Finite Group Databasebeta

← #18009674

Subgroups — #18009674

Order 4736.

124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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
1D37⋊#108C211yesmaximal, characteristic
2C2×#11924606C211yesmaximal, characteristic
3M32×D37C211yesmaximal, characteristic
4C2×#10596953—21no—
5D37⋊M16—21no—
6#11924607C412yes—
7#11924606—21no—
8#11924606—21no—
9#11924606C412yes—
10C2×C8×D37C2211yescharacteristic
11#11924476C411yescharacteristic
12#11924475—21no—
13C16×D37—21no—
14M32×C37C411yescharacteristic
15C2×C4×D37D411yescharacteristic
16#10596957—41no—
17C2×#64438—41no—
18#10596953—22no—
19#10596953—22no—
20#10596953—41no—
21D37⋊C8—41no—
22C2×C8×C37C2×C411yescharacteristic
23C2×#64436Q811yescharacteristic
24C8×D37C2×C411yescharacteristic
25C8×D37C2×C411yescharacteristic
26C8×D37D411yescharacteristic
27C8×D37D411yescharacteristic
28C16×C37—21no—
29#10596925—21no—
30C22×D37Q1611yescharacteristic
31C2×C4×C37C4⋊C411yescharacteristic
32C2×Dic37D811yescharacteristic
33C4×D37C22⋊C411yescharacteristic
34C4×D37C22⋊C411yescharacteristic
35C4×D37SD1611yescharacteristic
36C4×D37SD1611yescharacteristic
37#64438—42no—
38#64438—42no—
39C8×C37C4211yescharacteristic
40C8×C37C22⋊C411yescharacteristic
41#64436C4⋊C411yescharacteristic
42#64436C4⋊C411yescharacteristic
43C22×C37#10711yescharacteristic
44C2×D37—41no—
45C2×D37#10311yescharacteristic
46C2×D37#10311yescharacteristic
47C4×C37#9511yescharacteristic
48C4×C37#10611yescharacteristic
49Dic37#10211yescharacteristic
50Dic37#10211yescharacteristic
51#1388—371nomaximal, Sylow
52C2×C37—21no—
53C2×C37#34011yescharacteristic
54D37—21no—
55D37—21no—
56C2×M32—371no—
57C2×#108—371no—
58C2×#108—371no—
59C37#138811yescharacteristic, complemented, Sylow
60C2×M16—741no—
61C2×M16—741no—
62C22×C8—371no—
63M32—371no—
64M32—741no—
65M32#386611yescharacteristic
66C2×C16—741no—
67#108—372no—
68#108—372no—
69#108—741no—
70#108—741no—
71C22×C4—371no—
72M16—742no—
73M16—742no—
74M16—1481no—
75M16—1481no—
76C2×C8—371no—
77C2×C8—371no—
78C2×C8—371no—
79C2×C8—371no—
80C2×C8—371no—
81C2×C8—1481no—
82C2×C8—1481no—
83C2×C8C2×#386611yescharacteristic
84C16—21no—
85C16—741no—
86C23—371no—
87C2×C4—371no—
88C2×C4—371no—
89C2×C4—371no—
90C2×C4—371no—
91C2×C4—371no—
92C2×C4C4⋊#386611yescharacteristic
93C8—371no—
94C8—371no—
95C8—1482no—
96C8—1482no—
97C8C4×#386611yescharacteristic
98C8C22⋊#386611yescharacteristic
99C22—371no—
100C22—371no—
101C22—1481no—
102C22#1192460511yescharacteristic
103C4—371no—
104C4—371no—
105C4(C2×#3866)⋊C411yescharacteristic
106C4#1192460411yescharacteristic
107C2—21no—
108C2—741no—
109C2—741no—
110C2#1455840711yescharacteristic
subgroupG/H
centerC2#14558407
commutatorC8×C37C42
FrattiniC2×C8C2×#3866
FittingM32×C37C4
socleC2×C37#340
prime radicalC22×D37Q16
cosocleC2×C8×D37C22
hypercenterM32#3866
hypocenterC37#1388
LCSG ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
59. C37#1388semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1082
C2×#119246062
M32×D372
#138837