Finite Group Databasebeta

← C11×#7832 #14585025

Subgroups — C11×#7832 #14585025

Order 2816.

322 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2810C211yesmaximal, characteristic
2C11×#2100C213yesmaximal
3C11×#1271C213yesmaximal
4C11×#400—23no—
5C11×#389C2213yes—
6C11×#387—23no—
7C11×#384C2211yescharacteristic
8C11×#340—23no—
9C11×#340—23no—
10C11×#336C2213yes—
11C22×C8×C11—23no—
12C2×C11×C4⋊C4—23no—
13C2×C11×C4⋊C4—23no—
14C2×C11×C4⋊C4D413yes—
15C2×C11×C4⋊C4D413yes—
16C2×C42×C11—21no—
17C2×C42×C11C2311yescharacteristic
18C11×#95—23no—
19C11×#95—23no—
20C11×#95—21no—
21C11×#95—23no—
22#7832C1111yesmaximal, characteristic, direct product factor, Sylow
23C22×C4×C11—23no—
24C22×C4×C11—23no—
25C22×C4×C11—41no—
26C22×C4×C11C2×D413yes—
27C2×C8×C11—43no—
28C2×C8×C11—43no—
29C2×C8×C11—43no—
30C11×C4⋊C4—23no—
31C11×C4⋊C4—23no—
32C11×C4⋊C4—43no—
33C11×C4⋊C4—46no—
34C11×C4⋊C4—43no—
35C11×C4⋊C4—43no—
36C42×C11—41no—
37C42×C11—81no—
38#2810C2×C1111yescharacteristic
39#2100C2×C1113yes—
40#1271C2×C1113yes—
41C23×C11#12011yescharacteristic
42C2×C4×C11—23no—
43C2×C4×C11—23no—
44C2×C4×C11—43no—
45C2×C4×C11—43no—
46C2×C4×C11—43no—
47C2×C4×C11—43no—
48C2×C4×C11—43no—
49C2×C4×C11—43no—
50C2×C4×C11—83no—
51C2×C4×C11#13513yes—
52C2×C4×C11#13713yes—
53C8×C11—83no—
54#400—23no—
55#389C22×C1113yes—
56#387—23no—
57#384C22×C1111yescharacteristic
58#340—23no—
59#340—23no—
60#336C22×C1113yes—
61C22×C11#45213yes—
62C22×C11#45413yes—
63C22×C11#45811yescharacteristic
64C4×C11—23no—
65C4×C11—23no—
66C4×C11—83no—
67C4×C11—83no—
68C4×C11—161no—
69C22×C8—23no—
70C2×C4⋊C4—23no—
71C2×C4⋊C4—23no—
72C2×C4⋊C4D4×C1113yes—
73C2×C4⋊C4D4×C1113yes—
74C2×C42—21no—
75C2×C42C23×C1111yescharacteristic
76#95—23no—
77#95—23no—
78#95—21no—
79#95—23no—
80C2×C11#161513yes—
81C2×C11#163813yes—
82C2×C11#165811yescharacteristic
83C22×C4—23no—
84C22×C4—23no—
85C22×C4—41no—
86C22×C4C2×D4×C1113yes—
87C2×C8—43no—
88C2×C8—43no—
89C2×C8—43no—
90C4⋊C4—23no—
91C4⋊C4—23no—
92C4⋊C4—43no—
93C4⋊C4—46no—
94C4⋊C4—43no—
95C4⋊C4—43no—
96C42—41no—
97C42—81no—
98C11#783211yescharacteristic, direct product factor, Sylow
99C23C11×#12011yescharacteristic
100C2×C4—23no—
101C2×C4—23no—
102C2×C4—43no—
103C2×C4—43no—
104C2×C4—43no—
105C2×C4—43no—
106C2×C4—43no—
107C2×C4—43no—
108C2×C4—83no—
109C2×C4C11×#13513yes—
110C2×C4C11×#13713yes—
111C8—83no—
112C22C11×#45213yes—
113C22C11×#45413yes—
114C22C11×#45811yescharacteristic
115C4—23no—
116C4—23no—
117C4—83no—
118C4—83no—
119C4—161no—
120C2C11×#161513yes—
121C2C11×#163813yes—
122C2C11×#165811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C11#120
commutator, Frattini, cosocleC2×C42C23×C11
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
22. #7832C11direct (N × H)
98. C11#7832direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28102
C11×#21002
C11×#12712
#783211