Finite Group Databasebeta

← #37524860

Subgroups — #37524860

Order 22932.

104 conjugacy classes of subgroups; only the 15 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 15 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#26039556C211yesmaximal, characteristic
2#21439672C311yesmaximal, characteristic, complemented
3#21439623—31nomaximal
4#19153212C411yescharacteristic, complemented, Hall
5D13×#3862C2×C311yescharacteristic
6#16838473D311yescharacteristic
7C7×#10587717—21no—
8C7×C7⋊#261—31noHall
9C13×#3862C3×C411yescharacteristic, complemented
10#14274263Dic311yescharacteristic, complemented
11C7×#63271—21no—
12#10596868⋊C3—131nomaximal, Hall
13ΓL(1,𝔽8)×D13⋊C3—141no—
14C72×D13C3×D311yescharacteristic
15#11763985—211no—
16#11763982—211no—
17C2×ΓL(1,𝔽8)2—131no—
18ΓL(1,𝔽8)×C13⋊C3—141no—
19C72×C13C3×Dic311yescharacteristic, complemented, Hall
20#10596873—391no—
21#10596868—131no—
22#10587717—21no—
23#10587716—141no—
24#10587716—421no—
25#10587716—421no—
26ΓL(1,𝔽8)×D13—141no—
27C7×D13⋊C3—141no—
28C3⋊AGL(1,𝔽13)—491nomaximal, Hall
29ΓL(1,𝔽8)2—521noHall
30C7⋊#261—31no—
31C7×#261—211no—
32C2×#3862—131no—
33C2×#3861—131no—
34C2×C7×ΓL(1,𝔽8)—261no—
35#63271—21no—
36#63270—141no—
37#63270—421no—
38#63270—421no—
39C7×C13⋊C3—141no—
40C13×ΓL(1,𝔽8)—141no—
41C3×D13⋊C3—491no—
42C7×Dic7—391noHall
43C7×D13—21no—
44C7×D13—31no—
45C7×D13—31no—
46C3⋊#261—491no—
47AGL(1,𝔽13)—1471no—
48#3862AGL(1,𝔽13)11yescharacteristic, complemented
49#3861—521no—
50C7×ΓL(1,𝔽8)—521no—
51C2×C3×ΓL(1,𝔽8)—1821no—
52C3×C13⋊C3—491noHall
53C2×C72—131no—
54C7×C13—21no—
55C7×C13—31no—
56C7×C13—31no—
57C4×ΓL(1,𝔽8)—2731no—
58ΓL(1,𝔽8)⋊C4—2731no—
59C3×D13—981no—
60D13⋊C3—141no—
61D13⋊C3—981no—
62C3×ΓL(1,𝔽8)—3641no—
63#261—211noHall
64C72C3⋊AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
65C2×C3×C7—1821no—
66C2×ΓL(1,𝔽8)—261no—
67C2×ΓL(1,𝔽8)—5461no—
68C2×ΓL(1,𝔽8)—5461no—
69C2×ΓL(1,𝔽8)—1821no—
70C2×ΓL(1,𝔽8)—1821no—
71C3×C13—981no—
72C13⋊C3—141no—
73C13⋊C3—981no—
74C3×Dic3—6371noHall
75C4×C7—2731no—
76Dic7—391no—
77D13#64418⋊C311yescharacteristic
78C3×C7—3641no—
79ΓL(1,𝔽8)—141no—
80ΓL(1,𝔽8)—521no—
81ΓL(1,𝔽8)—10921no—
82ΓL(1,𝔽8)—10921no—
83ΓL(1,𝔽8)—3641no—
84C2×C32—6371no—
85C2×C7—261no—
86C2×C7—391no—
87C2×C7—781no—
88C13#10596868⋊C311yescharacteristic, complemented, Sylow
89C3×C4—19111no—
90Dic3—6371no—
91C32—6371noSylow
92C7—21no—
93C7—31no—
94C7—61no—
95C2×C3—1821no—
96C2×C3—12741no—
97C2×C3—12741no—
98C4—2731noSylow
99C3—981no—
100C3—1821no—
101C3—25481no—
102C2—131no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, hypocenterC13×#3862C3×C4
Fitting, socleC72×C13C3×Dic3
prime radical#26039556C2
cosocleD13×#3862C2×C3
LCSG ▷ C13×#3862
UCSC1

Complements

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

NH ≅ G/Ntype
2. #21439672C3semidirect
4. #19153212C4semidirect
9. C13×#3862C3×C4semidirect
10. #14274263Dic3semidirect
19. C72×C13C3×Dic3semidirect
48. #3862AGL(1,𝔽13)semidirect
64. C72C3⋊AGL(1,𝔽13)semidirect
88. C13#10596868⋊C3semidirect

Maximal subgroups

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

subgroupindex
#260395562
#214396723
#214396233
#10596868⋊C313
C3⋊AGL(1,𝔽13)49