Finite Group Databasebeta

← #16848091

Subgroups — #16848091

Order 3968.

1088 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 245 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×C4×D31C211yesmaximal, characteristic
2C2×#11758454C212yesmaximal, complemented
3#14520912C211yesmaximal, characteristic, complemented
4#14520908C214yesmaximal, complemented
5#14520904C212yesmaximal
6#14520896C214yesmaximal, complemented
7C31×#381C211yesmaximal, characteristic, complemented
8C24×D31C2211yescharacteristic
9C23×C4×C31C2211yescharacteristic
10C23×Dic31C2211yescharacteristic
11C22×C4×D31—28no—
12C22×C4×D31C418yescomplemented
13C22×C4×D31C2212yes—
14C22×C4×D31C2212yes—
15C2×C22⋊C4×C31C2212yes—
16C2×C22⋊Dic31C2212yes—
17C2×(C2×D31)⋊C4C2218yes—
18C2×Dic31⋊C4C2214yescomplemented
19C2×C4×Dic31C2214yescomplemented
20#11758454—28no—
21C31×#95C2214yescomplemented
22C31⋊#95C2214yescomplemented
23C24×C31C2311yescharacteristic
24C23×D31—24no—
25C23×D31—28no—
26C23×D31C2×C414yes—
27C23×D31C2312yes—
28C22×C4×C31—24no—
29C22×C4×C31C2×C414yes—
30C22×C4×C31C2314yes—
31C22×C4×C31C2312yes—
32C22×Dic31C2×C414yes—
33C22×Dic31D418yes—
34C22×Dic31C2314yes—
35C22×Dic31C2311yescharacteristic
36C22×Dic31C2311yescharacteristic
37C2×C4×D31—232no—
38C2×C4×D31—28no—
39C2×C4×D31—28no—
40C2×C4×D31C2×C418yes—
41C2×C4×D31C2×C418yes—
42C22⋊C4×C31—24no—
43C22⋊Dic31—24no—
44(C2×D31)⋊C4—216no—
45Dic31⋊C4—28no—
46C4×Dic31—28no—
47C23×C31—24no—
48C23×C31C22×C412yes—
49C23×C31C2×D414yes—
50C23×C31C2411yescharacteristic
51C22×D31—232no—
52C22×D31—28no—
53C22×D31—24no—
54C22×D31—24no—
55C22×D31—216no—
56C22×D31C22×C414yes—
57C22×D31#4118yes—
58C2×C4×C31—28no—
59C2×C4×C31—24no—
60C2×C4×C31—24no—
61C2×C4×C31—28no—
62C2×C4×C31C22×C414yes—
63C2×Dic31—24no—
64C2×Dic31—28no—
65C2×Dic31C22⋊C4116yescomplemented
66C2×Dic31C22×C412yes—
67C2×Dic31C22×C412yes—
68C2×Dic31C2×D414yes—
69C2×Dic31C2×D414yes—
70C4×D31—216no—
71C4×D31—216no—
72#2280—311nomaximal, Sylow
73C22×C31—24no—
74C22×C31—28no—
75C22×C31C2×C22⋊C414yes—
76C22×C31C23×C411yescharacteristic
77C22×C31C22×D412yes—
78C22×C31C2×#4114yes—
79C2×D31—232no—
80C2×D31—24no—
81C2×D31—24no—
82C2×D31—216no—
83C2×D31#11718yescomplemented
84C4×C31—24no—
85C4×C31—44no—
86Dic31—44no—
87Dic31C2×C22⋊C414yes—
88Dic31C2×C22⋊C414yes—
89C24×C4—311no—
90C2×#117—312no—
91#381—311no—
92#381D3111yescharacteristic, complemented
93#380—314no—
94#379—312no—
95C4×C22⋊C4—314no—
96C2×C31—24no—
97C2×C31C22×C22⋊C411yescharacteristic
98C2×C31C2×#11712yes—
99C2×C31#52514yes—
100D31—28no—
101C25—311no—
102C23×C4—311no—
103C23×C4—318no—
104C23×C4—312no—
105C23×C4—312no—
106C23×C4—628no—
107C23×C4C2×D3111yescharacteristic
108#117—628no—
109C2×C4⋊C4—314no—
110C2×C22⋊C4—312no—
111C2×C22⋊C4—318no—
112C2×C22⋊C4C2×D3112yes—
113C2×C42—314no—
114#95—314no—
115#95C2×D3114yescomplemented
116C31#228011yescharacteristic, complemented, Sylow
117C24—312no—
118C24—314no—
119C24—628no—
120C24—624no—
121C24C22×D3111yescharacteristic
122C22×C4—24no—
123C22×C4—314no—
124C22×C4—318no—
125C22×C4—311no—
126C22×C4—311no—
127C22×C4—318no—
128C22×C4—318no—
129C22×C4—314no—
130C22×C4—6232no—
131C22×C4—628no—
132C22×C4—628no—
133C22×C4C4×D3114yes—
134C22×C4C22×D3114yes—
135C22×C4C22×D3112yes—
136C4⋊C4—628no—
137C22⋊C4—24no—
138C22⋊C4—6216no—
139C22⋊C4—624no—
140C42—628no—
141C23—24no—
142C23—314no—
143C23—318no—
144C23—6216no—
145C23—6232no—
146C23—628no—
147C23—624no—
148C23—624no—
149C23C2×C4×D3112yes—
150C23D4×D3114yes—
151C23C23×D3111yescharacteristic
152C2×C4—28no—
153C2×C4—24no—
154C2×C4—24no—
155C2×C4—28no—
156C2×C4—3116no—
157C2×C4—312no—
158C2×C4—312no—
159C2×C4—314no—
160C2×C4—314no—
161C2×C4—6216no—
162C2×C4—6216no—
163C2×C4—624no—
164C2×C4—628no—
165C2×C4C2×C4×D3114yes—
166C22—24no—
167C22—28no—
168C22—318no—
169C22—6232no—
170C22—624no—
171C22—624no—
172C22—6216no—
173C22C22⋊C4×D3114yes—
174C22C22×C4×D3111yescharacteristic
175C22C2×D4×D3112yes—
176C22#41×D3114yes—
177C4—24no—
178C4—44no—
179C4—314no—
180C4—314no—
181C4—1244no—
182C2—24no—
183C2—628no—
184C2C2×C22⋊C4×D3111yescharacteristic
185C2#117×D3112yes—
186C2#1452155714yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#381C2
socle, cosocleC23×C31C24
prime radicalC24×D31C22
hypercenter#381D31
hypocenterC31#2280
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#11758454C2semidirect
3. #14520912C2semidirect
4. #14520908C2semidirect
6. #14520896C2semidirect
7. C31×#381C2semidirect
12. C22×C4×D31C4semidirect
18. C2×Dic31⋊C4C22semidirect
19. C2×C4×Dic31C22semidirect
21. C31×#95C22semidirect
22. C31⋊#95C22semidirect
65. C2×Dic31C22⋊C4semidirect
83. C2×D31#117semidirect
92. #381D31semidirect
115. #95C2×D31semidirect
116. C31#2280semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D312
C2×#117584542
#145209122
#145209082
#145209042
#145208962
C31×#3812
#228031