Finite Group Databasebeta

← #13074734

Subgroups — #13074734

Order 1408.

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×#66997C211yesmaximal, characteristic
2C2×#66942C211yesmaximal, characteristic
3C11×#395C211yesmaximal, characteristic
4#10622842C211yesmaximal, characteristic
5#10622597C212yesmaximal
6#10622592C211yesmaximal, characteristic
7#10622589C212yesmaximal
8#10622270C212yesmaximal
9#10622269C211yesmaximal, characteristic
10#10622263C212yesmaximal
11#10622261C211yesmaximal, characteristic
12C22×Q8×C11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16#66997—24no—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2211yescharacteristic
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2211yescharacteristic
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×Dic11⋊C4C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×C4×Dic11C2211yescharacteristic
28C2×C4×Dic11C2212yes—
29#66942—24no—
30C11×#95C2211yescharacteristic
31C11×#95C2212yes—
32C11⋊#95C2212yes—
33C11⋊#95C2211yescharacteristic
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C2×Q8×C11—22no—
38C2×Q8×C11—42no—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2312yes—
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2312yes—
49C22×Dic11C2311yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—42no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—42no—
54C4⋊Dic11—22no—
55C4⋊Dic11—42no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—24no—
60Dic11⋊C4—24no—
61Dic11⋊C4—22no—
62Dic11⋊C4—42no—
63Dic11⋊C4—42no—
64C4×Dic11D414yes—
65C4×Dic11Q818yescomplemented
66#2660—111nomaximal, Sylow
67C23×C11C2411yescharacteristic
68Q8×C11—44no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×Q814yes—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—21no—
87C2×Dic11—21no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11—22no—
92C2×Dic11—21no—
93C2×Dic11—21no—
94C2×Dic11C2×D412yes—
95C2×Dic11C2×D412yes—
96C2×Dic11C2×Q814yes—
97C2×Dic11C2×Q814yes—
98Dic22—44no—
99C2×C4⋊Q8—111no—
100C2×#125—111no—
101#398—112no—
102#398—112no—
103#395—111no—
104#395—111no—
105#395—111no—
106#395D1111yescharacteristic
107#384—112no—
108#382—112no—
109#376—111no—
110C22×C11C22×D411yescharacteristic
111C22×C11C22×Q812yes—
112C22×C11H(5,𝔽2)12yes—
113C22×C112−1+411yescharacteristic
114C22×C112−1+411yescharacteristic
115C4×C11—22no—
116C4×C11—24no—
117C4×C11—41no—
118C4×C11—42no—
119C4×C11—41no—
120Dic11—22no—
121Dic11—24no—
122Dic11—42no—
123Dic11—41no—
124Dic11—41no—
125Dic11C4⋊Q814yes—
126C22×Q8—111no—
127C22×Q8C2×D1111yescharacteristic
128C4⋊Q8—224no—
129#125—224no—
130C2×C4⋊C4—111no—
131C2×C4⋊C4—111no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4—111no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—112no—
136C2×C4⋊C4—112no—
137C2×C4⋊C4—112no—
138C2×C4⋊C4—112no—
139C2×C4⋊C4—112no—
140C2×C4⋊C4C2×D1111yescharacteristic
141C2×C4⋊C4C2×D1112yes—
142C2×C42—111no—
143C2×C42—112no—
144#95—111no—
145#95—112no—
146#95—112no—
147#95—112no—
148#95—112no—
149#95C2×D1111yescharacteristic
150#95C2×D1112yes—
151C2×C11C2×C4⋊Q811yescharacteristic
152C2×C11#53511yescharacteristic
153C2×C11#53611yescharacteristic
154C2×C11#54412yes—
155C2×C11#54412yes—
156C2×Q8—22no—
157C2×Q8—42no—
158C2×Q8—222no—
159C2×Q8—442no—
160C22×C4—111no—
161C22×C4—112no—
162C22×C4—111no—
163C22×C4—111no—
164C22×C4—112no—
165C22×C4—111no—
166C22×C4C22×D1111yescharacteristic
167C22×C4C22×D1112yes—
168C22×C4C22×D1111yescharacteristic
169C22×C4C22×D1111yescharacteristic
170C22×C4C22×D1112yes—
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—222no—
174C4⋊C4—222no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—224no—
178C4⋊C4—224no—
179C4⋊C4—222no—
180C4⋊C4—442no—
181C4⋊C4—442no—
182C4⋊C4—442no—
183C42—114no—
184C42—118no—
185C11#266011yescharacteristic, complemented, Sylow
186C23C23×D1111yescharacteristic
187Q8—44no—
188Q8—444no—
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—112no—
201C2×C4—114no—
202C2×C4—112no—
203C2×C4—114no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—221no—
207C2×C4—221no—
208C2×C4—221no—
209C2×C4—221no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—222no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—221no—
216C2×C4D4×D1112yes—
217C2×C4Q8×D1114yes—
218C22C2×D4×D1111yescharacteristic
219C22#6703712yes—
220C22C2×Q8×D1112yes—
221C22#6704011yescharacteristic
222C22#6704311yescharacteristic
223C4—22no—
224C4—24no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—114no—
229C4—224no—
230C4—222no—
231C4—442no—
232C4—441no—
233C4—441no—
234C2#1062312311yescharacteristic
235C2#1062315412yes—
236C2#1062315911yescharacteristic
237C2D11×C4⋊Q811yescharacteristic
238C2#1062326012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#395C2
hypercenter#395D11
hypocenterC11#2660
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
65. C4×Dic11Q8semidirect
185. C11#2660semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
C2×#669422
C11×#3952
#106228422
#106225972
#106225922
#106225892
#106222702
#106222692
#106222632
#106222612
#266011