Finite Group Databasebeta

← #27193038

Subgroups — #27193038

Order 13184.

172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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#20267848C211yesmaximal, characteristic
2#20267637C211yesmaximal, characteristic
3C4×M16×C103C211yesmaximal, characteristic
4C2×C4×Dic103—21no—
5C4⋊(C103⋊C8)C412yescomplemented
6C22⋊(C103⋊C8)—21no—
7#15692932—21no—
8C103⋊#95—21no—
9C103⋊#95C412yes—
10C2×M16×C103—21no—
11C2×C42×C103C2211yescharacteristic
12#97×C103C412yescomplemented
13C4×C8×C103—21no—
14C22×Dic103—22no—
15C2×C103⋊C8—22no—
16C4×Dic103—24no—
17C22×C4×C103C2×C411yescharacteristic
18C22×C4×C103D411yescharacteristic
19C22×C4×C103D411yescharacteristic
20M16×C103—24no—
21C2×C8×C103—22no—
22C42×C103C2×C411yescharacteristic
23C42×C103C2×C411yescharacteristic
24C42×C103D411yescharacteristic
25C42×C103Q811yescharacteristic
26C23×C103C22⋊C411yescharacteristic
27C2×C4×C103—22no—
28C2×C4×C103—22no—
29C2×C4×C103—41no—
30C2×C4×C103C4211yescharacteristic
31C2×C4×C103C22⋊C411yescharacteristic
32C2×C4×C103C22⋊C411yescharacteristic
33C2×C4×C103C4⋊C411yescharacteristic
34C2×C4×C103C4⋊C411yescharacteristic
35C2×C4×C103C4⋊C411yescharacteristic
36C2×Dic103—24no—
37C2×Dic103—42no—
38C2×Dic103—42no—
39C8×C103—24no—
40C103⋊C8—42no—
41C22×C103—21no—
42C22×C103—21no—
43C22×C103#9511yescharacteristic
44C22×C103#10412yes—
45C4×C103—21no—
46C4×C103—21no—
47C4×C103—21no—
48C4×C103—21no—
49C4×C103—21no—
50C4×C103#10412yes—
51Dic103—44no—
52C2×C103—22no—
53C2×C103#33911yescharacteristic
54C2×C103#33911yescharacteristic
55C2×C103#34411yescharacteristic
56#1300—1031nomaximal, Sylow
57C103#130011yescharacteristic, complemented, Sylow
58#432—1031no—
59C4×M16D10311yescharacteristic
60#376—1031no—
61C2×M16—21no—
62C2×C42—2061no—
63C2×C42C2×D10311yescharacteristic
64C4⋊C8—1032no—
65C22⋊C8—2061no—
66#97—2061no—
67#97Dic10312yescomplemented
68C4×C8—21no—
69#95—1032no—
70#95—2061no—
71C22×C4—2062no—
72C22×C4C4×D10311yescharacteristic
73C22×C4D41211yescharacteristic
74C22×C4C22⋊D10311yescharacteristic
75M16—24no—
76C2×C8—22no—
77C2×C8—2062no—
78C42—2064no—
79C42Dic20611yescharacteristic
80C42C4×D10311yescharacteristic
81C42C2×Dic10311yescharacteristic
82C42C22⋊D10311yescharacteristic
83C23(C2×D103)⋊C411yescharacteristic
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—41no—
87C2×C4—4122no—
88C2×C4—4122no—
89C2×C4—2064no—
90C2×C4C4×Dic10311yescharacteristic
91C2×C4(C2×D103)⋊C411yescharacteristic
92C2×C4C22⋊Dic10311yescharacteristic
93C2×C4Dic103⋊C411yescharacteristic
94C2×C4Dic103⋊C411yescharacteristic
95C2×C4C4⋊Dic10311yescharacteristic
96C8—24no—
97C8—4122no—
98C22—21no—
99C22—21no—
100C22C103⋊#9511yescharacteristic
101C22#1569294912yes—
102C4—21no—
103C4—21no—
104C4—21no—
105C4—21no—
106C4—21no—
107C4—4124no—
108C4#1569294712yes—
109C2—22no—
110C2#2026755111yescharacteristic
111C2#2026755211yescharacteristic
112C2#2026756311yescharacteristic
subgroupG/H
centerC2×C4(C2×D103)⋊C4
commutatorC2×C4×C103C42
FrattiniC2×C42C2×D103
FittingC4×M16×C103C2
socleC22×C103#95
prime radicalC23×C103C22⋊C4
cosocleC2×C42×C103C22
hypercenterC4×M16D103
hypocenterC103#1300
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
5. C4⋊(C103⋊C8)C4semidirect
12. #97×C103C4semidirect
57. C103#1300semidirect
67. #97Dic103semidirect

Maximal subgroups

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

subgroupindex
#202678482
#202676372
C4×M16×C1032
#1300103