Finite Group Databasebeta

← #18009992

Subgroups — #18009992

Order 4736.

346 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 64 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, complemented
2C4×C22⋊#3866C211yesmaximal, characteristic, complemented
3#14558384C214yesmaximal, complemented
4C2×#11924507C211yesmaximal, characteristic
5C2×#10596953—21no—
6C2×C22⋊#3866—21no—
7C2×C4×#3866—21no—
8#11924593C2212yescomplemented
9C22⋊#64438—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—24no—
38C2×#64438—22no—
39C4×#3866—42no—
40#10596953—42no—
41C22⋊Dic37—22no—
42C22⋊Dic37—22no—
43C4⋊Dic37—21no—
44C4⋊Dic37C2×C412yes—
45C23×C37—22no—
46C23×C37—42no—
47C23×C37—42no—
48C23×C37—42no—
49C23×C37C22⋊C411yescharacteristic
50C22×D37—22no—
51C22×D37—22no—
52C22×D37—41no—
53C22×D37C22⋊C411yescharacteristic
54C22×D37C2×D411yescharacteristic
55C2×#3866—24no—
56C2×#3866—42no—
57C2×#3866—42no—
58D4×C37—42no—
59D4×C37—42no—
60C2×C4×C37—22no—
61C2×C4×C37C22⋊C411yescharacteristic
62C2×C4×C37C22×C411yescharacteristic
63C22⋊D37—44no—
64C22⋊D37—44no—
65C2×Dic37—22no—
66C2×Dic37—41no—
67C2×Dic37—42no—
68C2×Dic37C22⋊C411yescharacteristic
69C2×Dic37C2×D411yescharacteristic
70C4×D37—22no—
71C4×D37—22no—
72C4×D37—41no—
73C4×D37—41no—
74#64438—42no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—42no—
78C22×C37—42no—
79C22×C37—42no—
80C22×C37—84no—
81C22×C37#10412yes—
82C22×C37C2×C22⋊C411yescharacteristic
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—21no—
86C2×D37—21no—
87C2×D37—21no—
88C2×D37—44no—
89C2×D37AGL(1,ℤ/8)12yes—
90#3866—44no—
91C4×C37—21no—
92C4×C37#9912yes—
93Dic37—21no—
94Dic37—21no—
95Dic37—42no—
96#1507—371nomaximal, Sylow
97C2×C37—22no—
98C2×C37—82no—
99C2×C37C2×#9911yescharacteristic
100C2×C37#41811yescharacteristic
101C2×C37C2×#10411yescharacteristic
102D37—22no—
103D37—41no—
104C2×#121—371no—
105#407—371no—
106C4×C22⋊C4—371no—
107#327—374no—
108C37#150711yescharacteristic, complemented, Sylow
109C22×D4—741no—
110C22×D4#386611yescharacteristic, complemented
111C23×C4—371no—
112C2×M16—741no—
113#121—372no—
114#121—372no—
115#121—741no—
116#121—741no—
117C2×C4⋊C4—371no—
118C2×C22⋊C4—741no—
119C2×C22⋊C4—741no—
120C2×C42—741no—
121C22⋊C8—372no—
122C22⋊C8—741no—
123#95—372no—
124C24—21no—
125C24—371no—
126C2×D4—21no—
127C2×D4—42no—
128C2×D4—742no—
129C2×D4—742no—
130C2×D4—1484no—
131C2×D4C2×#386612yes—
132C22×C4—371no—
133C22×C4—371no—
134C22×C4—371no—
135C22×C4—371no—
136C22×C4—371no—
137C22×C4—742no—
138C22×C4—741no—
139C22×C4—1482no—
140C22×C4C2×#386611yescharacteristic
141M16—1482no—
142C2×C8—742no—
143C4⋊C4—372no—
144C4⋊C4—741no—
145C22⋊C4—742no—
146C22⋊C4—742no—
147C22⋊C4—744no—
148C42—1482no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—42no—
153C23—371no—
154C23—371no—
155C23—742no—
156C23—742no—
157C23—1481no—
158C23C22⋊#386611yescharacteristic
159D4—42no—
160D4—42no—
161D4—1484no—
162D4—1484no—
163C2×C4—22no—
164C2×C4—371no—
165C2×C4—371no—
166C2×C4—742no—
167C2×C4—742no—
168C2×C4—744no—
169C2×C4—742no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4—1481no—
173C2×C4—1482no—
174C2×C4—1482no—
175C2×C4—1482no—
176C2×C4C22⋊#386611yescharacteristic
177C2×C4C22×#386611yescharacteristic
178C8—1482no—
179C22—21no—
180C22—21no—
181C22—42no—
182C22—42no—
183C22—42no—
184C22—84no—
185C22—372no—
186C22—741no—
187C22—741no—
188C22—741no—
189C22—741no—
190C22—741no—
191C22—1484no—
192C22#1192460012yes—
193C22C2×C22⋊#386611yescharacteristic
194C4—21no—
195C4—741no—
196C4—741no—
197C4—1484no—
198C4—1482no—
199C4#1192459412yes—
200C2—22no—
201C2—82no—
202C2—742no—
203C2—1481no—
204C2C2×#1192459411yescharacteristic
205C2#1455852511yescharacteristic
206C2C2×#1192460011yescharacteristic
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#1507
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. #14558504C2semidirect
2. C4×C22⋊#3866C2semidirect
3. #14558384C2semidirect
8. #11924593C22semidirect
10. (C2×#3866)⋊C4C22semidirect
15. #11924507C4semidirect
17. C2×C4⋊Dic37C4semidirect
19. C22×D4×C37C4semidirect
108. C37#1507semidirect
110. C22×D4#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
#145583842
C2×#119245072
#150737