Finite Group Databasebeta

← #43244162

Subgroups — #43244162

Order 28096.

346 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C2×D4×D439C212yesmaximal, complemented
2#28380728C212yesmaximal, complemented
3#28380725C212yesmaximal, complemented
4#28380717C211yesmaximal, characteristic, complemented
5#28380715C212yesmaximal, complemented
6#28380713C212yesmaximal, complemented
7#28380711C212yesmaximal, complemented
8C2×(C2×D439)⋊C4C211yesmaximal, characteristic, complemented
9#121×C439C211yesmaximal, characteristic, complemented
10C23×D439C2211yescharacteristic
11C23×D439C2212yescomplemented
12C2×D1756C2212yes—
13C2×D1756C2211yescharacteristic, complemented
14C2×C22⋊D439C2212yes—
15C2×C22⋊D439C2212yescomplemented
16C2×C22⋊D439C2212yescomplemented
17D4×D439—28no—
18C22×Dic439C2211yescharacteristic, complemented
19C2×C4×D439C2212yescomplemented
20C4⋊Dic439C2211yescharacteristic, complemented
21Dic439⋊C4C2212yescomplemented
22C22⋊Dic439C2212yescomplemented
23(C2×D439)⋊C4C2212yescomplemented
24(C2×D439)⋊C4C2212yescomplemented
25(C2×D439)⋊C4C2212yescomplemented
26(C2×D439)⋊C4C2212yescomplemented
27C2×D4×C439C2212yescomplemented
28C2×D4×C439C2211yescharacteristic, complemented
29C22×C4×C439C2211yescharacteristic, complemented
30C4⋊C4×C439C2211yescharacteristic, complemented
31C22⋊C4×C439C2212yescomplemented
32C22×D439—24no—
33C22×D439—41no—
34C22×D439—41no—
35C22×D439—42no—
36C22×D439—42no—
37C22×D439D414yescomplemented
38C22×D439C2312yes—
39C22×D439C2312yes—
40D1756—24no—
41D1756—41no—
42C22⋊D439—24no—
43C22⋊D439—24no—
44C22⋊D439—42no—
45C2×Dic439—41no—
46C2×Dic439C2312yes—
47C2×Dic439C2312yes—
48C4×D439—24no—
49C23×C439C2312yes—
50C23×C439C2311yescharacteristic
51D4×C439—24no—
52D4×C439—41no—
53C2×C4×C439—41no—
54C2×C4×C439C2311yescharacteristic
55C2×C4×C439C2312yes—
56C2×C4×C439C2311yescharacteristic
57C22×C439—21no—
58C22×C439—21no—
59C22×C439—22no—
60C22×C439—22no—
61C22×C439—22no—
62C22×C439C2×D412yes—
63C22×C439C2411yescharacteristic
64C2×D439—22no—
65C2×D439—22no—
66C2×D439—22no—
67C2×D439—22no—
68C2×D439—22no—
69C2×D439—44no—
70C2×D439—48no—
71C2×D439C2×D414yes—
72C4×C439—22no—
73C4×C439—21no—
74C4×C439—21no—
75Dic439—22no—
76Dic439—22no—
77C2×C439—22no—
78C2×C439—42no—
79C2×C439C22×D411yescharacteristic
80C2×C439H(5,𝔽2)11yescharacteristic
81C2×C439H(5,𝔽2)11yescharacteristic
82D439—24no—
83D439—42no—
84C439#53411yescharacteristic, complemented, Sylow
85#534—4391nomaximal, Sylow
86C22×D4—4392no—
87#123—4392no—
88#123—4392no—
89#121—4392no—
90#121—4391no—
91#121D43911yescharacteristic, complemented
92#120—4392no—
93#120—4392no—
94C2×C22⋊C4—4391no—
95C24—4392no—
96C24—4391no—
97C2×D4—8788no—
98C2×D4—4392no—
99C2×D4—4392no—
100C2×D4—4392no—
101C2×D4—4392no—
102C2×D4—4391no—
103C2×D4C2×D43912yescomplemented
104C2×D4C2×D43911yescharacteristic, complemented
105C22×C4—4392no—
106C22×C4—4391no—
107C22×C4C2×D43911yescharacteristic, complemented
108C4⋊C4—4392no—
109C4⋊C4—4391no—
110C4⋊C4C2×D43911yescharacteristic, complemented
111C22⋊C4—4392no—
112C22⋊C4—4392no—
113C22⋊C4—4392no—
114C22⋊C4—4392no—
115C22⋊C4—4392no—
116C22⋊C4C2×D43912yescomplemented
117C23—8784no—
118C23—4392no—
119C23—4392no—
120C23—4394no—
121C23—17561no—
122C23—17561no—
123C23—17562no—
124C23—17562no—
125C23C22×D43912yes—
126C23C22×D43911yescharacteristic
127D4—24no—
128D4—41no—
129D4—8784no—
130D4—8784no—
131D4—8784no—
132D4—17561no—
133D4—17562no—
134C2×C4—41no—
135C2×C4—8784no—
136C2×C4—4392no—
137C2×C4—4392no—
138C2×C4—17561no—
139C2×C4C22×D43911yescharacteristic
140C2×C4C22×D43911yescharacteristic
141C2×C4C22×D43912yes—
142C22—21no—
143C22—21no—
144C22—22no—
145C22—22no—
146C22—22no—
147C22—8782no—
148C22—8782no—
149C22—8782no—
150C22—8782no—
151C22—8782no—
152C22—4394no—
153C22—17564no—
154C22—17568no—
155C22D4×D43912yes—
156C22C23×D43911yescharacteristic
157C4—22no—
158C4—21no—
159C4—21no—
160C4—8782no—
161C4—8782no—
162C2—22no—
163C2—42no—
164C2—8784no—
165C2—17562no—
166C2C2×D4×D43911yescharacteristic
167C2#2838078811yescharacteristic
168C2#2838078911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D439
commutator, socle, cosocleC22×C439C24
Fitting#121×C439C2
hypercenter#121D439
hypocenterC439#534
LCSG ▷ C22×C439 ▷ C439
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×D439C2semidirect
2. #28380728C2semidirect
3. #28380725C2semidirect
4. #28380717C2semidirect
5. #28380715C2semidirect
6. #28380713C2semidirect
7. #28380711C2semidirect
8. C2×(C2×D439)⋊C4C2semidirect
9. #121×C439C2semidirect
11. C23×D439C22semidirect
13. C2×D1756C22semidirect
15. C2×C22⋊D439C22semidirect
16. C2×C22⋊D439C22semidirect
18. C22×Dic439C22semidirect
19. C2×C4×D439C22semidirect
20. C4⋊Dic439C22semidirect
21. Dic439⋊C4C22semidirect
22. C22⋊Dic439C22semidirect
23. (C2×D439)⋊C4C22semidirect
24. (C2×D439)⋊C4C22semidirect
25. (C2×D439)⋊C4C22semidirect
26. (C2×D439)⋊C4C22semidirect
27. C2×D4×C439C22semidirect
28. C2×D4×C439C22semidirect
29. C22×C4×C439C22semidirect
30. C4⋊C4×C439C22semidirect
31. C22⋊C4×C439C22semidirect
37. C22×D439D4semidirect
84. C439#534semidirect
91. #121D439semidirect
103. C2×D4C2×D439semidirect
104. C2×D4C2×D439semidirect
107. C22×C4C2×D439semidirect
110. C4⋊C4C2×D439semidirect
116. C22⋊C4C2×D439semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D4392
#283807282
#283807252
#283807172
#283807152
#283807132
#283807112
C2×(C2×D439)⋊C42
#121×C4392
#534439