Finite Group Databasebeta

← AGL(1,ℤ/8)×D389 #38734883

Subgroups — AGL(1,ℤ/8)×D389 #38734883

Order 24896.

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×D389C211yesmaximal, characteristic, complemented
2C2×D4×D389C211yesmaximal, characteristic, complemented
3#27159412C211yesmaximal, characteristic, complemented
4#27159411C212yesmaximal, complemented
5#27159410C211yesmaximal, characteristic, complemented
6#27159409C211yesmaximal, characteristic, complemented
7#27159408C212yesmaximal, complemented
8SD16×D389C212yesmaximal, complemented
9D8×D389C212yesmaximal, complemented
10M16×D389C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C389C211yesmaximal, characteristic, complemented
12C23×D389—21no—
13#20261967C2211yescharacteristic, complemented
14#20261966—21no—
15#20261966C2211yescharacteristic, complemented
16#20261965—21no—
17#20261965C2211yescharacteristic, complemented
18Q8×D389C2211yescharacteristic, complemented
19C2×D1556C2211yescharacteristic, complemented
20C2×C22⋊D389—21no—
21D4×D389—21no—
22D4×D389—21no—
23D4×D389—21no—
24D4×D389C2212yes—
25D4×D389C2212yescomplemented
26D4×D389C2211yescharacteristic, complemented
27C2×C4×D389—21no—
28C2×C4×D389C2211yescharacteristic
29#20261955C2212yescomplemented
30#20261954C2212yescomplemented
31#20261953C2212yescomplemented
32D3112C2212yescomplemented
33#20261951C2212yescomplemented
34#20261951C2212yescomplemented
35#20261950C2211yescharacteristic, complemented
36#20261949C2212yescomplemented
37C8×D389C2212yescomplemented
38#41×C389C2211yescharacteristic, complemented
39C2×D4×C389C2211yescharacteristic, complemented
40SD16×C389C2212yescomplemented
41D8×C389C2212yescomplemented
42M16×C389C2211yescharacteristic, complemented
43C22×D389—21no—
44C22×D389—21no—
45C22×D389—22no—
46C22×D389—22no—
47C22×D389—44no—
48C22×D389D411yescharacteristic
49Dic778—21no—
50Dic778C2311yescharacteristic, complemented
51D1556—21no—
52D1556—21no—
53D1556C2312yes—
54D1556C2311yescharacteristic, complemented
55C22⋊D389—21no—
56C22⋊D389—21no—
57C22⋊D389—22no—
58C22⋊D389—22no—
59C22⋊D389—21no—
60C2×Dic389—21no—
61C2×Dic389D411yescharacteristic
62C4×D389—21no—
63C4×D389—21no—
64C4×D389—21no—
65C4×D389D411yescharacteristic
66C4×D389D411yescharacteristic
67C4×D389C2311yescharacteristic
68C4×D389C2311yescharacteristic
69#15691005C2312yescomplemented
70C23×C389—21no—
71Q8×C389C2311yescharacteristic, complemented
72D4×C389—21no—
73D4×C389—21no—
74D4×C389C2312yes—
75D4×C389C2311yescharacteristic, complemented
76C2×C4×C389—21no—
77C2×C4×C389C2311yescharacteristic
78C8×C389C2312yescomplemented
79C22×C389—22no—
80C22×C389—21no—
81C22×C389—42no—
82C22×C389C2×D411yescharacteristic
83C2×D389—22no—
84C2×D389—22no—
85C2×D389—21no—
86C2×D389—44no—
87C2×D389—42no—
88C2×D389—42no—
89C2×D389—44no—
90C2×D389C2×D411yescharacteristic
91C2×D389C2×D411yescharacteristic
92C4×C389—21no—
93C4×C389C2×D411yescharacteristic
94C4×C389C2411yescharacteristic
95Dic389—21no—
96Dic389C2×D411yescharacteristic
97Dic389C2×D411yescharacteristic
98C2×C389—21no—
99C2×C389—42no—
100C2×C389—41no—
101C2×C389C22×D411yescharacteristic
102D389—21no—
103D389—41no—
104D389—42no—
105D389AGL(1,ℤ/8)12yesdirect product factor
106C389C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—3891nomaximal, Sylow
108C2×#41—3891no—
109C22×D4—3891no—
110AGL(1,ℤ/8)—3891no—
111AGL(1,ℤ/8)—3891no—
112AGL(1,ℤ/8)—3892no—
113AGL(1,ℤ/8)—3892no—
114AGL(1,ℤ/8)—3891no—
115AGL(1,ℤ/8)D38911yescharacteristic, direct product factor
116C2×SD16—3892no—
117C2×D8—3892no—
118C2×M16—3891no—
119C24—7781no—
120#41—7781no—
121#41—7781no—
122#41—3891no—
123#41—3891no—
124#41—3891no—
125#41C2×D38911yescharacteristic, complemented
126C2×Q8—3891no—
127C2×D4—7781no—
128C2×D4—7781no—
129C2×D4—7781no—
130C2×D4—7781no—
131C2×D4—3892no—
132C2×D4—3892no—
133C2×D4—3891no—
134C2×D4—3891no—
135C2×D4C2×D38911yescharacteristic, complemented
136C22×C4—7781no—
137C22×C4—3891no—
138SD16—3892no—
139SD16—3892no—
140SD16—3892no—
141SD16C2×D38912yescomplemented
142D8—3892no—
143D8—3892no—
144D8—3892no—
145D8C2×D38912yescomplemented
146M16—3891no—
147M16—3892no—
148M16C2×D38911yescharacteristic, complemented
149C2×C8—3892no—
150C23—21no—
151C23—7781no—
152C23—7782no—
153C23—7782no—
154C23—7781no—
155C23—15564no—
156C23—3891no—
157Q8—7781no—
158Q8—3891no—
159Q8C22×D38911yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—7781no—
163D4—7781no—
164D4—7781no—
165D4—7782no—
166D4—7782no—
167D4—7781no—
168D4—7781no—
169D4—3892no—
170D4—3891no—
171D4C22×D38912yes—
172D4C22×D38911yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—7781no—
175C2×C4—7781no—
176C2×C4—7781no—
177C2×C4—7781no—
178C2×C4—3891no—
179C2×C4—3891no—
180C2×C4—3891no—
181C2×C4—3891no—
182C2×C4—3891no—
183C2×C4C22×D38911yescharacteristic
184C8—3892no—
185C8C22×D38912yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—7782no—
190C22—7781no—
191C22—7782no—
192C22—15562no—
193C22—15564no—
194C22—15564no—
195C22—15562no—
196C22—3891no—
197C22—3891no—
198C22D4×D38911yescharacteristic
199C4—21no—
200C4—7781no—
201C4—3891no—
202C4—3891no—
203C4D4×D38911yescharacteristic
204C4C23×D38911yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—7781no—
209C2—15562no—
210C2—15561no—
211C2—3892no—
212C2C2×D4×D38911yescharacteristic
subgroupG/H
centerC2C2×D4×D389
commutator, cosocleC4×C389C24
FrattiniC4C23×D389
FittingAGL(1,ℤ/8)×C389C2
socleC2×C389C22×D4
hypercenterAGL(1,ℤ/8)D389
hypocenterC389C2×AGL(1,ℤ/8)
LCSG ▷ C4×C389 ▷ C2×C389 ▷ C389
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D389C2semidirect
2. C2×D4×D389C2semidirect
3. #27159412C2semidirect
4. #27159411C2semidirect
5. #27159410C2semidirect
6. #27159409C2semidirect
7. #27159408C2semidirect
8. SD16×D389C2semidirect
9. D8×D389C2semidirect
10. M16×D389C2semidirect
11. AGL(1,ℤ/8)×C389C2semidirect
13. #20261967C22semidirect
15. #20261966C22semidirect
17. #20261965C22semidirect
18. Q8×D389C22semidirect
19. C2×D1556C22semidirect
25. D4×D389C22semidirect
26. D4×D389C22semidirect
29. #20261955C22semidirect
30. #20261954C22semidirect
31. #20261953C22semidirect
32. D3112C22semidirect
33. #20261951C22semidirect
34. #20261951C22semidirect
35. #20261950C22semidirect
36. #20261949C22semidirect
37. C8×D389C22semidirect
38. #41×C389C22semidirect
39. C2×D4×C389C22semidirect
40. SD16×C389C22semidirect
41. D8×C389C22semidirect
42. M16×C389C22semidirect
50. Dic778C23semidirect
54. D1556C23semidirect
69. #15691005C23semidirect
71. Q8×C389C23semidirect
75. D4×C389C23semidirect
78. C8×C389C23semidirect
105. D389AGL(1,ℤ/8)direct (N × H)
106. C389C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D389direct (N × H)
125. #41C2×D389semidirect
135. C2×D4C2×D389semidirect
141. SD16C2×D389semidirect
145. D8C2×D389semidirect
148. M16C2×D389semidirect
159. Q8C22×D389semidirect
172. D4C22×D389semidirect
185. C8C22×D389semidirect

Maximal subgroups

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

subgroupindex
#41×D3892
C2×D4×D3892
#271594122
#271594112
#271594102
#271594092
#271594082
SD16×D3892
D8×D3892
M16×D3892
AGL(1,ℤ/8)×C3892
C2×AGL(1,ℤ/8)389