Finite Group Databasebeta

← #44566928

Subgroups — #44566928

Order 32192.

334 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 105 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×#22548883C211yesmaximal, characteristic, complemented
2C2×D4×D503C211yesmaximal, characteristic, complemented
3#30632851C211yesmaximal, characteristic, complemented
4#30632846C212yesmaximal, complemented
5#30632844C211yesmaximal, characteristic, complemented
6#30632835C212yesmaximal, complemented
7#30632832C212yesmaximal, complemented
8#30632826C211yesmaximal, characteristic, complemented
9C4×C22⋊D503C211yesmaximal, characteristic, complemented
10C22⋊C4×D503C212yesmaximal, complemented
11#121×C503C211yesmaximal, characteristic, complemented
12C23×D503C2212yes—
13#22548883—24no—
14C2×Dic1006C2211yescharacteristic, complemented
15C2×D2012C2211yescharacteristic
16C2×C22⋊D503C2211yescharacteristic
17C2×C22⋊D503C2212yes—
18C2×C22⋊D503C2212yescomplemented
19D4×D503—24no—
20C2×C4×D503C2211yescharacteristic
21C2×C4×D503C2212yescomplemented
22C2×C4×D503C2212yescomplemented
23C4⋊Dic503C2212yescomplemented
24Dic503⋊C4C2211yescharacteristic, complemented
25C22⋊Dic503C2212yescomplemented
26C22⋊Dic503C2211yescharacteristic, complemented
27C22⋊Dic503C2212yescomplemented
28(C2×D503)⋊C4C2211yescharacteristic
29(C2×D503)⋊C4C2212yes—
30(C2×D503)⋊C4C2212yescomplemented
31C4×Dic503C2211yescharacteristic, complemented
32C2×D4×C503C2211yescharacteristic
33C2×D4×C503C2212yescomplemented
34C22×C4×C503C2211yescharacteristic, complemented
35C4⋊C4×C503C2211yescharacteristic, complemented
36C22⋊C4×C503C2212yescomplemented
37C22×D503—24no—
38C22×D503—24no—
39C22×D503—42no—
40C22×D503C2312yes—
41C22×D503C2311yescharacteristic
42Dic1006—22no—
43D2012D414yescomplemented
44C22⋊D503—24no—
45C22⋊D503—24no—
46C22⋊D503—22no—
47C2×Dic503C2311yescharacteristic
48C2×Dic503C2311yescharacteristic
49C2×Dic503C2312yes—
50C2×Dic503C2311yescharacteristic
51C4×D503—24no—
52C4×D503—22no—
53C4×D503—42no—
54C23×C503C2312yes—
55C23×C503C2311yescharacteristic
56D4×C503—22no—
57D4×C503—42no—
58C2×C4×C503—22no—
59C2×C4×C503C2311yescharacteristic
60C2×C4×C503C2312yes—
61C2×C4×C503C2311yescharacteristic
62C22×C503—21no—
63C22×C503—22no—
64C22×C503—21no—
65C22×C503—22no—
66C22×C503—21no—
67C22×C503—22no—
68C22×C503C2411yescharacteristic
69C2×D503—21no—
70C2×D503—22no—
71C2×D503—22no—
72C2×D503—21no—
73C2×D503—48no—
74C2×D503C2×D414yes—
75C2×D503#4112yescomplemented
76C4×C503—21no—
77C4×C503—22no—
78C4×C503C2×D412yes—
79Dic503—21no—
80Dic503—22no—
81Dic503—21no—
82Dic503—21no—
83C2×C503—42no—
84C2×C503—41no—
85C2×C503C22×D411yescharacteristic
86C2×C503C2×#4111yescharacteristic
87C2×C503H(5,𝔽2)11yescharacteristic
88D503—22no—
89D503—24no—
90C503#54611yescharacteristic, complemented, Sylow
91#546—5031nomaximal, Sylow
92C2×#41—5031no—
93C22×D4—5031no—
94#124—5031no—
95#123—5032no—
96C22⋊Q8—5031no—
97#121—5032no—
98#121D50311yescharacteristic, complemented
99#120—5032no—
100C4×D4—5031no—
101C4×D4—5031no—
102C2×C22⋊C4—5032no—
103C24—5032no—
104#41—10064no—
105C2×Q8—5031no—
106C2×D4—10064no—
107C2×D4—5031no—
108C2×D4—5032no—
109C2×D4—5032no—
110C2×D4—5031no—
111C2×D4C2×D50311yescharacteristic
112C2×D4C2×D50312yescomplemented
113C22×C4—5032no—
114C22×C4—5032no—
115C22×C4—5031no—
116C22×C4C2×D50311yescharacteristic, complemented
117C4⋊C4—5031no—
118C4⋊C4—5032no—
119C4⋊C4C2×D50311yescharacteristic, complemented
120C22⋊C4—5032no—
121C22⋊C4—5031no—
122C22⋊C4—5032no—
123C22⋊C4—5031no—
124C22⋊C4—5032no—
125C22⋊C4—5032no—
126C22⋊C4C2×D50312yescomplemented
127C42—5031no—
128C23—20122no—
129C23—10064no—
130C23—10064no—
131C23—5031no—
132C23—5032no—
133C23C22×D50312yes—
134C23C22×D50311yescharacteristic
135Q8—10062no—
136D4—22no—
137D4—42no—
138D4—10064no—
139D4—10064no—
140D4—10062no—
141D4—5034no—
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×C4C22×D50312yes—
151C2×C4C22×D50311yescharacteristic
152C2×C4C22×D50311yescharacteristic
153C22—21no—
154C22—22no—
155C22—21no—
156C22—22no—
157C22—21no—
158C22—22no—
159C22—20128no—
160C22—10061no—
161C22—10062no—
162C22—10062no—
163C22—10061no—
164C22—5034no—
165C22—5032no—
166C22C23×D50311yescharacteristic
167C4—21no—
168C4—22no—
169C4—10061no—
170C4—10062no—
171C4—10061no—
172C4—10061no—
173C4D4×D50312yes—
174C2—42no—
175C2—41no—
176C2—10062no—
177C2—10064no—
178C2C2×D4×D50311yescharacteristic
179C2#41×D50311yescharacteristic
180C2#3063290911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#121×C503C2
hypercenter#121D503
hypocenterC503#546
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22548883C2semidirect
2. C2×D4×D503C2semidirect
3. #30632851C2semidirect
4. #30632846C2semidirect
5. #30632844C2semidirect
6. #30632835C2semidirect
7. #30632832C2semidirect
8. #30632826C2semidirect
9. C4×C22⋊D503C2semidirect
10. C22⋊C4×D503C2semidirect
11. #121×C503C2semidirect
14. C2×Dic1006C22semidirect
18. C2×C22⋊D503C22semidirect
21. C2×C4×D503C22semidirect
22. C2×C4×D503C22semidirect
23. C4⋊Dic503C22semidirect
24. Dic503⋊C4C22semidirect
25. C22⋊Dic503C22semidirect
26. C22⋊Dic503C22semidirect
27. C22⋊Dic503C22semidirect
30. (C2×D503)⋊C4C22semidirect
31. C4×Dic503C22semidirect
33. C2×D4×C503C22semidirect
34. C22×C4×C503C22semidirect
35. C4⋊C4×C503C22semidirect
36. C22⋊C4×C503C22semidirect
43. D2012D4semidirect
75. C2×D503#41semidirect
90. C503#546semidirect
98. #121D503semidirect
112. C2×D4C2×D503semidirect
116. C22×C4C2×D503semidirect
119. C4⋊C4C2×D503semidirect
126. C22⋊C4C2×D503semidirect

Maximal subgroups

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

subgroupindex
C2×#225488832
C2×D4×D5032
#306328512
#306328462
#306328442
#306328352
#306328322
#306328262
C4×C22⋊D5032
C22⋊C4×D5032
#121×C5032
#546503