Finite Group Databasebeta

← C11×#10935 #14588128

Subgroups — C11×#10935 #14588128

Order 2816.

2594 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 2594 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×#379C213yesmaximal
2C11×#2273C211yesmaximal, characteristic, complemented
3C2×C11×#342C213yesmaximal, complemented
4C26×C11C2211yescharacteristic
5C22×C11×C22⋊C4—26no—
6C22×C11×C22⋊C4C2213yes—
7C22×C11×C22⋊C4C2213yes—
8C11×#379—26no—
9C11×#379C4112yescomplemented
10C4×C11×C22⋊C4—26no—
11C11×#342—26no—
12C25×C11—23no—
13C25×C11—23no—
14C25×C11—26no—
15C25×C11—48no—
16C25×C11C2×C416yes—
17C25×C11C2311yescharacteristic
18C23×C4×C11—23no—
19C23×C4×C11D416yes—
20C2×C11×C22⋊C4—26no—
21C2×C11×C22⋊C4—26no—
22C2×C11×C22⋊C4—26no—
23C2×C11×C22⋊C4—26no—
24C2×C11×C22⋊C4—23no—
25C2×C11×C22⋊C4—224no—
26C2×C11×C22⋊C4—424no—
27C2×C11×C22⋊C4C2×C416yes—
28C2×C11×C22⋊C4C2×C416yes—
29C2×C11×C22⋊C4D416yes—
30C2×C42×C11—24no—
31C11×#95—24no—
32#10935C1111yesmaximal, characteristic, direct product factor, Sylow
33C24×C11—224no—
34C24×C11—26no—
35C24×C11—212no—
36C24×C11—26no—
37C24×C11—212no—
38C24×C11—424no—
39C24×C11—44no—
40C24×C11—412no—
41C24×C11—424no—
42C24×C11—448no—
43C24×C11—41no—
44C24×C11—46no—
45C24×C11—43no—
46C24×C11—43no—
47C24×C11—42no—
48C24×C11—41no—
49C24×C11C4214yescomplemented
50C24×C11C22×C413yes—
51C24×C11C2×D413yes—
52C24×C11C2×D413yes—
53C24×C11#4116yes—
54C22×C4×C11—26no—
55C22×C4×C11—26no—
56C22×C4×C11—26no—
57C22×C4×C11—412no—
58C22×C4×C11—412no—
59C22×C4×C11—46no—
60C22×C4×C11C22⋊C4112yescomplemented
61C11×C22⋊C4—212no—
62C11×C22⋊C4—212no—
63C11×C22⋊C4—212no—
64C11×C22⋊C4—448no—
65C11×C22⋊C4—43no—
66C11×C22⋊C4—43no—
67C42×C11—84no—
68C2×#379C2×C1113yes—
69#2273C2×C1111yescharacteristic, complemented
70C2×#342C2×C1113yescomplemented
71C23×C11—212no—
72C23×C11—224no—
73C23×C11—248no—
74C23×C11—212no—
75C23×C11—48no—
76C23×C11—46no—
77C23×C11—46no—
78C23×C11—412no—
79C23×C11—412no—
80C23×C11—448no—
81C23×C11—424no—
82C23×C11—424no—
83C23×C11—424no—
84C23×C11—448no—
85C23×C11—424no—
86C23×C11—416no—
87C23×C11—48no—
88C23×C11—46no—
89C23×C11—412no—
90C23×C11—46no—
91C23×C11—48no—
92C23×C11C2×C4211yescharacteristic
93C23×C11C2×C22⋊C413yes—
94C23×C11#11713yes—
95C23×C11C4×D416yes—
96C23×C11C4×D416yes—
97C23×C11#12011yescharacteristic
98C23×C11#12116yes—
99C23×C11#12313yes—
100C23×C11#12413yes—
101C23×C11#12612yes—
102C23×C11#12711yescharacteristic
103C2×C4×C11—212no—
104C2×C4×C11—412no—
105C2×C4×C11—412no—
106C2×C4×C11—412no—
107C2×C4×C11—46no—
108C2×C4×C11—86no—
109C2×C4×C11—812no—
110C26C22×C1111yescharacteristic
111C22×C22⋊C4—26no—
112C22×C22⋊C4C22×C1113yes—
113C22×C22⋊C4C22×C1113yes—
114#379—26no—
115#379C4×C11112yescomplemented
116C4×C22⋊C4—26no—
117#342—26no—
118C22×C11—26no—
119C22×C11—212no—
120C22×C11—26no—
121C22×C11—212no—
122C22×C11—224no—
123C22×C11—41no—
124C22×C11—43no—
125C22×C11—46no—
126C22×C11—43no—
127C22×C11—42no—
128C22×C11—41no—
129C22×C11—424no—
130C22×C11—412no—
131C22×C11—448no—
132C22×C11—424no—
133C22×C11—44no—
134C22×C11C4×C22⋊C413yes—
135C22×C11#38613yes—
136C22×C11#38816yes—
137C22×C11#39013yes—
138C22×C11B(4,𝔽2)14yes—
139C4×C11—412no—
140C4×C11—86no—
141C25—23no—
142C25—23no—
143C25—26no—
144C25—48no—
145C25C2×C4×C1116yes—
146C25C23×C1111yescharacteristic
147C23×C4—23no—
148C23×C4D4×C1116yes—
149C2×C22⋊C4—26no—
150C2×C22⋊C4—26no—
151C2×C22⋊C4—26no—
152C2×C22⋊C4—26no—
153C2×C22⋊C4—23no—
154C2×C22⋊C4—224no—
155C2×C22⋊C4—424no—
156C2×C22⋊C4C2×C4×C1116yes—
157C2×C22⋊C4C2×C4×C1116yes—
158C2×C22⋊C4D4×C1116yes—
159C2×C42—24no—
160#95—24no—
161C2×C11—23no—
162C2×C11—23no—
163C2×C11—26no—
164C2×C11—48no—
165C2×C11#143711yescharacteristic
166C2×C11#188916yes—
167C24—224no—
168C24—26no—
169C24—212no—
170C24—26no—
171C24—212no—
172C24—424no—
173C24—44no—
174C24—412no—
175C24—424no—
176C24—448no—
177C24—41no—
178C24—46no—
179C24—43no—
180C24—43no—
181C24—42no—
182C24—41no—
183C24C42×C1114yescomplemented
184C24C22×C4×C1113yes—
185C24C2×D4×C1113yes—
186C24C2×D4×C1113yes—
187C24C11×#4116yes—
188C22×C4—26no—
189C22×C4—26no—
190C22×C4—26no—
191C22×C4—412no—
192C22×C4—412no—
193C22×C4—46no—
194C22×C4C11×C22⋊C4112yescomplemented
195C22⋊C4—212no—
196C22⋊C4—212no—
197C22⋊C4—212no—
198C22⋊C4—448no—
199C22⋊C4—43no—
200C22⋊C4—43no—
201C42—84no—
202C11#1093511yescharacteristic, direct product factor, Sylow
203C23—212no—
204C23—224no—
205C23—248no—
206C23—212no—
207C23—48no—
208C23—46no—
209C23—46no—
210C23—412no—
211C23—412no—
212C23—448no—
213C23—424no—
214C23—424no—
215C23—424no—
216C23—448no—
217C23—424no—
218C23—416no—
219C23—48no—
220C23—46no—
221C23—412no—
222C23—46no—
223C23—48no—
224C23C2×C42×C1111yescharacteristic
225C23C2×C11×C22⋊C413yes—
226C23C11×#11713yes—
227C23C4×D4×C1116yes—
228C23C4×D4×C1116yes—
229C23C11×#12011yescharacteristic
230C23C11×#12116yes—
231C23C11×#12313yes—
232C23C11×#12413yes—
233C23C11×#12612yes—
234C23C11×#12711yescharacteristic
235C2×C4—212no—
236C2×C4—412no—
237C2×C4—412no—
238C2×C4—412no—
239C2×C4—46no—
240C2×C4—86no—
241C2×C4—812no—
242C22—26no—
243C22—212no—
244C22—26no—
245C22—212no—
246C22—224no—
247C22—41no—
248C22—43no—
249C22—46no—
250C22—43no—
251C22—42no—
252C22—41no—
253C22—424no—
254C22—412no—
255C22—448no—
256C22—424no—
257C22—44no—
258C22C4×C11×C22⋊C413yes—
259C22C11×#38613yes—
260C22C11×#38816yes—
261C22C11×#39013yes—
262C22C11×B(4,𝔽2)14yes—
263C4—412no—
264C4—86no—
265C2—23no—
266C2—23no—
267C2—26no—
268C2—48no—
269C2C11×#143711yescharacteristic
270C2C11×#188916yes—
subgroupG/H
center, socleC23×C11#120
commutatorC23C2×C42×C11
Frattini, cosocleC25C23×C11
prime radicalC26×C11C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
2. C11×#2273C2semidirect
3. C2×C11×#342C2semidirect
9. C11×#379C4semidirect
32. #10935C11direct (N × H)
49. C24×C11C42semidirect
60. C22×C4×C11C22⋊C4semidirect
69. #2273C2×C11semidirect
70. C2×#342C2×C11semidirect
115. #379C4×C11semidirect
183. C24C42×C11semidirect
194. C22×C4C11×C22⋊C4semidirect
202. C11#10935direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#3792
C11×#22732
C2×C11×#3422
#1093511