Finite Group Databasebeta

← AGL(1,ℤ/8)×D37 #14558317

Subgroups — AGL(1,ℤ/8)×D37 #14558317

Order 2368.

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×D37C211yesmaximal, characteristic, complemented
2C2×D4×D37C211yesmaximal, characteristic, complemented
3#11924564C211yesmaximal, characteristic, complemented
4#11924563C212yesmaximal, complemented
5#11924562C211yesmaximal, characteristic, complemented
6#11924561C211yesmaximal, characteristic, complemented
7#11924560C212yesmaximal, complemented
8SD16×D37C212yesmaximal, complemented
9D8×D37C212yesmaximal, complemented
10M16×D37C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C37C211yesmaximal, characteristic, complemented
12C23×D37—21no—
13#41×C37C2211yescharacteristic, complemented
14C2×D4×C37C2211yescharacteristic, complemented
15C2×C22⋊D37—21no—
16#10596966C2211yescharacteristic, complemented
17Q8×D37C2211yescharacteristic, complemented
18#10596964—21no—
19#10596964C2211yescharacteristic, complemented
20D4×D37—21no—
21D4×D37—21no—
22D4×D37—21no—
23D4×D37C2212yes—
24D4×D37C2212yescomplemented
25D4×D37C2211yescharacteristic, complemented
26#10596962—21no—
27#10596962C2211yescharacteristic, complemented
28C2×D148C2211yescharacteristic, complemented
29C2×C4×D37—21no—
30C2×C4×D37C2211yescharacteristic
31SD16×C37C2212yescomplemented
32D8×C37C2212yescomplemented
33M16×C37C2211yescharacteristic, complemented
34#10596941C2212yescomplemented
35#10596940C2212yescomplemented
36#10596939C2212yescomplemented
37#10596939C2212yescomplemented
38#10596934C2211yescharacteristic, complemented
39D296C2212yescomplemented
40#10596930C2212yescomplemented
41#10596929C2212yescomplemented
42C8×D37C2212yescomplemented
43C23×C37—21no—
44C22×D37—21no—
45C22×D37—21no—
46C22×D37—22no—
47C22×D37—22no—
48C22×D37—44no—
49C22×D37D411yescharacteristic
50Q8×C37C2311yescharacteristic, complemented
51D4×C37—21no—
52D4×C37—21no—
53D4×C37C2312yes—
54D4×C37C2311yescharacteristic, complemented
55C2×C4×C37—21no—
56C2×C4×C37C2311yescharacteristic
57C22⋊D37—21no—
58C22⋊D37—21no—
59C22⋊D37—21no—
60C22⋊D37—22no—
61C22⋊D37—22no—
62C2×Dic37—21no—
63C2×Dic37D411yescharacteristic
64D148—21no—
65D148—21no—
66D148C2312yes—
67D148C2311yescharacteristic, complemented
68C4×D37—21no—
69C4×D37—21no—
70C4×D37—21no—
71C4×D37D411yescharacteristic
72C4×D37D411yescharacteristic
73C4×D37C2311yescharacteristic
74C4×D37C2311yescharacteristic
75Dic74—21no—
76Dic74C2311yescharacteristic, complemented
77C8×C37C2312yescomplemented
78#64436C2312yescomplemented
79C22×C37—21no—
80C22×C37—22no—
81C22×C37—42no—
82C22×C37C2×D411yescharacteristic
83C2×D37—22no—
84C2×D37—21no—
85C2×D37—22no—
86C2×D37—44no—
87C2×D37—42no—
88C2×D37—42no—
89C2×D37—44no—
90C2×D37C2×D411yescharacteristic
91C2×D37C2×D411yescharacteristic
92C4×C37—21no—
93C4×C37C2×D411yescharacteristic
94C4×C37C2411yescharacteristic
95Dic37—21no—
96Dic37C2×D411yescharacteristic
97Dic37C2×D411yescharacteristic
98C2×C37—21no—
99C2×C37—42no—
100C2×C37—41no—
101C2×C37C22×D411yescharacteristic
102D37—21no—
103D37—41no—
104D37—42no—
105D37AGL(1,ℤ/8)12yesdirect product factor
106C2×AGL(1,ℤ/8)—371nomaximal, Sylow
107C37C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
108C2×#41—371no—
109C22×D4—371no—
110AGL(1,ℤ/8)—371no—
111AGL(1,ℤ/8)—371no—
112AGL(1,ℤ/8)—372no—
113AGL(1,ℤ/8)—372no—
114AGL(1,ℤ/8)—371no—
115AGL(1,ℤ/8)D3711yescharacteristic, direct product factor
116C2×SD16—372no—
117C2×D8—372no—
118C2×M16—371no—
119C24—741no—
120#41—371no—
121#41—371no—
122#41—371no—
123#41—741no—
124#41—741no—
125#41C2×D3711yescharacteristic, complemented
126C2×Q8—371no—
127C2×D4—372no—
128C2×D4—372no—
129C2×D4—371no—
130C2×D4—371no—
131C2×D4—741no—
132C2×D4—741no—
133C2×D4—741no—
134C2×D4—741no—
135C2×D4C2×D3711yescharacteristic, complemented
136C22×C4—371no—
137C22×C4—741no—
138SD16—372no—
139SD16—372no—
140SD16—372no—
141SD16C2×D3712yescomplemented
142D8—372no—
143D8—372no—
144D8—372no—
145D8C2×D3712yescomplemented
146M16—371no—
147M16—372no—
148M16C2×D3711yescharacteristic, complemented
149C2×C8—372no—
150C23—21no—
151C23—371no—
152C23—741no—
153C23—742no—
154C23—742no—
155C23—741no—
156C23—1484no—
157Q8—371no—
158Q8—741no—
159Q8C22×D3711yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—371no—
163D4—372no—
164D4—741no—
165D4—742no—
166D4—742no—
167D4—741no—
168D4—741no—
169D4—741no—
170D4—741no—
171D4C22×D3712yes—
172D4C22×D3711yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—371no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—371no—
178C2×C4—371no—
179C2×C4—741no—
180C2×C4—741no—
181C2×C4—741no—
182C2×C4—741no—
183C2×C4C22×D3711yescharacteristic
184C8—372no—
185C8C22×D3712yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—371no—
190C22—371no—
191C22—742no—
192C22—741no—
193C22—742no—
194C22—1482no—
195C22—1484no—
196C22—1482no—
197C22—1484no—
198C22D4×D3711yescharacteristic
199C4—21no—
200C4—371no—
201C4—371no—
202C4—741no—
203C4D4×D3711yescharacteristic
204C4C23×D3711yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—372no—
209C2—741no—
210C2—1482no—
211C2—1481no—
212C2C2×D4×D3711yescharacteristic
subgroupG/H
centerC2C2×D4×D37
commutator, cosocleC4×C37C24
FrattiniC4C23×D37
FittingAGL(1,ℤ/8)×C37C2
socleC2×C37C22×D4
hypercenterAGL(1,ℤ/8)D37
hypocenterC37C2×AGL(1,ℤ/8)
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D37C2semidirect
2. C2×D4×D37C2semidirect
3. #11924564C2semidirect
4. #11924563C2semidirect
5. #11924562C2semidirect
6. #11924561C2semidirect
7. #11924560C2semidirect
8. SD16×D37C2semidirect
9. D8×D37C2semidirect
10. M16×D37C2semidirect
11. AGL(1,ℤ/8)×C37C2semidirect
13. #41×C37C22semidirect
14. C2×D4×C37C22semidirect
16. #10596966C22semidirect
17. Q8×D37C22semidirect
19. #10596964C22semidirect
24. D4×D37C22semidirect
25. D4×D37C22semidirect
27. #10596962C22semidirect
28. C2×D148C22semidirect
31. SD16×C37C22semidirect
32. D8×C37C22semidirect
33. M16×C37C22semidirect
34. #10596941C22semidirect
35. #10596940C22semidirect
36. #10596939C22semidirect
37. #10596939C22semidirect
38. #10596934C22semidirect
39. D296C22semidirect
40. #10596930C22semidirect
41. #10596929C22semidirect
42. C8×D37C22semidirect
50. Q8×C37C23semidirect
54. D4×C37C23semidirect
67. D148C23semidirect
76. Dic74C23semidirect
77. C8×C37C23semidirect
78. #64436C23semidirect
105. D37AGL(1,ℤ/8)direct (N × H)
107. C37C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D37direct (N × H)
125. #41C2×D37semidirect
135. C2×D4C2×D37semidirect
141. SD16C2×D37semidirect
145. D8C2×D37semidirect
148. M16C2×D37semidirect
159. Q8C22×D37semidirect
172. D4C22×D37semidirect
185. C8C22×D37semidirect

Maximal subgroups

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

subgroupindex
#41×D372
C2×D4×D372
#119245642
#119245632
#119245622
#119245612
#119245602
SD16×D372
D8×D372
M16×D372
AGL(1,ℤ/8)×C372
C2×AGL(1,ℤ/8)37