Finite Group Databasebeta

← #13076888

Subgroups — #13076888

Order 1408.

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

normal subgroups only

This group has 356 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
1C11×#382C211yesmaximal, characteristic
2#10622599C212yesmaximal
3#10622592C212yesmaximal
4#10622549C212yesmaximal
5#10622273C214yesmaximal
6#10622269C214yesmaximal
7C22×Dic22C2212yes—
8C2×C11×C4⋊C4C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C42×C11C2211yescharacteristic
11C2×C4⋊Dic11C2212yes—
12C2×C4⋊Dic11C2212yes—
13C2×C4⋊Dic11C2212yes—
14C2×Dic11⋊C4C2214yes—
15C11×#95C2214yes—
16C11⋊#95C2214yes—
17C11⋊#95C2214yes—
18C11⋊#95C2212yes—
19C11⋊#95C2212yes—
20C11⋊#95C2214yes—
21C22×C4×C11C2312yes—
22C22×C4×C11C2312yes—
23C22×C4×C11C2311yescharacteristic
24C22×C4×C11C2312yes—
25C22×Dic11C2314yes—
26C22×Dic11C2314yes—
27C2×Dic22—44no—
28C2×Dic22—42no—
29C11×C4⋊C4—41no—
30C11×C4⋊C4—41no—
31C42×C11Q814yescomplemented
32C4⋊Dic11—42no—
33C4⋊Dic11—42no—
34C4⋊Dic11—42no—
35Dic11⋊C4—44no—
36#2844—111nomaximal, Sylow
37C23×C11C2411yescharacteristic
38C2×C4×C11—22no—
39C2×C4×C11—21no—
40C2×C4×C11—21no—
41C2×C4×C11—22no—
42C2×C4×C11—24no—
43C2×C4×C11—22no—
44C2×C4×C11—22no—
45C2×C4×C11—24no—
46C2×C4×C11C2×Q812yes—
47C2×C4×C11C2×Q814yes—
48C2×Dic11—24no—
49C2×Dic11—24no—
50C2×Dic11—24no—
51C2×Dic11—24no—
52C2×Dic11—24no—
53C2×Dic11—24no—
54Dic22—48no—
55#400—112no—
56#400—114no—
57#395—112no—
58#395—114no—
59#382—112no—
60#382D1111yescharacteristic
61C22×C11C22×Q811yescharacteristic
62C22×C11H(5,𝔽2)11yescharacteristic
63C22×C11H(5,𝔽2)12yes—
64C22×C112−1+411yescharacteristic
65C22×C112−1+412yes—
66C4×C11—22no—
67C4×C11—24no—
68C4×C11—42no—
69C4×C11—42no—
70Dic11—44no—
71Dic11—44no—
72C22×Q8—112no—
73C2×C4⋊C4—112no—
74C2×C4⋊C4—112no—
75C2×C4⋊C4—114no—
76C2×C4⋊C4—112no—
77C2×C4⋊C4C2×D1111yescharacteristic
78C2×C4⋊C4C2×D1111yescharacteristic
79C2×C42C2×D1111yescharacteristic
80#95—114no—
81#95—114no—
82#95—112no—
83#95—114no—
84#95—112no—
85#95C2×D1114yes—
86C2×C11#54411yescharacteristic
87C2×C11#54412yes—
88C2×C11H(3,𝔽4)11yescharacteristic
89C2×C11#56311yescharacteristic
90C2×C11#56312yes—
91C2×Q8—442no—
92C2×Q8—444no—
93C22×C4—114no—
94C22×C4—114no—
95C22×C4C22×D1112yes—
96C22×C4C22×D1112yes—
97C22×C4C22×D1111yescharacteristic
98C22×C4C22×D1112yes—
99C4⋊C4—41no—
100C4⋊C4—41no—
101C4⋊C4—444no—
102C4⋊C4—442no—
103C4⋊C4—442no—
104C4⋊C4—442no—
105C42Dic2214yescomplemented
106C11#284411yescharacteristic, complemented, Sylow
107C23C23×D1111yescharacteristic
108Q8—448no—
109C2×C4—21no—
110C2×C4—21no—
111C2×C4—22no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—22no—
115C2×C4—24no—
116C2×C4—24no—
117C2×C4—224no—
118C2×C4—224no—
119C2×C4—224no—
120C2×C4—224no—
121C2×C4—224no—
122C2×C4—224no—
123C2×C4C2×Dic2212yes—
124C2×C4C2×Dic2214yes—
125C22C22×Dic2211yescharacteristic
126C22#6703711yescharacteristic
127C22#6704011yescharacteristic
128C22#6704212yes—
129C22#6704312yes—
130C4—22no—
131C4—24no—
132C4—42no—
133C4—42no—
134C4—444no—
135C4—444no—
136C2#1062303111yescharacteristic
137C2#1062305012yes—
138C2#1062320311yescharacteristic
139C2#1062321411yescharacteristic
140C2#1062323012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#382C2
hypercenter#382D11
hypocenterC11#2844
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
31. C42×C11Q8semidirect
105. C42Dic22semidirect
106. C11#2844semidirect

Maximal subgroups

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

subgroupindex
C11×#3822
#106225992
#106225922
#106225492
#106222732
#106222692
#284411