Finite Group Databasebeta

← #7674539

Subgroups — #7674539

Order 512.

4954 conjugacy classes of subgroups.

The subgroup lattice has 957 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#43937C218yesmaximal, complemented
2#43055C218yesmaximal, complemented
3#39693C214yesmaximal, complemented
4#39692C214yesmaximal, complemented
5#39689C214yesmaximal, complemented
6#39688C214yesmaximal, complemented
7#39497C214yesmaximal, complemented
8#39494C214yesmaximal, complemented
9#37879C214yesmaximal, complemented
10#37874C214yesmaximal, complemented
11#35575C212yesmaximal, complemented
12#35543C212yesmaximal, complemented
13#35333C211yesmaximal, characteristic, complemented
14#35275C211yesmaximal, characteristic, complemented
15#35253C212yesmaximal, complemented
16C2×#2629C211yesmaximal, characteristic, complemented
17#34217C211yesmaximal, characteristic, complemented
18#34202C212yesmaximal
19#34183C211yesmaximal, characteristic, complemented
20#34065C211yesmaximal, characteristic
21#34052C211yesmaximal, characteristic, complemented
22C2×#544C2212yes—
23C22×#125C2211yescharacteristic
24C2×#525C2211yescharacteristic
25C2×#520C2212yes—
26C2×C4×#41C2211yescharacteristic
27C22×#117C2211yescharacteristic
28C22×#117C2212yes—
29#2868C2212yescomplemented
30#2859C2212yescomplemented
31#2857C2214yes—
32#2851C2214yes—
33#2851C2214yescomplemented
34#2802C2218yescomplemented
35#2802C2218yescomplemented
36#2792C2218yescomplemented
37#2791C2218yescomplemented
38#2790C2218yes—
39#2790C2218yes—
40#2790C2218yescomplemented
41#2788C2218yescomplemented
42#2784C2218yes—
43#2780C2218yes—
44#2780C2218yes—
45#2780C2218yes—
46#2768C2218yescomplemented
47#2729C2218yes—
48#2729C2218yescomplemented
49#2720C2218yes—
50#2660C2214yescomplemented
51#2629C2214yes—
52#2629C2214yes—
53#2629C2214yes—
54#2629C2214yes—
55#2629C2214yes—
56#2629C2212yescomplemented
57#2629C2212yescomplemented
58#2628C2214yes—
59#2588C2218yescomplemented
60#2587C2218yes—
61#2587C2218yes—
62#2587C2218yescomplemented
63#2585C2218yescomplemented
64#2583C2218yescomplemented
65#2579C2218yes—
66#2579C2218yes—
67#2574C2218yes—
68#2571C2214yescomplemented
69#2570C2214yescomplemented
70#2570C2214yescomplemented
71#2566C2218yes—
72#2566C2214yescomplemented
73#2565C2214yescomplemented
74#2564C2218yes—
75#2552C2214yescomplemented
76#2552C2214yescomplemented
77#2551C2214yescomplemented
78#2550C2218yescomplemented
79#2522C2218yes—
80#2522C2218yescomplemented
81#2509C2214yescomplemented
82#2508C2214yescomplemented
83#2507C2214yescomplemented
84#2507C2218yescomplemented
85#2506C2214yescomplemented
86#2505C2218yes—
87#2473C2218yes—
88#2473C2218yescomplemented
89#2454C2214yescomplemented
90#2453C2214yescomplemented
91#2452C2218yes—
92#2452C2214yescomplemented
93#2451C2214yescomplemented
94#2449C2218yes—
95#2442C2214yes—
96#2442C2214yescomplemented
97#2441C2214yes—
98#2441C2214yescomplemented
99#2440C2218yes—
100#2440C2214yes—
101#2440C2214yescomplemented
102#2439C2214yes—
103#2439C2214yescomplemented
104#2438C2218yes—
105#2437C2218yes—
106#2417C2218yes—
107C2×#398C2214yes—
108C2×#396C2214yes—
109#2370C2214yescomplemented
110#2370C2214yescomplemented
111#2359C2218yes—
112#2358C2218yes—
113#2354C2214yes—
114#2352C2214yes—
115#2352C2214yes—
116Q8×C4⋊C4C2214yescomplemented
117D4×C4⋊C4C2218yes—
118D4×C4⋊C4C2214yes—
119D4×C4⋊C4C2214yescomplemented
120#2345C2218yes—
121#2330C2212yescomplemented
122#2330C2212yescomplemented
123#2324C2212yes—
124#2324C2214yes—
125#2324C2212yes—
126#2323C2212yes—
127#2323C2214yes—
128#2323C2212yes—
129#2322C2214yes—
130#2321C2214yes—
131#2317C2212yes—
132#2317C2212yes—
133#2317C2212yes—
134#2317C2212yes—
135#2317C2212yes—
136#2317C2212yes—
137#2317C2212yes—
138#2317C2214yescomplemented
139#2316C2214yes—
140#2316C2212yes—
141#2315C2214yes—
142#2311C2212yes—
143C4×#125C2214yescomplemented
144C4×C22⋊Q8C2214yes—
145C4×#121C2214yes—
146#2297C2211yescharacteristic
147#2296C2214yes—
148#2296C2214yes—
149#2296C2211yescharacteristic
150#2293C2214yes—
151C2×#389C2212yes—
152#2290C2214yes—
153#2285C2211yescharacteristic
154#2285C2211yescharacteristic
155#2285C2212yes—
156#2285C2212yescomplemented
157C2×#384C2211yescharacteristic
158C2×#384C2212yescomplemented
159#2280C2211yescharacteristic
160C2×#380C2212yes—
161#2274C2212yes—
162C4×#117C2211yescharacteristic
163C22×#41C2311yescharacteristic
164C24×C4C2311yescharacteristic
165#544—48no—
166C2×C4⋊Q8C2314yes—
167C2×C4⋊Q8C2314yes—
168C2×C4⋊Q8C2318yes—
169C2×#125—28no—
170C2×#125C2312yes—
171C2×#125C2314yes—
172C2×#125C2312yes—
173C2×#125C2314yes—
174C2×#125C2314yes—
175C2×#125C2318yes—
176#525Q8116yescomplemented
177C2×#123C2312yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2318yes—
180C2×C22⋊Q8C2318yes—
181C2×C22⋊Q8C2312yes—
182C2×#121C2312yes—
183C2×#120C2312yes—
184#520—48no—
185C4×#41—28no—
186C2×C4×Q8C2312yes—
187C2×C4×Q8C2314yes—
188C2×C4×D4C2312yes—
189C2×C4×D4C2314yes—
190C2×C4×D4C2318yes—
191C2×C4×D4C2314yes—
192C2×C4×D4C2318yes—
193C2×C4×D4C2314yes—
194C2×#117—28no—
195C2×#117—48no—
196C2×#117C2312yes—
197C2×#117C2311yescharacteristic
198C2×#117C2312yes—
199C2×#117C2311yescharacteristic
200C2×#117C2312yes—
201C2×#117C2312yes—
202C2×#117C2312yes—
203C2×#117C2312yes—
204C2×#117C2312yes—
205C2×#117C2314yes—
206C2×#117C2312yes—
207C2×#117C2312yes—
208C2×#117C2314yes—
209C2×#117C2314yes—
210C2×#117C2311yescharacteristic
211C22×C4⋊C4C2312yes—
212C22×C4⋊C4C2312yes—
213C22×C4⋊C4C2312yes—
214C22×C4⋊C4C2314yes—
215C22×C4⋊C4C2312yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2314yes—
218C22×C4⋊C4C2318yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2314yes—
223C22×C22⋊C4C2314yes—
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226C22×C42C2314yes—
227C22×C42C2311yescharacteristic
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2318yes—
232#400C2318yes—
233#400C2318yes—
234#399C2318yes—
235#399C2318yes—
236#398C2318yes—
237#398C2318yes—
238#398C2318yes—
239#398C2318yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2318yes—
248#398C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#396C2318yes—
253#396C2318yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#395C2318yes—
263#395C2318yes—
264#395C2318yes—
265#395C2318yes—
266#393C2318yes—
267#393C2318yes—
268#391C2314yes—
269#391C2318yes—
270#391C2311yescharacteristic
271#391C2311yescharacteristic
272#391C2318yes—
273#390C2314yes—
274#390C2318yes—
275#390C2314yes—
276#390C2314yes—
277#390C2311yescharacteristic
278#390C2311yescharacteristic
279#389C2314yes—
280#389C2314yes—
281#389C2314yes—
282#389C2314yes—
283#389C2314yes—
284#389C2314yes—
285#389C2318yes—
286#389C2314yes—
287#389C2314yes—
288#389C2314yes—
289#389C2314yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2314yes—
294#389C2314yes—
295#389C2314yes—
296#389C2314yes—
297#389C2314yes—
298#389C2314yes—
299#389C2314yes—
300#389C2318yes—
301#389C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2312yes—
305#389C2312yes—
306#389C2318yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2318yes—
312#389C2318yes—
313#389C2318yes—
314#389C2314yes—
315#389C2314yes—
316#388C2314yes—
317#388C2318yes—
318#388C2314yes—
319#388C2314yes—
320#388C2314yes—
321#388C2314yes—
322#388C2314yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#387C2318yes—
327#387C2318yes—
328#387C2318yes—
329#387C2318yes—
330#387C2318yes—
331#387C2318yes—
332#387C2318yes—
333#387C2318yes—
334#387C2318yes—
335#387C2318yes—
336#387C2318yes—
337#387C2314yes—
338#387C2314yes—
339#387C2318yes—
340#387C2318yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#386C2314yes—
345#386C2318yes—
346#386C2314yes—
347#386C2314yes—
348#386C2318yes—
349#386C2318yes—
350#385C2318yes—
351#385C2318yes—
352#385C2314yes—
353#385C2318yes—
354#385C2318yes—
355#385C2318yes—
356#385C2318yes—
357#385C2314yes—
358#385C2314yes—
359#385C2314yes—
360#385C2314yes—
361#385C2314yes—
362#385C2314yes—
363#385C2314yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#384C2314yes—
375#384C2318yes—
376#384C2312yes—
377#384C2314yes—
378#384C2314yes—
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2312yes—
384#384C2312yes—
385#384C2318yes—
386#384C2314yes—
387#384C2312yes—
388#382C2312yes—
389#382C2314yes—
390#382C2318yes—
391#382C2312yes—
392#382C2314yes—
393#382C2314yes—
394#382C2312yes—
395#382C2312yes—
396#381C2312yes—
397#380C2314yes—
398#380C2318yes—
399#380C2314yes—
400#380C2314yes—
401#380C2314yes—
402#380C2314yes—
403#380C2314yes—
404#380C2318yes—
405#380C2312yes—
406#380C2314yes—
407#380C2312yes—
408#380C2318yes—
409#380C2318yes—
410#380C2314yes—
411#380C2314yes—
412#380C2314yes—
413#379C2312yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2318yes—
421C4×C4⋊C4C2312yes—
422C4×C4⋊C4C2312yes—
423C4×C4⋊C4C2314yes—
424C4×C4⋊C4C2314yes—
425C4×C4⋊C4C2318yes—
426C4×C4⋊C4C2314yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2314yes—
429C4×C22⋊C4C2318yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2318yes—
432C4×C22⋊C4C2318yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435#376C2312yes—
436C2×#95C2314yes—
437C2×#95C2314yes—
438C43C2312yes—
439C25C2411yescharacteristic
440C2×#41—24no—
441C2×#41—24no—
442C2×#41C2×Q818yes—
443C22×Q8C2411yescharacteristic
444C22×Q8C2418yes—
445C22×D4C2412yes—
446C22×D4C2411yescharacteristic
447C22×D4C2414yes—
448C23×C4—24no—
449C23×C4—24no—
450C23×C4C2×Q818yes—
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2412yes—
454C23×C4C2412yes—
455C23×C4C2414yes—
456C23×C4C2414yes—
457C23×C4C2412yes—
458C23×C4C2414yes—
459C23×C4C2414yes—
460C23×C4C2414yes—
461C23×C4C2418yes—
462C23×C4C2412yes—
463C23×C4C2411yescharacteristic
464C4⋊Q8—48no—
465C4⋊Q8—48no—
466C4⋊Q8—88no—
467#125—28no—
468#125—28no—
469#125—216no—
470#125—48no—
471#125—48no—
472#125—88no—
473#123C2×Q8116yes—
474C22⋊Q8—416no—
475C22⋊Q8—88no—
476C22⋊Q8—88no—
477C22⋊Q8C2×Q8116yes—
478#121C2×Q8116yes—
479#120C2×Q8116yes—
480C4×Q8—28no—
481C4×Q8—48no—
482C4×D4—216no—
483C4×D4—28no—
484C4×D4—48no—
485C4×D4—416no—
486C4×D4—88no—
487C4×D4C2×Q8132yes—
488#117—24no—
489#117—28no—
490#117—28no—
491#117—24no—
492#117—28no—
493#117—28no—
494#117—28no—
495#117—28no—
496#117—28no—
497#117—48no—
498#117—48no—
499#117—44no—
500#117—44no—
501#117—48no—
502#117C2×Q818yes—
503C2×C4⋊C4—28no—
504C2×C4⋊C4—216no—
505C2×C4⋊C4—28no—
506C2×C4⋊C4—28no—
507C2×C4⋊C4—44no—
508C2×C4⋊C4—44no—
509C2×C4⋊C4—48no—
510C2×C4⋊C4—88no—
511C2×C4⋊C4—84no—
512C2×C4⋊C4—84no—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2414yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2412yes—
517C2×C4⋊C4C2412yes—
518C2×C4⋊C4C2412yes—
519C2×C4⋊C4C2412yes—
520C2×C4⋊C4C2412yes—
521C2×C4⋊C4C2412yes—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2418yes—
526C2×C4⋊C4C2418yes—
527C2×C4⋊C4C2412yes—
528C2×C4⋊C4C2414yes—
529C2×C4⋊C4C2411yescharacteristic
530C2×C4⋊C4C2411yescharacteristic
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2418yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2414yes—
561C2×C22⋊C4—28no—
562C2×C22⋊C4—48no—
563C2×C22⋊C4—84no—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2412yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2412yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2412yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2414yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2414yes—
586C2×C22⋊C4C2414yes—
587C2×C42—24no—
588C2×C42—28no—
589C2×C42—48no—
590C2×C42#4118yes—
591C2×C42C2414yes—
592C2×C42C2414yes—
593C2×C42C2412yes—
594C2×C42C2412yes—
595C2×C42C2411yescharacteristic
596C2×C42C2411yescharacteristic
597C2×C42C2412yes—
598C2×C42C2414yes—
599C2×C42C2414yes—
600C2×C42C2414yes—
601C2×C42C2418yes—
602C2×C42C2418yes—
603C2×C42C2414yes—
604C2×C42C2414yes—
605C2×C42C2418yes—
606C2×C42C2412yes—
607C2×C42C2411yescharacteristic
608C2×C42C2412yes—
609C2×C42C2411yescharacteristic
610#95C2418yes—
611#95C2418yes—
612#95C2418yes—
613#95C2418yes—
614#95C2414yes—
615#95C2414yes—
616#95C2418yes—
617#95C2418yes—
618#95C2414yes—
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2414yes—
624#95C2414yes—
625#95C2414yes—
626#95C2414yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2414yes—
637#95C2418yes—
638#95C2414yes—
639#95C2414yes—
640#95C2418yes—
641#95C2418yes—
642C24—22no—
643C24—22no—
644C24—42no—
645C24—42no—
646C24C22×Q814yes—
647C24C2512yes—
648C24C2512yes—
649C24C2511yescharacteristic
650#41—232no—
651C2×Q8—22no—
652C2×Q8—22no—
653C2×Q8—48no—
654C2×Q8—48no—
655C2×Q8—48no—
656C2×Q8C22×Q814yes—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—44no—
662C2×D4—44no—
663C2×D4C22×Q818yes—
664C2×D4C22×Q814yes—
665C2×D4C22×Q8116yes—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—232no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—42no—
680C22×C4—44no—
681C22×C4—42no—
682C22×C4—44no—
683C22×C4—44no—
684C22×C4—44no—
685C22×C4—44no—
686C22×C4—44no—
687C22×C4—42no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—42no—
694C22×C4—44no—
695C22×C4—48no—
696C22×C4—48no—
697C22×C4—48no—
698C22×C4C22×Q818yes—
699C22×C4C22×Q818yes—
700C22×C4C22×Q818yes—
701C22×C4C22×Q814yes—
702C22×C4C22×Q814yes—
703C22×C4C2×#4118yes—
704C22×C4C2×#4114yes—
705C22×C4H(5,𝔽2)14yes—
706C22×C4C2514yes—
707C22×C4C2512yes—
708C22×C4C2514yes—
709C22×C4C2512yes—
710C22×C4C2518yes—
711C22×C4C2514yes—
712C22×C4C2512yes—
713C22×C4C2512yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2518yes—
717C22×C4C2514yes—
718C22×C4C2512yes—
719C22×C4C2512yes—
720C22×C4C2512yes—
721C22×C4C2512yes—
722C22×C4C2511yescharacteristic
723C22×C4C2511yescharacteristic
724C4⋊C4—24no—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—216no—
729C4⋊C4—216no—
730C4⋊C4—28no—
731C4⋊C4—28no—
732C4⋊C4—28no—
733C4⋊C4—24no—
734C4⋊C4—28no—
735C4⋊C4—28no—
736C4⋊C4—24no—
737C4⋊C4—24no—
738C4⋊C4—24no—
739C4⋊C4—24no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—44no—
743C4⋊C4—44no—
744C4⋊C4—48no—
745C4⋊C4—44no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—48no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C4⋊C4—44no—
755C4⋊C4—44no—
756C4⋊C4—48no—
757C4⋊C4—48no—
758C4⋊C4—44no—
759C4⋊C4—48no—
760C4⋊C4—48no—
761C4⋊C4—48no—
762C4⋊C4—48no—
763C4⋊C4—48no—
764C4⋊C4—44no—
765C4⋊C4—48no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—48no—
769C4⋊C4—44no—
770C4⋊C4C22×Q818yes—
771C4⋊C4C22×Q8116yes—
772C22⋊C4—24no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—24no—
776C22⋊C4—24no—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—28no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—44no—
791C22⋊C4—44no—
792C22⋊C4C22×Q818yes—
793C22⋊C4C22×Q8116yes—
794C22⋊C4C22×Q8116yes—
795C42—24no—
796C42—24no—
797C42—22no—
798C42—22no—
799C42—28no—
800C42—28no—
801C42—28no—
802C42—24no—
803C42—44no—
804C42—44no—
805C42—44no—
806C42—48no—
807C42—48no—
808C42—48no—
809C42—44no—
810C42C22×Q818yes—
811C42C2×#4114yes—
812C42C2×#4114yes—
813C42C2×#4118yes—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—28no—
827C23—48no—
828C23—84no—
829C23—82no—
830C23—82no—
831C23C23×Q814yes—
832C23C23×Q814yes—
833C23C23×Q812yes—
834C23C22×#4112yes—
835C23C2×H(5,𝔽2)12yes—
836C23C2611yescharacteristic
837Q8—28no—
838Q8—168no—
839D4—216no—
840D4—28no—
841D4—416no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—28no—
853C2×C4—216no—
854C2×C4—216no—
855C2×C4—216no—
856C2×C4—24no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—28no—
867C2×C4—24no—
868C2×C4—28no—
869C2×C4—24no—
870C2×C4—22no—
871C2×C4—28no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—24no—
880C2×C4—28no—
881C2×C4—22no—
882C2×C4—24no—
883C2×C4—24no—
884C2×C4—22no—
885C2×C4—24no—
886C2×C4—24no—
887C2×C4—48no—
888C2×C4—416no—
889C2×C4—84no—
890C2×C4—88no—
891C2×C4—88no—
892C2×C4—88no—
893C2×C4—88no—
894C2×C4—168no—
895C2×C4#554116yes—
896C2×C4C23×Q818yes—
897C2×C4C23×Q814yes—
898C2×C4C23×Q814yes—
899C2×C4C23×Q812yes—
900C2×C4C23×Q812yes—
901C2×C4C22×#4114yes—
902C2×C4C22×#4114yes—
903C2×C4C22×#4112yes—
904C2×C4C22×#4112yes—
905C2×C4C2×H(5,𝔽2)12yes—
906C2×C4C2×H(5,𝔽2)12yes—
907C22—24no—
908C22—24no—
909C22—22no—
910C22—22no—
911C22—24no—
912C22—28no—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—44no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—88no—
924C22C2×#55414yes—
925C22C24×Q811yescharacteristic
926C22C23×#4111yescharacteristic
927C22C22×H(5,𝔽2)11yescharacteristic
928C22H(7,𝔽2)12yes—
929C222−1+612yes—
930C4—28no—
931C4—24no—
932C4—24no—
933C4—24no—
934C4—24no—
935C4—44no—
936C4—42no—
937C4—42no—
938C4—48no—
939C4—44no—
940C4—48no—
941C4—44no—
942C4—42no—
943C4—42no—
944C4—44no—
945C4—44no—
946C4C2×#55414yes—
947C4C2×#55414yes—
948C2—24no—
949C2—44no—
950C2—44no—
951C2C22×#55411yescharacteristic
952C2#6285412yes—
953C2#6285612yes—
954C2#6288011yescharacteristic
955C2#6288811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#525C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #43937C2semidirect
2. #43055C2semidirect
3. #39693C2semidirect
4. #39692C2semidirect
5. #39689C2semidirect
6. #39688C2semidirect
7. #39497C2semidirect
8. #39494C2semidirect
9. #37879C2semidirect
10. #37874C2semidirect
11. #35575C2semidirect
12. #35543C2semidirect
13. #35333C2semidirect
14. #35275C2semidirect
15. #35253C2semidirect
16. C2×#2629C2semidirect
17. #34217C2semidirect
19. #34183C2semidirect
21. #34052C2semidirect
29. #2868C22semidirect
30. #2859C22semidirect
33. #2851C22semidirect
34. #2802C22semidirect
35. #2802C22semidirect
36. #2792C22semidirect
37. #2791C22semidirect
40. #2790C22semidirect
41. #2788C22semidirect
46. #2768C22semidirect
48. #2729C22semidirect
50. #2660C22semidirect
56. #2629C22semidirect
57. #2629C22semidirect
59. #2588C22semidirect
62. #2587C22semidirect
63. #2585C22semidirect
64. #2583C22semidirect
68. #2571C22semidirect
69. #2570C22semidirect
70. #2570C22semidirect
72. #2566C22semidirect
73. #2565C22semidirect
75. #2552C22semidirect
76. #2552C22semidirect
77. #2551C22semidirect
78. #2550C22semidirect
80. #2522C22semidirect
81. #2509C22semidirect
82. #2508C22semidirect
83. #2507C22semidirect
84. #2507C22semidirect
85. #2506C22semidirect
88. #2473C22semidirect
89. #2454C22semidirect
90. #2453C22semidirect
92. #2452C22semidirect
93. #2451C22semidirect
96. #2442C22semidirect
98. #2441C22semidirect
101. #2440C22semidirect
103. #2439C22semidirect
109. #2370C22semidirect
110. #2370C22semidirect
116. Q8×C4⋊C4C22semidirect
119. D4×C4⋊C4C22semidirect
121. #2330C22semidirect
122. #2330C22semidirect
138. #2317C22semidirect
143. C4×#125C22semidirect
156. #2285C22semidirect
158. C2×#384C22semidirect
176. #525Q8semidirect

Maximal subgroups

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

subgroupindex
#439372
#430552
#396932
#396922
#396892
#396882
#394972
#394942
#378792
#378742
#355752
#355432
#353332
#352752
#352532
C2×#26292
#342172
#342022
#341832
#340652
#340522