Finite Group Databasebeta

← #7711865

Subgroups — #7711865

Order 512.

5852 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59861C214yesmaximal, complemented
2#59819C214yesmaximal, complemented
3#45808C214yesmaximal, complemented
4#45806C214yesmaximal, complemented
5#39841C218yesmaximal, complemented
6#39460C218yesmaximal, complemented
7#37898C212yesmaximal, complemented
8#37883C212yesmaximal, complemented
9#37710C212yesmaximal, complemented
10#37694C212yesmaximal, complemented
11#37437C212yesmaximal, complemented
12#37316C212yesmaximal, complemented
13#37315C212yesmaximal, complemented
14#36625C211yesmaximal, characteristic, complemented
15C2×#2856C211yesmaximal, characteristic, complemented
16#36369C214yesmaximal, complemented
17#36262C214yesmaximal, complemented
18#35295C212yesmaximal, complemented
19#35259C212yesmaximal, complemented
20#34363C212yesmaximal, complemented
21C4×#525C211yesmaximal, characteristic, complemented
22C2×#551C2218yes—
23C2×#540C2212yescomplemented
24C2×#533C2211yescharacteristic, complemented
25C22×#127C2211yescharacteristic
26C2×#525C2211yescharacteristic
27C22×#121C2212yes—
28C22×#121C2214yes—
29C2×C4×#41C2211yescharacteristic, complemented
30C23×C42C2211yescharacteristic
31#2860C2214yescomplemented
32#2857C2212yes—
33#2857C2212yescomplemented
34#2856C2212yes—
35#2856C2212yes—
36#2856C2214yes—
37#2856C2212yes—
38#2856C2212yes—
39#2856C2214yes—
40#2855C2214yescomplemented
41#2854C2214yescomplemented
42#2851C2212yes—
43#2851C2212yescomplemented
44#2848C2214yes—
45#2816C2214yescomplemented
46#2815C2214yescomplemented
47#2808C2214yescomplemented
48#2808C2214yescomplemented
49#2804C2214yescomplemented
50#2793C2218yescomplemented
51#2791C2218yescomplemented
52#2733C2214yescomplemented
53#2732C2214yescomplemented
54#2727C2214yescomplemented
55#2724C2214yescomplemented
56#2709C2218yescomplemented
57#2703C2218yescomplemented
58#2703C2218yescomplemented
59#2691C2218yescomplemented
60#2691C2218yescomplemented
61#2682C2214yescomplemented
62#2681C2218yescomplemented
63#2681C2218yescomplemented
64#2676C2218yescomplemented
65#2676C2218yescomplemented
66#2673C2218yescomplemented
67#2661C2218yescomplemented
68#2647C2212yescomplemented
69#2641C2212yescomplemented
70#2629C2212yescomplemented
71#2624C2214yescomplemented
72#2619C2212yescomplemented
73#2615C2214yescomplemented
74#2613C2218yes—
75#2602C2218yescomplemented
76#2601C2218yescomplemented
77#2597C2218yescomplemented
78#2597C2218yescomplemented
79#2593C2218yescomplemented
80#2561C2218yes—
81#2561C2214yes—
82#2560C2218yescomplemented
83#2559C2218yescomplemented
84#2559C2218yescomplemented
85#2557C2218yescomplemented
86#2554C2218yescomplemented
87#2554C2218yescomplemented
88#2539C2214yes—
89#2534C2218yes—
90#2512C2214yescomplemented
91#2507C2214yescomplemented
92#2497C2214yescomplemented
93#2491C2214yescomplemented
94#2486C2214yes—
95#2484C2218yes—
96#2479C2218yescomplemented
97#2476C2218yescomplemented
98#2476C2218yescomplemented
99#2464C2218yescomplemented
100#2464C2218yescomplemented
101#2458C2218yescomplemented
102#2458C2218yescomplemented
103#2456C2218yescomplemented
104#2456C2218yescomplemented
105#2456C2218yescomplemented
106#2452C2214yescomplemented
107#2445C2214yescomplemented
108#2428C2214yescomplemented
109#2426C2218yescomplemented
110#2422C2214yescomplemented
111#2414C2214yescomplemented
112#2414C2214yescomplemented
113#2413C2218yes—
114#2410C2218yes—
115#2408C2214yes—
116#2405C2218yes—
117#2377C2218yescomplemented
118#2374C2218yescomplemented
119#2363C2214yescomplemented
120#2363C2214yescomplemented
121#2363C2218yescomplemented
122#2344C2214yes—
123#2342C2218yes—
124#2342C2218yes—
125D4×C22⋊C4C2214yes—
126#2333C2214yescomplemented
127#2333C2214yescomplemented
128#2330C2212yescomplemented
129#2328C2212yescomplemented
130#2324C2214yescomplemented
131#2324C2214yescomplemented
132#2314C2212yescomplemented
133#2309C2214yes—
134#2308C2214yes—
135C4×C22⋊Q8C2214yes—
136C4×C22⋊Q8C2212yes—
137C4×C22⋊Q8C2214yescomplemented
138C4×C22⋊Q8C2212yescomplemented
139C4×#123C2214yescomplemented
140C4×#121C2212yes—
141C4×#121C2214yescomplemented
142C4×#121C2212yescomplemented
143C4×#120C2214yes—
144#2297C2211yescharacteristic, complemented
145#2296C2212yescomplemented
146#2296C2211yescharacteristic, complemented
147#2293C2214yescomplemented
148C2×#390C2212yes—
149C2×#390C2214yes—
150#2290C2212yes—
151#2290C2212yescomplemented
152#2285C2211yescharacteristic, complemented
153C2×#384C2211yescharacteristic
154#2280C2212yes—
155#2280C2211yescharacteristic
156C42×D4C2212yes—
157C42×D4C2212yescomplemented
158C4×#117C2211yescharacteristic, complemented
159C22×#41C2311yescharacteristic
160C23×D4C2314yes—
161C23×D4C2312yes—
162C23×D4C2314yes—
163C24×C4C2312yes—
164C24×C4C2311yescharacteristic
165#551—432no—
166#540—48no—
167#533—44no—
168C2×C4⋊Q8C2312yes—
169C2×#127—44no—
170C2×#127C2312yes—
171C2×#127C2314yes—
172C2×#127C2312yes—
173C2×#126C2318yes—
174C2×#126C2318yes—
175C2×#125C2312yes—
176C2×#124C2318yes—
177#525—28no—
178C2×#123C2312yes—
179C2×#123C2318yes—
180C2×#123C2318yes—
181C2×#123C2318yes—
182C2×#123C2318yes—
183C2×#123C2318yes—
184C2×C22⋊Q8C2311yescharacteristic
185C2×C22⋊Q8C2311yescharacteristic
186C2×C22⋊Q8C2314yes—
187C2×C22⋊Q8C2318yes—
188C2×C22⋊Q8C2314yes—
189C2×C22⋊Q8C2314yes—
190C2×#121—216no—
191C2×#121—416no—
192C2×#121C2314yes—
193C2×#121C2314yes—
194C2×#121C2314yes—
195C2×#121C2314yes—
196C2×#121C2311yescharacteristic
197C2×#121C2311yescharacteristic
198C2×#121C2314yes—
199C2×#121C2314yes—
200C2×#121C2318yes—
201C2×#121C2314yes—
202C2×#121C2314yes—
203C2×#121C2318yes—
204C2×#121C2314yes—
205C2×#121C2314yes—
206C2×#121C2318yes—
207C2×#121C2318yes—
208C2×#120C2312yes—
209C2×#120C2318yes—
210C4×#41—44no—
211C2×C4×Q8C2312yes—
212C2×C4×Q8C2314yes—
213C2×C4×D4C2312yes—
214C2×C4×D4C2312yes—
215C2×C4×D4C2314yes—
216C2×C4×D4C2314yes—
217C2×C4×D4C2314yes—
218C2×C4×D4C2318yes—
219C2×C4×D4C2312yes—
220C2×C4×D4C2314yes—
221C2×C4×D4C2314yes—
222C2×#117C2312yes—
223C2×#117C2311yescharacteristic
224C2×#117C2318yes—
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2318yes—
228C2×#117C2312yes—
229C2×#117C2312yes—
230C22×C4⋊C4C2312yes—
231C22×C4⋊C4C2314yes—
232C22×C22⋊C4C2314yes—
233C22×C22⋊C4C2318yes—
234C22×C22⋊C4C2318yes—
235C22×C42—44no—
236C22×C42C2311yescharacteristic
237C22×C42C2311yescharacteristic
238C22×C42C2311yescharacteristic
239C22×C42C2312yes—
240C22×C42C2312yes—
241C22×C42C2311yescharacteristic
242C22×C42C2311yescharacteristic
243C22×C42C2312yes—
244C22×C42C2311yescharacteristic
245C22×C42C2312yes—
246#400C2318yes—
247#400C2318yes—
248#399C2318yes—
249#398C2318yes—
250#398C2318yes—
251#398C2318yes—
252#398C2318yes—
253#398C2318yes—
254#397C2318yes—
255#397C2318yes—
256#397C2318yes—
257#397C2318yes—
258#396C2318yes—
259#396C2318yes—
260#396C2318yes—
261#396C2318yes—
262#394C2318yes—
263#394C2318yes—
264#394C2318yes—
265#394C2318yes—
266#394C2318yes—
267#394C2318yes—
268#394C2318yes—
269#394C2318yes—
270#394C2318yes—
271#394C2318yes—
272#394C2318yes—
273#394C2318yes—
274#394C2318yes—
275#393C2318yes—
276#393C2318yes—
277#393C2318yes—
278#392C2318yes—
279#392C2318yes—
280#392C2318yes—
281#392C2318yes—
282#392C2318yes—
283#392C2318yes—
284#392C2318yes—
285#392C2318yes—
286#391C2314yes—
287#391C2314yes—
288#391C2312yes—
289#390C2318yes—
290#390C2318yes—
291#390C2318yes—
292#390C2318yes—
293#390C2318yes—
294#390C2314yes—
295#390C2314yes—
296#390C2314yes—
297#390C2314yes—
298#390C2318yes—
299#390C2318yes—
300#390C2314yes—
301#390C2314yes—
302#390C2314yes—
303#390C2314yes—
304#390C2314yes—
305#390C2318yes—
306#390C2318yes—
307#390C2314yes—
308#390C2312yes—
309#389C2314yes—
310#389C2314yes—
311#389C2314yes—
312#389C2318yes—
313#389C2314yes—
314#389C2314yes—
315#389C2314yes—
316#389C2314yes—
317#389C2318yes—
318#389C2314yes—
319#389C2312yes—
320#389C2312yes—
321#388C2318yes—
322#388C2318yes—
323#388C2318yes—
324#388C2318yes—
325#388C2318yes—
326#388C2318yes—
327#388C2318yes—
328#388C2318yes—
329#388C2318yes—
330#388C2318yes—
331#388C2318yes—
332#388C2318yes—
333#388C2318yes—
334#388C2318yes—
335#388C2318yes—
336#388C2318yes—
337#388C2318yes—
338#388C2318yes—
339#388C2314yes—
340#388C2314yes—
341#387C2318yes—
342#387C2318yes—
343#387C2318yes—
344#387C2318yes—
345#387C2318yes—
346#387C2318yes—
347#387C2314yes—
348#387C2318yes—
349#387C2318yes—
350#387C2314yes—
351#386C2318yes—
352#386C2318yes—
353#386C2318yes—
354#386C2318yes—
355#386C2318yes—
356#386C2318yes—
357#386C2318yes—
358#386C2318yes—
359#386C2318yes—
360#386C2318yes—
361#386C2318yes—
362#386C2314yes—
363#386C2314yes—
364#386C2314yes—
365#386C2318yes—
366#385C2318yes—
367#385C2318yes—
368#385C2318yes—
369#385C2318yes—
370#385C2318yes—
371#385C2318yes—
372#385C2318yes—
373#385C2314yes—
374#385C2314yes—
375#385C2314yes—
376#384C2312yes—
377#384C2312yes—
378#384C2314yes—
379#384C2312yes—
380#382C2312yes—
381#381C2314yes—
382#381C2318yes—
383#381C2318yes—
384#381C2312yes—
385#380C2314yes—
386#380C2314yes—
387#380C2314yes—
388#380C2314yes—
389#380C2314yes—
390#380C2314yes—
391#380C2312yes—
392#380C2314yes—
393#380C2312yes—
394#379C2318yes—
395#379C2318yes—
396#379C2312yes—
397#379C2314yes—
398C4×C4⋊C4C2314yes—
399C4×C4⋊C4C2314yes—
400C4×C4⋊C4C2314yes—
401C4×C4⋊C4C2314yes—
402C4×C4⋊C4C2318yes—
403C4×C4⋊C4C2312yes—
404C4×C4⋊C4C2314yes—
405C4×C4⋊C4C2312yes—
406C4×C4⋊C4C2312yes—
407C4×C4⋊C4C2312yes—
408C4×C22⋊C4C2318yes—
409C4×C22⋊C4C2314yes—
410C4×C22⋊C4C2314yes—
411C4×C22⋊C4C2314yes—
412C4×C22⋊C4C2318yes—
413C4×C22⋊C4C2318yes—
414C4×C22⋊C4C2312yes—
415C4×C22⋊C4C2318yes—
416C4×C22⋊C4C2314yes—
417C4×C22⋊C4C2312yes—
418C4×C22⋊C4C2314yes—
419C4×C22⋊C4C2312yes—
420C4×C22⋊C4C2312yes—
421C4×C22⋊C4C2314yes—
422C4×C22⋊C4C2314yes—
423#376C2312yes—
424C43C2312yes—
425C25C2414yes—
426C25C2411yescharacteristic
427C2×#41—24no—
428C2×#41—42no—
429C2×#41—42no—
430C22×Q8C2411yescharacteristic
431C22×Q8C2414yes—
432C22×D4—216no—
433C22×D4—28no—
434C22×D4—44no—
435C22×D4—48no—
436C22×D4—44no—
437C22×D4—48no—
438C22×D4—48no—
439C22×D4—416no—
440C22×D4C2412yes—
441C22×D4C2414yes—
442C22×D4C2412yes—
443C22×D4C2412yes—
444C22×D4C2411yescharacteristic
445C22×D4C2418yes—
446C22×D4C2418yes—
447C22×D4C2414yes—
448C22×D4C2418yes—
449C22×D4C2414yes—
450C22×D4C2414yes—
451C22×D4C2418yes—
452C22×D4C2418yes—
453C23×C4—28no—
454C23×C4—42no—
455C23×C4—44no—
456C23×C4—42no—
457C23×C4—44no—
458C23×C4#4118yes—
459C23×C4C2414yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2412yes—
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2414yes—
470C23×C4C2418yes—
471C23×C4C2418yes—
472C23×C4C2411yescharacteristic
473C23×C4C2411yescharacteristic
474C23×C4C2411yescharacteristic
475C23×C4C2412yes—
476C4⋊Q8—44no—
477#127—28no—
478#127—44no—
479#127—48no—
480#126—416no—
481#126—416no—
482#125—28no—
483#124—416no—
484#123—28no—
485#123—416no—
486#123—416no—
487#123—416no—
488#123—416no—
489#123—416no—
490C22⋊Q8—24no—
491C22⋊Q8—24no—
492C22⋊Q8—216no—
493C22⋊Q8—416no—
494C22⋊Q8—48no—
495C22⋊Q8—48no—
496#121—216no—
497#121—216no—
498#121—216no—
499#121—216no—
500#121—24no—
501#121—24no—
502#121—48no—
503#121—416no—
504#121—48no—
505#121—416no—
506#121—48no—
507#121—48no—
508#121—416no—
509#121—416no—
510#121—48no—
511#121—48no—
512#120—28no—
513#120—416no—
514C4×Q8—44no—
515C4×Q8—48no—
516C4×D4—28no—
517C4×D4—28no—
518C4×D4—216no—
519C4×D4—44no—
520C4×D4—48no—
521C4×D4—48no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—416no—
525#117—24no—
526#117—28no—
527#117—42no—
528#117—42no—
529#117—416no—
530#117—416no—
531#117—44no—
532#117—44no—
533C2×C4⋊C4—28no—
534C2×C4⋊C4—48no—
535C2×C4⋊C4C2414yes—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2414yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2411yescharacteristic
542C2×C4⋊C4C2411yescharacteristic
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2414yes—
547C2×C4⋊C4C2418yes—
548C2×C4⋊C4C2418yes—
549C2×C4⋊C4C2414yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2418yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2418yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2412yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2418yes—
560C2×C4⋊C4C2414yes—
561C2×C22⋊C4—216no—
562C2×C22⋊C4—232no—
563C2×C22⋊C4—416no—
564C2×C22⋊C4C2414yes—
565C2×C22⋊C4C2418yes—
566C2×C22⋊C4C2418yes—
567C2×C22⋊C4C2418yes—
568C2×C22⋊C4C2418yes—
569C2×C22⋊C4C2418yes—
570C2×C22⋊C4C2418yes—
571C2×C22⋊C4C2418yes—
572C2×C22⋊C4C2414yes—
573C2×C22⋊C4C2412yes—
574C2×C22⋊C4C2412yes—
575C2×C22⋊C4C2412yes—
576C2×C22⋊C4C2414yes—
577C2×C22⋊C4C2412yes—
578C2×C22⋊C4C2412yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2412yes—
583C2×C22⋊C4C2418yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2414yes—
587C2×C22⋊C4C2418yes—
588C2×C22⋊C4C2418yes—
589C2×C22⋊C4C2414yes—
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⋊C4C2418yes—
600C2×C42—24no—
601C2×C42—24no—
602C2×C42—24no—
603C2×C42—44no—
604C2×C42—42no—
605C2×C42—42no—
606C2×C42—44no—
607C2×C42—44no—
608C2×C42—44no—
609C2×C42—42no—
610C2×C42C2412yes—
611C2×C42C2414yes—
612C2×C42C2412yes—
613C2×C42C2412yes—
614C2×C42C2412yes—
615C2×C42C2412yes—
616C2×C42C2411yescharacteristic
617C2×C42C2412yes—
618C2×C42C2411yescharacteristic
619C2×C42C2411yescharacteristic
620C2×C42C2418yes—
621C2×C42C2418yes—
622C2×C42C2414yes—
623C2×C42C2414yes—
624C2×C42C2414yes—
625C2×C42C2414yes—
626C2×C42C2412yes—
627C2×C42C2412yes—
628C2×C42C2412yes—
629C2×C42C2411yescharacteristic
630#95C2414yes—
631#95C2414yes—
632#95C2414yes—
633#95C2414yes—
634#95C2418yes—
635#95C2414yes—
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2418yes—
640#95C2418yes—
641#95C2418yes—
642#95C2418yes—
643#95C2418yes—
644#95C2418yes—
645#95C2418yes—
646#95C2418yes—
647#95C2418yes—
648#95C2418yes—
649#95C2418yes—
650#95C2418yes—
651C24—24no—
652C24—28no—
653C24—216no—
654C24—41no—
655C24—41no—
656C24—42no—
657C24—44no—
658C24—48no—
659C24—44no—
660C24C2×#4114yes—
661C24C2518yes—
662C24C2512yes—
663C24C2511yescharacteristic
664C24C2511yescharacteristic
665C24C2511yescharacteristic
666#41—416no—
667C2×Q8—22no—
668C2×Q8—28no—
669C2×Q8—41no—
670C2×Q8—41no—
671C2×Q8—44no—
672C2×Q8—44no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—28no—
677C2×D4—216no—
678C2×D4—216no—
679C2×D4—28no—
680C2×D4—22no—
681C2×D4—28no—
682C2×D4—28no—
683C2×D4—216no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—44no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—48no—
693C2×D4—44no—
694C2×D4—48no—
695C2×D4—44no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—44no—
703C2×D4—44no—
704C2×D4—44no—
705C2×D4—48no—
706C2×D4—44no—
707C2×D4—48no—
708C2×D4—48no—
709C2×D4—48no—
710C2×D4—816no—
711C2×D4—832no—
712C2×D4—832no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—24no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—24no—
721C22×C4—22no—
722C22×C4—28no—
723C22×C4—216no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—24no—
727C22×C4—24no—
728C22×C4—24no—
729C22×C4—24no—
730C22×C4—24no—
731C22×C4—24no—
732C22×C4—24no—
733C22×C4—24no—
734C22×C4—24no—
735C22×C4—28no—
736C22×C4—416no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4—41no—
742C22×C4—42no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—42no—
746C22×C4—42no—
747C22×C4—41no—
748C22×C4—42no—
749C22×C4—44no—
750C22×C4—48no—
751C22×C4—44no—
752C22×C4—48no—
753C22×C4—48no—
754C22×C4—48no—
755C22×C4—48no—
756C22×C4—48no—
757C22×C4—432no—
758C22×C4C2×#4114yes—
759C22×C4C2×#4114yes—
760C22×C4C2×#4114yes—
761C22×C4C2×#4114yes—
762C22×C4C2×#4114yes—
763C22×C4C2×#4114yes—
764C22×C4H(5,𝔽2)18yes—
765C22×C4C2512yes—
766C22×C4C2512yes—
767C22×C4C2514yes—
768C22×C4C2518yes—
769C22×C4C2514yes—
770C22×C4C2518yes—
771C22×C4C2518yes—
772C22×C4C2512yes—
773C22×C4C2511yescharacteristic
774C22×C4C2511yescharacteristic
775C22×C4C2511yescharacteristic
776C22×C4C2512yes—
777C22×C4C2512yes—
778C22×C4C2512yes—
779C22×C4C2512yes—
780C22×C4C2511yescharacteristic
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—22no—
784C4⋊C4—22no—
785C4⋊C4—24no—
786C4⋊C4—24no—
787C4⋊C4—28no—
788C4⋊C4—28no—
789C4⋊C4—216no—
790C4⋊C4—28no—
791C4⋊C4—216no—
792C4⋊C4—28no—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—216no—
796C4⋊C4—44no—
797C4⋊C4—48no—
798C4⋊C4—44no—
799C4⋊C4—42no—
800C4⋊C4—42no—
801C4⋊C4—48no—
802C4⋊C4—48no—
803C4⋊C4—48no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C4⋊C4—48no—
807C22⋊C4—24no—
808C22⋊C4—24no—
809C22⋊C4—24no—
810C22⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—216no—
813C22⋊C4—216no—
814C22⋊C4—24no—
815C22⋊C4—24no—
816C22⋊C4—216no—
817C22⋊C4—216no—
818C22⋊C4—216no—
819C22⋊C4—216no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—42no—
826C22⋊C4—44no—
827C22⋊C4—42no—
828C22⋊C4—48no—
829C22⋊C4—44no—
830C22⋊C4—48no—
831C22⋊C4—44no—
832C22⋊C4—48no—
833C22⋊C4—48no—
834C22⋊C4—48no—
835C22⋊C4—48no—
836C22⋊C4—48no—
837C22⋊C4—48no—
838C22⋊C4—48no—
839C22⋊C4—48no—
840C22⋊C4—48no—
841C22⋊C4—48no—
842C22⋊C4—48no—
843C42—24no—
844C42—22no—
845C42—24no—
846C42—24no—
847C42—24no—
848C42—22no—
849C42—22no—
850C42—24no—
851C42—28no—
852C42—24no—
853C42—42no—
854C42—42no—
855C42—42no—
856C42—44no—
857C42—44no—
858C42—48no—
859C42—48no—
860C42—44no—
861C42—44no—
862C42H(5,𝔽2)14yes—
863C23—21no—
864C23—21no—
865C23—22no—
866C23—21no—
867C23—21no—
868C23—22no—
869C23—22no—
870C23—21no—
871C23—22no—
872C23—21no—
873C23—22no—
874C23—28no—
875C23—22no—
876C23—28no—
877C23—28no—
878C23—28no—
879C23—22no—
880C23—24no—
881C23—28no—
882C23—24no—
883C23—28no—
884C23—28no—
885C23—28no—
886C23—22no—
887C23—44no—
888C23—44no—
889C23—48no—
890C23—48no—
891C23—416no—
892C23—88no—
893C23—816no—
894C23—816no—
895C23—88no—
896C23C22×#4112yes—
897C23C22×#4112yes—
898C23C22×#4112yes—
899C23C2×H(5,𝔽2)14yes—
900C23C2611yescharacteristic
901Q8—44no—
902Q8—88no—
903D4—44no—
904D4—48no—
905D4—48no—
906D4—48no—
907D4—416no—
908D4—88no—
909D4—816no—
910D4—88no—
911D4—88no—
912D4—816no—
913D4—816no—
914D4—816no—
915D4—168no—
916C2×C4—216no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—21no—
920C2×C4—22no—
921C2×C4—21no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—21no—
926C2×C4—22no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—21no—
930C2×C4—22no—
931C2×C4—28no—
932C2×C4—28no—
933C2×C4—28no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—28no—
937C2×C4—22no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—24no—
941C2×C4—28no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—28no—
945C2×C4—28no—
946C2×C4—28no—
947C2×C4—28no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—24no—
951C2×C4—28no—
952C2×C4—22no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—28no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—48no—
960C2×C4—48no—
961C2×C4—48no—
962C2×C4—48no—
963C2×C4—48no—
964C2×C4—416no—
965C2×C4—48no—
966C2×C4—88no—
967C2×C4—816no—
968C2×C4—168no—
969C2×C4C22×#4112yes—
970C2×C4C22×#4112yes—
971C2×C4C22×#4112yes—
972C2×C4C22×#4112yes—
973C2×C4C2×H(5,𝔽2)14yes—
974C2×C4C2×H(5,𝔽2)14yes—
975C2×C4C2×H(5,𝔽2)14yes—
976C2×C4C2×H(5,𝔽2)12yes—
977C2×C4#58514yes—
978C2×C4#58512yes—
979C22—24no—
980C22—22no—
981C22—22no—
982C22—24no—
983C22—22no—
984C22—22no—
985C22—22no—
986C22—22no—
987C22—22no—
988C22—22no—
989C22—416no—
990C22—42no—
991C22—42no—
992C22—42no—
993C22—42no—
994C22—48no—
995C22—44no—
996C22—48no—
997C22—42no—
998C22—48no—
999C22—42no—
1000C22—48no—
1001C22—42no—
1002C22—48no—
1003C22—44no—
1004C22—48no—
1005C22—48no—
1006C22—1616no—
1007C22#350814yes—
1008C22C23×#4111yescharacteristic
1009C22C22×H(5,𝔽2)12yes—
1010C22C22×H(5,𝔽2)11yescharacteristic
1011C22C2×#58511yescharacteristic
1012C22C2×#58512yes—
1013C4—22no—
1014C4—22no—
1015C4—22no—
1016C4—24no—
1017C4—24no—
1018C4—24no—
1019C4—24no—
1020C4—44no—
1021C4—48no—
1022C4—42no—
1023C4—48no—
1024C4—42no—
1025C4—42no—
1026C4—44no—
1027C4—48no—
1028C4#350514yes—
1029C2—24no—
1030C2—42no—
1031C2—42no—
1032C2—82no—
1033C2—88no—
1034C2#6275912yes—
1035C2C2×#350511yescharacteristic
1036C2C2×#350811yescharacteristic
1037C2#6281511yescharacteristic
1038C2#6281812yes—
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. #59861C2semidirect
2. #59819C2semidirect
3. #45808C2semidirect
4. #45806C2semidirect
5. #39841C2semidirect
6. #39460C2semidirect
7. #37898C2semidirect
8. #37883C2semidirect
9. #37710C2semidirect
10. #37694C2semidirect
11. #37437C2semidirect
12. #37316C2semidirect
13. #37315C2semidirect
14. #36625C2semidirect
15. C2×#2856C2semidirect
16. #36369C2semidirect
17. #36262C2semidirect
18. #35295C2semidirect
19. #35259C2semidirect
20. #34363C2semidirect
21. C4×#525C2semidirect
23. C2×#540C22semidirect
24. C2×#533C22semidirect
29. C2×C4×#41C22semidirect
31. #2860C22semidirect
33. #2857C22semidirect
40. #2855C22semidirect
41. #2854C22semidirect
43. #2851C22semidirect
45. #2816C22semidirect
46. #2815C22semidirect
47. #2808C22semidirect
48. #2808C22semidirect
49. #2804C22semidirect
50. #2793C22semidirect
51. #2791C22semidirect
52. #2733C22semidirect
53. #2732C22semidirect
54. #2727C22semidirect
55. #2724C22semidirect
56. #2709C22semidirect
57. #2703C22semidirect
58. #2703C22semidirect
59. #2691C22semidirect
60. #2691C22semidirect
61. #2682C22semidirect
62. #2681C22semidirect
63. #2681C22semidirect
64. #2676C22semidirect
65. #2676C22semidirect
66. #2673C22semidirect
67. #2661C22semidirect
68. #2647C22semidirect
69. #2641C22semidirect
70. #2629C22semidirect
71. #2624C22semidirect
72. #2619C22semidirect
73. #2615C22semidirect
75. #2602C22semidirect
76. #2601C22semidirect
77. #2597C22semidirect
78. #2597C22semidirect
79. #2593C22semidirect
82. #2560C22semidirect
83. #2559C22semidirect
84. #2559C22semidirect
85. #2557C22semidirect
86. #2554C22semidirect
87. #2554C22semidirect
90. #2512C22semidirect
91. #2507C22semidirect
92. #2497C22semidirect
93. #2491C22semidirect
96. #2479C22semidirect
97. #2476C22semidirect
98. #2476C22semidirect
99. #2464C22semidirect
100. #2464C22semidirect
101. #2458C22semidirect
102. #2458C22semidirect
103. #2456C22semidirect
104. #2456C22semidirect
105. #2456C22semidirect
106. #2452C22semidirect
107. #2445C22semidirect
108. #2428C22semidirect
109. #2426C22semidirect
110. #2422C22semidirect
111. #2414C22semidirect
112. #2414C22semidirect
117. #2377C22semidirect
118. #2374C22semidirect
119. #2363C22semidirect
120. #2363C22semidirect
121. #2363C22semidirect
126. #2333C22semidirect
127. #2333C22semidirect
128. #2330C22semidirect
129. #2328C22semidirect
130. #2324C22semidirect
131. #2324C22semidirect
132. #2314C22semidirect
137. C4×C22⋊Q8C22semidirect
138. C4×C22⋊Q8C22semidirect
139. C4×#123C22semidirect
141. C4×#121C22semidirect
142. C4×#121C22semidirect
144. #2297C22semidirect
145. #2296C22semidirect
146. #2296C22semidirect
147. #2293C22semidirect
151. #2290C22semidirect
152. #2285C22semidirect
157. C42×D4C22semidirect
158. C4×#117C22semidirect

Maximal subgroups

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

subgroupindex
#598612
#598192
#458082
#458062
#398412
#394602
#378982
#378832
#377102
#376942
#374372
#373162
#373152
#366252
C2×#28562
#363692
#362622
#352952
#352592
#343632
C4×#5252