Finite Group Databasebeta

← #23782339

Subgroups — #23782339

Order 10432.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#19104720C211yesmaximal, characteristic, complemented
5#19104720C211yesmaximal, characteristic, complemented
6#19104718C211yesmaximal, characteristic, complemented
7#19104713C211yesmaximal, characteristic, complemented
8#19104712C211yesmaximal, characteristic, complemented
9#19104705C211yesmaximal, characteristic
10C4×D652C211yesmaximal, characteristic, complemented
11(C22⋊D163)⋊C4C211yesmaximal, characteristic, complemented
12#19104692C211yesmaximal, characteristic, complemented
13C2×(C2×D163)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D163C211yesmaximal, characteristic, complemented
15#117×C163C211yesmaximal, characteristic, complemented
16C23×D163C2211yescharacteristic
17C2×Dic326C2211yescharacteristic, complemented
18C2×D652C2211yescharacteristic
19C2×D652C2211yescharacteristic
20C2×C22⋊D163C2211yescharacteristic
21C22×Dic163C2211yescharacteristic
22C2×C4×D163C2211yescharacteristic
23C2×C4×D163C2211yescharacteristic
24C2×C4×D163C2211yescharacteristic, complemented
25C4⋊Dic163C2211yescharacteristic, complemented
26Dic163⋊C4C2211yescharacteristic, complemented
27Dic163⋊C4C2211yescharacteristic, complemented
28Dic163⋊C4C2211yescharacteristic, complemented
29Dic163⋊C4C2211yescharacteristic, complemented
30Dic163⋊C4C2211yescharacteristic, complemented
31C22⋊Dic163C2211yescharacteristic
32(C2×D163)⋊C4C2211yescharacteristic
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, complemented
41(C2×D163)⋊C4C2211yescharacteristic, complemented
42(C2×D163)⋊C4C2211yescharacteristic, complemented
43C4×Dic163C2211yescharacteristic, complemented
44C22×C4×C163C2211yescharacteristic
45C4⋊C4×C163C2211yescharacteristic, complemented
46C4⋊C4×C163C2211yescharacteristic, complemented
47C22⋊C4×C163C2211yescharacteristic
48C22⋊C4×C163C2211yescharacteristic
49C42×C163C2211yescharacteristic, complemented
50C42×C163C2211yescharacteristic, complemented
51C22×D163—22no—
52C22×D163—22no—
53C22×D163—41no—
54C22×D163C2311yescharacteristic
55C22×D163C2311yescharacteristic
56C22×D163C2311yescharacteristic
57Dic326—41no—
58D652—22no—
59D652—41no—
60C22⋊D163—22no—
61C2×Dic163—41no—
62C2×Dic163C2311yescharacteristic
63C2×Dic163C2311yescharacteristic
64C2×Dic163C2311yescharacteristic
65C2×Dic163C2311yescharacteristic
66C2×Dic163C2311yescharacteristic
67C4×D163—22no—
68C4×D163—41no—
69C4×D163—41no—
70C23×C163C2311yescharacteristic
71C2×C4×C163—22no—
72C2×C4×C163C2311yescharacteristic
73C2×C4×C163C2311yescharacteristic
74C2×C4×C163C2311yescharacteristic
75C2×C4×C163C2311yescharacteristic
76C2×C4×C163C2311yescharacteristic
77C2×C4×C163C2311yescharacteristic
78C22×C163—21no—
79C22×C163—21no—
80C22×C163#4112yes—
81C22×C163C2411yescharacteristic
82C2×D163—21no—
83C2×D163—21no—
84C2×D163—21no—
85C2×D163—21no—
86C2×D163—21no—
87C2×D163—21no—
88C2×D163—21no—
89C2×D163—21no—
90C2×D163—44no—
91C2×D163#4112yes—
92C4×C163—21no—
93C4×C163—21no—
94C4×C163—21no—
95C4×C163—21no—
96C4×C163—21no—
97C4×C163—21no—
98Dic163—21no—
99Dic163—21no—
100Dic163—21no—
101Dic163—21no—
102Dic163—21no—
103C2×C163—22no—
104C2×C163C2×#4111yescharacteristic
105C2×C163C2×#4111yescharacteristic
106C2×C163H(5,𝔽2)11yescharacteristic
107D163—22no—
108D163—41no—
109D163—41no—
110C163#55111yescharacteristic, complemented, Sylow
111#551—1631nomaximal, Sylow
112#126—1631no—
113#126—1631no—
114#124—1631no—
115#123—1631no—
116#123—1631no—
117#123—1631no—
118C22⋊Q8—1631no—
119C22⋊Q8—1631no—
120#120—1631no—
121C4×D4—1631no—
122C4×D4—1631no—
123#117—1631no—
124#117D16311yescharacteristic, complemented
125C2×C22⋊C4—1631no—
126C2×C22⋊C4—1631no—
127C24—1631no—
128C2×Q8—1631no—
129C2×D4—1631no—
130C2×D4—1631no—
131C2×D4—1631no—
132C22×C4—1631no—
133C22×C4—1631no—
134C22×C4—1631no—
135C22×C4—1631no—
136C22×C4C2×D16311yescharacteristic
137C4⋊C4—1631no—
138C4⋊C4—1631no—
139C4⋊C4—1631no—
140C4⋊C4—1631no—
141C4⋊C4—1631no—
142C4⋊C4—1631no—
143C4⋊C4C2×D16311yescharacteristic, complemented
144C4⋊C4C2×D16311yescharacteristic, complemented
145C22⋊C4—1631no—
146C22⋊C4—1631no—
147C22⋊C4—1631no—
148C22⋊C4—1631no—
149C22⋊C4—1631no—
150C22⋊C4—1631no—
151C22⋊C4—1631no—
152C22⋊C4—1631no—
153C22⋊C4—1631no—
154C22⋊C4—1631no—
155C22⋊C4—1631no—
156C22⋊C4—1631no—
157C22⋊C4C2×D16311yescharacteristic
158C22⋊C4C2×D16311yescharacteristic
159C42—1631no—
160C42C2×D16311yescharacteristic, complemented
161C42C2×D16311yescharacteristic, complemented
162C23—3262no—
163C23—3262no—
164C23—6521no—
165C23—1631no—
166C23—1631no—
167C23—1631no—
168C23C22×D16311yescharacteristic
169Q8—6521no—
170D4—3262no—
171D4—3262no—
172D4—6521no—
173C2×C4—22no—
174C2×C4—3262no—
175C2×C4—6521no—
176C2×C4—6521no—
177C2×C4—6521no—
178C2×C4—1631no—
179C2×C4—1631no—
180C2×C4—1631no—
181C2×C4—1631no—
182C2×C4—1631no—
183C2×C4C22×D16311yescharacteristic
184C2×C4C22×D16311yescharacteristic
185C2×C4C22×D16311yescharacteristic
186C2×C4C22×D16311yescharacteristic
187C2×C4C22×D16311yescharacteristic
188C2×C4C22×D16311yescharacteristic
189C22—21no—
190C22—21no—
191C22—3261no—
192C22—3261no—
193C22—3261no—
194C22—3261no—
195C22—3261no—
196C22—3261no—
197C22—3261no—
198C22—3261no—
199C22—6524no—
200C22—1632no—
201C22#1457969912yes—
202C22C23×D16311yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—3261no—
210C4—3261no—
211C4—3261no—
212C4—3261no—
213C4—3261no—
214C2—22no—
215C2—3262no—
216C2—6521no—
217C2—6521no—
218C2#41×D16311yescharacteristic
219C2C2×#1457969911yescharacteristic
220C2#1910478111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
Fitting#117×C163C2
prime radical#19104705C2
hypercenter#117D163
hypocenterC163#551
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #19104730C2semidirect
2. #19104729C2semidirect
3. #19104723C2semidirect
4. #19104720C2semidirect
5. #19104720C2semidirect
6. #19104718C2semidirect
7. #19104713C2semidirect
8. #19104712C2semidirect
10. C4×D652C2semidirect
11. (C22⋊D163)⋊C4C2semidirect
12. #19104692C2semidirect
13. C2×(C2×D163)⋊C4C2semidirect
14. C22⋊C4×D163C2semidirect
15. #117×C163C2semidirect
17. C2×Dic326C22semidirect
24. C2×C4×D163C22semidirect
25. C4⋊Dic163C22semidirect
26. Dic163⋊C4C22semidirect
27. Dic163⋊C4C22semidirect
28. Dic163⋊C4C22semidirect
29. Dic163⋊C4C22semidirect
30. Dic163⋊C4C22semidirect
40. (C2×D163)⋊C4C22semidirect
41. (C2×D163)⋊C4C22semidirect
42. (C2×D163)⋊C4C22semidirect
43. C4×Dic163C22semidirect
45. C4⋊C4×C163C22semidirect
46. C4⋊C4×C163C22semidirect
49. C42×C163C22semidirect
50. C42×C163C22semidirect
110. C163#551semidirect
124. #117D163semidirect
143. C4⋊C4C2×D163semidirect
144. C4⋊C4C2×D163semidirect
160. C42C2×D163semidirect
161. C42C2×D163semidirect