Finite Group Databasebeta

← AGL(1,ℤ/8)×D101 #20265961

Subgroups — AGL(1,ℤ/8)×D101 #20265961

Order 6464.

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×D101C211yesmaximal, characteristic, complemented
2C2×D4×D101C211yesmaximal, characteristic, complemented
3#15692283C211yesmaximal, characteristic, complemented
4#15692282C212yesmaximal, complemented
5#15692281C211yesmaximal, characteristic, complemented
6#15692280C211yesmaximal, characteristic, complemented
7#15692279C212yesmaximal, complemented
8SD16×D101C212yesmaximal, complemented
9D8×D101C212yesmaximal, complemented
10M16×D101C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C101C211yesmaximal, characteristic, complemented
12C23×D101—21no—
13#13108075C2211yescharacteristic, complemented
14#13108074—21no—
15#13108074C2211yescharacteristic, complemented
16#13108073—21no—
17#13108073C2211yescharacteristic, complemented
18Q8×D101C2211yescharacteristic, complemented
19C2×D404C2211yescharacteristic, complemented
20C2×C22⋊D101—21no—
21D4×D101—21no—
22D4×D101—21no—
23D4×D101—21no—
24D4×D101C2212yes—
25D4×D101C2212yescomplemented
26D4×D101C2211yescharacteristic, complemented
27C2×C4×D101—21no—
28C2×C4×D101C2211yescharacteristic
29#13108063C2212yescomplemented
30#13108062C2212yescomplemented
31#13108061C2212yescomplemented
32D808C2212yescomplemented
33#13108059C2212yescomplemented
34#13108059C2212yescomplemented
35#13108058C2211yescharacteristic, complemented
36#13108057C2212yescomplemented
37C8×D101C2212yescomplemented
38#41×C101C2211yescharacteristic, complemented
39C2×D4×C101C2211yescharacteristic, complemented
40SD16×C101C2212yescomplemented
41D8×C101C2212yescomplemented
42M16×C101C2211yescharacteristic, complemented
43C23×C101—21no—
44C22×D101—21no—
45C22×D101—21no—
46C22×D101—22no—
47C22×D101—22no—
48C22×D101—44no—
49C22×D101D411yescharacteristic
50Q8×C101C2311yescharacteristic, complemented
51D4×C101—21no—
52D4×C101—21no—
53D4×C101C2312yes—
54D4×C101C2311yescharacteristic, complemented
55C2×C4×C101—21no—
56C2×C4×C101C2311yescharacteristic
57C22⋊D101—21no—
58C22⋊D101—21no—
59C22⋊D101—22no—
60C22⋊D101—22no—
61C22⋊D101—21no—
62C2×Dic101—21no—
63C2×Dic101D411yescharacteristic
64D404—21no—
65D404—21no—
66D404C2312yes—
67D404C2311yescharacteristic, complemented
68C4×D101—21no—
69C4×D101—21no—
70C4×D101—21no—
71C4×D101D411yescharacteristic
72C4×D101D411yescharacteristic
73C4×D101C2311yescharacteristic
74C4×D101C2311yescharacteristic
75Dic202—21no—
76Dic202C2311yescharacteristic, complemented
77C8×C101C2312yescomplemented
78#11717579C2312yescomplemented
79C22×C101—21no—
80C22×C101—22no—
81C22×C101—42no—
82C22×C101C2×D411yescharacteristic
83C2×D101—22no—
84C2×D101—21no—
85C2×D101—22no—
86C2×D101—44no—
87C2×D101—42no—
88C2×D101—42no—
89C2×D101—44no—
90C2×D101C2×D411yescharacteristic
91C2×D101C2×D411yescharacteristic
92C4×C101—21no—
93C4×C101C2×D411yescharacteristic
94C4×C101C2411yescharacteristic
95Dic101—21no—
96Dic101C2×D411yescharacteristic
97Dic101C2×D411yescharacteristic
98C2×C101—21no—
99C2×C101—42no—
100C2×C101—41no—
101C2×C101C22×D411yescharacteristic
102D101—21no—
103D101—41no—
104D101—42no—
105D101AGL(1,ℤ/8)12yesdirect product factor
106C101C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—1011nomaximal, Sylow
108C2×#41—1011no—
109C22×D4—1011no—
110AGL(1,ℤ/8)—1011no—
111AGL(1,ℤ/8)—1011no—
112AGL(1,ℤ/8)—1012no—
113AGL(1,ℤ/8)—1012no—
114AGL(1,ℤ/8)—1011no—
115AGL(1,ℤ/8)D10111yescharacteristic, direct product factor
116C2×SD16—1012no—
117C2×D8—1012no—
118C2×M16—1011no—
119C24—2021no—
120#41—1011no—
121#41—1011no—
122#41—1011no—
123#41—2021no—
124#41—2021no—
125#41C2×D10111yescharacteristic, complemented
126C2×Q8—1011no—
127C2×D4—1012no—
128C2×D4—1012no—
129C2×D4—1011no—
130C2×D4—1011no—
131C2×D4—2021no—
132C2×D4—2021no—
133C2×D4—2021no—
134C2×D4—2021no—
135C2×D4C2×D10111yescharacteristic, complemented
136C22×C4—1011no—
137C22×C4—2021no—
138SD16—1012no—
139SD16—1012no—
140SD16—1012no—
141SD16C2×D10112yescomplemented
142D8—1012no—
143D8—1012no—
144D8—1012no—
145D8C2×D10112yescomplemented
146M16—1011no—
147M16—1012no—
148M16C2×D10111yescharacteristic, complemented
149C2×C8—1012no—
150C23—21no—
151C23—1011no—
152C23—4044no—
153C23—2021no—
154C23—2022no—
155C23—2022no—
156C23—2021no—
157Q8—1011no—
158Q8—2021no—
159Q8C22×D10111yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—1011no—
163D4—1012no—
164D4—2021no—
165D4—2022no—
166D4—2022no—
167D4—2021no—
168D4—2021no—
169D4—2021no—
170D4—2021no—
171D4C22×D10112yes—
172D4C22×D10111yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—1011no—
175C2×C4—1011no—
176C2×C4—1011no—
177C2×C4—1011no—
178C2×C4—1011no—
179C2×C4—2021no—
180C2×C4—2021no—
181C2×C4—2021no—
182C2×C4—2021no—
183C2×C4C22×D10111yescharacteristic
184C8—1012no—
185C8C22×D10112yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—1011no—
190C22—1011no—
191C22—4042no—
192C22—4044no—
193C22—4042no—
194C22—4044no—
195C22—2022no—
196C22—2021no—
197C22—2022no—
198C22D4×D10111yescharacteristic
199C4—21no—
200C4—1011no—
201C4—1011no—
202C4—2021no—
203C4D4×D10111yescharacteristic
204C4C23×D10111yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—1012no—
209C2—4042no—
210C2—4041no—
211C2—2021no—
212C2C2×D4×D10111yescharacteristic
subgroupG/H
centerC2C2×D4×D101
commutatorC4×C101C24
FrattiniC4C23×D101
FittingAGL(1,ℤ/8)×C101C2
socleC2×C101C22×D4
hypercenterAGL(1,ℤ/8)D101
hypocenterC101C2×AGL(1,ℤ/8)
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D101C2semidirect
2. C2×D4×D101C2semidirect
3. #15692283C2semidirect
4. #15692282C2semidirect
5. #15692281C2semidirect
6. #15692280C2semidirect
7. #15692279C2semidirect
8. SD16×D101C2semidirect
9. D8×D101C2semidirect
10. M16×D101C2semidirect
11. AGL(1,ℤ/8)×C101C2semidirect
13. #13108075C22semidirect
15. #13108074C22semidirect
17. #13108073C22semidirect
18. Q8×D101C22semidirect
19. C2×D404C22semidirect
25. D4×D101C22semidirect
26. D4×D101C22semidirect
29. #13108063C22semidirect
30. #13108062C22semidirect
31. #13108061C22semidirect
32. D808C22semidirect
33. #13108059C22semidirect
34. #13108059C22semidirect
35. #13108058C22semidirect
36. #13108057C22semidirect
37. C8×D101C22semidirect
38. #41×C101C22semidirect
39. C2×D4×C101C22semidirect
40. SD16×C101C22semidirect
41. D8×C101C22semidirect
42. M16×C101C22semidirect
50. Q8×C101C23semidirect
54. D4×C101C23semidirect
67. D404C23semidirect
76. Dic202C23semidirect
77. C8×C101C23semidirect
78. #11717579C23semidirect
105. D101AGL(1,ℤ/8)direct (N × H)
106. C101C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D101direct (N × H)
125. #41C2×D101semidirect
135. C2×D4C2×D101semidirect
141. SD16C2×D101semidirect
145. D8C2×D101semidirect
148. M16C2×D101semidirect
159. Q8C22×D101semidirect
172. D4C22×D101semidirect
185. C8C22×D101semidirect