Finite Group Databasebeta

← C11×#1529 #13064367

Subgroups — C11×#1529 #13064367

Order 1408.

216 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C11×#529C211yesmaximal, characteristic
2C11×#432C211yesmaximal, characteristic, complemented
3C4×C11×M16C211yesmaximal, characteristic, complemented
4C11×#330C212yesmaximal, complemented
5C11×#329C212yesmaximal, complemented
6C2×C11×M16—21no—
7C11×#126—21no—
8C11×#125C2211yescharacteristic
9C11×#124C2211yescharacteristic
10C11×#123—21no—
11C11×C22⋊Q8C411yescharacteristic
12C11×#121C411yescharacteristic
13C4×Q8×C11C411yescharacteristic
14C4×D4×C11—21no—
15C4×D4×C11C411yescharacteristic
16C11×#117—21no—
17C2×C42×C11C2211yescharacteristic
18C11×C4⋊C8—21no—
19C11×C22⋊C8—21no—
20C11×#97C2212yes—
21C11×#97C2212yes—
22C4×C8×C11—21no—
23C2×Q8×C11C2×C411yescharacteristic
24C2×D4×C11—21no—
25C2×D4×C11C2×C411yescharacteristic
26C22×C4×C11—21no—
27C22×C4×C11C2×C411yescharacteristic
28C22×C4×C11D411yescharacteristic
29C22×C4×C11D411yescharacteristic
30C11×M16—24no—
31C2×C8×C11—22no—
32C2×C8×C11—22no—
33C11×C4⋊C4—21no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4C2×C411yescharacteristic
38C11×C4⋊C4C2×C411yescharacteristic
39C11×C22⋊C4—21no—
40C11×C22⋊C4—21no—
41C11×C22⋊C4—21no—
42C11×C22⋊C4—21no—
43C11×C22⋊C4—21no—
44C42×C11—21no—
45C42×C11C2×C411yescharacteristic
46C42×C11D411yescharacteristic
47C42×C11D411yescharacteristic
48C42×C11C2311yescharacteristic
49#1529C1111yesmaximal, characteristic, direct product factor, Sylow
50C23×C11—21no—
51C23×C11C22⋊C411yescharacteristic
52Q8×C11—41no—
53D4×C11—41no—
54D4×C11—42no—
55C2×C4×C11—22no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—41no—
60C2×C4×C11—41no—
61C2×C4×C11—42no—
62C2×C4×C11C22⋊C411yescharacteristic
63C2×C4×C11C22⋊C411yescharacteristic
64C2×C4×C11C22⋊C411yescharacteristic
65C2×C4×C11C22×C411yescharacteristic
66C2×C4×C11C2×D411yescharacteristic
67C2×C4×C11C2×D411yescharacteristic
68C8×C11—24no—
69C8×C11—42no—
70#529C2×C1111yescharacteristic
71#432C2×C1111yescharacteristic, complemented
72C4×M16C2×C1111yescharacteristic, complemented
73#330C2×C1112yescomplemented
74#329C2×C1112yescomplemented
75C22×C11—21no—
76C22×C11—21no—
77C22×C11—21no—
78C22×C11—41no—
79C22×C11—41no—
80C22×C11—41no—
81C22×C11C2×C22⋊C411yescharacteristic
82C4×C11—21no—
83C4×C11—21no—
84C4×C11—21no—
85C4×C11—21no—
86C4×C11—21no—
87C4×C11—41no—
88C4×C11—41no—
89C4×C11—41no—
90C4×C11#10412yes—
91C2×M16—21no—
92#126—21no—
93#125C22×C1111yescharacteristic
94#124C22×C1111yescharacteristic
95#123—21no—
96C22⋊Q8C4×C1111yescharacteristic
97#121C4×C1111yescharacteristic
98C4×Q8C4×C1111yescharacteristic
99C4×D4—21no—
100C4×D4C4×C1111yescharacteristic
101#117—21no—
102C2×C42C22×C1111yescharacteristic
103C4⋊C8—21no—
104C22⋊C8—21no—
105#97C22×C1112yes—
106#97C22×C1112yes—
107C4×C8—21no—
108C2×C11—41no—
109C2×C11—81no—
110C2×C11#41311yescharacteristic
111C2×C11C2×#10411yescharacteristic
112C2×C11#42111yescharacteristic
113C2×Q8C2×C4×C1111yescharacteristic
114C2×D4—21no—
115C2×D4C2×C4×C1111yescharacteristic
116C22×C4—21no—
117C22×C4C2×C4×C1111yescharacteristic
118C22×C4D4×C1111yescharacteristic
119C22×C4D4×C1111yescharacteristic
120M16—24no—
121C2×C8—22no—
122C2×C8—22no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4C2×C4×C1111yescharacteristic
128C4⋊C4C2×C4×C1111yescharacteristic
129C22⋊C4—21no—
130C22⋊C4—21no—
131C22⋊C4—21no—
132C22⋊C4—21no—
133C22⋊C4—21no—
134C42—21no—
135C42C2×C4×C1111yescharacteristic
136C42D4×C1111yescharacteristic
137C42D4×C1111yescharacteristic
138C42C23×C1111yescharacteristic
139C11#152911yescharacteristic, direct product factor, Sylow
140C23—21no—
141C23C11×C22⋊C411yescharacteristic
142Q8—41no—
143D4—41no—
144D4—42no—
145C2×C4—22no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—42no—
152C2×C4C11×C22⋊C411yescharacteristic
153C2×C4C11×C22⋊C411yescharacteristic
154C2×C4C11×C22⋊C411yescharacteristic
155C2×C4C22×C4×C1111yescharacteristic
156C2×C4C2×D4×C1111yescharacteristic
157C2×C4C2×D4×C1111yescharacteristic
158C8—24no—
159C8—42no—
160C22—21no—
161C22—21no—
162C22—21no—
163C22—41no—
164C22—41no—
165C22—41no—
166C22C2×C11×C22⋊C411yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—21no—
171C4—21no—
172C4—41no—
173C4—41no—
174C4—41no—
175C4C11×#10412yes—
176C2—41no—
177C2—81no—
178C2C11×#41311yescharacteristic
179C2C2×C11×#10411yescharacteristic
180C2C11×#42111yescharacteristic
subgroupG/H
center, socleC22×C11C2×C22⋊C4
commutatorC2×C4C22×C4×C11
Frattini, cosocleC42C23×C11
prime radicalC11×#121C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#432C2semidirect
3. C4×C11×M16C2semidirect
4. C11×#330C2semidirect
5. C11×#329C2semidirect
49. #1529C11direct (N × H)
71. #432C2×C11semidirect
72. C4×M16C2×C11semidirect
73. #330C2×C11semidirect
74. #329C2×C11semidirect
139. C11#1529direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5292
C11×#4322
C4×C11×M162
C11×#3302
C11×#3292
#152911