Finite Group Databasebeta

← C2×#10597756 #11929244

Subgroups — C2×#10597756 #11929244

Order 1248.

472 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 124 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
1C23×D39C211yesmaximal, characteristic, complemented
2C22×D3×D13C211yesmaximal, characteristic, complemented
3C2×C13×#67C211yesmaximal, characteristic, complemented
4C2×C3×C22⋊D13C211yesmaximal, characteristic, complemented
5#10597756C218yesmaximal, direct product factor
6C2×#64604C211yesmaximal, characteristic, complemented
7C2×#64603C211yesmaximal, characteristic, complemented
8C2×#64601C211yesmaximal, characteristic, complemented
9C2×D4×D13—31nomaximal, Hall
10C23×C3×C13C2211yescharacteristic, complemented
11C22×D39—24no—
12C22×D39C2211yescharacteristic
13C22×D39C2214yescomplemented
14C22×D39C2211yescharacteristic, complemented
15C22×D3×C13C2211yescharacteristic, complemented
16C22×C3×D13C2211yescharacteristic, complemented
17C2×D3×D13—24no—
18C2×D3×D13C2214yescomplemented
19C13×#67C2214yescomplemented
20C2×Dic3×C13C2211yescharacteristic, complemented
21C3×C22⋊D13C2214yescomplemented
22C2×C3×Dic13C2211yescharacteristic, complemented
23#64604C2214yescomplemented
24#64603C2214yescomplemented
25#64601C2214yescomplemented
26C23×D13—31no—
27C23×D13—31no—
28C2×D4×C13—31no—
29C2×C22⋊D13—31no—
30C2×C22⋊D13D311yescharacteristic, complemented
31D4×D13—38no—
32C2×D52—31no—
33C2×C4×D13—31no—
34C22×C3×C13—22no—
35C22×C3×C13C2311yescharacteristic
36C22×C3×C13C2312yescomplemented
37C2×D39—22no—
38C2×D39—28no—
39C2×D39D414yescomplemented
40C2×D39C2312yes—
41C2×D39C2312yescomplemented
42C2×D3×C13—22no—
43C2×D3×C13C2312yescomplemented
44C2×C3×D13—22no—
45C2×C3×D13C2312yescomplemented
46D3×D13—28no—
47C3×Dic13C2312yescomplemented
48Dic3×C13C2312yescomplemented
49C23×C13—31no—
50C23×C13C2×D311yescharacteristic, complemented
51C22×D13—31no—
52C22×D13—31no—
53C22×D13—34no—
54C22×D13—34no—
55C22×D13—64no—
56C22×D13—64no—
57C22×D13C2×D311yescharacteristic, complemented
58D4×C13—34no—
59C2×C4×C13—31no—
60C22⋊D13—34no—
61C22⋊D13C2×D314yescomplemented
62C2×Dic13C2×D311yescharacteristic, complemented
63D52—34no—
64C4×D13—34no—
65C2×D3×D4—131nomaximal, Hall
66C2×C3×C13—22no—
67C2×C3×C13C2×D412yescomplemented
68C2×C3×C13C2411yescharacteristic
69D39—22no—
70D39C2×D414yescomplemented
71C3×D13—22no—
72D3×C13—22no—
73C22×C13—22no—
74C22×C13—32no—
75C22×C13—62no—
76C22×C13C22×D311yescharacteristic
77C22×C13C22×D312yescomplemented
78C2×D13—22no—
79C2×D13—34no—
80C2×D13—32no—
81C2×D13—32no—
82C2×D13—68no—
83C2×D13—68no—
84C2×D13—62no—
85C2×D13C22×D312yescomplemented
86C4×C13—32no—
87Dic13C22×D312yescomplemented
88C23×D3—131no—
89C23×D3—131no—
90C2×C3×D4—131no—
91C2×#67—131no—
92C2×#67D1311yescharacteristic, complemented
93D3×D4—138no—
94C2×D12—131no—
95C2×C4×D3—131no—
96C3×C13C22×D411yescharacteristic, complemented, Hall
97C22×D4—391noSylow
98C2×C13—22no—
99C2×C13—62no—
100C2×C13D3×D412yescomplemented
101C2×C13C23×D311yescharacteristic
102D13—22no—
103D13—34no—
104D13—62no—
105C23×C3—131no—
106C23×C3C2×D1311yescharacteristic, complemented
107C22×D3—131no—
108C22×D3—131no—
109C22×D3—134no—
110C22×D3—134no—
111C22×D3—264no—
112C22×D3—264no—
113C22×D3C2×D1311yescharacteristic, complemented
114C3×D4—134no—
115C2×C3×C4—131no—
116#67—134no—
117#67C2×D1314yescomplemented
118C2×Dic3C2×D1311yescharacteristic, complemented
119D12—134no—
120C4×D3—134no—
121C24—391no—
122C24—391no—
123C2×D4—31no—
124C2×D4—131no—
125C2×D4—391no—
126C2×D4—391no—
127C2×D4—398no—
128C22×C4—391no—
129C13C2×D3×D411yescharacteristic, complemented, Sylow
130C22×C3—22no—
131C22×C3—132no—
132C22×C3—262no—
133C22×C3C22×D1311yescharacteristic
134C22×C3C22×D1312yescomplemented
135C2×D3—22no—
136C2×D3—134no—
137C2×D3—132no—
138C2×D3—132no—
139C2×D3—268no—
140C2×D3—268no—
141C2×D3—262no—
142C2×D3C22×D1312yescomplemented
143C3×C4—132no—
144Dic3C22×D1312yescomplemented
145C23—31no—
146C23—131no—
147C23—394no—
148C23—391no—
149C23—391no—
150C23—394no—
151C23—784no—
152C23—784no—
153C23D3×D1311yescharacteristic, complemented
154D4—34no—
155D4—134no—
156D4—394no—
157D4—394no—
158C2×C4—31no—
159C2×C4—131no—
160C2×C4—394no—
161C2×C3—22no—
162C2×C3—262no—
163C2×C3D4×D1312yescomplemented
164C2×C3C23×D1311yescharacteristic
165D3—22no—
166D3—134no—
167D3—262no—
168C22—22no—
169C22—32no—
170C22—62no—
171C22—132no—
172C22—262no—
173C22—394no—
174C22—392no—
175C22—392no—
176C22—788no—
177C22—788no—
178C22—782no—
179C22C2×D3×D1311yescharacteristic
180C22C2×D3×D1312yescomplemented
181C4—32no—
182C4—132no—
183C3C2×D4×D1311yescharacteristic, complemented, Sylow
184C2—22no—
185C2—62no—
186C2—262no—
187C2—394no—
188C2—782no—
189C2#1059775612yesdirect product factor
190C2C22×D3×D1311yescharacteristic
subgroupG/H
centerC22C2×D3×D13
commutator, cosocleC2×C3×C13C24
FrattiniC2C22×D3×D13
FittingC23×C3×C13C22
socleC22×C3×C13C23
hypercenterC23D3×D13
hypocenterC3×C13C22×D4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C23×D39C2semidirect
2. C22×D3×D13C2semidirect
3. C2×C13×#67C2semidirect
4. C2×C3×C22⋊D13C2semidirect
5. #10597756C2direct (N × H)
6. C2×#64604C2semidirect
7. C2×#64603C2semidirect
8. C2×#64601C2semidirect
10. C23×C3×C13C22semidirect
13. C22×D39C22semidirect
14. C22×D39C22semidirect
15. C22×D3×C13C22semidirect
16. C22×C3×D13C22semidirect
18. C2×D3×D13C22semidirect
19. C13×#67C22semidirect
20. C2×Dic3×C13C22semidirect
21. C3×C22⋊D13C22semidirect
22. C2×C3×Dic13C22semidirect
23. #64604C22semidirect
24. #64603C22semidirect
25. #64601C22semidirect
30. C2×C22⋊D13D3semidirect
36. C22×C3×C13C23semidirect
39. C2×D39D4semidirect
41. C2×D39C23semidirect
43. C2×D3×C13C23semidirect
45. C2×C3×D13C23semidirect
47. C3×Dic13C23semidirect
48. Dic3×C13C23semidirect
50. C23×C13C2×D3semidirect
57. C22×D13C2×D3semidirect
61. C22⋊D13C2×D3semidirect
62. C2×Dic13C2×D3semidirect
67. C2×C3×C13C2×D4semidirect
70. D39C2×D4semidirect
77. C22×C13C22×D3semidirect
85. C2×D13C22×D3semidirect
87. Dic13C22×D3semidirect
92. C2×#67D13semidirect
96. C3×C13C22×D4semidirect
100. C2×C13D3×D4semidirect
106. C23×C3C2×D13semidirect
113. C22×D3C2×D13semidirect
117. #67C2×D13semidirect
118. C2×Dic3C2×D13semidirect
129. C13C2×D3×D4semidirect
134. C22×C3C22×D13semidirect
142. C2×D3C22×D13semidirect
144. Dic3C22×D13semidirect
153. C23D3×D13semidirect
163. C2×C3D4×D13semidirect
180. C22C2×D3×D13semidirect
183. C3C2×D4×D13semidirect
189. C2#10597756direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D392
C22×D3×D132
C2×C13×#672
C2×C3×C22⋊D132
#105977562
C2×#646042
C2×#646032
C2×#646012
C2×D4×D133
C2×D3×D413