Finite Group Databasebeta

← #17996763

Subgroups — #17996763

Order 4736.

124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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#14557934C211yesmaximal, characteristic
2#14557627C211yesmaximal, characteristic
3#14557358C211yesmaximal, characteristic
4#14557351C211yesmaximal, characteristic
5#14557338C211yesmaximal, characteristic
6#14557336C211yesmaximal, characteristic
7C37×#367C211yesmaximal, characteristic
8C2×Dic148C2211yescharacteristic
9#11924527—21no—
10#11924501—21no—
11C2×#10596925C2211yescharacteristic
12#11924470C2211yescharacteristic
13#11924467—21no—
14#11924459—21no—
15C8×Dic37C2211yescharacteristic
16C2×C16×C37C2211yescharacteristic
17#107×C37C2211yescharacteristic
18#107×C37C2211yescharacteristic
19C2×Dic74—21no—
20C2×C8×C37C2311yescharacteristic
21C4⋊C4×C37—21no—
22C4⋊C4×C37—21no—
23C4⋊Dic37—21no—
24C4⋊Dic37—41no—
25#10596936—41no—
26#10596936—41no—
27C4×Dic37—41no—
28C4×Dic37D411yescharacteristic
29C2×#64436D411yescharacteristic
30Dic148—21no—
31Dic148Q812yes—
32C16×C37—21no—
33#10596925—21no—
34C2×C4×C37—41no—
35C2×C4×C37—41no—
36C2×C4×C37C2×D411yescharacteristic
37C2×Dic37—41no—
38C2×Dic37—41no—
39C2×Dic37D811yescharacteristic
40C2×Dic37D811yescharacteristic
41Dic74—22no—
42Dic74—41no—
43C8×C37C2×Q811yescharacteristic
44C8×C37#4111yescharacteristic
45#64436—21no—
46C22×C37C2×D811yescharacteristic
47C4×C37—81no—
48C4×C37—81no—
49C4×C37C22⋊Q811yescharacteristic
50C4×C37#13711yescharacteristic
51Dic37—21no—
52Dic37—21no—
53Dic37—42no—
54Dic37—81no—
55#2229—371nomaximal, Sylow
56C2×C37#47411yescharacteristic
57C2×C37#50811yescharacteristic
58C2×C37#51011yescharacteristic
59#499—371no—
60C4×Q16—371no—
61#367D3711yescharacteristic
62#366—371no—
63C4⋊C16—371no—
64#358—371no—
65#358—371no—
66C37#222911yescharacteristic, complemented, Sylow
67C2×Q16—371no—
68#125—741no—
69C4×Q8—741no—
70C2×C16—371no—
71C2×C16C2×D3711yescharacteristic
72#107—371no—
73#107C2×D3711yescharacteristic
74#107C2×D3711yescharacteristic
75#106—741no—
76#103—741no—
77C4×C8—371no—
78C2×Q8—741no—
79Q16—372no—
80Q16—741no—
81C2×C8—371no—
82C2×C8C22×D3711yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—741no—
86C4⋊C4—1481no—
87C4⋊C4—1481no—
88C4⋊C4—1481no—
89C42—371no—
90C42—1481no—
91C16—21no—
92C16—741no—
93Q8—742no—
94Q8—1481no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—371no—
98C2×C4—371no—
99C2×C4—1481no—
100C2×C4—1481no—
101C2×C4D4×D3711yescharacteristic
102C8—741no—
103C8#1059696211yescharacteristic
104C8Q8×D3711yescharacteristic
105C22D8×D3711yescharacteristic
106C4—81no—
107C4—81no—
108C4—2961no—
109C4—741no—
110C4—741no—
111C4—1482no—
112C4#1192451411yescharacteristic
113C4#1192456811yescharacteristic
114C2#1455781211yescharacteristic
115C2#1455796411yescharacteristic
116C2#1455797211yescharacteristic
subgroupG/H
centerC22D8×D37
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#367C2
socle, prime radicalC22×C37C2×D8
hypercenter#367D37
hypocenterC37#2229
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
66. C37#2229semidirect

Maximal subgroups

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

subgroupindex
#145579342
#145576272
#145573582
#145573512
#145573382
#145573362
C37×#3672
#222937