Finite Group Databasebeta

← #13067149

Subgroups — #13067149

Order 1408.

274 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 81 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
2#10622824C211yesmaximal, characteristic
3#10622820C211yesmaximal, characteristic
4#10622176C214yesmaximal, complemented
5C22×Q8×C11C411yescharacteristic, complemented
6C23×C4×C11C2211yescharacteristic
7C11×C22⋊Q8—21no—
8C11×C22⋊Q8—21no—
9C11×C22⋊Q8C412yescomplemented
10C11×C22⋊Q8C2212yes—
11C2×C11×C4⋊C4—21no—
12C2×C11×C4⋊C4C411yescharacteristic, complemented
13C2×C11×C22⋊C4—21no—
14C2×C22⋊Dic11—21no—
15C2×#4318—21no—
16C11⋊#95—21no—
17C11⋊#95C2212yes—
18C22⋊(C11⋊C8)—21no—
19C22⋊(C11⋊C8)C2212yes—
20C24×C11D411yescharacteristic
21C2×Q8×C11—21no—
22C2×Q8×C11—42no—
23C2×Q8×C11C2×C412yes—
24C22×C4×C11—21no—
25C22×C4×C11—21no—
26C22×C4×C11—42no—
27C22×C4×C11C2×C411yescharacteristic
28C22×C4×C11C2×C411yescharacteristic
29C22×C4×C11D411yescharacteristic
30C22×C4×C11D411yescharacteristic
31C22×C4×C11D411yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×Dic11—22no—
34C11×C4⋊C4—22no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—22no—
37C11×C4⋊C4C2×C412yes—
38C11×C22⋊C4—22no—
39C11×C22⋊C4—22no—
40C22⋊Dic11—42no—
41#4318—42no—
42C2×C11⋊C8—22no—
43#1511—111nomaximal, Sylow
44C23×C11—22no—
45C23×C11—22no—
46C23×C11—41no—
47C23×C11C22⋊C411yescharacteristic
48C23×C11C22⋊C411yescharacteristic
49C23×C11C2×D411yescharacteristic
50Q8×C11—42no—
51Q8×C11—42no—
52C2×C4×C11—22no—
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—41no—
57C2×C4×C11—41no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—42no—
61C2×C4×C11—42no—
62C2×C4×C11C22⋊C411yescharacteristic
63C2×C4×C11C22⋊C411yescharacteristic
64C2×C4×C11C22×C411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C2×Dic11—42no—
67C2×Dic11—42no—
68C2×Dic11—42no—
69C11⋊C8—42no—
70C2×C22⋊Q8D1111yescharacteristic
71#407—111no—
72#381—111no—
73#328—114no—
74C22×C11—21no—
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11—21no—
79C22×C11—21no—
80C22×C11—21no—
81C22×C11—44no—
82C22×C11#9912yes—
83C22×C11C2×C22⋊C411yescharacteristic
84C22×C11#13712yes—
85C4×C11—21no—
86C4×C11—21no—
87C4×C11—21no—
88C4×C11—21no—
89C4×C11—42no—
90C4×C11—42no—
91Dic11—82no—
92C22×Q8Dic1111yescharacteristic, complemented
93C23×C4C2×D1111yescharacteristic
94C2×M16—221no—
95C22⋊Q8—21no—
96C22⋊Q8—21no—
97C22⋊Q8Dic1112yescomplemented
98C22⋊Q8C2×D1112yes—
99C2×C4⋊C4—21no—
100C2×C4⋊C4Dic1111yescharacteristic, complemented
101C2×C22⋊C4—21no—
102C2×C22⋊C4—221no—
103C22⋊C8—112no—
104C22⋊C8—221no—
105#95—112no—
106#95—221no—
107C2×C11—22no—
108C2×C11—22no—
109C2×C11—41no—
110C2×C11C2×#9911yescharacteristic
111C2×C11#41911yescharacteristic
112C2×C11#42111yescharacteristic
113C24C22⋊D1111yescharacteristic
114C2×Q8—21no—
115C2×Q8—42no—
116C2×Q8C2×Dic1112yes—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—42no—
120C22×C4—222no—
121C22×C4C2×Dic1111yescharacteristic
122C22×C4C2×Dic1111yescharacteristic
123C22×C4C22⋊D1111yescharacteristic
124C22×C4C22⋊D1111yescharacteristic
125C22×C4C22⋊D1111yescharacteristic
126C22×C4C22×D1111yescharacteristic
127M16—442no—
128C2×C8—222no—
129C4⋊C4—22no—
130C4⋊C4—21no—
131C4⋊C4—22no—
132C4⋊C4C2×Dic1112yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—442no—
136C11#151111yescharacteristic, complemented, Sylow
137C23—22no—
138C23—22no—
139C23—41no—
140C23C22⋊Dic1111yescharacteristic
141C23C22⋊Dic1111yescharacteristic
142C23C2×C22⋊D1111yescharacteristic
143Q8—42no—
144Q8—42no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—442no—
156C2×C4—442no—
157C2×C4—442no—
158C2×C4C22⋊Dic1111yescharacteristic
159C2×C4C22⋊Dic1111yescharacteristic
160C2×C4C22×Dic1111yescharacteristic
161C2×C4C2×C22⋊D1111yescharacteristic
162C8—442no—
163C22—21no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—44no—
171C22#6689812yes—
172C22#6699512yes—
173C22C2×C22⋊Dic1111yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—42no—
179C4—42no—
180C4—882no—
181C2—22no—
182C2—22no—
183C2—41no—
184C2C2×#6689811yescharacteristic
185C2#1062283811yescharacteristic
186C2#1062284911yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic11
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×C22⋊Q8C2
socleC22×C11C2×C22⋊C4
prime radicalC24×C11D4
cosocleC22×C4×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#1511
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10622176C2semidirect
5. C22×Q8×C11C4semidirect
9. C11×C22⋊Q8C4semidirect
12. C2×C11×C4⋊C4C4semidirect
92. C22×Q8Dic11semidirect
97. C22⋊Q8Dic11semidirect
100. C2×C4⋊C4Dic11semidirect
136. C11#1511semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
#106228242
#106228202
#106221762
#151111