Finite Group Databasebeta

← AGL(1,ℤ/8)×D283 #31827249

Subgroups — AGL(1,ℤ/8)×D283 #31827249

Order 18112.

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×D283C211yesmaximal, characteristic, complemented
2C2×D4×D283C211yesmaximal, characteristic, complemented
3#22583638C211yesmaximal, characteristic, complemented
4#22583637C212yesmaximal, complemented
5#22583636C211yesmaximal, characteristic, complemented
6#22583635C211yesmaximal, characteristic, complemented
7#22583634C212yesmaximal, complemented
8SD16×D283C212yesmaximal, complemented
9D8×D283C212yesmaximal, complemented
10M16×D283C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C283C211yesmaximal, characteristic, complemented
12C23×D283—21no—
13#17985393C2211yescharacteristic, complemented
14#17985392—21no—
15#17985392C2211yescharacteristic, complemented
16#17985391—21no—
17#17985391C2211yescharacteristic, complemented
18Q8×D283C2211yescharacteristic, complemented
19C2×D1132C2211yescharacteristic, complemented
20C2×C22⋊D283—21no—
21D4×D283—21no—
22D4×D283—21no—
23D4×D283—21no—
24D4×D283C2212yes—
25D4×D283C2212yescomplemented
26D4×D283C2211yescharacteristic, complemented
27C2×C4×D283—21no—
28C2×C4×D283C2211yescharacteristic
29#17985381C2212yescomplemented
30#17985380C2212yescomplemented
31#17985379C2212yescomplemented
32D2264C2212yescomplemented
33#17985377C2212yescomplemented
34#17985377C2212yescomplemented
35#17985376C2211yescharacteristic, complemented
36#17985375C2212yescomplemented
37C8×D283C2212yescomplemented
38#41×C283C2211yescharacteristic, complemented
39C2×D4×C283C2211yescharacteristic, complemented
40SD16×C283C2212yescomplemented
41D8×C283C2212yescomplemented
42M16×C283C2211yescharacteristic, complemented
43C22×D283—21no—
44C22×D283—21no—
45C22×D283—22no—
46C22×D283—22no—
47C22×D283—44no—
48C22×D283D411yescharacteristic
49Dic566—21no—
50Dic566C2311yescharacteristic, complemented
51D1132—21no—
52D1132—21no—
53D1132C2312yes—
54D1132C2311yescharacteristic, complemented
55C22⋊D283—21no—
56C22⋊D283—21no—
57C22⋊D283—22no—
58C22⋊D283—22no—
59C22⋊D283—21no—
60C2×Dic283—21no—
61C2×Dic283D411yescharacteristic
62C4×D283—21no—
63C4×D283—21no—
64C4×D283—21no—
65C4×D283D411yescharacteristic
66C4×D283D411yescharacteristic
67C4×D283C2311yescharacteristic
68C4×D283C2311yescharacteristic
69C283⋊C8C2312yescomplemented
70C23×C283—21no—
71Q8×C283C2311yescharacteristic, complemented
72D4×C283—21no—
73D4×C283—21no—
74D4×C283C2312yes—
75D4×C283C2311yescharacteristic, complemented
76C2×C4×C283—21no—
77C2×C4×C283C2311yescharacteristic
78C8×C283C2312yescomplemented
79C22×C283—21no—
80C22×C283—22no—
81C22×C283—42no—
82C22×C283C2×D411yescharacteristic
83C2×D283—22no—
84C2×D283—21no—
85C2×D283—22no—
86C2×D283—44no—
87C2×D283—42no—
88C2×D283—42no—
89C2×D283—44no—
90C2×D283C2×D411yescharacteristic
91C2×D283C2×D411yescharacteristic
92C4×C283—21no—
93C4×C283C2×D411yescharacteristic
94C4×C283C2411yescharacteristic
95Dic283—21no—
96Dic283C2×D411yescharacteristic
97Dic283C2×D411yescharacteristic
98C2×C283—21no—
99C2×C283—42no—
100C2×C283—41no—
101C2×C283C22×D411yescharacteristic
102D283—21no—
103D283—41no—
104D283—42no—
105D283AGL(1,ℤ/8)12yesdirect product factor
106C283C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—2831nomaximal, Sylow
108C2×#41—2831no—
109C22×D4—2831no—
110AGL(1,ℤ/8)—2831no—
111AGL(1,ℤ/8)—2831no—
112AGL(1,ℤ/8)—2832no—
113AGL(1,ℤ/8)—2832no—
114AGL(1,ℤ/8)—2831no—
115AGL(1,ℤ/8)D28311yescharacteristic, direct product factor
116C2×SD16—2832no—
117C2×D8—2832no—
118C2×M16—2831no—
119C24—5661no—
120#41—2831no—
121#41—2831no—
122#41—2831no—
123#41—5661no—
124#41—5661no—
125#41C2×D28311yescharacteristic, complemented
126C2×Q8—2831no—
127C2×D4—2832no—
128C2×D4—2832no—
129C2×D4—2831no—
130C2×D4—2831no—
131C2×D4—5661no—
132C2×D4—5661no—
133C2×D4—5661no—
134C2×D4—5661no—
135C2×D4C2×D28311yescharacteristic, complemented
136C22×C4—2831no—
137C22×C4—5661no—
138SD16—2832no—
139SD16—2832no—
140SD16—2832no—
141SD16C2×D28312yescomplemented
142D8—2832no—
143D8—2832no—
144D8—2832no—
145D8C2×D28312yescomplemented
146M16—2831no—
147M16—2832no—
148M16C2×D28311yescharacteristic, complemented
149C2×C8—2832no—
150C23—21no—
151C23—2831no—
152C23—5661no—
153C23—5662no—
154C23—5662no—
155C23—5661no—
156C23—11324no—
157Q8—2831no—
158Q8—5661no—
159Q8C22×D28311yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—2831no—
163D4—2832no—
164D4—5661no—
165D4—5662no—
166D4—5662no—
167D4—5661no—
168D4—5661no—
169D4—5661no—
170D4—5661no—
171D4C22×D28312yes—
172D4C22×D28311yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—2831no—
175C2×C4—2831no—
176C2×C4—2831no—
177C2×C4—2831no—
178C2×C4—2831no—
179C2×C4—5661no—
180C2×C4—5661no—
181C2×C4—5661no—
182C2×C4—5661no—
183C2×C4C22×D28311yescharacteristic
184C8—2832no—
185C8C22×D28312yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—2831no—
190C22—2831no—
191C22—5662no—
192C22—5661no—
193C22—5662no—
194C22—11322no—
195C22—11324no—
196C22—11322no—
197C22—11324no—
198C22D4×D28311yescharacteristic
199C4—21no—
200C4—2831no—
201C4—2831no—
202C4—5661no—
203C4D4×D28311yescharacteristic
204C4C23×D28311yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—2832no—
209C2—5661no—
210C2—11322no—
211C2—11321no—
212C2C2×D4×D28311yescharacteristic
subgroupG/H
centerC2C2×D4×D283
commutator, cosocleC4×C283C24
FrattiniC4C23×D283
FittingAGL(1,ℤ/8)×C283C2
socleC2×C283C22×D4
hypercenterAGL(1,ℤ/8)D283
hypocenterC283C2×AGL(1,ℤ/8)
LCSG ▷ C4×C283 ▷ C2×C283 ▷ C283
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D283C2semidirect
2. C2×D4×D283C2semidirect
3. #22583638C2semidirect
4. #22583637C2semidirect
5. #22583636C2semidirect
6. #22583635C2semidirect
7. #22583634C2semidirect
8. SD16×D283C2semidirect
9. D8×D283C2semidirect
10. M16×D283C2semidirect
11. AGL(1,ℤ/8)×C283C2semidirect
13. #17985393C22semidirect
15. #17985392C22semidirect
17. #17985391C22semidirect
18. Q8×D283C22semidirect
19. C2×D1132C22semidirect
25. D4×D283C22semidirect
26. D4×D283C22semidirect
29. #17985381C22semidirect
30. #17985380C22semidirect
31. #17985379C22semidirect
32. D2264C22semidirect
33. #17985377C22semidirect
34. #17985377C22semidirect
35. #17985376C22semidirect
36. #17985375C22semidirect
37. C8×D283C22semidirect
38. #41×C283C22semidirect
39. C2×D4×C283C22semidirect
40. SD16×C283C22semidirect
41. D8×C283C22semidirect
42. M16×C283C22semidirect
50. Dic566C23semidirect
54. D1132C23semidirect
69. C283⋊C8C23semidirect
71. Q8×C283C23semidirect
75. D4×C283C23semidirect
78. C8×C283C23semidirect
105. D283AGL(1,ℤ/8)direct (N × H)
106. C283C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D283direct (N × H)
125. #41C2×D283semidirect
135. C2×D4C2×D283semidirect
141. SD16C2×D283semidirect
145. D8C2×D283semidirect
148. M16C2×D283semidirect
159. Q8C22×D283semidirect
172. D4C22×D283semidirect
185. C8C22×D283semidirect

Maximal subgroups

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

subgroupindex
#41×D2832
C2×D4×D2832
#225836382
#225836372
#225836362
#225836352
#225836342
SD16×D2832
D8×D2832
M16×D2832
AGL(1,ℤ/8)×C2832
C2×AGL(1,ℤ/8)283