Finite Group Databasebeta

← #44566841

Subgroups — #44566841

Order 32192.

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
1C22×C22⋊D503C211yesmaximal, characteristic, complemented
2C2×D4×D503C211yesmaximal, characteristic, complemented
3#30632848C211yesmaximal, characteristic, complemented
4#30632846C212yesmaximal, complemented
5#30632845C211yesmaximal, characteristic, complemented
6#30632837C212yesmaximal, complemented
7#30632835C212yesmaximal, complemented
8#30632833C211yesmaximal, characteristic, complemented
9#30632832C212yesmaximal, complemented
10C22⋊C4×D503C211yesmaximal, characteristic, complemented
11#120×C503C211yesmaximal, characteristic, complemented
12C23×D503C2211yescharacteristic
13C23×D503C2211yescharacteristic, complemented
14C2×D2012C2211yescharacteristic, complemented
15C2×C22⋊D503—24no—
16C2×C22⋊D503C2212yes—
17C2×C22⋊D503C2211yescharacteristic
18C2×C22⋊D503C2211yescharacteristic, complemented
19C2×C22⋊D503C2212yescomplemented
20C2×C22⋊D503C2212yescomplemented
21D4×D503—24no—
22C22×Dic503C2211yescharacteristic, complemented
23C2×C4×D503C2211yescharacteristic, complemented
24C2×C4×D503C2212yescomplemented
25C4⋊Dic503C2212yescomplemented
26Dic503⋊C4C2212yescomplemented
27C22⋊Dic503C2211yescharacteristic, complemented
28C22⋊Dic503C2212yescomplemented
29C22⋊Dic503C2212yescomplemented
30(C2×D503)⋊C4C2212yescomplemented
31(C2×D503)⋊C4C2212yescomplemented
32C24×C503C2211yescharacteristic, complemented
33C2×D4×C503C2211yescharacteristic
34C2×D4×C503C2212yescomplemented
35C22⋊C4×C503C2211yescharacteristic, complemented
36C22⋊C4×C503C2212yescomplemented
37C22×D503—22no—
38C22×D503—42no—
39C22×D503—42no—
40C22×D503D414yescomplemented
41C22×D503C2311yescharacteristic
42C22×D503C2311yescharacteristic
43C22×D503C2311yescharacteristic
44D2012—22no—
45C22⋊D503—22no—
46C22⋊D503—22no—
47C22⋊D503—24no—
48C22⋊D503—24no—
49C22⋊D503—42no—
50C2×Dic503—22no—
51C2×Dic503C2312yes—
52C2×Dic503C2312yes—
53C2×Dic503C2311yescharacteristic
54C4×D503—22no—
55C4×D503—42no—
56C23×C503—22no—
57C23×C503—42no—
58C23×C503C2312yes—
59C23×C503C2311yescharacteristic
60C23×C503C2311yescharacteristic
61D4×C503—22no—
62D4×C503—42no—
63C2×C4×C503C2311yescharacteristic
64C2×C4×C503C2312yes—
65C22×C503—22no—
66C22×C503—21no—
67C22×C503—22no—
68C22×C503—22no—
69C22×C503—22no—
70C22×C503—22no—
71C22×C503—44no—
72C22×C503C2×D412yes—
73C22×C503C2411yescharacteristic
74C2×D503—22no—
75C2×D503—22no—
76C2×D503—21no—
77C2×D503—22no—
78C2×D503—44no—
79C2×D503—44no—
80C2×D503C2×D412yes—
81C2×D503C2×D412yes—
82C4×C503—21no—
83C4×C503—22no—
84Dic503—21no—
85Dic503—22no—
86Dic503—22no—
87C2×C503—22no—
88C2×C503—41no—
89C2×C503—42no—
90C2×C503C22×D411yescharacteristic
91C2×C503H(5,𝔽2)12yes—
92D503—22no—
93D503—22no—
94D503—41no—
95C503#53411yescharacteristic, complemented, Sylow
96#534—5031nomaximal, Sylow
97C22×D4—5031no—
98C22×D4—5031no—
99#123—5031no—
100#123—5032no—
101#123—5031no—
102#121—5032no—
103#121—5032no—
104#120—5031no—
105#120—5032no—
106#120D50311yescharacteristic, complemented
107C2×C22⋊C4—5031no—
108C24—5031no—
109C24—5031no—
110C24C2×D50311yescharacteristic, complemented
111C2×D4—10064no—
112C2×D4—10064no—
113C2×D4—5032no—
114C2×D4—5032no—
115C2×D4—5031no—
116C2×D4—5031no—
117C2×D4—5032no—
118C2×D4—5031no—
119C2×D4C2×D50311yescharacteristic
120C2×D4C2×D50312yescomplemented
121C22×C4—5032no—
122C22×C4—5031no—
123C22×C4—5031no—
124C4⋊C4—5032no—
125C4⋊C4—5032no—
126C22⋊C4—5031no—
127C22⋊C4—5032no—
128C22⋊C4—5032no—
129C22⋊C4—5032no—
130C22⋊C4—5032no—
131C22⋊C4C2×D50311yescharacteristic, complemented
132C22⋊C4C2×D50312yescomplemented
133C23—22no—
134C23—42no—
135C23—20122no—
136C23—20122no—
137C23—10062no—
138C23—5034no—
139C23—5031no—
140C23—5031no—
141C23—5031no—
142C23C22×D50311yescharacteristic
143C23C22×D50312yes—
144C23C22×D50311yescharacteristic
145D4—22no—
146D4—42no—
147D4—20122no—
148D4—10062no—
149D4—10062no—
150D4—10064no—
151D4—10064no—
152D4—10062no—
153C2×C4—20122no—
154C2×C4—10062no—
155C2×C4—10062no—
156C2×C4—5032no—
157C2×C4—5031no—
158C2×C4—5032no—
159C2×C4C22×D50312yes—
160C2×C4C22×D50311yescharacteristic
161C22—22no—
162C22—21no—
163C22—22no—
164C22—22no—
165C22—22no—
166C22—22no—
167C22—44no—
168C22—20124no—
169C22—20124no—
170C22—10061no—
171C22—10062no—
172C22—10062no—
173C22—10062no—
174C22—5032no—
175C22—5032no—
176C22D4×D50312yes—
177C22C23×D50311yescharacteristic
178C4—21no—
179C4—22no—
180C4—10061no—
181C4—10062no—
182C4—10062no—
183C2—22no—
184C2—42no—
185C2—41no—
186C2—20121no—
187C2—10062no—
188C2—10062no—
189C2C2×D4×D50311yescharacteristic
190C2#3063290912yes—
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#120×C503C2
hypercenter#120D503
hypocenterC503#534
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊D503C2semidirect
2. C2×D4×D503C2semidirect
3. #30632848C2semidirect
4. #30632846C2semidirect
5. #30632845C2semidirect
6. #30632837C2semidirect
7. #30632835C2semidirect
8. #30632833C2semidirect
9. #30632832C2semidirect
10. C22⋊C4×D503C2semidirect
11. #120×C503C2semidirect
13. C23×D503C22semidirect
14. C2×D2012C22semidirect
18. C2×C22⋊D503C22semidirect
19. C2×C22⋊D503C22semidirect
20. C2×C22⋊D503C22semidirect
22. C22×Dic503C22semidirect
23. C2×C4×D503C22semidirect
24. C2×C4×D503C22semidirect
25. C4⋊Dic503C22semidirect
26. Dic503⋊C4C22semidirect
27. C22⋊Dic503C22semidirect
28. C22⋊Dic503C22semidirect
29. C22⋊Dic503C22semidirect
30. (C2×D503)⋊C4C22semidirect
31. (C2×D503)⋊C4C22semidirect
32. C24×C503C22semidirect
34. C2×D4×C503C22semidirect
35. C22⋊C4×C503C22semidirect
36. C22⋊C4×C503C22semidirect
40. C22×D503D4semidirect
95. C503#534semidirect
106. #120D503semidirect
110. C24C2×D503semidirect
120. C2×D4C2×D503semidirect
131. C22⋊C4C2×D503semidirect
132. C22⋊C4C2×D503semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊D5032
C2×D4×D5032
#306328482
#306328462
#306328452
#306328372
#306328352
#306328332
#306328322
C22⋊C4×D5032
#120×C5032
#534503