Finite Group Databasebeta

← #18010001

Subgroups — #18010001

Order 4736.

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

normal subgroups only

This group has 326 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#14558505C211yesmaximal, characteristic, complemented
2#14558476C211yesmaximal, characteristic, complemented
3#14558384C214yesmaximal, complemented
4C2×#11924507C211yesmaximal, characteristic
5C2×#10596957—21no—
6C2×C22⋊#3866—21no—
7#11924593—21no—
8#11924593C2212yescomplemented
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4C2212yescomplemented
11C22×C22⋊D37—21no—
12C22×C4×D37C2211yescharacteristic
13#11924507—21no—
14#11924507—21no—
15#11924507C412yescomplemented
16#11924507C2212yes—
17C2×C4⋊Dic37C411yescharacteristic, complemented
18C2×C22⋊Dic37—21no—
19C22×D4×C37C411yescharacteristic, complemented
20C24×C37—21no—
21C23×D37D411yescharacteristic
22C22×#3866—22no—
23C2×D4×C37—21no—
24C2×D4×C37—42no—
25C2×D4×C37C2×C412yes—
26C22×C4×C37C2×C411yescharacteristic
27C2×C22⋊D37—22no—
28C2×C22⋊D37—22no—
29C2×C22⋊D37—44no—
30C22×Dic37—21no—
31C22×Dic37D411yescharacteristic
32C2×C4×D37—42no—
33C2×C4×D37C2×C411yescharacteristic
34C2×C4×D37D411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37C2311yescharacteristic
37C22⋊#3866—42no—
38#10596957—42no—
39C2×#64438—22no—
40C22⋊Dic37—22no—
41C22⋊Dic37—22no—
42C4⋊Dic37—21no—
43C4⋊Dic37C2×C412yes—
44C23×C37—22no—
45C23×C37—42no—
46C23×C37—42no—
47C23×C37—42no—
48C23×C37C22⋊C411yescharacteristic
49C22×D37—22no—
50C22×D37—22no—
51C22×D37—41no—
52C22×D37C22⋊C411yescharacteristic
53C22×D37C2×D411yescharacteristic
54C2×#3866—42no—
55C2×#3866—42no—
56C2×#3866—42no—
57D4×C37—42no—
58D4×C37—42no—
59C2×C4×C37—22no—
60C2×C4×C37C22⋊C411yescharacteristic
61C2×C4×C37C22×C411yescharacteristic
62C22⋊D37—44no—
63C22⋊D37—44no—
64C2×Dic37—22no—
65C2×Dic37—22no—
66C2×Dic37—42no—
67C2×Dic37C22⋊C411yescharacteristic
68C2×Dic37C2×D411yescharacteristic
69C4×D37—41no—
70C4×D37—41no—
71C4×D37—41no—
72C4×D37—41no—
73#64438—42no—
74C22×C37—21no—
75C22×C37—21no—
76C22×C37—42no—
77C22×C37—42no—
78C22×C37—42no—
79C22×C37—84no—
80C22×C37#9912yes—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—21no—
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—21no—
86C2×D37—21no—
87C2×D37—44no—
88C2×D37AGL(1,ℤ/8)12yes—
89#3866—82no—
90C4×C37—21no—
91C4×C37—21no—
92Dic37—21no—
93Dic37—21no—
94Dic37—42no—
95#1510—371nomaximal, Sylow
96C2×C37—22no—
97C2×C37—82no—
98C2×C37C2×#9911yescharacteristic
99C2×C37#41811yescharacteristic
100C2×C37#42111yescharacteristic
101D37—22no—
102D37—41no—
103C2×#121—371no—
104#407—371no—
105#381—371no—
106#327—374no—
107C37#151011yescharacteristic, complemented, Sylow
108C22×D4—741no—
109C22×D4#386611yescharacteristic, complemented
110C23×C4—371no—
111C2×M16—741no—
112#121—372no—
113#121—372no—
114#121—741no—
115#121—741no—
116C2×C4⋊C4—371no—
117C2×C22⋊C4—741no—
118C2×C22⋊C4—741no—
119C22⋊C8—372no—
120C22⋊C8—741no—
121#95—372no—
122#95—741no—
123C24—21no—
124C24—371no—
125C2×D4—21no—
126C2×D4—42no—
127C2×D4—742no—
128C2×D4—742no—
129C2×D4—1484no—
130C2×D4C2×#386612yes—
131C22×C4—371no—
132C22×C4—371no—
133C22×C4—371no—
134C22×C4—371no—
135C22×C4—371no—
136C22×C4—741no—
137C22×C4—742no—
138C22×C4—1482no—
139C22×C4C2×#386611yescharacteristic
140M16—1482no—
141C2×C8—742no—
142C4⋊C4—372no—
143C4⋊C4—741no—
144C22⋊C4—742no—
145C22⋊C4—742no—
146C22⋊C4—1482no—
147C23—22no—
148C23—42no—
149C23—42no—
150C23—42no—
151C23—371no—
152C23—371no—
153C23—742no—
154C23—742no—
155C23—1481no—
156C23C22⋊#386611yescharacteristic
157D4—42no—
158D4—42no—
159D4—1484no—
160D4—1484no—
161C2×C4—22no—
162C2×C4—371no—
163C2×C4—371no—
164C2×C4—742no—
165C2×C4—742no—
166C2×C4—1481no—
167C2×C4—1481no—
168C2×C4—1481no—
169C2×C4—1481no—
170C2×C4—1482no—
171C2×C4—1482no—
172C2×C4—1482no—
173C2×C4—1482no—
174C2×C4C22⋊#386611yescharacteristic
175C2×C4C22×#386611yescharacteristic
176C8—1482no—
177C22—21no—
178C22—21no—
179C22—42no—
180C22—42no—
181C22—42no—
182C22—84no—
183C22—372no—
184C22—741no—
185C22—741no—
186C22—741no—
187C22—741no—
188C22—741no—
189C22—1484no—
190C22#1192459412yes—
191C22C2×C22⋊#386611yescharacteristic
192C4—21no—
193C4—21no—
194C4—2962no—
195C4—741no—
196C4—741no—
197C4—1482no—
198C2—22no—
199C2—82no—
200C2—742no—
201C2—1481no—
202C2C2×#1192459411yescharacteristic
203C2#1455852511yescharacteristic
204C2#1455853111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22×D4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924507C2
cosocleC2×C4×D37C23
hypercenterC22×D4#3866
hypocenterC37#1510
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14558505C2semidirect
2. #14558476C2semidirect
3. #14558384C2semidirect
8. #11924593C22semidirect
10. (C2×#3866)⋊C4C22semidirect
15. #11924507C4semidirect
17. C2×C4⋊Dic37C4semidirect
19. C22×D4×C37C4semidirect
107. C37#1510semidirect
109. C22×D4#3866semidirect

Maximal subgroups

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

subgroupindex
#145585052
#145584762
#145583842
C2×#119245072
#151037