Finite Group Databasebeta

← AGL(1,ℤ/8)×D541 #46830959

Subgroups — AGL(1,ℤ/8)×D541 #46830959

Order 34624.

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×D541C211yesmaximal, characteristic, complemented
2C2×D4×D541C211yesmaximal, characteristic, complemented
3#31772656C211yesmaximal, characteristic, complemented
4#31772655C212yesmaximal, complemented
5#31772654C211yesmaximal, characteristic, complemented
6#31772653C211yesmaximal, characteristic, complemented
7#31772652C212yesmaximal, complemented
8SD16×D541C212yesmaximal, complemented
9D8×D541C212yesmaximal, complemented
10M16×D541C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C541C211yesmaximal, characteristic, complemented
12C23×D541—21no—
13#22575837C2211yescharacteristic, complemented
14#22575836—21no—
15#22575836C2211yescharacteristic, complemented
16#22575835—21no—
17#22575835C2211yescharacteristic, complemented
18Q8×D541C2211yescharacteristic, complemented
19C2×D2164C2211yescharacteristic, complemented
20C2×C22⋊D541—21no—
21D4×D541—21no—
22D4×D541—21no—
23D4×D541—21no—
24D4×D541C2212yes—
25D4×D541C2212yescomplemented
26D4×D541C2211yescharacteristic, complemented
27C2×C4×D541—21no—
28C2×C4×D541C2211yescharacteristic
29#22575825C2212yescomplemented
30#22575824C2212yescomplemented
31#22575823C2212yescomplemented
32D4328C2212yescomplemented
33#22575821C2212yescomplemented
34#22575821C2212yescomplemented
35#22575820C2211yescharacteristic, complemented
36#22575819C2212yescomplemented
37C8×D541C2212yescomplemented
38#41×C541C2211yescharacteristic, complemented
39C2×D4×C541C2211yescharacteristic, complemented
40SD16×C541C2212yescomplemented
41D8×C541C2212yescomplemented
42M16×C541C2211yescharacteristic, complemented
43C22×D541—21no—
44C22×D541—21no—
45C22×D541—22no—
46C22×D541—22no—
47C22×D541—44no—
48C22×D541D411yescharacteristic
49Dic1082—21no—
50Dic1082C2311yescharacteristic, complemented
51D2164—21no—
52D2164—21no—
53D2164C2312yes—
54D2164C2311yescharacteristic, complemented
55C22⋊D541—21no—
56C22⋊D541—21no—
57C22⋊D541—22no—
58C22⋊D541—22no—
59C22⋊D541—21no—
60C2×Dic541—21no—
61C2×Dic541D411yescharacteristic
62C4×D541—21no—
63C4×D541—21no—
64C4×D541—21no—
65C4×D541D411yescharacteristic
66C4×D541D411yescharacteristic
67C4×D541C2311yescharacteristic
68C4×D541C2311yescharacteristic
69#16864513C2312yescomplemented
70C23×C541—21no—
71Q8×C541C2311yescharacteristic, complemented
72D4×C541—21no—
73D4×C541—21no—
74D4×C541C2312yes—
75D4×C541C2311yescharacteristic, complemented
76C2×C4×C541—21no—
77C2×C4×C541C2311yescharacteristic
78C8×C541C2312yescomplemented
79C22×C541—22no—
80C22×C541—21no—
81C22×C541—42no—
82C22×C541C2×D411yescharacteristic
83C2×D541—22no—
84C2×D541—21no—
85C2×D541—22no—
86C2×D541—44no—
87C2×D541—42no—
88C2×D541—42no—
89C2×D541—44no—
90C2×D541C2×D411yescharacteristic
91C2×D541C2×D411yescharacteristic
92C4×C541—21no—
93C4×C541C2×D411yescharacteristic
94C4×C541C2411yescharacteristic
95Dic541—21no—
96Dic541C2×D411yescharacteristic
97Dic541C2×D411yescharacteristic
98C2×C541—21no—
99C2×C541—42no—
100C2×C541—41no—
101C2×C541C22×D411yescharacteristic
102D541—21no—
103D541—41no—
104D541—42no—
105D541AGL(1,ℤ/8)12yesdirect product factor
106C541C2×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
107C2×AGL(1,ℤ/8)—5411nomaximal, Sylow
108C2×#41—5411no—
109C22×D4—5411no—
110AGL(1,ℤ/8)—5411no—
111AGL(1,ℤ/8)—5411no—
112AGL(1,ℤ/8)—5412no—
113AGL(1,ℤ/8)—5412no—
114AGL(1,ℤ/8)—5411no—
115AGL(1,ℤ/8)D54111yescharacteristic, direct product factor
116C2×SD16—5412no—
117C2×D8—5412no—
118C2×M16—5411no—
119C24—10821no—
120#41—5411no—
121#41—5411no—
122#41—5411no—
123#41—10821no—
124#41—10821no—
125#41C2×D54111yescharacteristic, complemented
126C2×Q8—5411no—
127C2×D4—5412no—
128C2×D4—5412no—
129C2×D4—5411no—
130C2×D4—5411no—
131C2×D4—10821no—
132C2×D4—10821no—
133C2×D4—10821no—
134C2×D4—10821no—
135C2×D4C2×D54111yescharacteristic, complemented
136C22×C4—5411no—
137C22×C4—10821no—
138SD16—5412no—
139SD16—5412no—
140SD16—5412no—
141SD16C2×D54112yescomplemented
142D8—5412no—
143D8—5412no—
144D8—5412no—
145D8C2×D54112yescomplemented
146M16—5411no—
147M16—5412no—
148M16C2×D54111yescharacteristic, complemented
149C2×C8—5412no—
150C23—21no—
151C23—5411no—
152C23—10821no—
153C23—10822no—
154C23—10822no—
155C23—10821no—
156C23—21644no—
157Q8—5411no—
158Q8—10821no—
159Q8C22×D54111yescharacteristic, complemented
160D4—21no—
161D4—21no—
162D4—5412no—
163D4—5411no—
164D4—10821no—
165D4—10822no—
166D4—10822no—
167D4—10821no—
168D4—10821no—
169D4—10821no—
170D4—10821no—
171D4C22×D54112yes—
172D4C22×D54111yescharacteristic, complemented
173C2×C4—21no—
174C2×C4—5411no—
175C2×C4—5411no—
176C2×C4—5411no—
177C2×C4—5411no—
178C2×C4—5411no—
179C2×C4—10821no—
180C2×C4—10821no—
181C2×C4—10821no—
182C2×C4—10821no—
183C2×C4C22×D54111yescharacteristic
184C8—5412no—
185C8C22×D54112yescomplemented
186C22—21no—
187C22—22no—
188C22—42no—
189C22—5411no—
190C22—5411no—
191C22—10822no—
192C22—10821no—
193C22—10822no—
194C22—21642no—
195C22—21644no—
196C22—21642no—
197C22—21644no—
198C22D4×D54111yescharacteristic
199C4—21no—
200C4—5411no—
201C4—5411no—
202C4—10821no—
203C4D4×D54111yescharacteristic
204C4C23×D54111yescharacteristic
205C2—21no—
206C2—42no—
207C2—41no—
208C2—5412no—
209C2—10821no—
210C2—21642no—
211C2—21641no—
212C2C2×D4×D54111yescharacteristic
subgroupG/H
centerC2C2×D4×D541
commutator, cosocleC4×C541C24
FrattiniC4C23×D541
FittingAGL(1,ℤ/8)×C541C2
socleC2×C541C22×D4
hypercenterAGL(1,ℤ/8)D541
hypocenterC541C2×AGL(1,ℤ/8)
LCSG ▷ C4×C541 ▷ C2×C541 ▷ C541
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #41×D541C2semidirect
2. C2×D4×D541C2semidirect
3. #31772656C2semidirect
4. #31772655C2semidirect
5. #31772654C2semidirect
6. #31772653C2semidirect
7. #31772652C2semidirect
8. SD16×D541C2semidirect
9. D8×D541C2semidirect
10. M16×D541C2semidirect
11. AGL(1,ℤ/8)×C541C2semidirect
13. #22575837C22semidirect
15. #22575836C22semidirect
17. #22575835C22semidirect
18. Q8×D541C22semidirect
19. C2×D2164C22semidirect
25. D4×D541C22semidirect
26. D4×D541C22semidirect
29. #22575825C22semidirect
30. #22575824C22semidirect
31. #22575823C22semidirect
32. D4328C22semidirect
33. #22575821C22semidirect
34. #22575821C22semidirect
35. #22575820C22semidirect
36. #22575819C22semidirect
37. C8×D541C22semidirect
38. #41×C541C22semidirect
39. C2×D4×C541C22semidirect
40. SD16×C541C22semidirect
41. D8×C541C22semidirect
42. M16×C541C22semidirect
50. Dic1082C23semidirect
54. D2164C23semidirect
69. #16864513C23semidirect
71. Q8×C541C23semidirect
75. D4×C541C23semidirect
78. C8×C541C23semidirect
105. D541AGL(1,ℤ/8)direct (N × H)
106. C541C2×AGL(1,ℤ/8)semidirect
115. AGL(1,ℤ/8)D541direct (N × H)
125. #41C2×D541semidirect
135. C2×D4C2×D541semidirect
141. SD16C2×D541semidirect
145. D8C2×D541semidirect
148. M16C2×D541semidirect
159. Q8C22×D541semidirect
172. D4C22×D541semidirect
185. C8C22×D541semidirect

Maximal subgroups

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

subgroupindex
#41×D5412
C2×D4×D5412
#317726562
#317726552
#317726542
#317726532
#317726522
SD16×D5412
D8×D5412
M16×D5412
AGL(1,ℤ/8)×C5412
C2×AGL(1,ℤ/8)541