Finite Group Databasebeta

← #7646606

Subgroups — #7646606

Order 512.

4816 conjugacy classes of subgroups.

The subgroup lattice has 1187 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42694C214yesmaximal, complemented
2#42692C214yesmaximal, complemented
3#42662C214yesmaximal, complemented
4#42660C214yesmaximal, complemented
5#39761C212yesmaximal, complemented
6#39737C212yesmaximal, complemented
7#39505C212yesmaximal, complemented
8#39479C212yesmaximal, complemented
9#39194C212yesmaximal, complemented
10#39158C212yesmaximal, complemented
11#38978C212yesmaximal, complemented
12#38940C212yesmaximal, complemented
13#37492C214yesmaximal, complemented
14#36988C218yesmaximal, complemented
15#35544C212yesmaximal, complemented
16#35542C212yesmaximal, complemented
17#35280C211yesmaximal, characteristic, complemented
18#35275C211yesmaximal, characteristic, complemented
19#35228C214yesmaximal, complemented
20#35157C212yesmaximal, complemented
21#35151C212yesmaximal, complemented
22#34946C211yesmaximal, characteristic, complemented
23#34935C211yesmaximal, characteristic
24#34213C211yesmaximal, characteristic, complemented
25C2×#2354C211yesmaximal, characteristic, complemented
26#34060C211yesmaximal, characteristic, complemented
27C2×#544C2212yes—
28C2×#533C2211yescharacteristic
29C2×#525C2212yes—
30C2×C4×#41C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×#117C2212yes—
33#2868C2212yescomplemented
34#2859C2212yescomplemented
35#2857C2212yescomplemented
36#2857C2212yescomplemented
37#2855C2218yes—
38#2853C2218yes—
39#2830C2218yes—
40#2829C2218yes—
41#2801C2218yescomplemented
42#2800C2218yescomplemented
43#2795C2218yescomplemented
44#2793C2218yescomplemented
45#2777C2218yescomplemented
46#2775C2218yescomplemented
47#2772C2218yescomplemented
48#2772C2218yescomplemented
49#2759C2218yescomplemented
50#2754C2218yescomplemented
51#2741C2218yescomplemented
52#2737C2218yescomplemented
53#2731C2218yescomplemented
54#2716C2218yescomplemented
55#2702C2218yescomplemented
56#2700C2218yescomplemented
57#2662C2218yes—
58#2660C2214yescomplemented
59#2655C2218yescomplemented
60#2651C2218yes—
61#2650C2218yescomplemented
62#2644C2214yes—
63#2640C2214yes—
64#2629C2214yescomplemented
65#2626C2218yes—
66#2624C2214yes—
67#2622C2218yes—
68#2620C2214yes—
69#2582C2212yescomplemented
70#2582C2212yescomplemented
71#2563C2211yescharacteristic
72#2563C2211yescharacteristic
73#2563C2214yescomplemented
74#2562C2212yes—
75#2562C2212yes—
76#2562C2214yescomplemented
77#2562C2214yescomplemented
78#2561C2214yes—
79#2552C2212yescomplemented
80#2552C2212yescomplemented
81#2551C2212yescomplemented
82#2551C2212yescomplemented
83#2547C2211yescharacteristic
84#2547C2211yescharacteristic
85#2547C2214yescomplemented
86#2538C2211yescharacteristic
87#2538C2211yescharacteristic
88#2538C2212yescomplemented
89#2538C2212yescomplemented
90#2537C2211yescharacteristic
91#2537C2211yescharacteristic
92#2536C2212yes—
93#2535C2212yes—
94#2534C2214yes—
95#2525C2218yescomplemented
96#2520C2218yescomplemented
97#2512C2214yes—
98#2511C2214yescomplemented
99#2509C2214yescomplemented
100#2503C2212yes—
101#2500C2214yescomplemented
102#2500C2214yescomplemented
103#2499C2214yescomplemented
104#2499C2214yescomplemented
105#2497C2214yescomplemented
106#2497C2214yescomplemented
107#2496C2214yescomplemented
108#2496C2214yescomplemented
109#2495C2214yescomplemented
110#2495C2214yescomplemented
111#2494C2214yescomplemented
112#2494C2214yescomplemented
113#2494C2214yescomplemented
114#2493C2218yes—
115#2492C2214yescomplemented
116#2492C2214yescomplemented
117#2491C2214yes—
118#2491C2214yescomplemented
119#2490C2214yescomplemented
120#2489C2214yescomplemented
121#2488C2218yes—
122#2486C2212yes—
123#2485C2214yescomplemented
124#2485C2214yescomplemented
125#2485C2214yescomplemented
126#2485C2214yescomplemented
127#2480C2218yes—
128#2472C2218yes—
129#2448C2214yes—
130#2441C2214yescomplemented
131#2441C2214yescomplemented
132#2441C2214yescomplemented
133#2441C2214yescomplemented
134#2440C2214yes—
135#2440C2214yes—
136#2439C2214yescomplemented
137#2439C2214yescomplemented
138#2439C2214yescomplemented
139#2439C2214yescomplemented
140#2435C2212yes—
141#2426C2214yes—
142#2417C2214yes—
143#2417C2214yes—
144#2408C2212yes—
145#2398C2214yes—
146#2392C2214yes—
147#2370C2214yescomplemented
148#2369C2212yescomplemented
149#2365C2212yescomplemented
150#2355C2212yescomplemented
151#2355C2214yescomplemented
152#2354C2212yes—
153#2354C2212yes—
154#2354C2212yes—
155#2354C2212yes—
156#2354C2214yes—
157#2354C2214yes—
158Q8×C4⋊C4C2212yescomplemented
159#2331C2214yescomplemented
160#2329C2214yes—
161#2323C2214yescomplemented
162#2320C2212yescomplemented
163#2320C2214yescomplemented
164#2319C2212yescomplemented
165#2318C2214yes—
166#2317C2211yescharacteristic
167#2317C2211yescharacteristic
168#2317C2212yes—
169#2317C2212yes—
170#2316C2212yes—
171#2314C2212yescomplemented
172#2314C2212yescomplemented
173#2314C2214yescomplemented
174#2311C2211yescharacteristic
175#2311C2211yescharacteristic
176#2311C2212yes—
177C4×#124C2212yes—
178C4×#124C2212yes—
179C4×C22⋊Q8C2214yes—
180C4×#121C2212yes—
181C4×#121C2212yes—
182#2295C2212yescomplemented
183#2293C2212yescomplemented
184C2×#390C2212yes—
185#2290C2214yes—
186C2×#388C2214yes—
187#2285C2211yescharacteristic
188#2285C2212yescomplemented
189C2×#384C2211yescharacteristic
190#2283C2212yescomplemented
191#2280C2212yes—
192#2280C2212yes—
193#2280C2212yes—
194C2×#380C2212yes—
195#2274C2212yes—
196C4×#117C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C23×D4C2311yescharacteristic
201C24×C4C2312yes—
202#544—48no—
203#533—28no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2314yes—
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×#126C2318yes—
211C2×#125C2312yes—
212C2×#125C2314yes—
213C2×#125C2314yes—
214C2×#124C2312yes—
215C2×#124C2312yes—
216C2×#124C2318yes—
217#525—48no—
218C2×#123C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2318yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2314yes—
226C2×#121C2312yes—
227C2×#121C2312yes—
228C2×#121C2312yes—
229C2×#121C2312yes—
230C2×#120C2314yes—
231C4×#41—28no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×D4—28no—
238C2×C4×D4C2312yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2312yes—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2312yes—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2314yes—
249C2×C4×D4C2314yes—
250C2×#117—48no—
251C2×#117C2312yes—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C2×#117C2312yes—
257C2×#117C2314yes—
258C2×#117C2314yes—
259C2×#117C2314yes—
260C2×#117C2314yes—
261C2×#117C2314yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2312yes—
267C22×C4⋊C4C2312yes—
268C22×C22⋊C4C2312yes—
269C22×C22⋊C4C2314yes—
270C22×C22⋊C4C2314yes—
271C22×C42C2312yes—
272C22×C42C2314yes—
273C22×C42C2312yes—
274C22×C42C2311yescharacteristic
275#401C2318yes—
276#400C2314yes—
277#400C2314yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#399C2318yes—
284#399C2318yes—
285#398C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2314yes—
289#398C2318yes—
290#397C2314yes—
291#397C2314yes—
292#397C2318yes—
293#397C2318yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2314yes—
301#397C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2314yes—
310#396C2314yes—
311#395C2318yes—
312#395C2318yes—
313#394C2314yes—
314#394C2314yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2314yes—
320#394C2318yes—
321#394C2318yes—
322#394C2314yes—
323#394C2314yes—
324#393C2314yes—
325#393C2314yes—
326#393C2318yes—
327#393C2318yes—
328#393C2318yes—
329#393C2318yes—
330#392C2314yes—
331#391C2312yes—
332#391C2312yes—
333#391C2314yes—
334#391C2312yes—
335#391C2314yes—
336#391C2312yes—
337#391C2314yes—
338#391C2318yes—
339#391C2318yes—
340#391C2318yes—
341#391C2318yes—
342#391C2314yes—
343#390C2312yes—
344#390C2312yes—
345#390C2318yes—
346#390C2312yes—
347#390C2312yes—
348#390C2314yes—
349#390C2318yes—
350#390C2314yes—
351#390C2314yes—
352#390C2312yes—
353#390C2312yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2312yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2312yes—
367#389C2314yes—
368#389C2318yes—
369#389C2314yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2312yes—
374#389C2318yes—
375#389C2314yes—
376#389C2314yes—
377#389C2314yes—
378#388C2314yes—
379#388C2314yes—
380#388C2314yes—
381#388C2314yes—
382#388C2318yes—
383#388C2318yes—
384#388C2318yes—
385#388C2318yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2318yes—
391#388C2318yes—
392#388C2318yes—
393#388C2318yes—
394#388C2318yes—
395#388C2318yes—
396#388C2318yes—
397#388C2318yes—
398#388C2318yes—
399#388C2318yes—
400#388C2318yes—
401#388C2314yes—
402#388C2314yes—
403#387C2314yes—
404#387C2314yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2318yes—
410#387C2318yes—
411#387C2318yes—
412#387C2318yes—
413#387C2318yes—
414#387C2318yes—
415#387C2318yes—
416#387C2318yes—
417#387C2318yes—
418#387C2318yes—
419#387C2318yes—
420#387C2318yes—
421#386C2314yes—
422#386C2314yes—
423#386C2318yes—
424#386C2314yes—
425#386C2314yes—
426#385C2314yes—
427#385C2314yes—
428#385C2318yes—
429#385C2318yes—
430#384C2312yes—
431#384C2312yes—
432#384C2314yes—
433#384C2314yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2311yescharacteristic
439#384C2312yes—
440#384C2311yescharacteristic
441#384C2314yes—
442#383C2314yes—
443#383C2318yes—
444#382C2312yes—
445#382C2312yes—
446#382C2318yes—
447#382C2312yes—
448#382C2312yes—
449#382C2314yes—
450#382C2314yes—
451#382C2314yes—
452#382C2312yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2312yes—
460#380C2312yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2314yes—
467#380C2314yes—
468#380C2314yes—
469#380C2314yes—
470#380C2312yes—
471#380C2312yes—
472#380C2312yes—
473#380C2312yes—
474#380C2314yes—
475#380C2318yes—
476#380C2314yes—
477#380C2312yes—
478#380C2312yes—
479#380C2314yes—
480#380C2314yes—
481#380C2314yes—
482#380C2312yes—
483#380C2312yes—
484#380C2312yes—
485#380C2312yes—
486#380C2312yes—
487#379C2314yes—
488#379C2314yes—
489#379C2314yes—
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2311yescharacteristic
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2312yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2312yes—
504C4×C4⋊C4C2318yes—
505C4×C4⋊C4C2314yes—
506C4×C4⋊C4C2318yes—
507C4×C4⋊C4C2312yes—
508C4×C4⋊C4C2312yes—
509C4×C4⋊C4C2314yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2318yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2314yes—
517C4×C22⋊C4C2314yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2312yes—
520#376C2312yes—
521#376C2314yes—
522C2×#95C2312yes—
523C2×#95C2314yes—
524C43C2312yes—
525C25C2412yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41—24no—
529C22×Q8C2412yes—
530C22×Q8C2411yescharacteristic
531C22×Q8C2412yes—
532C22×Q8C2418yes—
533C22×D4—24no—
534C22×D4—42no—
535C22×D4—42no—
536C22×D4C2412yes—
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2412yes—
541C22×D4C2414yes—
542C22×D4C2414yes—
543C23×C4—28no—
544C23×C4—28no—
545C23×C4—28no—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2412yes—
552C23×C4C2412yes—
553C23×C4C2411yescharacteristic
554C23×C4C2414yes—
555C23×C4C2412yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C4⋊Q8—24no—
561C4⋊Q8—24no—
562C4⋊Q8—48no—
563C4⋊Q8—48no—
564C4⋊Q8—48no—
565C4⋊Q8—84no—
566#126—88no—
567#125—28no—
568#125—48no—
569#125—48no—
570#124—44no—
571#124—44no—
572#124—88no—
573#123—48no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—416no—
577C22⋊Q8—48no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—84no—
581#121—44no—
582#121—44no—
583#121—44no—
584#121—44no—
585#120—48no—
586C4×Q8—24no—
587C4×Q8—24no—
588C4×Q8—28no—
589C4×Q8—28no—
590C4×Q8—48no—
591C4×D4—28no—
592C4×D4—28no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—28no—
596C4×D4—28no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—48no—
602C4×D4—48no—
603#117—24no—
604#117—28no—
605#117—28no—
606#117—24no—
607#117—24no—
608#117—28no—
609#117—48no—
610#117—48no—
611#117—48no—
612#117—48no—
613#117—48no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—28no—
617C2×C4⋊C4—24no—
618C2×C4⋊C4—44no—
619C2×C4⋊C4—82no—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2412yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2412yes—
667C2×C4⋊C4C2418yes—
668C2×C22⋊C4—28no—
669C2×C22⋊C4—48no—
670C2×C22⋊C4—84no—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2412yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2412yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2418yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2418yes—
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⋊C4C2414yes—
705C2×C22⋊C4C2414yes—
706C2×C22⋊C4C2414yes—
707C2×C22⋊C4C2414yes—
708C2×C42—28no—
709C2×C42—44no—
710C2×C42—48no—
711C2×C42#4118yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2414yes—
715C2×C42C2414yes—
716C2×C42C2414yes—
717C2×C42C2412yes—
718C2×C42C2412yes—
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2412yes—
722C2×C42C2418yes—
723C2×C42C2418yes—
724C2×C42C2418yes—
725C2×C42C2418yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#95C2418yes—
734#95C2418yes—
735#95C2414yes—
736#95C2414yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2414yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773C24—24no—
774C24—24no—
775C24—24no—
776C24—42no—
777C24—42no—
778C24—42no—
779C24—42no—
780C24C2512yes—
781C24C2512yes—
782C24C2512yes—
783C24C2511yescharacteristic
784#41—416no—
785C2×Q8—22no—
786C2×Q8—24no—
787C2×Q8—24no—
788C2×Q8—22no—
789C2×Q8—22no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—48no—
795C2×Q8—48no—
796C2×Q8—48no—
797C2×D4—24no—
798C2×D4—24no—
799C2×D4—24no—
800C2×D4—24no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4—22no—
807C2×D4—22no—
808C2×D4—22no—
809C2×D4—22no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—416no—
813C2×D4—44no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—44no—
818C2×D4—44no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—28no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—24no—
834C22×C4—24no—
835C22×C4—24no—
836C22×C4—24no—
837C22×C4—24no—
838C22×C4—24no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—24no—
846C22×C4—42no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—432no—
857C22×C4C2×#4114yes—
858C22×C4C2×#4114yes—
859C22×C4C2×#4114yes—
860C22×C4H(5,𝔽2)14yes—
861C22×C42−1+414yes—
862C22×C4C2512yes—
863C22×C4C2512yes—
864C22×C4C2512yes—
865C22×C4C2512yes—
866C22×C4C2514yes—
867C22×C4C2512yes—
868C22×C4C2514yes—
869C22×C4C2514yes—
870C22×C4C2512yes—
871C22×C4C2512yes—
872C22×C4C2512yes—
873C22×C4C2514yes—
874C22×C4C2514yes—
875C22×C4C2514yes—
876C22×C4C2512yes—
877C22×C4C2518yes—
878C22×C4C2511yescharacteristic
879C22×C4C2511yescharacteristic
880C22×C4C2511yescharacteristic
881C22×C4C2511yescharacteristic
882C22×C4C2511yescharacteristic
883C22×C4C2511yescharacteristic
884C4⋊C4—24no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—28no—
894C4⋊C4—28no—
895C4⋊C4—24no—
896C4⋊C4—24no—
897C4⋊C4—24no—
898C4⋊C4—24no—
899C4⋊C4—28no—
900C4⋊C4—28no—
901C4⋊C4—24no—
902C4⋊C4—24no—
903C4⋊C4—22no—
904C4⋊C4—22no—
905C4⋊C4—24no—
906C4⋊C4—24no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—28no—
910C4⋊C4—24no—
911C4⋊C4—24no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C4—42no—
916C4⋊C4—44no—
917C4⋊C4—48no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—44no—
921C4⋊C4—44no—
922C4⋊C4—48no—
923C4⋊C4—48no—
924C4⋊C4—48no—
925C4⋊C4—48no—
926C4⋊C4—48no—
927C4⋊C4—48no—
928C4⋊C4—44no—
929C4⋊C4—48no—
930C4⋊C4—48no—
931C4⋊C4—42no—
932C22⋊C4—24no—
933C22⋊C4—28no—
934C22⋊C4—28no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—24no—
940C22⋊C4—24no—
941C22⋊C4—24no—
942C22⋊C4—24no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—44no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—44no—
965C22⋊C4—44no—
966C22⋊C4—44no—
967C22⋊C4—44no—
968C22⋊C4—44no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—28no—
973C42—28no—
974C42—24no—
975C42—24no—
976C42—28no—
977C42—24no—
978C42—24no—
979C42—44no—
980C42—48no—
981C42—48no—
982C42—42no—
983C42—48no—
984C42—48no—
985C42—42no—
986C42C2×#4114yes—
987C42C2×#4114yes—
988C42C2×#4114yes—
989C42C2×#4114yes—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—48no—
1016C23—48no—
1017C23—48no—
1018C23—84no—
1019C23—84no—
1020C23—84no—
1021C23—84no—
1022C23C22×#4112yes—
1023C23C2×H(5,𝔽2)12yes—
1024C23C2×2−1+412yes—
1025C23C2611yescharacteristic
1026Q8—44no—
1027Q8—48no—
1028Q8—84no—
1029Q8—168no—
1030D4—48no—
1031D4—48no—
1032D4—44no—
1033D4—44no—
1034D4—44no—
1035D4—88no—
1036D4—88no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—28no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—24no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—28no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—24no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—28no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—24no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—28no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—24no—
1091C2×C4—24no—
1092C2×C4—44no—
1093C2×C4—48no—
1094C2×C4—48no—
1095C2×C4—48no—
1096C2×C4—48no—
1097C2×C4—48no—
1098C2×C4—48no—
1099C2×C4—48no—
1100C2×C4—48no—
1101C2×C4—84no—
1102C2×C4—84no—
1103C2×C4—88no—
1104C2×C4#542116yes—
1105C2×C4C22×#4112yes—
1106C2×C4C22×#4112yes—
1107C2×C4C22×#4112yes—
1108C2×C4C22×#4112yes—
1109C2×C4C22×#4112yes—
1110C2×C4C22×#4112yes—
1111C2×C4C2×H(5,𝔽2)12yes—
1112C2×C4C2×H(5,𝔽2)12yes—
1113C2×C4C2×2−1+412yes—
1114C2×C4C2×2−1+412yes—
1115C2×C4#58512yes—
1116C2×C4#58512yes—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—22no—
1122C22—22no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22—816no—
1145C22C2×#54214yes—
1146C22C23×#4111yescharacteristic
1147C22C22×H(5,𝔽2)11yescharacteristic
1148C22C22×2−1+411yescharacteristic
1149C22C2×#58511yescharacteristic
1150C22C2×#58511yescharacteristic
1151C22H(7,𝔽2)11yescharacteristic
1152C222−1+611yescharacteristic
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—42no—
1157C4—44no—
1158C4—42no—
1159C4—44no—
1160C4—42no—
1161C4—44no—
1162C4—44no—
1163C4—42no—
1164C4—44no—
1165C4—42no—
1166C4—42no—
1167C4—42no—
1168C4—48no—
1169C4—44no—
1170C4—42no—
1171C4—42no—
1172C4C2×#54214yes—
1173C4C2×#54214yes—
1174C4#349314yes—
1175C2—24no—
1176C2—82no—
1177C2—82no—
1178C2—82no—
1179C2C22×#54211yescharacteristic
1180C2C2×#349311yescharacteristic
1181C2#6285611yescharacteristic
1182C2#6292511yescharacteristic
1183C2#6292911yescharacteristic
1184C2#6295511yescharacteristic
1185C2#6295911yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#34935C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42694C2semidirect
2. #42692C2semidirect
3. #42662C2semidirect
4. #42660C2semidirect
5. #39761C2semidirect
6. #39737C2semidirect
7. #39505C2semidirect
8. #39479C2semidirect
9. #39194C2semidirect
10. #39158C2semidirect
11. #38978C2semidirect
12. #38940C2semidirect
13. #37492C2semidirect
14. #36988C2semidirect
15. #35544C2semidirect
16. #35542C2semidirect
17. #35280C2semidirect
18. #35275C2semidirect
19. #35228C2semidirect
20. #35157C2semidirect
21. #35151C2semidirect
22. #34946C2semidirect
24. #34213C2semidirect
25. C2×#2354C2semidirect
26. #34060C2semidirect
33. #2868C22semidirect
34. #2859C22semidirect
35. #2857C22semidirect
36. #2857C22semidirect
41. #2801C22semidirect
42. #2800C22semidirect
43. #2795C22semidirect
44. #2793C22semidirect
45. #2777C22semidirect
46. #2775C22semidirect
47. #2772C22semidirect
48. #2772C22semidirect
49. #2759C22semidirect
50. #2754C22semidirect
51. #2741C22semidirect
52. #2737C22semidirect
53. #2731C22semidirect
54. #2716C22semidirect
55. #2702C22semidirect
56. #2700C22semidirect
58. #2660C22semidirect
59. #2655C22semidirect
61. #2650C22semidirect
64. #2629C22semidirect
69. #2582C22semidirect
70. #2582C22semidirect
73. #2563C22semidirect
76. #2562C22semidirect
77. #2562C22semidirect
79. #2552C22semidirect
80. #2552C22semidirect
81. #2551C22semidirect
82. #2551C22semidirect
85. #2547C22semidirect
88. #2538C22semidirect
89. #2538C22semidirect
95. #2525C22semidirect
96. #2520C22semidirect
98. #2511C22semidirect
99. #2509C22semidirect
101. #2500C22semidirect
102. #2500C22semidirect
103. #2499C22semidirect
104. #2499C22semidirect
105. #2497C22semidirect
106. #2497C22semidirect
107. #2496C22semidirect
108. #2496C22semidirect
109. #2495C22semidirect
110. #2495C22semidirect
111. #2494C22semidirect
112. #2494C22semidirect
113. #2494C22semidirect
115. #2492C22semidirect
116. #2492C22semidirect
118. #2491C22semidirect
119. #2490C22semidirect
120. #2489C22semidirect
123. #2485C22semidirect
124. #2485C22semidirect
125. #2485C22semidirect
126. #2485C22semidirect
130. #2441C22semidirect
131. #2441C22semidirect
132. #2441C22semidirect
133. #2441C22semidirect
136. #2439C22semidirect
137. #2439C22semidirect
138. #2439C22semidirect
139. #2439C22semidirect
147. #2370C22semidirect
148. #2369C22semidirect
149. #2365C22semidirect
150. #2355C22semidirect
151. #2355C22semidirect
158. Q8×C4⋊C4C22semidirect
159. #2331C22semidirect
161. #2323C22semidirect
162. #2320C22semidirect
163. #2320C22semidirect
164. #2319C22semidirect
171. #2314C22semidirect
172. #2314C22semidirect
173. #2314C22semidirect
182. #2295C22semidirect
183. #2293C22semidirect
188. #2285C22semidirect
190. #2283C22semidirect

Maximal subgroups

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

subgroupindex
#426942
#426922
#426622
#426602
#397612
#397372
#395052
#394792
#391942
#391582
#389782
#389402
#374922
#369882
#355442
#355422
#352802
#352752
#352282
#351572
#351512
#349462
#349352
#342132
C2×#23542
#340602