Finite Group Databasebeta

← C11×#11916 #14589109

Subgroups — C11×#11916 #14589109

Order 2816.

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

normal subgroups only

This group has 274 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×#3139C211yesmaximal, characteristic
2C11×#2165C212yesmaximal
3C11×#1356C214yesmaximal, complemented
4C11×#533C411yescharacteristic
5C2×C11×C4⋊Q8C411yescharacteristic
6C11×#491C412yes—
7C11×#491C2212yes—
8C11×#487—22no—
9C11×#419—22no—
10C4×C11×M16C2211yescharacteristic
11C11×#364—22no—
12C11×#349—22no—
13C11×#347C2214yes—
14C22×Q8×C11—21no—
15C2×C11×M16D412yes—
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8—21no—
18C11×C4⋊Q8—41no—
19C11×C4⋊Q8C2×C412yes—
20C11×#125C2×C412yes—
21C11×C22⋊Q8—41no—
22C4×Q8×C11—41no—
23C11×#117—21no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11C2×C411yescharacteristic
26C11×M32—24no—
27C11×#103—24no—
28C11×#103—24no—
29C11×#97C2×C411yescharacteristic
30C11×#97C2311yescharacteristic
31C4×C8×C11D412yes—
32#11916C1111yesmaximal, characteristic, direct product factor, Sylow
33C2×Q8×C11—22no—
34C2×Q8×C11—41no—
35C2×Q8×C11—44no—
36C2×Q8×C11—41no—
37C22×C4×C11—21no—
38C22×C4×C11—41no—
39C22×C4×C11C22⋊C411yescharacteristic
40C11×M16—42no—
41C2×C8×C11C22⋊C412yes—
42C2×C8×C11C2×D412yes—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—42no—
45C11×C4⋊C4—41no—
46C11×C4⋊C4—42no—
47C11×C4⋊C4—42no—
48C11×C22⋊C4—41no—
49C42×C11—21no—
50C42×C11—41no—
51C42×C11C22⋊C411yescharacteristic
52C42×C11C22×C411yescharacteristic
53C11×C16—44no—
54#3139C2×C1111yescharacteristic
55#2165C2×C1112yes—
56#1356C2×C1114yescomplemented
57C23×C11#10011yescharacteristic
58Q8×C11—44no—
59Q8×C11—82no—
60Q8×C11—82no—
61C2×C4×C11—21no—
62C2×C4×C11—22no—
63C2×C4×C11—21no—
64C2×C4×C11—42no—
65C2×C4×C11—42no—
66C2×C4×C11—42no—
67C2×C4×C11—82no—
68C2×C4×C11#10011yescharacteristic
69C2×C4×C11C2×C22⋊C411yescharacteristic
70C8×C11—22no—
71C8×C11—22no—
72#533C4×C1111yescharacteristic
73C2×C4⋊Q8C4×C1111yescharacteristic
74#491C4×C1112yes—
75#491C22×C1112yes—
76#487—22no—
77#419—22no—
78C4×M16C22×C1111yescharacteristic
79#364—22no—
80#349—22no—
81#347C22×C1114yes—
82C22×C11—21no—
83C22×C11—41no—
84C22×C11C2×#10011yescharacteristic
85C4×C11—22no—
86C4×C11—21no—
87C4×C11—41no—
88C4×C11—82no—
89C4×C11—82no—
90C4×C11#42112yes—
91C22×Q8—21no—
92C2×M16D4×C1112yes—
93C4⋊Q8—21no—
94C4⋊Q8—21no—
95C4⋊Q8—41no—
96C4⋊Q8C2×C4×C1112yes—
97#125C2×C4×C1112yes—
98C22⋊Q8—41no—
99C4×Q8—41no—
100#117—21no—
101C2×C4⋊C4—41no—
102C2×C42C2×C4×C1111yescharacteristic
103M32—24no—
104#103—24no—
105#103—24no—
106#97C2×C4×C1111yescharacteristic
107#97C23×C1111yescharacteristic
108C4×C8D4×C1112yes—
109C2×C11—21no—
110C2×C11—41no—
111C2×C11#153311yescharacteristic
112C2×Q8—22no—
113C2×Q8—41no—
114C2×Q8—44no—
115C2×Q8—41no—
116C22×C4—21no—
117C22×C4—41no—
118C22×C4C11×C22⋊C411yescharacteristic
119M16—42no—
120C2×C8C11×C22⋊C412yes—
121C2×C8C2×D4×C1112yes—
122C4⋊C4—22no—
123C4⋊C4—42no—
124C4⋊C4—42no—
125C4⋊C4—42no—
126C4⋊C4—41no—
127C22⋊C4—41no—
128C42—21no—
129C42—41no—
130C42C11×C22⋊C411yescharacteristic
131C42C22×C4×C1111yescharacteristic
132C16—44no—
133C11#1191611yescharacteristic, direct product factor, Sylow
134C23C11×#10011yescharacteristic
135Q8—44no—
136Q8—82no—
137Q8—82no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—42no—
143C2×C4—42no—
144C2×C4—82no—
145C2×C4C11×#10011yescharacteristic
146C2×C4C2×C11×C22⋊C411yescharacteristic
147C8—22no—
148C8—22no—
149C22—21no—
150C22—41no—
151C22C2×C11×#10011yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—82no—
156C4—82no—
157C4C11×#42112yes—
158C2—21no—
159C2—41no—
160C2C11×#153311yescharacteristic
subgroupG/H
center, socleC2×C11#1533
commutatorC42C22×C4×C11
Frattini, cosocle#97C23×C11
prime radicalC23×C11#100
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C11 ◁ C2×C4×C11 ◁ C4×C11×M16 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1356C2semidirect
32. #11916C11direct (N × H)
56. #1356C2×C11semidirect
133. C11#11916direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#31392
C11×#21652
C11×#13562
#1191611