Finite Group Databasebeta

← C2×S4×D13 #11929326

Subgroups — C2×S4×D13 #11929326

Order 1248.

262 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 35 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×A4×D13C211yesmaximal, characteristic, complemented
2C2×A4⋊D13C211yesmaximal, characteristic, complemented
3C2×C13×S4C211yesmaximal, characteristic, complemented
4S4×D13C214yesmaximal, direct product factor
5C2×D4×D13—31nomaximal, Hall
6C2×A4×C13C2211yescharacteristic, complemented
7C2×D3×D13—41nomaximal
8A4×D13C2212yescomplemented
9A4⋊D13C2212yescomplemented
10C13×S4C2212yescomplemented
11C23×D13—31no—
12C23×D13D311yescharacteristic, complemented
13C2×D4×C13—31no—
14C2×C22⋊D13—31no—
15C2×C22⋊D13—31no—
16D4×D13—34no—
17D4×D13—34no—
18C2×D52—31no—
19C2×C4×D13—31no—
20C2×D39—41no—
21C2×D3×C13—41no—
22C2×C3×D13—41no—
23A4×C13C2311yescharacteristic, complemented
24D3×D13—44no—
25C23×C13—31no—
26C23×C13C2×D311yescharacteristic, complemented
27C22×D13—31no—
28C22×D13—31no—
29C22×D13—32no—
30C22×D13—31no—
31C22×D13—34no—
32C22×D13—61no—
33C22×D13—62no—
34C22×D13—61no—
35C22×D13C2×D312yescomplemented
36D4×C13—32no—
37D4×C13—32no—
38C2×C4×C13—31no—
39C22⋊D13—34no—
40C22⋊D13—32no—
41C22⋊D13—32no—
42C2×Dic13—31no—
43D52—34no—
44C4×D13—34no—
45C22×S4—131nomaximal, Hall
46C2×C3×C13—41no—
47D39—42no—
48C3×D13—42no—
49D3×C13—42no—
50C22×C13—31no—
51C22×C13—31no—
52C22×C13—32no—
53C22×C13—61no—
54C22×C13—61no—
55C22×C13C22×D311yescharacteristic, complemented
56C2×D13—31no—
57C2×D13—32no—
58C2×D13—32no—
59C2×D13—32no—
60C2×D13—32no—
61C2×D13—61no—
62C2×D13—64no—
63C2×D13—61no—
64C2×D13—61no—
65C2×D13—64no—
66C2×D13S411yescharacteristic, direct product factor
67C4×C13—32no—
68Dic13—32no—
69C22×A4—131no—
70C2×S4—131no—
71C2×S4—134no—
72C2×S4D1311yescharacteristic, direct product factor
73C3×C13—41noHall
74C22×D4—391noSylow
75C2×C13—31no—
76C2×C13—31no—
77C2×C13—62no—
78C2×C13C2×S411yescharacteristic, complemented
79D13—32no—
80D13—62no—
81D13C2×S412yesdirect product factor
82C22×D3—521no—
83C2×A4—132no—
84C2×A4C2×D1311yescharacteristic, complemented
85S4—132no—
86S4C2×D1312yesdirect product factor
87C24—131no—
88C24—391no—
89C2×D4—31no—
90C2×D4—391no—
91C2×D4—394no—
92C2×D4—394no—
93C2×D4—391no—
94C2×D4—391no—
95C22×C4—391no—
96C13C22×S411yescharacteristic, complemented, Sylow
97C22×C3—521no—
98C2×D3—41no—
99C2×D3—524no—
100C2×D3—521no—
101A4C22×D1311yescharacteristic, complemented
102C23—31no—
103C23—132no—
104C23—391no—
105C23—392no—
106C23—391no—
107C23—391no—
108C23—394no—
109C23—781no—
110C23—782no—
111C23—781no—
112C23D3×D1311yescharacteristic, complemented
113D4—32no—
114D4—32no—
115D4—394no—
116D4—392no—
117D4—394no—
118D4—392no—
119C2×C4—31no—
120C2×C4—394no—
121C2×C4—391no—
122C2×C3—41no—
123C2×C3—522no—
124D3—42no—
125D3—522no—
126C22—31no—
127C22—31no—
128C22—32no—
129C22—61no—
130C22—61no—
131C22—131no—
132C22—392no—
133C22—392no—
134C22—392no—
135C22—392no—
136C22—391no—
137C22—781no—
138C22—781no—
139C22—784no—
140C22—784no—
141C22—781no—
142C22C2×D3×D1311yescharacteristic, complemented
143C4—32no—
144C4—392no—
145C3—41noSylow
146C2—31no—
147C2—31no—
148C2—62no—
149C2—132no—
150C2—392no—
151C2—782no—
152C2S4×D1311yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2S4×D13
commutator, cosocle, hypocenterA4×C13C23
FrattiniC1G
Fitting, socleC23×C13C2×D3
LCSG ▷ A4×C13
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×A4×D13C2semidirect
2. C2×A4⋊D13C2semidirect
3. C2×C13×S4C2semidirect
4. S4×D13C2direct (N × H)
6. C2×A4×C13C22semidirect
8. A4×D13C22semidirect
9. A4⋊D13C22semidirect
10. C13×S4C22semidirect
12. C23×D13D3semidirect
23. A4×C13C23semidirect
26. C23×C13C2×D3semidirect
35. C22×D13C2×D3semidirect
55. C22×C13C22×D3semidirect
66. C2×D13S4direct (N × H)
72. C2×S4D13direct (N × H)
78. C2×C13C2×S4semidirect
81. D13C2×S4direct (N × H)
84. C2×A4C2×D13semidirect
86. S4C2×D13direct (N × H)
96. C13C22×S4semidirect
101. A4C22×D13semidirect
112. C23D3×D13semidirect
142. C22C2×D3×D13semidirect
152. C2S4×D13direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×D132
C2×A4⋊D132
C2×C13×S42
S4×D132
C2×D4×D133
C2×D3×D134
C22×S413