Finite Group Databasebeta

← #23782344

Subgroups — #23782344

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#19104721C211yesmaximal, characteristic, complemented
4#19104718C211yesmaximal, characteristic, complemented
5#19104717C211yesmaximal, characteristic, complemented
6#19104716C211yesmaximal, characteristic, complemented
7#19104714C211yesmaximal, characteristic, complemented
8#19104713C211yesmaximal, characteristic, complemented
9#19104703C211yesmaximal, characteristic
10C4×C22⋊D163C211yesmaximal, characteristic, complemented
11#19104692C211yesmaximal, characteristic, complemented
12#19104691C211yesmaximal, characteristic, complemented
13C2×(C2×D163)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D163C211yesmaximal, characteristic, complemented
15C4×D4×C163C211yesmaximal, characteristic, complemented
16C23×D163C2211yescharacteristic
17C2×Dic326C2211yescharacteristic, complemented
18C2×C22⋊D163C2211yescharacteristic
19C2×C22⋊D163C2211yescharacteristic
20C22×Dic163C2211yescharacteristic
21C2×C4×D163C2211yescharacteristic
22C2×C4×D163C2211yescharacteristic
23C4⋊Dic163C2211yescharacteristic, complemented
24Dic163⋊C4C2211yescharacteristic, complemented
25Dic163⋊C4C2211yescharacteristic, complemented
26Dic163⋊C4C2211yescharacteristic, complemented
27Dic163⋊C4C2211yescharacteristic, complemented
28Dic163⋊C4C2211yescharacteristic, complemented
29Dic163⋊C4C2211yescharacteristic, complemented
30C22⋊Dic163C2211yescharacteristic
31C22⋊Dic163C2211yescharacteristic
32C22⋊Dic163C2211yescharacteristic, complemented
33C22⋊Dic163C2211yescharacteristic, complemented
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
42C4×Dic163C2211yescharacteristic, 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—22no—
53C22×D163—41no—
54C22×D163C2311yescharacteristic
55C22×D163C2311yescharacteristic
56Dic326—41no—
57C22⋊D163—22no—
58C22⋊D163—41no—
59C2×Dic163—22no—
60C2×Dic163C2311yescharacteristic
61C2×Dic163C2311yescharacteristic
62C2×Dic163C2311yescharacteristic
63C2×Dic163C2311yescharacteristic
64C2×Dic163C2311yescharacteristic
65C2×Dic163C2311yescharacteristic
66C4×D163—22no—
67C4×D163—41no—
68C23×C163C2311yescharacteristic
69C23×C163C2311yescharacteristic
70D4×C163—22no—
71C2×C4×C163—41no—
72C2×C4×C163—41no—
73C2×C4×C163C2311yescharacteristic
74C2×C4×C163C2311yescharacteristic
75C2×C4×C163C2311yescharacteristic
76C2×C4×C163C2311yescharacteristic
77C2×C4×C163C2311yescharacteristic
78C22×C163—21no—
79C22×C163—21no—
80C22×C163—21no—
81C22×C163—21no—
82C22×C163—21no—
83C22×C163#4112yes—
84C22×C163C2411yescharacteristic
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—
97Dic163—21no—
98Dic163—21no—
99Dic163—21no—
100Dic163—21no—
101Dic163—21no—
102Dic163—21no—
103C2×C163—22no—
104C2×C163—41no—
105C2×C163C2×#4111yescharacteristic
106C2×C163C2×#4111yescharacteristic
107C2×C163H(5,𝔽2)11yescharacteristic
108D163—22no—
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×D4D16311yescharacteristic, complemented
123#117—1631no—
124#117—1631no—
125C2×C22⋊C4—1631no—
126C2×C22⋊C4—1631no—
127C24—1631no—
128C2×Q8—1631no—
129C2×D4—1631no—
130C2×D4—1631no—
131C2×D4C2×D16311yescharacteristic
132C22×C4—1631no—
133C22×C4—1631no—
134C22×C4—1631no—
135C22×C4C2×D16311yescharacteristic
136C22×C4C2×D16311yescharacteristic, complemented
137C4⋊C4—1631no—
138C4⋊C4—1631no—
139C4⋊C4—1631no—
140C4⋊C4—1631no—
141C4⋊C4—1631no—
142C4⋊C4—1631no—
143C4⋊C4—1631no—
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, complemented
159C42—1631no—
160C42—1631no—
161C42C2×D16311yescharacteristic, complemented
162C23—3262no—
163C23—3262no—
164C23—6521no—
165C23—1631no—
166C23—1631no—
167C23C22×D16311yescharacteristic
168C23C22×D16311yescharacteristic
169Q8—6521no—
170D4—22no—
171D4—3262no—
172D4—6521no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—3262no—
176C2×C4—3262no—
177C2×C4—6521no—
178C2×C4—1631no—
179C2×C4—1631no—
180C2×C4—1631no—
181C2×C4—1631no—
182C2×C4—1631no—
183C2×C4—1631no—
184C2×C4C22×D16311yescharacteristic
185C2×C4C22×D16311yescharacteristic
186C2×C4C22×D16311yescharacteristic
187C2×C4C22×D16311yescharacteristic
188C2×C4C22×D16311yescharacteristic
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
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—3261no—
209C4—3261no—
210C4—3261no—
211C4—3261no—
212C4—3261no—
213C4—3261no—
214C2—22no—
215C2—41no—
216C2—3262no—
217C2—6521no—
218C2#41×D16311yescharacteristic
219C2C2×#1457969911yescharacteristic
220C2#1910478011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D163
commutator, socle, cosocleC22×C163C24
FittingC4×D4×C163C2
prime radical#19104703C2
hypercenterC4×D4D163
hypocenterC163#551
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. #19104721C2semidirect
4. #19104718C2semidirect
5. #19104717C2semidirect
6. #19104716C2semidirect
7. #19104714C2semidirect
8. #19104713C2semidirect
10. C4×C22⋊D163C2semidirect
11. #19104692C2semidirect
12. #19104691C2semidirect
13. C2×(C2×D163)⋊C4C2semidirect
14. C22⋊C4×D163C2semidirect
15. C4×D4×C163C2semidirect
17. C2×Dic326C22semidirect
23. C4⋊Dic163C22semidirect
24. Dic163⋊C4C22semidirect
25. Dic163⋊C4C22semidirect
26. Dic163⋊C4C22semidirect
27. Dic163⋊C4C22semidirect
28. Dic163⋊C4C22semidirect
29. Dic163⋊C4C22semidirect
32. C22⋊Dic163C22semidirect
33. C22⋊Dic163C22semidirect
42. C4×Dic163C22semidirect
43. C4×Dic163C22semidirect
46. C22×C4×C163C22semidirect
47. C4⋊C4×C163C22semidirect
49. C22⋊C4×C163C22semidirect
50. C42×C163C22semidirect
110. C163#551semidirect
122. C4×D4D163semidirect
136. C22×C4C2×D163semidirect
144. C4⋊C4C2×D163semidirect
158. C22⋊C4C2×D163semidirect
161. C42C2×D163semidirect