Finite Group Databasebeta

← #6568344

Subgroups — #6568344

Order 512.

1574 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39510C211yesmaximal, characteristic, complemented
2#34493C211yesmaximal, characteristic
3#30180C211yesmaximal, characteristic, complemented
4#30178C211yesmaximal, characteristic, complemented
5#29870C211yesmaximal, characteristic, complemented
6#29256C211yesmaximal, characteristic, complemented
7#29115C211yesmaximal, characteristic, complemented
8#29115C211yesmaximal, characteristic, complemented
9#28722C211yesmaximal, characteristic, complemented
10#27591C211yesmaximal, characteristic, complemented
11#27591C211yesmaximal, characteristic, complemented
12#27536C211yesmaximal, characteristic, complemented
13#27534C211yesmaximal, characteristic, complemented
14#27525C211yesmaximal, characteristic, complemented
15#27523C211yesmaximal, characteristic, complemented
16#27125C211yesmaximal, characteristic, complemented
17#27123C211yesmaximal, characteristic, complemented
18#27108C211yesmaximal, characteristic, complemented
19#27106C211yesmaximal, characteristic, complemented
20#26311C211yesmaximal, characteristic, complemented
21#26309C211yesmaximal, characteristic, complemented
22#25891C211yesmaximal, characteristic
23#25891C211yesmaximal, characteristic
24#23784C211yesmaximal, characteristic, complemented
25#23771C211yesmaximal, characteristic, complemented
26#23767C211yesmaximal, characteristic, complemented
27#23231C211yesmaximal, characteristic, complemented
28#23229C211yesmaximal, characteristic, complemented
29#23076C211yesmaximal, characteristic, complemented
30#23072C211yesmaximal, characteristic, complemented
31#22838C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#490C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37#2859C2211yescharacteristic, complemented
38#2800—21no—
39#2800—21no—
40#2776—21no—
41#2776—21no—
42#2629C2211yescharacteristic, complemented
43#2629C2211yescharacteristic, complemented
44#2594—21no—
45#2594—21no—
46#2562C2211yescharacteristic
47#2562C2211yescharacteristic
48#2525—21no—
49#2525—21no—
50#2495C2211yescharacteristic, complemented
51#2495C2211yescharacteristic, complemented
52#2494C2211yescharacteristic, complemented
53#2494C2211yescharacteristic, complemented
54#2375—21no—
55#2375—21no—
56#2370C2211yescharacteristic, complemented
57#2370C2211yescharacteristic, complemented
58#2366C2211yescharacteristic
59#2363—21no—
60#2363C2211yescharacteristic
61#2363C2211yescharacteristic
62#2354C2211yescharacteristic
63#2354C2211yescharacteristic
64D4×C22⋊C4—21no—
65D4×C22⋊C4C2211yescharacteristic
66D4×C22⋊C4C2211yescharacteristic
67#2324—21no—
68#2324C2211yescharacteristic
69#2324C2211yescharacteristic
70#2321—21no—
71#2321—21no—
72#2314C2211yescharacteristic, complemented
73#2314C2211yescharacteristic, complemented
74#2309—21no—
75#2309C2211yescharacteristic
76#2309C2211yescharacteristic
77C4×#127C2211yescharacteristic
78C4×#125C2211yescharacteristic, complemented
79#2293C2211yescharacteristic
80#2293C2211yescharacteristic
81#2101C2211yescharacteristic, complemented
82#2092C2211yescharacteristic
83#2092C2211yescharacteristic, complemented
84#2092C2211yescharacteristic, complemented
85#2088C2211yescharacteristic, complemented
86#2086C2211yescharacteristic, complemented
87#2085C2211yescharacteristic, complemented
88#2085C2211yescharacteristic, complemented
89#2084C2211yescharacteristic, complemented
90#2083C2211yescharacteristic, complemented
91#2077C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2077C2211yescharacteristic, complemented
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic, complemented
104#2071C2211yescharacteristic, complemented
105#2071C2211yescharacteristic, complemented
106#2071C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2065C2211yescharacteristic
109#2059C2211yescharacteristic, complemented
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic, complemented
120#2025C2211yescharacteristic, complemented
121#1992C2211yescharacteristic, complemented
122#1992C2211yescharacteristic, complemented
123#1989C2211yescharacteristic, complemented
124#1989C2211yescharacteristic, complemented
125#1982C2211yescharacteristic
126#1982C2211yescharacteristic
127#1955C2211yescharacteristic
128#1955C2211yescharacteristic
129#1948C2211yescharacteristic, complemented
130#1947C2211yescharacteristic, complemented
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic, complemented
134#1936C2211yescharacteristic, complemented
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic, complemented
142#1926C2211yescharacteristic, complemented
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic, complemented
146#1925C2211yescharacteristic, complemented
147#1924C2211yescharacteristic, complemented
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic, complemented
150#1923C2211yescharacteristic, complemented
151#1921C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1864C2211yescharacteristic, complemented
156#1864C2211yescharacteristic, complemented
157#1864C2211yescharacteristic, complemented
158#1864C2211yescharacteristic, complemented
159#1862C2211yescharacteristic, complemented
160#1862C2211yescharacteristic, complemented
161#1862C2211yescharacteristic, complemented
162#1862C2211yescharacteristic, complemented
163#1854C2211yescharacteristic, complemented
164#1854C2211yescharacteristic, complemented
165#1854C2211yescharacteristic, complemented
166#1854C2211yescharacteristic, complemented
167#1831C2211yescharacteristic, complemented
168#1825C2211yescharacteristic, complemented
169#1825C2211yescharacteristic, complemented
170#1825C2211yescharacteristic, complemented
171#1825C2211yescharacteristic, complemented
172#1818C2211yescharacteristic, complemented
173#1818C2211yescharacteristic, complemented
174#1804C2211yescharacteristic, complemented
175#1804C2211yescharacteristic, complemented
176#1804C2211yescharacteristic, complemented
177#1804C2211yescharacteristic, complemented
178#1786C2211yescharacteristic
179#1786C2211yescharacteristic
180#1786C2211yescharacteristic
181#1786C2211yescharacteristic
182#1786C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1786C2211yescharacteristic
186#1776C2211yescharacteristic, complemented
187#1776C2211yescharacteristic, complemented
188#1776C2211yescharacteristic, complemented
189#1776C2211yescharacteristic, complemented
190C4×#107C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1767C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206D42—24no—
207D42—24no—
208C2×#127C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#121—21no—
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×#120—21no—
216C2×#120—21no—
217C2×C4×D4—21no—
218C2×C4×D4—21no—
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227C2×#117—21no—
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C22×C22⋊C4—21no—
233C22×C22⋊C4—21no—
234#490—24no—
235#490—24no—
236#478—24no—
237#478—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292#401—21no—
293#401—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#394—21no—
311#394—21no—
312#390—21no—
313#390—21no—
314#390—21no—
315#390—21no—
316#390—21no—
317#390—21no—
318#390—21no—
319#390—21no—
320#390—21no—
321#390—21no—
322#390—21no—
323#390—21no—
324#390D411yescharacteristic
325#390D411yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389D411yescharacteristic
341#389D411yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#388—21no—
351#388—21no—
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#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#388D411yescharacteristic
373#388D411yescharacteristic
374#388D411yescharacteristic
375#388D411yescharacteristic
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#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#385—21no—
399#385—21no—
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#383—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#380—21no—
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#379—21no—
420#379—21no—
421#379—21no—
422#379—21no—
423#379—21no—
424#379—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445C43C2311yescharacteristic
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
484C25—21no—
485C25—21no—
486C22×D4—28no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—22no—
490C22×D4—22no—
491C22×D4—22no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4—82no—
506C22×D4—82no—
507C22×D4C2×D411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526#127—22no—
527#127#4114yes—
528#125—22no—
529#125—22no—
530#125—22no—
531#125—22no—
532#125—41no—
533#125—41no—
534#121—28no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#120—28no—
540#120—28no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—82no—
553C4×D4—82no—
554C4×D4—82no—
555C4×D4#4114yes—
556#117—41no—
557#117—41no—
558#117—41no—
559#117—41no—
560#117—41no—
561#117—41no—
562#117—41no—
563#117—41no—
564#117—82no—
565#117—82no—
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—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
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⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—82no—
642C2×C22⋊C4—82no—
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2×D411yescharacteristic
667C2×C42C2×D411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673#107—22no—
674#107—22no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#106—22no—
680#106—22no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—41no—
688C4⋊C8—41no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—22no—
700#102—22no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713C22⋊C8—41no—
714C22⋊C8—41no—
715C22⋊C8—41no—
716C22⋊C8—41no—
717C22⋊C8—41no—
718C22⋊C8—41no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721#97—22no—
722#97—22no—
723#97—41no—
724#97—41no—
725C4×C8—41no—
726C4×C8—41no—
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#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766C24—24no—
767C24—24no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—81no—
772C24—81no—
773C24—81no—
774C24—81no—
775C24—81no—
776C24—81no—
777C24—81no—
778C24—81no—
779C24—81no—
780C24—81no—
781C24—81no—
782C24—81no—
783C24C22×D411yescharacteristic
784C24C22×D411yescharacteristic
785C2×D4—24no—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—24no—
789C2×D4—22no—
790C2×D4—24no—
791C2×D4—24no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—41no—
808C2×D4—41no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4—82no—
818C2×D4—82no—
819C2×D4—82no—
820C2×D4—82no—
821C2×D4—82no—
822C2×D4—82no—
823C2×D4—82no—
824C2×D4—82no—
825C2×D4—816no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4C2×#4112yes—
831C2×D4C2×#4112yes—
832C2×D4C2×#4112yes—
833C22×C4—21no—
834C22×C4—24no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—42no—
860C22×C4—42no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C2511yescharacteristic
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C4⋊C4—22no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4C2×#4112yes—
963C22⋊C4—24no—
964C22⋊C4—24no—
965C22⋊C4—24no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—41no—
969C22⋊C4—41no—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—42no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—41no—
1017C42—41no—
1018C42—41no—
1019C42—41no—
1020C42—42no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C42—81no—
1026C42—81no—
1027C42—81no—
1028C42—81no—
1029C42—81no—
1030C42—81no—
1031C42C2×#4112yes—
1032C42C2×#4112yes—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—84no—
1069C23—84no—
1070C23—84no—
1071C23—84no—
1072C23—84no—
1073C23—84no—
1074C23—162no—
1075C23—162no—
1076C23—162no—
1077C23—162no—
1078C23—162no—
1079C23—162no—
1080C23—162no—
1081C23—162no—
1082C23C23×D411yescharacteristic
1083D4—22no—
1084D4—22no—
1085D4—22no—
1086D4—22no—
1087D4—22no—
1088D4—22no—
1089D4—48no—
1090D4—44no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
1100D4—84no—
1101D4—84no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—48no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—162no—
1185C2×C4—162no—
1186C2×C4—162no—
1187C2×C4—162no—
1188C2×C4#52512yes—
1189C2×C4#52512yes—
1190C2×C4C22×#4111yescharacteristic
1191C2×C4C22×#4111yescharacteristic
1192C2×C4#58511yescharacteristic
1193C2×C4#58511yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C8—41no—
1197C8—41no—
1198C8—41no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—42no—
1213C22—41no—
1214C22—41no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—42no—
1219C22—41no—
1220C22—41no—
1221C22—42no—
1222C22—41no—
1223C22—41no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—168no—
1240C22—168no—
1241C22C2×#52511yescharacteristic
1242C22#348511yescharacteristic
1243C22#350011yescharacteristic
1244C22#358411yescharacteristic
1245C22#358511yescharacteristic
1246C22#358511yescharacteristic
1247C22#358511yescharacteristic
1248C4—22no—
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—42no—
1259C4—41no—
1260C4—41no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4#351011yescharacteristic
1274C4#351011yescharacteristic
1275C4#352111yescharacteristic
1276C4#352111yescharacteristic
1277C2—81no—
1278C2—81no—
1279C2—82no—
1280C2—82no—
1281C2—82no—
1282C2#3603311yescharacteristic
1283C2#6056411yescharacteristic
1284C2#6060111yescharacteristic
1285C2#6179711yescharacteristic
1286C2#6181311yescharacteristic
1287C2#6256411yescharacteristic
1288C2#6260711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39510C2semidirect
3. #30180C2semidirect
4. #30178C2semidirect
5. #29870C2semidirect
6. #29256C2semidirect
7. #29115C2semidirect
8. #29115C2semidirect
9. #28722C2semidirect
10. #27591C2semidirect
11. #27591C2semidirect
12. #27536C2semidirect
13. #27534C2semidirect
14. #27525C2semidirect
15. #27523C2semidirect
16. #27125C2semidirect
17. #27123C2semidirect
18. #27108C2semidirect
19. #27106C2semidirect
20. #26311C2semidirect
21. #26309C2semidirect
24. #23784C2semidirect
25. #23771C2semidirect
26. #23767C2semidirect
27. #23231C2semidirect
28. #23229C2semidirect
29. #23076C2semidirect
30. #23072C2semidirect
31. #22838C2semidirect
37. #2859C22semidirect
42. #2629C22semidirect
43. #2629C22semidirect
50. #2495C22semidirect
51. #2495C22semidirect
52. #2494C22semidirect
53. #2494C22semidirect
56. #2370C22semidirect
57. #2370C22semidirect
72. #2314C22semidirect
73. #2314C22semidirect
78. C4×#125C22semidirect
81. #2101C22semidirect
83. #2092C22semidirect
84. #2092C22semidirect
85. #2088C22semidirect
86. #2086C22semidirect
87. #2085C22semidirect
88. #2085C22semidirect
89. #2084C22semidirect
90. #2083C22semidirect
91. #2077C22semidirect
92. #2077C22semidirect
93. #2077C22semidirect
94. #2077C22semidirect
95. #2076C22semidirect
96. #2076C22semidirect
97. #2075C22semidirect
98. #2075C22semidirect
103. #2071C22semidirect
104. #2071C22semidirect
105. #2071C22semidirect
106. #2071C22semidirect
109. #2059C22semidirect
119. #2025C22semidirect
120. #2025C22semidirect
121. #1992C22semidirect
122. #1992C22semidirect
123. #1989C22semidirect
124. #1989C22semidirect
129. #1948C22semidirect
130. #1947C22semidirect
133. #1936C22semidirect
134. #1936C22semidirect
137. #1934C22semidirect
138. #1934C22semidirect
141. #1926C22semidirect
142. #1926C22semidirect
145. #1925C22semidirect
146. #1925C22semidirect
147. #1924C22semidirect
148. #1924C22semidirect
149. #1923C22semidirect
150. #1923C22semidirect
151. #1921C22semidirect
152. #1920C22semidirect
153. #1919C22semidirect
154. #1918C22semidirect
155. #1864C22semidirect
156. #1864C22semidirect
157. #1864C22semidirect
158. #1864C22semidirect
159. #1862C22semidirect
160. #1862C22semidirect
161. #1862C22semidirect
162. #1862C22semidirect
163. #1854C22semidirect
164. #1854C22semidirect
165. #1854C22semidirect
166. #1854C22semidirect
167. #1831C22semidirect
168. #1825C22semidirect
169. #1825C22semidirect
170. #1825C22semidirect
171. #1825C22semidirect
172. #1818C22semidirect
173. #1818C22semidirect
174. #1804C22semidirect
175. #1804C22semidirect
176. #1804C22semidirect
177. #1804C22semidirect
186. #1776C22semidirect
187. #1776C22semidirect
188. #1776C22semidirect
189. #1776C22semidirect
190. C4×#107C22semidirect
191. C4×#106C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
194. #1767C22semidirect
197. #1762C22semidirect
198. #1762C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#395102
#344932
#301802
#301782
#298702
#292562
#291152
#287222
#275912
#275362
#275342
#275252
#275232
#271252
#271232
#271082
#271062
#263112
#263092
#258912
#237842
#237712
#237672
#232312
#232292
#230762
#230722
#228382