Finite Group Databasebeta

← #7659317

Subgroups — #7659317

Order 512.

4992 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52301C212yesmaximal, complemented
2#52163C211yesmaximal, characteristic
3#42921C214yesmaximal, complemented
4#42502C212yesmaximal, complemented
5#42419C214yesmaximal, complemented
6#41199C218yesmaximal, complemented
7#40380C218yesmaximal, complemented
8#39908C214yesmaximal, complemented
9#39702C214yesmaximal, complemented
10#39632C212yesmaximal, complemented
11#37374C212yesmaximal, complemented
12#37306C211yesmaximal, characteristic, complemented
13#37162C212yesmaximal, complemented
14#36929C214yesmaximal, complemented
15#36546C214yesmaximal, complemented
16#36449C212yesmaximal, complemented
17#35738C212yesmaximal, complemented
18#35726C214yesmaximal, complemented
19#34276C211yesmaximal, characteristic, complemented
20#34200C212yesmaximal, complemented
21C2×#554C2212yes—
22C2×#536C2211yescharacteristic
23C2×#525C2212yes—
24C2×#520C2211yescharacteristic
25C2×#519C2211yescharacteristic, complemented
26C23×C4⋊C4C2212yescomplemented
27#2863C2214yescomplemented
28#2857C2212yescomplemented
29#2848C2218yescomplemented
30#2848C2214yescomplemented
31#2839C2218yescomplemented
32#2835C2214yescomplemented
33#2811C2212yescomplemented
34#2809C2212yescomplemented
35#2806C2214yescomplemented
36#2804C2214yes—
37#2804C2212yes—
38#2788C2218yescomplemented
39#2782C2214yes—
40#2782C2218yes—
41#2770C2218yescomplemented
42#2769C2214yescomplemented
43#2764C2218yescomplemented
44#2750C2218yes—
45#2735C2218yescomplemented
46#2732C2212yes—
47#2729C2218yescomplemented
48#2728C2218yes—
49#2728C2212yes—
50#2724C2211yescharacteristic
51#2724C2214yescomplemented
52#2720C2218yescomplemented
53#2717C2214yes—
54#2708C2218yes—
55#2708C2214yes—
56#2697C2212yes—
57#2697C2214yescomplemented
58#2692C2218yescomplemented
59#2690C2218yescomplemented
60#2684C2214yes—
61#2684C2218yes—
62#2683C2212yes—
63#2679C2211yescharacteristic
64#2668C2214yes—
65#2666C2218yescomplemented
66#2652C2218yescomplemented
67#2652C2218yescomplemented
68#2652C2218yescomplemented
69#2646C2214yescomplemented
70#2634C2214yescomplemented
71#2633C2218yescomplemented
72#2628C2212yescomplemented
73#2625C2214yescomplemented
74#2611C2214yescomplemented
75#2598C2214yes—
76#2589C2218yescomplemented
77#2589C2218yescomplemented
78#2583C2218yescomplemented
79#2579C2218yes—
80#2578C2218yes—
81#2578C2218yescomplemented
82#2577C2218yescomplemented
83#2571C2212yescomplemented
84#2568C2212yescomplemented
85#2556C2218yescomplemented
86#2547C2212yes—
87#2536C2212yes—
88#2533C2218yescomplemented
89#2530C2218yescomplemented
90#2523C2218yescomplemented
91#2511C2214yescomplemented
92#2506C2214yescomplemented
93#2502C2214yescomplemented
94#2495C2214yescomplemented
95#2495C2214yescomplemented
96#2492C2214yescomplemented
97#2487C2214yes—
98#2485C2214yescomplemented
99#2477C2218yescomplemented
100#2473C2218yescomplemented
101#2473C2218yescomplemented
102#2465C2218yescomplemented
103#2463C2214yes—
104#2460C2218yes—
105#2453C2218yescomplemented
106#2450C2218yescomplemented
107#2449C2218yes—
108#2449C2218yes—
109#2440C2214yescomplemented
110#2440C2214yescomplemented
111#2439C2214yescomplemented
112#2427C2214yes—
113#2421C2214yescomplemented
114#2421C2214yescomplemented
115#2417C2214yes—
116#2417C2214yes—
117#2415C2214yes—
118#2409C2214yescomplemented
119#2398C2218yes—
120#2398C2214yes—
121#2395C2214yes—
122#2392C2212yes—
123#2365C2212yescomplemented
124#2362C2214yescomplemented
125#2361C2218yes—
126#2360C2218yescomplemented
127#2360C2214yescomplemented
128#2360C2214yescomplemented
129#2359C2218yescomplemented
130#2356C2212yescomplemented
131#2352C2214yes—
132#2352C2214yescomplemented
133D4×C4⋊C4C2212yes—
134D4×C4⋊C4C2214yes—
135D4×C4⋊C4C2214yescomplemented
136#2345C2214yescomplemented
137#2337C2218yes—
138#2327C2212yescomplemented
139#2326C2212yes—
140#2325C2214yes—
141#2322C2214yes—
142#2322C2214yescomplemented
143#2317C2211yescharacteristic, complemented
144#2317C2212yescomplemented
145#2311C2212yes—
146C4×C4⋊Q8C2212yescomplemented
147C4×#124C2214yes—
148C4×#124C2212yes—
149C4×#121C2212yes—
150C4×#120C2214yes—
151C4×#120C2218yes—
152C4×#120C2214yes—
153C4×#120C2214yescomplemented
154#2297C2211yescharacteristic
155C2×#391C2211yescharacteristic, complemented
156#2280C2212yescomplemented
157#2274C2212yescomplemented
158C4×#117C2211yescharacteristic, complemented
159C22×#41C2311yescharacteristic
160C23×Q8C2311yescharacteristic
161C24×C4C2312yes—
162C24×C4C2314yes—
163#554—48no—
164#536—28no—
165C2×C4⋊Q8C2312yes—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2312yes—
168C2×#125C2314yes—
169C2×#125C2318yes—
170C2×#124C2312yes—
171C2×#124C2314yes—
172#525—216no—
173C2×#123C2312yes—
174C2×#123C2312yes—
175C2×#123C2314yes—
176C2×C22⋊Q8C2314yes—
177C2×C22⋊Q8C2314yes—
178C2×C22⋊Q8C2318yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2318yes—
182C2×C22⋊Q8C2318yes—
183C2×C22⋊Q8C2314yes—
184C2×#121C2312yes—
185C2×#121C2314yes—
186C2×#120C2312yes—
187C2×#120C2312yes—
188C2×#120C2314yes—
189#520—44no—
190#519—44no—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2312yes—
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2314yes—
197C2×C4×D4C2314yes—
198C2×C4×D4C2314yes—
199C2×C4×D4C2312yes—
200C2×C4×D4C2314yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2312yes—
203C2×C4×D4C2312yes—
204C2×C4×D4C2318yes—
205C2×C4×D4C2318yes—
206C2×C4×D4C2314yes—
207C2×#117C2312yes—
208C2×#117C2311yescharacteristic
209C2×#117C2311yescharacteristic
210C2×#117C2312yes—
211C2×#117C2312yes—
212C2×#117C2311yescharacteristic
213C2×#117C2314yes—
214C22×C4⋊C4—48no—
215C22×C4⋊C4C2314yes—
216C22×C4⋊C4C2312yes—
217C22×C4⋊C4C2312yes—
218C22×C4⋊C4C2311yescharacteristic
219C22×C4⋊C4C2314yes—
220C22×C4⋊C4C2318yes—
221C22×C4⋊C4C2314yes—
222C22×C42C2311yescharacteristic
223#400C2314yes—
224#400C2314yes—
225#400C2318yes—
226#400C2318yes—
227#400C2318yes—
228#400C2318yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2318yes—
233#400C2318yes—
234#400C2314yes—
235#400C2318yes—
236#400C2318yes—
237#399C2314yes—
238#399C2318yes—
239#399C2314yes—
240#398C2318yes—
241#398C2318yes—
242#398C2318yes—
243#398C2318yes—
244#398C2318yes—
245#398C2318yes—
246#398C2318yes—
247#398C2314yes—
248#398C2312yes—
249#398C2314yes—
250#398C2318yes—
251#397C2314yes—
252#397C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2312yes—
257#397C2318yes—
258#397C2318yes—
259#397C2314yes—
260#397C2314yes—
261#397C2318yes—
262#397C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2314yes—
266#396C2318yes—
267#395C2318yes—
268#395C2318yes—
269#395C2314yes—
270#395C2318yes—
271#394C2314yes—
272#394C2318yes—
273#394C2314yes—
274#394C2312yes—
275#394C2314yes—
276#394C2314yes—
277#394C2318yes—
278#393C2314yes—
279#393C2318yes—
280#393C2318yes—
281#393C2318yes—
282#392C2312yes—
283#391C2311yescharacteristic
284#391C2312yes—
285#391C2314yes—
286#391C2314yes—
287#391C2318yes—
288#391C2312yes—
289#391C2311yescharacteristic
290#391C2318yes—
291#391C2314yes—
292#391C2314yes—
293#391C2318yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#390C2314yes—
298#390C2311yescharacteristic
299#390C2311yescharacteristic
300#390C2312yes—
301#389C2318yes—
302#389C2314yes—
303#389C2314yes—
304#389C2318yes—
305#389C2314yes—
306#389C2318yes—
307#389C2318yes—
308#389C2314yes—
309#389C2318yes—
310#389C2318yes—
311#389C2314yes—
312#389C2314yes—
313#389C2312yes—
314#389C2314yes—
315#389C2314yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2314yes—
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#386C2314yes—
344#386C2314yes—
345#386C2314yes—
346#386C2318yes—
347#386C2314yes—
348#386C2318yes—
349#386C2318yes—
350#386C2318yes—
351#386C2314yes—
352#386C2318yes—
353#386C2314yes—
354#386C2318yes—
355#386C2314yes—
356#385C2314yes—
357#385C2314yes—
358#385C2314yes—
359#385C2318yes—
360#385C2318yes—
361#385C2318yes—
362#385C2318yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2314yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2318yes—
375#385C2314yes—
376#385C2318yes—
377#385C2314yes—
378#384C2312yes—
379#384C2312yes—
380#384C2314yes—
381#383C2314yes—
382#383C2318yes—
383#383C2318yes—
384#382C2314yes—
385#382C2314yes—
386#382C2312yes—
387#382C2312yes—
388#381C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2318yes—
392#380C2318yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2318yes—
397#380C2314yes—
398#380C2314yes—
399#380C2312yes—
400#379C2314yes—
401#379C2318yes—
402#379C2314yes—
403C4×C4⋊C4C2318yes—
404C4×C4⋊C4C2312yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2318yes—
408C4×C4⋊C4C2312yes—
409C4×C4⋊C4C2314yes—
410C4×C4⋊C4C2314yes—
411C4×C22⋊C4C2318yes—
412C4×C22⋊C4C2314yes—
413C4×C22⋊C4C2314yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2318yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2318yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423#376C2312yes—
424#376C2314yes—
425C2×#95C2314yes—
426C43C2312yes—
427C25C2412yes—
428C2×#41—42no—
429C2×#41—42no—
430C2×#41#4118yes—
431C22×Q8—24no—
432C22×Q8—42no—
433C22×Q8—42no—
434C22×Q8C2412yes—
435C22×Q8C2412yes—
436C22×Q8C2414yes—
437C22×Q8C2414yes—
438C22×Q8C2411yescharacteristic
439C22×D4C2414yes—
440C22×D4C2412yes—
441C22×D4C2414yes—
442C22×D4C2411yescharacteristic
443C22×D4C2412yes—
444C22×D4C2412yes—
445C23×C4—28no—
446C23×C4—44no—
447C23×C4—44no—
448C23×C4—48no—
449C23×C4—88no—
450C23×C4C2414yes—
451C23×C4C2412yes—
452C23×C4C2411yescharacteristic
453C23×C4C2414yes—
454C23×C4C2418yes—
455C23×C4C2414yes—
456C23×C4C2412yes—
457C23×C4C2412yes—
458C23×C4C2412yes—
459C23×C4C2418yes—
460C23×C4C2414yes—
461C23×C4C2412yes—
462C4⋊Q8—28no—
463C4⋊Q8—44no—
464C4⋊Q8—44no—
465#125—48no—
466#125—88no—
467#124—28no—
468#124—216no—
469#123—28no—
470#123—28no—
471#123—216no—
472C22⋊Q8—216no—
473C22⋊Q8—216no—
474C22⋊Q8—416no—
475C22⋊Q8—48no—
476C22⋊Q8—48no—
477C22⋊Q8—84no—
478C22⋊Q8—88no—
479C22⋊Q8—88no—
480#121—216no—
481#121—28no—
482#120—28no—
483#120—28no—
484#120—216no—
485C4×Q8—28no—
486C4×Q8—44no—
487C4×Q8—44no—
488C4×Q8—44no—
489C4×Q8—44no—
490C4×Q8—84no—
491C4×D4—216no—
492C4×D4—216no—
493C4×D4—44no—
494C4×D4—44no—
495C4×D4—48no—
496C4×D4—44no—
497C4×D4—48no—
498C4×D4—88no—
499C4×D4—84no—
500C4×D4—88no—
501#117—28no—
502#117—24no—
503#117—24no—
504#117—42no—
505#117—48no—
506#117—44no—
507#117—44no—
508C2×C4⋊C4—28no—
509C2×C4⋊C4—216no—
510C2×C4⋊C4—48no—
511C2×C4⋊C4—416no—
512C2×C4⋊C4—48no—
513C2×C4⋊C4—44no—
514C2×C4⋊C4—42no—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2414yes—
517C2×C4⋊C4C2418yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2411yescharacteristic
520C2×C4⋊C4C2414yes—
521C2×C4⋊C4C2414yes—
522C2×C4⋊C4C2412yes—
523C2×C4⋊C4C2414yes—
524C2×C4⋊C4C2414yes—
525C2×C4⋊C4C2414yes—
526C2×C4⋊C4C2412yes—
527C2×C4⋊C4C2418yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2412yes—
531C2×C4⋊C4C2411yescharacteristic
532C2×C4⋊C4C2411yescharacteristic
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2418yes—
536C2×C4⋊C4C2412yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2418yes—
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2412yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2418yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2411yescharacteristic
552C2×C22⋊C4C2412yes—
553C2×C22⋊C4C2412yes—
554C2×C22⋊C4C2412yes—
555C2×C22⋊C4C2412yes—
556C2×C22⋊C4C2414yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2418yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2412yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2414yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C42—42no—
581C2×C42C2414yes—
582C2×C42C2412yes—
583C2×C42C2414yes—
584C2×C42C2412yes—
585C2×C42C2412yes—
586C2×C42C2412yes—
587C2×C42C2414yes—
588C2×C42C2414yes—
589C2×C42C2414yes—
590C2×C42C2414yes—
591C2×C42C2414yes—
592C2×C42C2418yes—
593C2×C42C2418yes—
594C2×C42C2411yescharacteristic
595C2×C42C2411yescharacteristic
596#95C2418yes—
597#95C2418yes—
598#95C2412yes—
599#95C2414yes—
600#95C2414yes—
601#95C2414yes—
602#95C2418yes—
603#95C2418yes—
604#95C2418yes—
605#95C2414yes—
606#95C2418yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2414yes—
612#95C2418yes—
613#95C2418yes—
614#95C2418yes—
615#95C2418yes—
616#95C2414yes—
617#95C2414yes—
618#95C2418yes—
619#95C2414yes—
620#95C2418yes—
621#95C2414yes—
622#95C2412yes—
623#95C2414yes—
624#95C2418yes—
625#95C2418yes—
626#95C2418yes—
627#95C2414yes—
628#95C2418yes—
629#95C2418yes—
630C24—24no—
631C24—28no—
632C24—42no—
633C24—42no—
634C24—44no—
635C24C2512yes—
636C24C2511yescharacteristic
637C24C2514yes—
638#41—416no—
639C2×Q8—24no—
640C2×Q8—24no—
641C2×Q8—24no—
642C2×Q8—28no—
643C2×Q8—24no—
644C2×Q8—42no—
645C2×Q8—41no—
646C2×Q8—42no—
647C2×Q8—41no—
648C2×Q8—44no—
649C2×Q8—44no—
650C2×Q8—44no—
651C2×Q8—48no—
652C2×Q8—416no—
653C2×Q8C2×#4114yes—
654C2×D4—28no—
655C2×D4—28no—
656C2×D4—28no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—42no—
660C2×D4—41no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—42no—
667C2×D4—41no—
668C2×D4C2×#4114yes—
669C2×D4C2×#4118yes—
670C2×D42−1+418yes—
671C22×C4—24no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—24no—
675C22×C4—24no—
676C22×C4—24no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
681C22×C4—28no—
682C22×C4—216no—
683C22×C4—24no—
684C22×C4—44no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—44no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—48no—
692C22×C4—44no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4—48no—
696C22×C4—48no—
697C22×C4—42no—
698C22×C4—48no—
699C22×C4—48no—
700C22×C4—42no—
701C22×C4—44no—
702C22×C4—432no—
703C22×C4—832no—
704C22×C4C2×#4114yes—
705C22×C4C2×#4118yes—
706C22×C4C2512yes—
707C22×C4C2512yes—
708C22×C4C2518yes—
709C22×C4C2514yes—
710C22×C4C2514yes—
711C22×C4C2512yes—
712C22×C4C2514yes—
713C22×C4C2514yes—
714C22×C4C2514yes—
715C22×C4C2514yes—
716C22×C4C2518yes—
717C22×C4C2512yes—
718C22×C4C2511yescharacteristic
719C22×C4C2512yes—
720C22×C4C2512yes—
721C22×C4C2512yes—
722C22×C4C2511yescharacteristic
723C4⋊C4—28no—
724C4⋊C4—24no—
725C4⋊C4—28no—
726C4⋊C4—28no—
727C4⋊C4—216no—
728C4⋊C4—24no—
729C4⋊C4—28no—
730C4⋊C4—216no—
731C4⋊C4—28no—
732C4⋊C4—22no—
733C4⋊C4—28no—
734C4⋊C4—24no—
735C4⋊C4—28no—
736C4⋊C4—44no—
737C4⋊C4—48no—
738C4⋊C4—42no—
739C4⋊C4—41no—
740C4⋊C4—41no—
741C4⋊C4—44no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—44no—
745C4⋊C4—44no—
746C4⋊C4—48no—
747C4⋊C4—48no—
748C4⋊C4—42no—
749C4⋊C4—48no—
750C4⋊C4—48no—
751C4⋊C4—48no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—48no—
755C4⋊C4—48no—
756C4⋊C4—48no—
757C4⋊C4—44no—
758C4⋊C4—44no—
759C4⋊C4H(5,𝔽2)14yes—
760C22⋊C4—24no—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—28no—
764C22⋊C4—28no—
765C22⋊C4—216no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—216no—
769C22⋊C4—216no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—24no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—44no—
776C22⋊C4—42no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—48no—
781C22⋊C4—48no—
782C22⋊C4—48no—
783C22⋊C4—48no—
784C22⋊C4—48no—
785C22⋊C4—48no—
786C22⋊C4—44no—
787C22⋊C4—44no—
788C42—28no—
789C42—24no—
790C42—24no—
791C42—28no—
792C42—24no—
793C42—28no—
794C42—24no—
795C42—41no—
796C42—41no—
797C42—44no—
798C42—44no—
799C42—44no—
800C42—44no—
801C42—48no—
802C42—48no—
803C23—24no—
804C23—21no—
805C23—24no—
806C23—22no—
807C23—24no—
808C23—24no—
809C23—22no—
810C23—24no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—416no—
818C23—48no—
819C23—48no—
820C23—416no—
821C23—48no—
822C23C22×#4114yes—
823C23C22×#4112yes—
824C23C2×2−1+418yes—
825C23C2611yescharacteristic
826Q8—44no—
827Q8—48no—
828Q8—48no—
829Q8—88no—
830Q8—164no—
831D4—48no—
832D4—44no—
833D4—48no—
834D4—416no—
835D4—416no—
836D4—48no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—216no—
845C2×C4—28no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—24no—
855C2×C4—24no—
856C2×C4—24no—
857C2×C4—28no—
858C2×C4—24no—
859C2×C4—24no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—28no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—28no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—28no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—28no—
874C2×C4—22no—
875C2×C4—24no—
876C2×C4—28no—
877C2×C4—28no—
878C2×C4—416no—
879C2×C4—48no—
880C2×C4—48no—
881C2×C4—416no—
882C2×C4—84no—
883C2×C4—88no—
884C2×C4—816no—
885C2×C4—816no—
886C2×C4—88no—
887C2×C4—162no—
888C2×C4C22×#4112yes—
889C2×C4C22×#4114yes—
890C2×C4C22×#4112yes—
891C2×C4C2×H(5,𝔽2)14yes—
892C2×C4C2×H(5,𝔽2)12yes—
893C2×C4C2×2−1+414yes—
894C2×C4#58512yes—
895C22—28no—
896C22—24no—
897C22—28no—
898C22—28no—
899C22—28no—
900C22—22no—
901C22—24no—
902C22—432no—
903C22—44no—
904C22—41no—
905C22—42no—
906C22—44no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—44no—
911C22—44no—
912C22—44no—
913C22C23×#4111yescharacteristic
914C22C22×H(5,𝔽2)11yescharacteristic
915C22C22×2−1+412yes—
916C22C2×#58511yescharacteristic
917C22H(7,𝔽2)12yes—
918C4—24no—
919C4—24no—
920C4—24no—
921C4—22no—
922C4—44no—
923C4—44no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—44no—
928C4—48no—
929C4—42no—
930C4—42no—
931C4—48no—
932C4—44no—
933C4—44no—
934C4#345914yes—
935C2—42no—
936C2—48no—
937C2—44no—
938C2C2×#345911yescharacteristic
939C2#6290212yes—
940C2#6300012yes—
941C2#6301611yescharacteristic
942C2#6304511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radical#52163C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52301C2semidirect
3. #42921C2semidirect
4. #42502C2semidirect
5. #42419C2semidirect
6. #41199C2semidirect
7. #40380C2semidirect
8. #39908C2semidirect
9. #39702C2semidirect
10. #39632C2semidirect
11. #37374C2semidirect
12. #37306C2semidirect
13. #37162C2semidirect
14. #36929C2semidirect
15. #36546C2semidirect
16. #36449C2semidirect
17. #35738C2semidirect
18. #35726C2semidirect
19. #34276C2semidirect
20. #34200C2semidirect
25. C2×#519C22semidirect
26. C23×C4⋊C4C22semidirect
27. #2863C22semidirect
28. #2857C22semidirect
29. #2848C22semidirect
30. #2848C22semidirect
31. #2839C22semidirect
32. #2835C22semidirect
33. #2811C22semidirect
34. #2809C22semidirect
35. #2806C22semidirect
38. #2788C22semidirect
41. #2770C22semidirect
42. #2769C22semidirect
43. #2764C22semidirect
45. #2735C22semidirect
47. #2729C22semidirect
51. #2724C22semidirect
52. #2720C22semidirect
57. #2697C22semidirect
58. #2692C22semidirect
59. #2690C22semidirect
65. #2666C22semidirect
66. #2652C22semidirect
67. #2652C22semidirect
68. #2652C22semidirect
69. #2646C22semidirect
70. #2634C22semidirect
71. #2633C22semidirect
72. #2628C22semidirect
73. #2625C22semidirect
74. #2611C22semidirect
76. #2589C22semidirect
77. #2589C22semidirect
78. #2583C22semidirect
81. #2578C22semidirect
82. #2577C22semidirect
83. #2571C22semidirect
84. #2568C22semidirect
85. #2556C22semidirect
88. #2533C22semidirect
89. #2530C22semidirect
90. #2523C22semidirect
91. #2511C22semidirect
92. #2506C22semidirect
93. #2502C22semidirect
94. #2495C22semidirect
95. #2495C22semidirect
96. #2492C22semidirect
98. #2485C22semidirect
99. #2477C22semidirect
100. #2473C22semidirect
101. #2473C22semidirect
102. #2465C22semidirect
105. #2453C22semidirect
106. #2450C22semidirect
109. #2440C22semidirect
110. #2440C22semidirect
111. #2439C22semidirect
113. #2421C22semidirect
114. #2421C22semidirect
118. #2409C22semidirect
123. #2365C22semidirect
124. #2362C22semidirect
126. #2360C22semidirect
127. #2360C22semidirect
128. #2360C22semidirect
129. #2359C22semidirect
130. #2356C22semidirect
132. #2352C22semidirect
135. D4×C4⋊C4C22semidirect
136. #2345C22semidirect
138. #2327C22semidirect
142. #2322C22semidirect
143. #2317C22semidirect
144. #2317C22semidirect
146. C4×C4⋊Q8C22semidirect
153. C4×#120C22semidirect
155. C2×#391C22semidirect
156. #2280C22semidirect
157. #2274C22semidirect
158. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#523012
#521632
#429212
#425022
#424192
#411992
#403802
#399082
#397022
#396322
#373742
#373062
#371622
#369292
#365462
#364492
#357382
#357262
#342762
#342002