Finite Group Databasebeta

← #6530117

Subgroups — #6530117

Order 512.

1430 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34969C211yesmaximal, characteristic
2#34239C211yesmaximal, characteristic, complemented
3#29288C211yesmaximal, characteristic, complemented
4#29278C211yesmaximal, characteristic, complemented
5#28285C211yesmaximal, characteristic, complemented
6#28208C211yesmaximal, characteristic, complemented
7#27634C211yesmaximal, characteristic, complemented
8#27632C211yesmaximal, characteristic
9#27476C211yesmaximal, characteristic, complemented
10#27472C211yesmaximal, characteristic, complemented
11#27410C211yesmaximal, characteristic
12#27406C211yesmaximal, characteristic
13#27349C211yesmaximal, characteristic, complemented
14#27345C211yesmaximal, characteristic, complemented
15#27179C211yesmaximal, characteristic
16#27175C211yesmaximal, characteristic
17#27156C211yesmaximal, characteristic, complemented
18#27152C211yesmaximal, characteristic, complemented
19#27026C211yesmaximal, characteristic, complemented
20#27022C211yesmaximal, characteristic, complemented
21#26887C211yesmaximal, characteristic, complemented
22#26883C211yesmaximal, characteristic, complemented
23#26717C211yesmaximal, characteristic, complemented
24#26713C211yesmaximal, characteristic, complemented
25#24307C211yesmaximal, characteristic, complemented
26#24305C211yesmaximal, characteristic
27#22121C211yesmaximal, characteristic, complemented
28#22121C211yesmaximal, characteristic, complemented
29#21926C211yesmaximal, characteristic, complemented
30#21617C211yesmaximal, characteristic, complemented
31#21617C211yesmaximal, characteristic, complemented
32C22×#125C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37#2530—21no—
38#2527—21no—
39#2511C2211yescharacteristic
40#2509C2211yescharacteristic
41#2494C2211yescharacteristic
42#2492C2211yescharacteristic
43#2477—21no—
44#2470—21no—
45#2452C2211yescharacteristic
46#2447C2211yescharacteristic
47#2427C2211yescharacteristic
48#2422C2211yescharacteristic
49#2401—21no—
50#2398—21no—
51#2371—21no—
52#2371—21no—
53#2370C2211yescharacteristic
54#2370C2211yescharacteristic
55#2370C2211yescharacteristic
56#2370C2211yescharacteristic
57#2345C2211yescharacteristic
58#2345C2211yescharacteristic
59#2344—21no—
60#2344—21no—
61#2344C2211yescharacteristic
62#2344C2211yescharacteristic
63#2336—21no—
64#2336—21no—
65#2313—21no—
66C4×C4⋊Q8C2211yescharacteristic
67C4×#125C2211yescharacteristic
68C4×#125C2211yescharacteristic
69C4×#125C2211yescharacteristic
70C4×#125C2211yescharacteristic
71C4×#124C2211yescharacteristic
72C4×C22⋊Q8—21no—
73C4×C22⋊Q8C2211yescharacteristic
74C4×#123—21no—
75C4×#121C2211yescharacteristic
76#2295C2211yescharacteristic
77#2283C2211yescharacteristic
78#2274—21no—
79C42×D4C2211yescharacteristic
80C4×#117C2211yescharacteristic
81#2100C2211yescharacteristic
82#2100C2211yescharacteristic
83#2088C2211yescharacteristic
84#2088C2211yescharacteristic
85#2087C2211yescharacteristic
86#2087C2211yescharacteristic
87#2085C2211yescharacteristic
88#2085C2211yescharacteristic
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic
91#2076C2211yescharacteristic
92#2075C2211yescharacteristic
93#2068C2211yescharacteristic
94#2067C2211yescharacteristic
95#2066C2211yescharacteristic
96#2065C2211yescharacteristic
97#2059C2211yescharacteristic
98#2059C2211yescharacteristic
99#2059C2211yescharacteristic
100#2059C2211yescharacteristic
101#2058C2211yescharacteristic
102#2057C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2036C2211yescharacteristic
106#2035C2211yescharacteristic
107#2034C2211yescharacteristic
108#2033C2211yescharacteristic
109#2026C2211yescharacteristic
110#2026C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#1989C2211yescharacteristic
114#1989C2211yescharacteristic
115#1989C2211yescharacteristic
116#1989C2211yescharacteristic
117#1988C2211yescharacteristic
118#1988C2211yescharacteristic
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1949C2211yescharacteristic
122#1949C2211yescharacteristic
123#1949C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1948C2211yescharacteristic
128#1947C2211yescharacteristic
129#1944C2211yescharacteristic
130#1944C2211yescharacteristic
131#1943C2211yescharacteristic
132#1943C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1928C2211yescharacteristic
138#1928C2211yescharacteristic
139#1928C2211yescharacteristic
140#1928C2211yescharacteristic
141#1927C2211yescharacteristic
142#1927C2211yescharacteristic
143#1927C2211yescharacteristic
144#1927C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1924C2211yescharacteristic
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1921C2211yescharacteristic
154#1921C2211yescharacteristic
155#1921C2211yescharacteristic
156#1920C2211yescharacteristic
157#1920C2211yescharacteristic
158#1920C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1919C2211yescharacteristic
162#1919C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1918C2211yescharacteristic
167#1918C2211yescharacteristic
168#1918C2211yescharacteristic
169#1917C2211yescharacteristic
170#1917C2211yescharacteristic
171#1917C2211yescharacteristic
172#1917C2211yescharacteristic
173#1874C2211yescharacteristic
174#1874C2211yescharacteristic
175#1872C2211yescharacteristic
176#1872C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1853C2211yescharacteristic
182#1853C2211yescharacteristic
183#1852C2211yescharacteristic
184#1852C2211yescharacteristic
185#1842C2211yescharacteristic
186#1831C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1797C2211yescharacteristic
192#1797C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197#1767C2211yescharacteristic
198#1767C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×#125—24no—
205C2×#125—24no—
206C2×#125—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224C2×#117—21no—
225C2×#117D411yescharacteristic
226C2×#117D411yescharacteristic
227C22×C4⋊C4—21no—
228C22×C4⋊C4—21no—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C42—21no—
232C22×C42C2311yescharacteristic
233#479—24no—
234#479—24no—
235#478—24no—
236#478—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#102C2311yescharacteristic
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×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285#401—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#397—21no—
292#397—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#396—21no—
297#394—21no—
298#394—21no—
299#393—21no—
300#393—21no—
301#391—21no—
302#391—21no—
303#391C2311yescharacteristic
304#391C2311yescharacteristic
305#391C2311yescharacteristic
306#391C2311yescharacteristic
307#390C2311yescharacteristic
308#390C2311yescharacteristic
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389C2311yescharacteristic
316#389C2311yescharacteristic
317#389C2311yescharacteristic
318#389C2311yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#388—21no—
330#388—21no—
331#388—21no—
332#388—21no—
333#388—21no—
334#387—21no—
335#387—21no—
336#387—21no—
337#387—21no—
338#387—21no—
339#387—21no—
340#387—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#387—21no—
354#387—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#386—21no—
366#386—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#384C2311yescharacteristic
372#383—21no—
373#382C2311yescharacteristic
374#382C2311yescharacteristic
375#382C2311yescharacteristic
376#381—21no—
377#381—21no—
378#381—21no—
379#381—21no—
380#380—21no—
381#380—21no—
382#380—21no—
383#380C2311yescharacteristic
384#380C2311yescharacteristic
385#380C2311yescharacteristic
386#380C2311yescharacteristic
387C4×C4⋊C4—21no—
388C4×C4⋊C4—21no—
389C4×C4⋊C4—21no—
390C4×C4⋊C4—21no—
391C4×C4⋊C4—21no—
392C4×C4⋊C4—21no—
393C4×C4⋊C4—21no—
394C4×C4⋊C4—21no—
395C4×C4⋊C4—21no—
396C4×C4⋊C4—21no—
397C4×C4⋊C4—21no—
398C4×C4⋊C4—21no—
399C4×C4⋊C4—21no—
400C4×C4⋊C4—21no—
401C4×C4⋊C4—21no—
402C4×C4⋊C4D411yescharacteristic
403C4×C4⋊C4D411yescharacteristic
404C4×C4⋊C4C2311yescharacteristic
405C4×C4⋊C4C2311yescharacteristic
406C4×C4⋊C4C2311yescharacteristic
407C4×C4⋊C4C2311yescharacteristic
408C4×C4⋊C4C2311yescharacteristic
409C4×C4⋊C4C2311yescharacteristic
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426C4×C22⋊C4—21no—
427C4×C22⋊C4—21no—
428C4×C22⋊C4—21no—
429C4×C22⋊C4—21no—
430C4×C22⋊C4D411yescharacteristic
431C4×C22⋊C4D411yescharacteristic
432C4×C22⋊C4C2311yescharacteristic
433C4×C22⋊C4C2311yescharacteristic
434#376—21no—
435#376—21no—
436#376D411yescharacteristic
437#376D411yescharacteristic
438C43C2311yescharacteristic
439C43C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
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×D4—21no—
487C22×D4C2411yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4C2×D411yescharacteristic
494C23×C4C2×D411yescharacteristic
495C23×C4C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C22×C8C2411yescharacteristic
501C22×C8C2411yescharacteristic
502C22×C8C2411yescharacteristic
503C22×C8C2411yescharacteristic
504C4⋊Q8—22no—
505C4⋊Q8—41no—
506#125—28no—
507#125—28no—
508#125—22no—
509#125—22no—
510#125—22no—
511#125—22no—
512#125—22no—
513#125—22no—
514#125#4114yes—
515#125#4114yes—
516#124—22no—
517#124—41no—
518#123—44no—
519C22⋊Q8—22no—
520C22⋊Q8—41no—
521C22⋊Q8—44no—
522#121—22no—
523#121—41no—
524C4×Q8—22no—
525C4×Q8—22no—
526C4×Q8—82no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—22no—
530C4×D4—22no—
531C4×D4—41no—
532C4×D4—41no—
533C4×D4—82no—
534#117—42no—
535#117—42no—
536#117—44no—
537#117—44no—
538C2×C4⋊C4—28no—
539C2×C4⋊C4—28no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
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⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
607C2×C22⋊C4C2×D411yescharacteristic
608C2×C22⋊C4C2×D411yescharacteristic
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—82no—
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644#107—22no—
645#107—22no—
646#107—22no—
647#107—22no—
648#107—22no—
649#107—41no—
650#107—41no—
651#107—41no—
652#106—22no—
653#106—22no—
654#106—22no—
655#106—22no—
656#106—22no—
657#106—41no—
658#106—41no—
659#106—41no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—41no—
673#103—41no—
674#103—41no—
675#103—41no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—41no—
683#102—41no—
684C22⋊C8—41no—
685C22⋊C8—41no—
686C22⋊C8—41no—
687C22⋊C8—41no—
688#97—41no—
689#97—41no—
690#97—41no—
691#97—41no—
692#95—21no—
693#95—21no—
694#95—21no—
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#95—21no—
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C24C22×D411yescharacteristic
748C2×Q8—21no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8—21no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—42no—
755C2×Q8—42no—
756C2×Q8—81no—
757C2×D4—21no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—42no—
763C2×D4—42no—
764C2×D4—81no—
765C2×D42−1+412yes—
766C22×C4—24no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—24no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—41no—
793C22×C4—41no—
794C22×C4—41no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—42no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—81no—
805C22×C4—81no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C2511yescharacteristic
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
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—
846C4⋊C4—24no—
847C4⋊C4—24no—
848C4⋊C4—24no—
849C4⋊C4—24no—
850C4⋊C4—24no—
851C4⋊C4—24no—
852C4⋊C4—24no—
853C4⋊C4—24no—
854C4⋊C4—24no—
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
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—41no—
881C4⋊C4—41no—
882C4⋊C4—41no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
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⋊C4C2×#4112yes—
903C4⋊C4C2×#4112yes—
904C4⋊C4C2×#4112yes—
905C4⋊C4C2×#4112yes—
906C4⋊C42−1+412yes—
907C22⋊C4—22no—
908C22⋊C4—22no—
909C22⋊C4—22no—
910C22⋊C4—41no—
911C22⋊C4—42no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—42no—
920C22⋊C4—42no—
921C22⋊C4—42no—
922C22⋊C4—42no—
923C22⋊C4—42no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C42—22no—
927C42—22no—
928C42—22no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—41no—
940C42—41no—
941C42—41no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—42no—
947C42—42no—
948C42—42no—
949C42—42no—
950C42—42no—
951C42—42no—
952C42—42no—
953C42—81no—
954C42—81no—
955C42—81no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42C2×#4112yes—
962C42C2×#4112yes—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—22no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23#57512yes—
977C23C23×D411yescharacteristic
978Q8—41no—
979Q8—41no—
980Q8—41no—
981Q8—41no—
982Q8—84no—
983D4—22no—
984D4—22no—
985D4—41no—
986D4—41no—
987D4—84no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—22no—
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—44no—
1030C2×C4—48no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
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—82no—
1076C2×C4—84no—
1077C2×C4—84no—
1078C2×C4—84no—
1079C2×C4—84no—
1080C2×C4#52512yes—
1081C2×C4#52512yes—
1082C2×C4#57512yes—
1083C2×C4C22×#4111yescharacteristic
1084C2×C4C22×#4111yescharacteristic
1085C2×C4C2×2−1+411yescharacteristic
1086C2×C4C2×2−1+411yescharacteristic
1087C2×C4#58511yescharacteristic
1088C2×C4#58511yescharacteristic
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C8—41no—
1096C8—41no—
1097C22—22no—
1098C22—22no—
1099C22—22no—
1100C22—41no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22C2×#52511yescharacteristic
1112C22#348911yescharacteristic
1113C22#348911yescharacteristic
1114C22C2×#57511yescharacteristic
1115C22C2×#57511yescharacteristic
1116C22#358511yescharacteristic
1117C22#358611yescharacteristic
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—41no—
1122C4—41no—
1123C4—42no—
1124C4—42no—
1125C4—41no—
1126C4—42no—
1127C4—42no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—42no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4#351611yescharacteristic
1147C4#351811yescharacteristic
1148C4#352311yescharacteristic
1149C4#352411yescharacteristic
1150C2—42no—
1151C2—82no—
1152C2#3566311yescharacteristic
1153C2#6054611yescharacteristic
1154C2#6056711yescharacteristic
1155C2#6211911yescharacteristic
1156C2#6211911yescharacteristic
1157C2#6212011yescharacteristic
1158C2#6212111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34239C2semidirect
3. #29288C2semidirect
4. #29278C2semidirect
5. #28285C2semidirect
6. #28208C2semidirect
7. #27634C2semidirect
9. #27476C2semidirect
10. #27472C2semidirect
13. #27349C2semidirect
14. #27345C2semidirect
17. #27156C2semidirect
18. #27152C2semidirect
19. #27026C2semidirect
20. #27022C2semidirect
21. #26887C2semidirect
22. #26883C2semidirect
23. #26717C2semidirect
24. #26713C2semidirect
25. #24307C2semidirect
27. #22121C2semidirect
28. #22121C2semidirect
29. #21926C2semidirect
30. #21617C2semidirect
31. #21617C2semidirect

Maximal subgroups

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

subgroupindex
#349692
#342392
#292882
#292782
#282852
#282082
#276342
#276322
#274762
#274722
#274102
#274062
#273492
#273452
#271792
#271752
#271562
#271522
#270262
#270222
#268872
#268832
#267172
#267132
#243072
#243052
#221212
#219262
#216172