Finite Group Databasebeta

← AGL(1,ℤ/8)×D439 #43244388

Subgroups — AGL(1,ℤ/8)×D439 #43244388

Order 28096.

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×D439C211yesmaximal, characteristic, complemented
2C2×D4×D439C211yesmaximal, characteristic, complemented
3#28380771C211yesmaximal, characteristic, complemented
4#28380770C212yesmaximal, complemented
5#28380769C211yesmaximal, characteristic, complemented
6#28380768C211yesmaximal, characteristic, complemented
7#28380767C212yesmaximal, complemented
8SD16×D439C212yesmaximal, complemented
9D8×D439C212yesmaximal, complemented
10M16×D439C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C439C211yesmaximal, characteristic, complemented
12C23×D439—21no—
13#20296330C2211yescharacteristic, complemented
14#20296329—21no—
15#20296329C2211yescharacteristic, complemented
16#20296328—21no—
17#20296328C2211yescharacteristic, complemented
18Q8×D439C2211yescharacteristic, complemented
19C2×D1756C2211yescharacteristic, complemented
20C2×C22⋊D439—21no—
21D4×D439—21no—
22D4×D439—21no—
23D4×D439—21no—
24D4×D439C2212yes—
25D4×D439C2212yescomplemented
26D4×D439C2211yescharacteristic, complemented
27C2×C4×D439—21no—
28C2×C4×D439C2211yescharacteristic
29#20296318C2212yescomplemented
30#20296317C2212yescomplemented
31#20296316C2212yescomplemented
32D3512C2212yescomplemented
33#20296314C2212yescomplemented
34#20296314C2212yescomplemented
35#20296313C2211yescharacteristic, complemented
36#20296312C2212yescomplemented
37C8×D439C2212yescomplemented
38#41×C439C2211yescharacteristic, complemented
39C2×D4×C439C2211yescharacteristic, complemented
40SD16×C439C2212yescomplemented
41D8×C439C2212yescomplemented
42M16×C439C2211yescharacteristic, complemented
43C22×D439—21no—
44C22×D439—21no—
45C22×D439—22no—
46C22×D439—22no—
47C22×D439—44no—
48C22×D439D411yescharacteristic
49Dic878—21no—
50Dic878C2311yescharacteristic, complemented
51D1756—21no—
52D1756—21no—
53D1756C2312yes—
54D1756C2311yescharacteristic, complemented
55C22⋊D439—21no—
56C22⋊D439—21no—
57C22⋊D439—22no—
58C22⋊D439—22no—
59C22⋊D439—21no—
60C2×Dic439—21no—
61C2×Dic439D411yescharacteristic
62C4×D439—21no—
63C4×D439—21no—
64C4×D439—21no—
65C4×D439D411yescharacteristic
66C4×D439D411yescharacteristic
67C4×D439C2311yescharacteristic
68C4×D439C2311yescharacteristic
69C439⋊C8C2312yescomplemented
70C23×C439—21no—
71Q8×C439C2311yescharacteristic, complemented
72D4×C439—21no—
73D4×C439—21no—
74D4×C439C2312yes—
75D4×C439C2311yescharacteristic, complemented
76C2×C4×C439—21no—
77C2×C4×C439C2311yescharacteristic
78C8×C439C2312yescomplemented
79C22×C439—21no—
80C22×C439—22no—
81C22×C439—42no—
82C22×C439C2×D411yescharacteristic
83C2×D439—22no—
84C2×D439—21no—
85C2×D439—22no—
86C2×D439—44no—
87C2×D439—42no—
88C2×D439—42no—
89C2×D439—44no—
90C2×D439C2×D411yescharacteristic
91C2×D439C2×D411yescharacteristic
92C4×C439—21no—
93C4×C439C2×D411yescharacteristic
94C4×C439C2411yescharacteristic
95Dic439—21no—
96Dic439C2×D411yescharacteristic
97Dic439C2×D411yescharacteristic
98C2×C439—21no—
99C2×C439—42no—
100C2×C439—41no—
101C2×C439C22×D411yescharacteristic
102D439—21no—
103D439—41no—
104D439—42no—
105D439AGL(1,ℤ/8)12yesdirect product factor
106C439C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—4391nomaximal, Sylow
108C2×#41—4391no—
109C22×D4—4391no—
110AGL(1,ℤ/8)—4391no—
111AGL(1,ℤ/8)—4391no—
112AGL(1,ℤ/8)—4392no—
113AGL(1,ℤ/8)—4392no—
114AGL(1,ℤ/8)—4391no—
115AGL(1,ℤ/8)D43911yescharacteristic, direct product factor
116C2×SD16—4392no—
117C2×D8—4392no—
118C2×M16—4391no—
119C24—8781no—
120#41—8781no—
121#41—8781no—
122#41—4391no—
123#41—4391no—
124#41—4391no—
125#41C2×D43911yescharacteristic, complemented
126C2×Q8—4391no—
127C2×D4—8781no—
128C2×D4—8781no—
129C2×D4—8781no—
130C2×D4—8781no—
131C2×D4—4392no—
132C2×D4—4392no—
133C2×D4—4391no—
134C2×D4—4391no—
135C2×D4C2×D43911yescharacteristic, complemented
136C22×C4—8781no—
137C22×C4—4391no—
138SD16—4392no—
139SD16—4392no—
140SD16—4392no—
141SD16C2×D43912yescomplemented
142D8—4392no—
143D8—4392no—
144D8—4392no—
145D8C2×D43912yescomplemented
146M16—4391no—
147M16—4392no—
148M16C2×D43911yescharacteristic, complemented
149C2×C8—4392no—
150C23—21no—
151C23—8781no—
152C23—8782no—
153C23—8782no—
154C23—8781no—
155C23—4391no—
156C23—17564no—
157Q8—8781no—
158Q8—4391no—
159Q8C22×D43911yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—8781no—
163D4—8781no—
164D4—8781no—
165D4—8782no—
166D4—8782no—
167D4—8781no—
168D4—8781no—
169D4—4391no—
170D4—4392no—
171D4C22×D43912yes—
172D4C22×D43911yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—8781no—
175C2×C4—8781no—
176C2×C4—8781no—
177C2×C4—8781no—
178C2×C4—4391no—
179C2×C4—4391no—
180C2×C4—4391no—
181C2×C4—4391no—
182C2×C4—4391no—
183C2×C4C22×D43911yescharacteristic
184C8—4392no—
185C8C22×D43912yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—8782no—
190C22—8781no—
191C22—8782no—
192C22—4391no—
193C22—4391no—
194C22—17562no—
195C22—17564no—
196C22—17564no—
197C22—17562no—
198C22D4×D43911yescharacteristic
199C4—21no—
200C4—8781no—
201C4—4391no—
202C4—4391no—
203C4D4×D43911yescharacteristic
204C4C23×D43911yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—8781no—
209C2—4392no—
210C2—17562no—
211C2—17561no—
212C2C2×D4×D43911yescharacteristic
subgroupG/H
centerC2C2×D4×D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
FittingAGL(1,ℤ/8)×C439C2
socleC2×C439C22×D4
hypercenterAGL(1,ℤ/8)D439
hypocenterC439C2×AGL(1,ℤ/8)
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D439C2semidirect
2. C2×D4×D439C2semidirect
3. #28380771C2semidirect
4. #28380770C2semidirect
5. #28380769C2semidirect
6. #28380768C2semidirect
7. #28380767C2semidirect
8. SD16×D439C2semidirect
9. D8×D439C2semidirect
10. M16×D439C2semidirect
11. AGL(1,ℤ/8)×C439C2semidirect
13. #20296330C22semidirect
15. #20296329C22semidirect
17. #20296328C22semidirect
18. Q8×D439C22semidirect
19. C2×D1756C22semidirect
25. D4×D439C22semidirect
26. D4×D439C22semidirect
29. #20296318C22semidirect
30. #20296317C22semidirect
31. #20296316C22semidirect
32. D3512C22semidirect
33. #20296314C22semidirect
34. #20296314C22semidirect
35. #20296313C22semidirect
36. #20296312C22semidirect
37. C8×D439C22semidirect
38. #41×C439C22semidirect
39. C2×D4×C439C22semidirect
40. SD16×C439C22semidirect
41. D8×C439C22semidirect
42. M16×C439C22semidirect
50. Dic878C23semidirect
54. D1756C23semidirect
69. C439⋊C8C23semidirect
71. Q8×C439C23semidirect
75. D4×C439C23semidirect
78. C8×C439C23semidirect
105. D439AGL(1,ℤ/8)direct (N × H)
106. C439C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D439direct (N × H)
125. #41C2×D439semidirect
135. C2×D4C2×D439semidirect
141. SD16C2×D439semidirect
145. D8C2×D439semidirect
148. M16C2×D439semidirect
159. Q8C22×D439semidirect
172. D4C22×D439semidirect
185. C8C22×D439semidirect

Maximal subgroups

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

subgroupindex
#41×D4392
C2×D4×D4392
#283807712
#283807702
#283807692
#283807682
#283807672
SD16×D4392
D8×D4392
M16×D4392
AGL(1,ℤ/8)×C4392
C2×AGL(1,ℤ/8)439