Finite Group Databasebeta

← C3×#88135 #11928772

Subgroups — C3×#88135 #11928772

Order 1248.

188 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 86 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×C3×C22⋊D13C211yesmaximal, characteristic
2C22×C3×Dic13C211yesmaximal, characteristic, complemented
3C2×C3×C4×D13C211yesmaximal, characteristic, complemented
4C3×C13×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#6103C211yesmaximal, characteristic, complemented
6C3×#6101C211yesmaximal, characteristic, complemented
7C3×C4×Dic13C211yesmaximal, characteristic, complemented
8#88135C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C13C2211yescharacteristic
10C22×C3×D13C2211yescharacteristic
11C2×C3×C4×C13C2211yescharacteristic
12C2×C3×C4×C13C2211yescharacteristic
13C3×C22⋊D13C414yescomplemented
14C2×C3×Dic13—22no—
15C2×C3×Dic13C2211yescharacteristic
16C2×C3×Dic13C2211yescharacteristic
17C2×C3×Dic13C2211yescharacteristic
18C3×C4×D13—22no—
19C2×C22⋊D13C2×C311yescharacteristic
20C22×Dic13C2×C311yescharacteristic, complemented
21C2×C4×D13C2×C311yescharacteristic, complemented
22C13×C22⋊C4C2×C311yescharacteristic, complemented
23#6103C2×C311yescharacteristic, complemented
24#6101C2×C311yescharacteristic, complemented
25C4×Dic13C2×C311yescharacteristic, complemented
26C22×C3×C13—21no—
27C22×C3×C13—21no—
28C22×C3×C13C2×C412yescomplemented
29C22×C3×C13C2311yescharacteristic
30C2×C3×D13—21no—
31C2×C3×D13—21no—
32C2×C3×D13C2×C412yescomplemented
33C3×C4×C13—21no—
34C3×C4×C13—21no—
35C3×Dic13—21no—
36C3×Dic13C2×C412yescomplemented
37C3×Dic13D412yescomplemented
38C23×C13C22×C311yescharacteristic
39C22×D13C22×C311yescharacteristic
40C2×C4×C13C22×C311yescharacteristic
41C2×C4×C13C22×C311yescharacteristic
42C22⋊D13C3×C414yescomplemented
43C2×Dic13—22no—
44C2×Dic13C22×C311yescharacteristic
45C2×Dic13C22×C311yescharacteristic
46C2×Dic13C22×C311yescharacteristic
47C4×D13—22no—
48C3×C4×D4—131nomaximal, Hall
49C2×C3×C13—22no—
50C2×C3×C13C22×C411yescharacteristic
51C2×C3×C13C2×D411yescharacteristic
52C2×C3×C13#4111yescharacteristic
53C3×D13—22no—
54C22×C13—21no—
55C22×C13—21no—
56C22×C13C2×C3×C412yescomplemented
57C22×C13C23×C311yescharacteristic
58C2×D13—21no—
59C2×D13—21no—
60C2×D13C2×C3×C412yescomplemented
61C4×C13—21no—
62C4×C13—21no—
63Dic13—21no—
64Dic13C2×C3×C412yescomplemented
65Dic13C3×D412yescomplemented
66C2×C3×D4—131no—
67C22×C3×C4—131no—
68C22×C3×C4—131no—
69C3×C4⋊C4—131no—
70C3×C22⋊C4—131no—
71C3×C22⋊C4D1311yescharacteristic, complemented
72C3×C42—131no—
73C3×C13C4×D411yescharacteristic, complemented, Hall
74C4×D4—131noSylow
75C2×C13—22no—
76C2×C13C22×C3×C411yescharacteristic
77C2×C13C2×C3×D411yescharacteristic
78C2×C13C3×#4111yescharacteristic
79D13—22no—
80C23×C3—131no—
81C23×C3C2×D1311yescharacteristic
82C3×D4—134no—
83C2×C3×C4—131no—
84C2×C3×C4—131no—
85C2×C3×C4—131no—
86C2×C3×C4—262no—
87C2×C3×C4—262no—
88C2×C3×C4C2×D1311yescharacteristic
89C2×C3×C4C2×D1311yescharacteristic
90C2×D4—131no—
91C22×C4—131no—
92C22×C4—131no—
93C4⋊C4—131no—
94C22⋊C4—131no—
95C22⋊C4C3×D1311yescharacteristic, complemented
96C42—131no—
97C13C3×C4×D411yescharacteristic, complemented, Sylow
98C22×C3—21no—
99C22×C3—21no—
100C22×C3—132no—
101C22×C3—261no—
102C22×C3—261no—
103C22×C3C4×D1312yescomplemented
104C22×C3C22×D1311yescharacteristic
105C3×C4—21no—
106C3×C4—21no—
107C3×C4—132no—
108C3×C4—132no—
109C3×C4—261no—
110C23—131no—
111C23C2×C3×D1311yescharacteristic
112D4—134no—
113C2×C4—131no—
114C2×C4—131no—
115C2×C4—131no—
116C2×C4—262no—
117C2×C4—262no—
118C2×C4C2×C3×D1311yescharacteristic
119C2×C4C2×C3×D1311yescharacteristic
120C2×C3—22no—
121C2×C3—262no—
122C2×C3C2×C4×D1311yescharacteristic
123C2×C3D4×D1311yescharacteristic
124C2×C3#612911yescharacteristic
125C22—21no—
126C22—21no—
127C22—132no—
128C22—261no—
129C22—261no—
130C22C3×C4×D1312yescomplemented
131C22C22×C3×D1311yescharacteristic
132C4—21no—
133C4—21no—
134C4—132no—
135C4—132no—
136C4—261no—
137C3#8813511yescharacteristic, direct product factor, Sylow
138C2—22no—
139C2—262no—
140C2C2×C3×C4×D1311yescharacteristic
141C2C3×D4×D1311yescharacteristic
142C2C3×#612911yescharacteristic
subgroupG/H
centerC22×C3C22×D13
commutatorC2×C13C22×C3×C4
FrattiniC22C22×C3×D13
FittingC3×C13×C22⋊C4C2
socleC22×C3×C13C23
prime radicalC2×C3×C22⋊D13C2
cosocleC22×C13C23×C3
hypercenterC3×C22⋊C4D13
hypocenterC13C3×C4×D4
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. C22×C3×Dic13C2semidirect
3. C2×C3×C4×D13C2semidirect
4. C3×C13×C22⋊C4C2semidirect
5. C3×#6103C2semidirect
6. C3×#6101C2semidirect
7. C3×C4×Dic13C2semidirect
8. #88135C3direct (N × H)
13. C3×C22⋊D13C4semidirect
20. C22×Dic13C2×C3semidirect
21. C2×C4×D13C2×C3semidirect
22. C13×C22⋊C4C2×C3semidirect
23. #6103C2×C3semidirect
24. #6101C2×C3semidirect
25. C4×Dic13C2×C3semidirect
28. C22×C3×C13C2×C4semidirect
32. C2×C3×D13C2×C4semidirect
36. C3×Dic13C2×C4semidirect
37. C3×Dic13D4semidirect
42. C22⋊D13C3×C4semidirect
56. C22×C13C2×C3×C4semidirect
60. C2×D13C2×C3×C4semidirect
64. Dic13C2×C3×C4semidirect
65. Dic13C3×D4semidirect
71. C3×C22⋊C4D13semidirect
73. C3×C13C4×D4semidirect
95. C22⋊C4C3×D13semidirect
97. C13C3×C4×D4semidirect
103. C22×C3C4×D13semidirect
130. C22C3×C4×D13semidirect
137. C3#88135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C22⋊D132
C22×C3×Dic132
C2×C3×C4×D132
C3×C13×C22⋊C42
C3×#61032
C3×#61012
C3×C4×Dic132
#881353
C3×C4×D413