Finite Group Databasebeta

← C11×#1483 #13064321

Subgroups — C11×#1483 #13064321

Order 1408.

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

normal subgroups only

This group has 234 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
1C11×#529C211yesmaximal, characteristic
2C2×C11×C4⋊C8C211yesmaximal, characteristic, complemented
3C4×C11×M16C211yesmaximal, characteristic, complemented
4C11×Q8⋊C8C212yesmaximal, complemented
5C11×D4⋊C8C212yesmaximal, complemented
6C2×C11×M16—21no—
7C22×C8×C11—21no—
8C11×#126—21no—
9C11×#125C411yescharacteristic
10C11×#124C411yescharacteristic
11C11×#123—21no—
12C11×C22⋊Q8C411yescharacteristic
13C11×#121C411yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15C4×D4×C11—21no—
16C4×D4×C11C2211yescharacteristic
17C11×#117—21no—
18C2×C42×C11C2211yescharacteristic
19C11×C4⋊C8—21no—
20C11×C4⋊C8C2212yes—
21C11×#97—21no—
22C4×C8×C11C2212yes—
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—
33C2×C8×C11—42no—
34C11×C4⋊C4—21no—
35C11×C4⋊C4—21no—
36C11×C4⋊C4—21no—
37C11×C4⋊C4—21no—
38C11×C4⋊C4C2×C411yescharacteristic
39C11×C4⋊C4C2×C411yescharacteristic
40C11×C22⋊C4—21no—
41C11×C22⋊C4—21no—
42C11×C22⋊C4—21no—
43C11×C22⋊C4—21no—
44C11×C22⋊C4—21no—
45C42×C11—21no—
46C42×C11C2×C411yescharacteristic
47C42×C11D411yescharacteristic
48C42×C11D411yescharacteristic
49C42×C11C2311yescharacteristic
50#1483C1111yesmaximal, characteristic, direct product factor, Sylow
51C23×C11—21no—
52C23×C11C22⋊C411yescharacteristic
53Q8×C11—22no—
54D4×C11—22no—
55D4×C11—42no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—41no—
64C2×C4×C11—41no—
65C2×C4×C11C22⋊C411yescharacteristic
66C2×C4×C11C22⋊C411yescharacteristic
67C2×C4×C11C22⋊C411yescharacteristic
68C2×C4×C11C22×C411yescharacteristic
69C2×C4×C11C2×D411yescharacteristic
70C2×C4×C11C2×D411yescharacteristic
71C8×C11—24no—
72C8×C11—42no—
73#529C2×C1111yescharacteristic
74C2×C4⋊C8C2×C1111yescharacteristic, complemented
75C4×M16C2×C1111yescharacteristic, complemented
76Q8⋊C8C2×C1112yescomplemented
77D4⋊C8C2×C1112yescomplemented
78C22×C11—21no—
79C22×C11—21no—
80C22×C11—41no—
81C22×C11—41no—
82C22×C11—41no—
83C22×C11#10412yes—
84C22×C11C2×C22⋊C411yescharacteristic
85C4×C11—21no—
86C4×C11—21no—
87C4×C11—21no—
88C4×C11—21no—
89C4×C11—41no—
90C4×C11—41no—
91C4×C11—41no—
92C4×C11#13112yes—
93C4×C11AGL(1,ℤ/8)11yescharacteristic
94C4×C11#13711yescharacteristic
95C2×M16—21no—
96C22×C8—21no—
97#126—21no—
98#125C4×C1111yescharacteristic
99#124C4×C1111yescharacteristic
100#123—21no—
101C22⋊Q8C4×C1111yescharacteristic
102#121C4×C1111yescharacteristic
103C4×Q8C22×C1111yescharacteristic
104C4×D4—21no—
105C4×D4C22×C1111yescharacteristic
106#117—21no—
107C2×C42C22×C1111yescharacteristic
108C4⋊C8—21no—
109C4⋊C8C22×C1112yes—
110#97—21no—
111C4×C8C22×C1112yes—
112C2×C11—22no—
113C2×C11—81no—
114C2×C11#40811yescharacteristic
115C2×C11#41711yescharacteristic
116C2×C11C2×#10411yescharacteristic
117C2×Q8C2×C4×C1111yescharacteristic
118C2×D4—21no—
119C2×D4C2×C4×C1111yescharacteristic
120C22×C4—21no—
121C22×C4C2×C4×C1111yescharacteristic
122C22×C4D4×C1111yescharacteristic
123C22×C4D4×C1111yescharacteristic
124M16—24no—
125C2×C8—22no—
126C2×C8—22no—
127C2×C8—42no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4C2×C4×C1111yescharacteristic
133C4⋊C4C2×C4×C1111yescharacteristic
134C22⋊C4—21no—
135C22⋊C4—21no—
136C22⋊C4—21no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C42—21no—
140C42C2×C4×C1111yescharacteristic
141C42D4×C1111yescharacteristic
142C42D4×C1111yescharacteristic
143C42C23×C1111yescharacteristic
144C11#148311yescharacteristic, direct product factor, Sylow
145C23—21no—
146C23C11×C22⋊C411yescharacteristic
147Q8—22no—
148D4—22no—
149D4—42no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4C11×C22⋊C411yescharacteristic
160C2×C4C11×C22⋊C411yescharacteristic
161C2×C4C11×C22⋊C411yescharacteristic
162C2×C4C22×C4×C1111yescharacteristic
163C2×C4C2×D4×C1111yescharacteristic
164C2×C4C2×D4×C1111yescharacteristic
165C8—24no—
166C8—42no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22C11×#10412yes—
173C22C2×C11×C22⋊C411yescharacteristic
174C4—21no—
175C4—21no—
176C4—21no—
177C4—21no—
178C4—41no—
179C4—41no—
180C4—41no—
181C4C11×#13112yes—
182C4C11×AGL(1,ℤ/8)11yescharacteristic
183C4C11×#13711yescharacteristic
184C2—22no—
185C2—81no—
186C2C11×#40811yescharacteristic
187C2C11×#41711yescharacteristic
188C2C2×C11×#10411yescharacteristic
subgroupG/H
centerC2×C4×C11C2×D4
commutatorC2×C4C22×C4×C11
Frattini, cosocleC42C23×C11
socleC22×C11C2×C22⋊C4
prime radicalC11×#121C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×C4⋊C8C2semidirect
3. C4×C11×M16C2semidirect
4. C11×Q8⋊C8C2semidirect
5. C11×D4⋊C8C2semidirect
50. #1483C11direct (N × H)
74. C2×C4⋊C8C2×C11semidirect
75. C4×M16C2×C11semidirect
76. Q8⋊C8C2×C11semidirect
77. D4⋊C8C2×C11semidirect
144. C11#1483direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5292
C2×C11×C4⋊C82
C4×C11×M162
C11×Q8⋊C82
C11×D4⋊C82
#148311