Finite Group Databasebeta

← #16848292

Subgroups — #16848292

Order 3968.

1104 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 1104 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×#11758454C212yesmaximal, complemented
3#14520949C218yesmaximal, complemented
4#14520905C211yesmaximal, characteristic, complemented
5#14520904C212yesmaximal, complemented
6C31×#379C211yesmaximal, characteristic, complemented
7C25×C31C2211yescharacteristic
8C24×D31C2211yescharacteristic
9C22×C22⋊D31—28no—
10C22×C22⋊D31C418yescomplemented
11C22×C22⋊D31C2214yes—
12C23×Dic31C2211yescharacteristic
13C2×C22⋊C4×C31C2212yes—
14C2×C22⋊C4×C31C2214yescomplemented
15C2×C22⋊Dic31C2212yes—
16C2×C22⋊Dic31C2214yescomplemented
17C2×(C2×D31)⋊C4C2218yescomplemented
18C2×Dic31⋊C4C2214yescomplemented
19C2×C4×Dic31C2214yescomplemented
20#11758454—28no—
21C24×C31—24no—
22C24×C31—44no—
23C24×C31C2×C414yes—
24C24×C31C2312yes—
25C24×C31C2311yescharacteristic
26C23×D31—24no—
27C23×D31—44no—
28C23×D31C2×C414yes—
29C23×D31C2312yes—
30C22×C4×C31C2314yes—
31C2×C22⋊D31—232no—
32C2×C22⋊D31—28no—
33C2×C22⋊D31—28no—
34C2×C22⋊D31C2×C4116yes—
35C22×Dic31C2×C414yes—
36C22×Dic31D418yes—
37C22×Dic31C2314yes—
38C22×Dic31C2312yes—
39C22⋊C4×C31—24no—
40C22⋊C4×C31—44no—
41C22⋊Dic31—24no—
42C22⋊Dic31—44no—
43(C2×D31)⋊C4—48no—
44Dic31⋊C4—28no—
45C4×Dic31—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—24no—
59C22×D31—28no—
60C22×D31—48no—
61C22×D31—416no—
62C22×D31C22×C414yes—
63C2×C4×C31—24no—
64C2×C4×C31—28no—
65C22⋊D31—232no—
66C2×Dic31—24no—
67C2×Dic31—28no—
68C2×Dic31C22⋊C4116yescomplemented
69C2×Dic31C22×C414yes—
70C2×Dic31C2×D414yes—
71C2×Dic31C2×D414yes—
72#2309—311nomaximal, Sylow
73C22×C31—24no—
74C22×C31—28no—
75C22×C31—24no—
76C22×C31—24no—
77C22×C31—24no—
78C22×C31—416no—
79C22×C31—48no—
80C22×C31C2×C22⋊C414yes—
81C22×C31C23×C411yescharacteristic
82C22×C31C22×D412yes—
83C22×C31H(5,𝔽2)14yes—
84C2×D31—24no—
85C2×D31—28no—
86C2×D31—416no—
87C2×D31—48no—
88C4×C31—44no—
89Dic31—44no—
90Dic31C2×C22⋊C418yes—
91C23×D4—311no—
92C2×#117—312no—
93#390—318no—
94#379—311no—
95#379—312no—
96#379D3111yescharacteristic, complemented
97C2×C31—24no—
98C2×C31—44no—
99C2×C31C22×C22⋊C411yescharacteristic
100C2×C31#51812yes—
101C2×C31#53514yes—
102D31—44no—
103C25—311no—
104C25C2×D3111yescharacteristic
105C22×D4—318no—
106C22×D4—314no—
107C22×D4—628no—
108C23×C4—311no—
109#117—628no—
110C2×C4⋊C4—314no—
111C2×C22⋊C4—312no—
112C2×C22⋊C4—314no—
113C2×C22⋊C4—318no—
114C2×C22⋊C4C2×D3112yes—
115C2×C22⋊C4C2×D3114yescomplemented
116C2×C42—314no—
117C31#230911yescharacteristic, complemented, Sylow
118C24—24no—
119C24—44no—
120C24—312no—
121C24—314no—
122C24—624no—
123C24—1244no—
124C24C4×D3114yes—
125C24C22×D3112yes—
126C24C22×D3111yescharacteristic
127C2×D4—3116no—
128C2×D4—6232no—
129C2×D4—628no—
130C2×D4—628no—
131C22×C4—314no—
132C22×C4—318no—
133C22×C4—312no—
134C22×C4—314no—
135C22×C4C22×D3114yes—
136C4⋊C4—628no—
137C22⋊C4—24no—
138C22⋊C4—44no—
139C22⋊C4—624no—
140C22⋊C4—1248no—
141C22⋊C4—1244no—
142C42—628no—
143C23—24no—
144C23—28no—
145C23—24no—
146C23—24no—
147C23—24no—
148C23—48no—
149C23—416no—
150C23—314no—
151C23—628no—
152C23—624no—
153C23—628no—
154C23—1248no—
155C23—12416no—
156C23C2×C4×D3114yes—
157C23C2×C4×D3112yes—
158C23D4×D3114yes—
159C23C23×D3111yescharacteristic
160D4—6232no—
161C2×C4—24no—
162C2×C4—28no—
163C2×C4—3116no—
164C2×C4—314no—
165C2×C4—314no—
166C2×C4—314no—
167C2×C4—624no—
168C2×C4—628no—
169C22—28no—
170C22—24no—
171C22—24no—
172C22—24no—
173C22—24no—
174C22—416no—
175C22—48no—
176C22—624no—
177C22—628no—
178C22—12416no—
179C22—1248no—
180C22C22⋊C4×D3114yes—
181C22C22×C4×D3111yescharacteristic
182C22C2×D4×D3112yes—
183C22#1175856114yes—
184C4—44no—
185C4—318no—
186C4—1244no—
187C2—24no—
188C2—44no—
189C2—1244no—
190C2C2×C22⋊C4×D3111yescharacteristic
191C2#1452152212yes—
192C2#1452161414yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#379C2
socle, cosocleC23×C31C24
prime radicalC23×C22⋊D31C2
hypercenter#379D31
hypocenterC31#2309
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
2. C2×#11758454C2semidirect
3. #14520949C2semidirect
4. #14520905C2semidirect
5. #14520904C2semidirect
6. C31×#379C2semidirect
10. C22×C22⋊D31C4semidirect
14. C2×C22⋊C4×C31C22semidirect
16. C2×C22⋊Dic31C22semidirect
17. C2×(C2×D31)⋊C4C22semidirect
18. C2×Dic31⋊C4C22semidirect
19. C2×C4×Dic31C22semidirect
68. C2×Dic31C22⋊C4semidirect
96. #379D31semidirect
115. C2×C22⋊C4C2×D31semidirect
117. C31#2309semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊D312
C2×#117584542
#145209492
#145209052
#145209042
C31×#3792
#230931