Finite Group Databasebeta

← #44442880

Subgroups — #44442880

Order 29504.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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#28414164C211yesmaximal, characteristic, complemented
2#28414163C211yesmaximal, characteristic, complemented
3#28414146C211yesmaximal, characteristic, complemented
4#28414145C212yesmaximal, complemented
5#28414142C212yesmaximal, complemented
6#28414139C212yesmaximal, complemented
7#28414138C211yesmaximal, characteristic, complemented
8C2×#20301486C211yesmaximal, characteristic, complemented
9D8×D461C212yesmaximal, complemented
10#28414126C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C461C211yesmaximal, characteristic, complemented
12#20301502C2212yescomplemented
13#20301501—21no—
14#20301501C2211yescharacteristic
15#20301501C2211yescharacteristic, complemented
16#20301500—21no—
17#20301500C2212yescomplemented
18C2×D1844—21no—
19C2×D1844C2211yescharacteristic, complemented
20C2×C22⋊D461—22no—
21D4×D461—21no—
22D4×D461—22no—
23D4×D461C2212yescomplemented
24D4×D461C2212yescomplemented
25#20301491C2211yescharacteristic, complemented
26#20301490C2212yescomplemented
27#20301489C2211yescharacteristic, complemented
28#20301488C2211yescharacteristic, complemented
29D3688C2212yescomplemented
30#20301486C2211yescharacteristic, complemented
31#20301486C2212yescomplemented
32#20301486C2212yescomplemented
33#20301484C2212yescomplemented
34C2×#16814779C2211yescharacteristic, complemented
35C8×D461C2212yescomplemented
36#41×C461C2211yescharacteristic, complemented
37C2×D4×C461C2211yescharacteristic, complemented
38SD16×C461C2212yescomplemented
39D8×C461C2212yescomplemented
40M16×C461C2211yescharacteristic, complemented
41C22×D461—21no—
42C22×D461—22no—
43C22×D461—22no—
44Dic922D411yescharacteristic
45Dic922C2311yescharacteristic
46D1844—22no—
47D1844—21no—
48D1844D411yescharacteristic
49D1844C2312yes—
50D1844C2311yescharacteristic
51C22⋊D461—21no—
52C22⋊D461—22no—
53C22⋊D461—22no—
54C22⋊D461—22no—
55C22⋊D461D412yes—
56C2×Dic461—22no—
57C4×D461—21no—
58C4×D461—22no—
59C4×D461C2312yes—
60#16814779C2311yescharacteristic
61#16814779C2311yescharacteristic
62C23×C461—21no—
63Q8×C461C2311yescharacteristic
64D4×C461—21no—
65D4×C461—21no—
66D4×C461C2311yescharacteristic
67D4×C461C2312yes—
68C2×C4×C461—21no—
69C2×C4×C461C2311yescharacteristic
70C8×C461C2312yes—
71C22×C461—21no—
72C22×C461—22no—
73C22×C461—81no—
74C22×C461C2×D411yescharacteristic
75C2×D461—21no—
76C2×D461—22no—
77C2×D461—82no—
78C2×D461—82no—
79C2×D461—81no—
80C2×D461C2×D412yes—
81C4×C461—21no—
82C4×C461C2×D411yescharacteristic
83C4×C461C2411yescharacteristic
84Dic461—21no—
85Dic461C2×D412yes—
86C2×C461—21no—
87C2×C461—41no—
88C2×C461—42no—
89C2×C461C22×D411yescharacteristic
90D461—22no—
91D461—41no—
92D461—42no—
93C461#57611yescharacteristic, complemented, Sylow
94#576—4611nomaximal, Sylow
95H(5,𝔽2)—4611no—
96H(5,𝔽2)—4611no—
97AGL(1,ℤ/8)—4612no—
98AGL(1,ℤ/8)—4612no—
99AGL(1,ℤ/8)—4611no—
100AGL(1,ℤ/8)D46111yescharacteristic, complemented
101#135—4611no—
102#135—4612no—
103C2×D8—4611no—
104C2×D8—4612no—
105#131—4611no—
106#41—9221no—
107#41—9221no—
108#41—4612no—
109#41—4612no—
110#41—4611no—
111#41—4611no—
112#41C2×D46111yescharacteristic, complemented
113C2×D4—9221no—
114C2×D4—9222no—
115C2×D4—9221no—
116C2×D4—9222no—
117C2×D4—4612no—
118C2×D4—4612no—
119C2×D4—4611no—
120C2×D4C2×D46111yescharacteristic, complemented
121Q16—4611no—
122SD16—4611no—
123SD16—4611no—
124SD16—4612no—
125SD16C2×D46112yescomplemented
126D8—4612no—
127D8—4611no—
128D8—4612no—
129D8—4612no—
130D8C2×D46112yescomplemented
131M16—4612no—
132M16C2×D46111yescharacteristic, complemented
133C2×C8—4611no—
134C2×C8—4612no—
135C23—21no—
136C23—9222no—
137C23—9222no—
138C23—9221no—
139Q8—4611no—
140Q8—4611no—
141Q8C22×D46111yescharacteristic
142D4—21no—
143D4—21no—
144D4—9222no—
145D4—9222no—
146D4—9221no—
147D4—9222no—
148D4—9222no—
149D4—9221no—
150D4—4612no—
151D4—4611no—
152D4—4612no—
153D4—4611no—
154D4C22×D46112yes—
155D4C22×D46111yescharacteristic
156C2×C4—21no—
157C2×C4—9222no—
158C2×C4—9222no—
159C2×C4—9221no—
160C2×C4—4612no—
161C2×C4C22×D46111yescharacteristic
162C8—4611no—
163C8—4611no—
164C8C22×D46112yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—36881no—
169C22—36882no—
170C22—36882no—
171C22—9222no—
172C22—9221no—
173C22—4612no—
174C22D4×D46111yescharacteristic
175C4—21no—
176C4—9221no—
177C4—4612no—
178C4D4×D46111yescharacteristic
179C4C23×D46111yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—18442no—
184C2—18441no—
185C2—9222no—
186C2C2×D4×D46111yescharacteristic
subgroupG/H
centerC2C2×D4×D461
commutator, cosocleC4×C461C24
FrattiniC4C23×D461
FittingAGL(1,ℤ/8)×C461C2
socleC2×C461C22×D4
hypercenterAGL(1,ℤ/8)D461
hypocenterC461#576
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28414164C2semidirect
2. #28414163C2semidirect
3. #28414146C2semidirect
4. #28414145C2semidirect
5. #28414142C2semidirect
6. #28414139C2semidirect
7. #28414138C2semidirect
8. C2×#20301486C2semidirect
9. D8×D461C2semidirect
10. #28414126C2semidirect
11. AGL(1,ℤ/8)×C461C2semidirect
12. #20301502C22semidirect
15. #20301501C22semidirect
17. #20301500C22semidirect
19. C2×D1844C22semidirect
23. D4×D461C22semidirect
24. D4×D461C22semidirect
25. #20301491C22semidirect
26. #20301490C22semidirect
27. #20301489C22semidirect
28. #20301488C22semidirect
29. D3688C22semidirect
30. #20301486C22semidirect
31. #20301486C22semidirect
32. #20301486C22semidirect
33. #20301484C22semidirect
34. C2×#16814779C22semidirect
35. C8×D461C22semidirect
36. #41×C461C22semidirect
37. C2×D4×C461C22semidirect
38. SD16×C461C22semidirect
39. D8×C461C22semidirect
40. M16×C461C22semidirect
93. C461#576semidirect
100. AGL(1,ℤ/8)D461semidirect
112. #41C2×D461semidirect
120. C2×D4C2×D461semidirect
125. SD16C2×D461semidirect
130. D8C2×D461semidirect
132. M16C2×D461semidirect

Maximal subgroups

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

subgroupindex
#284141642
#284141632
#284141462
#284141452
#284141422
#284141392
#284141382
C2×#203014862
D8×D4612
#284141262
AGL(1,ℤ/8)×C4612
#576461