Finite Group Databasebeta

← #43244401

Subgroups — #43244401

Order 28096.

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

normal subgroups only

This group has 262 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#41×D439C212yesmaximal, complemented
2#28380775C212yesmaximal, complemented
3#28380772C212yesmaximal, complemented
4#28380770C212yesmaximal, complemented
5#28380767C212yesmaximal, complemented
6#28380765C211yesmaximal, characteristic, complemented
7#28380763C212yesmaximal, complemented
8C2×#20296312C211yesmaximal, characteristic, complemented
9#135×C439C211yesmaximal, characteristic, complemented
10#20296330C2212yes—
11#20296329—22no—
12#20296329C2212yescomplemented
13#20296328—22no—
14#20296328C2212yes—
15Q8×D439C2212yescomplemented
16D4×D439—22no—
17D4×D439C2212yescomplemented
18C2×C4×D439—22no—
19C2×C4×D439C2211yescharacteristic
20Dic1756C2211yescharacteristic, complemented
21#20296319C2212yescomplemented
22#20296318C2212yescomplemented
23#20296317C2212yescomplemented
24#20296316C2212yescomplemented
25D3512C2211yescharacteristic, complemented
26#20296314C2212yescomplemented
27#20296312C2212yescomplemented
28#20296312C2212yescomplemented
29C2×C439⋊C8C2211yescharacteristic, complemented
30#41×C439C2212yescomplemented
31Q16×C439C2211yescharacteristic, complemented
32SD16×C439C2212yescomplemented
33D8×C439C2211yescharacteristic, complemented
34C2×C8×C439C2211yescharacteristic, complemented
35C22×D439—22no—
36C22×D439D411yescharacteristic
37Dic878—22no—
38Dic878C2312yes—
39D1756—22no—
40D1756C2312yes—
41C22⋊D439—22no—
42C22⋊D439—22no—
43C22⋊D439—22no—
44C2×Dic439—22no—
45C2×Dic439D411yescharacteristic
46C4×D439—22no—
47C4×D439—22no—
48C4×D439—22no—
49C4×D439D412yes—
50C4×D439C2312yes—
51C439⋊C8C2312yes—
52Q8×C439C2312yes—
53D4×C439—22no—
54D4×C439C2312yes—
55C2×C4×C439—22no—
56C2×C4×C439C2311yescharacteristic
57C8×C439C2311yescharacteristic
58C8×C439C2311yescharacteristic
59C22×C439—22no—
60C22×C439C2×D411yescharacteristic
61C2×D439—22no—
62C2×D439—41no—
63C2×D439—44no—
64C2×D439C2×D412yes—
65C4×C439—22no—
66C4×C439C2×D411yescharacteristic
67C4×C439C2411yescharacteristic
68Dic439—22no—
69Dic439C2×D412yes—
70C2×C439—21no—
71C2×C439—42no—
72C2×C439C22×D411yescharacteristic
73D439—22no—
74D439—42no—
75C439#57511yescharacteristic, complemented, Sylow
76#575—4391nomaximal, Sylow
77C2×#41—4392no—
78#137—4392no—
79#137—4392no—
80AGL(1,ℤ/8)—4392no—
81AGL(1,ℤ/8)—4392no—
82#135—4392no—
83#135—4391no—
84#135D43911yescharacteristic, complemented
85C2×M16—4391no—
86#41—8782no—
87#41—8782no—
88#41—4392no—
89#41—4392no—
90#41—4392no—
91#41C2×D43912yescomplemented
92C2×Q8—4392no—
93C2×D4—8782no—
94C2×D4—4392no—
95C22×C4—8782no—
96C22×C4—4391no—
97Q16—4392no—
98Q16—4391no—
99Q16C2×D43911yescharacteristic, complemented
100SD16—4392no—
101SD16—4392no—
102SD16—4392no—
103SD16C2×D43912yescomplemented
104D8—4392no—
105D8—4391no—
106D8C2×D43911yescharacteristic, complemented
107M16—4392no—
108M16—4392no—
109C2×C8—4391no—
110C2×C8C2×D43911yescharacteristic, complemented
111C23—8782no—
112C23—4391no—
113Q8—8782no—
114Q8—4392no—
115Q8C22×D43912yes—
116D4—22no—
117D4—8782no—
118D4—8782no—
119D4—8782no—
120D4—8782no—
121D4—4392no—
122D4C22×D43912yes—
123C2×C4—22no—
124C2×C4—8782no—
125C2×C4—8782no—
126C2×C4—8782no—
127C2×C4—8782no—
128C2×C4—4391no—
129C2×C4—4392no—
130C2×C4—4392no—
131C2×C4C22×D43911yescharacteristic
132C8—4392no—
133C8C22×D43911yescharacteristic
134C8C22×D43911yescharacteristic
135C22—22no—
136C22—8782no—
137C22—4392no—
138C22—17561no—
139C22—17564no—
140C22D4×D43911yescharacteristic
141C4—22no—
142C4—8782no—
143C4—4392no—
144C4D4×D43911yescharacteristic
145C4C23×D43911yescharacteristic
146C2—21no—
147C2—42no—
148C2—8782no—
149C2—17562no—
150C2C2×D4×D43911yescharacteristic
subgroupG/H
centerC4D4×D439
commutator, cosocleC4×C439C24
FrattiniC4C23×D439
Fitting#135×C439C2
socleC2×C439C22×D4
hypercenter#135D439
hypocenterC439#575
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D439C2semidirect
2. #28380775C2semidirect
3. #28380772C2semidirect
4. #28380770C2semidirect
5. #28380767C2semidirect
6. #28380765C2semidirect
7. #28380763C2semidirect
8. C2×#20296312C2semidirect
9. #135×C439C2semidirect
12. #20296329C22semidirect
15. Q8×D439C22semidirect
17. D4×D439C22semidirect
20. Dic1756C22semidirect
21. #20296319C22semidirect
22. #20296318C22semidirect
23. #20296317C22semidirect
24. #20296316C22semidirect
25. D3512C22semidirect
26. #20296314C22semidirect
27. #20296312C22semidirect
28. #20296312C22semidirect
29. C2×C439⋊C8C22semidirect
30. #41×C439C22semidirect
31. Q16×C439C22semidirect
32. SD16×C439C22semidirect
33. D8×C439C22semidirect
34. C2×C8×C439C22semidirect
75. C439#575semidirect
84. #135D439semidirect
91. #41C2×D439semidirect
99. Q16C2×D439semidirect
103. SD16C2×D439semidirect
106. D8C2×D439semidirect
110. C2×C8C2×D439semidirect

Maximal subgroups

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

subgroupindex
#41×D4392
#283807752
#283807722
#283807702
#283807672
#283807652
#283807632
C2×#202963122
#135×C4392
#575439