Finite Group Databasebeta

← AGL(1,ℤ/8)×D313 #34094936

Subgroups — AGL(1,ℤ/8)×D313 #34094936

Order 20032.

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×D313C211yesmaximal, characteristic, complemented
2C2×D4×D313C211yesmaximal, characteristic, complemented
3#23756525C211yesmaximal, characteristic, complemented
4#23756524C212yesmaximal, complemented
5#23756523C211yesmaximal, characteristic, complemented
6#23756522C211yesmaximal, characteristic, complemented
7#23756521C212yesmaximal, complemented
8SD16×D313C212yesmaximal, complemented
9D8×D313C212yesmaximal, complemented
10M16×D313C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C313C211yesmaximal, characteristic, complemented
12C23×D313—21no—
13#19097562C2211yescharacteristic, complemented
14#19097561—21no—
15#19097561C2211yescharacteristic, complemented
16#19097560—21no—
17#19097560C2211yescharacteristic, complemented
18Q8×D313C2211yescharacteristic, complemented
19C2×D1252C2211yescharacteristic, complemented
20C2×C22⋊D313—21no—
21D4×D313—21no—
22D4×D313—21no—
23D4×D313—21no—
24D4×D313C2212yes—
25D4×D313C2212yescomplemented
26D4×D313C2211yescharacteristic, complemented
27C2×C4×D313—21no—
28C2×C4×D313C2211yescharacteristic
29#19097550C2212yescomplemented
30#19097549C2212yescomplemented
31#19097548C2212yescomplemented
32D2504C2212yescomplemented
33#19097546C2212yescomplemented
34#19097546C2212yescomplemented
35#19097545C2211yescharacteristic, complemented
36#19097544C2212yescomplemented
37C8×D313C2212yescomplemented
38#41×C313C2211yescharacteristic, complemented
39C2×D4×C313C2211yescharacteristic, complemented
40SD16×C313C2212yescomplemented
41D8×C313C2212yescomplemented
42M16×C313C2211yescharacteristic, complemented
43C22×D313—21no—
44C22×D313—21no—
45C22×D313—22no—
46C22×D313—22no—
47C22×D313—44no—
48C22×D313D411yescharacteristic
49Dic626—21no—
50Dic626C2311yescharacteristic, complemented
51D1252—21no—
52D1252—21no—
53D1252C2312yes—
54D1252C2311yescharacteristic, complemented
55C22⋊D313—21no—
56C22⋊D313—21no—
57C22⋊D313—22no—
58C22⋊D313—22no—
59C22⋊D313—21no—
60C2×Dic313—21no—
61C2×Dic313D411yescharacteristic
62C4×D313—21no—
63C4×D313—21no—
64C4×D313—21no—
65C4×D313D411yescharacteristic
66C4×D313D411yescharacteristic
67C4×D313C2311yescharacteristic
68C4×D313C2311yescharacteristic
69#14578809C2312yescomplemented
70C23×C313—21no—
71Q8×C313C2311yescharacteristic, complemented
72D4×C313—21no—
73D4×C313—21no—
74D4×C313C2312yes—
75D4×C313C2311yescharacteristic, complemented
76C2×C4×C313—21no—
77C2×C4×C313C2311yescharacteristic
78C8×C313C2312yescomplemented
79C22×C313—21no—
80C22×C313—22no—
81C22×C313—42no—
82C22×C313C2×D411yescharacteristic
83C2×D313—22no—
84C2×D313—21no—
85C2×D313—22no—
86C2×D313—44no—
87C2×D313—42no—
88C2×D313—42no—
89C2×D313—44no—
90C2×D313C2×D411yescharacteristic
91C2×D313C2×D411yescharacteristic
92C4×C313—21no—
93C4×C313C2×D411yescharacteristic
94C4×C313C2411yescharacteristic
95Dic313—21no—
96Dic313C2×D411yescharacteristic
97Dic313C2×D411yescharacteristic
98C2×C313—21no—
99C2×C313—42no—
100C2×C313—41no—
101C2×C313C22×D411yescharacteristic
102D313—21no—
103D313—41no—
104D313—42no—
105D313AGL(1,ℤ/8)12yesdirect product factor
106C313C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—3131nomaximal, Sylow
108C2×#41—3131no—
109C22×D4—3131no—
110AGL(1,ℤ/8)—3131no—
111AGL(1,ℤ/8)—3131no—
112AGL(1,ℤ/8)—3132no—
113AGL(1,ℤ/8)—3132no—
114AGL(1,ℤ/8)—3131no—
115AGL(1,ℤ/8)D31311yescharacteristic, direct product factor
116C2×SD16—3132no—
117C2×D8—3132no—
118C2×M16—3131no—
119C24—6261no—
120#41—3131no—
121#41—3131no—
122#41—3131no—
123#41—6261no—
124#41—6261no—
125#41C2×D31311yescharacteristic, complemented
126C2×Q8—3131no—
127C2×D4—3132no—
128C2×D4—3132no—
129C2×D4—3131no—
130C2×D4—3131no—
131C2×D4—6261no—
132C2×D4—6261no—
133C2×D4—6261no—
134C2×D4—6261no—
135C2×D4C2×D31311yescharacteristic, complemented
136C22×C4—3131no—
137C22×C4—6261no—
138SD16—3132no—
139SD16—3132no—
140SD16—3132no—
141SD16C2×D31312yescomplemented
142D8—3132no—
143D8—3132no—
144D8—3132no—
145D8C2×D31312yescomplemented
146M16—3131no—
147M16—3132no—
148M16C2×D31311yescharacteristic, complemented
149C2×C8—3132no—
150C23—21no—
151C23—3131no—
152C23—6261no—
153C23—6262no—
154C23—6262no—
155C23—6261no—
156C23—12524no—
157Q8—3131no—
158Q8—6261no—
159Q8C22×D31311yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—3131no—
163D4—3132no—
164D4—6261no—
165D4—6262no—
166D4—6262no—
167D4—6261no—
168D4—6261no—
169D4—6261no—
170D4—6261no—
171D4C22×D31312yes—
172D4C22×D31311yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—3131no—
175C2×C4—3131no—
176C2×C4—3131no—
177C2×C4—3131no—
178C2×C4—3131no—
179C2×C4—6261no—
180C2×C4—6261no—
181C2×C4—6261no—
182C2×C4—6261no—
183C2×C4C22×D31311yescharacteristic
184C8—3132no—
185C8C22×D31312yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—3131no—
190C22—3131no—
191C22—6262no—
192C22—6261no—
193C22—6262no—
194C22—12522no—
195C22—12524no—
196C22—12522no—
197C22—12524no—
198C22D4×D31311yescharacteristic
199C4—21no—
200C4—3131no—
201C4—3131no—
202C4—6261no—
203C4D4×D31311yescharacteristic
204C4C23×D31311yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—3132no—
209C2—6261no—
210C2—12522no—
211C2—12521no—
212C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC2C2×D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
FittingAGL(1,ℤ/8)×C313C2
socleC2×C313C22×D4
hypercenterAGL(1,ℤ/8)D313
hypocenterC313C2×AGL(1,ℤ/8)
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D313C2semidirect
2. C2×D4×D313C2semidirect
3. #23756525C2semidirect
4. #23756524C2semidirect
5. #23756523C2semidirect
6. #23756522C2semidirect
7. #23756521C2semidirect
8. SD16×D313C2semidirect
9. D8×D313C2semidirect
10. M16×D313C2semidirect
11. AGL(1,ℤ/8)×C313C2semidirect
13. #19097562C22semidirect
15. #19097561C22semidirect
17. #19097560C22semidirect
18. Q8×D313C22semidirect
19. C2×D1252C22semidirect
25. D4×D313C22semidirect
26. D4×D313C22semidirect
29. #19097550C22semidirect
30. #19097549C22semidirect
31. #19097548C22semidirect
32. D2504C22semidirect
33. #19097546C22semidirect
34. #19097546C22semidirect
35. #19097545C22semidirect
36. #19097544C22semidirect
37. C8×D313C22semidirect
38. #41×C313C22semidirect
39. C2×D4×C313C22semidirect
40. SD16×C313C22semidirect
41. D8×C313C22semidirect
42. M16×C313C22semidirect
50. Dic626C23semidirect
54. D1252C23semidirect
69. #14578809C23semidirect
71. Q8×C313C23semidirect
75. D4×C313C23semidirect
78. C8×C313C23semidirect
105. D313AGL(1,ℤ/8)direct (N × H)
106. C313C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D313direct (N × H)
125. #41C2×D313semidirect
135. C2×D4C2×D313semidirect
141. SD16C2×D313semidirect
145. D8C2×D313semidirect
148. M16C2×D313semidirect
159. Q8C22×D313semidirect
172. D4C22×D313semidirect
185. C8C22×D313semidirect

Maximal subgroups

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

subgroupindex
#41×D3132
C2×D4×D3132
#237565252
#237565242
#237565232
#237565222
#237565212
SD16×D3132
D8×D3132
M16×D3132
AGL(1,ℤ/8)×C3132
C2×AGL(1,ℤ/8)313