Finite Group Databasebeta

← AGL(1,ℤ/8)×D163 #23782449

Subgroups — AGL(1,ℤ/8)×D163 #23782449

Order 10432.

298 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 101 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#41×D163C211yesmaximal, characteristic, complemented
2C2×D4×D163C211yesmaximal, characteristic, complemented
3#19104763C211yesmaximal, characteristic, complemented
4#19104762C212yesmaximal, complemented
5#19104761C211yesmaximal, characteristic, complemented
6#19104760C211yesmaximal, characteristic, complemented
7#19104759C212yesmaximal, complemented
8SD16×D163C212yesmaximal, complemented
9D8×D163C212yesmaximal, complemented
10M16×D163C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C163C211yesmaximal, characteristic, complemented
12C23×D163—21no—
13#14579700C2211yescharacteristic, complemented
14#14579699—21no—
15#14579699C2211yescharacteristic, complemented
16#14579698—21no—
17#14579698C2211yescharacteristic, complemented
18Q8×D163C2211yescharacteristic, complemented
19C2×D652C2211yescharacteristic, complemented
20C2×C22⋊D163—21no—
21D4×D163—21no—
22D4×D163—21no—
23D4×D163—21no—
24D4×D163C2212yes—
25D4×D163C2212yescomplemented
26D4×D163C2211yescharacteristic, complemented
27C2×C4×D163—21no—
28C2×C4×D163C2211yescharacteristic
29#14579688C2212yescomplemented
30#14579687C2212yescomplemented
31#14579686C2212yescomplemented
32D1304C2212yescomplemented
33#14579684C2212yescomplemented
34#14579684C2212yescomplemented
35#14579683C2211yescharacteristic, complemented
36#14579682C2212yescomplemented
37C8×D163C2212yescomplemented
38#41×C163C2211yescharacteristic, complemented
39C2×D4×C163C2211yescharacteristic, complemented
40SD16×C163C2212yescomplemented
41D8×C163C2212yescomplemented
42M16×C163C2211yescharacteristic, complemented
43C22×D163—21no—
44C22×D163—21no—
45C22×D163—22no—
46C22×D163—22no—
47C22×D163—44no—
48C22×D163D411yescharacteristic
49Dic326—21no—
50Dic326C2311yescharacteristic, complemented
51D652—21no—
52D652—21no—
53D652C2312yes—
54D652C2311yescharacteristic, complemented
55C22⋊D163—21no—
56C22⋊D163—21no—
57C22⋊D163—22no—
58C22⋊D163—22no—
59C22⋊D163—21no—
60C2×Dic163—21no—
61C2×Dic163D411yescharacteristic
62C4×D163—21no—
63C4×D163—21no—
64C4×D163—21no—
65C4×D163D411yescharacteristic
66C4×D163D411yescharacteristic
67C4×D163C2311yescharacteristic
68C4×D163C2311yescharacteristic
69C163⋊C8C2312yescomplemented
70C23×C163—21no—
71Q8×C163C2311yescharacteristic, complemented
72D4×C163—21no—
73D4×C163—21no—
74D4×C163C2312yes—
75D4×C163C2311yescharacteristic, complemented
76C2×C4×C163—21no—
77C2×C4×C163C2311yescharacteristic
78C8×C163C2312yescomplemented
79C22×C163—21no—
80C22×C163—22no—
81C22×C163—42no—
82C22×C163C2×D411yescharacteristic
83C2×D163—22no—
84C2×D163—21no—
85C2×D163—22no—
86C2×D163—44no—
87C2×D163—42no—
88C2×D163—42no—
89C2×D163—44no—
90C2×D163C2×D411yescharacteristic
91C2×D163C2×D411yescharacteristic
92C4×C163—21no—
93C4×C163C2×D411yescharacteristic
94C4×C163C2411yescharacteristic
95Dic163—21no—
96Dic163C2×D411yescharacteristic
97Dic163C2×D411yescharacteristic
98C2×C163—21no—
99C2×C163—42no—
100C2×C163—41no—
101C2×C163C22×D411yescharacteristic
102D163—21no—
103D163—41no—
104D163—42no—
105D163AGL(1,ℤ/8)12yesdirect product factor
106C163C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—1631nomaximal, Sylow
108C2×#41—1631no—
109C22×D4—1631no—
110AGL(1,ℤ/8)—1631no—
111AGL(1,ℤ/8)—1631no—
112AGL(1,ℤ/8)—1632no—
113AGL(1,ℤ/8)—1632no—
114AGL(1,ℤ/8)—1631no—
115AGL(1,ℤ/8)D16311yescharacteristic, direct product factor
116C2×SD16—1632no—
117C2×D8—1632no—
118C2×M16—1631no—
119C24—3261no—
120#41—3261no—
121#41—3261no—
122#41—1631no—
123#41—1631no—
124#41—1631no—
125#41C2×D16311yescharacteristic, complemented
126C2×Q8—1631no—
127C2×D4—3261no—
128C2×D4—3261no—
129C2×D4—3261no—
130C2×D4—3261no—
131C2×D4—1632no—
132C2×D4—1632no—
133C2×D4—1631no—
134C2×D4—1631no—
135C2×D4C2×D16311yescharacteristic, complemented
136C22×C4—3261no—
137C22×C4—1631no—
138SD16—1632no—
139SD16—1632no—
140SD16—1632no—
141SD16C2×D16312yescomplemented
142D8—1632no—
143D8—1632no—
144D8—1632no—
145D8C2×D16312yescomplemented
146M16—1631no—
147M16—1632no—
148M16C2×D16311yescharacteristic, complemented
149C2×C8—1632no—
150C23—21no—
151C23—3261no—
152C23—3262no—
153C23—3262no—
154C23—3261no—
155C23—6524no—
156C23—1631no—
157Q8—3261no—
158Q8—1631no—
159Q8C22×D16311yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—3261no—
163D4—3261no—
164D4—3261no—
165D4—3262no—
166D4—3262no—
167D4—3261no—
168D4—3261no—
169D4—1631no—
170D4—1632no—
171D4C22×D16312yes—
172D4C22×D16311yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—3261no—
175C2×C4—3261no—
176C2×C4—3261no—
177C2×C4—3261no—
178C2×C4—1631no—
179C2×C4—1631no—
180C2×C4—1631no—
181C2×C4—1631no—
182C2×C4—1631no—
183C2×C4C22×D16311yescharacteristic
184C8—1632no—
185C8C22×D16312yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—3262no—
190C22—3261no—
191C22—3262no—
192C22—6522no—
193C22—6524no—
194C22—6524no—
195C22—6522no—
196C22—1631no—
197C22—1631no—
198C22D4×D16311yescharacteristic
199C4—21no—
200C4—3261no—
201C4—1631no—
202C4—1631no—
203C4D4×D16311yescharacteristic
204C4C23×D16311yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—3261no—
209C2—6522no—
210C2—6521no—
211C2—1632no—
212C2C2×D4×D16311yescharacteristic
subgroupG/H
centerC2C2×D4×D163
commutator, cosocleC4×C163C24
FrattiniC4C23×D163
FittingAGL(1,ℤ/8)×C163C2
socleC2×C163C22×D4
hypercenterAGL(1,ℤ/8)D163
hypocenterC163C2×AGL(1,ℤ/8)
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D163C2semidirect
2. C2×D4×D163C2semidirect
3. #19104763C2semidirect
4. #19104762C2semidirect
5. #19104761C2semidirect
6. #19104760C2semidirect
7. #19104759C2semidirect
8. SD16×D163C2semidirect
9. D8×D163C2semidirect
10. M16×D163C2semidirect
11. AGL(1,ℤ/8)×C163C2semidirect
13. #14579700C22semidirect
15. #14579699C22semidirect
17. #14579698C22semidirect
18. Q8×D163C22semidirect
19. C2×D652C22semidirect
25. D4×D163C22semidirect
26. D4×D163C22semidirect
29. #14579688C22semidirect
30. #14579687C22semidirect
31. #14579686C22semidirect
32. D1304C22semidirect
33. #14579684C22semidirect
34. #14579684C22semidirect
35. #14579683C22semidirect
36. #14579682C22semidirect
37. C8×D163C22semidirect
38. #41×C163C22semidirect
39. C2×D4×C163C22semidirect
40. SD16×C163C22semidirect
41. D8×C163C22semidirect
42. M16×C163C22semidirect
50. Dic326C23semidirect
54. D652C23semidirect
69. C163⋊C8C23semidirect
71. Q8×C163C23semidirect
75. D4×C163C23semidirect
78. C8×C163C23semidirect
105. D163AGL(1,ℤ/8)direct (N × H)
106. C163C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D163direct (N × H)
125. #41C2×D163semidirect
135. C2×D4C2×D163semidirect
141. SD16C2×D163semidirect
145. D8C2×D163semidirect
148. M16C2×D163semidirect
159. Q8C22×D163semidirect
172. D4C22×D163semidirect
185. C8C22×D163semidirect