Finite Group Databasebeta

← #8460596

Subgroups — #8460596

Order 512.

5537 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59420C211yesmaximal, characteristic, complemented
2#59314C212yesmaximal, complemented
3#58982C214yesmaximal, complemented
4#54985C218yesmaximal, complemented
5#52992C214yesmaximal, complemented
6#47832C214yesmaximal, complemented
7#45675C214yesmaximal, complemented
8#45353C214yesmaximal, complemented
9#42535C214yesmaximal, complemented
10#42477C214yesmaximal, complemented
11#39726C212yesmaximal, complemented
12#39633C212yesmaximal, complemented
13#39367C214yesmaximal, complemented
14#38078C214yesmaximal, complemented
15#37629C211yesmaximal, characteristic, complemented
16#37330C214yesmaximal, complemented
17#36258C212yesmaximal, complemented
18#36179C211yesmaximal, characteristic, complemented
19#35280C212yesmaximal, complemented
20#34720C212yesmaximal, complemented
21C2×#559C2211yescharacteristic
22C2×#554C2214yescomplemented
23C2×#547C2214yescomplemented
24C2×#547C2212yescomplemented
25C2×#546C2214yes—
26C2×D42C2211yescharacteristic
27C2×#543C2214yescomplemented
28C2×#533C2212yescomplemented
29C2×C4×#41C2212yes—
30#2868C2211yescharacteristic, complemented
31#2857C2214yescomplemented
32#2857C2214yescomplemented
33#2856C2212yes—
34#2854C2214yes—
35#2841C2214yescomplemented
36#2836C2218yescomplemented
37#2830C2214yescomplemented
38#2827C2218yescomplemented
39#2814C2218yescomplemented
40#2798C2218yescomplemented
41#2790C2218yescomplemented
42#2771C2214yescomplemented
43#2741C2218yescomplemented
44#2735C2214yescomplemented
45#2732C2218yescomplemented
46#2729C2218yescomplemented
47#2720C2218yescomplemented
48#2708C2218yescomplemented
49#2707C2218yescomplemented
50#2707C2218yescomplemented
51#2704C2218yescomplemented
52#2697C2214yes—
53#2697C2218yescomplemented
54#2696C2218yescomplemented
55#2694C2218yescomplemented
56#2694C2218yescomplemented
57#2693C2218yescomplemented
58#2692C2218yescomplemented
59#2692C2218yescomplemented
60#2687C2218yescomplemented
61#2687C2218yescomplemented
62#2683C2218yescomplemented
63#2681C2218yescomplemented
64#2681C2218yescomplemented
65#2681C2218yescomplemented
66#2647C2214yescomplemented
67#2644C2214yescomplemented
68#2640C2214yescomplemented
69#2638C2214yescomplemented
70#2630C2218yescomplemented
71#2629C2218yescomplemented
72#2626C2218yescomplemented
73#2620C2214yescomplemented
74#2616C2214yescomplemented
75#2592C2214yescomplemented
76#2582C2214yescomplemented
77#2582C2212yescomplemented
78#2582C2211yescharacteristic, complemented
79#2551C2211yescharacteristic, complemented
80#2548C2212yes—
81#2545C2214yescomplemented
82#2542C2214yes—
83#2542C2212yescomplemented
84#2542C2214yescomplemented
85#2538C2212yes—
86#2538C2214yes—
87#2538C2212yes—
88#2538C2214yescomplemented
89#2534C2214yes—
90#2506C2214yescomplemented
91#2502C2214yescomplemented
92#2501C2214yescomplemented
93#2501C2214yescomplemented
94#2501C2214yescomplemented
95#2497C2214yescomplemented
96#2492C2214yescomplemented
97#2487C2214yescomplemented
98#2477C2214yescomplemented
99#2475C2214yescomplemented
100#2463C2214yescomplemented
101#2460C2214yescomplemented
102#2452C2214yes—
103#2452C2212yes—
104#2452C2214yescomplemented
105#2452C2214yescomplemented
106#2451C2214yescomplemented
107#2449C2218yescomplemented
108#2447C2214yescomplemented
109#2446C2212yescomplemented
110#2440C2214yescomplemented
111#2440C2214yescomplemented
112#2440C2214yescomplemented
113#2439C2212yescomplemented
114#2437C2218yescomplemented
115#2437C2214yescomplemented
116#2437C2218yescomplemented
117#2435C2214yes—
118#2432C2212yes—
119#2427C2214yes—
120#2427C2212yes—
121#2427C2214yescomplemented
122#2426C2214yes—
123#2426C2214yescomplemented
124#2424C2218yes—
125#2423C2214yescomplemented
126#2421C2212yescomplemented
127#2420C2214yes—
128#2418C2218yescomplemented
129#2418C2218yescomplemented
130#2417C2214yescomplemented
131#2417C2214yescomplemented
132#2417C2218yescomplemented
133#2416C2214yes—
134#2415C2212yescomplemented
135#2414C2214yes—
136#2411C2218yes—
137#2408C2214yes—
138#2407C2212yes—
139#2407C2218yescomplemented
140#2404C2214yescomplemented
141#2398C2214yescomplemented
142#2392C2214yescomplemented
143#2378C2214yescomplemented
144#2361C2214yes—
145Q8×C4⋊C4C2212yescomplemented
146D4×C4⋊C4C2212yes—
147D4×C22⋊C4C2214yes—
148D4×C22⋊C4C2214yes—
149#2326C2214yes—
150#2324C2214yescomplemented
151#2316C2214yescomplemented
152#2311C2214yes—
153C4×#127C2211yescharacteristic
154C4×#124C2212yes—
155C4×C22⋊Q8C2212yescomplemented
156C4×C22⋊Q8C2214yescomplemented
157C4×#121C2212yes—
158#2295C2212yescomplemented
159C2×#390C2214yes—
160#2290C2214yescomplemented
161C2×#384C2212yescomplemented
162C42×D4C2211yescharacteristic, complemented
163C22×#41C2312yes—
164C22×#41C2314yes—
165C23×D4C2314yes—
166#559—44no—
167#554—416no—
168#547—416no—
169#547—48no—
170#546—416no—
171D42—44no—
172#543—416no—
173#533—48no—
174C2×C4⋊Q8C2312yes—
175C2×C4⋊Q8C2312yes—
176C2×C4⋊Q8C2314yes—
177C2×C4⋊Q8C2312yes—
178C2×C4⋊Q8C2314yes—
179C2×#127C2311yescharacteristic
180C2×#125C2314yes—
181C2×#125C2318yes—
182C2×#124C2312yes—
183C2×#124C2314yes—
184C2×#124C2314yes—
185C2×#123C2318yes—
186C2×#123C2318yes—
187C2×#123C2318yes—
188C2×#123C2318yes—
189C2×#123C2314yes—
190C2×C22⋊Q8C2312yes—
191C2×C22⋊Q8C2314yes—
192C2×C22⋊Q8C2314yes—
193C2×C22⋊Q8C2318yes—
194C2×C22⋊Q8C2314yes—
195C2×C22⋊Q8C2314yes—
196C2×C22⋊Q8C2314yes—
197C2×C22⋊Q8C2318yes—
198C2×C22⋊Q8C2312yes—
199C2×C22⋊Q8C2318yes—
200C2×C22⋊Q8C2312yes—
201C2×C22⋊Q8C2314yes—
202C2×C22⋊Q8C2318yes—
203C2×C22⋊Q8C2318yes—
204C2×C22⋊Q8C2318yes—
205C2×C22⋊Q8C2318yes—
206C2×#121C2314yes—
207C2×#121C2312yes—
208C2×#121C2314yes—
209C2×#121C2314yes—
210C2×#121C2314yes—
211C2×#121C2318yes—
212C2×#120C2318yes—
213C2×#120C2314yes—
214C4×#41—48no—
215C2×C4×Q8C2312yes—
216C2×C4×Q8C2312yes—
217C2×C4×Q8C2314yes—
218C2×C4×Q8C2312yes—
219C2×C4×Q8C2314yes—
220C2×C4×D4C2312yes—
221C2×C4×D4C2312yes—
222C2×C4×D4C2314yes—
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2314yes—
225C2×C4×D4C2312yes—
226C2×C4×D4C2314yes—
227C2×C4×D4C2314yes—
228C2×C4×D4C2312yes—
229C2×C4×D4C2318yes—
230C2×C4×D4C2314yes—
231C2×C4×D4C2314yes—
232C2×#117C2314yes—
233C2×#117C2312yes—
234C2×#117C2314yes—
235C22×C4⋊C4C2314yes—
236C22×C4⋊C4C2314yes—
237C22×C4⋊C4C2314yes—
238C22×C4⋊C4C2314yes—
239C22×C22⋊C4C2314yes—
240C22×C22⋊C4C2318yes—
241C22×C22⋊C4C2318yes—
242C22×C42C2312yes—
243C22×C42C2314yes—
244#400C2314yes—
245#400C2318yes—
246#400C2314yes—
247#400C2318yes—
248#400C2318yes—
249#399C2314yes—
250#399C2318yes—
251#399C2318yes—
252#399C2318yes—
253#399C2314yes—
254#399C2318yes—
255#398C2318yes—
256#398C2318yes—
257#398C2314yes—
258#398C2318yes—
259#398C2318yes—
260#398C2318yes—
261#398C2318yes—
262#398C2318yes—
263#398C2318yes—
264#398C2314yes—
265#397C2314yes—
266#397C2318yes—
267#397C2318yes—
268#397C2318yes—
269#397C2318yes—
270#397C2318yes—
271#397C2314yes—
272#397C2314yes—
273#397C2314yes—
274#396C2318yes—
275#396C2318yes—
276#396C2318yes—
277#396C2318yes—
278#396C2318yes—
279#396C2318yes—
280#396C2318yes—
281#396C2318yes—
282#396C2318yes—
283#396C2318yes—
284#396C2318yes—
285#396C2314yes—
286#396C2314yes—
287#395C2314yes—
288#395C2318yes—
289#395C2318yes—
290#394C2318yes—
291#394C2318yes—
292#394C2318yes—
293#394C2314yes—
294#394C2318yes—
295#394C2318yes—
296#394C2318yes—
297#394C2314yes—
298#394C2318yes—
299#394C2314yes—
300#394C2314yes—
301#394C2314yes—
302#393C2318yes—
303#393C2314yes—
304#393C2318yes—
305#393C2314yes—
306#393C2314yes—
307#393C2318yes—
308#392C2318yes—
309#392C2314yes—
310#391C2314yes—
311#391C2314yes—
312#391C2314yes—
313#391C2318yes—
314#391C2312yes—
315#391C2318yes—
316#391C2312yes—
317#391C2312yes—
318#391C2312yes—
319#391C2314yes—
320#390C2312yes—
321#390C2314yes—
322#390C2314yes—
323#390C2314yes—
324#390C2314yes—
325#390C2318yes—
326#390C2314yes—
327#390C2312yes—
328#390C2314yes—
329#390C2314yes—
330#390C2314yes—
331#390C2314yes—
332#390C2318yes—
333#390C2318yes—
334#390C2312yes—
335#389C2314yes—
336#389C2314yes—
337#389C2314yes—
338#389C2314yes—
339#389C2318yes—
340#389C2318yes—
341#389C2314yes—
342#389C2318yes—
343#389C2312yes—
344#389C2314yes—
345#389C2314yes—
346#389C2318yes—
347#389C2314yes—
348#389C2312yes—
349#389C2314yes—
350#389C2312yes—
351#389C2312yes—
352#388C2318yes—
353#388C2318yes—
354#388C2318yes—
355#388C2318yes—
356#388C2318yes—
357#388C2318yes—
358#388C2318yes—
359#388C2318yes—
360#388C2314yes—
361#388C2314yes—
362#388C2314yes—
363#388C2314yes—
364#388C2314yes—
365#387C2314yes—
366#387C2314yes—
367#387C2318yes—
368#387C2314yes—
369#387C2318yes—
370#387C2314yes—
371#387C2314yes—
372#387C2314yes—
373#387C2314yes—
374#386C2318yes—
375#386C2318yes—
376#386C2318yes—
377#386C2318yes—
378#386C2318yes—
379#386C2318yes—
380#386C2318yes—
381#386C2318yes—
382#386C2314yes—
383#386C2314yes—
384#386C2314yes—
385#385C2318yes—
386#385C2318yes—
387#385C2318yes—
388#385C2318yes—
389#385C2318yes—
390#385C2318yes—
391#385C2314yes—
392#385C2318yes—
393#385C2318yes—
394#385C2314yes—
395#385C2314yes—
396#385C2314yes—
397#385C2314yes—
398#384C2311yescharacteristic
399#384C2314yes—
400#384C2312yes—
401#384C2314yes—
402#384C2314yes—
403#384C2314yes—
404#384C2312yes—
405#384C2314yes—
406#382C2312yes—
407#381C2314yes—
408#381C2314yes—
409#380C2318yes—
410#380C2318yes—
411#380C2318yes—
412#380C2318yes—
413#380C2312yes—
414#380C2318yes—
415#380C2314yes—
416#380C2314yes—
417#380C2314yes—
418#380C2318yes—
419#380C2314yes—
420#380C2314yes—
421#380C2312yes—
422#379C2318yes—
423#379C2318yes—
424#379C2314yes—
425C4×C4⋊C4C2314yes—
426C4×C4⋊C4C2312yes—
427C4×C4⋊C4C2314yes—
428C4×C4⋊C4C2312yes—
429C4×C4⋊C4C2314yes—
430C4×C4⋊C4C2311yescharacteristic
431C4×C22⋊C4C2314yes—
432C4×C22⋊C4C2314yes—
433C4×C22⋊C4C2314yes—
434C4×C22⋊C4C2312yes—
435C4×C22⋊C4C2314yes—
436C4×C22⋊C4C2312yes—
437C4×C22⋊C4C2312yes—
438#376C2314yes—
439C43C2311yescharacteristic
440C25C2414yes—
441C2×#41—28no—
442C2×#41—28no—
443C2×#41—416no—
444C2×#41—44no—
445C2×#41—48no—
446C22×Q8C2412yes—
447C22×Q8C2412yes—
448C22×Q8C2414yes—
449C22×Q8C2414yes—
450C22×Q8C2414yes—
451C22×D4—216no—
452C22×D4—48no—
453C22×D4—48no—
454C22×D4C2411yescharacteristic
455C22×D4C2414yes—
456C22×D4C2414yes—
457C22×D4C2414yes—
458C22×D4C2412yes—
459C22×D4C2412yes—
460C22×D4C2418yes—
461C22×D4C2418yes—
462C23×C4C2412yes—
463C23×C4C2414yes—
464C23×C4C2414yes—
465C23×C4C2412yes—
466C23×C4C2412yes—
467C23×C4C2414yes—
468C23×C4C2414yes—
469C23×C4C2418yes—
470C23×C4C2418yes—
471C23×C4C2414yes—
472C4⋊Q8—44no—
473C4⋊Q8—48no—
474C4⋊Q8—48no—
475C4⋊Q8—44no—
476C4⋊Q8—44no—
477#127—24no—
478#125—48no—
479#125—416no—
480#124—28no—
481#124—48no—
482#124—48no—
483#123—416no—
484#123—416no—
485#123—416no—
486#123—416no—
487#123—48no—
488C22⋊Q8—28no—
489C22⋊Q8—216no—
490C22⋊Q8—216no—
491C22⋊Q8—416no—
492C22⋊Q8—416no—
493C22⋊Q8—416no—
494C22⋊Q8—416no—
495C22⋊Q8—416no—
496C22⋊Q8—416no—
497C22⋊Q8—48no—
498C22⋊Q8—48no—
499C22⋊Q8—44no—
500C22⋊Q8—44no—
501C22⋊Q8—416no—
502C22⋊Q8—48no—
503C22⋊Q8—48no—
504#121—28no—
505#121—216no—
506#121—48no—
507#121—416no—
508#121—48no—
509#121—48no—
510#120—48no—
511#120—416no—
512C4×Q8—28no—
513C4×Q8—28no—
514C4×Q8—48no—
515C4×Q8—44no—
516C4×Q8—48no—
517C4×D4—216no—
518C4×D4—28no—
519C4×D4—24no—
520C4×D4—28no—
521C4×D4—44no—
522C4×D4—48no—
523C4×D4—48no—
524C4×D4—48no—
525C4×D4—48no—
526C4×D4—44no—
527C4×D4—48no—
528C4×D4—416no—
529#117—48no—
530#117—48no—
531#117—44no—
532C2×C4⋊C4—216no—
533C2×C4⋊C4—48no—
534C2×C4⋊C4—48no—
535C2×C4⋊C4—48no—
536C2×C4⋊C4C2414yes—
537C2×C4⋊C4C2414yes—
538C2×C4⋊C4C2412yes—
539C2×C4⋊C4C2414yes—
540C2×C4⋊C4C2418yes—
541C2×C4⋊C4C2418yes—
542C2×C4⋊C4C2412yes—
543C2×C4⋊C4C2414yes—
544C2×C4⋊C4C2412yes—
545C2×C4⋊C4C2412yes—
546C2×C4⋊C4C2412yes—
547C2×C4⋊C4C2414yes—
548C2×C4⋊C4C2414yes—
549C2×C4⋊C4C2412yes—
550C2×C4⋊C4C2414yes—
551C2×C4⋊C4C2414yes—
552C2×C4⋊C4C2414yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2414yes—
555C2×C4⋊C4C2418yes—
556C2×C4⋊C4C2418yes—
557C2×C4⋊C4C2414yes—
558C2×C4⋊C4C2414yes—
559C2×C4⋊C4C2414yes—
560C2×C4⋊C4C2418yes—
561C2×C4⋊C4C2418yes—
562C2×C4⋊C4C2414yes—
563C2×C4⋊C4C2414yes—
564C2×C4⋊C4C2414yes—
565C2×C4⋊C4C2418yes—
566C2×C4⋊C4C2414yes—
567C2×C4⋊C4C2418yes—
568C2×C4⋊C4C2418yes—
569C2×C4⋊C4C2418yes—
570C2×C4⋊C4C2418yes—
571C2×C4⋊C4C2414yes—
572C2×C4⋊C4C2414yes—
573C2×C4⋊C4C2411yescharacteristic
574C2×C22⋊C4—48no—
575C2×C22⋊C4—416no—
576C2×C22⋊C4—416no—
577C2×C22⋊C4C2414yes—
578C2×C22⋊C4C2414yes—
579C2×C22⋊C4C2414yes—
580C2×C22⋊C4C2418yes—
581C2×C22⋊C4C2418yes—
582C2×C22⋊C4C2414yes—
583C2×C22⋊C4C2414yes—
584C2×C22⋊C4C2414yes—
585C2×C22⋊C4C2412yes—
586C2×C22⋊C4C2412yes—
587C2×C22⋊C4C2412yes—
588C2×C22⋊C4C2414yes—
589C2×C22⋊C4C2414yes—
590C2×C22⋊C4C2414yes—
591C2×C22⋊C4C2418yes—
592C2×C22⋊C4C2418yes—
593C2×C22⋊C4C2418yes—
594C2×C22⋊C4C2418yes—
595C2×C22⋊C4C2418yes—
596C2×C22⋊C4C2414yes—
597C2×C22⋊C4C2414yes—
598C2×C22⋊C4C2414yes—
599C2×C22⋊C4C2414yes—
600C2×C22⋊C4C2418yes—
601C2×C22⋊C4C2418yes—
602C2×C22⋊C4C2414yes—
603C2×C22⋊C4C2418yes—
604C2×C22⋊C4C2418yes—
605C2×C22⋊C4C2414yes—
606C2×C22⋊C4C2418yes—
607C2×C22⋊C4C2418yes—
608C2×C22⋊C4C2414yes—
609C2×C22⋊C4C2414yes—
610C2×C22⋊C4C2414yes—
611C2×C22⋊C4C2418yes—
612C2×C42—28no—
613C2×C42—48no—
614C2×C42C2412yes—
615C2×C42C2414yes—
616C2×C42C2414yes—
617C2×C42C2412yes—
618C2×C42C2411yescharacteristic
619C2×C42C2414yes—
620C2×C42C2412yes—
621C2×C42C2412yes—
622C2×C42C2412yes—
623C2×C42C2414yes—
624C2×C42C2418yes—
625C2×C42C2414yes—
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628#95C2414yes—
629#95C2414yes—
630#95C2414yes—
631#95C2414yes—
632#95C2412yes—
633#95C2411yescharacteristic
634#95C2412yes—
635#95C2411yescharacteristic
636#95C2414yes—
637#95C2414yes—
638#95C2414yes—
639#95C2414yes—
640#95C2414yes—
641#95C2414yes—
642#95C2414yes—
643#95C2414yes—
644#95C2414yes—
645#95C2414yes—
646#95C2414yes—
647#95C2414yes—
648#95C2414yes—
649#95C2418yes—
650#95C2418yes—
651#95C2418yes—
652#95C2414yes—
653#95C2418yes—
654#95C2418yes—
655#95C2418yes—
656#95C2418yes—
657#95C2418yes—
658#95C2414yes—
659C24—216no—
660C24—44no—
661C24—48no—
662C24—44no—
663C24—44no—
664C24C2514yes—
665C24C2512yes—
666C24C2514yes—
667#41—432no—
668#41—832no—
669C2×Q8—24no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—24no—
676C2×Q8—24no—
677C2×Q8—44no—
678C2×Q8—48no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—48no—
682C2×D4—24no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—216no—
688C2×D4—216no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—24no—
692C2×D4—28no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—28no—
696C2×D4—44no—
697C2×D4—44no—
698C2×D4—42no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—48no—
702C2×D4—48no—
703C2×D4—42no—
704C2×D4—832no—
705C2×D42−1+418yes—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—28no—
709C22×C4—216no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—24no—
715C22×C4—24no—
716C22×C4—28no—
717C22×C4—24no—
718C22×C4—28no—
719C22×C4—28no—
720C22×C4—28no—
721C22×C4—44no—
722C22×C4—42no—
723C22×C4—44no—
724C22×C4—48no—
725C22×C4—48no—
726C22×C4—48no—
727C22×C4—44no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—44no—
731C22×C4—48no—
732C22×C4—44no—
733C22×C4—44no—
734C22×C4H(5,𝔽2)18yes—
735C22×C4C2511yescharacteristic
736C22×C4C2514yes—
737C22×C4C2512yes—
738C22×C4C2514yes—
739C22×C4C2514yes—
740C22×C4C2514yes—
741C22×C4C2514yes—
742C22×C4C2512yes—
743C22×C4C2514yes—
744C22×C4C2514yes—
745C22×C4C2518yes—
746C22×C4C2514yes—
747C22×C4C2511yescharacteristic
748C22×C4C2512yes—
749C22×C4C2511yescharacteristic
750C22×C4C2512yes—
751C22×C4C2512yes—
752C4⋊C4—28no—
753C4⋊C4—28no—
754C4⋊C4—216no—
755C4⋊C4—24no—
756C4⋊C4—28no—
757C4⋊C4—216no—
758C4⋊C4—24no—
759C4⋊C4—28no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—28no—
763C4⋊C4—24no—
764C4⋊C4—28no—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—24no—
769C4⋊C4—42no—
770C4⋊C4—44no—
771C4⋊C4—48no—
772C4⋊C4—48no—
773C4⋊C4—44no—
774C4⋊C4—44no—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—48no—
778C4⋊C4—48no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C4⋊C4—44no—
782C4⋊C4—48no—
783C4⋊C4—48no—
784C4⋊C4—48no—
785C4⋊C4—44no—
786C4⋊C4—48no—
787C4⋊C4—48no—
788C4⋊C4—44no—
789C4⋊C4H(5,𝔽2)14yes—
790C22⋊C4—28no—
791C22⋊C4—24no—
792C22⋊C4—28no—
793C22⋊C4—28no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—28no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—216no—
800C22⋊C4—216no—
801C22⋊C4—28no—
802C22⋊C4—24no—
803C22⋊C4—24no—
804C22⋊C4—48no—
805C22⋊C4—48no—
806C22⋊C4—48no—
807C22⋊C4—48no—
808C22⋊C4—48no—
809C22⋊C4—44no—
810C22⋊C4—48no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C22⋊C4—44no—
815C22⋊C4—44no—
816C22⋊C4—48no—
817C22⋊C4—48no—
818C22⋊C4—44no—
819C22⋊C4—48no—
820C22⋊C4—48no—
821C22⋊C4—44no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—44no—
825C42—24no—
826C42—24no—
827C42—24no—
828C42—28no—
829C42—28no—
830C42—24no—
831C42—22no—
832C42—28no—
833C42—24no—
834C42—44no—
835C42—44no—
836C42—41no—
837C42—48no—
838C42H(5,𝔽2)14yes—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—24no—
846C23—22no—
847C23—22no—
848C23—24no—
849C23—22no—
850C23—24no—
851C23—24no—
852C23—28no—
853C23—24no—
854C23—28no—
855C23—24no—
856C23—416no—
857C23—816no—
858C23—816no—
859C23—164no—
860C23—164no—
861C23C2×H(5,𝔽2)14yes—
862C23C2×2−1+418yes—
863C23C2611yescharacteristic
864Q8—48no—
865Q8—48no—
866Q8—88no—
867Q8—88no—
868Q8—164no—
869D4—28no—
870D4—216no—
871D4—416no—
872D4—416no—
873D4—416no—
874D4—84no—
875D4—816no—
876D4—816no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—21no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—216no—
885C2×C4—22no—
886C2×C4—24no—
887C2×C4—24no—
888C2×C4—24no—
889C2×C4—21no—
890C2×C4—22no—
891C2×C4—24no—
892C2×C4—24no—
893C2×C4—24no—
894C2×C4—24no—
895C2×C4—24no—
896C2×C4—28no—
897C2×C4—22no—
898C2×C4—24no—
899C2×C4—24no—
900C2×C4—28no—
901C2×C4—28no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—24no—
906C2×C4—24no—
907C2×C4—28no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—24no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—22no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—48no—
920C2×C4—416no—
921C2×C4—48no—
922C2×C4—416no—
923C2×C4—88no—
924C2×C4—88no—
925C2×C4—816no—
926C2×C4—168no—
927C2×C4—164no—
928C2×C4C2×H(5,𝔽2)12yes—
929C2×C4C2×H(5,𝔽2)12yes—
930C2×C4C2×H(5,𝔽2)14yes—
931C2×C4C2×H(5,𝔽2)14yes—
932C2×C4C2×H(5,𝔽2)14yes—
933C2×C4C2×H(5,𝔽2)14yes—
934C2×C4C2×2−1+414yes—
935C22—24no—
936C22—28no—
937C22—28no—
938C22—24no—
939C22—24no—
940C22—28no—
941C22—42no—
942C22—44no—
943C22—42no—
944C22—44no—
945C22—42no—
946C22—44no—
947C22—42no—
948C22—44no—
949C22—48no—
950C22—44no—
951C22—44no—
952C22—44no—
953C22—48no—
954C22—1616no—
955C22C22×H(5,𝔽2)11yescharacteristic
956C22C22×H(5,𝔽2)12yes—
957C22C22×H(5,𝔽2)11yescharacteristic
958C22C22×2−1+412yes—
959C222−1+611yescharacteristic
960C4—24no—
961C4—22no—
962C4—22no—
963C4—24no—
964C4—42no—
965C4—44no—
966C4—44no—
967C4—44no—
968C4—41no—
969C4—44no—
970C4—48no—
971C4—44no—
972C4—44no—
973C4—44no—
974C4—42no—
975C4—44no—
976C4#353618yes—
977C2—44no—
978C2—48no—
979C2—84no—
980C2C2×#353612yes—
981C2#6283211yescharacteristic
982C2#6291411yescharacteristic
983C2#6294212yes—
984C2#6301611yescharacteristic
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. #59420C2semidirect
2. #59314C2semidirect
3. #58982C2semidirect
4. #54985C2semidirect
5. #52992C2semidirect
6. #47832C2semidirect
7. #45675C2semidirect
8. #45353C2semidirect
9. #42535C2semidirect
10. #42477C2semidirect
11. #39726C2semidirect
12. #39633C2semidirect
13. #39367C2semidirect
14. #38078C2semidirect
15. #37629C2semidirect
16. #37330C2semidirect
17. #36258C2semidirect
18. #36179C2semidirect
19. #35280C2semidirect
20. #34720C2semidirect
22. C2×#554C22semidirect
23. C2×#547C22semidirect
24. C2×#547C22semidirect
27. C2×#543C22semidirect
28. C2×#533C22semidirect
30. #2868C22semidirect
31. #2857C22semidirect
32. #2857C22semidirect
35. #2841C22semidirect
36. #2836C22semidirect
37. #2830C22semidirect
38. #2827C22semidirect
39. #2814C22semidirect
40. #2798C22semidirect
41. #2790C22semidirect
42. #2771C22semidirect
43. #2741C22semidirect
44. #2735C22semidirect
45. #2732C22semidirect
46. #2729C22semidirect
47. #2720C22semidirect
48. #2708C22semidirect
49. #2707C22semidirect
50. #2707C22semidirect
51. #2704C22semidirect
53. #2697C22semidirect
54. #2696C22semidirect
55. #2694C22semidirect
56. #2694C22semidirect
57. #2693C22semidirect
58. #2692C22semidirect
59. #2692C22semidirect
60. #2687C22semidirect
61. #2687C22semidirect
62. #2683C22semidirect
63. #2681C22semidirect
64. #2681C22semidirect
65. #2681C22semidirect
66. #2647C22semidirect
67. #2644C22semidirect
68. #2640C22semidirect
69. #2638C22semidirect
70. #2630C22semidirect
71. #2629C22semidirect
72. #2626C22semidirect
73. #2620C22semidirect
74. #2616C22semidirect
75. #2592C22semidirect
76. #2582C22semidirect
77. #2582C22semidirect
78. #2582C22semidirect
79. #2551C22semidirect
81. #2545C22semidirect
83. #2542C22semidirect
84. #2542C22semidirect
88. #2538C22semidirect
90. #2506C22semidirect
91. #2502C22semidirect
92. #2501C22semidirect
93. #2501C22semidirect
94. #2501C22semidirect
95. #2497C22semidirect
96. #2492C22semidirect
97. #2487C22semidirect
98. #2477C22semidirect
99. #2475C22semidirect
100. #2463C22semidirect
101. #2460C22semidirect
104. #2452C22semidirect
105. #2452C22semidirect
106. #2451C22semidirect
107. #2449C22semidirect
108. #2447C22semidirect
109. #2446C22semidirect
110. #2440C22semidirect
111. #2440C22semidirect
112. #2440C22semidirect
113. #2439C22semidirect
114. #2437C22semidirect
115. #2437C22semidirect
116. #2437C22semidirect
121. #2427C22semidirect
123. #2426C22semidirect
125. #2423C22semidirect
126. #2421C22semidirect
128. #2418C22semidirect
129. #2418C22semidirect
130. #2417C22semidirect
131. #2417C22semidirect
132. #2417C22semidirect
134. #2415C22semidirect
139. #2407C22semidirect
140. #2404C22semidirect
141. #2398C22semidirect
142. #2392C22semidirect
143. #2378C22semidirect
145. Q8×C4⋊C4C22semidirect
150. #2324C22semidirect
151. #2316C22semidirect
155. C4×C22⋊Q8C22semidirect
156. C4×C22⋊Q8C22semidirect
158. #2295C22semidirect
160. #2290C22semidirect
161. C2×#384C22semidirect
162. C42×D4C22semidirect

Maximal subgroups

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

subgroupindex
#594202
#593142
#589822
#549852
#529922
#478322
#456752
#453532
#425352
#424772
#397262
#396332
#393672
#380782
#376292
#373302
#362582
#361792
#352802
#347202