Finite Group Databasebeta

← #11928526

Subgroups — #11928526

Order 1248.

184 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 66 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
1C2×C4×D39C211yesmaximal, characteristic
2C2×#64601C211yesmaximal, characteristic
3C2×#64601C211yesmaximal, characteristic
4C13×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C3×#6101C211yesmaximal, characteristic, complemented
6Dic3⋊Dic13C211yesmaximal, characteristic, complemented
7#10597611C211yesmaximal, characteristic, complemented
8C4⋊C4×D13—31nomaximal, Hall
9C22×D39C2211yescharacteristic
10C2×C3×C4×C13C2211yescharacteristic
11C2×Dic39C2211yescharacteristic
12C4×D39—22no—
13C2×Dic3×C13C2211yescharacteristic
14C2×Dic3×C13C2211yescharacteristic
15C2×C3×Dic13C2211yescharacteristic
16C2×C3×Dic13C2211yescharacteristic
17#64601—22no—
18#64601C414yescomplemented
19C2×C4×D13—31no—
20C2×C4×D13—31no—
21C2×C4×D13—31no—
22C13×C4⋊C4—31no—
23C4⋊Dic13—31no—
24#6101—31no—
25#6101D311yescharacteristic, complemented
26C22×C3×C13C2311yescharacteristic
27C2×D39C2×C412yes—
28C2×D39D412yes—
29C2×D39Q812yes—
30C3×C4×C13—21no—
31Dic39—21no—
32C3×Dic13—21no—
33C3×Dic13C2×C412yescomplemented
34Dic3×C13—21no—
35Dic3×C13C2×C412yescomplemented
36C22×D13—31no—
37C2×C4×C13—31no—
38C2×C4×C13—31no—
39C2×C4×C13C2×D311yescharacteristic
40C2×Dic13—31no—
41C2×Dic13C2×D311yescharacteristic
42C2×Dic13C2×D311yescharacteristic
43C4×D13—34no—
44C4×D13—62no—
45C4×D13—62no—
46D3×C4⋊C4—131nomaximal, Hall
47C2×C3×C13C22×C411yescharacteristic
48C2×C3×C13C2×D411yescharacteristic
49C2×C3×C13C2×Q811yescharacteristic
50D39C4⋊C414yescomplemented
51C22×C13C22×D311yescharacteristic
52C2×D13—32no—
53C2×D13—32no—
54C2×D13—32no—
55C4×C13—21no—
56C4×C13—32no—
57C4×C13—61no—
58Dic13—21no—
59Dic13—61no—
60Dic13C4×D312yescomplemented
61C2×C4×D3—131no—
62C2×C4×D3—131no—
63C2×C4×D3—131no—
64C3×C4⋊C4—131no—
65C4⋊Dic3—131no—
66Dic3⋊C4—131no—
67Dic3⋊C4D1311yescharacteristic, complemented
68C3×C13C2×C4⋊C411yescharacteristic, complemented, Hall
69C2×C4⋊C4—391noSylow
70C2×C13C2×C4×D311yescharacteristic
71C2×C13D3×D411yescharacteristic
72C2×C13D3×Q811yescharacteristic
73D13—34no—
74C22×D3—131no—
75C2×C3×C4—131no—
76C2×C3×C4—131no—
77C2×C3×C4C2×D1311yescharacteristic
78C2×Dic3—131no—
79C2×Dic3C2×D1311yescharacteristic
80C2×Dic3C2×D1311yescharacteristic
81C4×D3—134no—
82C4×D3—262no—
83C4×D3—262no—
84C22×C4—391no—
85C22×C4—391no—
86C22×C4—391no—
87C4⋊C4—31no—
88C4⋊C4—131no—
89C4⋊C4—391no—
90C4⋊C4—391no—
91C13D3×C4⋊C411yescharacteristic, complemented, Sylow
92C22×C3C22×D1311yescharacteristic
93C2×D3—132no—
94C2×D3—132no—
95C2×D3—132no—
96C3×C4—21no—
97C3×C4—132no—
98C3×C4—261no—
99Dic3—21no—
100Dic3—261no—
101Dic3C4×D1312yescomplemented
102C23—391no—
103C2×C4—31no—
104C2×C4—31no—
105C2×C4—131no—
106C2×C4—131no—
107C2×C4—394no—
108C2×C4—391no—
109C2×C4—782no—
110C2×C4—782no—
111C2×C4D3×D1311yescharacteristic
112C2×C3C2×C4×D1311yescharacteristic
113C2×C3D4×D1311yescharacteristic
114C2×C3Q8×D1311yescharacteristic
115D3—134no—
116C22—392no—
117C22—392no—
118C22—392no—
119C22C2×D3×D1311yescharacteristic
120C4—21no—
121C4—32no—
122C4—61no—
123C4—132no—
124C4—261no—
125C4—781no—
126C3C4⋊C4×D1311yescharacteristic, complemented, Sylow
127C2—394no—
128C2D39⋊Q811yescharacteristic
129C2C4×D3×D1311yescharacteristic
130C2#1059775611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutatorC2×C3×C13C22×C4
FittingC2×C3×C4×C13C22
socle, cosocleC22×C3×C13C23
prime radicalC22×D39C22
hypercenterC2×C4D3×D13
hypocenterC3×C13C2×C4⋊C4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. C13×Dic3⋊C4C2semidirect
5. C3×#6101C2semidirect
6. Dic3⋊Dic13C2semidirect
7. #10597611C2semidirect
18. #64601C4semidirect
25. #6101D3semidirect
33. C3×Dic13C2×C4semidirect
35. Dic3×C13C2×C4semidirect
50. D39C4⋊C4semidirect
60. Dic13C4×D3semidirect
67. Dic3⋊C4D13semidirect
68. C3×C13C2×C4⋊C4semidirect
91. C13D3×C4⋊C4semidirect
101. Dic3C4×D13semidirect
126. C3C4⋊C4×D13semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D392
C2×#646012
C13×Dic3⋊C42
C3×#61012
Dic3⋊Dic132
#105976112
C4⋊C4×D133
D3×C4⋊C413