Finite Group Databasebeta

← #44566794

Subgroups — #44566794

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×#22548884C211yesmaximal, characteristic, complemented
2C22×C4×D503C211yesmaximal, characteristic, complemented
3#30632849C212yesmaximal, complemented
4#30632840C211yesmaximal, characteristic, complemented
5#30632839C211yesmaximal, characteristic, complemented
6#30632838C211yesmaximal, characteristic, complemented
7#30632834C212yesmaximal, complemented
8#30632826C212yesmaximal, complemented
9(C22⋊D503)⋊C4C212yesmaximal, complemented
10#30632822C211yesmaximal, characteristic, complemented
11C22⋊Q8×C503C211yesmaximal, characteristic, complemented
12C23×D503C2211yescharacteristic
13#22548884—24no—
14C2×D2012C2212yes—
15C2×D2012C2212yes—
16C2×D2012C2211yescharacteristic, complemented
17C2×C22⋊D503C2212yes—
18C22×Dic503C2211yescharacteristic
19C2×C4×D503—24no—
20C2×C4×D503C2211yescharacteristic
21C2×C4×D503C2211yescharacteristic
22C2×C4×D503C2211yescharacteristic
23C2×C4×D503C2211yescharacteristic
24C2×C4×D503C2212yescomplemented
25C4⋊Dic503C2211yescharacteristic, complemented
26Dic503⋊C4C2212yescomplemented
27(C2×D503)⋊C4C2212yes—
28(C2×D503)⋊C4C2212yes—
29(C2×D503)⋊C4C2212yescomplemented
30(C2×D503)⋊C4C2212yescomplemented
31C4×Dic503C2212yescomplemented
32C2×Q8×C503C2211yescharacteristic, complemented
33C22×C4×C503C2211yescharacteristic
34C4⋊C4×C503C2211yescharacteristic, complemented
35C4⋊C4×C503C2212yescomplemented
36C22⋊C4×C503C2212yes—
37C22×D503—22no—
38C22×D503—22no—
39C22×D503—22no—
40C22×D503C2312yes—
41C22×D503C2311yescharacteristic
42C22×D503C2311yescharacteristic
43D2012—24no—
44D2012—24no—
45D2012—22no—
46C22⋊D503—24no—
47C2×Dic503—22no—
48C2×Dic503C2312yes—
49C2×Dic503C2311yescharacteristic
50C2×Dic503C2311yescharacteristic
51C4×D503—22no—
52C4×D503—22no—
53C4×D503—22no—
54C4×D503—24no—
55C4×D503D414yescomplemented
56C23×C503C2311yescharacteristic
57Q8×C503—22no—
58C2×C4×C503—22no—
59C2×C4×C503C2312yes—
60C2×C4×C503C2312yes—
61C2×C4×C503C2311yescharacteristic
62C2×C4×C503C2311yescharacteristic
63C22×C503—21no—
64C22×C503—21no—
65C22×C503#4112yescomplemented
66C22×C503C2411yescharacteristic
67C2×D503—28no—
68C2×D503—21no—
69C2×D503—21no—
70C2×D503—21no—
71C2×D503—21no—
72C2×D503—22no—
73C2×D503—22no—
74C2×D503—22no—
75C2×D503C2×D412yes—
76C2×D503#4112yescomplemented
77C4×C503—21no—
78C4×C503—22no—
79C4×C503—22no—
80C4×C503C2×D412yes—
81Dic503—21no—
82Dic503—22no—
83Dic503C2×D412yes—
84C2×C503—22no—
85C2×C503C22×D411yescharacteristic
86C2×C503C2×#4111yescharacteristic
87C2×C503C2×#4111yescharacteristic
88D503—22no—
89D503—22no—
90D503—42no—
91C503#52511yescharacteristic, complemented, Sylow
92#525—5031nomaximal, Sylow
93C2×#41—5031no—
94C23×C4—5031no—
95#123—5032no—
96C22⋊Q8—5031no—
97C22⋊Q8D50311yescharacteristic, complemented
98#121—5031no—
99#121—5031no—
100#120—5032no—
101C4×D4—5032no—
102C4×D4—5032no—
103#117—5031no—
104C24—5031no—
105#41—10064no—
106C2×Q8C2×D50311yescharacteristic, complemented
107C2×D4—5032no—
108C2×D4—5032no—
109C2×D4—5032no—
110C2×D4—5031no—
111C22×C4—10064no—
112C22×C4—5031no—
113C22×C4—5031no—
114C22×C4—5032no—
115C22×C4—5031no—
116C22×C4—5031no—
117C22×C4—5031no—
118C22×C4C2×D50311yescharacteristic
119C4⋊C4—5031no—
120C4⋊C4—5032no—
121C4⋊C4C2×D50311yescharacteristic, complemented
122C4⋊C4C2×D50312yescomplemented
123C22⋊C4—5032no—
124C22⋊C4—5032no—
125C22⋊C4—5032no—
126C22⋊C4—5032no—
127C22⋊C4C2×D50312yes—
128C42—5032no—
129C23—10062no—
130C23—10062no—
131C23—10062no—
132C23—5032no—
133C23—5031no—
134C23—5031no—
135C23C22×D50311yescharacteristic
136Q8—22no—
137D4—10064no—
138D4—10064no—
139D4—10064no—
140D4—10062no—
141C2×C4—22no—
142C2×C4—10062no—
143C2×C4—10062no—
144C2×C4—10064no—
145C2×C4—10062no—
146C2×C4—10062no—
147C2×C4—5032no—
148C2×C4—5031no—
149C2×C4—5031no—
150C2×C4—5034no—
151C2×C4C22×D50312yes—
152C2×C4C22×D50311yescharacteristic
153C2×C4C22×D50312yes—
154C2×C4C22×D50311yescharacteristic
155C22—21no—
156C22—21no—
157C22—10068no—
158C22—10062no—
159C22—10062no—
160C22—10062no—
161C22—10061no—
162C22—10061no—
163C22—10061no—
164C22—10061no—
165C22—5032no—
166C22—5032no—
167C22#2254888412yescomplemented
168C22C23×D50311yescharacteristic
169C4—21no—
170C4—22no—
171C4—22no—
172C4—10061no—
173C4—10062no—
174C4—5032no—
175C4D4×D50312yes—
176C2—22no—
177C2—20122no—
178C2—10062no—
179C2—10062no—
180C2C2×D4×D50311yescharacteristic
181C2#41×D50311yescharacteristic
182C2C2×#2254888411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
FittingC22⋊Q8×C503C2
hypercenterC22⋊Q8D503
hypocenterC503#525
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#22548884C2semidirect
2. C22×C4×D503C2semidirect
3. #30632849C2semidirect
4. #30632840C2semidirect
5. #30632839C2semidirect
6. #30632838C2semidirect
7. #30632834C2semidirect
8. #30632826C2semidirect
9. (C22⋊D503)⋊C4C2semidirect
10. #30632822C2semidirect
11. C22⋊Q8×C503C2semidirect
16. C2×D2012C22semidirect
24. C2×C4×D503C22semidirect
25. C4⋊Dic503C22semidirect
26. Dic503⋊C4C22semidirect
29. (C2×D503)⋊C4C22semidirect
30. (C2×D503)⋊C4C22semidirect
31. C4×Dic503C22semidirect
32. C2×Q8×C503C22semidirect
34. C4⋊C4×C503C22semidirect
35. C4⋊C4×C503C22semidirect
55. C4×D503D4semidirect
65. C22×C503#41semidirect
76. C2×D503#41semidirect
91. C503#525semidirect
97. C22⋊Q8D503semidirect
106. C2×Q8C2×D503semidirect
121. C4⋊C4C2×D503semidirect
122. C4⋊C4C2×D503semidirect
167. C22#22548884semidirect

Maximal subgroups

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

subgroupindex
C2×#225488842
C22×C4×D5032
#306328492
#306328402
#306328392
#306328382
#306328342
#306328262
(C22⋊D503)⋊C42
#306328222
C22⋊Q8×C5032
#525503