Finite Group Databasebeta

← #26026370

Subgroups — #26026370

Order 11392.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C2×#15668010C211yesmaximal, characteristic
2C2×#15668002C211yesmaximal, characteristic
3#19151532C212yesmaximal
4#19151531C212yesmaximal
5#19151519C211yesmaximal, characteristic
6#19151518C211yesmaximal, characteristic
7#19151517C211yesmaximal, characteristic
8#19151467C212yesmaximal
9#19151462C212yesmaximal
10#19151443C211yesmaximal, characteristic
11#395×C89C211yesmaximal, characteristic
12C22×Dic178C2211yescharacteristic
13#15668010—24no—
14#15668002—24no—
15C2×C4⋊Dic89C2211yescharacteristic
16C2×C4⋊Dic89C2212yes—
17C2×#13083553C2212yes—
18C2×#13083553C2212yes—
19C2×#13083553C2211yescharacteristic
20C2×#13083553C2211yescharacteristic
21C2×#13083553C2211yescharacteristic
22C2×#13083553C2211yescharacteristic
23C2×#13083553C2212yes—
24C2×#13083553C2212yes—
25C2×C4×Dic89C2211yescharacteristic
26C2×C4×Dic89C2212yes—
27#15667919C2211yescharacteristic
28#15667919C2212yes—
29#15667919C2212yes—
30#15667919C2212yes—
31#15667919C2212yes—
32C22×Q8×C89C2211yescharacteristic
33C2×C4⋊C4×C89C2211yescharacteristic
34C2×C4⋊C4×C89C2212yes—
35#95×C89C2211yescharacteristic
36#95×C89C2212yes—
37C2×Dic178—22no—
38C2×Dic178—42no—
39C22×Dic89C2312yes—
40C22×Dic89C2311yescharacteristic
41C22×Dic89C2311yescharacteristic
42C22×Dic89C2311yescharacteristic
43C22×Dic89C2312yes—
44C22×Dic89C2311yescharacteristic
45C4⋊Dic89—22no—
46C4⋊Dic89—42no—
47#13083553—22no—
48#13083553—22no—
49#13083553—22no—
50#13083553—22no—
51#13083553—24no—
52#13083553—24no—
53#13083553—42no—
54#13083553—42no—
55C4×Dic89D414yes—
56C4×Dic89Q818yescomplemented
57C2×Q8×C89—22no—
58C2×Q8×C89—42no—
59C22×C4×C89C2311yescharacteristic
60C22×C4×C89C2312yes—
61C22×C4×C89C2311yescharacteristic
62C22×C4×C89C2311yescharacteristic
63C22×C4×C89C2312yes—
64C4⋊C4×C89—22no—
65C4⋊C4×C89—42no—
66C23×C89C2411yescharacteristic
67Q8×C89—44no—
68C2×C4×C89—22no—
69C2×C4×C89—22no—
70C2×C4×C89—22no—
71C2×C4×C89—21no—
72C2×C4×C89—21no—
73C2×C4×C89—22no—
74C2×C4×C89—22no—
75C2×C4×C89—22no—
76C2×C4×C89—22no—
77C2×C4×C89—21no—
78C2×C4×C89—21no—
79C2×C4×C89C2×D412yes—
80C2×C4×C89C2×Q814yes—
81C2×Dic89—22no—
82C2×Dic89—21no—
83C2×Dic89—21no—
84C2×Dic89—22no—
85C2×Dic89—21no—
86C2×Dic89—21no—
87C2×Dic89—22no—
88C2×Dic89—22no—
89C2×Dic89—22no—
90C2×Dic89—22no—
91C2×Dic89—21no—
92C2×Dic89—21no—
93C2×Dic89C2×D412yes—
94C2×Dic89C2×D412yes—
95C2×Dic89C2×Q814yes—
96C2×Dic89C2×Q814yes—
97Dic178—44no—
98C22×C89C22×D411yescharacteristic
99C22×C89C22×Q812yes—
100C22×C89H(5,𝔽2)12yes—
101C22×C892−1+411yescharacteristic
102C22×C892−1+411yescharacteristic
103C4×C89—22no—
104C4×C89—24no—
105C4×C89—41no—
106C4×C89—42no—
107C4×C89—41no—
108Dic89—22no—
109Dic89—24no—
110Dic89—42no—
111Dic89—41no—
112Dic89—41no—
113Dic89C4⋊Q814yes—
114C2×C89C2×C4⋊Q811yescharacteristic
115C2×C89#53511yescharacteristic
116C2×C89#53611yescharacteristic
117C2×C89#54412yes—
118C2×C89#54412yes—
119#2660—891nomaximal, Sylow
120C89#266011yescharacteristic, complemented, Sylow
121C2×C4⋊Q8—891no—
122C2×#125—891no—
123#398—892no—
124#398—892no—
125#395—891no—
126#395—891no—
127#395—891no—
128#395D8911yescharacteristic
129#384—892no—
130#382—892no—
131#376—891no—
132C22×Q8—891no—
133C22×Q8C2×D8911yescharacteristic
134C4⋊Q8—1784no—
135#125—1784no—
136C2×C4⋊C4—892no—
137C2×C4⋊C4—892no—
138C2×C4⋊C4—892no—
139C2×C4⋊C4—891no—
140C2×C4⋊C4—891no—
141C2×C4⋊C4—891no—
142C2×C4⋊C4—891no—
143C2×C4⋊C4—891no—
144C2×C4⋊C4—892no—
145C2×C4⋊C4—892no—
146C2×C4⋊C4C2×D8911yescharacteristic
147C2×C4⋊C4C2×D8912yes—
148C2×C42—891no—
149C2×C42—892no—
150#95—891no—
151#95—892no—
152#95—892no—
153#95—892no—
154#95—892no—
155#95C2×D8911yescharacteristic
156#95C2×D8912yes—
157C2×Q8—22no—
158C2×Q8—42no—
159C2×Q8—3562no—
160C2×Q8—1782no—
161C22×C4—891no—
162C22×C4—892no—
163C22×C4—891no—
164C22×C4—891no—
165C22×C4—892no—
166C22×C4—891no—
167C22×C4C22×D8911yescharacteristic
168C22×C4C22×D8912yes—
169C22×C4C22×D8911yescharacteristic
170C22×C4C22×D8911yescharacteristic
171C22×C4C22×D8912yes—
172C4⋊C4—22no—
173C4⋊C4—42no—
174C4⋊C4—3562no—
175C4⋊C4—3562no—
176C4⋊C4—3562no—
177C4⋊C4—1782no—
178C4⋊C4—1782no—
179C4⋊C4—1782no—
180C4⋊C4—1782no—
181C4⋊C4—1784no—
182C4⋊C4—1784no—
183C4⋊C4—1782no—
184C42—894no—
185C42—898no—
186C23C23×D8911yescharacteristic
187Q8—44no—
188Q8—3564no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—892no—
201C2×C4—894no—
202C2×C4—892no—
203C2×C4—894no—
204C2×C4—1781no—
205C2×C4—1781no—
206C2×C4—1782no—
207C2×C4—1782no—
208C2×C4—1782no—
209C2×C4—1782no—
210C2×C4—1781no—
211C2×C4—1781no—
212C2×C4—1782no—
213C2×C4—1781no—
214C2×C4—1781no—
215C2×C4—1782no—
216C2×C4D4×D8912yes—
217C2×C4Q8×D8914yes—
218C22C2×D4×D8911yescharacteristic
219C22C2×Q8×D8912yes—
220C22#1566805712yes—
221C22#1566805911yescharacteristic
222C22#1566806011yescharacteristic
223C4—22no—
224C4—24no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—894no—
229C4—3562no—
230C4—3561no—
231C4—3561no—
232C4—1782no—
233C4—1784no—
234C2C4⋊Q8×D8911yescharacteristic
235C2#1915216311yescharacteristic
236C2#1915217111yescharacteristic
237C2#1915222512yes—
238C2#1915222712yes—
subgroupG/H
center, FrattiniC23C23×D89
commutator, socle, prime radical, cosocleC23×C89C24
Fitting#395×C89C2
hypercenter#395D89
hypocenterC89#2660
LCSG ▷ C23×C89 ▷ C89
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
56. C4×Dic89Q8semidirect
120. C89#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#156680102
C2×#156680022
#191515322
#191515312
#191515192
#191515182
#191515172
#191514672
#191514622
#191514432
#395×C892
#266089