Finite Group Databasebeta

← C13⋊C3×#5997⋊C3 #37524875

Subgroups — C13⋊C3×#5997⋊C3 #37524875

Order 22932.

168 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 27 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×#64424C211yesmaximal, characteristic
2C13⋊C3×#5997C311yesmaximal, characteristic, complemented
3#21439684C311yesmaximal, characteristic, complemented
4#21439683C311yesmaximal, characteristic, complemented
5C13×#5997⋊C3C311yesmaximal, characteristic, complemented
6C13⋊C3×#3861C411yescharacteristic, complemented, Hall
7C13⋊C3×C7⋊D7C2×C311yescharacteristic
8#16838449C2×C311yescharacteristic
9#16838448C2×C311yescharacteristic
10C13×#64424C2×C311yescharacteristic
11C13×#5997C3211yescharacteristic, complemented, Hall
12#14274263C3×C411yescharacteristic, complemented
13#14274262C3×C411yescharacteristic, complemented
14C13×#3861C3×C411yescharacteristic, complemented
15C72×C13⋊C3C3×C411yescharacteristic, complemented
16C3×#5997⋊C3—131nomaximal, Hall
17C13⋊C3×AGL(1,𝔽7)—143no—
18C13⋊C3×AGL(1,𝔽7)—141no—
19C13×C7⋊D7C2×C3211yescharacteristic
20C3×#64424—131no—
21ΓL(1,𝔽8)×C13⋊C3—143no—
22ΓL(1,𝔽8)×C13⋊C3—141no—
23C72×C13C32×C411yescharacteristic, complemented, Hall
24C3×#5997—131no—
25#5997⋊C3—131no—
26#5997⋊C3—131no—
27#5997⋊C3C13⋊C311yescharacteristic, direct product factor
28#10587721—141no—
29#10587721—143no—
30#10587720—141no—
31#10587720—143no—
32C13×AGL(1,𝔽7)—141no—
33C13×AGL(1,𝔽7)—143no—
34D7×C13⋊C3—423no—
35D7×C13⋊C3—421no—
36C3×C4×C13⋊C3—491nomaximal, Hall
37C3×#3861—131noHall
38C3×C7⋊D7—131no—
39#64424—131no—
40#64424—131no—
41#64424C2×C13⋊C311yescharacteristic
42#63271—141no—
43#63271—143no—
44#63270—141no—
45#63270—143no—
46C7×C13⋊C3—23no—
47C7×C13⋊C3—21no—
48C13×ΓL(1,𝔽8)—141no—
49C13×ΓL(1,𝔽8)—143no—
50C2×C3×C13⋊C3—491no—
51#5997C3×C13⋊C311yescharacteristic, complemented, Hall
52C13×D7—421no—
53C13×D7—423no—
54C3×C4×C13—491no—
55C4×C13⋊C3—491no—
56C4×C13⋊C3—491no—
57C4×C13⋊C3—1471no—
58C3×C72—131no—
59#3861—131no—
60#3861—131no—
61#3861C4×C13⋊C311yescharacteristic, complemented
62C3×AGL(1,𝔽7)—1823no—
63C3×AGL(1,𝔽7)—1821no—
64C3×C13⋊C3—491noHall
65C7⋊D7C2×C3×C13⋊C311yescharacteristic
66C7×C13—21no—
67C7×C13—23no—
68C2×C3×C13—491no—
69C2×C13⋊C3—491no—
70C2×C13⋊C3—491no—
71C2×C13⋊C3—1471no—
72C3×ΓL(1,𝔽8)—1823no—
73C3×ΓL(1,𝔽8)—1821no—
74C4×C13—1471noHall
75C72C3×C4×C13⋊C311yescharacteristic, complemented, Sylow
76C3×D7—5463no—
77C3×D7—1821no—
78AGL(1,𝔽7)—141no—
79AGL(1,𝔽7)—143no—
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, direct product factor
88C32×C4—6371noHall
89C2×C13—1471no—
90C3×C7—263no—
91C3×C7—261no—
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—141no—
100D7—423no—
101C13C3×#5997⋊C311yescharacteristic, complemented, Sylow
102C3×C4—491no—
103C3×C4—19111no—
104C3×C4—6371no—
105C3×C4—6371no—
106C32—6371noSylow
107C7—21no—
108C7—23no—
109C2×C3—491no—
110C2×C3—19111no—
111C2×C3—6371no—
112C2×C3—6371no—
113C4—1471noSylow
114C3—131no—
115C3—491no—
116C3—6371no—
117C3—6371no—
118C2—1471no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C13C32×C4
prime radicalC13⋊C3×#64424C2
cosocleC13×C7⋊D7C2×C32
LCSG ▷ C72×C13
UCSC1

Complements

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

NH ≅ G/Ntype
2. C13⋊C3×#5997C3semidirect
3. #21439684C3semidirect
4. #21439683C3semidirect
5. C13×#5997⋊C3C3semidirect
6. C13⋊C3×#3861C4semidirect
11. C13×#5997C32semidirect
12. #14274263C3×C4semidirect
13. #14274262C3×C4semidirect
14. C13×#3861C3×C4semidirect
15. C72×C13⋊C3C3×C4semidirect
23. C72×C13C32×C4semidirect
27. #5997⋊C3C13⋊C3direct (N × H)
51. #5997C3×C13⋊C3semidirect
61. #3861C4×C13⋊C3semidirect
75. C72C3×C4×C13⋊C3semidirect
87. C13⋊C3#5997⋊C3direct (N × H)
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
C13⋊C3×#59973
#214396843
#214396833
C13×#5997⋊C33
C3×#5997⋊C313
C3×C4×C13⋊C349