Finite Group Databasebeta

← #43244408

Subgroups — #43244408

Order 28096.

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#28380789C211yesmaximal, characteristic, complemented
2#28380788C211yesmaximal, characteristic, complemented
3#28380771C211yesmaximal, characteristic, complemented
4#28380770C212yesmaximal, complemented
5#28380767C212yesmaximal, complemented
6#28380764C212yesmaximal, complemented
7#28380763C211yesmaximal, characteristic, complemented
8C2×#20296314C211yesmaximal, characteristic, complemented
9D8×D439C212yesmaximal, complemented
10#28380751C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C439C211yesmaximal, characteristic, complemented
12#20296330C2212yescomplemented
13#20296329—21no—
14#20296329C2211yescharacteristic
15#20296329C2211yescharacteristic, complemented
16#20296328—21no—
17#20296328C2212yescomplemented
18C2×D1756—21no—
19C2×D1756C2211yescharacteristic, complemented
20C2×C22⋊D439—22no—
21D4×D439—21no—
22D4×D439—22no—
23D4×D439C2212yescomplemented
24D4×D439C2212yescomplemented
25#20296319C2211yescharacteristic, complemented
26#20296318C2212yescomplemented
27#20296317C2211yescharacteristic, complemented
28#20296316C2211yescharacteristic, complemented
29D3512C2212yescomplemented
30#20296314C2211yescharacteristic, complemented
31#20296314C2212yescomplemented
32#20296314C2212yescomplemented
33#20296312C2212yescomplemented
34C2×C439⋊C8C2211yescharacteristic, complemented
35C8×D439C2212yescomplemented
36#41×C439C2211yescharacteristic, complemented
37C2×D4×C439C2211yescharacteristic, complemented
38SD16×C439C2212yescomplemented
39D8×C439C2212yescomplemented
40M16×C439C2211yescharacteristic, complemented
41C22×D439—21no—
42C22×D439—22no—
43C22×D439—22no—
44Dic878D411yescharacteristic
45Dic878C2311yescharacteristic
46D1756—22no—
47D1756—21no—
48D1756D411yescharacteristic
49D1756C2312yes—
50D1756C2311yescharacteristic
51C22⋊D439—21no—
52C22⋊D439—22no—
53C22⋊D439—22no—
54C22⋊D439—22no—
55C22⋊D439D412yes—
56C2×Dic439—22no—
57C4×D439—21no—
58C4×D439—22no—
59C4×D439C2312yes—
60C439⋊C8C2311yescharacteristic
61C439⋊C8C2311yescharacteristic
62C23×C439—21no—
63Q8×C439C2311yescharacteristic
64D4×C439—21no—
65D4×C439—21no—
66D4×C439C2311yescharacteristic
67D4×C439C2312yes—
68C2×C4×C439—21no—
69C2×C4×C439C2311yescharacteristic
70C8×C439C2312yes—
71C22×C439—21no—
72C22×C439—22no—
73C22×C439—81no—
74C22×C439C2×D411yescharacteristic
75C2×D439—21no—
76C2×D439—22no—
77C2×D439—82no—
78C2×D439—82no—
79C2×D439—81no—
80C2×D439C2×D412yes—
81C4×C439—21no—
82C4×C439C2×D411yescharacteristic
83C4×C439C2411yescharacteristic
84Dic439—21no—
85Dic439C2×D412yes—
86C2×C439—21no—
87C2×C439—41no—
88C2×C439—42no—
89C2×C439C22×D411yescharacteristic
90D439—22no—
91D439—41no—
92D439—42no—
93C439#57611yescharacteristic, complemented, Sylow
94#576—4391nomaximal, Sylow
95H(5,𝔽2)—4391no—
96H(5,𝔽2)—4391no—
97AGL(1,ℤ/8)—4392no—
98AGL(1,ℤ/8)—4392no—
99AGL(1,ℤ/8)—4391no—
100AGL(1,ℤ/8)D43911yescharacteristic, complemented
101#135—4391no—
102#135—4392no—
103C2×D8—4391no—
104C2×D8—4392no—
105#131—4391no—
106#41—8781no—
107#41—8781no—
108#41—4392no—
109#41—4392no—
110#41—4391no—
111#41—4391no—
112#41C2×D43911yescharacteristic, complemented
113C2×D4—8781no—
114C2×D4—8782no—
115C2×D4—8781no—
116C2×D4—8782no—
117C2×D4—4392no—
118C2×D4—4392no—
119C2×D4—4391no—
120C2×D4C2×D43911yescharacteristic, complemented
121Q16—4391no—
122SD16—4391no—
123SD16—4391no—
124SD16—4392no—
125SD16C2×D43912yescomplemented
126D8—4392no—
127D8—4391no—
128D8—4392no—
129D8—4392no—
130D8C2×D43912yescomplemented
131M16—4392no—
132M16C2×D43911yescharacteristic, complemented
133C2×C8—4391no—
134C2×C8—4392no—
135C23—21no—
136C23—8782no—
137C23—8782no—
138C23—8781no—
139Q8—4391no—
140Q8—4391no—
141Q8C22×D43911yescharacteristic
142D4—21no—
143D4—21no—
144D4—8782no—
145D4—8782no—
146D4—8781no—
147D4—8782no—
148D4—8782no—
149D4—8781no—
150D4—4392no—
151D4—4391no—
152D4—4392no—
153D4—4391no—
154D4C22×D43912yes—
155D4C22×D43911yescharacteristic
156C2×C4—21no—
157C2×C4—8782no—
158C2×C4—8782no—
159C2×C4—8781no—
160C2×C4—4392no—
161C2×C4C22×D43911yescharacteristic
162C8—4391no—
163C8—4391no—
164C8C22×D43912yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—8782no—
169C22—8781no—
170C22—4392no—
171C22—35121no—
172C22—35122no—
173C22—35122no—
174C22D4×D43911yescharacteristic
175C4—21no—
176C4—8781no—
177C4—4392no—
178C4D4×D43911yescharacteristic
179C4C23×D43911yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—8782no—
184C2—17562no—
185C2—17561no—
186C2C2×D4×D43911yescharacteristic
subgroupG/H
centerC2C2×D4×D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
FittingAGL(1,ℤ/8)×C439C2
socleC2×C439C22×D4
hypercenterAGL(1,ℤ/8)D439
hypocenterC439#576
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #28380789C2semidirect
2. #28380788C2semidirect
3. #28380771C2semidirect
4. #28380770C2semidirect
5. #28380767C2semidirect
6. #28380764C2semidirect
7. #28380763C2semidirect
8. C2×#20296314C2semidirect
9. D8×D439C2semidirect
10. #28380751C2semidirect
11. AGL(1,ℤ/8)×C439C2semidirect
12. #20296330C22semidirect
15. #20296329C22semidirect
17. #20296328C22semidirect
19. C2×D1756C22semidirect
23. D4×D439C22semidirect
24. D4×D439C22semidirect
25. #20296319C22semidirect
26. #20296318C22semidirect
27. #20296317C22semidirect
28. #20296316C22semidirect
29. D3512C22semidirect
30. #20296314C22semidirect
31. #20296314C22semidirect
32. #20296314C22semidirect
33. #20296312C22semidirect
34. C2×C439⋊C8C22semidirect
35. C8×D439C22semidirect
36. #41×C439C22semidirect
37. C2×D4×C439C22semidirect
38. SD16×C439C22semidirect
39. D8×C439C22semidirect
40. M16×C439C22semidirect
93. C439#576semidirect
100. AGL(1,ℤ/8)D439semidirect
112. #41C2×D439semidirect
120. C2×D4C2×D439semidirect
125. SD16C2×D439semidirect
130. D8C2×D439semidirect
132. M16C2×D439semidirect

Maximal subgroups

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

subgroupindex
#283807892
#283807882
#283807712
#283807702
#283807672
#283807642
#283807632
C2×#202963142
D8×D4392
#283807512
AGL(1,ℤ/8)×C4392
#576439