Finite Group Databasebeta

← C11×#1508 #13064346

Subgroups — C11×#1508 #13064346

Order 1408.

294 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 96 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×C22⋊Q8C211yesmaximal, characteristic
2C11×#407C211yesmaximal, characteristic
3C4×C11×C22⋊C4C211yesmaximal, characteristic
4C11×#328C214yesmaximal, complemented
5C22×Q8×C11C411yescharacteristic, complemented
6C23×C4×C11C2211yescharacteristic
7C2×C11×M16—21no—
8C11×C22⋊Q8—21no—
9C11×C22⋊Q8—21no—
10C11×C22⋊Q8C412yescomplemented
11C11×C22⋊Q8C2212yes—
12C2×C11×C4⋊C4—21no—
13C2×C11×C4⋊C4C411yescharacteristic, complemented
14C2×C11×C22⋊C4—21no—
15C2×C11×C22⋊C4—21no—
16C2×C42×C11—21no—
17C11×C22⋊C8—21no—
18C11×C22⋊C8C2212yes—
19C11×#95C2212yes—
20C24×C11D411yescharacteristic
21C2×Q8×C11—21no—
22C2×Q8×C11—42no—
23C2×Q8×C11C2×C412yes—
24C22×C4×C11—21no—
25C22×C4×C11—21no—
26C22×C4×C11—22no—
27C22×C4×C11—42no—
28C22×C4×C11C2×C411yescharacteristic
29C22×C4×C11C2×C411yescharacteristic
30C22×C4×C11D411yescharacteristic
31C22×C4×C11D411yescharacteristic
32C22×C4×C11D411yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C11×M16—42no—
35C2×C8×C11—22no—
36C11×C4⋊C4—22no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—22no—
39C11×C4⋊C4C2×C412yes—
40C11×C22⋊C4—24no—
41C11×C22⋊C4—22no—
42C11×C22⋊C4—22no—
43C42×C11—42no—
44#1508C1111yesmaximal, characteristic, direct product factor, Sylow
45C23×C11—22no—
46C23×C11—22no—
47C23×C11—41no—
48C23×C11C22⋊C411yescharacteristic
49C23×C11C22⋊C411yescharacteristic
50C23×C11C2×D411yescharacteristic
51Q8×C11—42no—
52Q8×C11—42no—
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—24no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—41no—
62C2×C4×C11—42no—
63C2×C4×C11—42no—
64C2×C4×C11—42no—
65C2×C4×C11—42no—
66C2×C4×C11C22⋊C411yescharacteristic
67C2×C4×C11C22⋊C411yescharacteristic
68C2×C4×C11C22×C411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C8×C11—42no—
71C2×C22⋊Q8C2×C1111yescharacteristic
72#407C2×C1111yescharacteristic
73C4×C22⋊C4C2×C1111yescharacteristic
74#328C2×C1114yescomplemented
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11—21no—
79C22×C11—21no—
80C22×C11—21no—
81C22×C11—21no—
82C22×C11—44no—
83C22×C11#10412yes—
84C22×C11C2×C22⋊C411yescharacteristic
85C22×C11#13712yes—
86C4×C11—21no—
87C4×C11—21no—
88C4×C11—21no—
89C4×C11—44no—
90C4×C11—42no—
91C4×C11—42no—
92C4×C11#9912yes—
93C22×Q8C4×C1111yescharacteristic, complemented
94C23×C4C22×C1111yescharacteristic
95C2×M16—21no—
96C22⋊Q8—21no—
97C22⋊Q8—21no—
98C22⋊Q8C4×C1112yescomplemented
99C22⋊Q8C22×C1112yes—
100C2×C4⋊C4—21no—
101C2×C4⋊C4C4×C1111yescharacteristic, complemented
102C2×C22⋊C4—21no—
103C2×C22⋊C4—21no—
104C2×C42—21no—
105C22⋊C8—21no—
106C22⋊C8C22×C1112yes—
107#95C22×C1112yes—
108C2×C11—22no—
109C2×C11—22no—
110C2×C11—41no—
111C2×C11C2×#9911yescharacteristic
112C2×C11#41911yescharacteristic
113C2×C11C2×#10411yescharacteristic
114C24D4×C1111yescharacteristic
115C2×Q8—21no—
116C2×Q8—42no—
117C2×Q8C2×C4×C1112yes—
118C22×C4—21no—
119C22×C4—21no—
120C22×C4—22no—
121C22×C4—42no—
122C22×C4C2×C4×C1111yescharacteristic
123C22×C4C2×C4×C1111yescharacteristic
124C22×C4D4×C1111yescharacteristic
125C22×C4D4×C1111yescharacteristic
126C22×C4D4×C1111yescharacteristic
127C22×C4C23×C1111yescharacteristic
128M16—42no—
129C2×C8—22no—
130C4⋊C4—22no—
131C4⋊C4—21no—
132C4⋊C4—22no—
133C4⋊C4C2×C4×C1112yes—
134C22⋊C4—24no—
135C22⋊C4—22no—
136C22⋊C4—22no—
137C42—42no—
138C11#150811yescharacteristic, direct product factor, Sylow
139C23—22no—
140C23—22no—
141C23—41no—
142C23C11×C22⋊C411yescharacteristic
143C23C11×C22⋊C411yescharacteristic
144C23C2×D4×C1111yescharacteristic
145Q8—42no—
146Q8—42no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—24no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4C11×C22⋊C411yescharacteristic
161C2×C4C11×C22⋊C411yescharacteristic
162C2×C4C22×C4×C1111yescharacteristic
163C2×C4C2×D4×C1111yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—21no—
168C22—21no—
169C22—21no—
170C22—21no—
171C22—21no—
172C22—44no—
173C22C11×#10412yes—
174C22C2×C11×C22⋊C411yescharacteristic
175C22C11×#13712yes—
176C4—21no—
177C4—21no—
178C4—21no—
179C4—44no—
180C4—42no—
181C4—42no—
182C4C11×#9912yes—
183C2—22no—
184C2—22no—
185C2—41no—
186C2C2×C11×#9911yescharacteristic
187C2C11×#41911yescharacteristic
188C2C2×C11×#10411yescharacteristic
subgroupG/H
center, socleC22×C11C2×C22⋊C4
commutatorC2×C4C22×C4×C11
Frattini, cosocleC22×C4C23×C11
prime radicalC24×C11D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
4. C11×#328C2semidirect
5. C22×Q8×C11C4semidirect
10. C11×C22⋊Q8C4semidirect
13. C2×C11×C4⋊C4C4semidirect
44. #1508C11direct (N × H)
74. #328C2×C11semidirect
93. C22×Q8C4×C11semidirect
98. C22⋊Q8C4×C11semidirect
101. C2×C4⋊C4C4×C11semidirect
138. C11#1508direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C11×#4072
C4×C11×C22⋊C42
C11×#3282
#150811