Finite Group Databasebeta

← C11×#1901 #13064739

Subgroups — C11×#1901 #13064739

Order 1408.

338 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 116 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
1C22×C11×M16C211yesmaximal, characteristic
2C2×C11×C22⋊Q8C211yesmaximal, characteristic
3C2×C11×#101C212yesmaximal, complemented
4C11×#407C211yesmaximal, characteristic
5C11×#343C212yesmaximal, complemented
6C22×Q8×C11C2211yescharacteristic
7C23×C4×C11C2211yescharacteristic
8C2×C11×M16—21no—
9C2×C11×M16—24no—
10C2×C11×M16C2212yes—
11C2×C11×M16C2212yes—
12C22×C8×C11—21no—
13C11×C22⋊Q8—21no—
14C11×C22⋊Q8—21no—
15C11×C22⋊Q8—21no—
16C11×C22⋊Q8—21no—
17C2×C11×C4⋊C4C412yes—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C412yes—
20C11×#101—24no—
21C11×C22⋊C8—21no—
22C11×C22⋊C8—21no—
23C24×C11C2×C411yescharacteristic
24C2×Q8×C11—22no—
25C2×Q8×C11—21no—
26C2×Q8×C11—21no—
27C2×Q8×C11—22no—
28C22×C4×C11—22no—
29C22×C4×C11—22no—
30C22×C4×C11C2×C412yes—
31C22×C4×C11C2×C411yescharacteristic
32C22×C4×C11C2×C412yes—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D411yescharacteristic
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C11×M16—24no—
39C11×M16—22no—
40C11×M16—22no—
41C11×M16—22no—
42C11×M16D414yes—
43C2×C8×C11—24no—
44C2×C8×C11—22no—
45C2×C8×C11—22no—
46C11×C4⋊C4—22no—
47C11×C4⋊C4—22no—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C22⋊C4—22no—
51C11×C22⋊C4—22no—
52#1901C1111yesmaximal, characteristic, direct product factor, Sylow
53C23×C11—22no—
54C23×C11—22no—
55C23×C11—41no—
56C23×C11C22⋊C411yescharacteristic
57C23×C11C22⋊C411yescharacteristic
58C23×C11C22×C411yescharacteristic
59Q8×C11—41no—
60Q8×C11—42no—
61Q8×C11—41no—
62C2×C4×C11—22no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—24no—
72C2×C4×C11—42no—
73C2×C4×C11C22⋊C411yescharacteristic
74C2×C4×C11C22⋊C411yescharacteristic
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11#4112yes—
79C8×C11—24no—
80C8×C11—42no—
81C22×M16C2×C1111yescharacteristic
82C2×C22⋊Q8C2×C1111yescharacteristic
83C2×#101C2×C1112yescomplemented
84#407C2×C1111yescharacteristic
85#343C2×C1112yescomplemented
86C22×C11—21no—
87C22×C11—21no—
88C22×C11—21no—
89C22×C11—21no—
90C22×C11—21no—
91C22×C11—21no—
92C22×C11—21no—
93C22×C11—44no—
94C22×C11#10112yescomplemented
95C22×C11C2×C22⋊C411yescharacteristic
96C22×C11C4×D412yes—
97C4×C11—21no—
98C4×C11—21no—
99C4×C11—42no—
100C4×C11—42no—
101C4×C11#12011yescharacteristic
102C4×C11#12112yes—
103C4×C11#12311yescharacteristic
104C22×Q8C22×C1111yescharacteristic
105C23×C4C22×C1111yescharacteristic
106C2×M16—21no—
107C2×M16—24no—
108C2×M16C22×C1112yes—
109C2×M16C22×C1112yes—
110C22×C8—21no—
111C22⋊Q8—21no—
112C22⋊Q8—21no—
113C22⋊Q8—21no—
114C22⋊Q8—21no—
115C2×C4⋊C4C4×C1112yes—
116C2×C4⋊C4C22×C1111yescharacteristic
117C2×C22⋊C4C4×C1112yes—
118#101—24no—
119C22⋊C8—21no—
120C22⋊C8—21no—
121C2×C11—22no—
122C2×C11—22no—
123C2×C11—41no—
124C2×C11#38611yescharacteristic
125C2×C11C2×#10111yescharacteristic
126C2×C11#41311yescharacteristic
127C24C2×C4×C1111yescharacteristic
128C2×Q8—22no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4C2×C4×C1112yes—
135C22×C4C2×C4×C1111yescharacteristic
136C22×C4C2×C4×C1112yes—
137C22×C4D4×C1111yescharacteristic
138C22×C4D4×C1111yescharacteristic
139C22×C4D4×C1111yescharacteristic
140C22×C4D4×C1111yescharacteristic
141C22×C4C23×C1111yescharacteristic
142M16—24no—
143M16—22no—
144M16—22no—
145M16—22no—
146M16D4×C1114yes—
147C2×C8—24no—
148C2×C8—22no—
149C2×C8—22no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—21no—
153C4⋊C4—21no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C11#190111yescharacteristic, direct product factor, Sylow
157C23—22no—
158C23—22no—
159C23—41no—
160C23C11×C22⋊C411yescharacteristic
161C23C11×C22⋊C411yescharacteristic
162C23C22×C4×C1111yescharacteristic
163Q8—41no—
164Q8—42no—
165Q8—41no—
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—42no—
177C2×C4C11×C22⋊C411yescharacteristic
178C2×C4C11×C22⋊C411yescharacteristic
179C2×C4C2×D4×C1112yes—
180C2×C4C2×D4×C1111yescharacteristic
181C2×C4C2×D4×C1111yescharacteristic
182C2×C4C11×#4112yes—
183C8—24no—
184C8—42no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—44no—
193C22C11×#10112yescomplemented
194C22C2×C11×C22⋊C411yescharacteristic
195C22C4×D4×C1112yes—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—42no—
200C4C11×#12011yescharacteristic
201C4C11×#12112yes—
202C4C11×#12311yescharacteristic
203C2—22no—
204C2—22no—
205C2—41no—
206C2C11×#38611yescharacteristic
207C2C2×C11×#10111yescharacteristic
208C2C11×#41311yescharacteristic
subgroupG/H
center, socleC22×C11C2×C22⋊C4
commutatorC23C22×C4×C11
Frattini, cosocleC22×C4C23×C11
prime radicalC24×C11C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C11×#101C2semidirect
5. C11×#343C2semidirect
52. #1901C11direct (N × H)
83. C2×#101C2×C11semidirect
85. #343C2×C11semidirect
94. C22×C11#101semidirect
156. C11#1901direct (N × H)
193. C22C11×#101semidirect

Maximal subgroups

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

subgroupindex
C22×C11×M162
C2×C11×C22⋊Q82
C2×C11×#1012
C11×#4072
C11×#3432
#190111