Finite Group Databasebeta

← AGL(1,ℤ/8)×D157 #23758057

Subgroups — AGL(1,ℤ/8)×D157 #23758057

Order 10048.

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×D157C211yesmaximal, characteristic, complemented
2C2×D4×D157C211yesmaximal, characteristic, complemented
3#19097799C211yesmaximal, characteristic, complemented
4#19097798C212yesmaximal, complemented
5#19097797C211yesmaximal, characteristic, complemented
6#19097796C211yesmaximal, characteristic, complemented
7#19097795C212yesmaximal, complemented
8SD16×D157C212yesmaximal, complemented
9D8×D157C212yesmaximal, complemented
10M16×D157C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C157C211yesmaximal, characteristic, complemented
12C23×D157—21no—
13#14578955C2211yescharacteristic, complemented
14#14578954—21no—
15#14578954C2211yescharacteristic, complemented
16#14578953—21no—
17#14578953C2211yescharacteristic, complemented
18Q8×D157C2211yescharacteristic, complemented
19C2×D628C2211yescharacteristic, complemented
20C2×C22⋊D157—21no—
21D4×D157—21no—
22D4×D157—21no—
23D4×D157—21no—
24D4×D157C2212yes—
25D4×D157C2212yescomplemented
26D4×D157C2211yescharacteristic, complemented
27C2×C4×D157—21no—
28C2×C4×D157C2211yescharacteristic
29#14578943C2212yescomplemented
30#14578942C2212yescomplemented
31#14578941C2212yescomplemented
32D1256C2212yescomplemented
33#14578939C2212yescomplemented
34#14578939C2212yescomplemented
35#14578938C2211yescharacteristic, complemented
36#14578937C2212yescomplemented
37C8×D157C2212yescomplemented
38#41×C157C2211yescharacteristic, complemented
39C2×D4×C157C2211yescharacteristic, complemented
40SD16×C157C2212yescomplemented
41D8×C157C2212yescomplemented
42M16×C157C2211yescharacteristic, complemented
43C22×D157—21no—
44C22×D157—21no—
45C22×D157—22no—
46C22×D157—22no—
47C22×D157—44no—
48C22×D157D411yescharacteristic
49Dic314—21no—
50Dic314C2311yescharacteristic, complemented
51D628—21no—
52D628—21no—
53D628C2312yes—
54D628C2311yescharacteristic, complemented
55C22⋊D157—21no—
56C22⋊D157—21no—
57C22⋊D157—22no—
58C22⋊D157—22no—
59C22⋊D157—21no—
60C2×Dic157—21no—
61C2×Dic157D411yescharacteristic
62C4×D157—21no—
63C4×D157—21no—
64C4×D157—21no—
65C4×D157D411yescharacteristic
66C4×D157D411yescharacteristic
67C4×D157C2311yescharacteristic
68C4×D157C2311yescharacteristic
69#11929434C2312yescomplemented
70C23×C157—21no—
71Q8×C157C2311yescharacteristic, complemented
72D4×C157—21no—
73D4×C157—21no—
74D4×C157C2312yes—
75D4×C157C2311yescharacteristic, complemented
76C2×C4×C157—21no—
77C2×C4×C157C2311yescharacteristic
78C8×C157C2312yescomplemented
79C22×C157—21no—
80C22×C157—22no—
81C22×C157—42no—
82C22×C157C2×D411yescharacteristic
83C2×D157—22no—
84C2×D157—21no—
85C2×D157—22no—
86C2×D157—44no—
87C2×D157—42no—
88C2×D157—42no—
89C2×D157—44no—
90C2×D157C2×D411yescharacteristic
91C2×D157C2×D411yescharacteristic
92C4×C157—21no—
93C4×C157C2×D411yescharacteristic
94C4×C157C2411yescharacteristic
95Dic157—21no—
96Dic157C2×D411yescharacteristic
97Dic157C2×D411yescharacteristic
98C2×C157—21no—
99C2×C157—42no—
100C2×C157—41no—
101C2×C157C22×D411yescharacteristic
102D157—21no—
103D157—41no—
104D157—42no—
105D157AGL(1,ℤ/8)12yesdirect product factor
106C157C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—1571nomaximal, Sylow
108C2×#41—1571no—
109C22×D4—1571no—
110AGL(1,ℤ/8)—1571no—
111AGL(1,ℤ/8)—1571no—
112AGL(1,ℤ/8)—1572no—
113AGL(1,ℤ/8)—1572no—
114AGL(1,ℤ/8)—1571no—
115AGL(1,ℤ/8)D15711yescharacteristic, direct product factor
116C2×SD16—1572no—
117C2×D8—1572no—
118C2×M16—1571no—
119C24—3141no—
120#41—3141no—
121#41—3141no—
122#41—1571no—
123#41—1571no—
124#41—1571no—
125#41C2×D15711yescharacteristic, complemented
126C2×Q8—1571no—
127C2×D4—3141no—
128C2×D4—3141no—
129C2×D4—3141no—
130C2×D4—3141no—
131C2×D4—1572no—
132C2×D4—1572no—
133C2×D4—1571no—
134C2×D4—1571no—
135C2×D4C2×D15711yescharacteristic, complemented
136C22×C4—3141no—
137C22×C4—1571no—
138SD16—1572no—
139SD16—1572no—
140SD16—1572no—
141SD16C2×D15712yescomplemented
142D8—1572no—
143D8—1572no—
144D8—1572no—
145D8C2×D15712yescomplemented
146M16—1571no—
147M16—1572no—
148M16C2×D15711yescharacteristic, complemented
149C2×C8—1572no—
150C23—21no—
151C23—3141no—
152C23—3142no—
153C23—3142no—
154C23—3141no—
155C23—6284no—
156C23—1571no—
157Q8—3141no—
158Q8—1571no—
159Q8C22×D15711yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—3141no—
163D4—3141no—
164D4—3141no—
165D4—3142no—
166D4—3142no—
167D4—3141no—
168D4—3141no—
169D4—1571no—
170D4—1572no—
171D4C22×D15712yes—
172D4C22×D15711yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—3141no—
175C2×C4—3141no—
176C2×C4—3141no—
177C2×C4—3141no—
178C2×C4—1571no—
179C2×C4—1571no—
180C2×C4—1571no—
181C2×C4—1571no—
182C2×C4—1571no—
183C2×C4C22×D15711yescharacteristic
184C8—1572no—
185C8C22×D15712yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—3142no—
190C22—3141no—
191C22—3142no—
192C22—6282no—
193C22—6284no—
194C22—6284no—
195C22—6282no—
196C22—1571no—
197C22—1571no—
198C22D4×D15711yescharacteristic
199C4—21no—
200C4—3141no—
201C4—1571no—
202C4—1571no—
203C4D4×D15711yescharacteristic
204C4C23×D15711yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—3141no—
209C2—6282no—
210C2—6281no—
211C2—1572no—
212C2C2×D4×D15711yescharacteristic
subgroupG/H
centerC2C2×D4×D157
commutator, cosocleC4×C157C24
FrattiniC4C23×D157
FittingAGL(1,ℤ/8)×C157C2
socleC2×C157C22×D4
hypercenterAGL(1,ℤ/8)D157
hypocenterC157C2×AGL(1,ℤ/8)
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D157C2semidirect
2. C2×D4×D157C2semidirect
3. #19097799C2semidirect
4. #19097798C2semidirect
5. #19097797C2semidirect
6. #19097796C2semidirect
7. #19097795C2semidirect
8. SD16×D157C2semidirect
9. D8×D157C2semidirect
10. M16×D157C2semidirect
11. AGL(1,ℤ/8)×C157C2semidirect
13. #14578955C22semidirect
15. #14578954C22semidirect
17. #14578953C22semidirect
18. Q8×D157C22semidirect
19. C2×D628C22semidirect
25. D4×D157C22semidirect
26. D4×D157C22semidirect
29. #14578943C22semidirect
30. #14578942C22semidirect
31. #14578941C22semidirect
32. D1256C22semidirect
33. #14578939C22semidirect
34. #14578939C22semidirect
35. #14578938C22semidirect
36. #14578937C22semidirect
37. C8×D157C22semidirect
38. #41×C157C22semidirect
39. C2×D4×C157C22semidirect
40. SD16×C157C22semidirect
41. D8×C157C22semidirect
42. M16×C157C22semidirect
50. Dic314C23semidirect
54. D628C23semidirect
69. #11929434C23semidirect
71. Q8×C157C23semidirect
75. D4×C157C23semidirect
78. C8×C157C23semidirect
105. D157AGL(1,ℤ/8)direct (N × H)
106. C157C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D157direct (N × H)
125. #41C2×D157semidirect
135. C2×D4C2×D157semidirect
141. SD16C2×D157semidirect
145. D8C2×D157semidirect
148. M16C2×D157semidirect
159. Q8C22×D157semidirect
172. D4C22×D157semidirect
185. C8C22×D157semidirect