Finite Group Databasebeta

← #27193221

Subgroups — #27193221

Order 13184.

160 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C22×C103⋊C16C211yesmaximal, characteristic
2C2×C8×Dic103C211yesmaximal, characteristic
3C22×C16×C103C211yesmaximal, characteristic
4C22×C103⋊C8C411yescharacteristic
5C2×C4×Dic103C411yescharacteristic
6C2×C103⋊C16—21no—
7C2×C103⋊C16—21no—
8C2×C103⋊C16C412yescomplemented
9C8×Dic103—21no—
10C8×Dic103—21no—
11C22×C8×C103C2211yescharacteristic
12C2×C16×C103—21no—
13C2×C16×C103—21no—
14C2×C16×C103C412yescomplemented
15C22×Dic103C812yes—
16C2×C103⋊C8—21no—
17C2×C103⋊C8—21no—
18C2×C103⋊C8C812yes—
19C4×Dic103—21no—
20C4×Dic103—21no—
21C103⋊C16—22no—
22C22×C4×C103C2×C411yescharacteristic
23C2×C8×C103C2×C411yescharacteristic
24C2×C8×C103C2×C411yescharacteristic
25C2×C8×C103D411yescharacteristic
26C2×C8×C103D411yescharacteristic
27C2×C8×C103D411yescharacteristic
28C2×C8×C103Q811yescharacteristic
29C16×C103—22no—
30C23×C103C2×C811yescharacteristic
31C2×C4×C103C4211yescharacteristic
32C2×C4×C103C22⋊C411yescharacteristic
33C2×C4×C103C4⋊C411yescharacteristic
34C2×C4×C103C2×C811yescharacteristic
35C2×C4×C103M1611yescharacteristic
36C2×C4×C103M1611yescharacteristic
37C2×Dic103—22no—
38C2×Dic103—22no—
39C2×Dic103C1614yescomplemented
40C8×C103C22⋊C411yescharacteristic
41C8×C103C22⋊C411yescharacteristic
42C8×C103C4⋊C411yescharacteristic
43C8×C103C4⋊C411yescharacteristic
44C103⋊C8—22no—
45C22×C103C4×C811yescharacteristic
46C22×C103C22⋊C811yescharacteristic
47C22×C103C4⋊C811yescharacteristic
48C22×C103C2×C1612yes—
49C22×C103M3212yes—
50C4×C103#9511yescharacteristic
51C4×C103#9711yescharacteristic
52C4×C103C22⋊C811yescharacteristic
53C4×C103C4⋊C811yescharacteristic
54Dic103—24no—
55C2×C103#33611yescharacteristic
56C2×C103C4×C1611yescharacteristic
57C2×C103#34611yescharacteristic
58C2×C103C22⋊C1612yes—
59C2×C103C4⋊C1612yes—
60#1374—1031nomaximal, Sylow
61C103#137411yescharacteristic, complemented, Sylow
62C22×C16—1031no—
63C22×C16D10311yescharacteristic
64C2×C4×C8—1031no—
65C22×C8—1031no—
66C22×C8C2×D10311yescharacteristic
67C2×C42—1031no—
68C2×C16—21no—
69C2×C16—21no—
70C2×C16—1032no—
71C2×C16—2061no—
72C2×C16—2061no—
73C2×C16Dic10312yescomplemented
74C4×C8—2061no—
75C4×C8—2061no—
76C22×C4—1032no—
77C22×C4C4×D10311yescharacteristic
78C2×C8—1032no—
79C2×C8—2061no—
80C2×C8—2061no—
81C2×C8Dic20611yescharacteristic
82C2×C8C4×D10311yescharacteristic
83C2×C8D41211yescharacteristic
84C2×C8C2×Dic10311yescharacteristic
85C2×C8C22⋊D10311yescharacteristic
86C2×C8C22⋊D10311yescharacteristic
87C42—2061no—
88C42—2061no—
89C16—22no—
90C16—2062no—
91C23C8×D10311yescharacteristic
92C2×C4—1034no—
93C2×C4—2062no—
94C2×C4—2062no—
95C2×C4C4×Dic10311yescharacteristic
96C2×C4(C2×D103)⋊C411yescharacteristic
97C2×C4Dic103⋊C411yescharacteristic
98C2×C4C8×D10311yescharacteristic
99C2×C4#1311008811yescharacteristic
100C2×C4#1311008811yescharacteristic
101C8—2062no—
102C8(C2×D103)⋊C411yescharacteristic
103C8C22⋊Dic10311yescharacteristic
104C8Dic103⋊C411yescharacteristic
105C8C4⋊Dic10311yescharacteristic
106C22C8×Dic10311yescharacteristic
107C22(C2×D103)⋊C811yescharacteristic
108C22Dic103⋊C811yescharacteristic
109C22C16×D10312yes—
110C22#1569296012yes—
111C4—2064no—
112C4C103⋊#9511yescharacteristic
113C4#1569293111yescharacteristic
114C4(C2×D103)⋊C811yescharacteristic
115C4Dic103⋊C811yescharacteristic
116C2#2026754511yescharacteristic
117C2C16×Dic10311yescharacteristic
118C2#2026756611yescharacteristic
119C2(C2×D103)⋊C1612yes—
120C2Dic103⋊C1612yes—
subgroupG/H
center, FrattiniC22×C8C2×D103
commutatorC2×C103C4×C16
FittingC22×C16×C103C2
socle, prime radicalC23×C103C2×C8
cosocleC22×C8×C103C22
hypercenterC22×C16D103
hypocenterC103#1374
LCSG ▷ C2×C103 ▷ C103
UCSC1 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
8. C2×C103⋊C16C4semidirect
14. C2×C16×C103C4semidirect
39. C2×Dic103C16semidirect
61. C103#1374semidirect
73. C2×C16Dic103semidirect

Maximal subgroups

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

subgroupindex
C22×C103⋊C162
C2×C8×Dic1032
C22×C16×C1032
#1374103