Finite Group Databasebeta

← #26032066

Subgroups — #26032066

Order 11392.

494 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152252C211yesmaximal, characteristic, complemented
2D4×D356C211yesmaximal, characteristic, complemented
3#19151945C211yesmaximal, characteristic, complemented
4#19151912C212yesmaximal, complemented
5#19151879C211yesmaximal, characteristic, complemented
6#19151834C212yesmaximal, complemented
7#19151794C211yesmaximal, characteristic, complemented
8#19151734C212yesmaximal, complemented
9C4×D712C211yesmaximal, characteristic, complemented
10C2×#15667934C212yesmaximal, complemented
11C8×D4×C89C211yesmaximal, characteristic, complemented
12C2×#13083573—21no—
13C22×D356C2212yes—
14C2×D4×D89—21no—
15C2×D712C2211yescharacteristic
16C2×D712C2212yescomplemented
17#15668012C2211yescharacteristic, complemented
18#15668009C2211yescharacteristic
19#15667996—22no—
20#15667992—21no—
21#15667987—21no—
22#15667986C2212yes—
23#15667986C2212yescomplemented
24#15667982—22no—
25C4×D356C2211yescharacteristic
26C4×D356C2211yescharacteristic, complemented
27C2×C4⋊Dic89C2212yescomplemented
28#15667946C2212yescomplemented
29#15667946C2211yescharacteristic, complemented
30#15667934C2212yes—
31#15667934C2211yescharacteristic
32#15667934C2212yescomplemented
33#15667934C2212yescomplemented
34#15667934C2211yescharacteristic, complemented
35#15667934C2212yescomplemented
36C22×C8×C89C2212yescomplemented
37C4×D4×C89C2211yescharacteristic
38C4⋊C8×C89C2211yescharacteristic, complemented
39C22⋊C8×C89C2212yescomplemented
40C4×C8×C89C2211yescharacteristic, complemented
41C23×D89—22no—
42#13083573—44no—
43C2×Dic178—21no—
44C2×D356—24no—
45C2×D356—22no—
46C2×D356—21no—
47C2×D356—21no—
48C2×D356—42no—
49C2×D356C2311yescharacteristic
50C2×D356C2312yes—
51C2×D356C2311yescharacteristic
52C2×C22⋊D89—22no—
53C2×C22⋊D89—22no—
54D4×D89—44no—
55C22×Dic89—22no—
56C2×C4×D89—21no—
57C2×C4×D89—21no—
58D712—22no—
59D712—42no—
60C4⋊Dic89—22no—
61C4⋊Dic89—21no—
62C4⋊Dic89C2311yescharacteristic
63C4⋊Dic89C2311yescharacteristic
64C4⋊Dic89C2312yes—
65#13083551—21no—
66#13083551—21no—
67#13083551—22no—
68#13083551—22no—
69C2×D4×C89D411yescharacteristic
70C22×C4×C89C2312yes—
71C2×C8×C89—42no—
72C2×C8×C89C2311yescharacteristic
73C2×C8×C89C2312yes—
74C2×C8×C89C2311yescharacteristic
75C4⋊C4×C89D411yescharacteristic
76C22⋊C4×C89D412yes—
77C42×C89C2311yescharacteristic
78C23×C89C2×D412yes—
79C22×D89—21no—
80C22×D89—21no—
81C22×D89—22no—
82C22×D89—44no—
83C22×D89—44no—
84C22×D89—82no—
85D4×C89D814yescomplemented
86C2×C4×C89—22no—
87C2×C4×C89—22no—
88C2×C4×C89C2×D411yescharacteristic
89C2×C4×C89C2×D412yes—
90C2×C4×C89C2×D411yescharacteristic
91C2×C4×C89C2411yescharacteristic
92C22⋊D89—44no—
93C22⋊D89—44no—
94C2×Dic89—21no—
95C2×Dic89—21no—
96C2×Dic89—22no—
97C2×Dic89—44no—
98D356—21no—
99D356—22no—
100D356—21no—
101D356—21no—
102D356—22no—
103D356—44no—
104D356—42no—
105D356—81no—
106D356#4112yescomplemented
107C4×D89—42no—
108C4×D89—42no—
109Dic178—42no—
110C8×C89—21no—
111C8×C89—21no—
112C8×C89—22no—
113C22×C89—22no—
114C22×C89—22no—
115C22×C89C2×D814yes—
116C22×C89C22×D411yescharacteristic
117C2×D89—22no—
118C2×D89—41no—
119C2×D89—41no—
120C2×D89—42no—
121C2×D89—41no—
122C2×D89—41no—
123C2×D89—42no—
124C2×D89—42no—
125C2×D89—41no—
126C2×D89—88no—
127C4×C89—22no—
128C4×C89—21no—
129C4×C89C2×D812yes—
130C4×C89C2×#4111yescharacteristic
131C4×C89H(5,𝔽2)11yescharacteristic
132Dic89—42no—
133Dic89—41no—
134Dic89—41no—
135C2×C89—24no—
136C2×C89#54611yescharacteristic
137C2×C89C22×D811yescharacteristic
138C2×C89#57711yescharacteristic
139D89—42no—
140D89—81no—
141D89—82no—
142#3294—891nomaximal, Sylow
143C89#329411yescharacteristic, complemented, Sylow
144#547—891no—
145D42—891no—
146#486—891no—
147#480—892no—
148#474—891no—
149#466—892no—
150#459—891no—
151#447—892no—
152C4×D8—891no—
153C8×D4D8911yescharacteristic, complemented
154C2×#102—892no—
155C2×#41—1781no—
156C22×D4—892no—
157C22×D4—1781no—
158C2×D8—892no—
159C2×D8—891no—
160C22×C8C2×D8912yescomplemented
161C4⋊Q8—891no—
162#127—891no—
163#123—1782no—
164C22⋊Q8—1781no—
165#121—892no—
166#121—892no—
167#121—1781no—
168#120—1782no—
169C4×D4—891no—
170C4×D4—891no—
171C4×D4C2×D8911yescharacteristic
172C2×C4⋊C4—892no—
173#107—891no—
174#107—892no—
175C4⋊C8C2×D8911yescharacteristic, complemented
176#102—891no—
177#102—892no—
178#102—892no—
179#102—892no—
180#102—891no—
181#102—892no—
182C22⋊C8C2×D8912yescomplemented
183C4×C8C2×D8911yescharacteristic, complemented
184C24—1782no—
185#41—3564no—
186C2×Q8—1781no—
187C2×D4—891no—
188C2×D4—892no—
189C2×D4—891no—
190C2×D4—3562no—
191C2×D4—3564no—
192C2×D4—1784no—
193C2×D4—1782no—
194C2×D4—1782no—
195C2×D4—1782no—
196C2×D4—1781no—
197C2×D4—1781no—
198C2×D4D35611yescharacteristic
199C22×C4—1782no—
200C22×C4—1781no—
201C22×C4—1781no—
202C22×C4C22×D8912yes—
203D8—3562no—
204D8—1782no—
205C2×C8—42no—
206C2×C8C22×D8911yescharacteristic
207C2×C8C22×D8911yescharacteristic
208C2×C8C22×D8912yes—
209C4⋊C4—891no—
210C4⋊C4—892no—
211C4⋊C4—891no—
212C4⋊C4—1782no—
213C4⋊C4—1781no—
214C4⋊C4D35611yescharacteristic
215C22⋊C4—1781no—
216C22⋊C4—1781no—
217C22⋊C4—1782no—
218C22⋊C4—1782no—
219C22⋊C4D35612yes—
220C42C22×D8911yescharacteristic
221C23—3564no—
222C23—3564no—
223C23—1781no—
224C23—1782no—
225C23—1781no—
226C23—7122no—
227C23C2×D35612yes—
228Q8—3562no—
229D4—892no—
230D4—3564no—
231D4—3564no—
232D4—3564no—
233D4—3562no—
234D4—1781no—
235D4—1782no—
236D4—1781no—
237D4—1782no—
238D4—1781no—
239D4—7121no—
240D4D71214yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—3564no—
244C2×C4—3562no—
245C2×C4—3562no—
246C2×C4—1781no—
247C2×C4—1781no—
248C2×C4—1782no—
249C2×C4C2×D35611yescharacteristic
250C2×C4C2×D35612yes—
251C2×C4C2×D35611yescharacteristic
252C2×C4C23×D8911yescharacteristic
253C8—21no—
254C8—21no—
255C8—22no—
256C22—22no—
257C22—22no—
258C22—3561no—
259C22—3561no—
260C22—3562no—
261C22—3561no—
262C22—3562no—
263C22—3561no—
264C22—3561no—
265C22—3562no—
266C22—1782no—
267C22—7128no—
268C22C2×D71214yes—
269C22C22×D35611yescharacteristic
270C4—21no—
271C4—22no—
272C4—3561no—
273C4—3561no—
274C4—3562no—
275C4C2×D71212yes—
276C4#41×D8911yescharacteristic
277C4#1566805711yescharacteristic
278C2—24no—
279C2—3562no—
280C2—7121no—
281C2—7122no—
282C2#1915224311yescharacteristic
283C2C22×D71211yescharacteristic
284C2#1915241011yescharacteristic
subgroupG/H
centerC22C22×D356
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
FittingC8×D4×C89C2
socleC22×C89C22×D4
hypercenterC8×D4D89
hypocenterC89#3294
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. #19152252C2semidirect
2. D4×D356C2semidirect
3. #19151945C2semidirect
4. #19151912C2semidirect
5. #19151879C2semidirect
6. #19151834C2semidirect
7. #19151794C2semidirect
8. #19151734C2semidirect
9. C4×D712C2semidirect
10. C2×#15667934C2semidirect
11. C8×D4×C89C2semidirect
16. C2×D712C22semidirect
17. #15668012C22semidirect
23. #15667986C22semidirect
26. C4×D356C22semidirect
27. C2×C4⋊Dic89C22semidirect
28. #15667946C22semidirect
29. #15667946C22semidirect
32. #15667934C22semidirect
33. #15667934C22semidirect
34. #15667934C22semidirect
35. #15667934C22semidirect
36. C22×C8×C89C22semidirect
38. C4⋊C8×C89C22semidirect
39. C22⋊C8×C89C22semidirect
40. C4×C8×C89C22semidirect
85. D4×C89D8semidirect
106. D356#41semidirect
143. C89#3294semidirect
153. C8×D4D89semidirect
160. C22×C8C2×D89semidirect
175. C4⋊C8C2×D89semidirect
182. C22⋊C8C2×D89semidirect
183. C4×C8C2×D89semidirect
240. D4D712semidirect

Maximal subgroups

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

subgroupindex
#191522522
D4×D3562
#191519452
#191519122
#191518792
#191518342
#191517942
#191517342
C4×D7122
C2×#156679342
C8×D4×C892
#329489