Finite Group Databasebeta

← C11×#10391 #14587584

Subgroups — C11×#10391 #14587584

Order 2816.

542 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2840C211yesmaximal, characteristic
2C11×#1819C213yesmaximal
3C11×#1304C213yesmaximal
4C22×C11×C22⋊C4C2211yescharacteristic
5C11×#393—26no—
6C11×#379C2213yes—
7C11×#379C2213yes—
8C11×#342—26no—
9C25×C11C2311yescharacteristic
10C22×Q8×C11—22no—
11C23×C4×C11Q812yescomplemented
12C2×C11×C22⋊C4—23no—
13C2×C11×C22⋊C4—23no—
14C2×C11×C22⋊C4—23no—
15C2×C11×C22⋊C4—26no—
16C2×C11×C22⋊C4—26no—
17C2×C11×C22⋊C4D416yes—
18C11×#95—26no—
19#10391C1111yesmaximal, characteristic, direct product factor, Sylow
20C24×C11—42no—
21C24×C11—82no—
22C24×C11C2×D413yes—
23C24×C11C2×Q811yescharacteristic
24C24×C11#4113yes—
25C2×Q8×C11—84no—
26C2×Q8×C11—82no—
27C22×C4×C11—26no—
28C22×C4×C11—26no—
29C22×C4×C11—43no—
30C22×C4×C11—82no—
31C11×C22⋊C4—41no—
32C11×C22⋊C4—43no—
33C11×C22⋊C4—46no—
34C11×C22⋊C4—46no—
35C11×C22⋊C4—86no—
36C11×C22⋊C4—86no—
37#2840C2×C1111yescharacteristic
38#1819C2×C1113yes—
39#1304C2×C1113yes—
40C23×C11—26no—
41C23×C11—42no—
42C23×C11—41no—
43C23×C11—46no—
44C23×C11—46no—
45C23×C11—43no—
46C23×C11—88no—
47C23×C11#12011yescharacteristic
48C23×C11C22⋊Q813yes—
49C23×C11#12413yes—
50Q8×C11—88no—
51C2×C4×C11—412no—
52C2×C4×C11—42no—
53C2×C4×C11—46no—
54C2×C4×C11—86no—
55C2×C4×C11—83no—
56C2×C4×C11—86no—
57C22×C22⋊C4C22×C1111yescharacteristic
58#393—26no—
59#379C22×C1113yes—
60#379C22×C1113yes—
61#342—26no—
62C22×C11—22no—
63C22×C11—23no—
64C22×C11—23no—
65C22×C11—26no—
66C22×C11—26no—
67C22×C11—44no—
68C22×C11—86no—
69C22×C11—86no—
70C22×C11#39311yescharacteristic
71C22×C11#45812yes—
72C4×C11—86no—
73C4×C11—82no—
74C4×C11—163no—
75C25C23×C1111yescharacteristic
76C22×Q8—22no—
77C23×C4Q8×C1112yescomplemented
78C2×C22⋊C4—23no—
79C2×C22⋊C4—23no—
80C2×C22⋊C4—23no—
81C2×C22⋊C4—26no—
82C2×C22⋊C4—26no—
83C2×C22⋊C4D4×C1116yes—
84#95—26no—
85C2×C11—22no—
86C2×C11—43no—
87C2×C11—43no—
88C2×C11#203011yescharacteristic
89C2×C11#203212yes—
90C24—42no—
91C24—82no—
92C24C2×D4×C1113yes—
93C24C2×Q8×C1111yescharacteristic
94C24C11×#4113yes—
95C2×Q8—84no—
96C2×Q8—82no—
97C22×C4—26no—
98C22×C4—26no—
99C22×C4—43no—
100C22×C4—82no—
101C22⋊C4—41no—
102C22⋊C4—43no—
103C22⋊C4—46no—
104C22⋊C4—46no—
105C22⋊C4—86no—
106C22⋊C4—86no—
107C11#1039111yescharacteristic, direct product factor, Sylow
108C23—26no—
109C23—42no—
110C23—41no—
111C23—46no—
112C23—46no—
113C23—43no—
114C23—88no—
115C23C11×#12011yescharacteristic
116C23C11×C22⋊Q813yes—
117C23C11×#12413yes—
118Q8—88no—
119C2×C4—412no—
120C2×C4—42no—
121C2×C4—46no—
122C2×C4—86no—
123C2×C4—83no—
124C2×C4—86no—
125C22—22no—
126C22—23no—
127C22—23no—
128C22—26no—
129C22—26no—
130C22—44no—
131C22—86no—
132C22—86no—
133C22C11×#39311yescharacteristic
134C22C11×#45812yes—
135C4—86no—
136C4—82no—
137C4—163no—
138C2—22no—
139C2—43no—
140C2—43no—
141C2C11×#203011yescharacteristic
142C2C11×#203212yes—
subgroupG/H
center, socleC22×C11#393
commutator, Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
11. C23×C4×C11Q8semidirect
19. #10391C11direct (N × H)
77. C23×C4Q8×C11semidirect
107. C11#10391direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#28402
C11×#18192
C11×#13042
#1039111