Finite Group Databasebeta

← #7681078

Subgroups — #7681078

Order 512.

5322 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59867C214yesmaximal, complemented
2#59425C214yesmaximal, complemented
3#59196C218yesmaximal
4#45390C214yesmaximal, complemented
5#45149C214yesmaximal, complemented
6#44795C218yesmaximal, complemented
7#39067C214yesmaximal, complemented
8#38251C214yesmaximal, complemented
9#38057C214yesmaximal, complemented
10#36279C214yesmaximal, complemented
11#35674C211yesmaximal, characteristic, complemented
12#35674C211yesmaximal, characteristic, complemented
13#35662C211yesmaximal, characteristic, complemented
14#35630C211yesmaximal, characteristic, complemented
15#35320C211yesmaximal, characteristic, complemented
16#35313C211yesmaximal, characteristic, complemented
17#35311C211yesmaximal, characteristic
18#34739C211yesmaximal, characteristic
19C2×#2434C211yesmaximal, characteristic
20#34254C211yesmaximal, characteristic, complemented
21#34209C211yesmaximal, characteristic, complemented
22#34203C211yesmaximal, characteristic
23#34173C211yesmaximal, characteristic
24#34109C211yesmaximal, characteristic
25C2×#2310C211yesmaximal, characteristic
26C24×Q8C2211yescharacteristic
27C2×#533C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C22×C22⋊Q8C2211yescharacteristic
31C2×#519C2211yescharacteristic
32C2×#519C2211yescharacteristic
33C2×#519C2211yescharacteristic
34C22×#117C2211yescharacteristic
35C22×#117C2211yescharacteristic
36#2863C2214yescomplemented
37#2862C2214yescomplemented
38#2855C2214yes—
39#2799C2218yescomplemented
40#2789C2218yescomplemented
41#2762C2218yescomplemented
42#2762C2218yescomplemented
43#2758C2218yescomplemented
44#2758C2218yescomplemented
45#2755C2218yescomplemented
46#2755C2218yescomplemented
47#2745C2218yes—
48#2744C2218yes—
49#2739C2218yes—
50#2738C2218yes—
51#2645C2214yescomplemented
52#2642C2214yescomplemented
53#2625C2214yes—
54#2612C2218yescomplemented
55#2605C2218yescomplemented
56#2605C2218yescomplemented
57#2588C2218yescomplemented
58#2588C2218yescomplemented
59#2586C2218yescomplemented
60#2582C2214yescomplemented
61#2581C2214yescomplemented
62#2575C2218yes—
63#2573C2218yes—
64#2569C2218yes—
65#2568C2214yescomplemented
66#2568C2214yescomplemented
67#2527C2218yes—
68#2520C2218yescomplemented
69#2520C2218yescomplemented
70#2515C2218yes—
71#2514C2214yescomplemented
72#2514C2214yescomplemented
73#2514C2214yescomplemented
74#2511C2214yescomplemented
75#2511C2214yescomplemented
76#2511C2214yescomplemented
77#2505C2218yes—
78#2505C2218yes—
79#2503C2212yes—
80#2503C2218yes—
81#2502C2212yes—
82#2499C2212yes—
83#2499C2212yes—
84#2493C2218yes—
85#2493C2218yes—
86#2493C2218yes—
87#2493C2218yes—
88#2484C2218yes—
89#2484C2218yes—
90#2484C2214yes—
91#2483C2214yes—
92#2453C2214yescomplemented
93#2451C2214yescomplemented
94#2446C2214yescomplemented
95#2446C2214yescomplemented
96#2446C2214yescomplemented
97#2446C2214yescomplemented
98#2446C2214yescomplemented
99#2446C2214yescomplemented
100#2446C2214yescomplemented
101#2446C2214yescomplemented
102#2442C2212yes—
103#2441C2212yes—
104#2440C2212yes—
105#2439C2212yes—
106#2438C2218yes—
107#2438C2218yes—
108#2438C2214yes—
109#2437C2214yes—
110#2434C2214yes—
111#2434C2214yes—
112#2434C2212yes—
113#2434C2212yes—
114#2434C2212yes—
115#2434C2212yes—
116#2396C2214yes—
117C2×#395C2214yes—
118#2368C2218yes—
119#2365C2214yescomplemented
120#2365C2214yescomplemented
121#2362C2214yes—
122#2360C2214yes—
123#2356C2214yescomplemented
124#2355C2214yescomplemented
125#2347C2212yes—
126#2346C2212yes—
127#2345C2212yes—
128#2344C2212yes—
129#2344C2218yes—
130#2344C2214yes—
131#2343C2218yes—
132#2343C2218yes—
133#2343C2214yes—
134#2342C2214yes—
135#2342C2214yes—
136Q8×C22⋊C4C2214yes—
137Q8×C22⋊C4C2214yes—
138Q8×C22⋊C4C2214yes—
139Q8×C22⋊C4C2214yes—
140#2327C2214yescomplemented
141#2323C2214yes—
142#2320C2214yescomplemented
143#2317C2211yescharacteristic
144#2317C2211yescharacteristic
145#2316C2211yescharacteristic
146#2310C2211yescharacteristic
147#2310C2211yescharacteristic
148#2310C2211yescharacteristic
149#2310C2212yes—
150#2310C2211yescharacteristic
151#2310C2211yescharacteristic
152#2310C2211yescharacteristic
153#2310C2212yes—
154#2310C2214yes—
155#2310C2214yes—
156#2310C2211yescharacteristic
157#2310C2211yescharacteristic
158#2310C2211yescharacteristic
159#2310C2214yes—
160C4×C4⋊Q8C2214yescomplemented
161C4×C22⋊Q8C2214yes—
162C4×C22⋊Q8C2214yes—
163#2298C2212yes—
164#2298C2212yes—
165#2296C2211yescharacteristic
166#2296C2211yescharacteristic
167#2296C2211yescharacteristic
168#2296C2211yescharacteristic
169#2295C2214yescomplemented
170C2×#391C2212yes—
171C2×#391C2211yescharacteristic
172C2×#391C2211yescharacteristic
173C2×#391C2214yes—
174C2×#391C2212yes—
175C2×#385C2214yes—
176#2285C2211yescharacteristic
177#2283C2212yes—
178#2280C2214yes—
179#2280C2211yescharacteristic
180#2280C2211yescharacteristic
181C2×#381C2214yes—
182#2274C2211yescharacteristic
183C4×#117C2211yescharacteristic
184C4×#117C2212yes—
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C23×Q8—28no—
188C23×Q8—28no—
189C23×Q8—44no—
190C23×Q8C2311yescharacteristic
191C23×Q8C2311yescharacteristic
192C23×Q8C2312yes—
193C23×Q8C2312yes—
194C23×Q8C2312yes—
195C23×Q8C2312yes—
196C23×Q8C2312yes—
197C23×Q8C2311yescharacteristic
198C24×C4C2312yes—
199C24×C4C2311yescharacteristic
200#533—44no—
201C2×C4⋊Q8—28no—
202C2×C4⋊Q8—44no—
203C2×C4⋊Q8C2312yes—
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2314yes—
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2312yes—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×#125C2312yes—
211C2×C22⋊Q8—28no—
212C2×C22⋊Q8C2312yes—
213C2×C22⋊Q8C2312yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2314yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218#519—28no—
219#519—44no—
220#519—44no—
221C2×C4×Q8C2314yes—
222C2×C4×Q8C2314yes—
223C2×C4×Q8C2314yes—
224C2×C4×Q8C2314yes—
225C2×C4×Q8C2314yes—
226C2×C4×Q8C2314yes—
227C2×C4×Q8C2314yes—
228C2×#117—28no—
229C2×#117—44no—
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2312yes—
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2312yes—
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2314yes—
243C2×#117C2314yes—
244C2×#117C2312yes—
245C2×#117C2312yes—
246C2×#117C2312yes—
247C2×#117C2314yes—
248C2×#117C2314yes—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2312yes—
251C22×C4⋊C4C2314yes—
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2312yes—
255C22×C4⋊C4C2314yes—
256C22×C22⋊C4C2312yes—
257C22×C22⋊C4C2312yes—
258C22×C22⋊C4C2312yes—
259C22×C22⋊C4C2312yes—
260C22×C42C2312yes—
261C22×C42C2311yescharacteristic
262C22×C42C2311yescharacteristic
263C22×C42C2312yes—
264#401C2318yes—
265#401C2318yes—
266#400C2318yes—
267#400C2318yes—
268#400C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2314yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#399C2314yes—
284#398C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2314yes—
291#398C2314yes—
292#398C2318yes—
293#397C2318yes—
294#397C2318yes—
295#396C2314yes—
296#396C2314yes—
297#395C2318yes—
298#395C2314yes—
299#395C2318yes—
300#395C2318yes—
301#395C2318yes—
302#395C2318yes—
303#393C2314yes—
304#391C2314yes—
305#391C2314yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2312yes—
310#391C2318yes—
311#391C2318yes—
312#391C2318yes—
313#391C2318yes—
314#391C2314yes—
315#391C2312yes—
316#391C2312yes—
317#391C2314yes—
318#391C2312yes—
319#391C2314yes—
320#391C2312yes—
321#391C2314yes—
322#391C2314yes—
323#391C2312yes—
324#391C2312yes—
325#391C2318yes—
326#391C2318yes—
327#391C2318yes—
328#391C2318yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#391C2318yes—
337#391C2318yes—
338#391C2312yes—
339#391C2314yes—
340#391C2318yes—
341#391C2314yes—
342#391C2312yes—
343#391C2312yes—
344#391C2312yes—
345#391C2314yes—
346#389C2318yes—
347#389C2318yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2312yes—
354#389C2318yes—
355#389C2312yes—
356#389C2312yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2312yes—
363#388C2314yes—
364#388C2318yes—
365#388C2314yes—
366#388C2318yes—
367#388C2314yes—
368#388C2314yes—
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#387C2314yes—
390#387C2318yes—
391#387C2314yes—
392#387C2314yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2314yes—
402#387C2318yes—
403#385C2318yes—
404#385C2318yes—
405#385C2314yes—
406#385C2314yes—
407#385C2318yes—
408#385C2314yes—
409#385C2314yes—
410#385C2318yes—
411#385C2314yes—
412#385C2314yes—
413#385C2318yes—
414#385C2318yes—
415#385C2314yes—
416#385C2314yes—
417#384C2312yes—
418#384C2312yes—
419#384C2312yes—
420#383C2318yes—
421#383C2314yes—
422#383C2318yes—
423#383C2318yes—
424#382C2318yes—
425#382C2318yes—
426#382C2312yes—
427#382C2312yes—
428#382C2318yes—
429#382C2312yes—
430#382C2314yes—
431#381C2318yes—
432#381C2318yes—
433#381C2314yes—
434#381C2312yes—
435#381C2314yes—
436#381C2312yes—
437#381C2314yes—
438#381C2314yes—
439#381C2314yes—
440#381C2314yes—
441#381C2314yes—
442#381C2314yes—
443#381C2314yes—
444#381C2314yes—
445#381C2318yes—
446#380C2314yes—
447#380C2314yes—
448#380C2318yes—
449#380C2314yes—
450#380C2312yes—
451#380C2312yes—
452#380C2312yes—
453#380C2312yes—
454#380C2318yes—
455#380C2314yes—
456#379C2312yes—
457#379C2312yes—
458C4×C4⋊C4C2318yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2312yes—
462C4×C4⋊C4C2314yes—
463C4×C4⋊C4C2314yes—
464C4×C4⋊C4C2314yes—
465C4×C4⋊C4C2318yes—
466C4×C4⋊C4C2318yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2312yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2312yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C22⋊C4C2318yes—
477C4×C22⋊C4C2318yes—
478C4×C22⋊C4C2318yes—
479C4×C22⋊C4C2312yes—
480C4×C22⋊C4C2312yes—
481C4×C22⋊C4C2312yes—
482C4×C22⋊C4C2312yes—
483C4×C22⋊C4C2314yes—
484C4×C22⋊C4C2314yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2311yescharacteristic
490C4×C22⋊C4C2311yescharacteristic
491C4×C22⋊C4C2311yescharacteristic
492C4×C22⋊C4C2311yescharacteristic
493#376C2312yes—
494#376C2312yes—
495#376C2318yes—
496#376C2314yes—
497C2×#95C2318yes—
498C2×#95C2312yes—
499C2×#95C2314yes—
500C2×#95C2318yes—
501C2×#95C2314yes—
502C43C2312yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C22×Q8—28no—
506C22×Q8—28no—
507C22×Q8—28no—
508C22×Q8—28no—
509C22×Q8—24no—
510C22×Q8—24no—
511C22×Q8—24no—
512C22×Q8—28no—
513C22×Q8—28no—
514C22×Q8—28no—
515C22×Q8—28no—
516C22×Q8—28no—
517C22×Q8—28no—
518C22×Q8—24no—
519C22×Q8—24no—
520C22×Q8—24no—
521C22×Q8—24no—
522C22×Q8—24no—
523C22×Q8—44no—
524C22×Q8—44no—
525C22×Q8—44no—
526C22×Q8—44no—
527C22×Q8—44no—
528C22×Q8—464no—
529C22×Q8#4118yes—
530C22×Q8C2412yes—
531C22×Q8C2412yes—
532C22×Q8C2412yes—
533C22×Q8C2412yes—
534C22×Q8C2414yes—
535C22×Q8C2414yes—
536C22×Q8C2412yes—
537C22×Q8C2412yes—
538C22×Q8C2414yes—
539C23×C4—24no—
540C23×C4—24no—
541C23×C4—28no—
542C23×C4—28no—
543C23×C4—44no—
544C23×C4#4118yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2414yes—
552C23×C4C2411yescharacteristic
553C23×C4C2412yes—
554C23×C4C2411yescharacteristic
555C23×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558C23×C4C2412yes—
559C23×C4C2414yes—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C4⋊Q8—28no—
563C4⋊Q8—28no—
564C4⋊Q8—216no—
565C4⋊Q8—44no—
566C4⋊Q8—48no—
567C4⋊Q8—44no—
568C4⋊Q8—44no—
569#125—44no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—28no—
574C22⋊Q8—216no—
575C22⋊Q8—48no—
576C4×Q8—216no—
577C4×Q8—216no—
578C4×Q8—48no—
579C4×Q8—48no—
580C4×Q8—48no—
581C4×Q8—48no—
582C4×Q8—48no—
583#117—28no—
584#117—24no—
585#117—24no—
586#117—28no—
587#117—24no—
588#117—24no—
589#117—216no—
590#117—24no—
591#117—24no—
592#117—24no—
593#117—24no—
594#117—24no—
595#117—24no—
596#117—216no—
597#117—44no—
598#117—44no—
599#117—48no—
600#117—48no—
601#117—44no—
602C2×C4⋊C4—24no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—28no—
605C2×C4⋊C4—24no—
606C2×C4⋊C4—216no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4—48no—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2412yes—
616C2×C4⋊C4C2412yes—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2414yes—
621C2×C4⋊C4C2418yes—
622C2×C4⋊C4C2418yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2418yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C22⋊C4—28no—
650C2×C22⋊C4—28no—
651C2×C22⋊C4—28no—
652C2×C22⋊C4—44no—
653C2×C22⋊C4C2412yes—
654C2×C22⋊C4C2412yes—
655C2×C22⋊C4C2412yes—
656C2×C22⋊C4C2412yes—
657C2×C22⋊C4C2412yes—
658C2×C22⋊C4C2412yes—
659C2×C22⋊C4C2414yes—
660C2×C22⋊C4C2414yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2414yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2412yes—
674C2×C42—28no—
675C2×C42—24no—
676C2×C42—24no—
677C2×C42—44no—
678C2×C42C2412yes—
679C2×C42C2412yes—
680C2×C42C2412yes—
681C2×C42C2412yes—
682C2×C42C2412yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2412yes—
686C2×C42C2412yes—
687C2×C42C2418yes—
688C2×C42C2412yes—
689C2×C42C2414yes—
690C2×C42C2414yes—
691C2×C42C2412yes—
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2412yes—
697C2×C42C2414yes—
698C2×C42C2418yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2414yes—
702C2×C42C2418yes—
703#95C2412yes—
704#95C2418yes—
705#95C2418yes—
706#95C2412yes—
707#95C2412yes—
708#95C2412yes—
709#95C2418yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2418yes—
714#95C2418yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2414yes—
722#95C2414yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2418yes—
728#95C2414yes—
729#95C2418yes—
730#95C2418yes—
731#95C2418yes—
732#95C2418yes—
733#95C2414yes—
734#95C2418yes—
735#95C2414yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2418yes—
743#95C2418yes—
744#95C2414yes—
745#95C2414yes—
746#95C2414yes—
747#95C2414yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751C24—22no—
752C24—22no—
753C24—24no—
754C24—42no—
755C24C2×#4114yes—
756C24C2511yescharacteristic
757C24C2511yescharacteristic
758C24C2511yescharacteristic
759C2×Q8—232no—
760C2×Q8—24no—
761C2×Q8—24no—
762C2×Q8—24no—
763C2×Q8—24no—
764C2×Q8—24no—
765C2×Q8—24no—
766C2×Q8—28no—
767C2×Q8—28no—
768C2×Q8—28no—
769C2×Q8—28no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—24no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—28no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—432no—
786C2×Q8—432no—
787C2×Q8—432no—
788C2×Q8—432no—
789C2×Q8—432no—
790C2×Q8—416no—
791C2×Q8—416no—
792C2×Q8C2×#4118yes—
793C2×Q8C2×#4118yes—
794C22×C4—22no—
795C22×C4—24no—
796C22×C4—22no—
797C22×C4—24no—
798C22×C4—232no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—24no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—24no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—432no—
835C22×C4C2×#4114yes—
836C22×C4C2×#4118yes—
837C22×C4C2×#4114yes—
838C22×C4C2×#4114yes—
839C22×C4C2×#4114yes—
840C22×C4C2×#4114yes—
841C22×C4C2×#4114yes—
842C22×C4C2×#4114yes—
843C22×C4H(5,𝔽2)14yes—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2514yes—
847C22×C4C2512yes—
848C22×C4C2514yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2514yes—
859C22×C4C2511yescharacteristic
860C22×C4C2514yes—
861C22×C4C2511yescharacteristic
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—216no—
877C4⋊C4—216no—
878C4⋊C4—216no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C22⋊C4—24no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—24no—
922C22⋊C4—24no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C42−1+418yes—
927C42—24no—
928C42—24no—
929C42—24no—
930C42—24no—
931C42—22no—
932C42—24no—
933C42—22no—
934C42—216no—
935C42—24no—
936C42—24no—
937C42—24no—
938C42—22no—
939C42—22no—
940C42—24no—
941C42—24no—
942C42—24no—
943C42—24no—
944C42—28no—
945C42—28no—
946C42—44no—
947C42—44no—
948C42—44no—
949C42—48no—
950C42—48no—
951C42—48no—
952C23—21no—
953C23—21no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—21no—
958C23—21no—
959C23—22no—
960C23—22no—
961C23—28no—
962C23—28no—
963C23—44no—
964C23—48no—
965C23—48no—
966C23C22×#4112yes—
967C23C22×#4112yes—
968C23C22×#4112yes—
969C23C22×#4112yes—
970C23C2×H(5,𝔽2)12yes—
971C23C2×2−1+414yes—
972C23C2611yescharacteristic
973Q8—216no—
974Q8—216no—
975Q8—416no—
976Q8—416no—
977Q8—48no—
978Q8—48no—
979Q8—48no—
980Q8—48no—
981Q8—88no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—24no—
986C2×C4—22no—
987C2×C4—21no—
988C2×C4—24no—
989C2×C4—21no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—28no—
993C2×C4—216no—
994C2×C4—28no—
995C2×C4—28no—
996C2×C4—28no—
997C2×C4—28no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—24no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—24no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—48no—
1039C2×C4—48no—
1040C2×C4—416no—
1041C2×C4—416no—
1042C2×C4—48no—
1043C2×C4—48no—
1044C2×C4—48no—
1045C2×C4—84no—
1046C2×C4—84no—
1047C2×C4—88no—
1048C2×C4#551116yes—
1049C2×C4C22×#4112yes—
1050C2×C4C22×#4118yes—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C2×H(5,𝔽2)12yes—
1057C2×C4C2×H(5,𝔽2)12yes—
1058C2×C4C2×2−1+414yes—
1059C2×C4C2×2−1+414yes—
1060C22—24no—
1061C22—24no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—24no—
1066C22—24no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—22no—
1071C22—416no—
1072C22—42no—
1073C22—42no—
1074C22C2×#55114yes—
1075C22#350914yes—
1076C22C23×#4111yescharacteristic
1077C22C23×#4111yescharacteristic
1078C22C22×H(5,𝔽2)11yescharacteristic
1079C22C22×2−1+412yes—
1080C222−1+612yes—
1081C4—24no—
1082C4—24no—
1083C4—22no—
1084C4—22no—
1085C4—28no—
1086C4—44no—
1087C4—44no—
1088C4—42no—
1089C4—42no—
1090C4—42no—
1091C4—42no—
1092C4—42no—
1093C4—44no—
1094C4—44no—
1095C4—42no—
1096C4—44no—
1097C4—44no—
1098C4—44no—
1099C4—44no—
1100C4—44no—
1101C4C2×#55114yes—
1102C4C2×#55114yes—
1103C2—24no—
1104C2—24no—
1105C2—42no—
1106C2C22×#55111yescharacteristic
1107C2C2×#350911yescharacteristic
1108C2#6286011yescharacteristic
1109C2#6294212yes—
1110C2#6299812yes—
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. #59867C2semidirect
2. #59425C2semidirect
4. #45390C2semidirect
5. #45149C2semidirect
6. #44795C2semidirect
7. #39067C2semidirect
8. #38251C2semidirect
9. #38057C2semidirect
10. #36279C2semidirect
11. #35674C2semidirect
12. #35674C2semidirect
13. #35662C2semidirect
14. #35630C2semidirect
15. #35320C2semidirect
16. #35313C2semidirect
20. #34254C2semidirect
21. #34209C2semidirect
36. #2863C22semidirect
37. #2862C22semidirect
39. #2799C22semidirect
40. #2789C22semidirect
41. #2762C22semidirect
42. #2762C22semidirect
43. #2758C22semidirect
44. #2758C22semidirect
45. #2755C22semidirect
46. #2755C22semidirect
51. #2645C22semidirect
52. #2642C22semidirect
54. #2612C22semidirect
55. #2605C22semidirect
56. #2605C22semidirect
57. #2588C22semidirect
58. #2588C22semidirect
59. #2586C22semidirect
60. #2582C22semidirect
61. #2581C22semidirect
65. #2568C22semidirect
66. #2568C22semidirect
68. #2520C22semidirect
69. #2520C22semidirect
71. #2514C22semidirect
72. #2514C22semidirect
73. #2514C22semidirect
74. #2511C22semidirect
75. #2511C22semidirect
76. #2511C22semidirect
92. #2453C22semidirect
93. #2451C22semidirect
94. #2446C22semidirect
95. #2446C22semidirect
96. #2446C22semidirect
97. #2446C22semidirect
98. #2446C22semidirect
99. #2446C22semidirect
100. #2446C22semidirect
101. #2446C22semidirect
119. #2365C22semidirect
120. #2365C22semidirect
123. #2356C22semidirect
124. #2355C22semidirect
140. #2327C22semidirect
142. #2320C22semidirect
160. C4×C4⋊Q8C22semidirect
169. #2295C22semidirect

Maximal subgroups

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

subgroupindex
#598672
#594252
#591962
#453902
#451492
#447952
#390672
#382512
#380572
#362792
#356742
#356622
#356302
#353202
#353132
#353112
#347392
C2×#24342
#342542
#342092
#342032
#341732
#341092
C2×#23102