Finite Group Databasebeta

← AGL(1,ℤ/8)×D109 #20295810

Subgroups — AGL(1,ℤ/8)×D109 #20295810

Order 6976.

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×D109C211yesmaximal, characteristic, complemented
2C2×D4×D109C211yesmaximal, characteristic, complemented
3#16812727C211yesmaximal, characteristic, complemented
4#16812726C212yesmaximal, complemented
5#16812725C211yesmaximal, characteristic, complemented
6#16812724C211yesmaximal, characteristic, complemented
7#16812723C212yesmaximal, complemented
8SD16×D109C212yesmaximal, complemented
9D8×D109C212yesmaximal, complemented
10M16×D109C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C109C211yesmaximal, characteristic, complemented
12C23×D109—21no—
13#13182030C2211yescharacteristic, complemented
14#13182029—21no—
15#13182029C2211yescharacteristic, complemented
16#13182028—21no—
17#13182028C2211yescharacteristic, complemented
18Q8×D109C2211yescharacteristic, complemented
19C2×D436C2211yescharacteristic, complemented
20C2×C22⋊D109—21no—
21D4×D109—21no—
22D4×D109—21no—
23D4×D109—21no—
24D4×D109C2212yes—
25D4×D109C2212yescomplemented
26D4×D109C2211yescharacteristic, complemented
27C2×C4×D109—21no—
28C2×C4×D109C2211yescharacteristic
29#13182018C2212yescomplemented
30#13182017C2212yescomplemented
31#13182016C2212yescomplemented
32D872C2212yescomplemented
33#13182014C2212yescomplemented
34#13182014C2212yescomplemented
35#13182013C2211yescharacteristic, complemented
36#13182012C2212yescomplemented
37C8×D109C2212yescomplemented
38#41×C109C2211yescharacteristic, complemented
39C2×D4×C109C2211yescharacteristic, complemented
40SD16×C109C2212yescomplemented
41D8×C109C2212yescomplemented
42M16×C109C2211yescharacteristic, complemented
43C23×C109—21no—
44C22×D109—21no—
45C22×D109—21no—
46C22×D109—22no—
47C22×D109—22no—
48C22×D109—44no—
49C22×D109D411yescharacteristic
50Q8×C109C2311yescharacteristic, complemented
51D4×C109—21no—
52D4×C109—21no—
53D4×C109C2312yes—
54D4×C109C2311yescharacteristic, complemented
55C2×C4×C109—21no—
56C2×C4×C109C2311yescharacteristic
57C22⋊D109—21no—
58C22⋊D109—21no—
59C22⋊D109—22no—
60C22⋊D109—22no—
61C22⋊D109—21no—
62C2×Dic109—21no—
63C2×Dic109D411yescharacteristic
64D436—21no—
65D436—21no—
66D436C2312yes—
67D436C2311yescharacteristic, complemented
68C4×D109—21no—
69C4×D109—21no—
70C4×D109—21no—
71C4×D109D411yescharacteristic
72C4×D109D411yescharacteristic
73C4×D109C2311yescharacteristic
74C4×D109C2311yescharacteristic
75Dic218—21no—
76Dic218C2311yescharacteristic, complemented
77C8×C109C2312yescomplemented
78#11724784C2312yescomplemented
79C22×C109—21no—
80C22×C109—22no—
81C22×C109—42no—
82C22×C109C2×D411yescharacteristic
83C2×D109—22no—
84C2×D109—21no—
85C2×D109—22no—
86C2×D109—44no—
87C2×D109—42no—
88C2×D109—42no—
89C2×D109—44no—
90C2×D109C2×D411yescharacteristic
91C2×D109C2×D411yescharacteristic
92C4×C109—21no—
93C4×C109C2×D411yescharacteristic
94C4×C109C2411yescharacteristic
95Dic109—21no—
96Dic109C2×D411yescharacteristic
97Dic109C2×D411yescharacteristic
98C2×C109—21no—
99C2×C109—42no—
100C2×C109—41no—
101C2×C109C22×D411yescharacteristic
102D109—21no—
103D109—41no—
104D109—42no—
105D109AGL(1,ℤ/8)12yesdirect product factor
106C109C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—1091nomaximal, Sylow
108C2×#41—1091no—
109C22×D4—1091no—
110AGL(1,ℤ/8)—1091no—
111AGL(1,ℤ/8)—1091no—
112AGL(1,ℤ/8)—1092no—
113AGL(1,ℤ/8)—1092no—
114AGL(1,ℤ/8)—1091no—
115AGL(1,ℤ/8)D10911yescharacteristic, direct product factor
116C2×SD16—1092no—
117C2×D8—1092no—
118C2×M16—1091no—
119C24—2181no—
120#41—1091no—
121#41—1091no—
122#41—1091no—
123#41—2181no—
124#41—2181no—
125#41C2×D10911yescharacteristic, complemented
126C2×Q8—1091no—
127C2×D4—1092no—
128C2×D4—1092no—
129C2×D4—1091no—
130C2×D4—1091no—
131C2×D4—2181no—
132C2×D4—2181no—
133C2×D4—2181no—
134C2×D4—2181no—
135C2×D4C2×D10911yescharacteristic, complemented
136C22×C4—1091no—
137C22×C4—2181no—
138SD16—1092no—
139SD16—1092no—
140SD16—1092no—
141SD16C2×D10912yescomplemented
142D8—1092no—
143D8—1092no—
144D8—1092no—
145D8C2×D10912yescomplemented
146M16—1091no—
147M16—1092no—
148M16C2×D10911yescharacteristic, complemented
149C2×C8—1092no—
150C23—21no—
151C23—1091no—
152C23—4364no—
153C23—2181no—
154C23—2182no—
155C23—2182no—
156C23—2181no—
157Q8—1091no—
158Q8—2181no—
159Q8C22×D10911yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—1091no—
163D4—1092no—
164D4—2181no—
165D4—2182no—
166D4—2182no—
167D4—2181no—
168D4—2181no—
169D4—2181no—
170D4—2181no—
171D4C22×D10912yes—
172D4C22×D10911yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—1091no—
175C2×C4—1091no—
176C2×C4—1091no—
177C2×C4—1091no—
178C2×C4—1091no—
179C2×C4—2181no—
180C2×C4—2181no—
181C2×C4—2181no—
182C2×C4—2181no—
183C2×C4C22×D10911yescharacteristic
184C8—1092no—
185C8C22×D10912yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—1091no—
190C22—1091no—
191C22—4362no—
192C22—4364no—
193C22—4362no—
194C22—4364no—
195C22—2182no—
196C22—2181no—
197C22—2182no—
198C22D4×D10911yescharacteristic
199C4—21no—
200C4—1091no—
201C4—1091no—
202C4—2181no—
203C4D4×D10911yescharacteristic
204C4C23×D10911yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—1092no—
209C2—4362no—
210C2—4361no—
211C2—2181no—
212C2C2×D4×D10911yescharacteristic
subgroupG/H
centerC2C2×D4×D109
commutatorC4×C109C24
FrattiniC4C23×D109
FittingAGL(1,ℤ/8)×C109C2
socleC2×C109C22×D4
hypercenterAGL(1,ℤ/8)D109
hypocenterC109C2×AGL(1,ℤ/8)
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D109C2semidirect
2. C2×D4×D109C2semidirect
3. #16812727C2semidirect
4. #16812726C2semidirect
5. #16812725C2semidirect
6. #16812724C2semidirect
7. #16812723C2semidirect
8. SD16×D109C2semidirect
9. D8×D109C2semidirect
10. M16×D109C2semidirect
11. AGL(1,ℤ/8)×C109C2semidirect
13. #13182030C22semidirect
15. #13182029C22semidirect
17. #13182028C22semidirect
18. Q8×D109C22semidirect
19. C2×D436C22semidirect
25. D4×D109C22semidirect
26. D4×D109C22semidirect
29. #13182018C22semidirect
30. #13182017C22semidirect
31. #13182016C22semidirect
32. D872C22semidirect
33. #13182014C22semidirect
34. #13182014C22semidirect
35. #13182013C22semidirect
36. #13182012C22semidirect
37. C8×D109C22semidirect
38. #41×C109C22semidirect
39. C2×D4×C109C22semidirect
40. SD16×C109C22semidirect
41. D8×C109C22semidirect
42. M16×C109C22semidirect
50. Q8×C109C23semidirect
54. D4×C109C23semidirect
67. D436C23semidirect
76. Dic218C23semidirect
77. C8×C109C23semidirect
78. #11724784C23semidirect
105. D109AGL(1,ℤ/8)direct (N × H)
106. C109C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D109direct (N × H)
125. #41C2×D109semidirect
135. C2×D4C2×D109semidirect
141. SD16C2×D109semidirect
145. D8C2×D109semidirect
148. M16C2×D109semidirect
159. Q8C22×D109semidirect
172. D4C22×D109semidirect
185. C8C22×D109semidirect