Finite Group Databasebeta

← #7985167

Subgroups — #7985167

Order 512.

5055 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C211yesmaximal, characteristic, complemented
2#59217C212yesmaximal, complemented
3#59125C212yesmaximal, complemented
4#59036C212yesmaximal, complemented
5#48102C218yesmaximal, complemented
6#45605C214yesmaximal, complemented
7#45307C214yesmaximal, complemented
8#44984C214yesmaximal, complemented
9#42851C214yesmaximal, complemented
10#42613C214yesmaximal, complemented
11#39158C212yesmaximal, complemented
12#39156C212yesmaximal, complemented
13#39149C212yesmaximal, complemented
14#39146C212yesmaximal, complemented
15#39021C214yesmaximal, complemented
16#36551C212yesmaximal, complemented
17#36444C212yesmaximal, complemented
18#36188C211yesmaximal, characteristic, complemented
19#36134C211yesmaximal, characteristic, complemented
20D4×C4⋊Q8C211yesmaximal, characteristic, complemented
21#35239C212yesmaximal, complemented
22#35200C212yesmaximal, complemented
23#34943C211yesmaximal, characteristic, complemented
24#34943C211yesmaximal, characteristic, complemented
25#34371C212yesmaximal, complemented
26C4×#547C211yesmaximal, characteristic, complemented
27C2×#556C2212yes—
28C2×D4×Q8C2212yes—
29C2×#548C2214yes—
30C2×#547C2211yescharacteristic
31C2×#533C2212yes—
32C22×C4⋊Q8C2212yes—
33C2×C4×#41C2212yes—
34#2868C2211yescharacteristic
35#2857C2212yes—
36#2857C2214yes—
37#2857C2212yes—
38#2857C2212yes—
39#2851C2214yes—
40#2851C2214yes—
41#2831C2218yes—
42#2806C2214yes—
43#2805C2218yes—
44#2787C2218yes—
45#2781C2218yes—
46#2777C2218yes—
47#2776C2218yes—
48#2770C2218yes—
49#2759C2218yes—
50#2746C2218yes—
51#2740C2218yes—
52#2739C2218yes—
53#2715C2218yes—
54#2700C2218yes—
55#2692C2218yes—
56#2691C2218yes—
57#2689C2218yes—
58#2674C2218yes—
59#2666C2218yes—
60#2649C2218yes—
61#2645C2214yes—
62#2644C2214yes—
63#2638C2218yes—
64#2599C2218yes—
65#2589C2218yes—
66#2584C2214yes—
67#2582C2214yes—
68#2572C2214yes—
69#2572C2214yes—
70#2571C2211yescharacteristic
71#2571C2211yescharacteristic
72#2570C2214yes—
73#2568C2212yes—
74#2567C2212yes—
75#2563C2211yescharacteristic
76#2563C2211yescharacteristic
77#2563C2211yescharacteristic
78#2563C2211yescharacteristic
79#2562C2214yes—
80#2552C2212yes—
81#2552C2212yes—
82#2552C2212yes—
83#2551C2212yes—
84#2551C2212yes—
85#2550C2214yes—
86#2547C2214yes—
87#2547C2212yes—
88#2547C2212yes—
89#2546C2212yes—
90#2542C2212yes—
91#2538C2212yes—
92#2538C2214yes—
93#2537C2211yescharacteristic
94#2537C2214yes—
95#2537C2211yescharacteristic
96#2509C2214yes—
97#2507C2214yes—
98#2499C2214yes—
99#2499C2214yes—
100#2497C2214yes—
101#2497C2214yes—
102#2496C2214yes—
103#2496C2214yes—
104#2495C2212yes—
105#2495C2212yes—
106#2495C2212yes—
107#2495C2212yes—
108#2494C2214yes—
109#2494C2214yes—
110#2491C2214yes—
111#2490C2214yes—
112#2487C2214yes—
113#2485C2214yes—
114#2485C2214yes—
115#2476C2218yes—
116#2466C2218yes—
117#2465C2218yes—
118#2454C2214yes—
119#2450C2218yes—
120#2443C2218yes—
121#2442C2214yes—
122#2441C2214yes—
123#2440C2214yes—
124#2440C2214yes—
125#2440C2214yes—
126#2439C2214yes—
127#2438C2218yes—
128#2434C2214yes—
129#2432C2214yes—
130#2429C2214yes—
131#2429C2214yes—
132#2427C2218yes—
133#2427C2214yes—
134#2423C2214yes—
135#2423C2214yes—
136#2421C2214yes—
137#2420C2212yes—
138#2420C2212yes—
139#2420C2212yes—
140#2420C2212yes—
141#2416C2214yes—
142#2415C2214yes—
143#2415C2218yes—
144#2409C2214yes—
145#2398C2214yes—
146#2398C2214yes—
147#2381C2218yes—
148#2369C2212yes—
149#2365C2212yes—
150#2365C2211yescharacteristic
151#2365C2212yes—
152#2365C2212yes—
153#2365C2212yes—
154#2363C2214yes—
155#2362C2212yes—
156#2361C2212yes—
157#2359C2214yes—
158#2354C2212yes—
159#2354C2211yescharacteristic
160Q8×C4⋊C4C2212yes—
161Q8×C4⋊C4C2212yes—
162D4×C4⋊C4C2212yes—
163D4×C4⋊C4C2212yes—
164D4×C4⋊C4C2211yescharacteristic
165D4×C4⋊C4C2214yes—
166#2345C2214yes—
167#2345C2214yes—
168#2344C2212yes—
169Q8×C22⋊C4C2214yes—
170Q8×C22⋊C4C2214yes—
171#2339C2212yes—
172#2331C2214yes—
173#2331C2214yes—
174#2330C2214yes—
175#2327C2214yes—
176#2327C2214yes—
177#2326C2214yes—
178#2313C2218yes—
179C4×C4⋊Q8C2211yescharacteristic
180C4×C4⋊Q8C2211yescharacteristic
181C4×C4⋊Q8C2211yescharacteristic
182C4×C22⋊Q8C2212yes—
183C4×#123C2214yes—
184C4×#121C2212yes—
185C4×#121C2212yes—
186C4×#121C2214yes—
187C4×#121C2212yes—
188C4×#121C2212yes—
189C4×#121C2212yes—
190#2285C2212yes—
191#2283C2212yes—
192#2283C2212yes—
193#2283C2212yes—
194#2283C2212yes—
195C42×D4C2211yescharacteristic
196C42×D4C2211yescharacteristic
197C42×D4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2312yes—
200C23×Q8C2314yes—
201#556—48no—
202D4×Q8—48no—
203#548—416no—
204#547—28no—
205#533—48no—
206C2×C4⋊Q8—216no—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2312yes—
212C2×C4⋊Q8C2312yes—
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2312yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126C2318yes—
218C2×#125C2314yes—
219C2×#125C2314yes—
220C2×#124C2314yes—
221C2×#124C2318yes—
222C2×#123C2314yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2318yes—
225C2×C22⋊Q8C2314yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2318yes—
231C2×#121C2312yes—
232C2×#121C2312yes—
233C2×#121C2312yes—
234C2×#121C2312yes—
235C2×#121C2312yes—
236C2×#121C2318yes—
237C4×#41—48no—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2314yes—
243C2×C4×Q8C2312yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2314yes—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2314yes—
257C2×C4×D4C2318yes—
258C2×C4×D4C2314yes—
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2314yes—
261C2×C4×D4C2314yes—
262C2×#117C2314yes—
263C2×#117C2312yes—
264C2×#117C2314yes—
265C2×#117C2314yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2312yes—
268C22×C4⋊C4C2314yes—
269C22×C4⋊C4C2312yes—
270C22×C42C2312yes—
271C22×C42C2312yes—
272C22×C42C2312yes—
273C22×C42C2314yes—
274#401C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2314yes—
279#400C2314yes—
280#400C2314yes—
281#400C2318yes—
282#400C2314yes—
283#400C2318yes—
284#399C2318yes—
285#399C2318yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#397C2314yes—
294#397C2318yes—
295#397C2318yes—
296#397C2318yes—
297#397C2318yes—
298#397C2318yes—
299#397C2314yes—
300#397C2314yes—
301#397C2314yes—
302#397C2318yes—
303#397C2318yes—
304#396C2318yes—
305#396C2318yes—
306#396C2318yes—
307#396C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#394C2318yes—
313#394C2314yes—
314#394C2314yes—
315#394C2318yes—
316#394C2318yes—
317#394C2314yes—
318#394C2318yes—
319#394C2314yes—
320#393C2314yes—
321#393C2314yes—
322#393C2314yes—
323#393C2314yes—
324#393C2318yes—
325#391C2312yes—
326#391C2312yes—
327#391C2312yes—
328#391C2314yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2318yes—
333#391C2314yes—
334#391C2318yes—
335#391C2312yes—
336#391C2314yes—
337#391C2318yes—
338#391C2318yes—
339#391C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2312yes—
343#390C2312yes—
344#390C2312yes—
345#390C2314yes—
346#390C2318yes—
347#389C2312yes—
348#389C2312yes—
349#389C2312yes—
350#389C2312yes—
351#389C2312yes—
352#389C2312yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2312yes—
358#389C2312yes—
359#389C2312yes—
360#389C2312yes—
361#389C2318yes—
362#389C2314yes—
363#389C2314yes—
364#389C2318yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2312yes—
370#389C2314yes—
371#389C2314yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2318yes—
379#388C2318yes—
380#388C2318yes—
381#388C2314yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2314yes—
389#388C2318yes—
390#388C2314yes—
391#388C2318yes—
392#388C2318yes—
393#387C2314yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2314yes—
409#387C2314yes—
410#387C2318yes—
411#387C2318yes—
412#386C2314yes—
413#386C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2314yes—
417#386C2314yes—
418#386C2318yes—
419#386C2318yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2314yes—
427#385C2318yes—
428#385C2314yes—
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2314yes—
433#384C2314yes—
434#384C2314yes—
435#384C2312yes—
436#384C2312yes—
437#384C2312yes—
438#384C2312yes—
439#383C2314yes—
440#383C2314yes—
441#383C2314yes—
442#383C2314yes—
443#382C2312yes—
444#382C2312yes—
445#382C2312yes—
446#382C2312yes—
447#382C2314yes—
448#382C2312yes—
449#382C2312yes—
450#382C2312yes—
451#382C2312yes—
452#381C2314yes—
453#381C2314yes—
454#381C2314yes—
455#381C2314yes—
456#381C2314yes—
457#380C2312yes—
458#380C2312yes—
459#380C2314yes—
460#380C2314yes—
461#380C2312yes—
462#380C2312yes—
463#380C2312yes—
464#380C2312yes—
465#380C2312yes—
466#380C2312yes—
467#380C2312yes—
468#380C2312yes—
469#380C2318yes—
470#380C2318yes—
471#380C2312yes—
472#380C2314yes—
473#380C2314yes—
474#380C2312yes—
475#380C2312yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2318yes—
481#380C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2311yescharacteristic
493C4×C4⋊C4C2311yescharacteristic
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2312yes—
500C4×C4⋊C4C2314yes—
501C4×C4⋊C4C2311yescharacteristic
502C4×C4⋊C4C2311yescharacteristic
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C4⋊C4C2311yescharacteristic
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2318yes—
508C4×C22⋊C4C2312yes—
509C4×C22⋊C4C2312yes—
510C4×C22⋊C4C2312yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516C4×C22⋊C4C2312yes—
517C4×C22⋊C4C2312yes—
518C4×C22⋊C4C2314yes—
519C4×C22⋊C4C2314yes—
520C4×C22⋊C4C2312yes—
521C4×C22⋊C4C2312yes—
522#376C2314yes—
523#376C2314yes—
524C2×#95C2314yes—
525C43C2311yescharacteristic
526C2×#41—28no—
527C2×#41—28no—
528C2×#41—44no—
529C22×Q8—216no—
530C22×Q8—48no—
531C22×Q8—48no—
532C22×Q8C2414yes—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2412yes—
536C22×Q8C2418yes—
537C22×D4C2411yescharacteristic
538C22×D4C2414yes—
539C22×D4C2414yes—
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C22×D4C2414yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2412yes—
547C23×C4C2412yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2414yes—
551C23×C4C2412yes—
552C23×C4C2418yes—
553C23×C4C2412yes—
554C23×C4C2414yes—
555C4⋊Q8—216no—
556C4⋊Q8—216no—
557C4⋊Q8—216no—
558C4⋊Q8—28no—
559C4⋊Q8—24no—
560C4⋊Q8—28no—
561C4⋊Q8—24no—
562C4⋊Q8—48no—
563C4⋊Q8—44no—
564C4⋊Q8#4118yes—
565#126—416no—
566#125—48no—
567#125—48no—
568#124—216no—
569#124—416no—
570#123—216no—
571C22⋊Q8—28no—
572C22⋊Q8—416no—
573C22⋊Q8—48no—
574C22⋊Q8—416no—
575C22⋊Q8—48no—
576C22⋊Q8—48no—
577C22⋊Q8—48no—
578C22⋊Q8—48no—
579#121—28no—
580#121—28no—
581#121—28no—
582#121—28no—
583#121—416no—
584#121—44no—
585C4×Q8—28no—
586C4×Q8—44no—
587C4×Q8—44no—
588C4×Q8—44no—
589C4×Q8—48no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×D4—24no—
594C4×D4—24no—
595C4×D4—24no—
596C4×D4—24no—
597C4×D4—24no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4—24no—
601C4×D4—42no—
602C4×D4—44no—
603C4×D4—48no—
604C4×D4—48no—
605C4×D4—48no—
606C4×D4—48no—
607C4×D4—48no—
608C4×D4—416no—
609#117—48no—
610#117—48no—
611#117—44no—
612#117—48no—
613C2×C4⋊C4—216no—
614C2×C4⋊C4—216no—
615C2×C4⋊C4—28no—
616C2×C4⋊C4—44no—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2418yes—
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2412yes—
657C2×C4⋊C4C2414yes—
658C2×C4⋊C4C2418yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2414yes—
662C2×C4⋊C4C2412yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2412yes—
665C2×C4⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2418yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2412yes—
671C2×C22⋊C4C2412yes—
672C2×C22⋊C4C2412yes—
673C2×C22⋊C4C2412yes—
674C2×C22⋊C4C2412yes—
675C2×C22⋊C4C2412yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2418yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2414yes—
686C2×C22⋊C4C2412yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2414yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2414yes—
695C2×C22⋊C4C2414yes—
696C2×C42—28no—
697C2×C42—28no—
698C2×C42—28no—
699C2×C42—48no—
700C2×C42C2412yes—
701C2×C42C2414yes—
702C2×C42C2414yes—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2414yes—
707C2×C42C2411yescharacteristic
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2414yes—
716C2×C42C2418yes—
717C2×C42C2418yes—
718C2×C42C2418yes—
719C2×C42C2414yes—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#95C2412yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2412yes—
738#95C2412yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2412yes—
744#95C2412yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2414yes—
766#95C2418yes—
767#95C2418yes—
768#95C2418yes—
769#95C2418yes—
770C24C2512yes—
771C24C2512yes—
772C24C2512yes—
773#41—432no—
774C2×Q8—28no—
775C2×Q8—216no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—28no—
780C2×Q8—28no—
781C2×Q8—24no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—48no—
786C2×Q8—48no—
787C2×Q8—42no—
788C2×Q8—832no—
789C2×Q8C2×#4118yes—
790C2×D4—28no—
791C2×D4—28no—
792C2×D4—28no—
793C2×D4—28no—
794C2×D4—22no—
795C2×D4—22no—
796C2×D4—28no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4H(5,𝔽2)14yes—
807C2×D42−1+414yes—
808C22×C4—24no—
809C22×C4—28no—
810C22×C4—24no—
811C22×C4—24no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—24no—
815C22×C4—28no—
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—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—216no—
833C22×C4—24no—
834C22×C4—44no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—44no—
844C22×C4C2512yes—
845C22×C4C2512yes—
846C22×C4C2512yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2514yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2511yescharacteristic
856C22×C4C2514yes—
857C22×C4C2514yes—
858C22×C4C2512yes—
859C22×C4C2518yes—
860C22×C4C2511yescharacteristic
861C22×C4C2514yes—
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2511yescharacteristic
865C22×C4C2511yescharacteristic
866C22×C4C2511yescharacteristic
867C4⋊C4—22no—
868C4⋊C4—28no—
869C4⋊C4—216no—
870C4⋊C4—216no—
871C4⋊C4—28no—
872C4⋊C4—28no—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—24no—
876C4⋊C4—28no—
877C4⋊C4—24no—
878C4⋊C4—28no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—28no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—22no—
887C4⋊C4—24no—
888C4⋊C4—24no—
889C4⋊C4—24no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—44no—
895C4⋊C4—42no—
896C4⋊C4—48no—
897C4⋊C4—42no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—48no—
903C4⋊C4—42no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4C2×#4118yes—
915C4⋊C4C2×#4118yes—
916C22⋊C4—216no—
917C22⋊C4—24no—
918C22⋊C4—216no—
919C22⋊C4—28no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—28no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—24no—
929C22⋊C4—24no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—42no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—24no—
952C42—28no—
953C42—22no—
954C42—28no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—22no—
959C42—22no—
960C42—28no—
961C42—44no—
962C42—44no—
963C42—41no—
964C42—48no—
965C42—48no—
966C42—48no—
967C42C2×#4114yes—
968C42H(5,𝔽2)14yes—
969C422−1+414yes—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23C2×H(5,𝔽2)14yes—
990C23C2×2−1+414yes—
991C23C2611yescharacteristic
992Q8—216no—
993Q8—48no—
994Q8—416no—
995Q8—84no—
996Q8—816no—
997D4—28no—
998D4—28no—
999D4—416no—
1000D4—416no—
1001D4—44no—
1002D4—88no—
1003C2×C4—24no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—28no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—24no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—21no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—24no—
1027C2×C4—24no—
1028C2×C4—28no—
1029C2×C4—28no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—24no—
1043C2×C4—24no—
1044C2×C4—24no—
1045C2×C4—21no—
1046C2×C4—24no—
1047C2×C4—24no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—24no—
1057C2×C4—22no—
1058C2×C4—24no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—416no—
1062C2×C4—48no—
1063C2×C4—48no—
1064C2×C4—48no—
1065C2×C4—48no—
1066C2×C4—48no—
1067C2×C4—48no—
1068C2×C4—84no—
1069C2×C4—816no—
1070C2×C4—88no—
1071C2×C4C22×#4112yes—
1072C2×C4C22×#4118yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4112yes—
1075C2×C4C2×H(5,𝔽2)12yes—
1076C2×C4C2×H(5,𝔽2)12yes—
1077C2×C4C2×H(5,𝔽2)12yes—
1078C2×C4C2×H(5,𝔽2)12yes—
1079C2×C4C2×2−1+412yes—
1080C2×C4C2×2−1+412yes—
1081C2×C4C2×2−1+412yes—
1082C2×C4C2×2−1+412yes—
1083C2×C4#58512yes—
1084C22—24no—
1085C22—24no—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—24no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22C23×#4111yescharacteristic
1106C22C22×H(5,𝔽2)11yescharacteristic
1107C22C22×H(5,𝔽2)11yescharacteristic
1108C22C22×2−1+411yescharacteristic
1109C22C22×2−1+411yescharacteristic
1110C22C2×#58511yescharacteristic
1111C222−1+611yescharacteristic
1112C4—22no—
1113C4—28no—
1114C4—22no—
1115C4—22no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—41no—
1120C4—44no—
1121C4—44no—
1122C4—42no—
1123C4—42no—
1124C4—48no—
1125C4—42no—
1126C4—42no—
1127C4—42no—
1128C4—44no—
1129C4—44no—
1130C4—42no—
1131C4—44no—
1132C4#351814yes—
1133C4#351914yes—
1134C4#355214yes—
1135C2—44no—
1136C2—44no—
1137C2—82no—
1138C2C2×#355211yescharacteristic
1139C2C2×#351911yescharacteristic
1140C2C2×#351811yescharacteristic
1141C2#6291511yescharacteristic
1142C2#6292511yescharacteristic
1143C2#6299811yescharacteristic
1144C2#6301311yescharacteristic
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. #59871C2semidirect
2. #59217C2semidirect
3. #59125C2semidirect
4. #59036C2semidirect
5. #48102C2semidirect
6. #45605C2semidirect
7. #45307C2semidirect
8. #44984C2semidirect
9. #42851C2semidirect
10. #42613C2semidirect
11. #39158C2semidirect
12. #39156C2semidirect
13. #39149C2semidirect
14. #39146C2semidirect
15. #39021C2semidirect
16. #36551C2semidirect
17. #36444C2semidirect
18. #36188C2semidirect
19. #36134C2semidirect
20. D4×C4⋊Q8C2semidirect
21. #35239C2semidirect
22. #35200C2semidirect
23. #34943C2semidirect
24. #34943C2semidirect
25. #34371C2semidirect
26. C4×#547C2semidirect

Maximal subgroups

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

subgroupindex
#598712
#592172
#591252
#590362
#481022
#456052
#453072
#449842
#428512
#426132
#391582
#391562
#391492
#391462
#390212
#365512
#364442
#361882
#361342
D4×C4⋊Q82
#352392
#352002
#349432
#343712
C4×#5472