Finite Group Databasebeta

← #16844054

Subgroups — #16844054

Order 3968.

236 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 77 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×C4×Dic62C211yesmaximal, characteristic
2#14521106C211yesmaximal, characteristic
3#14520774C214yesmaximal
4C31×#432C211yesmaximal, characteristic
5C22×Dic62C411yescharacteristic
6C2×C42×C31C2211yescharacteristic
7C2×C4⋊Dic31C411yescharacteristic
8C2×Dic31⋊C4C2212yes—
9C2×C4×Dic31C412yes—
10C4×Dic62—21no—
11C4×Dic62—21no—
12C4×Dic62—21no—
13C4×Dic62—21no—
14C31×C4⋊C8—21no—
15C31×C22⋊C8C2212yes—
16C31×#97—21no—
17C22⋊(C31⋊C8)C2212yes—
18C4⋊(C31⋊C8)—21no—
19#11758391—21no—
20C22×C4×C31C2×C411yescharacteristic
21C22×C4×C31C2×C411yescharacteristic
22C22×C4×C31C2311yescharacteristic
23C22×Dic31C2×C412yes—
24C22×Dic31C2×C412yes—
25C2×Dic62—21no—
26C2×Dic62—21no—
27C2×Dic62—24no—
28C2×C8×C31—22no—
29C42×C31D411yescharacteristic
30C42×C31D411yescharacteristic
31C42×C31D411yescharacteristic
32C42×C31D411yescharacteristic
33C4⋊Dic31—21no—
34C4⋊Dic31—21no—
35Dic31⋊C4—22no—
36Dic31⋊C4—22no—
37C4×Dic31—22no—
38C4×Dic31—22no—
39C2×C31⋊C8—22no—
40C23×C31C22×C411yescharacteristic
41C2×C4×C31—22no—
42C2×C4×C31—22no—
43C2×C4×C31—41no—
44C2×C4×C31C22⋊C411yescharacteristic
45C2×C4×C31C22⋊C411yescharacteristic
46C2×C4×C31C22⋊C411yescharacteristic
47C2×C4×C31C22⋊C411yescharacteristic
48C2×C4×C31C2×D411yescharacteristic
49C2×C4×C31C2×D411yescharacteristic
50C2×Dic31—22no—
51C2×Dic31—22no—
52C2×Dic31—22no—
53C2×Dic31—42no—
54C2×Dic31M1614yes—
55Dic62—24no—
56Dic62—24no—
57C8×C31—42no—
58C31⋊C8—42no—
59#1467—311nomaximal, Sylow
60C22×C31—21no—
61C22×C31—21no—
62C22×C31C2×C22⋊C411yescharacteristic
63C22×C31C2×M1612yes—
64C4×C31—21no—
65C4×C31—21no—
66C4×C31—21no—
67C4×C31—21no—
68C4×C31—21no—
69C4×C31#10112yes—
70Dic31—24no—
71Dic31—42no—
72C2×C4×Q8—311no—
73#432—311no—
74#432D3111yescharacteristic
75#324—314no—
76C2×C31—22no—
77C2×C31#40711yescharacteristic
78C2×C31#41011yescharacteristic
79C2×C31C2×#10111yescharacteristic
80C22×Q8—311no—
81C4×Q8—621no—
82C4×Q8—621no—
83C4×Q8—621no—
84C4×Q8—621no—
85C2×C4⋊C4—311no—
86C2×C4⋊C4—312no—
87C2×C42—312no—
88C2×C42C2×D3111yescharacteristic
89C4⋊C8—21no—
90C4⋊C8—621no—
91C22⋊C8—312no—
92C22⋊C8C2×D3112yes—
93#97—21no—
94#97—621no—
95C31#146711yescharacteristic, complemented, Sylow
96C2×Q8—624no—
97C2×Q8—621no—
98C2×Q8—621no—
99C22×C4—312no—
100C22×C4—312no—
101C22×C4C4×D3111yescharacteristic
102C22×C4C4×D3111yescharacteristic
103C22×C4C22×D3111yescharacteristic
104C2×C8—22no—
105C2×C8—622no—
106C4⋊C4—621no—
107C4⋊C4—621no—
108C4⋊C4—622no—
109C4⋊C4—622no—
110C42—622no—
111C42—622no—
112C42D12411yescharacteristic
113C42D12411yescharacteristic
114C42C22⋊D3111yescharacteristic
115C42C22⋊D3111yescharacteristic
116C23C2×C4×D3111yescharacteristic
117Q8—624no—
118Q8—624no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—314no—
123C2×C4—622no—
124C2×C4—622no—
125C2×C4—622no—
126C2×C4—1242no—
127C2×C4(C2×D31)⋊C411yescharacteristic
128C2×C4(C2×D31)⋊C411yescharacteristic
129C2×C4(C2×D31)⋊C411yescharacteristic
130C2×C4(C2×D31)⋊C411yescharacteristic
131C2×C4C2×D12411yescharacteristic
132C2×C4C2×C22⋊D3111yescharacteristic
133C8—42no—
134C8—1242no—
135C22—21no—
136C22—21no—
137C22M16×D3112yes—
138C22C2×(C2×D31)⋊C411yescharacteristic
139C4—21no—
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—624no—
145C4—1242no—
146C4#1175841212yes—
147C2—22no—
148C2#1452101211yescharacteristic
149C2#1452102211yescharacteristic
150C2C2×#1175841211yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutator, prime radicalC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#432C2
socleC22×C31C2×C22⋊C4
cosocleC22×C4×C31C23
hypercenter#432D31
hypocenterC31#1467
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
95. C31#1467semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic622
#145211062
#145207742
C31×#4322
#146731