Finite Group Databasebeta

← #11928614

Subgroups — #11928614

Order 1248.

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

normal subgroups only

This group has 264 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
1C22×D3×D13C211yesmaximal, characteristic
2C2×C4×D39C211yesmaximal, characteristic, complemented
3C2×#64601C211yesmaximal, characteristic, complemented
4C13×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×#6103C211yesmaximal, characteristic, complemented
6(C2×D3)⋊Dic13C211yesmaximal, characteristic, complemented
7#10597608C211yesmaximal, characteristic, complemented
8C22⋊C4×D13—31nomaximal, Hall
9C22×D39C2211yescharacteristic
10C22×D3×C13C2211yescharacteristic
11C22×C3×D13C2211yescharacteristic
12C2×D3×D13—22no—
13C2×D3×D13—22no—
14C2×D3×D13C414yescomplemented
15C2×C3×C4×C13C2211yescharacteristic, complemented
16C2×Dic39C2211yescharacteristic, complemented
17C4×D39—22no—
18C2×Dic3×C13C2211yescharacteristic, complemented
19C2×C3×Dic13C2211yescharacteristic, complemented
20#64601—22no—
21C23×D13—31no—
22C2×C4×D13—31no—
23C2×C4×D13—31no—
24C13×C22⋊C4—31no—
25C22⋊Dic13—31no—
26#6103—31no—
27#6103D311yescharacteristic, complemented
28C22×C3×C13C2311yescharacteristic
29C2×D39C2×C412yes—
30C2×D39D412yes—
31C2×D39D412yes—
32C2×D3×C13—21no—
33C2×D3×C13—21no—
34C2×D3×C13C2×C412yescomplemented
35C2×C3×D13—21no—
36C2×C3×D13—21no—
37C2×C3×D13C2×C412yescomplemented
38D3×D13—28no—
39C3×C4×C13—21no—
40Dic39—21no—
41C3×Dic13—21no—
42Dic3×C13—21no—
43C23×C13—31no—
44C22×D13—31no—
45C22×D13—34no—
46C22×D13—62no—
47C22×D13—62no—
48C22×D13C2×D311yescharacteristic
49C2×C4×C13—31no—
50C2×C4×C13C2×D311yescharacteristic, complemented
51C2×Dic13—31no—
52C2×Dic13C2×D311yescharacteristic, complemented
53C4×D13—62no—
54C4×D13—62no—
55D3×C22⋊C4—131nomaximal, Hall
56C2×C3×C13C22×C411yescharacteristic
57C2×C3×C13C2×D411yescharacteristic
58C2×C3×C13C2×D411yescharacteristic
59D39C22⋊C414yescomplemented
60C3×D13—22no—
61D3×C13—22no—
62C22×C13—32no—
63C22×C13—61no—
64C22×C13—61no—
65C22×C13C22×D311yescharacteristic
66C2×D13—21no—
67C2×D13—21no—
68C2×D13—32no—
69C2×D13—32no—
70C2×D13—32no—
71C2×D13—68no—
72C2×D13C4×D312yescomplemented
73C4×C13—21no—
74C4×C13—61no—
75Dic13—21no—
76Dic13—61no—
77C23×D3—131no—
78C2×C4×D3—131no—
79C2×C4×D3—131no—
80C3×C22⋊C4—131no—
81#217—131no—
82(C2×D3)⋊C4—131no—
83(C2×D3)⋊C4D1311yescharacteristic, complemented
84C3×C13C2×C22⋊C411yescharacteristic, complemented, Hall
85C2×C22⋊C4—391noSylow
86C2×C13—62no—
87C2×C13C2×C4×D311yescharacteristic
88C2×C13D3×D411yescharacteristic
89C2×C13D3×D411yescharacteristic
90D13—22no—
91D13—34no—
92C23×C3—131no—
93C22×D3—131no—
94C22×D3—134no—
95C22×D3—262no—
96C22×D3—262no—
97C22×D3C2×D1311yescharacteristic
98C2×C3×C4—131no—
99C2×C3×C4C2×D1311yescharacteristic, complemented
100C2×Dic3—131no—
101C2×Dic3C2×D1311yescharacteristic, complemented
102C4×D3—262no—
103C4×D3—262no—
104C24—391no—
105C22×C4—391no—
106C22×C4—391no—
107C22⋊C4—31no—
108C22⋊C4—131no—
109C22⋊C4—391no—
110C22⋊C4—391no—
111C13D3×C22⋊C411yescharacteristic, complemented, Sylow
112C22×C3—132no—
113C22×C3—261no—
114C22×C3—261no—
115C22×C3C22×D1311yescharacteristic
116C2×D3—21no—
117C2×D3—21no—
118C2×D3—132no—
119C2×D3—132no—
120C2×D3—132no—
121C2×D3—268no—
122C2×D3C4×D1312yescomplemented
123C3×C4—21no—
124C3×C4—261no—
125Dic3—21no—
126Dic3—261no—
127C23—31no—
128C23—131no—
129C23—394no—
130C23—391no—
131C23—782no—
132C23—782no—
133C2×C4—31no—
134C2×C4—131no—
135C2×C4—391no—
136C2×C4—782no—
137C2×C4—782no—
138C2×C4D3×D1311yescharacteristic, complemented
139C2×C3—262no—
140C2×C3C2×C4×D1311yescharacteristic
141C2×C3D4×D1311yescharacteristic
142C2×C3D4×D1311yescharacteristic
143D3—22no—
144D3—134no—
145C22—32no—
146C22—61no—
147C22—61no—
148C22—132no—
149C22—261no—
150C22—261no—
151C22—392no—
152C22—392no—
153C22—392no—
154C22—788no—
155C22C2×D3×D1311yescharacteristic
156C4—21no—
157C4—61no—
158C4—261no—
159C4—781no—
160C3C22⋊C4×D1311yescharacteristic, complemented, Sylow
161C2—62no—
162C2—262no—
163C2—394no—
164C2C4×D3×D1311yescharacteristic
165C2#1059774311yescharacteristic
166C2#1059775611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutatorC2×C3×C13C22×C4
FittingC2×C3×C4×C13C22
socle, cosocleC22×C3×C13C23
prime radicalC22×D3×D13C2
hypercenterC2×C4D3×D13
hypocenterC3×C13C2×C22⋊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
2. C2×C4×D39C2semidirect
3. C2×#64601C2semidirect
4. C13×(C2×D3)⋊C4C2semidirect
5. C3×#6103C2semidirect
6. (C2×D3)⋊Dic13C2semidirect
7. #10597608C2semidirect
14. C2×D3×D13C4semidirect
15. C2×C3×C4×C13C22semidirect
16. C2×Dic39C22semidirect
18. C2×Dic3×C13C22semidirect
19. C2×C3×Dic13C22semidirect
27. #6103D3semidirect
34. C2×D3×C13C2×C4semidirect
37. C2×C3×D13C2×C4semidirect
50. C2×C4×C13C2×D3semidirect
52. C2×Dic13C2×D3semidirect
59. D39C22⋊C4semidirect
72. C2×D13C4×D3semidirect
83. (C2×D3)⋊C4D13semidirect
84. C3×C13C2×C22⋊C4semidirect
99. C2×C3×C4C2×D13semidirect
101. C2×Dic3C2×D13semidirect
111. C13D3×C22⋊C4semidirect
122. C2×D3C4×D13semidirect
138. C2×C4D3×D13semidirect
160. C3C22⋊C4×D13semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D132
C2×C4×D392
C2×#646012
C13×(C2×D3)⋊C42
C3×#61032
(C2×D3)⋊Dic132
#105976082
C22⋊C4×D133
D3×C22⋊C413