Finite Group Databasebeta

← #11929215

Subgroups — #11929215

Order 1248.

332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 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×D156C211yesmaximal, characteristic, complemented
2C13×#235C211yesmaximal, characteristic, complemented
3C3×#6127C211yesmaximal, characteristic, complemented
4#10597756C214yesmaximal, complemented
5D3×D52C212yesmaximal, complemented
6D12×D13C212yesmaximal, complemented
7#10597739C212yesmaximal, complemented
8#10597735C212yesmaximal, complemented
9#88256—31nomaximal, Hall
10C22×D39C2212yescomplemented
11C2×D3×D13C2214yescomplemented
12C2×C3×C4×C13C2211yescharacteristic, complemented
13D156C2212yescomplemented
14D156C2212yescomplemented
15C13×#67C2212yescomplemented
16C13×D12C2211yescharacteristic, complemented
17C4×D3×C13C2212yescomplemented
18C13×Dic6C2211yescharacteristic, complemented
19C3×C22⋊D13C2212yescomplemented
20C3×D52C2211yescharacteristic, complemented
21C3×C4×D13C2212yescomplemented
22C3×Dic26C2211yescharacteristic, complemented
23#64604C2214yescomplemented
24#64603C2214yescomplemented
25#64601C2214yescomplemented
26C13×#41—31no—
27#6131—32no—
28D4×D13—34no—
29D4×D13—32no—
30#6127—32no—
31#6127D311yescharacteristic, complemented
32C2×D52—31no—
33C2×D52—32no—
34C22×C3×C13C2311yescharacteristic
35C2×D39—42no—
36C2×D39C2314yes—
37C2×D3×C13C2312yes—
38C2×C3×D13C2312yes—
39D3×D13—44no—
40C3×C4×C13C2311yescharacteristic
41C3×C4×C13C2311yescharacteristic
42C3×Dic13C2312yes—
43Dic3×C13C2312yes—
44C22×D13—32no—
45C22×D13—34no—
46Q8×C13—31no—
47D4×C13—32no—
48D4×C13—31no—
49C2×C4×C13—32no—
50C2×C4×C13C2×D311yescharacteristic, complemented
51C22⋊D13—34no—
52C22⋊D13C2×D312yescomplemented
53D52—34no—
54D52—32no—
55D52—32no—
56D52C2×D311yescharacteristic, complemented
57C4×D13—34no—
58C4×D13C2×D312yescomplemented
59Dic26C2×D311yescharacteristic, complemented
60#1009—131nomaximal, Hall
61C2×C3×C13—21no—
62C2×C3×C13C2411yescharacteristic
63D39—24no—
64C3×D13—22no—
65D3×C13—22no—
66C22×C13—32no—
67C22×C13C22×D311yescharacteristic
68C2×D13—34no—
69C2×D13—124no—
70C2×D13—122no—
71C2×D13C22×D312yes—
72C4×C13—32no—
73C4×C13C22×D311yescharacteristic
74C4×C13C22×D311yescharacteristic
75Dic13C22×D312yes—
76C3×#41—131no—
77#239—132no—
78D3×D4—134no—
79D3×D4—132no—
80#235—132no—
81#235D1311yescharacteristic, complemented
82C2×D12—131no—
83C2×D12—132no—
84C3×C13H(5,𝔽2)11yescharacteristic, complemented, Hall
85H(5,𝔽2)—391noSylow
86C2×C13—21no—
87C2×C13—62no—
88C2×C13C23×D311yescharacteristic
89D13—22no—
90D13—64no—
91C22×D3—132no—
92C22×D3—134no—
93C3×Q8—131no—
94C3×D4—132no—
95C3×D4—131no—
96C2×C3×C4—132no—
97C2×C3×C4C2×D1311yescharacteristic, complemented
98#67—134no—
99#67C2×D1312yescomplemented
100D12—134no—
101D12—132no—
102D12—132no—
103D12C2×D1311yescharacteristic, complemented
104C4×D3—134no—
105C4×D3C2×D1312yescomplemented
106Dic6C2×D1311yescharacteristic, complemented
107#41—31no—
108#41—131no—
109#41—392no—
110#41—392no—
111C2×D4—392no—
112C2×D4—392no—
113C2×D4—394no—
114C2×D4—391no—
115C13#100911yescharacteristic, complemented, Sylow
116C22×C3—132no—
117C22×C3C22×D1311yescharacteristic
118C2×D3—134no—
119C2×D3—524no—
120C2×D3—522no—
121C2×D3C22×D1312yes—
122C3×C4—132no—
123C3×C4C22×D1311yescharacteristic
124C3×C4C22×D1311yescharacteristic
125Dic3C22×D1312yes—
126C23—394no—
127C23—392no—
128Q8—31no—
129Q8—131no—
130D4—32no—
131D4—31no—
132D4—132no—
133D4—131no—
134D4—394no—
135D4—394no—
136D4—392no—
137D4—392no—
138C2×C4—32no—
139C2×C4—132no—
140C2×C4—394no—
141C2×C4D3×D1311yescharacteristic, complemented
142C2×C3—21no—
143C2×C3—262no—
144C2×C3C23×D1311yescharacteristic
145D3—22no—
146D3—264no—
147C22—32no—
148C22—132no—
149C22—394no—
150C22—1562no—
151C22—1564no—
152C22C2×D3×D1311yescharacteristic
153C4—32no—
154C4—132no—
155C4C2×D3×D1311yescharacteristic
156C4C2×D3×D1311yescharacteristic
157C3#8825611yescharacteristic, complemented, Sylow
158C2—21no—
159C2—62no—
160C2—262no—
161C2—784no—
162C2C22×D3×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D13
commutator, socle, cosocleC2×C3×C13C24
FittingC2×C3×C4×C13C22
hypercenterC2×C4D3×D13
hypocenterC3×C13H(5,𝔽2)
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D156C2semidirect
2. C13×#235C2semidirect
3. C3×#6127C2semidirect
4. #10597756C2semidirect
5. D3×D52C2semidirect
6. D12×D13C2semidirect
7. #10597739C2semidirect
8. #10597735C2semidirect
10. C22×D39C22semidirect
11. C2×D3×D13C22semidirect
12. C2×C3×C4×C13C22semidirect
13. D156C22semidirect
14. D156C22semidirect
15. C13×#67C22semidirect
16. C13×D12C22semidirect
17. C4×D3×C13C22semidirect
18. C13×Dic6C22semidirect
19. C3×C22⋊D13C22semidirect
20. C3×D52C22semidirect
21. C3×C4×D13C22semidirect
22. C3×Dic26C22semidirect
23. #64604C22semidirect
24. #64603C22semidirect
25. #64601C22semidirect
31. #6127D3semidirect
50. C2×C4×C13C2×D3semidirect
52. C22⋊D13C2×D3semidirect
56. D52C2×D3semidirect
58. C4×D13C2×D3semidirect
59. Dic26C2×D3semidirect
81. #235D13semidirect
84. C3×C13H(5,𝔽2)semidirect
97. C2×C3×C4C2×D13semidirect
99. #67C2×D13semidirect
103. D12C2×D13semidirect
105. C4×D3C2×D13semidirect
106. Dic6C2×D13semidirect
115. C13#1009semidirect
141. C2×C4D3×D13semidirect
157. C3#88256semidirect

Maximal subgroups

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

subgroupindex
C2×D1562
C13×#2352
C3×#61272
#105977562
D3×D522
D12×D132
#105977392
#105977352
#882563
#100913