Finite Group Databasebeta

← #16845041

Subgroups — #16845041

Order 3968.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C31⋊#564C211yesmaximal, characteristic
2#14521459C211yesmaximal, characteristic
3#14521458C211yesmaximal, characteristic
4#14521418C211yesmaximal, characteristic
5#14520790C211yesmaximal, characteristic
6#14520790C211yesmaximal, characteristic
7C31×#330C211yesmaximal, characteristic
8C31×#125C2211yescharacteristic
9#11758467—21no—
10#11758467—21no—
11#11758466—21no—
12#11758466—21no—
13#11758466—21no—
14#11758466—21no—
15#11758447C2211yescharacteristic
16#11758447C2211yescharacteristic
17#11758446C2211yescharacteristic
18C31×#97C2211yescharacteristic
19C31×#97C2211yescharacteristic
20#11758406—21no—
21#11758405—21no—
22#11758404—21no—
23#11758404—21no—
24#11758396—21no—
25#11758395—21no—
26#11758391C2211yescharacteristic
27C2×Dic62—21no—
28C2×C8×C31—21no—
29C2×C8×C31—21no—
30C4⋊C4×C31—21no—
31C4⋊C4×C31—21no—
32C4⋊C4×C31D411yescharacteristic
33C4⋊C4×C31D411yescharacteristic
34C42×C31C2311yescharacteristic
35C4⋊Dic31—21no—
36C4⋊Dic31—21no—
37C4⋊Dic31—21no—
38C4⋊Dic31—21no—
39C4⋊Dic31D411yescharacteristic
40C4⋊Dic31D411yescharacteristic
41C4⋊Dic31D411yescharacteristic
42C4⋊Dic31D411yescharacteristic
43Dic31⋊C4—21no—
44Dic31⋊C4—21no—
45Dic31⋊C4—21no—
46Dic31⋊C4—21no—
47Dic31⋊C4—21no—
48Dic31⋊C4—21no—
49Dic31⋊C4—21no—
50Dic31⋊C4—21no—
51C4×Dic31—21no—
52C4×Dic31—21no—
53C2×C31⋊C8—21no—
54C2×C4×C31—21no—
55C2×C4×C31—21no—
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×Dic31—21no—
60C2×Dic31—21no—
61C2×Dic31—21no—
62C2×Dic31—21no—
63C2×Dic31—41no—
64Dic62—42no—
65C8×C31—22no—
66C8×C31—41no—
67C31⋊C8—22no—
68#1663—311nomaximal, Sylow
69C22×C31#12011yescharacteristic
70C4×C31—21no—
71C4×C31—21no—
72C4×C31—21no—
73C4×C31—41no—
74C4×C31—41no—
75Dic31—41no—
76Dic31—41no—
77Dic31—41no—
78Dic31—41no—
79Dic31—81no—
80#564—311no—
81#501—311no—
82#501—311no—
83#491—311no—
84#330—311no—
85#330—311no—
86#330D3111yescharacteristic
87C2×C31#45411yescharacteristic
88C2×C31#45611yescharacteristic
89C2×C31#45611yescharacteristic
90C4⋊Q8—311no—
91#125—311no—
92#125—311no—
93#125—621no—
94#125—621no—
95#125—621no—
96#125—621no—
97#125—621no—
98#125—621no—
99#125C2×D3111yescharacteristic
100#107—621no—
101#107—621no—
102#106—621no—
103#106—621no—
104#103—621no—
105#103—621no—
106#97—311no—
107#97C2×D3111yescharacteristic
108#97C2×D3111yescharacteristic
109C31#166311yescharacteristic, complemented, Sylow
110C2×Q8—621no—
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—621no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—311no—
117C4⋊C4—311no—
118C4⋊C4—311no—
119C4⋊C4—311no—
120C4⋊C4—621no—
121C4⋊C4—621no—
122C4⋊C4—621no—
123C4⋊C4—621no—
124C4⋊C4—621no—
125C4⋊C4—621no—
126C4⋊C4—621no—
127C4⋊C4—621no—
128C4⋊C4—621no—
129C4⋊C4—621no—
130C4⋊C4—621no—
131C4⋊C4—621no—
132C4⋊C4D12411yescharacteristic
133C4⋊C4D12411yescharacteristic
134C42—621no—
135C42—621no—
136C42C22×D3111yescharacteristic
137Q8—1242no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—621no—
141C2×C4—621no—
142C2×C4—621no—
143C2×C4—621no—
144C2×C4—1241no—
145C2×C4C2×D12411yescharacteristic
146C2×C4D4×D3111yescharacteristic
147C2×C4D4×D3111yescharacteristic
148C8—22no—
149C8—41no—
150C8—622no—
151C22#1175845911yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—1241no—
158C4—1241no—
159C4—1241no—
160C4—1241no—
161C4—2481no—
162C2#1452122311yescharacteristic
163C2#1452123311yescharacteristic
164C2#1452123411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#330C2
socle, prime radicalC22×C31#120
hypercenter#330D31
hypocenterC31#1663
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
109. C31#1663semidirect

Maximal subgroups

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

subgroupindex
C31⋊#5642
#145214592
#145214582
#145214182
#145207902
C31×#3302
#166331