Finite Group Databasebeta

← #43244414

Subgroups — #43244414

Order 28096.

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

normal subgroups only

This group has 258 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#28380790C211yesmaximal, characteristic, complemented
2#28380788C211yesmaximal, characteristic, complemented
3#28380776C211yesmaximal, characteristic, complemented
4#28380772C212yesmaximal, complemented
5#28380767C212yesmaximal, complemented
6#28380763C211yesmaximal, characteristic, complemented
7#28380762C212yesmaximal, complemented
8C2×#20296317C211yesmaximal, characteristic, complemented
9SD16×D439C212yesmaximal, complemented
10#28380751C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C439C211yesmaximal, characteristic, complemented
12#20296329—21no—
13#20296329C2211yescharacteristic
14#20296329C2211yescharacteristic
15#20296328—21no—
16#20296328—22no—
17#20296328C2212yes—
18#20296328C2212yescomplemented
19C2×Dic878—21no—
20C2×Dic878C2211yescharacteristic, complemented
21Q8×D439C2212yescomplemented
22C2×C22⋊D439—22no—
23D4×D439—21no—
24D4×D439C2212yes—
25Dic1756C2212yescomplemented
26#20296319C2211yescharacteristic, complemented
27#20296318C2212yescomplemented
28#20296317C2212yescomplemented
29#20296317C2212yescomplemented
30#20296317C2211yescharacteristic, complemented
31#20296316C2211yescharacteristic, complemented
32#20296314C2211yescharacteristic, complemented
33#20296312C2212yescomplemented
34C2×C439⋊C8C2211yescharacteristic, complemented
35C8×D439C2212yescomplemented
36#41×C439C2211yescharacteristic, complemented
37C2×D4×C439C2211yescharacteristic
38SD16×C439C2212yescomplemented
39D8×C439C2212yescomplemented
40M16×C439C2211yescharacteristic, complemented
41C22×D439—22no—
42Dic878—21no—
43Dic878—22no—
44Dic878D411yescharacteristic
45Dic878C2312yes—
46Dic878C2311yescharacteristic
47D1756D411yescharacteristic
48D1756C2311yescharacteristic
49C22⋊D439—21no—
50C22⋊D439—22no—
51C22⋊D439—22no—
52C22⋊D439—22no—
53C22⋊D439D412yes—
54C2×Dic439—21no—
55C2×Dic439—22no—
56C2×Dic439—22no—
57C4×D439—22no—
58C4×D439—21no—
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—82no—
77C2×D439C2×D412yes—
78C4×C439—21no—
79C4×C439C2×D411yescharacteristic
80C4×C439C2411yescharacteristic
81Dic439—21no—
82Dic439—22no—
83Dic439C2×D412yes—
84C2×C439—21no—
85C2×C439—42no—
86C2×C439—41no—
87C2×C439C22×D411yescharacteristic
88D439—22no—
89D439—41no—
90C439#57711yescharacteristic, complemented, Sylow
91#577—4391nomaximal, Sylow
922−1+4—4391no—
93H(5,𝔽2)—4391no—
94#137—4392no—
95#137—4391no—
96AGL(1,ℤ/8)—4392no—
97AGL(1,ℤ/8)D43911yescharacteristic, complemented
98#135—4391no—
99#135—4392no—
100C2×SD16—4391no—
101C2×SD16—4392no—
102#131—4391no—
103#41—8781no—
104#41—8781no—
105#41—8782no—
106#41—4392no—
107#41—4392no—
108#41—4391no—
109#41—4391no—
110#41C2×D43911yescharacteristic, complemented
111C2×Q8—8781no—
112C2×Q8—4392no—
113C2×Q8—4391no—
114C2×D4—8781no—
115C2×D4—8782no—
116C2×D4—4392no—
117C2×D4C2×D43911yescharacteristic
118Q16—4391no—
119Q16—4392no—
120SD16—4391no—
121SD16—4392no—
122SD16—4392no—
123SD16—4391no—
124SD16—4392no—
125SD16C2×D43912yescomplemented
126D8—4391no—
127D8C2×D43912yescomplemented
128M16—4392no—
129M16C2×D43911yescharacteristic, complemented
130C2×C8—4391no—
131C2×C8—4392no—
132C23—21no—
133C23—8782no—
134Q8—8782no—
135Q8—8781no—
136Q8—4392no—
137Q8—4391no—
138Q8—4391no—
139Q8C22×D43911yescharacteristic
140D4—21no—
141D4—21no—
142D4—8782no—
143D4—8782no—
144D4—8781no—
145D4—8782no—
146D4—4392no—
147D4—4391no—
148D4—4391no—
149D4C22×D43911yescharacteristic
150D4C22×D43912yes—
151C2×C4—21no—
152C2×C4—8782no—
153C2×C4—8781no—
154C2×C4—8782no—
155C2×C4—8782no—
156C2×C4—8781no—
157C2×C4—4392no—
158C2×C4C22×D43911yescharacteristic
159C8—4391no—
160C8—4391no—
161C8C22×D43912yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—8781no—
166C22—4392no—
167C22—35122no—
168C22D4×D43911yescharacteristic
169C4—21no—
170C4—8781no—
171C4—8782no—
172C4—4392no—
173C4D4×D43911yescharacteristic
174C4C23×D43911yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—8782no—
179C2—17561no—
180C2C2×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#577
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. #28380790C2semidirect
2. #28380788C2semidirect
3. #28380776C2semidirect
4. #28380772C2semidirect
5. #28380767C2semidirect
6. #28380763C2semidirect
7. #28380762C2semidirect
8. C2×#20296317C2semidirect
9. SD16×D439C2semidirect
10. #28380751C2semidirect
11. AGL(1,ℤ/8)×C439C2semidirect
18. #20296328C22semidirect
20. C2×Dic878C22semidirect
21. Q8×D439C22semidirect
25. Dic1756C22semidirect
26. #20296319C22semidirect
27. #20296318C22semidirect
28. #20296317C22semidirect
29. #20296317C22semidirect
30. #20296317C22semidirect
31. #20296316C22semidirect
32. #20296314C22semidirect
33. #20296312C22semidirect
34. C2×C439⋊C8C22semidirect
35. C8×D439C22semidirect
36. #41×C439C22semidirect
38. SD16×C439C22semidirect
39. D8×C439C22semidirect
40. M16×C439C22semidirect
90. C439#577semidirect
97. AGL(1,ℤ/8)D439semidirect
110. #41C2×D439semidirect
125. SD16C2×D439semidirect
127. D8C2×D439semidirect
129. M16C2×D439semidirect

Maximal subgroups

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

subgroupindex
#283807902
#283807882
#283807762
#283807722
#283807672
#283807632
#283807622
C2×#202963172
SD16×D4392
#283807512
AGL(1,ℤ/8)×C4392
#577439