Finite Group Databasebeta

← C24×C22⋊#6157 #28330798

Subgroups — C24×C22⋊#6157 #28330798

Order 13568.

43678 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 43678 conjugacy classes of subgroups — too many to draw. Only its 8408 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
1C25×#6157C212yesmaximal, complemented
2C23×C22⋊#6157C2160yesmaximal, direct product factor
3C26×D53C211yesmaximal, characteristic
4C24×#6157—232no—
5C24×#6157C22160yescomplemented
6C22×C22⋊#6157C221560yesdirect product factor
7C25×D53—232no—
8C25×D53C411yescharacteristic, complemented
9C25×D53C4130yescomplemented
10C25×D53C2211yescharacteristic
11C25×D53C22130yes—
12C26×C53C411yescharacteristic, complemented
13C23×#6157—2480no—
14C23×#6157C231280yescomplemented
15C2×C22⋊#6157C231960yesdirect product factor
16C24×D53—216no—
17C24×D53—2480no—
18C24×D53—2480no—
19C24×D53C2×C4115yes—
20C24×D53C2×C41420yescomplemented
21C24×D53C2×C4130yescomplemented
22C24×D53D4132yes—
23C24×D53C231140yes—
24C24×D53C23115yes—
25C25×C53—216no—
26C25×C53C2×C411yescharacteristic
27C25×C53C2×C4130yescomplemented
28C24×C53—2240no—
29C24×C53C22⋊C4116yescomplemented
30C24×C53C22×C4115yes—
31C24×C53C22×C41140yescomplemented
32C23×D53—2240no—
33C23×D53—23360no—
34C23×D53—21120no—
35C23×D53C22⋊C41240yescomplemented
36C23×D53C22×C41105yes—
37C23×D53C22×C41840yescomplemented
38C23×D53C22×C41140yescomplemented
39C23×D53C2×D41240yes—
40C23×D53C241120yes—
41C23×D53C24135yes—
42C22×#6157—21120no—
43C22×#6157C241240yescomplemented
44C22⋊#6157C241256yesdirect product factor
45C23×C53—2560no—
46C23×C53C2×C22⋊C41120yescomplemented
47C23×C53C23×C4135yes—
48C23×C53C23×C41120yescomplemented
49C22×D53—2560no—
50C22×D53—23360no—
51C22×D53—2480no—
52C22×D53C2×C22⋊C41840yescomplemented
53C22×D53C23×C41105yes—
54C22×D53C23×C41240yescomplemented
55C22×D53C23×C41120yescomplemented
56C22×D53C22×D41280yes—
57C22×D53C25116yes—
58C22×D53C25115yes—
59C2×#6157—2480no—
60C2×#6157C25132yescomplemented
61C24×C22⋊C4—531nomaximal, Sylow
62C22×C53—2240no—
63C22×C53C22×C22⋊C41140yescomplemented
64C22×C53C24×C4115yes—
65C22×C53C24×C4116yescomplemented
66C2×D53—2240no—
67C2×D53—232no—
68C2×D53—2480no—
69C2×D53C22×C22⋊C41420yescomplemented
70C2×D53C24×C4115yes—
71C2×D53C24×C4116yescomplemented
72C2×D53C23×D4160yes—
73C2×D53C2611yescharacteristic
74#6157—232no—
75C27—531no—
76C25×C4—532no—
77C23×C22⋊C4—5360no—
78C2×C53—216no—
79C2×C53C23×C22⋊C4130yescomplemented
80C2×C53C25×C411yescharacteristic
81D53—216no—
82D53C23×C22⋊C4130yescomplemented
83D53C24×D412yes—
84C26—531no—
85C26—531no—
86C26—5330no—
87C26—5330no—
88C26—10632no—
89C26#615711yescharacteristic, complemented
90C24×C4—5360no—
91C24×C4—10632no—
92C22×C22⋊C4—53560no—
93C53C24×C22⋊C411yescharacteristic, complemented, Sylow
94C25—216no—
95C25—5332no—
96C25—5315no—
97C25—5315no—
98C25—5330no—
99C25—53140no—
100C25—53420no—
101C25—106480no—
102C25—106480no—
103C25—10616no—
104C25C2×#615711yescharacteristic
105C25C2×#6157130yescomplemented
106C23×C4—53280no—
107C23×C4—106480no—
108C2×C22⋊C4—53960no—
109C24—2240no—
110C24—53240no—
111C24—53240no—
112C24—53105no—
113C24—5335no—
114C24—53140no—
115C24—53840no—
116C24—53120no—
117C24—1063360no—
118C24—1061120no—
119C24—106240no—
120C24C22⋊#6157116yesdirect product factor
121C24C22×#6157115yes—
122C24C22×#61571140yescomplemented
123C22×C4—53240no—
124C22×C4—1061120no—
125C22⋊C4—53256no—
126C23—2560no—
127C23—53840no—
128C23—53280no—
129C23—53105no—
130C23—5315no—
131C23—53120no—
132C23—53240no—
133C23—5316no—
134C23—106480no—
135C23—1063360no—
136C23—106560no—
137C23C2×C22⋊#61571120yesdirect product factor
138C23C23×#6157135yes—
139C23C23×#61571120yescomplemented
140C2×C4—5332no—
141C2×C4—106480no—
142C22—2240no—
143C22—5360no—
144C22—53420no—
145C22—531no—
146C22—5315no—
147C22—5316no—
148C22—10632no—
149C22—106480no—
150C22—106240no—
151C22C22×C22⋊#61571140yesdirect product factor
152C22C24×#6157115yes—
153C22C24×#6157116yescomplemented
154C4—10632no—
155C2—216no—
156C2—532no—
157C2—5330no—
158C2—10616no—
159C2C23×C22⋊#6157130yesdirect product factor
160C2C25×#615711yescharacteristic
subgroupG/H
centerC25C2×#6157
commutatorC2×C53C25×C4
FrattiniC2C25×#6157
FittingC26×C53C4
socleC25×C53C2×C4
prime radicalC26×D53C2
cosocleC2×D53C26
hypercenterC26#6157
hypocenterC53C24×C22⋊C4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C25 ◁ C26

Complements

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

NH ≅ G/Ntype
1. C25×#6157C2semidirect
2. C23×C22⋊#6157C2direct (N × H)
5. C24×#6157C22semidirect
6. C22×C22⋊#6157C22direct (N × H)
8. C25×D53C4semidirect
9. C25×D53C4semidirect
12. C26×C53C4semidirect
14. C23×#6157C23semidirect
15. C2×C22⋊#6157C23direct (N × H)
20. C24×D53C2×C4semidirect
21. C24×D53C2×C4semidirect
27. C25×C53C2×C4semidirect
29. C24×C53C22⋊C4semidirect
31. C24×C53C22×C4semidirect
35. C23×D53C22⋊C4semidirect
37. C23×D53C22×C4semidirect
38. C23×D53C22×C4semidirect
43. C22×#6157C24semidirect
44. C22⋊#6157C24direct (N × H)
46. C23×C53C2×C22⋊C4semidirect
48. C23×C53C23×C4semidirect
52. C22×D53C2×C22⋊C4semidirect
54. C22×D53C23×C4semidirect
55. C22×D53C23×C4semidirect
60. C2×#6157C25semidirect
63. C22×C53C22×C22⋊C4semidirect
65. C22×C53C24×C4semidirect
69. C2×D53C22×C22⋊C4semidirect
71. C2×D53C24×C4semidirect
79. C2×C53C23×C22⋊C4semidirect
82. D53C23×C22⋊C4semidirect
89. C26#6157semidirect
93. C53C24×C22⋊C4semidirect
105. C25C2×#6157semidirect
120. C24C22⋊#6157direct (N × H)
122. C24C22×#6157semidirect
137. C23C2×C22⋊#6157direct (N × H)
139. C23C23×#6157semidirect
151. C22C22×C22⋊#6157direct (N × H)
153. C22C24×#6157semidirect
159. C2C23×C22⋊#6157direct (N × H)

Maximal subgroups

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

subgroupindex
C25×#61572
C23×C22⋊#61572
C26×D532
C24×C22⋊C453