Finite Group Databasebeta

← #44566919

Subgroups — #44566919

Order 32192.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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×D503C211yesmaximal, characteristic, complemented
2#30632853C211yesmaximal, characteristic, complemented
3#30632847C212yesmaximal, complemented
4#30632840C211yesmaximal, characteristic, complemented
5#30632838C211yesmaximal, characteristic, complemented
6#30632836C212yesmaximal, complemented
7#30632832C212yesmaximal, complemented
8D4×Dic503C211yesmaximal, characteristic, complemented
9C4×C22⋊D503C211yesmaximal, characteristic, complemented
10C2×(C2×D503)⋊C4C212yesmaximal, complemented
11C2×#41×C503C211yesmaximal, characteristic, complemented
12C23×D503C2212yes—
13C2×D2012C2211yescharacteristic
14C2×C22⋊D503C2211yescharacteristic
15C2×C22⋊D503C2212yes—
16C2×C22⋊D503C2212yescomplemented
17D4×D503—24no—
18C22×Dic503C2212yescomplemented
19C2×C4×D503C2211yescharacteristic
20C4⋊Dic503C2211yescharacteristic, complemented
21Dic503⋊C4C2211yescharacteristic, complemented
22Dic503⋊C4C2212yescomplemented
23C22⋊Dic503C2211yescharacteristic, complemented
24C22⋊Dic503C2212yescomplemented
25(C2×D503)⋊C4C2211yescharacteristic
26(C2×D503)⋊C4C2212yes—
27(C2×D503)⋊C4C2212yescomplemented
28(C2×D503)⋊C4C2212yescomplemented
29(C2×D503)⋊C4C2212yescomplemented
30C4×Dic503C2211yescharacteristic, complemented
31#41×C503—24no—
32C2×Q8×C503C2211yescharacteristic, complemented
33C2×D4×C503C2211yescharacteristic
34C2×D4×C503C2212yescomplemented
35C22×C4×C503C2212yescomplemented
36C22×C4×C503C2211yescharacteristic, complemented
37C22×D503—24no—
38C22×D503—24no—
39C22×D503—42no—
40C22×D503C2312yes—
41C22×D503C2311yescharacteristic
42D2012—22no—
43C22⋊D503—24no—
44C22⋊D503—22no—
45C22⋊D503—42no—
46C2×Dic503—42no—
47C2×Dic503C2311yescharacteristic
48C2×Dic503C2311yescharacteristic
49C2×Dic503C2312yes—
50C2×Dic503C2311yescharacteristic
51C4×D503—22no—
52C23×C503C2311yescharacteristic
53C23×C503C2312yes—
54Q8×C503—22no—
55D4×C503—24no—
56D4×C503D414yescomplemented
57C2×C4×C503—24no—
58C2×C4×C503—22no—
59C2×C4×C503C2311yescharacteristic
60C2×C4×C503C2312yes—
61C2×C4×C503C2311yescharacteristic
62C22×C503—22no—
63C22×C503—22no—
64C22×C503—21no—
65C22×C503—21no—
66C22×C503—21no—
67C22×C503C2×D414yes—
68C22×C503C2411yescharacteristic
69C2×D503—21no—
70C2×D503—21no—
71C2×D503—22no—
72C2×D503—22no—
73C2×D503—22no—
74C2×D503—48no—
75C2×D503#4112yescomplemented
76C4×C503—21no—
77C4×C503—22no—
78C4×C503C2×D412yes—
79Dic503—21no—
80Dic503—21no—
81Dic503—21no—
82Dic503—22no—
83C2×C503—24no—
84C2×C503—41no—
85C2×C503C22×D411yescharacteristic
86C2×C503C2×#4111yescharacteristic
87C2×C503H(5,𝔽2)11yescharacteristic
88D503—22no—
89D503—42no—
90C503#54611yescharacteristic, complemented, Sylow
91#546—5031nomaximal, Sylow
92C2×#41D50311yescharacteristic, complemented
93C22×D4—5031no—
94#124—5031no—
95#123—5032no—
96C22⋊Q8—5031no—
97#121—5032no—
98#121—5031no—
99#120—5032no—
100C4×D4—5031no—
101C4×D4—5031no—
102C2×C22⋊C4—5032no—
103C24—5032no—
104#41—24no—
105C2×Q8C2×D50311yescharacteristic, complemented
106C2×D4—10064no—
107C2×D4—5032no—
108C2×D4—5031no—
109C2×D4—5032no—
110C2×D4—5031no—
111C2×D4C2×D50311yescharacteristic
112C2×D4C2×D50312yescomplemented
113C22×C4—5032no—
114C22×C4—5031no—
115C22×C4C2×D50312yescomplemented
116C22×C4C2×D50311yescharacteristic, complemented
117C4⋊C4—5031no—
118C4⋊C4—5031no—
119C4⋊C4—5032no—
120C22⋊C4—5032no—
121C22⋊C4—5031no—
122C22⋊C4—5031no—
123C22⋊C4—5032no—
124C22⋊C4—5032no—
125C22⋊C4—5032no—
126C22⋊C4—5032no—
127C42—5031no—
128C23—20122no—
129C23—10064no—
130C23—10064no—
131C23—5032no—
132C23—5031no—
133C23C22×D50311yescharacteristic
134C23C22×D50312yes—
135Q8—22no—
136D4—24no—
137D4—20122no—
138D4—10062no—
139D4—10064no—
140D4—10062no—
141D4C22⋊D50314yescomplemented
142C2×C4—24no—
143C2×C4—22no—
144C2×C4—20122no—
145C2×C4—10062no—
146C2×C4—5031no—
147C2×C4—5031no—
148C2×C4—5032no—
149C2×C4—5031no—
150C2×C4C22×D50311yescharacteristic
151C2×C4C22×D50312yes—
152C2×C4C22×D50311yescharacteristic
153C22—22no—
154C22—22no—
155C22—21no—
156C22—21no—
157C22—21no—
158C22—20128no—
159C22—10062no—
160C22—10062no—
161C22—10062no—
162C22—10061no—
163C22—10061no—
164C22—5032no—
165C22C2×C22⋊D50314yes—
166C22C23×D50311yescharacteristic
167C4—21no—
168C4—22no—
169C4—10061no—
170C4—10061no—
171C4—10061no—
172C4—10062no—
173C4C2×C22⋊D50312yes—
174C2—24no—
175C2—41no—
176C2—20122no—
177C2—10062no—
178C2C22×C22⋊D50311yescharacteristic
179C2#41×D50311yescharacteristic
180C2#3063291011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
FittingC2×#41×C503C2
hypercenterC2×#41D503
hypocenterC503#546
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×D4×D503C2semidirect
2. #30632853C2semidirect
3. #30632847C2semidirect
4. #30632840C2semidirect
5. #30632838C2semidirect
6. #30632836C2semidirect
7. #30632832C2semidirect
8. D4×Dic503C2semidirect
9. C4×C22⋊D503C2semidirect
10. C2×(C2×D503)⋊C4C2semidirect
11. C2×#41×C503C2semidirect
16. C2×C22⋊D503C22semidirect
18. C22×Dic503C22semidirect
20. C4⋊Dic503C22semidirect
21. Dic503⋊C4C22semidirect
22. Dic503⋊C4C22semidirect
23. C22⋊Dic503C22semidirect
24. C22⋊Dic503C22semidirect
27. (C2×D503)⋊C4C22semidirect
28. (C2×D503)⋊C4C22semidirect
29. (C2×D503)⋊C4C22semidirect
30. C4×Dic503C22semidirect
32. C2×Q8×C503C22semidirect
34. C2×D4×C503C22semidirect
35. C22×C4×C503C22semidirect
36. C22×C4×C503C22semidirect
56. D4×C503D4semidirect
75. C2×D503#41semidirect
90. C503#546semidirect
92. C2×#41D503semidirect
105. C2×Q8C2×D503semidirect
112. C2×D4C2×D503semidirect
115. C22×C4C2×D503semidirect
116. C22×C4C2×D503semidirect
141. D4C22⋊D503semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D5032
#306328532
#306328472
#306328402
#306328382
#306328362
#306328322
D4×Dic5032
C4×C22⋊D5032
C2×(C2×D503)⋊C42
C2×#41×C5032
#546503