Finite Group Databasebeta

← D3×D13×#3862 #37525367

Subgroups — D3×D13×#3862 #37525367

Order 22932.

216 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 50 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
1D39×#3862C211yesmaximal, characteristic, complemented
2D3×C13×#3862C211yesmaximal, characteristic, complemented
3C3×D13×#3862C211yesmaximal, characteristic, complemented
4D3×C72×D13C311yesmaximal, characteristic, complemented
5C2×D13×#3862—31nomaximal
6C3×C13×#3862C2211yescharacteristic, complemented, Hall
7C72×D39C2×C311yescharacteristic, complemented
8D3×C72×C13C2×C311yescharacteristic, complemented
9C3×C72×D13C2×C311yescharacteristic, complemented
10C2×C13×#3862—31no—
11D13×#3862—21no—
12D13×#3862—31no—
13D13×#3862D311yescharacteristic, direct product factor
14D3×ΓL(1,𝔽8)×D13—72nomaximal
15C2×C72×D13—31noHall
16C3×C72×C13C22×C311yescharacteristic, complemented
17C13×#3862—21no—
18C13×#3862C2×D311yescharacteristic, complemented
19C2×D3×#3862—131nomaximal, Hall
20ΓL(1,𝔽8)×D39—72no—
21D3×C13×ΓL(1,𝔽8)—72no—
22C3×ΓL(1,𝔽8)×D13—72no—
23C2×C72×C13—31no—
24C72×D13—31no—
25C72×D13C3×D311yescharacteristic, complemented
26D3×C7×D13—32no—
27D3×C7×D13ΓL(1,𝔽8)12yescomplemented
28C2×ΓL(1,𝔽8)×D13—212no—
29C2×C3×#3862—131no—
30D3×#3862—131no—
31D3×#3862D1311yescharacteristic, direct product factor
32C3×C13×ΓL(1,𝔽8)—72no—
33C72×C13C2×C3×D311yescharacteristic, complemented, Hall
34C2×D3×C72—131no—
35C22×#3862—391no—
36C7×D39—32no—
37C7×D39C2×ΓL(1,𝔽8)12yescomplemented
38D3×C7×C13—32no—
39D3×C7×C13C2×ΓL(1,𝔽8)12yescomplemented
40C3×C7×D13—32no—
41C3×C7×D13C2×ΓL(1,𝔽8)12yescomplemented
42C2×C13×ΓL(1,𝔽8)—212no—
43ΓL(1,𝔽8)×D13—72no—
44ΓL(1,𝔽8)×D13—142no—
45ΓL(1,𝔽8)×D13—212no—
46C3×D3×D13—491noHall
47C3×#3862C2×D1311yescharacteristic, complemented, Hall
48C2×C7×D13—32no—
49C2×C7×D13—92no—
50C2×C3×C72—131no—
51D3×C72—131no—
52D3×C72C3×D1311yescharacteristic, complemented
53C2×#3862—31no—
54C2×#3862—131no—
55C2×#3862—261no—
56C2×#3862—391no—
57C3×C7×C13—32no—
58C3×C7×C13C22×ΓL(1,𝔽8)12yescomplemented
59C13×ΓL(1,𝔽8)—72no—
60C13×ΓL(1,𝔽8)—142no—
61C2×D3×ΓL(1,𝔽8)—912no—
62C3×D39—491no—
63C3×D3×C13—491no—
64C32×D13—491no—
65C22×C72—391noHall
66C2×C7×C13—32no—
67C2×C7×C13—92no—
68C7×D13—32no—
69C7×D13—32no—
70C7×D13—92no—
71C7×D13D3×ΓL(1,𝔽8)12yescomplemented
72C2×C3×D13—1471no—
73D3×D13#386211yescharacteristic, direct product factor
74C3×C72C2×C3×D1311yescharacteristic, complemented
75#3862—21no—
76#3862D3×D1311yescharacteristic, direct product factor
77C2×C3×ΓL(1,𝔽8)—912no—
78D3×ΓL(1,𝔽8)—72no—
79D3×ΓL(1,𝔽8)—912no—
80C32×C13—491noHall
81C2×C72—31no—
82C2×C72—131no—
83C2×C72—391no—
84C7×C13—32no—
85C7×C13C2×D3×ΓL(1,𝔽8)12yescomplemented
86C2×D3×C7—132no—
87C2×D3×C7—392no—
88C22×ΓL(1,𝔽8)—2732no—
89C2×C3×C13—1471no—
90D39C2×#386211yescharacteristic, complemented
91C3×D13—491no—
92C3×D13—981no—
93C3×D13—1471no—
94C3×D13C2×#386211yescharacteristic, complemented
95D3×C13C2×#386211yescharacteristic, complemented
96C3×ΓL(1,𝔽8)—72no—
97C2×D13—31noHall
98C72C3×D3×D1311yescharacteristic, complemented, Sylow
99C2×C3×C7—132no—
100C2×C3×C7—392no—
101D3×C7—32no—
102D3×C7—132no—
103D3×C7—392no—
104D3×C7ΓL(1,𝔽8)×D1312yescomplemented
105C2×ΓL(1,𝔽8)—2732no—
106C2×ΓL(1,𝔽8)—212no—
107C2×ΓL(1,𝔽8)—912no—
108C2×ΓL(1,𝔽8)—1822no—
109C3×C13—491no—
110C3×C13—981no—
111C3×C13C22×#386211yescharacteristic, complemented
112C2×C3×D3—6371noHall
113C22×C7—392no—
114C22×C7—1172no—
115C2×C13—31no—
116D13—31no—
117D13D3×#386211yescharacteristic, direct product factor
118C3×C7—32no—
119C3×C7C2×ΓL(1,𝔽8)×D1312yescomplemented
120ΓL(1,𝔽8)—72no—
121ΓL(1,𝔽8)—142no—
122C2×C32—6371no—
123C3×D3—491no—
124C3×D3—6371no—
125C2×C7—32no—
126C2×C7—92no—
127C2×C7—132no—
128C2×C7—392no—
129C2×C7—392no—
130C2×C7—1172no—
131C13C2×D3×#386211yescharacteristic, complemented, Sylow
132C22×C3—19111no—
133C2×D3—131no—
134C32—491noSylow
135C7—32no—
136C7D3×ΓL(1,𝔽8)×D1312yescomplemented
137C2×C3—131no—
138C2×C3—19111no—
139C2×C3—6371no—
140C2×C3—1471no—
141C2×C3—12741no—
142D3—131no—
143D3D13×#386211yescharacteristic, direct product factor
144C22—391noSylow
145C3—491no—
146C3—981no—
147C3C2×D13×#386211yescharacteristic, complemented
148C2—31no—
149C2—131no—
150C2—391no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C72×C13C22×C3
LCSG ▷ C3×C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
1. D39×#3862C2semidirect
2. D3×C13×#3862C2semidirect
3. C3×D13×#3862C2semidirect
4. D3×C72×D13C3semidirect
6. C3×C13×#3862C22semidirect
7. C72×D39C2×C3semidirect
8. D3×C72×C13C2×C3semidirect
9. C3×C72×D13C2×C3semidirect
13. D13×#3862D3direct (N × H)
16. C3×C72×C13C22×C3semidirect
18. C13×#3862C2×D3semidirect
25. C72×D13C3×D3semidirect
27. D3×C7×D13ΓL(1,𝔽8)semidirect
31. D3×#3862D13direct (N × H)
33. C72×C13C2×C3×D3semidirect
37. C7×D39C2×ΓL(1,𝔽8)semidirect
39. D3×C7×C13C2×ΓL(1,𝔽8)semidirect
41. C3×C7×D13C2×ΓL(1,𝔽8)semidirect
47. C3×#3862C2×D13semidirect
52. D3×C72C3×D13semidirect
58. C3×C7×C13C22×ΓL(1,𝔽8)semidirect
71. C7×D13D3×ΓL(1,𝔽8)semidirect
73. D3×D13#3862direct (N × H)
74. C3×C72C2×C3×D13semidirect
76. #3862D3×D13direct (N × H)
85. C7×C13C2×D3×ΓL(1,𝔽8)semidirect
90. D39C2×#3862semidirect
94. C3×D13C2×#3862semidirect
95. D3×C13C2×#3862semidirect
98. C72C3×D3×D13semidirect
104. D3×C7ΓL(1,𝔽8)×D13semidirect
111. C3×C13C22×#3862semidirect
117. D13D3×#3862direct (N × H)
119. C3×C7C2×ΓL(1,𝔽8)×D13semidirect
131. C13C2×D3×#3862semidirect
136. C7D3×ΓL(1,𝔽8)×D13semidirect
143. D3D13×#3862direct (N × H)
147. C3C2×D13×#3862semidirect

Maximal subgroups

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

subgroupindex
D39×#38622
D3×C13×#38622
C3×D13×#38622
D3×C72×D133
C2×D13×#38623
D3×ΓL(1,𝔽8)×D137
C2×D3×#386213