Finite Group Databasebeta

← #37524682

Subgroups — #37524682

Order 22932.

104 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 19 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
1C2×#19153212C211yesmaximal, characteristic
2C13×#10596868C311yesmaximal, characteristic, complemented
3#21439534—31nomaximal
4#19153212C411yescharacteristic, complemented, Hall
5C2×C13×#3862C2×C311yescharacteristic
6C2×#14274263D311yescharacteristic
7C2×C7×#63271—21no—
8C7×C13×Dic7—31noHall
9C13×#3862C3×C411yescharacteristic, complemented
10#14274263Dic311yescharacteristic, complemented
11C7×#63271—21no—
12#10596868⋊C3—131nomaximal, Hall
13C2×ΓL(1,𝔽8)×C13⋊C3—141no—
14C2×C72×C13C3×D311yescharacteristic
15C4×#63270—211no—
16#11763961—211no—
17C2×ΓL(1,𝔽8)2—131no—
18ΓL(1,𝔽8)×C13⋊C3—141no—
19C72×C13C3×Dic311yescharacteristic, complemented, Hall
20#10596873—391no—
21#10596868C13⋊C311yescharacteristic, complemented
22C2×#63271—21no—
23C2×#63270—141no—
24C2×#63270—421no—
25C2×#63270—421no—
26C2×C13×ΓL(1,𝔽8)—141no—
27C2×C7×C13⋊C3—141no—
28Dic3×C13⋊C3—491nomaximal, Hall
29ΓL(1,𝔽8)2—131noHall
30C4×C7×C13—211no—
31C13×Dic7—31no—
32C2×#3862C2×C13⋊C311yescharacteristic
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—
41C2×C3×C13⋊C3—491no—
42C7×Dic7—31noHall
43C2×C7×C13—21no—
44C2×C7×C13—61no—
45C2×C7×C13—61no—
46Dic3×C13—491no—
47C4×C13⋊C3—1471no—
48#3862C4×C13⋊C311yescharacteristic, complemented
49#3861—131no—
50C7×ΓL(1,𝔽8)—261no—
51C2×C3×ΓL(1,𝔽8)—1821no—
52C3×C13⋊C3—491noHall
53C2×C72D3×C13⋊C311yescharacteristic
54C7×C13—21no—
55C7×C13—61no—
56C7×C13—61no—
57C4×ΓL(1,𝔽8)—2731no—
58ΓL(1,𝔽8)⋊C4—2731no—
59C2×C3×C13—981no—
60C2×C13⋊C3—141no—
61C2×C13⋊C3—981no—
62C3×ΓL(1,𝔽8)—1821no—
63C4×C13—211noHall
64C72Dic3×C13⋊C311yescharacteristic, complemented, Sylow
65C2×C3×C7—1821no—
66C2×ΓL(1,𝔽8)—141no—
67C2×ΓL(1,𝔽8)—261no—
68C2×ΓL(1,𝔽8)—5461no—
69C2×ΓL(1,𝔽8)—5461no—
70C2×ΓL(1,𝔽8)—1821no—
71C3×C13—981no—
72C13⋊C3—141no—
73C13⋊C3—981no—
74C3×Dic3—6371noHall
75C4×C7—211no—
76Dic7—31no—
77C2×C13#64418⋊C311yescharacteristic
78C3×C7—1821no—
79ΓL(1,𝔽8)—141no—
80ΓL(1,𝔽8)—261no—
81ΓL(1,𝔽8)—5461no—
82ΓL(1,𝔽8)—5461no—
83ΓL(1,𝔽8)—1821no—
84C2×C32—12741no—
85C2×C7—21no—
86C2×C7—31no—
87C2×C7—61no—
88C13#10596868⋊C311yescharacteristic, complemented, Sylow
89C3×C4—19111no—
90Dic3—491no—
91C32—12741noSylow
92C7—21no—
93C7—31no—
94C7—61no—
95C2×C3—981no—
96C2×C3—1821no—
97C2×C3—12741no—
98C4—211noSylow
99C3—981no—
100C3—1821no—
101C3—12741no—
102C2#2603956411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#26039564
commutator, hypocenterC13×#3862C3×C4
Fitting, socleC2×C72×C13C3×D3
prime radicalC2×#19153212C2
cosocleC2×C13×#3862C2×C3
LCSG ▷ C13×#3862
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. C13×#10596868C3semidirect
4. #19153212C4semidirect
9. C13×#3862C3×C4semidirect
10. #14274263Dic3semidirect
19. C72×C13C3×Dic3semidirect
21. #10596868C13⋊C3semidirect
48. #3862C4×C13⋊C3semidirect
64. C72Dic3×C13⋊C3semidirect
88. C13#10596868⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×#191532122
C13×#105968683
#214395343
#10596868⋊C313
Dic3×C13⋊C349