Finite Group Databasebeta

← #16854034

Subgroups — #16854034

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
1C2×#11758506C211yesmaximal, characteristic
2C22×C4×Dic31C211yesmaximal, characteristic, complemented
3#14520941C214yesmaximal, complemented
4#14520934C214yesmaximal, complemented
5#14520926C212yesmaximal
6#14520924C212yesmaximal, complemented
7C31×#381C211yesmaximal, characteristic, complemented
8C23×C4×C31C2211yescharacteristic
9C22×C22⋊D31C2211yescharacteristic
10C23×Dic31C2212yes—
11C2×C22⋊C4×C31C2212yes—
12C2×C22⋊Dic31C2211yescharacteristic
13#11758506—24no—
14C2×(C2×D31)⋊C4C2214yes—
15C2×(C2×D31)⋊C4C2212yes—
16C2×C4⋊Dic31C2214yes—
17C2×Dic31⋊C4C2212yes—
18C2×C4×Dic31—24no—
19C2×C4×Dic31C2214yes—
20C31×#95C2214yes—
21C31⋊#95C2214yes—
22C31⋊#95C2214yes—
23C24×C31C2311yescharacteristic
24C23×D31C2311yescharacteristic
25C22×C4×C31—24no—
26C22×C4×C31D414yes—
27C22×C4×C31C2314yes—
28C22×C4×C31C2312yes—
29C2×C22⋊D31—22no—
30C2×C22⋊D31—24no—
31C22×Dic31—24no—
32C22×Dic31—28no—
33C22×Dic31C2311yescharacteristic
34C22×Dic31C2312yes—
35C22×Dic31C2314yes—
36C22⋊C4×C31—24no—
37C22⋊Dic31—22no—
38(C2×D31)⋊C4—24no—
39(C2×D31)⋊C4—28no—
40C4⋊Dic31—28no—
41Dic31⋊C4—24no—
42C4×Dic31—28no—
43C23×C31—24no—
44C23×C31C2×D412yes—
45C23×C31#4114yes—
46C23×C31C2411yescharacteristic
47C22×D31—21no—
48C22×D31—24no—
49C22×D31—22no—
50C2×C4×C31—28no—
51C2×C4×C31—24no—
52C2×C4×C31—24no—
53C2×C4×C31—24no—
54C2×C4×C31—24no—
55C2×C4×C31C2×D414yes—
56C22⋊D31—44no—
57C2×Dic31—216no—
58C2×Dic31—24no—
59C2×Dic31—24no—
60C2×Dic31—21no—
61C2×Dic31—22no—
62C2×Dic31—24no—
63C2×Dic31—22no—
64C2×Dic31#4118yes—
65#2853—311nomaximal, Sylow
66C22×C31—24no—
67C22×C31—28no—
68C22×C31#12314yes—
69C22×C31C22×D411yescharacteristic
70C22×C31C2×#4112yes—
71C22×C31C2×#4114yes—
72C2×D31—41no—
73C2×D31—42no—
74C2×D31—44no—
75C4×C31—24no—
76C4×C31—44no—
77Dic31—28no—
78Dic31—41no—
79Dic31—42no—
80C2×#123—311no—
81C22×C42—311no—
82#388—314no—
83#387—314no—
84#386—312no—
85#385—312no—
86#381D3111yescharacteristic, complemented
87C2×C31—24no—
88C2×C31C2×#12311yescharacteristic
89C2×C31#52512yes—
90C2×C31#52914yes—
91D31—81no—
92C22×D4—311no—
93C23×C4—312no—
94C23×C4C2×D3111yescharacteristic
95#123—624no—
96C2×C4⋊C4—312no—
97C2×C4⋊C4—314no—
98C2×C22⋊C4—311no—
99C2×C22⋊C4—312no—
100C2×C22⋊C4—314no—
101C2×C22⋊C4C2×D3112yes—
102C2×C42—314no—
103C2×C42—624no—
104#95—314no—
105#95—314no—
106#95C2×D3114yes—
107C31#285311yescharacteristic, complemented, Sylow
108C24—311no—
109C24C22×D3111yescharacteristic
110C2×D4—622no—
111C2×D4—624no—
112C22×C4—24no—
113C22×C4—314no—
114C22×C4—311no—
115C22×C4—312no—
116C22×C4—628no—
117C22×C4—624no—
118C22×C4D12414yes—
119C22×C4C22×D3114yes—
120C22×C4C22×D3112yes—
121C4⋊C4—628no—
122C4⋊C4—624no—
123C22⋊C4—24no—
124C22⋊C4—628no—
125C22⋊C4—622no—
126C22⋊C4—624no—
127C42—628no—
128C23—24no—
129C23—621no—
130C23—622no—
131C23—624no—
132C23C2×D12412yes—
133C23#9249714yes—
134C23C23×D3111yescharacteristic
135D4—1244no—
136C2×C4—28no—
137C2×C4—24no—
138C2×C4—24no—
139C2×C4—24no—
140C2×C4—24no—
141C2×C4—318no—
142C2×C4—6216no—
143C2×C4—624no—
144C2×C4—624no—
145C2×C4—622no—
146C2×C4—621no—
147C2×C4—622no—
148C2×C4—624no—
149C2×C4C2×D12414yes—
150C22—24no—
151C22—28no—
152C22—1241no—
153C22—1242no—
154C22—1244no—
155C22#1175846314yes—
156C22C22×D12411yescharacteristic
157C22C2×#9249712yes—
158C22#41×D3114yes—
159C4—24no—
160C4—44no—
161C4—628no—
162C4—1241no—
163C4—1242no—
164C2—24no—
165C2—2481no—
166C2C2×#1175846311yescharacteristic
167C2#1452156112yes—
168C2#1452157614yes—
subgroupG/H
center, FrattiniC23C23×D31
commutator, socle, cosocleC23×C31C24
FittingC31×#381C2
prime radicalC22×C22⋊D31C22
hypercenter#381D31
hypocenterC31#2853
LCSG ▷ C23×C31 ▷ C31
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic31C2semidirect
3. #14520941C2semidirect
4. #14520934C2semidirect
6. #14520924C2semidirect
7. C31×#381C2semidirect
86. #381D31semidirect
107. C31#2853semidirect

Maximal subgroups

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

subgroupindex
C2×#117585062
C22×C4×Dic312
#145209412
#145209342
#145209262
#145209242
C31×#3812
#285331