Finite Group Databasebeta

← #18010032

Subgroups — #18010032

Order 4736.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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
1D37⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#14558475C211yesmaximal, characteristic, complemented
3#14558384C214yesmaximal, complemented
4C2×#11924507C211yesmaximal, characteristic
5C2×D37⋊C8—21no—
6C2×C4⋊#3866—21no—
7C2×C22⋊#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—42no—
30C2×C22⋊D37—42no—
31C22×Dic37—21no—
32C22×Dic37D411yescharacteristic
33C2×C4×D37—42no—
34C2×C4×D37C2×C411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37C2311yescharacteristic
38C22⋊#3866—42no—
39C2×#64438—22no—
40C4⋊#3866—42no—
41D37⋊C8—42no—
42C22⋊Dic37—22no—
43C22⋊Dic37—22no—
44C4⋊Dic37—21no—
45C4⋊Dic37C2×C412yes—
46C23×C37—22no—
47C23×C37—42no—
48C23×C37—42no—
49C23×C37—42no—
50C23×C37C22⋊C411yescharacteristic
51C22×D37—41no—
52C22×D37—41no—
53C22×D37C22⋊C411yescharacteristic
54C22×D37D812yes—
55C22×D37SD1612yes—
56C22×D37C2×D411yescharacteristic
57C2×#3866—42no—
58C2×#3866—42no—
59C2×#3866—42no—
60D4×C37—42no—
61D4×C37—42no—
62C2×C4×C37—22no—
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22×C411yescharacteristic
65C22⋊D37—44no—
66C22⋊D37—42no—
67C22⋊D37—42no—
68C2×Dic37—22no—
69C2×Dic37—41no—
70C2×Dic37—42no—
71C2×Dic37C22⋊C411yescharacteristic
72C2×Dic37C2×D411yescharacteristic
73C4×D37—22no—
74C4×D37—22no—
75C4×D37—41no—
76C4×D37—41no—
77#64438—42no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—42no—
81C22×C37—42no—
82C22×C37—42no—
83C22×C37—84no—
84C22×C37#10212yes—
85C22×C37C2×C22⋊C411yescharacteristic
86C2×D37—21no—
87C2×D37—21no—
88C2×D37—21no—
89C2×D37—21no—
90C2×D37—42no—
91C2×D37—42no—
92C2×D37#10212yes—
93C2×D37C2×D811yescharacteristic
94C2×D37C2×SD1611yescharacteristic
95#3866—82no—
96C4×C37—21no—
97C4×C37#9912yes—
98Dic37—21no—
99Dic37—21no—
100Dic37—42no—
101#1519—371nomaximal, Sylow
102C2×C37—22no—
103C2×C37—82no—
104C2×C37C2×#9911yescharacteristic
105C2×C37C2×#10211yescharacteristic
106C2×C37#42111yescharacteristic
107D37—21no—
108D37—22no—
109D37—21no—
110C2×#121—371no—
111C2×C22⋊C8—371no—
112#380—371no—
113#327—374no—
114C37#151911yescharacteristic, complemented, Sylow
115C22×D4—741no—
116C22×D4#386611yescharacteristic, complemented
117C23×C4—371no—
118C22×C8—741no—
119#121—372no—
120#121—372no—
121#121—741no—
122#121—741no—
123C2×C4⋊C4—371no—
124C2×C4⋊C4—741no—
125C2×C22⋊C4—741no—
126C2×C22⋊C4—741no—
127C22⋊C8—372no—
128C22⋊C8—741no—
129#95—372no—
130C24—21no—
131C24—371no—
132C2×D4—21no—
133C2×D4—42no—
134C2×D4—742no—
135C2×D4—742no—
136C2×D4—1482no—
137C2×D4—1482no—
138C2×D4C2×#386612yes—
139C22×C4—371no—
140C22×C4—371no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—741no—
145C22×C4—742no—
146C22×C4—1482no—
147C22×C4C2×#386611yescharacteristic
148C2×C8—742no—
149C2×C8—1482no—
150C4⋊C4—372no—
151C4⋊C4—741no—
152C4⋊C4—1482no—
153C22⋊C4—742no—
154C22⋊C4—742no—
155C22⋊C4—1482no—
156C23—22no—
157C23—42no—
158C23—42no—
159C23—42no—
160C23—371no—
161C23—371no—
162C23—372no—
163C23—372no—
164C23—1481no—
165C23—1481no—
166C23C22⋊#386611yescharacteristic
167D4—42no—
168D4—42no—
169D4—1482no—
170D4—1484no—
171D4—1482no—
172C2×C4—22no—
173C2×C4—371no—
174C2×C4—371no—
175C2×C4—742no—
176C2×C4—742no—
177C2×C4—742no—
178C2×C4—1481no—
179C2×C4—1481no—
180C2×C4—1482no—
181C2×C4—1482no—
182C2×C4—1482no—
183C2×C4—1481no—
184C2×C4—1482no—
185C2×C4C22⋊#386611yescharacteristic
186C2×C4C22×#386611yescharacteristic
187C8—1482no—
188C22—21no—
189C22—21no—
190C22—42no—
191C22—42no—
192C22—42no—
193C22—84no—
194C22—371no—
195C22—372no—
196C22—371no—
197C22—741no—
198C22—741no—
199C22—741no—
200C22—741no—
201C22—1482no—
202C22—1482no—
203C22#1192459812yes—
204C22C2×C22⋊#386611yescharacteristic
205C4—21no—
206C4—2962no—
207C4—741no—
208C4—741no—
209C4—1482no—
210C4#1192459412yes—
211C2—22no—
212C2—82no—
213C2—741no—
214C2—742no—
215C2—741no—
216C2C2×#1192459411yescharacteristic
217C2C2×#1192459811yescharacteristic
218C2#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#1519
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. D37⋊(C22⋊C8)C2semidirect
2. #14558475C2semidirect
3. #14558384C2semidirect
8. #11924593C22semidirect
10. (C2×#3866)⋊C4C22semidirect
15. #11924507C4semidirect
17. C2×C4⋊Dic37C4semidirect
19. C22×D4×C37C4semidirect
114. C37#1519semidirect
116. C22×D4#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C22⋊C8)2
#145584752
#145583842
C2×#119245072
#151937