Finite Group Databasebeta

← AGL(1,ℤ/8)×D593 #49183499

Subgroups — AGL(1,ℤ/8)×D593 #49183499

Order 37952.

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×D593C211yesmaximal, characteristic, complemented
2C2×D4×D593C211yesmaximal, characteristic, complemented
3#34039313C211yesmaximal, characteristic, complemented
4#34039312C212yesmaximal, complemented
5#34039311C211yesmaximal, characteristic, complemented
6#34039310C211yesmaximal, characteristic, complemented
7#34039309C212yesmaximal, complemented
8SD16×D593C212yesmaximal, complemented
9D8×D593C212yesmaximal, complemented
10M16×D593C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C593C211yesmaximal, characteristic, complemented
12C23×D593—21no—
13#23748734C2211yescharacteristic, complemented
14#23748733—21no—
15#23748733C2211yescharacteristic, complemented
16#23748732—21no—
17#23748732C2211yescharacteristic, complemented
18Q8×D593C2211yescharacteristic, complemented
19C2×D2372C2211yescharacteristic, complemented
20C2×C22⋊D593—21no—
21D4×D593—21no—
22D4×D593—21no—
23D4×D593—21no—
24D4×D593C2212yes—
25D4×D593C2212yescomplemented
26D4×D593C2211yescharacteristic, complemented
27C2×C4×D593—21no—
28C2×C4×D593C2211yescharacteristic
29#23748722C2212yescomplemented
30#23748721C2212yescomplemented
31#23748720C2212yescomplemented
32D4744C2212yescomplemented
33#23748718C2212yescomplemented
34#23748718C2212yescomplemented
35#23748717C2211yescharacteristic, complemented
36#23748716C2212yescomplemented
37C8×D593C2212yescomplemented
38#41×C593C2211yescharacteristic, complemented
39C2×D4×C593C2211yescharacteristic, complemented
40SD16×C593C2212yescomplemented
41D8×C593C2212yescomplemented
42M16×C593C2211yescharacteristic, complemented
43C22×D593—21no—
44C22×D593—21no—
45C22×D593—22no—
46C22×D593—22no—
47C22×D593—44no—
48C22×D593D411yescharacteristic
49Dic1186—21no—
50Dic1186C2311yescharacteristic, complemented
51D2372—21no—
52D2372—21no—
53D2372C2312yes—
54D2372C2311yescharacteristic, complemented
55C22⋊D593—21no—
56C22⋊D593—21no—
57C22⋊D593—22no—
58C22⋊D593—22no—
59C22⋊D593—21no—
60C2×Dic593—21no—
61C2×Dic593D411yescharacteristic
62C4×D593—21no—
63C4×D593—21no—
64C4×D593—21no—
65C4×D593D411yescharacteristic
66C4×D593D411yescharacteristic
67C4×D593C2311yescharacteristic
68C4×D593C2311yescharacteristic
69#18011654C2312yescomplemented
70C23×C593—21no—
71Q8×C593C2311yescharacteristic, complemented
72D4×C593—21no—
73D4×C593—21no—
74D4×C593C2312yes—
75D4×C593C2311yescharacteristic, complemented
76C2×C4×C593—21no—
77C2×C4×C593C2311yescharacteristic
78C8×C593C2312yescomplemented
79C22×C593—21no—
80C22×C593—22no—
81C22×C593—42no—
82C22×C593C2×D411yescharacteristic
83C2×D593—22no—
84C2×D593—21no—
85C2×D593—22no—
86C2×D593—44no—
87C2×D593—42no—
88C2×D593—42no—
89C2×D593—44no—
90C2×D593C2×D411yescharacteristic
91C2×D593C2×D411yescharacteristic
92C4×C593—21no—
93C4×C593C2×D411yescharacteristic
94C4×C593C2411yescharacteristic
95Dic593—21no—
96Dic593C2×D411yescharacteristic
97Dic593C2×D411yescharacteristic
98C2×C593—21no—
99C2×C593—42no—
100C2×C593—41no—
101C2×C593C22×D411yescharacteristic
102D593—21no—
103D593—41no—
104D593—42no—
105D593AGL(1,ℤ/8)12yesdirect product factor
106C593C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—5931nomaximal, Sylow
108C2×#41—5931no—
109C22×D4—5931no—
110AGL(1,ℤ/8)—5931no—
111AGL(1,ℤ/8)—5931no—
112AGL(1,ℤ/8)—5932no—
113AGL(1,ℤ/8)—5932no—
114AGL(1,ℤ/8)—5931no—
115AGL(1,ℤ/8)D59311yescharacteristic, direct product factor
116C2×SD16—5932no—
117C2×D8—5932no—
118C2×M16—5931no—
119C24—11861no—
120#41—5931no—
121#41—5931no—
122#41—5931no—
123#41—11861no—
124#41—11861no—
125#41C2×D59311yescharacteristic, complemented
126C2×Q8—5931no—
127C2×D4—5932no—
128C2×D4—5932no—
129C2×D4—5931no—
130C2×D4—5931no—
131C2×D4—11861no—
132C2×D4—11861no—
133C2×D4—11861no—
134C2×D4—11861no—
135C2×D4C2×D59311yescharacteristic, complemented
136C22×C4—5931no—
137C22×C4—11861no—
138SD16—5932no—
139SD16—5932no—
140SD16—5932no—
141SD16C2×D59312yescomplemented
142D8—5932no—
143D8—5932no—
144D8—5932no—
145D8C2×D59312yescomplemented
146M16—5931no—
147M16—5932no—
148M16C2×D59311yescharacteristic, complemented
149C2×C8—5932no—
150C23—21no—
151C23—23724no—
152C23—5931no—
153C23—11861no—
154C23—11862no—
155C23—11862no—
156C23—11861no—
157Q8—5931no—
158Q8—11861no—
159Q8C22×D59311yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—5932no—
163D4—5931no—
164D4—11861no—
165D4—11862no—
166D4—11862no—
167D4—11861no—
168D4—11861no—
169D4—11861no—
170D4—11861no—
171D4C22×D59312yes—
172D4C22×D59311yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—5931no—
175C2×C4—5931no—
176C2×C4—5931no—
177C2×C4—5931no—
178C2×C4—5931no—
179C2×C4—11861no—
180C2×C4—11861no—
181C2×C4—11861no—
182C2×C4—11861no—
183C2×C4C22×D59311yescharacteristic
184C8—5932no—
185C8C22×D59312yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—23722no—
190C22—23724no—
191C22—23722no—
192C22—23724no—
193C22—5931no—
194C22—5931no—
195C22—11862no—
196C22—11861no—
197C22—11862no—
198C22D4×D59311yescharacteristic
199C4—21no—
200C4—5931no—
201C4—5931no—
202C4—11861no—
203C4D4×D59311yescharacteristic
204C4C23×D59311yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—23722no—
209C2—23721no—
210C2—5932no—
211C2—11861no—
212C2C2×D4×D59311yescharacteristic
subgroupG/H
centerC2C2×D4×D593
commutator, cosocleC4×C593C24
FrattiniC4C23×D593
FittingAGL(1,ℤ/8)×C593C2
socleC2×C593C22×D4
hypercenterAGL(1,ℤ/8)D593
hypocenterC593C2×AGL(1,ℤ/8)
LCSG ▷ C4×C593 ▷ C2×C593 ▷ C593
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D593C2semidirect
2. C2×D4×D593C2semidirect
3. #34039313C2semidirect
4. #34039312C2semidirect
5. #34039311C2semidirect
6. #34039310C2semidirect
7. #34039309C2semidirect
8. SD16×D593C2semidirect
9. D8×D593C2semidirect
10. M16×D593C2semidirect
11. AGL(1,ℤ/8)×C593C2semidirect
13. #23748734C22semidirect
15. #23748733C22semidirect
17. #23748732C22semidirect
18. Q8×D593C22semidirect
19. C2×D2372C22semidirect
25. D4×D593C22semidirect
26. D4×D593C22semidirect
29. #23748722C22semidirect
30. #23748721C22semidirect
31. #23748720C22semidirect
32. D4744C22semidirect
33. #23748718C22semidirect
34. #23748718C22semidirect
35. #23748717C22semidirect
36. #23748716C22semidirect
37. C8×D593C22semidirect
38. #41×C593C22semidirect
39. C2×D4×C593C22semidirect
40. SD16×C593C22semidirect
41. D8×C593C22semidirect
42. M16×C593C22semidirect
50. Dic1186C23semidirect
54. D2372C23semidirect
69. #18011654C23semidirect
71. Q8×C593C23semidirect
75. D4×C593C23semidirect
78. C8×C593C23semidirect
105. D593AGL(1,ℤ/8)direct (N × H)
106. C593C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D593direct (N × H)
125. #41C2×D593semidirect
135. C2×D4C2×D593semidirect
141. SD16C2×D593semidirect
145. D8C2×D593semidirect
148. M16C2×D593semidirect
159. Q8C22×D593semidirect
172. D4C22×D593semidirect
185. C8C22×D593semidirect

Maximal subgroups

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

subgroupindex
#41×D5932
C2×D4×D5932
#340393132
#340393122
#340393112
#340393102
#340393092
SD16×D5932
D8×D5932
M16×D5932
AGL(1,ℤ/8)×C5932
C2×AGL(1,ℤ/8)593