Finite Group Databasebeta

← #16854030

Subgroups — #16854030

Order 3968.

582 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×C4×Dic31C211yesmaximal, characteristic, complemented
2#14520937C214yesmaximal, complemented
3#14520930C214yesmaximal, complemented
4#14520929C212yesmaximal
5#14520921C212yesmaximal, complemented
6#14520912C211yesmaximal, characteristic, complemented
7C2×C31×#123C211yesmaximal, characteristic
8C22×D4×C31C2211yescharacteristic
9C23×C4×C31C2211yescharacteristic
10C23×Dic31C2212yes—
11C31×#123—24no—
12C2×C4⋊C4×C31C2212yes—
13C2×C22⋊C4×C31C2211yescharacteristic
14C2×C22⋊C4×C31C2212yes—
15C2×C22⋊Dic31C2212yes—
16C2×C22⋊Dic31C2214yes—
17C2×Dic31⋊C4C2214yes—
18C2×C4×Dic31—24no—
19C2×C4×Dic31C2214yes—
20C31⋊#95C2214yes—
21C31⋊#95C2214yes—
22C31⋊#95C2214yes—
23C24×C31C2311yescharacteristic
24C24×C31C2311yescharacteristic
25C2×D4×C31—22no—
26C2×D4×C31—24no—
27C22×C4×C31—24no—
28C22×C4×C31D414yes—
29C22×C4×C31C2311yescharacteristic
30C22×C4×C31C2312yes—
31C22×C4×C31C2312yes—
32C22×Dic31—24no—
33C22×Dic31—28no—
34C22×Dic31C2314yes—
35C22×Dic31C2314yes—
36C4⋊C4×C31—24no—
37C22⋊C4×C31—22no—
38C22⋊C4×C31—24no—
39C22⋊Dic31—24no—
40C22⋊Dic31—28no—
41Dic31⋊C4—28no—
42C4×Dic31—28no—
43C23×C31—24no—
44C23×C31—21no—
45C23×C31—24no—
46C23×C31—22no—
47C23×C31C2×D412yes—
48C23×C31#4114yes—
49C23×C31C2411yescharacteristic
50D4×C31—44no—
51C2×C4×C31—28no—
52C2×C4×C31—24no—
53C2×C4×C31—22no—
54C2×C4×C31—21no—
55C2×C4×C31—24no—
56C2×C4×C31—22no—
57C2×C4×C31C2×D414yes—
58C2×Dic31—216no—
59C2×Dic31—24no—
60C2×Dic31—24no—
61C2×Dic31—24no—
62C2×Dic31—24no—
63C2×Dic31—24no—
64C2×Dic31#4118yes—
65#2853—311nomaximal, Sylow
66C22×C31—24no—
67C22×C31—28no—
68C22×C31—41no—
69C22×C31—42no—
70C22×C31—44no—
71C22×C31#12314yes—
72C22×C31C22×D411yescharacteristic
73C22×C31C2×#4112yes—
74C22×C31C2×#4114yes—
75C4×C31—24no—
76C4×C31—41no—
77C4×C31—42no—
78Dic31—28no—
79Dic31—44no—
80C2×#123D3111yescharacteristic
81C22×C42—311no—
82#388—314no—
83#387—314no—
84#386—312no—
85#385—312no—
86#381—311no—
87C2×C31—24no—
88C2×C31—81no—
89C2×C31C2×#12311yescharacteristic
90C2×C31#52512yes—
91C2×C31#52914yes—
92C22×D4C2×D3111yescharacteristic
93C23×C4—312no—
94C23×C4C2×D3111yescharacteristic
95#123—24no—
96C2×C4⋊C4—314no—
97C2×C4⋊C4C2×D3112yes—
98C2×C22⋊C4—312no—
99C2×C22⋊C4—314no—
100C2×C22⋊C4C2×D3111yescharacteristic
101C2×C22⋊C4C2×D3112yes—
102C2×C42—314no—
103C2×C42—624no—
104#95—314no—
105#95—314no—
106#95—314no—
107C31#285311yescharacteristic, complemented, Sylow
108C24C22×D3111yescharacteristic
109C24C22×D3111yescharacteristic
110C2×D4—24no—
111C2×D4—22no—
112C22×C4—24no—
113C22×C4—314no—
114C22×C4—314no—
115C22×C4—628no—
116C22×C4—624no—
117C22×C4C22⋊D3114yes—
118C22×C4C22×D3111yescharacteristic
119C22×C4C22×D3112yes—
120C22×C4C22×D3112yes—
121C4⋊C4—24no—
122C4⋊C4—628no—
123C22⋊C4—22no—
124C22⋊C4—24no—
125C22⋊C4—628no—
126C22⋊C4—624no—
127C42—628no—
128C23—24no—
129C23—22no—
130C23—24no—
131C23—21no—
132C23#9249714yes—
133C23C2×C22⋊D3112yes—
134C23C23×D3111yescharacteristic
135D4—44no—
136C2×C4—28no—
137C2×C4—24no—
138C2×C4—22no—
139C2×C4—24no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—318no—
143C2×C4—6216no—
144C2×C4—624no—
145C2×C4—624no—
146C2×C4—624no—
147C2×C4—624no—
148C2×C4—624no—
149C2×C4C2×C22⋊D3114yes—
150C22—24no—
151C22—28no—
152C22—41no—
153C22—42no—
154C22—44no—
155C22#1175851214yes—
156C22C2×#9249712yes—
157C22#41×D3114yes—
158C22C22×C22⋊D3111yescharacteristic
159C4—24no—
160C4—41no—
161C4—42no—
162C4—628no—
163C4—1244no—
164C2—24no—
165C2—81no—
166C2C2×#1175851211yescharacteristic
167C2#1452155612yes—
168C2#1452157614yes—
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC2×C31×#123C2
prime radicalC22×D4×C31C22
hypercenterC2×#123D31
hypocenterC31#2853
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C22×C4×Dic31C2semidirect
2. #14520937C2semidirect
3. #14520930C2semidirect
5. #14520921C2semidirect
6. #14520912C2semidirect
107. C31#2853semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic312
#145209372
#145209302
#145209292
#145209212
#145209122
C2×C31×#1232
#285331