Finite Group Databasebeta

← #16843718

Subgroups — #16843718

Order 3968.

124 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 35 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#14520979C211yesmaximal, characteristic
2#14520818C211yesmaximal, characteristic
3C31×#324C211yesmaximal, characteristic
4C2×C4⋊C4×C31C2211yescharacteristic
5C2×C4⋊Dic31C411yescharacteristic
6C2×Dic31⋊C4—21no—
7C2×#92474—21no—
8C31×C22⋊C8—21no—
9C31⋊#95—21no—
10C31⋊#95C411yescharacteristic
11C22×C4×C31C2×C411yescharacteristic
12C22×C4×C31D411yescharacteristic
13C22×C4×C31D411yescharacteristic
14C22×Dic31—21no—
15C22×Dic31—21no—
16C2×C8×C31—41no—
17C4⋊C4×C31—41no—
18C4⋊Dic31—41no—
19Dic31⋊C4—41no—
20Dic31⋊C4—41no—
21#92474—22no—
22#92474—41no—
23C2×C31⋊C8—41no—
24C23×C31C22⋊C411yescharacteristic
25C2×C4×C31—21no—
26C2×C4×C31—21no—
27C2×C4×C31—21no—
28C2×C4×C31—21no—
29C2×C4×C31—41no—
30C2×C4×C31—41no—
31C2×C4×C31D811yescharacteristic
32C2×C4×C31SD1611yescharacteristic
33C2×Dic31—22no—
34C2×Dic31—41no—
35C2×Dic31—41no—
36C2×Dic31—41no—
37C2×Dic31—41no—
38C2×Dic31—41no—
39C8×C31—81no—
40C31⋊C8—42no—
41#1346—311nomaximal, Sylow
42C22×C31—21no—
43C22×C31—21no—
44C22×C31#9911yescharacteristic
45C22×C31#10211yescharacteristic
46C22×C31#10411yescharacteristic
47C4×C31—21no—
48C4×C31—21no—
49C4×C31—41no—
50C4×C31—41no—
51Dic31—42no—
52Dic31—81no—
53#398—311no—
54#343—311no—
55#324D3111yescharacteristic
56C2×C31—21no—
57C2×C31—21no—
58C2×C31#32711yescharacteristic
59C2×C31#35211yescharacteristic
60C2×C31#35611yescharacteristic
61C2×M16—621no—
62C2×C4⋊C4—311no—
63C2×C4⋊C4—621no—
64C2×C4⋊C4C2×D3111yescharacteristic
65C22⋊C8—21no—
66#95—311no—
67#95—621no—
68C31#134611yescharacteristic, complemented, Sylow
69C22×C4—621no—
70C22×C4—621no—
71C22×C4C4×D3111yescharacteristic
72C22×C4D12411yescharacteristic
73C22×C4C22⋊D3111yescharacteristic
74M16—622no—
75M16—1241no—
76C2×C8—41no—
77C2×C8—1241no—
78C4⋊C4—41no—
79C4⋊C4—1241no—
80C4⋊C4—1241no—
81C4⋊C4—1241no—
82C23(C2×D31)⋊C411yescharacteristic
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4—622no—
90C2×C4—1241no—
91C2×C4—1241no—
92C2×C4—1241no—
93C2×C4—1241no—
94C2×C4—1241no—
95C2×C4#9247011yescharacteristic
96C2×C4D24811yescharacteristic
97C8—81no—
98C8—1242no—
99C22—21no—
100C22—21no—
101C22#1175839411yescharacteristic
102C22#1175840911yescharacteristic
103C22#1175841311yescharacteristic
104C4—21no—
105C4—21no—
106C4—41no—
107C4—41no—
108C4—1242no—
109C4—2481no—
110C2—21no—
111C2—21no—
112C2#1452078411yescharacteristic
113C2#1452083811yescharacteristic
114C2#1452084711yescharacteristic
subgroupG/H
centerC22#11758394
commutatorC22×C4×C31C2×C4
FrattiniC2×C4⋊C4C2×D31
FittingC31×#324C2
socleC22×C31#99
prime radicalC23×C31C22⋊C4
cosocleC2×C4⋊C4×C31C22
hypercenter#324D31
hypocenterC31#1346
LCSG ▷ C22×C4×C31 ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
68. C31#1346semidirect

Maximal subgroups

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

subgroupindex
#145209792
#145208182
C31×#3242
#134631