Finite Group Databasebeta

← #18010496

Subgroups — #18010496

Order 4736.

316 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 70 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#14558505C212yesmaximal
2#14558413C214yesmaximal, complemented
3C2×C4⋊C4×D37C211yesmaximal, characteristic
4C2×#10596957C2214yes—
5#11924593—22no—
6#11924593—22no—
7C22×C4×D37C412yes—
8C22×C4×D37C2211yescharacteristic
9C2×C4⋊Dic37C411yescharacteristic
10C2×#10596936C2212yes—
11C4⋊C4×D37—22no—
12C4⋊C4×D37—22no—
13C2×C4⋊C4×C37C411yescharacteristic
14C23×D37C2×C411yescharacteristic
15C22×C4×C37C2×C412yes—
16C22×C4×C37C2×C411yescharacteristic
17C22×Dic37C2×C412yes—
18C22×Dic37C2311yescharacteristic
19C2×C4×D37—24no—
20C2×C4×D37—22no—
21C2×C4×D37—22no—
22C2×C4×D37—44no—
23C2×C4×D37D412yes—
24C2×C4×D37D412yes—
25#10596957—28no—
26C2×#64438—24no—
27C4⋊C4×C37—22no—
28C4⋊Dic37—22no—
29#10596936—24no—
30C23×C37C22×C411yescharacteristic
31C22×D37—22no—
32C22×D37—22no—
33C22×D37—22no—
34C22×D37C22⋊C411yescharacteristic
35C22×D37C22⋊C411yescharacteristic
36C2×C4×C37—22no—
37C2×C4×C37—22no—
38C2×C4×C37—42no—
39C2×C4×C37C22⋊C412yes—
40C2×Dic37—22no—
41C2×Dic37—42no—
42C2×Dic37C2×D412yes—
43C2×Dic37#4114yes—
44C4×D37—24no—
45C4×D37—24no—
46C4×D37—44no—
47C4×D37—44no—
48#64438—44no—
49C22×C37—21no—
50C22×C37—21no—
51C22×C37C2×C22⋊C411yescharacteristic
52C22×C37#11712yes—
53C2×D37—28no—
54C2×D37—21no—
55C2×D37—21no—
56C2×D37—21no—
57C2×D37—21no—
58C2×D37#10012yes—
59C2×D37#10112yes—
60C4×C37—22no—
61C4×C37—42no—
62Dic37—42no—
63Dic37#12314yes—
64#1821—371nomaximal, Sylow
65C2×C37—22no—
66C2×C37#38111yescharacteristic
67C2×C37C2×#10011yescharacteristic
68C2×C37C2×#10111yescharacteristic
69D37—22no—
70D37—22no—
71C22×C4⋊C4—371no—
72#407—372no—
73#343—374no—
74C37#182111yescharacteristic, complemented, Sylow
75C23×C4—371no—
76C23×C4—372no—
77C2×M16—374no—
78C2×C4⋊C4—372no—
79C2×C4⋊C4—371no—
80C2×C4⋊C4—742no—
81C2×C4⋊C4—742no—
82C2×C4⋊C4#386611yescharacteristic
83C22⋊C8—742no—
84C22⋊C8—742no—
85C24—371no—
86C22×C4—371no—
87C22×C4—372no—
88C22×C4—372no—
89C22×C4—372no—
90C22×C4—744no—
91C22×C4—742no—
92C22×C4—742no—
93C22×C4—1484no—
94C22×C4C2×#386612yes—
95C22×C4C2×#386611yescharacteristic
96M16—748no—
97C2×C8—744no—
98C4⋊C4—22no—
99C4⋊C4—744no—
100C4⋊C4—742no—
101C23—371no—
102C23—371no—
103C23—742no—
104C23—742no—
105C23—742no—
106C23C22×#386611yescharacteristic
107C2×C4—22no—
108C2×C4—22no—
109C2×C4—42no—
110C2×C4—372no—
111C2×C4—374no—
112C2×C4—744no—
113C2×C4—744no—
114C2×C4—742no—
115C2×C4—1484no—
116C2×C4—1484no—
117C2×C4—1482no—
118C2×C4C22⋊#386612yes—
119C8—1484no—
120C22—21no—
121C22—21no—
122C22—372no—
123C22—372no—
124C22—748no—
125C22—741no—
126C22—741no—
127C22—741no—
128C22—741no—
129C22C2×C22⋊#386611yescharacteristic
130C22#1192461512yes—
131C4—22no—
132C4—42no—
133C4—374no—
134C4—1482no—
135C2—22no—
136C2—742no—
137C2—742no—
138C2#1455847611yescharacteristic
139C2D37⋊#10011yescharacteristic
140C2D37⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1821
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #14558413C2semidirect
74. C37#1821semidirect

Maximal subgroups

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

subgroupindex
#145585052
#145584132
C2×C4⋊C4×D372
#182137