Finite Group Databasebeta

← #7697253

Subgroups — #7697253

Order 512.

5409 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#60045C212yesmaximal, complemented
2#60034C214yesmaximal, complemented
3#59864C211yesmaximal, characteristic, complemented
4#59199C212yesmaximal, complemented
5#52288C212yesmaximal, complemented
6#52103C211yesmaximal, characteristic, complemented
7#45115C212yesmaximal, complemented
8#44922C214yesmaximal, complemented
9#44831C214yesmaximal, complemented
10#44244C218yesmaximal, complemented
11#40406C218yesmaximal, complemented
12#39493C212yesmaximal, complemented
13#38762C214yesmaximal, complemented
14#37839C214yesmaximal, complemented
15#36426C212yesmaximal, complemented
16#36415C211yesmaximal, characteristic, complemented
17#36087C212yesmaximal, complemented
18#35828C214yesmaximal, complemented
19#34316C212yesmaximal, complemented
20#34202C214yesmaximal, complemented
21C2×#555C2211yescharacteristic, complemented
22C2×#547C2212yes—
23C2×#547C2211yescharacteristic
24C2×#525C2214yes—
25C2×#520C2212yes—
26C22×#117C2212yescomplemented
27#2862C2211yescharacteristic, complemented
28#2853C2214yescomplemented
29#2850C2212yescomplemented
30#2847C2212yescomplemented
31#2806C2214yescomplemented
32#2805C2214yescomplemented
33#2804C2212yes—
34#2804C2214yes—
35#2804C2212yescomplemented
36#2799C2214yescomplemented
37#2796C2218yescomplemented
38#2780C2218yescomplemented
39#2777C2218yescomplemented
40#2748C2214yes—
41#2742C2214yescomplemented
42#2740C2218yescomplemented
43#2732C2214yes—
44#2708C2218yescomplemented
45#2706C2218yes—
46#2703C2218yes—
47#2696C2218yescomplemented
48#2693C2214yes—
49#2692C2218yescomplemented
50#2683C2211yescharacteristic
51#2682C2212yes—
52#2681C2214yes—
53#2680C2212yes—
54#2679C2211yescharacteristic
55#2678C2214yes—
56#2669C2212yes—
57#2650C2218yescomplemented
58#2632C2214yescomplemented
59#2628C2214yescomplemented
60#2615C2212yes—
61#2602C2218yescomplemented
62#2598C2214yes—
63#2598C2218yes—
64#2589C2218yescomplemented
65#2580C2218yescomplemented
66#2575C2218yescomplemented
67#2572C2214yes—
68#2572C2218yes—
69#2571C2212yescomplemented
70#2570C2214yescomplemented
71#2564C2218yes—
72#2563C2211yescharacteristic
73#2563C2214yescomplemented
74#2557C2218yescomplemented
75#2557C2218yescomplemented
76#2547C2211yescharacteristic, complemented
77#2540C2214yes—
78#2539C2218yescomplemented
79#2535C2214yescomplemented
80#2524C2218yescomplemented
81#2523C2214yescomplemented
82#2516C2218yescomplemented
83#2505C2218yescomplemented
84#2504C2212yescomplemented
85#2501C2212yescomplemented
86#2499C2212yescomplemented
87#2497C2214yescomplemented
88#2495C2214yescomplemented
89#2488C2218yescomplemented
90#2487C2212yes—
91#2487C2214yes—
92#2487C2212yescomplemented
93#2486C2214yescomplemented
94#2477C2218yescomplemented
95#2471C2218yes—
96#2471C2218yes—
97#2470C2218yescomplemented
98#2465C2218yescomplemented
99#2464C2218yescomplemented
100#2461C2218yescomplemented
101#2458C2218yescomplemented
102#2456C2218yes—
103#2440C2214yescomplemented
104#2439C2214yescomplemented
105#2437C2214yescomplemented
106#2431C2212yes—
107#2430C2218yes—
108#2416C2214yescomplemented
109#2414C2214yes—
110#2411C2214yescomplemented
111#2404C2214yes—
112#2404C2218yes—
113#2396C2214yescomplemented
114#2396C2218yescomplemented
115#2392C2214yes—
116#2388C2212yes—
117#2374C2218yescomplemented
118#2366C2212yes—
119#2365C2212yescomplemented
120#2363C2214yescomplemented
121#2362C2214yescomplemented
122#2359C2218yes—
123#2359C2218yescomplemented
124#2358C2214yes—
125#2358C2218yes—
126#2358C2218yescomplemented
127#2354C2212yes—
128#2354C2212yescomplemented
129#2354C2214yescomplemented
130#2352C2214yes—
131#2352C2214yes—
132#2352C2214yescomplemented
133#2352C2214yescomplemented
134D4×C4⋊C4C2214yes—
135D4×C4⋊C4C2214yescomplemented
136#2347C2212yescomplemented
137#2345C2214yescomplemented
138#2344C2212yescomplemented
139#2341C2214yes—
140#2335C2218yescomplemented
141#2324C2218yes—
142#2324C2214yescomplemented
143#2323C2218yescomplemented
144#2317C2214yescomplemented
145#2311C2214yes—
146C4×C4⋊Q8C2212yescomplemented
147C4×#127C2211yescharacteristic
148C4×C22⋊Q8C2214yescomplemented
149C4×C22⋊Q8C2218yescomplemented
150C4×#121C2218yes—
151C4×#120C2212yes—
152#2297C2214yes—
153#2297C2212yes—
154#2297C2214yes—
155#2293C2212yes—
156C2×#380C2214yescomplemented
157#2274C2214yescomplemented
158C42×D4C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C22×#41C2312yes—
161C22×#41C2314yes—
162C24×C4C2312yes—
163#555—44no—
164#547—216no—
165#547—44no—
166C2×C4⋊Q8C2312yes—
167C2×C4⋊Q8C2311yescharacteristic
168C2×C4⋊Q8C2311yescharacteristic
169C2×#127C2311yescharacteristic
170C2×#124C2314yes—
171C2×#124C2312yes—
172#525—232no—
173C2×#123C2318yes—
174C2×#123C2314yes—
175C2×#123C2314yes—
176C2×#123C2314yes—
177C2×#123C2318yes—
178C2×#123C2318yes—
179C2×C22⋊Q8C2314yes—
180C2×C22⋊Q8C2314yes—
181C2×C22⋊Q8C2314yes—
182C2×C22⋊Q8C2312yes—
183C2×C22⋊Q8C2318yes—
184C2×#121C2314yes—
185C2×#121C2314yes—
186C2×#121C2314yes—
187C2×#121C2312yes—
188C2×#121C2312yes—
189C2×#121C2312yes—
190C2×#121C2318yes—
191C2×#120C2314yes—
192C2×#120C2312yes—
193C2×#120C2314yes—
194C2×#120C2314yes—
195#520—48no—
196C2×C4×Q8C2314yes—
197C2×C4×Q8C2314yes—
198C2×C4×Q8C2314yes—
199C2×C4×D4C2314yes—
200C2×C4×D4C2312yes—
201C2×C4×D4C2314yes—
202C2×C4×D4C2314yes—
203C2×C4×D4C2311yescharacteristic
204C2×C4×D4C2311yescharacteristic
205C2×C4×D4C2311yescharacteristic
206C2×C4×D4C2318yes—
207C2×C4×D4C2314yes—
208C2×C4×D4C2318yes—
209C2×C4×D4C2318yes—
210C2×C4×D4C2312yes—
211C2×#117—48no—
212C2×#117C2314yes—
213C2×#117C2312yes—
214C2×#117C2314yes—
215C2×#117C2314yes—
216C2×#117C2318yes—
217C2×#117C2312yes—
218C2×#117C2314yes—
219C2×#117C2314yes—
220C22×C4⋊C4C2314yes—
221C22×C4⋊C4C2312yes—
222C22×C4⋊C4C2314yes—
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2312yes—
225C22×C22⋊C4C2314yes—
226C22×C22⋊C4C2318yes—
227C22×C42C2314yes—
228C22×C42C2312yes—
229#400C2318yes—
230#400C2318yes—
231#400C2314yes—
232#400C2314yes—
233#400C2318yes—
234#400C2318yes—
235#400C2318yes—
236#399C2318yes—
237#399C2318yes—
238#399C2314yes—
239#399C2314yes—
240#399C2314yes—
241#399C2314yes—
242#398C2318yes—
243#398C2318yes—
244#398C2314yes—
245#398C2318yes—
246#397C2314yes—
247#397C2318yes—
248#397C2318yes—
249#397C2314yes—
250#397C2318yes—
251#397C2318yes—
252#396C2314yes—
253#396C2314yes—
254#396C2318yes—
255#396C2318yes—
256#396C2318yes—
257#395C2318yes—
258#395C2318yes—
259#395C2312yes—
260#394C2312yes—
261#394C2314yes—
262#394C2314yes—
263#394C2318yes—
264#394C2314yes—
265#394C2314yes—
266#394C2318yes—
267#393C2314yes—
268#393C2318yes—
269#393C2318yes—
270#393C2318yes—
271#393C2318yes—
272#393C2314yes—
273#393C2312yes—
274#392C2314yes—
275#392C2318yes—
276#392C2318yes—
277#392C2318yes—
278#392C2314yes—
279#392C2312yes—
280#392C2314yes—
281#391C2314yes—
282#391C2318yes—
283#391C2314yes—
284#391C2312yes—
285#391C2312yes—
286#391C2318yes—
287#391C2312yes—
288#391C2314yes—
289#390C2314yes—
290#390C2311yescharacteristic
291#390C2311yescharacteristic
292#390C2312yes—
293#390C2318yes—
294#390C2318yes—
295#390C2314yes—
296#390C2318yes—
297#390C2318yes—
298#390C2314yes—
299#390C2318yes—
300#390C2312yes—
301#390C2318yes—
302#390C2312yes—
303#389C2314yes—
304#389C2314yes—
305#389C2314yes—
306#389C2314yes—
307#389C2318yes—
308#389C2318yes—
309#389C2318yes—
310#389C2318yes—
311#389C2314yes—
312#389C2312yes—
313#389C2312yes—
314#388C2318yes—
315#388C2318yes—
316#388C2318yes—
317#388C2318yes—
318#388C2318yes—
319#388C2318yes—
320#388C2318yes—
321#388C2318yes—
322#388C2314yes—
323#388C2314yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
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#386C2314yes—
343#386C2318yes—
344#386C2318yes—
345#386C2318yes—
346#386C2318yes—
347#386C2318yes—
348#386C2318yes—
349#386C2318yes—
350#386C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2314yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2314yes—
359#386C2314yes—
360#386C2314yes—
361#386C2312yes—
362#385C2314yes—
363#385C2318yes—
364#385C2318yes—
365#385C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2314yes—
371#385C2318yes—
372#385C2318yes—
373#385C2312yes—
374#385C2314yes—
375#384C2311yescharacteristic
376#384C2312yes—
377#384C2314yes—
378#383C2314yes—
379#383C2318yes—
380#382C2312yes—
381#382C2318yes—
382#382C2314yes—
383#382C2314yes—
384#381C2318yes—
385#381C2314yes—
386#380C2314yes—
387#380C2312yes—
388#380C2312yes—
389#380C2314yes—
390#380C2314yes—
391#380C2318yes—
392#380C2318yes—
393#380C2314yes—
394#380C2314yes—
395#380C2314yes—
396#380C2314yes—
397#380C2314yes—
398#380C2318yes—
399#379C2312yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2311yescharacteristic
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2318yes—
406C4×C4⋊C4C2318yes—
407C4×C4⋊C4C2314yes—
408C4×C4⋊C4C2314yes—
409C4×C4⋊C4C2312yes—
410C4×C4⋊C4C2314yes—
411C4×C4⋊C4C2318yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2318yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2318yes—
417C4×C22⋊C4C2314yes—
418C4×C22⋊C4C2312yes—
419C4×C22⋊C4C2314yes—
420C4×C22⋊C4C2318yes—
421C4×C22⋊C4C2312yes—
422C4×C22⋊C4C2318yes—
423C4×C22⋊C4C2318yes—
424C4×C22⋊C4C2312yes—
425C2×#95C2318yes—
426C43C2311yescharacteristic
427C25C2412yes—
428C2×#41—216no—
429C2×#41—28no—
430C2×#41—216no—
431C2×#41—44no—
432C2×#41—44no—
433C2×#41—82no—
434C2×#41—84no—
435C2×#41—84no—
436C22×Q8C2412yes—
437C22×Q8C2414yes—
438C22×Q8C2412yes—
439C22×Q8C2412yes—
440C22×D4C2411yescharacteristic
441C22×D4C2414yes—
442C22×D4C2414yes—
443C22×D4C2412yes—
444C22×D4C2414yes—
445C22×D4C2414yes—
446C22×D4C2411yescharacteristic
447C22×D4C2418yes—
448C22×D4C2414yes—
449C22×D4C2414yes—
450C22×D4C2412yes—
451C22×D4C2411yescharacteristic
452C23×C4—216no—
453C23×C4—44no—
454C23×C4C2412yes—
455C23×C4C2412yes—
456C23×C4C2414yes—
457C23×C4C2414yes—
458C23×C4C2412yes—
459C23×C4C2412yes—
460C23×C4C2414yes—
461C23×C4C2418yes—
462C23×C4C2414yes—
463C23×C4C2414yes—
464C23×C4C2418yes—
465C23×C4C2414yes—
466C4⋊Q8—28no—
467C4⋊Q8—42no—
468C4⋊Q8—42no—
469#127—24no—
470#124—48no—
471#124—82no—
472#123—216no—
473#123—216no—
474#123—232no—
475#123—48no—
476#123—88no—
477#123—88no—
478C22⋊Q8—216no—
479C22⋊Q8—216no—
480C22⋊Q8—216no—
481C22⋊Q8—44no—
482C22⋊Q8—88no—
483#121—216no—
484#121—216no—
485#121—216no—
486#121—44no—
487#121—44no—
488#121—44no—
489#121—88no—
490#120—216no—
491#120—28no—
492#120—216no—
493#120—84no—
494C4×Q8—48no—
495C4×Q8—84no—
496C4×Q8—84no—
497C4×D4—216no—
498C4×D4—216no—
499C4×D4—24no—
500C4×D4—216no—
501C4×D4—28no—
502C4×D4—416no—
503C4×D4—48no—
504C4×D4—42no—
505C4×D4—42no—
506C4×D4—88no—
507C4×D4—88no—
508C4×D4#41116yescomplemented
509#117—216no—
510#117—28no—
511#117—216no—
512#117—44no—
513#117—416no—
514#117—48no—
515#117—84no—
516#117—84no—
517C2×C4⋊C4—216no—
518C2×C4⋊C4—28no—
519C2×C4⋊C4—44no—
520C2×C4⋊C4—44no—
521C2×C4⋊C4—48no—
522C2×C4⋊C4C2414yes—
523C2×C4⋊C4C2412yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2412yes—
526C2×C4⋊C4C2414yes—
527C2×C4⋊C4C2414yes—
528C2×C4⋊C4C2418yes—
529C2×C4⋊C4C2414yes—
530C2×C4⋊C4C2414yes—
531C2×C4⋊C4C2414yes—
532C2×C4⋊C4C2414yes—
533C2×C4⋊C4C2414yes—
534C2×C4⋊C4C2414yes—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2418yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2411yescharacteristic
539C2×C4⋊C4C2412yes—
540C2×C4⋊C4C2414yes—
541C2×C4⋊C4C2412yes—
542C2×C4⋊C4C2418yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2411yescharacteristic
545C2×C4⋊C4C2418yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2418yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2411yescharacteristic
554C2×C22⋊C4—48no—
555C2×C22⋊C4—88no—
556C2×C22⋊C4C2418yes—
557C2×C22⋊C4C2414yes—
558C2×C22⋊C4C2414yes—
559C2×C22⋊C4C2414yes—
560C2×C22⋊C4C2414yes—
561C2×C22⋊C4C2414yes—
562C2×C22⋊C4C2414yes—
563C2×C22⋊C4C2414yes—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2414yes—
566C2×C22⋊C4C2412yes—
567C2×C22⋊C4C2414yes—
568C2×C22⋊C4C2414yes—
569C2×C22⋊C4C2412yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2418yes—
574C2×C22⋊C4C2418yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2412yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2412yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2414yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2418yes—
590C2×C22⋊C4C2414yes—
591C2×C42—48no—
592C2×C42—82no—
593C2×C42C2414yes—
594C2×C42C2418yes—
595C2×C42C2414yes—
596C2×C42C2411yescharacteristic
597C2×C42C2411yescharacteristic
598C2×C42C2418yes—
599C2×C42C2418yes—
600C2×C42C2418yes—
601C2×C42C2418yes—
602C2×C42C2412yes—
603C2×C42C2414yes—
604C2×C42C2412yes—
605C2×C42C2411yescharacteristic
606C2×C42C2412yes—
607#95C2418yes—
608#95C2418yes—
609#95C2418yes—
610#95C2418yes—
611#95C2414yes—
612#95C2414yes—
613#95C2412yes—
614#95C2418yes—
615#95C2418yes—
616#95C2418yes—
617#95C2418yes—
618#95C2412yes—
619#95C2418yes—
620#95C2418yes—
621#95C2418yes—
622#95C2418yes—
623#95C2418yes—
624#95C2418yes—
625#95C2418yes—
626#95C2412yes—
627#95C2414yes—
628#95C2414yes—
629#95C2414yes—
630#95C2418yes—
631#95C2414yes—
632#95C2414yes—
633#95C2418yes—
634#95C2418yes—
635C24—28no—
636C24—24no—
637C24—42no—
638C24—44no—
639C24—42no—
640C24C2512yes—
641C24C2512yes—
642C24C2514yes—
643C24C2512yes—
644#41—432no—
645#41—816no—
646#41—832no—
647C2×Q8—28no—
648C2×Q8—28no—
649C2×Q8—24no—
650C2×Q8—42no—
651C2×Q8—44no—
652C2×Q8—44no—
653C2×Q8—42no—
654C2×Q8—42no—
655C2×Q8—44no—
656C2×Q8—42no—
657C2×D4—28no—
658C2×D4—28no—
659C2×D4—28no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—216no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—24no—
667C2×D4—28no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—44no—
671C2×D4—42no—
672C2×D4—41no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—41no—
677C2×D4—42no—
678C2×D4—41no—
679C2×D4—48no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—48no—
684C2×D4—44no—
685C2×D4—41no—
686C2×D4—44no—
687C2×D4—48no—
688C2×D4C2×#4118yes—
689C2×D42−1+414yes—
690C22×C4—28no—
691C22×C4—28no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—216no—
695C22×C4—28no—
696C22×C4—28no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—28no—
700C22×C4—28no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—44no—
708C22×C4—44no—
709C22×C4—44no—
710C22×C4—44no—
711C22×C4—432no—
712C22×C4—44no—
713C22×C4—48no—
714C22×C4—48no—
715C22×C4—48no—
716C22×C4—48no—
717C22×C4—44no—
718C22×C4—48no—
719C22×C4—48no—
720C22×C4—48no—
721C22×C4C2×#41116yes—
722C22×C4C2514yes—
723C22×C4C2514yes—
724C22×C4C2514yes—
725C22×C4C2512yes—
726C22×C4C2518yes—
727C22×C4C2512yes—
728C22×C4C2514yes—
729C22×C4C2518yes—
730C22×C4C2514yes—
731C22×C4C2511yescharacteristic
732C22×C4C2512yes—
733C22×C4C2512yes—
734C22×C4C2514yes—
735C22×C4C2512yes—
736C22×C4C2511yescharacteristic
737C22×C4C2511yescharacteristic
738C4⋊C4—24no—
739C4⋊C4—28no—
740C4⋊C4—216no—
741C4⋊C4—28no—
742C4⋊C4—28no—
743C4⋊C4—28no—
744C4⋊C4—28no—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C4⋊C4—24no—
748C4⋊C4—28no—
749C4⋊C4—28no—
750C4⋊C4—24no—
751C4⋊C4—44no—
752C4⋊C4—48no—
753C4⋊C4—44no—
754C4⋊C4—41no—
755C4⋊C4—42no—
756C4⋊C4—42no—
757C4⋊C4—44no—
758C4⋊C4—48no—
759C4⋊C4—41no—
760C4⋊C4—44no—
761C4⋊C4—48no—
762C4⋊C4—42no—
763C4⋊C4—48no—
764C4⋊C4—48no—
765C4⋊C4—48no—
766C4⋊C4—48no—
767C4⋊C4—42no—
768C4⋊C4C2×#4118yes—
769C4⋊C4H(5,𝔽2)14yes—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—24no—
773C22⋊C4—28no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—28no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—216no—
781C22⋊C4—216no—
782C22⋊C4—28no—
783C22⋊C4—24no—
784C22⋊C4—28no—
785C22⋊C4—48no—
786C22⋊C4—48no—
787C22⋊C4—48no—
788C22⋊C4—48no—
789C22⋊C4—48no—
790C22⋊C4—44no—
791C22⋊C4—42no—
792C22⋊C4—44no—
793C22⋊C4—48no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—48no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—48no—
804C22⋊C4C2×#41116yes—
805C42—28no—
806C42—216no—
807C42—28no—
808C42—22no—
809C42—22no—
810C42—48no—
811C42—41no—
812C42—44no—
813C42—42no—
814C42—48no—
815C42—48no—
816C42—48no—
817C42—42no—
818C42C2×#4118yes—
819C23—24no—
820C23—24no—
821C23—24no—
822C23—22no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—22no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—48no—
840C23—416no—
841C23—88no—
842C23—84no—
843C23—84no—
844C23C22×#4118yes—
845C23C2×2−1+414yes—
846C23C2611yescharacteristic
847Q8—48no—
848Q8—416no—
849Q8—84no—
850Q8—162no—
851D4—48no—
852D4—44no—
853D4—416no—
854D4—416no—
855D4—416no—
856D4—48no—
857D4—44no—
858D4—82no—
859D4—88no—
860D4—816no—
861D4—88no—
862D4—164no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—21no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—21no—
872C2×C4—22no—
873C2×C4—232no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—24no—
878C2×C4—24no—
879C2×C4—28no—
880C2×C4—22no—
881C2×C4—28no—
882C2×C4—21no—
883C2×C4—24no—
884C2×C4—24no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—24no—
890C2×C4—24no—
891C2×C4—24no—
892C2×C4—28no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—28no—
898C2×C4—24no—
899C2×C4—28no—
900C2×C4—48no—
901C2×C4—48no—
902C2×C4—416no—
903C2×C4—416no—
904C2×C4—416no—
905C2×C4—48no—
906C2×C4—48no—
907C2×C4—816no—
908C2×C4—88no—
909C2×C4—164no—
910C2×C4—168no—
911C2×C4C22×#4114yes—
912C2×C4C22×#4114yes—
913C2×C4C22×#4118yes—
914C2×C4C22×#4114yes—
915C2×C4C2×H(5,𝔽2)14yes—
916C2×C4C2×H(5,𝔽2)12yes—
917C2×C4C2×2−1+412yes—
918C22—28no—
919C22—28no—
920C22—28no—
921C22—24no—
922C22—28no—
923C22—44no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—42no—
930C22—44no—
931C22—44no—
932C22—42no—
933C22—42no—
934C22—44no—
935C22—44no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—816no—
941C22C23×#4112yes—
942C22C22×H(5,𝔽2)11yescharacteristic
943C22C22×2−1+411yescharacteristic
944C22H(7,𝔽2)12yes—
945C22H(7,𝔽2)11yescharacteristic
946C4—24no—
947C4—24no—
948C4—24no—
949C4—22no—
950C4—28no—
951C4—44no—
952C4—48no—
953C4—44no—
954C4—41no—
955C4—44no—
956C4—48no—
957C4—44no—
958C4—44no—
959C4—42no—
960C4—42no—
961C4#348114yes—
962C2—44no—
963C2—48no—
964C2—82no—
965C2—82no—
966C2C2×#348111yescharacteristic
967C2#6285512yes—
968C2#6289411yescharacteristic
969C2#6300012yes—
970C2#6306611yescharacteristic
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. #60045C2semidirect
2. #60034C2semidirect
3. #59864C2semidirect
4. #59199C2semidirect
5. #52288C2semidirect
6. #52103C2semidirect
7. #45115C2semidirect
8. #44922C2semidirect
9. #44831C2semidirect
10. #44244C2semidirect
11. #40406C2semidirect
12. #39493C2semidirect
13. #38762C2semidirect
14. #37839C2semidirect
15. #36426C2semidirect
16. #36415C2semidirect
17. #36087C2semidirect
18. #35828C2semidirect
19. #34316C2semidirect
20. #34202C2semidirect
21. C2×#555C22semidirect
26. C22×#117C22semidirect
27. #2862C22semidirect
28. #2853C22semidirect
29. #2850C22semidirect
30. #2847C22semidirect
31. #2806C22semidirect
32. #2805C22semidirect
35. #2804C22semidirect
36. #2799C22semidirect
37. #2796C22semidirect
38. #2780C22semidirect
39. #2777C22semidirect
41. #2742C22semidirect
42. #2740C22semidirect
44. #2708C22semidirect
47. #2696C22semidirect
49. #2692C22semidirect
57. #2650C22semidirect
58. #2632C22semidirect
59. #2628C22semidirect
61. #2602C22semidirect
64. #2589C22semidirect
65. #2580C22semidirect
66. #2575C22semidirect
69. #2571C22semidirect
70. #2570C22semidirect
73. #2563C22semidirect
74. #2557C22semidirect
75. #2557C22semidirect
76. #2547C22semidirect
78. #2539C22semidirect
79. #2535C22semidirect
80. #2524C22semidirect
81. #2523C22semidirect
82. #2516C22semidirect
83. #2505C22semidirect
84. #2504C22semidirect
85. #2501C22semidirect
86. #2499C22semidirect
87. #2497C22semidirect
88. #2495C22semidirect
89. #2488C22semidirect
92. #2487C22semidirect
93. #2486C22semidirect
94. #2477C22semidirect
97. #2470C22semidirect
98. #2465C22semidirect
99. #2464C22semidirect
100. #2461C22semidirect
101. #2458C22semidirect
103. #2440C22semidirect
104. #2439C22semidirect
105. #2437C22semidirect
108. #2416C22semidirect
110. #2411C22semidirect
113. #2396C22semidirect
114. #2396C22semidirect
117. #2374C22semidirect
119. #2365C22semidirect
120. #2363C22semidirect
121. #2362C22semidirect
123. #2359C22semidirect
126. #2358C22semidirect
128. #2354C22semidirect
129. #2354C22semidirect
132. #2352C22semidirect
133. #2352C22semidirect
135. D4×C4⋊C4C22semidirect
136. #2347C22semidirect
137. #2345C22semidirect
138. #2344C22semidirect
140. #2335C22semidirect
142. #2324C22semidirect
143. #2323C22semidirect
144. #2317C22semidirect
146. C4×C4⋊Q8C22semidirect
148. C4×C22⋊Q8C22semidirect
149. C4×C22⋊Q8C22semidirect
156. C2×#380C22semidirect
157. #2274C22semidirect
158. C42×D4C22semidirect
508. C4×D4#41semidirect

Maximal subgroups

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

subgroupindex
#600452
#600342
#598642
#591992
#522882
#521032
#451152
#449222
#448312
#442442
#404062
#394932
#387622
#378392
#364262
#364152
#360872
#358282
#343162
#342022