Finite Group Databasebeta

← #7616637

Subgroups — #7616637

Order 512.

1325 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45058C211yesmaximal, characteristic, complemented
2#44986C211yesmaximal, characteristic
3#32291C211yesmaximal, characteristic, complemented
4#32289C211yesmaximal, characteristic, complemented
5#30779C211yesmaximal, characteristic, complemented
6#30778C211yesmaximal, characteristic, complemented
7#29281C211yesmaximal, characteristic, complemented
8#29267C211yesmaximal, characteristic, complemented
9#28857C211yesmaximal, characteristic, complemented
10#28843C211yesmaximal, characteristic, complemented
11#28651C211yesmaximal, characteristic, complemented
12#28610C211yesmaximal, characteristic
13#28079C211yesmaximal, characteristic, complemented
14#28070C211yesmaximal, characteristic, complemented
15#27714C211yesmaximal, characteristic, complemented
16#27704C211yesmaximal, characteristic, complemented
17#27184C211yesmaximal, characteristic, complemented
18#27179C211yesmaximal, characteristic, complemented
19#27061C211yesmaximal, characteristic, complemented
20#27056C211yesmaximal, characteristic, complemented
21#26325C211yesmaximal, characteristic, complemented
22#26303C211yesmaximal, characteristic, complemented
23#26282C211yesmaximal, characteristic, complemented
24#26238C211yesmaximal, characteristic
25#22925C211yesmaximal, characteristic, complemented
26#22921C211yesmaximal, characteristic, complemented
27#22742C211yesmaximal, characteristic, complemented
28#22712C211yesmaximal, characteristic, complemented
29#21725C211yesmaximal, characteristic, complemented
30#21654C211yesmaximal, characteristic, complemented
31#21637C211yesmaximal, characteristic, complemented
32C2×#500C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×#435C2211yescharacteristic
38#2808—21no—
39#2803—21no—
40#2796—21no—
41#2793—21no—
42#2789—21no—
43#2759—21no—
44#2710—21no—
45#2700—21no—
46#2605—21no—
47#2596—21no—
48#2592—21no—
49#2592C2211yescharacteristic
50#2589—21no—
51#2567C2211yescharacteristic
52#2547C2211yescharacteristic
53#2540C2211yescharacteristic
54#2527—21no—
55#2500C2211yescharacteristic
56#2499—21no—
57#2499C2211yescharacteristic
58#2497C2211yescharacteristic
59#2495C2211yescharacteristic
60#2494C2211yescharacteristic
61#2494C2211yescharacteristic
62#2492C2211yescharacteristic
63#2491C2211yescharacteristic
64#2474—21no—
65#2458—21no—
66#2440C2211yescharacteristic
67#2439C2211yescharacteristic
68#2423C2211yescharacteristic
69#2422C2211yescharacteristic
70#2398C2211yescharacteristic
71#2363C2211yescharacteristic
72#2362C2211yescharacteristic
73#2355C2211yescharacteristic
74#2354C2211yescharacteristic
75#2352C2211yescharacteristic
76Q8×C4⋊C4C2211yescharacteristic
77#2346C2211yescharacteristic
78#2344C2211yescharacteristic
79#2331C2211yescharacteristic
80#2331C2211yescharacteristic
81#2331C2211yescharacteristic
82#2326C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2097C2211yescharacteristic
88#2095C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2083C2211yescharacteristic
92#2083C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2074C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic
104#2057C2211yescharacteristic
105#2036C2211yescharacteristic
106#2036C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2024C2211yescharacteristic
114#2023C2211yescharacteristic
115#1993C2211yescharacteristic
116#1993C2211yescharacteristic
117#1990C2211yescharacteristic
118#1988C2211yescharacteristic
119#1987C2211yescharacteristic
120#1984C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1958C2211yescharacteristic
124#1954C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1947C2211yescharacteristic
132#1947C2211yescharacteristic
133#1943C2211yescharacteristic
134#1943C2211yescharacteristic
135#1942C2211yescharacteristic
136#1942C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1928C2211yescharacteristic
146#1927C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1921C2211yescharacteristic
157#1921C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1865C2211yescharacteristic
168#1864C2211yescharacteristic
169#1863C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1852C2211yescharacteristic
177#1846C2211yescharacteristic
178#1836C2211yescharacteristic
179#1836C2211yescharacteristic
180#1834C2211yescharacteristic
181#1832C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192#1763C2211yescharacteristic
193#1762C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#124—21no—
209C2×#124—21no—
210C2×#124C2311yescharacteristic
211C2×#123—21no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227#500—24no—
228#489—24no—
229#484—24no—
230#482—24no—
231#446—24no—
232#435—24no—
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#401—21no—
284#401—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400D411yescharacteristic
289#400D411yescharacteristic
290#399—21no—
291#399—21no—
292#398—21no—
293#398—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397D411yescharacteristic
304#397D411yescharacteristic
305#396—21no—
306#396—21no—
307#395—21no—
308#395—21no—
309#395—21no—
310#394—21no—
311#394—21no—
312#394—21no—
313#394—21no—
314#394D411yescharacteristic
315#394D411yescharacteristic
316#393—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#393D411yescharacteristic
321#393D411yescharacteristic
322#392—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#390—21no—
338#390—21no—
339#390—21no—
340#390—21no—
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—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#386—21no—
398#386—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#383—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#381—21no—
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423C4×C4⋊C4—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#376—21no—
443#376C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×D4—21no—
490C22×D4—21no—
491C22×D4C2×D411yescharacteristic
492C22×D4C2411yescharacteristic
493C23×C4—21no—
494C23×C4—21no—
495C23×C4C2411yescharacteristic
496C23×C4C2411yescharacteristic
497C2×M16—22no—
498C2×M16—41no—
499C2×M16—41no—
500C22×C8—22no—
501C22×C8—41no—
502C22×C8—41no—
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—22no—
514C4⋊Q8—22no—
515C4⋊Q8—41no—
516C4⋊Q8—41no—
517#124—22no—
518#124—22no—
519#124—82no—
520#124—82no—
521#123—82no—
522C22⋊Q8—22no—
523C22⋊Q8—41no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526C22⋊Q8—82no—
527#121—22no—
528#121—41no—
529#121—41no—
530#121—41no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—82no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—41no—
539C4×D4—41no—
540#117—22no—
541#117—41no—
542#117—41no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117—82no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—21no—
630C2×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645#107—22no—
646#107—22no—
647#107—22no—
648#107—22no—
649#107—41no—
650#107—41no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107#4114yes—
655#106—22no—
656#106—41no—
657#106—41no—
658#106—41no—
659#106—41no—
660#106—41no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—41no—
678#102—41no—
679#102—41no—
680#102—41no—
681C22⋊C8—22no—
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—22no—
685C22⋊C8—41no—
686C22⋊C8—41no—
687#97—22no—
688#97—41no—
689#97—41no—
690#97#4114yes—
691C4×C8—22no—
692C4×C8—22no—
693C4×C8—22no—
694C4×C8—41no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24C22×D411yescharacteristic
751C24C22×D411yescharacteristic
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—41no—
761C2×Q8—42no—
762C2×Q8—42no—
763C2×Q8—42no—
764C2×Q8—81no—
765C2×Q8—81no—
766C2×Q8—81no—
767C2×Q8—81no—
768C2×Q8—81no—
769C2×Q8—81no—
770C2×D4—22no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—41no—
778C2×D4—41no—
779C2×D4—42no—
780C2×D4—81no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4—81no—
784C2×D4—81no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C2511yescharacteristic
831M16—82no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—82no—
854C2×C8C2×#4112yes—
855C2×C8C2×#4112yes—
856C2×C8C2×#4112yes—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4C2×#4112yes—
913C4⋊C4C2×#4112yes—
914C22⋊C4—22no—
915C22⋊C4—22no—
916C22⋊C4—22no—
917C22⋊C4—22no—
918C22⋊C4—41no—
919C22⋊C4—41no—
920C22⋊C4—41no—
921C22⋊C4—41no—
922C22⋊C4—41no—
923C22⋊C4—41no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—81no—
934C22⋊C4—81no—
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⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42C2×#4112yes—
971C422−1+412yes—
972C23—21no—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23C23×D411yescharacteristic
994Q8—44no—
995Q8—41no—
996Q8—41no—
997Q8—41no—
998Q8—41no—
999Q8—162no—
1000Q8—162no—
1001Q8—162no—
1002D4—41no—
1003D4—41no—
1004D4—41no—
1005D4—41no—
1006D4—82no—
1007D4—162no—
1008D4—162no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—84no—
1096C2×C4—162no—
1097C2×C4#54712yes—
1098C2×C4#54712yes—
1099C2×C4#57812yes—
1100C2×C4C22×#4111yescharacteristic
1101C2×C4C22×#4111yescharacteristic
1102C2×C4C2×2−1+411yescharacteristic
1103C2×C4#58511yescharacteristic
1104C2×C4#58511yescharacteristic
1105C2×C4#58511yescharacteristic
1106C8—22no—
1107C8—22no—
1108C8—22no—
1109C8—41no—
1110C8—41no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C22—41no—
1115C22—41no—
1116C22—41no—
1117C22—41no—
1118C22—41no—
1119C22—41no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22C2×#54711yescharacteristic
1136C22D4×#4111yescharacteristic
1137C22#350011yescharacteristic
1138C22C2×#57811yescharacteristic
1139C22#358411yescharacteristic
1140C22#358511yescharacteristic
1141C22#358511yescharacteristic
1142C4—22no—
1143C4—22no—
1144C4—22no—
1145C4—41no—
1146C4—41no—
1147C4—42no—
1148C4—42no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4#348011yescharacteristic
1170C4#350711yescharacteristic
1171C4#351011yescharacteristic
1172C4#355711yescharacteristic
1173C2—81no—
1174C2—81no—
1175C2—161no—
1176C2#5982911yescharacteristic
1177C2#6127311yescharacteristic
1178C2#6127411yescharacteristic
1179C2#6147811yescharacteristic
1180C2#6150511yescharacteristic
1181C2#6260711yescharacteristic
1182C2#6261911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2540C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45058C2semidirect
3. #32291C2semidirect
4. #32289C2semidirect
5. #30779C2semidirect
6. #30778C2semidirect
7. #29281C2semidirect
8. #29267C2semidirect
9. #28857C2semidirect
10. #28843C2semidirect
11. #28651C2semidirect
13. #28079C2semidirect
14. #28070C2semidirect
15. #27714C2semidirect
16. #27704C2semidirect
17. #27184C2semidirect
18. #27179C2semidirect
19. #27061C2semidirect
20. #27056C2semidirect
21. #26325C2semidirect
22. #26303C2semidirect
23. #26282C2semidirect
25. #22925C2semidirect
26. #22921C2semidirect
27. #22742C2semidirect
28. #22712C2semidirect
29. #21725C2semidirect
30. #21654C2semidirect
31. #21637C2semidirect

Maximal subgroups

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

subgroupindex
#450582
#449862
#322912
#322892
#307792
#307782
#292812
#292672
#288572
#288432
#286512
#286102
#280792
#280702
#277142
#277042
#271842
#271792
#270612
#270562
#263252
#263032
#262822
#262382
#229252
#229212
#227422
#227122
#217252
#216542
#216372