Finite Group Databasebeta

← AGL(1,ℤ/8)×D97 #20261519

Subgroups — AGL(1,ℤ/8)×D97 #20261519

Order 6208.

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×D97C211yesmaximal, characteristic, complemented
2C2×D4×D97C211yesmaximal, characteristic, complemented
3#15690838C211yesmaximal, characteristic, complemented
4#15690837C212yesmaximal, complemented
5#15690836C211yesmaximal, characteristic, complemented
6#15690835C211yesmaximal, characteristic, complemented
7#15690834C212yesmaximal, complemented
8SD16×D97C212yesmaximal, complemented
9D8×D97C212yesmaximal, complemented
10M16×D97C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C97C211yesmaximal, characteristic, complemented
12C23×D97—21no—
13#13095512C2211yescharacteristic, complemented
14#13095511—21no—
15#13095511C2211yescharacteristic, complemented
16#13095510—21no—
17#13095510C2211yescharacteristic, complemented
18Q8×D97C2211yescharacteristic, complemented
19C2×D388C2211yescharacteristic, complemented
20C2×C22⋊D97—21no—
21D4×D97—21no—
22D4×D97—21no—
23D4×D97—21no—
24D4×D97C2212yes—
25D4×D97C2212yescomplemented
26D4×D97C2211yescharacteristic, complemented
27C2×C4×D97—21no—
28C2×C4×D97C2211yescharacteristic
29#13095500C2212yescomplemented
30#13095499C2212yescomplemented
31#13095498C2212yescomplemented
32D776C2212yescomplemented
33#13095496C2212yescomplemented
34#13095496C2212yescomplemented
35#13095495C2211yescharacteristic, complemented
36#13095494C2212yescomplemented
37C8×D97C2212yescomplemented
38#41×C97C2211yescharacteristic, complemented
39C2×D4×C97C2211yescharacteristic, complemented
40SD16×C97C2212yescomplemented
41D8×C97C2212yescomplemented
42M16×C97C2211yescharacteristic, complemented
43C23×C97—21no—
44C22×D97—21no—
45C22×D97—21no—
46C22×D97—22no—
47C22×D97—22no—
48C22×D97—44no—
49C22×D97D411yescharacteristic
50Q8×C97C2311yescharacteristic, complemented
51D4×C97—21no—
52D4×C97—21no—
53D4×C97C2312yes—
54D4×C97C2311yescharacteristic, complemented
55C2×C4×C97—21no—
56C2×C4×C97C2311yescharacteristic
57C22⋊D97—21no—
58C22⋊D97—21no—
59C22⋊D97—22no—
60C22⋊D97—22no—
61C22⋊D97—21no—
62C2×Dic97—21no—
63C2×Dic97D411yescharacteristic
64D388—21no—
65D388—21no—
66D388C2312yes—
67D388C2311yescharacteristic, complemented
68C4×D97—21no—
69C4×D97—21no—
70C4×D97—21no—
71C4×D97D411yescharacteristic
72C4×D97D411yescharacteristic
73C4×D97C2311yescharacteristic
74C4×D97C2311yescharacteristic
75Dic194—21no—
76Dic194C2311yescharacteristic, complemented
77C8×C97C2312yescomplemented
78#11715895C2312yescomplemented
79C22×C97—21no—
80C22×C97—22no—
81C22×C97—42no—
82C22×C97C2×D411yescharacteristic
83C2×D97—22no—
84C2×D97—21no—
85C2×D97—22no—
86C2×D97—44no—
87C2×D97—42no—
88C2×D97—42no—
89C2×D97—44no—
90C2×D97C2×D411yescharacteristic
91C2×D97C2×D411yescharacteristic
92C4×C97—21no—
93C4×C97C2×D411yescharacteristic
94C4×C97C2411yescharacteristic
95Dic97—21no—
96Dic97C2×D411yescharacteristic
97Dic97C2×D411yescharacteristic
98C2×C97—21no—
99C2×C97—42no—
100C2×C97—41no—
101C2×C97C22×D411yescharacteristic
102D97—21no—
103D97—41no—
104D97—42no—
105D97AGL(1,ℤ/8)12yesdirect product factor
106C97C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—971nomaximal, Sylow
108C2×#41—971no—
109C22×D4—971no—
110AGL(1,ℤ/8)—971no—
111AGL(1,ℤ/8)—971no—
112AGL(1,ℤ/8)—972no—
113AGL(1,ℤ/8)—972no—
114AGL(1,ℤ/8)—971no—
115AGL(1,ℤ/8)D9711yescharacteristic, direct product factor
116C2×SD16—972no—
117C2×D8—972no—
118C2×M16—971no—
119C24—1941no—
120#41—971no—
121#41—971no—
122#41—971no—
123#41—1941no—
124#41—1941no—
125#41C2×D9711yescharacteristic, complemented
126C2×Q8—971no—
127C2×D4—972no—
128C2×D4—972no—
129C2×D4—971no—
130C2×D4—971no—
131C2×D4—1941no—
132C2×D4—1941no—
133C2×D4—1941no—
134C2×D4—1941no—
135C2×D4C2×D9711yescharacteristic, complemented
136C22×C4—971no—
137C22×C4—1941no—
138SD16—972no—
139SD16—972no—
140SD16—972no—
141SD16C2×D9712yescomplemented
142D8—972no—
143D8—972no—
144D8—972no—
145D8C2×D9712yescomplemented
146M16—971no—
147M16—972no—
148M16C2×D9711yescharacteristic, complemented
149C2×C8—972no—
150C23—21no—
151C23—971no—
152C23—3884no—
153C23—1941no—
154C23—1942no—
155C23—1942no—
156C23—1941no—
157Q8—971no—
158Q8—1941no—
159Q8C22×D9711yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—971no—
163D4—972no—
164D4—1941no—
165D4—1942no—
166D4—1942no—
167D4—1941no—
168D4—1941no—
169D4—1941no—
170D4—1941no—
171D4C22×D9712yes—
172D4C22×D9711yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—971no—
175C2×C4—971no—
176C2×C4—971no—
177C2×C4—971no—
178C2×C4—971no—
179C2×C4—1941no—
180C2×C4—1941no—
181C2×C4—1941no—
182C2×C4—1941no—
183C2×C4C22×D9711yescharacteristic
184C8—972no—
185C8C22×D9712yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—971no—
190C22—971no—
191C22—3882no—
192C22—3884no—
193C22—3882no—
194C22—3884no—
195C22—1942no—
196C22—1941no—
197C22—1942no—
198C22D4×D9711yescharacteristic
199C4—21no—
200C4—971no—
201C4—971no—
202C4—1941no—
203C4D4×D9711yescharacteristic
204C4C23×D9711yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—972no—
209C2—3882no—
210C2—3881no—
211C2—1941no—
212C2C2×D4×D9711yescharacteristic
subgroupG/H
centerC2C2×D4×D97
commutatorC4×C97C24
FrattiniC4C23×D97
FittingAGL(1,ℤ/8)×C97C2
socleC2×C97C22×D4
hypercenterAGL(1,ℤ/8)D97
hypocenterC97C2×AGL(1,ℤ/8)
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D97C2semidirect
2. C2×D4×D97C2semidirect
3. #15690838C2semidirect
4. #15690837C2semidirect
5. #15690836C2semidirect
6. #15690835C2semidirect
7. #15690834C2semidirect
8. SD16×D97C2semidirect
9. D8×D97C2semidirect
10. M16×D97C2semidirect
11. AGL(1,ℤ/8)×C97C2semidirect
13. #13095512C22semidirect
15. #13095511C22semidirect
17. #13095510C22semidirect
18. Q8×D97C22semidirect
19. C2×D388C22semidirect
25. D4×D97C22semidirect
26. D4×D97C22semidirect
29. #13095500C22semidirect
30. #13095499C22semidirect
31. #13095498C22semidirect
32. D776C22semidirect
33. #13095496C22semidirect
34. #13095496C22semidirect
35. #13095495C22semidirect
36. #13095494C22semidirect
37. C8×D97C22semidirect
38. #41×C97C22semidirect
39. C2×D4×C97C22semidirect
40. SD16×C97C22semidirect
41. D8×C97C22semidirect
42. M16×C97C22semidirect
50. Q8×C97C23semidirect
54. D4×C97C23semidirect
67. D388C23semidirect
76. Dic194C23semidirect
77. C8×C97C23semidirect
78. #11715895C23semidirect
105. D97AGL(1,ℤ/8)direct (N × H)
106. C97C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D97direct (N × H)
125. #41C2×D97semidirect
135. C2×D4C2×D97semidirect
141. SD16C2×D97semidirect
145. D8C2×D97semidirect
148. M16C2×D97semidirect
159. Q8C22×D97semidirect
172. D4C22×D97semidirect
185. C8C22×D97semidirect