Finite Group Databasebeta

← #14558271

Subgroups — #14558271

Order 2368.

252 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 91 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#11924532C211yesmaximal, characteristic, complemented
2#11924531C211yesmaximal, characteristic, complemented
3#11924529C211yesmaximal, characteristic, complemented
4#11924521C211yesmaximal, characteristic, complemented
5#11924520C211yesmaximal, characteristic, complemented
6#11924519C211yesmaximal, characteristic, complemented
7#11924510C211yesmaximal, characteristic, complemented
8#11924509C211yesmaximal, characteristic, complemented
9#11924508C211yesmaximal, characteristic, complemented
10#11924508C211yesmaximal, characteristic, complemented
11#11924507C211yesmaximal, characteristic, complemented
12#11924506C211yesmaximal, characteristic, complemented
13#11924504C211yesmaximal, characteristic, complemented
14#11924504C211yesmaximal, characteristic, complemented
15#121×C37C211yesmaximal, characteristic, complemented
16C23×D37C2211yescharacteristic
17C2×D4×C37C2211yescharacteristic
18C2×D4×C37C2211yescharacteristic
19C2×D4×C37C2211yescharacteristic, complemented
20C22×C4×C37C2211yescharacteristic, complemented
21C2×C22⋊D37C2211yescharacteristic
22C2×C22⋊D37C2211yescharacteristic
23C2×C22⋊D37C2211yescharacteristic
24C2×C22⋊D37C2211yescharacteristic
25C2×C22⋊D37C2211yescharacteristic
26C2×C22⋊D37C2211yescharacteristic, complemented
27C2×C22⋊D37C2211yescharacteristic, complemented
28C22×Dic37C2211yescharacteristic, complemented
29C2×D148C2211yescharacteristic
30C2×D148C2211yescharacteristic
31C2×C4×D37C2211yescharacteristic, complemented
32C4⋊C4×C37C2211yescharacteristic, complemented
33C22⋊C4×C37C2211yescharacteristic
34C22⋊C4×C37C2211yescharacteristic, complemented
35C22⋊Dic37C2211yescharacteristic
36C22⋊Dic37C2211yescharacteristic
37C22⋊Dic37C2211yescharacteristic, complemented
38#10596938C2211yescharacteristic
39#10596938C2211yescharacteristic
40#10596938C2211yescharacteristic
41#10596938C2211yescharacteristic
42#10596938C2211yescharacteristic
43#10596938C2211yescharacteristic
44#10596938C2211yescharacteristic, complemented
45C4⋊Dic37C2211yescharacteristic, complemented
46C4⋊Dic37C2211yescharacteristic, complemented
47#10596936C2211yescharacteristic, complemented
48#10596936C2211yescharacteristic, complemented
49#10596936C2211yescharacteristic, complemented
50C4×Dic37C2211yescharacteristic, complemented
51C23×C37C2311yescharacteristic
52C23×C37C2311yescharacteristic
53C23×C37C2311yescharacteristic
54C22×D37—41no—
55C22×D37—41no—
56C22×D37—41no—
57C22×D37C2311yescharacteristic
58C22×D37C2311yescharacteristic
59C22×D37C2311yescharacteristic
60D4×C37—41no—
61D4×C37—41no—
62D4×C37—41no—
63C2×C4×C37—41no—
64C2×C4×C37C2311yescharacteristic
65C2×C4×C37C2311yescharacteristic
66C2×C4×C37C2311yescharacteristic
67C2×C4×C37C2311yescharacteristic
68C22⋊D37—41no—
69C22⋊D37—41no—
70C22⋊D37—41no—
71C22⋊D37—41no—
72C22⋊D37—41no—
73C22⋊D37—41no—
74C22⋊D37—41no—
75C2×Dic37—41no—
76C2×Dic37C2311yescharacteristic
77C2×Dic37C2311yescharacteristic
78C2×Dic37C2311yescharacteristic
79C2×Dic37C2311yescharacteristic
80C2×Dic37C2311yescharacteristic
81D148—41no—
82D148—41no—
83C4×D37—41no—
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—21no—
93C22×C37C2411yescharacteristic
94C2×D37—21no—
95C2×D37—21no—
96C2×D37—21no—
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—21no—
101C2×D37—21no—
102C2×D37—21no—
103C2×D37—44no—
104C4×C37—21no—
105C4×C37—21no—
106C4×C37—21no—
107C4×C37—21no—
108Dic37—21no—
109Dic37—21no—
110Dic37—21no—
111Dic37—21no—
112Dic37—21no—
113C2×C37—41no—
114C2×C37—41no—
115C2×C37—41no—
116C2×C37H(5,𝔽2)11yescharacteristic
117C2×C37H(5,𝔽2)11yescharacteristic
118C2×C37H(5,𝔽2)11yescharacteristic
119D37—41no—
120D37—41no—
121D37—41no—
122#560—371nomaximal, Sylow
123C37#56011yescharacteristic, complemented, Sylow
124#127—371no—
125#126—371no—
126#126—371no—
127#123—371no—
128#123—371no—
129#123—371no—
130#121—371no—
131#121—371no—
132#121—371no—
133#121—371no—
134#121—371no—
135#121D3711yescharacteristic, complemented
136#120—371no—
137#120—371no—
138#120—371no—
139C24—371no—
140C2×D4—371no—
141C2×D4—371no—
142C2×D4—371no—
143C2×D4—371no—
144C2×D4—371no—
145C2×D4—371no—
146C2×D4—371no—
147C2×D4—371no—
148C2×D4—371no—
149C2×D4C2×D3711yescharacteristic
150C2×D4C2×D3711yescharacteristic
151C2×D4C2×D3711yescharacteristic, complemented
152C22×C4—371no—
153C22×C4—371no—
154C22×C4C2×D3711yescharacteristic, complemented
155C4⋊C4—371no—
156C4⋊C4—371no—
157C4⋊C4—371no—
158C4⋊C4—371no—
159C4⋊C4—371no—
160C4⋊C4C2×D3711yescharacteristic, complemented
161C22⋊C4—371no—
162C22⋊C4—371no—
163C22⋊C4—371no—
164C22⋊C4—371no—
165C22⋊C4—371no—
166C22⋊C4—371no—
167C22⋊C4—371no—
168C22⋊C4—371no—
169C22⋊C4—371no—
170C22⋊C4—371no—
171C22⋊C4C2×D3711yescharacteristic
172C22⋊C4C2×D3711yescharacteristic, complemented
173C42—371no—
174C23—371no—
175C23—371no—
176C23—371no—
177C23—1481no—
178C23—1481no—
179C23—1481no—
180C23C22×D3711yescharacteristic
181C23C22×D3711yescharacteristic
182C23C22×D3711yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—1481no—
187D4—1481no—
188D4—1481no—
189D4—1481no—
190D4—1481no—
191D4—1481no—
192D4—1481no—
193D4—1481no—
194D4—1481no—
195C2×C4—41no—
196C2×C4—371no—
197C2×C4—371no—
198C2×C4—371no—
199C2×C4—371no—
200C2×C4—371no—
201C2×C4—1481no—
202C2×C4—1481no—
203C2×C4C22×D3711yescharacteristic
204C2×C4C22×D3711yescharacteristic
205C2×C4C22×D3711yescharacteristic
206C2×C4C22×D3711yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—741no—
217C22—741no—
218C22—741no—
219C22—741no—
220C22—741no—
221C22—741no—
222C22—741no—
223C22—741no—
224C22—741no—
225C22—1484no—
226C22C23×D3711yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—741no—
232C4—741no—
233C4—741no—
234C4—741no—
235C4—741no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—1481no—
240C2—1481no—
241C2—1481no—
242C2#1192458111yescharacteristic
243C2#1192458111yescharacteristic
244C2#1192458211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D37
commutator, socle, cosocleC22×C37C24
Fitting#121×C37C2
hypercenter#121D37
hypocenterC37#560
LCSG ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #11924532C2semidirect
2. #11924531C2semidirect
3. #11924529C2semidirect
4. #11924521C2semidirect
5. #11924520C2semidirect
6. #11924519C2semidirect
7. #11924510C2semidirect
8. #11924509C2semidirect
9. #11924508C2semidirect
10. #11924508C2semidirect
11. #11924507C2semidirect
12. #11924506C2semidirect
13. #11924504C2semidirect
14. #11924504C2semidirect
15. #121×C37C2semidirect
19. C2×D4×C37C22semidirect
20. C22×C4×C37C22semidirect
26. C2×C22⋊D37C22semidirect
27. C2×C22⋊D37C22semidirect
28. C22×Dic37C22semidirect
31. C2×C4×D37C22semidirect
32. C4⋊C4×C37C22semidirect
34. C22⋊C4×C37C22semidirect
37. C22⋊Dic37C22semidirect
44. #10596938C22semidirect
45. C4⋊Dic37C22semidirect
46. C4⋊Dic37C22semidirect
47. #10596936C22semidirect
48. #10596936C22semidirect
49. #10596936C22semidirect
50. C4×Dic37C22semidirect
123. C37#560semidirect
135. #121D37semidirect
151. C2×D4C2×D37semidirect
154. C22×C4C2×D37semidirect
160. C4⋊C4C2×D37semidirect
172. C22⋊C4C2×D37semidirect

Maximal subgroups

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

subgroupindex
#119245322
#119245312
#119245292
#119245212
#119245202
#119245192
#119245102
#119245092
#119245082
#119245072
#119245062
#119245042
#121×C372
#56037