Finite Group Databasebeta

← #21439678⋊C3 #37524873

Subgroups — #21439678⋊C3 #37524873

Order 22932.

168 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 23 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
1(C13⋊C3)⋊#64424C211yesmaximal, characteristic
2#21439686C311yesmaximal, characteristic, complemented
3#21439682C311yesmaximal, characteristic, complemented
4#21439679C311yesmaximal, characteristic, complemented
5#21439678C311yesmaximal, characteristic, complemented
6C13⋊C3×#3861C411yescharacteristic, complemented, Hall
7(C13⋊C3)⋊(C7⋊D7)C2×C311yescharacteristic
8#16838450C2×C311yescharacteristic
9#16838447C2×C311yescharacteristic
10#16838446C2×C311yescharacteristic
11#14579330C3211yescharacteristic, complemented, Hall
12#14274263C3×C411yescharacteristic, complemented
13#14274262C3×C411yescharacteristic, complemented
14C13×#3861C3×C411yescharacteristic, complemented
15C72×C13⋊C3C3×C411yescharacteristic, complemented
16C3×#5997⋊C3—131nomaximal, Hall
17ΓL(1,𝔽8)⋊(D13⋊C3)—141no—
18ΓL(1,𝔽8)⋊(D13⋊C3)—143no—
19C7⋊D91C2×C3211yescharacteristic
20C3×#64424—131no—
21ΓL(1,𝔽8)×C13⋊C3—141no—
22ΓL(1,𝔽8)×C13⋊C3—143no—
23C72×C13C32×C411yescharacteristic, complemented, Hall
24C3×#5997—131no—
25#5997⋊C3—131no—
26#5997⋊C3—131no—
27#5997⋊C3—391no—
28#10587723—141no—
29#10587723—143no—
30#10587722—141no—
31#10587722—143no—
32ΓL(1,𝔽8)⋊D13—141no—
33ΓL(1,𝔽8)⋊D13—143no—
34(C13⋊C3)⋊D7—421no—
35(C13⋊C3)⋊D7—423no—
36C3×AGL(1,𝔽13)—491nomaximal, Hall
37C3×#3861—131noHall
38C3×C7⋊D7—131no—
39#64424—131no—
40#64424—131no—
41#64424—131no—
42#63271—141no—
43#63271—143no—
44#63270—141no—
45#63270—143no—
46C7×C13⋊C3—21no—
47C7×C13⋊C3—23no—
48C13×ΓL(1,𝔽8)—141no—
49C13×ΓL(1,𝔽8)—143no—
50C3×D13⋊C3—491no—
51#5997—391noHall
52D91—421no—
53D91—423no—
54C3×#261—491no—
55AGL(1,𝔽13)—491no—
56AGL(1,𝔽13)—491no—
57AGL(1,𝔽13)—1471no—
58C3×C72—131no—
59#3861—131no—
60#3861—131no—
61#3861AGL(1,𝔽13)11yescharacteristic, complemented
62C3×AGL(1,𝔽7)—1821no—
63C3×AGL(1,𝔽7)—1823no—
64C3×C13⋊C3—491noHall
65C7⋊D7—131no—
66C7×C13—21no—
67C7×C13—23no—
68C3×D13—491no—
69D13⋊C3—491no—
70D13⋊C3—491no—
71D13⋊C3—1471no—
72C3×ΓL(1,𝔽8)—1821no—
73C3×ΓL(1,𝔽8)—1823no—
74#261—1471noHall
75C72C3×AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
76C3×D7—5461no—
77C3×D7—5463no—
78AGL(1,𝔽7)—5461no—
79AGL(1,𝔽7)—5463no—
80AGL(1,𝔽7)—1821no—
81AGL(1,𝔽7)—1821no—
82AGL(1,𝔽7)—1823no—
83AGL(1,𝔽7)—1823no—
84C3×C13—491no—
85C13⋊C3—491no—
86C13⋊C3—491no—
87C13⋊C3#5997⋊C311yescharacteristic, complemented
88C32×C4—6371noHall
89D13—1471no—
90C3×C7—261no—
91C3×C7—263no—
92ΓL(1,𝔽8)—141no—
93ΓL(1,𝔽8)—143no—
94ΓL(1,𝔽8)—1821no—
95ΓL(1,𝔽8)—1823no—
96ΓL(1,𝔽8)—1821no—
97ΓL(1,𝔽8)—1823no—
98C2×C32—6371no—
99D7—5461no—
100D7—16383no—
101C13C3×#5997⋊C311yescharacteristic, complemented, Sylow
102C3×C4—19111no—
103C3×C4—19111no—
104C3×C4—6371no—
105C3×C4—6371no—
106C32—6371noSylow
107C7—21no—
108C7—23no—
109C2×C3—19111no—
110C2×C3—19111no—
111C2×C3—6371no—
112C2×C3—6371no—
113C4—57331noSylow
114C3—131no—
115C3—491no—
116C3—6371no—
117C3—6371no—
118C2—57331no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C13C32×C4
prime radical(C13⋊C3)⋊#64424C2
cosocleC7⋊D91C2×C32
LCSG ▷ C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
2. #21439686C3semidirect
3. #21439682C3semidirect
4. #21439679C3semidirect
5. #21439678C3semidirect
6. C13⋊C3×#3861C4semidirect
11. #14579330C32semidirect
12. #14274263C3×C4semidirect
13. #14274262C3×C4semidirect
14. C13×#3861C3×C4semidirect
15. C72×C13⋊C3C3×C4semidirect
23. C72×C13C32×C4semidirect
61. #3861AGL(1,𝔽13)semidirect
75. C72C3×AGL(1,𝔽13)semidirect
87. C13⋊C3#5997⋊C3semidirect
101. C13C3×#5997⋊C3semidirect

Maximal subgroups

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

subgroupindex
(C13⋊C3)⋊#644242
#214396863
#214396823
#214396793
#214396783
C3×#5997⋊C313
C3×AGL(1,𝔽13)49