Finite Group Databasebeta

← C22×#10622284 #14919950

Subgroups — C22×#10622284 #14919950

Order 2816.

13646 conjugacy classes of subgroups; only the 1539 normal subgroups are shown.

normal subgroups only

This group has 13646 conjugacy classes of subgroups — too many to draw. Only its 1539 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
1C24×D44C213yesmaximal, complemented
2C23×(C2×D11)⋊C4C213yesmaximal, complemented
3C2×#10622284C2124yesmaximal, direct product factor
4C22×C11×#95C211yesmaximal, characteristic, complemented
5C25×D11C2213yes—
6C24×C4×C11C2213yes—
7C24×Dic11C2211yescharacteristic
8C23×D44—248no—
9C23×D44—224no—
10C23×D44C22136yescomplemented
11C22×(C2×D11)⋊C4—224no—
12C22×(C2×D11)⋊C4C22136yescomplemented
13C2×C11×#95C22112yescomplemented
14#10622284C22164yesdirect product factor
15C25×C11C2311yescharacteristic
16C24×D11—212no—
17C24×D11—224no—
18C24×D11—224no—
19C24×D11—212no—
20C24×D11D4124yescomplemented
21C24×D11C23118yes—
22C23×C4×C11—224no—
23C23×C4×C11D4124yescomplemented
24C23×C4×C11C23118yes—
25C23×Dic11—212no—
26C23×Dic11C2316yes—
27C22×D44—2384no—
28C22×D44—2288no—
29C22×D44—2144no—
30C22×D44C23148yescomplemented
31C2×(C2×D11)⋊C4—2144no—
32C2×(C2×D11)⋊C4C23148yescomplemented
33C11×#95C23116yescomplemented
34C22×#392—111nomaximal, Sylow
35C24×C11C2×D4112yes—
36C24×C11C2×D4112yes—
37C24×C11#4114yes—
38C24×C11C2413yes—
39C23×D11—2192no—
40C23×D11—296no—
41C23×D11—236no—
42C23×D11—272no—
43C23×D11—272no—
44C23×D11—236no—
45C23×D11—448no—
46C23×D11—496no—
47C23×D11—448no—
48C23×D11C2×D4172yescomplemented
49C23×D11C24112yes—
50C22×C4×C11—296no—
51C22×C4×C11—272no—
52C22×C4×C11C2×D4172yescomplemented
53C22×C4×C11C24112yes—
54C22×Dic11—236no—
55C22×Dic11—416no—
56C22×Dic11C2414yes—
57C2×D44—21152no—
58C2×D44—2192no—
59C2×D44—296no—
60(C2×D11)⋊C4—296no—
61C24×D4—113no—
62C23×C22⋊C4—113no—
63C2×#392—1124no—
64C22×#95D1111yescharacteristic, complemented
65C23×C11#120148yes—
66C23×C11#121148yes—
67C23×C11#127116yes—
68C23×C11C22×D4118yes—
69C23×C11C22×D4118yes—
70C23×C11C2×#4116yes—
71C23×C11C2511yescharacteristic
72C22×D11—2288no—
73C22×D11—2144no—
74C22×D11—212no—
75C22×D11—224no—
76C22×D11—224no—
77C22×D11—212no—
78C22×D11—472no—
79C22×D11—4144no—
80C22×D11—472no—
81C22×D11—4384no—
82C22×D11C22×D4124yescomplemented
83C2×C4×C11—2144no—
84C2×C4×C11—224no—
85C2×C4×C11C22×D4124yescomplemented
86C2×Dic11—212no—
87C2×Dic11—424no—
88D44—2384no—
89C26—113no—
90C23×D4—1136no—
91C23×D4—2248no—
92C23×D4—2224no—
93C24×C4—111no—
94C24×C4C2×D1113yes—
95C22×C22⋊C4—1136no—
96C22×C22⋊C4—2224no—
97#392—1164no—
98C2×#95C2×D11112yescomplemented
99C22×C11#392164yescomplemented
100C22×C11C2×#120136yes—
101C22×C11C2×#121136yes—
102C22×C11C2×#127112yes—
103C22×C11C23×D413yes—
104C22×C11C23×D413yes—
105C22×C11C22×#4111yescharacteristic
106C2×D11—248no—
107C2×D11—224no—
108C2×D11—4288no—
109C2×D11—412no—
110C2×D11—424no—
111C2×D11—412no—
112C4×C11—224no—
113Dic11—44no—
114C25—1124no—
115C25—1118no—
116C25—2212no—
117C25—2224no—
118C25—2224no—
119C25—2212no—
120C25C22×D1111yescharacteristic
121C22×D4—1148no—
122C22×D4—22288no—
123C22×D4—22384no—
124C22×D4—22144no—
125C23×C4—224no—
126C23×C4—116no—
127C23×C4—2212no—
128C23×C4D44124yescomplemented
129C23×C4C22×D11118yes—
130C2×C22⋊C4—1148no—
131C2×C22⋊C4—22144no—
132#95C22×D11116yescomplemented
133C2×C11C2×#392124yescomplemented
134C2×C11C22×#12013yes—
135C2×C11C22×#12113yes—
136C2×C11C22×#12711yescharacteristic
137D11—424no—
138C24—1172no—
139C24—1112no—
140C24—22192no—
141C24—2296no—
142C24—2236no—
143C24—2272no—
144C24—2272no—
145C24—2236no—
146C24—4448no—
147C24—4448no—
148C24—4496no—
149C24C2×D44112yes—
150C24D4×D11112yes—
151C24#434314yes—
152C24C23×D1113yes—
153C2×D4—22192no—
154C2×D4—221152no—
155C2×D4—2296no—
156C22×C4—296no—
157C22×C4—272no—
158C22×C4—114no—
159C22×C4—2236no—
160C22×C4—4416no—
161C22×C4C2×D44172yescomplemented
162C22×C4C23×D11112yes—
163C22⋊C4—2296no—
164C11C22×#39211yescharacteristic, complemented, Sylow
165C23—1124no—
166C23—22288no—
167C23—22144no—
168C23—2212no—
169C23—2224no—
170C23—2224no—
171C23—2212no—
172C23—4472no—
173C23—4472no—
174C23—44144no—
175C23—44384no—
176C23#66927116yes—
177C23#66935148yes—
178C23#66948148yes—
179C23C22×D44118yes—
180C23C2×D4×D11118yes—
181C23C2×#434316yes—
182C23C24×D1111yescharacteristic
183D4—22384no—
184C2×C4—2144no—
185C2×C4—224no—
186C2×C4—2212no—
187C2×C4—4424no—
188C2×C4C22×D44124yescomplemented
189C22—2248no—
190C22—2224no—
191C22—4412no—
192C22—44288no—
193C22—4412no—
194C22—4424no—
195C22#10622284164yesdirect product factor
196C22C2×#66927112yes—
197C22C2×#66935136yes—
198C22C2×#66948136yes—
199C22C23×D4413yes—
200C22C22×D4×D1113yes—
201C22C22×#434311yescharacteristic
202C4—224no—
203C4—444no—
204C2—4424no—
205C2C2×#10622284124yesdirect product factor
206C2C22×#6693513yes—
207C2C22×#6694813yes—
208C2C22×#6692711yescharacteristic
subgroupG/H
centerC25C22×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#95C2
socleC25×C11C23
hypercenterC22×#95D11
hypocenterC11C22×#392
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C25 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C24×D44C2semidirect
2. C23×(C2×D11)⋊C4C2semidirect
3. C2×#10622284C2direct (N × H)
4. C22×C11×#95C2semidirect
10. C23×D44C22semidirect
12. C22×(C2×D11)⋊C4C22semidirect
13. C2×C11×#95C22semidirect
14. #10622284C22direct (N × H)
20. C24×D11D4semidirect
23. C23×C4×C11D4semidirect
30. C22×D44C23semidirect
32. C2×(C2×D11)⋊C4C23semidirect
33. C11×#95C23semidirect
48. C23×D11C2×D4semidirect
52. C22×C4×C11C2×D4semidirect
64. C22×#95D11semidirect
82. C22×D11C22×D4semidirect
85. C2×C4×C11C22×D4semidirect
98. C2×#95C2×D11semidirect
99. C22×C11#392semidirect
128. C23×C4D44semidirect
132. #95C22×D11semidirect
133. C2×C11C2×#392semidirect
161. C22×C4C2×D44semidirect
164. C11C22×#392semidirect
188. C2×C4C22×D44semidirect
195. C22#10622284direct (N × H)
205. C2C2×#10622284direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D442
C23×(C2×D11)⋊C42
C2×#106222842
C22×C11×#952
C22×#39211