Finite Group Databasebeta

← #16845014

Subgroups — #16845014

Order 3968.

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

normal subgroups only

This group has 182 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, complemented
2#14521415C211yesmaximal, characteristic
3#14521414C212yesmaximal
4#14520790C212yesmaximal, complemented
5C31×#330C211yesmaximal, characteristic, complemented
6C31×#125C2211yescharacteristic
7#11758467—22no—
8#11758466—22no—
9#11758466—22no—
10#11758451C2211yescharacteristic
11#11758447C2212yes—
12C31×#97C2212yes—
13#11758409—22no—
14#11758409—22no—
15#11758397—22no—
16#11758391C2211yescharacteristic
17C2×D124—21no—
18C2×D124—22no—
19C2×C8×C31—22no—
20C4⋊C4×C31—22no—
21C4⋊C4×C31D412yes—
22C42×C31C2311yescharacteristic
23C4⋊Dic31—22no—
24C4⋊Dic31D412yes—
25C4⋊Dic31D412yes—
26Dic31⋊C4—22no—
27Dic31⋊C4—22no—
28Dic31⋊C4—22no—
29Dic31⋊C4—22no—
30C4×Dic31—22no—
31C2×C31⋊C8—21no—
32C22×D31—41no—
33C2×C4×C31—22no—
34C2×C4×C31C2×D411yescharacteristic
35C2×C4×C31C2×D412yes—
36C2×Dic31—22no—
37C2×Dic31—22no—
38D124—42no—
39D124—44no—
40C8×C31—42no—
41C31⋊C8—41no—
42#1658—311nomaximal, Sylow
43C22×C31#12011yescharacteristic
44C2×D31—82no—
45C2×D31—81no—
46C4×C31—21no—
47C4×C31—22no—
48C4×C31—42no—
49Dic31—42no—
50Dic31—42no—
51#564—311no—
52#490—311no—
53#490—312no—
54#330—312no—
55#330D3111yescharacteristic, complemented
56C2×C31#45412yes—
57C2×C31#45411yescharacteristic
58D31—161no—
59#127—311no—
60#125—312no—
61#125—622no—
62#125—622no—
63#125—622no—
64#125C2×D3111yescharacteristic
65#102—622no—
66#102—622no—
67#102—622no—
68#97—311no—
69#97C2×D3112yes—
70C31#165811yescharacteristic, complemented, Sylow
71C2×D4—621no—
72C2×D4—622no—
73C2×C8—22no—
74C2×C8—621no—
75C4⋊C4—22no—
76C4⋊C4—312no—
77C4⋊C4—312no—
78C4⋊C4—622no—
79C4⋊C4—622no—
80C4⋊C4—622no—
81C4⋊C4—622no—
82C4⋊C4—622no—
83C4⋊C4D12412yes—
84C42—622no—
85C42C22×D3111yescharacteristic
86C23—1241no—
87D4—1244no—
88D4—1242no—
89C2×C4—22no—
90C2×C4—622no—
91C2×C4—622no—
92C2×C4C2×D12411yescharacteristic
93C2×C4D4×D3112yes—
94C8—42no—
95C8—1241no—
96C22—2482no—
97C22—2481no—
98C22#1175845911yescharacteristic
99C4—22no—
100C4—21no—
101C4—42no—
102C4—1242no—
103C4—1242no—
104C2—4961no—
105C2#1452122312yes—
106C2#1452122411yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×#330C2
socleC22×C31#120
prime radical#11758451C22
hypercenter#330D31
hypocenterC31#1658
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. C31⋊#564C2semidirect
4. #14520790C2semidirect
5. C31×#330C2semidirect
55. #330D31semidirect
70. C31#1658semidirect

Maximal subgroups

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

subgroupindex
C31⋊#5642
#145214152
#145214142
#145207902
C31×#3302
#165831