Finite Group Databasebeta

← D13⋊C3×#64418 #37524869

Subgroups — D13⋊C3×#64418 #37524869

Order 22932.

152 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 22 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⋊C3×#64418C211yesmaximal, characteristic, complemented
2(C13⋊C3)⋊#64418C211yesmaximal, characteristic, complemented
3D13⋊C3×#3862C211yesmaximal, characteristic, complemented
4D13×#64418C311yesmaximal, characteristic, complemented
5C7×D7×D13⋊C3—31nomaximal
6C13⋊C3×#3862C2211yescharacteristic, complemented, Hall
7C13⋊#64418C2×C311yescharacteristic, complemented
8C13×#64418C2×C311yescharacteristic, complemented
9D13×#3862C2×C311yescharacteristic, complemented
10D13⋊#3862—21no—
11C7×D7×C13⋊C3—31no—
12C7×(C13⋊C3)⋊D7—31no—
13C72×D13⋊C3D311yescharacteristic, complemented
14C7×D7×D13—31noHall
15C13⋊#3862—21no—
16C13×#3862C22×C311yescharacteristic, complemented
17C72×C13⋊C3C2×D311yescharacteristic, complemented
18C2×C3×#64418—131nomaximal, Hall
19ΓL(1,𝔽8)×D13⋊C3—141no—
20C7×D91—31no—
21C7×C13×D7—31no—
22C72×D13C3×D311yescharacteristic, complemented
23C2×C7×D13⋊C3—211no—
24D7×D13⋊C3—31no—
25C2×C3×#3862—131no—
26C3×#64418—131no—
27C3×#64418—261no—
28ΓL(1,𝔽8)×C13⋊C3—141no—
29C72×C13C2×C3×D311yescharacteristic, complemented, Hall
30C2×C3×C7×D7—391no—
31C2×#64418—131no—
32C2×C7×C13⋊C3—211no—
33#10587717—141no—
34#10587716—141no—
35ΓL(1,𝔽8)×D13—141no—
36(C13⋊C3)⋊D7—31no—
37D7×C13⋊C3—31no—
38C7×D13⋊C3—21no—
39C7×D13⋊C3—31no—
40C7×D13⋊C3—61no—
41C7×D13⋊C3—211no—
42D3×D13⋊C3—491nomaximal, Hall
43C3×#3862—261noHall
44C2×C7×D13—211no—
45D7×D13—31no—
46C2×C3×C72—131no—
47C3×C7×D7—391no—
48C3×C7×D7—781no—
49C2×#3862—131no—
50C2×#3862—261no—
51#64418—131no—
52#64418D13⋊C311yescharacteristic, direct product factor
53#63271—141no—
54#63270—141no—
55C7×C13⋊C3—21no—
56C7×C13⋊C3—31no—
57C7×C13⋊C3—61no—
58C13×ΓL(1,𝔽8)—141no—
59C3⋊(D13⋊C3)—491no—
60D3×C13⋊C3—491no—
61C3×D13⋊C3—981no—
62C2×C7×D7—391noHall
63C2×C7×C13—211no—
64D91—31no—
65C7×D13—21no—
66C7×D13—61no—
67C7×D13—61no—
68C7×D13—211no—
69C13×D7—31no—
70D3×D13—491no—
71C2×D13⋊C3—211no—
72C3×C72—261no—
73#3862—521no—
74#3862C2×D13⋊C311yescharacteristic, complemented
75C2×C3×ΓL(1,𝔽8)—1821no—
76C3×C13⋊C3—981noHall
77C2×C72—131no—
78C7×D7—31no—
79C7×D7—391no—
80C7×C13—21no—
81C7×C13—61no—
82C7×C13—61no—
83C22×C3×C7—2731no—
84C2×C3×D7—391no—
85D39—491no—
86C3×D13—491no—
87D3×C13—491no—
88C2×C13⋊C3—211no—
89D13⋊C3—211no—
90D13⋊C3—981no—
91D13⋊C3#6441811yescharacteristic, direct product factor
92C3×ΓL(1,𝔽8)—3641no—
93C2×D13—211noHall
94C72D3×D13⋊C311yescharacteristic, complemented, Sylow
95C2×C3×C7—2731no—
96C2×C3×C7—261no—
97C2×C3×C7—5461no—
98C2×C3×C7—781no—
99C2×C3×C7—781no—
100C3×D7—391no—
101C3×D7—781no—
102C2×ΓL(1,𝔽8)—1821no—
103C2×ΓL(1,𝔽8)—1821no—
104C2×ΓL(1,𝔽8)—1821no—
105C3×C13—491no—
106C13⋊C3—981no—
107C13⋊C3C2×#6441811yescharacteristic, complemented
108C2×C3×D3—6371noHall
109C22×C7—2731no—
110C2×D7—391no—
111C2×C13—211no—
112D13—211no—
113D13C3×#6441811yescharacteristic, complemented
114C3×C7—521no—
115C3×C7—1561no—
116C3×C7—1561no—
117ΓL(1,𝔽8)—141no—
118ΓL(1,𝔽8)—3641no—
119ΓL(1,𝔽8)—3641no—
120C2×C32—12741no—
121C3×D3—6371no—
122C3×D3—12741no—
123C2×C7—2731no—
124C2×C7—211no—
125C2×C7—261no—
126C2×C7—781no—
127C2×C7—781no—
128D7—31no—
129D7—391no—
130C13C2×C3×#6441811yescharacteristic, complemented, Sylow
131C22×C3—2731no—
132C2×D3—6371no—
133C32—25481noSylow
134C7—21no—
135C7—61no—
136C7—61no—
137C2×C3—131no—
138C2×C3—2731no—
139C2×C3—5461no—
140C2×C3—12741no—
141C2×C3—12741no—
142D3—491no—
143D3—6371no—
144C22—2731noSylow
145C3—261no—
146C3—981no—
147C3—25481no—
148C2—131no—
149C2—2731no—
150C2—211no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC13×#3862C22×C3
Fitting, socleC72×C13C2×C3×D3
LCSG ▷ C13×#3862
UCSC1

Complements

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

NH ≅ G/Ntype
1. C13⋊C3×#64418C2semidirect
2. (C13⋊C3)⋊#64418C2semidirect
3. D13⋊C3×#3862C2semidirect
4. D13×#64418C3semidirect
6. C13⋊C3×#3862C22semidirect
7. C13⋊#64418C2×C3semidirect
8. C13×#64418C2×C3semidirect
9. D13×#3862C2×C3semidirect
13. C72×D13⋊C3D3semidirect
16. C13×#3862C22×C3semidirect
17. C72×C13⋊C3C2×D3semidirect
22. C72×D13C3×D3semidirect
29. C72×C13C2×C3×D3semidirect
52. #64418D13⋊C3direct (N × H)
74. #3862C2×D13⋊C3semidirect
91. D13⋊C3#64418direct (N × H)
94. C72D3×D13⋊C3semidirect
107. C13⋊C3C2×#64418semidirect
113. D13C3×#64418semidirect
130. C13C2×C3×#64418semidirect

Maximal subgroups

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

subgroupindex
C13⋊C3×#644182
(C13⋊C3)⋊#644182
D13⋊C3×#38622
D13×#644183
C7×D7×D13⋊C33
C2×C3×#6441813
D3×D13⋊C349