414yes—
782#95C2418yes—
783#95C2414yes—
784#95C2418yes—
785#95C2414yes—
786#95C2418yes—
787#95C2414yes—
788#95C2414yes—
789#95C2414yes—
790#95C2418yes—
791#95C2418yes—
792#95C2418yes—
793#95C2418yes—
794#95C2418yes—
795C24—22no—
796C24—22no—
797C24—22no—
798C24—22no—
799C24—41no—
800C24—41no—
801C24C22×Q814yes—
802C24C2511yescharacteristic
803C24C2511yescharacteristic
804C24C2511yescharacteristic
805C2×Q8—232no—
806C2×Q8—24no—
807C2×Q8—24no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—42no—
815C2×Q8—42no—
816C2×Q8—48no—
817C2×Q8—48no—
818C2×Q8—48no—
819C2×Q8C22×Q818yes—
820C2×Q8C22×Q818yes—
821C22×C4—22no—
822C22×C4—24no—
823C22×C4—22no—
824C22×C4—24no—
825C22×C4—22no—
826C22×C4—232no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—24no—
846C22×C4—24no—
847C22×C4—28no—
848C22×C4—28no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—41no—
864C22×C4—41no—
865C22×C4—41no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—41no—
872C22×C4—41no—
873C22×C4—416no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—42no—
882C22×C4—416no—
883C22×C4C22×Q818yes—
884C22×C4C22×Q814yes—
885C22×C4C22×Q814yes—
886C22×C4C22×Q814yes—
887C22×C4C22×Q814yes—
888C22×C4C22×Q814yes—
889C22×C4C22×Q818yes—
890C22×C4C22×Q814yes—
891C22×C4C2×#4114yes—
892C22×C4C2×#4114yes—
893C22×C4C2×#4114yes—
894C22×C4H(5,𝔽2)14yes—
895C22×C42−1+414yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C22×C4C2514yes—
899C22×C4C2514yes—
900C22×C4C2514yes—
901C22×C4C2514yes—
902C22×C4C2514yes—
903C22×C4C2514yes—
904C22×C4C2514yes—
905C22×C4C2514yes—
906C22×C4C2514yes—
907C22×C4C2514yes—
908C22×C4C2511yescharacteristic
909C22×C4C2514yes—
910C22×C4C2514yes—
911C22×C4C2511yescharacteristic
912C22×C4C2511yescharacteristic
913C22×C4C2511yescharacteristic
914C22×C4C2511yescharacteristic
915C22×C4C2511yescharacteristic
916C22×C4C2511yescharacteristic
917C22×C4C2511yescharacteristic
918C22×C4C2511yescharacteristic
919C22×C4C2511yescharacteristic
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—24no—
925C4⋊C4—24no—
926C4⋊C4—28no—
927C4⋊C4—28no—
928C4⋊C4—24no—
929C4⋊C4—24no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—28no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—28no—
943C4⋊C4—24no—
944C4⋊C4—28no—
945C4⋊C4—28no—
946C4⋊C4—24no—
947C4⋊C4—28no—
948C4⋊C4—24no—
949C4⋊C4—44no—
950C4⋊C4—42no—
951C4⋊C4—44no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—44no—
955C4⋊C4—42no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—48no—
959C4⋊C4—48no—
960C4⋊C4—48no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—44no—
964C4⋊C4—48no—
965C4⋊C4—48no—
966C4⋊C4—48no—
967C4⋊C4—44no—
968C4⋊C4—48no—
969C4⋊C4—48no—
970C4⋊C4—48no—
971C4⋊C4—48no—
972C4⋊C4—48no—
973C4⋊C4—48no—
974C4⋊C4—48no—
975C4⋊C4C22×Q818yes—
976C4⋊C4C22×Q818yes—
977C4⋊C4C22×Q8116yes—
978C4⋊C4C22×Q8116yes—
979C22⋊C4—28no—
980C22⋊C4—28no—
981C22⋊C4—28no—
982C22⋊C4—28no—
983C22⋊C4—28no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—44no—
987C22⋊C4—44no—
988C22⋊C4—44no—
989C22⋊C4—44no—
990C22⋊C4—44no—
991C22⋊C4C22×Q8116yes—
992C22⋊C4C22×Q8116yes—
993C42—22no—
994C42—22no—
995C42—22no—
996C42—22no—
997C42—22no—
998C42—22no—
999C42—22no—
1000C42—22no—
1001C42—22no—
1002C42—22no—
1003C42—22no—
1004C42—22no—
1005C42—28no—
1006C42—28no—
1007C42—28no—
1008C42—28no—
1009C42—28no—
1010C42—28no—
1011C42—28no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—48no—
1016C42—48no—
1017C42—48no—
1018C42—48no—
1019C42C2×#4114yes—
1020C42C2×#4114yes—
1021C42C2×#4114yes—
1022C42C2×#4114yes—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—28no—
1038C23—28no—
1039C23—44no—
1040C23—44no—
1041C23—44no—
1042C23—44no—
1043C23—44no—
1044C23C23×Q812yes—
1045C23C23×Q812yes—
1046C23C23×Q812yes—
1047C23C22×#4112yes—
1048C23C2×H(5,𝔽2)12yes—
1049C23C2×2−1+412yes—
1050C23#58512yes—
1051C23C2611yescharacteristic
1052Q8—216no—
1053Q8—216no—
1054Q8—48no—
1055Q8—84no—
1056Q8—168no—
1057C2×C4—28no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—24no—
1063C2×C4—21no—
1064C2×C4—24no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—24no—
1068C2×C4—21no—
1069C2×C4—24no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—28no—
1077C2×C4—216no—
1078C2×C4—28no—
1079C2×C4—28no—
1080C2×C4—28no—
1081C2×C4—28no—
1082C2×C4—28no—
1083C2×C4—28no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—24no—
1093C2×C4—24no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—24no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—21no—
1101C2×C4—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—24no—
1120C2×C4—44no—
1121C2×C4—48no—
1122C2×C4—44no—
1123C2×C4—44no—
1124C2×C4—44no—
1125C2×C4—44no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—44no—
1129C2×C4—44no—
1130C2×C4—84no—
1131C2×C4—88no—
1132C2×C4—84no—
1133C2×C4—88no—
1134C2×C4#554116yes—
1135C2×C4C23×Q818yes—
1136C2×C4C23×Q818yes—
1137C2×C4C23×Q812yes—
1138C2×C4C23×Q812yes—
1139C2×C4C23×Q812yes—
1140C2×C4C23×Q812yes—
1141C2×C4C22×#4112yes—
1142C2×C4C22×#4112yes—
1143C2×C4C22×#4112yes—
1144C2×C4C22×#4112yes—
1145C2×C4C22×#4112yes—
1146C2×C4C22×#4112yes—
1147C2×C4C2×H(5,𝔽2)12yes—
1148C2×C4C2×H(5,𝔽2)12yes—
1149C2×C4C2×2−1+412yes—
1150C2×C4C2×2−1+412yes—
1151C2×C4#58512yes—
1152C2×C4#58512yes—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—22no—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—416no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22C2×#55414yes—
1174C22#350214yes—
1175C22C24×Q811yescharacteristic
1176C22C23×#4111yescharacteristic
1177C22C22×H(5,𝔽2)11yescharacteristic
1178C22C22×2−1+411yescharacteristic
1179C22C2×#58511yescharacteristic
1180C22C2×#58511yescharacteristic
1181C22C2×#58511yescharacteristic
1182C4—22no—
1183C4—22no—
1184C4—28no—
1185C4—22no—
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—22no—
1190C4—28no—
1191C4—41no—
1192C4—44no—
1193C4—41no—
1194C4—44no—
1195C4—44no—
1196C4—44no—
1197C4—44no—
1198C4—44no—
1199C4—44no—
1200C4—44no—
1201C4—44no—
1202C4—44no—
1203C4C2×#55414yes—
1204C4C2×#55414yes—
1205C4#349514yes—
1206C2—24no—
1207C2—24no—
1208C2—42no—
1209C2C22×#55411yescharacteristic
1210C2C2×#350211yescharacteristic
1211C2C2×#349511yescharacteristic
1212C2#6281311yescharacteristic
1213C2#6281411yescharacteristic
1214C2#6283011yescharacteristic
1215C2#6283511yescharacteristic
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. #59325C2semidirect
2. #59324C2semidirect
3. #59322C2semidirect
4. #59321C2semidirect
5. #59259C2semidirect
6. #59245C2semidirect
7. #39609C2semidirect
8. #39607C2semidirect
9. #39603C2semidirect
10. #37877C2semidirect
13. #36571C2semidirect
14. #36564C2semidirect
15. #36552C2semidirect
16. #36193C2semidirect
18. #35668C2semidirect
19. #35585C2semidirect
21. #35179C2semidirect
22. #35167C2semidirect
23. #34213C2semidirect
25. #34182C2semidirect
49. #2792C22semidirect
50. #2791C22semidirect
52. #2774C22semidirect
54. #2755C22semidirect
61. #2590C22semidirect
62. #2588C22semidirect
63. #2586C22semidirect
64. #2585C22semidirect
66. #2582C22semidirect
67. #2582C22semidirect
68. #2581C22semidirect
71. #2568C22semidirect
72. #2568C22semidirect
73. #2567C22semidirect
74. #2567C22semidirect
75. #2567C22semidirect
76. #2565C22semidirect
77. #2565C22semidirect
78. #2565C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
81. #2552C22semidirect
82. #2551C22semidirect
83. #2551C22semidirect
84. #2550C22semidirect
85. #2550C22semidirect
88. #2520C22semidirect
89. #2520C22semidirect
90. #2511C22semidirect
91. #2511C22semidirect
92. #2509C22semidirect
93. #2509C22semidirect
94. #2508C22semidirect
95. #2508C22semidirect
96. #2508C22semidirect
97. #2507C22semidirect
98. #2507C22semidirect
99. #2507C22semidirect
100. #2507C22semidirect
101. #2506C22semidirect
102. #2506C22semidirect
110. #2453C22semidirect
111. #2453C22semidirect
112. #2451C22semidirect
113. #2451C22semidirect
125. #2370C22semidirect
126. #2370C22semidirect
127. #2369C22semidirect
128. #2369C22semidirect
130. #2365C22semidirect
136. #2355C22semidirect
137. #2355C22semidirect
138. #2355C22semidirect
139. #2351C22semidirect
140. #2351C22semidirect
141. Q8×C4⋊C4C22semidirect
142. Q8×C4⋊C4C22semidirect
143. Q8×C4⋊C4C22semidirect
144. Q8×C4⋊C4C22semidirect
145. Q8×C4⋊C4C22semidirect
218. C2×C22⋊Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#593252
#593242
#593222
#593212
#592592
#592452
#396092
#396072
#396032
#378772
#378732
#366252
#365712
#365642
#365522
#361932
#361902
#356682
#355852
#352532
#351792
#351672
#342132
#342032
#341822
C2×C4×C22⋊Q82
C2×#22852