Finite Group Databasebeta

← #23782248

Subgroups — #23782248

Order 10432.

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#19104730C211yesmaximal, characteristic, complemented
2#19104729C211yesmaximal, characteristic, complemented
3#19104723C211yesmaximal, characteristic, complemented
4#19104721C211yesmaximal, characteristic, complemented
5#19104720C211yesmaximal, characteristic, complemented
6#19104718C211yesmaximal, characteristic, complemented
7#19104712C211yesmaximal, characteristic, complemented
8#19104709C211yesmaximal, characteristic, complemented
9#19104708C211yesmaximal, characteristic, complemented
10#19104707C211yesmaximal, characteristic, complemented
11#19104705C211yesmaximal, characteristic, complemented
12#19104703C211yesmaximal, characteristic, complemented
13C4×C22⋊D163C211yesmaximal, characteristic, complemented
14C2×(C2×D163)⋊C4C211yesmaximal, characteristic, complemented
15C4×D4×C163C211yesmaximal, characteristic, complemented
16C23×D163C2211yescharacteristic
17C2×Dic326C2211yescharacteristic, complemented
18C2×D652C2211yescharacteristic
19C2×D652C2211yescharacteristic
20C2×C22⋊D163C2211yescharacteristic
21C2×C22⋊D163C2211yescharacteristic
22C2×C22⋊D163C2211yescharacteristic
23C2×C22⋊D163C2211yescharacteristic, complemented
24C22×Dic163C2211yescharacteristic
25C2×C4×D163C2211yescharacteristic, complemented
26C4⋊Dic163C2211yescharacteristic, complemented
27Dic163⋊C4C2211yescharacteristic, complemented
28Dic163⋊C4C2211yescharacteristic, complemented
29Dic163⋊C4C2211yescharacteristic, complemented
30Dic163⋊C4C2211yescharacteristic, complemented
31C22⋊Dic163C2211yescharacteristic
32C22⋊Dic163C2211yescharacteristic, complemented
33(C2×D163)⋊C4C2211yescharacteristic
34(C2×D163)⋊C4C2211yescharacteristic
35(C2×D163)⋊C4C2211yescharacteristic
36(C2×D163)⋊C4C2211yescharacteristic
37(C2×D163)⋊C4C2211yescharacteristic
38(C2×D163)⋊C4C2211yescharacteristic
39(C2×D163)⋊C4C2211yescharacteristic
40(C2×D163)⋊C4C2211yescharacteristic
41(C2×D163)⋊C4C2211yescharacteristic, complemented
42(C2×D163)⋊C4C2211yescharacteristic, complemented
43C4×Dic163C2211yescharacteristic, complemented
44C2×D4×C163C2211yescharacteristic
45C22×C4×C163C2211yescharacteristic
46C22×C4×C163C2211yescharacteristic, complemented
47C4⋊C4×C163C2211yescharacteristic, complemented
48C22⋊C4×C163C2211yescharacteristic
49C22⋊C4×C163C2211yescharacteristic, complemented
50C42×C163C2211yescharacteristic, complemented
51C22×D163—22no—
52C22×D163—41no—
53C22×D163—41no—
54C22×D163C2311yescharacteristic
55C22×D163C2311yescharacteristic
56C22×D163C2311yescharacteristic
57Dic326—41no—
58D652—41no—
59D652—41no—
60C22⋊D163—22no—
61C22⋊D163—41no—
62C22⋊D163—41no—
63C22⋊D163—41no—
64C2×Dic163—41no—
65C2×Dic163C2311yescharacteristic
66C2×Dic163C2311yescharacteristic
67C2×Dic163C2311yescharacteristic
68C2×Dic163C2311yescharacteristic
69C2×Dic163C2311yescharacteristic
70C4×D163—41no—
71C23×C163C2311yescharacteristic
72C23×C163C2311yescharacteristic
73D4×C163—22no—
74C2×C4×C163—41no—
75C2×C4×C163—41no—
76C2×C4×C163C2311yescharacteristic
77C2×C4×C163C2311yescharacteristic
78C2×C4×C163C2311yescharacteristic
79C2×C4×C163C2311yescharacteristic
80C2×C4×C163C2311yescharacteristic
81C22×C163—21no—
82C22×C163—21no—
83C22×C163—21no—
84C22×C163—21no—
85C22×C163—21no—
86C22×C163#4112yes—
87C22×C163C2411yescharacteristic
88C2×D163—21no—
89C2×D163—21no—
90C2×D163—21no—
91C2×D163—21no—
92C2×D163—21no—
93C2×D163—21no—
94C2×D163—21no—
95C2×D163—21no—
96C2×D163—21no—
97C2×D163—44no—
98C4×C163—21no—
99C4×C163—21no—
100C4×C163—21no—
101C4×C163—21no—
102C4×C163—21no—
103Dic163—21no—
104Dic163—21no—
105Dic163—21no—
106Dic163—21no—
107Dic163—21no—
108C2×C163—22no—
109C2×C163—41no—
110C2×C163C2×#4111yescharacteristic
111C2×C163H(5,𝔽2)11yescharacteristic
112C2×C163H(5,𝔽2)11yescharacteristic
113D163—41no—
114D163—41no—
115D163—41no—
116C163#53811yescharacteristic, complemented, Sylow
117#538—1631nomaximal, Sylow
118#126—1631no—
119#126—1631no—
120#124—1631no—
121#124—1631no—
122#123—1631no—
123#123—1631no—
124C22⋊Q8—1631no—
125#121—1631no—
126#121—1631no—
127#121—1631no—
128#120—1631no—
129#120—1631no—
130C4×D4—1631no—
131C4×D4D16311yescharacteristic, complemented
132C2×C22⋊C4—1631no—
133C24—1631no—
134C2×Q8—1631no—
135C2×D4—1631no—
136C2×D4—1631no—
137C2×D4—1631no—
138C2×D4—1631no—
139C2×D4—1631no—
140C2×D4—1631no—
141C2×D4C2×D16311yescharacteristic
142C22×C4—1631no—
143C22×C4—1631no—
144C22×C4C2×D16311yescharacteristic
145C22×C4C2×D16311yescharacteristic, complemented
146C4⋊C4—1631no—
147C4⋊C4—1631no—
148C4⋊C4—1631no—
149C4⋊C4—1631no—
150C4⋊C4—1631no—
151C4⋊C4C2×D16311yescharacteristic, complemented
152C22⋊C4—1631no—
153C22⋊C4—1631no—
154C22⋊C4—1631no—
155C22⋊C4—1631no—
156C22⋊C4—1631no—
157C22⋊C4—1631no—
158C22⋊C4—1631no—
159C22⋊C4—1631no—
160C22⋊C4—1631no—
161C22⋊C4—1631no—
162C22⋊C4—1631no—
163C22⋊C4—1631no—
164C22⋊C4C2×D16311yescharacteristic
165C22⋊C4C2×D16311yescharacteristic, complemented
166C42—1631no—
167C42C2×D16311yescharacteristic, complemented
168C23—3262no—
169C23—6521no—
170C23—6521no—
171C23—1631no—
172C23—1631no—
173C23—1631no—
174C23C22×D16311yescharacteristic
175C23C22×D16311yescharacteristic
176Q8—6521no—
177D4—22no—
178D4—3262no—
179D4—6521no—
180D4—6521no—
181D4—6521no—
182D4—6521no—
183D4—6521no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—6521no—
187C2×C4—6521no—
188C2×C4—1631no—
189C2×C4—1631no—
190C2×C4—1631no—
191C2×C4—1631no—
192C2×C4—1631no—
193C2×C4C22×D16311yescharacteristic
194C2×C4C22×D16311yescharacteristic
195C2×C4C22×D16311yescharacteristic
196C2×C4C22×D16311yescharacteristic
197C2×C4C22×D16311yescharacteristic
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—3261no—
204C22—3261no—
205C22—3261no—
206C22—3261no—
207C22—3261no—
208C22—3261no—
209C22—3261no—
210C22—3261no—
211C22—3261no—
212C22—6524no—
213C22#1457969912yes—
214C22C23×D16311yescharacteristic
215C4—21no—
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—3261no—
221C4—3261no—
222C4—3261no—
223C4—3261no—
224C4—3261no—
225C2—22no—
226C2—41no—
227C2—6521no—
228C2—6521no—
229C2—6521no—
230C2C2×#1457969911yescharacteristic
231C2#1910478011yescharacteristic
232C2#1910478111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
FittingC4×D4×C163C2
hypercenterC4×D4D163
hypocenterC163#538
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #19104730C2semidirect
2. #19104729C2semidirect
3. #19104723C2semidirect
4. #19104721C2semidirect
5. #19104720C2semidirect
6. #19104718C2semidirect
7. #19104712C2semidirect
8. #19104709C2semidirect
9. #19104708C2semidirect
10. #19104707C2semidirect
11. #19104705C2semidirect
12. #19104703C2semidirect
13. C4×C22⋊D163C2semidirect
14. C2×(C2×D163)⋊C4C2semidirect
15. C4×D4×C163C2semidirect
17. C2×Dic326C22semidirect
23. C2×C22⋊D163C22semidirect
25. C2×C4×D163C22semidirect
26. C4⋊Dic163C22semidirect
27. Dic163⋊C4C22semidirect
28. Dic163⋊C4C22semidirect
29. Dic163⋊C4C22semidirect
30. Dic163⋊C4C22semidirect
32. C22⋊Dic163C22semidirect
41. (C2×D163)⋊C4C22semidirect
42. (C2×D163)⋊C4C22semidirect
43. C4×Dic163C22semidirect
46. C22×C4×C163C22semidirect
47. C4⋊C4×C163C22semidirect
49. C22⋊C4×C163C22semidirect
50. C42×C163C22semidirect
116. C163#538semidirect
131. C4×D4D163semidirect
145. C22×C4C2×D163semidirect
151. C4⋊C4C2×D163semidirect
165. C22⋊C4C2×D163semidirect
167. C42C2×D163semidirect