Finite Group Databasebeta

← #14583637

Subgroups — #14583637

Order 2752.

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#13063321C211yesmaximal, characteristic, complemented
2#13063320C211yesmaximal, characteristic, complemented
3#13063318C211yesmaximal, characteristic, complemented
4#13063310C211yesmaximal, characteristic, complemented
5#13063309C211yesmaximal, characteristic, complemented
6#13063308C211yesmaximal, characteristic, complemented
7#13063299C211yesmaximal, characteristic, complemented
8#13063298C211yesmaximal, characteristic, complemented
9#13063297C211yesmaximal, characteristic, complemented
10#13063297C211yesmaximal, characteristic, complemented
11#13063296C211yesmaximal, characteristic, complemented
12#13063295C211yesmaximal, characteristic, complemented
13#13063293C211yesmaximal, characteristic, complemented
14#13063293C211yesmaximal, characteristic, complemented
15#121×C43C211yesmaximal, characteristic, complemented
16C23×D43C2211yescharacteristic
17C2×D4×C43C2211yescharacteristic
18C2×D4×C43C2211yescharacteristic
19C2×D4×C43C2211yescharacteristic, complemented
20C22×C4×C43C2211yescharacteristic, complemented
21C2×C22⋊D43C2211yescharacteristic
22C2×C22⋊D43C2211yescharacteristic
23C2×C22⋊D43C2211yescharacteristic
24C2×C22⋊D43C2211yescharacteristic
25C2×C22⋊D43C2211yescharacteristic
26C2×C22⋊D43C2211yescharacteristic, complemented
27C2×C22⋊D43C2211yescharacteristic, complemented
28C22×Dic43C2211yescharacteristic, complemented
29C2×D172C2211yescharacteristic
30C2×D172C2211yescharacteristic
31C2×C4×D43C2211yescharacteristic, complemented
32C4⋊C4×C43C2211yescharacteristic, complemented
33C22⋊C4×C43C2211yescharacteristic
34C22⋊C4×C43C2211yescharacteristic, complemented
35C22⋊Dic43C2211yescharacteristic
36C22⋊Dic43C2211yescharacteristic
37C22⋊Dic43C2211yescharacteristic, complemented
38(C2×D43)⋊C4C2211yescharacteristic
39(C2×D43)⋊C4C2211yescharacteristic
40(C2×D43)⋊C4C2211yescharacteristic
41(C2×D43)⋊C4C2211yescharacteristic
42(C2×D43)⋊C4C2211yescharacteristic
43(C2×D43)⋊C4C2211yescharacteristic
44(C2×D43)⋊C4C2211yescharacteristic, complemented
45C4⋊Dic43C2211yescharacteristic, complemented
46C4⋊Dic43C2211yescharacteristic, complemented
47Dic43⋊C4C2211yescharacteristic, complemented
48Dic43⋊C4C2211yescharacteristic, complemented
49Dic43⋊C4C2211yescharacteristic, complemented
50C4×Dic43C2211yescharacteristic, complemented
51C23×C43C2311yescharacteristic
52C23×C43C2311yescharacteristic
53C23×C43C2311yescharacteristic
54C22×D43—41no—
55C22×D43—41no—
56C22×D43—41no—
57C22×D43C2311yescharacteristic
58C22×D43C2311yescharacteristic
59C22×D43C2311yescharacteristic
60D4×C43—41no—
61D4×C43—41no—
62D4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43C2311yescharacteristic
65C2×C4×C43C2311yescharacteristic
66C2×C4×C43C2311yescharacteristic
67C2×C4×C43C2311yescharacteristic
68C22⋊D43—41no—
69C22⋊D43—41no—
70C22⋊D43—41no—
71C22⋊D43—41no—
72C22⋊D43—41no—
73C22⋊D43—41no—
74C22⋊D43—41no—
75C2×Dic43—41no—
76C2×Dic43C2311yescharacteristic
77C2×Dic43C2311yescharacteristic
78C2×Dic43C2311yescharacteristic
79C2×Dic43C2311yescharacteristic
80C2×Dic43C2311yescharacteristic
81D172—41no—
82D172—41no—
83C4×D43—41no—
84C22×C43—21no—
85C22×C43—21no—
86C22×C43—21no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43—21no—
92C22×C43—21no—
93C22×C43C2411yescharacteristic
94C2×D43—21no—
95C2×D43—21no—
96C2×D43—21no—
97C2×D43—21no—
98C2×D43—21no—
99C2×D43—21no—
100C2×D43—21no—
101C2×D43—21no—
102C2×D43—21no—
103C2×D43—44no—
104C4×C43—21no—
105C4×C43—21no—
106C4×C43—21no—
107C4×C43—21no—
108Dic43—21no—
109Dic43—21no—
110Dic43—21no—
111Dic43—21no—
112Dic43—21no—
113C2×C43—41no—
114C2×C43—41no—
115C2×C43—41no—
116C2×C43H(5,𝔽2)11yescharacteristic
117C2×C43H(5,𝔽2)11yescharacteristic
118C2×C43H(5,𝔽2)11yescharacteristic
119D43—41no—
120D43—41no—
121D43—41no—
122#560—431nomaximal, Sylow
123C43#56011yescharacteristic, complemented, Sylow
124#127—431no—
125#126—431no—
126#126—431no—
127#123—431no—
128#123—431no—
129#123—431no—
130#121—431no—
131#121—431no—
132#121—431no—
133#121—431no—
134#121—431no—
135#121D4311yescharacteristic, complemented
136#120—431no—
137#120—431no—
138#120—431no—
139C24—431no—
140C2×D4—431no—
141C2×D4—431no—
142C2×D4—431no—
143C2×D4—431no—
144C2×D4—431no—
145C2×D4—431no—
146C2×D4—431no—
147C2×D4—431no—
148C2×D4—431no—
149C2×D4C2×D4311yescharacteristic
150C2×D4C2×D4311yescharacteristic
151C2×D4C2×D4311yescharacteristic, complemented
152C22×C4—431no—
153C22×C4—431no—
154C22×C4C2×D4311yescharacteristic, complemented
155C4⋊C4—431no—
156C4⋊C4—431no—
157C4⋊C4—431no—
158C4⋊C4—431no—
159C4⋊C4—431no—
160C4⋊C4C2×D4311yescharacteristic, complemented
161C22⋊C4—431no—
162C22⋊C4—431no—
163C22⋊C4—431no—
164C22⋊C4—431no—
165C22⋊C4—431no—
166C22⋊C4—431no—
167C22⋊C4—431no—
168C22⋊C4—431no—
169C22⋊C4—431no—
170C22⋊C4—431no—
171C22⋊C4C2×D4311yescharacteristic
172C22⋊C4C2×D4311yescharacteristic, complemented
173C42—431no—
174C23—431no—
175C23—431no—
176C23—431no—
177C23—1721no—
178C23—1721no—
179C23—1721no—
180C23C22×D4311yescharacteristic
181C23C22×D4311yescharacteristic
182C23C22×D4311yescharacteristic
183D4—41no—
184D4—41no—
185D4—41no—
186D4—1721no—
187D4—1721no—
188D4—1721no—
189D4—1721no—
190D4—1721no—
191D4—1721no—
192D4—1721no—
193D4—1721no—
194D4—1721no—
195C2×C4—41no—
196C2×C4—431no—
197C2×C4—431no—
198C2×C4—431no—
199C2×C4—431no—
200C2×C4—431no—
201C2×C4—1721no—
202C2×C4—1721no—
203C2×C4C22×D4311yescharacteristic
204C2×C4C22×D4311yescharacteristic
205C2×C4C22×D4311yescharacteristic
206C2×C4C22×D4311yescharacteristic
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—21no—
216C22—861no—
217C22—861no—
218C22—861no—
219C22—861no—
220C22—861no—
221C22—861no—
222C22—861no—
223C22—861no—
224C22—861no—
225C22—1724no—
226C22C23×D4311yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—861no—
232C4—861no—
233C4—861no—
234C4—861no—
235C4—861no—
236C2—41no—
237C2—41no—
238C2—41no—
239C2—1721no—
240C2—1721no—
241C2—1721no—
242C2#1306337011yescharacteristic
243C2#1306337011yescharacteristic
244C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#121×C43C2
hypercenter#121D43
hypocenterC43#560
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #13063321C2semidirect
2. #13063320C2semidirect
3. #13063318C2semidirect
4. #13063310C2semidirect
5. #13063309C2semidirect
6. #13063308C2semidirect
7. #13063299C2semidirect
8. #13063298C2semidirect
9. #13063297C2semidirect
10. #13063297C2semidirect
11. #13063296C2semidirect
12. #13063295C2semidirect
13. #13063293C2semidirect
14. #13063293C2semidirect
15. #121×C43C2semidirect
19. C2×D4×C43C22semidirect
20. C22×C4×C43C22semidirect
26. C2×C22⋊D43C22semidirect
27. C2×C22⋊D43C22semidirect
28. C22×Dic43C22semidirect
31. C2×C4×D43C22semidirect
32. C4⋊C4×C43C22semidirect
34. C22⋊C4×C43C22semidirect
37. C22⋊Dic43C22semidirect
44. (C2×D43)⋊C4C22semidirect
45. C4⋊Dic43C22semidirect
46. C4⋊Dic43C22semidirect
47. Dic43⋊C4C22semidirect
48. Dic43⋊C4C22semidirect
49. Dic43⋊C4C22semidirect
50. C4×Dic43C22semidirect
123. C43#560semidirect
135. #121D43semidirect
151. C2×D4C2×D43semidirect
154. C22×C4C2×D43semidirect
160. C4⋊C4C2×D43semidirect
172. C22⋊C4C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633212
#130633202
#130633182
#130633102
#130633092
#130633082
#130632992
#130632982
#130632972
#130632962
#130632952
#130632932
#121×C432
#56043