Finite Group Databasebeta

← #7616700

Subgroups — #7616700

Order 512.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59643C211yesmaximal, characteristic
2#59435C211yesmaximal, characteristic, complemented
3#32308C211yesmaximal, characteristic, complemented
4#32307C211yesmaximal, characteristic, complemented
5#30794C211yesmaximal, characteristic, complemented
6#30792C211yesmaximal, characteristic, complemented
7#29276C211yesmaximal, characteristic, complemented
8#29261C211yesmaximal, characteristic, complemented
9#28862C211yesmaximal, characteristic, complemented
10#28847C211yesmaximal, characteristic, complemented
11#28651C211yesmaximal, characteristic, complemented
12#28612C211yesmaximal, characteristic
13#28080C211yesmaximal, characteristic, complemented
14#28070C211yesmaximal, characteristic, complemented
15#27716C211yesmaximal, characteristic, complemented
16#27709C211yesmaximal, characteristic, complemented
17#27173C211yesmaximal, characteristic, complemented
18#27166C211yesmaximal, characteristic, complemented
19#27039C211yesmaximal, characteristic, complemented
20#27034C211yesmaximal, characteristic, complemented
21#26328C211yesmaximal, characteristic, complemented
22#26315C211yesmaximal, characteristic, complemented
23#26295C211yesmaximal, characteristic, complemented
24#26245C211yesmaximal, characteristic
25#22928C211yesmaximal, characteristic, complemented
26#22921C211yesmaximal, characteristic, complemented
27#22742C211yesmaximal, characteristic, complemented
28#22710C211yesmaximal, characteristic, complemented
29#21731C211yesmaximal, characteristic, complemented
30C4×#489C211yesmaximal, characteristic, complemented
31#21632C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic
33C2×#489C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#446C2211yescharacteristic
37C2×#435C2211yescharacteristic
38#2775—21no—
39#2775—21no—
40#2773—21no—
41#2710—21no—
42#2607—21no—
43#2604—21no—
44#2604—21no—
45#2592C2211yescharacteristic
46#2571—21no—
47#2567C2211yescharacteristic
48#2563C2211yescharacteristic
49#2557—21no—
50#2540C2211yescharacteristic
51#2516—21no—
52#2512—21no—
53#2501C2211yescharacteristic
54#2499C2211yescharacteristic
55#2496C2211yescharacteristic
56#2496C2211yescharacteristic
57#2495C2211yescharacteristic
58#2495C2211yescharacteristic
59#2492C2211yescharacteristic
60#2491C2211yescharacteristic
61#2458—21no—
62#2448—21no—
63#2448—21no—
64#2441C2211yescharacteristic
65#2441C2211yescharacteristic
66#2423C2211yescharacteristic
67#2420C2211yescharacteristic
68#2374—21no—
69#2363C2211yescharacteristic
70#2360C2211yescharacteristic
71#2356—21no—
72#2355C2211yescharacteristic
73#2354C2211yescharacteristic
74#2352C2211yescharacteristic
75Q8×C4⋊C4C2211yescharacteristic
76#2346C2211yescharacteristic
77#2346C2211yescharacteristic
78C4×C4⋊Q8C2211yescharacteristic
79C4×C4⋊Q8C2211yescharacteristic
80C4×#125C2211yescharacteristic
81C4×#124C2211yescharacteristic
82C4×#124C2211yescharacteristic
83#2101C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2097C2211yescharacteristic
88#2096C2211yescharacteristic
89#2094C2211yescharacteristic
90#2092C2211yescharacteristic
91#2085C2211yescharacteristic
92#2084C2211yescharacteristic
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2075C2211yescharacteristic
97#2072C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic
102#2065C2211yescharacteristic
103#2058C2211yescharacteristic
104#2058C2211yescharacteristic
105#2036C2211yescharacteristic
106#2035C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2026C2211yescharacteristic
114#2025C2211yescharacteristic
115#1993C2211yescharacteristic
116#1993C2211yescharacteristic
117#1992C2211yescharacteristic
118#1988C2211yescharacteristic
119#1988C2211yescharacteristic
120#1985C2211yescharacteristic
121#1983C2211yescharacteristic
122#1983C2211yescharacteristic
123#1959C2211yescharacteristic
124#1955C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1948C2211yescharacteristic
131#1948C2211yescharacteristic
132#1947C2211yescharacteristic
133#1942C2211yescharacteristic
134#1942C2211yescharacteristic
135#1941C2211yescharacteristic
136#1941C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1934C2211yescharacteristic
144#1933C2211yescharacteristic
145#1928C2211yescharacteristic
146#1927C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1920C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1895C2211yescharacteristic
162#1894C2211yescharacteristic
163#1893C2211yescharacteristic
164#1892C2211yescharacteristic
165#1875C2211yescharacteristic
166#1873C2211yescharacteristic
167#1865C2211yescharacteristic
168#1864C2211yescharacteristic
169#1863C2211yescharacteristic
170#1862C2211yescharacteristic
171#1854C2211yescharacteristic
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1853C2211yescharacteristic
176#1852C2211yescharacteristic
177#1847C2211yescharacteristic
178#1836C2211yescharacteristic
179#1836C2211yescharacteristic
180#1834C2211yescharacteristic
181#1831C2211yescharacteristic
182#1825C2211yescharacteristic
183#1824C2211yescharacteristic
184#1809C2211yescharacteristic
185#1807C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#124—21no—
211C2×#124D411yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8—21no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230#501—24no—
231#489—24no—
232#485—24no—
233#482—24no—
234#446—24no—
235#435—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#399—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#399—21no—
296#399—21no—
297#398—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#395—21no—
309#395—21no—
310#394—21no—
311#394—21no—
312#393—21no—
313#393—21no—
314#393—21no—
315#393—21no—
316#393—21no—
317#392—21no—
318#391—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391—21no—
323#391D411yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#390—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390D411yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388D411yescharacteristic
372#388D411yescharacteristic
373#388D411yescharacteristic
374#388D411yescharacteristic
375#387—21no—
376#387—21no—
377#387—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#386—21no—
389#386—21no—
390#386—21no—
391#385—21no—
392#384—21no—
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#383—21no—
399#383—21no—
400#382—21no—
401#382—21no—
402#382—21no—
403#382D411yescharacteristic
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#381—21no—
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376—21no—
442#376—21no—
443C43C2311yescharacteristic
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×Q8C2×D411yescharacteristic
487C22×Q8C2411yescharacteristic
488C22×D4—21no—
489C22×D4—21no—
490C22×D4C2×D411yescharacteristic
491C22×D4C2411yescharacteristic
492C23×C4—21no—
493C23×C4—21no—
494C23×C4C2411yescharacteristic
495C23×C4C2411yescharacteristic
496C2×M16—22no—
497C2×M16—41no—
498C2×M16—41no—
499C22×C8—22no—
500C22×C8—41no—
501C22×C8—41no—
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C4⋊Q8—22no—
511C4⋊Q8—22no—
512C4⋊Q8—22no—
513C4⋊Q8—41no—
514#126—82no—
515#126—82no—
516#125—22no—
517#125—41no—
518#124—22no—
519#124—22no—
520#124—42no—
521#124—82no—
522#123—44no—
523#123—82no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526C22⋊Q8—41no—
527C22⋊Q8—41no—
528#121—22no—
529#121—41no—
530#121—41no—
531#121—41no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—44no—
537C4×Q8—82no—
538C4×Q8—82no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—41no—
542C4×D4—41no—
543#117—22no—
544#117—22no—
545#117—41no—
546#117—41no—
547#117—41no—
548#117—41no—
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—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42C2×D411yescharacteristic
646C2×C42C2×D411yescharacteristic
647C2×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654#107—22no—
655#107—41no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107#4114yes—
660#106—22no—
661#106—22no—
662#106—22no—
663#106—22no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—22no—
673C4⋊C8—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—41no—
679#103—41no—
680#103—41no—
681#103—41no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690C22⋊C8—22no—
691C22⋊C8—22no—
692C22⋊C8—22no—
693C22⋊C8—22no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696#97—22no—
697#97—22no—
698#97—22no—
699#97—41no—
700#97#4114yes—
701C4×C8—22no—
702C4×C8—41no—
703C4×C8—41no—
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#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24C22×D411yescharacteristic
754C24C22×D411yescharacteristic
755C2×Q8—22no—
756C2×Q8—22no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
763C2×Q8—41no—
764C2×Q8—42no—
765C2×Q8—42no—
766C2×Q8—42no—
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—42no—
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—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
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⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4C2×#4112yes—
916C4⋊C4C2×#4112yes—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—22no—
923C22⋊C4—41no—
924C22⋊C4—41no—
925C22⋊C4—41no—
926C22⋊C4—41no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
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—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C42—22no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—41no—
961C42—41no—
962C42—41no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—42no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42C2×#4112yes—
978C422−1+412yes—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23C23×D411yescharacteristic
1001Q8—44no—
1002Q8—41no—
1003Q8—41no—
1004Q8—41no—
1005Q8—41no—
1006Q8—84no—
1007Q8—84no—
1008D4—41no—
1009D4—41no—
1010D4—41no—
1011D4—41no—
1012D4—82no—
1013D4—162no—
1014D4—162no—
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—21no—
1035C2×C4—21no—
1036C2×C4—22no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—22no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
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—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—162no—
1101C2×C4—162no—
1102C2×C4#54712yes—
1103C2×C4#54712yes—
1104C2×C4#57512yes—
1105C2×C4#57712yes—
1106C2×C4C22×#4111yescharacteristic
1107C2×C4C22×#4111yescharacteristic
1108C2×C4C2×2−1+411yescharacteristic
1109C2×C4#58511yescharacteristic
1110C2×C4#58511yescharacteristic
1111C2×C4#58511yescharacteristic
1112C8—22no—
1113C8—22no—
1114C8—22no—
1115C8—41no—
1116C8—41no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—41no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22C2×#54711yescharacteristic
1142C22D4×#4111yescharacteristic
1143C22#350011yescharacteristic
1144C22C2×#57511yescharacteristic
1145C22C2×#57711yescharacteristic
1146C22#358511yescharacteristic
1147C22#358611yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—41no—
1153C4—41no—
1154C4—41no—
1155C4—42no—
1156C4—42no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4#348011yescharacteristic
1176C4#350711yescharacteristic
1177C4#351011yescharacteristic
1178C4#355711yescharacteristic
1179C2—81no—
1180C2—81no—
1181C2—161no—
1182C2#5982911yescharacteristic
1183C2#6125311yescharacteristic
1184C2#6127911yescharacteristic
1185C2#6145011yescharacteristic
1186C2#6150911yescharacteristic
1187C2#6258011yescharacteristic
1188C2#6260311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2540C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59435C2semidirect
3. #32308C2semidirect
4. #32307C2semidirect
5. #30794C2semidirect
6. #30792C2semidirect
7. #29276C2semidirect
8. #29261C2semidirect
9. #28862C2semidirect
10. #28847C2semidirect
11. #28651C2semidirect
13. #28080C2semidirect
14. #28070C2semidirect
15. #27716C2semidirect
16. #27709C2semidirect
17. #27173C2semidirect
18. #27166C2semidirect
19. #27039C2semidirect
20. #27034C2semidirect
21. #26328C2semidirect
22. #26315C2semidirect
23. #26295C2semidirect
25. #22928C2semidirect
26. #22921C2semidirect
27. #22742C2semidirect
28. #22710C2semidirect
29. #21731C2semidirect
30. C4×#489C2semidirect
31. #21632C2semidirect

Maximal subgroups

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

subgroupindex
#596432
#594352
#323082
#323072
#307942
#307922
#292762
#292612
#288622
#288472
#286512
#286122
#280802
#280702
#277162
#277092
#271732
#271662
#270392
#270342
#263282
#263152
#262952
#262452
#229282
#229212
#227422
#227102
#217312
C4×#4892
#216322