Finite Group Databasebeta

← #44566842

Subgroups — #44566842

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×D2012C211yesmaximal, characteristic, complemented
2C2×D4×D503C211yesmaximal, characteristic, complemented
3#30632849C212yesmaximal, complemented
4#30632847C211yesmaximal, characteristic, complemented
5#30632839C212yesmaximal, complemented
6#30632837C212yesmaximal, complemented
7#30632834C211yesmaximal, characteristic, complemented
8#30632834C212yesmaximal, complemented
9#30632832C211yesmaximal, characteristic, complemented
10C22⋊C4×D503C211yesmaximal, characteristic, complemented
11#123×C503C211yesmaximal, characteristic, complemented
12C23×D503C2211yescharacteristic
13C23×D503C2211yescharacteristic, complemented
14C23×D503C2211yescharacteristic, complemented
15C2×D2012—24no—
16C2×D2012C2212yes—
17C2×D2012C2212yescomplemented
18C2×D2012C2211yescharacteristic, complemented
19C2×D2012C2212yescomplemented
20C2×C22⋊D503C2211yescharacteristic
21C2×C22⋊D503C2211yescharacteristic, complemented
22C2×C22⋊D503C2212yescomplemented
23D4×D503—24no—
24C2×C4×D503C2211yescharacteristic, complemented
25C2×C4×D503C2212yescomplemented
26Dic503⋊C4C2212yescomplemented
27C22⋊Dic503C2211yescharacteristic, complemented
28(C2×D503)⋊C4C2212yescomplemented
29(C2×D503)⋊C4C2212yescomplemented
30(C2×D503)⋊C4C2212yescomplemented
31(C2×D503)⋊C4C2212yescomplemented
32C2×D4×C503C2211yescharacteristic
33C22×C4×C503C2211yescharacteristic, complemented
34C4⋊C4×C503C2212yescomplemented
35C22⋊C4×C503C2211yescharacteristic, complemented
36C22⋊C4×C503C2212yescomplemented
37C22×D503—22no—
38C22×D503—22no—
39C22×D503—42no—
40C22×D503—42no—
41C22×D503—42no—
42C22×D503D414yescomplemented
43C22×D503C2311yescharacteristic
44C22×D503C2312yes—
45C22×D503C2311yescharacteristic
46C22×D503C2311yescharacteristic
47D2012—22no—
48D2012—24no—
49D2012—24no—
50D2012—42no—
51C22⋊D503—22no—
52C22⋊D503—22no—
53C22⋊D503—42no—
54C2×Dic503C2312yes—
55C2×Dic503C2311yescharacteristic
56C4×D503—22no—
57C4×D503—42no—
58C23×C503C2311yescharacteristic
59C23×C503C2311yescharacteristic
60D4×C503—22no—
61C2×C4×C503—22no—
62C2×C4×C503C2312yes—
63C2×C4×C503C2312yes—
64C2×C4×C503C2311yescharacteristic
65C22×C503—22no—
66C22×C503—21no—
67C22×C503—22no—
68C22×C503C2×D412yes—
69C22×C503C2411yescharacteristic
70C2×D503—22no—
71C2×D503—22no—
72C2×D503—21no—
73C2×D503—22no—
74C2×D503—22no—
75C2×D503—22no—
76C2×D503—22no—
77C2×D503—44no—
78C2×D503—44no—
79C2×D503—44no—
80C2×D503C2×D412yes—
81C2×D503C2×D412yes—
82C4×C503—22no—
83C4×C503—21no—
84C4×C503—22no—
85Dic503—21no—
86Dic503—22no—
87C2×C503—22no—
88C2×C503—41no—
89C2×C503C22×D411yescharacteristic
90C2×C503H(5,𝔽2)12yes—
91D503—22no—
92D503—22no—
93D503—41no—
94D503—42no—
95C503#53411yescharacteristic, complemented, Sylow
96#534—5031nomaximal, Sylow
97C22×D4—5031no—
98C22×D4—5031no—
99#123—5031no—
100#123—5032no—
101#123D50311yescharacteristic, complemented
102#121—5032no—
103#121—5032no—
104#120—5031no—
105#120—5032no—
106#120—5031no—
107C2×C22⋊C4—5031no—
108C24—5031no—
109C24—5031no—
110C24—5031no—
111C2×D4—10064no—
112C2×D4—10064no—
113C2×D4—5032no—
114C2×D4—5031no—
115C2×D4—5031no—
116C2×D4—5032no—
117C2×D4—5032no—
118C2×D4—5031no—
119C2×D4—5032no—
120C2×D4C2×D50311yescharacteristic
121C22×C4—5032no—
122C22×C4—5031no—
123C22×C4C2×D50311yescharacteristic, complemented
124C4⋊C4—5032no—
125C4⋊C4C2×D50312yescomplemented
126C22⋊C4—5031no—
127C22⋊C4—5032no—
128C22⋊C4—5032no—
129C22⋊C4—5032no—
130C22⋊C4—5032no—
131C22⋊C4C2×D50311yescharacteristic, complemented
132C22⋊C4C2×D50312yescomplemented
133C23—20122no—
134C23—20122no—
135C23—20122no—
136C23—10062no—
137C23—10062no—
138C23—5034no—
139C23—5032no—
140C23—5031no—
141C23—5031no—
142C23—5031no—
143C23C22×D50311yescharacteristic
144C23C22×D50311yescharacteristic
145D4—22no—
146D4—20122no—
147D4—20122no—
148D4—10064no—
149D4—10064no—
150D4—10062no—
151D4—10062no—
152D4—10062no—
153C2×C4—22no—
154C2×C4—20122no—
155C2×C4—10062no—
156C2×C4—5032no—
157C2×C4—5031no—
158C2×C4C22×D50312yes—
159C2×C4C22×D50311yescharacteristic
160C2×C4C22×D50312yes—
161C22—22no—
162C22—21no—
163C22—22no—
164C22—20124no—
165C22—20124no—
166C22—20124no—
167C22—10062no—
168C22—10061no—
169C22—10062no—
170C22—10062no—
171C22—10062no—
172C22—10062no—
173C22—10062no—
174C22—5032no—
175C22—5032no—
176C22D4×D50312yes—
177C22C23×D50311yescharacteristic
178C4—22no—
179C4—21no—
180C4—22no—
181C4—10061no—
182C4—10062no—
183C2—22no—
184C2—41no—
185C2—20122no—
186C2—20121no—
187C2—10062no—
188C2—10062no—
189C2C2×D4×D50311yescharacteristic
190C2#3063291012yes—
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#123×C503C2
hypercenter#123D503
hypocenterC503#534
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C22×D2012C2semidirect
2. C2×D4×D503C2semidirect
3. #30632849C2semidirect
4. #30632847C2semidirect
5. #30632839C2semidirect
6. #30632837C2semidirect
7. #30632834C2semidirect
8. #30632834C2semidirect
9. #30632832C2semidirect
10. C22⋊C4×D503C2semidirect
11. #123×C503C2semidirect
13. C23×D503C22semidirect
14. C23×D503C22semidirect
17. C2×D2012C22semidirect
18. C2×D2012C22semidirect
19. C2×D2012C22semidirect
21. C2×C22⋊D503C22semidirect
22. C2×C22⋊D503C22semidirect
24. C2×C4×D503C22semidirect
25. C2×C4×D503C22semidirect
26. Dic503⋊C4C22semidirect
27. C22⋊Dic503C22semidirect
28. (C2×D503)⋊C4C22semidirect
29. (C2×D503)⋊C4C22semidirect
30. (C2×D503)⋊C4C22semidirect
31. (C2×D503)⋊C4C22semidirect
33. C22×C4×C503C22semidirect
34. C4⋊C4×C503C22semidirect
35. C22⋊C4×C503C22semidirect
36. C22⋊C4×C503C22semidirect
42. C22×D503D4semidirect
95. C503#534semidirect
101. #123D503semidirect
123. C22×C4C2×D503semidirect
125. C4⋊C4C2×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×D20122
C2×D4×D5032
#306328492
#306328472
#306328392
#306328372
#306328342
#306328322
C22⋊C4×D5032
#123×C5032
#534503