Finite Group Databasebeta

← AGL(1,ℤ/8)×D107 #20293411

Subgroups — AGL(1,ℤ/8)×D107 #20293411

Order 6848.

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×D107C211yesmaximal, characteristic, complemented
2C2×D4×D107C211yesmaximal, characteristic, complemented
3#16812137C211yesmaximal, characteristic, complemented
4#16812136C212yesmaximal, complemented
5#16812135C211yesmaximal, characteristic, complemented
6#16812134C211yesmaximal, characteristic, complemented
7#16812133C212yesmaximal, complemented
8SD16×D107C212yesmaximal, complemented
9D8×D107C212yesmaximal, complemented
10M16×D107C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C107C211yesmaximal, characteristic, complemented
12C23×D107—21no—
13#13133819C2211yescharacteristic, complemented
14#13133818—21no—
15#13133818C2211yescharacteristic, complemented
16#13133817—21no—
17#13133817C2211yescharacteristic, complemented
18Q8×D107C2211yescharacteristic, complemented
19C2×D428C2211yescharacteristic, complemented
20C2×C22⋊D107—21no—
21D4×D107—21no—
22D4×D107—21no—
23D4×D107—21no—
24D4×D107C2212yes—
25D4×D107C2212yescomplemented
26D4×D107C2211yescharacteristic, complemented
27C2×C4×D107—21no—
28C2×C4×D107C2211yescharacteristic
29#13133807C2212yescomplemented
30#13133806C2212yescomplemented
31#13133805C2212yescomplemented
32D856C2212yescomplemented
33#13133803C2212yescomplemented
34#13133803C2212yescomplemented
35#13133802C2211yescharacteristic, complemented
36#13133801C2212yescomplemented
37C8×D107C2212yescomplemented
38#41×C107C2211yescharacteristic, complemented
39C2×D4×C107C2211yescharacteristic, complemented
40SD16×C107C2212yescomplemented
41D8×C107C2212yescomplemented
42M16×C107C2211yescharacteristic, complemented
43C23×C107—21no—
44C22×D107—21no—
45C22×D107—21no—
46C22×D107—22no—
47C22×D107—22no—
48C22×D107—44no—
49C22×D107D411yescharacteristic
50Q8×C107C2311yescharacteristic, complemented
51D4×C107—21no—
52D4×C107—21no—
53D4×C107C2312yes—
54D4×C107C2311yescharacteristic, complemented
55C2×C4×C107—21no—
56C2×C4×C107C2311yescharacteristic
57C22⋊D107—21no—
58C22⋊D107—21no—
59C22⋊D107—22no—
60C22⋊D107—22no—
61C22⋊D107—21no—
62C2×Dic107—21no—
63C2×Dic107D411yescharacteristic
64D428—21no—
65D428—21no—
66D428C2312yes—
67D428C2311yescharacteristic, complemented
68C4×D107—21no—
69C4×D107—21no—
70C4×D107—21no—
71C4×D107D411yescharacteristic
72C4×D107D411yescharacteristic
73C4×D107C2311yescharacteristic
74C4×D107C2311yescharacteristic
75Dic214—21no—
76Dic214C2311yescharacteristic, complemented
77C8×C107C2312yescomplemented
78C107⋊C8C2312yescomplemented
79C22×C107—21no—
80C22×C107—22no—
81C22×C107—42no—
82C22×C107C2×D411yescharacteristic
83C2×D107—22no—
84C2×D107—21no—
85C2×D107—22no—
86C2×D107—44no—
87C2×D107—42no—
88C2×D107—42no—
89C2×D107—44no—
90C2×D107C2×D411yescharacteristic
91C2×D107C2×D411yescharacteristic
92C4×C107—21no—
93C4×C107C2×D411yescharacteristic
94C4×C107C2411yescharacteristic
95Dic107—21no—
96Dic107C2×D411yescharacteristic
97Dic107C2×D411yescharacteristic
98C2×C107—21no—
99C2×C107—42no—
100C2×C107—41no—
101C2×C107C22×D411yescharacteristic
102D107—21no—
103D107—41no—
104D107—42no—
105D107AGL(1,ℤ/8)12yesdirect product factor
106C107C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—1071nomaximal, Sylow
108C2×#41—1071no—
109C22×D4—1071no—
110AGL(1,ℤ/8)—1071no—
111AGL(1,ℤ/8)—1071no—
112AGL(1,ℤ/8)—1072no—
113AGL(1,ℤ/8)—1072no—
114AGL(1,ℤ/8)—1071no—
115AGL(1,ℤ/8)D10711yescharacteristic, direct product factor
116C2×SD16—1072no—
117C2×D8—1072no—
118C2×M16—1071no—
119C24—2141no—
120#41—1071no—
121#41—1071no—
122#41—1071no—
123#41—2141no—
124#41—2141no—
125#41C2×D10711yescharacteristic, complemented
126C2×Q8—1071no—
127C2×D4—1072no—
128C2×D4—1072no—
129C2×D4—1071no—
130C2×D4—1071no—
131C2×D4—2141no—
132C2×D4—2141no—
133C2×D4—2141no—
134C2×D4—2141no—
135C2×D4C2×D10711yescharacteristic, complemented
136C22×C4—1071no—
137C22×C4—2141no—
138SD16—1072no—
139SD16—1072no—
140SD16—1072no—
141SD16C2×D10712yescomplemented
142D8—1072no—
143D8—1072no—
144D8—1072no—
145D8C2×D10712yescomplemented
146M16—1071no—
147M16—1072no—
148M16C2×D10711yescharacteristic, complemented
149C2×C8—1072no—
150C23—21no—
151C23—1071no—
152C23—4284no—
153C23—2141no—
154C23—2142no—
155C23—2142no—
156C23—2141no—
157Q8—1071no—
158Q8—2141no—
159Q8C22×D10711yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—1071no—
163D4—1072no—
164D4—2141no—
165D4—2142no—
166D4—2142no—
167D4—2141no—
168D4—2141no—
169D4—2141no—
170D4—2141no—
171D4C22×D10712yes—
172D4C22×D10711yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—1071no—
175C2×C4—1071no—
176C2×C4—1071no—
177C2×C4—1071no—
178C2×C4—1071no—
179C2×C4—2141no—
180C2×C4—2141no—
181C2×C4—2141no—
182C2×C4—2141no—
183C2×C4C22×D10711yescharacteristic
184C8—1072no—
185C8C22×D10712yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—1071no—
190C22—1071no—
191C22—4282no—
192C22—4284no—
193C22—4282no—
194C22—4284no—
195C22—2142no—
196C22—2141no—
197C22—2142no—
198C22D4×D10711yescharacteristic
199C4—21no—
200C4—1071no—
201C4—1071no—
202C4—2141no—
203C4D4×D10711yescharacteristic
204C4C23×D10711yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—1072no—
209C2—4282no—
210C2—4281no—
211C2—2141no—
212C2C2×D4×D10711yescharacteristic
subgroupG/H
centerC2C2×D4×D107
commutatorC4×C107C24
FrattiniC4C23×D107
FittingAGL(1,ℤ/8)×C107C2
socleC2×C107C22×D4
hypercenterAGL(1,ℤ/8)D107
hypocenterC107C2×AGL(1,ℤ/8)
LCSG ▷ C4×C107 ▷ C2×C107 ▷ C107
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D107C2semidirect
2. C2×D4×D107C2semidirect
3. #16812137C2semidirect
4. #16812136C2semidirect
5. #16812135C2semidirect
6. #16812134C2semidirect
7. #16812133C2semidirect
8. SD16×D107C2semidirect
9. D8×D107C2semidirect
10. M16×D107C2semidirect
11. AGL(1,ℤ/8)×C107C2semidirect
13. #13133819C22semidirect
15. #13133818C22semidirect
17. #13133817C22semidirect
18. Q8×D107C22semidirect
19. C2×D428C22semidirect
25. D4×D107C22semidirect
26. D4×D107C22semidirect
29. #13133807C22semidirect
30. #13133806C22semidirect
31. #13133805C22semidirect
32. D856C22semidirect
33. #13133803C22semidirect
34. #13133803C22semidirect
35. #13133802C22semidirect
36. #13133801C22semidirect
37. C8×D107C22semidirect
38. #41×C107C22semidirect
39. C2×D4×C107C22semidirect
40. SD16×C107C22semidirect
41. D8×C107C22semidirect
42. M16×C107C22semidirect
50. Q8×C107C23semidirect
54. D4×C107C23semidirect
67. D428C23semidirect
76. Dic214C23semidirect
77. C8×C107C23semidirect
78. C107⋊C8C23semidirect
105. D107AGL(1,ℤ/8)direct (N × H)
106. C107C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D107direct (N × H)
125. #41C2×D107semidirect
135. C2×D4C2×D107semidirect
141. SD16C2×D107semidirect
145. D8C2×D107semidirect
148. M16C2×D107semidirect
159. Q8C22×D107semidirect
172. D4C22×D107semidirect
185. C8C22×D107semidirect