Finite Group Databasebeta

← #43244411

Subgroups — #43244411

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#28380789C211yesmaximal, characteristic, complemented
3#28380775C212yesmaximal, complemented
4#28380773C211yesmaximal, characteristic, complemented
5#28380768C211yesmaximal, characteristic, complemented
6#28380767C212yesmaximal, complemented
7#28380764C212yesmaximal, complemented
8C2×#20296318C211yesmaximal, characteristic, complemented
9SD16×D439C212yesmaximal, complemented
10#28380749C211yesmaximal, characteristic, complemented
11#135×C439C211yesmaximal, characteristic, complemented
12#20296330C2212yes—
13#20296329—21no—
14#20296329—21no—
15#20296329C2211yescharacteristic
16#20296328—22no—
17#20296328C2212yescomplemented
18C2×Dic878—21no—
19C2×Dic878C2211yescharacteristic, complemented
20Q8×D439C2212yescomplemented
21C2×D1756—21no—
22C2×D1756C2211yescharacteristic
23D4×D439—22no—
24D4×D439C2212yes—
25#20296319C2212yescomplemented
26#20296318C2212yescomplemented
27#20296318C2212yescomplemented
28#20296317C2212yescomplemented
29#20296316C2212yescomplemented
30#20296314C2212yescomplemented
31#20296313C2211yescharacteristic, complemented
32#20296312C2212yescomplemented
33C8×D439C2212yescomplemented
34#41×C439C2211yescharacteristic
35#41×C439C2211yescharacteristic, complemented
36Q16×C439C2211yescharacteristic, complemented
37SD16×C439C2211yescharacteristic, complemented
38SD16×C439C2211yescharacteristic, complemented
39D8×C439C2211yescharacteristic, complemented
40C2×C8×C439C2211yescharacteristic, complemented
41C22×D439—21no—
42C22×D439—22no—
43Dic878—21no—
44Dic878—22no—
45Dic878D411yescharacteristic
46Dic878C2312yes—
47D1756—22no—
48D1756—21no—
49D1756D411yescharacteristic
50D1756C2312yes—
51C22⋊D439—22no—
52C22⋊D439—22no—
53C22⋊D439D412yes—
54C2×Dic439—21no—
55C2×Dic439—22no—
56C4×D439—22no—
57C4×D439—22no—
58C4×D439C2312yes—
59C439⋊C8C2312yes—
60Q8×C439C2311yescharacteristic
61Q8×C439C2311yescharacteristic
62D4×C439—21no—
63D4×C439—21no—
64D4×C439C2311yescharacteristic
65D4×C439C2311yescharacteristic
66C2×C4×C439—21no—
67C2×C4×C439—21no—
68C2×C4×C439C2311yescharacteristic
69C8×C439C2311yescharacteristic
70C8×C439C2311yescharacteristic
71C22×C439—21no—
72C22×C439—21no—
73C22×C439C2×D411yescharacteristic
74C2×D439—22no—
75C2×D439—82no—
76C2×D439—81no—
77C2×D439C2×D412yes—
78C4×C439—21no—
79C4×C439—21no—
80C4×C439C2×D411yescharacteristic
81C4×C439C2411yescharacteristic
82Dic439—22no—
83Dic439C2×D412yes—
84C2×C439—21no—
85C2×C439—41no—
86C2×C439—41no—
87C2×C439C22×D411yescharacteristic
88D439—22no—
89D439—42no—
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#135D43911yescharacteristic, complemented
100C2×SD16—4392no—
101C2×SD16—4391no—
102#131—4391no—
103#41—8781no—
104#41—8781no—
105#41—8782no—
106#41—4392no—
107#41—4392no—
108#41—4391no—
109#41C2×D43911yescharacteristic
110#41C2×D43911yescharacteristic, complemented
111C2×Q8—8781no—
112C2×Q8—4392no—
113C2×Q8—4391no—
114C2×D4—8781no—
115C2×D4—8782no—
116C2×D4—4392no—
117C2×D4—4391no—
118Q16—4392no—
119Q16C2×D43911yescharacteristic, complemented
120SD16—4392no—
121SD16—4392no—
122SD16—4392no—
123SD16—4392no—
124SD16C2×D43911yescharacteristic, complemented
125SD16C2×D43911yescharacteristic, complemented
126D8—4392no—
127D8C2×D43911yescharacteristic, complemented
128M16—4391no—
129M16—4392no—
130C2×C8—4392no—
131C2×C8C2×D43911yescharacteristic, complemented
132C23—8782no—
133C23—8781no—
134Q8—8782no—
135Q8—8781no—
136Q8—4392no—
137Q8—4391no—
138Q8C22×D43911yescharacteristic
139Q8C22×D43911yescharacteristic
140D4—21no—
141D4—21no—
142D4—8782no—
143D4—8782no—
144D4—8782no—
145D4—8781no—
146D4—4392no—
147D4—4391no—
148D4—4392no—
149D4C22×D43911yescharacteristic
150D4C22×D43911yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—8782no—
154C2×C4—8782no—
155C2×C4—8781no—
156C2×C4—8782no—
157C2×C4—4392no—
158C2×C4C22×D43911yescharacteristic
159C8—4392no—
160C8C22×D43911yescharacteristic
161C8C22×D43911yescharacteristic
162C22—21no—
163C22—21no—
164C22—8782no—
165C22—4392no—
166C22—35121no—
167C22—35122no—
168C22D4×D43911yescharacteristic
169C4—21no—
170C4—21no—
171C4—8782no—
172C4—4392no—
173C4D4×D43911yescharacteristic
174C4C23×D43911yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—8782no—
179C2—17562no—
180C2C2×D4×D43911yescharacteristic
subgroupG/H
centerC2C2×D4×D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
Fitting#135×C439C2
socleC2×C439C22×D4
hypercenter#135D439
hypocenterC439#577
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #28380790C2semidirect
2. #28380789C2semidirect
3. #28380775C2semidirect
4. #28380773C2semidirect
5. #28380768C2semidirect
6. #28380767C2semidirect
7. #28380764C2semidirect
8. C2×#20296318C2semidirect
9. SD16×D439C2semidirect
10. #28380749C2semidirect
11. #135×C439C2semidirect
17. #20296328C22semidirect
19. C2×Dic878C22semidirect
20. Q8×D439C22semidirect
25. #20296319C22semidirect
26. #20296318C22semidirect
27. #20296318C22semidirect
28. #20296317C22semidirect
29. #20296316C22semidirect
30. #20296314C22semidirect
31. #20296313C22semidirect
32. #20296312C22semidirect
33. C8×D439C22semidirect
35. #41×C439C22semidirect
36. Q16×C439C22semidirect
37. SD16×C439C22semidirect
38. SD16×C439C22semidirect
39. D8×C439C22semidirect
40. C2×C8×C439C22semidirect
90. C439#577semidirect
99. #135D439semidirect
110. #41C2×D439semidirect
119. Q16C2×D439semidirect
124. SD16C2×D439semidirect
125. SD16C2×D439semidirect
127. D8C2×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
#283807902
#283807892
#283807752
#283807732
#283807682
#283807672
#283807642
C2×#202963182
SD16×D4392
#283807492
#135×C4392
#577439