Finite Group Databasebeta

← C11×#10936 #14588129

Subgroups — C11×#10936 #14588129

Order 2816.

1258 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 302 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
1C2×C11×#381C213yesmaximal
2C11×#2273C211yesmaximal, characteristic
3C2×C11×#342C213yesmaximal
4C24×C4×C11C2211yescharacteristic
5C22×C11×C22⋊C4C2213yes—
6C22×C11×C22⋊C4C2213yes—
7C11×#381—26no—
8C11×#381C4112yescomplemented
9C4×C11×C22⋊C4—26no—
10C2×C11×#95—26no—
11C11×#342—26no—
12C25×C11C2311yescharacteristic
13C23×C4×C11—23no—
14C23×C4×C11—23no—
15C23×C4×C11—26no—
16C23×C4×C11—23no—
17C23×C4×C11C2×C416yes—
18C23×C4×C11D416yes—
19C2×C11×C22⋊C4—26no—
20C2×C11×C22⋊C4—26no—
21C2×C11×C22⋊C4—26no—
22C2×C11×C22⋊C4—26no—
23C2×C11×C22⋊C4—23no—
24C2×C11×C22⋊C4C2×C416yes—
25C2×C11×C22⋊C4C2×C416yes—
26C2×C11×C22⋊C4D416yes—
27C2×C42×C11—24no—
28C11×#95—24no—
29C11×#95—224no—
30#10936C1111yesmaximal, characteristic, direct product factor, Sylow
31C24×C11—44no—
32C24×C11C22×C413yes—
33C24×C11C2×D413yes—
34C24×C11C2×D413yes—
35C24×C11#4116yes—
36C22×C4×C11—26no—
37C22×C4×C11—26no—
38C22×C4×C11—212no—
39C22×C4×C11—212no—
40C22×C4×C11—26no—
41C22×C4×C11—26no—
42C22×C4×C11—26no—
43C22×C4×C11—41no—
44C22×C4×C11—46no—
45C22×C4×C11—43no—
46C22×C4×C11—43no—
47C22×C4×C11—42no—
48C22×C4×C11—41no—
49C22×C4×C11—412no—
50C22×C4×C11—412no—
51C22×C4×C11—46no—
52C22×C4×C11C4214yescomplemented
53C22×C4×C11C22⋊C4112yes—
54C11×C22⋊C4—212no—
55C11×C22⋊C4—212no—
56C11×C22⋊C4—212no—
57C11×C22⋊C4—43no—
58C11×C22⋊C4—43no—
59C42×C11—84no—
60C2×#381C2×C1113yes—
61#2273C2×C1111yescharacteristic
62C2×#342C2×C1113yes—
63C23×C11—212no—
64C23×C11—46no—
65C23×C11—46no—
66C23×C11—412no—
67C23×C11C2×C4211yescharacteristic
68C23×C11C2×C22⋊C413yes—
69C23×C11#11713yes—
70C23×C11C4×D416yes—
71C23×C11C4×D416yes—
72C23×C11#12011yescharacteristic
73C23×C11#12116yes—
74C23×C11#12313yes—
75C23×C11#12413yes—
76C23×C11#12612yes—
77C23×C11#12711yescharacteristic
78C2×C4×C11—212no—
79C2×C4×C11—212no—
80C2×C4×C11—46no—
81C2×C4×C11—412no—
82C2×C4×C11—46no—
83C2×C4×C11—412no—
84C2×C4×C11—412no—
85C2×C4×C11—412no—
86C2×C4×C11—46no—
87C2×C4×C11—86no—
88C2×C4×C11—812no—
89C24×C4C22×C1111yescharacteristic
90C22×C22⋊C4C22×C1113yes—
91C22×C22⋊C4C22×C1113yes—
92#381—26no—
93#381C4×C11112yescomplemented
94C4×C22⋊C4—26no—
95C2×#95—26no—
96#342—26no—
97C22×C11—26no—
98C22×C11—212no—
99C22×C11—26no—
100C22×C11—212no—
101C22×C11—41no—
102C22×C11—43no—
103C22×C11—46no—
104C22×C11—43no—
105C22×C11—42no—
106C22×C11—41no—
107C22×C11C4×C22⋊C413yes—
108C22×C11#38613yes—
109C22×C11#38816yes—
110C22×C11#39013yes—
111C22×C11#45814yes—
112C4×C11—412no—
113C4×C11—44no—
114C4×C11—86no—
115C25C23×C1111yescharacteristic
116C23×C4—23no—
117C23×C4—23no—
118C23×C4—26no—
119C23×C4—23no—
120C23×C4C2×C4×C1116yes—
121C23×C4D4×C1116yes—
122C2×C22⋊C4—26no—
123C2×C22⋊C4—26no—
124C2×C22⋊C4—26no—
125C2×C22⋊C4—26no—
126C2×C22⋊C4—23no—
127C2×C22⋊C4C2×C4×C1116yes—
128C2×C22⋊C4C2×C4×C1116yes—
129C2×C22⋊C4D4×C1116yes—
130C2×C42—24no—
131#95—24no—
132#95—224no—
133C2×C11—23no—
134C2×C11—23no—
135C2×C11—26no—
136C2×C11#143711yescharacteristic
137C2×C11#189016yes—
138C24—44no—
139C24C22×C4×C1113yes—
140C24C2×D4×C1113yes—
141C24C2×D4×C1113yes—
142C24C11×#4116yes—
143C22×C4—26no—
144C22×C4—26no—
145C22×C4—212no—
146C22×C4—212no—
147C22×C4—26no—
148C22×C4—26no—
149C22×C4—26no—
150C22×C4—41no—
151C22×C4—46no—
152C22×C4—43no—
153C22×C4—43no—
154C22×C4—42no—
155C22×C4—41no—
156C22×C4—412no—
157C22×C4—412no—
158C22×C4—46no—
159C22×C4C42×C1114yescomplemented
160C22×C4C11×C22⋊C4112yes—
161C22⋊C4—212no—
162C22⋊C4—212no—
163C22⋊C4—212no—
164C22⋊C4—43no—
165C22⋊C4—43no—
166C42—84no—
167C11#1093611yescharacteristic, direct product factor, Sylow
168C23—212no—
169C23—46no—
170C23—46no—
171C23—412no—
172C23C2×C42×C1111yescharacteristic
173C23C2×C11×C22⋊C413yes—
174C23C11×#11713yes—
175C23C4×D4×C1116yes—
176C23C4×D4×C1116yes—
177C23C11×#12011yescharacteristic
178C23C11×#12116yes—
179C23C11×#12313yes—
180C23C11×#12413yes—
181C23C11×#12612yes—
182C23C11×#12711yescharacteristic
183C2×C4—212no—
184C2×C4—212no—
185C2×C4—46no—
186C2×C4—412no—
187C2×C4—46no—
188C2×C4—412no—
189C2×C4—412no—
190C2×C4—412no—
191C2×C4—46no—
192C2×C4—86no—
193C2×C4—812no—
194C22—26no—
195C22—212no—
196C22—26no—
197C22—212no—
198C22—41no—
199C22—43no—
200C22—46no—
201C22—43no—
202C22—42no—
203C22—41no—
204C22C4×C11×C22⋊C413yes—
205C22C11×#38613yes—
206C22C11×#38816yes—
207C22C11×#39013yes—
208C22C11×#45814yes—
209C4—412no—
210C4—44no—
211C4—86no—
212C2—23no—
213C2—23no—
214C2—26no—
215C2C11×#143711yescharacteristic
216C2C11×#189016yes—
subgroupG/H
center, socleC23×C11#120
commutatorC23C2×C42×C11
Frattini, cosocleC25C23×C11
prime radicalC25×C11C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
8. C11×#381C4semidirect
30. #10936C11direct (N × H)
52. C22×C4×C11C42semidirect
93. #381C4×C11semidirect
159. C22×C4C42×C11semidirect
167. C11#10936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3812
C11×#22732
C2×C11×#3422
#1093611