Finite Group Databasebeta

← #44566791

Subgroups — #44566791

Order 32192.

330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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
2C22×C4×D503C211yesmaximal, characteristic, complemented
3#30632846C212yesmaximal, complemented
4#30632844C211yesmaximal, characteristic, complemented
5#30632843C211yesmaximal, characteristic, complemented
6#30632835C211yesmaximal, characteristic, complemented
7#30632832C212yesmaximal, complemented
8D4×Dic503C212yesmaximal, complemented
9(C22⋊D503)⋊C4C212yesmaximal, complemented
10#30632822C211yesmaximal, characteristic, complemented
11#121×C503C211yesmaximal, characteristic, complemented
12C23×D503C2211yescharacteristic
13#22548882—24no—
14C2×Dic1006C2211yescharacteristic, complemented
15C2×C22⋊D503C2212yes—
16C2×C22⋊D503C2212yes—
17C22×Dic503C2211yescharacteristic
18C22×Dic503C2212yescomplemented
19C2×C4×D503—24no—
20C2×C4×D503C2211yescharacteristic
21C2×C4×D503C2211yescharacteristic
22C2×C4×D503C2211yescharacteristic
23C2×C4×D503C2211yescharacteristic
24C4⋊Dic503C2211yescharacteristic, complemented
25C4⋊Dic503C2212yescomplemented
26Dic503⋊C4C2212yescomplemented
27C22⋊Dic503C2212yes—
28C22⋊Dic503C2212yescomplemented
29(C2×D503)⋊C4C2212yes—
30(C2×D503)⋊C4C2212yes—
31C4×Dic503C2212yescomplemented
32C2×D4×C503C2212yes—
33C2×D4×C503C2211yescharacteristic, complemented
34C22×C4×C503C2211yescharacteristic
35C4⋊C4×C503C2211yescharacteristic, complemented
36C22⋊C4×C503C2212yescomplemented
37C22×D503—22no—
38C22×D503—22no—
39C22×D503—22no—
40C22×D503C2311yescharacteristic
41C22×D503C2311yescharacteristic
42Dic1006—22no—
43C22⋊D503—24no—
44C22⋊D503—24no—
45C2×Dic503—22no—
46C2×Dic503—24no—
47C2×Dic503C2312yes—
48C2×Dic503C2312yes—
49C2×Dic503C2311yescharacteristic
50C2×Dic503C2311yescharacteristic
51C4×D503—22no—
52C4×D503—22no—
53C4×D503—22no—
54C4×D503D414yescomplemented
55C23×C503C2312yes—
56C23×C503C2311yescharacteristic
57D4×C503—24no—
58D4×C503—22no—
59C2×C4×C503—22no—
60C2×C4×C503C2311yescharacteristic
61C2×C4×C503C2312yes—
62C2×C4×C503C2311yescharacteristic
63C22×C503—21no—
64C22×C503—21no—
65C22×C503—22no—
66C22×C503—22no—
67C22×C503—22no—
68C22×C503#4112yescomplemented
69C22×C503C2411yescharacteristic
70C2×D503—28no—
71C2×D503—21no—
72C2×D503—21no—
73C2×D503—21no—
74C2×D503—21no—
75C2×D503C2×D412yes—
76C2×D503#4112yescomplemented
77C4×C503—21no—
78C4×C503—22no—
79C4×C503C2×D412yes—
80Dic503—21no—
81Dic503—22no—
82Dic503—22no—
83Dic503C2×D412yes—
84C2×C503—22no—
85C2×C503—42no—
86C2×C503C22×D411yescharacteristic
87C2×C503C2×#4111yescharacteristic
88C2×C503C2×#4111yescharacteristic
89D503—22no—
90D503—22no—
91C503#52511yescharacteristic, complemented, Sylow
92#525—5031nomaximal, Sylow
93C2×#41—5031no—
94C23×C4—5031no—
95#123—5032no—
96C22⋊Q8—5031no—
97C22⋊Q8—5031no—
98#121—5031no—
99#121D50311yescharacteristic, complemented
100#120—5032no—
101C4×D4—5032no—
102C4×D4—5032no—
103#117—5031no—
104C24—5031no—
105#41—10064no—
106C2×Q8—5031no—
107C2×D4—5032no—
108C2×D4—5032no—
109C2×D4C2×D50312yes—
110C2×D4C2×D50311yescharacteristic, complemented
111C22×C4—10064no—
112C22×C4—5031no—
113C22×C4—5032no—
114C22×C4—5031no—
115C22×C4—5031no—
116C22×C4—5031no—
117C22×C4—5031no—
118C22×C4C2×D50311yescharacteristic
119C4⋊C4—5031no—
120C4⋊C4—5032no—
121C4⋊C4—5032no—
122C4⋊C4C2×D50311yescharacteristic, complemented
123C22⋊C4—5032no—
124C22⋊C4—5032no—
125C22⋊C4—5032no—
126C22⋊C4—5032no—
127C22⋊C4C2×D50312yescomplemented
128C42—5032no—
129C23—10062no—
130C23—10062no—
131C23—10062no—
132C23—5031no—
133C23—5031no—
134C23C22×D50312yes—
135C23C22×D50311yescharacteristic
136Q8—10062no—
137D4—24no—
138D4—22no—
139D4—10064no—
140D4—10064no—
141C2×C4—22no—
142C2×C4—10062no—
143C2×C4—10062no—
144C2×C4—10062no—
145C2×C4—10064no—
146C2×C4—10062no—
147C2×C4—5032no—
148C2×C4—5031no—
149C2×C4—5032no—
150C2×C4—5031no—
151C2×C4—5034no—
152C2×C4C22×D50312yes—
153C2×C4C22×D50311yescharacteristic
154C2×C4C22×D50311yescharacteristic
155C22—21no—
156C22—21no—
157C22—22no—
158C22—22no—
159C22—22no—
160C22—10068no—
161C22—10061no—
162C22—10061no—
163C22—10061no—
164C22—10061no—
165C22—5032no—
166C22—5032no—
167C22#2254888212yescomplemented
168C22C23×D50311yescharacteristic
169C4—21no—
170C4—22no—
171C4—10061no—
172C4—10062no—
173C4—10062no—
174C4—5032no—
175C4D4×D50312yes—
176C2—22no—
177C2—42no—
178C2—10062no—
179C2—10062no—
180C2C2×D4×D50311yescharacteristic
181C2#41×D50311yescharacteristic
182C2C2×#2254888211yescharacteristic
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#121×C503C2
hypercenter#121D503
hypocenterC503#525
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#22548882C2semidirect
2. C22×C4×D503C2semidirect
3. #30632846C2semidirect
4. #30632844C2semidirect
5. #30632843C2semidirect
6. #30632835C2semidirect
7. #30632832C2semidirect
8. D4×Dic503C2semidirect
9. (C22⋊D503)⋊C4C2semidirect
10. #30632822C2semidirect
11. #121×C503C2semidirect
14. C2×Dic1006C22semidirect
18. C22×Dic503C22semidirect
24. C4⋊Dic503C22semidirect
25. C4⋊Dic503C22semidirect
26. Dic503⋊C4C22semidirect
28. C22⋊Dic503C22semidirect
31. C4×Dic503C22semidirect
33. C2×D4×C503C22semidirect
35. C4⋊C4×C503C22semidirect
36. C22⋊C4×C503C22semidirect
54. C4×D503D4semidirect
68. C22×C503#41semidirect
76. C2×D503#41semidirect
91. C503#525semidirect
99. #121D503semidirect
110. C2×D4C2×D503semidirect
122. C4⋊C4C2×D503semidirect
127. C22⋊C4C2×D503semidirect
167. C22#22548882semidirect

Maximal subgroups

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

subgroupindex
C2×#225488822
C22×C4×D5032
#306328462
#306328442
#306328432
#306328352
#306328322
D4×Dic5032
(C22⋊D503)⋊C42
#306328222
#121×C5032
#525503