Finite Group Databasebeta

← #13076683

Subgroups — #13076683

Order 1408.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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
2C2×#66923C211yesmaximal, characteristic
3#10622599C212yesmaximal
4#10622597C214yesmaximal
5#10622596C212yesmaximal
6#10622595C212yesmaximal
7#10622593C212yesmaximal
8#10622549C211yesmaximal, characteristic
9C11×#125—24no—
10C2×C11×C4⋊C4C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2212yes—
14C2×C42×C11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2214yes—
21#66923—24no—
22C11⋊#95C2212yes—
23C11⋊#95C2212yes—
24C11⋊#95C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2214yes—
27C22×C4×C11C2312yes—
28C22×C4×C11C2312yes—
29C22×C4×C11C2311yescharacteristic
30C22×C4×C11C2311yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C22×Dic11C2314yes—
33C22×Dic11C2312yes—
34C22×Dic11C2312yes—
35C11×C4⋊C4—22no—
36C11×C4⋊C4—22no—
37C11×C4⋊C4—24no—
38C11×C4⋊C4—24no—
39C42×C11D414yes—
40C4⋊Dic11—22no—
41C4⋊Dic11—22no—
42C4⋊Dic11—42no—
43Dic11⋊C4—24no—
44Dic11⋊C4—24no—
45Dic11⋊C4—44no—
46#2822—111nomaximal, Sylow
47C23×C11C2411yescharacteristic
48C2×C4×C11—21no—
49C2×C4×C11—22no—
50C2×C4×C11—22no—
51C2×C4×C11—21no—
52C2×C4×C11—22no—
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—24no—
56C2×C4×C11—22no—
57C2×C4×C11C2×D412yes—
58C2×C4×C11C2×D412yes—
59C2×C4×C11C2×D412yes—
60C2×Dic11—22no—
61C2×Dic11—22no—
62C2×Dic11—22no—
63C2×Dic11—24no—
64C2×Dic11—24no—
65C2×Dic11—24no—
66C2×Dic11—22no—
67C2×Dic11—24no—
68C2×#125—111no—
69C2×#125D1111yescharacteristic
70#400—112no—
71#400—112no—
72#398—112no—
73#398—112no—
74#398—114no—
75#382—111no—
76C22×C11C22×D411yescharacteristic
77C22×C11H(5,𝔽2)11yescharacteristic
78C22×C112−1+412yes—
79C22×C112−1+412yes—
80C22×C112−1+411yescharacteristic
81C4×C11—22no—
82C4×C11—22no—
83C4×C11—22no—
84C4×C11—42no—
85C4×C11—42no—
86Dic11—42no—
87Dic11—42no—
88Dic11—44no—
89#125—24no—
90#125—224no—
91C2×C4⋊C4—112no—
92C2×C4⋊C4—111no—
93C2×C4⋊C4—112no—
94C2×C4⋊C4—111no—
95C2×C4⋊C4—112no—
96C2×C4⋊C4—114no—
97C2×C4⋊C4C2×D1112yes—
98C2×C4⋊C4C2×D1111yescharacteristic
99C2×C4⋊C4C2×D1112yes—
100C2×C4⋊C4C2×D1111yescharacteristic
101C2×C42C2×D1111yescharacteristic
102#95—112no—
103#95—112no—
104#95—114no—
105#95—114no—
106#95—114no—
107C2×C11#53611yescharacteristic
108C2×C11#53611yescharacteristic
109C2×C11#53711yescharacteristic
110C2×C11#56312yes—
111C2×C11#56412yes—
112C22×C4—114no—
113C22×C4—112no—
114C22×C4—112no—
115C22×C4C22×D1112yes—
116C22×C4C22×D1112yes—
117C22×C4C22×D1111yescharacteristic
118C22×C4C22×D1111yescharacteristic
119C22×C4C22×D1111yescharacteristic
120C4⋊C4—24no—
121C4⋊C4—22no—
122C4⋊C4—24no—
123C4⋊C4—22no—
124C4⋊C4—224no—
125C4⋊C4—224no—
126C4⋊C4—222no—
127C4⋊C4—222no—
128C4⋊C4—444no—
129C4⋊C4—442no—
130C42C22⋊D1114yes—
131C11#282211yescharacteristic, complemented, Sylow
132C23C23×D1111yescharacteristic
133C2×C4—22no—
134C2×C4—21no—
135C2×C4—22no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—24no—
139C2×C4—22no—
140C2×C4—22no—
141C2×C4—22no—
142C2×C4—224no—
143C2×C4—224no—
144C2×C4—222no—
145C2×C4—224no—
146C2×C4—222no—
147C2×C4—224no—
148C2×C4—222no—
149C2×C4—222no—
150C2×C4C2×C22⋊D1112yes—
151C2×C4C2×C22⋊D1112yes—
152C2×C4C2×C22⋊D1112yes—
153C22#6704012yes—
154C22#6704211yescharacteristic
155C22#6704312yes—
156C22#6704311yescharacteristic
157C22C22×C22⋊D1111yescharacteristic
158C4—22no—
159C4—22no—
160C4—22no—
161C4—42no—
162C4—42no—
163C4—442no—
164C4—442no—
165C4—444no—
166C2C11⋊#56412yes—
167C2#1062323012yes—
168C2#1062334711yescharacteristic
169C2#1062335611yescharacteristic
170C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC2×C11×#125C2
hypercenterC2×#125D11
hypocenterC11#2822
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
131. C11#2822semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
C2×#669232
#106225992
#106225972
#106225962
#106225952
#106225932
#106225492
#282211