Finite Group Databasebeta

← #7630911

Subgroups — #7630911

Order 512.

4830 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36039C214yesmaximal, complemented
2#35843C214yesmaximal, complemented
3#35810C218yesmaximal, complemented
4#35779C218yesmaximal
5#35747C214yesmaximal, complemented
6#35708C214yesmaximal, complemented
7#35345C212yesmaximal, complemented
8#35336C212yesmaximal, complemented
9#35335C211yesmaximal, characteristic, complemented
10#35294C212yesmaximal, complemented
11#35284C212yesmaximal, complemented
12#35282C214yesmaximal, complemented
13#35275C211yesmaximal, characteristic, complemented
14#35265C212yesmaximal, complemented
15#35253C212yesmaximal
16#34634C211yesmaximal, characteristic
17#34625C214yesmaximal, complemented
18C2×#2629C211yesmaximal, characteristic
19#34272C212yesmaximal, complemented
20#34217C211yesmaximal, characteristic, complemented
21#34214C211yesmaximal, characteristic, complemented
22#34180C212yesmaximal
23#33996C211yesmaximal, characteristic
24C2×#544C2212yes—
25C2×#533C2211yescharacteristic
26C22×#125C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C22×#117C2211yescharacteristic
30#2868C2212yescomplemented
31#2864C2214yescomplemented
32#2859C2212yescomplemented
33#2859C2212yescomplemented
34#2859C2212yescomplemented
35#2859C2214yescomplemented
36#2857C2214yes—
37#2851C2214yes—
38#2667C2218yes—
39#2666C2218yescomplemented
40#2666C2218yescomplemented
41#2665C2218yes—
42#2660C2214yescomplemented
43#2660C2214yescomplemented
44#2647C2214yescomplemented
45#2647C2214yescomplemented
46#2629C2214yes—
47#2629C2211yescharacteristic
48#2629C2212yes—
49#2629C2211yescharacteristic
50#2629C2212yes—
51#2629C2214yes—
52#2629C2212yes—
53#2629C2214yes—
54#2629C2212yes—
55#2629C2211yescharacteristic
56#2629C2211yescharacteristic
57#2628C2212yes—
58#2628C2214yes—
59#2628C2212yes—
60#2627C2214yes—
61#2626C2214yes—
62#2608C2218yes—
63#2608C2218yes—
64#2606C2218yescomplemented
65#2606C2218yescomplemented
66#2590C2218yescomplemented
67#2590C2218yescomplemented
68#2587C2218yes—
69#2587C2218yes—
70#2586C2218yescomplemented
71#2585C2218yescomplemented
72#2584C2214yescomplemented
73#2584C2214yescomplemented
74#2583C2218yes—
75#2574C2218yes—
76#2570C2218yescomplemented
77#2556C2218yes—
78#2552C2214yescomplemented
79#2551C2214yescomplemented
80#2550C2218yescomplemented
81#2522C2218yes—
82#2520C2218yescomplemented
83#2509C2214yescomplemented
84#2508C2214yescomplemented
85#2507C2214yescomplemented
86#2507C2218yescomplemented
87#2506C2214yescomplemented
88#2505C2218yes—
89#2497C2218yes—
90#2473C2218yes—
91#2465C2218yes—
92#2462C2218yescomplemented
93#2446C2218yescomplemented
94#2442C2214yes—
95#2441C2214yes—
96#2441C2218yes—
97#2440C2214yes—
98#2440C2218yes—
99#2439C2214yes—
100#2439C2218yes—
101#2438C2218yes—
102#2437C2218yes—
103#2429C2218yes—
104#2402C2218yescomplemented
105#2399C2218yescomplemented
106#2396C2218yes—
107#2396C2214yes—
108#2396C2218yes—
109#2396C2214yes—
110C2×#398C2214yes—
111C2×#396C2214yes—
112#2370C2214yescomplemented
113#2370C2214yescomplemented
114#2370C2214yescomplemented
115#2370C2214yescomplemented
116#2369C2214yescomplemented
117#2368C2218yes—
118#2365C2214yescomplemented
119#2360C2218yes—
120#2360C2218yes—
121#2355C2214yescomplemented
122Q8×C4⋊C4C2214yescomplemented
123#2347C2214yes—
124#2346C2214yes—
125#2345C2214yes—
126#2345C2218yes—
127#2344C2214yes—
128#2343C2218yes—
129#2342C2218yes—
130#2331C2214yescomplemented
131#2330C2212yescomplemented
132#2330C2212yescomplemented
133#2330C2212yescomplemented
134#2330C2214yescomplemented
135#2330C2212yescomplemented
136#2317C2212yes—
137#2317C2212yes—
138#2317C2212yes—
139#2317C2212yes—
140#2316C2212yes—
141#2314C2214yes—
142#2314C2214yes—
143C4×C4⋊Q8C2214yescomplemented
144C4×C4⋊Q8C2214yescomplemented
145C4×#125C2214yescomplemented
146C4×#125C2214yescomplemented
147#2296C2212yes—
148C2×#389C2212yes—
149#2285C2214yes—
150#2285C2211yescharacteristic
151C2×#384C2211yescharacteristic
152#2283C2214yes—
153#2280C2212yes—
154C2×#380C2212yes—
155#2274C2212yes—
156#2274C2212yes—
157#2274C2212yes—
158#2274C2212yes—
159#2274C2212yes—
160#2274C2212yes—
161#2274C2214yes—
162#2273C2214yes—
163C4×#117C2211yescharacteristic
164C4×#117C2212yes—
165C4×#117C2212yes—
166C4×#117C2212yes—
167C4×#117C2211yescharacteristic
168C4×#117C2211yescharacteristic
169C4×#117C2212yes—
170C4×#117C2211yescharacteristic
171C24×C4C2311yescharacteristic
172#544—216no—
173#533—28no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2314yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2318yes—
178C2×#125—28no—
179C2×#125C2312yes—
180C2×#125C2314yes—
181C2×#125C2314yes—
182C2×#125C2312yes—
183C2×#125C2311yescharacteristic
184C2×#125C2311yescharacteristic
185C2×#125C2314yes—
186C2×#125C2318yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×C4×Q8C2314yes—
191C2×C4×Q8C2318yes—
192C2×C4×Q8C2318yes—
193C2×#117—28no—
194C2×#117—28no—
195C2×#117Q8116yescomplemented
196C2×#117C2311yescharacteristic
197C2×#117C2312yes—
198C2×#117C2312yes—
199C2×#117C2312yes—
200C2×#117C2311yescharacteristic
201C2×#117C2311yescharacteristic
202C2×#117C2311yescharacteristic
203C2×#117C2311yescharacteristic
204C2×#117C2312yes—
205C2×#117C2312yes—
206C2×#117C2312yes—
207C2×#117C2311yescharacteristic
208C2×#117C2311yescharacteristic
209C2×#117C2318yes—
210C2×#117C2312yes—
211C2×#117C2311yescharacteristic
212C2×#117C2312yes—
213C2×#117C2312yes—
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2314yes—
219C22×C4⋊C4C2312yes—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2314yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2314yes—
228C22×C22⋊C4C2312yes—
229C22×C42C2312yes—
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233#400C2318yes—
234#400C2314yes—
235#400C2318yes—
236#400C2318yes—
237#400C2314yes—
238#400C2318yes—
239#400C2318yes—
240#399C2314yes—
241#399C2314yes—
242#399C2318yes—
243#398C2314yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2314yes—
253#398C2318yes—
254#398C2314yes—
255#398C2318yes—
256#398C2318yes—
257#398C2314yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#396C2318yes—
262#396C2314yes—
263#396C2318yes—
264#396C2314yes—
265#396C2318yes—
266#396C2318yes—
267#396C2318yes—
268#396C2314yes—
269#396C2314yes—
270#396C2318yes—
271#395C2318yes—
272#395C2318yes—
273#395C2314yes—
274#395C2318yes—
275#395C2314yes—
276#395C2318yes—
277#395C2318yes—
278#393C2314yes—
279#393C2314yes—
280#393C2318yes—
281#391C2318yes—
282#391C2318yes—
283#391C2318yes—
284#391C2318yes—
285#391C2318yes—
286#389C2312yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2312yes—
291#389C2314yes—
292#389C2314yes—
293#389C2318yes—
294#389C2318yes—
295#389C2318yes—
296#389C2318yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2314yes—
301#389C2314yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2318yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2312yes—
311#389C2318yes—
312#389C2314yes—
313#389C2318yes—
314#389C2318yes—
315#389C2318yes—
316#389C2318yes—
317#389C2318yes—
318#389C2312yes—
319#389C2318yes—
320#389C2318yes—
321#389C2314yes—
322#389C2314yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2318yes—
338#387C2318yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2318yes—
348#387C2318yes—
349#385C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2318yes—
353#385C2318yes—
354#385C2318yes—
355#385C2314yes—
356#385C2314yes—
357#384C2312yes—
358#384C2314yes—
359#384C2314yes—
360#384C2314yes—
361#384C2318yes—
362#384C2314yes—
363#384C2311yescharacteristic
364#384C2312yes—
365#384C2311yescharacteristic
366#384C2314yes—
367#383C2318yes—
368#382C2312yes—
369#382C2314yes—
370#382C2314yes—
371#382C2314yes—
372#382C2318yes—
373#382C2318yes—
374#382C2314yes—
375#381C2318yes—
376#381C2314yes—
377#380C2312yes—
378#380C2314yes—
379#380C2312yes—
380#380C2318yes—
381#380C2318yes—
382#380C2318yes—
383#380C2314yes—
384#380C2314yes—
385#380C2314yes—
386#380C2312yes—
387#380C2314yes—
388#380C2312yes—
389#379C2314yes—
390C4×C4⋊C4C2314yes—
391C4×C4⋊C4C2314yes—
392C4×C4⋊C4C2314yes—
393C4×C4⋊C4C2318yes—
394C4×C4⋊C4C2318yes—
395C4×C4⋊C4C2318yes—
396C4×C4⋊C4C2318yes—
397C4×C4⋊C4C2314yes—
398C4×C4⋊C4C2318yes—
399C4×C4⋊C4C2318yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2318yes—
402C4×C4⋊C4C2312yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2312yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2318yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2318yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2314yes—
437C4×C22⋊C4C2314yes—
438C4×C22⋊C4C2314yes—
439C4×C22⋊C4C2314yes—
440C4×C22⋊C4C2314yes—
441#376C2312yes—
442#376C2312yes—
443#376C2318yes—
444#376C2312yes—
445#376C2312yes—
446C2×#95C2314yes—
447C2×#95C2314yes—
448C43C2312yes—
449C43C2312yes—
450C43C2312yes—
451C43C2312yes—
452C25C2411yescharacteristic
453C22×Q8C2414yes—
454C22×Q8C2418yes—
455C23×C4—24no—
456C23×C4—24no—
457C23×C4C2×Q818yes—
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2414yes—
464C23×C4C2414yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2412yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C4⋊Q8—216no—
472C4⋊Q8—28no—
473C4⋊Q8—216no—
474C4⋊Q8—88no—
475#125—216no—
476#125—216no—
477#125—28no—
478#125—28no—
479#125—24no—
480#125—24no—
481#125—216no—
482#125—88no—
483C22⋊Q8—216no—
484C22⋊Q8—232no—
485C22⋊Q8—88no—
486C4×Q8—216no—
487C4×Q8—88no—
488C4×Q8—88no—
489#117—24no—
490#117—28no—
491#117—28no—
492#117—24no—
493#117—24no—
494#117—28no—
495#117—28no—
496#117—28no—
497#117—28no—
498#117—24no—
499#117—24no—
500#117—24no—
501#117—24no—
502#117—88no—
503#117C2×Q8116yes—
504#117C2×Q8116yes—
505#117C2×Q8116yes—
506#117C2×Q818yes—
507#117C2×Q818yes—
508#117#4118yes—
509C2×C4⋊C4—28no—
510C2×C4⋊C4—216no—
511C2×C4⋊C4—28no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—24no—
514C2×C4⋊C4—24no—
515C2×C4⋊C4—84no—
516C2×C4⋊C4—84no—
517C2×C4⋊C4C2×Q8116yes—
518C2×C4⋊C4C2411yescharacteristic
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2418yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2412yes—
533C2×C4⋊C4C2412yes—
534C2×C4⋊C4C2412yes—
535C2×C4⋊C4C2412yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2418yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2414yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2412yes—
565C2×C4⋊C4C2411yescharacteristic
566C2×C4⋊C4C2411yescharacteristic
567C2×C22⋊C4—28no—
568C2×C22⋊C4—28no—
569C2×C22⋊C4—84no—
570C2×C22⋊C4C2×Q8116yes—
571C2×C22⋊C4C2412yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2412yes—
590C2×C42—24no—
591C2×C42—28no—
592C2×C42C2×Q8116yes—
593C2×C42#4118yes—
594C2×C42C2412yes—
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597C2×C42C2412yes—
598C2×C42C2412yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2418yes—
603C2×C42C2418yes—
604C2×C42C2414yes—
605C2×C42C2414yes—
606C2×C42C2418yes—
607C2×C42C2414yes—
608C2×C42C2414yes—
609C2×C42C2414yes—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2414yes—
613C2×C42C2418yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2414yes—
617C2×C42C2412yes—
618C2×C42C2411yescharacteristic
619C2×C42C2412yes—
620C2×C42C2411yescharacteristic
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2418yes—
635#95C2418yes—
636#95C2414yes—
637#95C2418yes—
638#95C2418yes—
639#95C2418yes—
640#95C2418yes—
641#95C2414yes—
642#95C2414yes—
643#95C2418yes—
644#95C2418yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653#95C2414yes—
654#95C2418yes—
655#95C2418yes—
656#95C2414yes—
657C24—22no—
658C24—22no—
659C24—42no—
660C24—42no—
661C24C22×Q814yes—
662C24C2511yescharacteristic
663C24C2511yescharacteristic
664C24C2511yescharacteristic
665C2×Q8—28no—
666C2×Q8—216no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—48no—
670C2×Q8—48no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—232no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—24no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—42no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—42no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—42no—
698C22×C4—44no—
699C22×C4C22×Q814yes—
700C22×C4C22×Q814yes—
701C22×C4C22×Q814yes—
702C22×C4C22×Q814yes—
703C22×C4C22×Q814yes—
704C22×C4C22×Q8116yes—
705C22×C4C22×Q814yes—
706C22×C4C2×#4118yes—
707C22×C4C2×#4114yes—
708C22×C4C2×#4114yes—
709C22×C4C2512yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2518yes—
716C22×C4C2514yes—
717C22×C4C2518yes—
718C22×C4C2512yes—
719C22×C4C2511yescharacteristic
720C22×C4C2511yescharacteristic
721C22×C4C2514yes—
722C22×C4C2514yes—
723C22×C4C2512yes—
724C22×C4C2512yes—
725C22×C4C2512yes—
726C22×C4C2512yes—
727C22×C4C2511yescharacteristic
728C22×C4C2511yescharacteristic
729C4⋊C4—24no—
730C4⋊C4—24no—
731C4⋊C4—24no—
732C4⋊C4—24no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—216no—
738C4⋊C4—216no—
739C4⋊C4—28no—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—24no—
744C4⋊C4—24no—
745C4⋊C4—24no—
746C4⋊C4—24no—
747C4⋊C4—28no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—216no—
751C4⋊C4—216no—
752C4⋊C4—216no—
753C4⋊C4—48no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—48no—
760C4⋊C4—44no—
761C4⋊C4—48no—
762C4⋊C4—44no—
763C4⋊C4—48no—
764C4⋊C4—48no—
765C4⋊C4—44no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—48no—
769C4⋊C4—48no—
770C4⋊C4—44no—
771C4⋊C4—48no—
772C4⋊C4—44no—
773C4⋊C4C22×Q8116yes—
774C4⋊C4C22×Q818yes—
775C4⋊C4C22×Q818yes—
776C4⋊C4C2×#4114yes—
777C4⋊C4C2×#4114yes—
778C22⋊C4—24no—
779C22⋊C4—28no—
780C22⋊C4—28no—
781C22⋊C4—24no—
782C22⋊C4—24no—
783C22⋊C4—24no—
784C22⋊C4—24no—
785C22⋊C4—24no—
786C22⋊C4—24no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—44no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C22⋊C4C22×Q8116yes—
794C22⋊C4C22×Q818yes—
795C22⋊C4C22×Q818yes—
796C22⋊C4C2×#4118yes—
797C42—24no—
798C42—24no—
799C42—24no—
800C42—22no—
801C42—22no—
802C42—24no—
803C42—28no—
804C42—28no—
805C42—44no—
806C42—44no—
807C42—48no—
808C42—44no—
809C42—44no—
810C42—48no—
811C42—48no—
812C42—44no—
813C42—44no—
814C42—48no—
815C42—44no—
816C42—44no—
817C42C22×Q8116yes—
818C42C22×Q818yes—
819C42C22×Q818yes—
820C42C2×#4118yes—
821C42C2×#4118yes—
822C42C2×#4114yes—
823C42C2×#4114yes—
824C23—22no—
825C23—22no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—28no—
835C23—48no—
836C23—84no—
837C23—82no—
838C23—82no—
839C23C23×Q812yes—
840C23C23×Q812yes—
841C23C23×Q812yes—
842C23C22×#4112yes—
843C23C22×#4112yes—
844C23C2611yescharacteristic
845Q8—416no—
846Q8—816no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—24no—
852C2×C4—24no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—28no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—28no—
875C2×C4—28no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—24no—
882C2×C4—28no—
883C2×C4—28no—
884C2×C4—28no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—24no—
890C2×C4—28no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—416no—
895C2×C4—48no—
896C2×C4—84no—
897C2×C4—84no—
898C2×C4—84no—
899C2×C4—88no—
900C2×C4—88no—
901C2×C4#533116yes—
902C2×C4C23×Q812yes—
903C2×C4C23×Q818yes—
904C2×C4C23×Q818yes—
905C2×C4C23×Q812yes—
906C2×C4C23×Q812yes—
907C2×C4C23×Q812yes—
908C2×C4C22×#4114yes—
909C2×C4C22×#4114yes—
910C2×C4C22×#4114yes—
911C2×C4C22×#4114yes—
912C2×C4C22×#4112yes—
913C2×C4C22×#4112yes—
914C2×C4C22×#4112yes—
915C2×C4C22×#4112yes—
916C22—24no—
917C22—24no—
918C22—22no—
919C22—22no—
920C22—24no—
921C22—24no—
922C22—22no—
923C22—22no—
924C22—42no—
925C22—42no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—88no—
931C22C2×#53314yes—
932C22C24×Q811yescharacteristic
933C22C23×#4111yescharacteristic
934C22C23×#4111yescharacteristic
935C22H(7,𝔽2)12yes—
936C222−1+612yes—
937C4—28no—
938C4—28no—
939C4—24no—
940C4—24no—
941C4—24no—
942C4—24no—
943C4—22no—
944C4—22no—
945C4—42no—
946C4—42no—
947C4—48no—
948C4—44no—
949C4—44no—
950C4—42no—
951C4—48no—
952C4—44no—
953C4—44no—
954C4—42no—
955C4C2×#53314yes—
956C4C2×#53314yes—
957C2—24no—
958C2—42no—
959C2—42no—
960C2C22×#53311yescharacteristic
961C2#6285412yes—
962C2#6285612yes—
963C2#6285811yescharacteristic
964C2#6286111yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC25C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36039C2semidirect
2. #35843C2semidirect
3. #35810C2semidirect
5. #35747C2semidirect
6. #35708C2semidirect
7. #35345C2semidirect
8. #35336C2semidirect
9. #35335C2semidirect
10. #35294C2semidirect
11. #35284C2semidirect
12. #35282C2semidirect
13. #35275C2semidirect
14. #35265C2semidirect
17. #34625C2semidirect
19. #34272C2semidirect
20. #34217C2semidirect
21. #34214C2semidirect
30. #2868C22semidirect
31. #2864C22semidirect
32. #2859C22semidirect
33. #2859C22semidirect
34. #2859C22semidirect
35. #2859C22semidirect
39. #2666C22semidirect
40. #2666C22semidirect
42. #2660C22semidirect
43. #2660C22semidirect
44. #2647C22semidirect
45. #2647C22semidirect
64. #2606C22semidirect
65. #2606C22semidirect
66. #2590C22semidirect
67. #2590C22semidirect
70. #2586C22semidirect
71. #2585C22semidirect
72. #2584C22semidirect
73. #2584C22semidirect
76. #2570C22semidirect
78. #2552C22semidirect
79. #2551C22semidirect
80. #2550C22semidirect
82. #2520C22semidirect
83. #2509C22semidirect
84. #2508C22semidirect
85. #2507C22semidirect
86. #2507C22semidirect
87. #2506C22semidirect
92. #2462C22semidirect
93. #2446C22semidirect
104. #2402C22semidirect
105. #2399C22semidirect
112. #2370C22semidirect
113. #2370C22semidirect
114. #2370C22semidirect
115. #2370C22semidirect
116. #2369C22semidirect
118. #2365C22semidirect
121. #2355C22semidirect
122. Q8×C4⋊C4C22semidirect
130. #2331C22semidirect
131. #2330C22semidirect
132. #2330C22semidirect
133. #2330C22semidirect
134. #2330C22semidirect
135. #2330C22semidirect
143. C4×C4⋊Q8C22semidirect
144. C4×C4⋊Q8C22semidirect
145. C4×#125C22semidirect
146. C4×#125C22semidirect
195. C2×#117Q8semidirect

Maximal subgroups

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

subgroupindex
#360392
#358432
#358102
#357792
#357472
#357082
#353452
#353362
#353352
#352942
#352842
#352822
#352752
#352652
#352532
#346342
#346252
C2×#26292
#342722
#342172
#342142
#341802
#339962