Finite Group Databasebeta

← #27193235

Subgroups — #27193235

Order 13184.

152 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 89 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×#15692955C211yesmaximal, characteristic
3C2×#107×C103C211yesmaximal, characteristic
4C2×C4⋊Dic103—21no—
5C2×C103⋊C16—21no—
6C2×C103⋊C16—21no—
7C2×C103⋊C16C412yescomplemented
8#15692955—21no—
9#15692955C412yescomplemented
10C22×C8×C103C2211yescharacteristic
11C2×C4⋊C4×C103—21no—
12#107×C103—21no—
13#107×C103C412yescomplemented
14C22×Dic103—41no—
15C4⋊Dic103—22no—
16C4⋊Dic103—41no—
17C103⋊C16—22no—
18C22×C4×C103—41no—
19C22×C4×C103D411yescharacteristic
20C2×C8×C103C2×C411yescharacteristic
21C2×C8×C103C2×C411yescharacteristic
22C2×C8×C103C2×C411yescharacteristic
23C2×C8×C103D411yescharacteristic
24C2×C8×C103D411yescharacteristic
25C2×C8×C103Q811yescharacteristic
26C4⋊C4×C103—22no—
27C4⋊C4×C103—41no—
28C23×C103D811yescharacteristic
29C2×C4×C103—42no—
30C2×C4×C103—81no—
31C2×C4×C103—81no—
32C2×C4×C103C22⋊C411yescharacteristic
33C2×C4×C103C22⋊C411yescharacteristic
34C2×C4×C103C4⋊C411yescharacteristic
35C2×C4×C103SD1611yescharacteristic
36C2×C4×C103SD1611yescharacteristic
37C2×C4×C103Q1611yescharacteristic
38C2×Dic103—42no—
39C2×Dic103—81no—
40C2×Dic103—81no—
41C8×C103C4211yescharacteristic
42C8×C103C22⋊C411yescharacteristic
43C8×C103C4⋊C411yescharacteristic
44C8×C103C4⋊C411yescharacteristic
45C22×C103#10211yescharacteristic
46C22×C103#10211yescharacteristic
47C22×C103#10711yescharacteristic
48C22×C103D1611yescharacteristic
49C22×C103SD3211yescharacteristic
50C22×C103SD3211yescharacteristic
51C22×C103Q3211yescharacteristic
52C4×C103—82no—
53C4×C103#9511yescharacteristic
54C4×C103#10311yescharacteristic
55C4×C103#10311yescharacteristic
56C4×C103#10611yescharacteristic
57Dic103—82no—
58C2×C103#34011yescharacteristic
59C2×C103#35711yescharacteristic
60C2×C103#35711yescharacteristic
61C2×C103#35811yescharacteristic
62C2×C103#35811yescharacteristic
63C2×C103#36611yescharacteristic
64C2×C103#36711yescharacteristic
65#1380—1031nomaximal, Sylow
66C103#138011yescharacteristic, complemented, Sylow
67C22×C16—1031no—
68C2×#107—1031no—
69C2×#107D10311yescharacteristic
70C22×C8C2×D10311yescharacteristic
71C2×C4⋊C4—21no—
72C2×C4⋊C4—2061no—
73C2×C16—1032no—
74C2×C16—2061no—
75C2×C16—2061no—
76#107—21no—
77#107—1032no—
78#107—2061no—
79#107Dic10312yescomplemented
80C22×C4—41no—
81C22×C4—4121no—
82C22×C4C22⋊D10311yescharacteristic
83C2×C8Dic20611yescharacteristic
84C2×C8C4×D10311yescharacteristic
85C2×C8C4×D10311yescharacteristic
86C2×C8D41211yescharacteristic
87C2×C8C2×Dic10311yescharacteristic
88C2×C8C22⋊D10311yescharacteristic
89C4⋊C4—22no—
90C4⋊C4—41no—
91C4⋊C4—4121no—
92C4⋊C4—2062no—
93C16—2062no—
94C23#1311009011yescharacteristic
95C2×C4—42no—
96C2×C4—81no—
97C2×C4—81no—
98C2×C4—8241no—
99C2×C4—8241no—
100C2×C4—4122no—
101C2×C4(C2×D103)⋊C411yescharacteristic
102C2×C4C22⋊Dic10311yescharacteristic
103C2×C4Dic103⋊C411yescharacteristic
104C2×C4#1311009211yescharacteristic
105C2×C4#1311009311yescharacteristic
106C2×C4#1311009511yescharacteristic
107C8C4×Dic10311yescharacteristic
108C8(C2×D103)⋊C411yescharacteristic
109C8Dic103⋊C411yescharacteristic
110C8C4⋊Dic10311yescharacteristic
111C22#1569294111yescharacteristic
112C22#1569294211yescharacteristic
113C22#1569295411yescharacteristic
114C22#1569296211yescharacteristic
115C22#1569296411yescharacteristic
116C22#1569296511yescharacteristic
117C22#1569296711yescharacteristic
118C4—82no—
119C4—8242no—
120C4C103⋊#9511yescharacteristic
121C4#1569294411yescharacteristic
122C4#1569294511yescharacteristic
123C4#1569295211yescharacteristic
124C2#2026755311yescharacteristic
125C2#2026759111yescharacteristic
126C2#2026759211yescharacteristic
127C2#2026759411yescharacteristic
128C2#2026759511yescharacteristic
129C2#2026761611yescharacteristic
130C2#2026761811yescharacteristic
subgroupG/H
centerC23#13110090
commutatorC8×C103C42
FrattiniC22×C8C2×D103
FittingC2×#107×C103C2
socle, prime radicalC23×C103D8
cosocleC22×C8×C103C22
hypercenterC2×#107D103
hypocenterC103#1380
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
7. C2×C103⋊C16C4semidirect
9. #15692955C4semidirect
13. #107×C103C4semidirect
66. C103#1380semidirect
79. #107Dic103semidirect

Maximal subgroups

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

subgroupindex
C22×C103⋊C162
C2×#156929552
C2×#107×C1032
#1380103