Finite Group Databasebeta

← #13074447

Subgroups — #13074447

Order 1408.

472 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 157 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×#125C211yesmaximal, characteristic, complemented
2C2×#66925C211yesmaximal, characteristic
3#10622607C214yesmaximal
4#10622600C212yesmaximal
5#10622597C214yesmaximal, complemented
6#10622586C212yesmaximal, complemented
7#10622548C211yesmaximal, characteristic, complemented
8C22×C4×D11C2211yescharacteristic
9C11×#125—24no—
10C2×C11×C4⋊C4C2212yes—
11C2×C11×C4⋊C4C2214yes—
12C2×C42×C11C2211yescharacteristic
13C2×(C2×D11)⋊C4C2212yes—
14C2×(C2×D11)⋊C4C2214yes—
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2214yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2214yes—
19C2×C4×Dic11C2211yescharacteristic
20#66925—24no—
21C11⋊#95C2214yes—
22C11⋊#95C2214yes—
23C23×D11C2311yescharacteristic
24C22×C4×C11C2314yes—
25C22×C4×C11C2312yes—
26C22×C4×C11C2311yescharacteristic
27C22×Dic11C2312yes—
28C22×Dic11C2314yes—
29C22×Dic11C2311yescharacteristic
30C2×C4×D11—22no—
31C2×C4×D11—22no—
32C2×C4×D11Q814yes—
33C11×C4⋊C4—28no—
34C11×C4⋊C4—24no—
35C42×C11D414yes—
36(C2×D11)⋊C4—24no—
37(C2×D11)⋊C4—44no—
38C4⋊Dic11—24no—
39C4⋊Dic11—44no—
40Dic11⋊C4—24no—
41Dic11⋊C4—44no—
42C4×Dic11—22no—
43#2629—111nomaximal, Sylow
44C23×C11C2411yescharacteristic
45C22×D11—21no—
46C22×D11—21no—
47C22×D11—22no—
48C22×D11—22no—
49C22×D11C2×Q812yes—
50C2×C4×C11—22no—
51C2×C4×C11—22no—
52C2×C4×C11—24no—
53C2×C4×C11—24no—
54C2×C4×C11—24no—
55C2×C4×C11C2×D414yes—
56C2×C4×C11C2×D412yes—
57C2×C4×C11C2×Q812yes—
58C2×C4×C11#4112yes—
59C2×Dic11—21no—
60C2×Dic11—21no—
61C2×Dic11—22no—
62C2×Dic11—24no—
63C2×Dic11—22no—
64C2×Dic11—24no—
65C2×Dic11—24no—
66C2×Dic11—22no—
67C2×Dic11C2×Q812yes—
68C4×D11—28no—
69C2×#125D1111yescharacteristic, complemented
70C2×#117—111no—
71#398—114no—
72#396—114no—
73#389—112no—
74#384—111no—
75#380—112no—
76C22×C11C22×D411yescharacteristic
77C22×C11C22×Q811yescharacteristic
78C22×C11C2×#4111yescharacteristic
79C22×C11H(5,𝔽2)12yes—
80C22×C112−1+412yes—
81C2×D11—22no—
82C2×D11—24no—
83C2×D11—42no—
84C2×D11—41no—
85C2×D11—41no—
86C4×C11—24no—
87C4×C11—44no—
88C4×C11C22⋊Q814yes—
89Dic11—22no—
90Dic11—42no—
91Dic11—44no—
92C23×C4—111no—
93#125—24no—
94#117—224no—
95C2×C4⋊C4—112no—
96C2×C4⋊C4—112no—
97C2×C4⋊C4—114no—
98C2×C4⋊C4—114no—
99C2×C4⋊C4C2×D1112yes—
100C2×C4⋊C4C2×D1114yes—
101C2×C22⋊C4—112no—
102C2×C22⋊C4—114no—
103C2×C42—111no—
104C2×C42C2×D1111yescharacteristic
105#95—114no—
106#95—114no—
107C2×C11C2×C22⋊Q811yescharacteristic
108C2×C11#53712yes—
109C2×C11#54011yescharacteristic
110C2×C11#54111yescharacteristic
111C2×C11#54412yes—
112D11—42no—
113C24—111no—
114C22×C4—111no—
115C22×C4—114no—
116C22×C4—112no—
117C22×C4—114no—
118C22×C4—222no—
119C22×C4—222no—
120C22×C4C22×D1114yes—
121C22×C4C22×D1112yes—
122C22×C4C22×D1111yescharacteristic
123C4⋊C4—28no—
124C4⋊C4—24no—
125C4⋊C4—224no—
126C4⋊C4—224no—
127C4⋊C4—444no—
128C4⋊C4—444no—
129C22⋊C4—224no—
130C22⋊C4—444no—
131C42—222no—
132C42C22⋊D1114yes—
133C11#262911yescharacteristic, complemented, Sylow
134C23—112no—
135C23—221no—
136C23—222no—
137C23—222no—
138C23—221no—
139C23C23×D1111yescharacteristic
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—24no—
143C2×C4—24no—
144C2×C4—24no—
145C2×C4—112no—
146C2×C4—221no—
147C2×C4—221no—
148C2×C4—228no—
149C2×C4—224no—
150C2×C4—224no—
151C2×C4—222no—
152C2×C4—224no—
153C2×C4—222no—
154C2×C4—222no—
155C2×C4Q8×D1112yes—
156C2×C4#434312yes—
157C2×C4C2×C22⋊D1114yes—
158C2×C4C2×C22⋊D1112yes—
159C22—222no—
160C22—224no—
161C22—442no—
162C22—441no—
163C22—441no—
164C22C2×Q8×D1111yescharacteristic
165C22C2×#434311yescharacteristic
166C22#6704212yes—
167C22#6704312yes—
168C22C22×C22⋊D1111yescharacteristic
169C4—24no—
170C4—44no—
171C4—222no—
172C4—442no—
173C4—444no—
174C4#6699914yes—
175C2—442no—
176C2#1062322012yes—
177C2#1062322811yescharacteristic
178C2#1062322911yescharacteristic
179C2C2×#6699911yescharacteristic
180C2#1062336412yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#125C2
prime radicalC23×D11C23
hypercenterC2×#125D11
hypocenterC11#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C11×#125C2semidirect
5. #10622597C2semidirect
6. #10622586C2semidirect
7. #10622548C2semidirect
69. C2×#125D11semidirect
133. C11#2629semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
C2×#669252
#106226072
#106226002
#106225972
#106225862
#106225482
#262911