Finite Group Databasebeta

← #7682888

Subgroups — #7682888

Order 512.

5274 conjugacy classes of subgroups.

The subgroup lattice has 1137 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59698C214yesmaximal, complemented
2#59694C214yesmaximal, complemented
3#59385C218yesmaximal, complemented
4#59306C214yesmaximal, complemented
5#59305C214yesmaximal, complemented
6#45220C214yesmaximal, complemented
7#45120C214yesmaximal, complemented
8#45000C214yesmaximal, complemented
9#44972C214yesmaximal, complemented
10#43286C218yesmaximal, complemented
11#35661C211yesmaximal, characteristic, complemented
12#35633C211yesmaximal, characteristic, complemented
13#35621C211yesmaximal, characteristic, complemented
14#35619C211yesmaximal, characteristic, complemented
15#35557C211yesmaximal, characteristic, complemented
16#35555C211yesmaximal, characteristic, complemented
17#34814C211yesmaximal, characteristic, complemented
18C2×#2502C211yesmaximal, characteristic, complemented
19#34743C211yesmaximal, characteristic
20#34268C211yesmaximal, characteristic, complemented
21#34254C211yesmaximal, characteristic, complemented
22#34207C211yesmaximal, characteristic, complemented
23#34200C211yesmaximal, characteristic, complemented
24#34200C211yesmaximal, characteristic, complemented
25#34183C211yesmaximal, characteristic, complemented
26C2×#536C2211yescharacteristic
27C2×#536C2211yescharacteristic
28C2×#532C2211yescharacteristic
29C2×#525C2211yescharacteristic
30C2×#525C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38#2802C2218yescomplemented
39#2790C2218yes—
40#2790C2218yescomplemented
41#2787C2218yescomplemented
42#2782C2218yes—
43#2770C2218yescomplemented
44#2765C2218yescomplemented
45#2757C2218yes—
46#2757C2218yescomplemented
47#2747C2218yescomplemented
48#2725C2218yescomplemented
49#2691C2218yes—
50#2606C2218yescomplemented
51#2603C2218yes—
52#2600C2218yes—
53#2597C2218yes—
54#2587C2218yes—
55#2587C2218yes—
56#2585C2218yescomplemented
57#2579C2218yes—
58#2579C2218yescomplemented
59#2578C2218yes—
60#2570C2214yescomplemented
61#2566C2218yes—
62#2552C2214yescomplemented
63#2547C2212yescomplemented
64#2546C2212yescomplemented
65#2545C2212yescomplemented
66#2544C2212yescomplemented
67#2538C2214yes—
68#2536C2214yes—
69#2534C2214yes—
70#2531C2218yescomplemented
71#2525C2218yescomplemented
72#2512C2214yescomplemented
73#2511C2214yescomplemented
74#2507C2218yescomplemented
75#2507C2214yescomplemented
76#2506C2214yescomplemented
77#2503C2212yescomplemented
78#2502C2214yes—
79#2502C2214yes—
80#2502C2214yes—
81#2502C2214yes—
82#2502C2212yescomplemented
83#2499C2212yescomplemented
84#2499C2212yescomplemented
85#2497C2212yes—
86#2497C2214yescomplemented
87#2496C2212yes—
88#2496C2214yescomplemented
89#2495C2212yes—
90#2494C2212yes—
91#2493C2214yes—
92#2486C2214yes—
93#2481C2218yes—
94#2480C2214yes—
95#2473C2218yes—
96#2468C2218yescomplemented
97#2466C2218yes—
98#2460C2218yes—
99#2447C2214yescomplemented
100#2446C2214yescomplemented
101#2442C2218yescomplemented
102#2429C2212yes—
103#2429C2214yes—
104#2429C2214yes—
105#2428C2212yes—
106#2427C2214yes—
107#2427C2212yes—
108#2426C2214yes—
109#2426C2212yes—
110#2425C2214yes—
111#2425C2218yes—
112#2424C2214yes—
113#2419C2218yes—
114#2417C2214yes—
115#2417C2214yescomplemented
116#2415C2214yes—
117#2415C2214yescomplemented
118#2413C2214yes—
119#2411C2214yes—
120#2401C2214yes—
121#2392C2214yes—
122C2×#398C2214yes—
123#2373C2218yes—
124#2367C2214yescomplemented
125#2365C2214yescomplemented
126#2361C2218yes—
127#2361C2214yes—
128#2361C2214yes—
129#2361C2218yes—
130#2360C2214yes—
131#2360C2214yes—
132#2359C2218yes—
133#2356C2214yescomplemented
134#2355C2214yescomplemented
135#2354C2214yescomplemented
136#2352C2214yes—
137#2352C2214yes—
138Q8×C4⋊C4C2214yescomplemented
139D4×C4⋊C4C2218yes—
140D4×C4⋊C4C2214yes—
141D4×C4⋊C4C2214yes—
142D4×C4⋊C4C2214yescomplemented
143D4×C4⋊C4C2214yescomplemented
144#2343C2218yes—
145#2326C2212yescomplemented
146#2326C2212yescomplemented
147#2323C2214yescomplemented
148#2322C2214yes—
149#2322C2214yes—
150#2320C2214yescomplemented
151#2317C2211yescharacteristic
152#2317C2211yescharacteristic
153#2317C2211yescharacteristic
154#2317C2212yescomplemented
155#2317C2212yescomplemented
156#2316C2211yescharacteristic
157#2311C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2310C2211yescharacteristic
161C4×C4⋊Q8C2212yescomplemented
162C4×#127C2212yescomplemented
163C4×#126C2214yes—
164C4×C22⋊Q8C2214yescomplemented
165C4×#121C2214yes—
166C4×#120C2214yes—
167C4×#120C2214yes—
168#2297C2211yescharacteristic
169#2296C2211yescharacteristic
170#2296C2211yescharacteristic
171#2296C2211yescharacteristic
172#2295C2214yescomplemented
173C2×#391C2211yescharacteristic
174C2×#391C2211yescharacteristic
175C2×#385C2214yes—
176#2285C2211yescharacteristic
177#2285C2212yescomplemented
178C2×#384C2211yescharacteristic
179C2×#384C2211yescharacteristic
180C2×#384C2212yescomplemented
181#2280C2211yescharacteristic
182#2280C2211yescharacteristic
183#2274C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192#536—28no—
193#536—44no—
194#532—28no—
195C2×C4⋊Q8C2311yescharacteristic
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×#127C2311yescharacteristic
199C2×#126C2314yes—
200C2×#126C2318yes—
201C2×#125C2318yes—
202C2×#124C2311yescharacteristic
203C2×#124C2311yescharacteristic
204C2×#124C2312yes—
205C2×#124C2312yes—
206#525—28no—
207#525—28no—
208C2×#123C2312yes—
209C2×#123C2312yes—
210C2×#123C2314yes—
211C2×#123C2314yes—
212C2×C22⋊Q8—44no—
213C2×C22⋊Q8C2314yes—
214C2×C22⋊Q8C2312yes—
215C2×C22⋊Q8C2312yes—
216C2×C22⋊Q8C2314yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2312yes—
219C2×C22⋊Q8C2312yes—
220C2×#121C2312yes—
221C2×#121C2312yes—
222C2×#121C2314yes—
223C2×#121C2314yes—
224C2×#120C2312yes—
225C2×#120C2312yes—
226#520—44no—
227#520—44no—
228#520—44no—
229#519—28no—
230C4×#41—28no—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2312yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×D4C2314yes—
238C2×C4×D4C2314yes—
239C2×C4×D4C2314yes—
240C2×C4×D4C2312yes—
241C2×C4×D4C2314yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2312yes—
244C2×C4×D4C2314yes—
245C2×C4×D4C2314yes—
246C2×C4×D4C2314yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2318yes—
249C2×C4×D4C2318yes—
250C2×C4×D4C2318yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2312yes—
257C2×#117C2314yes—
258C2×#117C2312yes—
259C2×#117C2312yes—
260C2×#117C2312yes—
261C2×#117C2311yescharacteristic
262C22×C4⋊C4—44no—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2318yes—
274C22×C4⋊C4C2314yes—
275C22×C4⋊C4C2314yes—
276C22×C22⋊C4C2312yes—
277C22×C22⋊C4C2312yes—
278C22×C42C2311yescharacteristic
279C22×C42C2312yes—
280C22×C42C2311yescharacteristic
281#401C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2314yes—
297#398C2318yes—
298#398C2318yes—
299#398C2318yes—
300#398C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2318yes—
304#397C2318yes—
305#397C2318yes—
306#397C2314yes—
307#397C2314yes—
308#397C2314yes—
309#397C2318yes—
310#396C2314yes—
311#396C2318yes—
312#396C2318yes—
313#396C2318yes—
314#396C2318yes—
315#396C2318yes—
316#396C2314yes—
317#396C2314yes—
318#394C2318yes—
319#394C2318yes—
320#394C2318yes—
321#394C2314yes—
322#394C2314yes—
323#394C2314yes—
324#392C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2314yes—
328#391C2312yes—
329#391C2312yes—
330#391C2312yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2314yes—
335#391C2312yes—
336#391C2312yes—
337#391C2312yes—
338#390C2312yes—
339#390C2312yes—
340#390C2318yes—
341#390C2314yes—
342#390C2318yes—
343#390C2312yes—
344#390C2312yes—
345#389C2318yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2318yes—
353#389C2318yes—
354#389C2312yes—
355#389C2318yes—
356#389C2318yes—
357#389C2312yes—
358#389C2318yes—
359#389C2314yes—
360#389C2318yes—
361#389C2318yes—
362#389C2318yes—
363#389C2318yes—
364#389C2312yes—
365#389C2312yes—
366#389C2312yes—
367#388C2314yes—
368#388C2314yes—
369#388C2314yes—
370#388C2318yes—
371#388C2318yes—
372#388C2318yes—
373#388C2318yes—
374#388C2318yes—
375#388C2318yes—
376#388C2318yes—
377#388C2318yes—
378#388C2318yes—
379#388C2318yes—
380#388C2314yes—
381#388C2318yes—
382#388C2314yes—
383#387C2314yes—
384#387C2314yes—
385#387C2314yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#386C2314yes—
401#386C2314yes—
402#386C2314yes—
403#386C2314yes—
404#386C2318yes—
405#386C2318yes—
406#386C2314yes—
407#386C2318yes—
408#386C2318yes—
409#386C2314yes—
410#385C2318yes—
411#385C2318yes—
412#385C2318yes—
413#385C2318yes—
414#385C2314yes—
415#385C2314yes—
416#385C2314yes—
417#385C2318yes—
418#385C2318yes—
419#385C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2314yes—
426#385C2314yes—
427#385C2318yes—
428#385C2314yes—
429#385C2318yes—
430#384C2312yes—
431#384C2318yes—
432#384C2314yes—
433#384C2312yes—
434#384C2312yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2314yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#383C2314yes—
443#383C2318yes—
444#382C2318yes—
445#382C2312yes—
446#382C2312yes—
447#382C2312yes—
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#381C2314yes—
451#381C2312yes—
452#381C2312yes—
453#381C2318yes—
454#380C2314yes—
455#380C2314yes—
456#380C2314yes—
457#380C2314yes—
458#380C2318yes—
459#380C2318yes—
460#380C2318yes—
461#380C2312yes—
462#380C2314yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#379C2312yes—
468#379C2312yes—
469C4×C4⋊C4C2312yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2318yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2318yes—
478C4×C4⋊C4C2318yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C22⋊C4C2312yes—
485C4×C22⋊C4C2314yes—
486C4×C22⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2318yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498#376C2312yes—
499#376C2318yes—
500C2×#95C2314yes—
501C2×#95C2314yes—
502C2×#95C2312yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41#4118yes—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×D4C2412yes—
519C22×D4C2411yescharacteristic
520C22×D4C2414yes—
521C22×D4C2414yes—
522C22×D4C2414yes—
523C22×D4C2412yes—
524C22×D4C2411yescharacteristic
525C23×C4—24no—
526C23×C4—24no—
527C23×C4—24no—
528C23×C4—44no—
529C23×C4—84no—
530C23×C4C2412yes—
531C23×C4C2411yescharacteristic
532C23×C4C2412yes—
533C23×C4C2412yes—
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2414yes—
543C23×C4C2414yes—
544C23×C4C2418yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C4⋊Q8—24no—
548C4⋊Q8—28no—
549C4⋊Q8—44no—
550#127—24no—
551#126—216no—
552#126—88no—
553#125—88no—
554#124—24no—
555#124—24no—
556#124—28no—
557#124—44no—
558#123—28no—
559#123—216no—
560#123—28no—
561#123—48no—
562C22⋊Q8—28no—
563C22⋊Q8—216no—
564C22⋊Q8—28no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—44no—
568C22⋊Q8—44no—
569#121—28no—
570#121—216no—
571#121—28no—
572#121—216no—
573#120—28no—
574#120—28no—
575C4×Q8—28no—
576C4×Q8—216no—
577C4×Q8—216no—
578C4×Q8—44no—
579C4×Q8—44no—
580C4×Q8—44no—
581C4×D4—216no—
582C4×D4—216no—
583C4×D4—28no—
584C4×D4—216no—
585C4×D4—216no—
586C4×D4—44no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—48no—
590C4×D4—48no—
591C4×D4—48no—
592C4×D4—88no—
593C4×D4—88no—
594C4×D4—88no—
595#117—24no—
596#117—24no—
597#117—24no—
598#117—24no—
599#117—24no—
600#117—216no—
601#117—28no—
602#117—44no—
603#117—44no—
604#117—44no—
605#117#4118yes—
606C2×C4⋊C4—24no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—48no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—44no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—88no—
617C2×C4⋊C4—84no—
618C2×C4⋊C4—84no—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2418yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2412yes—
662C2×C22⋊C4—28no—
663C2×C22⋊C4—44no—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2418yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2418yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2412yes—
697C2×C42—24no—
698C2×C42—24no—
699C2×C42—28no—
700C2×C42C2411yescharacteristic
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2412yes—
704C2×C42C2412yes—
705C2×C42C2418yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2414yes—
710C2×C42C2411yescharacteristic
711C2×C42C2414yes—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2418yes—
719C2×C42C2418yes—
720C2×C42C2412yes—
721#95C2418yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2412yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2414yes—
730#95C2418yes—
731#95C2414yes—
732#95C2414yes—
733#95C2418yes—
734#95C2414yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2414yes—
746#95C2414yes—
747#95C2418yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2418yes—
756C24—22no—
757C24—24no—
758C24—22no—
759C24—22no—
760C24—42no—
761C24C2512yes—
762C24C2512yes—
763C24C2512yes—
764C24C2511yescharacteristic
765#41—232no—
766#41—416no—
767C2×Q8—22no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—24no—
773C2×Q8—22no—
774C2×Q8—22no—
775C2×Q8—22no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—416no—
779C2×Q8C2×#4114yes—
780C2×D4—24no—
781C2×D4—24no—
782C2×D4—28no—
783C2×D4—28no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—28no—
788C2×D4—28no—
789C2×D4—22no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—28no—
796C2×D4—44no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4C2×#4118yes—
800C2×D4C2×#4114yes—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—24no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—22no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—28no—
827C22×C4—44no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—48no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—416no—
843C22×C4—816no—
844C22×C4C2×#4118yes—
845C22×C4C2×#4114yes—
846C22×C4C2×#4114yes—
847C22×C4H(5,𝔽2)14yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2511yescharacteristic
868C22×C4C2511yescharacteristic
869C4⋊C4—28no—
870C4⋊C4—24no—
871C4⋊C4—216no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—216no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—28no—
891C4⋊C4—28no—
892C4⋊C4—48no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—48no—
897C4⋊C4—48no—
898C4⋊C4—44no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—48no—
902C4⋊C4—48no—
903C4⋊C4—48no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4C2×#4118yes—
912C22⋊C4—24no—
913C22⋊C4—24no—
914C22⋊C4—24no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—216no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—28no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4C2×#4118yes—
944C22⋊C42−1+418yes—
945C42—22no—
946C42—22no—
947C42—24no—
948C42—28no—
949C42—24no—
950C42—22no—
951C42—22no—
952C42—24no—
953C42—24no—
954C42—216no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—28no—
959C42—44no—
960C42—44no—
961C42—44no—
962C42—44no—
963C42—48no—
964C42—48no—
965C42C2×#4118yes—
966C23—22no—
967C23—22no—
968C23—28no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—48no—
985C23—48no—
986C23—44no—
987C23—44no—
988C23C22×#4114yes—
989C23C22×#4112yes—
990C23C22×#4112yes—
991C23C2×H(5,𝔽2)12yes—
992C23C2×2−1+414yes—
993C23C2611yescharacteristic
994Q8—28no—
995Q8—48no—
996Q8—48no—
997Q8—44no—
998D4—216no—
999D4—28no—
1000D4—416no—
1001D4—416no—
1002D4—416no—
1003D4—48no—
1004D4—44no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—216no—
1014C2×C4—24no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—24no—
1018C2×C4—24no—
1019C2×C4—24no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—24no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—28no—
1046C2×C4—28no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—28no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—416no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—84no—
1061C2×C4—84no—
1062C2×C4—84no—
1063C2×C4—816no—
1064C2×C4—164no—
1065C2×C4—164no—
1066C2×C4—164no—
1067C2×C4#553116yes—
1068C2×C4C22×#4118yes—
1069C2×C4C22×#4114yes—
1070C2×C4C22×#4112yes—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4112yes—
1073C2×C4C22×#4112yes—
1074C2×C4C2×H(5,𝔽2)12yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×2−1+414yes—
1077C2×C4C2×2−1+414yes—
1078C22—24no—
1079C22—24no—
1080C22—22no—
1081C22—22no—
1082C22—24no—
1083C22—24no—
1084C22—28no—
1085C22—24no—
1086C22—24no—
1087C22—416no—
1088C22—44no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—44no—
1096C22—44no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22C2×#55314yes—
1101C22C23×#4111yescharacteristic
1102C22C23×#4111yescharacteristic
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C22×2−1+412yes—
1105C22H(7,𝔽2)12yes—
1106C4—24no—
1107C4—28no—
1108C4—24no—
1109C4—24no—
1110C4—44no—
1111C4—44no—
1112C4—42no—
1113C4—42no—
1114C4—44no—
1115C4—42no—
1116C4—42no—
1117C4—44no—
1118C4—44no—
1119C4—44no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—42no—
1124C4—44no—
1125C4C2×#55314yes—
1126C4C2×#55314yes—
1127C2—24no—
1128C2—44no—
1129C2—44no—
1130C2—82no—
1131C2C22×#55311yescharacteristic
1132C2#6283311yescharacteristic
1133C2#6287611yescharacteristic
1134C2#6300012yes—
1135C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34743C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59698C2semidirect
2. #59694C2semidirect
3. #59385C2semidirect
4. #59306C2semidirect
5. #59305C2semidirect
6. #45220C2semidirect
7. #45120C2semidirect
8. #45000C2semidirect
9. #44972C2semidirect
10. #43286C2semidirect
11. #35661C2semidirect
12. #35633C2semidirect
13. #35621C2semidirect
14. #35619C2semidirect
15. #35557C2semidirect
16. #35555C2semidirect
17. #34814C2semidirect
18. C2×#2502C2semidirect
20. #34268C2semidirect
21. #34254C2semidirect
22. #34207C2semidirect
23. #34200C2semidirect
24. #34200C2semidirect
25. #34183C2semidirect
38. #2802C22semidirect
40. #2790C22semidirect
41. #2787C22semidirect
43. #2770C22semidirect
44. #2765C22semidirect
46. #2757C22semidirect
47. #2747C22semidirect
48. #2725C22semidirect
50. #2606C22semidirect
56. #2585C22semidirect
58. #2579C22semidirect
60. #2570C22semidirect
62. #2552C22semidirect
63. #2547C22semidirect
64. #2546C22semidirect
65. #2545C22semidirect
66. #2544C22semidirect
70. #2531C22semidirect
71. #2525C22semidirect
72. #2512C22semidirect
73. #2511C22semidirect
74. #2507C22semidirect
75. #2507C22semidirect
76. #2506C22semidirect
77. #2503C22semidirect
82. #2502C22semidirect
83. #2499C22semidirect
84. #2499C22semidirect
86. #2497C22semidirect
88. #2496C22semidirect
96. #2468C22semidirect
99. #2447C22semidirect
100. #2446C22semidirect
101. #2442C22semidirect
115. #2417C22semidirect
117. #2415C22semidirect
124. #2367C22semidirect
125. #2365C22semidirect
133. #2356C22semidirect
134. #2355C22semidirect
135. #2354C22semidirect
138. Q8×C4⋊C4C22semidirect
142. D4×C4⋊C4C22semidirect
143. D4×C4⋊C4C22semidirect
145. #2326C22semidirect
146. #2326C22semidirect
147. #2323C22semidirect
150. #2320C22semidirect
154. #2317C22semidirect
155. #2317C22semidirect
161. C4×C4⋊Q8C22semidirect
162. C4×#127C22semidirect
164. C4×C22⋊Q8C22semidirect
172. #2295C22semidirect
177. #2285C22semidirect
180. C2×#384C22semidirect

Maximal subgroups

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

subgroupindex
#596982
#596942
#593852
#593062
#593052
#452202
#451202
#450002
#449722
#432862
#356612
#356332
#356212
#356192
#355572
#355552
#348142
C2×#25022
#347432
#342682
#342542
#342072
#342002
#341832