Finite Group Databasebeta

← #8701562

Subgroups — #8701562

Order 512.

5577 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59841C212yesmaximal, complemented
2#59822C212yesmaximal, complemented
3#59544C214yesmaximal, complemented
4#58384C214yesmaximal, complemented
5#57581C218yesmaximal, complemented
6#52307C211yesmaximal, characteristic, complemented
7#51783C214yesmaximal, complemented
8#48462C218yesmaximal, complemented
9#46016C212yesmaximal, complemented
10#45996C211yesmaximal, characteristic, complemented
11#45103C212yesmaximal, complemented
12#44886C214yesmaximal, complemented
13#42987C212yesmaximal, complemented
14#42434C214yesmaximal, complemented
15#39953C214yesmaximal, complemented
16#39174C212yesmaximal, complemented
17#37267C212yesmaximal, complemented
18#37249C214yesmaximal, complemented
19#36508C211yesmaximal, characteristic, complemented
20#36496C212yesmaximal, complemented
21C2×H(3,𝔽4)C2212yes—
22C2×#559C2212yes—
23C2×#557C2211yescharacteristic, complemented
24C2×#556C2211yescharacteristic
25C2×#555C2214yescomplemented
26C2×#554C2212yescomplemented
27C2×#550C2212yes—
28C2×#546C2214yescomplemented
29C2×#537C2214yes—
30C2×#535C2212yescomplemented
31#2862C2211yescharacteristic, complemented
32#2861C2212yes—
33#2861C2214yescomplemented
34#2858C2212yes—
35#2858C2212yes—
36#2819C2212yes—
37#2819C2214yescomplemented
38#2818C2214yes—
39#2816C2218yescomplemented
40#2811C2211yescharacteristic, complemented
41#2804C2214yescomplemented
42#2795C2218yescomplemented
43#2785C2212yescomplemented
44#2785C2214yescomplemented
45#2753C2218yescomplemented
46#2737C2218yescomplemented
47#2733C2212yes—
48#2733C2212yes—
49#2733C2212yes—
50#2733C2211yescharacteristic, complemented
51#2733C2214yescomplemented
52#2733C2214yescomplemented
53#2731C2214yescomplemented
54#2720C2218yescomplemented
55#2712C2218yescomplemented
56#2711C2218yescomplemented
57#2711C2218yescomplemented
58#2711C2218yescomplemented
59#2710C2218yescomplemented
60#2706C2218yescomplemented
61#2699C2214yescomplemented
62#2692C2218yescomplemented
63#2685C2218yescomplemented
64#2680C2214yescomplemented
65#2679C2212yes—
66#2678C2218yescomplemented
67#2676C2218yescomplemented
68#2676C2218yescomplemented
69#2673C2218yescomplemented
70#2671C2218yes—
71#2670C2218yes—
72#2670C2218yes—
73#2670C2218yescomplemented
74#2669C2218yescomplemented
75#2669C2218yescomplemented
76#2668C2214yescomplemented
77#2662C2214yes—
78#2661C2218yescomplemented
79#2641C2214yescomplemented
80#2635C2218yescomplemented
81#2632C2214yescomplemented
82#2620C2218yescomplemented
83#2616C2212yescomplemented
84#2610C2218yescomplemented
85#2609C2214yescomplemented
86#2592C2214yescomplemented
87#2574C2218yescomplemented
88#2567C2212yescomplemented
89#2566C2214yescomplemented
90#2566C2214yescomplemented
91#2565C2212yescomplemented
92#2548C2212yes—
93#2548C2214yescomplemented
94#2548C2214yescomplemented
95#2546C2211yescharacteristic, complemented
96#2545C2212yes—
97#2544C2214yescomplemented
98#2542C2211yescharacteristic
99#2542C2212yescomplemented
100#2541C2212yes—
101#2541C2218yescomplemented
102#2540C2214yes—
103#2537C2214yescomplemented
104#2532C2218yescomplemented
105#2519C2218yescomplemented
106#2492C2214yescomplemented
107#2491C2214yes—
108#2491C2214yescomplemented
109#2476C2218yescomplemented
110#2474C2218yescomplemented
111#2461C2218yescomplemented
112#2461C2218yescomplemented
113#2461C2218yescomplemented
114#2459C2218yescomplemented
115#2459C2218yescomplemented
116#2437C2214yescomplemented
117#2435C2212yescomplemented
118#2433C2214yes—
119#2432C2214yescomplemented
120#2432C2214yescomplemented
121#2431C2214yes—
122#2429C2214yescomplemented
123#2428C2214yes—
124#2427C2214yes—
125#2426C2214yescomplemented
126#2426C2214yescomplemented
127#2426C2214yescomplemented
128#2424C2218yes—
129#2424C2218yescomplemented
130#2424C2218yescomplemented
131#2417C2214yescomplemented
132#2416C2214yescomplemented
133#2414C2214yes—
134#2414C2218yescomplemented
135#2414C2218yescomplemented
136#2411C2218yescomplemented
137#2408C2212yes—
138#2407C2214yescomplemented
139#2388C2212yes—
140#2388C2214yescomplemented
141#2379C2214yescomplemented
142#2362C2214yescomplemented
143#2361C2214yescomplemented
144#2361C2214yescomplemented
145#2354C2218yescomplemented
146#2347C2212yescomplemented
147#2344C2214yescomplemented
148#2326C2214yescomplemented
149#2321C2218yescomplemented
150C4×C4⋊Q8C2212yescomplemented
151C4×#127C2214yescomplemented
152C4×#124C2211yescharacteristic
153C4×#124C2212yescomplemented
154C4×#124C2214yescomplemented
155C4×#124C2212yescomplemented
156#2295C2212yescomplemented
157#2293C2214yescomplemented
158C42×Q8C2211yescharacteristic, complemented
159C22×#41C2312yes—
160C22×#41C2314yes—
161C23×D4C2312yes—
162H(3,𝔽4)—48no—
163#559—48no—
164#557—44no—
165#556—44no—
166#555—416no—
167#554—48no—
168#550—48no—
169#546—416no—
170#537—416no—
171#535—48no—
172C2×C4⋊Q8C2312yes—
173C2×C4⋊Q8C2312yes—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2311yescharacteristic
176C2×C4⋊Q8C2311yescharacteristic
177C2×#127C2314yes—
178C2×#127C2314yes—
179C2×#127C2312yes—
180C2×#127C2312yes—
181C2×#127C2314yes—
182C2×#126C2314yes—
183C2×#125C2312yes—
184C2×#125C2314yes—
185C2×#125C2314yes—
186C2×#124C2314yes—
187C2×#124C2312yes—
188C2×#124C2311yescharacteristic
189C2×#124C2314yes—
190C2×#124C2312yes—
191C2×#124C2314yes—
192C2×#124C2314yes—
193C2×#124C2314yes—
194C2×#124C2312yes—
195C2×#124C2314yes—
196C2×#124C2318yes—
197C2×#124C2314yes—
198C2×#124C2318yes—
199C2×#124C2314yes—
200C2×#123C2318yes—
201C2×#123C2318yes—
202C2×C22⋊Q8C2314yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2314yes—
205C2×C22⋊Q8C2312yes—
206C2×C22⋊Q8C2314yes—
207C2×C22⋊Q8C2318yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2318yes—
211C2×#121C2318yes—
212C2×#121C2318yes—
213C2×#121C2314yes—
214C2×#121C2314yes—
215C2×#121C2318yes—
216C2×#121C2318yes—
217C2×#121C2318yes—
218C2×#121C2318yes—
219C2×#120C2318yes—
220C2×#120C2314yes—
221C2×#120C2318yes—
222C2×#120C2318yes—
223C2×#120C2318yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2312yes—
227C2×C4×Q8C2312yes—
228C2×C4×Q8C2312yes—
229C2×C4×Q8C2312yes—
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4C2314yes—
232C2×C4×D4C2314yes—
233C2×C4×D4C2318yes—
234C2×C4×D4C2318yes—
235C2×C4×D4C2314yes—
236C2×C4×D4C2314yes—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2314yes—
239C2×C4×D4C2312yes—
240C2×C4×D4C2312yes—
241C2×#117C2312yes—
242C2×#117C2318yes—
243C2×#117C2318yes—
244C22×C4⋊C4C2314yes—
245C22×C22⋊C4C2318yes—
246#400C2318yes—
247#399C2318yes—
248#399C2318yes—
249#399C2314yes—
250#398C2318yes—
251#398C2318yes—
252#398C2314yes—
253#397C2318yes—
254#397C2318yes—
255#396C2318yes—
256#396C2318yes—
257#396C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#395C2318yes—
262#395C2314yes—
263#395C2312yes—
264#395C2314yes—
265#394C2314yes—
266#394C2314yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2314yes—
273#394C2318yes—
274#394C2314yes—
275#394C2314yes—
276#394C2318yes—
277#394C2314yes—
278#394C2318yes—
279#394C2318yes—
280#394C2314yes—
281#394C2318yes—
282#394C2318yes—
283#394C2318yes—
284#394C2314yes—
285#394C2312yes—
286#394C2314yes—
287#394C2318yes—
288#394C2314yes—
289#394C2318yes—
290#394C2318yes—
291#393C2318yes—
292#393C2318yes—
293#393C2318yes—
294#393C2318yes—
295#393C2312yes—
296#393C2314yes—
297#392C2312yes—
298#392C2318yes—
299#392C2318yes—
300#392C2314yes—
301#392C2318yes—
302#392C2318yes—
303#392C2318yes—
304#392C2314yes—
305#392C2314yes—
306#392C2314yes—
307#392C2314yes—
308#392C2318yes—
309#392C2318yes—
310#392C2318yes—
311#392C2318yes—
312#391C2311yescharacteristic
313#391C2312yes—
314#391C2312yes—
315#391C2312yes—
316#391C2314yes—
317#391C2318yes—
318#391C2312yes—
319#391C2314yes—
320#391C2314yes—
321#391C2312yes—
322#391C2314yes—
323#390C2312yes—
324#390C2314yes—
325#390C2318yes—
326#390C2318yes—
327#390C2314yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2318yes—
332#390C2318yes—
333#390C2314yes—
334#390C2314yes—
335#390C2314yes—
336#390C2314yes—
337#390C2311yescharacteristic
338#390C2312yes—
339#390C2318yes—
340#390C2318yes—
341#390C2314yes—
342#390C2312yes—
343#390C2314yes—
344#390C2318yes—
345#390C2314yes—
346#389C2318yes—
347#389C2314yes—
348#389C2314yes—
349#389C2314yes—
350#388C2318yes—
351#388C2318yes—
352#388C2314yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2318yes—
361#388C2318yes—
362#388C2318yes—
363#388C2314yes—
364#388C2318yes—
365#388C2318yes—
366#388C2318yes—
367#388C2318yes—
368#388C2314yes—
369#388C2314yes—
370#388C2314yes—
371#388C2318yes—
372#388C2314yes—
373#388C2314yes—
374#388C2314yes—
375#388C2314yes—
376#387C2318yes—
377#387C2318yes—
378#387C2318yes—
379#387C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2318yes—
383#386C2318yes—
384#386C2318yes—
385#386C2318yes—
386#386C2318yes—
387#386C2318yes—
388#386C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2318yes—
392#385C2318yes—
393#385C2318yes—
394#385C2318yes—
395#385C2318yes—
396#384C2314yes—
397#384C2312yes—
398#384C2314yes—
399#383C2314yes—
400#382C2311yescharacteristic
401#382C2314yes—
402#382C2312yes—
403#382C2312yes—
404#382C2314yes—
405#381C2318yes—
406#380C2318yes—
407#380C2314yes—
408#380C2312yes—
409#380C2318yes—
410#379C2318yes—
411#379C2314yes—
412C4×C4⋊C4C2318yes—
413C4×C4⋊C4C2312yes—
414C4×C4⋊C4C2314yes—
415C4×C4⋊C4C2314yes—
416C4×C4⋊C4C2312yes—
417C4×C4⋊C4C2314yes—
418C4×C4⋊C4C2314yes—
419C4×C4⋊C4C2312yes—
420C4×C4⋊C4C2311yescharacteristic
421C4×C22⋊C4C2318yes—
422C4×C22⋊C4C2314yes—
423C4×C22⋊C4C2312yes—
424C4×C22⋊C4C2314yes—
425C4×C22⋊C4C2314yes—
426C4×C22⋊C4C2314yes—
427#376C2314yes—
428C43C2312yes—
429C43C2311yescharacteristic
430C43C2312yes—
431C25C2414yes—
432C2×#41—44no—
433C2×#41—48no—
434C2×#41—48no—
435C2×#41—48no—
436C2×#41—48no—
437C22×Q8C2411yescharacteristic
438C22×Q8C2412yes—
439C22×Q8C2412yes—
440C22×Q8C2412yes—
441C22×Q8C2412yes—
442C22×Q8C2414yes—
443C22×Q8C2411yescharacteristic
444C22×D4—44no—
445C22×D4—48no—
446C22×D4C2414yes—
447C22×D4C2412yes—
448C22×D4C2411yescharacteristic
449C22×D4C2414yes—
450C22×D4C2414yes—
451C22×D4C2418yes—
452C22×D4C2418yes—
453C22×D4C2412yes—
454C22×D4C2414yes—
455C22×D4C2418yes—
456C22×D4C2414yes—
457C22×D4C2414yes—
458C22×D4C2414yes—
459C22×D4C2418yes—
460C22×D4C2418yes—
461C22×D4C2412yes—
462C22×D4C2414yes—
463C23×C4C2414yes—
464C23×C4C2412yes—
465C23×C4C2418yes—
466C23×C4C2418yes—
467C23×C4C2418yes—
468C4⋊Q8—28no—
469C4⋊Q8—44no—
470C4⋊Q8—42no—
471C4⋊Q8—44no—
472C4⋊Q8—42no—
473#127—48no—
474#127—48no—
475#127—48no—
476#127—44no—
477#127—44no—
478#126—48no—
479#125—48no—
480#125—48no—
481#125—44no—
482#124—28no—
483#124—216no—
484#124—24no—
485#124—48no—
486#124—48no—
487#124—44no—
488#124—48no—
489#124—416no—
490#124—48no—
491#124—44no—
492#124—48no—
493#124—48no—
494#124—48no—
495#124—416no—
496#123—416no—
497#123—416no—
498C22⋊Q8—216no—
499C22⋊Q8—416no—
500C22⋊Q8—416no—
501C22⋊Q8—48no—
502C22⋊Q8—48no—
503C22⋊Q8—44no—
504#121—216no—
505#121—216no—
506#121—416no—
507#121—416no—
508#121—416no—
509#121—416no—
510#121—416no—
511#121—48no—
512#121—48no—
513#121—416no—
514#121—416no—
515#120—416no—
516#120—416no—
517#120—416no—
518#120—416no—
519#120—48no—
520C4×Q8—28no—
521C4×Q8—28no—
522C4×Q8—24no—
523C4×Q8—44no—
524C4×Q8—44no—
525C4×Q8—42no—
526C4×Q8—44no—
527C4×D4—216no—
528C4×D4—416no—
529C4×D4—48no—
530C4×D4—416no—
531C4×D4—48no—
532C4×D4—44no—
533C4×D4—48no—
534C4×D4—44no—
535C4×D4—42no—
536C4×D4—48no—
537#117—28no—
538#117—416no—
539#117—416no—
540C2×C4⋊C4—216no—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2414yes—
543C2×C4⋊C4C2418yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2414yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2412yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2418yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2411yescharacteristic
553C2×C4⋊C4C2414yes—
554C2×C4⋊C4C2412yes—
555C2×C4⋊C4C2414yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2412yes—
560C2×C4⋊C4C2411yescharacteristic
561C2×C4⋊C4C2412yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2418yes—
564C2×C4⋊C4C2418yes—
565C2×C4⋊C4C2412yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2412yes—
568C2×C4⋊C4C2412yes—
569C2×C4⋊C4C2411yescharacteristic
570C2×C22⋊C4—416no—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2418yes—
573C2×C22⋊C4C2414yes—
574C2×C22⋊C4C2414yes—
575C2×C22⋊C4C2418yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2418yes—
579C2×C22⋊C4C2418yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2418yes—
586C2×C22⋊C4C2418yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2412yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2418yes—
598C2×C22⋊C4C2418yes—
599C2×C22⋊C4C2418yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2414yes—
602C2×C22⋊C4C2418yes—
603C2×C22⋊C4C2414yes—
604C2×C22⋊C4C2414yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2414yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2418yes—
609C2×C42C2412yes—
610C2×C42C2414yes—
611C2×C42C2414yes—
612C2×C42C2412yes—
613C2×C42C2414yes—
614C2×C42C2414yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2412yes—
618C2×C42C2412yes—
619C2×C42C2411yescharacteristic
620C2×C42C2412yes—
621C2×C42C2411yescharacteristic
622C2×C42C2412yes—
623C2×C42C2418yes—
624C2×C42C2414yes—
625C2×C42C2411yescharacteristic
626C2×C42C2412yes—
627#95C2418yes—
628#95C2418yes—
629#95C2412yes—
630#95C2414yes—
631#95C2418yes—
632#95C2418yes—
633#95C2414yes—
634#95C2414yes—
635#95C2414yes—
636#95C2414yes—
637#95C2412yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2412yes—
642#95C2414yes—
643#95C2414yes—
644#95C2418yes—
645#95C2414yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650C24—48no—
651C24—44no—
652C24—44no—
653C24—48no—
654C24—44no—
655C24C2512yes—
656C24C2518yes—
657C24C2514yes—
658#41—816no—
659#41—832no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—24no—
663C2×Q8—28no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—41no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—44no—
671C2×Q8—42no—
672C2×Q8—42no—
673C2×Q8—42no—
674C2×Q8—44no—
675C2×Q8—44no—
676C2×Q8—44no—
677C2×Q8H(5,𝔽2)14yes—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—28no—
681C2×D4—22no—
682C2×D4—28no—
683C2×D4—216no—
684C2×D4—216no—
685C2×D4—24no—
686C2×D4—24no—
687C2×D4—28no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—44no—
691C2×D4—48no—
692C2×D4—41no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—42no—
696C2×D4—48no—
697C2×D4—44no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—48no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4—48no—
704C2×D4—48no—
705C2×D4—44no—
706C2×D4—44no—
707C2×D4—42no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—44no—
711C2×D4—44no—
712C2×D4—42no—
713C2×D4—41no—
714C2×D4—44no—
715C2×D4—48no—
716C2×D4—44no—
717C2×D4—48no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—44no—
725C2×D4—48no—
726C2×D4—816no—
727C22×C4—28no—
728C22×C4—24no—
729C22×C4—28no—
730C22×C4—28no—
731C22×C4—28no—
732C22×C4—216no—
733C22×C4—216no—
734C22×C4—48no—
735C22×C4—48no—
736C22×C4—48no—
737C22×C4—48no—
738C22×C4—48no—
739C22×C4—48no—
740C22×C4—48no—
741C22×C4C2514yes—
742C22×C4C2512yes—
743C22×C4C2514yes—
744C22×C4C2512yes—
745C22×C4C2518yes—
746C22×C4C2512yes—
747C22×C4C2514yes—
748C22×C4C2514yes—
749C22×C4C2514yes—
750C22×C4C2511yescharacteristic
751C22×C4C2512yes—
752C22×C4C2512yes—
753C22×C4C2514yes—
754C22×C4C2511yescharacteristic
755C22×C4C2512yes—
756C22×C4C2512yes—
757C22×C4C2511yescharacteristic
758C4⋊C4—216no—
759C4⋊C4—28no—
760C4⋊C4—24no—
761C4⋊C4—216no—
762C4⋊C4—28no—
763C4⋊C4—28no—
764C4⋊C4—24no—
765C4⋊C4—216no—
766C4⋊C4—48no—
767C4⋊C4—48no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4—41no—
771C4⋊C4—44no—
772C4⋊C4—42no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—42no—
777C4⋊C4—41no—
778C4⋊C4—44no—
779C4⋊C4—42no—
780C4⋊C4—48no—
781C4⋊C4—48no—
782C4⋊C4—42no—
783C4⋊C4—44no—
784C4⋊C4—42no—
785C4⋊C4H(5,𝔽2)18yes—
786C4⋊C4H(5,𝔽2)14yes—
787C22⋊C4—216no—
788C22⋊C4—216no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—216no—
792C22⋊C4—216no—
793C22⋊C4—28no—
794C22⋊C4—216no—
795C22⋊C4—216no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—216no—
799C22⋊C4—28no—
800C22⋊C4—44no—
801C22⋊C4—48no—
802C22⋊C4—48no—
803C22⋊C4—48no—
804C22⋊C4—48no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—48no—
808C22⋊C4—44no—
809C22⋊C4—48no—
810C22⋊C4—42no—
811C22⋊C4—48no—
812C22⋊C4—48no—
813C22⋊C4—48no—
814C22⋊C4—44no—
815C22⋊C4—48no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—44no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C22⋊C4—48no—
822C22⋊C4—44no—
823C22⋊C4—44no—
824C22⋊C4—44no—
825C42—28no—
826C42—24no—
827C42—28no—
828C42—28no—
829C42—24no—
830C42—28no—
831C42—28no—
832C42—24no—
833C42—24no—
834C42—22no—
835C42—24no—
836C42—22no—
837C42—28no—
838C42—24no—
839C42—41no—
840C42—42no—
841C42—48no—
842C42—44no—
843C23—22no—
844C23—24no—
845C23—28no—
846C23—22no—
847C23—24no—
848C23—28no—
849C23—28no—
850C23—28no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—28no—
856C23—24no—
857C23—24no—
858C23—28no—
859C23—28no—
860C23—24no—
861C23—22no—
862C23—88no—
863C23—816no—
864C23—168no—
865C23—164no—
866C23—164no—
867C23C2611yescharacteristic
868Q8—44no—
869Q8—44no—
870Q8—48no—
871Q8—84no—
872Q8—84no—
873Q8—84no—
874Q8—164no—
875D4—48no—
876D4—416no—
877D4—816no—
878D4—816no—
879D4—84no—
880D4—88no—
881D4—82no—
882D4—88no—
883D4—88no—
884D4—88no—
885D4—88no—
886D4—84no—
887D4—816no—
888D4—168no—
889D4—164no—
890D4—164no—
891D4—168no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—21no—
895C2×C4—24no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—21no—
901C2×C4—22no—
902C2×C4—24no—
903C2×C4—28no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—24no—
907C2×C4—24no—
908C2×C4—24no—
909C2×C4—21no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—28no—
918C2×C4—28no—
919C2×C4—24no—
920C2×C4—24no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—24no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—28no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—48no—
930C2×C4—416no—
931C2×C4—816no—
932C2×C4—816no—
933C2×C4—816no—
934C2×C4C2×H(5,𝔽2)14yes—
935C2×C4C2×H(5,𝔽2)12yes—
936C2×C4C2×H(5,𝔽2)14yes—
937C2×C4C2×H(5,𝔽2)18yes—
938C2×C4C2×H(5,𝔽2)14yes—
939C2×C4C2×H(5,𝔽2)12yes—
940C2×C4#58514yes—
941C22—44no—
942C22—42no—
943C22—48no—
944C22—44no—
945C22—48no—
946C22—44no—
947C22—48no—
948C22—44no—
949C22—44no—
950C22—48no—
951C22—42no—
952C22—44no—
953C22—48no—
954C22—42no—
955C22—44no—
956C22—44no—
957C22—48no—
958C22—44no—
959C22—48no—
960C22—1616no—
961C22C22×H(5,𝔽2)12yes—
962C22C22×H(5,𝔽2)11yescharacteristic
963C22C22×H(5,𝔽2)11yescharacteristic
964C22C2×#58512yes—
965C222−1+611yescharacteristic
966C4—28no—
967C4—24no—
968C4—24no—
969C4—22no—
970C4—24no—
971C4—44no—
972C4—42no—
973C4—44no—
974C4—42no—
975C4—44no—
976C4—48no—
977C4—42no—
978C4—41no—
979C4—42no—
980C4—44no—
981C4—44no—
982C4#354914yes—
983C2—84no—
984C2—88no—
985C2—82no—
986C2C2×#354911yescharacteristic
987C2#6289511yescharacteristic
988C2#6289712yes—
989C2#6301412yes—
990C2#6302411yescharacteristic
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. #59841C2semidirect
2. #59822C2semidirect
3. #59544C2semidirect
4. #58384C2semidirect
5. #57581C2semidirect
6. #52307C2semidirect
7. #51783C2semidirect
8. #48462C2semidirect
9. #46016C2semidirect
10. #45996C2semidirect
11. #45103C2semidirect
12. #44886C2semidirect
13. #42987C2semidirect
14. #42434C2semidirect
15. #39953C2semidirect
16. #39174C2semidirect
17. #37267C2semidirect
18. #37249C2semidirect
19. #36508C2semidirect
20. #36496C2semidirect
23. C2×#557C22semidirect
25. C2×#555C22semidirect
26. C2×#554C22semidirect
28. C2×#546C22semidirect
30. C2×#535C22semidirect
31. #2862C22semidirect
33. #2861C22semidirect
37. #2819C22semidirect
39. #2816C22semidirect
40. #2811C22semidirect
41. #2804C22semidirect
42. #2795C22semidirect
43. #2785C22semidirect
44. #2785C22semidirect
45. #2753C22semidirect
46. #2737C22semidirect
50. #2733C22semidirect
51. #2733C22semidirect
52. #2733C22semidirect
53. #2731C22semidirect
54. #2720C22semidirect
55. #2712C22semidirect
56. #2711C22semidirect
57. #2711C22semidirect
58. #2711C22semidirect
59. #2710C22semidirect
60. #2706C22semidirect
61. #2699C22semidirect
62. #2692C22semidirect
63. #2685C22semidirect
64. #2680C22semidirect
66. #2678C22semidirect
67. #2676C22semidirect
68. #2676C22semidirect
69. #2673C22semidirect
73. #2670C22semidirect
74. #2669C22semidirect
75. #2669C22semidirect
76. #2668C22semidirect
78. #2661C22semidirect
79. #2641C22semidirect
80. #2635C22semidirect
81. #2632C22semidirect
82. #2620C22semidirect
83. #2616C22semidirect
84. #2610C22semidirect
85. #2609C22semidirect
86. #2592C22semidirect
87. #2574C22semidirect
88. #2567C22semidirect
89. #2566C22semidirect
90. #2566C22semidirect
91. #2565C22semidirect
93. #2548C22semidirect
94. #2548C22semidirect
95. #2546C22semidirect
97. #2544C22semidirect
99. #2542C22semidirect
101. #2541C22semidirect
103. #2537C22semidirect
104. #2532C22semidirect
105. #2519C22semidirect
106. #2492C22semidirect
108. #2491C22semidirect
109. #2476C22semidirect
110. #2474C22semidirect
111. #2461C22semidirect
112. #2461C22semidirect
113. #2461C22semidirect
114. #2459C22semidirect
115. #2459C22semidirect
116. #2437C22semidirect
117. #2435C22semidirect
119. #2432C22semidirect
120. #2432C22semidirect
122. #2429C22semidirect
125. #2426C22semidirect
126. #2426C22semidirect
127. #2426C22semidirect
129. #2424C22semidirect
130. #2424C22semidirect
131. #2417C22semidirect
132. #2416C22semidirect
134. #2414C22semidirect
135. #2414C22semidirect
136. #2411C22semidirect
138. #2407C22semidirect
140. #2388C22semidirect
141. #2379C22semidirect
142. #2362C22semidirect
143. #2361C22semidirect
144. #2361C22semidirect
145. #2354C22semidirect
146. #2347C22semidirect
147. #2344C22semidirect
148. #2326C22semidirect
149. #2321C22semidirect
150. C4×C4⋊Q8C22semidirect
151. C4×#127C22semidirect
153. C4×#124C22semidirect
154. C4×#124C22semidirect
155. C4×#124C22semidirect
156. #2295C22semidirect
157. #2293C22semidirect
158. C42×Q8C22semidirect

Maximal subgroups

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

subgroupindex
#598412
#598222
#595442
#583842
#575812
#523072
#517832
#484622
#460162
#459962
#451032
#448862
#429872
#424342
#399532
#391742
#372672
#372492
#365082
#364962