Finite Group Databasebeta

← #18009868

Subgroups — #18009868

Order 4736.

204 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558553C211yesmaximal, characteristic
2#14558549C211yesmaximal, characteristic
3#14558379C212yesmaximal
4#14558378C212yesmaximal
5C2×#11924526C211yesmaximal, characteristic
6#11924603—21no—
7C4⋊#64438—21no—
8C22⋊#64438C2212yes—
9C22⋊#64438C2212yes—
10#11924591—21no—
11C4×#64438—21no—
12#11924526—21no—
13#11924526—21no—
14#11924526—21no—
15#11924526—21no—
16C2×C4⋊Dic37C2211yescharacteristic
17C2×#10596936C411yescharacteristic
18C2×#10596936C411yescharacteristic
19C2×#10596936C411yescharacteristic
20C2×#10596936C2211yescharacteristic
21C2×C4×Dic37C2211yescharacteristic
22C2×C4⋊C4×C37C411yescharacteristic
23C22×C4×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×C4×C37C2×C411yescharacteristic
26C22×Dic37C2×C411yescharacteristic
27C22×Dic37C2×C411yescharacteristic
28C22×Dic37C2×C411yescharacteristic
29C22×Dic37C2311yescharacteristic
30C2×#64438—22no—
31C2×#64438—22no—
32C4⋊C4×C37—21no—
33C4⋊C4×C37—21no—
34C4⋊Dic37—21no—
35C4⋊Dic37—21no—
36#10596936—21no—
37#10596936—21no—
38#10596936—21no—
39#10596936—21no—
40#10596936—21no—
41#10596936—21no—
42#10596936—21no—
43#10596936—21no—
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37D411yescharacteristic
48C23×C37C22×C411yescharacteristic
49C2×C4×C37—22no—
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37—22no—
53C2×C4×C37—41no—
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×Dic37—22no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37—22no—
60C2×Dic37—41no—
61C2×Dic37—41no—
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C2×D411yescharacteristic
65C2×Dic37C2×D411yescharacteristic
66#64438—42no—
67#64438—42no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37C2×C22⋊C411yescharacteristic
71C22×C37#13112yes—
72C4×C37—21no—
73C4×C37—21no—
74C4×C37—41no—
75C4×C37—41no—
76Dic37—21no—
77Dic37—21no—
78Dic37—21no—
79Dic37—41no—
80Dic37—41no—
81Dic37#10112yes—
82#1470—371nomaximal, Sylow
83C2×C37—22no—
84C2×C37#40811yescharacteristic
85C2×C37#41011yescharacteristic
86C2×C37C2×#10111yescharacteristic
87C2×#125—371no—
88#432—371no—
89#431—371no—
90#324—372no—
91#324—372no—
92C37#147011yescharacteristic, complemented, Sylow
93#125—741no—
94#125—741no—
95#125—741no—
96#125—741no—
97C2×C4⋊C4—371no—
98C2×C4⋊C4—371no—
99C2×C4⋊C4—371no—
100C2×C4⋊C4—371no—
101C2×C4⋊C4—371no—
102C2×C4⋊C4#386611yescharacteristic
103C2×C42—371no—
104C4⋊C8—741no—
105C4⋊C8—741no—
106C22⋊C8—372no—
107C22⋊C8—372no—
108#97—741no—
109C4×C8—741no—
110C22×C4—371no—
111C22×C4—371no—
112C22×C4—371no—
113C22×C4—371no—
114C22×C4C2×#386611yescharacteristic
115C22×C4C2×#386611yescharacteristic
116C22×C4C2×#386611yescharacteristic
117C2×C8—742no—
118C2×C8—742no—
119C4⋊C4—21no—
120C4⋊C4—21no—
121C4⋊C4—741no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4—741no—
126C4⋊C4—741no—
127C4⋊C4—741no—
128C4⋊C4—741no—
129C4⋊C4—741no—
130C4⋊C4—741no—
131C42—371no—
132C42—371no—
133C42—371no—
134C42—371no—
135C23C22×#386611yescharacteristic
136C2×C4—22no—
137C2×C4—21no—
138C2×C4—21no—
139C2×C4—22no—
140C2×C4—41no—
141C2×C4—371no—
142C2×C4—371no—
143C2×C4—371no—
144C2×C4—371no—
145C2×C4—742no—
146C2×C4—741no—
147C2×C4—741no—
148C2×C4—742no—
149C2×C4—1481no—
150C2×C4—1481no—
151C2×C4C22⋊#386611yescharacteristic
152C2×C4C22⋊#386611yescharacteristic
153C8—1482no—
154C8—1482no—
155C22—21no—
156C22—21no—
157C22C2×C22⋊#386611yescharacteristic
158C22#1192462312yes—
159C4—21no—
160C4—21no—
161C4—41no—
162C4—41no—
163C4—372no—
164C4—741no—
165C4—741no—
166C4—741no—
167C4—1481no—
168C4—1481no—
169C2—22no—
170C2#1455850611yescharacteristic
171C2#1455851211yescharacteristic
172C2D37⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutator, prime radicalC23×C37C22×C4
FrattiniC23C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
cosocleC22×Dic37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1470
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
92. C37#1470semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145585492
#145583792
#145583782
C2×#119245262
#147037