Finite Group Databasebeta

← AGL(1,ℤ/8)×D383 #37589135

Subgroups — AGL(1,ℤ/8)×D383 #37589135

Order 24512.

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×D383C211yesmaximal, characteristic, complemented
2C2×D4×D383C211yesmaximal, characteristic, complemented
3#27133869C211yesmaximal, characteristic, complemented
4#27133868C212yesmaximal, complemented
5#27133867C211yesmaximal, characteristic, complemented
6#27133866C211yesmaximal, characteristic, complemented
7#27133865C212yesmaximal, complemented
8SD16×D383C212yesmaximal, complemented
9D8×D383C212yesmaximal, complemented
10M16×D383C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C383C211yesmaximal, characteristic, complemented
12C23×D383—21no—
13#20259458C2211yescharacteristic, complemented
14#20259457—21no—
15#20259457C2211yescharacteristic, complemented
16#20259456—21no—
17#20259456C2211yescharacteristic, complemented
18Q8×D383C2211yescharacteristic, complemented
19C2×D1532C2211yescharacteristic, complemented
20C2×C22⋊D383—21no—
21D4×D383—21no—
22D4×D383—21no—
23D4×D383—21no—
24D4×D383C2212yes—
25D4×D383C2212yescomplemented
26D4×D383C2211yescharacteristic, complemented
27C2×C4×D383—21no—
28C2×C4×D383C2211yescharacteristic
29#20259446C2212yescomplemented
30#20259445C2212yescomplemented
31#20259444C2212yescomplemented
32D3064C2212yescomplemented
33#20259442C2212yescomplemented
34#20259442C2212yescomplemented
35#20259441C2211yescharacteristic, complemented
36#20259440C2212yescomplemented
37C8×D383C2212yescomplemented
38#41×C383C2211yescharacteristic, complemented
39C2×D4×C383C2211yescharacteristic, complemented
40SD16×C383C2212yescomplemented
41D8×C383C2212yescomplemented
42M16×C383C2211yescharacteristic, complemented
43C22×D383—21no—
44C22×D383—21no—
45C22×D383—22no—
46C22×D383—22no—
47C22×D383—44no—
48C22×D383D411yescharacteristic
49Dic766—21no—
50Dic766C2311yescharacteristic, complemented
51D1532—21no—
52D1532—21no—
53D1532C2312yes—
54D1532C2311yescharacteristic, complemented
55C22⋊D383—21no—
56C22⋊D383—21no—
57C22⋊D383—22no—
58C22⋊D383—22no—
59C22⋊D383—21no—
60C2×Dic383—21no—
61C2×Dic383D411yescharacteristic
62C4×D383—21no—
63C4×D383—21no—
64C4×D383—21no—
65C4×D383D411yescharacteristic
66C4×D383D411yescharacteristic
67C4×D383C2311yescharacteristic
68C4×D383C2311yescharacteristic
69C383⋊C8C2312yescomplemented
70C23×C383—21no—
71Q8×C383C2311yescharacteristic, complemented
72D4×C383—21no—
73D4×C383—21no—
74D4×C383C2312yes—
75D4×C383C2311yescharacteristic, complemented
76C2×C4×C383—21no—
77C2×C4×C383C2311yescharacteristic
78C8×C383C2312yescomplemented
79C22×C383—21no—
80C22×C383—22no—
81C22×C383—42no—
82C22×C383C2×D411yescharacteristic
83C2×D383—22no—
84C2×D383—21no—
85C2×D383—22no—
86C2×D383—44no—
87C2×D383—42no—
88C2×D383—42no—
89C2×D383—44no—
90C2×D383C2×D411yescharacteristic
91C2×D383C2×D411yescharacteristic
92C4×C383—21no—
93C4×C383C2×D411yescharacteristic
94C4×C383C2411yescharacteristic
95Dic383—21no—
96Dic383C2×D411yescharacteristic
97Dic383C2×D411yescharacteristic
98C2×C383—21no—
99C2×C383—42no—
100C2×C383—41no—
101C2×C383C22×D411yescharacteristic
102D383—21no—
103D383—41no—
104D383—42no—
105D383AGL(1,ℤ/8)12yesdirect product factor
106C383C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—3831nomaximal, Sylow
108C2×#41—3831no—
109C22×D4—3831no—
110AGL(1,ℤ/8)—3831no—
111AGL(1,ℤ/8)—3831no—
112AGL(1,ℤ/8)—3832no—
113AGL(1,ℤ/8)—3832no—
114AGL(1,ℤ/8)—3831no—
115AGL(1,ℤ/8)D38311yescharacteristic, direct product factor
116C2×SD16—3832no—
117C2×D8—3832no—
118C2×M16—3831no—
119C24—7661no—
120#41—3831no—
121#41—3831no—
122#41—3831no—
123#41—7661no—
124#41—7661no—
125#41C2×D38311yescharacteristic, complemented
126C2×Q8—3831no—
127C2×D4—3832no—
128C2×D4—3832no—
129C2×D4—3831no—
130C2×D4—3831no—
131C2×D4—7661no—
132C2×D4—7661no—
133C2×D4—7661no—
134C2×D4—7661no—
135C2×D4C2×D38311yescharacteristic, complemented
136C22×C4—3831no—
137C22×C4—7661no—
138SD16—3832no—
139SD16—3832no—
140SD16—3832no—
141SD16C2×D38312yescomplemented
142D8—3832no—
143D8—3832no—
144D8—3832no—
145D8C2×D38312yescomplemented
146M16—3831no—
147M16—3832no—
148M16C2×D38311yescharacteristic, complemented
149C2×C8—3832no—
150C23—21no—
151C23—3831no—
152C23—15324no—
153C23—7661no—
154C23—7662no—
155C23—7662no—
156C23—7661no—
157Q8—3831no—
158Q8—7661no—
159Q8C22×D38311yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—3831no—
163D4—3832no—
164D4—7661no—
165D4—7662no—
166D4—7662no—
167D4—7661no—
168D4—7661no—
169D4—7661no—
170D4—7661no—
171D4C22×D38312yes—
172D4C22×D38311yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—3831no—
175C2×C4—3831no—
176C2×C4—3831no—
177C2×C4—3831no—
178C2×C4—3831no—
179C2×C4—7661no—
180C2×C4—7661no—
181C2×C4—7661no—
182C2×C4—7661no—
183C2×C4C22×D38311yescharacteristic
184C8—3832no—
185C8C22×D38312yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—3831no—
190C22—3831no—
191C22—15322no—
192C22—15324no—
193C22—15322no—
194C22—15324no—
195C22—7662no—
196C22—7661no—
197C22—7662no—
198C22D4×D38311yescharacteristic
199C4—21no—
200C4—3831no—
201C4—3831no—
202C4—7661no—
203C4D4×D38311yescharacteristic
204C4C23×D38311yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—3832no—
209C2—15322no—
210C2—15321no—
211C2—7661no—
212C2C2×D4×D38311yescharacteristic
subgroupG/H
centerC2C2×D4×D383
commutator, cosocleC4×C383C24
FrattiniC4C23×D383
FittingAGL(1,ℤ/8)×C383C2
socleC2×C383C22×D4
hypercenterAGL(1,ℤ/8)D383
hypocenterC383C2×AGL(1,ℤ/8)
LCSG ▷ C4×C383 ▷ C2×C383 ▷ C383
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D383C2semidirect
2. C2×D4×D383C2semidirect
3. #27133869C2semidirect
4. #27133868C2semidirect
5. #27133867C2semidirect
6. #27133866C2semidirect
7. #27133865C2semidirect
8. SD16×D383C2semidirect
9. D8×D383C2semidirect
10. M16×D383C2semidirect
11. AGL(1,ℤ/8)×C383C2semidirect
13. #20259458C22semidirect
15. #20259457C22semidirect
17. #20259456C22semidirect
18. Q8×D383C22semidirect
19. C2×D1532C22semidirect
25. D4×D383C22semidirect
26. D4×D383C22semidirect
29. #20259446C22semidirect
30. #20259445C22semidirect
31. #20259444C22semidirect
32. D3064C22semidirect
33. #20259442C22semidirect
34. #20259442C22semidirect
35. #20259441C22semidirect
36. #20259440C22semidirect
37. C8×D383C22semidirect
38. #41×C383C22semidirect
39. C2×D4×C383C22semidirect
40. SD16×C383C22semidirect
41. D8×C383C22semidirect
42. M16×C383C22semidirect
50. Dic766C23semidirect
54. D1532C23semidirect
69. C383⋊C8C23semidirect
71. Q8×C383C23semidirect
75. D4×C383C23semidirect
78. C8×C383C23semidirect
105. D383AGL(1,ℤ/8)direct (N × H)
106. C383C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D383direct (N × H)
125. #41C2×D383semidirect
135. C2×D4C2×D383semidirect
141. SD16C2×D383semidirect
145. D8C2×D383semidirect
148. M16C2×D383semidirect
159. Q8C22×D383semidirect
172. D4C22×D383semidirect
185. C8C22×D383semidirect

Maximal subgroups

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

subgroupindex
#41×D3832
C2×D4×D3832
#271338692
#271338682
#271338672
#271338662
#271338652
SD16×D3832
D8×D3832
M16×D3832
AGL(1,ℤ/8)×C3832
C2×AGL(1,ℤ/8)383