Finite Group Databasebeta

← C11×#1897 #13064735

Subgroups — C11×#1897 #13064735

Order 1408.

358 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 112 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×#525C211yesmaximal, characteristic
2C2×C11×#117C211yesmaximal, characteristic, complemented
3C2×C11×#104C212yesmaximal, complemented
4C11×#407C211yesmaximal, characteristic, complemented
5C11×#339C212yesmaximal, complemented
6C2×C11×#41C2211yescharacteristic
7C23×C4×C11C2211yescharacteristic
8C2×C11×M16C2212yes—
9C11×#123—21no—
10C11×C22⋊Q8C412yescomplemented
11C11×#121C412yescomplemented
12C11×#120—21no—
13C4×D4×C11—22no—
14C11×#117—24no—
15C11×#117C2211yescharacteristic
16C2×C11×C4⋊C4—21no—
17C2×C11×C22⋊C4—21no—
18C2×C42×C11C2212yes—
19C11×#104—24no—
20C11×C22⋊C8—22no—
21C24×C11D411yescharacteristic
22C11×#41—22no—
23C11×#41—22no—
24C2×Q8×C11C2×C411yescharacteristic
25C2×D4×C11—22no—
26C2×D4×C11—21no—
27C2×D4×C11C2×C411yescharacteristic
28C22×C4×C11—22no—
29C22×C4×C11—22no—
30C22×C4×C11—22no—
31C22×C4×C11—21no—
32C22×C4×C11C2×C412yes—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D412yes—
35C22×C4×C11C2311yescharacteristic
36C11×M16—22no—
37C11×M16—22no—
38C2×C8×C11—22no—
39C11×C4⋊C4—24no—
40C11×C4⋊C4—22no—
41C11×C4⋊C4C2×C412yes—
42C11×C22⋊C4—24no—
43C11×C22⋊C4—22no—
44C11×C22⋊C4—21no—
45C11×C22⋊C4—22no—
46C42×C11—22no—
47C42×C11—21no—
48C42×C11D414yescomplemented
49#1897C1111yesmaximal, characteristic, direct product factor, Sylow
50C23×C11—21no—
51C23×C11—21no—
52C23×C11—21no—
53C23×C11—42no—
54C23×C11C22⋊C412yes—
55C23×C11C2×D411yescharacteristic
56Q8×C11—22no—
57D4×C11—22no—
58D4×C11—44no—
59D4×C11—41no—
60D4×C11—41no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—24no—
64C2×C4×C11—24no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—24no—
68C2×C4×C11—44no—
69C2×C4×C11—42no—
70C2×C4×C11C22⋊C412yes—
71C2×C4×C11C22×C411yescharacteristic
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11#4112yes—
75C8×C11—42no—
76#525C2×C1111yescharacteristic
77C2×#117C2×C1111yescharacteristic, complemented
78C2×#104C2×C1112yescomplemented
79#407C2×C1111yescharacteristic, complemented
80#339C2×C1112yescomplemented
81C22×C11—22no—
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—22no—
85C22×C11—42no—
86C22×C11—42no—
87C22×C11—41no—
88C22×C11—42no—
89C22×C11C2×C22⋊C411yescharacteristic
90C22×C11#12011yescharacteristic
91C22×C11#12311yescharacteristic
92C4×C11—22no—
93C4×C11—44no—
94C4×C11—41no—
95C4×C11—42no—
96C4×C11C4×D412yes—
97C4×C11#12112yes—
98C2×#41C22×C1111yescharacteristic
99C23×C4C22×C1111yescharacteristic
100C2×M16C22×C1112yes—
101#123—21no—
102C22⋊Q8C4×C1112yescomplemented
103#121C4×C1112yescomplemented
104#120—21no—
105C4×D4—22no—
106#117—24no—
107#117C22×C1111yescharacteristic
108C2×C4⋊C4—21no—
109C2×C22⋊C4—21no—
110C2×C42C22×C1112yes—
111#104—24no—
112C22⋊C8—22no—
113C2×C11—21no—
114C2×C11—21no—
115C2×C11—42no—
116C2×C11—81no—
117C2×C11#38611yescharacteristic
118C2×C11#42112yes—
119C24D4×C1111yescharacteristic
120#41—22no—
121#41—22no—
122C2×Q8C2×C4×C1111yescharacteristic
123C2×D4—22no—
124C2×D4—21no—
125C2×D4C2×C4×C1111yescharacteristic
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4C2×C4×C1112yes—
131C22×C4D4×C1111yescharacteristic
132C22×C4D4×C1112yes—
133C22×C4C23×C1111yescharacteristic
134M16—22no—
135M16—22no—
136C2×C8—22no—
137C4⋊C4—24no—
138C4⋊C4—22no—
139C4⋊C4C2×C4×C1112yes—
140C22⋊C4—24no—
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C42—22no—
145C42—21no—
146C42D4×C1114yescomplemented
147C11#189711yescharacteristic, direct product factor, Sylow
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C11×C22⋊C412yes—
153C23C2×D4×C1111yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—44no—
167C2×C4—42no—
168C2×C4C11×C22⋊C412yes—
169C2×C4C22×C4×C1111yescharacteristic
170C2×C4C2×D4×C1112yes—
171C2×C4C2×D4×C1111yescharacteristic
172C2×C4C11×#4112yes—
173C8—42no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—41no—
181C22—42no—
182C22C2×C11×C22⋊C411yescharacteristic
183C22C11×#12011yescharacteristic
184C22C11×#12311yescharacteristic
185C4—22no—
186C4—44no—
187C4—41no—
188C4—42no—
189C4C4×D4×C1112yes—
190C4C11×#12112yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2C11×#38611yescharacteristic
196C2C11×#42112yes—
subgroupG/H
centerC2×C4×C11C2×D4
commutatorC2×C4C22×C4×C11
Frattini, cosocleC22×C4C23×C11
socleC22×C11C2×C22⋊C4
prime radicalC11×#525C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C11×#117C2semidirect
3. C2×C11×#104C2semidirect
4. C11×#407C2semidirect
5. C11×#339C2semidirect
10. C11×C22⋊Q8C4semidirect
11. C11×#121C4semidirect
48. C42×C11D4semidirect
49. #1897C11direct (N × H)
77. C2×#117C2×C11semidirect
78. C2×#104C2×C11semidirect
79. #407C2×C11semidirect
80. #339C2×C11semidirect
102. C22⋊Q8C4×C11semidirect
103. #121C4×C11semidirect
146. C42D4×C11semidirect
147. C11#1897direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#5252
C2×C11×#1172
C2×C11×#1042
C11×#4072
C11×#3392
#189711