Finite Group Databasebeta

← C23×#3802 #11919168

Subgroups — C23×#3802 #11919168

Order 1152.

21785 conjugacy classes of subgroups; only the 4100 normal subgroups are shown.

normal subgroups only

This group has 21785 conjugacy classes of subgroups — too many to draw. Only its 4100 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×D32C212yesmaximal, complemented
2C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C23×C3×D12C212yesmaximal, complemented
4C23×#625C212yesmaximal, complemented
5C22×#3802C2156yesmaximal, direct product factor
6C23×D3×D4—32nomaximal
7C24×C3⋊D3C2211yescharacteristic
8C24×C3×D3C2214yescomplemented
9C23×D32—232no—
10C23×D32C22156yescomplemented
11C23×C32×C4C2211yescharacteristic, complemented
12C23×C3⋊Dic3C2211yescharacteristic, complemented
13C22×C4×C3⋊D3C22128yescomplemented
14C22×C3×D12C22156yescomplemented
15C22×#625C22156yescomplemented
16C2×#3802C221448yesdirect product factor
17C25×D3—34no—
18C23×C3×D4—32no—
19C23×#67—34no—
20C22×D3×D4—3112no—
21C23×D12D312yescomplemented
22C23×C4×D3—32no—
23C23×C4×D3—61no—
24C24×C32C2311yescharacteristic
25C23×C3⋊D3D4116yescomplemented
26C23×C3⋊D3C23114yes—
27C23×C3×D3—232no—
28C23×C3×D3C23156yescomplemented
29C22×D32—2448no—
30C22×D32C231224yescomplemented
31C22×C32×C4C23114yescomplemented
32C22×C3⋊Dic3C23114yescomplemented
33C2×C4×C3⋊D3C231112yescomplemented
34C2×C3×D12C231224yescomplemented
35C2×#625C231224yescomplemented
36#3802C231512yesdirect product factor
37C24×D4—91noSylow
38C25×C3—34no—
39C24×D3—32no—
40C24×D3—3112no—
41C24×D3—61no—
42C24×D3—664no—
43C24×D3C2×D314yescomplemented
44C22×C3×D4—356no—
45C23×C3×C4—21no—
46C23×C3×C4C2×D312yescomplemented
47C22×#67—3112no—
48C23×Dic3—32no—
49C23×Dic3—61no—
50C2×D3×D4—3896no—
51C22×D12C2×D3156yescomplemented
52C22×C4×D3—356no—
53C22×C4×D3—628no—
54C23×C32C2×D418yescomplemented
55C23×C32C2417yes—
56C22×C3⋊D3C2×D41112yescomplemented
57C22×C3⋊D3C24128yes—
58C22×C3×D3—2224no—
59C22×C3×D3C241112yescomplemented
60C2×D32—2896no—
61C2×D32C241128yescomplemented
62C2×C32×C4C24128yescomplemented
63C2×C3⋊Dic3C24128yescomplemented
64C4×C3⋊D3C24164yescomplemented
65C3×D12C241128yescomplemented
66#625C241128yescomplemented
67C26—92no—
68C23×D4—32no—
69C23×D4—956no—
70C23×D4—92no—
71C24×C4—91no—
72C24×C3—21no—
73C24×C3—356no—
74C24×C3—632no—
75C24×C3C22×D312yes—
76C23×D3—232no—
77C23×D3—332no—
78C23×D3—328no—
79C23×D3—3448no—
80C23×D3—616no—
81C23×D3—614no—
82C23×D3—6896no—
83C23×D3C22×D3156yescomplemented
84C2×C3×D4—3224no—
85C22×C3×C4—214no—
86C22×C3×C4C22×D3128yescomplemented
87C2×#67—3448no—
88C22×Dic3—328no—
89C22×Dic3—614no—
90D3×D4—31024no—
91C2×D12C22×D31224yescomplemented
92C2×C4×D3—3224no—
93C2×C4×D3—6112no—
94C22×C32C22×D4128yescomplemented
95C22×C32C2517yes—
96C2×C3⋊D3C22×D41112yescomplemented
97C2×C3⋊D3C2518yes—
98C2×C3×D3—2224no—
99C2×C3×D3C25132yescomplemented
100D32—2256no—
101C32×C4C2518yescomplemented
102C3⋊Dic3C2518yescomplemented
103C25—34no—
104C25—956no—
105C25—91no—
106C25—1832no—
107C22×D4—356no—
108C22×D4—9448no—
109C22×D4—956no—
110C23×C4—91no—
111C23×C4—928no—
112C23×C4D3211yescharacteristic, complemented
113C23×C3—27no—
114C23×C3—28no—
115C23×C3—3112no—
116C23×C3—6224no—
117C23×C3D3×D4116yescomplemented
118C23×C3C23×D3114yes—
119C22×D3—2224no—
120C22×D3—3224no—
121C22×D3—356no—
122C22×D3—3256no—
123C22×D3—6112no—
124C22×D3—628no—
125C22×D3—61792no—
126C22×D3C23×D31112yescomplemented
127C3×D4—3128no—
128C2×C3×C4—228no—
129C2×C3×C4C23×D3156yescomplemented
130#67—3256no—
131C2×Dic3—356no—
132C2×Dic3—628no—
133D12C23×D31128yescomplemented
134C4×D3—3128no—
135C4×D3—664no—
136C2×C32C23×D4114yescomplemented
137C2×C32C2611yescharacteristic
138C3⋊D3C23×D4116yescomplemented
139C3×D3—232no—
140C24—356no—
141C24—632no—
142C24—9224no—
143C24—914no—
144C24—916no—
145C24—18448no—
146C24C2×D3211yescharacteristic
147C2×D4—3224no—
148C2×D4—9512no—
149C2×D4—9224no—
150C22×C4—914no—
151C22×C4—9112no—
152C22×C4C2×D32114yescomplemented
153C22×C3—228no—
154C22×C3—27no—
155C22×C3—332no—
156C22×C3—6224no—
157C22×C3C2×D3×D4156yescomplemented
158C22×C3C24×D3114yes—
159C2×D3—2224no—
160C2×D3—3224no—
161C2×D3—316no—
162C2×D3—68no—
163C2×D3—6112no—
164C2×D3—6512no—
165C2×D3C24×D3132yescomplemented
166C3×C4—28no—
167C3×C4C24×D3116yescomplemented
168Dic3—316no—
169Dic3—68no—
170C32C24×D411yescharacteristic, complemented, Sylow
171C23—3112no—
172C23—6224no—
173C23—9128no—
174C23—9112no—
175C23—928no—
176C23—18896no—
177C23#380218yesdirect product factor
178C23C22×D3217yes—
179D4—3128no—
180D4—9128no—
181C2×C4—928no—
182C2×C4—964no—
183C2×C4C22×D32128yescomplemented
184C2×C3—214no—
185C2×C3—21no—
186C2×C3—632no—
187C2×C3C22×D3×D4128yescomplemented
188C2×C3C25×D312yes—
189D3—232no—
190D3—332no—
191D3—616no—
192C22—332no—
193C22—6224no—
194C22—9112no—
195C22—98no—
196C22—18256no—
197C22C2×#3802128yesdirect product factor
198C22C23×D3217yes—
199C4—98no—
200C4C23×D3218yescomplemented
201C3—21no—
202C3C23×D3×D412yescomplemented
203C2—632no—
204C2—916no—
205C2C22×#3802114yesdirect product factor
206C2C24×D3211yescharacteristic
subgroupG/H
centerC24C2×D32
commutator, cosocleC2×C32C26
FrattiniC2C24×D32
FittingC23×C32×C4C22
socleC24×C32C23
hypercenterC23×C4D32
hypocenterC32C24×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C24×D32C2semidirect
2. C23×C4×C3⋊D3C2semidirect
3. C23×C3×D12C2semidirect
4. C23×#625C2semidirect
5. C22×#3802C2direct (N × H)
8. C24×C3×D3C22semidirect
10. C23×D32C22semidirect
11. C23×C32×C4C22semidirect
12. C23×C3⋊Dic3C22semidirect
13. C22×C4×C3⋊D3C22semidirect
14. C22×C3×D12C22semidirect
15. C22×#625C22semidirect
16. C2×#3802C22direct (N × H)
21. C23×D12D3semidirect
25. C23×C3⋊D3D4semidirect
28. C23×C3×D3C23semidirect
30. C22×D32C23semidirect
31. C22×C32×C4C23semidirect
32. C22×C3⋊Dic3C23semidirect
33. C2×C4×C3⋊D3C23semidirect
34. C2×C3×D12C23semidirect
35. C2×#625C23semidirect
36. #3802C23direct (N × H)
43. C24×D3C2×D3semidirect
46. C23×C3×C4C2×D3semidirect
51. C22×D12C2×D3semidirect
54. C23×C32C2×D4semidirect
56. C22×C3⋊D3C2×D4semidirect
59. C22×C3×D3C24semidirect
61. C2×D32C24semidirect
62. C2×C32×C4C24semidirect
63. C2×C3⋊Dic3C24semidirect
64. C4×C3⋊D3C24semidirect
65. C3×D12C24semidirect
66. #625C24semidirect
83. C23×D3C22×D3semidirect
86. C22×C3×C4C22×D3semidirect
91. C2×D12C22×D3semidirect
94. C22×C32C22×D4semidirect
96. C2×C3⋊D3C22×D4semidirect
99. C2×C3×D3C25semidirect
101. C32×C4C25semidirect
102. C3⋊Dic3C25semidirect
112. C23×C4D32semidirect
117. C23×C3D3×D4semidirect
126. C22×D3C23×D3semidirect
129. C2×C3×C4C23×D3semidirect
133. D12C23×D3semidirect
136. C2×C32C23×D4semidirect
138. C3⋊D3C23×D4semidirect
152. C22×C4C2×D32semidirect
157. C22×C3C2×D3×D4semidirect
165. C2×D3C24×D3semidirect
167. C3×C4C24×D3semidirect
170. C32C24×D4semidirect
177. C23#3802direct (N × H)
183. C2×C4C22×D32semidirect
187. C2×C3C22×D3×D4semidirect
197. C22C2×#3802direct (N × H)
200. C4C23×D32semidirect
202. C3C23×D3×D4semidirect
205. C2C22×#3802direct (N × H)

Maximal subgroups

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

subgroupindex
C24×D322
C23×C4×C3⋊D32
C23×C3×D122
C23×#6252
C22×#38022
C23×D3×D43