Finite Group Databasebeta

← #16844685

Subgroups — #16844685

Order 3968.

238 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 57 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
1#14521204C212yesmaximal
2#14520969C211yesmaximal, characteristic
3#14520786C212yesmaximal
4#14520775C211yesmaximal, characteristic
5C31×#544C211yesmaximal, characteristic
6C22×Dic62C2211yescharacteristic
7C31×C4⋊Q8—22no—
8C31×#125—22no—
9C31×C22⋊Q8—21no—
10C31×C22⋊Q8C2212yes—
11C31×#117—21no—
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×#92482—22no—
14C2×Dic31⋊C4—21no—
15C31⋊#95—21no—
16C31⋊#95C2211yescharacteristic
17C22⋊(C31⋊C8)C2212yes—
18#11758398—22no—
19C2×Q8×C31—21no—
20C2×Q8×C31D412yes—
21C22×C4×C31D411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31C2311yescharacteristic
24C22×Dic31—21no—
25C22×Dic31—21no—
26C2×Dic62—22no—
27C2×Dic62—42no—
28C4⋊C4×C31—21no—
29C4⋊C4×C31—21no—
30C4⋊C4×C31—21no—
31C4⋊C4×C31—22no—
32C4⋊C4×C31—22no—
33C4⋊C4×C31—22no—
34C4⋊C4×C31D412yes—
35C22⋊C4×C31—22no—
36C42×C31—22no—
37#92482—44no—
38Dic31⋊C4—42no—
39C2×C31⋊C8—22no—
40C23×C31C2×D411yescharacteristic
41Q8×C31—42no—
42Q8×C31—81no—
43C2×C4×C31—21no—
44C2×C4×C31—21no—
45C2×C4×C31—22no—
46C2×C4×C31—22no—
47C2×C4×C31—21no—
48C2×C4×C31—41no—
49C2×C4×C31—41no—
50C2×C4×C31Q1612yescomplemented
51C2×C4×C31C2×D412yes—
52C2×Dic31—22no—
53C2×Dic31—22no—
54C2×Dic31—41no—
55C2×Dic31—41no—
56C2×Dic31—41no—
57C2×Dic31—41no—
58Dic62—24no—
59Dic62—42no—
60C31⋊C8—42no—
61#1605—311nomaximal, Sylow
62C22×C31—21no—
63C22×C31—21no—
64C22×C31#12011yescharacteristic
65C22×C31C2×Q1611yescharacteristic
66C22×C31#13711yescharacteristic
67C4×C31—22no—
68C4×C31—22no—
69C4×C31—42no—
70C4×C31—41no—
71C4×C31—42no—
72Dic31—42no—
73Dic31—42no—
74#544D3111yescharacteristic
75#451—312no—
76#395—311no—
77#328—312no—
78#324—311no—
79C2×C31—21no—
80C2×C31—21no—
81C2×C31#45111yescharacteristic
82C2×C31#45611yescharacteristic
83C2×C31B(4,𝔽2)11yescharacteristic
84C22×Q8—311no—
85C2×Q16—622no—
86C4⋊Q8—22no—
87#125—22no—
88C22⋊Q8—21no—
89C22⋊Q8C2×D3112yes—
90#117—21no—
91C2×C4⋊C4—621no—
92C2×C4⋊C4C2×D3111yescharacteristic
93#103—622no—
94C22⋊C8—312no—
95#95—311no—
96#95—621no—
97C31#160511yescharacteristic, complemented, Sylow
98C2×Q8—21no—
99C2×Q8—622no—
100C2×Q8—1242no—
101C2×Q8C22⋊D3112yes—
102C22×C4—621no—
103C22×C4—621no—
104C22×C4C22⋊D3111yescharacteristic
105C22×C4C22⋊D3111yescharacteristic
106C22×C4C22×D3111yescharacteristic
107Q16—1244no—
108C2×C8—622no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C4⋊C4—1242no—
116C4⋊C4C22⋊D3112yes—
117C22⋊C4—22no—
118C42—22no—
119C23C2×C22⋊D3111yescharacteristic
120Q8—42no—
121Q8—81no—
122Q8—624no—
123Q8—1242no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—21no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—622no—
132C2×C4—622no—
133C2×C4—1241no—
134C2×C4—1241no—
135C2×C4—1241no—
136C2×C4—1241no—
137C2×C4#9248212yescomplemented
138C2×C4C2×C22⋊D3112yes—
139C8—1242no—
140C22—21no—
141C22—21no—
142C22#1175851911yescharacteristic
143C22C2×#9248211yescharacteristic
144C22#1175853011yescharacteristic
145C4—22no—
146C4—22no—
147C4—42no—
148C4—41no—
149C4—42no—
150C4—1242no—
151C4—1242no—
152C2—21no—
153C2—21no—
154C2#1452120511yescharacteristic
155C2#1452123211yescharacteristic
156C2#1452123611yescharacteristic
subgroupG/H
centerC22#11758530
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#544C2
socleC22×C31#120
prime radicalC23×C31C2×D4
hypercenter#544D31
hypocenterC31#1605
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
50. C2×C4×C31Q16semidirect
97. C31#1605semidirect
137. C2×C4#92482semidirect

Maximal subgroups

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

subgroupindex
#145212042
#145209692
#145207862
#145207752
C31×#5442
#160531