Finite Group Databasebeta

← #13074732

Subgroups — #13074732

Order 1408.

524 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 165 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×C11×C22⋊Q8C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3#10622842C212yesmaximal, complemented
4C2×C11⋊#95C211yesmaximal, characteristic
5#10622596C212yesmaximal, complemented
6#10622593C212yesmaximal, complemented
7#10622592C212yesmaximal, complemented
8#10622555C214yesmaximal
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C22×Dic22C2211yescharacteristic
13C11×C22⋊Q8—24no—
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19#66977—24no—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2214yes—
22C2×Dic11⋊C4C2214yes—
23C11⋊#95C2214yes—
24C11⋊#95C2214yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C24×C11C2311yescharacteristic
28C2×Q8×C11—22no—
29C2×Q8×C11—42no—
30C22×C4×C11—42no—
31C22×C4×C11D414yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11—42no—
37C22×Dic11—42no—
38C22×Dic11Q818yescomplemented
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2314yes—
42C2×Dic22—22no—
43C2×Dic22—42no—
44C11×C4⋊C4—22no—
45C11×C4⋊C4—24no—
46C11×C22⋊C4—24no—
47C22⋊Dic11—24no—
48C4⋊Dic11—22no—
49Dic11⋊C4—24no—
50Dic11⋊C4—44no—
51Dic11⋊C4—44no—
52#2659—111nomaximal, Sylow
53C23×C11—21no—
54C23×C11—22no—
55C23×C11—21no—
56C23×C11C2×D412yes—
57C23×C11C2×Q814yes—
58C23×C11C2411yescharacteristic
59Q8×C11—44no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—24no—
66C2×C4×C11—22no—
67C2×C4×C11—44no—
68C2×C4×C11C2×D412yes—
69C2×C4×C11C2×D412yes—
70C2×Dic11—24no—
71C2×Dic11—24no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—24no—
76C2×Dic11—22no—
77C2×Dic11—48no—
78C2×Dic11C2×Q818yes—
79Dic22—44no—
80C2×C22⋊Q8—111no—
81C2×C22⋊Q8D1111yescharacteristic
82#398—112no—
83#398—112no—
84#395—112no—
85#395—112no—
86#380—114no—
87C2×#95—111no—
88C22×C11—22no—
89C22×C11—22no—
90C22×C11—24no—
91C22×C11—24no—
92C22×C11C4⋊Q814yes—
93C22×C11C22×D411yescharacteristic
94C22×C11C22×Q812yes—
95C22×C11H(5,𝔽2)12yes—
96C22×C11H(5,𝔽2)11yescharacteristic
97C22×C112−1+411yescharacteristic
98C4×C11—22no—
99C4×C11—22no—
100C4×C11—42no—
101C4×C11—42no—
102Dic11—28no—
103Dic11—42no—
104Dic11—42no—
105C22×Q8—111no—
106C22×Q8C2×D1111yescharacteristic
107C23×C4—112no—
108C23×C4C2×D1111yescharacteristic
109C22⋊Q8—24no—
110C22⋊Q8—224no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—114no—
114C2×C4⋊C4—114no—
115C2×C4⋊C4C2×D1112yes—
116C2×C4⋊C4C2×D1111yescharacteristic
117C2×C22⋊C4—112no—
118C2×C22⋊C4C2×D1112yes—
119#95—112no—
120#95—112no—
121#95—114no—
122#95—114no—
123C2×C11—24no—
124C2×C11C2×C4⋊Q811yescharacteristic
125C2×C11#53411yescharacteristic
126C2×C11#53711yescharacteristic
127C2×C11#54312yes—
128C2×C11#54412yes—
129C24C22×D1111yescharacteristic
130C2×Q8—22no—
131C2×Q8—42no—
132C2×Q8—222no—
133C2×Q8—442no—
134C22×C4—42no—
135C22×C4—114no—
136C22×C4—118no—
137C22×C4—112no—
138C22×C4—112no—
139C22×C4—442no—
140C22×C4—442no—
141C22×C4C22⋊D1114yes—
142C22×C4C22×D1112yes—
143C22×C4C22×D1112yes—
144C22×C4C22×D1111yescharacteristic
145C22×C4C22×D1111yescharacteristic
146C4⋊C4—22no—
147C4⋊C4—24no—
148C4⋊C4—224no—
149C4⋊C4—222no—
150C4⋊C4—444no—
151C4⋊C4—444no—
152C22⋊C4—24no—
153C22⋊C4—224no—
154C11#265911yescharacteristic, complemented, Sylow
155C23—22no—
156C23—21no—
157C23—21no—
158C23Q8×D1114yes—
159C23C2×C22⋊D1112yes—
160C23C23×D1111yescharacteristic
161Q8—44no—
162Q8—444no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—24no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—44no—
171C2×C4—118no—
172C2×C4—224no—
173C2×C4—224no—
174C2×C4—224no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—448no—
180C2×C4C2×C22⋊D1112yes—
181C2×C4C2×C22⋊D1112yes—
182C22—22no—
183C22—22no—
184C22—24no—
185C22—24no—
186C22#6699714yes—
187C22#6703712yes—
188C22C2×Q8×D1112yes—
189C22#6704211yescharacteristic
190C22#6704311yescharacteristic
191C22C22×C22⋊D1111yescharacteristic
192C4—22no—
193C4—22no—
194C4—42no—
195C4—42no—
196C4—228no—
197C4—442no—
198C4—442no—
199C2—24no—
200C2#1062315412yes—
201C2#1062316512yes—
202C2#1062333511yescharacteristic
203C2C2×#6699711yescharacteristic
204C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2659
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10622842C2semidirect
5. #10622596C2semidirect
6. #10622593C2semidirect
7. #10622592C2semidirect
38. C22×Dic11Q8semidirect
154. C11#2659semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669772
#106228422
C2×C11⋊#952
#106225962
#106225932
#106225922
#106225552
#265911