Finite Group Databasebeta

← #16848287

Subgroups — #16848287

Order 3968.

1160 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C23×C22⋊D31C211yesmaximal, characteristic
2C2×C22⋊C4×D31C212yesmaximal, complemented
3#14520925C218yesmaximal, complemented
4#14520910C212yesmaximal, complemented
5#14520905C211yesmaximal, characteristic, complemented
6C31×#379C211yesmaximal, characteristic, complemented
7C25×C31C2211yescharacteristic
8C24×D31C2211yescharacteristic
9C22×C22⋊D31—28no—
10C22×C22⋊D31C418yescomplemented
11C22×C22⋊D31C2214yes—
12C23×Dic31C2211yescharacteristic
13C22×C4×D31C2214yescomplemented
14C2×C22⋊C4×C31C2212yes—
15C2×C22⋊C4×C31C2214yescomplemented
16C2×C22⋊Dic31C2212yes—
17C2×C22⋊Dic31C2214yescomplemented
18C2×(C2×D31)⋊C4C2214yescomplemented
19C22⋊C4×D31—28no—
20C31⋊#95C2218yescomplemented
21C24×C31—24no—
22C24×C31—44no—
23C24×C31C2×C414yescomplemented
24C24×C31C2312yes—
25C24×C31C2311yescharacteristic
26C23×D31—44no—
27C23×D31C2×C414yes—
28C23×D31D418yes—
29C23×D31C2312yes—
30C22×C4×C31C2314yes—
31C2×C22⋊D31—232no—
32C2×C22⋊D31—28no—
33C2×C22⋊D31—28no—
34C2×C22⋊D31C2×C4116yescomplemented
35C22×Dic31—24no—
36C22×Dic31C2×C414yescomplemented
37C22×Dic31C2314yes—
38C22×Dic31C2312yes—
39C2×C4×D31—28no—
40C2×C4×D31—48no—
41C22⋊C4×C31—24no—
42C22⋊C4×C31—44no—
43C22⋊Dic31—24no—
44C22⋊Dic31—44no—
45(C2×D31)⋊C4—28no—
46C23×C31—24no—
47C23×C31—28no—
48C23×C31—24no—
49C23×C31—24no—
50C23×C31—24no—
51C23×C31—48no—
52C23×C31—416no—
53C23×C31C22×C414yes—
54C23×C31C22×C412yes—
55C23×C31C2×D414yes—
56C23×C31C2411yescharacteristic
57C22×D31—28no—
58C22×D31—48no—
59C22×D31—416no—
60C22×D31C22⋊C4116yescomplemented
61C22×D31C22×C414yes—
62C22×D31C2×D414yes—
63C22×D31C2×D414yes—
64C2×C4×C31—24no—
65C2×C4×C31—28no—
66C22⋊D31—232no—
67C2×Dic31—28no—
68C2×Dic31—24no—
69C2×Dic31—24no—
70C2×Dic31—28no—
71C2×Dic31C22×C414yes—
72C4×D31—416no—
73#2308—311nomaximal, Sylow
74C22×C31—24no—
75C22×C31—28no—
76C22×C31—24no—
77C22×C31—24no—
78C22×C31—24no—
79C22×C31—416no—
80C22×C31—48no—
81C22×C31C2×C22⋊C414yes—
82C22×C31C23×C411yescharacteristic
83C22×C31C22×D412yes—
84C22×C31H(5,𝔽2)14yes—
85C2×D31—28no—
86C2×D31—28no—
87C2×D31—28no—
88C2×D31—416no—
89C2×D31C2×C22⋊C418yes—
90C4×C31—44no—
91Dic31—24no—
92Dic31—44no—
93C23×D4—311no—
94C22×C22⋊C4—312no—
95#386—318no—
96#381—312no—
97#379—311no—
98#379D3111yescharacteristic, complemented
99C2×C31—24no—
100C2×C31—44no—
101C2×C31C22×C22⋊C411yescharacteristic
102C2×C31#51812yes—
103C2×C31#53414yes—
104D31—28no—
105C25—311no—
106C25C2×D3111yescharacteristic
107C22×D4—318no—
108C22×D4—314no—
109C22×D4—628no—
110C23×C4—311no—
111C23×C4—314no—
112C2×C22⋊C4—312no—
113C2×C22⋊C4—314no—
114C2×C22⋊C4—314no—
115C2×C22⋊C4—628no—
116C2×C22⋊C4C2×D3112yes—
117C2×C22⋊C4C2×D3114yescomplemented
118#95—318no—
119C31#230811yescharacteristic, complemented, Sylow
120C24—24no—
121C24—44no—
122C24—312no—
123C24—314no—
124C24—318no—
125C24—1244no—
126C24C4×D3114yescomplemented
127C24C22×D3112yes—
128C24C22×D3111yescharacteristic
129C2×D4—3116no—
130C2×D4—6232no—
131C2×D4—628no—
132C2×D4—628no—
133C22×C4—314no—
134C22×C4—312no—
135C22×C4—314no—
136C22×C4—628no—
137C22×C4—624no—
138C22×C4—1248no—
139C22×C4C22×D3114yes—
140C22⋊C4—24no—
141C22⋊C4—44no—
142C22⋊C4—628no—
143C22⋊C4—624no—
144C22⋊C4—1244no—
145C23—24no—
146C23—28no—
147C23—24no—
148C23—24no—
149C23—24no—
150C23—48no—
151C23—416no—
152C23—314no—
153C23—314no—
154C23—314no—
155C23—3116no—
156C23—628no—
157C23—12416no—
158C23—1248no—
159C23C2×C4×D3114yes—
160C23C2×C4×D3112yes—
161C23D4×D3114yes—
162C23C23×D3111yescharacteristic
163D4—6232no—
164C2×C4—24no—
165C2×C4—28no—
166C2×C4—314no—
167C2×C4—628no—
168C2×C4—624no—
169C2×C4—624no—
170C2×C4—628no—
171C2×C4—12416no—
172C22—28no—
173C22—24no—
174C22—24no—
175C22—24no—
176C22—24no—
177C22—416no—
178C22—48no—
179C22—318no—
180C22—628no—
181C22—628no—
182C22—628no—
183C22—12416no—
184C22C22⋊C4×D3114yes—
185C22C22×C4×D3111yescharacteristic
186C22C2×D4×D3112yes—
187C22#1175856114yes—
188C4—44no—
189C4—624no—
190C4—1244no—
191C2—24no—
192C2—44no—
193C2—628no—
194C2C2×C22⋊C4×D3111yescharacteristic
195C2#1452152212yes—
196C2#1452160914yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#379C2
socle, cosocleC23×C31C24
prime radicalC23×C22⋊D31C2
hypercenter#379D31
hypocenterC31#2308
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D31C2semidirect
3. #14520925C2semidirect
4. #14520910C2semidirect
5. #14520905C2semidirect
6. C31×#379C2semidirect
10. C22×C22⋊D31C4semidirect
13. C22×C4×D31C22semidirect
15. C2×C22⋊C4×C31C22semidirect
17. C2×C22⋊Dic31C22semidirect
18. C2×(C2×D31)⋊C4C22semidirect
20. C31⋊#95C22semidirect
23. C24×C31C2×C4semidirect
34. C2×C22⋊D31C2×C4semidirect
36. C22×Dic31C2×C4semidirect
60. C22×D31C22⋊C4semidirect
98. #379D31semidirect
117. C2×C22⋊C4C2×D31semidirect
119. C31#2308semidirect
126. C24C4×D31semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D312
C2×C22⋊C4×D312
#145209252
#145209102
#145209052
C31×#3792
#230831