Finite Group Databasebeta

← #44566789

Subgroups — #44566789

Order 32192.

330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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#30632847C211yesmaximal, characteristic, complemented
4#30632842C212yesmaximal, complemented
5#30632837C212yesmaximal, complemented
6#30632834C211yesmaximal, characteristic, complemented
7#30632832C211yesmaximal, characteristic, complemented
8#30632826C212yesmaximal, complemented
9(C22⋊D503)⋊C4C212yesmaximal, complemented
10#30632820C211yesmaximal, characteristic, complemented
11#123×C503C211yesmaximal, characteristic, complemented
12C23×D503C2211yescharacteristic
13#22548882—24no—
14C2×Dic1006C2211yescharacteristic, complemented
15C2×D2012C2212yes—
16C2×C22⋊D503C2212yes—
17C2×C22⋊D503C2211yescharacteristic
18C2×C22⋊D503C2211yescharacteristic, complemented
19C22×Dic503C2211yescharacteristic
20C22×Dic503C2211yescharacteristic, complemented
21C2×C4×D503—24no—
22C2×C4×D503C2212yes—
23C2×C4×D503C2212yes—
24C2×C4×D503C2211yescharacteristic, complemented
25Dic503⋊C4C2212yescomplemented
26Dic503⋊C4C2212yescomplemented
27C22⋊Dic503C2211yescharacteristic
28(C2×D503)⋊C4C2212yes—
29(C2×D503)⋊C4C2212yes—
30(C2×D503)⋊C4C2212yescomplemented
31C4×Dic503C2212yescomplemented
32C2×D4×C503C2211yescharacteristic
33C22×C4×C503C2211yescharacteristic
34C4⋊C4×C503C2212yescomplemented
35C22⋊C4×C503C2211yescharacteristic
36C22⋊C4×C503C2212yescomplemented
37C22×D503—22no—
38C22×D503—24no—
39C22×D503C2311yescharacteristic
40C22×D503C2312yes—
41Dic1006—22no—
42D2012—24no—
43C22⋊D503—22no—
44C22⋊D503—24no—
45C22⋊D503—22no—
46C2×Dic503—22no—
47C2×Dic503D414yescomplemented
48C2×Dic503C2312yes—
49C2×Dic503C2311yescharacteristic
50C2×Dic503C2311yescharacteristic
51C2×Dic503C2311yescharacteristic
52C4×D503—24no—
53C4×D503—24no—
54C4×D503—22no—
55C23×C503C2311yescharacteristic
56C23×C503C2311yescharacteristic
57D4×C503—22no—
58C2×C4×C503—22no—
59C2×C4×C503C2312yes—
60C2×C4×C503C2312yes—
61C2×C4×C503C2311yescharacteristic
62C22×C503—22no—
63C22×C503—21no—
64C22×C503—22no—
65C22×C503C2×D412yes—
66C22×C503C2411yescharacteristic
67C2×D503—28no—
68C2×D503—22no—
69C2×D503—22no—
70C2×D503—21no—
71C2×D503—22no—
72C2×D503#4114yescomplemented
73C4×C503—22no—
74C4×C503—21no—
75C4×C503—22no—
76Dic503—21no—
77Dic503—22no—
78Dic503C2×D412yes—
79Dic503C2×D412yes—
80C2×C503—22no—
81C2×C503—41no—
82C2×C503C22×D411yescharacteristic
83C2×C503C2×#4112yes—
84D503—24no—
85D503—41no—
86C503#52511yescharacteristic, complemented, Sylow
87#525—5031nomaximal, Sylow
88C2×#41—5031no—
89C23×C4—5031no—
90#123—5031no—
91#123D50311yescharacteristic, complemented
92C22⋊Q8—5032no—
93#121—5032no—
94#120—5031no—
95#120—5031no—
96C4×D4—5032no—
97C4×D4—5032no—
98#117—5031no—
99C24—5031no—
100#41—10064no—
101C2×Q8—5031no—
102C2×D4—5032no—
103C2×D4—5031no—
104C2×D4—5031no—
105C2×D4—5032no—
106C2×D4C2×D50311yescharacteristic
107C22×C4—10064no—
108C22×C4—5031no—
109C22×C4—5032no—
110C22×C4—5031no—
111C22×C4—5032no—
112C22×C4—5031no—
113C22×C4C2×D50311yescharacteristic
114C4⋊C4—5032no—
115C4⋊C4—5032no—
116C4⋊C4C2×D50312yescomplemented
117C22⋊C4—5031no—
118C22⋊C4—5032no—
119C22⋊C4—5032no—
120C22⋊C4—5032no—
121C22⋊C4C2×D50311yescharacteristic
122C22⋊C4C2×D50312yescomplemented
123C42—5032no—
124C23—10064no—
125C23—10062no—
126C23—5031no—
127C23—5032no—
128C23C22×D50311yescharacteristic
129C23C22×D50311yescharacteristic
130Q8—10062no—
131D4—22no—
132D4—10064no—
133D4—10064no—
134D4—10062no—
135D4—10062no—
136C2×C4—22no—
137C2×C4—10064no—
138C2×C4—10064no—
139C2×C4—10062no—
140C2×C4—10062no—
141C2×C4—5032no—
142C2×C4—5031no—
143C2×C4—5034no—
144C2×C4—5031no—
145C2×C4—5031no—
146C2×C4C22×D50312yes—
147C2×C4C22×D50311yescharacteristic
148C2×C4C22×D50312yes—
149C22—22no—
150C22—21no—
151C22—22no—
152C22—10068no—
153C22—10061no—
154C22—10062no—
155C22—10062no—
156C22—10062no—
157C22—5034no—
158C22D4×D50312yes—
159C22C23×D50311yescharacteristic
160C4—22no—
161C4—21no—
162C4—22no—
163C4—10061no—
164C4—10062no—
165C4—5032no—
166C4—5032no—
167C2—22no—
168C2—41no—
169C2—20121no—
170C2—10064no—
171C2C2×D4×D50311yescharacteristic
172C2#41×D50312yes—
subgroupG/H
center, FrattiniC22C23×D503
commutator, socle, cosocleC22×C503C24
Fitting#123×C503C2
hypercenter#123D503
hypocenterC503#525
LCSG ▷ C22×C503 ▷ C503
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#22548882C2semidirect
2. C22×C4×D503C2semidirect
3. #30632847C2semidirect
4. #30632842C2semidirect
5. #30632837C2semidirect
6. #30632834C2semidirect
7. #30632832C2semidirect
8. #30632826C2semidirect
9. (C22⋊D503)⋊C4C2semidirect
10. #30632820C2semidirect
11. #123×C503C2semidirect
14. C2×Dic1006C22semidirect
18. C2×C22⋊D503C22semidirect
20. C22×Dic503C22semidirect
24. C2×C4×D503C22semidirect
25. Dic503⋊C4C22semidirect
26. Dic503⋊C4C22semidirect
30. (C2×D503)⋊C4C22semidirect
31. C4×Dic503C22semidirect
34. C4⋊C4×C503C22semidirect
36. C22⋊C4×C503C22semidirect
47. C2×Dic503D4semidirect
72. C2×D503#41semidirect
86. C503#525semidirect
91. #123D503semidirect
116. C4⋊C4C2×D503semidirect
122. 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×C4×D5032
#306328472
#306328422
#306328372
#306328342
#306328322
#306328262
(C22⋊D503)⋊C42
#306328202
#123×C5032
#525503