Finite Group Databasebeta

← #7670660

Subgroups — #7670660

Order 512.

5694 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59941C214yesmaximal, complemented
2#59329C211yesmaximal, characteristic, complemented
3#59313C211yesmaximal, characteristic, complemented
4#59206C214yesmaximal, complemented
5#59136C212yesmaximal, complemented
6#59023C214yesmaximal, complemented
7#40055C214yesmaximal, complemented
8#40052C214yesmaximal, complemented
9#38772C218yesmaximal, complemented
10C2×#2857C211yesmaximal, characteristic, complemented
11#36492C212yesmaximal, complemented
12#36480C212yesmaximal, complemented
13#36368C214yesmaximal, complemented
14#36363C214yesmaximal, complemented
15#36301C212yesmaximal, complemented
16#36275C212yesmaximal, complemented
17#35357C214yesmaximal, complemented
18#35026C214yesmaximal, complemented
19#34308C214yesmaximal, complemented
20C4×#525C212yesmaximal, complemented
21C2×#554C2212yescomplemented
22C2×#547C2214yes—
23C22×C4⋊Q8C2211yescharacteristic
24C2×#525C2212yes—
25C22×C22⋊Q8C2212yes—
26C2×#520C2214yes—
27C2×C4×#41C2212yes—
28C23×C42C2211yescharacteristic
29#2864C2214yescomplemented
30#2863C2214yescomplemented
31#2857C2214yes—
32#2857C2214yes—
33#2857C2214yes—
34#2857C2212yes—
35#2857C2212yes—
36#2855C2214yescomplemented
37#2851C2214yescomplemented
38#2799C2214yescomplemented
39#2794C2214yescomplemented
40#2746C2218yes—
41#2745C2218yescomplemented
42#2739C2218yes—
43#2729C2218yescomplemented
44#2728C2214yescomplemented
45#2693C2218yes—
46#2687C2218yes—
47#2680C2214yescomplemented
48#2655C2218yescomplemented
49#2652C2218yescomplemented
50#2605C2218yescomplemented
51#2586C2214yescomplemented
52#2585C2218yescomplemented
53#2582C2211yescharacteristic, complemented
54#2578C2218yes—
55#2573C2218yescomplemented
56#2572C2214yescomplemented
57#2571C2211yescharacteristic, complemented
58#2570C2214yescomplemented
59#2567C2212yescomplemented
60#2563C2212yescomplemented
61#2562C2214yes—
62#2551C2211yescharacteristic, complemented
63#2550C2214yescomplemented
64#2537C2211yescharacteristic, complemented
65#2535C2214yes—
66#2534C2218yes—
67#2527C2218yescomplemented
68#2522C2218yes—
69#2511C2214yescomplemented
70#2509C2214yescomplemented
71#2503C2214yes—
72#2497C2214yes—
73#2494C2214yes—
74#2494C2214yescomplemented
75#2493C2218yes—
76#2492C2214yes—
77#2492C2214yescomplemented
78#2487C2214yes—
79#2486C2214yes—
80#2485C2214yes—
81#2484C2214yes—
82#2482C2214yes—
83#2477C2218yes—
84#2477C2218yes—
85#2477C2218yescomplemented
86#2465C2218yes—
87#2465C2218yes—
88#2463C2218yes—
89#2463C2218yes—
90#2457C2218yes—
91#2453C2214yescomplemented
92#2452C2214yescomplemented
93#2450C2218yes—
94#2449C2218yes—
95#2449C2218yes—
96#2442C2214yes—
97#2441C2214yes—
98#2440C2214yescomplemented
99#2440C2214yescomplemented
100#2439C2214yes—
101#2438C2218yescomplemented
102#2422C2214yescomplemented
103#2421C2214yescomplemented
104#2420C2214yes—
105#2419C2218yes—
106#2417C2214yes—
107#2417C2214yes—
108#2409C2218yes—
109#2407C2214yes—
110#2406C2214yes—
111#2404C2214yes—
112#2369C2212yescomplemented
113#2368C2218yescomplemented
114#2365C2214yescomplemented
115#2361C2214yes—
116#2361C2214yescomplemented
117#2360C2218yescomplemented
118#2359C2218yes—
119#2359C2218yescomplemented
120#2355C2212yescomplemented
121#2352C2214yes—
122#2352C2214yes—
123D4×C4⋊C4C2214yes—
124D4×C4⋊C4C2214yescomplemented
125D4×C4⋊C4C2212yescomplemented
126#2347C2214yes—
127#2344C2214yes—
128#2344C2214yescomplemented
129#2339C2218yes—
130#2339C2214yes—
131#2323C2218yescomplemented
132#2322C2218yes—
133#2322C2218yescomplemented
134#2313C2214yes—
135C4×C4⋊Q8C2214yescomplemented
136C4×C22⋊Q8C2212yes—
137C4×C22⋊Q8C2212yes—
138C4×C22⋊Q8C2212yes—
139C4×C22⋊Q8C2212yes—
140C4×#123C2214yes—
141C4×#123C2214yes—
142C4×#121C2212yes—
143C4×#121C2212yes—
144C4×#121C2212yes—
145C4×#121C2212yes—
146C4×#121C2214yescomplemented
147C4×#120C2214yes—
148C4×#120C2214yes—
149#2297C2212yes—
150#2296C2212yes—
151C2×#391C2212yes—
152#2293C2214yescomplemented
153C2×#389C2214yes—
154C2×#389C2214yescomplemented
155#2290C2214yes—
156#2290C2214yes—
157C2×#384C2211yescharacteristic
158#2280C2212yes—
159C2×#380C2214yes—
160C42×D4C2214yes—
161C42×D4C2214yes—
162C4×#117C2212yes—
163C22×#41C2312yes—
164C22×#41C2314yes—
165C23×Q8C2312yes—
166C24×C4C2312yes—
167C24×C4C2311yescharacteristic
168#554—48no—
169#547—232no—
170C2×C4⋊Q8—44no—
171C2×C4⋊Q8C2314yes—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2314yes—
174C2×C4⋊Q8C2312yes—
175C2×#125C2314yes—
176#525—216no—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×#123C2314yes—
180C2×C22⋊Q8—48no—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2312yes—
183C2×C22⋊Q8C2312yes—
184C2×C22⋊Q8C2314yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2318yes—
187C2×C22⋊Q8C2314yes—
188C2×C22⋊Q8C2318yes—
189C2×C22⋊Q8C2318yes—
190C2×#121C2314yes—
191C2×#121C2312yes—
192C2×#121C2312yes—
193C2×#120C2314yes—
194#520—416no—
195C4×#41—48no—
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2318yes—
198C2×C4×Q8C2312yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2314yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2312yes—
211C2×C4×D4C2314yes—
212C2×C4×D4C2314yes—
213C2×#117C2312yes—
214C2×#117C2312yes—
215C2×#117C2318yes—
216C2×#117C2314yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2314yes—
222C22×C4⋊C4C2318yes—
223C22×C4⋊C4C2314yes—
224C22×C4⋊C4C2314yes—
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4C2314yes—
227C22×C42—44no—
228C22×C42C2312yes—
229C22×C42C2311yescharacteristic
230C22×C42C2314yes—
231C22×C42C2312yes—
232C22×C42C2312yes—
233C22×C42C2312yes—
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236#401C2318yes—
237#400C2318yes—
238#400C2318yes—
239#400C2314yes—
240#400C2314yes—
241#400C2318yes—
242#400C2318yes—
243#400C2318yes—
244#400C2318yes—
245#400C2318yes—
246#399C2318yes—
247#398C2314yes—
248#398C2314yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#395C2318yes—
261#395C2314yes—
262#395C2318yes—
263#395C2314yes—
264#394C2318yes—
265#394C2314yes—
266#394C2314yes—
267#394C2318yes—
268#393C2318yes—
269#393C2318yes—
270#393C2318yes—
271#392C2318yes—
272#391C2318yes—
273#391C2314yes—
274#391C2314yes—
275#391C2318yes—
276#391C2314yes—
277#391C2312yes—
278#391C2314yes—
279#391C2314yes—
280#391C2314yes—
281#391C2318yes—
282#391C2314yes—
283#391C2318yes—
284#391C2312yes—
285#390C2314yes—
286#390C2312yes—
287#390C2312yes—
288#389C2312yes—
289#389C2318yes—
290#389C2314yes—
291#389C2314yes—
292#389C2314yes—
293#389C2312yes—
294#389C2314yes—
295#389C2314yes—
296#389C2318yes—
297#389C2318yes—
298#389C2318yes—
299#389C2318yes—
300#389C2318yes—
301#389C2312yes—
302#389C2314yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2314yes—
308#389C2314yes—
309#389C2312yes—
310#388C2318yes—
311#388C2318yes—
312#388C2318yes—
313#388C2318yes—
314#388C2318yes—
315#388C2314yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2314yes—
321#388C2314yes—
322#388C2314yes—
323#387C2318yes—
324#387C2318yes—
325#387C2318yes—
326#387C2318yes—
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#387C2314yes—
340#387C2318yes—
341#387C2314yes—
342#387C2314yes—
343#387C2314yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2314yes—
348#386C2318yes—
349#386C2314yes—
350#386C2318yes—
351#386C2318yes—
352#386C2318yes—
353#386C2314yes—
354#386C2314yes—
355#386C2314yes—
356#386C2314yes—
357#385C2318yes—
358#385C2318yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2314yes—
367#385C2314yes—
368#385C2314yes—
369#385C2314yes—
370#385C2314yes—
371#385C2314yes—
372#384C2314yes—
373#384C2314yes—
374#384C2311yescharacteristic
375#384C2311yescharacteristic
376#384C2312yes—
377#383C2318yes—
378#382C2314yes—
379#382C2314yes—
380#382C2314yes—
381#381C2314yes—
382#381C2314yes—
383#381C2318yes—
384#381C2318yes—
385#381C2318yes—
386#381C2314yes—
387#380C2312yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2314yes—
392#380C2318yes—
393#380C2318yes—
394#380C2318yes—
395#380C2314yes—
396#380C2314yes—
397#380C2312yes—
398#380C2314yes—
399#380C2314yes—
400#380C2318yes—
401#380C2312yes—
402#380C2312yes—
403#379C2314yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2314yes—
406C4×C4⋊C4C2314yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2312yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2314yes—
429C4×C22⋊C4C2314yes—
430C4×C22⋊C4C2314yes—
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2314yes—
435#376C2314yes—
436C2×#95C2318yes—
437C2×#95C2318yes—
438C43C2314yes—
439C25C2411yescharacteristic
440C2×#41—28no—
441C2×#41—232no—
442C2×#41—28no—
443C2×#41—48no—
444C2×#41—44no—
445C22×Q8—44no—
446C22×Q8—44no—
447C22×Q8—44no—
448C22×Q8C2412yes—
449C22×Q8C2414yes—
450C22×Q8C2414yes—
451C22×Q8C2414yes—
452C22×D4C2414yes—
453C22×D4C2414yes—
454C22×D4C2414yes—
455C22×D4C2412yes—
456C22×D4C2414yes—
457C23×C4—28no—
458C23×C4—24no—
459C23×C4—28no—
460C23×C4—42no—
461C23×C4—44no—
462C23×C4—42no—
463C23×C4C2414yes—
464C23×C4C2414yes—
465C23×C4C2411yescharacteristic
466C23×C4C2412yes—
467C23×C4C2418yes—
468C23×C4C2414yes—
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473C23×C4C2412yes—
474C23×C4C2412yes—
475C23×C4C2412yes—
476C23×C4C2414yes—
477C23×C4C2414yes—
478C23×C4C2418yes—
479C23×C4C2411yescharacteristic
480C4⋊Q8—216no—
481C4⋊Q8—28no—
482C4⋊Q8—48no—
483C4⋊Q8—44no—
484#125—48no—
485#123—232no—
486#123—216no—
487#123—232no—
488C22⋊Q8—28no—
489C22⋊Q8—28no—
490C22⋊Q8—232no—
491C22⋊Q8—416no—
492C22⋊Q8—416no—
493C22⋊Q8—48no—
494C22⋊Q8—416no—
495C22⋊Q8—48no—
496C22⋊Q8—48no—
497#121—28no—
498#121—216no—
499#121#41116yescomplemented
500#120—216no—
501C4×Q8—28no—
502C4×Q8—416no—
503C4×Q8—44no—
504C4×D4—216no—
505C4×D4—216no—
506C4×D4—216no—
507C4×D4—216no—
508C4×D4—216no—
509C4×D4—216no—
510C4×D4—28no—
511C4×D4—44no—
512C4×D4—48no—
513C4×D4—48no—
514C4×D4—48no—
515C4×D4—48no—
516C4×D4—416no—
517C4×D4—416no—
518#117—28no—
519#117—28no—
520#117—48no—
521#117—416no—
522#117—48no—
523#117—44no—
524C2×C4⋊C4—216no—
525C2×C4⋊C4—216no—
526C2×C4⋊C4—216no—
527C2×C4⋊C4—416no—
528C2×C4⋊C4—48no—
529C2×C4⋊C4—48no—
530C2×C4⋊C4—44no—
531C2×C4⋊C4C2412yes—
532C2×C4⋊C4C2418yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2412yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2412yes—
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2418yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2412yes—
565C2×C22⋊C4—48no—
566C2×C22⋊C4C2414yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2414yes—
571C2×C22⋊C4C2414yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2414yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2418yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
590C2×C42—28no—
591C2×C42—24no—
592C2×C42—48no—
593C2×C42—44no—
594C2×C42—44no—
595C2×C42—42no—
596C2×C42—44no—
597C2×C42—44no—
598C2×C42C2414yes—
599C2×C42C2412yes—
600C2×C42C2414yes—
601C2×C42C2414yes—
602C2×C42C2414yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2414yes—
606C2×C42C2412yes—
607C2×C42C2411yescharacteristic
608C2×C42C2412yes—
609C2×C42C2414yes—
610C2×C42C2418yes—
611C2×C42C2418yes—
612C2×C42C2414yes—
613C2×C42C2414yes—
614C2×C42C2412yes—
615C2×C42C2411yescharacteristic
616C2×C42C2412yes—
617C2×C42C2411yescharacteristic
618C2×C42C2411yescharacteristic
619#95C2414yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2414yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2414yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2414yes—
652#95C2414yes—
653#95C2418yes—
654#95C2414yes—
655C24—22no—
656C24—24no—
657C24—24no—
658C24—41no—
659C24—41no—
660C24C2514yes—
661C24C2512yes—
662C24C2511yescharacteristic
663#41—432no—
664#41—464no—
665C2×Q8—24no—
666C2×Q8—216no—
667C2×Q8—24no—
668C2×Q8—28no—
669C2×Q8—24no—
670C2×Q8—28no—
671C2×Q8—44no—
672C2×Q8—44no—
673C2×Q8—44no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—816no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—216no—
682C2×D4—28no—
683C2×D4—28no—
684C2×D4—24no—
685C2×D4—24no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4C2×#4118yes—
690C2×D4C2×#41116yes—
691C22×C4—22no—
692C22×C4—24no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—216no—
699C22×C4—24no—
700C22×C4—28no—
701C22×C4—216no—
702C22×C4—28no—
703C22×C4—24no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—216no—
707C22×C4—24no—
708C22×C4—24no—
709C22×C4—24no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—24no—
714C22×C4—24no—
715C22×C4—28no—
716C22×C4—24no—
717C22×C4—24no—
718C22×C4—24no—
719C22×C4—28no—
720C22×C4—24no—
721C22×C4—28no—
722C22×C4—41no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—41no—
730C22×C4—42no—
731C22×C4—432no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—48no—
737C22×C4—48no—
738C22×C4—48no—
739C22×C4—416no—
740C22×C4C2×#4118yes—
741C22×C4H(5,𝔽2)14yes—
742C22×C42−1+418yes—
743C22×C4C2512yes—
744C22×C4C2514yes—
745C22×C4C2514yes—
746C22×C4C2514yes—
747C22×C4C2514yes—
748C22×C4C2514yes—
749C22×C4C2514yes—
750C22×C4C2514yes—
751C22×C4C2518yes—
752C22×C4C2514yes—
753C22×C4C2514yes—
754C22×C4C2512yes—
755C22×C4C2511yescharacteristic
756C22×C4C2512yes—
757C22×C4C2512yes—
758C22×C4C2511yescharacteristic
759C22×C4C2512yes—
760C4⋊C4—28no—
761C4⋊C4—28no—
762C4⋊C4—216no—
763C4⋊C4—216no—
764C4⋊C4—24no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—216no—
769C4⋊C4—216no—
770C4⋊C4—216no—
771C4⋊C4—24no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—24no—
776C4⋊C4—28no—
777C4⋊C4—24no—
778C4⋊C4—24no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—44no—
782C4⋊C4—48no—
783C4⋊C4—42no—
784C4⋊C4—44no—
785C4⋊C4—42no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—48no—
791C4⋊C4—48no—
792C4⋊C4—48no—
793C4⋊C4C2×#4118yes—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—216no—
798C22⋊C4—216no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—28no—
809C22⋊C4—48no—
810C22⋊C4—48no—
811C22⋊C4—44no—
812C22⋊C4—48no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4C2×#41116yes—
818C42—28no—
819C42—28no—
820C42—24no—
821C42—24no—
822C42—24no—
823C42—22no—
824C42—24no—
825C42—28no—
826C42—28no—
827C42—28no—
828C42—28no—
829C42—42no—
830C42—41no—
831C42—42no—
832C42—41no—
833C42—44no—
834C42—44no—
835C42—48no—
836C42—48no—
837C42—44no—
838C42H(5,𝔽2)14yes—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—28no—
843C23—22no—
844C23—22no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—22no—
849C23—22no—
850C23—24no—
851C23—22no—
852C23—24no—
853C23—24no—
854C23—22no—
855C23—48no—
856C23—48no—
857C23—44no—
858C23—44no—
859C23C22×#4118yes—
860C23C22×#4114yes—
861C23C2×H(5,𝔽2)12yes—
862C23C2×2−1+414yes—
863C23C2611yescharacteristic
864Q8—416no—
865Q8—48no—
866Q8—88no—
867Q8—88no—
868D4—232no—
869D4—216no—
870D4—416no—
871D4—416no—
872D4—416no—
873C2×C4—28no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—21no—
880C2×C4—24no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—21no—
886C2×C4—216no—
887C2×C4—216no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—22no—
892C2×C4—24no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—28no—
903C2×C4—24no—
904C2×C4—28no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—28no—
916C2×C4—44no—
917C2×C4—48no—
918C2×C4—48no—
919C2×C4—48no—
920C2×C4—48no—
921C2×C4—48no—
922C2×C4—416no—
923C2×C4—432no—
924C2×C4—416no—
925C2×C4—416no—
926C2×C4—48no—
927C2×C4—88no—
928C2×C4—88no—
929C2×C4—168no—
930C2×C4C22×#4118yes—
931C2×C4C22×#4114yes—
932C2×C4C22×#4114yes—
933C2×C4C2×H(5,𝔽2)12yes—
934C2×C4C2×H(5,𝔽2)14yes—
935C2×C4C2×H(5,𝔽2)14yes—
936C2×C4C2×2−1+414yes—
937C2×C4C2×2−1+414yes—
938C2×C4#58512yes—
939C22—24no—
940C22—24no—
941C22—22no—
942C22—22no—
943C22—24no—
944C22—28no—
945C22—24no—
946C22—28no—
947C22—24no—
948C22—28no—
949C22—416no—
950C22—42no—
951C22—44no—
952C22—44no—
953C22—42no—
954C22—42no—
955C22—44no—
956C22—44no—
957C22—42no—
958C22#348114yes—
959C22C23×#4112yes—
960C22C22×H(5,𝔽2)11yescharacteristic
961C22C22×H(5,𝔽2)11yescharacteristic
962C22C22×2−1+412yes—
963C22C2×#58511yescharacteristic
964C4—24no—
965C4—24no—
966C4—22no—
967C4—22no—
968C4—24no—
969C4—28no—
970C4—44no—
971C4—42no—
972C4—44no—
973C4—44no—
974C4—44no—
975C4—44no—
976C4—48no—
977C4—44no—
978C4—44no—
979C4—44no—
980C4#352018yes—
981C2—24no—
982C2—48no—
983C2—44no—
984C2C2×#348111yescharacteristic
985C2C2×#352012yes—
986C2#6280512yes—
987C2#6281811yescharacteristic
988C2#6283311yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59941C2semidirect
2. #59329C2semidirect
3. #59313C2semidirect
4. #59206C2semidirect
5. #59136C2semidirect
6. #59023C2semidirect
7. #40055C2semidirect
8. #40052C2semidirect
9. #38772C2semidirect
10. C2×#2857C2semidirect
11. #36492C2semidirect
12. #36480C2semidirect
13. #36368C2semidirect
14. #36363C2semidirect
15. #36301C2semidirect
16. #36275C2semidirect
17. #35357C2semidirect
18. #35026C2semidirect
19. #34308C2semidirect
20. C4×#525C2semidirect
21. C2×#554C22semidirect
29. #2864C22semidirect
30. #2863C22semidirect
36. #2855C22semidirect
37. #2851C22semidirect
38. #2799C22semidirect
39. #2794C22semidirect
41. #2745C22semidirect
43. #2729C22semidirect
44. #2728C22semidirect
47. #2680C22semidirect
48. #2655C22semidirect
49. #2652C22semidirect
50. #2605C22semidirect
51. #2586C22semidirect
52. #2585C22semidirect
53. #2582C22semidirect
55. #2573C22semidirect
56. #2572C22semidirect
57. #2571C22semidirect
58. #2570C22semidirect
59. #2567C22semidirect
60. #2563C22semidirect
62. #2551C22semidirect
63. #2550C22semidirect
64. #2537C22semidirect
67. #2527C22semidirect
69. #2511C22semidirect
70. #2509C22semidirect
74. #2494C22semidirect
77. #2492C22semidirect
85. #2477C22semidirect
91. #2453C22semidirect
92. #2452C22semidirect
98. #2440C22semidirect
99. #2440C22semidirect
101. #2438C22semidirect
102. #2422C22semidirect
103. #2421C22semidirect
112. #2369C22semidirect
113. #2368C22semidirect
114. #2365C22semidirect
116. #2361C22semidirect
117. #2360C22semidirect
119. #2359C22semidirect
120. #2355C22semidirect
124. D4×C4⋊C4C22semidirect
125. D4×C4⋊C4C22semidirect
128. #2344C22semidirect
131. #2323C22semidirect
133. #2322C22semidirect
135. C4×C4⋊Q8C22semidirect
146. C4×#121C22semidirect
152. #2293C22semidirect
154. C2×#389C22semidirect
499. #121#41semidirect

Maximal subgroups

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

subgroupindex
#599412
#593292
#593132
#592062
#591362
#590232
#400552
#400522
#387722
C2×#28572
#364922
#364802
#363682
#363632
#363012
#362752
#353572
#350262
#343082
C4×#5252