Finite Group Databasebeta

← C2×C11×#1355 #14589102

Subgroups — C2×C11×#1355 #14589102

Order 2816.

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

normal subgroups only

This group has 366 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×#490C211yesmaximal, characteristic
2C2×C11×#347C212yesmaximal, complemented
3C11×#1355C214yesmaximal, direct product factor
4C2×C11×#127C411yescharacteristic
5C2×C11×#125C411yescharacteristic
6C2×C11×M32—22no—
7C11×#490—22no—
8C11×#490C412yes—
9C11×#490C2212yes—
10C2×C11×#102—22no—
11C2×C11×#97C2211yescharacteristic
12C11×#347—22no—
13C11×#347C2214yescomplemented
14C22×D4×C11—21no—
15C22×D4×C11—41no—
16C22×C8×C11D412yes—
17C11×#127—21no—
18C11×#127—41no—
19C11×#127C2×C412yes—
20C11×#125—21no—
21C11×#125—41no—
22C11×#125C2×C412yes—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—41no—
25C2×C42×C11C2×C411yescharacteristic
26C11×M32—24no—
27C11×M32—24no—
28C2×C11×C16—24no—
29C11×#102—24no—
30C11×#102—24no—
31C11×#97C2×C411yescharacteristic
32C11×#97D412yes—
33C11×#97C2311yescharacteristic
34C2×#1355C1111yesmaximal, characteristic, direct product factor, Sylow
35C24×C11—41no—
36C2×D4×C11—22no—
37C2×D4×C11—42no—
38C2×D4×C11—42no—
39C2×D4×C11—41no—
40C2×D4×C11—42no—
41C2×D4×C11—42no—
42C2×D4×C11—84no—
43C22×C4×C11—21no—
44C22×C4×C11—41no—
45C22×C4×C11C22⋊C411yescharacteristic
46C2×C8×C11—22no—
47C2×C8×C11—22no—
48C2×C8×C11C22⋊C412yes—
49C2×C8×C11C2×D412yes—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—42no—
52C11×C4⋊C4—42no—
53C11×C4⋊C4—41no—
54C42×C11—21no—
55C42×C11C22⋊C411yescharacteristic
56C42×C11C22×C411yescharacteristic
57C11×C16—28no—
58C2×#490C2×C1111yescharacteristic
59C2×#347C2×C1112yescomplemented
60#1355C2×C1114yesdirect product factor
61C23×C11—42no—
62C23×C11—84no—
63C23×C11—81no—
64C23×C11—81no—
65C23×C11#10011yescharacteristic
66D4×C11—44no—
67D4×C11—84no—
68D4×C11—84no—
69D4×C11—82no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—42no—
73C2×C4×C11—42no—
74C2×C4×C11—82no—
75C2×C4×C11#10011yescharacteristic
76C2×C4×C11#10412yes—
77C2×C4×C11#10412yes—
78C2×C4×C11C2×C22⋊C411yescharacteristic
79C8×C11—22no—
80C8×C11—22no—
81C2×#127C4×C1111yescharacteristic
82C2×#125C4×C1111yescharacteristic
83C2×M32—22no—
84#490—22no—
85#490C4×C1112yes—
86#490C22×C1112yes—
87C2×#102—22no—
88C2×#97C22×C1111yescharacteristic
89#347—22no—
90#347C22×C1114yescomplemented
91C22×C11—22no—
92C22×C11—84no—
93C22×C11—82no—
94C22×C11—162no—
95C22×C11—162no—
96C22×C11#32911yescharacteristic
97C22×C11#32911yescharacteristic
98C22×C11C2×#10011yescharacteristic
99C4×C11—41no—
100C4×C11—41no—
101C4×C11—82no—
102C4×C11#32912yes—
103C4×C11C2×#10412yes—
104C22×D4—21no—
105C22×D4—41no—
106C22×C8D4×C1112yes—
107#127—21no—
108#127—41no—
109#127C2×C4×C1112yes—
110#125—21no—
111#125—41no—
112#125C2×C4×C1112yes—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—41no—
115C2×C42C2×C4×C1111yescharacteristic
116M32—24no—
117M32—24no—
118C2×C16—24no—
119#102—24no—
120#102—24no—
121#97C2×C4×C1111yescharacteristic
122#97D4×C1112yes—
123#97C23×C1111yescharacteristic
124C2×C11—21no—
125C2×C11—21no—
126C2×C11—162no—
127C2×C11#135512yesdirect product factor
128C2×C11C2×#32911yescharacteristic
129C24—41no—
130C2×D4—22no—
131C2×D4—42no—
132C2×D4—42no—
133C2×D4—41no—
134C2×D4—42no—
135C2×D4—42no—
136C2×D4—84no—
137C22×C4—21no—
138C22×C4—41no—
139C22×C4C11×C22⋊C411yescharacteristic
140C2×C8—22no—
141C2×C8—22no—
142C2×C8C11×C22⋊C412yes—
143C2×C8C2×D4×C1112yes—
144C4⋊C4—22no—
145C4⋊C4—42no—
146C4⋊C4—42no—
147C4⋊C4—41no—
148C42—21no—
149C42C11×C22⋊C411yescharacteristic
150C42C22×C4×C1111yescharacteristic
151C16—28no—
152C11C2×#135511yescharacteristic, direct product factor, Sylow
153C23—42no—
154C23—84no—
155C23—81no—
156C23—81no—
157C23C11×#10011yescharacteristic
158D4—44no—
159D4—84no—
160D4—84no—
161D4—82no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—82no—
167C2×C4C11×#10011yescharacteristic
168C2×C4C11×#10412yes—
169C2×C4C11×#10412yes—
170C2×C4C2×C11×C22⋊C411yescharacteristic
171C8—22no—
172C8—22no—
173C22—22no—
174C22—84no—
175C22—82no—
176C22—162no—
177C22—162no—
178C22C11×#32911yescharacteristic
179C22C11×#32911yescharacteristic
180C22C2×C11×#10011yescharacteristic
181C4—41no—
182C4—41no—
183C4—82no—
184C4C11×#32912yes—
185C4C2×C11×#10412yes—
186C2—21no—
187C2—21no—
188C2—162no—
189C2C11×#135512yesdirect product factor
190C2C2×C11×#32911yescharacteristic
subgroupG/H
center, socleC22×C11#329
commutatorC42C22×C4×C11
Frattini, cosocle#97C23×C11
prime radicalC2×C11×#127C4
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
2. C2×C11×#347C2semidirect
3. C11×#1355C2direct (N × H)
13. C11×#347C22semidirect
34. C2×#1355C11direct (N × H)
59. C2×#347C2×C11semidirect
60. #1355C2×C11direct (N × H)
90. #347C22×C11semidirect
127. C2×C11#1355direct (N × H)
152. C11C2×#1355direct (N × H)
189. C2C11×#1355direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#4902
C2×C11×#3472
C11×#13552
C2×#135511