Finite Group Databasebeta

← #7631652

Subgroups — #7631652

Order 512.

4924 conjugacy classes of subgroups.

The subgroup lattice has 1114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36556C212yesmaximal, complemented
2#36552C212yesmaximal, complemented
3#36454C212yesmaximal, complemented
4#36450C212yesmaximal, complemented
5#36314C212yesmaximal, complemented
6#36313C212yesmaximal, complemented
7#36177C212yesmaximal, complemented
8#36175C212yesmaximal, complemented
9#35973C214yesmaximal, complemented
10#35870C214yesmaximal, complemented
11#35818C214yesmaximal, complemented
12#35789C214yesmaximal, complemented
13#35630C212yesmaximal, complemented
14#35619C212yesmaximal
15#35461C218yesmaximal, complemented
16#35320C211yesmaximal, characteristic, complemented
17#35316C211yesmaximal, characteristic
18#35026C214yesmaximal, complemented
19#34948C211yesmaximal, characteristic, complemented
20#34947C211yesmaximal, characteristic
21#34780C214yesmaximal, complemented
22#34266C212yesmaximal
23#34213C211yesmaximal, characteristic, complemented
24#34187C212yesmaximal, complemented
25C2×#2365C211yesmaximal, characteristic, complemented
26C4×#520C211yesmaximal, characteristic
27C2×#536C2212yes—
28C2×#533C2211yescharacteristic
29C22×C4⋊Q8C2211yescharacteristic
30C2×#520C2211yescharacteristic
31C2×#520C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33C22×C4×Q8C2212yes—
34#2864C2214yes—
35#2863C2214yes—
36#2862C2212yes—
37#2862C2212yes—
38#2857C2212yes—
39#2857C2212yes—
40#2855C2214yes—
41#2851C2214yes—
42#2655C2218yes—
43#2652C2218yes—
44#2642C2214yes—
45#2621C2214yes—
46#2590C2218yes—
47#2588C2218yes—
48#2585C2218yes—
49#2577C2218yes—
50#2575C2218yes—
51#2573C2218yes—
52#2571C2211yescharacteristic
53#2571C2211yescharacteristic
54#2570C2212yes—
55#2570C2212yes—
56#2569C2214yes—
57#2568C2212yes—
58#2568C2212yes—
59#2568C2211yescharacteristic
60#2568C2212yes—
61#2568C2212yes—
62#2567C2211yescharacteristic
63#2566C2212yes—
64#2565C2212yes—
65#2564C2214yes—
66#2563C2211yescharacteristic
67#2552C2211yescharacteristic
68#2552C2211yescharacteristic
69#2547C2212yes—
70#2547C2212yes—
71#2546C2212yes—
72#2546C2212yes—
73#2542C2211yescharacteristic
74#2533C2218yes—
75#2533C2218yes—
76#2530C2218yes—
77#2528C2218yes—
78#2528C2218yes—
79#2527C2218yes—
80#2524C2218yes—
81#2524C2218yes—
82#2523C2218yes—
83#2520C2218yes—
84#2517C2218yes—
85#2515C2218yes—
86#2514C2214yes—
87#2514C2214yes—
88#2514C2214yes—
89#2514C2214yes—
90#2514C2214yes—
91#2511C2214yes—
92#2511C2214yes—
93#2511C2214yes—
94#2511C2214yes—
95#2509C2214yes—
96#2508C2214yes—
97#2505C2218yes—
98#2503C2214yes—
99#2503C2214yes—
100#2503C2214yes—
101#2502C2214yes—
102#2499C2214yes—
103#2499C2214yes—
104#2495C2214yes—
105#2494C2214yes—
106#2493C2218yes—
107#2493C2218yes—
108#2493C2218yes—
109#2489C2214yes—
110#2486C2214yes—
111#2486C2214yes—
112#2453C2214yes—
113#2447C2214yes—
114#2447C2214yes—
115#2446C2214yes—
116#2446C2214yes—
117#2442C2212yes—
118#2442C2212yes—
119#2421C2214yes—
120#2419C2218yes—
121#2419C2218yes—
122#2417C2212yes—
123#2417C2212yes—
124#2402C2214yes—
125#2402C2218yes—
126#2401C2218yes—
127#2396C2214yes—
128#2370C2214yes—
129#2369C2212yes—
130#2367C2214yes—
131#2367C2214yes—
132#2365C2214yes—
133#2365C2214yes—
134#2365C2214yes—
135#2365C2212yes—
136#2365C2212yes—
137#2365C2212yes—
138#2365C2212yes—
139#2365C2214yes—
140#2365C2212yes—
141#2362C2214yes—
142#2362C2214yes—
143#2360C2214yes—
144#2360C2214yes—
145#2356C2214yes—
146#2356C2214yes—
147#2356C2214yes—
148#2356C2214yes—
149#2355C2214yes—
150#2355C2212yes—
151#2355C2214yes—
152#2355C2214yes—
153#2355C2214yes—
154#2355C2214yes—
155Q8×C4⋊C4C2212yes—
156#2329C2214yes—
157#2322C2218yes—
158#2317C2212yes—
159#2313C2218yes—
160#2310C2212yes—
161#2310C2212yes—
162#2310C2212yes—
163C4×#125C2212yes—
164C4×#125C2214yes—
165C4×#125C2212yes—
166C4×C22⋊Q8C2212yes—
167C4×C22⋊Q8C2212yes—
168C4×C22⋊Q8C2214yes—
169C4×C22⋊Q8C2214yes—
170C4×#123C2218yes—
171#2297C2212yes—
172#2296C2212yes—
173#2295C2214yes—
174C2×#391C2212yes—
175C2×#389C2212yes—
176C2×#387C2214yes—
177#2285C2212yes—
178#2285C2212yes—
179#2285C2211yescharacteristic
180#2283C2214yes—
181#2283C2218yes—
182#2276C2212yes—
183#2275C2214yes—
184#2275C2212yes—
185#2274C2211yescharacteristic
186#2274C2211yescharacteristic
187#2274C2212yes—
188#2274C2212yes—
189#2274C2212yes—
190C42×Q8C2212yes—
191C42×D4C2212yes—
192C42×D4C2214yes—
193C4×#117C2212yes—
194C4×#117C2211yescharacteristic
195C2×C4×C4⋊C4C2212yes—
196C2×C4×C4⋊C4C2211yescharacteristic
197C2×C4×C4⋊C4C2211yescharacteristic
198C2×C4×C4⋊C4C2212yes—
199C22×#41C2311yescharacteristic
200C23×Q8C2312yes—
201#536—216no—
202#533—28no—
203C2×C4⋊Q8—28no—
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2312yes—
206C2×C4⋊Q8C2312yes—
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2312yes—
209C2×C4⋊Q8C2312yes—
210C2×C4⋊Q8C2314yes—
211C2×#125C2312yes—
212C2×#125C2312yes—
213C2×#125C2312yes—
214C2×#124C2314yes—
215C2×#123C2318yes—
216C2×C22⋊Q8C2312yes—
217C2×C22⋊Q8C2314yes—
218C2×C22⋊Q8C2314yes—
219C2×C22⋊Q8C2312yes—
220C2×C22⋊Q8C2312yes—
221C2×C22⋊Q8C2312yes—
222#520—28no—
223#520—28no—
224C4×#41—28no—
225C2×C4×Q8—216no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2314yes—
231C2×C4×Q8C2314yes—
232C2×C4×Q8C2314yes—
233C2×C4×Q8C2314yes—
234C2×C4×Q8C2312yes—
235C2×C4×Q8C2312yes—
236C2×C4×Q8C2314yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2312yes—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2314yes—
241C2×C4×D4C2312yes—
242C2×C4×D4C2312yes—
243C2×C4×D4C2314yes—
244C2×C4×D4C2312yes—
245C2×#117C2312yes—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2312yes—
250C2×#117C2312yes—
251C2×#117C2312yes—
252C2×#117C2312yes—
253C22×C4⋊C4C2314yes—
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2312yes—
256C22×C4⋊C4C2312yes—
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2312yes—
259C22×C4⋊C4C2312yes—
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C42C2312yes—
263C22×C42C2314yes—
264C22×C42C2312yes—
265C22×C42C2314yes—
266C22×C42C2312yes—
267C22×C42C2311yescharacteristic
268#401C2318yes—
269#401C2318yes—
270#400C2314yes—
271#400C2318yes—
272#400C2318yes—
273#400C2318yes—
274#400C2318yes—
275#400C2314yes—
276#400C2314yes—
277#400C2314yes—
278#400C2314yes—
279#400C2318yes—
280#400C2318yes—
281#400C2318yes—
282#400C2318yes—
283#400C2318yes—
284#400C2318yes—
285#400C2318yes—
286#400C2318yes—
287#399C2314yes—
288#398C2314yes—
289#398C2314yes—
290#398C2314yes—
291#398C2314yes—
292#398C2314yes—
293#398C2314yes—
294#398C2318yes—
295#398C2318yes—
296#398C2318yes—
297#398C2318yes—
298#397C2318yes—
299#397C2318yes—
300#397C2318yes—
301#397C2318yes—
302#397C2318yes—
303#397C2318yes—
304#396C2314yes—
305#396C2314yes—
306#395C2314yes—
307#393C2314yes—
308#391C2312yes—
309#391C2312yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2314yes—
314#391C2314yes—
315#391C2314yes—
316#391C2314yes—
317#391C2314yes—
318#391C2314yes—
319#391C2314yes—
320#391C2314yes—
321#391C2314yes—
322#391C2314yes—
323#391C2314yes—
324#391C2314yes—
325#391C2314yes—
326#391C2312yes—
327#391C2312yes—
328#391C2318yes—
329#391C2314yes—
330#391C2314yes—
331#391C2314yes—
332#391C2314yes—
333#391C2314yes—
334#390C2312yes—
335#390C2312yes—
336#389C2312yes—
337#389C2312yes—
338#389C2312yes—
339#389C2314yes—
340#389C2312yes—
341#389C2312yes—
342#389C2312yes—
343#389C2312yes—
344#389C2312yes—
345#389C2312yes—
346#389C2312yes—
347#389C2314yes—
348#389C2314yes—
349#389C2318yes—
350#389C2318yes—
351#389C2318yes—
352#389C2318yes—
353#389C2314yes—
354#389C2314yes—
355#389C2314yes—
356#389C2314yes—
357#389C2314yes—
358#389C2314yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#387C2314yes—
364#387C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2318yes—
368#387C2318yes—
369#387C2314yes—
370#387C2314yes—
371#387C2318yes—
372#387C2318yes—
373#387C2318yes—
374#387C2318yes—
375#387C2318yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#387C2318yes—
381#387C2318yes—
382#387C2318yes—
383#387C2318yes—
384#387C2318yes—
385#387C2318yes—
386#387C2318yes—
387#387C2318yes—
388#387C2318yes—
389#387C2318yes—
390#387C2318yes—
391#387C2318yes—
392#387C2318yes—
393#387C2318yes—
394#387C2318yes—
395#387C2318yes—
396#387C2318yes—
397#387C2318yes—
398#386C2314yes—
399#386C2314yes—
400#385C2314yes—
401#385C2314yes—
402#385C2314yes—
403#385C2314yes—
404#385C2318yes—
405#385C2318yes—
406#385C2318yes—
407#385C2318yes—
408#385C2318yes—
409#384C2312yes—
410#384C2312yes—
411#384C2312yes—
412#384C2312yes—
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2314yes—
416#383C2318yes—
417#383C2318yes—
418#383C2318yes—
419#383C2318yes—
420#382C2314yes—
421#382C2312yes—
422#382C2312yes—
423#382C2312yes—
424#382C2312yes—
425#382C2314yes—
426#382C2314yes—
427#382C2314yes—
428#382C2312yes—
429#382C2312yes—
430#382C2312yes—
431#382C2314yes—
432#382C2318yes—
433#382C2318yes—
434#381C2318yes—
435#381C2318yes—
436#381C2318yes—
437#381C2318yes—
438#381C2318yes—
439#380C2312yes—
440#380C2312yes—
441#380C2314yes—
442#380C2314yes—
443#380C2314yes—
444#380C2312yes—
445#380C2314yes—
446#380C2314yes—
447#380C2314yes—
448#380C2314yes—
449#380C2314yes—
450#380C2312yes—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2318yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2314yes—
458C4×C4⋊C4C2318yes—
459C4×C4⋊C4C2314yes—
460C4×C4⋊C4C2314yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2312yes—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2312yes—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2318yes—
470C4×C4⋊C4C2318yes—
471C4×C4⋊C4C2314yes—
472C4×C4⋊C4C2314yes—
473C4×C4⋊C4C2314yes—
474C4×C4⋊C4C2314yes—
475C4×C4⋊C4C2312yes—
476C4×C4⋊C4C2314yes—
477C4×C4⋊C4C2312yes—
478C4×C4⋊C4C2312yes—
479C4×C4⋊C4C2312yes—
480C4×C4⋊C4C2312yes—
481C4×C4⋊C4C2312yes—
482C4×C4⋊C4C2314yes—
483C4×C4⋊C4C2314yes—
484C4×C4⋊C4C2314yes—
485C4×C4⋊C4C2314yes—
486C4×C4⋊C4C2318yes—
487C4×C4⋊C4C2312yes—
488C4×C4⋊C4C2312yes—
489C4×C4⋊C4C2318yes—
490C4×C4⋊C4C2314yes—
491C4×C4⋊C4C2311yescharacteristic
492C4×C4⋊C4C2312yes—
493C4×C4⋊C4C2314yes—
494C4×C4⋊C4C2314yes—
495C4×C4⋊C4C2312yes—
496C4×C4⋊C4C2312yes—
497C4×C4⋊C4C2312yes—
498C4×C4⋊C4C2312yes—
499C4×C4⋊C4C2314yes—
500C4×C22⋊C4C2314yes—
501C4×C22⋊C4C2318yes—
502C4×C22⋊C4C2312yes—
503C4×C22⋊C4C2314yes—
504C4×C22⋊C4C2314yes—
505C4×C22⋊C4C2314yes—
506C4×C22⋊C4C2314yes—
507C4×C22⋊C4C2314yes—
508C4×C22⋊C4C2318yes—
509C4×C22⋊C4C2318yes—
510C4×C22⋊C4C2314yes—
511C4×C22⋊C4C2314yes—
512C4×C22⋊C4C2312yes—
513C4×C22⋊C4C2314yes—
514C4×C22⋊C4C2314yes—
515#376C2318yes—
516#376C2318yes—
517#376C2312yes—
518#376C2314yes—
519C2×#95C2312yes—
520C2×#95C2312yes—
521C2×#95C2314yes—
522C2×#95C2314yes—
523C2×#95C2314yes—
524C43C2312yes—
525C43C2314yes—
526C2×#41—24no—
527C2×#41—24no—
528C2×#41#4118yes—
529C22×Q8—28no—
530C22×Q8—28no—
531C22×Q8—28no—
532C22×Q8C2412yes—
533C22×Q8C2414yes—
534C22×Q8C2414yes—
535C22×Q8C2411yescharacteristic
536C22×Q8C2412yes—
537C22×D4C2412yes—
538C22×D4C2411yescharacteristic
539C23×C4C2414yes—
540C23×C4C2412yes—
541C23×C4C2412yes—
542C23×C4C2411yescharacteristic
543C23×C4C2412yes—
544C23×C4C2412yes—
545C23×C4C2412yes—
546C23×C4C2414yes—
547C23×C4C2414yes—
548C23×C4C2412yes—
549C23×C4C2412yes—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C4⋊Q8—216no—
553C4⋊Q8—28no—
554C4⋊Q8—28no—
555C4⋊Q8—28no—
556C4⋊Q8—28no—
557C4⋊Q8—24no—
558C4⋊Q8—24no—
559#125—28no—
560#125—28no—
561#125—44no—
562#124—216no—
563#123—232no—
564C22⋊Q8—28no—
565C22⋊Q8—28no—
566C22⋊Q8—216no—
567C22⋊Q8—216no—
568C22⋊Q8—28no—
569C22⋊Q8—44no—
570C4×Q8—28no—
571C4×Q8—216no—
572C4×Q8—216no—
573C4×Q8—216no—
574C4×Q8—216no—
575C4×Q8—28no—
576C4×Q8—24no—
577C4×Q8—24no—
578C4×Q8—28no—
579C4×Q8—28no—
580C4×Q8—48no—
581C4×D4—216no—
582C4×D4—28no—
583C4×D4—28no—
584C4×D4—28no—
585C4×D4—216no—
586C4×D4—28no—
587C4×D4—24no—
588C4×D4—24no—
589#117—24no—
590#117—28no—
591#117—24no—
592#117—24no—
593#117—28no—
594#117—28no—
595#117—28no—
596#117—28no—
597C2×C4⋊C4—216no—
598C2×C4⋊C4—28no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—28no—
601C2×C4⋊C4—28no—
602C2×C4⋊C4—28no—
603C2×C4⋊C4—24no—
604C2×C4⋊C4—42no—
605C2×C4⋊C4#4118yes—
606C2×C4⋊C4C2412yes—
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2414yes—
610C2×C4⋊C4C2412yes—
611C2×C4⋊C4C2414yes—
612C2×C4⋊C4C2418yes—
613C2×C4⋊C4C2418yes—
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2414yes—
617C2×C4⋊C4C2414yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2414yes—
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2412yes—
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2412yes—
627C2×C4⋊C4C2412yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2412yes—
630C2×C4⋊C4C2412yes—
631C2×C4⋊C4C2412yes—
632C2×C4⋊C4C2412yes—
633C2×C4⋊C4C2414yes—
634C2×C4⋊C4C2414yes—
635C2×C4⋊C4C2412yes—
636C2×C4⋊C4C2412yes—
637C2×C4⋊C4C2418yes—
638C2×C4⋊C4C2418yes—
639C2×C4⋊C4C2414yes—
640C2×C4⋊C4C2412yes—
641C2×C4⋊C4C2414yes—
642C2×C4⋊C4C2414yes—
643C2×C4⋊C4C2412yes—
644C2×C4⋊C4C2418yes—
645C2×C4⋊C4C2414yes—
646C2×C4⋊C4C2414yes—
647C2×C4⋊C4C2414yes—
648C2×C4⋊C4C2414yes—
649C2×C4⋊C4C2414yes—
650C2×C4⋊C4C2414yes—
651C2×C4⋊C4C2412yes—
652C2×C4⋊C4C2412yes—
653C2×C4⋊C4C2414yes—
654C2×C4⋊C4C2414yes—
655C2×C4⋊C4C2418yes—
656C2×C4⋊C4C2414yes—
657C2×C4⋊C4C2412yes—
658C2×C4⋊C4C2412yes—
659C2×C4⋊C4C2411yescharacteristic
660C2×C22⋊C4C2412yes—
661C2×C22⋊C4C2412yes—
662C2×C22⋊C4C2412yes—
663C2×C22⋊C4C2414yes—
664C2×C22⋊C4C2412yes—
665C2×C22⋊C4C2412yes—
666C2×C22⋊C4C2414yes—
667C2×C22⋊C4C2414yes—
668C2×C22⋊C4C2414yes—
669C2×C22⋊C4C2418yes—
670C2×C22⋊C4C2418yes—
671C2×C22⋊C4C2414yes—
672C2×C22⋊C4C2414yes—
673C2×C22⋊C4C2414yes—
674C2×C22⋊C4C2414yes—
675C2×C42—216no—
676C2×C42—28no—
677C2×C42—28no—
678C2×C42—44no—
679C2×C42—48no—
680C2×C42#4118yes—
681C2×C42C2412yes—
682C2×C42C2414yes—
683C2×C42C2412yes—
684C2×C42C2412yes—
685C2×C42C2414yes—
686C2×C42C2414yes—
687C2×C42C2414yes—
688C2×C42C2412yes—
689C2×C42C2412yes—
690C2×C42C2418yes—
691C2×C42C2412yes—
692C2×C42C2412yes—
693C2×C42C2418yes—
694C2×C42C2412yes—
695C2×C42C2412yes—
696C2×C42C2414yes—
697C2×C42C2412yes—
698C2×C42C2412yes—
699C2×C42C2418yes—
700C2×C42C2414yes—
701C2×C42C2412yes—
702C2×C42C2412yes—
703C2×C42C2414yes—
704C2×C42C2414yes—
705C2×C42C2418yes—
706C2×C42C2414yes—
707C2×C42C2414yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712#95C2414yes—
713#95C2412yes—
714#95C2414yes—
715#95C2414yes—
716#95C2414yes—
717#95C2418yes—
718#95C2412yes—
719#95C2412yes—
720#95C2418yes—
721#95C2412yes—
722#95C2412yes—
723#95C2418yes—
724#95C2418yes—
725#95C2412yes—
726#95C2414yes—
727#95C2414yes—
728#95C2414yes—
729#95C2414yes—
730#95C2414yes—
731#95C2412yes—
732#95C2412yes—
733#95C2414yes—
734#95C2418yes—
735#95C2418yes—
736#95C2418yes—
737#95C2418yes—
738#95C2414yes—
739#95C2414yes—
740#95C2418yes—
741#95C2418yes—
742#95C2414yes—
743#95C2414yes—
744#95C2418yes—
745#95C2418yes—
746#95C2414yes—
747#95C2414yes—
748#95C2414yes—
749#95C2414yes—
750#95C2414yes—
751#95C2418yes—
752#95C2418yes—
753#95C2414yes—
754#95C2414yes—
755#95C2414yes—
756#95C2418yes—
757#95C2418yes—
758#95C2418yes—
759#95C2418yes—
760#95C2418yes—
761#95C2418yes—
762#95C2414yes—
763#95C2414yes—
764C24C2512yes—
765C24C2511yescharacteristic
766#41—232no—
767C2×Q8—22no—
768C2×Q8—22no—
769C2×Q8—28no—
770C2×Q8—28no—
771C2×Q8—24no—
772C2×Q8—28no—
773C2×Q8—28no—
774C2×Q8—28no—
775C2×Q8—28no—
776C2×Q8—24no—
777C2×Q8—24no—
778C2×Q8—24no—
779C2×Q8—42no—
780C2×Q8—42no—
781C2×Q8—432no—
782C2×Q8C2×#4114yes—
783C2×D4—24no—
784C2×D4—24no—
785C2×D4—22no—
786C2×D4—22no—
787C2×D4C2×#4118yes—
788C2×D4C2×#4114yes—
789C22×C4—24no—
790C22×C4—24no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—24no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—28no—
797C22×C4—24no—
798C22×C4—28no—
799C22×C4—24no—
800C22×C4—24no—
801C22×C4—24no—
802C22×C4—24no—
803C22×C4—24no—
804C22×C4—24no—
805C22×C4—28no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—42no—
811C22×C4—44no—
812C22×C4—42no—
813C22×C4—44no—
814C22×C4—42no—
815C22×C4—44no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—44no—
820C22×C4—42no—
821C22×C4C2×#4114yes—
822C22×C4C2×#4118yes—
823C22×C4C2×#4118yes—
824C22×C4C2×#4114yes—
825C22×C4C2×#4114yes—
826C22×C4C2×#4114yes—
827C22×C4C2×#4114yes—
828C22×C4C2512yes—
829C22×C4C2512yes—
830C22×C4C2512yes—
831C22×C4C2512yes—
832C22×C4C2512yes—
833C22×C4C2514yes—
834C22×C4C2512yes—
835C22×C4C2512yes—
836C22×C4C2514yes—
837C22×C4C2514yes—
838C22×C4C2514yes—
839C22×C4C2518yes—
840C22×C4C2512yes—
841C22×C4C2512yes—
842C22×C4C2514yes—
843C22×C4C2511yescharacteristic
844C22×C4C2511yescharacteristic
845C22×C4C2514yes—
846C22×C4C2511yescharacteristic
847C22×C4C2512yes—
848C22×C4C2512yes—
849C22×C4C2511yescharacteristic
850C22×C4C2511yescharacteristic
851C22×C4C2511yescharacteristic
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—216no—
859C4⋊C4—216no—
860C4⋊C4—28no—
861C4⋊C4—28no—
862C4⋊C4—28no—
863C4⋊C4—28no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—24no—
867C4⋊C4—24no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—24no—
871C4⋊C4—24no—
872C4⋊C4—24no—
873C4⋊C4—24no—
874C4⋊C4—28no—
875C4⋊C4—28no—
876C4⋊C4—24no—
877C4⋊C4—24no—
878C4⋊C4—216no—
879C4⋊C4—216no—
880C4⋊C4—24no—
881C4⋊C4—22no—
882C4⋊C4—28no—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—24no—
886C4⋊C4—22no—
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—42no—
890C4⋊C4—44no—
891C4⋊C4—44no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4C2×#4118yes—
904C4⋊C4C2×#4118yes—
905C4⋊C42−1+414yes—
906C22⋊C4—28no—
907C22⋊C4—24no—
908C22⋊C4—24no—
909C22⋊C4—24no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—216no—
913C22⋊C4—216no—
914C22⋊C4—28no—
915C22⋊C4—24no—
916C22⋊C4—24no—
917C22⋊C4—28no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C42—24no—
922C42—24no—
923C42—24no—
924C42—24no—
925C42—24no—
926C42—216no—
927C42—24no—
928C42—24no—
929C42—216no—
930C42—28no—
931C42—28no—
932C42—24no—
933C42—24no—
934C42—28no—
935C42—28no—
936C42—24no—
937C42—28no—
938C42—24no—
939C42—44no—
940C42—44no—
941C42—44no—
942C42—44no—
943C42—48no—
944C42—42no—
945C42—42no—
946C42—44no—
947C42—48no—
948C42C2×#4114yes—
949C42C2×#4114yes—
950C42C2×#4114yes—
951C42C2×#4114yes—
952C23—21no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23C22×#4114yes—
963C23C22×#4112yes—
964C23C22×#4112yes—
965C23C22×#4112yes—
966C23C2611yescharacteristic
967Q8—28no—
968Q8—416no—
969Q8—416no—
970Q8—48no—
971Q8—84no—
972D4—216no—
973D4—28no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—21no—
978C2×C4—24no—
979C2×C4—21no—
980C2×C4—24no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—216no—
987C2×C4—28no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—28no—
996C2×C4—24no—
997C2×C4—24no—
998C2×C4—24no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—24no—
1002C2×C4—22no—
1003C2×C4—28no—
1004C2×C4—28no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—24no—
1008C2×C4—24no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—24no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—24no—
1016C2×C4—24no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—24no—
1022C2×C4—24no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—24no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—24no—
1031C2×C4—24no—
1032C2×C4—22no—
1033C2×C4—48no—
1034C2×C4—44no—
1035C2×C4—48no—
1036C2×C4—416no—
1037C2×C4—48no—
1038C2×C4—88no—
1039C2×C4—84no—
1040C2×C4—84no—
1041C2×C4—84no—
1042C2×C4—88no—
1043C2×C4#529116yes—
1044C2×C4C22×#4118yes—
1045C2×C4C22×#4112yes—
1046C2×C4C22×#4114yes—
1047C2×C4C22×#4112yes—
1048C2×C4C22×#4112yes—
1049C2×C4C22×#4112yes—
1050C2×C4C22×#4112yes—
1051C2×C4C22×#4112yes—
1052C2×C4C22×#4112yes—
1053C2×C4C22×#4112yes—
1054C2×C4C22×#4112yes—
1055C2×C4C22×#4112yes—
1056C2×C4C2×2−1+414yes—
1057C2×C4C2×2−1+412yes—
1058C2×C4#58512yes—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—22no—
1063C22—22no—
1064C22—22no—
1065C22—24no—
1066C22—24no—
1067C22—24no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22C2×#52914yes—
1073C22C23×#4111yescharacteristic
1074C22C23×#4111yescharacteristic
1075C22C23×#4111yescharacteristic
1076C22C22×2−1+411yescharacteristic
1077C22C2×#58511yescharacteristic
1078C222−1+611yescharacteristic
1079C222−1+611yescharacteristic
1080C4—28no—
1081C4—24no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—24no—
1086C4—42no—
1087C4—42no—
1088C4—42no—
1089C4—44no—
1090C4—44no—
1091C4—42no—
1092C4—42no—
1093C4—42no—
1094C4—42no—
1095C4—44no—
1096C4—42no—
1097C4—44no—
1098C4—42no—
1099C4—44no—
1100C4—48no—
1101C4C2×#52914yes—
1102C4C2×#52914yes—
1103C4#350714yes—
1104C2—24no—
1105C2—44no—
1106C2C22×#52911yescharacteristic
1107C2C2×#350711yescharacteristic
1108C2#6286011yescharacteristic
1109C2#6299111yescharacteristic
1110C2#6299511yescharacteristic
1111C2#6299811yescharacteristic
1112C2#6300111yescharacteristic
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. #36556C2semidirect
2. #36552C2semidirect
3. #36454C2semidirect
4. #36450C2semidirect
5. #36314C2semidirect
6. #36313C2semidirect
7. #36177C2semidirect
8. #36175C2semidirect
9. #35973C2semidirect
10. #35870C2semidirect
11. #35818C2semidirect
12. #35789C2semidirect
13. #35630C2semidirect
15. #35461C2semidirect
16. #35320C2semidirect
18. #35026C2semidirect
19. #34948C2semidirect
21. #34780C2semidirect
23. #34213C2semidirect
24. #34187C2semidirect
25. C2×#2365C2semidirect

Maximal subgroups

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

subgroupindex
#365562
#365522
#364542
#364502
#363142
#363132
#361772
#361752
#359732
#358702
#358182
#357892
#356302
#356192
#354612
#353202
#353162
#350262
#349482
#349472
#347802
#342662
#342132
#341872
C2×#23652
C4×#5202