Finite Group Databasebeta

← #8095273

Subgroups — #8095273

Order 512.

4884 conjugacy classes of subgroups.

The subgroup lattice has 1135 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53145C214yesmaximal, complemented
2#53024C214yesmaximal, complemented
3#52992C214yesmaximal, complemented
4#52959C214yesmaximal, complemented
5#52550C218yesmaximal, complemented
6#46112C214yesmaximal, complemented
7#46005C214yesmaximal, complemented
8#45745C218yesmaximal, complemented
9#45603C214yesmaximal, complemented
10#45501C214yesmaximal, complemented
11#35673C211yesmaximal, characteristic, complemented
12#35662C211yesmaximal, characteristic, complemented
13#35661C211yesmaximal, characteristic, complemented
14#35633C211yesmaximal, characteristic, complemented
15#35532C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#35312C211yesmaximal, characteristic, complemented
18#35308C211yesmaximal, characteristic, complemented
19#35286C211yesmaximal, characteristic, complemented
20#35280C211yesmaximal, characteristic, complemented
21#35224C211yesmaximal, characteristic, complemented
22#35223C211yesmaximal, characteristic
23#34813C211yesmaximal, characteristic, complemented
24C2×#2502C211yesmaximal, characteristic, complemented
25#34742C211yesmaximal, characteristic, complemented
26C2×#544C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#533C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×#519C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C23×C4⋊C4C2211yescharacteristic
38#2862C2212yescomplemented
39#2861C2212yescomplemented
40#2859C2214yescomplemented
41#2857C2214yescomplemented
42#2857C2212yescomplemented
43#2850C2212yescomplemented
44#2848C2214yes—
45#2847C2214yes—
46#2845C2218yescomplemented
47#2841C2218yescomplemented
48#2839C2218yescomplemented
49#2837C2218yescomplemented
50#2836C2218yescomplemented
51#2836C2218yescomplemented
52#2831C2218yescomplemented
53#2827C2218yes—
54#2827C2218yes—
55#2814C2218yescomplemented
56#2806C2218yescomplemented
57#2802C2218yescomplemented
58#2788C2218yes—
59#2781C2218yes—
60#2781C2218yescomplemented
61#2779C2218yes—
62#2772C2218yescomplemented
63#2768C2218yes—
64#2768C2218yescomplemented
65#2747C2218yes—
66#2732C2218yes—
67#2711C2218yes—
68#2708C2218yes—
69#2704C2218yes—
70#2704C2218yescomplemented
71#2704C2218yescomplemented
72#2692C2218yes—
73#2687C2218yescomplemented
74#2681C2218yes—
75#2672C2218yes—
76#2647C2214yescomplemented
77#2642C2212yescomplemented
78#2640C2212yescomplemented
79#2629C2214yescomplemented
80#2627C2214yes—
81#2621C2212yescomplemented
82#2620C2212yescomplemented
83#2618C2214yes—
84#2582C2214yescomplemented
85#2582C2214yescomplemented
86#2581C2214yescomplemented
87#2571C2214yescomplemented
88#2567C2212yescomplemented
89#2566C2212yescomplemented
90#2565C2212yescomplemented
91#2552C2214yescomplemented
92#2542C2212yescomplemented
93#2538C2214yes—
94#2538C2214yescomplemented
95#2536C2214yes—
96#2534C2214yes—
97#2502C2214yes—
98#2502C2214yes—
99#2502C2214yes—
100#2502C2214yes—
101#2502C2212yescomplemented
102#2501C2212yescomplemented
103#2500C2212yescomplemented
104#2499C2212yescomplemented
105#2498C2218yes—
106#2492C2212yes—
107#2492C2214yescomplemented
108#2491C2212yes—
109#2490C2212yes—
110#2489C2212yes—
111#2489C2214yescomplemented
112#2488C2214yes—
113#2488C2218yes—
114#2486C2214yes—
115#2472C2214yes—
116#2453C2214yescomplemented
117#2451C2214yescomplemented
118#2449C2218yes—
119#2448C2214yescomplemented
120#2446C2214yescomplemented
121#2443C2218yes—
122#2442C2214yes—
123#2442C2214yes—
124#2442C2218yes—
125#2441C2214yescomplemented
126#2440C2214yes—
127#2440C2214yes—
128#2440C2214yescomplemented
129#2438C2218yes—
130#2429C2214yes—
131#2429C2214yes—
132#2429C2214yescomplemented
133#2427C2214yes—
134#2427C2214yescomplemented
135#2426C2214yes—
136#2425C2218yes—
137#2423C2212yes—
138#2423C2214yescomplemented
139#2423C2214yescomplemented
140#2422C2212yes—
141#2422C2214yescomplemented
142#2421C2212yes—
143#2421C2214yescomplemented
144#2420C2212yes—
145#2419C2214yes—
146#2418C2214yes—
147#2417C2214yes—
148#2417C2214yes—
149#2417C2218yes—
150#2417C2214yes—
151#2416C2214yes—
152#2416C2214yes—
153#2415C2214yes—
154#2413C2214yes—
155#2411C2214yes—
156#2398C2214yes—
157#2395C2214yes—
158C2×#398C2214yes—
159#2379C2218yes—
160#2376C2218yes—
161#2317C2211yescharacteristic
162#2317C2211yescharacteristic
163#2317C2211yescharacteristic
164#2316C2211yescharacteristic
165#2316C2211yescharacteristic
166#2316C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2311C2211yescharacteristic
170#2310C2211yescharacteristic
171C4×#124C2214yes—
172C4×#123C2214yes—
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2296C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#385C2214yes—
180#2285C2211yescharacteristic
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2280C2211yescharacteristic
184#2280C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C23×Q8C2311yescharacteristic
190C24×C4C2311yescharacteristic
191C24×C4C2312yes—
192#544—44no—
193#537—44no—
194#536—44no—
195#536—44no—
196#533—44no—
197C2×C4⋊Q8C2312yes—
198C2×C4⋊Q8C2312yes—
199C2×C4⋊Q8C2312yes—
200C2×C4⋊Q8C2312yes—
201C2×C4⋊Q8C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2318yes—
206C2×#124C2314yes—
207C2×#124C2312yes—
208C2×#124C2312yes—
209#525—44no—
210#525—44no—
211C2×#123C2314yes—
212C2×#123C2312yes—
213C2×#123C2312yes—
214C2×#123C2314yes—
215C2×#123C2314yes—
216C2×#123C2318yes—
217C2×C22⋊Q8—44no—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2314yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2318yes—
231C2×C22⋊Q8C2318yes—
232C2×#121C2314yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2312yes—
237C2×#121C2318yes—
238C2×#120C2312yes—
239C2×#120C2312yes—
240#520—44no—
241#519—44no—
242C4×#41—44no—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2312yes—
247C2×C4×Q8C2314yes—
248C2×C4×D4C2312yes—
249C2×C4×D4C2314yes—
250C2×C4×D4C2314yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2314yes—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2312yes—
261C2×#117C2314yes—
262C2×#117C2312yes—
263C22×C4⋊C4—44no—
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2312yes—
269C22×C4⋊C4C2314yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2314yes—
273C22×C4⋊C4C2314yes—
274C22×C22⋊C4C2312yes—
275C22×C22⋊C4C2312yes—
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2314yes—
287#400C2314yes—
288#400C2314yes—
289#399C2318yes—
290#399C2318yes—
291#399C2318yes—
292#399C2314yes—
293#398C2318yes—
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#398C2318yes—
309#398C2314yes—
310#398C2318yes—
311#398C2318yes—
312#398C2318yes—
313#397C2314yes—
314#397C2314yes—
315#397C2318yes—
316#397C2318yes—
317#397C2318yes—
318#397C2318yes—
319#397C2318yes—
320#397C2314yes—
321#397C2314yes—
322#397C2314yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2318yes—
329#396C2318yes—
330#396C2318yes—
331#396C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2318yes—
335#394C2314yes—
336#394C2314yes—
337#394C2318yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2314yes—
343#394C2314yes—
344#393C2314yes—
345#393C2318yes—
346#393C2314yes—
347#391C2311yescharacteristic
348#391C2312yes—
349#391C2312yes—
350#391C2312yes—
351#391C2314yes—
352#391C2312yes—
353#391C2312yes—
354#391C2311yescharacteristic
355#391C2318yes—
356#391C2314yes—
357#391C2318yes—
358#391C2312yes—
359#391C2312yes—
360#391C2311yescharacteristic
361#391C2318yes—
362#391C2312yes—
363#391C2312yes—
364#391C2311yescharacteristic
365#391C2312yes—
366#391C2314yes—
367#391C2314yes—
368#390C2311yescharacteristic
369#390C2312yes—
370#390C2312yes—
371#390C2312yes—
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2318yes—
375#390C2311yescharacteristic
376#390C2312yes—
377#390C2314yes—
378#389C2318yes—
379#389C2314yes—
380#389C2314yes—
381#389C2318yes—
382#389C2314yes—
383#389C2314yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2318yes—
391#389C2312yes—
392#389C2318yes—
393#389C2312yes—
394#389C2318yes—
395#389C2318yes—
396#389C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2314yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#387C2318yes—
413#387C2314yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2314yes—
420#386C2314yes—
421#386C2314yes—
422#386C2314yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2314yes—
428#386C2314yes—
429#386C2314yes—
430#386C2314yes—
431#385C2318yes—
432#385C2318yes—
433#385C2318yes—
434#385C2318yes—
435#385C2314yes—
436#385C2314yes—
437#385C2314yes—
438#385C2318yes—
439#385C2318yes—
440#385C2314yes—
441#385C2314yes—
442#385C2318yes—
443#385C2318yes—
444#384C2312yes—
445#384C2312yes—
446#384C2312yes—
447#384C2314yes—
448#384C2312yes—
449#384C2312yes—
450#384C2314yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#382C2312yes—
455#382C2312yes—
456#382C2318yes—
457#382C2312yes—
458#382C2314yes—
459#382C2318yes—
460#382C2312yes—
461#381C2314yes—
462#381C2314yes—
463#381C2312yes—
464#381C2312yes—
465#380C2314yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2318yes—
474#380C2318yes—
475#380C2312yes—
476#380C2312yes—
477#380C2318yes—
478#380C2314yes—
479#380C2312yes—
480#380C2312yes—
481#379C2312yes—
482#379C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2312yes—
488C4×C22⋊C4C2312yes—
489C4×C22⋊C4C2314yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2312yes—
492C4×C22⋊C4C2312yes—
493C4×C22⋊C4C2314yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2312yes—
499#376C2312yes—
500C2×#95C2312yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C25C2411yescharacteristic
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C22×Q8—24no—
512C22×Q8—24no—
513C22×Q8—24no—
514C22×Q8C2412yes—
515C22×Q8C2412yes—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2414yes—
519C22×Q8C2414yes—
520C22×D4C2412yes—
521C22×D4C2412yes—
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2414yes—
525C22×D4C2414yes—
526C22×D4C2414yes—
527C23×C4—24no—
528C23×C4—24no—
529C23×C4—24no—
530C23×C4—44no—
531C23×C4—84no—
532C23×C4C2412yes—
533C23×C4C2411yescharacteristic
534C23×C4C2412yes—
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2414yes—
544C23×C4C2418yes—
545C23×C4C2414yes—
546C23×C4C2411yescharacteristic
547C4⋊Q8—44no—
548C4⋊Q8—44no—
549C4⋊Q8—44no—
550C4⋊Q8—44no—
551C4⋊Q8—44no—
552#125—44no—
553#125—44no—
554#125—44no—
555#125—88no—
556#124—216no—
557#124—44no—
558#124—44no—
559#123—216no—
560#123—44no—
561#123—44no—
562#123—48no—
563#123—48no—
564#123—88no—
565C22⋊Q8—48no—
566C22⋊Q8—48no—
567C22⋊Q8—48no—
568C22⋊Q8—48no—
569C22⋊Q8—44no—
570C22⋊Q8—44no—
571C22⋊Q8—48no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—44no—
575C22⋊Q8—44no—
576C22⋊Q8—88no—
577C22⋊Q8—88no—
578C22⋊Q8—88no—
579#121—44no—
580#121—44no—
581#121—44no—
582#121—44no—
583#121—48no—
584#121—88no—
585#120—44no—
586#120—44no—
587C4×Q8—48no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—44no—
592C4×D4—44no—
593C4×D4—44no—
594C4×D4—48no—
595C4×D4—48no—
596C4×D4—48no—
597C4×D4—48no—
598#117—24no—
599#117—24no—
600#117—24no—
601#117—24no—
602#117—24no—
603#117—24no—
604#117—44no—
605#117—48no—
606#117—44no—
607C2×C4⋊C4—24no—
608C2×C4⋊C4—24no—
609C2×C4⋊C4—24no—
610C2×C4⋊C4—48no—
611C2×C4⋊C4—48no—
612C2×C4⋊C4—44no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—44no—
615C2×C4⋊C4—84no—
616C2×C4⋊C4—84no—
617C2×C4⋊C4C2412yes—
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2414yes—
633C2×C4⋊C4C2418yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2418yes—
636C2×C4⋊C4C2418yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
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⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2414yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2418yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2418yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2412yes—
699C2×C42—24no—
700C2×C42—24no—
701C2×C42—44no—
702C2×C42C2412yes—
703C2×C42C2411yescharacteristic
704C2×C42C2412yes—
705C2×C42C2412yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2418yes—
724#95C2418yes—
725#95C2418yes—
726#95C2418yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2418yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754C24—22no—
755C24—24no—
756C24—22no—
757C24—22no—
758C24—42no—
759C24C2512yes—
760C24C2512yes—
761C24C2512yes—
762C24C2511yescharacteristic
763#41—416no—
764#41—416no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—28no—
778C2×Q8—44no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—48no—
782C2×Q8—416no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—28no—
790C2×D4—28no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—22no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—44no—
798C2×D4—44no—
799C2×D4—44no—
800C2×D4—44no—
801C2×D4—44no—
802C2×D4—48no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—22no—
806C22×C4—24no—
807C22×C4—22no—
808C22×C4—24no—
809C22×C4—22no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
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—24no—
827C22×C4—24no—
828C22×C4—28no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—48no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—416no—
842C22×C4—816no—
843C22×C4H(5,𝔽2)14yes—
844C22×C4H(5,𝔽2)14yes—
845C22×C42−1+414yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2514yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2512yes—
853C22×C4C2512yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2512yes—
857C22×C4C2514yes—
858C22×C4C2512yes—
859C22×C4C2514yes—
860C22×C4C2514yes—
861C22×C4C2512yes—
862C22×C4C2514yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C4⋊C4—24no—
868C4⋊C4—24no—
869C4⋊C4—24no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—24no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—28no—
882C4⋊C4—28no—
883C4⋊C4—48no—
884C4⋊C4—44no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—44no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—48no—
910C4⋊C4—48no—
911C4⋊C4—44no—
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—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—44no—
945C22⋊C4—44no—
946C22⋊C42−1+418yes—
947C42—22no—
948C42—22no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—22no—
957C42—24no—
958C42—22no—
959C42—28no—
960C42—44no—
961C42—44no—
962C42—48no—
963C42—44no—
964C23—22no—
965C23—22no—
966C23—28no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—22no—
980C23—22no—
981C23—24no—
982C23—24no—
983C23—48no—
984C23—48no—
985C23—44no—
986C23—44no—
987C23C2×H(5,𝔽2)12yes—
988C23C2×H(5,𝔽2)12yes—
989C23C2×2−1+414yes—
990C23C2×2−1+412yes—
991C23C2611yescharacteristic
992Q8—48no—
993Q8—48no—
994Q8—44no—
995Q8—44no—
996Q8—88no—
997Q8—164no—
998D4—48no—
999D4—48no—
1000D4—44no—
1001D4—44no—
1002D4—88no—
1003D4—88no—
1004D4—164no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—24no—
1012C2×C4—24no—
1013C2×C4—24no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—24no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—24no—
1037C2×C4—24no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—28no—
1052C2×C4—28no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—88no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4—816no—
1066C2×C4—164no—
1067C2×C4#562116yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×H(5,𝔽2)12yes—
1072C2×C4C2×2−1+414yes—
1073C2×C4C2×2−1+414yes—
1074C2×C4C2×2−1+412yes—
1075C2×C4C2×2−1+412yes—
1076C22—22no—
1077C22—22no—
1078C22—24no—
1079C22—24no—
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—416no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—44no—
1093C22—44no—
1094C22—42no—
1095C22—42no—
1096C22—44no—
1097C22—44no—
1098C22C2×#56214yes—
1099C22C22×H(5,𝔽2)11yescharacteristic
1100C22C22×H(5,𝔽2)11yescharacteristic
1101C22C22×2−1+412yes—
1102C22C22×2−1+411yescharacteristic
1103C22H(7,𝔽2)12yes—
1104C4—24no—
1105C4—24no—
1106C4—42no—
1107C4—42no—
1108C4—44no—
1109C4—44no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—42no—
1114C4—44no—
1115C4—44no—
1116C4—44no—
1117C4—44no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—44no—
1122C4—42no—
1123C4C2×#56214yes—
1124C4C2×#56214yes—
1125C2—24no—
1126C2—44no—
1127C2—82no—
1128C2—82no—
1129C2C22×#56211yescharacteristic
1130C2#6283311yescharacteristic
1131C2#6287611yescharacteristic
1132C2#6294412yes—
1133C2#6294512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35223C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53145C2semidirect
2. #53024C2semidirect
3. #52992C2semidirect
4. #52959C2semidirect
5. #52550C2semidirect
6. #46112C2semidirect
7. #46005C2semidirect
8. #45745C2semidirect
9. #45603C2semidirect
10. #45501C2semidirect
11. #35673C2semidirect
12. #35662C2semidirect
13. #35661C2semidirect
14. #35633C2semidirect
15. #35532C2semidirect
16. #35530C2semidirect
17. #35312C2semidirect
18. #35308C2semidirect
19. #35286C2semidirect
20. #35280C2semidirect
21. #35224C2semidirect
23. #34813C2semidirect
24. C2×#2502C2semidirect
25. #34742C2semidirect
38. #2862C22semidirect
39. #2861C22semidirect
40. #2859C22semidirect
41. #2857C22semidirect
42. #2857C22semidirect
43. #2850C22semidirect
46. #2845C22semidirect
47. #2841C22semidirect
48. #2839C22semidirect
49. #2837C22semidirect
50. #2836C22semidirect
51. #2836C22semidirect
52. #2831C22semidirect
55. #2814C22semidirect
56. #2806C22semidirect
57. #2802C22semidirect
60. #2781C22semidirect
62. #2772C22semidirect
64. #2768C22semidirect
70. #2704C22semidirect
71. #2704C22semidirect
73. #2687C22semidirect
76. #2647C22semidirect
77. #2642C22semidirect
78. #2640C22semidirect
79. #2629C22semidirect
81. #2621C22semidirect
82. #2620C22semidirect
84. #2582C22semidirect
85. #2582C22semidirect
86. #2581C22semidirect
87. #2571C22semidirect
88. #2567C22semidirect
89. #2566C22semidirect
90. #2565C22semidirect
91. #2552C22semidirect
92. #2542C22semidirect
94. #2538C22semidirect
101. #2502C22semidirect
102. #2501C22semidirect
103. #2500C22semidirect
104. #2499C22semidirect
107. #2492C22semidirect
111. #2489C22semidirect
116. #2453C22semidirect
117. #2451C22semidirect
119. #2448C22semidirect
120. #2446C22semidirect
125. #2441C22semidirect
128. #2440C22semidirect
132. #2429C22semidirect
134. #2427C22semidirect
138. #2423C22semidirect
139. #2423C22semidirect
141. #2422C22semidirect
143. #2421C22semidirect

Maximal subgroups

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

subgroupindex
#531452
#530242
#529922
#529592
#525502
#461122
#460052
#457452
#456032
#455012
#356732
#356622
#356612
#356332
#355322
#355302
#353122
#353082
#352862
#352802
#352242
#352232
#348132
C2×#25022
#347422