Finite Group Databasebeta

← AGL(1,ℤ/8)×D193 #27136043

Subgroups — AGL(1,ℤ/8)×D193 #27136043

Order 12352.

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×D193C211yesmaximal, characteristic, complemented
2C2×D4×D193C211yesmaximal, characteristic, complemented
3#20259927C211yesmaximal, characteristic, complemented
4#20259926C212yesmaximal, complemented
5#20259925C211yesmaximal, characteristic, complemented
6#20259924C211yesmaximal, characteristic, complemented
7#20259923C212yesmaximal, complemented
8SD16×D193C212yesmaximal, complemented
9D8×D193C212yesmaximal, complemented
10M16×D193C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C193C211yesmaximal, characteristic, complemented
12C23×D193—21no—
13#15690556C2211yescharacteristic, complemented
14#15690555—21no—
15#15690555C2211yescharacteristic, complemented
16#15690554—21no—
17#15690554C2211yescharacteristic, complemented
18Q8×D193C2211yescharacteristic, complemented
19C2×D772C2211yescharacteristic, complemented
20C2×C22⋊D193—21no—
21D4×D193—21no—
22D4×D193—21no—
23D4×D193—21no—
24D4×D193C2212yes—
25D4×D193C2212yescomplemented
26D4×D193C2211yescharacteristic, complemented
27C2×C4×D193—21no—
28C2×C4×D193C2211yescharacteristic
29#15690544C2212yescomplemented
30#15690543C2212yescomplemented
31#15690542C2212yescomplemented
32D1544C2212yescomplemented
33#15690540C2212yescomplemented
34#15690540C2212yescomplemented
35#15690539C2211yescharacteristic, complemented
36#15690538C2212yescomplemented
37C8×D193C2212yescomplemented
38#41×C193C2211yescharacteristic, complemented
39C2×D4×C193C2211yescharacteristic, complemented
40SD16×C193C2212yescomplemented
41D8×C193C2212yescomplemented
42M16×C193C2211yescharacteristic, complemented
43C22×D193—21no—
44C22×D193—21no—
45C22×D193—22no—
46C22×D193—22no—
47C22×D193—44no—
48C22×D193D411yescharacteristic
49Dic386—21no—
50Dic386C2311yescharacteristic, complemented
51D772—21no—
52D772—21no—
53D772C2312yes—
54D772C2311yescharacteristic, complemented
55C22⋊D193—21no—
56C22⋊D193—21no—
57C22⋊D193—22no—
58C22⋊D193—22no—
59C22⋊D193—21no—
60C2×Dic193—21no—
61C2×Dic193D411yescharacteristic
62C4×D193—21no—
63C4×D193—21no—
64C4×D193—21no—
65C4×D193D411yescharacteristic
66C4×D193D411yescharacteristic
67C4×D193C2311yescharacteristic
68C4×D193C2311yescharacteristic
69#13095393C2312yescomplemented
70C23×C193—21no—
71Q8×C193C2311yescharacteristic, complemented
72D4×C193—21no—
73D4×C193—21no—
74D4×C193C2312yes—
75D4×C193C2311yescharacteristic, complemented
76C2×C4×C193—21no—
77C2×C4×C193C2311yescharacteristic
78C8×C193C2312yescomplemented
79C22×C193—21no—
80C22×C193—22no—
81C22×C193—42no—
82C22×C193C2×D411yescharacteristic
83C2×D193—22no—
84C2×D193—21no—
85C2×D193—22no—
86C2×D193—44no—
87C2×D193—42no—
88C2×D193—42no—
89C2×D193—44no—
90C2×D193C2×D411yescharacteristic
91C2×D193C2×D411yescharacteristic
92C4×C193—21no—
93C4×C193C2×D411yescharacteristic
94C4×C193C2411yescharacteristic
95Dic193—21no—
96Dic193C2×D411yescharacteristic
97Dic193C2×D411yescharacteristic
98C2×C193—21no—
99C2×C193—42no—
100C2×C193—41no—
101C2×C193C22×D411yescharacteristic
102D193—21no—
103D193—41no—
104D193—42no—
105D193AGL(1,ℤ/8)12yesdirect product factor
106C193C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—1931nomaximal, Sylow
108C2×#41—1931no—
109C22×D4—1931no—
110AGL(1,ℤ/8)—1931no—
111AGL(1,ℤ/8)—1931no—
112AGL(1,ℤ/8)—1932no—
113AGL(1,ℤ/8)—1932no—
114AGL(1,ℤ/8)—1931no—
115AGL(1,ℤ/8)D19311yescharacteristic, direct product factor
116C2×SD16—1932no—
117C2×D8—1932no—
118C2×M16—1931no—
119C24—3861no—
120#41—3861no—
121#41—3861no—
122#41—1931no—
123#41—1931no—
124#41—1931no—
125#41C2×D19311yescharacteristic, complemented
126C2×Q8—1931no—
127C2×D4—3861no—
128C2×D4—3861no—
129C2×D4—3861no—
130C2×D4—3861no—
131C2×D4—1932no—
132C2×D4—1932no—
133C2×D4—1931no—
134C2×D4—1931no—
135C2×D4C2×D19311yescharacteristic, complemented
136C22×C4—3861no—
137C22×C4—1931no—
138SD16—1932no—
139SD16—1932no—
140SD16—1932no—
141SD16C2×D19312yescomplemented
142D8—1932no—
143D8—1932no—
144D8—1932no—
145D8C2×D19312yescomplemented
146M16—1931no—
147M16—1932no—
148M16C2×D19311yescharacteristic, complemented
149C2×C8—1932no—
150C23—21no—
151C23—7724no—
152C23—3861no—
153C23—3862no—
154C23—3862no—
155C23—3861no—
156C23—1931no—
157Q8—3861no—
158Q8—1931no—
159Q8C22×D19311yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—3861no—
163D4—3861no—
164D4—3861no—
165D4—3862no—
166D4—3862no—
167D4—3861no—
168D4—3861no—
169D4—1931no—
170D4—1932no—
171D4C22×D19312yes—
172D4C22×D19311yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—3861no—
175C2×C4—3861no—
176C2×C4—3861no—
177C2×C4—3861no—
178C2×C4—1931no—
179C2×C4—1931no—
180C2×C4—1931no—
181C2×C4—1931no—
182C2×C4—1931no—
183C2×C4C22×D19311yescharacteristic
184C8—1932no—
185C8C22×D19312yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—7722no—
190C22—7724no—
191C22—7724no—
192C22—7722no—
193C22—3862no—
194C22—3861no—
195C22—3862no—
196C22—1931no—
197C22—1931no—
198C22D4×D19311yescharacteristic
199C4—21no—
200C4—3861no—
201C4—1931no—
202C4—1931no—
203C4D4×D19311yescharacteristic
204C4C23×D19311yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—7722no—
209C2—7721no—
210C2—3861no—
211C2—1932no—
212C2C2×D4×D19311yescharacteristic
subgroupG/H
centerC2C2×D4×D193
commutator, cosocleC4×C193C24
FrattiniC4C23×D193
FittingAGL(1,ℤ/8)×C193C2
socleC2×C193C22×D4
hypercenterAGL(1,ℤ/8)D193
hypocenterC193C2×AGL(1,ℤ/8)
LCSG ▷ C4×C193 ▷ C2×C193 ▷ C193
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D193C2semidirect
2. C2×D4×D193C2semidirect
3. #20259927C2semidirect
4. #20259926C2semidirect
5. #20259925C2semidirect
6. #20259924C2semidirect
7. #20259923C2semidirect
8. SD16×D193C2semidirect
9. D8×D193C2semidirect
10. M16×D193C2semidirect
11. AGL(1,ℤ/8)×C193C2semidirect
13. #15690556C22semidirect
15. #15690555C22semidirect
17. #15690554C22semidirect
18. Q8×D193C22semidirect
19. C2×D772C22semidirect
25. D4×D193C22semidirect
26. D4×D193C22semidirect
29. #15690544C22semidirect
30. #15690543C22semidirect
31. #15690542C22semidirect
32. D1544C22semidirect
33. #15690540C22semidirect
34. #15690540C22semidirect
35. #15690539C22semidirect
36. #15690538C22semidirect
37. C8×D193C22semidirect
38. #41×C193C22semidirect
39. C2×D4×C193C22semidirect
40. SD16×C193C22semidirect
41. D8×C193C22semidirect
42. M16×C193C22semidirect
50. Dic386C23semidirect
54. D772C23semidirect
69. #13095393C23semidirect
71. Q8×C193C23semidirect
75. D4×C193C23semidirect
78. C8×C193C23semidirect
105. D193AGL(1,ℤ/8)direct (N × H)
106. C193C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D193direct (N × H)
125. #41C2×D193semidirect
135. C2×D4C2×D193semidirect
141. SD16C2×D193semidirect
145. D8C2×D193semidirect
148. M16C2×D193semidirect
159. Q8C22×D193semidirect
172. D4C22×D193semidirect
185. C8C22×D193semidirect

Maximal subgroups

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

subgroupindex
#41×D1932
C2×D4×D1932
#202599272
#202599262
#202599252
#202599242
#202599232
SD16×D1932
D8×D1932
M16×D1932
AGL(1,ℤ/8)×C1932
C2×AGL(1,ℤ/8)193