Finite Group Databasebeta

← C4×(C22⋊D13)⋊C3 #11928293

Subgroups — C4×(C22⋊D13)⋊C3 #11928293

Order 1248.

188 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C22×C4×C13⋊C3C211yesmaximal, characteristic, complemented
2C2×(C22⋊D13)⋊C3C211yesmaximal, characteristic
3C2×C4×D13⋊C3C211yesmaximal, characteristic, complemented
4(C22⋊Dic13)⋊C3C211yesmaximal, characteristic, complemented
5#6103⋊C3C211yesmaximal, characteristic, complemented
6#6101⋊C3C211yesmaximal, characteristic, complemented
7C4×Dic13⋊C3C211yesmaximal, characteristic, complemented
8C4×C22⋊D13C311yesmaximal, characteristic, complemented, Hall
9C23×C13⋊C3C2211yescharacteristic
10C22×D13⋊C3C2211yescharacteristic
11C2×C4×C13⋊C3—22no—
12C2×C4×C13⋊C3C2211yescharacteristic
13C2×C4×C13⋊C3C2211yescharacteristic
14(C22⋊D13)⋊C3C414yesdirect product factor
15C2×Dic13⋊C3C2211yescharacteristic
16C2×Dic13⋊C3C2211yescharacteristic
17C2×Dic13⋊C3C2211yescharacteristic
18C4×D13⋊C3—22no—
19C22×C4×C13C2×C311yescharacteristic, complemented
20C2×C22⋊D13C2×C311yescharacteristic
21C2×C4×D13C2×C311yescharacteristic, complemented
22C22⋊Dic13C2×C311yescharacteristic, complemented
23#6103C2×C311yescharacteristic, complemented
24#6101C2×C311yescharacteristic, complemented
25C4×Dic13C2×C311yescharacteristic, complemented
26C22×C13⋊C3—21no—
27C22×C13⋊C3—21no—
28C22×C13⋊C3C2×C412yescomplemented
29C22×C13⋊C3C2311yescharacteristic
30C2×D13⋊C3—21no—
31C2×D13⋊C3—21no—
32C2×D13⋊C3C2×C412yescomplemented
33C4×C13⋊C3—21no—
34C4×C13⋊C3D412yescomplemented
35Dic13⋊C3—21no—
36Dic13⋊C3—21no—
37Dic13⋊C3C2×C412yescomplemented
38C23×C13C22×C311yescharacteristic
39C22×D13C22×C311yescharacteristic
40C2×C4×C13—22no—
41C2×C4×C13C22×C311yescharacteristic
42C2×C4×C13C22×C311yescharacteristic
43C22⋊D13C3×C414yescomplemented
44C2×Dic13C22×C311yescharacteristic
45C2×Dic13C22×C311yescharacteristic
46C2×Dic13C22×C311yescharacteristic
47C4×D13—22no—
48C3×C4×D4—131nomaximal, Hall
49C2×C13⋊C3—22no—
50C2×C13⋊C3C22×C411yescharacteristic
51C2×C13⋊C3C2×D411yescharacteristic
52C2×C13⋊C3#4111yescharacteristic
53D13⋊C3—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×C13C3×D412yescomplemented
63Dic13—21no—
64Dic13—21no—
65Dic13C2×C3×C412yescomplemented
66C2×C3×D4—131no—
67C22×C3×C4—131no—
68C22×C3×C4—131no—
69C3×C4⋊C4—131no—
70C3×C22⋊C4—131no—
71C3×C22⋊C4—131no—
72C3×C42—131no—
73C13⋊C3C4×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×C3—131no—
82C3×D4—134no—
83C2×C3×C4—131no—
84C2×C3×C4—131no—
85C2×C3×C4—131no—
86C2×C3×C4—131no—
87C2×C3×C4—131no—
88C2×C3×C4—262no—
89C2×C3×C4—262no—
90C2×D4—131no—
91C22×C4—131no—
92C22×C4D13⋊C311yescharacteristic, complemented
93C4⋊C4—131no—
94C22⋊C4—131no—
95C22⋊C4—131no—
96C42—131no—
97C13C3×C4×D411yescharacteristic, complemented, Sylow
98C22×C3—132no—
99C22×C3—132no—
100C22×C3—131no—
101C22×C3—261no—
102C22×C3—261no—
103C22×C3—261no—
104C22×C3—261no—
105C3×C4—132no—
106C3×C4—132no—
107C3×C4—261no—
108C3×C4—261no—
109C3×C4—261no—
110C23—131no—
111C23C2×D13⋊C311yescharacteristic
112D4—134no—
113C2×C4—22no—
114C2×C4—131no—
115C2×C4—131no—
116C2×C4—131no—
117C2×C4—262no—
118C2×C4C2×D13⋊C311yescharacteristic
119C2×C4C2×D13⋊C311yescharacteristic
120C2×C3—131no—
121C2×C3—131no—
122C2×C3—131no—
123C2×C3—262no—
124C2×C3—262no—
125C22—21no—
126C22—21no—
127C22—132no—
128C22—261no—
129C22—261no—
130C22C4×D13⋊C312yescomplemented
131C22C22×D13⋊C311yescharacteristic
132C4—21no—
133C4—132no—
134C4—261no—
135C4—261no—
136C4(C22⋊D13)⋊C312yesdirect product factor
137C3—131noSylow
138C2—22no—
139C2—262no—
140C2C2×C4×D13⋊C311yescharacteristic
141C2#6127⋊C311yescharacteristic
142C2C2×(C22⋊D13)⋊C311yescharacteristic
subgroupG/H
centerC2×C4C2×D13⋊C3
commutatorC2×C13C22×C3×C4
FrattiniC22C22×D13⋊C3
FittingC22×C4×C13C2×C3
socle, cosocleC22×C13C23×C3
prime radicalC2×(C22⋊D13)⋊C3C2
hypercenterC22×C4D13⋊C3
hypocenterC13C3×C4×D4
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C13⋊C3C2semidirect
3. C2×C4×D13⋊C3C2semidirect
4. (C22⋊Dic13)⋊C3C2semidirect
5. #6103⋊C3C2semidirect
6. #6101⋊C3C2semidirect
7. C4×Dic13⋊C3C2semidirect
8. C4×C22⋊D13C3semidirect
14. (C22⋊D13)⋊C3C4direct (N × H)
19. C22×C4×C13C2×C3semidirect
21. C2×C4×D13C2×C3semidirect
22. C22⋊Dic13C2×C3semidirect
23. #6103C2×C3semidirect
24. #6101C2×C3semidirect
25. C4×Dic13C2×C3semidirect
28. C22×C13⋊C3C2×C4semidirect
32. C2×D13⋊C3C2×C4semidirect
34. C4×C13⋊C3D4semidirect
37. Dic13⋊C3C2×C4semidirect
43. C22⋊D13C3×C4semidirect
56. C22×C13C2×C3×C4semidirect
60. C2×D13C2×C3×C4semidirect
62. C4×C13C3×D4semidirect
65. Dic13C2×C3×C4semidirect
73. C13⋊C3C4×D4semidirect
92. C22×C4D13⋊C3semidirect
97. C13C3×C4×D4semidirect
130. C22C4×D13⋊C3semidirect
136. C4(C22⋊D13)⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C13⋊C32
C2×(C22⋊D13)⋊C32
C2×C4×D13⋊C32
(C22⋊Dic13)⋊C32
#6103⋊C32
#6101⋊C32
C4×Dic13⋊C32
C4×C22⋊D133
C3×C4×D413