Finite Group Databasebeta

← C2×C11×#1356 #14589103

Subgroups — C2×C11×#1356 #14589103

Order 2816.

314 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C2×C11×#491C211yesmaximal, characteristic
2C2×C11×#347C212yesmaximal
3C11×#1356C214yesmaximal, direct product factor
4C2×C11×C4⋊Q8C411yescharacteristic
5C2×C11×#125C411yescharacteristic
6C2×C11×M32—22no—
7C11×#491—22no—
8C11×#491C412yes—
9C11×#491C2212yes—
10C2×C11×#103—22no—
11C2×C11×#97C2211yescharacteristic
12C11×#347—22no—
13C11×#347C2214yes—
14C22×Q8×C11—21no—
15C22×C8×C11D412yes—
16C11×C4⋊Q8—21no—
17C11×C4⋊Q8—41no—
18C11×C4⋊Q8C2×C412yes—
19C11×#125—21no—
20C11×#125—41no—
21C11×#125C2×C412yes—
22C2×C11×C4⋊C4—21no—
23C2×C11×C4⋊C4—41no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11C2×C411yescharacteristic
26C11×M32—24no—
27C11×M32—24no—
28C2×C11×C16—24no—
29C11×#103—24no—
30C11×#103—24no—
31C11×#97C2×C411yescharacteristic
32C11×#97D412yes—
33C11×#97C2311yescharacteristic
34C2×#1356C1111yesmaximal, characteristic, direct product factor, Sylow
35C2×Q8×C11—22no—
36C2×Q8×C11—41no—
37C2×Q8×C11—42no—
38C2×Q8×C11—42no—
39C22×C4×C11—21no—
40C22×C4×C11—41no—
41C22×C4×C11—41no—
42C22×C4×C11C22⋊C411yescharacteristic
43C2×C8×C11—22no—
44C2×C8×C11—22no—
45C2×C8×C11C22⋊C412yes—
46C2×C8×C11C2×D412yes—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—42no—
49C11×C4⋊C4—42no—
50C11×C4⋊C4—42no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—41no—
53C42×C11—21no—
54C42×C11C22⋊C411yescharacteristic
55C42×C11C22×C411yescharacteristic
56C11×C16—28no—
57C2×#491C2×C1111yescharacteristic
58C2×#347C2×C1112yes—
59#1356C2×C1114yesdirect product factor
60C23×C11#10011yescharacteristic
61Q8×C11—44no—
62Q8×C11—82no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—42no—
66C2×C4×C11—42no—
67C2×C4×C11—42no—
68C2×C4×C11—82no—
69C2×C4×C11—81no—
70C2×C4×C11—81no—
71C2×C4×C11#10011yescharacteristic
72C2×C4×C11#10412yes—
73C2×C4×C11#10412yes—
74C2×C4×C11C2×C22⋊C411yescharacteristic
75C8×C11—22no—
76C8×C11—22no—
77C2×C4⋊Q8C4×C1111yescharacteristic
78C2×#125C4×C1111yescharacteristic
79C2×M32—22no—
80#491—22no—
81#491C4×C1112yes—
82#491C22×C1112yes—
83C2×#103—22no—
84C2×#97C22×C1111yescharacteristic
85#347—22no—
86#347C22×C1114yes—
87C22×C11—22no—
88C22×C11#32911yescharacteristic
89C22×C11#32911yescharacteristic
90C22×C11C2×#10011yescharacteristic
91C4×C11—41no—
92C4×C11—41no—
93C4×C11—82no—
94C4×C11—82no—
95C4×C11#32912yes—
96C4×C11C2×#10412yes—
97C22×Q8—21no—
98C22×C8D4×C1112yes—
99C4⋊Q8—21no—
100C4⋊Q8—41no—
101C4⋊Q8C2×C4×C1112yes—
102#125—21no—
103#125—41no—
104#125C2×C4×C1112yes—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C42C2×C4×C1111yescharacteristic
109M32—24no—
110M32—24no—
111C2×C16—24no—
112#103—24no—
113#103—24no—
114#97C2×C4×C1111yescharacteristic
115#97D4×C1112yes—
116#97C23×C1111yescharacteristic
117C2×C11—21no—
118C2×C11—21no—
119C2×C11#135612yesdirect product factor
120C2×C11C2×#32911yescharacteristic
121C2×Q8—22no—
122C2×Q8—41no—
123C2×Q8—42no—
124C2×Q8—42no—
125C22×C4—21no—
126C22×C4—41no—
127C22×C4—41no—
128C22×C4C11×C22⋊C411yescharacteristic
129C2×C8—22no—
130C2×C8—22no—
131C2×C8C11×C22⋊C412yes—
132C2×C8C2×D4×C1112yes—
133C4⋊C4—22no—
134C4⋊C4—42no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C4⋊C4—42no—
138C4⋊C4—41no—
139C42—21no—
140C42C11×C22⋊C411yescharacteristic
141C42C22×C4×C1111yescharacteristic
142C16—28no—
143C11C2×#135611yescharacteristic, direct product factor, Sylow
144C23C11×#10011yescharacteristic
145Q8—44no—
146Q8—82no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—82no—
153C2×C4—81no—
154C2×C4—81no—
155C2×C4C11×#10011yescharacteristic
156C2×C4C11×#10412yes—
157C2×C4C11×#10412yes—
158C2×C4C2×C11×C22⋊C411yescharacteristic
159C8—22no—
160C8—22no—
161C22—22no—
162C22C11×#32911yescharacteristic
163C22C11×#32911yescharacteristic
164C22C2×C11×#10011yescharacteristic
165C4—41no—
166C4—41no—
167C4—82no—
168C4—82no—
169C4C11×#32912yes—
170C4C2×C11×#10412yes—
171C2—21no—
172C2—21no—
173C2C11×#135612yesdirect product factor
174C2C2×C11×#32911yescharacteristic
subgroupG/H
center, socleC22×C11#329
commutatorC42C22×C4×C11
Frattini, cosocle#97C23×C11
prime radicalC23×C11#100
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C2×C11×#97 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#1356C2direct (N × H)
34. C2×#1356C11direct (N × H)
59. #1356C2×C11direct (N × H)
119. C2×C11#1356direct (N × H)
143. C11C2×#1356direct (N × H)
173. C2C11×#1356direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4912
C2×C11×#3472
C11×#13562
C2×#135611