Finite Group Databasebeta

← #7630912

Subgroups — #7630912

Order 512.

4858 conjugacy classes of subgroups.

The subgroup lattice has 1039 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35958C214yesmaximal, complemented
2#35952C214yesmaximal, complemented
3#35951C218yesmaximal, complemented
4#35936C214yesmaximal, complemented
5#35934C214yesmaximal, complemented
6#35931C218yesmaximal, complemented
7#35339C211yesmaximal, characteristic, complemented
8#35334C211yesmaximal, characteristic
9#35333C211yesmaximal, characteristic
10#35304C214yesmaximal, complemented
11#35286C211yesmaximal, characteristic, complemented
12#35282C214yesmaximal, complemented
13#35282C214yesmaximal, complemented
14#35280C211yesmaximal, characteristic
15#35279C211yesmaximal, characteristic
16#34642C211yesmaximal, characteristic, complemented
17#34625C214yesmaximal, complemented
18C2×#2660C211yesmaximal, characteristic, complemented
19#34217C211yesmaximal, characteristic, complemented
20#34216C211yesmaximal, characteristic, complemented
21#34215C211yesmaximal, characteristic, complemented
22#34214C211yesmaximal, characteristic, complemented
23#34189C211yesmaximal, characteristic
24#34188C211yesmaximal, characteristic
25#33999C211yesmaximal, characteristic
26C2×#533C2211yescharacteristic
27C2×#533C2211yescharacteristic
28C22×C4⋊Q8C2211yescharacteristic
29C22×#125C2211yescharacteristic
30C2×C4×#41C2211yescharacteristic
31C2×C4×#41C2211yescharacteristic
32C2×C4×#41C2211yescharacteristic
33#2864C2214yes—
34#2859C2214yes—
35#2857C2214yes—
36#2857C2214yes—
37#2851C2214yes—
38#2851C2214yes—
39#2667C2218yes—
40#2666C2218yes—
41#2666C2218yes—
42#2665C2218yes—
43#2660C2212yes—
44#2660C2214yes—
45#2660C2214yes—
46#2660C2212yes—
47#2660C2212yes—
48#2660C2212yes—
49#2660C2212yes—
50#2660C2212yes—
51#2660C2212yes—
52#2660C2212yes—
53#2659C2214yes—
54#2659C2214yes—
55#2647C2214yes—
56#2647C2214yes—
57#2629C2214yes—
58#2629C2214yes—
59#2628C2214yes—
60#2628C2214yes—
61#2612C2218yes—
62#2612C2218yes—
63#2606C2218yes—
64#2605C2218yes—
65#2586C2218yes—
66#2586C2218yes—
67#2585C2218yes—
68#2585C2218yes—
69#2582C2214yes—
70#2581C2214yes—
71#2580C2214yes—
72#2579C2214yes—
73#2579C2214yes—
74#2574C2218yes—
75#2574C2218yes—
76#2571C2214yes—
77#2570C2214yes—
78#2570C2214yes—
79#2569C2218yes—
80#2569C2218yes—
81#2568C2212yes—
82#2567C2212yes—
83#2566C2212yes—
84#2566C2212yes—
85#2565C2212yes—
86#2565C2212yes—
87#2564C2218yes—
88#2563C2212yes—
89#2556C2218yes—
90#2556C2218yes—
91#2552C2214yes—
92#2549C2218yes—
93#2542C2212yes—
94#2538C2214yes—
95#2522C2218yes—
96#2522C2218yes—
97#2520C2218yes—
98#2520C2218yes—
99#2487C2214yes—
100#2465C2218yes—
101#2465C2218yes—
102#2462C2218yes—
103#2462C2218yes—
104#2442C2218yes—
105#2438C2218yes—
106#2438C2218yes—
107#2417C2218yes—
108#2409C2214yes—
109#2402C2218yes—
110#2399C2218yes—
111#2399C2214yes—
112#2399C2214yes—
113#2396C2218yes—
114#2396C2218yes—
115C2×#398C2214yes—
116C2×#395C2214yes—
117#2370C2214yes—
118#2370C2214yes—
119#2369C2214yes—
120#2368C2218yes—
121#2365C2214yes—
122#2360C2218yes—
123#2357C2214yes—
124#2356C2214yes—
125#2355C2214yes—
126#2355C2214yes—
127#2355C2214yes—
128#2355C2214yes—
129#2354C2214yes—
130#2353C2218yes—
131#2352C2218yes—
132Q8×C4⋊C4C2214yes—
133#2345C2214yes—
134#2345C2214yes—
135#2345C2214yes—
136Q8×C22⋊C4C2214yes—
137#2331C2214yes—
138#2331C2214yes—
139#2330C2214yes—
140#2330C2214yes—
141#2317C2211yescharacteristic
142#2317C2211yescharacteristic
143#2317C2211yescharacteristic
144#2317C2211yescharacteristic
145#2316C2211yescharacteristic
146#2316C2211yescharacteristic
147#2316C2211yescharacteristic
148#2316C2211yescharacteristic
149#2314C2214yes—
150#2314C2214yes—
151#2311C2211yescharacteristic
152#2311C2211yescharacteristic
153#2311C2211yescharacteristic
154#2311C2211yescharacteristic
155C4×C4⋊Q8C2214yes—
156C4×C4⋊Q8C2214yes—
157C4×#125C2214yes—
158C4×#125C2214yes—
159#2285C2211yescharacteristic
160#2285C2211yescharacteristic
161#2285C2214yes—
162#2285C2211yescharacteristic
163#2285C2211yescharacteristic
164C2×#384C2211yescharacteristic
165C2×#384C2211yescharacteristic
166#2283C2214yes—
167C2×#382C2211yescharacteristic
168C2×#382C2211yescharacteristic
169#2276C2212yes—
170#2276C2212yes—
171#2275C2214yes—
172#2275C2212yes—
173#2275C2214yes—
174#2275C2212yes—
175#2274C2211yescharacteristic
176#2274C2211yescharacteristic
177#2274C2211yescharacteristic
178#2274C2211yescharacteristic
179C4×#117C2211yescharacteristic
180C4×#117C2212yes—
181C4×#117C2211yescharacteristic
182C4×#117C2211yescharacteristic
183C4×#117C2212yes—
184C4×#117C2212yes—
185C2×#376C2211yescharacteristic
186C2×#376C2212yes—
187C22×#41C2311yescharacteristic
188C23×Q8C2312yes—
189#533—28no—
190#533—28no—
191C2×C4⋊Q8—28no—
192C2×C4⋊Q8C2312yes—
193C2×C4⋊Q8C2312yes—
194C2×C4⋊Q8C2312yes—
195C2×C4⋊Q8C2312yes—
196C2×C4⋊Q8C2312yes—
197C2×C4⋊Q8C2312yes—
198C2×#125—28no—
199C2×#125C2312yes—
200C2×#125C2312yes—
201C2×#125C2312yes—
202C2×#125C2312yes—
203C2×#125C2312yes—
204C2×#125C2312yes—
205C2×#125C2318yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2314yes—
208C2×C22⋊Q8C2318yes—
209C2×C22⋊Q8C2318yes—
210C4×#41—28no—
211C4×#41—28no—
212C4×#41Q8116yescomplemented
213C2×C4×Q8C2311yescharacteristic
214C2×C4×Q8C2311yescharacteristic
215C2×C4×Q8C2314yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2318yes—
219C2×C4×Q8C2318yes—
220C2×C4×Q8C2312yes—
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2314yes—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2312yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2312yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2312yes—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2312yes—
236C2×#117C2312yes—
237C2×#117C2318yes—
238C2×#117C2311yescharacteristic
239C2×#117C2312yes—
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C4⋊C4C2312yes—
245C22×C4⋊C4C2312yes—
246C22×C4⋊C4C2312yes—
247C22×C4⋊C4C2314yes—
248C22×C4⋊C4C2314yes—
249C22×C42C2312yes—
250C22×C42C2312yes—
251C22×C42C2311yescharacteristic
252C22×C42C2312yes—
253C22×C42C2311yescharacteristic
254C22×C42C2311yescharacteristic
255#400C2318yes—
256#400C2318yes—
257#400C2318yes—
258#400C2318yes—
259#400C2318yes—
260#400C2318yes—
261#399C2318yes—
262#399C2318yes—
263#398C2318yes—
264#398C2318yes—
265#398C2314yes—
266#398C2318yes—
267#398C2318yes—
268#398C2318yes—
269#398C2314yes—
270#398C2318yes—
271#398C2318yes—
272#398C2318yes—
273#398C2314yes—
274#398C2314yes—
275#398C2318yes—
276#398C2318yes—
277#398C2314yes—
278#398C2318yes—
279#398C2318yes—
280#398C2314yes—
281#398C2314yes—
282#398C2314yes—
283#396C2318yes—
284#396C2318yes—
285#396C2318yes—
286#396C2318yes—
287#395C2318yes—
288#395C2318yes—
289#395C2314yes—
290#395C2318yes—
291#395C2314yes—
292#395C2314yes—
293#395C2318yes—
294#395C2314yes—
295#395C2318yes—
296#395C2314yes—
297#395C2318yes—
298#395C2314yes—
299#395C2314yes—
300#395C2314yes—
301#393C2318yes—
302#393C2318yes—
303#391C2318yes—
304#391C2318yes—
305#391C2312yes—
306#391C2312yes—
307#391C2312yes—
308#391C2312yes—
309#391C2318yes—
310#391C2318yes—
311#391C2318yes—
312#391C2318yes—
313#391C2318yes—
314#391C2318yes—
315#390C2312yes—
316#390C2312yes—
317#390C2312yes—
318#390C2312yes—
319#389C2314yes—
320#389C2314yes—
321#389C2314yes—
322#389C2314yes—
323#389C2314yes—
324#389C2314yes—
325#389C2314yes—
326#389C2314yes—
327#389C2318yes—
328#389C2318yes—
329#389C2318yes—
330#389C2314yes—
331#389C2314yes—
332#389C2314yes—
333#389C2314yes—
334#389C2318yes—
335#389C2318yes—
336#389C2318yes—
337#389C2318yes—
338#389C2318yes—
339#389C2318yes—
340#389C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#387C2318yes—
361#387C2318yes—
362#387C2318yes—
363#387C2318yes—
364#387C2318yes—
365#387C2318yes—
366#387C2318yes—
367#387C2318yes—
368#387C2318yes—
369#386C2314yes—
370#386C2314yes—
371#386C2314yes—
372#386C2314yes—
373#385C2318yes—
374#385C2318yes—
375#385C2318yes—
376#385C2318yes—
377#385C2314yes—
378#385C2314yes—
379#385C2314yes—
380#385C2314yes—
381#384C2312yes—
382#384C2312yes—
383#384C2312yes—
384#384C2312yes—
385#384C2312yes—
386#384C2312yes—
387#384C2312yes—
388#384C2312yes—
389#384C2314yes—
390#384C2314yes—
391#384C2312yes—
392#384C2312yes—
393#384C2312yes—
394#384C2312yes—
395#383C2318yes—
396#382C2312yes—
397#382C2312yes—
398#382C2312yes—
399#382C2312yes—
400#382C2312yes—
401#382C2312yes—
402#382C2312yes—
403#382C2312yes—
404#382C2314yes—
405#382C2318yes—
406#382C2314yes—
407#382C2312yes—
408#382C2312yes—
409#382C2318yes—
410#382C2312yes—
411#382C2312yes—
412#381C2318yes—
413#380C2318yes—
414#380C2314yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2314yes—
419#380C2314yes—
420#380C2314yes—
421#380C2314yes—
422#380C2318yes—
423#380C2318yes—
424#380C2314yes—
425#380C2312yes—
426#380C2312yes—
427#380C2312yes—
428#380C2312yes—
429#380C2314yes—
430C4×C4⋊C4C2314yes—
431C4×C4⋊C4C2314yes—
432C4×C4⋊C4C2314yes—
433C4×C4⋊C4C2318yes—
434C4×C4⋊C4C2318yes—
435C4×C4⋊C4C2318yes—
436C4×C4⋊C4C2318yes—
437C4×C4⋊C4C2314yes—
438C4×C4⋊C4C2318yes—
439C4×C4⋊C4C2318yes—
440C4×C4⋊C4C2312yes—
441C4×C4⋊C4C2312yes—
442C4×C4⋊C4C2312yes—
443C4×C4⋊C4C2312yes—
444C4×C4⋊C4C2312yes—
445C4×C4⋊C4C2314yes—
446C4×C4⋊C4C2312yes—
447C4×C4⋊C4C2314yes—
448C4×C4⋊C4C2314yes—
449C4×C4⋊C4C2314yes—
450C4×C4⋊C4C2314yes—
451C4×C4⋊C4C2314yes—
452C4×C4⋊C4C2318yes—
453C4×C4⋊C4C2312yes—
454C4×C4⋊C4C2314yes—
455C4×C4⋊C4C2314yes—
456C4×C4⋊C4C2314yes—
457C4×C4⋊C4C2312yes—
458C4×C4⋊C4C2314yes—
459C4×C4⋊C4C2312yes—
460C4×C4⋊C4C2312yes—
461C4×C4⋊C4C2314yes—
462C4×C4⋊C4C2314yes—
463C4×C22⋊C4C2314yes—
464C4×C22⋊C4C2318yes—
465C4×C22⋊C4C2314yes—
466C4×C22⋊C4C2314yes—
467C4×C22⋊C4C2312yes—
468C4×C22⋊C4C2314yes—
469C4×C22⋊C4C2314yes—
470C4×C22⋊C4C2312yes—
471C4×C22⋊C4C2314yes—
472C4×C22⋊C4C2314yes—
473C4×C22⋊C4C2314yes—
474C4×C22⋊C4C2314yes—
475C4×C22⋊C4C2314yes—
476C4×C22⋊C4C2314yes—
477C4×C22⋊C4C2314yes—
478#376C2312yes—
479#376C2312yes—
480#376C2314yes—
481#376C2314yes—
482#376C2318yes—
483#376C2312yes—
484#376C2312yes—
485#376C2312yes—
486#376C2311yescharacteristic
487#376C2311yescharacteristic
488#376C2311yescharacteristic
489#376C2311yescharacteristic
490C2×#95C2314yes—
491C2×#95C2314yes—
492C2×#95C2314yes—
493C2×#95C2312yes—
494C2×#95C2312yes—
495C2×#95C2314yes—
496C43C2312yes—
497C43C2312yes—
498C43C2312yes—
499C2×#41—24no—
500C2×#41—24no—
501C2×#41C2×Q818yes—
502C22×Q8—28no—
503C22×Q8—84no—
504C22×Q8C2411yescharacteristic
505C22×Q8C2414yes—
506C22×Q8C2414yes—
507C22×Q8C2414yes—
508C22×Q8C2414yes—
509C22×D4C2412yes—
510C22×D4C2411yescharacteristic
511C23×C4C2412yes—
512C23×C4C2412yes—
513C23×C4C2412yes—
514C23×C4C2412yes—
515C23×C4C2412yes—
516C23×C4C2412yes—
517C23×C4C2414yes—
518C23×C4C2412yes—
519C23×C4C2412yes—
520C23×C4C2414yes—
521C23×C4C2411yescharacteristic
522C23×C4C2412yes—
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C4⋊Q8—28no—
526C4⋊Q8—28no—
527C4⋊Q8—28no—
528C4⋊Q8—28no—
529C4⋊Q8—28no—
530C4⋊Q8—28no—
531#125—28no—
532#125—28no—
533#125—28no—
534#125—28no—
535#125—28no—
536#125—28no—
537#125—88no—
538C22⋊Q8—216no—
539C22⋊Q8—216no—
540C22⋊Q8—88no—
541C22⋊Q8—88no—
542C4×Q8—28no—
543C4×Q8—24no—
544C4×Q8—24no—
545C4×Q8—216no—
546C4×Q8—216no—
547C4×Q8—88no—
548C4×Q8—88no—
549C4×Q8C2×Q8116yescomplemented
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—216no—
553C4×D4—28no—
554C4×D4—24no—
555C4×D4—24no—
556C4×D4C2×Q8132yes—
557C4×D4C2×Q8116yescomplemented
558#117—24no—
559#117—24no—
560#117—24no—
561#117—24no—
562#117—24no—
563#117—24no—
564#117—28no—
565#117—28no—
566#117—88no—
567#117C2×Q818yes—
568#117C2×Q8116yescomplemented
569C2×C4⋊C4—28no—
570C2×C4⋊C4—28no—
571C2×C4⋊C4—24no—
572C2×C4⋊C4—24no—
573C2×C4⋊C4—28no—
574C2×C4⋊C4—24no—
575C2×C4⋊C4—24no—
576C2×C4⋊C4—84no—
577C2×C4⋊C4—84no—
578C2×C4⋊C4C2412yes—
579C2×C4⋊C4C2412yes—
580C2×C4⋊C4C2412yes—
581C2×C4⋊C4C2412yes—
582C2×C4⋊C4C2414yes—
583C2×C4⋊C4C2414yes—
584C2×C4⋊C4C2414yes—
585C2×C4⋊C4C2414yes—
586C2×C4⋊C4C2412yes—
587C2×C4⋊C4C2412yes—
588C2×C4⋊C4C2412yes—
589C2×C4⋊C4C2412yes—
590C2×C4⋊C4C2414yes—
591C2×C4⋊C4C2414yes—
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2412yes—
595C2×C4⋊C4C2412yes—
596C2×C4⋊C4C2414yes—
597C2×C4⋊C4C2412yes—
598C2×C4⋊C4C2412yes—
599C2×C4⋊C4C2412yes—
600C2×C4⋊C4C2412yes—
601C2×C4⋊C4C2412yes—
602C2×C4⋊C4C2414yes—
603C2×C4⋊C4C2414yes—
604C2×C4⋊C4C2414yes—
605C2×C4⋊C4C2414yes—
606C2×C4⋊C4C2414yes—
607C2×C4⋊C4C2414yes—
608C2×C4⋊C4C2418yes—
609C2×C4⋊C4C2418yes—
610C2×C4⋊C4C2418yes—
611C2×C4⋊C4C2418yes—
612C2×C4⋊C4C2414yes—
613C2×C4⋊C4C2414yes—
614C2×C4⋊C4C2418yes—
615C2×C4⋊C4C2418yes—
616C2×C4⋊C4C2418yes—
617C2×C4⋊C4C2418yes—
618C2×C4⋊C4C2414yes—
619C2×C4⋊C4C2418yes—
620C2×C4⋊C4C2418yes—
621C2×C4⋊C4C2414yes—
622C2×C4⋊C4C2414yes—
623C2×C4⋊C4C2414yes—
624C2×C4⋊C4C2414yes—
625C2×C4⋊C4C2414yes—
626C2×C4⋊C4C2418yes—
627C2×C4⋊C4C2418yes—
628C2×C4⋊C4C2412yes—
629C2×C4⋊C4C2414yes—
630C2×C22⋊C4C2412yes—
631C2×C22⋊C4C2412yes—
632C2×C22⋊C4C2412yes—
633C2×C22⋊C4C2414yes—
634C2×C22⋊C4C2412yes—
635C2×C22⋊C4C2412yes—
636C2×C22⋊C4C2412yes—
637C2×C22⋊C4C2412yes—
638C2×C22⋊C4C2412yes—
639C2×C22⋊C4C2418yes—
640C2×C22⋊C4C2418yes—
641C2×C22⋊C4C2418yes—
642C2×C22⋊C4C2418yes—
643C2×C22⋊C4C2412yes—
644C2×C22⋊C4C2414yes—
645C2×C42—28no—
646C2×C42—28no—
647C2×C42C2×Q818yes—
648C2×C42C2×Q8116yescomplemented
649C2×C42#4118yes—
650C2×C42#4118yes—
651C2×C42C2412yes—
652C2×C42C2412yes—
653C2×C42C2412yes—
654C2×C42C2412yes—
655C2×C42C2412yes—
656C2×C42C2412yes—
657C2×C42C2412yes—
658C2×C42C2414yes—
659C2×C42C2412yes—
660C2×C42C2418yes—
661C2×C42C2418yes—
662C2×C42C2414yes—
663C2×C42C2414yes—
664C2×C42C2418yes—
665C2×C42C2414yes—
666C2×C42C2414yes—
667C2×C42C2414yes—
668C2×C42C2414yes—
669C2×C42C2418yes—
670C2×C42C2412yes—
671C2×C42C2411yescharacteristic
672C2×C42C2414yes—
673C2×C42C2412yes—
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2412yes—
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682#95C2412yes—
683#95C2412yes—
684#95C2414yes—
685#95C2414yes—
686#95C2414yes—
687#95C2414yes—
688#95C2412yes—
689#95C2412yes—
690#95C2412yes—
691#95C2412yes—
692#95C2412yes—
693#95C2412yes—
694#95C2414yes—
695#95C2414yes—
696#95C2418yes—
697#95C2418yes—
698#95C2418yes—
699#95C2418yes—
700#95C2414yes—
701#95C2418yes—
702#95C2418yes—
703#95C2414yes—
704#95C2418yes—
705#95C2418yes—
706#95C2418yes—
707#95C2418yes—
708#95C2414yes—
709#95C2414yes—
710#95C2418yes—
711#95C2418yes—
712#95C2418yes—
713#95C2414yes—
714#95C2414yes—
715#95C2418yes—
716#95C2418yes—
717#95C2418yes—
718#95C2418yes—
719#95C2414yes—
720#95C2414yes—
721#95C2418yes—
722#95C2418yes—
723#95C2418yes—
724C24C2512yes—
725C24C2511yescharacteristic
726#41—232no—
727C2×Q8—22no—
728C2×Q8—22no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—28no—
733C2×Q8—44no—
734C2×Q8—48no—
735C2×Q8—44no—
736C2×Q8—44no—
737C2×Q8—48no—
738C2×Q8—44no—
739C2×Q8—816no—
740C2×Q8C22×Q814yes—
741C2×D4—24no—
742C2×D4—24no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4C22×Q818yes—
746C2×D4C22×Q814yes—
747C22×C4—24no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—24no—
752C22×C4—24no—
753C22×C4—24no—
754C22×C4—28no—
755C22×C4—24no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—42no—
763C22×C4—42no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×Q818yes—
773C22×C4C22×Q818yes—
774C22×C4C22×Q8116yes—
775C22×C4C22×Q814yes—
776C22×C4C2×#4114yes—
777C22×C4C2×#4114yes—
778C22×C4C2×#4118yes—
779C22×C4C2×#4114yes—
780C22×C4C2×#4114yes—
781C22×C4C2512yes—
782C22×C4C2514yes—
783C22×C4C2514yes—
784C22×C4C2514yes—
785C22×C4C2514yes—
786C22×C4C2514yes—
787C22×C4C2514yes—
788C22×C4C2514yes—
789C22×C4C2514yes—
790C22×C4C2512yes—
791C22×C4C2514yes—
792C22×C4C2512yes—
793C22×C4C2512yes—
794C22×C4C2514yes—
795C22×C4C2512yes—
796C22×C4C2511yescharacteristic
797C22×C4C2512yes—
798C22×C4C2511yescharacteristic
799C22×C4C2511yescharacteristic
800C22×C4C2512yes—
801C22×C4C2511yescharacteristic
802C22×C4C2511yescharacteristic
803C22×C4C2511yescharacteristic
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—28no—
807C4⋊C4—28no—
808C4⋊C4—24no—
809C4⋊C4—24no—
810C4⋊C4—24no—
811C4⋊C4—24no—
812C4⋊C4—28no—
813C4⋊C4—28no—
814C4⋊C4—24no—
815C4⋊C4—24no—
816C4⋊C4—24no—
817C4⋊C4—24no—
818C4⋊C4—24no—
819C4⋊C4—28no—
820C4⋊C4—24no—
821C4⋊C4—24no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—24no—
825C4⋊C4—24no—
826C4⋊C4—24no—
827C4⋊C4—24no—
828C4⋊C4—28no—
829C4⋊C4—28no—
830C4⋊C4—28no—
831C4⋊C4—28no—
832C4⋊C4—28no—
833C4⋊C4—28no—
834C4⋊C4—48no—
835C4⋊C4—48no—
836C4⋊C4—48no—
837C4⋊C4—48no—
838C4⋊C4—44no—
839C4⋊C4—44no—
840C4⋊C4—44no—
841C4⋊C4—44no—
842C4⋊C4—48no—
843C4⋊C4—48no—
844C4⋊C4—44no—
845C4⋊C4—44no—
846C4⋊C4—48no—
847C4⋊C4—48no—
848C4⋊C4—48no—
849C4⋊C4—48no—
850C4⋊C4—44no—
851C4⋊C4—48no—
852C4⋊C4—48no—
853C4⋊C4—44no—
854C4⋊C4C22×Q818yes—
855C4⋊C4C22×Q8116yes—
856C22⋊C4—24no—
857C22⋊C4—24no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—24no—
861C22⋊C4—24no—
862C22⋊C4—24no—
863C22⋊C4—28no—
864C22⋊C4—24no—
865C22⋊C4—48no—
866C22⋊C4—48no—
867C22⋊C4—48no—
868C22⋊C4—48no—
869C22⋊C4C22×Q818yes—
870C22⋊C4C22×Q8116yes—
871C42—24no—
872C42—24no—
873C42—24no—
874C42—28no—
875C42—24no—
876C42—24no—
877C42—24no—
878C42—24no—
879C42—24no—
880C42—44no—
881C42—44no—
882C42—48no—
883C42—44no—
884C42—48no—
885C42—48no—
886C42—44no—
887C42—44no—
888C42—48no—
889C42—44no—
890C42C22×Q814yes—
891C42C22×Q814yes—
892C42C22×Q818yes—
893C42C22×Q818yes—
894C42C22×Q8116yes—
895C42C2×#4114yes—
896C42C2×#4114yes—
897C42C2×#4114yes—
898C42C2×#4114yes—
899C42C2×#4118yes—
900C42C2×#4114yes—
901C42C2×#4114yes—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—24no—
907C23—24no—
908C23C23×Q814yes—
909C23C23×Q812yes—
910C23C22×#4112yes—
911C23C22×#4112yes—
912C23C2611yescharacteristic
913Q8—28no—
914Q8—416no—
915Q8—416no—
916Q8—88no—
917Q8—88no—
918D4—216no—
919D4—28no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—216no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—22no—
940C2×C4—24no—
941C2×C4—24no—
942C2×C4—24no—
943C2×C4—24no—
944C2×C4—24no—
945C2×C4—24no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—28no—
954C2×C4—28no—
955C2×C4—28no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—28no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—48no—
965C2×C4—416no—
966C2×C4—48no—
967C2×C4—44no—
968C2×C4—44no—
969C2×C4—84no—
970C2×C4—88no—
971C2×C4—84no—
972C2×C4—84no—
973C2×C4—84no—
974C2×C4—84no—
975C2×C4—84no—
976C2×C4#533116yes—
977C2×C4C23×Q814yes—
978C2×C4C23×Q814yes—
979C2×C4C23×Q818yes—
980C2×C4C23×Q814yes—
981C2×C4C23×Q812yes—
982C2×C4C23×Q812yes—
983C2×C4C22×#4112yes—
984C2×C4C22×#4114yes—
985C2×C4C22×#4112yes—
986C2×C4C22×#4112yes—
987C2×C4C22×#4114yes—
988C2×C4C22×#4112yes—
989C2×C4C22×#4112yes—
990C2×C4C22×#4112yes—
991C2×C4C22×#4112yes—
992C2×C4C22×#4112yes—
993C22—24no—
994C22—22no—
995C22—24no—
996C22—22no—
997C22—28no—
998C22—24no—
999C22—42no—
1000C22—44no—
1001C22—42no—
1002C22C2×#53314yes—
1003C22C24×Q811yescharacteristic
1004C22C23×#4111yescharacteristic
1005C22C23×#4111yescharacteristic
1006C22H(7,𝔽2)12yes—
1007C222−1+612yes—
1008C4—24no—
1009C4—28no—
1010C4—24no—
1011C4—22no—
1012C4—22no—
1013C4—24no—
1014C4—24no—
1015C4—22no—
1016C4—22no—
1017C4—24no—
1018C4—42no—
1019C4—44no—
1020C4—44no—
1021C4—44no—
1022C4—44no—
1023C4—44no—
1024C4—44no—
1025C4—44no—
1026C4—44no—
1027C4—42no—
1028C4—44no—
1029C4C2×#53314yes—
1030C4C2×#53314yes—
1031C2—24no—
1032C2—44no—
1033C2C22×#53311yescharacteristic
1034C2#6285412yes—
1035C2#6285511yescharacteristic
1036C2#6285612yes—
1037C2#6286011yescharacteristic
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. #35958C2semidirect
2. #35952C2semidirect
3. #35951C2semidirect
4. #35936C2semidirect
5. #35934C2semidirect
6. #35931C2semidirect
7. #35339C2semidirect
10. #35304C2semidirect
11. #35286C2semidirect
12. #35282C2semidirect
13. #35282C2semidirect
16. #34642C2semidirect
17. #34625C2semidirect
18. C2×#2660C2semidirect
19. #34217C2semidirect
20. #34216C2semidirect
21. #34215C2semidirect
22. #34214C2semidirect
212. C4×#41Q8semidirect
549. C4×Q8C2×Q8semidirect
557. C4×D4C2×Q8semidirect
568. #117C2×Q8semidirect
648. C2×C42C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#359582
#359522
#359512
#359362
#359342
#359312
#353392
#353342
#353332
#353042
#352862
#352822
#352802
#352792
#346422
#346252
C2×#26602
#342172
#342162
#342152
#342142
#341892
#341882
#339992