Finite Group Databasebeta

← #44566846

Subgroups — #44566846

Order 32192.

334 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 334 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
1C2×#22548882C211yesmaximal, characteristic, complemented
2C22×C22⋊D503C211yesmaximal, characteristic, complemented
3#30632860C212yesmaximal, complemented
4#30632850C212yesmaximal, complemented
5#30632837C212yesmaximal, complemented
6#30632836C212yesmaximal, complemented
7#30632834C211yesmaximal, characteristic, complemented
8#30632833C211yesmaximal, characteristic, complemented
9#30632832C211yesmaximal, characteristic, complemented
10#30632820C211yesmaximal, characteristic, complemented
11#120×C503C211yesmaximal, characteristic, complemented
12C23×D503C2211yescharacteristic
13#22548882—24no—
14C2×Dic1006C2211yescharacteristic, complemented
15C2×D2012C2212yescomplemented
16C2×C22⋊D503—24no—
17C2×C22⋊D503C2211yescharacteristic
18C2×C22⋊D503C2212yes—
19C2×C22⋊D503C2212yes—
20C2×C22⋊D503C2211yescharacteristic, complemented
21C2×C22⋊D503C2212yescomplemented
22C2×C22⋊D503C2212yescomplemented
23C22×Dic503C2211yescharacteristic
24C22×Dic503C2211yescharacteristic, complemented
25C2×C4×D503C2211yescharacteristic, complemented
26Dic503⋊C4C2212yescomplemented
27C22⋊Dic503C2211yescharacteristic
28C22⋊Dic503C2212yescomplemented
29(C2×D503)⋊C4C2212yescomplemented
30(C2×D503)⋊C4C2212yescomplemented
31C4×Dic503C2212yescomplemented
32C24×C503C2211yescharacteristic
33C2×D4×C503C2211yescharacteristic
34C2×D4×C503C2212yescomplemented
35C22⋊C4×C503C2211yescharacteristic
36C22⋊C4×C503C2212yescomplemented
37C22×D503—22no—
38C22×D503—42no—
39C22×D503C2312yes—
40C22×D503C2311yescharacteristic
41Dic1006—22no—
42D2012—42no—
43C22⋊D503—22no—
44C22⋊D503—24no—
45C22⋊D503—24no—
46C22⋊D503—22no—
47C22⋊D503—42no—
48C22⋊D503—42no—
49C2×Dic503—22no—
50C2×Dic503D414yescomplemented
51C2×Dic503C2312yes—
52C2×Dic503C2311yescharacteristic
53C2×Dic503C2311yescharacteristic
54C2×Dic503C2311yescharacteristic
55C4×D503—22no—
56C23×C503—22no—
57C23×C503—42no—
58C23×C503C2312yes—
59C23×C503C2311yescharacteristic
60C23×C503C2311yescharacteristic
61D4×C503—22no—
62D4×C503—42no—
63C2×C4×C503C2312yes—
64C2×C4×C503C2311yescharacteristic
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—21no—
75C2×D503—22no—
76C2×D503—22no—
77C2×D503—22no—
78C2×D503—22no—
79C2×D503—44no—
80C4×C503—21no—
81C4×C503—22no—
82Dic503—21no—
83Dic503—22no—
84Dic503C2×D412yes—
85Dic503C2×D412yes—
86C2×C503—22no—
87C2×C503—41no—
88C2×C503—42no—
89C2×C503C22×D411yescharacteristic
90C2×C503H(5,𝔽2)12yes—
91D503—41no—
92D503—42no—
93C503#53511yescharacteristic, complemented, Sylow
94#535—5031nomaximal, Sylow
95C2×#41—5031no—
96C22×D4—5031no—
97#127—5032no—
98#124—5032no—
99#121—5032no—
100#121—5032no—
101#120—5031no—
102#120—5031no—
103#120—5031no—
104#120D50311yescharacteristic, complemented
105#117—5031no—
106C24—5031no—
107C24C2×D50311yescharacteristic
108#41—10064no—
109C2×Q8—5031no—
110C2×D4—10064no—
111C2×D4—5032no—
112C2×D4—5032no—
113C2×D4—5031no—
114C2×D4—5032no—
115C2×D4—5032no—
116C2×D4—5031no—
117C2×D4—5032no—
118C2×D4C2×D50311yescharacteristic
119C2×D4C2×D50312yescomplemented
120C22×C4—5031no—
121C22×C4—5031no—
122C22×C4—5031no—
123C4⋊C4—5032no—
124C22⋊C4—5031no—
125C22⋊C4—5032no—
126C22⋊C4—5032no—
127C22⋊C4—5032no—
128C22⋊C4C2×D50311yescharacteristic
129C22⋊C4C2×D50312yescomplemented
130C42—5032no—
131C23—22no—
132C23—42no—
133C23—20122no—
134C23—10062no—
135C23—5032no—
136C23—5031no—
137C23C22×D50312yes—
138C23C22×D50311yescharacteristic
139C23C22×D50311yescharacteristic
140Q8—10062no—
141D4—22no—
142D4—42no—
143D4—20122no—
144D4—20122no—
145D4—20122no—
146D4—10062no—
147D4—10064no—
148D4—10064no—
149D4—10062no—
150C2×C4—10062no—
151C2×C4—10062no—
152C2×C4—5032no—
153C2×C4—5031no—
154C2×C4—5034no—
155C2×C4—5031no—
156C2×C4—5031no—
157C2×C4C22×D50312yes—
158C2×C4C22×D50311yescharacteristic
159C22—22no—
160C22—21no—
161C22—22no—
162C22—22no—
163C22—22no—
164C22—22no—
165C22—44no—
166C22—20124no—
167C22—10061no—
168C22—10062no—
169C22—10062no—
170C22—10062no—
171C22—10062no—
172C22D4×D50312yes—
173C22C23×D50311yescharacteristic
174C4—21no—
175C4—22no—
176C4—10061no—
177C4—10062no—
178C4—5032no—
179C4—5032no—
180C2—22no—
181C2—42no—
182C2—41no—
183C2—20122no—
184C2—20121no—
185C2C2×D4×D50311yescharacteristic
186C2#3063290912yes—
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#120×C503C2
hypercenter#120D503
hypocenterC503#535
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C2×#22548882C2semidirect
2. C22×C22⋊D503C2semidirect
3. #30632860C2semidirect
4. #30632850C2semidirect
5. #30632837C2semidirect
6. #30632836C2semidirect
7. #30632834C2semidirect
8. #30632833C2semidirect
9. #30632832C2semidirect
10. #30632820C2semidirect
11. #120×C503C2semidirect
14. C2×Dic1006C22semidirect
15. C2×D2012C22semidirect
20. C2×C22⋊D503C22semidirect
21. C2×C22⋊D503C22semidirect
22. C2×C22⋊D503C22semidirect
24. C22×Dic503C22semidirect
25. C2×C4×D503C22semidirect
26. Dic503⋊C4C22semidirect
28. C22⋊Dic503C22semidirect
29. (C2×D503)⋊C4C22semidirect
30. (C2×D503)⋊C4C22semidirect
31. C4×Dic503C22semidirect
34. C2×D4×C503C22semidirect
36. C22⋊C4×C503C22semidirect
50. C2×Dic503D4semidirect
93. C503#535semidirect
104. #120D503semidirect
119. C2×D4C2×D503semidirect
129. C22⋊C4C2×D503semidirect

Maximal subgroups

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

subgroupindex
C2×#225488822
C22×C22⋊D5032
#306328602
#306328502
#306328372
#306328362
#306328342
#306328332
#306328322
#306328202
#120×C5032
#535503