Finite Group Databasebeta

← #16848288

Subgroups — #16848288

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×D124C211yesmaximal, characteristic
2C2×C22⋊C4×D31C212yesmaximal, complemented
3#14520927C218yesmaximal, complemented
4#14520912C211yesmaximal, characteristic, complemented
5#14520904C212yesmaximal, complemented
6C31×#381C211yesmaximal, characteristic, complemented
7C24×D31C2211yescharacteristic
8C24×D31C2211yescharacteristic
9C23×C4×C31C2211yescharacteristic
10C22×D124—28no—
11C22×D124C418yescomplemented
12C22×D124C2214yes—
13C22×C4×D31C2214yescomplemented
14C2×C22⋊C4×C31C2212yes—
15C2×C22⋊Dic31C2212yes—
16C2×(C2×D31)⋊C4C2214yescomplemented
17C2×(C2×D31)⋊C4C2218yescomplemented
18C22⋊C4×D31—28no—
19C31×#95C2214yescomplemented
20C31⋊#95C2214yescomplemented
21C24×C31C2311yescharacteristic
22C23×D31—24no—
23C23×D31—44no—
24C23×D31—44no—
25C23×D31C2×C414yes—
26C23×D31C2×C414yescomplemented
27C23×D31D418yes—
28C23×D31C2312yes—
29C23×D31C2312yes—
30C22×C4×C31—24no—
31C22×C4×C31C2×C414yescomplemented
32C22×C4×C31C2314yes—
33C22×C4×C31C2312yes—
34C22×Dic31C2314yes—
35C2×D124—232no—
36C2×D124—28no—
37C2×D124—28no—
38C2×D124C2×C4116yescomplemented
39C2×C4×D31—28no—
40C2×C4×D31—48no—
41C22⋊C4×C31—24no—
42C22⋊Dic31—24no—
43(C2×D31)⋊C4—28no—
44(C2×D31)⋊C4—48no—
45C23×C31—24no—
46C23×C31C22×C412yes—
47C23×C31C2×D414yes—
48C23×C31C2411yescharacteristic
49C22×D31—28no—
50C22×D31—28no—
51C22×D31—24no—
52C22×D31—28no—
53C22×D31—48no—
54C22×D31—48no—
55C22×D31—416no—
56C22×D31—416no—
57C22×D31C22⋊C4116yescomplemented
58C22×D31C22×C414yes—
59C22×D31C22×C414yes—
60C22×D31C2×D414yes—
61C22×D31C2×D414yes—
62C2×C4×C31—28no—
63C2×C4×C31—24no—
64C2×C4×C31—24no—
65C2×C4×C31—28no—
66C2×C4×C31C22×C414yes—
67C2×Dic31—24no—
68C2×Dic31—28no—
69D124—232no—
70C4×D31—416no—
71#2308—311nomaximal, Sylow
72C22×C31—24no—
73C22×C31—28no—
74C22×C31C2×C22⋊C414yes—
75C22×C31C23×C411yescharacteristic
76C22×C31C22×D412yes—
77C22×C31H(5,𝔽2)14yes—
78C2×D31—28no—
79C2×D31—28no—
80C2×D31—28no—
81C2×D31—24no—
82C2×D31—28no—
83C2×D31—416no—
84C2×D31—416no—
85C2×D31—48no—
86C2×D31C2×C22⋊C418yes—
87C4×C31—24no—
88C4×C31—44no—
89Dic31—44no—
90C23×D4—311no—
91C22×C22⋊C4—312no—
92#386—318no—
93#381—311no—
94#381D3111yescharacteristic, complemented
95#379—312no—
96C2×C31—24no—
97C2×C31C22×C22⋊C411yescharacteristic
98C2×C31#51812yes—
99C2×C31#53414yes—
100D31—28no—
101D31—44no—
102C25—311no—
103C25—311no—
104C22×D4—318no—
105C22×D4—314no—
106C22×D4—628no—
107C23×C4—314no—
108C23×C4C2×D3111yescharacteristic
109C2×C22⋊C4—312no—
110C2×C22⋊C4—314no—
111C2×C22⋊C4—318no—
112C2×C22⋊C4—628no—
113C2×C22⋊C4C2×D3112yes—
114#95—314no—
115#95C2×D3114yescomplemented
116C31#230811yescharacteristic, complemented, Sylow
117C24—312no—
118C24—314no—
119C24—318no—
120C24—312no—
121C24—314no—
122C24—624no—
123C24—1244no—
124C24—1244no—
125C24C22×D3111yescharacteristic
126C2×D4—3116no—
127C2×D4—6232no—
128C2×D4—628no—
129C2×D4—628no—
130C22×C4—24no—
131C22×C4—314no—
132C22×C4—628no—
133C22×C4—1248no—
134C22×C4C4×D3114yescomplemented
135C22×C4C22×D3114yes—
136C22×C4C22×D3112yes—
137C22⋊C4—24no—
138C22⋊C4—628no—
139C22⋊C4—624no—
140C22⋊C4—1248no—
141C23—24no—
142C23—314no—
143C23—314no—
144C23—314no—
145C23—3116no—
146C23—314no—
147C23—628no—
148C23—628no—
149C23—624no—
150C23—628no—
151C23—12416no—
152C23—1248no—
153C23—1248no—
154C23—12416no—
155C23C2×C4×D3112yes—
156C23D4×D3114yes—
157C23C23×D3111yescharacteristic
158D4—6232no—
159C2×C4—28no—
160C2×C4—24no—
161C2×C4—24no—
162C2×C4—28no—
163C2×C4—624no—
164C2×C4—628no—
165C2×C4—12416no—
166C2×C4C2×C4×D3114yes—
167C22—28no—
168C22—24no—
169C22—318no—
170C22—628no—
171C22—628no—
172C22—628no—
173C22—624no—
174C22—628no—
175C22—12416no—
176C22—12416no—
177C22—1248no—
178C22C22⋊C4×D3114yes—
179C22C22×C4×D3111yescharacteristic
180C22C2×D4×D3112yes—
181C22#1175856614yes—
182C4—24no—
183C4—44no—
184C4—1244no—
185C2—24no—
186C2—628no—
187C2—1244no—
188C2C2×C22⋊C4×D3111yescharacteristic
189C2#1452152312yes—
190C2#1452161014yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#381C2
socle, cosocleC23×C31C24
prime radicalC23×D124C2
hypercenter#381D31
hypocenterC31#2308
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C4×D31C2semidirect
3. #14520927C2semidirect
4. #14520912C2semidirect
5. #14520904C2semidirect
6. C31×#381C2semidirect
11. C22×D124C4semidirect
13. C22×C4×D31C22semidirect
16. C2×(C2×D31)⋊C4C22semidirect
17. C2×(C2×D31)⋊C4C22semidirect
19. C31×#95C22semidirect
20. C31⋊#95C22semidirect
26. C23×D31C2×C4semidirect
31. C22×C4×C31C2×C4semidirect
38. C2×D124C2×C4semidirect
57. C22×D31C22⋊C4semidirect
94. #381D31semidirect
115. #95C2×D31semidirect
116. C31#2308semidirect
134. C22×C4C4×D31semidirect

Maximal subgroups

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

subgroupindex
C23×D1242
C2×C22⋊C4×D312
#145209272
#145209122
#145209042
C31×#3812
#230831