Finite Group Databasebeta

← #7712766

Subgroups — #7712766

Order 512.

5726 conjugacy classes of subgroups.

The subgroup lattice has 1009 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60029C214yesmaximal, complemented
2#58993C214yesmaximal, complemented
3#45758C214yesmaximal, complemented
4#45743C214yesmaximal, complemented
5#39818C214yesmaximal, complemented
6#39688C214yesmaximal, complemented
7#38823C214yesmaximal, complemented
8#38761C214yesmaximal, complemented
9#38487C214yesmaximal, complemented
10#38425C214yesmaximal, complemented
11#37523C212yesmaximal, complemented
12#37315C212yesmaximal, complemented
13#37308C211yesmaximal, characteristic, complemented
14#37298C211yesmaximal, characteristic, complemented
15#36624C212yesmaximal, complemented
16#36200C214yesmaximal, complemented
17#36126C214yesmaximal, complemented
18#35301C212yesmaximal, complemented
19#35261C212yesmaximal, complemented
20#34418C212yesmaximal, complemented
21C2×#2296C211yesmaximal, characteristic, complemented
22C2×#547C2218yes—
23C2×#540C2212yes—
24C2×#532C2212yes—
25C2×#532C2212yes—
26C2×#525C2214yes—
27C22×#117C2211yescharacteristic
28C22×#117C2211yescharacteristic
29C23×C42C2211yescharacteristic
30#2857C2212yes—
31#2857C2212yes—
32#2856C2212yes—
33#2856C2212yes—
34#2856C2212yes—
35#2854C2214yes—
36#2854C2214yes—
37#2854C2214yes—
38#2851C2212yes—
39#2850C2214yes—
40#2850C2214yes—
41#2847C2214yes—
42#2847C2214yes—
43#2826C2214yes—
44#2824C2214yes—
45#2808C2214yescomplemented
46#2805C2214yescomplemented
47#2803C2218yescomplemented
48#2788C2218yescomplemented
49#2784C2218yes—
50#2780C2218yes—
51#2742C2214yes—
52#2734C2214yescomplemented
53#2732C2214yescomplemented
54#2729C2218yescomplemented
55#2727C2214yescomplemented
56#2724C2214yescomplemented
57#2714C2218yes—
58#2701C2218yescomplemented
59#2691C2218yes—
60#2688C2218yes—
61#2682C2214yescomplemented
62#2682C2214yescomplemented
63#2681C2218yes—
64#2677C2214yes—
65#2675C2214yes—
66#2675C2214yes—
67#2663C2218yescomplemented
68#2649C2218yescomplemented
69#2629C2212yes—
70#2628C2212yes—
71#2628C2212yes—
72#2624C2214yes—
73#2619C2212yes—
74#2619C2212yes—
75#2619C2212yes—
76#2610C2214yes—
77#2610C2214yes—
78#2602C2218yescomplemented
79#2598C2214yes—
80#2598C2214yes—
81#2591C2214yes—
82#2587C2218yescomplemented
83#2583C2218yescomplemented
84#2570C2214yescomplemented
85#2566C2214yescomplemented
86#2559C2218yescomplemented
87#2551C2214yescomplemented
88#2541C2214yescomplemented
89#2539C2214yes—
90#2529C2218yescomplemented
91#2525C2218yescomplemented
92#2515C2218yescomplemented
93#2513C2214yescomplemented
94#2512C2214yescomplemented
95#2509C2214yescomplemented
96#2507C2214yescomplemented
97#2491C2218yescomplemented
98#2481C2218yes—
99#2476C2218yes—
100#2471C2218yes—
101#2464C2218yes—
102#2463C2214yes—
103#2461C2218yescomplemented
104#2461C2218yescomplemented
105#2456C2218yes—
106#2455C2214yes—
107#2452C2218yes—
108#2452C2214yescomplemented
109#2452C2214yescomplemented
110#2449C2218yes—
111#2445C2214yescomplemented
112#2445C2214yescomplemented
113#2443C2218yes—
114#2430C2218yes—
115#2430C2218yes—
116#2424C2218yes—
117#2419C2218yes—
118#2416C2218yes—
119#2413C2218yes—
120#2406C2214yes—
121#2404C2214yes—
122#2377C2218yes—
123#2373C2218yescomplemented
124#2370C2214yescomplemented
125#2366C2214yescomplemented
126#2361C2218yes—
127#2361C2218yescomplemented
128#2359C2218yes—
129#2357C2214yescomplemented
130D4×C4⋊C4C2214yescomplemented
131#2335C2218yescomplemented
132#2324C2214yes—
133#2324C2214yes—
134#2324C2214yes—
135#2322C2218yescomplemented
136#2314C2212yes—
137C4×#121C2214yes—
138C4×#121C2214yes—
139C4×#121C2214yes—
140C4×#121C2214yes—
141C4×#121C2214yes—
142#2297C2214yes—
143#2296C2214yes—
144#2296C2212yes—
145#2296C2211yescharacteristic
146#2296C2212yes—
147#2296C2211yescharacteristic
148#2296C2212yes—
149#2296C2211yescharacteristic
150#2296C2212yes—
151#2296C2211yescharacteristic
152C2×#389C2212yes—
153C2×#389C2212yes—
154C2×#385C2212yes—
155C2×#385C2212yes—
156#2285C2212yes—
157#2283C2212yes—
158C2×C4×C4⋊C4C2214yes—
159C22×#41C2314yes—
160C22×#41C2314yes—
161C24×C4C2311yescharacteristic
162C24×C4C2311yescharacteristic
163C24×C4C2311yescharacteristic
164#547—432no—
165#540—216no—
166#532—48no—
167#532—48no—
168C2×C4⋊Q8C2312yes—
169C2×C4⋊Q8C2312yes—
170C2×C4⋊Q8C2318yes—
171C2×#127C2312yes—
172C2×#127C2312yes—
173C2×#127C2312yes—
174C2×#126C2318yes—
175C2×#125C2312yes—
176C2×#124C2314yes—
177C2×#124C2314yes—
178#525—416no—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×C22⋊Q8C2318yes—
185C2×C22⋊Q8C2314yes—
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×#121C2314yes—
189C2×#121C2314yes—
190C2×#121C2314yes—
191C2×#121C2318yes—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2314yes—
197C2×#121C2314yes—
198C2×#121C2318yes—
199C2×#121C2318yes—
200C2×#121C2318yes—
201C2×#120C2318yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2318yes—
204C2×C4×D4C2314yes—
205C2×C4×D4C2314yes—
206C2×C4×D4C2314yes—
207C2×C4×D4C2318yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2314yes—
210C2×C4×D4C2318yes—
211C2×#117—28no—
212C2×#117—44no—
213C2×#117C2312yes—
214C2×#117C2311yescharacteristic
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2312yes—
219C2×#117C2311yescharacteristic
220C2×#117C2312yes—
221C2×#117C2311yescharacteristic
222C2×#117C2314yes—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C4⋊C4C2314yes—
227C22×C4⋊C4C2318yes—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2314yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C42—44no—
234C22×C42C2312yes—
235C22×C42C2312yes—
236C22×C42C2312yes—
237C22×C42C2311yescharacteristic
238C22×C42C2312yes—
239C22×C42C2312yes—
240C22×C42C2311yescharacteristic
241C22×C42C2312yes—
242C22×C42C2311yescharacteristic
243C22×C42C2311yescharacteristic
244#400C2318yes—
245#400C2318yes—
246#400C2318yes—
247#400C2314yes—
248#400C2314yes—
249#399C2314yes—
250#399C2314yes—
251#399C2318yes—
252#398C2318yes—
253#398C2318yes—
254#398C2318yes—
255#398C2318yes—
256#397C2318yes—
257#397C2318yes—
258#397C2318yes—
259#397C2318yes—
260#396C2318yes—
261#396C2318yes—
262#396C2318yes—
263#396C2318yes—
264#396C2318yes—
265#396C2318yes—
266#395C2314yes—
267#395C2318yes—
268#395C2314yes—
269#395C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2314yes—
275#394C2314yes—
276#394C2314yes—
277#394C2318yes—
278#394C2314yes—
279#394C2318yes—
280#394C2318yes—
281#393C2314yes—
282#393C2318yes—
283#393C2314yes—
284#393C2318yes—
285#392C2314yes—
286#392C2314yes—
287#392C2314yes—
288#392C2318yes—
289#392C2314yes—
290#392C2318yes—
291#392C2318yes—
292#391C2314yes—
293#391C2314yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2314yes—
298#390C2318yes—
299#390C2318yes—
300#390C2318yes—
301#390C2318yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2314yes—
306#390C2314yes—
307#390C2318yes—
308#390C2314yes—
309#389C2314yes—
310#389C2314yes—
311#389C2312yes—
312#389C2318yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2318yes—
320#389C2312yes—
321#389C2314yes—
322#389C2314yes—
323#389C2318yes—
324#389C2314yes—
325#389C2312yes—
326#389C2312yes—
327#389C2312yes—
328#389C2312yes—
329#389C2314yes—
330#389C2312yes—
331#389C2312yes—
332#389C2314yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2318yes—
345#388C2318yes—
346#388C2318yes—
347#388C2318yes—
348#388C2318yes—
349#387C2318yes—
350#387C2318yes—
351#387C2318yes—
352#387C2318yes—
353#387C2318yes—
354#387C2318yes—
355#387C2318yes—
356#387C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2318yes—
363#386C2318yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2318yes—
372#385C2318yes—
373#385C2318yes—
374#385C2312yes—
375#385C2318yes—
376#385C2318yes—
377#385C2318yes—
378#385C2318yes—
379#385C2318yes—
380#385C2318yes—
381#385C2318yes—
382#385C2318yes—
383#385C2312yes—
384#385C2312yes—
385#385C2312yes—
386#385C2312yes—
387#385C2312yes—
388#385C2314yes—
389#385C2312yes—
390#385C2314yes—
391#385C2314yes—
392#385C2312yes—
393#385C2314yes—
394#384C2312yes—
395#384C2312yes—
396#384C2312yes—
397#383C2314yes—
398#382C2312yes—
399#382C2312yes—
400#382C2312yes—
401#382C2314yes—
402#381C2318yes—
403#381C2314yes—
404#380C2314yes—
405#380C2314yes—
406#380C2318yes—
407#380C2314yes—
408#380C2314yes—
409#380C2314yes—
410#380C2314yes—
411C4×C4⋊C4C2314yes—
412C4×C4⋊C4C2314yes—
413C4×C4⋊C4C2314yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2314yes—
420C4×C4⋊C4C2314yes—
421C4×C4⋊C4C2314yes—
422C4×C4⋊C4C2314yes—
423C4×C4⋊C4C2314yes—
424C4×C22⋊C4C2318yes—
425C4×C22⋊C4C2318yes—
426C4×C22⋊C4C2318yes—
427C4×C22⋊C4C2314yes—
428C4×C22⋊C4C2318yes—
429#376C2314yes—
430C2×#95C2314yes—
431C2×#95C2314yes—
432C25C2411yescharacteristic
433C2×#41—216no—
434C2×#41—48no—
435C2×#41—48no—
436C2×#41—48no—
437C2×#41—416no—
438C22×Q8C2414yes—
439C22×Q8C2414yes—
440C22×D4C2414yes—
441C22×D4C2418yes—
442C22×D4C2418yes—
443C22×D4C2418yes—
444C22×D4C2414yes—
445C22×D4C2418yes—
446C22×D4C2414yes—
447C22×D4C2414yes—
448C22×D4C2414yes—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—28no—
453C23×C4—44no—
454C23×C4—42no—
455C23×C4—42no—
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2414yes—
461C23×C4C2412yes—
462C23×C4C2411yescharacteristic
463C23×C4C2412yes—
464C23×C4C2411yescharacteristic
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2412yes—
468C23×C4C2411yescharacteristic
469C23×C4C2411yescharacteristic
470C23×C4C2412yes—
471C23×C4C2418yes—
472C23×C4C2418yes—
473C23×C4C2412yes—
474C23×C4C2418yes—
475C23×C4C2411yescharacteristic
476C4⋊Q8—44no—
477C4⋊Q8—44no—
478C4⋊Q8—416no—
479#127—28no—
480#127—44no—
481#127—44no—
482#126—416no—
483#125—28no—
484#124—48no—
485#124—48no—
486#123—232no—
487#123—232no—
488#123—416no—
489#123—416no—
490#123—416no—
491C22⋊Q8—416no—
492C22⋊Q8—48no—
493C22⋊Q8—48no—
494C22⋊Q8—416no—
495#121—216no—
496#121—216no—
497#121—216no—
498#121—232no—
499#121—48no—
500#121—48no—
501#121—48no—
502#121—416no—
503#121—416no—
504#121—48no—
505#121—48no—
506#121—48no—
507#121—416no—
508#120—416no—
509C4×D4—216no—
510C4×D4—48no—
511C4×D4—48no—
512C4×D4—48no—
513C4×D4—48no—
514C4×D4—416no—
515C4×D4—416no—
516C4×D4—416no—
517C4×D4—416no—
518#117—24no—
519#117—28no—
520#117—28no—
521#117—28no—
522#117—42no—
523#117—42no—
524#117—44no—
525#117—44no—
526#117—42no—
527#117—42no—
528#117—48no—
529#117#4118yescomplemented
530C2×C4⋊C4—216no—
531C2×C4⋊C4—28no—
532C2×C4⋊C4—48no—
533C2×C4⋊C4—416no—
534C2×C4⋊C4—42no—
535C2×C4⋊C4—42no—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2418yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2414yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2414yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2411yescharacteristic
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2411yescharacteristic
556C2×C4⋊C4C2411yescharacteristic
557C2×C4⋊C4C2418yes—
558C2×C4⋊C4C2418yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2414yes—
561C2×C4⋊C4C2414yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2412yes—
570C2×C22⋊C4—28no—
571C2×C22⋊C4—44no—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2418yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2412yes—
584C2×C22⋊C4C2412yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2418yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2418yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2412yes—
600C2×C42—28no—
601C2×C42—28no—
602C2×C42—28no—
603C2×C42—42no—
604C2×C42—42no—
605C2×C42—44no—
606C2×C42—44no—
607C2×C42—42no—
608C2×C42—42no—
609C2×C42—44no—
610C2×C42C2412yes—
611C2×C42C2412yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2414yes—
615C2×C42C2412yes—
616C2×C42C2412yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2418yes—
621C2×C42C2418yes—
622C2×C42C2418yes—
623C2×C42C2412yes—
624C2×C42C2412yes—
625C2×C42C2412yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2418yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2414yes—
645#95C2414yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2418yes—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—24no—
657C24—42no—
658C24C2518yes—
659C24C2511yescharacteristic
660C24C2511yescharacteristic
661C24C2511yescharacteristic
662#41—832no—
663#41—832no—
664C2×Q8—28no—
665C2×Q8—44no—
666C2×Q8—48no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×D4—216no—
670C2×D4—216no—
671C2×D4—216no—
672C2×D4—216no—
673C2×D4—216no—
674C2×D4—28no—
675C2×D4—216no—
676C2×D4—28no—
677C2×D4—28no—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—44no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—44no—
693C2×D4—44no—
694C22×C4—232no—
695C22×C4—22no—
696C22×C4—24no—
697C22×C4—22no—
698C22×C4—24no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—24no—
713C22×C4—24no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—24no—
717C22×C4—28no—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—24no—
722C22×C4—24no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—216no—
726C22×C4—216no—
727C22×C4—41no—
728C22×C4—42no—
729C22×C4—41no—
730C22×C4—42no—
731C22×C4—41no—
732C22×C4—41no—
733C22×C4—44no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—42no—
737C22×C4—416no—
738C22×C4—48no—
739C22×C4—48no—
740C22×C4—44no—
741C22×C4—48no—
742C22×C4—48no—
743C22×C4—48no—
744C22×C4—48no—
745C22×C4—48no—
746C22×C4—416no—
747C22×C4C2×#4114yes—
748C22×C4H(5,𝔽2)14yes—
749C22×C4H(5,𝔽2)18yes—
750C22×C42−1+414yes—
751C22×C4C2512yes—
752C22×C4C2518yes—
753C22×C4C2512yes—
754C22×C4C2518yes—
755C22×C4C2512yes—
756C22×C4C2514yes—
757C22×C4C2512yes—
758C22×C4C2512yes—
759C22×C4C2518yes—
760C22×C4C2511yescharacteristic
761C22×C4C2514yes—
762C22×C4C2511yescharacteristic
763C22×C4C2512yes—
764C22×C4C2512yes—
765C22×C4C2511yescharacteristic
766C22×C4C2512yes—
767C22×C4C2511yescharacteristic
768C4⋊C4—28no—
769C4⋊C4—24no—
770C4⋊C4—28no—
771C4⋊C4—216no—
772C4⋊C4—28no—
773C4⋊C4—28no—
774C4⋊C4—28no—
775C4⋊C4—28no—
776C4⋊C4—216no—
777C4⋊C4—28no—
778C4⋊C4—216no—
779C4⋊C4—28no—
780C4⋊C4—28no—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—44no—
784C4⋊C4—44no—
785C4⋊C4—41no—
786C4⋊C4—42no—
787C4⋊C4—41no—
788C4⋊C4—41no—
789C4⋊C4—42no—
790C4⋊C4—41no—
791C4⋊C4—48no—
792C4⋊C4—48no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—48no—
798C4⋊C4—44no—
799C4⋊C4—48no—
800C4⋊C4—48no—
801C4⋊C4C2×#4118yes—
802C22⋊C4—24no—
803C22⋊C4—216no—
804C22⋊C4—28no—
805C22⋊C4—216no—
806C22⋊C4—216no—
807C22⋊C4—216no—
808C22⋊C4—216no—
809C22⋊C4—216no—
810C22⋊C4—216no—
811C22⋊C4—216no—
812C22⋊C4—42no—
813C22⋊C4—42no—
814C22⋊C4—42no—
815C22⋊C4—42no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—48no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4C2×#4118yes—
830C42—28no—
831C42—24no—
832C42—24no—
833C42—24no—
834C42—24no—
835C42—24no—
836C42—24no—
837C42—24no—
838C42—24no—
839C42—24no—
840C42—42no—
841C42—42no—
842C42—42no—
843C42—42no—
844C42—48no—
845C42—48no—
846C42—48no—
847C42C2×#4118yes—
848C23—21no—
849C23—21no—
850C23—22no—
851C23—28no—
852C23—21no—
853C23—21no—
854C23—21no—
855C23—22no—
856C23—22no—
857C23—21no—
858C23—22no—
859C23—22no—
860C23—28no—
861C23—28no—
862C23—28no—
863C23—28no—
864C23—28no—
865C23—28no—
866C23—28no—
867C23—48no—
868C23—48no—
869C23—44no—
870C23—44no—
871C23C22×#4112yes—
872C23C2×H(5,𝔽2)14yes—
873C23C2×H(5,𝔽2)12yes—
874C23C2×2−1+412yes—
875C23C2611yescharacteristic
876Q8—88no—
877Q8—88no—
878D4—432no—
879D4—416no—
880D4—88no—
881D4—816no—
882D4—88no—
883D4—816no—
884D4—816no—
885D4—88no—
886D4—88no—
887C2×C4—28no—
888C2×C4—28no—
889C2×C4—28no—
890C2×C4—21no—
891C2×C4—21no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—24no—
903C2×C4—22no—
904C2×C4—216no—
905C2×C4—28no—
906C2×C4—28no—
907C2×C4—28no—
908C2×C4—24no—
909C2×C4—28no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—28no—
916C2×C4—28no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—24no—
922C2×C4—24no—
923C2×C4—28no—
924C2×C4—24no—
925C2×C4—28no—
926C2×C4—28no—
927C2×C4—22no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—44no—
932C2×C4—48no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—416no—
936C2×C4—48no—
937C2×C4—48no—
938C2×C4—44no—
939C2×C4—48no—
940C2×C4—816no—
941C2×C4—816no—
942C2×C4—84no—
943C2×C4—816no—
944C2×C4C22×#4118yes—
945C2×C4C22×#4112yes—
946C2×C4C22×#4112yes—
947C2×C4C2×H(5,𝔽2)12yes—
948C2×C4C2×H(5,𝔽2)14yes—
949C2×C4C2×H(5,𝔽2)14yes—
950C2×C4C2×H(5,𝔽2)12yes—
951C2×C4C2×2−1+412yes—
952C2×C4C2×2−1+412yes—
953C2×C4#58514yes—
954C22—22no—
955C22—22no—
956C22—24no—
957C22—24no—
958C22—22no—
959C22—22no—
960C22—24no—
961C22—24no—
962C22—416no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—42no—
968C22—42no—
969C22—48no—
970C22—48no—
971C22—48no—
972C22—48no—
973C22—48no—
974C22—48no—
975C22—48no—
976C22#353714yes—
977C22C23×#4111yescharacteristic
978C22C22×H(5,𝔽2)11yescharacteristic
979C22C22×H(5,𝔽2)12yes—
980C22C22×2−1+411yescharacteristic
981C22C2×#58512yes—
982C4—24no—
983C4—24no—
984C4—24no—
985C4—22no—
986C4—22no—
987C4—22no—
988C4—28no—
989C4—42no—
990C4—42no—
991C4—48no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—44no—
996C4—48no—
997C4—48no—
998C4#349214yes—
999C2—24no—
1000C2—42no—
1001C2—42no—
1002C2—88no—
1003C2C2×#353711yescharacteristic
1004C2#6272911yescharacteristic
1005C2C2×#349211yescharacteristic
1006C2#6280012yes—
1007C2#6283512yes—
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. #60029C2semidirect
2. #58993C2semidirect
3. #45758C2semidirect
4. #45743C2semidirect
5. #39818C2semidirect
6. #39688C2semidirect
7. #38823C2semidirect
8. #38761C2semidirect
9. #38487C2semidirect
10. #38425C2semidirect
11. #37523C2semidirect
12. #37315C2semidirect
13. #37308C2semidirect
14. #37298C2semidirect
15. #36624C2semidirect
16. #36200C2semidirect
17. #36126C2semidirect
18. #35301C2semidirect
19. #35261C2semidirect
20. #34418C2semidirect
21. C2×#2296C2semidirect
45. #2808C22semidirect
46. #2805C22semidirect
47. #2803C22semidirect
48. #2788C22semidirect
52. #2734C22semidirect
53. #2732C22semidirect
54. #2729C22semidirect
55. #2727C22semidirect
56. #2724C22semidirect
58. #2701C22semidirect
61. #2682C22semidirect
62. #2682C22semidirect
67. #2663C22semidirect
68. #2649C22semidirect
78. #2602C22semidirect
82. #2587C22semidirect
83. #2583C22semidirect
84. #2570C22semidirect
85. #2566C22semidirect
86. #2559C22semidirect
87. #2551C22semidirect
88. #2541C22semidirect
90. #2529C22semidirect
91. #2525C22semidirect
92. #2515C22semidirect
93. #2513C22semidirect
94. #2512C22semidirect
95. #2509C22semidirect
96. #2507C22semidirect
97. #2491C22semidirect
103. #2461C22semidirect
104. #2461C22semidirect
108. #2452C22semidirect
109. #2452C22semidirect
111. #2445C22semidirect
112. #2445C22semidirect
123. #2373C22semidirect
124. #2370C22semidirect
125. #2366C22semidirect
127. #2361C22semidirect
129. #2357C22semidirect
130. D4×C4⋊C4C22semidirect
131. #2335C22semidirect
135. #2322C22semidirect
529. #117#41semidirect

Maximal subgroups

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

subgroupindex
#600292
#589932
#457582
#457432
#398182
#396882
#388232
#387612
#384872
#384252
#375232
#373152
#373082
#372982
#366242
#362002
#361262
#353012
#352612
#344182
C2×#22962