Finite Group Databasebeta

← C11×#1472 #13064310

Subgroups — C11×#1472 #13064310

Order 1408.

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

normal subgroups only

This group has 270 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
3C2×C11×C22⋊C8C211yesmaximal, characteristic
4C11×#324C214yesmaximal, complemented
5C22×Q8×C11C411yescharacteristic
6C23×C4×C11C2211yescharacteristic
7C2×C11×M16—21no—
8C22×C8×C11—21no—
9C11×C22⋊Q8—21no—
10C11×C22⋊Q8—21no—
11C11×C22⋊Q8—21no—
12C11×C22⋊Q8—21no—
13C2×C11×C4⋊C4C411yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C11×C22⋊C4C412yes—
16C11×C22⋊C8—21no—
17C11×C22⋊C8—21no—
18C11×C22⋊C8C2212yes—
19C11×C22⋊C8C2212yes—
20C24×C11C2×C411yescharacteristic
21C2×Q8×C11—21no—
22C2×Q8×C11—21no—
23C2×Q8×C11—42no—
24C22×C4×C11—42no—
25C22×C4×C11C2×C412yes—
26C22×C4×C11C2×C411yescharacteristic
27C22×C4×C11C2×C412yes—
28C22×C4×C11D411yescharacteristic
29C22×C4×C11D411yescharacteristic
30C22×C4×C11D411yescharacteristic
31C22×C4×C11D411yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C11×M16—42no—
34C2×C8×C11—22no—
35C2×C8×C11—22no—
36C2×C8×C11—42no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4—21no—
39C11×C4⋊C4—22no—
40C11×C4⋊C4—22no—
41C11×C22⋊C4—22no—
42C11×C22⋊C4—22no—
43#1472C1111yesmaximal, characteristic, direct product factor, Sylow
44C23×C11—22no—
45C23×C11—22no—
46C23×C11—41no—
47C23×C11C22⋊C411yescharacteristic
48C23×C11C22⋊C411yescharacteristic
49C23×C11C22×C411yescharacteristic
50Q8×C11—42no—
51Q8×C11—42no—
52C2×C4×C11—22no—
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—22no—
57C2×C4×C11—24no—
58C2×C4×C11—41no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—42no—
62C2×C4×C11C22⋊C411yescharacteristic
63C2×C4×C11C22⋊C411yescharacteristic
64C2×C4×C11C2×D411yescharacteristic
65C2×C4×C11C2×D411yescharacteristic
66C8×C11—42no—
67C8×C11—42no—
68C2×C22⋊Q8C2×C1111yescharacteristic
69#407C2×C1111yescharacteristic
70C2×C22⋊C8C2×C1111yescharacteristic
71#324C2×C1114yescomplemented
72C22×C11—21no—
73C22×C11—21no—
74C22×C11—21no—
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11—21no—
79C22×C11—44no—
80C22×C11#10112yes—
81C22×C11C2×C22⋊C411yescharacteristic
82C22×C11#13112yes—
83C4×C11—21no—
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—42no—
87C4×C11—42no—
88C4×C11#9912yes—
89C22×Q8C4×C1111yescharacteristic
90C23×C4C22×C1111yescharacteristic
91C2×M16—21no—
92C22×C8—21no—
93C22⋊Q8—21no—
94C22⋊Q8—21no—
95C22⋊Q8—21no—
96C22⋊Q8—21no—
97C2×C4⋊C4C4×C1111yescharacteristic
98C2×C4⋊C4C22×C1112yes—
99C2×C22⋊C4C4×C1112yes—
100C22⋊C8—21no—
101C22⋊C8—21no—
102C22⋊C8C22×C1112yes—
103C22⋊C8C22×C1112yes—
104C2×C11—22no—
105C2×C11—22no—
106C2×C11—41no—
107C2×C11#40811yescharacteristic
108C2×C11C2×#9911yescharacteristic
109C2×C11C2×#10111yescharacteristic
110C24C2×C4×C1111yescharacteristic
111C2×Q8—21no—
112C2×Q8—21no—
113C2×Q8—42no—
114C22×C4—42no—
115C22×C4C2×C4×C1112yes—
116C22×C4C2×C4×C1111yescharacteristic
117C22×C4C2×C4×C1112yes—
118C22×C4D4×C1111yescharacteristic
119C22×C4D4×C1111yescharacteristic
120C22×C4D4×C1111yescharacteristic
121C22×C4D4×C1111yescharacteristic
122C22×C4C23×C1111yescharacteristic
123M16—42no—
124C2×C8—22no—
125C2×C8—22no—
126C2×C8—42no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—22no—
130C4⋊C4—22no—
131C22⋊C4—22no—
132C22⋊C4—22no—
133C11#147211yescharacteristic, direct product factor, Sylow
134C23—22no—
135C23—22no—
136C23—41no—
137C23C11×C22⋊C411yescharacteristic
138C23C11×C22⋊C411yescharacteristic
139C23C22×C4×C1111yescharacteristic
140Q8—42no—
141Q8—42no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—24no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4C11×C22⋊C411yescharacteristic
153C2×C4C11×C22⋊C411yescharacteristic
154C2×C4C2×D4×C1111yescharacteristic
155C2×C4C2×D4×C1111yescharacteristic
156C8—42no—
157C8—42no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—21no—
164C22—21no—
165C22—44no—
166C22C11×#10112yes—
167C22C2×C11×C22⋊C411yescharacteristic
168C22C11×#13112yes—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—42no—
173C4—42no—
174C4C11×#9912yes—
175C2—22no—
176C2—22no—
177C2—41no—
178C2C11×#40811yescharacteristic
179C2C2×C11×#9911yescharacteristic
180C2C2×C11×#10111yescharacteristic
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
4. C11×#324C2semidirect
43. #1472C11direct (N × H)
71. #324C2×C11semidirect
133. C11#1472direct (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
C2×C11×C22⋊C82
C11×#3242
#147211