Finite Group Databasebeta

← AGL(1,ℤ/8)×D47 #15689907

Subgroups — AGL(1,ℤ/8)×D47 #15689907

Order 3008.

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×D47C211yesmaximal, characteristic, complemented
2C2×D4×D47C211yesmaximal, characteristic, complemented
3#13094052C211yesmaximal, characteristic, complemented
4#13094051C212yesmaximal, complemented
5#13094050C211yesmaximal, characteristic, complemented
6#13094049C211yesmaximal, characteristic, complemented
7#13094048C212yesmaximal, complemented
8SD16×D47C212yesmaximal, complemented
9D8×D47C212yesmaximal, complemented
10M16×D47C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C47C211yesmaximal, characteristic, complemented
12C23×D47—21no—
13#41×C47C2211yescharacteristic, complemented
14C2×D4×C47C2211yescharacteristic, complemented
15C2×C22⋊D47—21no—
16#10625354C2211yescharacteristic, complemented
17Q8×D47C2211yescharacteristic, complemented
18#10625352—21no—
19#10625352C2211yescharacteristic, complemented
20D4×D47—21no—
21D4×D47—21no—
22D4×D47—21no—
23D4×D47C2212yes—
24D4×D47C2212yescomplemented
25D4×D47C2211yescharacteristic, complemented
26#10625350—21no—
27#10625350C2211yescharacteristic, complemented
28C2×D188C2211yescharacteristic, complemented
29C2×C4×D47—21no—
30C2×C4×D47C2211yescharacteristic
31SD16×C47C2212yescomplemented
32D8×C47C2212yescomplemented
33M16×C47C2211yescharacteristic, complemented
34#10625336C2212yescomplemented
35#10625335C2212yescomplemented
36#10625334C2212yescomplemented
37#10625334C2212yescomplemented
38#10625329C2211yescharacteristic, complemented
39D376C2212yescomplemented
40#10625325C2212yescomplemented
41#10625324C2212yescomplemented
42C8×D47C2212yescomplemented
43C23×C47—21no—
44C22×D47—21no—
45C22×D47—21no—
46C22×D47—22no—
47C22×D47—22no—
48C22×D47—44no—
49C22×D47D411yescharacteristic
50Q8×C47C2311yescharacteristic, complemented
51D4×C47—21no—
52D4×C47—21no—
53D4×C47C2312yes—
54D4×C47C2311yescharacteristic, complemented
55C2×C4×C47—21no—
56C2×C4×C47C2311yescharacteristic
57C22⋊D47—21no—
58C22⋊D47—21no—
59C22⋊D47—21no—
60C22⋊D47—22no—
61C22⋊D47—22no—
62C2×Dic47—21no—
63C2×Dic47D411yescharacteristic
64D188—21no—
65D188—21no—
66D188C2312yes—
67D188C2311yescharacteristic, complemented
68C4×D47—21no—
69C4×D47—21no—
70C4×D47—21no—
71C4×D47D411yescharacteristic
72C4×D47D411yescharacteristic
73C4×D47C2311yescharacteristic
74C4×D47C2311yescharacteristic
75Dic94—21no—
76Dic94C2311yescharacteristic, complemented
77C8×C47C2312yescomplemented
78C47⋊C8C2312yescomplemented
79C22×C47—21no—
80C22×C47—22no—
81C22×C47—42no—
82C22×C47C2×D411yescharacteristic
83C2×D47—22no—
84C2×D47—21no—
85C2×D47—22no—
86C2×D47—44no—
87C2×D47—42no—
88C2×D47—42no—
89C2×D47—44no—
90C2×D47C2×D411yescharacteristic
91C2×D47C2×D411yescharacteristic
92C4×C47—21no—
93C4×C47C2×D411yescharacteristic
94C4×C47C2411yescharacteristic
95Dic47—21no—
96Dic47C2×D411yescharacteristic
97Dic47C2×D411yescharacteristic
98C2×C47—21no—
99C2×C47—42no—
100C2×C47—41no—
101C2×C47C22×D411yescharacteristic
102D47—21no—
103D47—41no—
104D47—42no—
105D47AGL(1,ℤ/8)12yesdirect product factor
106C2×AGL(1,ℤ/8)—471nomaximal, Sylow
107C47C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
108C2×#41—471no—
109C22×D4—471no—
110AGL(1,ℤ/8)—471no—
111AGL(1,ℤ/8)—471no—
112AGL(1,ℤ/8)—472no—
113AGL(1,ℤ/8)—472no—
114AGL(1,ℤ/8)—471no—
115AGL(1,ℤ/8)D4711yescharacteristic, direct product factor
116C2×SD16—472no—
117C2×D8—472no—
118C2×M16—471no—
119C24—941no—
120#41—471no—
121#41—471no—
122#41—471no—
123#41—941no—
124#41—941no—
125#41C2×D4711yescharacteristic, complemented
126C2×Q8—471no—
127C2×D4—472no—
128C2×D4—472no—
129C2×D4—471no—
130C2×D4—471no—
131C2×D4—941no—
132C2×D4—941no—
133C2×D4—941no—
134C2×D4—941no—
135C2×D4C2×D4711yescharacteristic, complemented
136C22×C4—471no—
137C22×C4—941no—
138SD16—472no—
139SD16—472no—
140SD16—472no—
141SD16C2×D4712yescomplemented
142D8—472no—
143D8—472no—
144D8—472no—
145D8C2×D4712yescomplemented
146M16—471no—
147M16—472no—
148M16C2×D4711yescharacteristic, complemented
149C2×C8—472no—
150C23—21no—
151C23—471no—
152C23—941no—
153C23—942no—
154C23—942no—
155C23—941no—
156C23—1884no—
157Q8—471no—
158Q8—941no—
159Q8C22×D4711yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—472no—
163D4—471no—
164D4—941no—
165D4—942no—
166D4—942no—
167D4—941no—
168D4—941no—
169D4—941no—
170D4—941no—
171D4C22×D4712yes—
172D4C22×D4711yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—471no—
175C2×C4—471no—
176C2×C4—471no—
177C2×C4—471no—
178C2×C4—471no—
179C2×C4—941no—
180C2×C4—941no—
181C2×C4—941no—
182C2×C4—941no—
183C2×C4C22×D4711yescharacteristic
184C8—472no—
185C8C22×D4712yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—471no—
190C22—471no—
191C22—942no—
192C22—941no—
193C22—942no—
194C22—1882no—
195C22—1884no—
196C22—1882no—
197C22—1884no—
198C22D4×D4711yescharacteristic
199C4—21no—
200C4—471no—
201C4—471no—
202C4—941no—
203C4D4×D4711yescharacteristic
204C4C23×D4711yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—472no—
209C2—941no—
210C2—1882no—
211C2—1881no—
212C2C2×D4×D4711yescharacteristic
subgroupG/H
centerC2C2×D4×D47
commutator, cosocleC4×C47C24
FrattiniC4C23×D47
FittingAGL(1,ℤ/8)×C47C2
socleC2×C47C22×D4
hypercenterAGL(1,ℤ/8)D47
hypocenterC47C2×AGL(1,ℤ/8)
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D47C2semidirect
2. C2×D4×D47C2semidirect
3. #13094052C2semidirect
4. #13094051C2semidirect
5. #13094050C2semidirect
6. #13094049C2semidirect
7. #13094048C2semidirect
8. SD16×D47C2semidirect
9. D8×D47C2semidirect
10. M16×D47C2semidirect
11. AGL(1,ℤ/8)×C47C2semidirect
13. #41×C47C22semidirect
14. C2×D4×C47C22semidirect
16. #10625354C22semidirect
17. Q8×D47C22semidirect
19. #10625352C22semidirect
24. D4×D47C22semidirect
25. D4×D47C22semidirect
27. #10625350C22semidirect
28. C2×D188C22semidirect
31. SD16×C47C22semidirect
32. D8×C47C22semidirect
33. M16×C47C22semidirect
34. #10625336C22semidirect
35. #10625335C22semidirect
36. #10625334C22semidirect
37. #10625334C22semidirect
38. #10625329C22semidirect
39. D376C22semidirect
40. #10625325C22semidirect
41. #10625324C22semidirect
42. C8×D47C22semidirect
50. Q8×C47C23semidirect
54. D4×C47C23semidirect
67. D188C23semidirect
76. Dic94C23semidirect
77. C8×C47C23semidirect
78. C47⋊C8C23semidirect
105. D47AGL(1,ℤ/8)direct (N × H)
107. C47C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D47direct (N × H)
125. #41C2×D47semidirect
135. C2×D4C2×D47semidirect
141. SD16C2×D47semidirect
145. D8C2×D47semidirect
148. M16C2×D47semidirect
159. Q8C22×D47semidirect
172. D4C22×D47semidirect
185. C8C22×D47semidirect

Maximal subgroups

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

subgroupindex
#41×D472
C2×D4×D472
#130940522
#130940512
#130940502
#130940492
#130940482
SD16×D472
D8×D472
M16×D472
AGL(1,ℤ/8)×C472
C2×AGL(1,ℤ/8)47