Finite Group Databasebeta

← #27193039

Subgroups — #27193039

Order 13184.

148 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 77 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#20267844C211yesmaximal, characteristic
2C2×C4⋊(C103⋊C8)C211yesmaximal, characteristic
3#423×C103C211yesmaximal, characteristic
4C22×C103⋊C8—21no—
5C4⋊(C103⋊C8)—21no—
6C4⋊(C103⋊C8)—21no—
7C4⋊(C103⋊C8)C412yes—
8C22⋊(C103⋊C8)C412yes—
9C4×C103⋊C8—21no—
10C2×M16×C103—21no—
11C2×C42×C103C2211yescharacteristic
12C4⋊C8×C103—21no—
13C4⋊C8×C103C412yes—
14C2×C103⋊C8—22no—
15C2×C103⋊C8—22no—
16C2×C103⋊C8—41no—
17C2×C103⋊C8—41no—
18C22×C4×C103C2×C411yescharacteristic
19C22×C4×C103D411yescharacteristic
20C22×C4×C103Q811yescharacteristic
21M16×C103—41no—
22M16×C103—41no—
23C2×C8×C103—22no—
24C42×C103C2×C411yescharacteristic
25C42×C103C2×C411yescharacteristic
26C42×C103D411yescharacteristic
27C42×C103D411yescharacteristic
28C23×C103C4⋊C411yescharacteristic
29C2×C4×C103—22no—
30C2×C4×C103—41no—
31C2×C4×C103C4211yescharacteristic
32C2×C4×C103C22⋊C411yescharacteristic
33C2×C4×C103C22⋊C411yescharacteristic
34C2×C4×C103C22⋊C411yescharacteristic
35C2×C4×C103C4⋊C411yescharacteristic
36C2×C4×C103C4⋊C411yescharacteristic
37C2×C4×C103D811yescharacteristic
38C2×C4×C103SD1611yescharacteristic
39C2×C4×C103SD1611yescharacteristic
40C2×C4×C103Q1611yescharacteristic
41C8×C103—42no—
42C103⋊C8—42no—
43C103⋊C8—42no—
44C22×C103—21no—
45C22×C103—21no—
46C22×C103#9511yescharacteristic
47C22×C103#10611yescharacteristic
48C22×C103#10711yescharacteristic
49C4×C103—21no—
50C4×C103—21no—
51C4×C103—21no—
52C4×C103#10211yescharacteristic
53C4×C103#10211yescharacteristic
54C4×C103#10311yescharacteristic
55C4×C103#10311yescharacteristic
56C4×C103#10812yes—
57C2×C103—21no—
58C2×C103—21no—
59C2×C103#34011yescharacteristic
60C2×C103#34111yescharacteristic
61C2×C103#34411yescharacteristic
62#1301—1031nomaximal, Sylow
63C103#130111yescharacteristic, complemented, Sylow
64#431—1031no—
65#423D10311yescharacteristic
66C2×C4⋊C8—1031no—
67C2×M16—21no—
68C22×C8—2061no—
69C2×C42C2×D10311yescharacteristic
70C4⋊C8—21no—
71C4⋊C8—1032no—
72C4⋊C8—2061no—
73C4⋊C8—2061no—
74C4⋊C8Dic10312yes—
75C22⋊C8—1032no—
76C4×C8—2061no—
77C22×C4Dic20611yescharacteristic
78C22×C4C4×D10311yescharacteristic
79C22×C4C22⋊D10311yescharacteristic
80M16—41no—
81M16—41no—
82C2×C8—22no—
83C2×C8—4121no—
84C2×C8—4121no—
85C2×C8—2062no—
86C2×C8—2062no—
87C42C4×D10311yescharacteristic
88C42D41211yescharacteristic
89C42C2×Dic10311yescharacteristic
90C42C22⋊D10311yescharacteristic
91C23Dic103⋊C411yescharacteristic
92C2×C4—22no—
93C2×C4—41no—
94C2×C4C4×Dic10311yescharacteristic
95C2×C4(C2×D103)⋊C411yescharacteristic
96C2×C4(C2×D103)⋊C411yescharacteristic
97C2×C4C22⋊Dic10311yescharacteristic
98C2×C4Dic103⋊C411yescharacteristic
99C2×C4C4⋊Dic10311yescharacteristic
100C2×C4#1311009011yescharacteristic
101C2×C4#1311009211yescharacteristic
102C2×C4#1311009311yescharacteristic
103C2×C4#1311009511yescharacteristic
104C8—42no—
105C8—4122no—
106C8—4122no—
107C22—21no—
108C22—21no—
109C22C103⋊#9511yescharacteristic
110C22#1569295211yescharacteristic
111C22#1569295411yescharacteristic
112C4—21no—
113C4—21no—
114C4—21no—
115C4#1569294111yescharacteristic
116C4#1569294211yescharacteristic
117C4#1569294411yescharacteristic
118C4#1569294511yescharacteristic
119C4#1569295612yes—
120C2—21no—
121C2—21no—
122C2#2026755311yescharacteristic
123C2#2026755511yescharacteristic
124C2#2026756211yescharacteristic
subgroupG/H
centerC2×C4C22⋊Dic103
commutatorC2×C4×C103C42
FrattiniC2×C42C2×D103
Fitting#423×C103C2
socleC22×C103#95
prime radicalC23×C103C4⋊C4
cosocleC2×C42×C103C22
hypercenter#423D103
hypocenterC103#1301
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
63. C103#1301semidirect

Maximal subgroups

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

subgroupindex
#202678442
C2×C4⋊(C103⋊C8)2
#423×C1032
#1301103