Finite Group Databasebeta

← #14583488

Subgroups — #14583488

Order 2752.

250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 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#13063320C211yesmaximal, characteristic, complemented
2#13063313C211yesmaximal, characteristic, complemented
3#13063311C211yesmaximal, characteristic, complemented
4#13063310C211yesmaximal, characteristic, complemented
5#13063307C211yesmaximal, characteristic, complemented
6#13063303C211yesmaximal, characteristic, complemented
7#13063300C211yesmaximal, characteristic, complemented
8#13063300C211yesmaximal, characteristic, complemented
9#13063298C211yesmaximal, characteristic, complemented
10#13063295C211yesmaximal, characteristic, complemented
11#13063295C211yesmaximal, characteristic, complemented
12C4×D172C211yesmaximal, characteristic, complemented
13#13063287C211yesmaximal, characteristic, complemented
14C22⋊C4×D43C211yesmaximal, characteristic, complemented
15#126×C43C211yesmaximal, characteristic, complemented
16C23×D43C2211yescharacteristic
17C2×C22⋊D43C2211yescharacteristic
18C2×C22⋊D43C2211yescharacteristic
19C2×D172C2211yescharacteristic
20C2×D172C2211yescharacteristic
21C2×D172C2211yescharacteristic
22C2×D172C2211yescharacteristic
23C2×D172C2211yescharacteristic, complemented
24C2×C4×D43C2211yescharacteristic
25C2×C4×D43C2211yescharacteristic
26C2×C4×D43C2211yescharacteristic, complemented
27C2×C4×D43C2211yescharacteristic, complemented
28C2×Dic86C2211yescharacteristic, complemented
29C4⋊C4×C43C2211yescharacteristic, complemented
30C4⋊C4×C43C2211yescharacteristic, complemented
31C4⋊C4×C43C2211yescharacteristic, complemented
32C22⋊C4×C43C2211yescharacteristic
33C22⋊C4×C43C2211yescharacteristic
34C22⋊C4×C43C2211yescharacteristic
35C42×C43C2211yescharacteristic, complemented
36C22⋊Dic43C2211yescharacteristic
37(C2×D43)⋊C4C2211yescharacteristic
38(C2×D43)⋊C4C2211yescharacteristic
39(C2×D43)⋊C4C2211yescharacteristic
40(C2×D43)⋊C4C2211yescharacteristic
41(C2×D43)⋊C4C2211yescharacteristic
42(C2×D43)⋊C4C2211yescharacteristic
43(C2×D43)⋊C4C2211yescharacteristic, complemented
44(C2×D43)⋊C4C2211yescharacteristic, complemented
45(C2×D43)⋊C4C2211yescharacteristic, complemented
46(C2×D43)⋊C4C2211yescharacteristic, complemented
47C4⋊Dic43C2211yescharacteristic, complemented
48Dic43⋊C4C2211yescharacteristic, complemented
49Dic43⋊C4C2211yescharacteristic, complemented
50C4×Dic43C2211yescharacteristic, complemented
51C23×C43C2311yescharacteristic
52C22×D43—22no—
53C22×D43—41no—
54C22×D43—41no—
55C22×D43C2311yescharacteristic
56C22×D43C2311yescharacteristic
57C22×D43C2311yescharacteristic
58C22×D43C2311yescharacteristic
59C2×C4×C43C2311yescharacteristic
60C2×C4×C43C2311yescharacteristic
61C2×C4×C43C2311yescharacteristic
62C2×C4×C43C2311yescharacteristic
63C2×C4×C43C2311yescharacteristic
64C2×C4×C43C2311yescharacteristic
65C22⋊D43—41no—
66C22⋊D43—41no—
67C2×Dic43C2311yescharacteristic
68C2×Dic43C2311yescharacteristic
69C2×Dic43C2311yescharacteristic
70C2×Dic43C2311yescharacteristic
71D172—22no—
72D172—22no—
73D172—41no—
74D172—41no—
75D172—41no—
76C4×D43—41no—
77C4×D43—41no—
78C4×D43—41no—
79C4×D43—41no—
80Dic86—41no—
81C22×C43—21no—
82C22×C43—21no—
83C22×C43—21no—
84C22×C43C2411yescharacteristic
85C2×D43—21no—
86C2×D43—21no—
87C2×D43—21no—
88C2×D43—21no—
89C2×D43—21no—
90C2×D43—21no—
91C2×D43—21no—
92C2×D43—21no—
93C2×D43—21no—
94C2×D43—21no—
95C2×D43—21no—
96C2×D43—44no—
97C2×D43#4112yes—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—21no—
103C4×C43—21no—
104Dic43—21no—
105Dic43—21no—
106Dic43—21no—
107Dic43—21no—
108C2×C43—41no—
109C2×C43C2×#4111yescharacteristic
110C2×C43H(5,𝔽2)11yescharacteristic
111C2×C43H(5,𝔽2)11yescharacteristic
112D43—22no—
113D43—41no—
114D43—41no—
115D43—41no—
116#538—431nomaximal, Sylow
117C43#53811yescharacteristic, complemented, Sylow
118#126—431no—
119#126D4311yescharacteristic, complemented
120#124—431no—
121#124—431no—
122#123—431no—
123#123—431no—
124C22⋊Q8—431no—
125#121—431no—
126#121—431no—
127#121—431no—
128#120—431no—
129#120—431no—
130C4×D4—431no—
131C4×D4—431no—
132C2×C22⋊C4—431no—
133C24—431no—
134C2×Q8—431no—
135C2×D4—431no—
136C2×D4—431no—
137C2×D4—431no—
138C2×D4—431no—
139C2×D4—431no—
140C2×D4—431no—
141C2×D4—431no—
142C22×C4—431no—
143C22×C4—431no—
144C22×C4—431no—
145C22×C4—431no—
146C4⋊C4—431no—
147C4⋊C4—431no—
148C4⋊C4—431no—
149C4⋊C4C2×D4311yescharacteristic, complemented
150C4⋊C4C2×D4311yescharacteristic, complemented
151C4⋊C4C2×D4311yescharacteristic, complemented
152C22⋊C4—431no—
153C22⋊C4—431no—
154C22⋊C4—431no—
155C22⋊C4—431no—
156C22⋊C4—431no—
157C22⋊C4—431no—
158C22⋊C4—431no—
159C22⋊C4—431no—
160C22⋊C4—431no—
161C22⋊C4—431no—
162C22⋊C4—431no—
163C22⋊C4C2×D4311yescharacteristic
164C22⋊C4C2×D4311yescharacteristic
165C22⋊C4C2×D4311yescharacteristic
166C42—431no—
167C42C2×D4311yescharacteristic, complemented
168C23—431no—
169C23—431no—
170C23—431no—
171C23—431no—
172C23—862no—
173C23—1721no—
174C23—1721no—
175C23C22×D4311yescharacteristic
176Q8—1721no—
177D4—862no—
178D4—862no—
179D4—1721no—
180D4—1721no—
181D4—1721no—
182D4—1721no—
183D4—1721no—
184C2×C4—431no—
185C2×C4—431no—
186C2×C4—431no—
187C2×C4—431no—
188C2×C4—1721no—
189C2×C4—1721no—
190C2×C4—1721no—
191C2×C4—1721no—
192C2×C4C22×D4311yescharacteristic
193C2×C4C22×D4311yescharacteristic
194C2×C4C22×D4311yescharacteristic
195C2×C4C22×D4311yescharacteristic
196C2×C4C22×D4311yescharacteristic
197C2×C4C22×D4311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—432no—
202C22—861no—
203C22—861no—
204C22—861no—
205C22—861no—
206C22—861no—
207C22—861no—
208C22—861no—
209C22—861no—
210C22—861no—
211C22—861no—
212C22—861no—
213C22—1724no—
214C22C23×D4311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—21no—
221C4—861no—
222C4—861no—
223C4—861no—
224C4—861no—
225C2—41no—
226C2—862no—
227C2—1721no—
228C2—1721no—
229C2—1721no—
230C2#41×D4311yescharacteristic
231C2#1306337111yescharacteristic
232C2#1306337111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
Fitting#126×C43C2
hypercenter#126D43
hypocenterC43#538
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
1. #13063320C2semidirect
2. #13063313C2semidirect
3. #13063311C2semidirect
4. #13063310C2semidirect
5. #13063307C2semidirect
6. #13063303C2semidirect
7. #13063300C2semidirect
8. #13063300C2semidirect
9. #13063298C2semidirect
10. #13063295C2semidirect
11. #13063295C2semidirect
12. C4×D172C2semidirect
13. #13063287C2semidirect
14. C22⋊C4×D43C2semidirect
15. #126×C43C2semidirect
23. C2×D172C22semidirect
26. C2×C4×D43C22semidirect
27. C2×C4×D43C22semidirect
28. C2×Dic86C22semidirect
29. C4⋊C4×C43C22semidirect
30. C4⋊C4×C43C22semidirect
31. C4⋊C4×C43C22semidirect
35. C42×C43C22semidirect
43. (C2×D43)⋊C4C22semidirect
44. (C2×D43)⋊C4C22semidirect
45. (C2×D43)⋊C4C22semidirect
46. (C2×D43)⋊C4C22semidirect
47. C4⋊Dic43C22semidirect
48. Dic43⋊C4C22semidirect
49. Dic43⋊C4C22semidirect
50. C4×Dic43C22semidirect
117. C43#538semidirect
119. #126D43semidirect
149. C4⋊C4C2×D43semidirect
150. C4⋊C4C2×D43semidirect
151. C4⋊C4C2×D43semidirect
167. C42C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633202
#130633132
#130633112
#130633102
#130633072
#130633032
#130633002
#130632982
#130632952
C4×D1722
#130632872
C22⋊C4×D432
#126×C432
#53843