Finite Group Databasebeta

← #7652078

Subgroups — #7652078

Order 512.

5664 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42936C214yesmaximal, complemented
2#42829C214yesmaximal, complemented
3#42552C214yesmaximal, complemented
4#42504C214yesmaximal, complemented
5#40845C218yesmaximal, complemented
6#40140C214yesmaximal, complemented
7#40006C214yesmaximal, complemented
8#39654C214yesmaximal, complemented
9#39632C214yesmaximal, complemented
10#38509C218yesmaximal, complemented
11#35660C211yesmaximal, characteristic, complemented
12#35659C211yesmaximal, characteristic, complemented
13#35633C211yesmaximal, characteristic, complemented
14#35628C211yesmaximal, characteristic, complemented
15#35557C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#35313C211yesmaximal, characteristic, complemented
18#35280C211yesmaximal, characteristic, complemented
19#35223C211yesmaximal, characteristic, complemented
20#34813C211yesmaximal, characteristic, complemented
21C2×#2502C211yesmaximal, characteristic, complemented
22#34743C211yesmaximal, characteristic, complemented
23#34259C211yesmaximal, characteristic, complemented
24#34207C211yesmaximal, characteristic, complemented
25#34200C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#532C2211yescharacteristic
31C2×#525C2211yescharacteristic
32C2×#525C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#520C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38C23×C4⋊C4C2211yescharacteristic
39#2863C2214yescomplemented
40#2857C2214yescomplemented
41#2847C2214yes—
42#2831C2218yescomplemented
43#2827C2218yescomplemented
44#2806C2218yescomplemented
45#2804C2218yes—
46#2788C2218yes—
47#2788C2218yescomplemented
48#2780C2218yes—
49#2778C2218yes—
50#2768C2218yescomplemented
51#2765C2218yescomplemented
52#2761C2218yescomplemented
53#2756C2218yescomplemented
54#2750C2218yes—
55#2749C2218yes—
56#2708C2218yes—
57#2702C2218yescomplemented
58#2695C2218yescomplemented
59#2676C2218yes—
60#2666C2218yescomplemented
61#2653C2218yes—
62#2653C2218yescomplemented
63#2646C2218yescomplemented
64#2645C2214yescomplemented
65#2636C2218yes—
66#2630C2218yescomplemented
67#2629C2214yescomplemented
68#2618C2214yes—
69#2592C2214yescomplemented
70#2587C2218yescomplemented
71#2582C2214yescomplemented
72#2574C2218yes—
73#2568C2214yescomplemented
74#2559C2218yes—
75#2538C2214yescomplemented
76#2534C2214yes—
77#2514C2214yescomplemented
78#2512C2214yescomplemented
79#2511C2214yescomplemented
80#2511C2214yescomplemented
81#2502C2214yes—
82#2502C2214yes—
83#2502C2214yes—
84#2502C2214yes—
85#2502C2212yescomplemented
86#2501C2212yescomplemented
87#2500C2212yescomplemented
88#2499C2212yescomplemented
89#2497C2214yescomplemented
90#2496C2214yescomplemented
91#2493C2218yes—
92#2492C2212yes—
93#2492C2214yescomplemented
94#2491C2212yes—
95#2490C2212yes—
96#2489C2212yes—
97#2489C2214yescomplemented
98#2488C2218yes—
99#2488C2214yes—
100#2486C2214yes—
101#2481C2218yes—
102#2472C2214yes—
103#2456C2218yes—
104#2450C2218yes—
105#2450C2218yescomplemented
106#2443C2218yes—
107#2436C2212yescomplemented
108#2434C2212yescomplemented
109#2432C2212yescomplemented
110#2431C2212yescomplemented
111#2430C2218yes—
112#2429C2214yes—
113#2429C2212yes—
114#2428C2212yes—
115#2427C2214yes—
116#2427C2212yes—
117#2426C2212yes—
118#2425C2214yes—
119#2424C2214yes—
120#2423C2214yescomplemented
121#2422C2214yescomplemented
122#2417C2214yes—
123#2417C2214yes—
124#2417C2218yes—
125#2417C2214yes—
126#2416C2214yes—
127#2416C2214yes—
128#2415C2214yes—
129#2409C2214yes—
130#2409C2214yes—
131#2409C2214yescomplemented
132#2407C2214yes—
133#2407C2214yes—
134#2407C2214yescomplemented
135#2406C2214yes—
136#2404C2214yes—
137#2398C2214yes—
138#2392C2214yes—
139C2×#398C2214yes—
140#2361C2214yes—
141#2361C2218yes—
142#2360C2214yes—
143#2354C2214yescomplemented
144#2352C2214yes—
145D4×C4⋊C4C2214yes—
146D4×C4⋊C4C2214yescomplemented
147Q8×C22⋊C4C2214yescomplemented
148#2339C2218yes—
149#2339C2214yescomplemented
150#2337C2218yes—
151#2326C2212yescomplemented
152#2326C2212yescomplemented
153#2325C2218yes—
154#2322C2214yes—
155#2317C2211yescharacteristic
156#2316C2211yescharacteristic
157#2316C2211yescharacteristic
158#2311C2211yescharacteristic
159#2311C2211yescharacteristic
160#2311C2211yescharacteristic
161#2311C2211yescharacteristic
162#2311C2211yescharacteristic
163#2311C2212yescomplemented
164#2310C2211yescharacteristic
165#2310C2211yescharacteristic
166#2310C2212yescomplemented
167C4×C4⋊Q8C2212yescomplemented
168C4×#127C2212yescomplemented
169C4×#124C2214yes—
170C4×#121C2214yes—
171C4×#120C2214yes—
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2212yescomplemented
176#2296C2211yescharacteristic
177C2×#391C2211yescharacteristic
178C2×#391C2211yescharacteristic
179C2×#391C2212yescomplemented
180C2×#385C2214yes—
181C2×#384C2211yescharacteristic
182C2×#384C2211yescharacteristic
183#2280C2211yescharacteristic
184#2274C2211yescharacteristic
185C4×#117C2211yescharacteristic
186C2×C4×C22⋊C4C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2312yes—
194C22×#41C2314yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2312yes—
198C23×Q8C2312yes—
199C24×C4C2311yescharacteristic
200C24×C4C2312yes—
201#537—44no—
202#536—44no—
203#533—44no—
204#532—28no—
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2312yes—
208C2×#127C2311yescharacteristic
209C2×#126C2318yes—
210C2×#125C2312yes—
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#124C2314yes—
214C2×#124C2312yes—
215#525—28no—
216#525—44no—
217#525—44no—
218C2×#123C2312yes—
219C2×#123C2312yes—
220C2×#123C2312yes—
221C2×#123C2314yes—
222C2×#123C2318yes—
223C2×C22⋊Q8—44no—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2314yes—
232C2×C22⋊Q8C2312yes—
233C2×C22⋊Q8C2318yes—
234C2×#121C2314yes—
235C2×#121C2312yes—
236C2×#121C2314yes—
237C2×#121C2314yes—
238C2×#121C2312yes—
239C2×#121C2312yes—
240C2×#121C2312yes—
241C2×#121C2312yes—
242C2×#121C2318yes—
243C2×#120C2312yes—
244C2×#120C2312yes—
245C2×#120C2312yes—
246#520—44no—
247#520—44no—
248C4×#41—44no—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2312yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2314yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2312yes—
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×C4×D4C2314yes—
263C2×C4×D4C2318yes—
264C2×C4×D4C2318yes—
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C2×#117C2311yescharacteristic
269C2×#117C2311yescharacteristic
270C2×#117C2312yes—
271C2×#117C2312yes—
272C2×#117C2312yes—
273C22×C4⋊C4—44no—
274C22×C4⋊C4C2311yescharacteristic
275C22×C4⋊C4C2311yescharacteristic
276C22×C4⋊C4C2311yescharacteristic
277C22×C4⋊C4C2312yes—
278C22×C4⋊C4C2312yes—
279C22×C4⋊C4C2314yes—
280C22×C4⋊C4C2312yes—
281C22×C4⋊C4C2314yes—
282C22×C4⋊C4C2312yes—
283C22×C4⋊C4C2314yes—
284C22×C4⋊C4C2314yes—
285C22×C22⋊C4C2312yes—
286C22×C22⋊C4C2312yes—
287C22×C42C2311yescharacteristic
288C22×C42C2311yescharacteristic
289C22×C42C2312yes—
290#401C2318yes—
291#400C2318yes—
292#400C2318yes—
293#400C2318yes—
294#400C2314yes—
295#400C2318yes—
296#400C2318yes—
297#400C2318yes—
298#400C2314yes—
299#400C2318yes—
300#399C2318yes—
301#398C2318yes—
302#398C2318yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2318yes—
308#398C2318yes—
309#398C2318yes—
310#398C2314yes—
311#397C2314yes—
312#397C2314yes—
313#397C2318yes—
314#397C2318yes—
315#397C2318yes—
316#397C2318yes—
317#397C2314yes—
318#396C2318yes—
319#396C2318yes—
320#396C2314yes—
321#396C2314yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#395C2318yes—
327#395C2318yes—
328#394C2318yes—
329#394C2318yes—
330#394C2318yes—
331#394C2314yes—
332#394C2314yes—
333#394C2314yes—
334#394C2314yes—
335#394C2318yes—
336#394C2318yes—
337#394C2314yes—
338#393C2318yes—
339#393C2318yes—
340#393C2318yes—
341#393C2314yes—
342#393C2314yes—
343#392C2318yes—
344#392C2318yes—
345#392C2314yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2312yes—
350#391C2314yes—
351#391C2314yes—
352#391C2314yes—
353#391C2311yescharacteristic
354#391C2312yes—
355#391C2312yes—
356#391C2318yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#391C2314yes—
361#391C2318yes—
362#391C2318yes—
363#391C2318yes—
364#391C2312yes—
365#391C2312yes—
366#391C2314yes—
367#391C2312yes—
368#391C2314yes—
369#391C2311yescharacteristic
370#391C2312yes—
371#390C2312yes—
372#390C2312yes—
373#390C2318yes—
374#390C2312yes—
375#390C2312yes—
376#390C2312yes—
377#390C2311yescharacteristic
378#390C2312yes—
379#390C2312yes—
380#390C2314yes—
381#390C2314yes—
382#390C2311yescharacteristic
383#389C2318yes—
384#389C2314yes—
385#389C2314yes—
386#389C2314yes—
387#389C2314yes—
388#389C2314yes—
389#389C2318yes—
390#389C2318yes—
391#389C2314yes—
392#389C2318yes—
393#389C2312yes—
394#389C2312yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2314yes—
400#388C2318yes—
401#388C2318yes—
402#388C2314yes—
403#388C2318yes—
404#388C2318yes—
405#388C2314yes—
406#388C2318yes—
407#388C2314yes—
408#388C2314yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#386C2314yes—
417#386C2314yes—
418#386C2314yes—
419#386C2314yes—
420#386C2314yes—
421#386C2318yes—
422#386C2318yes—
423#386C2318yes—
424#386C2318yes—
425#386C2318yes—
426#386C2318yes—
427#386C2318yes—
428#386C2314yes—
429#386C2318yes—
430#386C2318yes—
431#386C2318yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#385C2318yes—
437#385C2318yes—
438#385C2314yes—
439#385C2318yes—
440#385C2318yes—
441#385C2318yes—
442#385C2318yes—
443#385C2318yes—
444#385C2318yes—
445#385C2318yes—
446#385C2318yes—
447#385C2318yes—
448#385C2318yes—
449#385C2314yes—
450#385C2318yes—
451#384C2312yes—
452#384C2312yes—
453#384C2312yes—
454#384C2314yes—
455#384C2312yes—
456#384C2314yes—
457#384C2312yes—
458#383C2318yes—
459#382C2318yes—
460#382C2312yes—
461#382C2314yes—
462#381C2314yes—
463#381C2314yes—
464#381C2318yes—
465#381C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2314yes—
473#380C2314yes—
474#380C2318yes—
475#380C2318yes—
476#380C2312yes—
477#380C2312yes—
478#380C2318yes—
479#380C2314yes—
480#379C2312yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C22⋊C4C2318yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2318yes—
490C4×C22⋊C4C2314yes—
491C4×C22⋊C4C2314yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2312yes—
494C4×C22⋊C4C2312yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2312yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501#376C2312yes—
502C2×#95C2318yes—
503C2×#95C2314yes—
504C2×#95C2312yes—
505C2×#95C2314yes—
506C43C2312yes—
507C25C2411yescharacteristic
5082−1+4—464no—
509C2×#41—216no—
510C2×#41—28no—
511C2×#41—24no—
512C2×#41—28no—
513C2×#41—24no—
514C2×#41—24no—
515C2×#41—24no—
516C2×#41—24no—
517C2×#41—24no—
518C2×#41—24no—
519C2×#41—24no—
520C2×#41—48no—
521C2×#41—48no—
522C2×#41—44no—
523C2×#41—44no—
524C2×#41—44no—
525C2×#41—44no—
526C2×#41#4118yes—
527C22×Q8—28no—
528C22×Q8—28no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—44no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2411yescharacteristic
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2414yes—
542C22×Q8C2414yes—
543C22×D4C2412yes—
544C22×D4C2411yescharacteristic
545C22×D4C2412yes—
546C22×D4C2411yescharacteristic
547C22×D4C2414yes—
548C22×D4C2414yes—
549C22×D4C2412yes—
550C22×D4C2411yescharacteristic
551C22×D4C2414yes—
552C22×D4C2414yes—
553C22×D4C2414yes—
554C22×D4C2414yes—
555C23×C4—24no—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—44no—
559C23×C4—84no—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2412yes—
567C23×C4C2412yes—
568C23×C4C2412yes—
569C23×C4C2412yes—
570C23×C4C2412yes—
571C23×C4C2412yes—
572C23×C4C2414yes—
573C23×C4C2414yes—
574C23×C4C2414yes—
575C23×C4C2418yes—
576C23×C4C2414yes—
577C23×C4C2414yes—
578C23×C4C2411yescharacteristic
579C4⋊Q8—24no—
580C4⋊Q8—44no—
581C4⋊Q8—44no—
582#127—24no—
583#126—88no—
584#125—44no—
585#124—24no—
586#124—24no—
587#124—216no—
588#124—44no—
589#123—28no—
590#123—44no—
591#123—44no—
592#123—48no—
593#123—88no—
594C22⋊Q8—28no—
595C22⋊Q8—48no—
596C22⋊Q8—48no—
597C22⋊Q8—48no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600C22⋊Q8—48no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—88no—
604#121—28no—
605#121—216no—
606#121—216no—
607#121—44no—
608#121—44no—
609#121—44no—
610#121—44no—
611#121—48no—
612#121—88no—
613#120—28no—
614#120—44no—
615#120—44no—
616C4×Q8—48no—
617C4×Q8—44no—
618C4×Q8—44no—
619C4×Q8—44no—
620C4×D4—216no—
621C4×D4—216no—
622C4×D4—44no—
623C4×D4—44no—
624C4×D4—44no—
625C4×D4—48no—
626C4×D4—48no—
627C4×D4—48no—
628C4×D4—48no—
629C4×D4—48no—
630C4×D4—88no—
631C4×D4—88no—
632#117—24no—
633#117—24no—
634#117—24no—
635#117—24no—
636#117—24no—
637#117—44no—
638#117—44no—
639#117—44no—
640C2×C4⋊C4—24no—
641C2×C4⋊C4—24no—
642C2×C4⋊C4—24no—
643C2×C4⋊C4—48no—
644C2×C4⋊C4—48no—
645C2×C4⋊C4—44no—
646C2×C4⋊C4—44no—
647C2×C4⋊C4—44no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4—84no—
650C2×C4⋊C4—84no—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2412yes—
654C2×C4⋊C4C2412yes—
655C2×C4⋊C4C2412yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2412yes—
660C2×C4⋊C4C2412yes—
661C2×C4⋊C4C2412yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2414yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2418yes—
671C2×C4⋊C4C2418yes—
672C2×C4⋊C4C2418yes—
673C2×C4⋊C4C2418yes—
674C2×C4⋊C4C2414yes—
675C2×C4⋊C4C2414yes—
676C2×C4⋊C4C2414yes—
677C2×C4⋊C4C2418yes—
678C2×C4⋊C4C2414yes—
679C2×C4⋊C4C2414yes—
680C2×C4⋊C4C2414yes—
681C2×C4⋊C4C2414yes—
682C2×C4⋊C4C2418yes—
683C2×C4⋊C4C2418yes—
684C2×C4⋊C4C2418yes—
685C2×C4⋊C4C2414yes—
686C2×C22⋊C4—28no—
687C2×C22⋊C4—44no—
688C2×C22⋊C4C2412yes—
689C2×C22⋊C4C2412yes—
690C2×C22⋊C4C2412yes—
691C2×C22⋊C4C2412yes—
692C2×C22⋊C4C2412yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2412yes—
695C2×C22⋊C4C2412yes—
696C2×C22⋊C4C2414yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2414yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2414yes—
703C2×C22⋊C4C2414yes—
704C2×C22⋊C4C2418yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C22⋊C4C2414yes—
709C2×C22⋊C4C2414yes—
710C2×C22⋊C4C2414yes—
711C2×C22⋊C4C2414yes—
712C2×C22⋊C4C2414yes—
713C2×C22⋊C4C2418yes—
714C2×C22⋊C4C2418yes—
715C2×C22⋊C4C2418yes—
716C2×C22⋊C4C2414yes—
717C2×C22⋊C4C2414yes—
718C2×C22⋊C4C2418yes—
719C2×C22⋊C4C2418yes—
720C2×C22⋊C4C2414yes—
721C2×C22⋊C4C2414yes—
722C2×C22⋊C4C2418yes—
723C2×C22⋊C4C2414yes—
724C2×C22⋊C4C2412yes—
725C2×C42—24no—
726C2×C42—24no—
727C2×C42—44no—
728C2×C42C2412yes—
729C2×C42C2411yescharacteristic
730C2×C42C2412yes—
731C2×C42C2412yes—
732C2×C42C2412yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736C2×C42C2411yescharacteristic
737C2×C42C2414yes—
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2414yes—
741C2×C42C2414yes—
742C2×C42C2414yes—
743C2×C42C2414yes—
744C2×C42C2418yes—
745#95C2414yes—
746#95C2418yes—
747#95C2412yes—
748#95C2412yes—
749#95C2412yes—
750#95C2412yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2414yes—
757#95C2414yes—
758#95C2418yes—
759#95C2414yes—
760#95C2414yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764#95C2418yes—
765#95C2414yes—
766#95C2418yes—
767#95C2414yes—
768#95C2414yes—
769#95C2418yes—
770#95C2418yes—
771#95C2414yes—
772#95C2414yes—
773#95C2418yes—
774#95C2418yes—
775#95C2418yes—
776#95C2418yes—
777#95C2418yes—
778C24—22no—
779C24—24no—
780C24—22no—
781C24—22no—
782C24—42no—
783C24C2512yes—
784C24C2512yes—
785C24C2512yes—
786C24C2512yes—
787C24C2511yescharacteristic
788#41—232no—
789#41—432no—
790#41—464no—
791#41—432no—
792#41—416no—
793#41—416no—
794C2×Q8—22no—
795C2×Q8—28no—
796C2×Q8—24no—
797C2×Q8—22no—
798C2×Q8—24no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—22no—
802C2×Q8—22no—
803C2×Q8—24no—
804C2×Q8—24no—
805C2×Q8—24no—
806C2×Q8—22no—
807C2×Q8—22no—
808C2×Q8—24no—
809C2×Q8—28no—
810C2×Q8—44no—
811C2×Q8—44no—
812C2×Q8—44no—
813C2×Q8—44no—
814C2×Q8—432no—
815C2×Q8—432no—
816C2×Q8—416no—
817C2×Q8C2×#4114yes—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4—24no—
823C2×D4—28no—
824C2×D4—24no—
825C2×D4—24no—
826C2×D4—24no—
827C2×D4—24no—
828C2×D4—24no—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—28no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—22no—
836C2×D4—22no—
837C2×D4—22no—
838C2×D4—22no—
839C2×D4—22no—
840C2×D4—28no—
841C2×D4—44no—
842C2×D4—44no—
843C2×D4—44no—
844C2×D4—44no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—44no—
850C2×D4—48no—
851C2×D4C2×#4118yes—
852C2×D4C2×#4114yes—
853C22×C4—24no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—22no—
857C22×C4—28no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—24no—
864C22×C4—24no—
865C22×C4—24no—
866C22×C4—24no—
867C22×C4—24no—
868C22×C4—24no—
869C22×C4—24no—
870C22×C4—28no—
871C22×C4—24no—
872C22×C4—24no—
873C22×C4—24no—
874C22×C4—24no—
875C22×C4—24no—
876C22×C4—24no—
877C22×C4—24no—
878C22×C4—24no—
879C22×C4—24no—
880C22×C4—24no—
881C22×C4—24no—
882C22×C4—28no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—48no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—416no—
902C22×C4—816no—
903C22×C4C2×#4118yes—
904C22×C4C2×#4114yes—
905C22×C4H(5,𝔽2)14yes—
906C22×C4H(5,𝔽2)14yes—
907C22×C4C2512yes—
908C22×C4C2514yes—
909C22×C4C2512yes—
910C22×C4C2514yes—
911C22×C4C2512yes—
912C22×C4C2514yes—
913C22×C4C2514yes—
914C22×C4C2514yes—
915C22×C4C2512yes—
916C22×C4C2514yes—
917C22×C4C2512yes—
918C22×C4C2514yes—
919C22×C4C2512yes—
920C22×C4C2512yes—
921C22×C4C2514yes—
922C22×C4C2512yes—
923C22×C4C2512yes—
924C22×C4C2512yes—
925C22×C4C2511yescharacteristic
926C22×C4C2511yescharacteristic
927C4⋊C4—24no—
928C4⋊C4—28no—
929C4⋊C4—28no—
930C4⋊C4—24no—
931C4⋊C4—24no—
932C4⋊C4—24no—
933C4⋊C4—24no—
934C4⋊C4—24no—
935C4⋊C4—24no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—24no—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—28no—
942C4⋊C4—48no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—48no—
946C4⋊C4—48no—
947C4⋊C4—48no—
948C4⋊C4—48no—
949C4⋊C4—48no—
950C4⋊C4—44no—
951C4⋊C4—44no—
952C4⋊C4—44no—
953C4⋊C4—48no—
954C4⋊C4—44no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—48no—
959C4⋊C4—48no—
960C4⋊C4—48no—
961C4⋊C4—44no—
962C22⋊C4—24no—
963C22⋊C4—28no—
964C22⋊C4—28no—
965C22⋊C4—24no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—24no—
970C22⋊C4—28no—
971C22⋊C4—28no—
972C22⋊C4—28no—
973C22⋊C4—24no—
974C22⋊C4—24no—
975C22⋊C4—28no—
976C22⋊C4—28no—
977C22⋊C4—28no—
978C22⋊C4—48no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—44no—
986C22⋊C4—44no—
987C22⋊C4—48no—
988C22⋊C4—48no—
989C22⋊C4—48no—
990C22⋊C4—44no—
991C22⋊C4—44no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—44no—
995C22⋊C4—44no—
996C22⋊C4—48no—
997C22⋊C4—44no—
998C22⋊C42−1+418yescomplemented
999C42—24no—
1000C42—22no—
1001C42—22no—
1002C42—24no—
1003C42—22no—
1004C42—22no—
1005C42—24no—
1006C42—24no—
1007C42—24no—
1008C42—24no—
1009C42—24no—
1010C42—28no—
1011C42—44no—
1012C42—44no—
1013C42—44no—
1014C42—44no—
1015C42—48no—
1016C23—22no—
1017C23—22no—
1018C23—28no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—24no—
1026C23—24no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—48no—
1040C23—48no—
1041C23—44no—
1042C23—44no—
1043C23C22×#4114yes—
1044C23C22×#4112yes—
1045C23C2×H(5,𝔽2)12yes—
1046C23C2×H(5,𝔽2)12yes—
1047C23C2×2−1+414yes—
1048C23C2611yescharacteristic
1049Q8—28no—
1050Q8—416no—
1051Q8—48no—
1052Q8—44no—
1053Q8—48no—
1054Q8—44no—
1055Q8—88no—
1056D4—216no—
1057D4—28no—
1058D4—416no—
1059D4—416no—
1060D4—416no—
1061D4—48no—
1062D4—48no—
1063D4—44no—
1064D4—44no—
1065D4—88no—
1066D4—88no—
1067D4—164no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—216no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—24no—
1084C2×C4—24no—
1085C2×C4—24no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—24no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—28no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—28no—
1113C2×C4—24no—
1114C2×C4—28no—
1115C2×C4—48no—
1116C2×C4—48no—
1117C2×C4—416no—
1118C2×C4—416no—
1119C2×C4—44no—
1120C2×C4—48no—
1121C2×C4—48no—
1122C2×C4—48no—
1123C2×C4—48no—
1124C2×C4—48no—
1125C2×C4—88no—
1126C2×C4—84no—
1127C2×C4—84no—
1128C2×C4—84no—
1129C2×C4—816no—
1130C2×C4—164no—
1131C2×C4—164no—
1132C2×C4#538116yes—
1133C2×C4C22×#4114yes—
1134C2×C4C22×#4112yes—
1135C2×C4C22×#4112yes—
1136C2×C4C2×H(5,𝔽2)12yes—
1137C2×C4C2×H(5,𝔽2)12yes—
1138C2×C4C2×H(5,𝔽2)12yes—
1139C2×C4C2×H(5,𝔽2)12yes—
1140C2×C4C2×2−1+414yes—
1141C2×C4C2×2−1+414yes—
1142C22—24no—
1143C22—22no—
1144C22—22no—
1145C22—24no—
1146C22—24no—
1147C22—28no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—416no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—44no—
1158C22—42no—
1159C22—44no—
1160C22—44no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—44no—
1168C22—44no—
1169C22C2×#53814yes—
1170C22C23×#4111yescharacteristic
1171C22C22×H(5,𝔽2)11yescharacteristic
1172C22C22×H(5,𝔽2)11yescharacteristic
1173C22C22×2−1+412yes—
1174C22H(7,𝔽2)12yes—
1175C4—24no—
1176C4—24no—
1177C4—24no—
1178C4—42no—
1179C4—44no—
1180C4—42no—
1181C4—44no—
1182C4—44no—
1183C4—44no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—44no—
1188C4—42no—
1189C4—42no—
1190C4—44no—
1191C4—44no—
1192C4—44no—
1193C4C2×#53814yes—
1194C4C2×#53814yes—
1195C2—24no—
1196C2—44no—
1197C2—44no—
1198C2—82no—
1199C2—82no—
1200C2C22×#53811yescharacteristic
1201C2#6283311yescharacteristic
1202C2#6287611yescharacteristic
1203C2#6294412yes—
1204C2#6300012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42936C2semidirect
2. #42829C2semidirect
3. #42552C2semidirect
4. #42504C2semidirect
5. #40845C2semidirect
6. #40140C2semidirect
7. #40006C2semidirect
8. #39654C2semidirect
9. #39632C2semidirect
10. #38509C2semidirect
11. #35660C2semidirect
12. #35659C2semidirect
13. #35633C2semidirect
14. #35628C2semidirect
15. #35557C2semidirect
16. #35530C2semidirect
17. #35313C2semidirect
18. #35280C2semidirect
19. #35223C2semidirect
20. #34813C2semidirect
21. C2×#2502C2semidirect
22. #34743C2semidirect
23. #34259C2semidirect
24. #34207C2semidirect
25. #34200C2semidirect
39. #2863C22semidirect
40. #2857C22semidirect
42. #2831C22semidirect
43. #2827C22semidirect
44. #2806C22semidirect
47. #2788C22semidirect
50. #2768C22semidirect
51. #2765C22semidirect
52. #2761C22semidirect
53. #2756C22semidirect
57. #2702C22semidirect
58. #2695C22semidirect
60. #2666C22semidirect
62. #2653C22semidirect
63. #2646C22semidirect
64. #2645C22semidirect
66. #2630C22semidirect
67. #2629C22semidirect
69. #2592C22semidirect
70. #2587C22semidirect
71. #2582C22semidirect
73. #2568C22semidirect
75. #2538C22semidirect
77. #2514C22semidirect
78. #2512C22semidirect
79. #2511C22semidirect
80. #2511C22semidirect
85. #2502C22semidirect
86. #2501C22semidirect
87. #2500C22semidirect
88. #2499C22semidirect
89. #2497C22semidirect
90. #2496C22semidirect
93. #2492C22semidirect
97. #2489C22semidirect
105. #2450C22semidirect
107. #2436C22semidirect
108. #2434C22semidirect
109. #2432C22semidirect
110. #2431C22semidirect
120. #2423C22semidirect
121. #2422C22semidirect
131. #2409C22semidirect
134. #2407C22semidirect
143. #2354C22semidirect
146. D4×C4⋊C4C22semidirect
147. Q8×C22⋊C4C22semidirect
149. #2339C22semidirect
151. #2326C22semidirect
152. #2326C22semidirect
163. #2311C22semidirect
166. #2310C22semidirect
167. C4×C4⋊Q8C22semidirect
168. C4×#127C22semidirect
175. #2297C22semidirect
179. C2×#391C22semidirect
998. C22⋊C42−1+4semidirect

Maximal subgroups

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

subgroupindex
#429362
#428292
#425522
#425042
#408452
#401402
#400062
#396542
#396322
#385092
#356602
#356592
#356332
#356282
#355572
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#353132
#352802
#352232
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C2×#25022
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#342072
#342002