Finite Group Databasebeta

← #17996840

Subgroups — #17996840

Order 4736.

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

normal subgroups only

This group has 132 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#14557911C211yesmaximal, characteristic
3#14557338C211yesmaximal, characteristic
4#14557337C211yesmaximal, characteristic
5#14557336C211yesmaximal, characteristic
6#14557308C211yesmaximal, characteristic
7C37×#358C211yesmaximal, characteristic
8C2×Dic148C2211yescharacteristic
9C2×#10596942—21no—
10#11924534—21no—
11#11924527—21no—
12C2×#10596925C2211yescharacteristic
13#11924470C2211yescharacteristic
14#11924467—21no—
15C8×Dic37C2211yescharacteristic
16C2×Q16×C37C2211yescharacteristic
17C2×C16×C37C2211yescharacteristic
18#107×C37C2211yescharacteristic
19C2×Q8×C37—21no—
20C2×Dic74—21no—
21Q16×C37—21no—
22Q16×C37—21no—
23C2×C8×C37C2311yescharacteristic
24C4⋊C4×C37—21no—
25#10596942—42no—
26C4⋊Dic37—21no—
27C4⋊Dic37—41no—
28#10596936—41no—
29#10596936—41no—
30#10596936—41no—
31C4×Dic37D411yescharacteristic
32C2×#64436D411yescharacteristic
33Dic148—21no—
34Dic148—21no—
35C16×C37—21no—
36#10596925—21no—
37Q8×C37—41no—
38Q8×C37—41no—
39C2×C4×C37—41no—
40C2×C4×C37—41no—
41C2×C4×C37C2×D411yescharacteristic
42C2×Dic37—41no—
43C2×Dic37—41no—
44C2×Dic37D811yescharacteristic
45C2×Dic37D811yescharacteristic
46Dic74—41no—
47Dic74—41no—
48C8×C37#4111yescharacteristic
49C8×C37#4111yescharacteristic
50#64436SD1612yes—
51C22×C37C2×D811yescharacteristic
52C4×C37—81no—
53C4×C37—81no—
54C4×C37#12411yescharacteristic
55C4×C37C2×SD1611yescharacteristic
56Dic37—21no—
57Dic37—21no—
58Dic37—81no—
59Dic37—81no—
60#2245—371nomaximal, Sylow
61C2×C37#48611yescharacteristic
62C2×C37#51011yescharacteristic
63C2×C37#51011yescharacteristic
64#499—371no—
65#494—371no—
66#358—371no—
67#358—371no—
68#358—371no—
69#358D3711yescharacteristic
70#346—371no—
71C37#224511yescharacteristic, complemented, Sylow
72C2×Q16—371no—
73C2×Q16—741no—
74C2×Q16C2×D3711yescharacteristic
75C4⋊Q8—741no—
76#125—741no—
77C2×C16—371no—
78C2×C16C2×D3711yescharacteristic
79#107—371no—
80#107C2×D3711yescharacteristic
81#106—741no—
82C4×C8—371no—
83C2×Q8—21no—
84C2×Q8—741no—
85Q16—21no—
86Q16—21no—
87Q16—741no—
88Q16—741no—
89Q16—1482no—
90C2×C8—371no—
91C2×C8C22×D3711yescharacteristic
92C4⋊C4—21no—
93C4⋊C4—741no—
94C4⋊C4—1481no—
95C4⋊C4—1481no—
96C4⋊C4—1481no—
97C4⋊C4—1481no—
98C42—371no—
99C16—21no—
100C16—741no—
101Q8—41no—
102Q8—41no—
103Q8—1481no—
104Q8—1481no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—371no—
108C2×C4—371no—
109C2×C4—1481no—
110C2×C4—1481no—
111C2×C4D4×D3711yescharacteristic
112C8—372no—
113C8#1059696211yescharacteristic
114C8#1059696411yescharacteristic
115C22D8×D3711yescharacteristic
116C4—81no—
117C4—81no—
118C4—2961no—
119C4—2961no—
120C4—741no—
121C4—741no—
122C4#1192452211yescharacteristic
123C4SD16×D3711yescharacteristic
124C2#1455787811yescharacteristic
125C2#1455797211yescharacteristic
126C2#1455797511yescharacteristic
subgroupG/H
centerC22D8×D37
commutator, cosocleC2×C8×C37C23
FrattiniC2×C8C22×D37
FittingC37×#358C2
socle, prime radicalC22×C37C2×D8
hypercenter#358D37
hypocenterC37#2245
LCSG ▷ C2×C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
71. C37#2245semidirect

Maximal subgroups

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

subgroupindex
#145579342
#145579112
#145573382
#145573372
#145573362
#145573082
C37×#3582
#224537