Finite Group Databasebeta

← D13×#11725071 #37524488

Subgroups — D13×#11725071 #37524488

Order 22932.

112 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 19 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
1C13⋊#11725071C211yesmaximal, characteristic, complemented
2C13×#11725071C211yesmaximal, characteristic, complemented
3D13×#89205C211yesmaximal, characteristic, complemented
4C7×D13×D21—31nomaximal
5C13×#89205C2211yescharacteristic, complemented, Hall
6C7×D273—31no—
7C7×C13×D21—31no—
8C3×C72×D13D311yescharacteristic
9C7×D7×D13—91noHall
10C3×C72×C13C2×D311yescharacteristic
11C2×#11725071—131nomaximal, Hall
12D13×C7⋊C9—141no—
13C7×D91—91no—
14C7×C13×D7—91no—
15C72×D13D911yescharacteristic, complemented
16D13×D21—31no—
17D3×C7×D13—211no—
18C2×#89205—131no—
19#11725071—131no—
20#11725071D1311yescharacteristic, direct product factor
21C13×C7⋊C9—141no—
22C72×C13C2×D911yescharacteristic, complemented, Hall
23C2×C7×D21—391no—
24D273—31no—
25C13×D21—31no—
26C7×D39—211no—
27D3×C7×C13—211no—
28C3×C7×D13—21no—
29C3×C7×D13—31no—
30C3×C7×D13—61no—
31D9×D13—491nomaximal, Hall
32#89205C2×D1311yescharacteristic, complemented, Hall
33C2×C7×D13—631no—
34D7×D13—91no—
35C2×C3×C72—131no—
36C7×D21—31no—
37C7×D21—391no—
38C3×C7×C13—21no—
39C3×C7×C13—31no—
40C3×C7×C13—61no—
41D117—491no—
42C9×D13—981no—
43C13×D9—491no—
44C2×C7×D7—1171noHall
45C2×C7×C13—631no—
46D91—91no—
47C7×D13—21no—
48C7×D13—31no—
49C7×D13—61no—
50C7×D13—631no—
51C13×D7—91no—
52D3×D13—211no—
53C3×C72D3×D1311yescharacteristic
54C2×C7⋊C9—1821no—
55C9×C13—981noHall
56C2×C72—131no—
57C7×D7—91no—
58C7×D7—1171no—
59C7×C13—21no—
60C7×C13—31no—
61C7×C13—61no—
62C2×D21—391no—
63C2×D3×C7—2731no—
64D39—211no—
65C3×D13#6441811yescharacteristic
66D3×C13—211no—
67C7⋊C9—141no—
68C2×D13—631noHall
69C72D9×D1311yescharacteristic, complemented, Sylow
70C2×C3×C7—261no—
71C2×C3×C7—391no—
72C2×C3×C7—781no—
73D21—31no—
74D21—391no—
75D3×C7—2731no—
76D3×C7—211no—
77C3×C13C2×#6441811yescharacteristic
78C2×D9—6371noHall
79C22×C7—8191no—
80C2×D7—1171no—
81C2×C13—631no—
82D13—631no—
83D13#1172507111yescharacteristic, direct product factor
84C3×C7—21no—
85C3×C7—31no—
86C3×C7—61no—
87C2×C9—12741no—
88D9—491no—
89D9—6371no—
90C2×C7—261no—
91C2×C7—391no—
92C2×C7—8191no—
93C2×C7—631no—
94C2×C7—781no—
95D7—91no—
96D7—1171no—
97C13C2×#1172507111yescharacteristic, complemented, Sylow
98C2×D3—2731no—
99C9—981noSylow
100C7—21no—
101C7—31no—
102C7—61no—
103C2×C3—131no—
104D3—2731no—
105D3—211no—
106C22—8191noSylow
107C3D13×#6441811yescharacteristic
108C2—131no—
109C2—8191no—
110C2—631no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC13×#89205C22
FrattiniC3D13×#64418
Fitting, socleC3×C72×C13C2×D3
LCSG ▷ C13×#89205
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊#11725071C2semidirect
2. C13×#11725071C2semidirect
3. D13×#89205C2semidirect
5. C13×#89205C22semidirect
15. C72×D13D9semidirect
20. #11725071D13direct (N × H)
22. C72×C13C2×D9semidirect
32. #89205C2×D13semidirect
69. C72D9×D13semidirect
83. D13#11725071direct (N × H)
97. C13C2×#11725071semidirect

Maximal subgroups

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

subgroupindex
C13⋊#117250712
C13×#117250712
D13×#892052
C7×D13×D213
C2×#1172507113
D9×D1349