Finite Group Databasebeta

← AGL(1,ℤ/8)×D401 #38786898

Subgroups — AGL(1,ℤ/8)×D401 #38786898

Order 25664.

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×D401C211yesmaximal, characteristic, complemented
2C2×D4×D401C211yesmaximal, characteristic, complemented
3#27165765C211yesmaximal, characteristic, complemented
4#27165764C212yesmaximal, complemented
5#27165763C211yesmaximal, characteristic, complemented
6#27165762C211yesmaximal, characteristic, complemented
7#27165761C212yesmaximal, complemented
8SD16×D401C212yesmaximal, complemented
9D8×D401C212yesmaximal, complemented
10M16×D401C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C401C211yesmaximal, characteristic, complemented
12C23×D401—21no—
13#20264367C2211yescharacteristic, complemented
14#20264366—21no—
15#20264366C2211yescharacteristic, complemented
16#20264365—21no—
17#20264365C2211yescharacteristic, complemented
18Q8×D401C2211yescharacteristic, complemented
19C2×D1604C2211yescharacteristic, complemented
20C2×C22⋊D401—21no—
21D4×D401—21no—
22D4×D401—21no—
23D4×D401—21no—
24D4×D401C2212yes—
25D4×D401C2212yescomplemented
26D4×D401C2211yescharacteristic, complemented
27C2×C4×D401—21no—
28C2×C4×D401C2211yescharacteristic
29#20264355C2212yescomplemented
30#20264354C2212yescomplemented
31#20264353C2212yescomplemented
32D3208C2212yescomplemented
33#20264351C2212yescomplemented
34#20264351C2212yescomplemented
35#20264350C2211yescharacteristic, complemented
36#20264349C2212yescomplemented
37C8×D401C2212yescomplemented
38#41×C401C2211yescharacteristic, complemented
39C2×D4×C401C2211yescharacteristic, complemented
40SD16×C401C2212yescomplemented
41D8×C401C2212yescomplemented
42M16×C401C2211yescharacteristic, complemented
43C22×D401—21no—
44C22×D401—21no—
45C22×D401—22no—
46C22×D401—22no—
47C22×D401—44no—
48C22×D401D411yescharacteristic
49Dic802—21no—
50Dic802C2311yescharacteristic, complemented
51D1604—21no—
52D1604—21no—
53D1604C2312yes—
54D1604C2311yescharacteristic, complemented
55C22⋊D401—21no—
56C22⋊D401—21no—
57C22⋊D401—22no—
58C22⋊D401—22no—
59C22⋊D401—21no—
60C2×Dic401—21no—
61C2×Dic401D411yescharacteristic
62C4×D401—21no—
63C4×D401—21no—
64C4×D401—21no—
65C4×D401D411yescharacteristic
66C4×D401D411yescharacteristic
67C4×D401C2311yescharacteristic
68C4×D401C2311yescharacteristic
69#15691999C2312yescomplemented
70C23×C401—21no—
71Q8×C401C2311yescharacteristic, complemented
72D4×C401—21no—
73D4×C401—21no—
74D4×C401C2312yes—
75D4×C401C2311yescharacteristic, complemented
76C2×C4×C401—21no—
77C2×C4×C401C2311yescharacteristic
78C8×C401C2312yescomplemented
79C22×C401—21no—
80C22×C401—22no—
81C22×C401—42no—
82C22×C401C2×D411yescharacteristic
83C2×D401—22no—
84C2×D401—21no—
85C2×D401—22no—
86C2×D401—44no—
87C2×D401—42no—
88C2×D401—42no—
89C2×D401—44no—
90C2×D401C2×D411yescharacteristic
91C2×D401C2×D411yescharacteristic
92C4×C401—21no—
93C4×C401C2×D411yescharacteristic
94C4×C401C2411yescharacteristic
95Dic401—21no—
96Dic401C2×D411yescharacteristic
97Dic401C2×D411yescharacteristic
98C2×C401—21no—
99C2×C401—42no—
100C2×C401—41no—
101C2×C401C22×D411yescharacteristic
102D401—21no—
103D401—41no—
104D401—42no—
105D401AGL(1,ℤ/8)12yesdirect product factor
106C401C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—4011nomaximal, Sylow
108C2×#41—4011no—
109C22×D4—4011no—
110AGL(1,ℤ/8)—4011no—
111AGL(1,ℤ/8)—4011no—
112AGL(1,ℤ/8)—4012no—
113AGL(1,ℤ/8)—4012no—
114AGL(1,ℤ/8)—4011no—
115AGL(1,ℤ/8)D40111yescharacteristic, direct product factor
116C2×SD16—4012no—
117C2×D8—4012no—
118C2×M16—4011no—
119C24—8021no—
120#41—8021no—
121#41—8021no—
122#41—4011no—
123#41—4011no—
124#41—4011no—
125#41C2×D40111yescharacteristic, complemented
126C2×Q8—4011no—
127C2×D4—8021no—
128C2×D4—8021no—
129C2×D4—8021no—
130C2×D4—8021no—
131C2×D4—4012no—
132C2×D4—4012no—
133C2×D4—4011no—
134C2×D4—4011no—
135C2×D4C2×D40111yescharacteristic, complemented
136C22×C4—8021no—
137C22×C4—4011no—
138SD16—4012no—
139SD16—4012no—
140SD16—4012no—
141SD16C2×D40112yescomplemented
142D8—4012no—
143D8—4012no—
144D8—4012no—
145D8C2×D40112yescomplemented
146M16—4011no—
147M16—4012no—
148M16C2×D40111yescharacteristic, complemented
149C2×C8—4012no—
150C23—21no—
151C23—8021no—
152C23—8022no—
153C23—8022no—
154C23—8021no—
155C23—16044no—
156C23—4011no—
157Q8—8021no—
158Q8—4011no—
159Q8C22×D40111yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—8021no—
163D4—8021no—
164D4—8021no—
165D4—8022no—
166D4—8022no—
167D4—8021no—
168D4—8021no—
169D4—4011no—
170D4—4012no—
171D4C22×D40112yes—
172D4C22×D40111yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—8021no—
175C2×C4—8021no—
176C2×C4—8021no—
177C2×C4—8021no—
178C2×C4—4011no—
179C2×C4—4011no—
180C2×C4—4011no—
181C2×C4—4011no—
182C2×C4—4011no—
183C2×C4C22×D40111yescharacteristic
184C8—4012no—
185C8C22×D40112yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—8022no—
190C22—8021no—
191C22—8022no—
192C22—16042no—
193C22—16044no—
194C22—16044no—
195C22—16042no—
196C22—4011no—
197C22—4011no—
198C22D4×D40111yescharacteristic
199C4—21no—
200C4—8021no—
201C4—4011no—
202C4—4011no—
203C4D4×D40111yescharacteristic
204C4C23×D40111yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—8021no—
209C2—16042no—
210C2—16041no—
211C2—4012no—
212C2C2×D4×D40111yescharacteristic
subgroupG/H
centerC2C2×D4×D401
commutator, cosocleC4×C401C24
FrattiniC4C23×D401
FittingAGL(1,ℤ/8)×C401C2
socleC2×C401C22×D4
hypercenterAGL(1,ℤ/8)D401
hypocenterC401C2×AGL(1,ℤ/8)
LCSG ▷ C4×C401 ▷ C2×C401 ▷ C401
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D401C2semidirect
2. C2×D4×D401C2semidirect
3. #27165765C2semidirect
4. #27165764C2semidirect
5. #27165763C2semidirect
6. #27165762C2semidirect
7. #27165761C2semidirect
8. SD16×D401C2semidirect
9. D8×D401C2semidirect
10. M16×D401C2semidirect
11. AGL(1,ℤ/8)×C401C2semidirect
13. #20264367C22semidirect
15. #20264366C22semidirect
17. #20264365C22semidirect
18. Q8×D401C22semidirect
19. C2×D1604C22semidirect
25. D4×D401C22semidirect
26. D4×D401C22semidirect
29. #20264355C22semidirect
30. #20264354C22semidirect
31. #20264353C22semidirect
32. D3208C22semidirect
33. #20264351C22semidirect
34. #20264351C22semidirect
35. #20264350C22semidirect
36. #20264349C22semidirect
37. C8×D401C22semidirect
38. #41×C401C22semidirect
39. C2×D4×C401C22semidirect
40. SD16×C401C22semidirect
41. D8×C401C22semidirect
42. M16×C401C22semidirect
50. Dic802C23semidirect
54. D1604C23semidirect
69. #15691999C23semidirect
71. Q8×C401C23semidirect
75. D4×C401C23semidirect
78. C8×C401C23semidirect
105. D401AGL(1,ℤ/8)direct (N × H)
106. C401C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D401direct (N × H)
125. #41C2×D401semidirect
135. C2×D4C2×D401semidirect
141. SD16C2×D401semidirect
145. D8C2×D401semidirect
148. M16C2×D401semidirect
159. Q8C22×D401semidirect
172. D4C22×D401semidirect
185. C8C22×D401semidirect

Maximal subgroups

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

subgroupindex
#41×D4012
C2×D4×D4012
#271657652
#271657642
#271657632
#271657622
#271657612
SD16×D4012
D8×D4012
M16×D4012
AGL(1,ℤ/8)×C4012
C2×AGL(1,ℤ/8)401