Finite Group Databasebeta

← AGL(1,ℤ/8)×D443 #43248501

Subgroups — AGL(1,ℤ/8)×D443 #43248501

Order 28352.

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×D443C211yesmaximal, characteristic, complemented
2C2×D4×D443C211yesmaximal, characteristic, complemented
3#28381914C211yesmaximal, characteristic, complemented
4#28381913C212yesmaximal, complemented
5#28381912C211yesmaximal, characteristic, complemented
6#28381911C211yesmaximal, characteristic, complemented
7#28381910C212yesmaximal, complemented
8SD16×D443C212yesmaximal, complemented
9D8×D443C212yesmaximal, complemented
10M16×D443C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C443C211yesmaximal, characteristic, complemented
12C23×D443—21no—
13#20296788C2211yescharacteristic, complemented
14#20296787—21no—
15#20296787C2211yescharacteristic, complemented
16#20296786—21no—
17#20296786C2211yescharacteristic, complemented
18Q8×D443C2211yescharacteristic, complemented
19C2×D1772C2211yescharacteristic, complemented
20C2×C22⋊D443—21no—
21D4×D443—21no—
22D4×D443—21no—
23D4×D443—21no—
24D4×D443C2212yes—
25D4×D443C2212yescomplemented
26D4×D443C2211yescharacteristic, complemented
27C2×C4×D443—21no—
28C2×C4×D443C2211yescharacteristic
29#20296776C2212yescomplemented
30#20296775C2212yescomplemented
31#20296774C2212yescomplemented
32D3544C2212yescomplemented
33#20296772C2212yescomplemented
34#20296772C2212yescomplemented
35#20296771C2211yescharacteristic, complemented
36#20296770C2212yescomplemented
37C8×D443C2212yescomplemented
38#41×C443C2211yescharacteristic, complemented
39C2×D4×C443C2211yescharacteristic, complemented
40SD16×C443C2212yescomplemented
41D8×C443C2212yescomplemented
42M16×C443C2211yescharacteristic, complemented
43C22×D443—21no—
44C22×D443—21no—
45C22×D443—22no—
46C22×D443—22no—
47C22×D443—44no—
48C22×D443D411yescharacteristic
49Dic886—21no—
50Dic886C2311yescharacteristic, complemented
51D1772—21no—
52D1772—21no—
53D1772C2312yes—
54D1772C2311yescharacteristic, complemented
55C22⋊D443—21no—
56C22⋊D443—21no—
57C22⋊D443—22no—
58C22⋊D443—22no—
59C22⋊D443—21no—
60C2×Dic443—21no—
61C2×Dic443D411yescharacteristic
62C4×D443—21no—
63C4×D443—21no—
64C4×D443—21no—
65C4×D443D411yescharacteristic
66C4×D443D411yescharacteristic
67C4×D443C2311yescharacteristic
68C4×D443C2311yescharacteristic
69C443⋊C8C2312yescomplemented
70C23×C443—21no—
71Q8×C443C2311yescharacteristic, complemented
72D4×C443—21no—
73D4×C443—21no—
74D4×C443C2312yes—
75D4×C443C2311yescharacteristic, complemented
76C2×C4×C443—21no—
77C2×C4×C443C2311yescharacteristic
78C8×C443C2312yescomplemented
79C22×C443—21no—
80C22×C443—22no—
81C22×C443—42no—
82C22×C443C2×D411yescharacteristic
83C2×D443—22no—
84C2×D443—21no—
85C2×D443—22no—
86C2×D443—44no—
87C2×D443—42no—
88C2×D443—42no—
89C2×D443—44no—
90C2×D443C2×D411yescharacteristic
91C2×D443C2×D411yescharacteristic
92C4×C443—21no—
93C4×C443C2×D411yescharacteristic
94C4×C443C2411yescharacteristic
95Dic443—21no—
96Dic443C2×D411yescharacteristic
97Dic443C2×D411yescharacteristic
98C2×C443—21no—
99C2×C443—42no—
100C2×C443—41no—
101C2×C443C22×D411yescharacteristic
102D443—21no—
103D443—41no—
104D443—42no—
105D443AGL(1,ℤ/8)12yesdirect product factor
106C443C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—4431nomaximal, Sylow
108C2×#41—4431no—
109C22×D4—4431no—
110AGL(1,ℤ/8)—4431no—
111AGL(1,ℤ/8)—4431no—
112AGL(1,ℤ/8)—4432no—
113AGL(1,ℤ/8)—4432no—
114AGL(1,ℤ/8)—4431no—
115AGL(1,ℤ/8)D44311yescharacteristic, direct product factor
116C2×SD16—4432no—
117C2×D8—4432no—
118C2×M16—4431no—
119C24—8861no—
120#41—8861no—
121#41—8861no—
122#41—4431no—
123#41—4431no—
124#41—4431no—
125#41C2×D44311yescharacteristic, complemented
126C2×Q8—4431no—
127C2×D4—8861no—
128C2×D4—8861no—
129C2×D4—8861no—
130C2×D4—8861no—
131C2×D4—4432no—
132C2×D4—4432no—
133C2×D4—4431no—
134C2×D4—4431no—
135C2×D4C2×D44311yescharacteristic, complemented
136C22×C4—8861no—
137C22×C4—4431no—
138SD16—4432no—
139SD16—4432no—
140SD16—4432no—
141SD16C2×D44312yescomplemented
142D8—4432no—
143D8—4432no—
144D8—4432no—
145D8C2×D44312yescomplemented
146M16—4431no—
147M16—4432no—
148M16C2×D44311yescharacteristic, complemented
149C2×C8—4432no—
150C23—21no—
151C23—8861no—
152C23—8862no—
153C23—8862no—
154C23—8861no—
155C23—4431no—
156C23—17724no—
157Q8—8861no—
158Q8—4431no—
159Q8C22×D44311yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—8861no—
163D4—8861no—
164D4—8861no—
165D4—8862no—
166D4—8862no—
167D4—8861no—
168D4—8861no—
169D4—4431no—
170D4—4432no—
171D4C22×D44312yes—
172D4C22×D44311yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—8861no—
175C2×C4—8861no—
176C2×C4—8861no—
177C2×C4—8861no—
178C2×C4—4431no—
179C2×C4—4431no—
180C2×C4—4431no—
181C2×C4—4431no—
182C2×C4—4431no—
183C2×C4C22×D44311yescharacteristic
184C8—4432no—
185C8C22×D44312yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—8862no—
190C22—8861no—
191C22—8862no—
192C22—4431no—
193C22—4431no—
194C22—17722no—
195C22—17724no—
196C22—17724no—
197C22—17722no—
198C22D4×D44311yescharacteristic
199C4—21no—
200C4—8861no—
201C4—4431no—
202C4—4431no—
203C4D4×D44311yescharacteristic
204C4C23×D44311yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—8861no—
209C2—4432no—
210C2—17722no—
211C2—17721no—
212C2C2×D4×D44311yescharacteristic
subgroupG/H
centerC2C2×D4×D443
commutator, cosocleC4×C443C24
FrattiniC4C23×D443
FittingAGL(1,ℤ/8)×C443C2
socleC2×C443C22×D4
hypercenterAGL(1,ℤ/8)D443
hypocenterC443C2×AGL(1,ℤ/8)
LCSG ▷ C4×C443 ▷ C2×C443 ▷ C443
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D443C2semidirect
2. C2×D4×D443C2semidirect
3. #28381914C2semidirect
4. #28381913C2semidirect
5. #28381912C2semidirect
6. #28381911C2semidirect
7. #28381910C2semidirect
8. SD16×D443C2semidirect
9. D8×D443C2semidirect
10. M16×D443C2semidirect
11. AGL(1,ℤ/8)×C443C2semidirect
13. #20296788C22semidirect
15. #20296787C22semidirect
17. #20296786C22semidirect
18. Q8×D443C22semidirect
19. C2×D1772C22semidirect
25. D4×D443C22semidirect
26. D4×D443C22semidirect
29. #20296776C22semidirect
30. #20296775C22semidirect
31. #20296774C22semidirect
32. D3544C22semidirect
33. #20296772C22semidirect
34. #20296772C22semidirect
35. #20296771C22semidirect
36. #20296770C22semidirect
37. C8×D443C22semidirect
38. #41×C443C22semidirect
39. C2×D4×C443C22semidirect
40. SD16×C443C22semidirect
41. D8×C443C22semidirect
42. M16×C443C22semidirect
50. Dic886C23semidirect
54. D1772C23semidirect
69. C443⋊C8C23semidirect
71. Q8×C443C23semidirect
75. D4×C443C23semidirect
78. C8×C443C23semidirect
105. D443AGL(1,ℤ/8)direct (N × H)
106. C443C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D443direct (N × H)
125. #41C2×D443semidirect
135. C2×D4C2×D443semidirect
141. SD16C2×D443semidirect
145. D8C2×D443semidirect
148. M16C2×D443semidirect
159. Q8C22×D443semidirect
172. D4C22×D443semidirect
185. C8C22×D443semidirect

Maximal subgroups

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

subgroupindex
#41×D4432
C2×D4×D4432
#283819142
#283819132
#283819122
#283819112
#283819102
SD16×D4432
D8×D4432
M16×D4432
AGL(1,ℤ/8)×C4432
C2×AGL(1,ℤ/8)443