Finite Group Databasebeta

← #6894230

Subgroups — #6894230

Order 512.

1595 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37852C211yesmaximal, characteristic, complemented
2#37449C211yesmaximal, characteristic, complemented
3#32781C211yesmaximal, characteristic, complemented
4#32734C211yesmaximal, characteristic, complemented
5#32306C211yesmaximal, characteristic, complemented
6#32292C211yesmaximal, characteristic, complemented
7#32062C211yesmaximal, characteristic, complemented
8#31934C211yesmaximal, characteristic, complemented
9#31312C211yesmaximal, characteristic, complemented
10#31296C211yesmaximal, characteristic, complemented
11#31010C211yesmaximal, characteristic, complemented
12#30522C211yesmaximal, characteristic, complemented
13#30333C211yesmaximal, characteristic, complemented
14#30120C211yesmaximal, characteristic, complemented
15#29930C211yesmaximal, characteristic, complemented
16#29848C211yesmaximal, characteristic, complemented
17#29600C211yesmaximal, characteristic
18#28368C211yesmaximal, characteristic, complemented
19#27947C211yesmaximal, characteristic, complemented
20#27904C211yesmaximal, characteristic, complemented
21#27706C211yesmaximal, characteristic, complemented
22#27274C211yesmaximal, characteristic, complemented
23#25216C211yesmaximal, characteristic, complemented
24#25104C211yesmaximal, characteristic, complemented
25#24667C211yesmaximal, characteristic, complemented
26#24590C211yesmaximal, characteristic, complemented
27#24491C211yesmaximal, characteristic, complemented
28#24387C211yesmaximal, characteristic, complemented
29#24003C211yesmaximal, characteristic, complemented
30#23482C211yesmaximal, characteristic, complemented
31#22559C211yesmaximal, characteristic, complemented
32C2×#525C2211yescharacteristic
33C22×C22⋊Q8C2211yescharacteristic
34C2×#487C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#483C2211yescharacteristic
37C2×#483C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#463C2211yescharacteristic, complemented
41C2×#449C2211yescharacteristic
42C2×#448C2211yescharacteristic
43C2×#433C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#417C2211yescharacteristic
46C2×#417C2211yescharacteristic
47C2×#407C2211yescharacteristic
48#2847C2211yescharacteristic
49#2814—21no—
50#2814—21no—
51#2746—21no—
52#2741—21no—
53#2737—21no—
54#2717—21no—
55#2638—21no—
56#2638—21no—
57#2628C2211yescharacteristic
58#2624C2211yescharacteristic
59#2622—21no—
60#2622—21no—
61#2621C2211yescharacteristic
62#2621C2211yescharacteristic
63#2620C2211yescharacteristic
64#2620C2211yescharacteristic
65#2579—21no—
66#2579—21no—
67#2564—21no—
68#2510—21no—
69#2504C2211yescharacteristic
70#2504C2211yescharacteristic
71#2502C2211yescharacteristic
72#2499C2211yescharacteristic
73#2499C2211yescharacteristic
74#2495C2211yescharacteristic
75#2494C2211yescharacteristic
76#2491C2211yescharacteristic
77#2472—21no—
78#2440C2211yescharacteristic
79#2436C2211yescharacteristic
80#2434C2211yescharacteristic
81#2432C2211yescharacteristic
82#2432C2211yescharacteristic
83#2422C2211yescharacteristic
84#2418—21no—
85#2361C2211yescharacteristic
86#2345C2211yescharacteristic
87#2324C2211yescharacteristic
88#2314C2211yescharacteristic
89#2280C2211yescharacteristic
90C2×#380C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2094C2211yescharacteristic, complemented
97#2092C2211yescharacteristic, complemented
98#2092C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2083C2211yescharacteristic, complemented
102#2073C2211yescharacteristic, complemented
103#2072C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2065C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2054C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2042C2211yescharacteristic, complemented
116#2042C2211yescharacteristic, complemented
117#2042C2211yescharacteristic, complemented
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2035C2211yescharacteristic
127#2035C2211yescharacteristic
128#2035C2211yescharacteristic
129#2035C2211yescharacteristic
130#2034C2211yescharacteristic
131#2034C2211yescharacteristic
132#2034C2211yescharacteristic
133#2033C2211yescharacteristic
134#2033C2211yescharacteristic
135#2033C2211yescharacteristic
136#2024C2211yescharacteristic, complemented
137#2023C2211yescharacteristic, complemented
138#2013C2211yescharacteristic, complemented
139#2013C2211yescharacteristic, complemented
140#2012C2211yescharacteristic, complemented
141#2000C2211yescharacteristic
142#2000C2211yescharacteristic
143#2000C2211yescharacteristic
144#2000C2211yescharacteristic
145#1999C2211yescharacteristic
146#1999C2211yescharacteristic
147#1993C2211yescharacteristic, complemented
148#1983C2211yescharacteristic, complemented
149#1981C2211yescharacteristic, complemented
150#1981C2211yescharacteristic, complemented
151#1973C2211yescharacteristic, complemented
152#1972C2211yescharacteristic, complemented
153#1968C2211yescharacteristic, complemented
154#1968C2211yescharacteristic, complemented
155#1960C2211yescharacteristic, complemented
156#1959C2211yescharacteristic, complemented
157#1958C2211yescharacteristic, complemented
158#1949C2211yescharacteristic, complemented
159#1949C2211yescharacteristic, complemented
160#1948C2211yescharacteristic, complemented
161#1935C2211yescharacteristic, complemented
162#1935C2211yescharacteristic, complemented
163#1934C2211yescharacteristic, complemented
164#1933C2211yescharacteristic, complemented
165#1928C2211yescharacteristic, complemented
166#1928C2211yescharacteristic, complemented
167#1927C2211yescharacteristic, complemented
168#1927C2211yescharacteristic, complemented
169#1926C2211yescharacteristic, complemented
170#1925C2211yescharacteristic, complemented
171#1924C2211yescharacteristic
172#1924C2211yescharacteristic
173#1923C2211yescharacteristic
174#1923C2211yescharacteristic
175#1894C2211yescharacteristic
176#1894C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1874C2211yescharacteristic
180#1872C2211yescharacteristic
181#1872C2211yescharacteristic
182#1853C2211yescharacteristic
183#1853C2211yescharacteristic
184#1852C2211yescharacteristic
185#1851C2211yescharacteristic
186#1851C2211yescharacteristic
187#1847C2211yescharacteristic, complemented
188#1846C2211yescharacteristic, complemented
189#1834C2211yescharacteristic, complemented
190#1825C2211yescharacteristic
191#1818C2211yescharacteristic
192#1802C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1788C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1779C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1750C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#124—21no—
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218#525—42no—
219#525—42no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—42no—
226C2×C22⋊Q8—42no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253#487—42no—
254#483—42no—
255#483—42no—
256#482—42no—
257#468—42no—
258#468—42no—
259#463—42no—
260#449—42no—
261#448—42no—
262#433—42no—
263#428—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#417—42no—
281#417—42no—
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314#407—42no—
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#401—21no—
330#400—21no—
331#400—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#395—21no—
362#395—21no—
363#395—21no—
364#395—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#393—21no—
378#393—21no—
379#393—21no—
380#393—21no—
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#390—21no—
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—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#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#383—21no—
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#381D411yescharacteristic
446#381D411yescharacteristic
447#380—21no—
448#380—21no—
449#380—21no—
450#380D411yescharacteristic
451#380D411yescharacteristic
452#380D411yescharacteristic
453#380D411yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#379D411yescharacteristic
462#379D411yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4—21no—
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C2×#95—21no—
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#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—22no—
523C23×C4—22no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4—41no—
533C23×C4—41no—
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2×D411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×M16—22no—
553C2×M16—22no—
554C2×M16—22no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—82no—
577#123—44no—
578#123—82no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—44no—
592C22⋊Q8—44no—
593C22⋊Q8—82no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#120—44no—
605#120—82no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—44no—
609C4×D4—44no—
610C4×D4—82no—
611#117—22no—
612#117—22no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—44no—
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
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—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—82no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—41no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730#106—41no—
731#106—41no—
732C4⋊C8—22no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736#103—22no—
737#103—22no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#102—22no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778#97—41no—
779#97—41no—
780C4×C8—22no—
781C4×C8—41no—
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#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—22no—
826C24—22no—
827C24—21no—
828C24—21no—
829C24—41no—
830C24—41no—
831C24—41no—
832C24—41no—
833C24—41no—
834C24C22×D411yescharacteristic
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837#41—44no—
838#41—44no—
839#41—82no—
840#41—82no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—42no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—82no—
866C2×Q8—82no—
867C2×Q8—82no—
868C2×Q8—82no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—22no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—22no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—41no—
933C22×C4—41no—
934C22×C4—41no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—41no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—82no—
944C22×C4—82no—
945C22×C4—82no—
946C22×C4—82no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4H(5,𝔽2)12yes—
972C22×C4H(5,𝔽2)12yes—
973C22×C4C2511yescharacteristic
974SD16—82no—
975SD16—82no—
976SD16—82no—
977D8—82no—
978M16—44no—
979M16—82no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8H(5,𝔽2)12yes—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—42no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—44no—
1133C23—44no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—82no—
1149C23—82no—
1150C23—82no—
1151C23—82no—
1152C23—82no—
1153C23#53512yes—
1154C23#57712yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—84no—
1169Q8—162no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—84no—
1179D4—84no—
1180D4—84no—
1181D4—84no—
1182D4—162no—
1183D4—162no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—82no—
1271C2×C4—82no—
1272C2×C4—84no—
1273C2×C4—82no—
1274C2×C4—84no—
1275C2×C4—84no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4#53512yes—
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4#58511yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C8—22no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—88no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22C2×#53511yescharacteristic
1331C22#348511yescharacteristic
1332C22#349611yescharacteristic
1333C22C2×#57711yescharacteristic
1334C22#358511yescharacteristic
1335C22#358611yescharacteristic
1336C22#358611yescharacteristic
1337C4—22no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4#353311yescharacteristic
1363C4#353411yescharacteristic
1364C4#354211yescharacteristic
1365C4#354511yescharacteristic
1366C2—42no—
1367C2—42no—
1368C2—81no—
1369C2—161no—
1370C2—161no—
1371C2#4050911yescharacteristic
1372C2#6081011yescharacteristic
1373C2#6081311yescharacteristic
1374C2#6174511yescharacteristic
1375C2#6178211yescharacteristic
1376C2#6228411yescharacteristic
1377C2#6230811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#29600C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37852C2semidirect
2. #37449C2semidirect
3. #32781C2semidirect
4. #32734C2semidirect
5. #32306C2semidirect
6. #32292C2semidirect
7. #32062C2semidirect
8. #31934C2semidirect
9. #31312C2semidirect
10. #31296C2semidirect
11. #31010C2semidirect
12. #30522C2semidirect
13. #30333C2semidirect
14. #30120C2semidirect
15. #29930C2semidirect
16. #29848C2semidirect
18. #28368C2semidirect
19. #27947C2semidirect
20. #27904C2semidirect
21. #27706C2semidirect
22. #27274C2semidirect
23. #25216C2semidirect
24. #25104C2semidirect
25. #24667C2semidirect
26. #24590C2semidirect
27. #24491C2semidirect
28. #24387C2semidirect
29. #24003C2semidirect
30. #23482C2semidirect
31. #22559C2semidirect
34. C2×#487C22semidirect
40. C2×#463C22semidirect
91. #2101C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2097C22semidirect
96. #2094C22semidirect
97. #2092C22semidirect
98. #2092C22semidirect
99. #2085C22semidirect
100. #2084C22semidirect
101. #2083C22semidirect
102. #2073C22semidirect
103. #2072C22semidirect
104. #2072C22semidirect
105. #2068C22semidirect
106. #2068C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
110. #2065C22semidirect
111. #2055C22semidirect
112. #2054C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2042C22semidirect
116. #2042C22semidirect
117. #2042C22semidirect
136. #2024C22semidirect
137. #2023C22semidirect
138. #2013C22semidirect
139. #2013C22semidirect
140. #2012C22semidirect
147. #1993C22semidirect
148. #1983C22semidirect
149. #1981C22semidirect
150. #1981C22semidirect
151. #1973C22semidirect
152. #1972C22semidirect
153. #1968C22semidirect
154. #1968C22semidirect
155. #1960C22semidirect
156. #1959C22semidirect
157. #1958C22semidirect
158. #1949C22semidirect
159. #1949C22semidirect
160. #1948C22semidirect
161. #1935C22semidirect
162. #1935C22semidirect
163. #1934C22semidirect
164. #1933C22semidirect
165. #1928C22semidirect
166. #1928C22semidirect
167. #1927C22semidirect
168. #1927C22semidirect
169. #1926C22semidirect
170. #1925C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
187. #1847C22semidirect
188. #1846C22semidirect
189. #1834C22semidirect
192. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#378522
#374492
#327812
#327342
#323062
#322922
#320622
#319342
#313122
#312962
#310102
#305222
#303332
#301202
#299302
#298482
#296002
#283682
#279472
#279042
#277062
#272742
#252162
#251042
#246672
#245902
#244912
#243872
#240032
#234822
#225592