Finite Group Databasebeta

← #17994672

Subgroups — #17994672

Order 4736.

300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×#11924492C211yesmaximal, characteristic
2#14557394C212yesmaximal
3#14557300C211yesmaximal, characteristic
4#14557299C212yesmaximal
5C37×#342C211yesmaximal, characteristic
6C23×Dic37C2211yescharacteristic
7#11924492—24no—
8C2×#10596936C412yescomplemented
9C2×C22⋊Dic37C2212yes—
10C2×C22⋊Dic37C2211yescharacteristic
11C2×C4×Dic37C412yescomplemented
12#11924443—24no—
13C2×C22⋊C4×C37C2212yes—
14C2×C22⋊C4×C37C2211yescharacteristic
15C24×C37C2311yescharacteristic
16C22×C4×C37—22no—
17C22×C4×C37C2×C412yes—
18C22×Dic37—22no—
19C22×Dic37—21no—
20C22×Dic37—21no—
21C22×Dic37—22no—
22C22×Dic37C2×C411yescharacteristic
23C22×Dic37C2×C411yescharacteristic
24C22×Dic37C2×C412yes—
25C22×Dic37D414yes—
26C22⋊C4×C37—22no—
27C22⋊C4×C37—22no—
28C22⋊C4×C37—22no—
29C22⋊Dic37—22no—
30C22⋊Dic37—22no—
31C22⋊Dic37—22no—
32#10596936—24no—
33C4×Dic37—24no—
34C23×C37—42no—
35C23×C37C22×C411yescharacteristic
36C23×C37C2×D412yes—
37C23×C37#4112yes—
38C23×C37#4111yescharacteristic
39C23×C37#4111yescharacteristic
40C2×C4×C37—22no—
41C2×C4×C37—42no—
42C2×C4×C37—44no—
43C2×C4×C37—42no—
44C2×Dic37—21no—
45C2×Dic37—21no—
46C2×Dic37—21no—
47C2×Dic37—21no—
48C2×Dic37—24no—
49C2×Dic37—24no—
50C2×Dic37—22no—
51C2×Dic37—42no—
52C2×Dic37—44no—
53C2×Dic37—42no—
54C2×Dic37C22⋊C412yes—
55C2×Dic37C22⋊C412yes—
56C22×C37—22no—
57C22×C37—24no—
58C22×C37—42no—
59C22×C37—41no—
60C22×C37—41no—
61C22×C37C2×C22⋊C411yescharacteristic
62C22×C37#11711yescharacteristic
63C22×C37#11711yescharacteristic
64C22×C37#12312yes—
65C22×C37#12312yes—
66C4×C37—42no—
67C4×C37—82no—
68Dic37—22no—
69Dic37—22no—
70Dic37—42no—
71Dic37—82no—
72#1820—371nomaximal, Sylow
73C2×C37—22no—
74C2×C37—22no—
75C2×C37—21no—
76C2×C37—21no—
77C2×C37#38111yescharacteristic
78C2×C37#41012yes—
79C2×#117—371no—
80#381—372no—
81#342—372no—
82#342—371no—
83#342D3711yescharacteristic
84C37#182011yescharacteristic, complemented, Sylow
85C23×C4—371no—
86#117—744no—
87C2×C4⋊C4—372no—
88C2×C22⋊C4—371no—
89C2×C22⋊C4—372no—
90C2×C22⋊C4C2×D3712yes—
91C2×C22⋊C4C2×D3711yescharacteristic
92C2×C42—372no—
93#95—744no—
94C24C22×D3711yescharacteristic
95C22×C4—22no—
96C22×C4—371no—
97C22×C4—371no—
98C22×C4—374no—
99C22×C4—372no—
100C22×C4—742no—
101C22×C4—741no—
102C22×C4—741no—
103C22×C4—742no—
104C22×C4C4×D3712yes—
105C4⋊C4—744no—
106C22⋊C4—22no—
107C22⋊C4—22no—
108C22⋊C4—22no—
109C22⋊C4—742no—
110C22⋊C4—742no—
111C22⋊C4—742no—
112C42—744no—
113C23—42no—
114C23C2×C4×D3711yescharacteristic
115C23#1059696212yes—
116C23D4×D3712yes—
117C23#1059696411yescharacteristic
118C23#1059696611yescharacteristic
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—44no—
122C2×C4—42no—
123C2×C4—372no—
124C2×C4—372no—
125C2×C4—741no—
126C2×C4—741no—
127C2×C4—741no—
128C2×C4—741no—
129C2×C4—744no—
130C2×C4—744no—
131C2×C4—742no—
132C2×C4—1484no—
133C2×C4—1482no—
134C2×C4—1482no—
135C22—22no—
136C22—24no—
137C22—42no—
138C22—41no—
139C22—41no—
140C22C22⋊C4×D3711yescharacteristic
141C22#1192449311yescharacteristic
142C22#1192449411yescharacteristic
143C22#1192451812yes—
144C22#1192452112yes—
145C4—42no—
146C4—82no—
147C4—2962no—
148C4—742no—
149C4—742no—
150C4—1482no—
151C2—22no—
152C2—22no—
153C2—21no—
154C2—21no—
155C2#1455739511yescharacteristic
156C2#1455750512yes—
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#342C2
socleC22×C37C2×C22⋊C4
prime radical, cosocleC24×C37C23
hypercenter#342D37
hypocenterC37#1820
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
8. C2×#10596936C4semidirect
11. C2×C4×Dic37C4semidirect
84. C37#1820semidirect

Maximal subgroups

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

subgroupindex
C2×#119244922
#145573942
#145573002
#145572992
C37×#3422
#182037