Finite Group Databasebeta

← C11×#1870 #13064708

Subgroups — C11×#1870 #13064708

Order 1408.

408 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 136 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, complemented
2C2×C4×D4×C11C211yesmaximal, characteristic
3C2×C11×C22⋊C8C211yesmaximal, characteristic, complemented
4C2×C11×C22⋊C8C212yesmaximal, complemented
5C11×#336C212yesmaximal, complemented
6C22×D4×C11C411yescharacteristic
7C23×C4×C11C2211yescharacteristic
8C23×C4×C11C2211yescharacteristic
9C2×C11×M16—22no—
10C2×C11×M16—24no—
11C22×C8×C11C2212yes—
12C22×C8×C11C2212yes—
13C4×D4×C11—22no—
14C4×D4×C11—22no—
15C2×C11×C4⋊C4C411yescharacteristic
16C2×C11×C22⋊C4C411yescharacteristic
17C2×C11×C22⋊C4C411yescharacteristic
18C2×C42×C11C2211yescharacteristic
19C11×C22⋊C8—22no—
20C11×C22⋊C8—24no—
21C24×C11C2×C411yescharacteristic
22C24×C11C2×C411yescharacteristic
23C2×D4×C11—22no—
24C2×D4×C11—22no—
25C2×D4×C11—22no—
26C22×C4×C11—22no—
27C22×C4×C11—22no—
28C22×C4×C11—22no—
29C22×C4×C11—21no—
30C22×C4×C11—21no—
31C22×C4×C11—22no—
32C22×C4×C11C2×C411yescharacteristic
33C22×C4×C11C2×C411yescharacteristic
34C22×C4×C11C2×C411yescharacteristic
35C22×C4×C11C2×C411yescharacteristic
36C22×C4×C11D412yes—
37C22×C4×C11D412yes—
38C22×C4×C11C2311yescharacteristic
39C11×M16—28no—
40C2×C8×C11—22no—
41C2×C8×C11—22no—
42C2×C8×C11—22no—
43C2×C8×C11—22no—
44C2×C8×C11—22no—
45C2×C8×C11D414yescomplemented
46C11×C4⋊C4—22no—
47C11×C22⋊C4—22no—
48C11×C22⋊C4—22no—
49C42×C11—21no—
50C42×C11—21no—
51#1870C1111yesmaximal, characteristic, direct product factor, Sylow
52C23×C11—21no—
53C23×C11—22no—
54C23×C11—22no—
55C23×C11—21no—
56C23×C11—21no—
57C23×C11—21no—
58C23×C11—22no—
59C23×C11—22no—
60C23×C11C22⋊C412yes—
61C23×C11M1612yescomplemented
62C23×C11C22×C411yescharacteristic
63D4×C11—28no—
64C2×C4×C11—21no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—24no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—41no—
75C2×C4×C11—42no—
76C2×C4×C11—41no—
77C2×C4×C11C22⋊C412yes—
78C2×C4×C11M1612yescomplemented
79C2×C4×C11C2×D412yes—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11#4112yes—
83C8×C11—24no—
84C8×C11—42no—
85C22×M16C2×C1111yescharacteristic, complemented
86C2×C4×D4C2×C1111yescharacteristic
87C2×C22⋊C8C2×C1111yescharacteristic, complemented
88C2×C22⋊C8C2×C1112yescomplemented
89#336C2×C1112yescomplemented
90C22×C11—22no—
91C22×C11—22no—
92C22×C11—22no—
93C22×C11—22no—
94C22×C11—24no—
95C22×C11—41no—
96C22×C11—41no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11—42no—
100C22×C11C2×C22⋊C411yescharacteristic
101C22×C11C4×D412yes—
102C22×C11C2×M1611yescharacteristic
103C22×C11C2×M1611yescharacteristic
104C22×C11#13112yes—
105C4×C11—22no—
106C4×C11—22no—
107C4×C11—41no—
108C4×C11—41no—
109C4×C11#12011yescharacteristic
110C4×C11#12112yes—
111C4×C11#12311yescharacteristic
112C22×D4C4×C1111yescharacteristic
113C23×C4C22×C1111yescharacteristic
114C23×C4C22×C1111yescharacteristic
115C2×M16—22no—
116C2×M16—24no—
117C22×C8C22×C1112yes—
118C22×C8C22×C1112yes—
119C4×D4—22no—
120C4×D4—22no—
121C2×C4⋊C4C4×C1111yescharacteristic
122C2×C22⋊C4C4×C1111yescharacteristic
123C2×C22⋊C4C4×C1111yescharacteristic
124C2×C42C22×C1111yescharacteristic
125C22⋊C8—22no—
126C22⋊C8—24no—
127C2×C11—42no—
128C2×C11—42no—
129C2×C11#38611yescharacteristic
130C2×C11#40711yescharacteristic
131C2×C11#40811yescharacteristic
132C2×C11#43512yes—
133C2×C11#43612yes—
134C24C2×C4×C1111yescharacteristic
135C24C2×C4×C1111yescharacteristic
136C2×D4—22no—
137C2×D4—22no—
138C2×D4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—22no—
145C22×C4C2×C4×C1111yescharacteristic
146C22×C4C2×C4×C1111yescharacteristic
147C22×C4C2×C4×C1111yescharacteristic
148C22×C4C2×C4×C1111yescharacteristic
149C22×C4D4×C1112yes—
150C22×C4D4×C1112yes—
151C22×C4C23×C1111yescharacteristic
152M16—28no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8D4×C1114yescomplemented
159C4⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—22no—
162C42—21no—
163C42—21no—
164C11#187011yescharacteristic, direct product factor, Sylow
165C23—21no—
166C23—22no—
167C23—22no—
168C23—21no—
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23C11×C22⋊C412yes—
174C23C11×M1612yescomplemented
175C23C22×C4×C1111yescharacteristic
176D4—28no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4C11×C22⋊C412yes—
191C2×C4C11×M1612yescomplemented
192C2×C4C2×D4×C1112yes—
193C2×C4C2×D4×C1111yescharacteristic
194C2×C4C2×D4×C1111yescharacteristic
195C2×C4C11×#4112yes—
196C8—24no—
197C8—42no—
198C22—22no—
199C22—22no—
200C22—22no—
201C22—22no—
202C22—24no—
203C22—41no—
204C22—41no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22C2×C11×C22⋊C411yescharacteristic
209C22C4×D4×C1112yes—
210C22C2×C11×M1611yescharacteristic
211C22C2×C11×M1611yescharacteristic
212C22C11×#13112yes—
213C4—22no—
214C4—22no—
215C4—41no—
216C4—41no—
217C4C11×#12011yescharacteristic
218C4C11×#12112yes—
219C4C11×#12311yescharacteristic
220C2—42no—
221C2—42no—
222C2C11×#38611yescharacteristic
223C2C11×#40711yescharacteristic
224C2C11×#40811yescharacteristic
225C2C11×#43512yes—
226C2C11×#43612yes—
subgroupG/H
centerC22×C4×C11C23
commutatorC23C22×C4×C11
Frattini, cosocleC22×C4C23×C11
socleC23×C11C22×C4
prime radicalC22×D4×C11C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C11×M16C2semidirect
3. C2×C11×C22⋊C8C2semidirect
4. C2×C11×C22⋊C8C2semidirect
5. C11×#336C2semidirect
45. C2×C8×C11D4semidirect
51. #1870C11direct (N × H)
61. C23×C11M16semidirect
78. C2×C4×C11M16semidirect
85. C22×M16C2×C11semidirect
87. C2×C22⋊C8C2×C11semidirect
88. C2×C22⋊C8C2×C11semidirect
89. #336C2×C11semidirect
158. C2×C8D4×C11semidirect
164. C11#1870direct (N × H)
174. C23C11×M16semidirect
191. C2×C4C11×M16semidirect

Maximal subgroups

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

subgroupindex
C22×C11×M162
C2×C4×D4×C112
C2×C11×C22⋊C82
C11×#3362
#187011