Finite Group Databasebeta

← #44566925

Subgroups — #44566925

Order 32192.

334 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 115 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×#22548882C211yesmaximal, characteristic, complemented
2#30632851C211yesmaximal, characteristic, complemented
3#30632845C212yesmaximal, complemented
4#30632843C211yesmaximal, characteristic, complemented
5#30632836C212yesmaximal, complemented
6#30632835C211yesmaximal, characteristic, complemented
7#30632833C212yesmaximal, complemented
8D4×Dic503C211yesmaximal, characteristic, complemented
9C4×C22⋊D503C211yesmaximal, characteristic, complemented
10C2×C22⋊Dic503C212yesmaximal, complemented
11C22×D4×C503C211yesmaximal, characteristic, complemented
12#22548882—24no—
13C2×Dic1006C2211yescharacteristic, complemented
14C2×C22⋊D503C2211yescharacteristic
15C2×C22⋊D503C2212yescomplemented
16C2×C22⋊D503C2212yescomplemented
17C22×Dic503C2212yescomplemented
18C22×Dic503C2212yescomplemented
19C2×C4×D503C2211yescharacteristic, complemented
20C4⋊Dic503C2211yescharacteristic, complemented
21Dic503⋊C4C2211yescharacteristic, complemented
22Dic503⋊C4C2212yescomplemented
23C22⋊Dic503C2211yescharacteristic
24C22⋊Dic503C2212yes—
25C22⋊Dic503C2212yescomplemented
26C22⋊Dic503C2212yescomplemented
27C22⋊Dic503C2212yescomplemented
28C22⋊Dic503C2212yescomplemented
29(C2×D503)⋊C4C2211yescharacteristic, complemented
30C4×Dic503C2211yescharacteristic, complemented
31C24×C503C2212yes—
32C2×D4×C503—24no—
33C2×D4×C503C2211yescharacteristic
34C2×D4×C503C2212yes—
35C2×D4×C503C2211yescharacteristic
36C22×C4×C503C2211yescharacteristic
37C22×D503C2311yescharacteristic
38Dic1006—22no—
39C22⋊D503—24no—
40C22⋊D503—22no—
41C22⋊D503—42no—
42C2×Dic503—24no—
43C2×Dic503—42no—
44C2×Dic503C2311yescharacteristic
45C2×Dic503C2311yescharacteristic
46C2×Dic503C2312yes—
47C2×Dic503C2311yescharacteristic
48C2×Dic503C2312yes—
49C4×D503—22no—
50C23×C503—24no—
51C23×C503—24no—
52C23×C503—42no—
53C23×C503C2312yes—
54C23×C503C2312yes—
55C23×C503C2311yescharacteristic
56D4×C503—24no—
57D4×C503—22no—
58D4×C503D414yescomplemented
59C2×C4×C503—22no—
60C2×C4×C503C2311yescharacteristic
61C2×C4×C503C2311yescharacteristic
62C22×C503—21no—
63C22×C503—22no—
64C22×C503—21no—
65C22×C503—22no—
66C22×C503—22no—
67C22×C503—22no—
68C22×C503—22no—
69C22×C503—48no—
70C22×C503C2×D414yes—
71C22×C503#4112yescomplemented
72C22×C503C2411yescharacteristic
73C2×D503—21no—
74C2×D503—21no—
75C2×D503—21no—
76C4×C503—21no—
77C4×C503C2×D412yes—
78Dic503—21no—
79Dic503—22no—
80Dic503—21no—
81Dic503—21no—
82Dic503—22no—
83C2×C503—22no—
84C2×C503—24no—
85C2×C503—42no—
86C2×C503C22×D411yescharacteristic
87C2×C503C2×#4111yescharacteristic
88C2×C503H(5,𝔽2)11yescharacteristic
89D503—41no—
90C503#54611yescharacteristic, complemented, Sylow
91#546—5031nomaximal, Sylow
92C2×#41—5031no—
93C22×D4D50311yescharacteristic, complemented
94#124—5031no—
95#123—5032no—
96C22⋊Q8—5031no—
97#121—5031no—
98#121—5032no—
99#120—5032no—
100C4×D4—5031no—
101C4×D4—5031no—
102C2×C22⋊C4—5032no—
103C24C2×D50312yes—
104#41—10064no—
105C2×Q8—5031no—
106C2×D4—24no—
107C2×D4—5032no—
108C2×D4—5031no—
109C2×D4—5032no—
110C2×D4C2×D50312yes—
111C2×D4C2×D50311yescharacteristic
112C2×D4C2×D50311yescharacteristic
113C22×C4—5032no—
114C22×C4—5032no—
115C22×C4—5031no—
116C22×C4C2×D50311yescharacteristic
117C4⋊C4—5031no—
118C4⋊C4—5031no—
119C4⋊C4—5032no—
120C22⋊C4—5031no—
121C22⋊C4—5032no—
122C22⋊C4—5032no—
123C22⋊C4—5032no—
124C22⋊C4—5032no—
125C22⋊C4—5032no—
126C22⋊C4—5031no—
127C42—5031no—
128C23—24no—
129C23—24no—
130C23—42no—
131C23—5031no—
132C23C22×D50312yes—
133C23C22×D50312yes—
134C23C22×D50311yescharacteristic
135Q8—10062no—
136D4—24no—
137D4—22no—
138D4—20122no—
139D4—10064no—
140D4—10062no—
141D4C22⋊D50314yescomplemented
142C2×C4—22no—
143C2×C4—20122no—
144C2×C4—10064no—
145C2×C4—10062no—
146C2×C4—5031no—
147C2×C4—5031no—
148C2×C4—5032no—
149C2×C4—5031no—
150C2×C4—5032no—
151C2×C4C22×D50311yescharacteristic
152C2×C4C22×D50311yescharacteristic
153C22—21no—
154C22—22no—
155C22—22no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—48no—
161C22—10061no—
162C22—10061no—
163C22—10061no—
164C22C2×C22⋊D50314yes—
165C22#2254888212yescomplemented
166C22C23×D50311yescharacteristic
167C4—21no—
168C4—10061no—
169C4—10062no—
170C4—10061no—
171C4—10061no—
172C4—10062no—
173C4C2×C22⋊D50312yes—
174C2—22no—
175C2—24no—
176C2—42no—
177C2—20121no—
178C2C22×C22⋊D50311yescharacteristic
179C2C2×#2254888211yescharacteristic
180C2#3063290911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
FittingC22×D4×C503C2
hypercenterC22×D4D503
hypocenterC503#546
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#22548882C2semidirect
2. #30632851C2semidirect
3. #30632845C2semidirect
4. #30632843C2semidirect
5. #30632836C2semidirect
6. #30632835C2semidirect
7. #30632833C2semidirect
8. D4×Dic503C2semidirect
9. C4×C22⋊D503C2semidirect
10. C2×C22⋊Dic503C2semidirect
11. C22×D4×C503C2semidirect
13. C2×Dic1006C22semidirect
15. C2×C22⋊D503C22semidirect
16. C2×C22⋊D503C22semidirect
17. C22×Dic503C22semidirect
18. C22×Dic503C22semidirect
19. C2×C4×D503C22semidirect
20. C4⋊Dic503C22semidirect
21. Dic503⋊C4C22semidirect
22. Dic503⋊C4C22semidirect
25. C22⋊Dic503C22semidirect
26. C22⋊Dic503C22semidirect
27. C22⋊Dic503C22semidirect
28. C22⋊Dic503C22semidirect
29. (C2×D503)⋊C4C22semidirect
30. C4×Dic503C22semidirect
58. D4×C503D4semidirect
71. C22×C503#41semidirect
90. C503#546semidirect
93. C22×D4D503semidirect
141. D4C22⋊D503semidirect
165. C22#22548882semidirect

Maximal subgroups

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

subgroupindex
C2×#225488822
#306328512
#306328452
#306328432
#306328362
#306328352
#306328332
D4×Dic5032
C4×C22⋊D5032
C2×C22⋊Dic5032
C22×D4×C5032
#546503