Finite Group Databasebeta

← #17996178

Subgroups — #17996178

Order 4736.

148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 57 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#14557581C211yesmaximal, characteristic
2#14557559C211yesmaximal, characteristic
3#14557305C211yesmaximal, characteristic
4#14557304C211yesmaximal, characteristic
5#14557298C211yesmaximal, characteristic
6#14557291C211yesmaximal, characteristic
7C37×#341C211yesmaximal, characteristic
8C2×#10596934C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10C2×#10596934C2211yescharacteristic
11#11924495C2211yescharacteristic
12#11924471—22no—
13#11924465—22no—
14C2×M16×C37C2211yescharacteristic
15C2×M16×C37C2211yescharacteristic
16C22×C8×C37C2211yescharacteristic
17C22×C4×C37C2311yescharacteristic
18M16×C37—21no—
19M16×C37—21no—
20M16×C37—21no—
21M16×C37—21no—
22C2×C8×C37—21no—
23C2×C8×C37—21no—
24C2×C8×C37—21no—
25C2×C8×C37—21no—
26C2×C8×C37—21no—
27C22⋊Dic37Q812yes—
28C4⋊Dic37—21no—
29C4×Dic37—21no—
30#10596934—21no—
31#10596934—21no—
32#10596934—21no—
33#10596934—21no—
34#10596934—21no—
35#10596934—21no—
36C2×#64436—21no—
37C2×#64436—21no—
38C2×#64436D412yes—
39C23×C37C2×Q811yescharacteristic
40C2×C4×C37C2×D411yescharacteristic
41C2×C4×C37#4111yescharacteristic
42C2×C4×C37#4111yescharacteristic
43C2×C4×C37#4111yescharacteristic
44C2×C4×C37#4111yescharacteristic
45C2×C4×C37#4111yescharacteristic
46C2×Dic37—22no—
47C8×C37—41no—
48C8×C37—41no—
49C8×C37—41no—
50#64436—22no—
51#64436—41no—
52#64436—41no—
53C22×C37—41no—
54C22×C37C22⋊Q811yescharacteristic
55C22×C37#12511yescharacteristic
56C22×C37#12511yescharacteristic
57C4×C37#12311yescharacteristic
58C4×C37#12411yescharacteristic
59C4×C37#12611yescharacteristic
60C4×C37#12611yescharacteristic
61Dic37—42no—
62#2103—371nomaximal, Sylow
63C2×C37—21no—
64C2×C37—21no—
65C2×C37—21no—
66C2×C37#40011yescharacteristic
67#430—371no—
68#424—371no—
69#344—371no—
70#344—371no—
71#341—371no—
72#341D3711yescharacteristic
73#338—371no—
74C37#210311yescharacteristic, complemented, Sylow
75C2×M16—371no—
76C2×M16—371no—
77C2×M16—371no—
78C2×M16C2×D3711yescharacteristic
79C2×M16C2×D3711yescharacteristic
80C22×C8C2×D3711yescharacteristic
81#117—371no—
82#108—742no—
83C4⋊C8—742no—
84C22×C4C22×D3711yescharacteristic
85M16—21no—
86M16—21no—
87M16—21no—
88M16—21no—
89M16—741no—
90M16—741no—
91M16—741no—
92M16—741no—
93M16—741no—
94M16—741no—
95C2×C8—21no—
96C2×C8—21no—
97C2×C8—21no—
98C2×C8—21no—
99C2×C8—21no—
100C2×C8—372no—
101C2×C8—741no—
102C2×C8—741no—
103C4⋊C4—741no—
104C22⋊C4—372no—
105C42—741no—
106C23Q8×D3711yescharacteristic
107C2×C4—742no—
108C2×C4#1059696211yescharacteristic
109C2×C4#1059696211yescharacteristic
110C2×C4#1059696211yescharacteristic
111C2×C4D4×D3711yescharacteristic
112C2×C4#1059696411yescharacteristic
113C2×C4#1059696411yescharacteristic
114C8—41no—
115C8—41no—
116C8—41no—
117C8—742no—
118C8—1481no—
119C8—1481no—
120C22—41no—
121C22#1192451411yescharacteristic
122C22#1192452611yescharacteristic
123C22#1192452611yescharacteristic
124C4—1482no—
125C4#1192451811yescharacteristic
126C4#1192452211yescharacteristic
127C4#1192452911yescharacteristic
128C4#1192453011yescharacteristic
129C2—21no—
130C2—21no—
131C2—21no—
132C2#1455747411yescharacteristic
subgroupG/H
centerC4#11924522
commutator, cosocleC22×C4×C37C23
FrattiniC22×C4C22×D37
FittingC37×#341C2
socleC2×C37#400
prime radicalC23×C37C2×Q8
hypercenter#341D37
hypocenterC37#2103
LCSG ▷ C22×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #341

Complements

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

NH ≅ G/Ntype
74. C37#2103semidirect

Maximal subgroups

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

subgroupindex
#145575812
#145575592
#145573052
#145573042
#145572982
#145572912
C37×#3412
#210337