Finite Group Databasebeta

← #16845789

Subgroups — #16845789

Order 3968.

316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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
2#14521013C211yesmaximal, characteristic
3#14520817C214yesmaximal, complemented
4C31×#407C211yesmaximal, characteristic
5C23×C4×C31C2211yescharacteristic
6C23×Dic31C412yes—
7C2×M16×C31C2212yes—
8C2×C4⋊Dic31—21no—
9C2×C4⋊Dic31—21no—
10C2×C4⋊Dic31—21no—
11C2×C4⋊Dic31—21no—
12C2×C4⋊Dic31C412yes—
13C2×C4⋊Dic31C2212yes—
14C2×#92474C2212yes—
15C31×C22⋊C8—21no—
16C31×C22⋊C8—21no—
17C22⋊(C31⋊C8)—21no—
18C22⋊(C31⋊C8)—21no—
19C24×C31C2×C411yescharacteristic
20C22×C4×C31—24no—
21C22×C4×C31C2×C411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31D411yescharacteristic
24C22×C4×C31D411yescharacteristic
25C22×C4×C31D411yescharacteristic
26C22×C4×C31C2311yescharacteristic
27C22×Dic31—22no—
28C22×Dic31—22no—
29C22×Dic31—44no—
30C22×Dic31C2×C414yes—
31M16×C31—24no—
32C2×C8×C31—22no—
33C4⋊Dic31—22no—
34C4⋊Dic31—22no—
35C4⋊Dic31—22no—
36C4⋊Dic31—22no—
37#92474—24no—
38C2×C31⋊C8—22no—
39C23×C31—22no—
40C23×C31—22no—
41C23×C31—22no—
42C23×C31C22⋊C411yescharacteristic
43C23×C31C22⋊C411yescharacteristic
44C23×C31C22×C411yescharacteristic
45C2×C4×C31—22no—
46C2×C4×C31—22no—
47C2×C4×C31—22no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31C22⋊C411yescharacteristic
51C2×C4×C31C22⋊C411yescharacteristic
52C2×C4×C31C2×D411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31#4114yes—
55C2×Dic31—24no—
56C2×Dic31—44no—
57C2×Dic31—44no—
58C2×Dic31—44no—
59C8×C31—42no—
60C31⋊C8—42no—
61#1821—311nomaximal, Sylow
62C22×C31—28no—
63C22×C31—21no—
64C22×C31—21no—
65C22×C31—21no—
66C22×C31—21no—
67C22×C31—21no—
68C22×C31—21no—
69C22×C31#10012yes—
70C22×C31#10112yes—
71C22×C31C2×C22⋊C411yescharacteristic
72C22×C31#11712yes—
73C4×C31—21no—
74C4×C31—21no—
75C4×C31#12312yes—
76C4×C31#12312yes—
77Dic31—44no—
78C22×C4⋊C4—311no—
79#407—311no—
80#407D3111yescharacteristic
81#343—314no—
82C2×C31—22no—
83C2×C31—22no—
84C2×C31—22no—
85C2×C31#38111yescharacteristic
86C2×C31C2×#10011yescharacteristic
87C2×C31C2×#10111yescharacteristic
88C23×C4—312no—
89C23×C4C2×D3111yescharacteristic
90C2×M16—312no—
91C2×M16C2×D3112yes—
92C2×C4⋊C4—312no—
93C2×C4⋊C4—312no—
94C2×C4⋊C4—621no—
95C2×C4⋊C4—621no—
96C2×C4⋊C4—621no—
97C2×C4⋊C4—621no—
98C22⋊C8—21no—
99C22⋊C8—21no—
100C22⋊C8—621no—
101C22⋊C8—621no—
102C31#182111yescharacteristic, complemented, Sylow
103C24C4×D3111yescharacteristic
104C22×C4—24no—
105C22×C4—314no—
106C22×C4—622no—
107C22×C4—622no—
108C22×C4—1244no—
109C22×C4C4×D3111yescharacteristic
110C22×C4D12411yescharacteristic
111C22×C4D12411yescharacteristic
112C22×C4C22⋊D3111yescharacteristic
113C22×C4C22⋊D3111yescharacteristic
114C22×C4C22×D3111yescharacteristic
115M16—24no—
116M16—624no—
117C2×C8—22no—
118C2×C8—622no—
119C4⋊C4—622no—
120C4⋊C4—622no—
121C4⋊C4—622no—
122C4⋊C4—622no—
123C23—22no—
124C23—22no—
125C23—22no—
126C23(C2×D31)⋊C411yescharacteristic
127C23(C2×D31)⋊C411yescharacteristic
128C23C2×C4×D3111yescharacteristic
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—624no—
135C2×C4—1244no—
136C2×C4—1244no—
137C2×C4—1244no—
138C2×C4(C2×D31)⋊C411yescharacteristic
139C2×C4(C2×D31)⋊C411yescharacteristic
140C2×C4C2×D12411yescharacteristic
141C2×C4#9249714yes—
142C2×C4C2×C22⋊D3111yescharacteristic
143C8—42no—
144C8—1242no—
145C22—28no—
146C22—21no—
147C22—21no—
148C22—21no—
149C22—21no—
150C22—21no—
151C22—21no—
152C22#1175841112yes—
153C22#1175841212yes—
154C22#1175845412yes—
155C22C2×(C2×D31)⋊C411yescharacteristic
156C4—21no—
157C4—21no—
158C4—1244no—
159C4#1175846312yes—
160C4#1175851212yes—
161C2—22no—
162C2—22no—
163C2—22no—
164C2#1452091011yescharacteristic
165C2C2×#1175841111yescharacteristic
166C2C2×#1175841211yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#407C2
socleC22×C31C2×C22⋊C4
prime radicalC24×C31C2×C4
cosocleC22×C4×C31C23
hypercenter#407D31
hypocenterC31#1821
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #14520817C2semidirect
102. C31#1821semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊Dic312
#145210132
#145208172
C31×#4072
#182131