Finite Group Databasebeta

← AGL(1,ℤ/8)×D571 #49143050

Subgroups — AGL(1,ℤ/8)×D571 #49143050

Order 36544.

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×D571C211yesmaximal, characteristic, complemented
2C2×D4×D571C211yesmaximal, characteristic, complemented
3#32912722C211yesmaximal, characteristic, complemented
4#32912721C212yesmaximal, complemented
5#32912720C211yesmaximal, characteristic, complemented
6#32912719C211yesmaximal, characteristic, complemented
7#32912718C212yesmaximal, complemented
8SD16×D571C212yesmaximal, complemented
9D8×D571C212yesmaximal, complemented
10M16×D571C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C571C211yesmaximal, characteristic, complemented
12C23×D571—21no—
13#22603734C2211yescharacteristic, complemented
14#22603733—21no—
15#22603733C2211yescharacteristic, complemented
16#22603732—21no—
17#22603732C2211yescharacteristic, complemented
18Q8×D571C2211yescharacteristic, complemented
19C2×D2284C2211yescharacteristic, complemented
20C2×C22⋊D571—21no—
21D4×D571—21no—
22D4×D571—21no—
23D4×D571—21no—
24D4×D571C2212yes—
25D4×D571C2212yescomplemented
26D4×D571C2211yescharacteristic, complemented
27C2×C4×D571—21no—
28C2×C4×D571C2211yescharacteristic
29#22603722C2212yescomplemented
30#22603721C2212yescomplemented
31#22603720C2212yescomplemented
32D4568C2212yescomplemented
33#22603718C2212yescomplemented
34#22603718C2212yescomplemented
35#22603717C2211yescharacteristic, complemented
36#22603716C2212yescomplemented
37C8×D571C2212yescomplemented
38#41×C571C2211yescharacteristic, complemented
39C2×D4×C571C2211yescharacteristic, complemented
40SD16×C571C2212yescomplemented
41D8×C571C2212yescomplemented
42M16×C571C2211yescharacteristic, complemented
43C22×D571—21no—
44C22×D571—21no—
45C22×D571—22no—
46C22×D571—22no—
47C22×D571—44no—
48C22×D571D411yescharacteristic
49Dic1142—21no—
50Dic1142C2311yescharacteristic, complemented
51D2284—21no—
52D2284—21no—
53D2284C2312yes—
54D2284C2311yescharacteristic, complemented
55C22⋊D571—21no—
56C22⋊D571—21no—
57C22⋊D571—22no—
58C22⋊D571—22no—
59C22⋊D571—21no—
60C2×Dic571—21no—
61C2×Dic571D411yescharacteristic
62C4×D571—21no—
63C4×D571—21no—
64C4×D571—21no—
65C4×D571D411yescharacteristic
66C4×D571D411yescharacteristic
67C4×D571C2311yescharacteristic
68C4×D571C2311yescharacteristic
69C571⋊C8C2312yescomplemented
70C23×C571—21no—
71Q8×C571C2311yescharacteristic, complemented
72D4×C571—21no—
73D4×C571—21no—
74D4×C571C2312yes—
75D4×C571C2311yescharacteristic, complemented
76C2×C4×C571—21no—
77C2×C4×C571C2311yescharacteristic
78C8×C571C2312yescomplemented
79C22×C571—21no—
80C22×C571—22no—
81C22×C571—42no—
82C22×C571C2×D411yescharacteristic
83C2×D571—22no—
84C2×D571—21no—
85C2×D571—22no—
86C2×D571—44no—
87C2×D571—42no—
88C2×D571—42no—
89C2×D571—44no—
90C2×D571C2×D411yescharacteristic
91C2×D571C2×D411yescharacteristic
92C4×C571—21no—
93C4×C571C2×D411yescharacteristic
94C4×C571C2411yescharacteristic
95Dic571—21no—
96Dic571C2×D411yescharacteristic
97Dic571C2×D411yescharacteristic
98C2×C571—21no—
99C2×C571—42no—
100C2×C571—41no—
101C2×C571C22×D411yescharacteristic
102D571—21no—
103D571—41no—
104D571—42no—
105D571AGL(1,ℤ/8)12yesdirect product factor
106C571C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—5711nomaximal, Sylow
108C2×#41—5711no—
109C22×D4—5711no—
110AGL(1,ℤ/8)—5711no—
111AGL(1,ℤ/8)—5711no—
112AGL(1,ℤ/8)—5712no—
113AGL(1,ℤ/8)—5712no—
114AGL(1,ℤ/8)—5711no—
115AGL(1,ℤ/8)D57111yescharacteristic, direct product factor
116C2×SD16—5712no—
117C2×D8—5712no—
118C2×M16—5711no—
119C24—11421no—
120#41—5711no—
121#41—5711no—
122#41—5711no—
123#41—11421no—
124#41—11421no—
125#41C2×D57111yescharacteristic, complemented
126C2×Q8—5711no—
127C2×D4—5712no—
128C2×D4—5712no—
129C2×D4—5711no—
130C2×D4—5711no—
131C2×D4—11421no—
132C2×D4—11421no—
133C2×D4—11421no—
134C2×D4—11421no—
135C2×D4C2×D57111yescharacteristic, complemented
136C22×C4—5711no—
137C22×C4—11421no—
138SD16—5712no—
139SD16—5712no—
140SD16—5712no—
141SD16C2×D57112yescomplemented
142D8—5712no—
143D8—5712no—
144D8—5712no—
145D8C2×D57112yescomplemented
146M16—5711no—
147M16—5712no—
148M16C2×D57111yescharacteristic, complemented
149C2×C8—5712no—
150C23—21no—
151C23—5711no—
152C23—11421no—
153C23—11422no—
154C23—11422no—
155C23—11421no—
156C23—22844no—
157Q8—5711no—
158Q8—11421no—
159Q8C22×D57111yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—5711no—
163D4—5712no—
164D4—11421no—
165D4—11422no—
166D4—11422no—
167D4—11421no—
168D4—11421no—
169D4—11421no—
170D4—11421no—
171D4C22×D57112yes—
172D4C22×D57111yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—5711no—
175C2×C4—5711no—
176C2×C4—5711no—
177C2×C4—5711no—
178C2×C4—5711no—
179C2×C4—11421no—
180C2×C4—11421no—
181C2×C4—11421no—
182C2×C4—11421no—
183C2×C4C22×D57111yescharacteristic
184C8—5712no—
185C8C22×D57112yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—5711no—
190C22—5711no—
191C22—11422no—
192C22—11421no—
193C22—11422no—
194C22—22842no—
195C22—22844no—
196C22—22842no—
197C22—22844no—
198C22D4×D57111yescharacteristic
199C4—21no—
200C4—5711no—
201C4—5711no—
202C4—11421no—
203C4D4×D57111yescharacteristic
204C4C23×D57111yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—5712no—
209C2—11421no—
210C2—22842no—
211C2—22841no—
212C2C2×D4×D57111yescharacteristic
subgroupG/H
centerC2C2×D4×D571
commutator, cosocleC4×C571C24
FrattiniC4C23×D571
FittingAGL(1,ℤ/8)×C571C2
socleC2×C571C22×D4
hypercenterAGL(1,ℤ/8)D571
hypocenterC571C2×AGL(1,ℤ/8)
LCSG ▷ C4×C571 ▷ C2×C571 ▷ C571
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D571C2semidirect
2. C2×D4×D571C2semidirect
3. #32912722C2semidirect
4. #32912721C2semidirect
5. #32912720C2semidirect
6. #32912719C2semidirect
7. #32912718C2semidirect
8. SD16×D571C2semidirect
9. D8×D571C2semidirect
10. M16×D571C2semidirect
11. AGL(1,ℤ/8)×C571C2semidirect
13. #22603734C22semidirect
15. #22603733C22semidirect
17. #22603732C22semidirect
18. Q8×D571C22semidirect
19. C2×D2284C22semidirect
25. D4×D571C22semidirect
26. D4×D571C22semidirect
29. #22603722C22semidirect
30. #22603721C22semidirect
31. #22603720C22semidirect
32. D4568C22semidirect
33. #22603718C22semidirect
34. #22603718C22semidirect
35. #22603717C22semidirect
36. #22603716C22semidirect
37. C8×D571C22semidirect
38. #41×C571C22semidirect
39. C2×D4×C571C22semidirect
40. SD16×C571C22semidirect
41. D8×C571C22semidirect
42. M16×C571C22semidirect
50. Dic1142C23semidirect
54. D2284C23semidirect
69. C571⋊C8C23semidirect
71. Q8×C571C23semidirect
75. D4×C571C23semidirect
78. C8×C571C23semidirect
105. D571AGL(1,ℤ/8)direct (N × H)
106. C571C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D571direct (N × H)
125. #41C2×D571semidirect
135. C2×D4C2×D571semidirect
141. SD16C2×D571semidirect
145. D8C2×D571semidirect
148. M16C2×D571semidirect
159. Q8C22×D571semidirect
172. D4C22×D571semidirect
185. C8C22×D571semidirect

Maximal subgroups

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

subgroupindex
#41×D5712
C2×D4×D5712
#329127222
#329127212
#329127202
#329127192
#329127182
SD16×D5712
D8×D5712
M16×D5712
AGL(1,ℤ/8)×C5712
C2×AGL(1,ℤ/8)571