Finite Group Databasebeta

← AGL(1,ℤ/8)×D139 #22581737

Subgroups — AGL(1,ℤ/8)×D139 #22581737

Order 8896.

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×D139C211yesmaximal, characteristic, complemented
2C2×D4×D139C211yesmaximal, characteristic, complemented
3#17984870C211yesmaximal, characteristic, complemented
4#17984869C212yesmaximal, complemented
5#17984868C211yesmaximal, characteristic, complemented
6#17984867C211yesmaximal, characteristic, complemented
7#17984866C212yesmaximal, complemented
8SD16×D139C212yesmaximal, complemented
9D8×D139C212yesmaximal, complemented
10M16×D139C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C139C211yesmaximal, characteristic, complemented
12C23×D139—21no—
13#14555786C2211yescharacteristic, complemented
14#14555785—21no—
15#14555785C2211yescharacteristic, complemented
16#14555784—21no—
17#14555784C2211yescharacteristic, complemented
18Q8×D139C2211yescharacteristic, complemented
19C2×D556C2211yescharacteristic, complemented
20C2×C22⋊D139—21no—
21D4×D139—21no—
22D4×D139—21no—
23D4×D139—21no—
24D4×D139C2212yes—
25D4×D139C2212yescomplemented
26D4×D139C2211yescharacteristic, complemented
27C2×C4×D139—21no—
28C2×C4×D139C2211yescharacteristic
29#14555774C2212yescomplemented
30#14555773C2212yescomplemented
31#14555772C2212yescomplemented
32D1112C2212yescomplemented
33#14555770C2212yescomplemented
34#14555770C2212yescomplemented
35#14555769C2211yescharacteristic, complemented
36#14555768C2212yescomplemented
37C8×D139C2212yescomplemented
38#41×C139C2211yescharacteristic, complemented
39C2×D4×C139C2211yescharacteristic, complemented
40SD16×C139C2212yescomplemented
41D8×C139C2212yescomplemented
42M16×C139C2211yescharacteristic, complemented
43C22×D139—21no—
44C22×D139—21no—
45C22×D139—22no—
46C22×D139—22no—
47C22×D139—44no—
48C22×D139D411yescharacteristic
49Dic278—21no—
50Dic278C2311yescharacteristic, complemented
51D556—21no—
52D556—21no—
53D556C2312yes—
54D556C2311yescharacteristic, complemented
55C22⋊D139—21no—
56C22⋊D139—21no—
57C22⋊D139—22no—
58C22⋊D139—22no—
59C22⋊D139—21no—
60C2×Dic139—21no—
61C2×Dic139D411yescharacteristic
62C4×D139—21no—
63C4×D139—21no—
64C4×D139—21no—
65C4×D139D411yescharacteristic
66C4×D139D411yescharacteristic
67C4×D139C2311yescharacteristic
68C4×D139C2311yescharacteristic
69C139⋊C8C2312yescomplemented
70C23×C139—21no—
71Q8×C139C2311yescharacteristic, complemented
72D4×C139—21no—
73D4×C139—21no—
74D4×C139C2312yes—
75D4×C139C2311yescharacteristic, complemented
76C2×C4×C139—21no—
77C2×C4×C139C2311yescharacteristic
78C8×C139C2312yescomplemented
79C22×C139—21no—
80C22×C139—22no—
81C22×C139—42no—
82C22×C139C2×D411yescharacteristic
83C2×D139—22no—
84C2×D139—21no—
85C2×D139—22no—
86C2×D139—44no—
87C2×D139—42no—
88C2×D139—42no—
89C2×D139—44no—
90C2×D139C2×D411yescharacteristic
91C2×D139C2×D411yescharacteristic
92C4×C139—21no—
93C4×C139C2×D411yescharacteristic
94C4×C139C2411yescharacteristic
95Dic139—21no—
96Dic139C2×D411yescharacteristic
97Dic139C2×D411yescharacteristic
98C2×C139—21no—
99C2×C139—42no—
100C2×C139—41no—
101C2×C139C22×D411yescharacteristic
102D139—21no—
103D139—41no—
104D139—42no—
105D139AGL(1,ℤ/8)12yesdirect product factor
106C139C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—1391nomaximal, Sylow
108C2×#41—1391no—
109C22×D4—1391no—
110AGL(1,ℤ/8)—1391no—
111AGL(1,ℤ/8)—1391no—
112AGL(1,ℤ/8)—1392no—
113AGL(1,ℤ/8)—1392no—
114AGL(1,ℤ/8)—1391no—
115AGL(1,ℤ/8)D13911yescharacteristic, direct product factor
116C2×SD16—1392no—
117C2×D8—1392no—
118C2×M16—1391no—
119C24—2781no—
120#41—2781no—
121#41—2781no—
122#41—1391no—
123#41—1391no—
124#41—1391no—
125#41C2×D13911yescharacteristic, complemented
126C2×Q8—1391no—
127C2×D4—2781no—
128C2×D4—2781no—
129C2×D4—2781no—
130C2×D4—2781no—
131C2×D4—1392no—
132C2×D4—1392no—
133C2×D4—1391no—
134C2×D4—1391no—
135C2×D4C2×D13911yescharacteristic, complemented
136C22×C4—2781no—
137C22×C4—1391no—
138SD16—1392no—
139SD16—1392no—
140SD16—1392no—
141SD16C2×D13912yescomplemented
142D8—1392no—
143D8—1392no—
144D8—1392no—
145D8C2×D13912yescomplemented
146M16—1391no—
147M16—1392no—
148M16C2×D13911yescharacteristic, complemented
149C2×C8—1392no—
150C23—21no—
151C23—2781no—
152C23—2782no—
153C23—2782no—
154C23—2781no—
155C23—5564no—
156C23—1391no—
157Q8—2781no—
158Q8—1391no—
159Q8C22×D13911yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—2781no—
163D4—2781no—
164D4—2781no—
165D4—2782no—
166D4—2782no—
167D4—2781no—
168D4—2781no—
169D4—1391no—
170D4—1392no—
171D4C22×D13912yes—
172D4C22×D13911yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—2781no—
175C2×C4—2781no—
176C2×C4—2781no—
177C2×C4—2781no—
178C2×C4—1391no—
179C2×C4—1391no—
180C2×C4—1391no—
181C2×C4—1391no—
182C2×C4—1391no—
183C2×C4C22×D13911yescharacteristic
184C8—1392no—
185C8C22×D13912yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—2782no—
190C22—2781no—
191C22—2782no—
192C22—5562no—
193C22—5564no—
194C22—5564no—
195C22—5562no—
196C22—1391no—
197C22—1391no—
198C22D4×D13911yescharacteristic
199C4—21no—
200C4—2781no—
201C4—1391no—
202C4—1391no—
203C4D4×D13911yescharacteristic
204C4C23×D13911yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—2781no—
209C2—5562no—
210C2—5561no—
211C2—1392no—
212C2C2×D4×D13911yescharacteristic
subgroupG/H
centerC2C2×D4×D139
commutatorC4×C139C24
FrattiniC4C23×D139
FittingAGL(1,ℤ/8)×C139C2
socleC2×C139C22×D4
hypercenterAGL(1,ℤ/8)D139
hypocenterC139C2×AGL(1,ℤ/8)
LCSG ▷ C4×C139 ▷ C2×C139 ▷ C139
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D139C2semidirect
2. C2×D4×D139C2semidirect
3. #17984870C2semidirect
4. #17984869C2semidirect
5. #17984868C2semidirect
6. #17984867C2semidirect
7. #17984866C2semidirect
8. SD16×D139C2semidirect
9. D8×D139C2semidirect
10. M16×D139C2semidirect
11. AGL(1,ℤ/8)×C139C2semidirect
13. #14555786C22semidirect
15. #14555785C22semidirect
17. #14555784C22semidirect
18. Q8×D139C22semidirect
19. C2×D556C22semidirect
25. D4×D139C22semidirect
26. D4×D139C22semidirect
29. #14555774C22semidirect
30. #14555773C22semidirect
31. #14555772C22semidirect
32. D1112C22semidirect
33. #14555770C22semidirect
34. #14555770C22semidirect
35. #14555769C22semidirect
36. #14555768C22semidirect
37. C8×D139C22semidirect
38. #41×C139C22semidirect
39. C2×D4×C139C22semidirect
40. SD16×C139C22semidirect
41. D8×C139C22semidirect
42. M16×C139C22semidirect
50. Dic278C23semidirect
54. D556C23semidirect
69. C139⋊C8C23semidirect
71. Q8×C139C23semidirect
75. D4×C139C23semidirect
78. C8×C139C23semidirect
105. D139AGL(1,ℤ/8)direct (N × H)
106. C139C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D139direct (N × H)
125. #41C2×D139semidirect
135. C2×D4C2×D139semidirect
141. SD16C2×D139semidirect
145. D8C2×D139semidirect
148. M16C2×D139semidirect
159. Q8C22×D139semidirect
172. D4C22×D139semidirect
185. C8C22×D139semidirect