Finite Group Databasebeta

← #17992619

Subgroups — #17992619

Order 4736.

154 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 35 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#14557469C211yesmaximal, characteristic
2#14557257C211yesmaximal, characteristic
3C37×#342C211yesmaximal, characteristic
4C2×C4⋊Dic37C411yescharacteristic, complemented
5C2×#10596936—21no—
6C2×C22⋊Dic37—21no—
7C22⋊#64436—21no—
8#11924443C411yescharacteristic, complemented
9C2×C22⋊C4×C37—21no—
10C2×C22⋊C4×C37C2211yescharacteristic
11C24×C37D411yescharacteristic
12C22×C4×C37—41no—
13C22×C4×C37C2×C411yescharacteristic
14C22×C4×C37D411yescharacteristic
15C22×Dic37—21no—
16C22×Dic37—21no—
17C22⋊C4×C37—22no—
18C22⋊C4×C37—41no—
19C22⋊C4×C37—41no—
20C22⋊Dic37—42no—
21C4⋊Dic37—41no—
22#10596936—42no—
23C2×#64436—41no—
24C23×C37—21no—
25C23×C37—21no—
26C23×C37—41no—
27C23×C37—41no—
28C23×C37C22⋊C411yescharacteristic
29C23×C37SD1611yescharacteristic
30C23×C37Q1611yescharacteristic
31C2×C4×C37—21no—
32C2×C4×C37—21no—
33C2×C4×C37—41no—
34C2×C4×C37—41no—
35C2×C4×C37—42no—
36C2×C4×C37—81no—
37C2×C4×C37—81no—
38C2×Dic37—22no—
39C2×Dic37—41no—
40C2×Dic37—41no—
41C2×Dic37—41no—
42C2×Dic37—41no—
43C2×Dic37—41no—
44#64436—81no—
45C22×C37—21no—
46C22×C37—21no—
47C22×C37—21no—
48C22×C37—21no—
49C22×C37—41no—
50C22×C37—41no—
51C22×C37—41no—
52C22×C37—41no—
53C22×C37—81no—
54C22×C37#9911yescharacteristic
55C22×C37#10311yescharacteristic
56C22×C37#10411yescharacteristic
57C4×C37—41no—
58C4×C37—41no—
59C4×C37—82no—
60Dic37—42no—
61Dic37—81no—
62#1352—371nomaximal, Sylow
63C2×C37—21no—
64C2×C37—21no—
65C2×C37—41no—
66C2×C37—41no—
67C2×C37#32811yescharacteristic
68C2×C37#35211yescharacteristic
69C2×C37#35311yescharacteristic
70#399—371no—
71#342D3711yescharacteristic
72#323—371no—
73C37#135211yescharacteristic, complemented, Sylow
74C2×C4⋊C4—371no—
75C2×C4⋊C4—741no—
76C2×C22⋊C4—21no—
77C2×C22⋊C4—741no—
78C2×C22⋊C4C2×D3711yescharacteristic
79C22⋊C8—741no—
80#95—371no—
81C24C22⋊D3711yescharacteristic
82C22×C4—41no—
83C22×C4—741no—
84C22×C4—741no—
85C22×C4C4×D3711yescharacteristic
86C22×C4D14811yescharacteristic
87C2×C8—1481no—
88C4⋊C4—1481no—
89C4⋊C4—1482no—
90C22⋊C4—22no—
91C22⋊C4—41no—
92C22⋊C4—41no—
93C22⋊C4—1482no—
94C23—21no—
95C23—21no—
96C23—41no—
97C23—41no—
98C23#1059693811yescharacteristic
99C23#1059694011yescharacteristic
100C23#1059694211yescharacteristic
101C2×C4—21no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—41no—
105C2×C4—42no—
106C2×C4—81no—
107C2×C4—81no—
108C2×C4—742no—
109C2×C4—1481no—
110C2×C4—1481no—
111C2×C4—1481no—
112C2×C4—1481no—
113C2×C4—1481no—
114C8—2961no—
115C22—21no—
116C22—21no—
117C22—21no—
118C22—21no—
119C22—41no—
120C22—41no—
121C22—41no—
122C22—41no—
123C22—81no—
124C22#1192445011yescharacteristic
125C22#1192445911yescharacteristic
126C22#1192446411yescharacteristic
127C4—41no—
128C4—41no—
129C4—82no—
130C4—2961no—
131C4—1482no—
132C2—21no—
133C2—21no—
134C2—41no—
135C2—41no—
136C2#1455726911yescharacteristic
137C2#1455732211yescharacteristic
138C2#1455732511yescharacteristic
subgroupG/H
centerC22#11924450
commutatorC22×C4×C37C2×C4
FrattiniC2×C22⋊C4C2×D37
FittingC37×#342C2
socleC22×C37#99
prime radicalC24×C37D4
cosocleC2×C22⋊C4×C37C22
hypercenter#342D37
hypocenterC37#1352
LCSG ▷ C22×C4×C37 ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
4. C2×C4⋊Dic37C4semidirect
8. #11924443C4semidirect
73. C37#1352semidirect

Maximal subgroups

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

subgroupindex
#145574692
#145572572
C37×#3422
#135237