Finite Group Databasebeta

← C11×#11491 #14588684

Subgroups — C11×#11491 #14588684

Order 2816.

356 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2931C211yesmaximal, characteristic
2C11×#2163C212yesmaximal, complemented
3C11×#1315C214yesmaximal, complemented
4C2×C11×#131C412yes—
5C11×#532C411yescharacteristic
6C11×#436—22no—
7C8×D4×C11—22no—
8C11×#423C411yescharacteristic
9C11×#408C2212yes—
10C2×C4×C8×C11C2211yescharacteristic
11C11×C4⋊C16—22no—
12C11×C22⋊C16C2214yes—
13C11×#346—22no—
14C2×C11×#41C2×C412yes—
15C11×#131—44no—
16C2×C11×M16—22no—
17C2×C11×M16C2×C412yes—
18C22×C8×C11—22no—
19C22×C8×C11C2×C411yescharacteristic
20C22×C8×C11C2311yescharacteristic
21C11×C4⋊Q8C811yescharacteristic
22C11×#127C811yescharacteristic
23C11×#124C812yes—
24C11×#121—22no—
25C4×D4×C11—22no—
26C2×C42×C11C2×C411yescharacteristic
27C2×C11×C16—24no—
28C11×C4⋊C8—22no—
29C11×C22⋊C8—24no—
30C4×C8×C11D412yes—
31C4×C8×C11D412yes—
32#11491C1111yesmaximal, characteristic, direct product factor, Sylow
33C11×#41—42no—
34C11×#41—42no—
35C2×Q8×C11C2×C812yes—
36C2×D4×C11—22no—
37C2×D4×C11—22no—
38C2×D4×C11C2×C812yes—
39C22×C4×C11—22no—
40C22×C4×C11M1612yes—
41C22×C4×C11C22×C411yescharacteristic
42C11×M16—42no—
43C11×M16—44no—
44C2×C8×C11—22no—
45C2×C8×C11—22no—
46C2×C8×C11—41no—
47C2×C8×C11—44no—
48C2×C8×C11C22⋊C411yescharacteristic
49C2×C8×C11C22⋊C411yescharacteristic
50C2×C8×C11C2×D412yes—
51C11×C4⋊C4—22no—
52C11×C22⋊C4—24no—
53C42×C11C22⋊C412yes—
54C42×C11C2×C811yescharacteristic
55C42×C11C2×C811yescharacteristic
56C11×C16—44no—
57#2931C2×C1111yescharacteristic
58#2163C2×C1112yescomplemented
59#1315C2×C1114yescomplemented
60C23×C11—22no—
61C23×C11C2×M1611yescharacteristic
62Q8×C11—42no—
63D4×C11—42no—
64D4×C11—44no—
65D4×C11—44no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—42no—
70C2×C4×C11—42no—
71C2×C4×C11—42no—
72C2×C4×C11C22⋊C812yes—
73C2×C4×C11C22⋊C812yes—
74C2×C4×C11C2×C22⋊C411yescharacteristic
75C2×C4×C11C22×C811yescharacteristic
76C8×C11—22no—
77C8×C11—21no—
78C8×C11—42no—
79C8×C11#10012yes—
80C2×#131C4×C1112yes—
81#532C4×C1111yescharacteristic
82#436—22no—
83C8×D4—22no—
84#423C4×C1111yescharacteristic
85#408C22×C1112yes—
86C2×C4×C8C22×C1111yescharacteristic
87C4⋊C16—22no—
88C22⋊C16C22×C1114yes—
89#346—22no—
90C22×C11—22no—
91C22×C11—21no—
92C22×C11—44no—
93C22×C11—42no—
94C22×C11C2×C22⋊C811yescharacteristic
95C4×C11—22no—
96C4×C11—22no—
97C4×C11—21no—
98C4×C11—42no—
99C4×C11#41011yescharacteristic
100C4×C11C2×#10011yescharacteristic
101C2×#41C2×C4×C1112yes—
102#131—44no—
103C2×M16—22no—
104C2×M16C2×C4×C1112yes—
105C22×C8—22no—
106C22×C8C2×C4×C1111yescharacteristic
107C22×C8C23×C1111yescharacteristic
108C4⋊Q8C8×C1111yescharacteristic
109#127C8×C1111yescharacteristic
110#124C8×C1112yes—
111#121—22no—
112C4×D4—22no—
113C2×C42C2×C4×C1111yescharacteristic
114C2×C16—24no—
115C4⋊C8—22no—
116C22⋊C8—24no—
117C4×C8D4×C1112yes—
118C4×C8D4×C1112yes—
119C2×C11—41no—
120C2×C11—82no—
121C2×C11#146011yescharacteristic
122C2×C11#211712yes—
123#41—42no—
124#41—42no—
125C2×Q8C2×C8×C1112yes—
126C2×D4—22no—
127C2×D4—22no—
128C2×D4C2×C8×C1112yes—
129C22×C4—22no—
130C22×C4C11×M1612yes—
131C22×C4C22×C4×C1111yescharacteristic
132M16—44no—
133M16—42no—
134C2×C8—22no—
135C2×C8—22no—
136C2×C8—41no—
137C2×C8—44no—
138C2×C8C11×C22⋊C411yescharacteristic
139C2×C8C11×C22⋊C411yescharacteristic
140C2×C8C2×D4×C1112yes—
141C4⋊C4—22no—
142C22⋊C4—24no—
143C42C11×C22⋊C412yes—
144C42C2×C8×C1111yescharacteristic
145C42C2×C8×C1111yescharacteristic
146C16—44no—
147C11#1149111yescharacteristic, direct product factor, Sylow
148C23—22no—
149C23C2×C11×M1611yescharacteristic
150Q8—42no—
151D4—42no—
152D4—44no—
153D4—44no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4C11×C22⋊C812yes—
161C2×C4C11×C22⋊C812yes—
162C2×C4C2×C11×C22⋊C411yescharacteristic
163C2×C4C22×C8×C1111yescharacteristic
164C8—22no—
165C8—21no—
166C8—42no—
167C8C11×#10012yes—
168C22—21no—
169C22—22no—
170C22—42no—
171C22—44no—
172C22C2×C11×C22⋊C811yescharacteristic
173C4—21no—
174C4—22no—
175C4—22no—
176C4—42no—
177C4C11×#41011yescharacteristic
178C4C2×C11×#10011yescharacteristic
179C2—41no—
180C2—82no—
181C2C11×#146011yescharacteristic
182C2C11×#211712yes—
subgroupG/H
centerC2×C4×C11C2×C22⋊C4
commutatorC2×C4C22×C8×C11
Frattini, cosocleC22×C8C23×C11
socleC22×C11C2×C22⋊C8
prime radicalC11×#532C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C4×C8×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2163C2semidirect
3. C11×#1315C2semidirect
32. #11491C11direct (N × H)
58. #2163C2×C11semidirect
59. #1315C2×C11semidirect
147. C11#11491direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#29312
C11×#21632
C11×#13152
#1149111