Finite Group Databasebeta

← #11928718

Subgroups — #11928718

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×#64625C211yesmaximal, characteristic, complemented
3C2×C13×#67C211yesmaximal, characteristic, complemented
4C2×C3×C22⋊D13C211yesmaximal, characteristic, complemented
5#10597610C211yesmaximal, characteristic, complemented
6(C2×D3)⋊Dic13C211yesmaximal, characteristic, complemented
7#10597608C211yesmaximal, characteristic, complemented
8#88191—31nomaximal, Hall
9C23×C3×C13C2211yescharacteristic, complemented
10C22×D39C2211yescharacteristic
11C22×D3×C13C2211yescharacteristic
12C22×C3×D13C2211yescharacteristic
13C2×D3×D13—22no—
14C2×D3×D13—22no—
15C2×D3×D13—22no—
16#64625—22no—
17C2×Dic39C2211yescharacteristic, complemented
18C13×#67—22no—
19C2×Dic3×C13C2211yescharacteristic, complemented
20C3×C22⋊D13—22no—
21C2×C3×Dic13C2211yescharacteristic, complemented
22C23×D13—31no—
23C2×D4×C13—31no—
24C2×C22⋊D13—31no—
25C2×C22⋊D13D311yescharacteristic, complemented
26C22⋊Dic13—31no—
27#6103—31no—
28#6103—31no—
29C22×C3×C13—21no—
30C22×C3×C13—21no—
31C22×C3×C13—21no—
32C22×C3×C13C2311yescharacteristic
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—
43Dic39—21no—
44C3×Dic13—21no—
45Dic3×C13—21no—
46C23×C13—31no—
47C23×C13C2×D311yescharacteristic, complemented
48C22×D13—31no—
49C22×D13—62no—
50C22×D13—62no—
51C22×D13—62no—
52C22×D13C2×D311yescharacteristic
53D4×C13—62no—
54C2×C4×C13—31no—
55C22⋊D13—22no—
56C22⋊D13—62no—
57C2×Dic13—31no—
58C2×Dic13C2×D311yescharacteristic, complemented
59#937—131nomaximal, Hall
60C2×C3×C13—41no—
61C2×C3×C13C2×D411yescharacteristic
62C2×C3×C13C2×D411yescharacteristic
63C2×C3×C13C2×D411yescharacteristic
64D39—22no—
65C3×D13—22no—
66D3×C13—22no—
67C22×C13—21no—
68C22×C13—21no—
69C22×C13—21no—
70C22×C13—32no—
71C22×C13—61no—
72C22×C13—61no—
73C22×C13C22×D311yescharacteristic
74C2×D13—21no—
75C2×D13—21no—
76C2×D13—32no—
77C2×D13—68no—
78C2×D13—61no—
79C2×D13—61no—
80C2×D13#6712yescomplemented
81C4×C13—61no—
82Dic13—21no—
83Dic13—61no—
84C23×D3—131no—
85C2×C3×D4—131no—
86C2×#67—131no—
87C2×#67D1311yescharacteristic, complemented
88#217—131no—
89(C2×D3)⋊C4—131no—
90(C2×D3)⋊C4—131no—
91C3×C13#12011yescharacteristic, complemented, Hall
92#120—391noSylow
93C2×C13—41no—
94C2×C13—62no—
95C2×C13D3×D411yescharacteristic
96C2×C13D3×D411yescharacteristic
97C2×C13C2×#6711yescharacteristic
98D13—22no—
99D13—62no—
100C23×C3—131no—
101C23×C3C2×D1311yescharacteristic, complemented
102C22×D3—131no—
103C22×D3—262no—
104C22×D3—262no—
105C22×D3—262no—
106C22×D3C2×D1311yescharacteristic
107C3×D4—262no—
108C2×C3×C4—131no—
109#67—22no—
110#67—262no—
111C2×Dic3—131no—
112C2×Dic3C2×D1311yescharacteristic, complemented
113C24—391no—
114C2×D4—31no—
115C2×D4—131no—
116C2×D4—391no—
117C22⋊C4—391no—
118C22⋊C4—391no—
119C22⋊C4—391no—
120C13#93711yescharacteristic, complemented, Sylow
121C22×C3—21no—
122C22×C3—21no—
123C22×C3—21no—
124C22×C3—132no—
125C22×C3—261no—
126C22×C3—261no—
127C22×C3C22×D1311yescharacteristic
128C2×D3—21no—
129C2×D3—21no—
130C2×D3—132no—
131C2×D3—268no—
132C2×D3—261no—
133C2×D3—261no—
134C2×D3C22⋊D1312yescomplemented
135C3×C4—261no—
136Dic3—21no—
137Dic3—261no—
138C23—31no—
139C23—131no—
140C23—391no—
141C23—782no—
142C23—782no—
143C23—782no—
144C23D3×D1311yescharacteristic, complemented
145D4—62no—
146D4—262no—
147D4—782no—
148C2×C4—31no—
149C2×C4—131no—
150C2×C4—391no—
151C2×C3—41no—
152C2×C3—262no—
153C2×C3D4×D1311yescharacteristic
154C2×C3D4×D1311yescharacteristic
155C2×C3C2×C22⋊D1311yescharacteristic
156D3—22no—
157D3—262no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—32no—
162C22—61no—
163C22—61no—
164C22—132no—
165C22—261no—
166C22—261no—
167C22—392no—
168C22—788no—
169C22—781no—
170C22—781no—
171C22C2×D3×D1311yescharacteristic
172C4—61no—
173C4—261no—
174C4—781no—
175C3#8819111yescharacteristic, complemented, Sylow
176C2—41no—
177C2—62no—
178C2—262no—
179C2—782no—
180C2#67×D1311yescharacteristic
181C2D3×C22⋊D1311yescharacteristic
182C2#1059775611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×D13
commutator, socle, cosocleC22×C3×C13C23
FittingC23×C3×C13C22
hypercenterC23D3×D13
hypocenterC3×C13#120
LCSG ▷ C22×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×D3×D13C2semidirect
2. C2×#64625C2semidirect
3. C2×C13×#67C2semidirect
4. C2×C3×C22⋊D13C2semidirect
5. #10597610C2semidirect
6. (C2×D3)⋊Dic13C2semidirect
7. #10597608C2semidirect
9. C23×C3×C13C22semidirect
17. C2×Dic39C22semidirect
19. C2×Dic3×C13C22semidirect
21. C2×C3×Dic13C22semidirect
25. C2×C22⋊D13D3semidirect
35. C2×D39D4semidirect
38. C2×D3×C13D4semidirect
41. C2×C3×D13D4semidirect
47. C23×C13C2×D3semidirect
58. C2×Dic13C2×D3semidirect
80. C2×D13#67semidirect
87. C2×#67D13semidirect
91. C3×C13#120semidirect
101. C23×C3C2×D13semidirect
112. C2×Dic3C2×D13semidirect
120. C13#937semidirect
134. C2×D3C22⋊D13semidirect
144. C23D3×D13semidirect
175. C3#88191semidirect

Maximal subgroups

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

subgroupindex
C22×D3×D132
C2×#646252
C2×C13×#672
C2×C3×C22⋊D132
#105976102
(C2×D3)⋊Dic132
#105976082
#881913
#93713