Finite Group Databasebeta

← #7633066

Subgroups — #7633066

Order 512.

5246 conjugacy classes of subgroups.

The subgroup lattice has 1141 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36564C212yesmaximal, complemented
2#36480C212yesmaximal, complemented
3#36288C212yesmaximal, complemented
4#36278C214yesmaximal, complemented
5#36133C212yesmaximal, complemented
6#36129C214yesmaximal, complemented
7#35931C218yesmaximal, complemented
8#35843C214yesmaximal, complemented
9#35747C214yesmaximal, complemented
10#35585C212yesmaximal, complemented
11#35582C214yesmaximal, complemented
12#35581C214yesmaximal, complemented
13#35574C212yesmaximal
14#35280C211yesmaximal, characteristic
15#35199C212yesmaximal, complemented
16#35177C212yesmaximal, complemented
17#35173C211yesmaximal, characteristic, complemented
18#34950C212yesmaximal, complemented
19#34947C211yesmaximal, characteristic
20#34929C212yesmaximal, complemented
21C2×#2551C211yesmaximal, characteristic, complemented
22#34253C212yesmaximal
23#34216C212yesmaximal, complemented
24#34214C211yesmaximal, characteristic, complemented
25#34145C211yesmaximal, characteristic, complemented
26C4×#520C211yesmaximal, characteristic
27C2×#533C2211yescharacteristic
28C2×#533C2211yescharacteristic
29C2×#533C2214yes—
30C22×C4⋊Q8C2212yes—
31C22×C4⋊Q8C2212yes—
32C2×#520C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×C4×#41C2211yescharacteristic
35#2863C2214yes—
36#2862C2214yes—
37#2857C2214yes—
38#2857C2214yes—
39#2857C2212yes—
40#2857C2212yes—
41#2855C2214yes—
42#2666C2218yes—
43#2665C2218yes—
44#2659C2214yes—
45#2629C2214yes—
46#2612C2218yes—
47#2608C2218yes—
48#2606C2218yes—
49#2605C2218yes—
50#2590C2218yes—
51#2587C2218yes—
52#2586C2218yes—
53#2586C2218yes—
54#2584C2214yes—
55#2584C2214yes—
56#2582C2212yes—
57#2582C2212yes—
58#2579C2218yes—
59#2574C2218yes—
60#2569C2218yes—
61#2568C2211yescharacteristic
62#2567C2212yes—
63#2567C2212yes—
64#2567C2211yescharacteristic
65#2566C2212yes—
66#2565C2212yes—
67#2564C2214yes—
68#2563C2211yescharacteristic
69#2556C2218yes—
70#2551C2214yes—
71#2551C2212yes—
72#2551C2212yes—
73#2551C2212yes—
74#2551C2212yes—
75#2551C2214yes—
76#2550C2218yes—
77#2549C2218yes—
78#2546C2212yes—
79#2546C2212yes—
80#2542C2211yescharacteristic
81#2538C2212yes—
82#2538C2212yes—
83#2520C2218yes—
84#2509C2214yes—
85#2509C2214yes—
86#2508C2214yes—
87#2508C2214yes—
88#2507C2214yes—
89#2507C2214yes—
90#2507C2214yes—
91#2506C2214yes—
92#2506C2214yes—
93#2497C2214yes—
94#2492C2214yes—
95#2492C2214yes—
96#2465C2218yes—
97#2465C2218yes—
98#2462C2218yes—
99#2452C2214yes—
100#2452C2214yes—
101#2451C2214yes—
102#2451C2214yes—
103#2451C2214yes—
104#2451C2214yes—
105#2446C2218yes—
106#2446C2214yes—
107#2442C2218yes—
108#2440C2214yes—
109#2440C2214yes—
110#2439C2218yes—
111#2439C2214yes—
112#2439C2214yes—
113#2438C2218yes—
114#2429C2218yes—
115#2429C2214yes—
116#2417C2212yes—
117#2417C2214yes—
118#2417C2214yes—
119#2417C2212yes—
120#2409C2218yes—
121#2399C2218yes—
122#2396C2218yes—
123#2396C2214yes—
124C2×#395C2214yes—
125#2370C2212yes—
126#2370C2212yes—
127#2369C2214yes—
128#2369C2211yescharacteristic
129#2369C2211yescharacteristic
130#2369C2214yes—
131#2368C2214yes—
132#2365C2214yes—
133#2365C2211yescharacteristic
134#2365C2211yescharacteristic
135#2365C2214yes—
136#2360C2212yes—
137#2360C2214yes—
138#2360C2214yes—
139#2360C2212yes—
140#2355C2212yes—
141#2355C2212yes—
142#2353C2218yes—
143#2352C2218yes—
144Q8×C4⋊C4C2212yes—
145Q8×C4⋊C4C2212yes—
146#2347C2214yes—
147#2346C2214yes—
148#2345C2214yes—
149#2345C2218yes—
150#2344C2214yes—
151Q8×C22⋊C4C2218yes—
152#2331C2214yes—
153#2331C2214yes—
154#2330C2214yes—
155#2320C2214yes—
156#2319C2214yes—
157#2317C2212yes—
158#2316C2212yes—
159#2316C2212yes—
160#2316C2212yes—
161#2311C2212yes—
162C4×C4⋊Q8C2214yes—
163C4×C4⋊Q8C2212yes—
164C4×C4⋊Q8C2212yes—
165C4×C4⋊Q8C2214yes—
166C4×C4⋊Q8C2214yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2214yes—
169C4×C22⋊Q8C2212yes—
170#2297C2212yes—
171#2296C2212yes—
172#2295C2212yes—
173#2295C2214yes—
174#2295C2214yes—
175#2295C2214yes—
176#2293C2214yes—
177C2×#389C2212yes—
178C2×#389C2212yes—
179#2285C2212yes—
180C2×#384C2211yescharacteristic
181#2276C2212yes—
182#2275C2214yes—
183#2275C2212yes—
184#2274C2211yescharacteristic
185#2274C2212yes—
186#2274C2212yes—
187#2274C2212yes—
188#2274C2211yescharacteristic
189C42×Q8C2212yes—
190C42×Q8C2212yes—
191C42×D4C2214yes—
192C42×D4C2212yes—
193C4×#117C2211yescharacteristic
194C4×#117C2212yes—
195C4×#117C2212yes—
196C2×C4×C4⋊C4C2212yes—
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C23×Q8C2314yes—
201#533—28no—
202#533—28no—
203#533—416no—
204C2×C4⋊Q8—216no—
205C2×C4⋊Q8—48no—
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2314yes—
209C2×C4⋊Q8C2314yes—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2314yes—
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2314yes—
214C2×C4⋊Q8C2314yes—
215C2×C4⋊Q8C2314yes—
216C2×C4⋊Q8C2314yes—
217C2×C4⋊Q8C2318yes—
218C2×#125C2312yes—
219C2×#125C2312yes—
220C2×#125C2318yes—
221C2×C22⋊Q8C2312yes—
222C2×C22⋊Q8C2312yes—
223C2×C22⋊Q8C2312yes—
224C2×C22⋊Q8C2312yes—
225C2×C22⋊Q8C2312yes—
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2314yes—
228C2×C22⋊Q8C2318yes—
229C2×C22⋊Q8C2318yes—
230C2×C22⋊Q8C2314yes—
231#520—28no—
232#520Q8116yescomplemented
233C4×#41—28no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2312yes—
237C2×C4×Q8C2312yes—
238C2×C4×Q8C2312yes—
239C2×C4×Q8C2312yes—
240C2×C4×Q8C2312yes—
241C2×C4×Q8C2312yes—
242C2×C4×Q8C2312yes—
243C2×C4×Q8C2318yes—
244C2×C4×Q8C2314yes—
245C2×C4×Q8C2318yes—
246C2×C4×Q8C2314yes—
247C2×C4×Q8C2312yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2314yes—
252C2×C4×D4C2312yes—
253C2×C4×D4C2312yes—
254C2×C4×D4C2314yes—
255C2×C4×D4C2312yes—
256C2×#117C2312yes—
257C2×#117C2312yes—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C2×#117C2312yes—
261C2×#117C2312yes—
262C2×#117C2318yes—
263C2×#117C2311yescharacteristic
264C2×#117C2312yes—
265C22×C4⋊C4C2312yes—
266C22×C4⋊C4C2314yes—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2312yes—
270C22×C4⋊C4C2314yes—
271C22×C4⋊C4C2312yes—
272C22×C4⋊C4C2312yes—
273C22×C4⋊C4C2311yescharacteristic
274C22×C4⋊C4C2312yes—
275C22×C4⋊C4C2311yescharacteristic
276C22×C42C2312yes—
277C22×C42C2312yes—
278C22×C42C2314yes—
279C22×C42C2312yes—
280C22×C42C2311yescharacteristic
281#400C2314yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#399C2314yes—
287#398C2314yes—
288#398C2314yes—
289#398C2318yes—
290#398C2318yes—
291#398C2318yes—
292#398C2318yes—
293#398C2318yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#398C2318yes—
299#396C2314yes—
300#396C2314yes—
301#396C2318yes—
302#396C2318yes—
303#396C2318yes—
304#396C2318yes—
305#395C2314yes—
306#395C2318yes—
307#395C2318yes—
308#395C2318yes—
309#395C2318yes—
310#395C2318yes—
311#395C2318yes—
312#395C2318yes—
313#395C2318yes—
314#393C2314yes—
315#393C2318yes—
316#393C2318yes—
317#391C2314yes—
318#391C2318yes—
319#391C2318yes—
320#391C2318yes—
321#391C2314yes—
322#391C2312yes—
323#391C2312yes—
324#391C2314yes—
325#391C2314yes—
326#391C2314yes—
327#391C2312yes—
328#391C2312yes—
329#391C2318yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2318yes—
334#391C2318yes—
335#391C2318yes—
336#391C2312yes—
337#391C2314yes—
338#391C2312yes—
339#391C2318yes—
340#390C2312yes—
341#390C2312yes—
342#390C2314yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2314yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#389C2314yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2318yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#389C2312yes—
360#389C2314yes—
361#389C2314yes—
362#389C2314yes—
363#389C2314yes—
364#389C2314yes—
365#389C2314yes—
366#389C2314yes—
367#389C2318yes—
368#389C2318yes—
369#389C2318yes—
370#389C2318yes—
371#389C2318yes—
372#389C2318yes—
373#389C2314yes—
374#389C2314yes—
375#389C2314yes—
376#389C2314yes—
377#389C2312yes—
378#389C2312yes—
379#389C2314yes—
380#389C2312yes—
381#389C2312yes—
382#389C2312yes—
383#389C2312yes—
384#389C2314yes—
385#389C2314yes—
386#388C2318yes—
387#388C2318yes—
388#388C2318yes—
389#388C2318yes—
390#387C2314yes—
391#387C2314yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2314yes—
397#387C2318yes—
398#387C2318yes—
399#387C2318yes—
400#387C2318yes—
401#387C2318yes—
402#387C2318yes—
403#387C2318yes—
404#387C2318yes—
405#387C2318yes—
406#387C2318yes—
407#387C2318yes—
408#387C2318yes—
409#387C2314yes—
410#387C2314yes—
411#387C2314yes—
412#387C2314yes—
413#387C2314yes—
414#386C2314yes—
415#386C2314yes—
416#386C2318yes—
417#385C2314yes—
418#385C2314yes—
419#385C2314yes—
420#385C2318yes—
421#385C2318yes—
422#385C2318yes—
423#385C2314yes—
424#384C2312yes—
425#384C2312yes—
426#384C2312yes—
427#384C2314yes—
428#384C2314yes—
429#384C2312yes—
430#384C2312yes—
431#384C2312yes—
432#383C2318yes—
433#382C2312yes—
434#382C2312yes—
435#382C2314yes—
436#382C2318yes—
437#382C2318yes—
438#381C2318yes—
439#380C2312yes—
440#380C2312yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2314yes—
445#380C2318yes—
446#380C2318yes—
447#380C2318yes—
448#380C2314yes—
449#380C2318yes—
450#380C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2314yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2312yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2312yes—
457C4×C4⋊C4C2318yes—
458C4×C4⋊C4C2318yes—
459C4×C4⋊C4C2318yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2312yes—
464C4×C4⋊C4C2312yes—
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2312yes—
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2314yes—
469C4×C4⋊C4C2314yes—
470C4×C4⋊C4C2314yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2312yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2312yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C4⋊C4C2314yes—
481C4×C4⋊C4C2311yescharacteristic
482C4×C4⋊C4C2311yescharacteristic
483C4×C4⋊C4C2312yes—
484C4×C4⋊C4C2312yes—
485C4×C4⋊C4C2312yes—
486C4×C4⋊C4C2314yes—
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2314yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2312yes—
492C4×C4⋊C4C2314yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2314yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2312yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2314yes—
502C4×C22⋊C4C2314yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2318yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2314yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2312yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515C4×C22⋊C4C2314yes—
516#376C2314yes—
517#376C2312yes—
518#376C2318yes—
519#376C2314yes—
520C2×#95C2312yes—
521C2×#95C2314yes—
522C2×#95C2312yes—
523C2×#95C2314yes—
524C43C2312yes—
525C43C2314yes—
526C43C2314yes—
527C2×#41—24no—
528C2×#41—24no—
529C2×#41C2×Q818yes—
530C22×Q8—216no—
531C22×Q8—48no—
532C22×Q8—84no—
533C22×Q8C2412yes—
534C22×Q8C2412yes—
535C22×Q8C2418yes—
536C22×Q8C2411yescharacteristic
537C22×Q8C2412yes—
538C22×Q8C2412yes—
539C22×Q8C2418yes—
540C22×D4C2412yes—
541C22×D4C2411yescharacteristic
542C23×C4C2412yes—
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2411yescharacteristic
547C23×C4C2414yes—
548C23×C4C2414yes—
549C23×C4C2412yes—
550C23×C4C2412yes—
551C23×C4C2414yes—
552C23×C4C2412yes—
553C23×C4C2411yescharacteristic
554C23×C4C2411yescharacteristic
555C4⋊Q8—216no—
556C4⋊Q8—216no—
557C4⋊Q8—216no—
558C4⋊Q8—216no—
559C4⋊Q8—216no—
560C4⋊Q8—24no—
561C4⋊Q8—24no—
562C4⋊Q8—24no—
563C4⋊Q8—24no—
564C4⋊Q8—48no—
565C4⋊Q8—48no—
566C4⋊Q8—416no—
567#125—28no—
568#125—28no—
569#125—416no—
570C22⋊Q8—28no—
571C22⋊Q8—28no—
572C22⋊Q8—28no—
573C22⋊Q8—28no—
574C22⋊Q8—28no—
575C22⋊Q8—28no—
576C22⋊Q8—416no—
577C22⋊Q8—48no—
578C22⋊Q8—84no—
579C22⋊Q8—88no—
580C4×Q8—28no—
581C4×Q8—28no—
582C4×Q8—28no—
583C4×Q8—24no—
584C4×Q8—24no—
585C4×Q8—28no—
586C4×Q8—28no—
587C4×Q8—28no—
588C4×Q8—28no—
589C4×Q8—48no—
590C4×Q8—416no—
591C4×Q8—84no—
592C4×Q8—88no—
593C4×Q8C2×Q8116yescomplemented
594C4×D4—28no—
595C4×D4—28no—
596C4×D4—216no—
597C4×D4—28no—
598C4×D4—24no—
599C4×D4—24no—
600C4×D4C2×Q8132yes—
601C4×D4C2×Q8116yescomplemented
602#117—24no—
603#117—24no—
604#117—28no—
605#117—28no—
606#117—28no—
607#117—28no—
608#117—416no—
609#117C2×Q818yes—
610#117C2×Q8116yescomplemented
611C2×C4⋊C4—216no—
612C2×C4⋊C4—28no—
613C2×C4⋊C4—28no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—48no—
617C2×C4⋊C4—44no—
618C2×C4⋊C4—82no—
619C2×C4⋊C4C2×Q818yes—
620C2×C4⋊C4C2×Q8116yescomplemented
621C2×C4⋊C4#4118yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2418yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2414yes—
629C2×C4⋊C4C2414yes—
630C2×C4⋊C4C2418yes—
631C2×C4⋊C4C2418yes—
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2412yes—
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2412yes—
638C2×C4⋊C4C2412yes—
639C2×C4⋊C4C2412yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2412yes—
642C2×C4⋊C4C2412yes—
643C2×C4⋊C4C2414yes—
644C2×C4⋊C4C2414yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2412yes—
650C2×C4⋊C4C2412yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2414yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2418yes—
658C2×C4⋊C4C2414yes—
659C2×C4⋊C4C2418yes—
660C2×C4⋊C4C2414yes—
661C2×C4⋊C4C2418yes—
662C2×C4⋊C4C2418yes—
663C2×C4⋊C4C2418yes—
664C2×C4⋊C4C2418yes—
665C2×C4⋊C4C2418yes—
666C2×C4⋊C4C2418yes—
667C2×C4⋊C4C2414yes—
668C2×C4⋊C4C2414yes—
669C2×C4⋊C4C2418yes—
670C2×C4⋊C4C2414yes—
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2412yes—
673C2×C4⋊C4C2414yes—
674C2×C4⋊C4C2412yes—
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2412yes—
677C2×C4⋊C4C2412yes—
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C22⋊C4C2414yes—
681C2×C22⋊C4C2412yes—
682C2×C22⋊C4C2412yes—
683C2×C22⋊C4C2414yes—
684C2×C22⋊C4C2412yes—
685C2×C22⋊C4C2412yes—
686C2×C22⋊C4C2414yes—
687C2×C22⋊C4C2414yes—
688C2×C22⋊C4C2414yes—
689C2×C22⋊C4C2418yes—
690C2×C22⋊C4C2414yes—
691C2×C22⋊C4C2418yes—
692C2×C22⋊C4C2414yes—
693C2×C22⋊C4C2412yes—
694C2×C22⋊C4C2414yes—
695C2×C42—28no—
696C2×C42—28no—
697C2×C42—44no—
698C2×C42—48no—
699C2×C42#4118yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2414yes—
706C2×C42C2412yes—
707C2×C42C2412yes—
708C2×C42C2412yes—
709C2×C42C2412yes—
710C2×C42C2414yes—
711C2×C42C2414yes—
712C2×C42C2412yes—
713C2×C42C2412yes—
714C2×C42C2412yes—
715C2×C42C2412yes—
716C2×C42C2418yes—
717C2×C42C2412yes—
718C2×C42C2414yes—
719C2×C42C2414yes—
720C2×C42C2418yes—
721C2×C42C2414yes—
722C2×C42C2414yes—
723C2×C42C2414yes—
724C2×C42C2412yes—
725C2×C42C2414yes—
726C2×C42C2414yes—
727C2×C42C2412yes—
728C2×C42C2414yes—
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#95C2412yes—
734#95C2414yes—
735#95C2418yes—
736#95C2414yes—
737#95C2414yes—
738#95C2414yes—
739#95C2412yes—
740#95C2412yes—
741#95C2412yes—
742#95C2412yes—
743#95C2418yes—
744#95C2412yes—
745#95C2414yes—
746#95C2412yes—
747#95C2412yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2414yes—
752#95C2414yes—
753#95C2414yes—
754#95C2418yes—
755#95C2418yes—
756#95C2418yes—
757#95C2418yes—
758#95C2414yes—
759#95C2418yes—
760#95C2414yes—
761#95C2414yes—
762#95C2414yes—
763#95C2414yes—
764#95C2414yes—
765#95C2418yes—
766#95C2414yes—
767#95C2418yes—
768#95C2414yes—
769#95C2414yes—
770#95C2418yes—
771#95C2418yes—
772#95C2418yes—
773#95C2418yes—
774#95C2414yes—
775#95C2418yes—
776#95C2414yes—
777C24C2512yes—
778C24C2511yescharacteristic
779#41—232no—
780C2×Q8—22no—
781C2×Q8—22no—
782C2×Q8—24no—
783C2×Q8—24no—
784C2×Q8—24no—
785C2×Q8—216no—
786C2×Q8—24no—
787C2×Q8—216no—
788C2×Q8—24no—
789C2×Q8—24no—
790C2×Q8—216no—
791C2×Q8—24no—
792C2×Q8—24no—
793C2×Q8—42no—
794C2×Q8—48no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—48no—
798C2×Q8—48no—
799C2×Q8—42no—
800C2×Q8—832no—
801C2×Q8C22×Q814yes—
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—22no—
805C2×D4—22no—
806C2×D4C22×Q818yes—
807C2×D4C22×Q814yes—
808C22×C4—24no—
809C22×C4—24no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—24no—
813C22×C4—24no—
814C22×C4—28no—
815C22×C4—24no—
816C22×C4—24no—
817C22×C4—24no—
818C22×C4—24no—
819C22×C4—24no—
820C22×C4—24no—
821C22×C4—28no—
822C22×C4—42no—
823C22×C4—44no—
824C22×C4—42no—
825C22×C4—41no—
826C22×C4—44no—
827C22×C4—42no—
828C22×C4—41no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4C22×Q818yes—
839C22×C4C22×Q818yes—
840C22×C4C22×Q8116yes—
841C22×C4C22×Q814yes—
842C22×C4C2×#4114yes—
843C22×C4C2×#4114yes—
844C22×C4C2×#4118yes—
845C22×C4C2×#4114yes—
846C22×C4C2×#4114yes—
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2512yes—
850C22×C4C2512yes—
851C22×C4C2512yes—
852C22×C4C2514yes—
853C22×C4C2514yes—
854C22×C4C2514yes—
855C22×C4C2514yes—
856C22×C4C2518yes—
857C22×C4C2512yes—
858C22×C4C2512yes—
859C22×C4C2512yes—
860C22×C4C2512yes—
861C22×C4C2514yes—
862C22×C4C2511yescharacteristic
863C22×C4C2511yescharacteristic
864C22×C4C2514yes—
865C22×C4C2511yescharacteristic
866C22×C4C2512yes—
867C22×C4C2512yes—
868C22×C4C2511yescharacteristic
869C22×C4C2511yescharacteristic
870C22×C4C2511yescharacteristic
871C4⋊C4—22no—
872C4⋊C4—28no—
873C4⋊C4—216no—
874C4⋊C4—216no—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—22no—
878C4⋊C4—24no—
879C4⋊C4—24no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—24no—
883C4⋊C4—24no—
884C4⋊C4—24no—
885C4⋊C4—24no—
886C4⋊C4—28no—
887C4⋊C4—28no—
888C4⋊C4—28no—
889C4⋊C4—28no—
890C4⋊C4—24no—
891C4⋊C4—24no—
892C4⋊C4—24no—
893C4⋊C4—24no—
894C4⋊C4—24no—
895C4⋊C4—22no—
896C4⋊C4—216no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—28no—
900C4⋊C4—24no—
901C4⋊C4—22no—
902C4⋊C4—28no—
903C4⋊C4—28no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—48no—
910C4⋊C4—44no—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—48no—
915C4⋊C4—44no—
916C4⋊C4—48no—
917C4⋊C4—48no—
918C4⋊C4—48no—
919C4⋊C4—44no—
920C4⋊C4C22×Q818yes—
921C4⋊C4C22×Q818yes—
922C4⋊C4C22×Q814yes—
923C4⋊C4C22×Q8116yes—
924C4⋊C4C22×Q814yes—
925C4⋊C4C2×#4118yes—
926C4⋊C4C2×#4118yes—
927C4⋊C4H(5,𝔽2)14yes—
928C4⋊C42−1+414yes—
929C22⋊C4—24no—
930C22⋊C4—24no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—28no—
934C22⋊C4—24no—
935C22⋊C4—24no—
936C22⋊C4—28no—
937C22⋊C4—28no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4C22×Q818yes—
943C22⋊C4C22×Q8116yes—
944C42—24no—
945C42—24no—
946C42—24no—
947C42—24no—
948C42—24no—
949C42—24no—
950C42—24no—
951C42—28no—
952C42—24no—
953C42—28no—
954C42—28no—
955C42—24no—
956C42—28no—
957C42—28no—
958C42—24no—
959C42—28no—
960C42—44no—
961C42—44no—
962C42—44no—
963C42—44no—
964C42—42no—
965C42—44no—
966C42—48no—
967C42—42no—
968C42—44no—
969C42—44no—
970C42—48no—
971C42C22×Q818yes—
972C42C22×Q8116yes—
973C42C2×#4114yes—
974C42C2×#4114yes—
975C42C2×#4114yes—
976C42C2×#4114yes—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23C23×Q814yes—
988C23C23×Q812yes—
989C23C22×#4112yes—
990C23C22×#4112yes—
991C23C2611yescharacteristic
992Q8—28no—
993Q8—432no—
994Q8—48no—
995Q8—48no—
996Q8—48no—
997Q8—84no—
998Q8—816no—
999D4—216no—
1000D4—28no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—24no—
1007C2×C4—24no—
1008C2×C4—21no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—21no—
1013C2×C4—22no—
1014C2×C4—24no—
1015C2×C4—21no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—24no—
1020C2×C4—21no—
1021C2×C4—216no—
1022C2×C4—28no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—24no—
1029C2×C4—24no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—28no—
1034C2×C4—22no—
1035C2×C4—24no—
1036C2×C4—22no—
1037C2×C4—24no—
1038C2×C4—28no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—24no—
1042C2×C4—24no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—24no—
1046C2×C4—22no—
1047C2×C4—24no—
1048C2×C4—28no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—24no—
1054C2×C4—22no—
1055C2×C4—24no—
1056C2×C4—48no—
1057C2×C4—416no—
1058C2×C4—44no—
1059C2×C4—48no—
1060C2×C4—48no—
1061C2×C4—48no—
1062C2×C4—48no—
1063C2×C4—88no—
1064C2×C4—84no—
1065C2×C4—88no—
1066C2×C4#533116yescomplemented
1067C2×C4C23×Q814yes—
1068C2×C4C23×Q814yes—
1069C2×C4C23×Q814yes—
1070C2×C4C23×Q818yes—
1071C2×C4C23×Q812yes—
1072C2×C4C23×Q812yes—
1073C2×C4C22×#4112yes—
1074C2×C4C22×#4118yes—
1075C2×C4C22×#4112yes—
1076C2×C4C22×#4112yes—
1077C2×C4C22×#4112yes—
1078C2×C4C22×#4112yes—
1079C2×C4C22×#4112yes—
1080C2×C4C22×#4112yes—
1081C2×C4C22×#4112yes—
1082C2×C4C2×H(5,𝔽2)14yes—
1083C2×C4C2×H(5,𝔽2)12yes—
1084C2×C4C2×2−1+414yes—
1085C2×C4C2×2−1+412yes—
1086C22—22no—
1087C22—22no—
1088C22—22no—
1089C22—22no—
1090C22—22no—
1091C22—22no—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22C2×#53314yes—
1100C22C24×Q811yescharacteristic
1101C22C23×#4111yescharacteristic
1102C22C23×#4111yescharacteristic
1103C22C22×H(5,𝔽2)11yescharacteristic
1104C22C22×2−1+411yescharacteristic
1105C22H(7,𝔽2)11yescharacteristic
1106C222−1+611yescharacteristic
1107C4—24no—
1108C4—28no—
1109C4—28no—
1110C4—24no—
1111C4—24no—
1112C4—24no—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—24no—
1117C4—42no—
1118C4—42no—
1119C4—48no—
1120C4—42no—
1121C4—42no—
1122C4—42no—
1123C4—44no—
1124C4—44no—
1125C4—42no—
1126C4—44no—
1127C4—44no—
1128C4C2×#53314yes—
1129C4C2×#53314yes—
1130C4#351114yes—
1131C2—24no—
1132C2—44no—
1133C2C22×#53311yescharacteristic
1134C2C2×#351111yescharacteristic
1135C2#6285611yescharacteristic
1136C2Q8×H(5,𝔽2)11yescharacteristic
1137C2#6298311yescharacteristic
1138C2Q8×2−1+411yescharacteristic
1139C2#6299811yescharacteristic
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. #36564C2semidirect
2. #36480C2semidirect
3. #36288C2semidirect
4. #36278C2semidirect
5. #36133C2semidirect
6. #36129C2semidirect
7. #35931C2semidirect
8. #35843C2semidirect
9. #35747C2semidirect
10. #35585C2semidirect
11. #35582C2semidirect
12. #35581C2semidirect
15. #35199C2semidirect
16. #35177C2semidirect
17. #35173C2semidirect
18. #34950C2semidirect
20. #34929C2semidirect
21. C2×#2551C2semidirect
23. #34216C2semidirect
24. #34214C2semidirect
25. #34145C2semidirect
232. #520Q8semidirect
593. C4×Q8C2×Q8semidirect
601. C4×D4C2×Q8semidirect
610. #117C2×Q8semidirect
620. C2×C4⋊C4C2×Q8semidirect
1066. C2×C4#533semidirect

Maximal subgroups

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

subgroupindex
#365642
#364802
#362882
#362782
#361332
#361292
#359312
#358432
#357472
#355852
#355822
#355812
#355742
#352802
#351992
#351772
#351732
#349502
#349472
#349292
C2×#25512
#342532
#342162
#342142
#341452
C4×#5202