Finite Group Databasebeta

← C2×C11×#2029 #14600658

Subgroups — C2×C11×#2029 #14600658

Order 2816.

2818 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 350 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×#543C211yesmaximal, characteristic, complemented
2C2×C11×#379C213yesmaximal
3C11×#2029C218yesmaximal, direct product factor
4C2×C11×#342C213yesmaximal, complemented
5C26×C11C2211yescharacteristic
6C11×#543—26no—
7C11×#543C2214yescomplemented
8C2×C11×C22⋊Q8—26no—
9C22×C11×C22⋊C4—26no—
10C22×C11×C22⋊C4C2213yes—
11C22×C11×C22⋊C4C2213yes—
12C11×#379—26no—
13C11×#379C22112yes—
14C11×#342C22112yescomplemented
15C25×C11—23no—
16C25×C11—23no—
17C25×C11—26no—
18C25×C11—48no—
19C25×C11Q814yescomplemented
20C25×C11C2312yes—
21C25×C11C2311yescharacteristic
22C22×Q8×C11—22no—
23C23×C4×C11—23no—
24C23×C4×C11D416yes—
25C11×C22⋊Q8—224no—
26C11×C22⋊Q8—224no—
27C2×C11×C4⋊C4—26no—
28C2×C11×C22⋊C4—26no—
29C2×C11×C22⋊C4—26no—
30C2×C11×C22⋊C4—212no—
31C2×C11×C22⋊C4—23no—
32C2×C11×C22⋊C4—224no—
33C2×C11×C22⋊C4—424no—
34C2×C11×C22⋊C4D416yes—
35C2×C11×C22⋊C4C2316yes—
36C2×C11×C22⋊C4C2316yes—
37C2×#2029C1111yesmaximal, characteristic, direct product factor, Sylow
38C24×C11—224no—
39C24×C11—212no—
40C24×C11—26no—
41C24×C11—212no—
42C24×C11—26no—
43C24×C11—416no—
44C24×C11—48no—
45C24×C11—44no—
46C24×C11—412no—
47C24×C11—424no—
48C24×C11—448no—
49C24×C11—43no—
50C24×C11—41no—
51C24×C11—46no—
52C24×C11—46no—
53C24×C11C2×D413yes—
54C24×C11C2×D413yes—
55C24×C11C2×Q812yes—
56C24×C11C2×Q814yescomplemented
57C24×C11#4116yes—
58C24×C11C2411yescharacteristic
59C2×Q8×C11—28no—
60C2×Q8×C11—84no—
61C22×C4×C11—26no—
62C22×C4×C11—26no—
63C22×C4×C11—26no—
64C22×C4×C11—412no—
65C22×C4×C11—412no—
66C22×C4×C11—46no—
67C22×C4×C11C2×D4112yes—
68C11×C4⋊C4—224no—
69C11×C22⋊C4—212no—
70C11×C22⋊C4—212no—
71C11×C22⋊C4—212no—
72C11×C22⋊C4—448no—
73C11×C22⋊C4—46no—
74C2×#543C2×C1111yescharacteristic, complemented
75C2×#379C2×C1113yes—
76#2029C2×C1118yesdirect product factor
77C2×#342C2×C1113yescomplemented
78C23×C11—212no—
79C23×C11—224no—
80C23×C11—248no—
81C23×C11—212no—
82C23×C11—46no—
83C23×C11—44no—
84C23×C11—48no—
85C23×C11—412no—
86C23×C11—42no—
87C23×C11—412no—
88C23×C11—424no—
89C23×C11—448no—
90C23×C11—424no—
91C23×C11—448no—
92C23×C11—424no—
93C23×C11—448no—
94C23×C11—42no—
95C23×C11—46no—
96C23×C11—412no—
97C23×C11—44no—
98C23×C11—48no—
99C23×C11#12013yes—
100C23×C11#12011yescharacteristic
101C23×C11C22⋊Q816yes—
102C23×C11C22⋊Q816yes—
103C23×C11#12416yes—
104C23×C11#12416yes—
105C23×C11C22×D413yes—
106C23×C11C22×Q811yescharacteristic
107C23×C11C2×#4113yes—
108Q8×C11—88no—
109C2×C4×C11—212no—
110C2×C4×C11—412no—
111C2×C4×C11—412no—
112C2×C4×C11—412no—
113C2×C4×C11—46no—
114C2×C4×C11—86no—
115C2×C4×C11—812no—
116C26C22×C1111yescharacteristic
117#543—26no—
118#543C22×C1114yescomplemented
119C2×C22⋊Q8—26no—
120C22×C22⋊C4—26no—
121C22×C22⋊C4C22×C1113yes—
122C22×C22⋊C4C22×C1113yes—
123#379—26no—
124#379C22×C11112yes—
125#342C22×C11112yescomplemented
126C22×C11—26no—
127C22×C11—26no—
128C22×C11—212no—
129C22×C11—212no—
130C22×C11—224no—
131C22×C11—46no—
132C22×C11—46no—
133C22×C11—41no—
134C22×C11—43no—
135C22×C11—424no—
136C22×C11—412no—
137C22×C11—448no—
138C22×C11—44no—
139C22×C11—48no—
140C22×C11—416no—
141C22×C11#39316yes—
142C22×C11#39312yes—
143C22×C11B(4,𝔽2)14yes—
144C22×C11C2×#12011yescharacteristic
145C22×C11C2×C22⋊Q813yes—
146C22×C11C2×#12413yes—
147C4×C11—412no—
148C4×C11—86no—
149C25—23no—
150C25—23no—
151C25—26no—
152C25—48no—
153C25Q8×C1114yescomplemented
154C25C23×C1112yes—
155C25C23×C1111yescharacteristic
156C22×Q8—22no—
157C23×C4—23no—
158C23×C4D4×C1116yes—
159C22⋊Q8—224no—
160C22⋊Q8—224no—
161C2×C4⋊C4—26no—
162C2×C22⋊C4—26no—
163C2×C22⋊C4—26no—
164C2×C22⋊C4—212no—
165C2×C22⋊C4—23no—
166C2×C22⋊C4—224no—
167C2×C22⋊C4—424no—
168C2×C22⋊C4D4×C1116yes—
169C2×C22⋊C4C23×C1116yes—
170C2×C22⋊C4C23×C1116yes—
171C2×C11—23no—
172C2×C11—23no—
173C2×C11—26no—
174C2×C11—48no—
175C2×C11#202914yesdirect product factor
176C2×C11C2×#39311yescharacteristic
177C2×C11C2×B(4,𝔽2)12yes—
178C24—224no—
179C24—212no—
180C24—26no—
181C24—212no—
182C24—26no—
183C24—416no—
184C24—44no—
185C24—48no—
186C24—412no—
187C24—424no—
188C24—448no—
189C24—43no—
190C24—41no—
191C24—46no—
192C24—46no—
193C24C2×D4×C1113yes—
194C24C2×D4×C1113yes—
195C24C2×Q8×C1112yes—
196C24C2×Q8×C1114yescomplemented
197C24C11×#4116yes—
198C24C24×C1111yescharacteristic
199C2×Q8—28no—
200C2×Q8—84no—
201C22×C4—26no—
202C22×C4—26no—
203C22×C4—26no—
204C22×C4—412no—
205C22×C4—412no—
206C22×C4—46no—
207C22×C4C2×D4×C11112yes—
208C4⋊C4—224no—
209C22⋊C4—212no—
210C22⋊C4—212no—
211C22⋊C4—212no—
212C22⋊C4—448no—
213C22⋊C4—46no—
214C11C2×#202911yescharacteristic, direct product factor, Sylow
215C23—212no—
216C23—224no—
217C23—248no—
218C23—212no—
219C23—46no—
220C23—44no—
221C23—48no—
222C23—412no—
223C23—42no—
224C23—412no—
225C23—424no—
226C23—448no—
227C23—424no—
228C23—448no—
229C23—424no—
230C23—448no—
231C23—42no—
232C23—46no—
233C23—412no—
234C23—44no—
235C23—48no—
236C23C11×#12013yes—
237C23C11×#12011yescharacteristic
238C23C11×C22⋊Q816yes—
239C23C11×C22⋊Q816yes—
240C23C11×#12416yes—
241C23C11×#12416yes—
242C23C22×D4×C1113yes—
243C23C22×Q8×C1111yescharacteristic
244C23C2×C11×#4113yes—
245Q8—88no—
246C2×C4—212no—
247C2×C4—412no—
248C2×C4—412no—
249C2×C4—412no—
250C2×C4—46no—
251C2×C4—86no—
252C2×C4—812no—
253C22—26no—
254C22—26no—
255C22—212no—
256C22—212no—
257C22—224no—
258C22—46no—
259C22—46no—
260C22—41no—
261C22—43no—
262C22—424no—
263C22—412no—
264C22—448no—
265C22—44no—
266C22—48no—
267C22—416no—
268C22C11×#39316yes—
269C22C11×#39312yes—
270C22C11×B(4,𝔽2)14yes—
271C22C2×C11×#12011yescharacteristic
272C22C2×C11×C22⋊Q813yes—
273C22C2×C11×#12413yes—
274C4—412no—
275C4—86no—
276C2—23no—
277C2—23no—
278C2—26no—
279C2—48no—
280C2C11×#202914yesdirect product factor
281C2C2×C11×#39311yescharacteristic
282C2C2×C11×B(4,𝔽2)12yes—
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC26×C11C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C11×#543C2semidirect
3. C11×#2029C2direct (N × H)
4. C2×C11×#342C2semidirect
7. C11×#543C22semidirect
14. C11×#342C22semidirect
19. C25×C11Q8semidirect
37. C2×#2029C11direct (N × H)
56. C24×C11C2×Q8semidirect
74. C2×#543C2×C11semidirect
76. #2029C2×C11direct (N × H)
77. C2×#342C2×C11semidirect
118. #543C22×C11semidirect
125. #342C22×C11semidirect
153. C25Q8×C11semidirect
175. C2×C11#2029direct (N × H)
196. C24C2×Q8×C11semidirect
214. C11C2×#2029direct (N × H)
280. C2C11×#2029direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#5432
C2×C11×#3792
C11×#20292
C2×C11×#3422
C2×#202911