Finite Group Databasebeta

← #6475684

Subgroups — #6475684

Order 512.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35310C211yesmaximal, characteristic, complemented
2#34202C211yesmaximal, characteristic
3#33156C211yesmaximal, characteristic, complemented
4#33117C211yesmaximal, characteristic, complemented
5#32968C211yesmaximal, characteristic, complemented
6#32916C211yesmaximal, characteristic, complemented
7#29895C211yesmaximal, characteristic, complemented
8#29894C211yesmaximal, characteristic, complemented
9#29601C211yesmaximal, characteristic
10#29601C211yesmaximal, characteristic
11#29489C211yesmaximal, characteristic, complemented
12#29488C211yesmaximal, characteristic, complemented
13#29471C211yesmaximal, characteristic, complemented
14#29470C211yesmaximal, characteristic, complemented
15#29417C211yesmaximal, characteristic, complemented
16#29415C211yesmaximal, characteristic, complemented
17#29414C211yesmaximal, characteristic, complemented
18#29411C211yesmaximal, characteristic, complemented
19#27643C211yesmaximal, characteristic, complemented
20#27640C211yesmaximal, characteristic, complemented
21#24707C211yesmaximal, characteristic, complemented
22#24704C211yesmaximal, characteristic, complemented
23#24659C211yesmaximal, characteristic, complemented
24#24652C211yesmaximal, characteristic, complemented
25#24165C211yesmaximal, characteristic, complemented
26#24163C211yesmaximal, characteristic, complemented
27#22094C211yesmaximal, characteristic, complemented
28#22092C211yesmaximal, characteristic, complemented
29#22057C211yesmaximal, characteristic, complemented
30#22057C211yesmaximal, characteristic, complemented
31#20717C211yesmaximal, characteristic, complemented
32C2×#541C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C2×#520C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#479C2211yescharacteristic, complemented
39C2×#478C2211yescharacteristic, complemented
40C2×#462C2211yescharacteristic, complemented
41C2×#461C2211yescharacteristic, complemented
42C2×#452C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#432C2211yescharacteristic
45C2×#431C2211yescharacteristic
46#2857C2211yescharacteristic
47#2851C2211yescharacteristic
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2629C2211yescharacteristic
51#2625C2211yescharacteristic
52#2625C2211yescharacteristic
53#2621C2211yescharacteristic
54#2480—21no—
55#2480—21no—
56#2478—21no—
57#2478—21no—
58#2475—21no—
59#2475—21no—
60#2473—21no—
61#2473—21no—
62#2359—21no—
63#2359—21no—
64#2358—21no—
65#2358—21no—
66#2354—21no—
67#2352—21no—
68#2352—21no—
69D4×C4⋊C4—21no—
70#2324C2211yescharacteristic
71#2324C2211yescharacteristic
72#2323C2211yescharacteristic
73#2323C2211yescharacteristic
74#2323C2211yescharacteristic
75#2323C2211yescharacteristic
76#2317C2211yescharacteristic
77#2314C2211yescharacteristic
78#2311C2211yescharacteristic
79C4×C22⋊Q8C2211yescharacteristic
80C4×C22⋊Q8C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C2×#380C2211yescharacteristic
86#2274C2211yescharacteristic
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2076C2211yescharacteristic
90#2076C2211yescharacteristic
91#2076C2211yescharacteristic
92#2076C2211yescharacteristic
93#2075C2211yescharacteristic
94#2075C2211yescharacteristic
95#2036C2211yescharacteristic
96#2036C2211yescharacteristic
97#2036C2211yescharacteristic
98#2036C2211yescharacteristic
99#2036C2211yescharacteristic
100#2036C2211yescharacteristic
101#2036C2211yescharacteristic
102#2036C2211yescharacteristic
103#2035C2211yescharacteristic
104#2035C2211yescharacteristic
105#2035C2211yescharacteristic
106#2035C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2001C2211yescharacteristic
112#2001C2211yescharacteristic
113#2001C2211yescharacteristic
114#2001C2211yescharacteristic
115#2000C2211yescharacteristic
116#2000C2211yescharacteristic
117#2000C2211yescharacteristic
118#2000C2211yescharacteristic
119#1989C2211yescharacteristic, complemented
120#1989C2211yescharacteristic, complemented
121#1981C2211yescharacteristic, complemented
122#1981C2211yescharacteristic, complemented
123#1973C2211yescharacteristic, complemented
124#1973C2211yescharacteristic, complemented
125#1969C2211yescharacteristic, complemented
126#1969C2211yescharacteristic, complemented
127#1949C2211yescharacteristic, complemented
128#1949C2211yescharacteristic, complemented
129#1947C2211yescharacteristic, complemented
130#1947C2211yescharacteristic, complemented
131#1944C2211yescharacteristic, complemented
132#1943C2211yescharacteristic, complemented
133#1942C2211yescharacteristic, complemented
134#1941C2211yescharacteristic, complemented
135#1935C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1934C2211yescharacteristic, complemented
140#1934C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1927C2211yescharacteristic, complemented
149#1925C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1921C2211yescharacteristic, complemented
152#1921C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1920C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1880C2211yescharacteristic, complemented
160#1880C2211yescharacteristic, complemented
161#1878C2211yescharacteristic, complemented
162#1878C2211yescharacteristic, complemented
163#1878C2211yescharacteristic, complemented
164#1878C2211yescharacteristic, complemented
165#1877C2211yescharacteristic, complemented
166#1877C2211yescharacteristic, complemented
167#1872C2211yescharacteristic
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1872C2211yescharacteristic
171#1865C2211yescharacteristic, complemented
172#1865C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic, complemented
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1817C2211yescharacteristic
186#1817C2211yescharacteristic
187#1805C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1802C2211yescharacteristic, complemented
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1798C2211yescharacteristic
194#1798C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1779C2211yescharacteristic
198#1779C2211yescharacteristic
199#1750C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C24×C4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#541—42no—
210#541—42no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217#525—24no—
218#525—24no—
219C2×#123—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231#520—42no—
232#520—42no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117—42no—
247C2×#117—42no—
248C2×#117D411yescharacteristic
249C2×#117D411yescharacteristic
250C2×#117D411yescharacteristic
251C2×#117D411yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4—21no—
258C22×C4⋊C4D411yescharacteristic
259C22×C4⋊C4D411yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4D411yescharacteristic
264C22×C22⋊C4D411yescharacteristic
265C22×C42C2311yescharacteristic
266C22×C42C2311yescharacteristic
267#485—24no—
268#485—24no—
269#479—42no—
270#478—42no—
271#462—42no—
272#461—42no—
273#452—24no—
274#452—24no—
275#432—42no—
276#431—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400—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#396—21no—
348#396—21no—
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#384—21no—
422#384C2311yescharacteristic
423#382—21no—
424#382C2311yescharacteristic
425#380—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380—21no—
430#380—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C2×#95—21no—
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#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—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41#4114yes—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—41no—
518C23×C4—41no—
519C23×C4—41no—
520C23×C4—41no—
521C23×C4C2×D411yescharacteristic
522C23×C4C2×D411yescharacteristic
523C23×C4C2×D411yescharacteristic
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553#126—44no—
554#126—44no—
555#125—22no—
556#125—22no—
557#125—44no—
558#125—44no—
559#123—28no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#120—28no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×Q8—41no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×D4—28no—
590C4×D4—28no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—44no—
596C4×D4—44no—
597C4×D4—82no—
598C4×D4—82no—
599#117—22no—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—41no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—42no—
609#117—42no—
610#117—42no—
611#117—42no—
612#117—44no—
613#117#4114yes—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—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—42no—
643C2×C4⋊C4—42no—
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⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
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—42no—
697C2×C22⋊C4—42no—
698C2×C22⋊C4—82no—
699C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
708C2×C42—22no—
709C2×C42—22no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—41no—
721C2×C42—41no—
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—22no—
731#107—22no—
732#107—41no—
733#107—41no—
734#107—41no—
735#107—41no—
736#107—41no—
737#107—41no—
738#106—22no—
739#106—22no—
740#106—41no—
741#106—41no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#102—22no—
765#102—22no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782#97—41no—
783#97—41no—
784C4×C8—41no—
785C4×C8—41no—
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#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824C24—21no—
825C24—22no—
826C24—22no—
827C24—41no—
828C24—41no—
829C24—41no—
830C24—41no—
831C24—41no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
835#41—44no—
836#41—44no—
837#41—44no—
838#41—44no—
839C2×Q8—21no—
840C2×Q8—21no—
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×Q8C2×#4112yes—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4C2×#4112yes—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—24no—
885C22×C4—22no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—41no—
915C22×C4—41no—
916C22×C4—41no—
917C22×C4—41no—
918C22×C4—41no—
919C22×C4—41no—
920C22×C4—41no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—42no—
926C22×C4—44no—
927C22×C4—44no—
928C22×C4—44no—
929C22×C4—44no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C2×#4112yes—
955C22×C4C2×#4112yes—
956C22×C4C2511yescharacteristic
957Q16—82no—
958Q16—82no—
959SD16—82no—
960SD16—82no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C4⋊C4—24no—
986C4⋊C4—24no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
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—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4C2×#4112yes—
1044C4⋊C4C2×#4112yes—
1045C22⋊C4—24no—
1046C22⋊C4—24no—
1047C22⋊C4—24no—
1048C22⋊C4—24no—
1049C22⋊C4—24no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C42—24no—
1081C42—22no—
1082C42—22no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—41no—
1090C42—41no—
1091C42—42no—
1092C42—42no—
1093C42—42no—
1094C42—42no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42H(5,𝔽2)12yes—
1102C42H(5,𝔽2)12yes—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—44no—
1124C23—44no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—82no—
1132C23—82no—
1133C23—82no—
1134C23—82no—
1135C23—82no—
1136C23#52512yes—
1137C23#57812yes—
1138C23C23×D411yescharacteristic
1139Q8—22no—
1140Q8—22no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151D4—22no—
1152D4—22no—
1153D4—48no—
1154D4—48no—
1155D4—41no—
1156D4—41no—
1157D4—84no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
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—44no—
1196C2×C4—44no—
1197C2×C4—44no—
1198C2×C4—48no—
1199C2×C4—44no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—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—82no—
1251C2×C4—82no—
1252C2×C4—82no—
1253C2×C4—162no—
1254C2×C4—162no—
1255C2×C4—162no—
1256C2×C4—162no—
1257C2×C4#52512yes—
1258C2×C4#53412yes—
1259C2×C4#53412yes—
1260C2×C4C22×#4111yescharacteristic
1261C2×C4C22×#4111yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8—41no—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—22no—
1278C22—22no—
1279C22—22no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—41no—
1284C22—41no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—42no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—88no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22C2×#52511yescharacteristic
1304C22C2×#53411yescharacteristic
1305C22#344911yescharacteristic
1306C22C2×#57811yescharacteristic
1307C22#358411yescharacteristic
1308C22#358511yescharacteristic
1309C22#358611yescharacteristic
1310C4—22no—
1311C4—22no—
1312C4—22no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—42no—
1320C4—42no—
1321C4—41no—
1322C4—41no—
1323C4—42no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4#350511yescharacteristic
1337C4#350511yescharacteristic
1338C4#350611yescharacteristic
1339C4#350611yescharacteristic
1340C2—42no—
1341C2—42no—
1342C2—81no—
1343C2—82no—
1344C2#3503111yescharacteristic
1345C2#6058611yescharacteristic
1346C2#6058911yescharacteristic
1347C2#6077011yescharacteristic
1348C2#6077211yescharacteristic
1349C2#6098311yescharacteristic
1350C2#6098511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35310C2semidirect
3. #33156C2semidirect
4. #33117C2semidirect
5. #32968C2semidirect
6. #32916C2semidirect
7. #29895C2semidirect
8. #29894C2semidirect
11. #29489C2semidirect
12. #29488C2semidirect
13. #29471C2semidirect
14. #29470C2semidirect
15. #29417C2semidirect
16. #29415C2semidirect
17. #29414C2semidirect
18. #29411C2semidirect
19. #27643C2semidirect
20. #27640C2semidirect
21. #24707C2semidirect
22. #24704C2semidirect
23. #24659C2semidirect
24. #24652C2semidirect
25. #24165C2semidirect
26. #24163C2semidirect
27. #22094C2semidirect
28. #22092C2semidirect
29. #22057C2semidirect
30. #22057C2semidirect
31. #20717C2semidirect
38. C2×#479C22semidirect
39. C2×#478C22semidirect
40. C2×#462C22semidirect
41. C2×#461C22semidirect
119. #1989C22semidirect
120. #1989C22semidirect
121. #1981C22semidirect
122. #1981C22semidirect
123. #1973C22semidirect
124. #1973C22semidirect
125. #1969C22semidirect
126. #1969C22semidirect
127. #1949C22semidirect
128. #1949C22semidirect
129. #1947C22semidirect
130. #1947C22semidirect
131. #1944C22semidirect
132. #1943C22semidirect
133. #1942C22semidirect
134. #1941C22semidirect
135. #1935C22semidirect
136. #1935C22semidirect
137. #1935C22semidirect
138. #1935C22semidirect
139. #1934C22semidirect
140. #1934C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
146. #1928C22semidirect
147. #1927C22semidirect
148. #1927C22semidirect
149. #1925C22semidirect
150. #1925C22semidirect
151. #1921C22semidirect
152. #1921C22semidirect
153. #1921C22semidirect
154. #1920C22semidirect
155. #1919C22semidirect
156. #1918C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1880C22semidirect
160. #1880C22semidirect
161. #1878C22semidirect
162. #1878C22semidirect
163. #1878C22semidirect
164. #1878C22semidirect
165. #1877C22semidirect
166. #1877C22semidirect
171. #1865C22semidirect
172. #1865C22semidirect
173. #1865C22semidirect
174. #1864C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
177. #1863C22semidirect
178. #1862C22semidirect
187. #1805C22semidirect
188. #1804C22semidirect
189. #1803C22semidirect
190. #1802C22semidirect

Maximal subgroups

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

subgroupindex
#353102
#342022
#331562
#331172
#329682
#329162
#298952
#298942
#296012
#294892
#294882
#294712
#294702
#294172
#294152
#294142
#294112
#276432
#276402
#247072
#247042
#246592
#246522
#241652
#241632
#220942
#220922
#220572
#207172