Finite Group Databasebeta

← #11928617

Subgroups — #11928617

Order 1248.

260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 54 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, complemented
2C2×D156C211yesmaximal, characteristic, complemented
3C2×#64604C211yesmaximal, characteristic, complemented
4C2×#64603C211yesmaximal, characteristic, complemented
5C13×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6C3×#6103C211yesmaximal, characteristic, complemented
7#10597610C211yesmaximal, characteristic, complemented
8#88136—31nomaximal, Hall
9C22×D39C2211yescharacteristic
10C22×D39C2211yescharacteristic, complemented
11C22×D3×C13C2211yescharacteristic
12C22×C3×D13C2211yescharacteristic
13C2×D3×D13—22no—
14C2×D3×D13—22no—
15C2×D3×D13—22no—
16C2×C3×C4×C13C2211yescharacteristic, complemented
17D156—22no—
18C2×Dic3×C13C2211yescharacteristic, complemented
19C2×C3×Dic13C2211yescharacteristic, complemented
20#64604—22no—
21#64603—22no—
22C23×D13—31no—
23C2×C22⋊D13—31no—
24C2×D52—31no—
25C2×D52—31no—
26C13×C22⋊C4—31no—
27#6103—31no—
28#6103D311yescharacteristic, complemented
29C22×C3×C13C2311yescharacteristic
30C2×D39—21no—
31C2×D39—21no—
32C2×D39—21no—
33C2×D39—21no—
34C2×D39—21no—
35C2×D39D412yescomplemented
36C2×D3×C13—21no—
37C2×D3×C13—21no—
38C2×D3×C13D412yescomplemented
39C2×C3×D13—21no—
40C2×C3×D13—21no—
41C2×C3×D13D412yescomplemented
42D3×D13—28no—
43C3×C4×C13—21no—
44C3×Dic13—21no—
45Dic3×C13—21no—
46C23×C13—31no—
47C22×D13—31no—
48C22×D13—31no—
49C22×D13—62no—
50C22×D13—62no—
51C22×D13—62no—
52C22×D13C2×D311yescharacteristic
53C2×C4×C13—31no—
54C2×C4×C13C2×D311yescharacteristic, complemented
55C22⋊D13—62no—
56C2×Dic13C2×D311yescharacteristic, complemented
57D52—62no—
58D52—62no—
59#882—131nomaximal, Hall
60C2×C3×C13C2×D411yescharacteristic
61C2×C3×C13C2×D411yescharacteristic
62C2×C3×C13C2×D411yescharacteristic
63D39—22no—
64D39—41no—
65C3×D13—22no—
66D3×C13—22no—
67C22×C13—32no—
68C22×C13—61no—
69C22×C13—61no—
70C22×C13C22×D311yescharacteristic
71C2×D13—21no—
72C2×D13—21no—
73C2×D13—32no—
74C2×D13—68no—
75C2×D13—61no—
76C2×D13—61no—
77C2×D13—61no—
78C2×D13—61no—
79C2×D13—61no—
80C2×D13D1212yescomplemented
81C4×C13—21no—
82C4×C13—61no—
83Dic13—21no—
84C23×D3—131no—
85C2×#67—131no—
86C2×D12—131no—
87C2×D12—131no—
88C3×C22⋊C4—131no—
89(C2×D3)⋊C4—131no—
90(C2×D3)⋊C4D1311yescharacteristic, complemented
91C3×C13#12011yescharacteristic, complemented, Hall
92#120—391noSylow
93C2×C13—62no—
94C2×C13C2×D1211yescharacteristic
95C2×C13D3×D411yescharacteristic
96C2×C13D3×D411yescharacteristic
97D13—22no—
98D13—62no—
99D13—121no—
100C23×C3—131no—
101C22×D3—131no—
102C22×D3—131no—
103C22×D3—262no—
104C22×D3—262no—
105C22×D3—262no—
106C22×D3C2×D1311yescharacteristic
107C2×C3×C4—131no—
108C2×C3×C4C2×D1311yescharacteristic, complemented
109#67—262no—
110C2×Dic3C2×D1311yescharacteristic, complemented
111D12—262no—
112D12—262no—
113C24—391no—
114C2×D4—391no—
115C2×D4—391no—
116C2×D4—391no—
117C22⋊C4—31no—
118C22⋊C4—131no—
119C22⋊C4—391no—
120C13#88211yescharacteristic, complemented, Sylow
121C22×C3—132no—
122C22×C3—261no—
123C22×C3—261no—
124C22×C3C22×D1311yescharacteristic
125C2×D3—21no—
126C2×D3—21no—
127C2×D3—132no—
128C2×D3—268no—
129C2×D3—261no—
130C2×D3—261no—
131C2×D3—261no—
132C2×D3—261no—
133C2×D3—261no—
134C2×D3D5212yescomplemented
135C3×C4—21no—
136C3×C4—261no—
137Dic3—21no—
138C23—31no—
139C23—131no—
140C23—391no—
141C23—391no—
142C23—782no—
143C23—782no—
144C23—782no—
145D4—782no—
146D4—782no—
147D4—782no—
148C2×C4—31no—
149C2×C4—131no—
150C2×C4D3×D1311yescharacteristic, complemented
151C2×C3—262no—
152C2×C3C2×D5211yescharacteristic
153C2×C3D4×D1311yescharacteristic
154C2×C3D4×D1311yescharacteristic
155D3—22no—
156D3—262no—
157D3—521no—
158C22—32no—
159C22—61no—
160C22—61no—
161C22—132no—
162C22—261no—
163C22—261no—
164C22—392no—
165C22—788no—
166C22—781no—
167C22—781no—
168C22—781no—
169C22—781no—
170C22—781no—
171C22C2×D3×D1311yescharacteristic
172C4—21no—
173C4—61no—
174C4—261no—
175C3#8813611yescharacteristic, complemented, Sylow
176C2—62no—
177C2—262no—
178C2—782no—
179C2—1561no—
180C2D12×D1311yescharacteristic
181C2D3×D5211yescharacteristic
182C2#1059775611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutator, socle, cosocleC22×C3×C13C23
FittingC2×C3×C4×C13C22
hypercenterC2×C4D3×D13
hypocenterC3×C13#120
LCSG ▷ C22×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C22×D3×D13C2semidirect
2. C2×D156C2semidirect
3. C2×#64604C2semidirect
4. C2×#64603C2semidirect
5. C13×(C2×D3)⋊C4C2semidirect
6. C3×#6103C2semidirect
7. #10597610C2semidirect
10. C22×D39C22semidirect
16. C2×C3×C4×C13C22semidirect
18. C2×Dic3×C13C22semidirect
19. C2×C3×Dic13C22semidirect
28. #6103D3semidirect
35. C2×D39D4semidirect
38. C2×D3×C13D4semidirect
41. C2×C3×D13D4semidirect
54. C2×C4×C13C2×D3semidirect
56. C2×Dic13C2×D3semidirect
80. C2×D13D12semidirect
90. (C2×D3)⋊C4D13semidirect
91. C3×C13#120semidirect
108. C2×C3×C4C2×D13semidirect
110. C2×Dic3C2×D13semidirect
120. C13#882semidirect
134. C2×D3D52semidirect
150. C2×C4D3×D13semidirect
175. C3#88136semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D132
C2×D1562
C2×#646042
C2×#646032
C13×(C2×D3)⋊C42
C3×#61032
#105976102
#881363
#88213