Finite Group Databasebeta

← C2×C11×#2030 #14600659

Subgroups — C2×C11×#2030 #14600659

Order 2816.

1482 conjugacy classes of subgroups; only the 350 normal subgroups are shown.

normal subgroups only

This group has 1482 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
2C2×C11×#381C213yesmaximal
3C11×#2030C218yesmaximal, direct product factor
4C2×C11×#342C213yesmaximal
5C24×C4×C11C2211yescharacteristic
6C11×#543—26no—
7C11×#543C2214yes—
8C2×C11×C22⋊Q8—26no—
9C22×C11×C22⋊C4C2213yes—
10C22×C11×C22⋊C4C2213yes—
11C11×#381—26no—
12C11×#381C22112yes—
13C2×C11×#95—26no—
14C11×#342C22112yes—
15C25×C11C2311yescharacteristic
16C22×Q8×C11—22no—
17C23×C4×C11—23no—
18C23×C4×C11—23no—
19C23×C4×C11—26no—
20C23×C4×C11—23no—
21C23×C4×C11D416yes—
22C23×C4×C11Q814yescomplemented
23C23×C4×C11C2312yes—
24C11×C22⋊Q8—224no—
25C11×C22⋊Q8—224no—
26C2×C11×C4⋊C4—26no—
27C2×C11×C22⋊C4—26no—
28C2×C11×C22⋊C4—26no—
29C2×C11×C22⋊C4—212no—
30C2×C11×C22⋊C4—23no—
31C2×C11×C22⋊C4D416yes—
32C2×C11×C22⋊C4C2316yes—
33C2×C11×C22⋊C4C2316yes—
34C11×#95—224no—
35C2×#2030C1111yesmaximal, characteristic, direct product factor, Sylow
36C24×C11—44no—
37C24×C11C2×D413yes—
38C24×C11C2×D413yes—
39C24×C11C2×Q812yes—
40C24×C11#4116yes—
41C24×C11C2411yescharacteristic
42C2×Q8×C11—28no—
43C2×Q8×C11—84no—
44C22×C4×C11—26no—
45C22×C4×C11—212no—
46C22×C4×C11—212no—
47C22×C4×C11—26no—
48C22×C4×C11—26no—
49C22×C4×C11—26no—
50C22×C4×C11—26no—
51C22×C4×C11—43no—
52C22×C4×C11—41no—
53C22×C4×C11—46no—
54C22×C4×C11—46no—
55C22×C4×C11—412no—
56C22×C4×C11—412no—
57C22×C4×C11—46no—
58C22×C4×C11C2×D4112yes—
59C22×C4×C11C2×Q814yescomplemented
60C11×C4⋊C4—224no—
61C11×C22⋊C4—212no—
62C11×C22⋊C4—212no—
63C11×C22⋊C4—212no—
64C11×C22⋊C4—46no—
65C2×#543C2×C1111yescharacteristic
66C2×#381C2×C1113yes—
67#2030C2×C1118yesdirect product factor
68C2×#342C2×C1113yes—
69C23×C11—212no—
70C23×C11—46no—
71C23×C11—44no—
72C23×C11—412no—
73C23×C11—42no—
74C23×C11#12013yes—
75C23×C11#12011yescharacteristic
76C23×C11C22⋊Q816yes—
77C23×C11C22⋊Q816yes—
78C23×C11#12416yes—
79C23×C11#12416yes—
80C23×C11C22×D413yes—
81C23×C11C22×Q811yescharacteristic
82C23×C11C2×#4113yes—
83Q8×C11—88no—
84C2×C4×C11—212no—
85C2×C4×C11—212no—
86C2×C4×C11—42no—
87C2×C4×C11—46no—
88C2×C4×C11—412no—
89C2×C4×C11—44no—
90C2×C4×C11—412no—
91C2×C4×C11—412no—
92C2×C4×C11—412no—
93C2×C4×C11—46no—
94C2×C4×C11—86no—
95C2×C4×C11—812no—
96C24×C4C22×C1111yescharacteristic
97#543—26no—
98#543C22×C1114yes—
99C2×C22⋊Q8—26no—
100C22×C22⋊C4C22×C1113yes—
101C22×C22⋊C4C22×C1113yes—
102#381—26no—
103#381C22×C11112yes—
104C2×#95—26no—
105#342C22×C11112yes—
106C22×C11—26no—
107C22×C11—26no—
108C22×C11—212no—
109C22×C11—212no—
110C22×C11—46no—
111C22×C11—46no—
112C22×C11—41no—
113C22×C11—43no—
114C22×C11#39316yes—
115C22×C11#39312yes—
116C22×C11#45814yes—
117C22×C11C2×#12011yescharacteristic
118C22×C11C2×C22⋊Q813yes—
119C22×C11C2×#12413yes—
120C4×C11—44no—
121C4×C11—412no—
122C4×C11—86no—
123C25C23×C1111yescharacteristic
124C22×Q8—22no—
125C23×C4—23no—
126C23×C4—23no—
127C23×C4—26no—
128C23×C4—23no—
129C23×C4D4×C1116yes—
130C23×C4Q8×C1114yescomplemented
131C23×C4C23×C1112yes—
132C22⋊Q8—224no—
133C22⋊Q8—224no—
134C2×C4⋊C4—26no—
135C2×C22⋊C4—26no—
136C2×C22⋊C4—26no—
137C2×C22⋊C4—212no—
138C2×C22⋊C4—23no—
139C2×C22⋊C4D4×C1116yes—
140C2×C22⋊C4C23×C1116yes—
141C2×C22⋊C4C23×C1116yes—
142#95—224no—
143C2×C11—23no—
144C2×C11—23no—
145C2×C11—26no—
146C2×C11#203014yesdirect product factor
147C2×C11C2×#39311yescharacteristic
148C2×C11C2×#45812yes—
149C24—44no—
150C24C2×D4×C1113yes—
151C24C2×D4×C1113yes—
152C24C2×Q8×C1112yes—
153C24C11×#4116yes—
154C24C24×C1111yescharacteristic
155C2×Q8—28no—
156C2×Q8—84no—
157C22×C4—26no—
158C22×C4—212no—
159C22×C4—212no—
160C22×C4—26no—
161C22×C4—26no—
162C22×C4—26no—
163C22×C4—26no—
164C22×C4—43no—
165C22×C4—41no—
166C22×C4—46no—
167C22×C4—46no—
168C22×C4—412no—
169C22×C4—412no—
170C22×C4—46no—
171C22×C4C2×D4×C11112yes—
172C22×C4C2×Q8×C1114yescomplemented
173C4⋊C4—224no—
174C22⋊C4—212no—
175C22⋊C4—212no—
176C22⋊C4—212no—
177C22⋊C4—46no—
178C11C2×#203011yescharacteristic, direct product factor, Sylow
179C23—212no—
180C23—46no—
181C23—44no—
182C23—412no—
183C23—42no—
184C23C11×#12013yes—
185C23C11×#12011yescharacteristic
186C23C11×C22⋊Q816yes—
187C23C11×C22⋊Q816yes—
188C23C11×#12416yes—
189C23C11×#12416yes—
190C23C22×D4×C1113yes—
191C23C22×Q8×C1111yescharacteristic
192C23C2×C11×#4113yes—
193Q8—88no—
194C2×C4—212no—
195C2×C4—212no—
196C2×C4—42no—
197C2×C4—46no—
198C2×C4—412no—
199C2×C4—44no—
200C2×C4—412no—
201C2×C4—412no—
202C2×C4—412no—
203C2×C4—46no—
204C2×C4—86no—
205C2×C4—812no—
206C22—26no—
207C22—26no—
208C22—212no—
209C22—212no—
210C22—46no—
211C22—46no—
212C22—41no—
213C22—43no—
214C22C11×#39316yes—
215C22C11×#39312yes—
216C22C11×#45814yes—
217C22C2×C11×#12011yescharacteristic
218C22C2×C11×C22⋊Q813yes—
219C22C2×C11×#12413yes—
220C4—44no—
221C4—412no—
222C4—86no—
223C2—23no—
224C2—23no—
225C2—26no—
226C2C11×#203014yesdirect product factor
227C2C2×C11×#39311yescharacteristic
228C2C2×C11×#45812yes—
subgroupG/H
center, socleC23×C11#120
commutator, Frattini, cosocleC24C24×C11
prime radicalC25×C11C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C11 ◁ C25×C11 ◁ G

Complements

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

NH ≅ G/Ntype
3. C11×#2030C2direct (N × H)
22. C23×C4×C11Q8semidirect
35. C2×#2030C11direct (N × H)
59. C22×C4×C11C2×Q8semidirect
67. #2030C2×C11direct (N × H)
130. C23×C4Q8×C11semidirect
146. C2×C11#2030direct (N × H)
172. C22×C4C2×Q8×C11semidirect
178. C11C2×#2030direct (N × H)
226. C2C11×#2030direct (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×#3812
C11×#20302
C2×C11×#3422
C2×#203011