Finite Group Databasebeta

← #7683794

Subgroups — #7683794

Order 512.

5438 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59373C218yesmaximal, complemented
2#59280C214yesmaximal, complemented
3#59275C214yesmaximal, complemented
4#59271C214yesmaximal, complemented
5#59239C214yesmaximal, complemented
6#45327C214yesmaximal, complemented
7#45290C214yesmaximal, complemented
8#45129C214yesmaximal, complemented
9#45003C214yesmaximal, complemented
10#44083C218yesmaximal, complemented
11#35659C211yesmaximal, characteristic
12#35644C211yesmaximal, characteristic, complemented
13#35630C211yesmaximal, characteristic, complemented
14#35630C211yesmaximal, characteristic, complemented
15#35620C211yesmaximal, characteristic, complemented
16#35532C211yesmaximal, characteristic, complemented
17C2×#2499C211yesmaximal, characteristic, complemented
18#34742C211yesmaximal, characteristic, complemented
19#34742C211yesmaximal, characteristic, complemented
20#34259C211yesmaximal, characteristic, complemented
21#34259C211yesmaximal, characteristic, complemented
22#34201C211yesmaximal, characteristic, complemented
23#34201C211yesmaximal, characteristic, complemented
24#34189C211yesmaximal, characteristic, complemented
25#34188C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#544C2211yescharacteristic
28C2×#525C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35C22×#117C2211yescharacteristic
36#2798C2218yes—
37#2778C2218yes—
38#2762C2218yescomplemented
39#2759C2218yes—
40#2754C2218yes—
41#2749C2218yes—
42#2745C2218yescomplemented
43#2744C2218yescomplemented
44#2743C2218yescomplemented
45#2740C2218yes—
46#2737C2218yes—
47#2696C2218yes—
48#2605C2218yescomplemented
49#2588C2218yescomplemented
50#2578C2218yescomplemented
51#2576C2218yescomplemented
52#2575C2218yescomplemented
53#2573C2218yescomplemented
54#2569C2218yescomplemented
55#2568C2212yescomplemented
56#2567C2212yescomplemented
57#2566C2212yescomplemented
58#2566C2212yescomplemented
59#2565C2212yescomplemented
60#2565C2212yescomplemented
61#2563C2212yescomplemented
62#2561C2214yes—
63#2542C2212yescomplemented
64#2532C2218yes—
65#2526C2218yes—
66#2520C2218yescomplemented
67#2516C2218yes—
68#2514C2214yescomplemented
69#2514C2214yescomplemented
70#2514C2214yescomplemented
71#2514C2214yescomplemented
72#2511C2214yescomplemented
73#2511C2214yescomplemented
74#2511C2214yescomplemented
75#2511C2214yescomplemented
76#2510C2218yes—
77#2510C2218yes—
78#2503C2214yes—
79#2499C2214yes—
80#2499C2214yes—
81#2499C2214yes—
82#2499C2214yes—
83#2498C2218yes—
84#2493C2218yes—
85#2493C2218yes—
86#2493C2218yescomplemented
87#2492C2214yes—
88#2492C2214yes—
89#2489C2214yes—
90#2489C2214yes—
91#2488C2218yes—
92#2477C2218yescomplemented
93#2471C2218yes—
94#2450C2218yes—
95#2449C2218yes—
96#2442C2214yescomplemented
97#2441C2214yescomplemented
98#2440C2214yescomplemented
99#2439C2214yescomplemented
100#2423C2212yes—
101#2423C2212yes—
102#2422C2212yes—
103#2422C2212yes—
104#2421C2212yes—
105#2421C2212yes—
106#2420C2212yes—
107#2420C2212yes—
108#2419C2214yes—
109#2419C2214yes—
110#2418C2214yes—
111#2418C2214yes—
112#2409C2214yes—
113#2409C2214yes—
114#2407C2214yes—
115#2407C2214yes—
116#2406C2214yes—
117#2404C2214yes—
118#2395C2214yes—
119#2395C2214yes—
120C2×#397C2214yes—
121#2368C2218yescomplemented
122#2363C2214yes—
123#2363C2214yes—
124#2362C2214yes—
125#2362C2214yes—
126#2357C2214yescomplemented
127#2356C2214yescomplemented
128#2355C2214yescomplemented
129#2354C2214yes—
130#2354C2214yes—
131#2354C2214yescomplemented
132#2353C2218yes—
133#2352C2218yes—
134#2352C2214yes—
135#2352C2214yes—
136#2343C2218yescomplemented
137Q8×C22⋊C4C2214yescomplemented
138Q8×C22⋊C4C2214yescomplemented
139#2339C2218yes—
140#2339C2218yes—
141#2339C2214yescomplemented
142#2339C2214yescomplemented
143#2321C2214yes—
144#2321C2214yes—
145#2317C2211yescharacteristic
146#2317C2211yescharacteristic
147#2314C2214yescomplemented
148#2314C2214yescomplemented
149#2311C2211yescharacteristic
150#2311C2211yescharacteristic
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2212yescomplemented
154#2311C2212yescomplemented
155#2310C2211yescharacteristic
156#2310C2211yescharacteristic
157#2310C2211yescharacteristic
158#2310C2212yescomplemented
159#2310C2212yescomplemented
160C4×#123C2214yes—
161C4×#123C2214yes—
162C4×#123C2214yes—
163C4×#123C2214yes—
164#2297C2211yescharacteristic
165#2297C2211yescharacteristic
166#2297C2212yescomplemented
167#2297C2212yescomplemented
168#2296C2211yescharacteristic
169#2296C2211yescharacteristic
170C2×#391C2211yescharacteristic
171C2×#391C2211yescharacteristic
172C2×#391C2212yescomplemented
173C2×#391C2212yescomplemented
174C2×#387C2214yes—
175#2285C2211yescharacteristic
176#2285C2211yescharacteristic
177#2285C2214yescomplemented
178C2×#384C2211yescharacteristic
179#2283C2214yescomplemented
180C2×#382C2211yescharacteristic
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—28no—
189C2×2−1+4—44no—
190C22×#41C2312yes—
191C22×#41C2312yes—
192C22×#41C2314yes—
193C22×#41C2311yescharacteristic
194C22×#41C2311yescharacteristic
195C23×Q8C2311yescharacteristic
196C23×Q8C2312yes—
197C23×Q8C2312yes—
198C24×C4C2311yescharacteristic
199#544—44no—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204#525—28no—
205#525—28no—
206C2×#123C2312yes—
207C2×#123C2312yes—
208C2×#123C2314yes—
209C2×#123C2314yes—
210C2×C22⋊Q8—44no—
211C2×C22⋊Q8C2312yes—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2318yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2314yes—
217C2×#121C2312yes—
218C2×#121C2312yes—
219C2×#120C2312yes—
220C2×#120C2312yes—
221#520—44no—
222#520—44no—
223C4×#41—28no—
224C4×#41—28no—
225C2×C4×Q8C2312yes—
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×D4C2314yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2312yes—
232C2×C4×D4C2312yes—
233C2×C4×D4C2314yes—
234C2×C4×D4C2314yes—
235C2×C4×D4C2312yes—
236C2×C4×D4C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×#117—44no—
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2312yes—
247C2×#117C2312yes—
248C2×#117C2312yes—
249C2×#117C2312yes—
250C2×#117C2318yes—
251C2×#117C2314yes—
252C2×#117C2314yes—
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2312yes—
258C22×C4⋊C4C2314yes—
259C22×C4⋊C4C2312yes—
260C22×C22⋊C4C2312yes—
261C22×C22⋊C4C2312yes—
262C22×C22⋊C4C2312yes—
263C22×C42C2311yescharacteristic
264C22×C42C2311yescharacteristic
265C22×C42C2312yes—
266C22×C42C2312yes—
267C22×C42C2312yes—
268#401C2318yes—
269#401C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2314yes—
277#400C2314yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#399C2318yes—
282#399C2314yes—
283#399C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2314yes—
287#398C2314yes—
288#397C2318yes—
289#397C2314yes—
290#397C2314yes—
291#397C2314yes—
292#397C2314yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2314yes—
298#397C2314yes—
299#396C2318yes—
300#396C2318yes—
301#395C2318yes—
302#395C2318yes—
303#394C2318yes—
304#394C2314yes—
305#394C2314yes—
306#394C2314yes—
307#394C2314yes—
308#393C2318yes—
309#393C2318yes—
310#393C2318yes—
311#392C2318yes—
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#391C2312yes—
315#391C2312yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2312yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2311yescharacteristic
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2318yes—
330#391C2318yes—
331#391C2311yescharacteristic
332#391C2318yes—
333#391C2318yes—
334#391C2318yes—
335#391C2314yes—
336#391C2314yes—
337#391C2318yes—
338#391C2312yes—
339#391C2312yes—
340#390C2311yescharacteristic
341#390C2312yes—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2312yes—
345#390C2312yes—
346#390C2312yes—
347#390C2318yes—
348#390C2318yes—
349#390C2311yescharacteristic
350#389C2318yes—
351#389C2314yes—
352#389C2314yes—
353#389C2312yes—
354#389C2312yes—
355#389C2312yes—
356#389C2312yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2318yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2318yes—
369#388C2314yes—
370#388C2314yes—
371#388C2314yes—
372#388C2314yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2314yes—
383#387C2318yes—
384#387C2318yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2314yes—
395#386C2314yes—
396#386C2314yes—
397#386C2314yes—
398#386C2314yes—
399#386C2318yes—
400#386C2318yes—
401#386C2318yes—
402#386C2318yes—
403#386C2318yes—
404#386C2314yes—
405#386C2314yes—
406#386C2318yes—
407#386C2318yes—
408#386C2318yes—
409#386C2314yes—
410#386C2314yes—
411#385C2318yes—
412#385C2318yes—
413#385C2314yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#385C2318yes—
418#385C2314yes—
419#385C2314yes—
420#385C2314yes—
421#384C2312yes—
422#384C2312yes—
423#384C2312yes—
424#384C2312yes—
425#384C2312yes—
426#384C2314yes—
427#384C2312yes—
428#383C2318yes—
429#383C2318yes—
430#383C2318yes—
431#382C2312yes—
432#382C2312yes—
433#382C2312yes—
434#382C2312yes—
435#382C2312yes—
436#382C2318yes—
437#382C2318yes—
438#382C2314yes—
439#382C2312yes—
440#381C2314yes—
441#381C2314yes—
442#381C2314yes—
443#381C2318yes—
444#381C2318yes—
445#381C2314yes—
446#381C2314yes—
447#381C2318yes—
448#381C2312yes—
449#381C2312yes—
450#380C2318yes—
451#380C2314yes—
452#380C2314yes—
453#380C2314yes—
454#380C2314yes—
455#380C2318yes—
456#380C2318yes—
457#380C2318yes—
458#380C2314yes—
459#380C2312yes—
460#380C2312yes—
461#380C2314yes—
462#380C2312yes—
463#380C2312yes—
464#379C2312yes—
465#379C2312yes—
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2318yes—
475C4×C4⋊C4C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2314yes—
481C4×C22⋊C4C2314yes—
482C4×C22⋊C4C2318yes—
483C4×C22⋊C4C2318yes—
484C4×C22⋊C4C2318yes—
485C4×C22⋊C4C2318yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2318yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497#376C2318yes—
498C2×#95C2318yes—
499C2×#95C2314yes—
500C2×#95C2314yes—
501C2×#95C2318yes—
502C2×#95C2314yes—
503C2×#95C2312yes—
504C25C2411yescharacteristic
5052−1+4—464no—
506C2×#41—28no—
507C2×#41—28no—
508C2×#41—216no—
509C2×#41—216no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—28no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—48no—
517C2×#41—44no—
518C2×#41—44no—
519C2×#41#4118yes—
520C2×#41#4118yes—
521C22×Q8—28no—
522C22×Q8—28no—
523C22×Q8—28no—
524C22×Q8—28no—
525C22×Q8—24no—
526C22×Q8—24no—
527C22×Q8—24no—
528C22×Q8—44no—
529C22×Q8—44no—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2414yes—
533C22×Q8C2411yescharacteristic
534C22×Q8C2411yescharacteristic
535C22×Q8C2414yes—
536C22×D4C2414yes—
537C22×D4C2412yes—
538C22×D4C2412yes—
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2414yes—
542C22×D4C2414yes—
543C23×C4—24no—
544C23×C4—24no—
545C23×C4—24no—
546C23×C4C2412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2414yes—
553C23×C4C2414yes—
554C23×C4C2412yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2414yes—
561C23×C4C2414yes—
562C23×C4C2414yes—
563C23×C4C2411yescharacteristic
564C4⋊Q8—44no—
565C4⋊Q8—44no—
566#125—44no—
567#125—44no—
568#123—28no—
569#123—28no—
570#123—48no—
571#123—48no—
572C22⋊Q8—28no—
573C22⋊Q8—28no—
574C22⋊Q8—48no—
575C22⋊Q8—416no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578#121—28no—
579#121—28no—
580#120—28no—
581#120—28no—
582C4×Q8—28no—
583C4×Q8—28no—
584C4×Q8—44no—
585C4×Q8—44no—
586C4×D4—216no—
587C4×D4—28no—
588C4×D4—216no—
589C4×D4—28no—
590C4×D4—216no—
591C4×D4—216no—
592C4×D4—44no—
593C4×D4—44no—
594C4×D4—48no—
595C4×D4—48no—
596#117—28no—
597#117—28no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—24no—
603#117—24no—
604#117—48no—
605#117—48no—
606#117—416no—
607#117—44no—
608#117—44no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—24no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—48no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2414yes—
652C2×C22⋊C4—44no—
653C2×C22⋊C4—44no—
654C2×C22⋊C4—44no—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2412yes—
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2414yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2414yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2418yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2418yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C42—28no—
688C2×C42—24no—
689C2×C42—28no—
690C2×C42—24no—
691C2×C42—44no—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2412yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2418yes—
707C2×C42C2414yes—
708C2×C42C2414yes—
709C2×C42C2418yes—
710C2×C42C2418yes—
711C2×C42C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2414yes—
715#95C2414yes—
716#95C2418yes—
717#95C2418yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2418yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753C24—22no—
754C24—22no—
755C24—22no—
756C24—42no—
757C24—42no—
758C24C2512yes—
759C24C2512yes—
760C24C2512yes—
761C24C2511yescharacteristic
762#41—232no—
763#41—232no—
764#41—432no—
765#41—432no—
766#41—464no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—28no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—48no—
782C2×Q8—432no—
783C2×Q8—432no—
784C2×Q8—416no—
785C2×Q8C2×#4114yes—
786C2×Q8C2×#4114yes—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—28no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4C2×#4118yes—
805C2×D4C2×#4118yes—
806C2×D4C2×#4114yes—
807C2×D4C2×#4114yes—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—28no—
817C22×C4—28no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—22no—
821C22×C4—24no—
822C22×C4—28no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—28no—
837C22×C4—44no—
838C22×C4—42no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—42no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—42no—
848C22×C4—44no—
849C22×C4—44no—
850C22×C4—48no—
851C22×C4—48no—
852C22×C4—416no—
853C22×C4C2×#4118yes—
854C22×C4C2×#4118yes—
855C22×C4C2×#4114yes—
856C22×C4C2×#4114yes—
857C22×C4H(5,𝔽2)14yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2514yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2512yes—
870C22×C4C2514yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2512yes—
875C22×C4C2512yes—
876C22×C4C2512yes—
877C22×C4C2511yescharacteristic
878C22×C4C2511yescharacteristic
879C4⋊C4—28no—
880C4⋊C4—28no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—22no—
894C4⋊C4—22no—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—216no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—48no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—28no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C42—22no—
948C42—22no—
949C42—24no—
950C42—24no—
951C42—22no—
952C42—22no—
953C42—28no—
954C42—24no—
955C42—28no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—48no—
962C42—48no—
963C42—48no—
964C42—48no—
965C42—44no—
966C42—44no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—44no—
985C23—44no—
986C23—44no—
987C23—84no—
988C23—84no—
989C23C22×#4114yes—
990C23C22×#4114yes—
991C23C22×#4112yes—
992C23C22×#4112yes—
993C23C2×H(5,𝔽2)12yes—
994C23C2611yescharacteristic
995Q8—28no—
996Q8—28no—
997Q8—416no—
998Q8—48no—
999Q8—48no—
1000Q8—164no—
1001D4—216no—
1002D4—216no—
1003D4—28no—
1004D4—28no—
1005D4—416no—
1006D4—88no—
1007D4—88no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—216no—
1015C2×C4—216no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—24no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—28no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—48no—
1058C2×C4—416no—
1059C2×C4—416no—
1060C2×C4—416no—
1061C2×C4—44no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—84no—
1066C2×C4—88no—
1067C2×C4—84no—
1068C2×C4—84no—
1069C2×C4—84no—
1070C2×C4—164no—
1071C2×C4—164no—
1072C2×C4#551116yes—
1073C2×C4C22×#4114yes—
1074C2×C4C22×#4114yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C2×H(5,𝔽2)12yes—
1080C2×C4C2×H(5,𝔽2)12yes—
1081C2×C4#58514yes—
1082C22—24no—
1083C22—24no—
1084C22—22no—
1085C22—22no—
1086C22—28no—
1087C22—28no—
1088C22—24no—
1089C22—24no—
1090C22—44no—
1091C22—44no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—88no—
1104C22C2×#55114yes—
1105C22C23×#4111yescharacteristic
1106C22C23×#4111yescharacteristic
1107C22C22×H(5,𝔽2)11yescharacteristic
1108C22C2×#58512yes—
1109C222−1+612yes—
1110C4—24no—
1111C4—24no—
1112C4—24no—
1113C4—44no—
1114C4—42no—
1115C4—44no—
1116C4—44no—
1117C4—42no—
1118C4—42no—
1119C4—44no—
1120C4—44no—
1121C4—44no—
1122C4—42no—
1123C4—42no—
1124C4—42no—
1125C4—44no—
1126C4—42no—
1127C4—42no—
1128C4—44no—
1129C4C2×#55114yes—
1130C4C2×#55114yes—
1131C2—24no—
1132C2—44no—
1133C2—44no—
1134C2—82no—
1135C2C22×#55111yescharacteristic
1136C2#6283611yescharacteristic
1137C2#6288711yescharacteristic
1138C2#6299312yes—
1139C2#6300912yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35659C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59373C2semidirect
2. #59280C2semidirect
3. #59275C2semidirect
4. #59271C2semidirect
5. #59239C2semidirect
6. #45327C2semidirect
7. #45290C2semidirect
8. #45129C2semidirect
9. #45003C2semidirect
10. #44083C2semidirect
12. #35644C2semidirect
13. #35630C2semidirect
14. #35630C2semidirect
15. #35620C2semidirect
16. #35532C2semidirect
17. C2×#2499C2semidirect
18. #34742C2semidirect
19. #34742C2semidirect
20. #34259C2semidirect
21. #34259C2semidirect
22. #34201C2semidirect
23. #34201C2semidirect
24. #34189C2semidirect
25. #34188C2semidirect
38. #2762C22semidirect
42. #2745C22semidirect
43. #2744C22semidirect
44. #2743C22semidirect
48. #2605C22semidirect
49. #2588C22semidirect
50. #2578C22semidirect
51. #2576C22semidirect
52. #2575C22semidirect
53. #2573C22semidirect
54. #2569C22semidirect
55. #2568C22semidirect
56. #2567C22semidirect
57. #2566C22semidirect
58. #2566C22semidirect
59. #2565C22semidirect
60. #2565C22semidirect
61. #2563C22semidirect
63. #2542C22semidirect
66. #2520C22semidirect
68. #2514C22semidirect
69. #2514C22semidirect
70. #2514C22semidirect
71. #2514C22semidirect
72. #2511C22semidirect
73. #2511C22semidirect
74. #2511C22semidirect
75. #2511C22semidirect
86. #2493C22semidirect
92. #2477C22semidirect
96. #2442C22semidirect
97. #2441C22semidirect
98. #2440C22semidirect
99. #2439C22semidirect
121. #2368C22semidirect
126. #2357C22semidirect
127. #2356C22semidirect
128. #2355C22semidirect
131. #2354C22semidirect
136. #2343C22semidirect
137. Q8×C22⋊C4C22semidirect
138. Q8×C22⋊C4C22semidirect
141. #2339C22semidirect
142. #2339C22semidirect
147. #2314C22semidirect
148. #2314C22semidirect
153. #2311C22semidirect
154. #2311C22semidirect
158. #2310C22semidirect
159. #2310C22semidirect
166. #2297C22semidirect
167. #2297C22semidirect
172. C2×#391C22semidirect
173. C2×#391C22semidirect
177. #2285C22semidirect
179. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#593732
#592802
#592752
#592712
#592392
#453272
#452902
#451292
#450032
#440832
#356592
#356442
#356302
#356202
#355322
C2×#24992
#347422
#342592
#342012
#341892
#341882