Finite Group Databasebeta

← C3×C22⋊C4×D13 #11928771

Subgroups — C3×C22⋊C4×D13 #11928771

Order 1248.

264 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 98 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×C3×D13C211yesmaximal, characteristic
2C2×C3×C4×D13C212yesmaximal, complemented
3C3×C13×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×C22⋊Dic13C211yesmaximal, characteristic, complemented
5C3×#6103C212yesmaximal, complemented
6C22⋊C4×D13C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C13C2211yescharacteristic
8C22×C3×D13—24no—
9C22×C3×D13C414yescomplemented
10C22×C3×D13C2211yescharacteristic
11C22×C3×D13C2211yescharacteristic
12C2×C3×C4×C13C2212yescomplemented
13C2×C3×Dic13C2212yescomplemented
14C3×C4×D13—24no—
15C23×D13C2×C311yescharacteristic
16C2×C4×D13C2×C312yescomplemented
17C13×C22⋊C4C2×C311yescharacteristic, complemented
18C22⋊Dic13C2×C311yescharacteristic, complemented
19#6103C2×C312yescomplemented
20C22×C3×C13—22no—
21C22×C3×C13C2×C412yescomplemented
22C22×C3×C13C2311yescharacteristic
23C2×C3×D13—22no—
24C2×C3×D13—28no—
25C2×C3×D13C2×C412yes—
26C2×C3×D13C2×C412yescomplemented
27C2×C3×D13D414yes—
28C3×C4×C13—22no—
29C3×Dic13—22no—
30C23×C13C22×C311yescharacteristic
31C22×D13—24no—
32C22×D13C3×C414yescomplemented
33C22×D13C22×C311yescharacteristic
34C22×D13C22×C311yescharacteristic
35C2×C4×C13C22×C312yescomplemented
36C2×Dic13C22×C312yescomplemented
37C4×D13—24no—
38C2×C3×C22⋊C4—131nomaximal, Hall
39C2×C3×C13—22no—
40C2×C3×C13C22×C411yescharacteristic
41C2×C3×C13C2×D412yes—
42C3×D13—22no—
43C3×D13C22⋊C414yesdirect product factor
44C22×C13—22no—
45C22×C13C2×C3×C412yescomplemented
46C22×C13C23×C311yescharacteristic
47C2×D13—22no—
48C2×D13—28no—
49C2×D13C2×C3×C412yes—
50C2×D13C2×C3×C412yescomplemented
51C2×D13C3×D414yes—
52C4×C13—22no—
53Dic13—22no—
54C24×C3—131no—
55C22×C3×C4—132no—
56C3×C22⋊C4—131no—
57C3×C22⋊C4—132no—
58C3×C22⋊C4D1311yescharacteristic, direct product factor
59C3×C13C2×C22⋊C411yescharacteristic, complemented, Hall
60C2×C22⋊C4—131noSylow
61C2×C13—22no—
62C2×C13C22×C3×C411yescharacteristic
63C2×C13C2×C3×D412yes—
64D13—22no—
65D13C3×C22⋊C414yesdirect product factor
66C23×C3—131no—
67C23×C3—134no—
68C23×C3—131no—
69C23×C3—264no—
70C23×C3C2×D1311yescharacteristic
71C2×C3×C4—132no—
72C2×C3×C4—264no—
73C2×C3×C4C2×D1312yescomplemented
74C24—131no—
75C22×C4—132no—
76C22⋊C4—131no—
77C22⋊C4—132no—
78C22⋊C4C3×D1311yescharacteristic, direct product factor
79C13C2×C3×C22⋊C411yescharacteristic, complemented, Sylow
80C22×C3—22no—
81C22×C3—132no—
82C22×C3—134no—
83C22×C3—132no—
84C22×C3—268no—
85C22×C3—262no—
86C22×C3C4×D1312yescomplemented
87C22×C3C22×D1311yescharacteristic
88C3×C4—22no—
89C3×C4—262no—
90C23—131no—
91C23—134no—
92C23—131no—
93C23—264no—
94C23C2×C3×D1311yescharacteristic
95C2×C4—132no—
96C2×C4—264no—
97C2×C4C2×C3×D1312yescomplemented
98C2×C3—22no—
99C2×C3—134no—
100C2×C3—262no—
101C2×C3C2×C4×D1311yescharacteristic
102C2×C3D4×D1312yes—
103C22—22no—
104C22—132no—
105C22—134no—
106C22—132no—
107C22—268no—
108C22—262no—
109C22C3×C4×D1312yescomplemented
110C22C22×C3×D1311yescharacteristic
111C4—22no—
112C4—262no—
113C3C22⋊C4×D1311yescharacteristic, direct product factor, Sylow
114C2—22no—
115C2—134no—
116C2—262no—
117C2C2×C3×C4×D1311yescharacteristic
118C2C3×D4×D1312yes—
subgroupG/H
centerC22×C3C22×D13
commutatorC2×C13C22×C3×C4
FrattiniC22C22×C3×D13
FittingC3×C13×C22⋊C4C2
socleC22×C3×C13C23
prime radicalC23×C3×D13C2
cosocleC22×C13C23×C3
hypercenterC3×C22⋊C4D13
hypocenterC13C2×C3×C22⋊C4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×D13C2semidirect
3. C3×C13×C22⋊C4C2semidirect
4. C3×C22⋊Dic13C2semidirect
5. C3×#6103C2semidirect
6. C22⋊C4×D13C3direct (N × H)
9. C22×C3×D13C4semidirect
12. C2×C3×C4×C13C22semidirect
13. C2×C3×Dic13C22semidirect
16. C2×C4×D13C2×C3semidirect
17. C13×C22⋊C4C2×C3semidirect
18. C22⋊Dic13C2×C3semidirect
19. #6103C2×C3semidirect
21. C22×C3×C13C2×C4semidirect
26. C2×C3×D13C2×C4semidirect
32. C22×D13C3×C4semidirect
35. C2×C4×C13C22×C3semidirect
36. C2×Dic13C22×C3semidirect
43. C3×D13C22⋊C4direct (N × H)
45. C22×C13C2×C3×C4semidirect
50. C2×D13C2×C3×C4semidirect
58. C3×C22⋊C4D13direct (N × H)
59. C3×C13C2×C22⋊C4semidirect
65. D13C3×C22⋊C4direct (N × H)
73. C2×C3×C4C2×D13semidirect
78. C22⋊C4C3×D13direct (N × H)
79. C13C2×C3×C22⋊C4semidirect
86. C22×C3C4×D13semidirect
97. C2×C4C2×C3×D13semidirect
109. C22C3×C4×D13semidirect
113. C3C22⋊C4×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D132
C2×C3×C4×D132
C3×C13×C22⋊C42
C3×C22⋊Dic132
C3×#61032
C22⋊C4×D133
C2×C3×C22⋊C413