Finite Group Databasebeta

← #26031072

Subgroups — #26031072

Order 11392.

410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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
1C22⋊Q8×D89C212yesmaximal
2#19151930C212yesmaximal, complemented
3#19151927C212yesmaximal, complemented
4#19151856C211yesmaximal, characteristic, complemented
5#19151854C212yesmaximal, complemented
6#19151755C212yesmaximal, complemented
7#19151752C212yesmaximal, complemented
8#19151561C211yesmaximal, characteristic
9#470×C89C211yesmaximal, characteristic, complemented
10C2×Q8×D89C2212yes—
11C22×C4×D89C2211yescharacteristic
12C2×Dic356C2211yescharacteristic, complemented
13C2×#13083564C2212yescomplemented
14C2×#13083558C2211yescharacteristic
15#15667992C2212yes—
16#15667991C2212yes—
17#15667990—22no—
18#15667989—22no—
19#15667988C2212yes—
20C4⋊C4×D89—22no—
21C4⋊C4×D89C2212yes—
22C22⋊C4×D89—22no—
23#15667944C2211yescharacteristic, complemented
24#15667943C2212yescomplemented
25#15667937C2212yescomplemented
26#15667936C2212yescomplemented
27#15667935C2212yescomplemented
28#15667924C2212yes—
29#15667924C2212yes—
30C2×Q16×C89C2211yescharacteristic, complemented
31C2×M16×C89C2211yescharacteristic
32C22⋊Q8×C89C2212yes—
33#106×C89C2211yescharacteristic, complemented
34#103×C89C2212yescomplemented
35C23×D89D411yescharacteristic
36C2×Dic178—22no—
37C2×Dic178C2312yes—
38Q8×D89—42no—
39Q8×D89—42no—
40C22×Dic89D411yescharacteristic
41C2×C4×D89—22no—
42C2×C4×D89—22no—
43C2×C4×D89—41no—
44C2×C4×D89—41no—
45C2×C4×D89D412yes—
46C2×C4×D89C2312yes—
47Dic356—41no—
48#13083564—42no—
49#13083558—41no—
50C2×#10623494C2312yes—
51C4⋊Dic89—22no—
52C4⋊Dic89C2312yes—
53#13083553—22no—
54#13083553—22no—
55#13083553—22no—
56C22⋊Dic89—22no—
57#13083551—22no—
58#13083551—22no—
59C2×Q8×C89C2312yes—
60C22×C4×C89C2311yescharacteristic
61Q16×C89—41no—
62M16×C89—41no—
63C2×C8×C89C2311yescharacteristic
64C2×C8×C89C2311yescharacteristic
65C4⋊C4×C89—22no—
66C4⋊C4×C89C2312yes—
67C22⋊C4×C89—22no—
68C23×C89C2×D411yescharacteristic
69C22×D89—24no—
70C22×D89—41no—
71C22×D89C2×D412yes—
72Q8×C89—22no—
73Q8×C89—22no—
74C2×C4×C89—21no—
75C2×C4×C89—21no—
76C2×C4×C89—22no—
77C2×C4×C89—22no—
78C2×C4×C89C2×D411yescharacteristic
79C2×C4×C89C2411yescharacteristic
80C2×Dic89—22no—
81C2×Dic89—22no—
82C2×Dic89—41no—
83C2×Dic89C2×D412yes—
84C4×D89—22no—
85C4×D89—22no—
86C4×D89—42no—
87C4×D89—44no—
88C4×D89—44no—
89Dic178—22no—
90Dic178—22no—
91Dic178—44no—
92C8×C89—21no—
93C8×C89—21no—
94#10623494—22no—
95C22×C89—21no—
96C22×C89—22no—
97C22×C89C22×D411yescharacteristic
98C2×D89—22no—
99C2×D89—22no—
100C2×D89—44no—
101C2×D89#13714yes—
102C4×C89—21no—
103C4×C89—42no—
104C4×C89—42no—
105C4×C89H(5,𝔽2)11yescharacteristic
106C4×C89H(5,𝔽2)11yescharacteristic
107Dic89—22no—
108Dic89—42no—
109Dic89—42no—
110C2×C89—41no—
111C2×C89#53411yescharacteristic
112C2×C89C2×#13712yes—
113D89—24no—
114#3195—891nomaximal, Sylow
115C89#319511yescharacteristic, complemented, Sylow
116C2×C22⋊Q8—892no—
117#483—892no—
118#483—892no—
119#470—891no—
120#470—892no—
121#470D8911yescharacteristic, complemented
122#451—892no—
123#451—892no—
124#407—891no—
125C22×Q8—892no—
126C23×C4—891no—
127C2×Q16—892no—
128C2×Q16—891no—
129C2×Q16C2×D8911yescharacteristic, complemented
130C2×M16—891no—
131C2×M16C2×D8911yescharacteristic
132C22⋊Q8—892no—
133C22⋊Q8—892no—
134C22⋊Q8—892no—
135C22⋊Q8—1782no—
136C22⋊Q8—1782no—
137C22⋊Q8C2×D8912yes—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—1782no—
140C2×C22⋊C4—1782no—
141#106—891no—
142#106—892no—
143#106C2×D8911yescharacteristic, complemented
144#103—892no—
145#103—892no—
146#103—892no—
147#103C2×D8912yescomplemented
148C22⋊C8—892no—
149C22⋊C8—892no—
150C24—891no—
151C2×Q8—892no—
152C2×Q8—3562no—
153C2×Q8—3562no—
154C2×Q8—1782no—
155C2×Q8C22×D8912yes—
156C22×C4—891no—
157C22×C4—892no—
158C22×C4—892no—
159C22×C4—3561no—
160C22×C4—3561no—
161C22×C4—1782no—
162C22×C4—1782no—
163C22×C4C22×D8911yescharacteristic
164Q16—41no—
165Q16—3561no—
166Q16—3562no—
167M16—41no—
168M16—3561no—
169C2×C8—892no—
170C2×C8C22×D8911yescharacteristic
171C2×C8C22×D8911yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—892no—
174C4⋊C4—1782no—
175C4⋊C4—1782no—
176C4⋊C4—1782no—
177C4⋊C4—1782no—
178C4⋊C4C22×D8912yes—
179C22⋊C4—22no—
180C22⋊C4—1782no—
181C22⋊C4—1782no—
182C22⋊C4—1782no—
183C23—892no—
184C23—3561no—
185C23—1784no—
186C23D4×D8911yescharacteristic
187Q8—22no—
188Q8—22no—
189Q8—3564no—
190Q8—1782no—
191Q8—1782no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—892no—
197C2×C4—3562no—
198C2×C4—3564no—
199C2×C4—3564no—
200C2×C4—3561no—
201C2×C4—1782no—
202C2×C4—1782no—
203C2×C4—1782no—
204C2×C4—1782no—
205C2×C4D4×D8911yescharacteristic
206C2×C4C23×D8911yescharacteristic
207C8—21no—
208C8—21no—
209C8—1782no—
210C22—22no—
211C22—21no—
212C22—894no—
213C22—3564no—
214C22—1782no—
215C22—1782no—
216C22C2×D4×D8911yescharacteristic
217C4—21no—
218C4—42no—
219C4—42no—
220C4—3562no—
221C4—3562no—
222C4—1782no—
223C4#1566805711yescharacteristic
224C4#1566805811yescharacteristic
225C2—41no—
226C2—1784no—
227C2#1915215611yescharacteristic
228C2#137×D8912yes—
subgroupG/H
centerC22C2×D4×D89
commutator, cosocleC2×C4×C89C24
FrattiniC2×C4C23×D89
Fitting#470×C89C2
socleC22×C89C22×D4
prime radicalC23×D89D4
hypercenter#470D89
hypocenterC89#3195
LCSG ▷ C2×C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #19151930C2semidirect
3. #19151927C2semidirect
4. #19151856C2semidirect
5. #19151854C2semidirect
6. #19151755C2semidirect
7. #19151752C2semidirect
9. #470×C89C2semidirect
12. C2×Dic356C22semidirect
13. C2×#13083564C22semidirect
23. #15667944C22semidirect
24. #15667943C22semidirect
25. #15667937C22semidirect
26. #15667936C22semidirect
27. #15667935C22semidirect
30. C2×Q16×C89C22semidirect
33. #106×C89C22semidirect
34. #103×C89C22semidirect
115. C89#3195semidirect
121. #470D89semidirect
129. C2×Q16C2×D89semidirect
143. #106C2×D89semidirect
147. #103C2×D89semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D892
#191519302
#191519272
#191518562
#191518542
#191517552
#191517522
#191515612
#470×C892
#319589