Finite Group Databasebeta

← C2×D39⋊Q8 #11929202

Subgroups — C2×D39⋊Q8 #11929202

Order 1248.

312 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 124 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×C4×D39C211yesmaximal, characteristic
2C2×C13×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×Dic26C211yesmaximal, characteristic, complemented
4C2×#64605C212yesmaximal, complemented
5C2×#64601C212yesmaximal
6D39⋊Q8C218yesmaximal, direct product factor
7C2×Q8×D13—31nomaximal, Hall
8C22×D39C2211yescharacteristic
9C2×C3×C4×C13C2211yescharacteristic
10C2×Dic39C2211yescharacteristic
11C4×D39C2214yes—
12C2×Dic3×C13C2212yes—
13C13×Dic6C2214yescomplemented
14C2×C3×Dic13C2212yes—
15C3×Dic26C2214yescomplemented
16#64605C2218yescomplemented
17#64601C2218yes—
18C2×Q8×C13—31no—
19Q8×D13—38no—
20C2×C4×D13—31no—
21C2×C4×D13—32no—
22C2×Dic26—32no—
23C2×Dic26D311yescharacteristic, complemented
24C22×C3×C13C2311yescharacteristic
25C2×D39Q814yescomplemented
26C2×D39C2312yes—
27C3×C4×C13C2312yes—
28Dic39C2312yes—
29C3×Dic13C2314yes—
30Dic3×C13C2314yes—
31C22×D13—31no—
32Q8×C13—34no—
33C2×C4×C13—32no—
34C2×C4×C13C2×D311yescharacteristic
35C2×Dic13—31no—
36C2×Dic13C2×D312yes—
37C4×D13—34no—
38C4×D13—38no—
39Dic26—38no—
40Dic26C2×D314yescomplemented
41C2×D3×Q8—131nomaximal, Hall
42C2×C3×C13C2×Q812yescomplemented
43C2×C3×C13C2411yescharacteristic
44D39C2×Q814yescomplemented
45C22×C13C22×D311yescharacteristic
46C2×D13—34no—
47C2×D13—32no—
48C4×C13—34no—
49C4×C13C22×D312yes—
50Dic13—32no—
51Dic13C22×D314yes—
52C2×C3×Q8—131no—
53D3×Q8—138no—
54C2×C4×D3—131no—
55C2×C4×D3—132no—
56C2×Dic6—132no—
57C2×Dic6D1311yescharacteristic, complemented
58C3×C13C22×Q811yescharacteristic, complemented, Hall
59C22×Q8—391noSylow
60C2×C13D3×Q812yescomplemented
61C2×C13C23×D311yescharacteristic
62D13—34no—
63C22×D3—131no—
64C3×Q8—134no—
65C2×C3×C4—132no—
66C2×C3×C4C2×D1311yescharacteristic
67C2×Dic3—131no—
68C2×Dic3C2×D1312yes—
69C4×D3—134no—
70C4×D3—138no—
71Dic6—138no—
72Dic6C2×D1314yescomplemented
73C2×Q8—31no—
74C2×Q8—131no—
75C2×Q8—392no—
76C2×Q8—398no—
77C22×C4—392no—
78C22×C4—391no—
79C13C2×D3×Q811yescharacteristic, complemented, Sylow
80C22×C3C22×D1311yescharacteristic
81C2×D3—134no—
82C2×D3—132no—
83C3×C4—134no—
84C3×C4C22×D1312yes—
85Dic3—132no—
86Dic3C22×D1314yes—
87C23—391no—
88Q8—34no—
89Q8—134no—
90Q8—398no—
91C2×C4—32no—
92C2×C4—132no—
93C2×C4—398no—
94C2×C4—391no—
95C2×C4—394no—
96C2×C4D3×D1311yescharacteristic
97C2×C3Q8×D1312yescomplemented
98C2×C3C23×D1311yescharacteristic
99D3—134no—
100C22—394no—
101C22—392no—
102C22C2×D3×D1311yescharacteristic
103C4—34no—
104C4—134no—
105C4—392no—
106C4C2×D3×D1312yes—
107C3C2×Q8×D1311yescharacteristic, complemented, Sylow
108C2—394no—
109C2D39⋊Q812yesdirect product factor
110C2C22×D3×D1311yescharacteristic
subgroupG/H
centerC22C2×D3×D13
commutator, cosocleC2×C3×C13C24
FrattiniC2C22×D3×D13
FittingC2×C3×C4×C13C22
socleC22×C3×C13C23
prime radicalC22×D39C22
hypercenterC2×C4D3×D13
hypocenterC3×C13C22×Q8
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C13×Dic6C2semidirect
3. C2×C3×Dic26C2semidirect
4. C2×#64605C2semidirect
6. D39⋊Q8C2direct (N × H)
13. C13×Dic6C22semidirect
15. C3×Dic26C22semidirect
16. #64605C22semidirect
23. C2×Dic26D3semidirect
25. C2×D39Q8semidirect
40. Dic26C2×D3semidirect
42. C2×C3×C13C2×Q8semidirect
44. D39C2×Q8semidirect
57. C2×Dic6D13semidirect
58. C3×C13C22×Q8semidirect
60. C2×C13D3×Q8semidirect
72. Dic6C2×D13semidirect
79. C13C2×D3×Q8semidirect
97. C2×C3Q8×D13semidirect
107. C3C2×Q8×D13semidirect
109. C2D39⋊Q8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D392
C2×C13×Dic62
C2×C3×Dic262
C2×#646052
C2×#646012
D39⋊Q82
C2×Q8×D133
C2×D3×Q813