Finite Group Databasebeta

← C11×#1875 #13064713

Subgroups — C11×#1875 #13064713

Order 1408.

412 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 128 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×#121C211yesmaximal, characteristic
2C2×C11×#117C211yesmaximal, characteristic, complemented
3C2×C11×#102C212yesmaximal, complemented
4C2×C11×C22⋊C8C211yesmaximal, characteristic, complemented
5C11×#340C212yesmaximal, complemented
6C22×D4×C11—21no—
7C22×D4×C11C2211yescharacteristic
8C23×C4×C11C2211yescharacteristic
9C22×C8×C11C2212yes—
10C11×#121—22no—
11C11×#121C414yescomplemented
12C11×#117—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C22⋊C4—21no—
16C2×C11×C22⋊C4—21no—
17C2×C42×C11—21no—
18C11×#102—24no—
19C11×C22⋊C8—22no—
20C24×C11—21no—
21C24×C11D411yescharacteristic
22C2×D4×C11—24no—
23C2×D4×C11—22no—
24C2×D4×C11—21no—
25C2×D4×C11—22no—
26C2×D4×C11—44no—
27C2×D4×C11C2×C412yes—
28C22×C4×C11—22no—
29C22×C4×C11—22no—
30C22×C4×C11—22no—
31C22×C4×C11—21no—
32C22×C4×C11C2×C412yes—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D412yes—
35C22×C4×C11C2311yescharacteristic
36C2×C8×C11—22no—
37C2×C8×C11—22no—
38C2×C8×C11—22no—
39C11×C4⋊C4—22no—
40C11×C4⋊C4—21no—
41C11×C4⋊C4C2×C412yes—
42C11×C4⋊C4D414yescomplemented
43C11×C22⋊C4—24no—
44C11×C22⋊C4—24no—
45C42×C11—24no—
46#1875C1111yesmaximal, characteristic, direct product factor, Sylow
47C23×C11—21no—
48C23×C11—21no—
49C23×C11—22no—
50C23×C11—22no—
51C23×C11—22no—
52C23×C11—41no—
53C23×C11—41no—
54C23×C11—42no—
55C23×C11—42no—
56C23×C11C22⋊C412yes—
57C23×C11C2×D411yescharacteristic
58D4×C11—24no—
59D4×C11—48no—
60D4×C11—42no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—24no—
64C2×C4×C11—24no—
65C2×C4×C11—22no—
66C2×C4×C11—24no—
67C2×C4×C11—42no—
68C2×C4×C11—42no—
69C2×C4×C11—42no—
70C2×C4×C11C22⋊C412yes—
71C2×C4×C11C22×C411yescharacteristic
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11#4112yes—
75C8×C11—42no—
76C2×#121C2×C1111yescharacteristic
77C2×#117C2×C1111yescharacteristic, complemented
78C2×#102C2×C1112yescomplemented
79C2×C22⋊C8C2×C1111yescharacteristic, complemented
80#340C2×C1112yescomplemented
81C22×C11—22no—
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—42no—
85C22×C11—42no—
86C22×C11—42no—
87C22×C11—42no—
88C22×C11—42no—
89C22×C11—82no—
90C22×C11—82no—
91C22×C11C2×C22⋊C411yescharacteristic
92C22×C11#12011yescharacteristic
93C22×C11#12311yescharacteristic
94C22×C11#13512yes—
95C22×C11AGL(1,ℤ/8)12yes—
96C4×C11—22no—
97C4×C11—42no—
98C4×C11—44no—
99C4×C11C4×D412yes—
100C4×C11#12112yes—
101C22×D4—21no—
102C22×D4C22×C1111yescharacteristic
103C23×C4C22×C1111yescharacteristic
104C22×C8C22×C1112yes—
105#121—22no—
106#121C4×C1114yescomplemented
107#117—24no—
108C2×C4⋊C4C22×C1111yescharacteristic
109C2×C4⋊C4C22×C1112yes—
110C2×C22⋊C4—21no—
111C2×C22⋊C4—21no—
112C2×C42—21no—
113#102—24no—
114C22⋊C8—22no—
115C2×C11—42no—
116C2×C11—82no—
117C2×C11#38611yescharacteristic
118C2×C11#41611yescharacteristic
119C2×C11#41811yescharacteristic
120C2×C11#44912yes—
121C2×C11#48212yes—
122C24—21no—
123C24D4×C1111yescharacteristic
124C2×D4—24no—
125C2×D4—22no—
126C2×D4—21no—
127C2×D4—22no—
128C2×D4—44no—
129C2×D4C2×C4×C1112yes—
130C22×C4—22no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—21no—
134C22×C4C2×C4×C1112yes—
135C22×C4D4×C1111yescharacteristic
136C22×C4D4×C1112yes—
137C22×C4C23×C1111yescharacteristic
138C2×C8—22no—
139C2×C8—22no—
140C2×C8—22no—
141C4⋊C4—22no—
142C4⋊C4—21no—
143C4⋊C4C2×C4×C1112yes—
144C4⋊C4D4×C1114yescomplemented
145C22⋊C4—24no—
146C22⋊C4—24no—
147C42—24no—
148C11#187511yescharacteristic, direct product factor, Sylow
149C23—21no—
150C23—21no—
151C23—22no—
152C23—22no—
153C23—22no—
154C23—41no—
155C23—41no—
156C23—42no—
157C23—42no—
158C23C11×C22⋊C412yes—
159C23C2×D4×C1111yescharacteristic
160D4—24no—
161D4—48no—
162D4—42no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4C11×C22⋊C412yes—
173C2×C4C22×C4×C1111yescharacteristic
174C2×C4C2×D4×C1112yes—
175C2×C4C2×D4×C1111yescharacteristic
176C2×C4C11×#4112yes—
177C8—42no—
178C22—22no—
179C22—22no—
180C22—22no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—42no—
185C22—42no—
186C22—82no—
187C22—82no—
188C22C2×C11×C22⋊C411yescharacteristic
189C22C11×#12011yescharacteristic
190C22C11×#12311yescharacteristic
191C22C11×#13512yes—
192C22C11×AGL(1,ℤ/8)12yes—
193C4—22no—
194C4—42no—
195C4—44no—
196C4C4×D4×C1112yes—
197C4C11×#12112yes—
198C2—42no—
199C2—82no—
200C2C11×#38611yescharacteristic
201C2C11×#41611yescharacteristic
202C2C11×#41811yescharacteristic
203C2C11×#44912yes—
204C2C11×#48212yes—
subgroupG/H
center, socleC23×C11C2×D4
commutatorC2×C4C22×C4×C11
Frattini, cosocleC22×C4C23×C11
prime radicalC2×C11×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#117C2semidirect
3. C2×C11×#102C2semidirect
4. C2×C11×C22⋊C8C2semidirect
5. C11×#340C2semidirect
11. C11×#121C4semidirect
42. C11×C4⋊C4D4semidirect
46. #1875C11direct (N × H)
77. C2×#117C2×C11semidirect
78. C2×#102C2×C11semidirect
79. C2×C22⋊C8C2×C11semidirect
80. #340C2×C11semidirect
106. #121C4×C11semidirect
144. C4⋊C4D4×C11semidirect
148. C11#1875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1212
C2×C11×#1172
C2×C11×#1022
C2×C11×C22⋊C82
C11×#3402
#187511