Finite Group Databasebeta

← #43244410

Subgroups — #43244410

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#28380791C211yesmaximal, characteristic, complemented
2#28380788C211yesmaximal, characteristic, complemented
3#28380774C211yesmaximal, characteristic, complemented
4#28380772C212yesmaximal, complemented
5#28380770C212yesmaximal, complemented
6#28380769C211yesmaximal, characteristic, complemented
7#28380765C211yesmaximal, characteristic, complemented
8#28380764C212yesmaximal, complemented
9SD16×D439C212yesmaximal, complemented
10#28380749C211yesmaximal, characteristic, complemented
11C2×SD16×C439C211yesmaximal, characteristic, complemented
12#20296330—21no—
13#20296330C2212yescomplemented
14#20296329—22no—
15#20296329C2211yescharacteristic
16#20296329C2211yescharacteristic
17#20296329C2211yescharacteristic, complemented
18#20296328—21no—
19#20296328C2212yes—
20Q8×D439—21no—
21Q8×D439C2212yescomplemented
22C2×C22⋊D439—22no—
23D4×D439—21no—
24D4×D439C2212yes—
25Dic1756C2211yescharacteristic, complemented
26#20296319C2212yescomplemented
27#20296318C2211yescharacteristic, complemented
28#20296318C2211yescharacteristic, complemented
29#20296317C2212yescomplemented
30#20296316C2212yescomplemented
31D3512C2211yescharacteristic, complemented
32#20296314C2212yescomplemented
33#20296313C2211yescharacteristic, complemented
34#20296312C2212yescomplemented
35C8×D439C2212yescomplemented
36C2×Q8×C439C2211yescharacteristic, complemented
37C2×D4×C439C2211yescharacteristic
38SD16×C439C2212yescomplemented
39SD16×C439C2212yescomplemented
40C2×C8×C439C2211yescharacteristic, complemented
41C22×D439—22no—
42Dic878—22no—
43Dic878D411yescharacteristic
44Dic878C2311yescharacteristic
45Dic878C2311yescharacteristic
46D1756—22no—
47D1756D411yescharacteristic
48D1756C2311yescharacteristic
49D1756C2311yescharacteristic
50C22⋊D439—21no—
51C22⋊D439—21no—
52C22⋊D439—22no—
53C22⋊D439—22no—
54C22⋊D439D412yes—
55C2×Dic439—22no—
56C4×D439—22no—
57C4×D439—21no—
58C4×D439—21no—
59C4×D439—22no—
60C4×D439C2312yes—
61C439⋊C8C2312yes—
62C23×C439—21no—
63Q8×C439—21no—
64Q8×C439C2312yes—
65D4×C439—21no—
66D4×C439C2312yes—
67C2×C4×C439—21no—
68C2×C4×C439C2311yescharacteristic
69C8×C439C2311yescharacteristic
70C8×C439C2311yescharacteristic
71C22×C439—22no—
72C22×C439—81no—
73C22×C439C2×D411yescharacteristic
74C2×D439—21no—
75C2×D439—21no—
76C2×D439—82no—
77C2×D439C2×D412yes—
78C4×C439—22no—
79C4×C439C2×D411yescharacteristic
80C4×C439C2411yescharacteristic
81Dic439—21no—
82Dic439—21no—
83Dic439C2×D412yes—
84C2×C439—21no—
85C2×C439—42no—
86C2×C439C22×D411yescharacteristic
87D439—22no—
88D439—41no—
89D439—41no—
90C439#57711yescharacteristic, complemented, Sylow
91#577—4391nomaximal, Sylow
922−1+4—4391no—
93H(5,𝔽2)—4391no—
94#137—4391no—
95#137—4392no—
96AGL(1,ℤ/8)—4391no—
97AGL(1,ℤ/8)—4392no—
98#135—4392no—
99#135—4391no—
100C2×SD16—4392no—
101C2×SD16D43911yescharacteristic, complemented
102#131—4391no—
103#41—8782no—
104#41—8781no—
105#41—8781no—
106#41—4392no—
107#41—4392no—
108#41—4391no—
109#41—4391no—
110#41—4391no—
111C2×Q8—8781no—
112C2×Q8—4392no—
113C2×Q8C2×D43911yescharacteristic, complemented
114C2×D4—8781no—
115C2×D4—8782no—
116C2×D4—4392no—
117C2×D4C2×D43911yescharacteristic
118Q16—4392no—
119Q16—4391no—
120SD16—4392no—
121SD16—4392no—
122SD16—4391no—
123SD16—4391no—
124SD16C2×D43912yescomplemented
125SD16C2×D43912yescomplemented
126D8—4392no—
127D8—4391no—
128M16—4391no—
129M16—4392no—
130C2×C8—4392no—
131C2×C8C2×D43911yescharacteristic, complemented
132C23—21no—
133C23—8782no—
134Q8—21no—
135Q8—8782no—
136Q8—4391no—
137Q8—4391no—
138Q8—4391no—
139Q8C22×D43912yes—
140D4—21no—
141D4—8782no—
142D4—8782no—
143D4—8781no—
144D4—8781no—
145D4—8782no—
146D4—4392no—
147D4—4391no—
148D4—4391no—
149D4—4391no—
150D4C22×D43912yes—
151C2×C4—21no—
152C2×C4—8782no—
153C2×C4—8782no—
154C2×C4—8782no—
155C2×C4—8781no—
156C2×C4—8781no—
157C2×C4—4392no—
158C2×C4C22×D43911yescharacteristic
159C8—4392no—
160C8C22×D43911yescharacteristic
161C8C22×D43911yescharacteristic
162C22—22no—
163C22—81no—
164C22—8781no—
165C22—8781no—
166C22—4392no—
167C22—35122no—
168C22D4×D43911yescharacteristic
169C4—22no—
170C4—8781no—
171C4—8781no—
172C4—4392no—
173C4D4×D43911yescharacteristic
174C4C23×D43911yescharacteristic
175C2—21no—
176C2—42no—
177C2—8782no—
178C2—17561no—
179C2—17561no—
180C2C2×D4×D43911yescharacteristic
subgroupG/H
centerC2C2×D4×D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
FittingC2×SD16×C439C2
socleC2×C439C22×D4
hypercenterC2×SD16D439
hypocenterC439#577
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #28380791C2semidirect
2. #28380788C2semidirect
3. #28380774C2semidirect
4. #28380772C2semidirect
5. #28380770C2semidirect
6. #28380769C2semidirect
7. #28380765C2semidirect
8. #28380764C2semidirect
9. SD16×D439C2semidirect
10. #28380749C2semidirect
11. C2×SD16×C439C2semidirect
13. #20296330C22semidirect
17. #20296329C22semidirect
21. Q8×D439C22semidirect
25. Dic1756C22semidirect
26. #20296319C22semidirect
27. #20296318C22semidirect
28. #20296318C22semidirect
29. #20296317C22semidirect
30. #20296316C22semidirect
31. D3512C22semidirect
32. #20296314C22semidirect
33. #20296313C22semidirect
34. #20296312C22semidirect
35. C8×D439C22semidirect
36. C2×Q8×C439C22semidirect
38. SD16×C439C22semidirect
39. SD16×C439C22semidirect
40. C2×C8×C439C22semidirect
90. C439#577semidirect
101. C2×SD16D439semidirect
113. C2×Q8C2×D439semidirect
124. SD16C2×D439semidirect
125. SD16C2×D439semidirect
131. C2×C8C2×D439semidirect

Maximal subgroups

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

subgroupindex
#283807912
#283807882
#283807742
#283807722
#283807702
#283807692
#283807652
#283807642
SD16×D4392
#283807492
C2×SD16×C4392
#577439