Finite Group Databasebeta

← C37×#10624929 #41004718

Subgroups — C37×#10624929 #41004718

Order 26973.

960 conjugacy classes of subgroups; only the 470 normal subgroups are shown.

normal subgroups only

This group has 960 conjugacy classes of subgroups — too many to draw. Only its 470 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×#737C313yesmaximal, complemented
2C3×C37×#737C311yesmaximal, characteristic, complemented
3C37×#6913C3118yesmaximal, complemented
4C37×#6912C312yesmaximal, complemented
5C37×#6911C311yesmaximal, characteristic, complemented
6C37×#6910C313yesmaximal, complemented
7C37×#6909C313yesmaximal, complemented
8C37×#6908C319yesmaximal, complemented
9C37×#737—312no—
10C37×#737—36no—
11C37×#737—36no—
12C37×#737—33no—
13C37×#737C3219yescomplemented
14C37×#737C32118yescomplemented
15C3×3−1+2×C37—36no—
16C3×3−1+2×C37C3216yes—
17C3×3−1+2×C37C3211yescharacteristic
18C3×3−1+2×C37C3211yescharacteristic
19C3×3−1+2×C37C3216yescomplemented
20C3×H(3,𝔽3)×C37C3211yescharacteristic
21C3×H(3,𝔽3)×C37C3213yes—
22C32×C9×C37—33no—
23C32×C9×C37C3211yescharacteristic
24C32×C9×C37C3213yescomplemented
25C37×#733C32118yescomplemented
26C37×#732C3219yes—
27C37×#731C32127yescomplemented
28C37×AΣL(1,𝔽27)C32127yescomplemented
29C33×C37—33no—
30C33×C37C3313yes—
31C33×C37C3311yescharacteristic
323−1+2×C37—312no—
333−1+2×C37—33no—
343−1+2×C37—33no—
353−1+2×C37—318no—
363−1+2×C37—336no—
373−1+2×C37—318no—
383−1+2×C37C33118yes—
39H(3,𝔽3)×C37—33no—
40H(3,𝔽3)×C37—36no—
41H(3,𝔽3)×C37C3319yes—
42C3×C9×C37—36no—
43C3×C9×C37—318no—
44C3×C9×C37—36no—
45C3×C9×C37—39no—
46C3×C9×C37—33no—
47C3×C9×C37H(3,𝔽3)16yes—
48C3×C9×C37H(3,𝔽3)13yes—
49C3×C9×C37C3313yes—
50C3×C9×C37C3313yes—
51C3×C9×C37C3312yes—
52C3×C9×C37C3311yescharacteristic
53#10624929C3711yesmaximal, characteristic, direct product factor, Sylow
54C32×C37—33no—
55C32×C37—39no—
56C32×C37—91no—
57C32×C37—93no—
58C32×C37—99no—
59C32×C37C3×H(3,𝔽3)13yes—
60C32×C37C3411yescharacteristic
61C9×C37—318no—
62C9×C37—33no—
63C9×C37—33no—
64C9×C37C3×H(3,𝔽3)16yes—
65C9×C37C3×H(3,𝔽3)12yes—
66C9×C37C3×H(3,𝔽3)11yescharacteristic
67C3×#737C3×C3713yescomplemented
68C3×#737C3×C3711yescharacteristic, complemented
69#6913C3×C37118yescomplemented
70#6912C3×C3712yescomplemented
71#6911C3×C3711yescharacteristic, complemented
72#6910C3×C3713yescomplemented
73#6909C3×C3713yescomplemented
74#6908C3×C3719yescomplemented
75C3×C37—33no—
76C3×C37—31no—
77C3×C37—93no—
78C3×C37—99no—
79C3×C37C32×H(3,𝔽3)11yescharacteristic
80#737—36no—
81#737—312no—
82#737—33no—
83#737—36no—
84#737C32×C37118yescomplemented
85#737C32×C3719yescomplemented
86C3×3−1+2—36no—
87C3×3−1+2C32×C3716yes—
88C3×3−1+2C32×C3711yescharacteristic
89C3×3−1+2C32×C3711yescharacteristic
90C3×3−1+2C32×C3716yescomplemented
91C3×H(3,𝔽3)C32×C3711yescharacteristic
92C3×H(3,𝔽3)C32×C3713yes—
93C32×C9—33no—
94C32×C9C32×C3711yescharacteristic
95C32×C9C32×C3713yescomplemented
96#733C32×C37118yescomplemented
97#732C32×C3719yes—
98#731C32×C37127yescomplemented
99AΣL(1,𝔽27)C32×C37127yescomplemented
100C37#1062492911yescharacteristic, direct product factor, Sylow
101C33—33no—
102C33C33×C3713yes—
103C33C33×C3711yescharacteristic
1043−1+2—312no—
1053−1+2—33no—
1063−1+2—33no—
1073−1+2—336no—
1083−1+2—318no—
1093−1+2—318no—
1103−1+2C33×C37118yes—
111H(3,𝔽3)—33no—
112H(3,𝔽3)—36no—
113H(3,𝔽3)C33×C3719yes—
114C3×C9—36no—
115C3×C9—39no—
116C3×C9—318no—
117C3×C9—33no—
118C3×C9—36no—
119C3×C9H(3,𝔽3)×C3713yes—
120C3×C9H(3,𝔽3)×C3716yes—
121C3×C9C33×C3713yes—
122C3×C9C33×C3713yes—
123C3×C9C33×C3711yescharacteristic
124C3×C9C33×C3712yes—
125C32—33no—
126C32—39no—
127C32—91no—
128C32—93no—
129C32—99no—
130C32C3×H(3,𝔽3)×C3713yes—
131C32C34×C3711yescharacteristic
132C9—318no—
133C9—33no—
134C9—33no—
135C9C3×H(3,𝔽3)×C3711yescharacteristic
136C9C3×H(3,𝔽3)×C3716yes—
137C9C3×H(3,𝔽3)×C3712yes—
138C3—33no—
139C3—31no—
140C3—99no—
141C3—93no—
142C3C32×H(3,𝔽3)×C3711yescharacteristic
subgroupG/H
centerC9×C37C3×H(3,𝔽3)
commutator, Frattini, cosocleC32C34×C37
socleC3×C37C32×H(3,𝔽3)
LCSG ▷ C32 ▷ C3 ▷ C1
UCSC1 ◁ C9×C37 ◁ C32×C9×C37 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×C37×#737C3semidirect
2. C3×C37×#737C3semidirect
3. C37×#6913C3semidirect
4. C37×#6912C3semidirect
5. C37×#6911C3semidirect
6. C37×#6910C3semidirect
7. C37×#6909C3semidirect
8. C37×#6908C3semidirect
13. C37×#737C32semidirect
14. C37×#737C32semidirect
19. C3×3−1+2×C37C32semidirect
24. C32×C9×C37C32semidirect
25. C37×#733C32semidirect
27. C37×#731C32semidirect
28. C37×AΣL(1,𝔽27)C32semidirect
53. #10624929C37direct (N × H)
67. C3×#737C3×C37semidirect
68. C3×#737C3×C37semidirect
69. #6913C3×C37semidirect
70. #6912C3×C37semidirect
71. #6911C3×C37semidirect
72. #6910C3×C37semidirect
73. #6909C3×C37semidirect
74. #6908C3×C37semidirect
84. #737C32×C37semidirect
85. #737C32×C37semidirect
90. C3×3−1+2C32×C37semidirect
95. C32×C9C32×C37semidirect
96. #733C32×C37semidirect
98. #731C32×C37semidirect
99. AΣL(1,𝔽27)C32×C37semidirect
100. C37#10624929direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C37×#7373
C37×#69133
C37×#69123
C37×#69113
C37×#69103
C37×#69093
C37×#69083
#1062492937