Finite Group Databasebeta

← #27192999

Subgroups — #27192999

Order 13184.

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

normal subgroups only

This group has 164 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
2C4×C4⋊Dic103C211yesmaximal, characteristic
3#432×C103C211yesmaximal, characteristic
4C2×C4⋊Dic103—21no—
5C2×C4×Dic103C412yes—
6C4⋊(C103⋊C8)C412yescomplemented
7C22⋊(C103⋊C8)—21no—
8#15692932—21no—
9C103⋊#95—21no—
10C2×C42×C103C2211yescharacteristic
11C4⋊C8×C103—21no—
12C22⋊C8×C103—21no—
13#97×C103C412yescomplemented
14C22×Dic103—22no—
15C2×C103⋊C8—22no—
16C4⋊Dic103—24no—
17C4×Dic103—42no—
18C22×C4×C103C2×C411yescharacteristic
19C22×C4×C103D411yescharacteristic
20C22×C4×C103D411yescharacteristic
21C2×C8×C103—22no—
22C42×C103C2×C411yescharacteristic
23C42×C103C2×C411yescharacteristic
24C42×C103D411yescharacteristic
25C42×C103Q811yescharacteristic
26C23×C103C22⋊C411yescharacteristic
27C2×C4×C103—21no—
28C2×C4×C103—21no—
29C2×C4×C103—22no—
30C2×C4×C103—41no—
31C2×C4×C103C4211yescharacteristic
32C2×C4×C103C22⋊C411yescharacteristic
33C2×C4×C103C22⋊C411yescharacteristic
34C2×C4×C103C4⋊C411yescharacteristic
35C2×C4×C103C4⋊C411yescharacteristic
36C2×C4×C103C4⋊C411yescharacteristic
37C2×Dic103—24no—
38C2×Dic103—42no—
39C2×Dic103—42no—
40C8×C103—42no—
41C103⋊C8—42no—
42C22×C103—21no—
43C22×C103—21no—
44C22×C103#9511yescharacteristic
45C22×C103#10011yescharacteristic
46C22×C103#10111yescharacteristic
47C4×C103—21no—
48C4×C103—21no—
49C4×C103—21no—
50C4×C103—21no—
51C4×C103—21no—
52C4×C103#10412yes—
53Dic103—44no—
54C2×C103—21no—
55C2×C103—21no—
56C2×C103H(3,ℤ/4)11yescharacteristic
57C2×C103#33911yescharacteristic
58C2×C103#34311yescharacteristic
59#1285—1031nomaximal, Sylow
60C103#128511yescharacteristic, complemented, Sylow
61#432—1031no—
62#432D10311yescharacteristic
63C4×C4⋊C4—1031no—
64C2×C4⋊C4—2061no—
65C2×C42—1032no—
66C2×C42C2×D10311yescharacteristic
67C4⋊C8—21no—
68C4⋊C8—1032no—
69C22⋊C8—21no—
70C22⋊C8—2061no—
71#97—2061no—
72#97Dic10312yescomplemented
73#95—2061no—
74C22×C4—2062no—
75C22×C4C4×D10311yescharacteristic
76C22×C4D41211yescharacteristic
77C22×C4C22⋊D10311yescharacteristic
78C2×C8—22no—
79C2×C8—2062no—
80C4⋊C4—2064no—
81C42—4122no—
82C42Dic20611yescharacteristic
83C42C4×D10311yescharacteristic
84C42C2×Dic10311yescharacteristic
85C42C22⋊D10311yescharacteristic
86C23(C2×D103)⋊C411yescharacteristic
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—41no—
91C2×C4—4122no—
92C2×C4—4122no—
93C2×C4—2064no—
94C2×C4C4×Dic10311yescharacteristic
95C2×C4(C2×D103)⋊C411yescharacteristic
96C2×C4C22⋊Dic10311yescharacteristic
97C2×C4Dic103⋊C411yescharacteristic
98C2×C4Dic103⋊C411yescharacteristic
99C2×C4C4⋊Dic10311yescharacteristic
100C8—42no—
101C8—4122no—
102C22—21no—
103C22—21no—
104C22C103⋊#9511yescharacteristic
105C22#1569293711yescharacteristic
106C22#1569293911yescharacteristic
107C4—21no—
108C4—21no—
109C4—21no—
110C4—21no—
111C4—21no—
112C4—4124no—
113C4#1569294712yes—
114C2—21no—
115C2—21no—
116C2#2026754711yescharacteristic
117C2#2026755211yescharacteristic
118C2#2026755911yescharacteristic
subgroupG/H
centerC22C103⋊#95
commutatorC2×C4×C103C42
FrattiniC2×C42C2×D103
Fitting#432×C103C2
socleC22×C103#95
prime radicalC23×C103C22⋊C4
cosocleC2×C42×C103C22
hypercenter#432D103
hypocenterC103#1285
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
6. C4⋊(C103⋊C8)C4semidirect
13. #97×C103C4semidirect
60. C103#1285semidirect
72. #97Dic103semidirect

Maximal subgroups

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

subgroupindex
#202678482
C4×C4⋊Dic1032
#432×C1032
#1285103