Finite Group Databasebeta

← C3×#88191 #11928829

Subgroups — C3×#88191 #11928829

Order 1248.

260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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, complemented
2C2×C3×D4×C13C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊D13C212yesmaximal, complemented
4C3×C22⋊Dic13C211yesmaximal, characteristic, complemented
5C3×#6103C212yesmaximal, complemented
6#88191C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C13C2211yescharacteristic
8C23×C3×C13C2211yescharacteristic, complemented
9C22×C3×D13—22no—
10C22×C3×D13—24no—
11C22×C3×D13C2212yes—
12C3×D4×C13—22no—
13C2×C3×C4×C13C2211yescharacteristic, complemented
14C3×C22⋊D13—24no—
15C2×C3×Dic13C2212yescomplemented
16C23×D13C2×C311yescharacteristic, complemented
17C2×D4×C13C2×C311yescharacteristic, complemented
18C2×C22⋊D13C2×C312yescomplemented
19C22⋊Dic13C2×C311yescharacteristic, complemented
20#6103C2×C312yescomplemented
21C22×C3×C13—22no—
22C22×C3×C13—22no—
23C22×C3×C13—21no—
24C22×C3×C13D412yescomplemented
25C22×C3×C13C2311yescharacteristic
26C2×C3×D13—28no—
27C2×C3×D13—22no—
28C2×C3×D13—22no—
29C2×C3×D13D414yescomplemented
30C3×C4×C13—21no—
31C3×Dic13—22no—
32C23×C13C22×C311yescharacteristic
33C23×C13C22×C311yescharacteristic, complemented
34C22×D13—22no—
35C22×D13—24no—
36C22×D13C22×C312yes—
37D4×C13—22no—
38C2×C4×C13C22×C311yescharacteristic, complemented
39C22⋊D13—24no—
40C2×Dic13C22×C312yescomplemented
41C3×#120—131nomaximal, Hall
42C2×C3×C13—22no—
43C2×C3×C13—41no—
44C2×C3×C13C2×D412yes—
45C2×C3×C13C2×D411yescharacteristic
46C3×D13—24no—
47C22×C13—22no—
48C22×C13—22no—
49C22×C13—21no—
50C22×C13C3×D412yescomplemented
51C22×C13C23×C311yescharacteristic
52C2×D13—28no—
53C2×D13—22no—
54C2×D13—22no—
55C2×D13C3×D414yescomplemented
56C4×C13—21no—
57Dic13—22no—
58C24×C3—131no—
59C2×C3×D4—132no—
60C2×C3×D4D1311yescharacteristic, complemented
61C3×C22⋊C4—131no—
62C3×C22⋊C4—132no—
63C3×C13#12011yescharacteristic, complemented, Hall
64#120—131noSylow
65C2×C13—22no—
66C2×C13—41no—
67C2×C13C2×C3×D412yes—
68C2×C13C2×C3×D411yescharacteristic
69D13—24no—
70C23×C3—132no—
71C23×C3—264no—
72C23×C3—262no—
73C23×C3C2×D1311yescharacteristic
74C23×C3C2×D1311yescharacteristic, complemented
75C3×D4—22no—
76C3×D4—264no—
77C2×C3×C4—132no—
78C2×C3×C4C2×D1311yescharacteristic, complemented
79C24—131no—
80C2×D4—132no—
81C2×D4C3×D1311yescharacteristic, complemented
82C22⋊C4—131no—
83C22⋊C4—132no—
84C13C3×#12011yescharacteristic, complemented, Sylow
85C22×C3—22no—
86C22×C3—22no—
87C22×C3—21no—
88C22×C3—134no—
89C22×C3—268no—
90C22×C3—262no—
91C22×C3—262no—
92C22×C3C22⋊D1312yescomplemented
93C22×C3C22×D1311yescharacteristic
94C3×C4—21no—
95C3×C4—262no—
96C23—132no—
97C23—264no—
98C23—262no—
99C23C2×C3×D1311yescharacteristic
100C23C2×C3×D1311yescharacteristic, complemented
101D4—22no—
102D4—264no—
103C2×C4—132no—
104C2×C4C2×C3×D1311yescharacteristic, complemented
105C2×C3—22no—
106C2×C3—41no—
107C2×C3—264no—
108C2×C3D4×D1312yes—
109C2×C3C2×C22⋊D1311yescharacteristic
110C22—22no—
111C22—22no—
112C22—21no—
113C22—134no—
114C22—268no—
115C22—262no—
116C22—262no—
117C22C3×C22⋊D1312yescomplemented
118C22C22×C3×D1311yescharacteristic
119C4—21no—
120C4—262no—
121C3#8819111yescharacteristic, direct product factor, Sylow
122C2—22no—
123C2—41no—
124C2—264no—
125C2C3×D4×D1312yes—
126C2C2×C3×C22⋊D1311yescharacteristic
subgroupG/H
centerC22×C3C22×D13
commutator, cosocleC22×C13C23×C3
FrattiniC22C22×C3×D13
FittingC2×C3×D4×C13C2
socleC22×C3×C13C23
hypercenterC2×C3×D4D13
hypocenterC13C3×#120
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D13C2semidirect
2. C2×C3×D4×C13C2semidirect
3. C2×C3×C22⋊D13C2semidirect
4. C3×C22⋊Dic13C2semidirect
5. C3×#6103C2semidirect
6. #88191C3direct (N × H)
8. C23×C3×C13C22semidirect
13. C2×C3×C4×C13C22semidirect
15. C2×C3×Dic13C22semidirect
16. C23×D13C2×C3semidirect
17. C2×D4×C13C2×C3semidirect
18. C2×C22⋊D13C2×C3semidirect
19. C22⋊Dic13C2×C3semidirect
20. #6103C2×C3semidirect
24. C22×C3×C13D4semidirect
29. C2×C3×D13D4semidirect
33. C23×C13C22×C3semidirect
38. C2×C4×C13C22×C3semidirect
40. C2×Dic13C22×C3semidirect
50. C22×C13C3×D4semidirect
55. C2×D13C3×D4semidirect
60. C2×C3×D4D13semidirect
63. C3×C13#120semidirect
74. C23×C3C2×D13semidirect
78. C2×C3×C4C2×D13semidirect
81. C2×D4C3×D13semidirect
84. C13C3×#120semidirect
92. C22×C3C22⋊D13semidirect
100. C23C2×C3×D13semidirect
104. C2×C4C2×C3×D13semidirect
117. C22C3×C22⋊D13semidirect
121. C3#88191direct (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×D4×C132
C2×C3×C22⋊D132
C3×C22⋊Dic132
C3×#61032
#881913
C3×#12013