Finite Group Databasebeta

← #18009477

Subgroups — #18009477

Order 4736.

246 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 48 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#14558504C211yesmaximal, characteristic
2C4×C22⋊#3866C211yesmaximal, characteristic
3#14557380C211yesmaximal, characteristic
4C2×#10596953C412yescomplemented
5C2×C22⋊#3866—21no—
6C2×C4×#3866—21no—
7#11924593—21no—
8C22⋊#64438—21no—
9(C2×#3866)⋊C4C412yescomplemented
10C22×C4×D37C2211yescharacteristic
11C2×#10596938—21no—
12C2×C4×Dic37—21no—
13#11924443C411yescharacteristic, complemented
14#95×C37C411yescharacteristic, complemented
15C23×D37D411yescharacteristic
16C22×#3866—22no—
17C22×C4×C37—21no—
18C22×C4×C37C2×C411yescharacteristic
19C22×Dic37—21no—
20C22×Dic37D411yescharacteristic
21C2×C4×D37—42no—
22C2×C4×D37C2×C411yescharacteristic
23C2×C4×D37C2×C411yescharacteristic
24C2×C4×D37D411yescharacteristic
25C2×C4×D37Q811yescharacteristic
26C22⋊#3866—22no—
27C22⋊#3866—22no—
28C2×#64438—22no—
29C4×#3866—42no—
30#10596953—42no—
31#10596938—24no—
32C4×Dic37—42no—
33C23×C37C22⋊C411yescharacteristic
34C22×D37—21no—
35C22×D37—21no—
36C22×D37—22no—
37C22×D37—41no—
38C22×D37C22⋊C411yescharacteristic
39C22×D37C4⋊C411yescharacteristic
40C2×#3866—24no—
41C2×#3866—42no—
42C2×#3866—42no—
43C2×C4×C37—22no—
44C2×C4×C37—41no—
45C2×C4×C37—41no—
46C2×C4×C37—41no—
47C2×C4×C37C4211yescharacteristic
48C2×C4×C37C4⋊C411yescharacteristic
49C2×Dic37—22no—
50C2×Dic37—22no—
51C2×Dic37—41no—
52C2×Dic37—41no—
53C2×Dic37C22⋊C411yescharacteristic
54C2×Dic37C4⋊C411yescharacteristic
55C4×D37—22no—
56C4×D37—22no—
57C4×D37—41no—
58C4×D37—41no—
59#64438—42no—
60C22×C37—21no—
61C22×C37—21no—
62C22×C37#9511yescharacteristic
63C22×C37#10411yescharacteristic
64C22×C37#10411yescharacteristic
65C2×D37—21no—
66C2×D37—21no—
67C2×D37—21no—
68C2×D37—21no—
69C2×D37—21no—
70C2×D37—42no—
71C2×D37—42no—
72C2×D37#10412yes—
73#3866—44no—
74C4×C37—21no—
75C4×C37—21no—
76C4×C37—42no—
77Dic37—21no—
78Dic37—42no—
79Dic37#9912yes—
80#1297—371nomaximal, Sylow
81C2×C37—21no—
82C2×C37—21no—
83C2×C37#33911yescharacteristic
84C2×C37#33911yescharacteristic
85C2×C37#34211yescharacteristic
86D37—22no—
87D37—41no—
88#407—371no—
89C4×C22⋊C4—371no—
90C4×C22⋊C4—371no—
91C37#129711yescharacteristic, complemented, Sylow
92C23×C4—371no—
93C2×M16—372no—
94C2×C22⋊C4—741no—
95C2×C22⋊C4—741no—
96C2×C42—741no—
97C2×C42—741no—
98C22⋊C8—741no—
99C22⋊C8—741no—
100#95—372no—
101#95—371no—
102#95#386611yescharacteristic, complemented
103C24—371no—
104C22×C4—21no—
105C22×C4—371no—
106C22×C4—371no—
107C22×C4—371no—
108C22×C4—371no—
109C22×C4—371no—
110C22×C4—742no—
111C22×C4—741no—
112C22×C4—1482no—
113C22×C4C2×#386611yescharacteristic
114M16—1482no—
115C2×C8—742no—
116C22⋊C4—744no—
117C22⋊C4—742no—
118C22⋊C4—742no—
119C42—1482no—
120C42—1482no—
121C23—371no—
122C23—371no—
123C23—742no—
124C23—741no—
125C23—741no—
126C23—1481no—
127C23C22⋊#386611yescharacteristic
128C2×C4—22no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—41no—
132C2×C4—371no—
133C2×C4—371no—
134C2×C4—742no—
135C2×C4—742no—
136C2×C4—742no—
137C2×C4—742no—
138C2×C4—744no—
139C2×C4—1481no—
140C2×C4—1481no—
141C2×C4—1481no—
142C2×C4—1482no—
143C2×C4—1482no—
144C2×C4—1481no—
145C2×C4C4×#386611yescharacteristic
146C2×C4C4⋊#386611yescharacteristic
147C8—1482no—
148C22—21no—
149C22—21no—
150C22—372no—
151C22—741no—
152C22—741no—
153C22—741no—
154C22—741no—
155C22—741no—
156C22—1482no—
157C22—1482no—
158C22(C2×#3866)⋊C411yescharacteristic
159C22#1192460011yescharacteristic
160C22#1192460111yescharacteristic
161C4—21no—
162C4—21no—
163C4—42no—
164C4—372no—
165C4—741no—
166C4—1482no—
167C4—1484no—
168C2—21no—
169C2—21no—
170C2—742no—
171C2—1481no—
172C2#1455840311yescharacteristic
173C2#1455840411yescharacteristic
174C2#1455841011yescharacteristic
subgroupG/H
centerC22(C2×#3866)⋊C4
commutatorC2×C4×C37C42
FrattiniC22×C4C2×#3866
Fitting#95×C37C4
socleC22×C37#95
prime radicalC23×D37D4
cosocleC22×C4×D37C22
hypercenter#95#3866
hypocenterC37#1297
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. C2×#10596953C4semidirect
9. (C2×#3866)⋊C4C4semidirect
13. #11924443C4semidirect
14. #95×C37C4semidirect
91. C37#1297semidirect
102. #95#3866semidirect

Maximal subgroups

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

subgroupindex
#145585042
C4×C22⋊#38662
#145573802
#129737