Finite Group Databasebeta

← #45686282

Subgroups — #45686282

Order 33300.

160 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 26 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
1C3⋊(C37⋊#3874)C211yesmaximal, characteristic, complemented
2C37×C3⋊#3874C211yesmaximal, characteristic, complemented
3C3×#19149853C211yesmaximal, characteristic, complemented
4D15⋊D185—31nomaximal
5#3874⋊D37—33nomaximal
6C3×C37×C52⋊C3C2211yescharacteristic, complemented, Hall
7C5×D555—31no—
8C5×D15×C37—31no—
9C3×C5⋊D185D311yescharacteristic, complemented
10#19149853D313yescomplemented
11C37⋊#3874—33no—
12C37×#3874—33no—
13D5×D185—91noHall
14C37×C52⋊C3C2×D313yescomplemented
15C3×C52×C37C2×D311yescharacteristic, complemented
16D15⋊D37—151no—
17D3×D185—151no—
18C5⋊D185C3⋊D311yescharacteristic, complemented
19C5×D185—91no—
20C5×D5×C37—91no—
21C3⋊D3×D37—251nomaximal, Hall
22D555—31no—
23D15×C37—31no—
24C5×D111—151no—
25C5×D3×C37—151no—
26C3×D185—151no—
27C3×D185—151no—
28C52×C37C2×C3⋊D311yescharacteristic, complemented, Hall
29((C5⋊D5)⋊C3)⋊D3—371nomaximal, Hall
30C2×D185—451no—
31D5×D37—451no—
32C3⋊D111—251no—
33C3⋊D3×C37—251no—
34C32×D37—251no—
35C3×C5×C37—31no—
36C3×C5×C37—31no—
37C3×(C5⋊D5)⋊C3—371no—
38C3⋊#3874—371no—
39C3⋊#3874D3711yescharacteristic, complemented
40D3×D37—751no—
41D3×D37—753no—
42C2×C5×C37—451no—
43D185—91no—
44D185—151no—
45D185—151no—
46C5×D37—451no—
47D5×C37—91no—
48C32×C37—251noHall
49D15⋊D5—1111no—
50#3874⋊C2—1113no—
51C3×C52⋊C3C2×D3711yescharacteristic, complemented, Hall
52D111—151no—
53D111—753no—
54C3×D37—253no—
55C3×D37—251no—
56D3×C37—151no—
57D3×C37—753no—
58C5×C37—31no—
59C5×C37—31no—
60C5×D15—31no—
61C5×D15—1111no—
62C3×C5⋊D5—371no—
63(C5⋊D5)⋊C3—373no—
64#3874—33no—
65#3874—1113no—
66C2×D37—2251noHall
67C3×C37—253no—
68C3×C37#3874⋊C211yescharacteristic, complemented
69D52—3331noHall
70C3×C52D3×D3711yescharacteristic, complemented
71C52⋊C3D3×D3713yescomplemented
72C2×C37—451no—
73D37—251no—
74D37—451no—
75D3×D5—5551no—
76D3×D5—5551no—
77C5⋊D5—371no—
78C5×D5—91no—
79C5×D5—3331no—
80C37((C5⋊D5)⋊C3)⋊D311yescharacteristic, complemented, Sylow
81C2×C3⋊D3—9251noHall
82D15—31no—
83D15—1111no—
84C3×D5—5551no—
85C3×D5—5551no—
86C5×D3—151no—
87C5×D3—5551no—
88C52C3⋊D3×D3711yescharacteristic, complemented, Sylow
89C2×D5—16651no—
90C2×D5—16651no—
91C2×C32—9251no—
92C3⋊D3—251no—
93C3⋊D3—9251no—
94C3×C5—31no—
95C3×C5—31no—
96C2×D3—27751no—
97C2×D3—27753no—
98C2×C5—451no—
99C2×C5—16651no—
100D5—91no—
101D5—5551no—
102D5—5551no—
103D5—3331no—
104C32—251noSylow
105C2×C3—9253no—
106C2×C3—9251no—
107D3—151no—
108D3—5551no—
109D3—753no—
110D3—27753no—
111C5—31no—
112C5—31no—
113C22—83251noSylow
114C3—253no—
115C3#3874⋊D3711yescharacteristic, complemented
116C2—451no—
117C2—16651no—
118C2—9251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC3×C37×C52⋊C3C22
Fitting, socleC3×C52×C37C2×D3
LCSG ▷ C3×C37×C52⋊C3
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3⋊(C37⋊#3874)C2semidirect
2. C37×C3⋊#3874C2semidirect
3. C3×#19149853C2semidirect
6. C3×C37×C52⋊C3C22semidirect
9. C3×C5⋊D185D3semidirect
10. #19149853D3semidirect
14. C37×C52⋊C3C2×D3semidirect
15. C3×C52×C37C2×D3semidirect
18. C5⋊D185C3⋊D3semidirect
28. C52×C37C2×C3⋊D3semidirect
39. C3⋊#3874D37semidirect
51. C3×C52⋊C3C2×D37semidirect
68. C3×C37#3874⋊C2semidirect
70. C3×C52D3×D37semidirect
71. C52⋊C3D3×D37semidirect
80. C37((C5⋊D5)⋊C3)⋊D3semidirect
88. C52C3⋊D3×D37semidirect
115. C3#3874⋊D37semidirect

Maximal subgroups

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

subgroupindex
C3⋊(C37⋊#3874)2
C37×C3⋊#38742
C3×#191498532
D15⋊D1853
#3874⋊D373
C3⋊D3×D3725
((C5⋊D5)⋊C3)⋊D337