Finite Group Databasebeta

← #7643149

Subgroups — #7643149

Order 512.

5492 conjugacy classes of subgroups.

The subgroup lattice has 1161 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40225C214yesmaximal, complemented
2#40214C214yesmaximal, complemented
3#40200C214yesmaximal, complemented
4#40190C214yesmaximal, complemented
5#39790C214yesmaximal, complemented
6#39783C214yesmaximal, complemented
7#39663C214yesmaximal, complemented
8#39654C214yesmaximal, complemented
9#36823C218yesmaximal, complemented
10#36641C211yesmaximal, characteristic, complemented
11#36639C211yesmaximal, characteristic, complemented
12#35667C211yesmaximal, characteristic, complemented
13#35666C211yesmaximal, characteristic, complemented
14#35662C211yesmaximal, characteristic, complemented
15#35660C211yesmaximal, characteristic
16#35628C211yesmaximal, characteristic, complemented
17#35621C211yesmaximal, characteristic, complemented
18#35557C211yesmaximal, characteristic, complemented
19#35530C211yesmaximal, characteristic, complemented
20#35182C211yesmaximal, characteristic, complemented
21#35153C211yesmaximal, characteristic, complemented
22#35058C218yesmaximal, complemented
23#34266C211yesmaximal, characteristic, complemented
24#34257C211yesmaximal, characteristic, complemented
25C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
26C22×2−1+4C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#536C2211yescharacteristic
32C2×#533C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C22×C4⋊Q8C2211yescharacteristic
35C2×#520C2211yescharacteristic
36C2×#519C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38C22×C4×Q8C2211yescharacteristic
39#2863C2212yes—
40#2863C2212yes—
41#2862C2212yes—
42#2861C2212yes—
43#2861C2212yes—
44#2860C2212yes—
45#2860C2212yes—
46#2858C2212yes—
47#2854C2214yes—
48#2853C2214yes—
49#2852C2214yes—
50#2852C2214yes—
51#2850C2214yes—
52#2850C2214yes—
53#2806C2218yes—
54#2803C2218yes—
55#2800C2218yes—
56#2788C2218yes—
57#2788C2218yes—
58#2780C2218yes—
59#2779C2218yes—
60#2775C2218yes—
61#2774C2218yes—
62#2770C2218yes—
63#2768C2218yes—
64#2768C2218yes—
65#2727C2218yes—
66#2715C2218yes—
67#2710C2218yes—
68#2695C2218yes—
69#2666C2218yes—
70#2662C2218yes—
71#2651C2218yes—
72#2650C2218yes—
73#2623C2214yes—
74#2618C2214yes—
75#2597C2218yes—
76#2595C2218yes—
77#2593C2218yes—
78#2592C2214yes—
79#2589C2218yes—
80#2587C2218yes—
81#2586C2218yes—
82#2582C2214yes—
83#2581C2214yes—
84#2574C2218yes—
85#2568C2214yes—
86#2554C2218yes—
87#2547C2212yes—
88#2546C2214yes—
89#2546C2212yes—
90#2545C2214yes—
91#2545C2212yes—
92#2544C2212yes—
93#2512C2214yes—
94#2511C2214yes—
95#2502C2212yes—
96#2501C2212yes—
97#2500C2212yes—
98#2499C2212yes—
99#2497C2214yes—
100#2496C2214yes—
101#2492C2214yes—
102#2489C2214yes—
103#2488C2218yes—
104#2481C2218yes—
105#2453C2214yes—
106#2451C2214yes—
107#2448C2214yes—
108#2446C2214yes—
109#2443C2218yes—
110#2438C2218yes—
111#2436C2212yes—
112#2434C2214yes—
113#2434C2212yes—
114#2434C2212yes—
115#2434C2212yes—
116#2432C2212yes—
117#2432C2212yes—
118#2432C2214yes—
119#2432C2212yes—
120#2431C2212yes—
121#2430C2218yes—
122#2429C2214yes—
123#2429C2214yes—
124#2429C2214yes—
125#2429C2214yes—
126#2426C2214yes—
127#2426C2214yes—
128#2425C2218yes—
129#2423C2214yes—
130#2423C2214yes—
131#2422C2214yes—
132#2421C2214yes—
133#2417C2214yes—
134#2415C2214yes—
135#2413C2218yes—
136#2409C2214yes—
137#2407C2214yes—
138#2406C2218yes—
139#2367C2214yes—
140#2365C2214yes—
141#2362C2214yes—
142#2360C2214yes—
143#2341C2214yes—
144#2341C2214yes—
145Q8×C22⋊C4C2214yes—
146Q8×C22⋊C4C2214yes—
147#2337C2218yes—
148#2335C2218yes—
149#2334C2218yes—
150#2334C2218yes—
151#2322C2214yes—
152#2317C2211yescharacteristic
153#2316C2211yescharacteristic
154#2311C2211yescharacteristic
155#2311C2211yescharacteristic
156#2311C2211yescharacteristic
157#2311C2214yes—
158#2310C2211yescharacteristic
159#2310C2211yescharacteristic
160C4×C4⋊Q8C2214yes—
161C4×C4⋊Q8C2214yes—
162C4×C4⋊Q8C2214yes—
163C4×C4⋊Q8C2214yes—
164C4×#126C2214yes—
165C4×#126C2214yes—
166C4×#124C2214yes—
167C4×#124C2214yes—
168C4×#123C2214yes—
169#2297C2211yescharacteristic
170#2297C2211yescharacteristic
171#2297C2211yescharacteristic
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2214yes—
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#389C2214yes—
183C2×#384C2211yescharacteristic
184#2274C2211yescharacteristic
185C2×C4×C4⋊C4C2214yes—
186C2×C43C2211yescharacteristic
187C2×2−1+4—28no—
188C2×2−1+4—44no—
189C2×2−1+4—44no—
190C22×#41C2311yescharacteristic
191C22×#41C2311yescharacteristic
192C22×#41C2311yescharacteristic
193C22×#41C2314yes—
194C22×#41C2312yes—
195C22×#41C2312yes—
196C23×Q8C2311yescharacteristic
197C23×Q8C2311yescharacteristic
198C23×Q8C2312yes—
199C23×Q8C2312yes—
200#537—44no—
201#536—28no—
202#536—44no—
203#536—44no—
204#536—44no—
205#533—44no—
206#532—44no—
207C2×C4⋊Q8—28no—
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2312yes—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2312yes—
216C2×C4⋊Q8C2312yes—
217C2×#127C2311yescharacteristic
218C2×#126C2314yes—
219C2×#126C2314yes—
220C2×#126C2318yes—
221C2×#125C2312yes—
222C2×#124C2314yes—
223C2×#124C2312yes—
224C2×#124C2312yes—
225C2×#124C2314yes—
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2312yes—
229C2×#124C2312yes—
230C2×#123C2314yes—
231C2×#123C2318yes—
232C2×#123C2314yes—
233C2×#123C2314yes—
234C2×#123C2314yes—
235C2×C22⋊Q8C2314yes—
236C2×C22⋊Q8C2314yes—
237C2×C22⋊Q8C2312yes—
238C2×C22⋊Q8C2312yes—
239C2×C22⋊Q8C2314yes—
240C2×C22⋊Q8C2312yes—
241C2×C22⋊Q8C2312yes—
242C2×C22⋊Q8C2314yes—
243C2×#121C2314yes—
244C2×#121C2314yes—
245C2×#121C2312yes—
246C2×#121C2312yes—
247#520—44no—
248#519—44no—
249C2×C4×Q8—44no—
250C2×C4×Q8—44no—
251C2×C4×Q8C2314yes—
252C2×C4×Q8C2314yes—
253C2×C4×Q8C2314yes—
254C2×C4×Q8C2314yes—
255C2×C4×Q8C2314yes—
256C2×C4×Q8C2314yes—
257C2×C4×Q8C2314yes—
258C2×C4×Q8C2312yes—
259C2×C4×D4C2314yes—
260C2×C4×D4C2312yes—
261C2×C4×D4C2314yes—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2314yes—
268C2×#117C2312yes—
269C22×C4⋊C4C2311yescharacteristic
270C22×C4⋊C4C2311yescharacteristic
271C22×C4⋊C4C2314yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2312yes—
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2314yes—
276C22×C42C2312yes—
277C22×C42C2311yescharacteristic
278C22×C42C2311yescharacteristic
279C22×C42C2311yescharacteristic
280C22×C42C2312yes—
281C22×C42C2312yes—
282C22×C42C2312yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2318yes—
289#399C2318yes—
290#399C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#394C2318yes—
315#394C2318yes—
316#394C2318yes—
317#394C2318yes—
318#394C2318yes—
319#394C2318yes—
320#393C2318yes—
321#393C2318yes—
322#392C2318yes—
323#391C2314yes—
324#391C2314yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2312yes—
329#391C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2314yes—
334#391C2312yes—
335#391C2312yes—
336#391C2318yes—
337#391C2312yes—
338#391C2312yes—
339#391C2318yes—
340#391C2318yes—
341#391C2318yes—
342#391C2314yes—
343#391C2314yes—
344#391C2312yes—
345#391C2312yes—
346#391C2312yes—
347#391C2312yes—
348#391C2312yes—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390C2312yes—
352#390C2318yes—
353#390C2312yes—
354#390C2312yes—
355#390C2318yes—
356#390C2312yes—
357#390C2318yes—
358#390C2314yes—
359#390C2314yes—
360#390C2312yes—
361#390C2312yes—
362#390C2312yes—
363#390C2312yes—
364#390C2312yes—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2314yes—
372#389C2314yes—
373#389C2314yes—
374#389C2318yes—
375#389C2312yes—
376#389C2312yes—
377#389C2318yes—
378#389C2318yes—
379#389C2318yes—
380#389C2318yes—
381#389C2318yes—
382#389C2312yes—
383#389C2312yes—
384#389C2312yes—
385#389C2312yes—
386#388C2314yes—
387#388C2314yes—
388#388C2314yes—
389#388C2314yes—
390#388C2314yes—
391#388C2314yes—
392#388C2314yes—
393#388C2318yes—
394#388C2318yes—
395#388C2314yes—
396#388C2318yes—
397#388C2318yes—
398#388C2314yes—
399#388C2318yes—
400#388C2318yes—
401#388C2318yes—
402#388C2318yes—
403#388C2314yes—
404#388C2318yes—
405#388C2318yes—
406#388C2318yes—
407#388C2318yes—
408#388C2314yes—
409#388C2314yes—
410#388C2314yes—
411#388C2314yes—
412#388C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2318yes—
420#387C2318yes—
421#387C2318yes—
422#387C2318yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#386C2312yes—
429#386C2312yes—
430#386C2314yes—
431#386C2314yes—
432#386C2314yes—
433#386C2312yes—
434#386C2318yes—
435#386C2318yes—
436#386C2318yes—
437#386C2312yes—
438#386C2312yes—
439#386C2314yes—
440#386C2314yes—
441#386C2312yes—
442#386C2314yes—
443#386C2314yes—
444#385C2314yes—
445#385C2318yes—
446#385C2312yes—
447#385C2318yes—
448#385C2318yes—
449#385C2318yes—
450#385C2318yes—
451#385C2318yes—
452#385C2318yes—
453#385C2318yes—
454#385C2312yes—
455#385C2314yes—
456#385C2314yes—
457#384C2314yes—
458#384C2312yes—
459#384C2312yes—
460#384C2312yes—
461#383C2314yes—
462#383C2314yes—
463#382C2318yes—
464#382C2312yes—
465#382C2314yes—
466#382C2314yes—
467#381C2314yes—
468#381C2314yes—
469#380C2314yes—
470#380C2314yes—
471#380C2318yes—
472#380C2318yes—
473#380C2314yes—
474#380C2314yes—
475#380C2318yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2314yes—
480C4×C4⋊C4C2318yes—
481C4×C4⋊C4C2318yes—
482C4×C4⋊C4C2318yes—
483C4×C4⋊C4C2318yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2318yes—
486C4×C4⋊C4C2314yes—
487C4×C22⋊C4C2314yes—
488C4×C22⋊C4C2314yes—
489C4×C22⋊C4C2312yes—
490C4×C22⋊C4C2312yes—
491C4×C22⋊C4C2318yes—
492C4×C22⋊C4C2314yes—
493C4×C22⋊C4C2318yes—
494C4×C22⋊C4C2318yes—
495C4×C22⋊C4C2314yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2312yes—
498C4×C22⋊C4C2312yes—
499C4×C22⋊C4C2312yes—
500C4×C22⋊C4C2312yes—
501C2×#95C2314yes—
502C2×#95C2314yes—
503C43C2312yes—
504C43C2312yes—
505C43C2312yes—
506C43C2312yes—
5072−1+4—464no—
508C2×#41—28no—
509C2×#41—28no—
510C2×#41—24no—
511C2×#41—216no—
512C2×#41—24no—
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—
526C22×Q8—28no—
527C22×Q8—28no—
528C22×Q8—24no—
529C22×Q8—24no—
530C22×Q8—24no—
531C22×Q8—24no—
532C22×Q8—24no—
533C22×Q8—44no—
534C22×Q8—44no—
535C22×Q8—44no—
536C22×Q8—44no—
537C22×Q8#4118yes—
538C22×Q8C2412yes—
539C22×Q8C2412yes—
540C22×Q8C2411yescharacteristic
541C22×Q8C2411yescharacteristic
542C22×Q8C2411yescharacteristic
543C22×Q8C2412yes—
544C22×Q8C2412yes—
545C22×Q8C2414yes—
546C22×Q8C2414yes—
547C22×D4C2412yes—
548C22×D4C2411yescharacteristic
549C22×D4C2412yes—
550C22×D4C2412yes—
551C22×D4C2411yescharacteristic
552C22×D4C2411yescharacteristic
553C22×D4C2414yes—
554C22×D4C2414yes—
555C22×D4C2414yes—
556C23×C4C2412yes—
557C23×C4C2412yes—
558C23×C4C2412yes—
559C23×C4C2412yes—
560C23×C4C2412yes—
561C23×C4C2411yescharacteristic
562C23×C4C2412yes—
563C23×C4C2412yes—
564C23×C4C2412yes—
565C23×C4C2412yes—
566C23×C4C2411yescharacteristic
567C23×C4C2414yes—
568C23×C4C2414yes—
569C23×C4C2414yes—
570C23×C4C2411yescharacteristic
571C4⋊Q8—28no—
572C4⋊Q8—28no—
573C4⋊Q8—216no—
574C4⋊Q8—28no—
575C4⋊Q8—44no—
576C4⋊Q8—42no—
577C4⋊Q8—44no—
578C4⋊Q8—44no—
579C4⋊Q8—44no—
580#127—42no—
581#126—216no—
582#126—48no—
583#126—416no—
584#125—44no—
585#124—28no—
586#124—216no—
587#124—48no—
588#124—42no—
589#124—42no—
590#124—44no—
591#124—44no—
592#124—44no—
593#123—216no—
594#123—416no—
595#123—48no—
596#123—48no—
597#123—48no—
598C22⋊Q8—216no—
599C22⋊Q8—48no—
600C22⋊Q8—44no—
601C22⋊Q8—44no—
602C22⋊Q8—48no—
603C22⋊Q8—48no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606#121—44no—
607#121—44no—
608#121—48no—
609#121—48no—
610C4×Q8—48no—
611C4×Q8—48no—
612C4×Q8—48no—
613C4×Q8—48no—
614C4×Q8—48no—
615C4×Q8—48no—
616C4×Q8—48no—
617C4×Q8—44no—
618C4×D4—44no—
619C4×D4—48no—
620C4×D4—48no—
621#117—24no—
622#117—24no—
623#117—24no—
624#117—24no—
625#117—24no—
626#117—48no—
627#117—44no—
628C2×C4⋊C4—216no—
629C2×C4⋊C4—24no—
630C2×C4⋊C4—24no—
631C2×C4⋊C4—48no—
632C2×C4⋊C4—44no—
633C2×C4⋊C4—44no—
634C2×C4⋊C4—44no—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2412yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2412yes—
647C2×C4⋊C4C2412yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2414yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2414yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2418yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2414yes—
670C2×C4⋊C4C2418yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2418yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
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⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2414yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2418yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2418yes—
696C2×C22⋊C4C2418yes—
697C2×C22⋊C4C2414yes—
698C2×C22⋊C4C2414yes—
699C2×C22⋊C4C2418yes—
700C2×C22⋊C4C2414yes—
701C2×C22⋊C4C2414yes—
702C2×C22⋊C4C2418yes—
703C2×C42—24no—
704C2×C42—24no—
705C2×C42—24no—
706C2×C42—28no—
707C2×C42—44no—
708C2×C42—44no—
709C2×C42—44no—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2412yes—
717C2×C42C2412yes—
718C2×C42C2411yescharacteristic
719C2×C42C2412yes—
720C2×C42C2412yes—
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2412yes—
725C2×C42C2412yes—
726C2×C42C2412yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2418yes—
730C2×C42C2418yes—
731C2×C42C2418yes—
732C2×C42C2418yes—
733C2×C42C2412yes—
734C2×C42C2412yes—
735C2×C42C2412yes—
736#95C2418yes—
737#95C2418yes—
738#95C2418yes—
739#95C2418yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2414yes—
757#95C2414yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770C24C2512yes—
771C24C2512yes—
772C24C2512yes—
773C24C2511yescharacteristic
774#41—464no—
775#41—432no—
776#41—432no—
777#41—416no—
778#41—416no—
779#41—416no—
780C2×Q8—232no—
781C2×Q8—24no—
782C2×Q8—24no—
783C2×Q8—22no—
784C2×Q8—28no—
785C2×Q8—22no—
786C2×Q8—22no—
787C2×Q8—24no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—24no—
791C2×Q8—24no—
792C2×Q8—22no—
793C2×Q8—24no—
794C2×Q8—24no—
795C2×Q8—24no—
796C2×Q8—22no—
797C2×Q8—22no—
798C2×Q8—22no—
799C2×Q8—22no—
800C2×Q8—22no—
801C2×Q8—28no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—44no—
806C2×Q8—432no—
807C2×Q8—432no—
808C2×Q8—416no—
809C2×Q8C2×#4118yes—
810C2×Q8C2×#4118yes—
811C2×D4—24no—
812C2×D4—24no—
813C2×D4—24no—
814C2×D4—24no—
815C2×D4—24no—
816C2×D4—24no—
817C2×D4—24no—
818C2×D4—24no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—28no—
822C2×D4—22no—
823C2×D4—22no—
824C2×D4—22no—
825C2×D4—22no—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—28no—
831C2×D4—44no—
832C2×D4—44no—
833C2×D4—44no—
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—48no—
837C22×C4—24no—
838C22×C4—22no—
839C22×C4—24no—
840C22×C4—24no—
841C22×C4—24no—
842C22×C4—24no—
843C22×C4—24no—
844C22×C4—24no—
845C22×C4—22no—
846C22×C4—24no—
847C22×C4—24no—
848C22×C4—24no—
849C22×C4—24no—
850C22×C4—24no—
851C22×C4—24no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—24no—
857C22×C4—24no—
858C22×C4—24no—
859C22×C4—24no—
860C22×C4—24no—
861C22×C4—24no—
862C22×C4—24no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4C2×#4118yes—
874C22×C4C2×#4114yes—
875C22×C4H(5,𝔽2)14yes—
876C22×C4H(5,𝔽2)14yes—
877C22×C4C2512yes—
878C22×C4C2512yes—
879C22×C4C2514yes—
880C22×C4C2512yes—
881C22×C4C2512yes—
882C22×C4C2514yes—
883C22×C4C2514yes—
884C22×C4C2514yes—
885C22×C4C2514yes—
886C22×C4C2514yes—
887C22×C4C2512yes—
888C22×C4C2512yes—
889C22×C4C2514yes—
890C22×C4C2512yes—
891C22×C4C2514yes—
892C22×C4C2512yes—
893C22×C4C2512yes—
894C22×C4C2512yes—
895C22×C4C2512yes—
896C22×C4C2511yescharacteristic
897C22×C4C2511yescharacteristic
898C4⋊C4—216no—
899C4⋊C4—216no—
900C4⋊C4—24no—
901C4⋊C4—216no—
902C4⋊C4—24no—
903C4⋊C4—24no—
904C4⋊C4—24no—
905C4⋊C4—24no—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—24no—
909C4⋊C4—24no—
910C4⋊C4—24no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—216no—
915C4⋊C4—28no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—48no—
919C4⋊C4—48no—
920C4⋊C4—48no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—48no—
928C4⋊C4—48no—
929C4⋊C4—44no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—44no—
933C4⋊C4—48no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—24no—
939C22⋊C4—216no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—28no—
943C22⋊C4—28no—
944C22⋊C4—28no—
945C22⋊C4—28no—
946C22⋊C4—28no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—44no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—48no—
958C22⋊C4—44no—
959C22⋊C4—48no—
960C22⋊C4—44no—
961C22⋊C4—44no—
962C22⋊C4—44no—
963C22⋊C4—44no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C42—24no—
967C42—22no—
968C42—22no—
969C42—24no—
970C42—24no—
971C42—24no—
972C42—24no—
973C42—22no—
974C42—22no—
975C42—24no—
976C42—24no—
977C42—24no—
978C42—24no—
979C42—24no—
980C42—24no—
981C42—24no—
982C42—24no—
983C42—24no—
984C42—42no—
985C42—42no—
986C42—48no—
987C42—48no—
988C42—44no—
989C42—48no—
990C42—48no—
991C422−1+418yescomplemented
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23C22×#4112yes—
1010C23C2×H(5,𝔽2)12yes—
1011C23C2×H(5,𝔽2)12yes—
1012C23C2611yescharacteristic
1013Q8—216no—
1014Q8—216no—
1015Q8—416no—
1016Q8—48no—
1017Q8—48no—
1018Q8—44no—
1019Q8—44no—
1020Q8—44no—
1021Q8—88no—
1022D4—416no—
1023D4—48no—
1024D4—48no—
1025D4—48no—
1026D4—44no—
1027D4—44no—
1028D4—44no—
1029D4—88no—
1030D4—164no—
1031C2×C4—216no—
1032C2×C4—28no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—24no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—216no—
1044C2×C4—24no—
1045C2×C4—22no—
1046C2×C4—24no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—24no—
1057C2×C4—24no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—24no—
1076C2×C4—24no—
1077C2×C4—28no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—28no—
1082C2×C4—48no—
1083C2×C4—416no—
1084C2×C4—416no—
1085C2×C4—44no—
1086C2×C4—48no—
1087C2×C4—48no—
1088C2×C4—48no—
1089C2×C4—48no—
1090C2×C4—84no—
1091C2×C4—84no—
1092C2×C4—164no—
1093C2×C4#538116yes—
1094C2×C4C22×#4118yes—
1095C2×C4C22×#4112yes—
1096C2×C4C22×#4112yes—
1097C2×C4C2×H(5,𝔽2)12yes—
1098C2×C4C2×H(5,𝔽2)12yes—
1099C2×C4C2×H(5,𝔽2)12yes—
1100C2×C4C2×H(5,𝔽2)12yes—
1101C2×C4C2×2−1+414yes—
1102C2×C4C2×2−1+414yes—
1103C2×C4C2×2−1+414yes—
1104C2×C4#58514yes—
1105C22—24no—
1106C22—22no—
1107C22—24no—
1108C22—22no—
1109C22—44no—
1110C22—44no—
1111C22—44no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—44no—
1116C22—44no—
1117C22—44no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22C2×#53814yes—
1125C22C23×#4111yescharacteristic
1126C22C22×H(5,𝔽2)11yescharacteristic
1127C22C22×H(5,𝔽2)11yescharacteristic
1128C22C22×2−1+412yes—
1129C22C2×#58512yes—
1130C4—24no—
1131C4—24no—
1132C4—24no—
1133C4—24no—
1134C4—28no—
1135C4—44no—
1136C4—42no—
1137C4—44no—
1138C4—42no—
1139C4—44no—
1140C4—44no—
1141C4—42no—
1142C4—44no—
1143C4—44no—
1144C4—42no—
1145C4—42no—
1146C4—42no—
1147C4—42no—
1148C4—44no—
1149C4C2×#53814yes—
1150C4C2×#53814yes—
1151C2—24no—
1152C2—82no—
1153C2—82no—
1154C2—82no—
1155C2C22×#53811yescharacteristic
1156C2#6278812yes—
1157C2#6283311yescharacteristic
1158C2#6283512yes—
1159C2#6283611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35660C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40225C2semidirect
2. #40214C2semidirect
3. #40200C2semidirect
4. #40190C2semidirect
5. #39790C2semidirect
6. #39783C2semidirect
7. #39663C2semidirect
8. #39654C2semidirect
9. #36823C2semidirect
10. #36641C2semidirect
11. #36639C2semidirect
12. #35667C2semidirect
13. #35666C2semidirect
14. #35662C2semidirect
16. #35628C2semidirect
17. #35621C2semidirect
18. #35557C2semidirect
19. #35530C2semidirect
20. #35182C2semidirect
21. #35153C2semidirect
22. #35058C2semidirect
23. #34266C2semidirect
24. #34257C2semidirect
25. C2×C4×C4⋊Q8C2semidirect
991. C422−1+4semidirect

Maximal subgroups

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

subgroupindex
#402252
#402142
#402002
#401902
#397902
#397832
#396632
#396542
#368232
#366412
#366392
#356672
#356662
#356622
#356602
#356282
#356212
#355572
#355302
#351822
#351532
#350582
#342662
#342572
C2×C4×C4⋊Q82