Finite Group Databasebeta

← #7525182

Subgroups — #7525182

Order 512.

1541 conjugacy classes of subgroups.

The subgroup lattice has 1263 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59200C211yesmaximal, characteristic
2#36427C211yesmaximal, characteristic
3#31795C211yesmaximal, characteristic, complemented
4#31691C211yesmaximal, characteristic, complemented
5#31439C211yesmaximal, characteristic, complemented
6#31323C211yesmaximal, characteristic, complemented
7#28780C211yesmaximal, characteristic, complemented
8#27707C211yesmaximal, characteristic, complemented
9#27668C211yesmaximal, characteristic, complemented
10#27105C211yesmaximal, characteristic, complemented
11#27058C211yesmaximal, characteristic, complemented
12#26419C211yesmaximal, characteristic, complemented
13#26311C211yesmaximal, characteristic, complemented
14#26207C211yesmaximal, characteristic, complemented
15#26012C211yesmaximal, characteristic, complemented
16#26003C211yesmaximal, characteristic, complemented
17#25239C211yesmaximal, characteristic, complemented
18#24964C211yesmaximal, characteristic, complemented
19#24946C211yesmaximal, characteristic, complemented
20#24944C211yesmaximal, characteristic, complemented
21#24596C211yesmaximal, characteristic, complemented
22#24561C211yesmaximal, characteristic, complemented
23#24554C211yesmaximal, characteristic, complemented
24#24106C211yesmaximal, characteristic, complemented
25#22939C211yesmaximal, characteristic, complemented
26#22846C211yesmaximal, characteristic
27#22707C211yesmaximal, characteristic, complemented
28#22622C211yesmaximal, characteristic, complemented
29#22496C211yesmaximal, characteristic, complemented
30#20845C211yesmaximal, characteristic, complemented
31#20699C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C22×#117C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#485C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×C8×D4C2211yescharacteristic
38C2×#428C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#407C2211yescharacteristic
41C22×C22⋊C8C2211yescharacteristic
42#2853—21no—
43#2848C2211yescharacteristic
44#2735—21no—
45#2685—21no—
46#2575—21no—
47#2573—21no—
48#2562C2211yescharacteristic
49#2526—21no—
50#2518—21no—
51#2516—21no—
52#2502C2211yescharacteristic
53#2497C2211yescharacteristic
54#2496C2211yescharacteristic
55#2487C2211yescharacteristic
56#2485C2211yescharacteristic
57#2485C2211yescharacteristic
58#2485C2211yescharacteristic
59#2482—21no—
60#2479—21no—
61#2479—21no—
62#2475—21no—
63#2475—21no—
64#2441C2211yescharacteristic
65#2441C2211yescharacteristic
66#2441C2211yescharacteristic
67#2441C2211yescharacteristic
68#2415C2211yescharacteristic
69#2415C2211yescharacteristic
70#2411—21no—
71#2373—21no—
72#2362C2211yescharacteristic
73#2362C2211yescharacteristic
74#2354C2211yescharacteristic
75#2354C2211yescharacteristic
76#2354C2211yescharacteristic
77#2354C2211yescharacteristic
78#2347C2211yescharacteristic
79#2346C2211yescharacteristic
80#2344C2211yescharacteristic
81C4×#120C2211yescharacteristic
82#2296—21no—
83#2280C2211yescharacteristic
84#2280C2211yescharacteristic
85#2100C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2084C2211yescharacteristic, complemented
95#2084C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic, complemented
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2035C2211yescharacteristic
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2026C2211yescharacteristic, complemented
117#1992C2211yescharacteristic, complemented
118#1992C2211yescharacteristic, complemented
119#1989C2211yescharacteristic, complemented
120#1989C2211yescharacteristic, complemented
121#1955C2211yescharacteristic
122#1947C2211yescharacteristic, complemented
123#1947C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1944C2211yescharacteristic, complemented
126#1943C2211yescharacteristic, complemented
127#1943C2211yescharacteristic, complemented
128#1942C2211yescharacteristic, complemented
129#1935C2211yescharacteristic, complemented
130#1933C2211yescharacteristic, complemented
131#1928C2211yescharacteristic, complemented
132#1928C2211yescharacteristic, complemented
133#1924C2211yescharacteristic
134#1923C2211yescharacteristic
135#1921C2211yescharacteristic, complemented
136#1921C2211yescharacteristic, complemented
137#1921C2211yescharacteristic, complemented
138#1920C2211yescharacteristic, complemented
139#1920C2211yescharacteristic, complemented
140#1919C2211yescharacteristic, complemented
141#1919C2211yescharacteristic, complemented
142#1918C2211yescharacteristic, complemented
143#1894C2211yescharacteristic
144#1894C2211yescharacteristic
145#1892C2211yescharacteristic
146#1892C2211yescharacteristic
147#1892C2211yescharacteristic, complemented
148#1873C2211yescharacteristic
149#1873C2211yescharacteristic
150#1873C2211yescharacteristic, complemented
151#1870C2211yescharacteristic
152#1869C2211yescharacteristic
153#1869C2211yescharacteristic
154#1865C2211yescharacteristic, complemented
155#1863C2211yescharacteristic, complemented
156#1854C2211yescharacteristic
157#1854C2211yescharacteristic
158#1854C2211yescharacteristic
159#1854C2211yescharacteristic
160#1854C2211yescharacteristic
161#1854C2211yescharacteristic
162#1854C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic, complemented
167#1854C2211yescharacteristic, complemented
168#1854C2211yescharacteristic, complemented
169#1851C2211yescharacteristic
170#1850C2211yescharacteristic
171#1834C2211yescharacteristic, complemented
172#1825C2211yescharacteristic
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic, complemented
179#1825C2211yescharacteristic, complemented
180#1824C2211yescharacteristic
181#1824C2211yescharacteristic
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic, complemented
188#1807C2211yescharacteristic
189#1807C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1753C2211yescharacteristic
195#1752C2211yescharacteristic
196#1736C2211yescharacteristic
197#1736C2211yescharacteristic
198#1735C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C24×C4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#552—24no—
210#552—42no—
211C2×#126—21no—
212C2×#126—21no—
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×#120D411yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227C2×#117—21no—
228C2×#117—21no—
229C2×#117—21no—
230C2×#117—24no—
231C2×#117—42no—
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245C22×C42—21no—
246#485—24no—
247#485—42no—
248#435—42no—
249C8×D4—24no—
250#428—24no—
251#428—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279#407—24no—
280C2×C22⋊C8—42no—
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#399—21no—
300#399—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#390—21no—
326#390—21no—
327#390—21no—
328#390—21no—
329#389—21no—
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389—21no—
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#386—21no—
383#386D411yescharacteristic
384#386D411yescharacteristic
385#386D411yescharacteristic
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385D411yescharacteristic
393#385D411yescharacteristic
394#385D411yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#383—21no—
400#382—21no—
401#381—21no—
402#381—21no—
403#381—21no—
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#379—21no—
421#379—21no—
422#379—21no—
423#379D411yescharacteristic
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376—21no—
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
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
490C25C2×D411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4C2×D411yescharacteristic
493C22×D4C2×D411yescharacteristic
494C22×D4C2×D411yescharacteristic
495C23×C4—21no—
496C23×C4—22no—
497C23×C4—22no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—21no—
501C23×C4—41no—
502C23×C4—41no—
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2×D411yescharacteristic
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—22no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533#126—44no—
534#126—44no—
535#125—22no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—44no—
540#123—44no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C22⋊Q8—22no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549#120—42no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—41no—
557C4×D4—41no—
558#117—22no—
559#117—22no—
560#117—22no—
561#117—22no—
562#117—22no—
563#117—22no—
564#117—22no—
565#117—22no—
566#117—22no—
567#117—44no—
568#117—44no—
569#117—41no—
570#117—41no—
571#117—41no—
572#117—41no—
573#117—41no—
574#117—44no—
575#117—44no—
576#117—41no—
577#117—41no—
578#117—41no—
579#117—41no—
580#117—41no—
581#117—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4#4114yes—
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
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—44no—
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
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—44no—
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696#107—22no—
697#107—22no—
698#107—22no—
699#107—41no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#106—22no—
705#106—22no—
706#106—22no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712C4⋊C8—22no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715#103—22no—
716#103—22no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723C22⋊C8—22no—
724C22⋊C8—22no—
725C22⋊C8—22no—
726C22⋊C8—22no—
727C22⋊C8—22no—
728C22⋊C8—22no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8#4114yes—
734#97—41no—
735#97—41no—
736C4×C8—22no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
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#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778C24—22no—
779C24—22no—
780C24—41no—
781C24—41no—
782C24—41no—
783C24—41no—
784C24—41no—
785C24C22×D411yescharacteristic
786C24C22×D411yescharacteristic
787C24C22×D411yescharacteristic
788C24C22×D411yescharacteristic
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—22no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—41no—
801C2×D4—41no—
802C2×D4—41no—
803C2×D4—41no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—24no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—41no—
848C22×C4—41no—
849C22×C4—41no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—42no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4H(5,𝔽2)12yes—
872C22×C42−1+412yes—
873C22×C4C2511yescharacteristic
874M16—44no—
875M16—44no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—82no—
899C2×C8—82no—
900C2×C8—82no—
901C2×C8C2×#4112yes—
902C2×C8C2×#4112yes—
903C4⋊C4—24no—
904C4⋊C4—22no—
905C4⋊C4—22no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—41no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4C2×#4112yes—
964C4⋊C4C2×#4112yes—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—42no—
1014C42—42no—
1015C42—42no—
1016C42—42no—
1017C42—42no—
1018C42—42no—
1019C42—42no—
1020C42—42no—
1021C42—42no—
1022C42—42no—
1023C42—42no—
1024C42—81no—
1025C42—81no—
1026C42—81no—
1027C42—81no—
1028C42—81no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—44no—
1056C23—44no—
1057C23—82no—
1058C23—82no—
1059C23—82no—
1060C23—82no—
1061C23—82no—
1062C23#54612yes—
1063C23#54712yes—
1064C23C23×D411yescharacteristic
1065Q8—41no—
1066Q8—41no—
1067Q8—41no—
1068Q8—41no—
1069D4—44no—
1070D4—82no—
1071D4—82no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—44no—
1110C2×C4—44no—
1111C2×C4—44no—
1112C2×C4—48no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—84no—
1168C2×C4#54612yes—
1169C2×C4#54712yes—
1170C2×C4#57512yes—
1171C2×C4C22×#4111yescharacteristic
1172C2×C4C22×#4111yescharacteristic
1173C2×C4C2×H(5,𝔽2)11yescharacteristic
1174C2×C4C2×2−1+411yescharacteristic
1175C2×C4#58511yescharacteristic
1176C2×C4#58511yescharacteristic
1177C8—22no—
1178C8—22no—
1179C8—41no—
1180C8—41no—
1181C8—41no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—41no—
1192C22—41no—
1193C22—41no—
1194C22—41no—
1195C22—41no—
1196C22—41no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—88no—
1214C22C2×#54611yescharacteristic
1215C22C2×#54711yescharacteristic
1216C22#348511yescharacteristic
1217C22C2×#57511yescharacteristic
1218C22#358411yescharacteristic
1219C22#358411yescharacteristic
1220C22#358611yescharacteristic
1221C4—22no—
1222C4—22no—
1223C4—22no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—42no—
1231C4—42no—
1232C4—41no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4#347511yescharacteristic
1248C4#349511yescharacteristic
1249C4#351311yescharacteristic
1250C4#353511yescharacteristic
1251C2—42no—
1252C2—42no—
1253C2—81no—
1254C2—81no—
1255C2#5901011yescharacteristic
1256C2#6115911yescharacteristic
1257C2#6117011yescharacteristic
1258C2#6124311yescharacteristic
1259C2#6127511yescharacteristic
1260C2#6174311yescharacteristic
1261C2#6176311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#120D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #31795C2semidirect
4. #31691C2semidirect
5. #31439C2semidirect
6. #31323C2semidirect
7. #28780C2semidirect
8. #27707C2semidirect
9. #27668C2semidirect
10. #27105C2semidirect
11. #27058C2semidirect
12. #26419C2semidirect
13. #26311C2semidirect
14. #26207C2semidirect
15. #26012C2semidirect
16. #26003C2semidirect
17. #25239C2semidirect
18. #24964C2semidirect
19. #24946C2semidirect
20. #24944C2semidirect
21. #24596C2semidirect
22. #24561C2semidirect
23. #24554C2semidirect
24. #24106C2semidirect
25. #22939C2semidirect
27. #22707C2semidirect
28. #22622C2semidirect
29. #22496C2semidirect
30. #20845C2semidirect
31. #20699C2semidirect
85. #2100C22semidirect
86. #2099C22semidirect
87. #2099C22semidirect
88. #2099C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2087C22semidirect
92. #2086C22semidirect
93. #2084C22semidirect
94. #2084C22semidirect
95. #2084C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
101. #2076C22semidirect
103. #2075C22semidirect
104. #2072C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
112. #2036C22semidirect
115. #2035C22semidirect
116. #2026C22semidirect
117. #1992C22semidirect
118. #1992C22semidirect
119. #1989C22semidirect
120. #1989C22semidirect
122. #1947C22semidirect
123. #1947C22semidirect
124. #1947C22semidirect
125. #1944C22semidirect
126. #1943C22semidirect
127. #1943C22semidirect
128. #1942C22semidirect
129. #1935C22semidirect
130. #1933C22semidirect
131. #1928C22semidirect
132. #1928C22semidirect
135. #1921C22semidirect
136. #1921C22semidirect
137. #1921C22semidirect
138. #1920C22semidirect
139. #1920C22semidirect
140. #1919C22semidirect
141. #1919C22semidirect
142. #1918C22semidirect
147. #1892C22semidirect
150. #1873C22semidirect
154. #1865C22semidirect
155. #1863C22semidirect
166. #1854C22semidirect
167. #1854C22semidirect
168. #1854C22semidirect
171. #1834C22semidirect
178. #1825C22semidirect
179. #1825C22semidirect
187. #1808C22semidirect
189. #1807C22semidirect
190. #1803C22semidirect
191. #1776C22semidirect
192. C4×#106C22semidirect
193. #1763C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#592002
#364272
#317952
#316912
#314392
#313232
#287802
#277072
#276682
#271052
#270582
#264192
#263112
#262072
#260122
#260032
#252392
#249642
#249462
#249442
#245962
#245612
#245542
#241062
#229392
#228462
#227072
#226222
#224962
#208452
#206992