Finite Group Databasebeta

← #8069366

Subgroups — #8069366

Order 512.

5549 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59951C212yesmaximal, complemented
2#59544C214yesmaximal, complemented
3#59002C214yesmaximal, complemented
4#59001C212yesmaximal, complemented
5#51923C214yesmaximal, complemented
6#49972C218yesmaximal, complemented
7#49842C218yesmaximal, complemented
8#49638C214yesmaximal, complemented
9#46232C214yesmaximal, complemented
10#46225C212yesmaximal, complemented
11#46016C212yesmaximal, complemented
12#46004C211yesmaximal, characteristic, complemented
13#39954C214yesmaximal, complemented
14#39886C214yesmaximal, complemented
15#38956C212yesmaximal, complemented
16#38905C212yesmaximal, complemented
17#36185C212yesmaximal, complemented
18#36125C211yesmaximal, characteristic, complemented
19#34368C212yesmaximal, complemented
20C4×H(3,𝔽4)C211yesmaximal, characteristic, complemented
21C2×H(3,𝔽4)C2211yescharacteristic
22C2×#556C2212yescomplemented
23C2×#555C2212yes—
24C2×#550C2211yescharacteristic, complemented
25C2×#548C2214yes—
26C2×#547C2211yescharacteristic
27C2×#547C2212yes—
28C2×#532C2212yes—
29C2×#525C2214yescomplemented
30C22×C22⋊Q8C2212yescomplemented
31#2862C2212yescomplemented
32#2858C2212yescomplemented
33#2858C2211yescharacteristic, complemented
34#2850C2214yes—
35#2850C2212yescomplemented
36#2847C2212yescomplemented
37#2844C2212yescomplemented
38#2819C2214yes—
39#2811C2212yescomplemented
40#2804C2212yes—
41#2804C2214yescomplemented
42#2795C2218yescomplemented
43#2769C2214yescomplemented
44#2763C2218yescomplemented
45#2753C2218yescomplemented
46#2737C2218yescomplemented
47#2733C2214yes—
48#2731C2214yes—
49#2723C2218yescomplemented
50#2714C2218yes—
51#2712C2218yescomplemented
52#2710C2218yescomplemented
53#2703C2218yes—
54#2703C2218yescomplemented
55#2703C2218yescomplemented
56#2696C2218yes—
57#2692C2218yescomplemented
58#2692C2218yescomplemented
59#2680C2218yescomplemented
60#2676C2218yes—
61#2672C2218yes—
62#2670C2214yescomplemented
63#2670C2218yescomplemented
64#2669C2214yes—
65#2669C2218yes—
66#2662C2218yescomplemented
67#2631C2218yes—
68#2623C2214yescomplemented
69#2619C2214yes—
70#2610C2218yes—
71#2610C2218yescomplemented
72#2603C2218yescomplemented
73#2598C2218yescomplemented
74#2593C2214yes—
75#2592C2214yescomplemented
76#2574C2218yescomplemented
77#2568C2212yescomplemented
78#2567C2212yescomplemented
79#2546C2211yescharacteristic, complemented
80#2544C2218yes—
81#2542C2212yes—
82#2541C2211yescharacteristic
83#2541C2212yes—
84#2540C2214yes—
85#2532C2218yescomplemented
86#2532C2218yescomplemented
87#2529C2218yescomplemented
88#2521C2218yescomplemented
89#2521C2218yescomplemented
90#2504C2214yescomplemented
91#2500C2214yes—
92#2499C2214yescomplemented
93#2492C2214yescomplemented
94#2492C2214yescomplemented
95#2491C2214yescomplemented
96#2474C2218yescomplemented
97#2464C2218yescomplemented
98#2463C2214yescomplemented
99#2461C2218yes—
100#2461C2218yescomplemented
101#2459C2218yes—
102#2456C2218yes—
103#2449C2218yescomplemented
104#2443C2218yes—
105#2436C2212yescomplemented
106#2434C2214yescomplemented
107#2432C2214yescomplemented
108#2432C2212yescomplemented
109#2431C2212yes—
110#2431C2214yes—
111#2431C2214yescomplemented
112#2431C2214yescomplemented
113#2429C2214yescomplemented
114#2428C2214yescomplemented
115#2427C2214yescomplemented
116#2427C2214yescomplemented
117#2427C2214yescomplemented
118#2426C2214yescomplemented
119#2424C2218yes—
120#2418C2218yescomplemented
121#2417C2214yes—
122#2415C2214yes—
123#2414C2214yes—
124#2411C2214yescomplemented
125#2409C2212yes—
126#2407C2214yes—
127#2404C2214yes—
128#2379C2214yes—
129#2379C2211yescharacteristic
130#2379C2212yes—
131#2379C2212yes—
132#2379C2212yes—
133#2379C2214yescomplemented
134#2375C2214yes—
135#2375C2212yes—
136#2369C2214yescomplemented
137#2366C2214yes—
138#2362C2214yescomplemented
139#2362C2214yescomplemented
140#2361C2214yescomplemented
141#2354C2218yescomplemented
142D4×C4⋊C4C2218yescomplemented
143#2347C2214yescomplemented
144#2344C2212yescomplemented
145#2324C2218yescomplemented
146#2324C2218yescomplemented
147#2311C2214yes—
148#2311C2214yescomplemented
149C4×#124C2214yes—
150C4×#124C2211yescharacteristic
151C4×#124C2212yes—
152C4×#124C2212yes—
153C4×#120C2212yes—
154C4×#120C2214yes—
155#2295C2214yescomplemented
156#2293C2212yescomplemented
157#2285C2214yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C22×#41C2312yes—
161C22×#41C2314yes—
162C23×Q8C2312yes—
163C24×C4C2312yes—
164H(3,𝔽4)—28no—
165#556—48no—
166#555—48no—
167#550—44no—
168#548—416no—
169#547—44no—
170#547—48no—
171#532—216no—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2312yes—
177C2×#127C2312yes—
178C2×#127C2312yes—
179C2×#127C2311yescharacteristic
180C2×#127C2314yes—
181C2×#126C2318yes—
182C2×#124C2312yes—
183C2×#124C2312yes—
184C2×#124C2314yes—
185C2×#124C2312yes—
186C2×#124C2314yes—
187C2×#124C2314yes—
188C2×#124C2318yes—
189C2×#124C2318yes—
190C2×#124C2312yes—
191C2×#124C2318yes—
192C2×#124C2311yescharacteristic
193#525—416no—
194C2×#123C2314yes—
195C2×#123C2318yes—
196C2×#123C2318yes—
197C2×C22⋊Q8—48no—
198C2×C22⋊Q8C2314yes—
199C2×C22⋊Q8C2314yes—
200C2×C22⋊Q8C2314yes—
201C2×C22⋊Q8C2312yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2314yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2318yes—
206C2×#121C2318yes—
207C2×#121C2314yes—
208C2×#121C2314yes—
209C2×#121C2312yes—
210C2×#121C2314yes—
211C2×#121C2312yes—
212C2×#121C2314yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2318yes—
216C2×#120C2312yes—
217C2×#120C2314yes—
218C2×#120C2318yes—
219C2×#120C2314yes—
220C2×C4×Q8C2314yes—
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2318yes—
224C2×C4×D4C2312yes—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2312yes—
227C2×C4×D4C2318yes—
228C2×C4×D4C2318yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2312yes—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2314yes—
233C2×C4×D4C2312yes—
234C2×#117C2314yes—
235C2×#117C2314yes—
236C2×#117C2314yes—
237C2×#117C2314yes—
238C2×#117C2314yes—
239C22×C4⋊C4C2312yes—
240C22×C4⋊C4C2314yes—
241C22×C4⋊C4C2314yes—
242C22×C22⋊C4C2314yes—
243C22×C42C2312yes—
244#400C2314yes—
245#400C2314yes—
246#400C2318yes—
247#400C2318yes—
248#399C2318yes—
249#399C2318yes—
250#398C2318yes—
251#398C2314yes—
252#398C2318yes—
253#397C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#395C2318yes—
262#395C2318yes—
263#395C2314yes—
264#395C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#394C2318yes—
276#393C2318yes—
277#393C2318yes—
278#393C2318yes—
279#393C2318yes—
280#393C2318yes—
281#393C2314yes—
282#392C2318yes—
283#392C2318yes—
284#392C2318yes—
285#392C2318yes—
286#392C2318yes—
287#392C2318yes—
288#392C2318yes—
289#392C2318yes—
290#392C2318yes—
291#392C2314yes—
292#391C2318yes—
293#391C2312yes—
294#391C2314yes—
295#391C2314yes—
296#391C2314yes—
297#391C2314yes—
298#391C2318yes—
299#391C2314yes—
300#391C2314yes—
301#391C2312yes—
302#391C2314yes—
303#391C2314yes—
304#391C2311yescharacteristic
305#391C2314yes—
306#391C2312yes—
307#390C2318yes—
308#390C2314yes—
309#390C2314yes—
310#390C2318yes—
311#390C2318yes—
312#390C2314yes—
313#390C2314yes—
314#390C2312yes—
315#390C2314yes—
316#390C2312yes—
317#390C2318yes—
318#390C2314yes—
319#390C2314yes—
320#390C2314yes—
321#390C2318yes—
322#390C2311yescharacteristic
323#390C2312yes—
324#389C2314yes—
325#389C2314yes—
326#389C2318yes—
327#389C2318yes—
328#389C2314yes—
329#388C2318yes—
330#388C2318yes—
331#388C2314yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2318yes—
340#388C2318yes—
341#388C2318yes—
342#388C2318yes—
343#388C2318yes—
344#388C2314yes—
345#388C2318yes—
346#388C2318yes—
347#388C2314yes—
348#388C2318yes—
349#388C2314yes—
350#388C2314yes—
351#388C2314yes—
352#388C2314yes—
353#388C2314yes—
354#388C2314yes—
355#387C2318yes—
356#387C2318yes—
357#387C2318yes—
358#387C2318yes—
359#387C2318yes—
360#386C2312yes—
361#386C2314yes—
362#386C2314yes—
363#386C2314yes—
364#386C2318yes—
365#386C2318yes—
366#386C2318yes—
367#386C2318yes—
368#386C2318yes—
369#386C2318yes—
370#386C2318yes—
371#386C2314yes—
372#386C2318yes—
373#386C2318yes—
374#386C2314yes—
375#386C2314yes—
376#386C2314yes—
377#386C2314yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#385C2318yes—
382#385C2314yes—
383#385C2318yes—
384#385C2318yes—
385#385C2318yes—
386#385C2314yes—
387#385C2318yes—
388#385C2318yes—
389#385C2312yes—
390#385C2314yes—
391#385C2314yes—
392#385C2314yes—
393#384C2314yes—
394#384C2314yes—
395#383C2318yes—
396#382C2314yes—
397#382C2314yes—
398#382C2314yes—
399#382C2311yescharacteristic
400#382C2314yes—
401#382C2312yes—
402#382C2312yes—
403#381C2314yes—
404#380C2318yes—
405#380C2318yes—
406#380C2318yes—
407#380C2318yes—
408#380C2312yes—
409#380C2314yes—
410#379C2312yes—
411#379C2314yes—
412C4×C4⋊C4C2312yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2318yes—
415C4×C4⋊C4C2318yes—
416C4×C4⋊C4C2314yes—
417C4×C4⋊C4C2318yes—
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2318yes—
420C4×C22⋊C4C2314yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2314yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2312yes—
427C4×C22⋊C4C2314yes—
428#376C2318yes—
429C43C2311yescharacteristic
430C43C2312yes—
431C25C2412yes—
432C2×#41—28no—
433C2×#41—28no—
434C2×#41—44no—
435C2×#41—44no—
436C2×#41—48no—
437C2×#41—48no—
438C2×#41—48no—
439C2×#41—82no—
440C2×#41—82no—
441C22×Q8—44no—
442C22×Q8—48no—
443C22×Q8C2414yes—
444C22×Q8C2412yes—
445C22×Q8C2412yes—
446C22×Q8C2414yes—
447C22×Q8C2414yes—
448C22×Q8C2411yescharacteristic
449C22×D4C2411yescharacteristic
450C22×D4C2412yes—
451C22×D4C2418yes—
452C22×D4C2412yes—
453C22×D4C2414yes—
454C22×D4C2412yes—
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2412yes—
458C22×D4C2418yes—
459C22×D4C2418yes—
460C22×D4C2418yes—
461C22×D4C2414yes—
462C22×D4C2412yes—
463C22×D4C2411yescharacteristic
464C23×C4—44no—
465C23×C4—48no—
466C23×C4C2412yes—
467C23×C4C2414yes—
468C23×C4C2414yes—
469C23×C4C2414yes—
470C23×C4C2414yes—
471C23×C4C2412yes—
472C23×C4C2414yes—
473C23×C4C2412yes—
474C23×C4C2418yes—
475C23×C4C2414yes—
476C4⋊Q8—28no—
477C4⋊Q8—42no—
478C4⋊Q8—44no—
479C4⋊Q8—44no—
480C4⋊Q8—44no—
481#127—28no—
482#127—44no—
483#127—42no—
484#127—84no—
485#126—416no—
486#124—28no—
487#124—216no—
488#124—28no—
489#124—28no—
490#124—416no—
491#124—416no—
492#124—48no—
493#124—48no—
494#124—88no—
495#124—82no—
496#124#4118yescomplemented
497#123—416no—
498#123—416no—
499#123—48no—
500C22⋊Q8—216no—
501C22⋊Q8—216no—
502C22⋊Q8—416no—
503C22⋊Q8—416no—
504C22⋊Q8—44no—
505C22⋊Q8—48no—
506C22⋊Q8—48no—
507C22⋊Q8—48no—
508#121—216no—
509#121—232no—
510#121—48no—
511#121—48no—
512#121—44no—
513#121—48no—
514#121—416no—
515#121—48no—
516#121—44no—
517#121—48no—
518#120—28no—
519#120—216no—
520#120—416no—
521#120—84no—
522C4×Q8—216no—
523C4×Q8—42no—
524C4×Q8—44no—
525C4×D4—28no—
526C4×D4—24no—
527C4×D4—28no—
528C4×D4—232no—
529C4×D4—416no—
530C4×D4—416no—
531C4×D4—416no—
532C4×D4—44no—
533C4×D4—42no—
534C4×D4—48no—
535C4×D4—44no—
536#117—216no—
537#117—48no—
538#117—48no—
539#117—84no—
540#117—84no—
541C2×C4⋊C4—28no—
542C2×C4⋊C4—48no—
543C2×C4⋊C4—48no—
544C2×C4⋊C4C2418yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2418yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2412yes—
563C2×C4⋊C4C2411yescharacteristic
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2414yes—
566C2×C4⋊C4C2412yes—
567C2×C4⋊C4C2414yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2412yes—
571C2×C22⋊C4—48no—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2418yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2412yes—
581C2×C22⋊C4C2414yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2418yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2414yes—
595C2×C22⋊C4C2414yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C42—28no—
610C2×C42C2418yes—
611C2×C42C2418yes—
612C2×C42C2412yes—
613C2×C42C2411yescharacteristic
614C2×C42C2412yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2412yes—
620C2×C42C2418yes—
621C2×C42C2414yes—
622C2×C42C2411yescharacteristic
623C2×C42C2414yes—
624C2×C42C2412yes—
625C2×C42C2411yescharacteristic
626#95C2418yes—
627#95C2418yes—
628#95C2418yes—
629#95C2418yes—
630#95C2414yes—
631#95C2412yes—
632#95C2414yes—
633#95C2414yes—
634#95C2414yes—
635#95C2418yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2414yes—
649#95C2414yes—
650#95C2418yes—
651#95C2418yes—
652C24—24no—
653C24—42no—
654C24—44no—
655C24—44no—
656C24—42no—
657C24C2514yes—
658C24C2514yes—
659C24C2512yes—
660C24C2512yes—
661#41—816no—
662#41—816no—
663#41—832no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—28no—
667C2×Q8—28no—
668C2×Q8—28no—
669C2×Q8—41no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8—44no—
673C2×Q8—48no—
674C2×Q8—42no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8—44no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—816no—
681C2×Q8C2×#4114yes—
682C2×D4—216no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—28no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—24no—
692C2×D4—216no—
693C2×D4—28no—
694C2×D4—41no—
695C2×D4—48no—
696C2×D4—41no—
697C2×D4—48no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—44no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—42no—
708C2×D4—48no—
709C2×D4—42no—
710C2×D4—42no—
711C2×D4—44no—
712C2×D4—42no—
713C2×D4—44no—
714C2×D4—48no—
715C2×D4—48no—
716C2×D4—48no—
717C2×D4—44no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4C2×#4114yes—
723C22×C4—28no—
724C22×C4—28no—
725C22×C4—24no—
726C22×C4—28no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—24no—
733C22×C4—28no—
734C22×C4—28no—
735C22×C4—28no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—44no—
741C22×C4—42no—
742C22×C4—48no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—48no—
746C22×C4—48no—
747C22×C4—48no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—816no—
751C22×C4C2512yes—
752C22×C4C2511yescharacteristic
753C22×C4C2514yes—
754C22×C4C2518yes—
755C22×C4C2512yes—
756C22×C4C2514yes—
757C22×C4C2514yes—
758C22×C4C2518yes—
759C22×C4C2512yes—
760C22×C4C2514yes—
761C22×C4C2511yescharacteristic
762C22×C4C2512yes—
763C22×C4C2512yes—
764C22×C4C2514yes—
765C22×C4C2512yes—
766C22×C4C2511yescharacteristic
767C4⋊C4—216no—
768C4⋊C4—24no—
769C4⋊C4—28no—
770C4⋊C4—216no—
771C4⋊C4—28no—
772C4⋊C4—216no—
773C4⋊C4—216no—
774C4⋊C4—42no—
775C4⋊C4—44no—
776C4⋊C4—48no—
777C4⋊C4—48no—
778C4⋊C4—42no—
779C4⋊C4—42no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—48no—
783C4⋊C4—41no—
784C4⋊C4—44no—
785C4⋊C4—48no—
786C4⋊C4—42no—
787C4⋊C4—41no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—42no—
791C4⋊C4—44no—
792C4⋊C4H(5,𝔽2)14yes—
793C4⋊C4H(5,𝔽2)18yes—
794C22⋊C4—24no—
795C22⋊C4—216no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—216no—
800C22⋊C4—216no—
801C22⋊C4—24no—
802C22⋊C4—28no—
803C22⋊C4—28no—
804C22⋊C4—216no—
805C22⋊C4—216no—
806C22⋊C4—48no—
807C22⋊C4—44no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—48no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—42no—
814C22⋊C4—44no—
815C22⋊C4—48no—
816C22⋊C4—44no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—42no—
820C22⋊C4—44no—
821C22⋊C4—44no—
822C22⋊C4—48no—
823C22⋊C4—44no—
824C22⋊C4—48no—
825C22⋊C4—44no—
826C22⋊C4—48no—
827C22⋊C4—48no—
828C22⋊C4—44no—
829C22⋊C4—48no—
830C22⋊C4C2×#41116yes—
831C42—28no—
832C42—24no—
833C42—24no—
834C42—216no—
835C42—216no—
836C42—24no—
837C42—22no—
838C42—24no—
839C42—28no—
840C42—42no—
841C42—44no—
842C42—42no—
843C42—48no—
844C42—44no—
845C42—41no—
846C42C2×#4114yes—
847C23—24no—
848C23—22no—
849C23—22no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—28no—
859C23—22no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—22no—
864C23—28no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—48no—
869C23—84no—
870C23—88no—
871C23—84no—
872C23—88no—
873C23C22×#4114yes—
874C23C2611yescharacteristic
875Q8—44no—
876Q8—416no—
877Q8—84no—
878Q8—84no—
879Q8—88no—
880Q8—164no—
881D4—44no—
882D4—432no—
883D4—44no—
884D4—48no—
885D4—84no—
886D4—84no—
887D4—84no—
888D4—88no—
889D4—88no—
890D4—88no—
891D4—816no—
892D4—816no—
893D4—164no—
894D4—162no—
895D4—168no—
896C2×C4—24no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—21no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—28no—
914C2×C4—24no—
915C2×C4—28no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—28no—
926C2×C4—22no—
927C2×C4—24no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—24no—
931C2×C4—22no—
932C2×C4—28no—
933C2×C4—416no—
934C2×C4—416no—
935C2×C4—48no—
936C2×C4—416no—
937C2×C4—48no—
938C2×C4—416no—
939C2×C4—84no—
940C2×C4—88no—
941C2×C4—88no—
942C2×C4—816no—
943C2×C4C22×#4114yes—
944C2×C4C22×#4112yes—
945C2×C4C22×#4114yes—
946C2×C4C2×H(5,𝔽2)18yes—
947C2×C4C2×H(5,𝔽2)14yes—
948C2×C4C2×H(5,𝔽2)12yes—
949C2×C4C2×H(5,𝔽2)14yes—
950C22—24no—
951C22—28no—
952C22—42no—
953C22—42no—
954C22—44no—
955C22—42no—
956C22—44no—
957C22—44no—
958C22—44no—
959C22—48no—
960C22—44no—
961C22—44no—
962C22—44no—
963C22—44no—
964C22—42no—
965C22—42no—
966C22—44no—
967C22—44no—
968C22—44no—
969C22—48no—
970C22—44no—
971C22—44no—
972C22—816no—
973C22C23×#4111yescharacteristic
974C22C22×H(5,𝔽2)11yescharacteristic
975C22C22×H(5,𝔽2)12yes—
976C22H(7,𝔽2)11yescharacteristic
977C222−1+612yes—
978C4—24no—
979C4—22no—
980C4—24no—
981C4—24no—
982C4—28no—
983C4—44no—
984C4—44no—
985C4—44no—
986C4—42no—
987C4—48no—
988C4—42no—
989C4—41no—
990C4—44no—
991C4—48no—
992C4—42no—
993C4#354914yes—
994C2—44no—
995C2—82no—
996C2—84no—
997C2—84no—
998C2C2×#354911yescharacteristic
999C2#6298311yescharacteristic
1000C2#6298512yes—
1001C2#6304811yescharacteristic
1002C2#6305212yes—
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. #59951C2semidirect
2. #59544C2semidirect
3. #59002C2semidirect
4. #59001C2semidirect
5. #51923C2semidirect
6. #49972C2semidirect
7. #49842C2semidirect
8. #49638C2semidirect
9. #46232C2semidirect
10. #46225C2semidirect
11. #46016C2semidirect
12. #46004C2semidirect
13. #39954C2semidirect
14. #39886C2semidirect
15. #38956C2semidirect
16. #38905C2semidirect
17. #36185C2semidirect
18. #36125C2semidirect
19. #34368C2semidirect
20. C4×H(3,𝔽4)C2semidirect
22. C2×#556C22semidirect
24. C2×#550C22semidirect
29. C2×#525C22semidirect
30. C22×C22⋊Q8C22semidirect
31. #2862C22semidirect
32. #2858C22semidirect
33. #2858C22semidirect
35. #2850C22semidirect
36. #2847C22semidirect
37. #2844C22semidirect
39. #2811C22semidirect
41. #2804C22semidirect
42. #2795C22semidirect
43. #2769C22semidirect
44. #2763C22semidirect
45. #2753C22semidirect
46. #2737C22semidirect
49. #2723C22semidirect
51. #2712C22semidirect
52. #2710C22semidirect
54. #2703C22semidirect
55. #2703C22semidirect
57. #2692C22semidirect
58. #2692C22semidirect
59. #2680C22semidirect
62. #2670C22semidirect
63. #2670C22semidirect
66. #2662C22semidirect
68. #2623C22semidirect
71. #2610C22semidirect
72. #2603C22semidirect
73. #2598C22semidirect
75. #2592C22semidirect
76. #2574C22semidirect
77. #2568C22semidirect
78. #2567C22semidirect
79. #2546C22semidirect
85. #2532C22semidirect
86. #2532C22semidirect
87. #2529C22semidirect
88. #2521C22semidirect
89. #2521C22semidirect
90. #2504C22semidirect
92. #2499C22semidirect
93. #2492C22semidirect
94. #2492C22semidirect
95. #2491C22semidirect
96. #2474C22semidirect
97. #2464C22semidirect
98. #2463C22semidirect
100. #2461C22semidirect
103. #2449C22semidirect
105. #2436C22semidirect
106. #2434C22semidirect
107. #2432C22semidirect
108. #2432C22semidirect
111. #2431C22semidirect
112. #2431C22semidirect
113. #2429C22semidirect
114. #2428C22semidirect
115. #2427C22semidirect
116. #2427C22semidirect
117. #2427C22semidirect
118. #2426C22semidirect
120. #2418C22semidirect
124. #2411C22semidirect
133. #2379C22semidirect
136. #2369C22semidirect
138. #2362C22semidirect
139. #2362C22semidirect
140. #2361C22semidirect
141. #2354C22semidirect
142. D4×C4⋊C4C22semidirect
143. #2347C22semidirect
144. #2344C22semidirect
145. #2324C22semidirect
146. #2324C22semidirect
148. #2311C22semidirect
155. #2295C22semidirect
156. #2293C22semidirect
157. #2285C22semidirect
158. C42×D4C22semidirect
496. #124#41semidirect

Maximal subgroups

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

subgroupindex
#599512
#595442
#590022
#590012
#519232
#499722
#498422
#496382
#462322
#462252
#460162
#460042
#399542
#398862
#389562
#389052
#361852
#361252
#343682
C4×H(3,𝔽4)2