Finite Group Databasebeta

← #14558118

Subgroups — #14558118

Order 2368.

250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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#11924529C211yesmaximal, characteristic, complemented
2#11924529C211yesmaximal, characteristic, complemented
3#11924523C211yesmaximal, characteristic, complemented
4#11924522C211yesmaximal, characteristic, complemented
5#11924518C211yesmaximal, characteristic, complemented
6#11924517C211yesmaximal, characteristic, complemented
7#11924513C211yesmaximal, characteristic, complemented
8#11924508C211yesmaximal, characteristic, complemented
9#11924508C211yesmaximal, characteristic, complemented
10#11924507C211yesmaximal, characteristic, complemented
11#11924505C211yesmaximal, characteristic, complemented
12D4×Dic37C211yesmaximal, characteristic, complemented
13#11924496C211yesmaximal, characteristic, complemented
14C2×C22⋊Dic37C211yesmaximal, characteristic, complemented
15#120×C37C211yesmaximal, characteristic, complemented
16C24×C37C2211yescharacteristic
17C2×D4×C37C2211yescharacteristic
18C2×D4×C37C2211yescharacteristic
19C2×D4×C37C2211yescharacteristic
20C2×C22⋊D37C2211yescharacteristic
21C2×C22⋊D37C2211yescharacteristic
22C2×C22⋊D37C2211yescharacteristic
23C2×C22⋊D37C2211yescharacteristic, complemented
24C22×Dic37C2211yescharacteristic
25C22×Dic37C2211yescharacteristic
26C22×Dic37C2211yescharacteristic, complemented
27C2×C4×D37C2211yescharacteristic, complemented
28C2×Dic74C2211yescharacteristic, complemented
29C22⋊C4×C37C2211yescharacteristic
30C22⋊C4×C37C2211yescharacteristic
31C22⋊C4×C37C2211yescharacteristic
32C22⋊Dic37C2211yescharacteristic
33C22⋊Dic37C2211yescharacteristic
34C22⋊Dic37C2211yescharacteristic
35C22⋊Dic37C2211yescharacteristic
36C22⋊Dic37C2211yescharacteristic
37C22⋊Dic37C2211yescharacteristic
38C22⋊Dic37C2211yescharacteristic
39C22⋊Dic37C2211yescharacteristic, complemented
40C22⋊Dic37C2211yescharacteristic, complemented
41#10596938C2211yescharacteristic, complemented
42#10596938C2211yescharacteristic, complemented
43C4⋊Dic37C2211yescharacteristic, complemented
44C4⋊Dic37C2211yescharacteristic, complemented
45#10596936C2211yescharacteristic, complemented
46#10596936C2211yescharacteristic, complemented
47#10596936C2211yescharacteristic, complemented
48#10596936C2211yescharacteristic, complemented
49C4×Dic37C2211yescharacteristic, complemented
50C4×Dic37C2211yescharacteristic, complemented
51C23×C37—22no—
52C23×C37—41no—
53C23×C37—41no—
54C23×C37C2311yescharacteristic
55C23×C37C2311yescharacteristic
56C23×C37C2311yescharacteristic
57C23×C37C2311yescharacteristic
58C22×D37C2311yescharacteristic
59D4×C37—22no—
60D4×C37—41no—
61D4×C37—41no—
62C2×C4×C37C2311yescharacteristic
63C2×C4×C37C2311yescharacteristic
64C2×C4×C37C2311yescharacteristic
65C22⋊D37—22no—
66C22⋊D37—41no—
67C22⋊D37—41no—
68C22⋊D37—41no—
69C2×Dic37—41no—
70C2×Dic37—41no—
71C2×Dic37—41no—
72C2×Dic37C2311yescharacteristic
73C2×Dic37C2311yescharacteristic
74C2×Dic37C2311yescharacteristic
75C2×Dic37C2311yescharacteristic
76C2×Dic37C2311yescharacteristic
77C2×Dic37C2311yescharacteristic
78C2×Dic37C2311yescharacteristic
79C4×D37—41no—
80Dic74—41no—
81C22×C37—21no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—21no—
85C22×C37—21no—
86C22×C37—21no—
87C22×C37—21no—
88C22×C37—21no—
89C22×C37—21no—
90C22×C37—21no—
91C22×C37—21no—
92C22×C37—44no—
93C22×C37#4112yes—
94C22×C37C2411yescharacteristic
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—21no—
98C4×C37—21no—
99C4×C37—21no—
100C4×C37—21no—
101Dic37—21no—
102Dic37—21no—
103Dic37—21no—
104Dic37—21no—
105Dic37—21no—
106Dic37—21no—
107Dic37—21no—
108C2×C37—22no—
109C2×C37—41no—
110C2×C37—41no—
111C2×C37—41no—
112C2×C37C2×#4111yescharacteristic
113C2×C37H(5,𝔽2)11yescharacteristic
114C2×C37H(5,𝔽2)11yescharacteristic
115D37—41no—
116#538—371nomaximal, Sylow
117C37#53811yescharacteristic, complemented, Sylow
118#126—371no—
119#126—371no—
120#124—371no—
121#124—371no—
122#123—371no—
123#123—371no—
124C22⋊Q8—371no—
125#121—371no—
126#121—371no—
127#121—371no—
128#120—371no—
129#120D3711yescharacteristic, complemented
130C4×D4—371no—
131C4×D4—371no—
132C2×C22⋊C4—371no—
133C24C2×D3711yescharacteristic
134C2×Q8—371no—
135C2×D4—371no—
136C2×D4—371no—
137C2×D4—371no—
138C2×D4—371no—
139C2×D4C2×D3711yescharacteristic
140C2×D4C2×D3711yescharacteristic
141C2×D4C2×D3711yescharacteristic
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—371no—
146C4⋊C4—371no—
147C4⋊C4—371no—
148C4⋊C4—371no—
149C4⋊C4—371no—
150C4⋊C4—371no—
151C4⋊C4—371no—
152C22⋊C4—371no—
153C22⋊C4—371no—
154C22⋊C4—371no—
155C22⋊C4—371no—
156C22⋊C4—371no—
157C22⋊C4—371no—
158C22⋊C4—371no—
159C22⋊C4—371no—
160C22⋊C4—371no—
161C22⋊C4—371no—
162C22⋊C4—371no—
163C22⋊C4C2×D3711yescharacteristic
164C22⋊C4C2×D3711yescharacteristic
165C22⋊C4C2×D3711yescharacteristic
166C42—371no—
167C42—371no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—371no—
172C23C22×D3711yescharacteristic
173C23C22×D3711yescharacteristic
174C23C22×D3711yescharacteristic
175C23C22×D3711yescharacteristic
176Q8—1481no—
177D4—22no—
178D4—41no—
179D4—41no—
180D4—742no—
181D4—1481no—
182D4—1481no—
183D4—1481no—
184C2×C4—371no—
185C2×C4—371no—
186C2×C4—371no—
187C2×C4—371no—
188C2×C4—371no—
189C2×C4—371no—
190C2×C4—371no—
191C2×C4—1481no—
192C2×C4—1481no—
193C2×C4—1481no—
194C2×C4—1481no—
195C2×C4C22×D3711yescharacteristic
196C2×C4C22×D3711yescharacteristic
197C2×C4C22×D3711yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—44no—
210C22—741no—
211C22—741no—
212C22—741no—
213C22#1059696412yes—
214C22C23×D3711yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—741no—
219C4—741no—
220C4—741no—
221C4—741no—
222C4—741no—
223C4—741no—
224C4—741no—
225C2—22no—
226C2—41no—
227C2—41no—
228C2—41no—
229C2—1481no—
230C2C2×#1059696411yescharacteristic
231C2#1192458111yescharacteristic
232C2#1192458111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D37
commutator, socle, cosocleC22×C37C24
Fitting#120×C37C2
hypercenter#120D37
hypocenterC37#538
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #11924529C2semidirect
2. #11924529C2semidirect
3. #11924523C2semidirect
4. #11924522C2semidirect
5. #11924518C2semidirect
6. #11924517C2semidirect
7. #11924513C2semidirect
8. #11924508C2semidirect
9. #11924508C2semidirect
10. #11924507C2semidirect
11. #11924505C2semidirect
12. D4×Dic37C2semidirect
13. #11924496C2semidirect
14. C2×C22⋊Dic37C2semidirect
15. #120×C37C2semidirect
23. C2×C22⋊D37C22semidirect
26. C22×Dic37C22semidirect
27. C2×C4×D37C22semidirect
28. C2×Dic74C22semidirect
39. C22⋊Dic37C22semidirect
40. C22⋊Dic37C22semidirect
41. #10596938C22semidirect
42. #10596938C22semidirect
43. C4⋊Dic37C22semidirect
44. C4⋊Dic37C22semidirect
45. #10596936C22semidirect
46. #10596936C22semidirect
47. #10596936C22semidirect
48. #10596936C22semidirect
49. C4×Dic37C22semidirect
50. C4×Dic37C22semidirect
117. C37#538semidirect
129. #120D37semidirect

Maximal subgroups

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

subgroupindex
#119245292
#119245232
#119245222
#119245182
#119245172
#119245132
#119245082
#119245072
#119245052
D4×Dic372
#119244962
C2×C22⋊Dic372
#120×C372
#53837