Finite Group Databasebeta

← #7549063

Subgroups — #7549063

Order 512.

1779 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59016C211yesmaximal, characteristic
2#36516C211yesmaximal, characteristic
3#32068C211yesmaximal, characteristic, complemented
4#31998C211yesmaximal, characteristic, complemented
5#31951C211yesmaximal, characteristic, complemented
6#31772C211yesmaximal, characteristic, complemented
7#28782C211yesmaximal, characteristic, complemented
8#27721C211yesmaximal, characteristic, complemented
9#27345C211yesmaximal, characteristic, complemented
10#27177C211yesmaximal, characteristic, complemented
11#26429C211yesmaximal, characteristic, complemented
12#26358C211yesmaximal, characteristic, complemented
13#26220C211yesmaximal, characteristic, complemented
14#26145C211yesmaximal, characteristic, complemented
15#25979C211yesmaximal, characteristic, complemented
16#25561C211yesmaximal, characteristic, complemented
17#25545C211yesmaximal, characteristic, complemented
18#25219C211yesmaximal, characteristic, complemented
19#25118C211yesmaximal, characteristic, complemented
20#24880C211yesmaximal, characteristic, complemented
21#24791C211yesmaximal, characteristic, complemented
22#24559C211yesmaximal, characteristic, complemented
23#24386C211yesmaximal, characteristic, complemented
24#24122C211yesmaximal, characteristic, complemented
25#23036C211yesmaximal, characteristic, complemented
26#22881C211yesmaximal, characteristic, complemented
27#22850C211yesmaximal, characteristic
28#22711C211yesmaximal, characteristic, complemented
29#22497C211yesmaximal, characteristic, complemented
30#20911C211yesmaximal, characteristic, complemented
31#20846C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#554C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#484C2211yescharacteristic, complemented
37C2×#483C2211yescharacteristic
38C2×#477C2211yescharacteristic, complemented
39C2×#470C2211yescharacteristic
40C2×#470C2211yescharacteristic
41C2×#467C2211yescharacteristic, complemented
42C2×#451C2211yescharacteristic
43C2×C4×Q16C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C2×#428C2211yescharacteristic
48C2×#419C2211yescharacteristic
49C2×#419C2211yescharacteristic
50C2×#407C2211yescharacteristic
51C2×#407C2211yescharacteristic
52#2855—21no—
53#2848C2211yescharacteristic
54#2704—21no—
55#2692—21no—
56#2561—21no—
57#2549—21no—
58#2538C2211yescharacteristic
59#2534—21no—
60#2503C2211yescharacteristic
61#2502C2211yescharacteristic
62#2492C2211yescharacteristic
63#2486C2211yescharacteristic
64#2477—21no—
65#2477—21no—
66#2475—21no—
67#2475—21no—
68#2473—21no—
69#2450—21no—
70#2440C2211yescharacteristic
71#2439C2211yescharacteristic
72#2439C2211yescharacteristic
73#2437—21no—
74#2423C2211yescharacteristic
75#2417—21no—
76#2417C2211yescharacteristic
77#2417C2211yescharacteristic
78#2415C2211yescharacteristic
79#2415C2211yescharacteristic
80#2409C2211yescharacteristic
81#2362C2211yescharacteristic
82#2362C2211yescharacteristic
83#2360C2211yescharacteristic
84#2358—21no—
85#2352C2211yescharacteristic
86#2352C2211yescharacteristic
87D4×C4⋊C4C2211yescharacteristic
88#2345C2211yescharacteristic
89Q8×C22⋊C4C2211yescharacteristic
90C4×#123—21no—
91C4×#120C2211yescharacteristic
92C2×#380C2211yescharacteristic
93#2100C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2097C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2084C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic, complemented
103#2074C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2058C2211yescharacteristic, complemented
110#2057C2211yescharacteristic, complemented
111#2056C2211yescharacteristic, complemented
112#2036C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic, complemented
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2001C2211yescharacteristic
123#2001C2211yescharacteristic
124#2001C2211yescharacteristic, complemented
125#1993C2211yescharacteristic, complemented
126#1990C2211yescharacteristic, complemented
127#1988C2211yescharacteristic, complemented
128#1971C2211yescharacteristic, complemented
129#1971C2211yescharacteristic, complemented
130#1954C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1948C2211yescharacteristic, complemented
133#1943C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1935C2211yescharacteristic, complemented
136#1933C2211yescharacteristic, complemented
137#1928C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1924C2211yescharacteristic
142#1924C2211yescharacteristic
143#1918C2211yescharacteristic, complemented
144#1918C2211yescharacteristic, complemented
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1894C2211yescharacteristic
148#1894C2211yescharacteristic
149#1892C2211yescharacteristic, complemented
150#1878C2211yescharacteristic, complemented
151#1878C2211yescharacteristic, complemented
152#1873C2211yescharacteristic
153#1873C2211yescharacteristic
154#1873C2211yescharacteristic
155#1873C2211yescharacteristic
156#1872C2211yescharacteristic
157#1872C2211yescharacteristic
158#1872C2211yescharacteristic
159#1872C2211yescharacteristic
160#1872C2211yescharacteristic
161#1872C2211yescharacteristic
162#1872C2211yescharacteristic, complemented
163#1872C2211yescharacteristic, complemented
164#1870C2211yescharacteristic
165#1870C2211yescharacteristic
166#1869C2211yescharacteristic
167#1865C2211yescharacteristic, complemented
168#1865C2211yescharacteristic, complemented
169#1865C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1853C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic, complemented
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic, complemented
183#1851C2211yescharacteristic
184#1851C2211yescharacteristic
185#1836C2211yescharacteristic, complemented
186#1824C2211yescharacteristic, complemented
187#1823C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1807C2211yescharacteristic, complemented
191#1805C2211yescharacteristic, complemented
192#1803C2211yescharacteristic, complemented
193#1787C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1736C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#554—24no—
213#554—42no—
214#554—42no—
215#554—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125—21no—
219C2×#125—21no—
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—24no—
229C2×C22⋊Q8—42no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#120D411yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117—21no—
252C2×#117—42no—
253C2×#117—42no—
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4—21no—
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4—21no—
267C22×C22⋊C4—21no—
268C22×C22⋊C4—21no—
269C22×C42—21no—
270#484—42no—
271#483—42no—
272#477—42no—
273#470—24no—
274#470—42no—
275#467—42no—
276#451—24no—
277C4×Q16—42no—
278#435—24no—
279#435—42no—
280#428—42no—
281#428—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×#106C2311yescharacteristic
292C2×#106C2311yescharacteristic
293C2×#106C2311yescharacteristic
294C2×#106C2311yescharacteristic
295C2×#106C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297C2×C4⋊C8C2311yescharacteristic
298C2×C4⋊C8C2311yescharacteristic
299#419—42no—
300#419—42no—
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321#407—24no—
322#407—42no—
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#395—21no—
358#395—21no—
359#394—21no—
360#394—21no—
361#393—21no—
362#393—21no—
363#393—21no—
364#393—21no—
365#391—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
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#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386D411yescharacteristic
414#386D411yescharacteristic
415#386D411yescharacteristic
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385D411yescharacteristic
427#385D411yescharacteristic
428#385D411yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#379—21no—
453#379D411yescharacteristic
454C4×C4⋊C4—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C2×#95—21no—
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#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25C2×D411yescharacteristic
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4C2×D411yescharacteristic
516C22×D4C2×D411yescharacteristic
517C22×D4C2×D411yescharacteristic
518C23×C4—21no—
519C23×C4—22no—
520C23×C4—22no—
521C23×C4—22no—
522C23×C4—22no—
523C23×C4—21no—
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×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—22no—
550C2×M16—22no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—22no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#125—44no—
573#125—44no—
574#123—44no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—44no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—44no—
596C22⋊Q8—44no—
597C22⋊Q8—44no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—82no—
601C22⋊Q8#4114yes—
602#120—24no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—44no—
616C4×D4—44no—
617C4×D4—82no—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—41no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—44no—
627#117—44no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
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—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4—44no—
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
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—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—44no—
716C2×C22⋊C4—44no—
717C2×C22⋊C4—82no—
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—44no—
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—22no—
746#107—22no—
747#107—22no—
748#107—41no—
749#107—41no—
750#106—22no—
751#106—41no—
752#106—41no—
753#106—41no—
754#106—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758C4⋊C8—22no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—22no—
767#103—22no—
768#103—22no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781C22⋊C8—22no—
782C22⋊C8—22no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—22no—
786C22⋊C8—22no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8#4114yes—
792#97—22no—
793#97—41no—
794C4×C8—41no—
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#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836C24—22no—
837C24—22no—
838C24—22no—
839C24—41no—
840C24—41no—
841C24—41no—
842C24—41no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846C24C22×D411yescharacteristic
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—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—42no—
865C2×Q8—42no—
866C2×Q8—42no—
867C2×Q8—44no—
868C2×Q8—44no—
869C2×Q8—42no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—82no—
876C2×Q8—82no—
877C2×Q8C2×#4112yes—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4#13714yes—
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—22no—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—24no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—22no—
905C22×C4—22no—
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—21no—
917C22×C4—21no—
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—41no—
931C22×C4—41no—
932C22×C4—41no—
933C22×C4—44no—
934C22×C4—44no—
935C22×C4—44no—
936C22×C4—44no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
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×C4C2×#4112yes—
971C22×C4C2×#4112yes—
972C22×C4H(5,𝔽2)12yes—
973C22×C42−1+412yes—
974C22×C4C2511yescharacteristic
975Q16—44no—
976Q16—82no—
977M16—44no—
978M16—44no—
979M16—82no—
980M16—82no—
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×C8—82no—
1004C2×C8C2×#4112yes—
1005C2×C8C2×#4112yes—
1006C4⋊C4—24no—
1007C4⋊C4—24no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
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—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—41no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4C2×#4112yes—
1065C4⋊C4H(5,𝔽2)12yes—
1066C4⋊C4H(5,𝔽2)12yes—
1067C22⋊C4—24no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—22no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—81no—
1116C42—81no—
1117C42—81no—
1118C42—81no—
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—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—44no—
1144C23—44no—
1145C23—44no—
1146C23—82no—
1147C23—82no—
1148C23—82no—
1149C23—82no—
1150C23#54612yes—
1151C23#54712yes—
1152C23C2×#13712yes—
1153C23C2×#13712yes—
1154C23C23×D411yescharacteristic
1155Q8—22no—
1156Q8—22no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—84no—
1168Q8—162no—
1169Q8—162no—
1170D4—44no—
1171D4—44no—
1172D4—44no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—44no—
1213C2×C4—44no—
1214C2×C4—44no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
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—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4#54612yes—
1276C2×C4#54712yes—
1277C2×C4C2×#13712yes—
1278C2×C4C22×#4111yescharacteristic
1279C2×C4C22×#4111yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×2−1+411yescharacteristic
1284C8—22no—
1285C8—22no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—22no—
1302C22—22no—
1303C22—22no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—88no—
1321C22C2×#54611yescharacteristic
1322C22C2×#54711yescharacteristic
1323C22#348411yescharacteristic
1324C22C22×#13711yescharacteristic
1325C22#358511yescharacteristic
1326C22#358611yescharacteristic
1327C22#358611yescharacteristic
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—42no—
1335C4—42no—
1336C4—41no—
1337C4—41no—
1338C4—42no—
1339C4—41no—
1340C4—41no—
1341C4—42no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4#348111yescharacteristic
1355C4#351911yescharacteristic
1356C4#352011yescharacteristic
1357C4#353611yescharacteristic
1358C2—42no—
1359C2—42no—
1360C2—42no—
1361C2—42no—
1362C2#5909011yescharacteristic
1363C2#6115711yescharacteristic
1364C2#6118011yescharacteristic
1365C2#6125411yescharacteristic
1366C2#6126911yescharacteristic
1367C2#6157311yescharacteristic
1368C2#6164711yescharacteristic
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. #32068C2semidirect
4. #31998C2semidirect
5. #31951C2semidirect
6. #31772C2semidirect
7. #28782C2semidirect
8. #27721C2semidirect
9. #27345C2semidirect
10. #27177C2semidirect
11. #26429C2semidirect
12. #26358C2semidirect
13. #26220C2semidirect
14. #26145C2semidirect
15. #25979C2semidirect
16. #25561C2semidirect
17. #25545C2semidirect
18. #25219C2semidirect
19. #25118C2semidirect
20. #24880C2semidirect
21. #24791C2semidirect
22. #24559C2semidirect
23. #24386C2semidirect
24. #24122C2semidirect
25. #23036C2semidirect
26. #22881C2semidirect
28. #22711C2semidirect
29. #22497C2semidirect
30. #20911C2semidirect
31. #20846C2semidirect
36. C2×#484C22semidirect
38. C2×#477C22semidirect
41. C2×#467C22semidirect
43. C2×C4×Q16C22semidirect
93. #2100C22semidirect
94. #2099C22semidirect
95. #2097C22semidirect
96. #2097C22semidirect
97. #2088C22semidirect
98. #2085C22semidirect
99. #2084C22semidirect
102. #2077C22semidirect
103. #2074C22semidirect
104. #2072C22semidirect
105. #2068C22semidirect
106. #2068C22semidirect
107. #2066C22semidirect
108. #2066C22semidirect
109. #2058C22semidirect
110. #2057C22semidirect
111. #2056C22semidirect
114. #2036C22semidirect
117. #2035C22semidirect
118. #2035C22semidirect
119. #2035C22semidirect
120. #2024C22semidirect
121. #2024C22semidirect
124. #2001C22semidirect
125. #1993C22semidirect
126. #1990C22semidirect
127. #1988C22semidirect
128. #1971C22semidirect
129. #1971C22semidirect
131. #1949C22semidirect
132. #1948C22semidirect
133. #1943C22semidirect
134. #1941C22semidirect
135. #1935C22semidirect
136. #1933C22semidirect
137. #1928C22semidirect
138. #1928C22semidirect
139. #1927C22semidirect
140. #1927C22semidirect
143. #1918C22semidirect
144. #1918C22semidirect
149. #1892C22semidirect
150. #1878C22semidirect
151. #1878C22semidirect
162. #1872C22semidirect
163. #1872C22semidirect
167. #1865C22semidirect
168. #1865C22semidirect
169. #1865C22semidirect
170. #1863C22semidirect
178. #1853C22semidirect
182. #1852C22semidirect
185. #1836C22semidirect
186. #1824C22semidirect
190. #1807C22semidirect
191. #1805C22semidirect
192. #1803C22semidirect
194. #1776C22semidirect
195. #1763C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#590162
#365162
#320682
#319982
#319512
#317722
#287822
#277212
#273452
#271772
#264292
#263582
#262202
#261452
#259792
#255612
#255452
#252192
#251182
#248802
#247912
#245592
#243862
#241222
#230362
#228812
#228502
#227112
#224972
#209112
#208462