Finite Group Databasebeta

← AGL(1,ℤ/8)×D281 #31824247

Subgroups — AGL(1,ℤ/8)×D281 #31824247

Order 17984.

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×D281C211yesmaximal, characteristic, complemented
2C2×D4×D281C211yesmaximal, characteristic, complemented
3#22582907C211yesmaximal, characteristic, complemented
4#22582906C212yesmaximal, complemented
5#22582905C211yesmaximal, characteristic, complemented
6#22582904C211yesmaximal, characteristic, complemented
7#22582903C212yesmaximal, complemented
8SD16×D281C212yesmaximal, complemented
9D8×D281C212yesmaximal, complemented
10M16×D281C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C281C211yesmaximal, characteristic, complemented
12C23×D281—21no—
13#17985139C2211yescharacteristic, complemented
14#17985138—21no—
15#17985138C2211yescharacteristic, complemented
16#17985137—21no—
17#17985137C2211yescharacteristic, complemented
18Q8×D281C2211yescharacteristic, complemented
19C2×D1124C2211yescharacteristic, complemented
20C2×C22⋊D281—21no—
21D4×D281—21no—
22D4×D281—21no—
23D4×D281—21no—
24D4×D281C2212yes—
25D4×D281C2212yescomplemented
26D4×D281C2211yescharacteristic, complemented
27C2×C4×D281—21no—
28C2×C4×D281C2211yescharacteristic
29#17985127C2212yescomplemented
30#17985126C2212yescomplemented
31#17985125C2212yescomplemented
32D2248C2212yescomplemented
33#17985123C2212yescomplemented
34#17985123C2212yescomplemented
35#17985122C2211yescharacteristic, complemented
36#17985121C2212yescomplemented
37C8×D281C2212yescomplemented
38#41×C281C2211yescharacteristic, complemented
39C2×D4×C281C2211yescharacteristic, complemented
40SD16×C281C2212yescomplemented
41D8×C281C2212yescomplemented
42M16×C281C2211yescharacteristic, complemented
43C22×D281—21no—
44C22×D281—21no—
45C22×D281—22no—
46C22×D281—22no—
47C22×D281—44no—
48C22×D281D411yescharacteristic
49Dic562—21no—
50Dic562C2311yescharacteristic, complemented
51D1124—21no—
52D1124—21no—
53D1124C2312yes—
54D1124C2311yescharacteristic, complemented
55C22⋊D281—21no—
56C22⋊D281—21no—
57C22⋊D281—22no—
58C22⋊D281—22no—
59C22⋊D281—21no—
60C2×Dic281—21no—
61C2×Dic281D411yescharacteristic
62C4×D281—21no—
63C4×D281—21no—
64C4×D281—21no—
65C4×D281D411yescharacteristic
66C4×D281D411yescharacteristic
67C4×D281C2311yescharacteristic
68C4×D281C2311yescharacteristic
69#14555886C2312yescomplemented
70C23×C281—21no—
71Q8×C281C2311yescharacteristic, complemented
72D4×C281—21no—
73D4×C281—21no—
74D4×C281C2312yes—
75D4×C281C2311yescharacteristic, complemented
76C2×C4×C281—21no—
77C2×C4×C281C2311yescharacteristic
78C8×C281C2312yescomplemented
79C22×C281—21no—
80C22×C281—22no—
81C22×C281—42no—
82C22×C281C2×D411yescharacteristic
83C2×D281—22no—
84C2×D281—21no—
85C2×D281—22no—
86C2×D281—44no—
87C2×D281—42no—
88C2×D281—42no—
89C2×D281—44no—
90C2×D281C2×D411yescharacteristic
91C2×D281C2×D411yescharacteristic
92C4×C281—21no—
93C4×C281C2×D411yescharacteristic
94C4×C281C2411yescharacteristic
95Dic281—21no—
96Dic281C2×D411yescharacteristic
97Dic281C2×D411yescharacteristic
98C2×C281—21no—
99C2×C281—42no—
100C2×C281—41no—
101C2×C281C22×D411yescharacteristic
102D281—21no—
103D281—41no—
104D281—42no—
105D281AGL(1,ℤ/8)12yesdirect product factor
106C281C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—2811nomaximal, Sylow
108C2×#41—2811no—
109C22×D4—2811no—
110AGL(1,ℤ/8)—2811no—
111AGL(1,ℤ/8)—2811no—
112AGL(1,ℤ/8)—2812no—
113AGL(1,ℤ/8)—2812no—
114AGL(1,ℤ/8)—2811no—
115AGL(1,ℤ/8)D28111yescharacteristic, direct product factor
116C2×SD16—2812no—
117C2×D8—2812no—
118C2×M16—2811no—
119C24—5621no—
120#41—2811no—
121#41—2811no—
122#41—2811no—
123#41—5621no—
124#41—5621no—
125#41C2×D28111yescharacteristic, complemented
126C2×Q8—2811no—
127C2×D4—2812no—
128C2×D4—2812no—
129C2×D4—2811no—
130C2×D4—2811no—
131C2×D4—5621no—
132C2×D4—5621no—
133C2×D4—5621no—
134C2×D4—5621no—
135C2×D4C2×D28111yescharacteristic, complemented
136C22×C4—2811no—
137C22×C4—5621no—
138SD16—2812no—
139SD16—2812no—
140SD16—2812no—
141SD16C2×D28112yescomplemented
142D8—2812no—
143D8—2812no—
144D8—2812no—
145D8C2×D28112yescomplemented
146M16—2811no—
147M16—2812no—
148M16C2×D28111yescharacteristic, complemented
149C2×C8—2812no—
150C23—21no—
151C23—2811no—
152C23—5621no—
153C23—5622no—
154C23—5622no—
155C23—5621no—
156C23—11244no—
157Q8—2811no—
158Q8—5621no—
159Q8C22×D28111yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—2811no—
163D4—2812no—
164D4—5621no—
165D4—5622no—
166D4—5622no—
167D4—5621no—
168D4—5621no—
169D4—5621no—
170D4—5621no—
171D4C22×D28112yes—
172D4C22×D28111yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—2811no—
175C2×C4—2811no—
176C2×C4—2811no—
177C2×C4—2811no—
178C2×C4—2811no—
179C2×C4—5621no—
180C2×C4—5621no—
181C2×C4—5621no—
182C2×C4—5621no—
183C2×C4C22×D28111yescharacteristic
184C8—2812no—
185C8C22×D28112yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—2811no—
190C22—2811no—
191C22—5622no—
192C22—5621no—
193C22—5622no—
194C22—11242no—
195C22—11244no—
196C22—11242no—
197C22—11244no—
198C22D4×D28111yescharacteristic
199C4—21no—
200C4—2811no—
201C4—2811no—
202C4—5621no—
203C4D4×D28111yescharacteristic
204C4C23×D28111yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—2812no—
209C2—5621no—
210C2—11242no—
211C2—11241no—
212C2C2×D4×D28111yescharacteristic
subgroupG/H
centerC2C2×D4×D281
commutator, cosocleC4×C281C24
FrattiniC4C23×D281
FittingAGL(1,ℤ/8)×C281C2
socleC2×C281C22×D4
hypercenterAGL(1,ℤ/8)D281
hypocenterC281C2×AGL(1,ℤ/8)
LCSG ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D281C2semidirect
2. C2×D4×D281C2semidirect
3. #22582907C2semidirect
4. #22582906C2semidirect
5. #22582905C2semidirect
6. #22582904C2semidirect
7. #22582903C2semidirect
8. SD16×D281C2semidirect
9. D8×D281C2semidirect
10. M16×D281C2semidirect
11. AGL(1,ℤ/8)×C281C2semidirect
13. #17985139C22semidirect
15. #17985138C22semidirect
17. #17985137C22semidirect
18. Q8×D281C22semidirect
19. C2×D1124C22semidirect
25. D4×D281C22semidirect
26. D4×D281C22semidirect
29. #17985127C22semidirect
30. #17985126C22semidirect
31. #17985125C22semidirect
32. D2248C22semidirect
33. #17985123C22semidirect
34. #17985123C22semidirect
35. #17985122C22semidirect
36. #17985121C22semidirect
37. C8×D281C22semidirect
38. #41×C281C22semidirect
39. C2×D4×C281C22semidirect
40. SD16×C281C22semidirect
41. D8×C281C22semidirect
42. M16×C281C22semidirect
50. Dic562C23semidirect
54. D1124C23semidirect
69. #14555886C23semidirect
71. Q8×C281C23semidirect
75. D4×C281C23semidirect
78. C8×C281C23semidirect
105. D281AGL(1,ℤ/8)direct (N × H)
106. C281C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D281direct (N × H)
125. #41C2×D281semidirect
135. C2×D4C2×D281semidirect
141. SD16C2×D281semidirect
145. D8C2×D281semidirect
148. M16C2×D281semidirect
159. Q8C22×D281semidirect
172. D4C22×D281semidirect
185. C8C22×D281semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#41×D2812
C2×D4×D2812
#225829072
#225829062
#225829052
#225829042
#225829032
SD16×D2812
D8×D2812
M16×D2812
AGL(1,ℤ/8)×C2812
C2×AGL(1,ℤ/8)281