Finite Group Databasebeta

← C11×#23467 #14600660

Subgroups — C11×#23467 #14600660

Order 2816.

1378 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 334 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×#3458C211yesmaximal, characteristic, complemented
2C11×#2280C213yesmaximal
3C11×#2030C214yesmaximal, complemented
4C11×#2029C214yesmaximal
5C11×#1740C213yesmaximal, complemented
6C24×C4×C11C2211yescharacteristic
7C11×#544—26no—
8C11×#543C2214yes—
9C11×#533—26no—
10C2×C11×#117C2213yes—
11C2×C11×#117C2213yes—
12C11×#381C2216yes—
13C11×#380—26no—
14C11×#379C2216yes—
15C4×C11×C22⋊C4—26no—
16C11×#342C22112yes—
17C25×C11C2311yescharacteristic
18C23×C4×C11—23no—
19C23×C4×C11—23no—
20C23×C4×C11—26no—
21C23×C4×C11Q814yescomplemented
22C23×C4×C11C2311yescharacteristic
23C23×C4×C11C2311yescharacteristic
24C11×C4⋊Q8—212no—
25C11×#125—212no—
26C11×C22⋊Q8—224no—
27C4×Q8×C11—28no—
28C11×#117—26no—
29C11×#117—26no—
30C11×#117—212no—
31C2×C11×C4⋊C4—23no—
32C2×C11×C4⋊C4D416yes—
33C2×C11×C22⋊C4—212no—
34C2×C11×C22⋊C4C2316yes—
35C2×C11×C22⋊C4C2316yes—
36C2×C42×C11—23no—
37C2×C42×C11D416yes—
38C11×#95—212no—
39#23467C1111yesmaximal, characteristic, direct product factor, Sylow
40C24×C11—23no—
41C24×C11—23no—
42C24×C11—44no—
43C24×C11C2×Q812yes—
44C24×C11C2411yescharacteristic
45C2×Q8×C11—28no—
46C22×C4×C11—23no—
47C22×C4×C11—23no—
48C22×C4×C11—212no—
49C22×C4×C11—212no—
50C22×C4×C11—26no—
51C22×C4×C11—43no—
52C22×C4×C11—41no—
53C22×C4×C11—46no—
54C22×C4×C11—46no—
55C22×C4×C11C2×D4112yes—
56C22×C4×C11C2×D413yes—
57C22×C4×C11C2×D413yes—
58C22×C4×C11C2×Q812yes—
59C22×C4×C11C2×Q812yes—
60C22×C4×C11#4116yes—
61C11×C4⋊C4—224no—
62C11×C4⋊C4—212no—
63C11×C4⋊C4—46no—
64C11×C22⋊C4—212no—
65C11×C22⋊C4—212no—
66C11×C22⋊C4—424no—
67C42×C11—26no—
68C42×C11—26no—
69C42×C11—46no—
70#3458C2×C1111yescharacteristic, complemented
71#2280C2×C1113yes—
72#2030C2×C1114yescomplemented
73#2029C2×C1114yes—
74#1740C2×C1113yescomplemented
75C23×C11—212no—
76C23×C11—26no—
77C23×C11—44no—
78C23×C11—42no—
79C23×C11—46no—
80C23×C11—412no—
81C23×C11—41no—
82C23×C11—43no—
83C23×C11C22×D413yes—
84C23×C11C22×Q811yescharacteristic
85C23×C11C2×#4113yes—
86Q8×C11—88no—
87C2×C4×C11—212no—
88C2×C4×C11—26no—
89C2×C4×C11—41no—
90C2×C4×C11—43no—
91C2×C4×C11—412no—
92C2×C4×C11—44no—
93C2×C4×C11—412no—
94C2×C4×C11—412no—
95C2×C4×C11—46no—
96C2×C4×C11#12013yes—
97C2×C4×C11#12011yescharacteristic
98C2×C4×C11C22⋊Q816yes—
99C2×C4×C11C22⋊Q816yes—
100C2×C4×C11#12416yes—
101C2×C4×C11#12416yes—
102C24×C4C22×C1111yescharacteristic
103#544—26no—
104#543C22×C1114yes—
105#533—26no—
106C2×#117C22×C1113yes—
107C2×#117C22×C1113yes—
108#381C22×C1116yes—
109#380—26no—
110#379C22×C1116yes—
111C4×C22⋊C4—26no—
112#342C22×C11112yes—
113C22×C11—26no—
114C22×C11—212no—
115C22×C11—41no—
116C22×C11—43no—
117C22×C11—412no—
118C22×C11—46no—
119C22×C11—42no—
120C22×C11—44no—
121C22×C11C2×#12011yescharacteristic
122C22×C11C2×C22⋊Q813yes—
123C22×C11C2×#12413yes—
124C4×C11—42no—
125C4×C11—412no—
126C4×C11—86no—
127C4×C11#39316yes—
128C4×C11#39312yes—
129C25C23×C1111yescharacteristic
130C23×C4—23no—
131C23×C4—23no—
132C23×C4—26no—
133C23×C4Q8×C1114yescomplemented
134C23×C4C23×C1111yescharacteristic
135C23×C4C23×C1111yescharacteristic
136C4⋊Q8—212no—
137#125—212no—
138C22⋊Q8—224no—
139C4×Q8—28no—
140#117—26no—
141#117—26no—
142#117—212no—
143C2×C4⋊C4—23no—
144C2×C4⋊C4D4×C1116yes—
145C2×C22⋊C4—212no—
146C2×C22⋊C4C23×C1116yes—
147C2×C22⋊C4C23×C1116yes—
148C2×C42—23no—
149C2×C42D4×C1116yes—
150#95—212no—
151C2×C11—23no—
152C2×C11—23no—
153C2×C11—44no—
154C2×C11C2×#39311yescharacteristic
155C2×C11#302512yes—
156C24—23no—
157C24—23no—
158C24—44no—
159C24C2×Q8×C1112yes—
160C24C24×C1111yescharacteristic
161C2×Q8—28no—
162C22×C4—23no—
163C22×C4—23no—
164C22×C4—212no—
165C22×C4—212no—
166C22×C4—26no—
167C22×C4—43no—
168C22×C4—41no—
169C22×C4—46no—
170C22×C4—46no—
171C22×C4C2×D4×C11112yes—
172C22×C4C2×D4×C1113yes—
173C22×C4C2×D4×C1113yes—
174C22×C4C2×Q8×C1112yes—
175C22×C4C2×Q8×C1112yes—
176C22×C4C11×#4116yes—
177C4⋊C4—224no—
178C4⋊C4—212no—
179C4⋊C4—46no—
180C22⋊C4—212no—
181C22⋊C4—212no—
182C22⋊C4—424no—
183C42—26no—
184C42—26no—
185C42—46no—
186C11#2346711yescharacteristic, direct product factor, Sylow
187C23—212no—
188C23—26no—
189C23—44no—
190C23—42no—
191C23—46no—
192C23—412no—
193C23—41no—
194C23—43no—
195C23C22×D4×C1113yes—
196C23C22×Q8×C1111yescharacteristic
197C23C2×C11×#4113yes—
198Q8—88no—
199C2×C4—212no—
200C2×C4—26no—
201C2×C4—41no—
202C2×C4—43no—
203C2×C4—412no—
204C2×C4—44no—
205C2×C4—412no—
206C2×C4—412no—
207C2×C4—46no—
208C2×C4C11×#12013yes—
209C2×C4C11×#12011yescharacteristic
210C2×C4C11×C22⋊Q816yes—
211C2×C4C11×C22⋊Q816yes—
212C2×C4C11×#12416yes—
213C2×C4C11×#12416yes—
214C22—26no—
215C22—212no—
216C22—41no—
217C22—43no—
218C22—412no—
219C22—46no—
220C22—42no—
221C22—44no—
222C22C2×C11×#12011yescharacteristic
223C22C2×C11×C22⋊Q813yes—
224C22C2×C11×#12413yes—
225C4—42no—
226C4—412no—
227C4—86no—
228C4C11×#39316yes—
229C4C11×#39312yes—
230C2—23no—
231C2—23no—
232C2—44no—
233C2C2×C11×#39311yescharacteristic
234C2C11×#302512yes—
subgroupG/H
centerC2×C4×C11#120
commutator, Frattini, cosocleC24C24×C11
socleC22×C11C2×#120
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C11 ◁ C23×C4×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C11×#3458C2semidirect
3. C11×#2030C2semidirect
5. C11×#1740C2semidirect
21. C23×C4×C11Q8semidirect
39. #23467C11direct (N × H)
70. #3458C2×C11semidirect
72. #2030C2×C11semidirect
74. #1740C2×C11semidirect
133. C23×C4Q8×C11semidirect
186. C11#23467direct (N × H)

Maximal subgroups

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

subgroupindex
C11×#34582
C11×#22802
C11×#20302
C11×#20292
C11×#17402
#2346711