Finite Group Databasebeta

← #7654868

Subgroups — #7654868

Order 512.

4636 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42921C214yesmaximal, complemented
2#42090C218yesmaximal, complemented
3#39633C212yesmaximal, complemented
4#39159C212yesmaximal, complemented
5#39078C214yesmaximal, complemented
6#39053C214yesmaximal, complemented
7#38976C212yesmaximal, complemented
8#38943C212yesmaximal, complemented
9#38248C214yesmaximal
10#37757C214yesmaximal, complemented
11#37641C211yesmaximal, characteristic, complemented
12#37630C212yesmaximal, complemented
13#36598C212yesmaximal, complemented
14#36552C212yesmaximal, complemented
15#36299C212yesmaximal, complemented
16#36133C212yesmaximal, complemented
17#35993C214yesmaximal, complemented
18#35280C211yesmaximal, characteristic
19#35275C211yesmaximal, characteristic, complemented
20#35206C212yesmaximal, complemented
21#35199C212yesmaximal, complemented
22#34979C211yesmaximal, characteristic
23#34929C212yesmaximal, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34154C211yesmaximal, characteristic, complemented
26#34127C211yesmaximal, characteristic
27C2×#544C2212yes—
28C2×#533C2211yescharacteristic
29C2×#533C2211yescharacteristic
30C2×#533C2214yes—
31C2×C4×#41C2211yescharacteristic
32#2868C2212yes—
33#2863C2214yes—
34#2862C2214yes—
35#2859C2212yes—
36#2857C2212yes—
37#2857C2212yes—
38#2855C2214yes—
39#2851C2214yes—
40#2839C2218yes—
41#2822C2214yes—
42#2790C2218yes—
43#2782C2218yes—
44#2770C2218yes—
45#2769C2218yes—
46#2766C2218yes—
47#2758C2218yes—
48#2745C2218yes—
49#2744C2218yes—
50#2729C2218yes—
51#2728C2218yes—
52#2719C2218yes—
53#2690C2218yes—
54#2666C2218yes—
55#2660C2214yes—
56#2655C2218yes—
57#2652C2218yes—
58#2647C2214yes—
59#2645C2214yes—
60#2645C2214yes—
61#2642C2214yes—
62#2629C2214yes—
63#2625C2214yes—
64#2625C2214yes—
65#2621C2214yes—
66#2611C2214yes—
67#2590C2218yes—
68#2582C2212yes—
69#2582C2212yes—
70#2582C2212yes—
71#2582C2212yes—
72#2577C2218yes—
73#2576C2218yes—
74#2571C2214yes—
75#2570C2218yes—
76#2568C2212yes—
77#2568C2212yes—
78#2568C2211yescharacteristic
79#2568C2214yes—
80#2556C2218yes—
81#2552C2212yes—
82#2552C2212yes—
83#2551C2212yes—
84#2551C2212yes—
85#2547C2211yescharacteristic
86#2546C2212yes—
87#2546C2212yes—
88#2546C2211yescharacteristic
89#2542C2211yescharacteristic
90#2538C2212yes—
91#2538C2212yes—
92#2520C2218yes—
93#2515C2218yes—
94#2515C2218yes—
95#2514C2214yes—
96#2511C2214yes—
97#2511C2214yes—
98#2511C2214yes—
99#2509C2214yes—
100#2508C2214yes—
101#2508C2214yes—
102#2506C2214yes—
103#2506C2214yes—
104#2505C2218yes—
105#2502C2214yes—
106#2499C2212yes—
107#2497C2214yes—
108#2495C2214yes—
109#2495C2214yes—
110#2492C2214yes—
111#2492C2214yes—
112#2489C2214yes—
113#2477C2218yes—
114#2475C2218yes—
115#2462C2218yes—
116#2453C2214yes—
117#2452C2214yes—
118#2451C2214yes—
119#2451C2214yes—
120#2447C2214yes—
121#2446C2214yes—
122#2446C2214yes—
123#2446C2218yes—
124#2440C2214yes—
125#2440C2214yes—
126#2440C2214yes—
127#2438C2218yes—
128#2432C2212yes—
129#2429C2214yes—
130#2421C2218yes—
131#2421C2214yes—
132#2417C2214yes—
133#2417C2214yes—
134#2415C2212yes—
135#2415C2212yes—
136#2396C2218yes—
137#2395C2214yes—
138#2371C2214yes—
139#2365C2211yescharacteristic
140#2365C2211yescharacteristic
141#2365C2214yes—
142#2365C2211yescharacteristic
143#2365C2211yescharacteristic
144#2362C2212yes—
145#2362C2212yes—
146#2362C2212yes—
147#2362C2212yes—
148#2360C2214yes—
149#2360C2214yes—
150#2360C2214yes—
151#2355C2212yes—
152#2355C2211yescharacteristic
153#2355C2211yescharacteristic
154#2355C2214yes—
155#2355C2212yes—
156#2352C2212yes—
157#2352C2212yes—
158Q8×C4⋊C4C2212yes—
159Q8×C4⋊C4C2212yes—
160D4×C4⋊C4C2211yescharacteristic
161D4×C4⋊C4C2211yescharacteristic
162#2347C2212yes—
163#2344C2214yes—
164#2343C2214yes—
165#2339C2212yes—
166#2331C2214yes—
167#2330C2214yes—
168#2326C2214yes—
169#2320C2214yes—
170#2320C2214yes—
171#2317C2212yes—
172#2317C2212yes—
173#2316C2212yes—
174#2311C2212yes—
175C4×C4⋊Q8C2212yes—
176C4×C4⋊Q8C2212yes—
177C4×C4⋊Q8C2214yes—
178C4×C4⋊Q8C2212yes—
179C4×#124C2212yes—
180C4×C22⋊Q8C2212yes—
181C4×C22⋊Q8C2212yes—
182C4×C22⋊Q8C2214yes—
183#2298C2214yes—
184#2295C2212yes—
185#2295C2212yes—
186#2295C2212yes—
187#2293C2214yes—
188#2290C2214yes—
189#2285C2211yescharacteristic
190C2×#384C2211yescharacteristic
191#2283C2212yes—
192#2274C2212yes—
193C42×Q8C2212yes—
194C42×Q8C2212yes—
195C42×D4C2212yes—
196C4×#117C2211yescharacteristic
197C4×#117C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200#544—48no—
201#533—28no—
202#533—28no—
203#533—416no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2314yes—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2314yes—
213C2×C4⋊Q8C2314yes—
214C2×#125C2312yes—
215C2×#125C2312yes—
216C2×#125C2314yes—
217C2×#125C2314yes—
218C2×#125C2318yes—
219C2×#124C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2314yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C4×#41—28no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2312yes—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2314yes—
241C2×C4×Q8C2314yes—
242C2×C4×Q8C2318yes—
243C2×C4×Q8C2312yes—
244C2×C4×D4C2312yes—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2312yes—
247C2×C4×D4C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×#117C2312yes—
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2312yes—
254C2×#117C2312yes—
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C2×#117C2312yes—
259C2×#117C2318yes—
260C22×C4⋊C4C2312yes—
261C22×C4⋊C4C2312yes—
262C22×C4⋊C4C2312yes—
263C22×C4⋊C4C2312yes—
264C22×C4⋊C4C2312yes—
265C22×C42C2312yes—
266C22×C42C2314yes—
267C22×C42C2311yescharacteristic
268#401C2318yes—
269#400C2318yes—
270#400C2318yes—
271#400C2318yes—
272#400C2318yes—
273#400C2314yes—
274#400C2318yes—
275#400C2318yes—
276#400C2318yes—
277#400C2318yes—
278#400C2318yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#399C2314yes—
286#398C2318yes—
287#398C2318yes—
288#398C2318yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2314yes—
299#398C2318yes—
300#397C2318yes—
301#397C2314yes—
302#397C2318yes—
303#397C2314yes—
304#397C2314yes—
305#397C2318yes—
306#397C2318yes—
307#396C2318yes—
308#396C2318yes—
309#396C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#394C2314yes—
314#394C2314yes—
315#393C2318yes—
316#391C2312yes—
317#391C2318yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2314yes—
328#391C2318yes—
329#391C2314yes—
330#391C2312yes—
331#391C2312yes—
332#391C2314yes—
333#391C2318yes—
334#391C2312yes—
335#391C2312yes—
336#391C2312yes—
337#391C2318yes—
338#391C2312yes—
339#391C2312yes—
340#391C2312yes—
341#391C2312yes—
342#390C2314yes—
343#390C2312yes—
344#389C2314yes—
345#389C2318yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2314yes—
352#389C2314yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2314yes—
360#389C2312yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2318yes—
366#389C2318yes—
367#389C2312yes—
368#389C2318yes—
369#389C2312yes—
370#389C2314yes—
371#389C2312yes—
372#389C2312yes—
373#389C2314yes—
374#389C2314yes—
375#389C2312yes—
376#389C2312yes—
377#389C2312yes—
378#388C2314yes—
379#388C2318yes—
380#388C2314yes—
381#388C2318yes—
382#388C2314yes—
383#388C2314yes—
384#388C2314yes—
385#388C2314yes—
386#388C2314yes—
387#388C2314yes—
388#388C2318yes—
389#388C2318yes—
390#387C2314yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2314yes—
401#387C2314yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2314yes—
406#387C2314yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2318yes—
412#387C2318yes—
413#387C2314yes—
414#387C2314yes—
415#387C2314yes—
416#387C2314yes—
417#387C2314yes—
418#387C2314yes—
419#387C2314yes—
420#386C2318yes—
421#386C2314yes—
422#386C2314yes—
423#385C2318yes—
424#385C2318yes—
425#385C2318yes—
426#385C2318yes—
427#385C2318yes—
428#385C2314yes—
429#385C2314yes—
430#385C2314yes—
431#385C2314yes—
432#385C2318yes—
433#384C2312yes—
434#384C2312yes—
435#384C2314yes—
436#384C2314yes—
437#384C2314yes—
438#384C2314yes—
439#384C2311yescharacteristic
440#384C2311yescharacteristic
441#384C2312yes—
442#384C2312yes—
443#384C2312yes—
444#383C2318yes—
445#383C2318yes—
446#383C2314yes—
447#382C2312yes—
448#382C2312yes—
449#382C2314yes—
450#382C2314yes—
451#382C2312yes—
452#382C2318yes—
453#382C2318yes—
454#382C2314yes—
455#382C2318yes—
456#382C2312yes—
457#381C2318yes—
458#381C2314yes—
459#380C2314yes—
460#380C2314yes—
461#380C2318yes—
462#380C2312yes—
463#380C2312yes—
464#380C2314yes—
465#380C2312yes—
466#380C2314yes—
467#380C2312yes—
468#380C2312yes—
469#380C2312yes—
470C4×C4⋊C4C2312yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2318yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2314yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2314yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2314yes—
482C4×C4⋊C4C2312yes—
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2312yes—
487C4×C4⋊C4C2314yes—
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491C4×C4⋊C4C2314yes—
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2312yes—
494C4×C4⋊C4C2311yescharacteristic
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2314yes—
497C4×C4⋊C4C2314yes—
498C4×C4⋊C4C2314yes—
499C4×C4⋊C4C2311yescharacteristic
500C4×C4⋊C4C2311yescharacteristic
501C4×C4⋊C4C2314yes—
502C4×C4⋊C4C2314yes—
503C4×C4⋊C4C2314yes—
504C4×C4⋊C4C2311yescharacteristic
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2318yes—
507C4×C22⋊C4C2312yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2314yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2314yes—
513C4×C22⋊C4C2312yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2312yes—
516#376C2314yes—
517#376C2314yes—
518#376C2312yes—
519#376C2312yes—
520C2×#95C2314yes—
521C43C2312yes—
522C43C2312yes—
523C43C2314yes—
524C2×#41—24no—
525C2×#41—24no—
526C2×#41—42no—
527C22×Q8C2412yes—
528C22×Q8C2412yes—
529C22×Q8C2412yes—
530C22×Q8C2412yes—
531C22×Q8C2411yescharacteristic
532C22×Q8C2418yes—
533C22×D4C2412yes—
534C22×D4C2411yescharacteristic
535C23×C4C2412yes—
536C23×C4C2412yes—
537C23×C4C2414yes—
538C23×C4C2412yes—
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C23×C4C2414yes—
543C23×C4C2414yes—
544C4⋊Q8—216no—
545C4⋊Q8—24no—
546C4⋊Q8—24no—
547C4⋊Q8—24no—
548C4⋊Q8—24no—
549C4⋊Q8—48no—
550C4⋊Q8—48no—
551C4⋊Q8—44no—
552C4⋊Q8—48no—
553C4⋊Q8—48no—
554#125—28no—
555#125—28no—
556#125—48no—
557#125—48no—
558#125—416no—
559#124—28no—
560C22⋊Q8—28no—
561C22⋊Q8—28no—
562C22⋊Q8—28no—
563C22⋊Q8—28no—
564C22⋊Q8—28no—
565C22⋊Q8—28no—
566C22⋊Q8—416no—
567C22⋊Q8—416no—
568C22⋊Q8—48no—
569C22⋊Q8—48no—
570C4×Q8—28no—
571C4×Q8—28no—
572C4×Q8—28no—
573C4×Q8—24no—
574C4×Q8—24no—
575C4×Q8—28no—
576C4×Q8—28no—
577C4×Q8—28no—
578C4×Q8—28no—
579C4×Q8—48no—
580C4×Q8—44no—
581C4×Q8—48no—
582C4×Q8—416no—
583C4×D4—28no—
584C4×D4—28no—
585C4×D4—28no—
586C4×D4—24no—
587C4×D4—24no—
588C4×D4—44no—
589#117—24no—
590#117—28no—
591#117—28no—
592#117—24no—
593#117—24no—
594#117—24no—
595#117—28no—
596#117—44no—
597#117—416no—
598#117—42no—
599C2×C4⋊C4—28no—
600C2×C4⋊C4—44no—
601C2×C4⋊C4—44no—
602C2×C4⋊C4—44no—
603C2×C4⋊C4—44no—
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2412yes—
609C2×C4⋊C4C2412yes—
610C2×C4⋊C4C2414yes—
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2412yes—
614C2×C4⋊C4C2412yes—
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2412yes—
619C2×C4⋊C4C2412yes—
620C2×C4⋊C4C2412yes—
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2412yes—
625C2×C4⋊C4C2412yes—
626C2×C4⋊C4C2414yes—
627C2×C4⋊C4C2414yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2414yes—
631C2×C4⋊C4C2414yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2412yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2414yes—
637C2×C4⋊C4C2414yes—
638C2×C4⋊C4C2414yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2414yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2412yes—
646C2×C4⋊C4C2418yes—
647C2×C4⋊C4C2418yes—
648C2×C4⋊C4C2418yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2418yes—
651C2×C4⋊C4C2418yes—
652C2×C4⋊C4C2418yes—
653C2×C4⋊C4C2418yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C22⋊C4C2414yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2412yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2412yes—
669C2×C22⋊C4C2412yes—
670C2×C22⋊C4C2414yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2418yes—
675C2×C22⋊C4C2414yes—
676C2×C22⋊C4C2412yes—
677C2×C22⋊C4C2414yes—
678C2×C22⋊C4C2418yes—
679C2×C42—28no—
680C2×C42—48no—
681C2×C42#4118yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2414yes—
685C2×C42C2414yes—
686C2×C42C2412yes—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2412yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2412yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2412yes—
697C2×C42C2412yes—
698C2×C42C2414yes—
699C2×C42C2414yes—
700C2×C42C2412yes—
701C2×C42C2412yes—
702C2×C42C2418yes—
703C2×C42C2412yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2418yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#95C2412yes—
713#95C2414yes—
714#95C2414yes—
715#95C2414yes—
716#95C2412yes—
717#95C2412yes—
718#95C2412yes—
719#95C2412yes—
720#95C2412yes—
721#95C2412yes—
722#95C2412yes—
723#95C2414yes—
724#95C2414yes—
725#95C2414yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2414yes—
732#95C2414yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2414yes—
738#95C2414yes—
739#95C2414yes—
740#95C2414yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2414yes—
745#95C2414yes—
746#95C2418yes—
747#95C2414yes—
748#95C2414yes—
749#95C2418yes—
750#95C2418yes—
751#95C2414yes—
752#95C2414yes—
753#95C2418yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762C24C2511yescharacteristic
763C24C2512yes—
764#41—416no—
765C2×Q8—22no—
766C2×Q8—24no—
767C2×Q8—24no—
768C2×Q8—24no—
769C2×Q8—24no—
770C2×Q8—24no—
771C2×Q8—24no—
772C2×Q8—216no—
773C2×Q8—24no—
774C2×Q8—24no—
775C2×Q8—24no—
776C2×Q8—24no—
777C2×Q8—22no—
778C2×Q8—24no—
779C2×Q8—24no—
780C2×Q8—22no—
781C2×Q8—48no—
782C2×Q8—48no—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4—42no—
788C2×D42−1+414yes—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—28no—
796C22×C4—24no—
797C22×C4—24no—
798C22×C4—24no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—28no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—44no—
806C22×C4—42no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—44no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4C2×#4114yes—
814C22×C4C2×#4114yes—
815C22×C4C2×#4114yes—
816C22×C4C2512yes—
817C22×C4C2512yes—
818C22×C4C2512yes—
819C22×C4C2512yes—
820C22×C4C2514yes—
821C22×C4C2514yes—
822C22×C4C2512yes—
823C22×C4C2514yes—
824C22×C4C2512yes—
825C22×C4C2512yes—
826C22×C4C2514yes—
827C22×C4C2514yes—
828C22×C4C2514yes—
829C22×C4C2512yes—
830C22×C4C2518yes—
831C22×C4C2511yescharacteristic
832C22×C4C2511yescharacteristic
833C22×C4C2511yescharacteristic
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2512yes—
837C22×C4C2511yescharacteristic
838C22×C4C2511yescharacteristic
839C22×C4C2511yescharacteristic
840C4⋊C4—22no—
841C4⋊C4—22no—
842C4⋊C4—24no—
843C4⋊C4—24no—
844C4⋊C4—24no—
845C4⋊C4—24no—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—28no—
849C4⋊C4—28no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—28no—
857C4⋊C4—22no—
858C4⋊C4—216no—
859C4⋊C4—28no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—24no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—24no—
866C4⋊C4—28no—
867C4⋊C4—28no—
868C4⋊C4—28no—
869C4⋊C4—22no—
870C4⋊C4—28no—
871C4⋊C4—28no—
872C4⋊C4—24no—
873C4⋊C4—22no—
874C4⋊C4—24no—
875C4⋊C4—44no—
876C4⋊C4—44no—
877C4⋊C4—44no—
878C4⋊C4—44no—
879C4⋊C4—42no—
880C4⋊C4—48no—
881C4⋊C4—42no—
882C4⋊C4—44no—
883C4⋊C4—48no—
884C4⋊C4—48no—
885C4⋊C4—48no—
886C4⋊C4—48no—
887C4⋊C4—48no—
888C4⋊C4—48no—
889C4⋊C4—48no—
890C4⋊C4—44no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—48no—
894C4⋊C4H(5,𝔽2)14yes—
895C4⋊C42−1+414yes—
896C4⋊C42−1+414yes—
897C22⋊C4—24no—
898C22⋊C4—28no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—24no—
904C22⋊C4—24no—
905C22⋊C4—24no—
906C22⋊C4—28no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—28no—
910C22⋊C4—42no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C42—24no—
916C42—24no—
917C42—24no—
918C42—28no—
919C42—28no—
920C42—24no—
921C42—28no—
922C42—24no—
923C42—28no—
924C42—24no—
925C42—24no—
926C42—24no—
927C42—24no—
928C42—28no—
929C42—24no—
930C42—28no—
931C42—24no—
932C42—24no—
933C42—24no—
934C42—24no—
935C42—44no—
936C42—44no—
937C42—42no—
938C42—48no—
939C42—44no—
940C42—48no—
941C42C2×#4114yes—
942C42C2×#4114yes—
943C42C2×#4114yes—
944C42C2×#4114yes—
945C23—22no—
946C23—22no—
947C23—21no—
948C23—22no—
949C23—21no—
950C23—21no—
951C23—22no—
952C23—21no—
953C23—22no—
954C23—21no—
955C23—22no—
956C23—21no—
957C23C22×#4112yes—
958C23C2×2−1+414yes—
959C23C2611yescharacteristic
960Q8—48no—
961Q8—48no—
962Q8—44no—
963Q8—48no—
964Q8—48no—
965Q8—816no—
966D4—28no—
967D4—48no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—28no—
981C2×C4—28no—
982C2×C4—28no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—24no—
987C2×C4—24no—
988C2×C4—24no—
989C2×C4—24no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—22no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—28no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—24no—
1010C2×C4—24no—
1011C2×C4—24no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—24no—
1020C2×C4—24no—
1021C2×C4—22no—
1022C2×C4—28no—
1023C2×C4—28no—
1024C2×C4—24no—
1025C2×C4—24no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—416no—
1029C2×C4—48no—
1030C2×C4—48no—
1031C2×C4—48no—
1032C2×C4—88no—
1033C2×C4—164no—
1034C2×C4C22×#4112yes—
1035C2×C4C22×#4112yes—
1036C2×C4C22×#4112yes—
1037C2×C4C22×#4112yes—
1038C2×C4C22×#4112yes—
1039C2×C4C22×#4112yes—
1040C2×C4C2×H(5,𝔽2)14yes—
1041C2×C4C2×H(5,𝔽2)12yes—
1042C2×C4C2×2−1+414yes—
1043C2×C4C2×2−1+414yes—
1044C2×C4C2×2−1+412yes—
1045C2×C4C2×2−1+412yes—
1046C2×C4C2×2−1+412yes—
1047C2×C4#58512yes—
1048C2×C4#58512yes—
1049C22—24no—
1050C22—24no—
1051C22—22no—
1052C22—22no—
1053C22—24no—
1054C22—22no—
1055C22—41no—
1056C22—42no—
1057C22—41no—
1058C22—41no—
1059C22—42no—
1060C22—41no—
1061C22—42no—
1062C22—42no—
1063C22C23×#4111yescharacteristic
1064C22C22×H(5,𝔽2)11yescharacteristic
1065C22C22×2−1+411yescharacteristic
1066C22C22×2−1+411yescharacteristic
1067C22C22×2−1+411yescharacteristic
1068C22C2×#58511yescharacteristic
1069C22C2×#58511yescharacteristic
1070C4—24no—
1071C4—24no—
1072C4—24no—
1073C4—22no—
1074C4—22no—
1075C4—22no—
1076C4—42no—
1077C4—44no—
1078C4—42no—
1079C4—44no—
1080C4—48no—
1081C4—42no—
1082C4—42no—
1083C4—42no—
1084C4—42no—
1085C4—44no—
1086C4—44no—
1087C4—42no—
1088C4—44no—
1089C4—42no—
1090C4—44no—
1091C4#346114yes—
1092C4#349514yes—
1093C4#351114yes—
1094C2—44no—
1095C2—42no—
1096C2C2×#346111yescharacteristic
1097C2C2×#351111yescharacteristic
1098C2C2×#349511yescharacteristic
1099C2#6301611yescharacteristic
1100C2#6302111yescharacteristic
1101C2#6303211yescharacteristic
1102C2#6303211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×#41C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42921C2semidirect
2. #42090C2semidirect
3. #39633C2semidirect
4. #39159C2semidirect
5. #39078C2semidirect
6. #39053C2semidirect
7. #38976C2semidirect
8. #38943C2semidirect
10. #37757C2semidirect
11. #37641C2semidirect
12. #37630C2semidirect
13. #36598C2semidirect
14. #36552C2semidirect
15. #36299C2semidirect
16. #36133C2semidirect
17. #35993C2semidirect
19. #35275C2semidirect
20. #35206C2semidirect
21. #35199C2semidirect
23. #34929C2semidirect
24. #34214C2semidirect
25. #34154C2semidirect

Maximal subgroups

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

subgroupindex
#429212
#420902
#396332
#391592
#390782
#390532
#389762
#389432
#382482
#377572
#376412
#376302
#365982
#365522
#362992
#361332
#359932
#352802
#352752
#352062
#351992
#349792
#349292
#342142
#341542
#341272