Finite Group Databasebeta

← #7506973

Subgroups — #7506973

Order 512.

1627 conjugacy classes of subgroups.

The subgroup lattice has 1329 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35596C211yesmaximal, characteristic, complemented
2#35538C211yesmaximal, characteristic
3#31973C211yesmaximal, characteristic, complemented
4#31937C211yesmaximal, characteristic, complemented
5#31902C211yesmaximal, characteristic, complemented
6#31867C211yesmaximal, characteristic, complemented
7#31839C211yesmaximal, characteristic, complemented
8#31810C211yesmaximal, characteristic, complemented
9#31771C211yesmaximal, characteristic, complemented
10#31743C211yesmaximal, characteristic, complemented
11#31725C211yesmaximal, characteristic, complemented
12#31693C211yesmaximal, characteristic, complemented
13#31672C211yesmaximal, characteristic, complemented
14#31350C211yesmaximal, characteristic, complemented
15#31286C211yesmaximal, characteristic, complemented
16#31024C211yesmaximal, characteristic, complemented
17#30631C211yesmaximal, characteristic, complemented
18#30527C211yesmaximal, characteristic, complemented
19#23781C211yesmaximal, characteristic, complemented
20#23766C211yesmaximal, characteristic, complemented
21#23715C211yesmaximal, characteristic, complemented
22#23714C211yesmaximal, characteristic, complemented
23#23684C211yesmaximal, characteristic, complemented
24#23582C211yesmaximal, characteristic, complemented
25C4×#486C211yesmaximal, characteristic, complemented
26#21584C211yesmaximal, characteristic, complemented
27#21459C211yesmaximal, characteristic, complemented
28#21399C211yesmaximal, characteristic, complemented
29#21274C211yesmaximal, characteristic, complemented
30#21266C211yesmaximal, characteristic, complemented
31#20744C211yesmaximal, characteristic, complemented
32C2×#540C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#486C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#450C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#440C2211yescharacteristic, complemented
39C2×C4×SD16C2211yescharacteristic
40C2×#433C2211yescharacteristic
41C2×#433C2211yescharacteristic, complemented
42#2602—21no—
43#2597—21no—
44#2588—21no—
45#2585—21no—
46#2560—21no—
47#2539—21no—
48#2530—21no—
49#2529—21no—
50#2511C2211yescharacteristic, complemented
51#2508C2211yescharacteristic, complemented
52#2499C2211yescharacteristic, complemented
53#2496C2211yescharacteristic
54#2492C2211yescharacteristic
55#2485C2211yescharacteristic
56#2469—21no—
57#2456—21no—
58#2455—21no—
59#2454C2211yescharacteristic
60#2445C2211yescharacteristic
61#2441C2211yescharacteristic
62#2440C2211yescharacteristic, complemented
63#2433C2211yescharacteristic
64#2428C2211yescharacteristic
65#2424—21no—
66#2422C2211yescharacteristic
67#2421—21no—
68#2418—21no—
69#2417C2211yescharacteristic
70#2414—21no—
71#2414C2211yescharacteristic
72#2411—21no—
73#2408C2211yescharacteristic
74#2324C2211yescharacteristic
75#2324C2211yescharacteristic
76#2323C2211yescharacteristic
77#2323C2211yescharacteristic, complemented
78#2314C2211yescharacteristic
79C4×C4⋊Q8C2211yescharacteristic, complemented
80C4×#127C2211yescharacteristic
81#2295C2211yescharacteristic, complemented
82#2293C2211yescharacteristic
83#2293C2211yescharacteristic
84#2274C2211yescharacteristic, complemented
85#2099C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2094C2211yescharacteristic, complemented
88#2093C2211yescharacteristic
89#2087C2211yescharacteristic, complemented
90#2087C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2076C2211yescharacteristic
98#2075C2211yescharacteristic, complemented
99#2073C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2058C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic, complemented
114#2055C2211yescharacteristic, complemented
115#2041C2211yescharacteristic
116#2041C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic, complemented
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2026C2211yescharacteristic, complemented
126#2023C2211yescharacteristic
127#2014C2211yescharacteristic
128#2014C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic, complemented
133#1990C2211yescharacteristic, complemented
134#1989C2211yescharacteristic, complemented
135#1989C2211yescharacteristic, complemented
136#1982C2211yescharacteristic
137#1982C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1957C2211yescharacteristic
141#1954C2211yescharacteristic
142#1954C2211yescharacteristic
143#1941C2211yescharacteristic, complemented
144#1941C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1939C2211yescharacteristic, complemented
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic, complemented
152#1934C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1925C2211yescharacteristic
157#1923C2211yescharacteristic
158#1923C2211yescharacteristic
159#1923C2211yescharacteristic, complemented
160#1923C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1919C2211yescharacteristic, complemented
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1875C2211yescharacteristic
166#1875C2211yescharacteristic
167#1875C2211yescharacteristic, complemented
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic, complemented
170#1873C2211yescharacteristic
171#1864C2211yescharacteristic
172#1862C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic, complemented
175#1834C2211yescharacteristic, complemented
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1823C2211yescharacteristic, complemented
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1802C2211yescharacteristic
182#1802C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1776C2211yescharacteristic, complemented
187#1776C2211yescharacteristic, complemented
188C4×#106C2211yescharacteristic, complemented
189#1767C2211yescharacteristic, complemented
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic, complemented
194C4×#103C2211yescharacteristic, complemented
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202C42×C8C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207#540—24no—
208#540—42no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×#127C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#123—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#120—21no—
229C2×#120—21no—
230C2×#120—21no—
231#518—24no—
232#518—42no—
233C2×C4×Q8—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253#486—24no—
254#481—24no—
255#450—24no—
256#440—42no—
257#440—42no—
258C4×SD16—24no—
259#433—42no—
260#433—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#399—21no—
324#399—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#393—21no—
345#392—21no—
346#392—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#391—21no—
351#391—21no—
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390D411yescharacteristic
362#390D411yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389D411yescharacteristic
374#389D411yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388D411yescharacteristic
399#388D411yescharacteristic
400#388D411yescharacteristic
401#388D411yescharacteristic
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#382C2311yescharacteristic
431#380—21no—
432#380—21no—
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#379—21no—
440C4×C4⋊C4—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
457C43C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4C2×D411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×SD16—22no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—41no—
539#127—22no—
540#127—22no—
541#127—41no—
542#127—41no—
543#126—82no—
544#125—22no—
545#125—41no—
546#123—44no—
547#123—44no—
548#123—82no—
549#123—82no—
550C22⋊Q8—22no—
551C22⋊Q8—41no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554C22⋊Q8—82no—
555#121—22no—
556#121—22no—
557#121—22no—
558#121—44no—
559#121—44no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—41no—
565#121—82no—
566#120—82no—
567#120—82no—
568#120—82no—
569C4×Q8—22no—
570C4×Q8—22no—
571C4×Q8—82no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—44no—
584C4×D4—44no—
585C4×D4—82no—
586C4×D4—82no—
587C4×D4#4114yes—
588#117—22no—
589#117—22no—
590#117—22no—
591#117—22no—
592#117—22no—
593#117—41no—
594#117—41no—
595#117—41no—
596#117—82no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—44no—
673C2×C22⋊C4—44no—
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#106—22no—
707#106—22no—
708#106—22no—
709#106—41no—
710#106—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717#103—22no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102#4114yes—
743C22⋊C8—22no—
744C22⋊C8—22no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751#97—22no—
752#97—22no—
753C4×C8—22no—
754C4×C8—22no—
755C4×C8—22no—
756C4×C8—41no—
757C4×C8—41no—
758C4×C8—41no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797C24—21no—
798C24—21no—
799C24—21no—
800C24—42no—
801C24—42no—
802C24—42no—
803C24—81no—
804C24—81no—
805C24—81no—
806C24—81no—
807C24C22×D411yescharacteristic
808C24C22×D411yescharacteristic
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—42no—
816C2×Q8—42no—
817C2×Q8—81no—
818C2×D4—22no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—41no—
839C2×D4—41no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—44no—
846C2×D4—44no—
847C2×D4—44no—
848C2×D4—44no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4C2×#4112yes—
869C2×D4C2×#4112yes—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—24no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—81no—
902C22×C4—81no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C2511yescharacteristic
926SD16—44no—
927SD16—44no—
928SD16—44no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8C2×#4112yes—
953C4⋊C4—22no—
954C4⋊C4—22no—
955C4⋊C4—22no—
956C4⋊C4—22no—
957C4⋊C4—22no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—41no—
981C4⋊C4—41no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4C2×#4112yes—
1006C4⋊C4C2×#4112yes—
1007C22⋊C4—24no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C42—22no—
1049C42—22no—
1050C42—22no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—41no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—81no—
1064C42—81no—
1065C42—81no—
1066C42—81no—
1067C42—81no—
1068C42—81no—
1069C42C2×#4112yes—
1070C42H(5,𝔽2)12yes—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—22no—
1078C23—21no—
1079C23—22no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—48no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—162no—
1108C23—162no—
1109C23—162no—
1110C23—162no—
1111C23—162no—
1112C23—162no—
1113C23C23×D411yescharacteristic
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—84no—
1119D4—22no—
1120D4—22no—
1121D4—22no—
1122D4—22no—
1123D4—48no—
1124D4—41no—
1125D4—41no—
1126D4—41no—
1127D4—41no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—82no—
1133D4—84no—
1134D4—84no—
1135D4—162no—
1136D4—162no—
1137D4—162no—
1138D4—162no—
1139D4—162no—
1140D4—162no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—84no—
1220C2×C4—162no—
1221C2×C4—162no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4#54612yes—
1226C2×C4#54612yes—
1227C2×C4#57612yes—
1228C2×C4#57712yes—
1229C2×C4#57712yes—
1230C2×C4C22×#4111yescharacteristic
1231C2×C4C22×#4111yescharacteristic
1232C2×C4C2×H(5,𝔽2)11yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C8—22no—
1237C8—41no—
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C22—42no—
1245C22—41no—
1246C22—41no—
1247C22—42no—
1248C22—41no—
1249C22—41no—
1250C22—42no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—42no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—42no—
1263C22—42no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—168no—
1280C22#344911yescharacteristic
1281C22C2×#54611yescharacteristic
1282C22D4×#4111yescharacteristic
1283C22C2×#57611yescharacteristic
1284C22C2×#57711yescharacteristic
1285C22C2×#57711yescharacteristic
1286C22#358411yescharacteristic
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—41no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4#345511yescharacteristic
1313C4#346011yescharacteristic
1314C4#347511yescharacteristic
1315C4#352911yescharacteristic
1316C2—81no—
1317C2—81no—
1318C2—82no—
1319C2—82no—
1320C2—161no—
1321C2#5212911yescharacteristic
1322C2#6100111yescharacteristic
1323C2#6100611yescharacteristic
1324C2#6121211yescharacteristic
1325C2#6121511yescharacteristic
1326C2#6148111yescharacteristic
1327C2#6148911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35538C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #35596C2semidirect
3. #31973C2semidirect
4. #31937C2semidirect
5. #31902C2semidirect
6. #31867C2semidirect
7. #31839C2semidirect
8. #31810C2semidirect
9. #31771C2semidirect
10. #31743C2semidirect
11. #31725C2semidirect
12. #31693C2semidirect
13. #31672C2semidirect
14. #31350C2semidirect
15. #31286C2semidirect
16. #31024C2semidirect
17. #30631C2semidirect
18. #30527C2semidirect
19. #23781C2semidirect
20. #23766C2semidirect
21. #23715C2semidirect
22. #23714C2semidirect
23. #23684C2semidirect
24. #23582C2semidirect
25. C4×#486C2semidirect
26. #21584C2semidirect
27. #21459C2semidirect
28. #21399C2semidirect
29. #21274C2semidirect
30. #21266C2semidirect
31. #20744C2semidirect
38. C2×#440C22semidirect
41. C2×#433C22semidirect
50. #2511C22semidirect
51. #2508C22semidirect
52. #2499C22semidirect
62. #2440C22semidirect
77. #2323C22semidirect
79. C4×C4⋊Q8C22semidirect
81. #2295C22semidirect
84. #2274C22semidirect
85. #2099C22semidirect
86. #2099C22semidirect
87. #2094C22semidirect
89. #2087C22semidirect
90. #2087C22semidirect
91. #2087C22semidirect
92. #2086C22semidirect
93. #2085C22semidirect
94. #2083C22semidirect
98. #2075C22semidirect
99. #2073C22semidirect
100. #2072C22semidirect
101. #2068C22semidirect
104. #2067C22semidirect
105. #2066C22semidirect
108. #2065C22semidirect
109. #2059C22semidirect
110. #2058C22semidirect
113. #2055C22semidirect
114. #2055C22semidirect
117. #2036C22semidirect
121. #2034C22semidirect
125. #2026C22semidirect
132. #2000C22semidirect
133. #1990C22semidirect
134. #1989C22semidirect
135. #1989C22semidirect
143. #1941C22semidirect
144. #1941C22semidirect
145. #1939C22semidirect
146. #1939C22semidirect
151. #1934C22semidirect
152. #1934C22semidirect
153. #1933C22semidirect
154. #1933C22semidirect
159. #1923C22semidirect
160. #1923C22semidirect
161. #1920C22semidirect
162. #1919C22semidirect
167. #1875C22semidirect
169. #1874C22semidirect
174. #1854C22semidirect
175. #1834C22semidirect
178. #1823C22semidirect
186. #1776C22semidirect
187. #1776C22semidirect
188. C4×#106C22semidirect
189. #1767C22semidirect
193. #1762C22semidirect
194. C4×#103C22semidirect
198. C4×#102C22semidirect
199. C4×#102C22semidirect
201. #1750C22semidirect
202. C42×C8C22semidirect

Maximal subgroups

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

subgroupindex
#355962
#355382
#319732
#319372
#319022
#318672
#318392
#318102
#317712
#317432
#317252
#316932
#316722
#313502
#312862
#310242
#306312
#305272
#237812
#237662
#237152
#237142
#236842
#235822
C4×#4862
#215842
#214592
#213992
#212742
#212662
#207442