Finite Group Databasebeta

← #7582618

Subgroups — #7582618

Order 512.

1398 conjugacy classes of subgroups.

The subgroup lattice has 1213 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59592C211yesmaximal, characteristic
2#36256C211yesmaximal, characteristic, complemented
3#31798C211yesmaximal, characteristic, complemented
4#31766C211yesmaximal, characteristic, complemented
5#30785C211yesmaximal, characteristic, complemented
6#30713C211yesmaximal, characteristic
7#29479C211yesmaximal, characteristic, complemented
8#29464C211yesmaximal, characteristic, complemented
9#29025C211yesmaximal, characteristic, complemented
10#28886C211yesmaximal, characteristic, complemented
11#28084C211yesmaximal, characteristic, complemented
12#27788C211yesmaximal, characteristic, complemented
13#27333C211yesmaximal, characteristic, complemented
14#27200C211yesmaximal, characteristic, complemented
15#27156C211yesmaximal, characteristic, complemented
16#27048C211yesmaximal, characteristic, complemented
17#26860C211yesmaximal, characteristic, complemented
18#26807C211yesmaximal, characteristic, complemented
19#26788C211yesmaximal, characteristic, complemented
20#26740C211yesmaximal, characteristic, complemented
21#26725C211yesmaximal, characteristic, complemented
22#26717C211yesmaximal, characteristic, complemented
23#26242C211yesmaximal, characteristic
24#24937C211yesmaximal, characteristic, complemented
25#23300C211yesmaximal, characteristic, complemented
26#23164C211yesmaximal, characteristic, complemented
27#23134C211yesmaximal, characteristic, complemented
28#23077C211yesmaximal, characteristic, complemented
29#22920C211yesmaximal, characteristic, complemented
30#21580C211yesmaximal, characteristic, complemented
31C4×#483C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#483C2211yescharacteristic
36C2×#475C2211yescharacteristic
37C2×#465C2211yescharacteristic
38#2855C2211yescharacteristic
39#2851—21no—
40#2773—21no—
41#2751—21no—
42#2595—21no—
43#2589—21no—
44#2585—21no—
45#2573—21no—
46#2557—21no—
47#2540C2211yescharacteristic
48#2528—21no—
49#2511C2211yescharacteristic
50#2506C2211yescharacteristic
51#2494C2211yescharacteristic
52#2493—21no—
53#2492C2211yescharacteristic
54#2491C2211yescharacteristic
55#2490C2211yescharacteristic
56#2489C2211yescharacteristic
57#2489C2211yescharacteristic
58#2486C2211yescharacteristic
59#2475—21no—
60#2455—21no—
61#2448C2211yescharacteristic
62#2447—21no—
63#2447C2211yescharacteristic
64#2442C2211yescharacteristic
65#2419—21no—
66#2417C2211yescharacteristic
67#2370C2211yescharacteristic
68#2370C2211yescharacteristic
69#2369C2211yescharacteristic
70#2361C2211yescharacteristic
71#2360C2211yescharacteristic
72#2360C2211yescharacteristic
73#2360C2211yescharacteristic
74#2357—21no—
75#2356C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77#2344C2211yescharacteristic
78C4×C22⋊Q8C2211yescharacteristic
79C4×#123C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2290—21no—
82C2×C4×C4⋊C4C2211yescharacteristic
83#2100C2211yescharacteristic
84#2097C2211yescharacteristic
85#2088C2211yescharacteristic
86#2084C2211yescharacteristic
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2076C2211yescharacteristic
90#2073C2211yescharacteristic
91#2068C2211yescharacteristic
92#2068C2211yescharacteristic
93#2065C2211yescharacteristic
94#2065C2211yescharacteristic
95#2059C2211yescharacteristic
96#2058C2211yescharacteristic
97#2058C2211yescharacteristic
98#2056C2211yescharacteristic
99#2042C2211yescharacteristic
100#2036C2211yescharacteristic
101#2036C2211yescharacteristic
102#2035C2211yescharacteristic
103#2035C2211yescharacteristic
104#2035C2211yescharacteristic
105#2034C2211yescharacteristic
106#2034C2211yescharacteristic
107#2033C2211yescharacteristic
108#2026C2211yescharacteristic
109#2026C2211yescharacteristic
110#2025C2211yescharacteristic
111#2015C2211yescharacteristic
112#2001C2211yescharacteristic
113#2001C2211yescharacteristic
114#2000C2211yescharacteristic
115#1993C2211yescharacteristic
116#1989C2211yescharacteristic
117#1989C2211yescharacteristic
118#1983C2211yescharacteristic
119#1971C2211yescharacteristic
120#1968C2211yescharacteristic
121#1968C2211yescharacteristic
122#1959C2211yescharacteristic
123#1955C2211yescharacteristic
124#1949C2211yescharacteristic
125#1948C2211yescharacteristic
126#1943C2211yescharacteristic
127#1943C2211yescharacteristic
128#1941C2211yescharacteristic
129#1936C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1934C2211yescharacteristic
135#1933C2211yescharacteristic
136#1933C2211yescharacteristic
137#1928C2211yescharacteristic
138#1927C2211yescharacteristic
139#1927C2211yescharacteristic
140#1927C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1924C2211yescharacteristic
149#1923C2211yescharacteristic
150#1923C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1919C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1892C2211yescharacteristic
166#1880C2211yescharacteristic
167#1878C2211yescharacteristic
168#1878C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic
176#1864C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1853C2211yescharacteristic
180#1852C2211yescharacteristic
181#1824C2211yescharacteristic
182#1823C2211yescharacteristic
183#1823C2211yescharacteristic
184#1807C2211yescharacteristic
185#1776C2211yescharacteristic
186#1776C2211yescharacteristic
187#1776C2211yescharacteristic
188C4×#106C2211yescharacteristic
189C4×#106C2211yescharacteristic
190C4×#106C2211yescharacteristic
191#1771C2211yescharacteristic
192#1770C2211yescharacteristic
193#1763C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1749C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202C2×#340C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124—21no—
211C2×#124C2311yescharacteristic
212C2×#123—21no—
213C2×#123D411yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117—21no—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C42—21no—
233C22×C42C2311yescharacteristic
234#499—24no—
235#483—24no—
236#483—24no—
237#481—24no—
238#475—24no—
239#465—24no—
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291#401—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#399—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#394—21no—
315#394—21no—
316#393—21no—
317#393—21no—
318#392—21no—
319#391—21no—
320#391—21no—
321#391—21no—
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#390—21no—
330#390—21no—
331#390—21no—
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#388—21no—
353#388—21no—
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#388D411yescharacteristic
363#388D411yescharacteristic
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387D411yescharacteristic
383#387D411yescharacteristic
384#386—21no—
385#386—21no—
386#386—21no—
387#386D411yescharacteristic
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385D411yescharacteristic
399#384C2311yescharacteristic
400#383—21no—
401#382—21no—
402#382—21no—
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#381—21no—
407#381—21no—
408#381D411yescharacteristic
409#380—21no—
410#380—21no—
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444#376—21no—
445C2×#95—21no—
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#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×Q8—21no—
485C22×Q8C2411yescharacteristic
486C22×Q8C2411yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4C2×D411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2×D411yescharacteristic
497C23×C4C2×D411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C2×Q16—41no—
501C2×Q16—41no—
502C2×Q16—41no—
503C2×SD16—22no—
504C2×SD16—41no—
505C2×SD16—41no—
506C22×C8—22no—
507C22×C8—41no—
508C22×C8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—41no—
519#125—22no—
520#125—22no—
521#125—41no—
522#125—41no—
523#125—82no—
524#124—41no—
525#124—41no—
526#124—82no—
527#123—42no—
528#123—82no—
529C22⋊Q8—22no—
530C22⋊Q8—22no—
531C22⋊Q8—22no—
532C22⋊Q8—41no—
533C22⋊Q8—41no—
534C22⋊Q8—41no—
535C22⋊Q8—41no—
536C22⋊Q8—41no—
537#121—22no—
538#121—22no—
539#121—41no—
540#121—41no—
541C4×Q8—22no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—44no—
550C4×D4—44no—
551C4×D4—82no—
552#117—82no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
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—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—41no—
649C2×C42—41no—
650C2×C42—82no—
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658#107—22no—
659#107—22no—
660#107—41no—
661#106—22no—
662#106—22no—
663#106—22no—
664#106—22no—
665#106—22no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106#4114yes—
671#106#4114yes—
672C4⋊C8—22no—
673C4⋊C8—41no—
674C4⋊C8—41no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695C22⋊C8—22no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700C22⋊C8—41no—
701C22⋊C8—41no—
702#97—41no—
703#97—41no—
704#97—41no—
705#97—41no—
706C4×C8—22no—
707C4×C8—41no—
708C4×C8—41no—
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#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762C24—21no—
763C24C22×D411yescharacteristic
764C24C22×D411yescharacteristic
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—42no—
778C2×Q8—81no—
779C2×Q8—81no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—42no—
793C2×D4—81no—
794C2×D4—81no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
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—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—41no—
825C22×C4—41no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C2511yescharacteristic
856Q16—82no—
857SD16—82no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—82no—
881C2×C8C2×#4112yes—
882C2×C8C2×#4112yes—
883C4⋊C4—22no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4C2×#4112yes—
938C4⋊C4C2×#4112yes—
939C4⋊C4C2×#4112yes—
940C4⋊C4C2×#4112yes—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—41no—
981C42—41no—
982C42—42no—
983C42—42no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C42—81no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23#57512yes—
1015C23#57712yes—
1016C23C23×D411yescharacteristic
1017Q8—41no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—162no—
1026D4—44no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—41no—
1031D4—84no—
1032D4—84no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—22no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—44no—
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—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—82no—
1123C2×C4—84no—
1124C2×C4—84no—
1125C2×C4—84no—
1126C2×C4—162no—
1127C2×C4—162no—
1128C2×C4#57712yes—
1129C2×C4C22×#4111yescharacteristic
1130C2×C4C22×#4111yescharacteristic
1131C2×C4#58511yescharacteristic
1132C2×C4#58511yescharacteristic
1133C2×C4#58511yescharacteristic
1134C2×C4#58511yescharacteristic
1135C8—22no—
1136C8—22no—
1137C8—41no—
1138C8—41no—
1139C8—41no—
1140C8—41no—
1141C8—41no—
1142C8—41no—
1143C22—22no—
1144C22—22no—
1145C22—22no—
1146C22—22no—
1147C22—22no—
1148C22—22no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—81no—
1158C22—81no—
1159C22—81no—
1160C22—81no—
1161C22—81no—
1162C22—81no—
1163C22—81no—
1164C22D4×#4111yescharacteristic
1165C22D4×#4111yescharacteristic
1166C22#348511yescharacteristic
1167C22C2×#57511yescharacteristic
1168C22C2×#57711yescharacteristic
1169C22C2×#57711yescharacteristic
1170C22#358611yescharacteristic
1171C4—22no—
1172C4—41no—
1173C4—42no—
1174C4—41no—
1175C4—42no—
1176C4—41no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—41no—
1181C4—41no—
1182C4—42no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—42no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4—81no—
1194C4—81no—
1195C4—81no—
1196C4—81no—
1197C4—81no—
1198C4#348011yescharacteristic
1199C4#351011yescharacteristic
1200C4#352411yescharacteristic
1201C4#356611yescharacteristic
1202C2—42no—
1203C2—42no—
1204C2—161no—
1205C2#5917511yescharacteristic
1206C2#6144511yescharacteristic
1207C2#6145511yescharacteristic
1208C2#6148311yescharacteristic
1209C2#6152011yescharacteristic
1210C2#6172911yescharacteristic
1211C2#6174511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2540C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36256C2semidirect
3. #31798C2semidirect
4. #31766C2semidirect
5. #30785C2semidirect
7. #29479C2semidirect
8. #29464C2semidirect
9. #29025C2semidirect
10. #28886C2semidirect
11. #28084C2semidirect
12. #27788C2semidirect
13. #27333C2semidirect
14. #27200C2semidirect
15. #27156C2semidirect
16. #27048C2semidirect
17. #26860C2semidirect
18. #26807C2semidirect
19. #26788C2semidirect
20. #26740C2semidirect
21. #26725C2semidirect
22. #26717C2semidirect
24. #24937C2semidirect
25. #23300C2semidirect
26. #23164C2semidirect
27. #23134C2semidirect
28. #23077C2semidirect
29. #22920C2semidirect
30. #21580C2semidirect
31. C4×#483C2semidirect

Maximal subgroups

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

subgroupindex
#595922
#362562
#317982
#317662
#307852
#307132
#294792
#294642
#290252
#288862
#280842
#277882
#273332
#272002
#271562
#270482
#268602
#268072
#267882
#267402
#267252
#267172
#262422
#249372
#233002
#231642
#231342
#230772
#229202
#215802
C4×#4832