Finite Group Databasebeta

← #8095350

Subgroups — #8095350

Order 512.

4846 conjugacy classes of subgroups.

The subgroup lattice has 1132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53130C214yesmaximal, complemented
2#53050C214yesmaximal, complemented
3#53021C214yesmaximal, complemented
4#53016C214yesmaximal, complemented
5#52321C218yesmaximal, complemented
6#45749C218yesmaximal, complemented
7#45653C214yesmaximal, complemented
8#45650C214yesmaximal, complemented
9#45501C214yesmaximal, complemented
10#45500C214yesmaximal, complemented
11#35628C211yesmaximal, characteristic, complemented
12#35621C211yesmaximal, characteristic, complemented
13#35592C211yesmaximal, characteristic, complemented
14#35574C211yesmaximal, characteristic, complemented
15#35555C211yesmaximal, characteristic, complemented
16#35530C211yesmaximal, characteristic, complemented
17#35308C211yesmaximal, characteristic, complemented
18#35307C211yesmaximal, characteristic, complemented
19#35280C211yesmaximal, characteristic, complemented
20#35273C211yesmaximal, characteristic
21#35182C211yesmaximal, characteristic, complemented
22#35153C211yesmaximal, characteristic, complemented
23C2×#2567C211yesmaximal, characteristic, complemented
24#34745C211yesmaximal, characteristic, complemented
25#34744C211yesmaximal, characteristic, complemented
26C2×#537C2211yescharacteristic
27C2×#537C2211yescharacteristic
28C2×#536C2211yescharacteristic
29C2×#536C2211yescharacteristic
30C2×#536C2211yescharacteristic
31C2×#533C2211yescharacteristic
32C2×#532C2211yescharacteristic
33C22×C4⋊Q8C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C22×C4×Q8C2211yescharacteristic
38#2857C2214yes—
39#2857C2212yes—
40#2857C2212yes—
41#2856C2212yes—
42#2855C2214yes—
43#2854C2214yes—
44#2853C2214yes—
45#2850C2212yes—
46#2841C2218yes—
47#2841C2218yes—
48#2837C2218yes—
49#2836C2218yes—
50#2832C2218yes—
51#2831C2218yes—
52#2831C2218yes—
53#2830C2218yes—
54#2820C2218yes—
55#2814C2218yes—
56#2806C2218yes—
57#2802C2218yes—
58#2802C2218yes—
59#2800C2218yes—
60#2800C2218yes—
61#2788C2218yes—
62#2788C2218yes—
63#2783C2218yes—
64#2779C2218yes—
65#2768C2218yes—
66#2755C2218yes—
67#2704C2218yes—
68#2704C2218yes—
69#2701C2218yes—
70#2700C2218yes—
71#2694C2218yes—
72#2692C2218yes—
73#2686C2218yes—
74#2681C2218yes—
75#2672C2218yes—
76#2629C2214yes—
77#2625C2214yes—
78#2623C2214yes—
79#2621C2212yes—
80#2620C2212yes—
81#2620C2212yes—
82#2620C2212yes—
83#2618C2214yes—
84#2592C2214yes—
85#2591C2214yes—
86#2582C2214yes—
87#2579C2214yes—
88#2570C2214yes—
89#2568C2214yes—
90#2567C2214yes—
91#2567C2214yes—
92#2567C2214yes—
93#2567C2214yes—
94#2552C2214yes—
95#2547C2212yes—
96#2546C2212yes—
97#2545C2212yes—
98#2544C2212yes—
99#2538C2214yes—
100#2538C2214yes—
101#2537C2214yes—
102#2507C2214yes—
103#2506C2214yes—
104#2502C2212yes—
105#2501C2212yes—
106#2500C2212yes—
107#2499C2212yes—
108#2492C2214yes—
109#2492C2214yes—
110#2492C2214yes—
111#2491C2214yes—
112#2491C2214yes—
113#2489C2214yes—
114#2488C2218yes—
115#2473C2218yes—
116#2454C2212yes—
117#2453C2212yes—
118#2452C2212yes—
119#2452C2214yes—
120#2451C2214yes—
121#2451C2212yes—
122#2450C2214yes—
123#2449C2214yes—
124#2448C2214yes—
125#2448C2212yes—
126#2447C2214yes—
127#2447C2212yes—
128#2446C2214yes—
129#2446C2214yes—
130#2446C2212yes—
131#2445C2212yes—
132#2444C2214yes—
133#2443C2218yes—
134#2443C2214yes—
135#2440C2214yes—
136#2439C2214yes—
137#2436C2214yes—
138#2429C2214yes—
139#2429C2214yes—
140#2429C2214yes—
141#2427C2214yes—
142#2426C2214yes—
143#2426C2214yes—
144#2425C2218yes—
145#2425C2218yes—
146#2423C2214yes—
147#2423C2214yes—
148#2422C2214yes—
149#2421C2214yes—
150#2419C2218yes—
151#2417C2214yes—
152#2417C2218yes—
153#2416C2218yes—
154#2415C2214yes—
155#2409C2214yes—
156#2396C2214yes—
157#2395C2214yes—
158C2×#395C2214yes—
159#2378C2218yes—
160#2376C2218yes—
161#2317C2211yescharacteristic
162#2317C2211yescharacteristic
163#2316C2211yescharacteristic
164#2316C2211yescharacteristic
165#2311C2211yescharacteristic
166#2311C2211yescharacteristic
167#2311C2211yescharacteristic
168#2311C2211yescharacteristic
169#2310C2211yescharacteristic
170C4×C22⋊Q8C2214yes—
171C4×#123C2214yes—
172#2297C2211yescharacteristic
173#2297C2211yescharacteristic
174#2297C2211yescharacteristic
175#2297C2211yescharacteristic
176#2297C2211yescharacteristic
177#2296C2211yescharacteristic
178#2296C2211yescharacteristic
179#2296C2211yescharacteristic
180C2×#391C2211yescharacteristic
181C2×#391C2211yescharacteristic
182C2×#389C2214yes—
183C2×#384C2211yescharacteristic
184C2×#384C2211yescharacteristic
185#2274C2211yescharacteristic
186C2×C4×C4⋊C4C2211yescharacteristic
187C22×#41C2311yescharacteristic
188C22×#41C2311yescharacteristic
189C22×#41C2311yescharacteristic
190C23×Q8C2311yescharacteristic
191C23×Q8C2312yes—
192#537—44no—
193#537—44no—
194#536—44no—
195#536—44no—
196#536—44no—
197#533—44no—
198#532—44no—
199C2×C4⋊Q8—44no—
200C2×C4⋊Q8C2314yes—
201C2×C4⋊Q8C2314yes—
202C2×C4⋊Q8C2312yes—
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2312yes—
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×#127C2311yescharacteristic
208C2×#125C2312yes—
209C2×#125C2318yes—
210C2×#124C2312yes—
211C2×#124C2312yes—
212C2×#124C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#124C2312yes—
215C2×#124C2318yes—
216C2×#123C2314yes—
217C2×#123C2314yes—
218C2×#123C2314yes—
219C2×#123C2314yes—
220C2×#123C2318yes—
221C2×C22⋊Q8C2314yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2314yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2314yes—
229C2×C22⋊Q8C2314yes—
230C2×C22⋊Q8C2312yes—
231C2×C22⋊Q8C2318yes—
232C2×C22⋊Q8C2318yes—
233C2×#121C2314yes—
234C2×#121C2312yes—
235C2×#121C2314yes—
236C2×#121C2312yes—
237C2×#121C2312yes—
238C2×#121C2314yes—
239C2×#121C2312yes—
240C2×#121C2318yes—
241#520—44no—
242C4×#41—44no—
243C4×#41—44no—
244C2×C4×Q8—44no—
245C2×C4×Q8C2314yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2314yes—
248C2×C4×Q8C2312yes—
249C2×C4×Q8C2312yes—
250C2×C4×Q8C2312yes—
251C2×C4×D4C2314yes—
252C2×C4×D4C2314yes—
253C2×C4×D4C2314yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×C4×D4C2312yes—
257C2×C4×D4C2312yes—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2312yes—
264C2×#117C2312yes—
265C2×#117C2312yes—
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2312yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2314yes—
274C22×C4⋊C4C2314yes—
275C22×C42C2311yescharacteristic
276C22×C42C2311yescharacteristic
277C22×C42C2311yescharacteristic
278C22×C42C2312yes—
279C22×C42C2312yes—
280C22×C42C2312yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2314yes—
285#400C2318yes—
286#400C2318yes—
287#400C2318yes—
288#400C2314yes—
289#399C2318yes—
290#399C2318yes—
291#399C2314yes—
292#399C2314yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#398C2314yes—
300#398C2318yes—
301#398C2318yes—
302#398C2314yes—
303#398C2318yes—
304#398C2318yes—
305#398C2318yes—
306#398C2318yes—
307#398C2314yes—
308#397C2314yes—
309#397C2318yes—
310#397C2318yes—
311#397C2318yes—
312#397C2318yes—
313#397C2318yes—
314#397C2314yes—
315#397C2318yes—
316#397C2314yes—
317#397C2318yes—
318#396C2314yes—
319#396C2318yes—
320#396C2318yes—
321#396C2318yes—
322#396C2318yes—
323#396C2318yes—
324#396C2318yes—
325#396C2318yes—
326#396C2318yes—
327#396C2318yes—
328#396C2314yes—
329#395C2318yes—
330#395C2318yes—
331#395C2318yes—
332#395C2318yes—
333#395C2318yes—
334#395C2314yes—
335#394C2318yes—
336#394C2318yes—
337#394C2314yes—
338#394C2318yes—
339#394C2318yes—
340#394C2318yes—
341#394C2318yes—
342#394C2318yes—
343#394C2314yes—
344#393C2318yes—
345#393C2318yes—
346#393C2314yes—
347#393C2318yes—
348#393C2318yes—
349#391C2314yes—
350#391C2314yes—
351#391C2312yes—
352#391C2312yes—
353#391C2312yes—
354#391C2312yes—
355#391C2314yes—
356#391C2312yes—
357#391C2312yes—
358#391C2312yes—
359#391C2312yes—
360#391C2314yes—
361#391C2312yes—
362#391C2318yes—
363#391C2318yes—
364#391C2318yes—
365#391C2318yes—
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2312yes—
369#391C2312yes—
370#391C2314yes—
371#391C2312yes—
372#390C2312yes—
373#390C2312yes—
374#390C2312yes—
375#390C2312yes—
376#390C2318yes—
377#390C2312yes—
378#390C2311yescharacteristic
379#390C2318yes—
380#390C2311yescharacteristic
381#390C2312yes—
382#390C2312yes—
383#390C2312yes—
384#389C2318yes—
385#389C2318yes—
386#389C2318yes—
387#389C2318yes—
388#389C2312yes—
389#389C2314yes—
390#389C2314yes—
391#389C2314yes—
392#389C2314yes—
393#389C2314yes—
394#389C2314yes—
395#389C2318yes—
396#389C2318yes—
397#389C2312yes—
398#389C2318yes—
399#389C2318yes—
400#389C2312yes—
401#389C2318yes—
402#389C2318yes—
403#389C2312yes—
404#389C2312yes—
405#389C2312yes—
406#389C2314yes—
407#388C2318yes—
408#388C2318yes—
409#388C2314yes—
410#388C2318yes—
411#388C2318yes—
412#388C2318yes—
413#388C2318yes—
414#388C2318yes—
415#388C2318yes—
416#388C2318yes—
417#388C2318yes—
418#388C2318yes—
419#388C2314yes—
420#387C2318yes—
421#387C2318yes—
422#387C2314yes—
423#387C2318yes—
424#387C2318yes—
425#387C2318yes—
426#387C2318yes—
427#387C2318yes—
428#387C2318yes—
429#387C2314yes—
430#387C2314yes—
431#387C2314yes—
432#386C2314yes—
433#386C2314yes—
434#386C2314yes—
435#386C2314yes—
436#386C2312yes—
437#386C2312yes—
438#386C2312yes—
439#386C2318yes—
440#386C2312yes—
441#386C2312yes—
442#386C2312yes—
443#386C2318yes—
444#386C2314yes—
445#386C2314yes—
446#386C2314yes—
447#385C2314yes—
448#385C2314yes—
449#385C2312yes—
450#385C2318yes—
451#385C2318yes—
452#385C2312yes—
453#385C2318yes—
454#385C2314yes—
455#385C2314yes—
456#385C2314yes—
457#385C2314yes—
458#385C2314yes—
459#384C2314yes—
460#384C2314yes—
461#384C2312yes—
462#384C2312yes—
463#384C2312yes—
464#384C2312yes—
465#384C2312yes—
466#384C2312yes—
467#382C2318yes—
468#382C2312yes—
469#382C2312yes—
470#381C2314yes—
471#381C2314yes—
472#381C2318yes—
473#380C2314yes—
474#380C2314yes—
475#380C2314yes—
476#380C2314yes—
477#380C2314yes—
478#380C2314yes—
479#380C2314yes—
480#380C2318yes—
481#380C2318yes—
482#380C2318yes—
483#380C2318yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2314yes—
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2312yes—
494C4×C22⋊C4C2314yes—
495C4×C22⋊C4C2312yes—
496C4×C22⋊C4C2314yes—
497C4×C22⋊C4C2314yes—
498C4×C22⋊C4C2314yes—
499C4×C22⋊C4C2314yes—
500C4×C22⋊C4C2312yes—
501C2×#95C2312yes—
502C2×#95C2314yes—
503C2×#95C2314yes—
504C2×#41—24no—
505C2×#41—24no—
506C2×#41—24no—
507C2×#41—24no—
508C2×#41—24no—
509C2×#41—24no—
510C2×#41—24no—
511C2×#41—24no—
512C2×#41—24no—
513C22×Q8—24no—
514C22×Q8—24no—
515C22×Q8—24no—
516C22×Q8—44no—
517C22×Q8—84no—
518C22×Q8C2412yes—
519C22×Q8C2411yescharacteristic
520C22×Q8C2412yes—
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×Q8C2414yes—
524C22×Q8C2418yes—
525C22×D4C2412yes—
526C22×D4C2412yes—
527C22×D4C2412yes—
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2414yes—
532C22×D4C2414yes—
533C22×D4C2414yes—
534C23×C4C2411yescharacteristic
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2412yes—
538C23×C4C2412yes—
539C23×C4C2412yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2411yescharacteristic
545C23×C4C2414yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2411yescharacteristic
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—44no—
552C4⋊Q8—42no—
553C4⋊Q8—44no—
554C4⋊Q8—44no—
555C4⋊Q8—44no—
556#127—42no—
557#125—44no—
558#125—88no—
559#124—42no—
560#124—42no—
561#124—44no—
562#124—44no—
563#124—44no—
564#124—88no—
565#123—216no—
566#123—48no—
567#123—48no—
568#123—48no—
569#123—88no—
570C22⋊Q8—216no—
571C22⋊Q8—48no—
572C22⋊Q8—44no—
573C22⋊Q8—44no—
574C22⋊Q8—48no—
575C22⋊Q8—48no—
576C22⋊Q8—44no—
577C22⋊Q8—44no—
578C22⋊Q8—44no—
579C22⋊Q8—44no—
580C22⋊Q8—88no—
581C22⋊Q8—88no—
582#121—44no—
583#121—44no—
584#121—44no—
585#121—44no—
586#121—48no—
587#121—48no—
588#121—48no—
589#121—88no—
590C4×Q8—48no—
591C4×Q8—48no—
592C4×Q8—48no—
593C4×Q8—44no—
594C4×Q8—44no—
595C4×Q8—44no—
596C4×D4—44no—
597C4×D4—44no—
598C4×D4—44no—
599C4×D4—48no—
600C4×D4—48no—
601C4×D4—48no—
602C4×D4—48no—
603#117—24no—
604#117—24no—
605#117—24no—
606#117—24no—
607#117—24no—
608#117—44no—
609#117—44no—
610#117—44no—
611C2×C4⋊C4—24no—
612C2×C4⋊C4—24no—
613C2×C4⋊C4—24no—
614C2×C4⋊C4—28no—
615C2×C4⋊C4—44no—
616C2×C4⋊C4—44no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—84no—
619C2×C4⋊C4—84no—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2412yes—
623C2×C4⋊C4C2412yes—
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2414yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2418yes—
640C2×C4⋊C4C2418yes—
641C2×C4⋊C4C2418yes—
642C2×C4⋊C4C2418yes—
643C2×C4⋊C4C2418yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2414yes—
652C2×C4⋊C4C2414yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2418yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2418yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2418yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2414yes—
663C2×C4⋊C4C2414yes—
664C2×C4⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2412yes—
667C2×C22⋊C4C2412yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2414yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2414yes—
679C2×C22⋊C4C2414yes—
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2414yes—
682C2×C22⋊C4C2414yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2418yes—
685C2×C22⋊C4C2418yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2418yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2414yes—
694C2×C22⋊C4C2418yes—
695C2×C22⋊C4C2414yes—
696C2×C22⋊C4C2414yes—
697C2×C42—24no—
698C2×C42—24no—
699C2×C42—24no—
700C2×C42—44no—
701C2×C42—44no—
702C2×C42—44no—
703C2×C42C2412yes—
704C2×C42C2411yescharacteristic
705C2×C42C2412yes—
706C2×C42C2411yescharacteristic
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2412yes—
711C2×C42C2412yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2414yes—
717C2×C42C2414yes—
718C2×C42C2414yes—
719C2×C42C2418yes—
720C2×C42C2418yes—
721#95C2412yes—
722#95C2412yes—
723#95C2412yes—
724#95C2412yes—
725#95C2418yes—
726#95C2418yes—
727#95C2418yes—
728#95C2418yes—
729#95C2418yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2414yes—
735#95C2414yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2414yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2418yes—
748#95C2418yes—
749#95C2418yes—
750#95C2418yes—
751#95C2418yes—
752#95C2418yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756C24C2512yes—
757C24C2512yes—
758C24C2512yes—
759C24C2511yescharacteristic
760#41—416no—
761#41—416no—
762#41—416no—
763C2×Q8—24no—
764C2×Q8—22no—
765C2×Q8—24no—
766C2×Q8—22no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—22no—
772C2×Q8—22no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—22no—
776C2×Q8—22no—
777C2×Q8—22no—
778C2×Q8—28no—
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—48no—
782C2×Q8—48no—
783C2×Q8—48no—
784C2×Q8—416no—
785C2×Q8—816no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—24no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—24no—
793C2×D4—24no—
794C2×D4—24no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—22no—
799C2×D4—22no—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—28no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—48no—
810C2×D4—48no—
811C22×C4—22no—
812C22×C4—24no—
813C22×C4—22no—
814C22×C4—24no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—24no—
822C22×C4—24no—
823C22×C4—24no—
824C22×C4—24no—
825C22×C4—24no—
826C22×C4—24no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—24no—
831C22×C4—24no—
832C22×C4—24no—
833C22×C4—28no—
834C22×C4—28no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4—48no—
847C22×C4H(5,𝔽2)14yes—
848C22×C4H(5,𝔽2)14yes—
849C22×C42−1+414yes—
850C22×C4C2514yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2512yes—
855C22×C4C2512yes—
856C22×C4C2512yes—
857C22×C4C2512yes—
858C22×C4C2514yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2514yes—
863C22×C4C2514yes—
864C22×C4C2514yes—
865C22×C4C2512yes—
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2512yes—
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—24no—
875C4⋊C4—24no—
876C4⋊C4—24no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—24no—
880C4⋊C4—24no—
881C4⋊C4—24no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—48no—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—48no—
906C4⋊C4—48no—
907C4⋊C4—44no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—44no—
914C4⋊C4—44no—
915C4⋊C42−1+418yes—
916C22⋊C4—24no—
917C22⋊C4—24no—
918C22⋊C4—24no—
919C22⋊C4—24no—
920C22⋊C4—24no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—44no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C42—22no—
949C42—22no—
950C42—22no—
951C42—22no—
952C42—24no—
953C42—24no—
954C42—24no—
955C42—24no—
956C42—24no—
957C42—24no—
958C42—24no—
959C42—24no—
960C42—24no—
961C42—44no—
962C42—44no—
963C42—48no—
964C42—44no—
965C42—48no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23C2×H(5,𝔽2)12yes—
984C23C2×H(5,𝔽2)12yes—
985C23C2×2−1+412yes—
986C23C2611yescharacteristic
987Q8—48no—
988Q8—48no—
989Q8—44no—
990Q8—44no—
991Q8—44no—
992Q8—88no—
993Q8—816no—
994D4—48no—
995D4—48no—
996D4—48no—
997D4—44no—
998D4—44no—
999D4—44no—
1000D4—88no—
1001D4—164no—
1002D4—164no—
1003C2×C4—28no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—24no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—22no—
1023C2×C4—24no—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—24no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—24no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—24no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—28no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—28no—
1048C2×C4—22no—
1049C2×C4—24no—
1050C2×C4—24no—
1051C2×C4—28no—
1052C2×C4—22no—
1053C2×C4—48no—
1054C2×C4—48no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—48no—
1059C2×C4—48no—
1060C2×C4—88no—
1061C2×C4—88no—
1062C2×C4—84no—
1063C2×C4—84no—
1064C2×C4—84no—
1065C2×C4—164no—
1066C2×C4#562116yes—
1067C2×C4C2×H(5,𝔽2)12yes—
1068C2×C4C2×H(5,𝔽2)12yes—
1069C2×C4C2×H(5,𝔽2)12yes—
1070C2×C4C2×H(5,𝔽2)12yes—
1071C2×C4C2×2−1+414yes—
1072C2×C4C2×2−1+414yes—
1073C2×C4C2×2−1+414yes—
1074C2×C4C2×2−1+412yes—
1075C2×C4C2×2−1+412yes—
1076C22—22no—
1077C22—22no—
1078C22—24no—
1079C22—24no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—44no—
1087C22—44no—
1088C22—44no—
1089C22—44no—
1090C22—44no—
1091C22—44no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22C2×#56214yes—
1096C22C22×H(5,𝔽2)11yescharacteristic
1097C22C22×H(5,𝔽2)11yescharacteristic
1098C22C22×2−1+412yes—
1099C22C22×2−1+411yescharacteristic
1100C22H(7,𝔽2)12yes—
1101C4—24no—
1102C4—24no—
1103C4—24no—
1104C4—42no—
1105C4—42no—
1106C4—44no—
1107C4—44no—
1108C4—44no—
1109C4—42no—
1110C4—44no—
1111C4—42no—
1112C4—42no—
1113C4—44no—
1114C4—44no—
1115C4—44no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—44no—
1120C4C2×#56214yes—
1121C4C2×#56214yes—
1122C2—24no—
1123C2—82no—
1124C2—82no—
1125C2—82no—
1126C2C22×#56211yescharacteristic
1127C2#6283311yescharacteristic
1128C2#6287611yescharacteristic
1129C2#6294312yes—
1130C2#6294412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#35273C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #53130C2semidirect
2. #53050C2semidirect
3. #53021C2semidirect
4. #53016C2semidirect
5. #52321C2semidirect
6. #45749C2semidirect
7. #45653C2semidirect
8. #45650C2semidirect
9. #45501C2semidirect
10. #45500C2semidirect
11. #35628C2semidirect
12. #35621C2semidirect
13. #35592C2semidirect
14. #35574C2semidirect
15. #35555C2semidirect
16. #35530C2semidirect
17. #35308C2semidirect
18. #35307C2semidirect
19. #35280C2semidirect
21. #35182C2semidirect
22. #35153C2semidirect
23. C2×#2567C2semidirect
24. #34745C2semidirect
25. #34744C2semidirect

Maximal subgroups

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

subgroupindex
#531302
#530502
#530212
#530162
#523212
#457492
#456532
#456502
#455012
#455002
#356282
#356212
#355922
#355742
#355552
#355302
#353082
#353072
#352802
#352732
#351822
#351532
C2×#25672
#347452
#347442