Finite Group Databasebeta

← C11×#1900 #13064738

Subgroups — C11×#1900 #13064738

Order 1408.

390 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 116 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×C11×#121C211yesmaximal, characteristic
3C2×C11×#100C212yesmaximal, complemented
4C11×#407C211yesmaximal, characteristic, complemented
5C11×#343C212yesmaximal, complemented
6C22×D4×C11C412yes—
7C22×D4×C11C2211yescharacteristic
8C23×C4×C11C2211yescharacteristic
9C2×C11×M16—21no—
10C2×C11×M16—24no—
11C2×C11×M16C2212yes—
12C2×C11×M16C2212yes—
13C22×C8×C11—21no—
14C11×#121—21no—
15C11×#121—21no—
16C11×#121—21no—
17C11×#121—21no—
18C2×C11×C4⋊C4C2211yescharacteristic
19C2×C11×C22⋊C4C412yes—
20C11×#100—24no—
21C11×C22⋊C8—21no—
22C11×C22⋊C8—21no—
23C24×C11C2×C411yescharacteristic
24C24×C11C2×C412yes—
25C2×D4×C11—22no—
26C2×D4×C11—22no—
27C2×D4×C11—22no—
28C2×D4×C11—21no—
29C2×D4×C11—21no—
30C2×D4×C11—22no—
31C2×D4×C11—44no—
32C22×C4×C11—22no—
33C22×C4×C11—22no—
34C22×C4×C11C2×C411yescharacteristic
35C22×C4×C11C2×C412yes—
36C22×C4×C11D411yescharacteristic
37C22×C4×C11D411yescharacteristic
38C22×C4×C11D411yescharacteristic
39C22×C4×C11D411yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C11×M16—24no—
42C11×M16—22no—
43C11×M16—22no—
44C11×M16—22no—
45C11×M16D414yescomplemented
46C2×C8×C11—24no—
47C2×C8×C11—22no—
48C2×C8×C11—22no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4—21no—
51C11×C22⋊C4—22no—
52C11×C22⋊C4—22no—
53#1900C1111yesmaximal, characteristic, direct product factor, Sylow
54C23×C11—22no—
55C23×C11—22no—
56C23×C11—22no—
57C23×C11—24no—
58C23×C11—41no—
59C23×C11—42no—
60C23×C11—42no—
61C23×C11C22⋊C411yescharacteristic
62C23×C11C22⋊C411yescharacteristic
63C23×C11C22×C411yescharacteristic
64D4×C11—44no—
65D4×C11—44no—
66D4×C11—41no—
67D4×C11—42no—
68D4×C11—41no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—21no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—42no—
78C2×C4×C11C22⋊C411yescharacteristic
79C2×C4×C11C22⋊C411yescharacteristic
80C2×C4×C11C2×D412yes—
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11#4112yes—
84C8×C11—24no—
85C8×C11—42no—
86C22×M16C2×C1111yescharacteristic, complemented
87C2×#121C2×C1111yescharacteristic
88C2×#100C2×C1112yescomplemented
89#407C2×C1111yescharacteristic, complemented
90#343C2×C1112yescomplemented
91C22×C11—21no—
92C22×C11—21no—
93C22×C11—21no—
94C22×C11—21no—
95C22×C11—21no—
96C22×C11—21no—
97C22×C11—21no—
98C22×C11—44no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11—42no—
102C22×C11—84no—
103C22×C11#10012yescomplemented
104C22×C11C2×C22⋊C411yescharacteristic
105C22×C11C4×D412yes—
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—42no—
109C4×C11#12011yescharacteristic
110C4×C11#12112yes—
111C4×C11#12311yescharacteristic
112C22×D4C4×C1112yes—
113C22×D4C22×C1111yescharacteristic
114C23×C4C22×C1111yescharacteristic
115C2×M16—21no—
116C2×M16—24no—
117C2×M16C22×C1112yes—
118C2×M16C22×C1112yes—
119C22×C8—21no—
120#121—21no—
121#121—21no—
122#121—21no—
123#121—21no—
124C2×C4⋊C4C22×C1111yescharacteristic
125C2×C22⋊C4C4×C1112yes—
126#100—24no—
127C22⋊C8—21no—
128C22⋊C8—21no—
129C2×C11—22no—
130C2×C11—22no—
131C2×C11—41no—
132C2×C11—82no—
133C2×C11#38611yescharacteristic
134C2×C11C2×#10011yescharacteristic
135C2×C11#41311yescharacteristic
136C24C2×C4×C1111yescharacteristic
137C24C2×C4×C1112yes—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4—44no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4C2×C4×C1111yescharacteristic
148C22×C4C2×C4×C1112yes—
149C22×C4D4×C1111yescharacteristic
150C22×C4D4×C1111yescharacteristic
151C22×C4D4×C1111yescharacteristic
152C22×C4D4×C1111yescharacteristic
153C22×C4C23×C1111yescharacteristic
154M16—24no—
155M16—22no—
156M16—22no—
157M16—22no—
158M16D4×C1114yescomplemented
159C2×C8—24no—
160C2×C8—22no—
161C2×C8—22no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C11#190011yescharacteristic, direct product factor, Sylow
167C23—22no—
168C23—22no—
169C23—22no—
170C23—24no—
171C23—41no—
172C23—42no—
173C23—42no—
174C23C11×C22⋊C411yescharacteristic
175C23C11×C22⋊C411yescharacteristic
176C23C22×C4×C1111yescharacteristic
177D4—44no—
178D4—44no—
179D4—41no—
180D4—42no—
181D4—41no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—42no—
191C2×C4C11×C22⋊C411yescharacteristic
192C2×C4C11×C22⋊C411yescharacteristic
193C2×C4C2×D4×C1112yes—
194C2×C4C2×D4×C1111yescharacteristic
195C2×C4C2×D4×C1111yescharacteristic
196C2×C4C11×#4112yes—
197C8—24no—
198C8—42no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—44no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22—84no—
211C22C11×#10012yescomplemented
212C22C2×C11×C22⋊C411yescharacteristic
213C22C4×D4×C1112yes—
214C4—21no—
215C4—21no—
216C4—42no—
217C4C11×#12011yescharacteristic
218C4C11×#12112yes—
219C4C11×#12311yescharacteristic
220C2—22no—
221C2—22no—
222C2—41no—
223C2—82no—
224C2C11×#38611yescharacteristic
225C2C2×C11×#10011yescharacteristic
226C2C11×#41311yescharacteristic
subgroupG/H
center, socleC22×C11C2×C22⋊C4
commutatorC23C22×C4×C11
Frattini, cosocleC22×C4C23×C11
prime radicalC2×C11×#121C2
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
1. C22×C11×M16C2semidirect
3. C2×C11×#100C2semidirect
4. C11×#407C2semidirect
5. C11×#343C2semidirect
45. C11×M16D4semidirect
53. #1900C11direct (N × H)
86. C22×M16C2×C11semidirect
88. C2×#100C2×C11semidirect
89. #407C2×C11semidirect
90. #343C2×C11semidirect
103. C22×C11#100semidirect
158. M16D4×C11semidirect
166. C11#1900direct (N × H)
211. C22C11×#100semidirect

Maximal subgroups

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

subgroupindex
C22×C11×M162
C2×C11×#1212
C2×C11×#1002
C11×#4072
C11×#3432
#190011