Finite Group Databasebeta

← #26032059

Subgroups — #26032059

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
1D4×D356C211yesmaximal, characteristic, complemented
2#19151946C211yesmaximal, characteristic, complemented
3#19151911C212yesmaximal, complemented
4#19151875C211yesmaximal, characteristic, complemented
5#19151832C212yesmaximal, complemented
6#19151793C211yesmaximal, characteristic, complemented
7#19151731C212yesmaximal, complemented
8C4×#13083559C211yesmaximal, characteristic, complemented
9D4×#10623494C211yesmaximal, characteristic, complemented
10C2×#15667932C212yesmaximal, complemented
11#547×C89C211yesmaximal, characteristic, complemented
12C22×D356C2212yes—
13C2×D4×D89—21no—
14C2×#13083559C2211yescharacteristic
15C2×#13083559C2212yescomplemented
16C22×#10623494C2212yescomplemented
17#15668009C2211yescharacteristic
18#15667987—21no—
19#15667986C2212yes—
20#15667982—22no—
21C4×D356C2211yescharacteristic
22#15667945C2212yescomplemented
23#15667945C2211yescharacteristic, complemented
24C4⋊#10623494C2211yescharacteristic, complemented
25#15667933C2211yescharacteristic, complemented
26#15667932C2212yes—
27#15667932C2211yescharacteristic
28#15667932C2212yescomplemented
29#15667932C2212yescomplemented
30#15667932C2212yescomplemented
31C22⋊#10623494C2212yescomplemented
32C4×#10623494C2211yescharacteristic, complemented
33C2×#41×C89—21no—
34C4⋊Q8×C89C2211yescharacteristic, complemented
35#123×C89—22no—
36C22⋊Q8×C89—21no—
37#121×C89C2212yescomplemented
38C4×D4×C89C2211yescharacteristic
39C4×D4×C89C2211yescharacteristic, complemented
40C2×C4⋊C4×C89C2212yescomplemented
41C23×D89—22no—
42C2×D356—24no—
43C2×D356—22no—
44C2×D356—21no—
45C2×D356—21no—
46C2×D356—42no—
47C2×D356C2312yes—
48C2×D356C2311yescharacteristic
49C2×C22⋊D89—22no—
50D4×D89—44no—
51C2×C4×D89—21no—
52#13083559—22no—
53#13083559—42no—
54C2×#10623494—42no—
55C2×#10623494C2311yescharacteristic
56C2×#10623494C2312yes—
57C2×#10623494C2311yescharacteristic
58C4⋊Dic89C2311yescharacteristic
59#13083551—21no—
60#13083551—22no—
61#41×C89—44no—
62C2×Q8×C89—21no—
63C2×D4×C89—22no—
64C2×D4×C89D411yescharacteristic
65C2×D4×C89C2311yescharacteristic
66C22×C4×C89—22no—
67C22×C4×C89—21no—
68C22×C4×C89C2312yes—
69C4⋊C4×C89—22no—
70C4⋊C4×C89—21no—
71C4⋊C4×C89D411yescharacteristic
72C4⋊C4×C89C2311yescharacteristic
73C4⋊C4×C89C2312yes—
74C22⋊C4×C89—21no—
75C22⋊C4×C89—22no—
76C22⋊C4×C89D412yes—
77C42×C89C2311yescharacteristic
78C23×C89—21no—
79C23×C89C2×D412yes—
80C22×D89—21no—
81C22×D89—22no—
82C22×D89—44no—
83C22×D89—44no—
84C22×D89—82no—
85Q8×C89—42no—
86D4×C89—21no—
87D4×C89—21no—
88D4×C89—44no—
89D4×C89D814yescomplemented
90C2×C4×C89—22no—
91C2×C4×C89—22no—
92C2×C4×C89—21no—
93C2×C4×C89—22no—
94C2×C4×C89—44no—
95C2×C4×C89—42no—
96C2×C4×C89C2×D411yescharacteristic
97C2×C4×C89C2×D412yes—
98C2×C4×C89C2×D411yescharacteristic
99C2×C4×C89C2411yescharacteristic
100C22⋊D89—44no—
101C2×Dic89—21no—
102D356—22no—
103D356—21no—
104D356—22no—
105D356—44no—
106D356—42no—
107D356—81no—
108D356#4112yescomplemented
109C4×D89—42no—
110#10623494—21no—
111#10623494—21no—
112#10623494—22no—
113C22×C89—22no—
114C22×C89—22no—
115C22×C89—41no—
116C22×C89—41no—
117C22×C89—41no—
118C22×C89C2×D814yes—
119C22×C89C22×D411yescharacteristic
120C2×D89—22no—
121C2×D89—41no—
122C2×D89—41no—
123C2×D89—42no—
124C2×D89—42no—
125C2×D89—42no—
126C2×D89—88no—
127C4×C89—22no—
128C4×C89—21no—
129C4×C89—41no—
130C4×C89—42no—
131C4×C89C2×D812yes—
132C4×C89C2×#4111yescharacteristic
133C4×C89H(5,𝔽2)11yescharacteristic
134Dic89—41no—
135C2×C89—24no—
136C2×C89—81no—
137C2×C89#54611yescharacteristic
138C2×C89C22×D811yescharacteristic
139C2×C89#57711yescharacteristic
140D89—42no—
141D89—82no—
142#3294—891nomaximal, Sylow
143C89#329411yescharacteristic, complemented, Sylow
144#547D8911yescharacteristic, complemented
145D42—891no—
146#486—891no—
147#480—892no—
148#474—891no—
149#466—892no—
150#459—891no—
151#447—892no—
152C4×D8—891no—
153C8×D4—891no—
154C2×#102—892no—
155C2×#41—21no—
156C22×D4—892no—
157C22×D4—1781no—
158C2×D8—892no—
159C2×D8—891no—
160C22×C8—892no—
161C4⋊Q8C2×D8911yescharacteristic, complemented
162#127—891no—
163#123—22no—
164C22⋊Q8—21no—
165#121—892no—
166#121—1781no—
167#121C2×D8912yescomplemented
168#120—1782no—
169C4×D4—891no—
170C4×D4C2×D8911yescharacteristic
171C4×D4C2×D8911yescharacteristic, complemented
172C2×C4⋊C4C2×D8912yescomplemented
173#107—891no—
174#107—892no—
175C4⋊C8—891no—
176#102—891no—
177#102—891no—
178#102—892no—
179#102—892no—
180#102—892no—
181#102—892no—
182C22⋊C8—892no—
183C4×C8—891no—
184C24—1782no—
185#41—44no—
186C2×Q8—21no—
187C2×D4—22no—
188C2×D4—891no—
189C2×D4—892no—
190C2×D4—3562no—
191C2×D4—3564no—
192C2×D4—1784no—
193C2×D4—1782no—
194C2×D4—1782no—
195C2×D4—1781no—
196C2×D4—1781no—
197C2×D4C22⋊D8911yescharacteristic
198C2×D4C22×D8911yescharacteristic
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—1781no—
202C22×C4C22×D8912yes—
203D8—3562no—
204D8—1782no—
205C2×C8—891no—
206C2×C8—891no—
207C2×C8—892no—
208C2×C8—3562no—
209C4⋊C4—22no—
210C4⋊C4—21no—
211C4⋊C4—891no—
212C4⋊C4C22⋊D8911yescharacteristic
213C4⋊C4C22×D8911yescharacteristic
214C4⋊C4C22×D8912yes—
215C22⋊C4—21no—
216C22⋊C4—22no—
217C22⋊C4—1781no—
218C22⋊C4—1782no—
219C22⋊C4C22⋊D8912yes—
220C42C22×D8911yescharacteristic
221C23—21no—
222C23—3564no—
223C23—3564no—
224C23—1782no—
225C23—1781no—
226C23—7122no—
227C23C2×C22⋊D8912yes—
228Q8—42no—
229D4—21no—
230D4—21no—
231D4—44no—
232D4—892no—
233D4—3564no—
234D4—3564no—
235D4—3562no—
236D4—1782no—
237D4—1782no—
238D4—1781no—
239D4—7121no—
240D4#1308355914yescomplemented
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—3562no—
248C2×C4—1781no—
249C2×C4C2×C22⋊D8911yescharacteristic
250C2×C4C2×C22⋊D8912yes—
251C2×C4C2×C22⋊D8911yescharacteristic
252C2×C4C23×D8911yescharacteristic
253C8—1781no—
254C8—1781no—
255C8—1782no—
256C22—22no—
257C22—22no—
258C22—41no—
259C22—41no—
260C22—41no—
261C22—3561no—
262C22—3561no—
263C22—3562no—
264C22—3562no—
265C22—3562no—
266C22—1782no—
267C22—7128no—
268C22C2×#1308355914yes—
269C22C22×C22⋊D8911yescharacteristic
270C4—21no—
271C4—22no—
272C4—41no—
273C4—42no—
274C4—3561no—
275C4C2×#1308355912yes—
276C4#41×D8911yescharacteristic
277C4#1566805811yescharacteristic
278C2—24no—
279C2—81no—
280C2—3562no—
281C2—7122no—
282C2#1915223611yescharacteristic
283C2C22×#1308355911yescharacteristic
284C2#1915240611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#547×C89C2
socleC22×C89C22×D4
hypercenter#547D89
hypocenterC89#3294
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. D4×D356C2semidirect
2. #19151946C2semidirect
3. #19151911C2semidirect
4. #19151875C2semidirect
5. #19151832C2semidirect
6. #19151793C2semidirect
7. #19151731C2semidirect
8. C4×#13083559C2semidirect
9. D4×#10623494C2semidirect
10. C2×#15667932C2semidirect
11. #547×C89C2semidirect
15. C2×#13083559C22semidirect
16. C22×#10623494C22semidirect
22. #15667945C22semidirect
23. #15667945C22semidirect
24. C4⋊#10623494C22semidirect
25. #15667933C22semidirect
28. #15667932C22semidirect
29. #15667932C22semidirect
30. #15667932C22semidirect
31. C22⋊#10623494C22semidirect
32. C4×#10623494C22semidirect
34. C4⋊Q8×C89C22semidirect
37. #121×C89C22semidirect
39. C4×D4×C89C22semidirect
40. C2×C4⋊C4×C89C22semidirect
89. D4×C89D8semidirect
108. D356#41semidirect
143. C89#3294semidirect
144. #547D89semidirect
161. C4⋊Q8C2×D89semidirect
167. #121C2×D89semidirect
171. C4×D4C2×D89semidirect
172. C2×C4⋊C4C2×D89semidirect
240. D4#13083559semidirect

Maximal subgroups

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

subgroupindex
D4×D3562
#191519462
#191519112
#191518752
#191518322
#191517932
#191517312
C4×#130835592
D4×#106234942
C2×#156679322
#547×C892
#329489