Finite Group Databasebeta

← D3×C22⋊#1039 #72260174

Subgroups — D3×C22⋊#1039 #72260174

Order 2400.

1056 conjugacy classes of subgroups; only the 294 normal subgroups are shown.

normal subgroups only

This group has 1056 conjugacy classes of subgroups — too many to draw. Only its 294 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
1C23×C52×D3C211yesmaximal, characteristic
2C2×D3×#1039C212yesmaximal, complemented
3#11925254C211yesmaximal, characteristic, complemented
4C3×C22⋊#1039C211yesmaximal, characteristic, complemented
5(C2×D3)⋊#1039C212yesmaximal, complemented
6C2×C22⋊#1039—31nomaximal, Hall
7C23×C3×C52C2211yescharacteristic
8C22×C52×D3—24no—
9C22×C52×D3C414yescomplemented
10C22×C52×D3C2211yescharacteristic
11C22×C52×D3C2211yescharacteristic
12C2×C3⋊#1039C2212yescomplemented
13C2×C3×#1039C2212yescomplemented
14D3×#1039—24no—
15D3×C22⋊Dic5—56nomaximal
16C24×C52—31no—
17C22×#1039—32no—
18C22⋊#1039—31no—
19C22⋊#1039—32no—
20C22⋊#1039D311yescharacteristic, direct product factor
21C22×C3×C52—22no—
22C22×C3×C52C2×C412yescomplemented
23C22×C3×C52C2311yescharacteristic
24C2×C52×D3—22no—
25C2×C52×D3—28no—
26C2×C52×D3C2×C412yes—
27C2×C52×D3C2×C412yescomplemented
28C2×C52×D3D414yes—
29C3⋊#1039—22no—
30C3×#1039—22no—
31C23×C5×D3D516yes—
32C2×D3×Dic5—512no—
33#6719—56no—
34C3×C22⋊Dic5—56no—
35(C2×D3)⋊Dic5—512no—
36C23×C52—31no—
37C23×C52—34no—
38C23×C52—31no—
39C23×C52—64no—
40C23×C52C2×D311yescharacteristic
41C2×#1039—32no—
42C2×#1039—64no—
43C2×#1039C2×D312yescomplemented
44C2×C22⋊Dic5—156no—
45C2×C3×C52—22no—
46C2×C3×C52C22×C411yescharacteristic
47C2×C3×C52C2×D412yes—
48C52×D3—22no—
49C52×D3C22⋊C414yescomplemented
50C23×C3×C5C2×D516yes—
51C22×C5×D3—224no—
52C22×C5×D3Dic5124yescomplemented
53C22×C5×D3C2×D516yes—
54C22×C5×D3C2×D516yes—
55C2×Dic15—512no—
56C2×C3×Dic5—512no—
57D3×Dic5—1024no—
58C22×C52—22no—
59C22×C52—32no—
60C22×C52—34no—
61C22×C52—32no—
62C22×C52—68no—
63C22×C52—62no—
64C22×C52C4×D312yescomplemented
65C22×C52C22×D311yescharacteristic
66#1039—22no—
67#1039—62no—
68D3×C22⋊C4—251noHall
69C24×C5—36no—
70C22×Dic5—1512no—
71C22⋊Dic5—56no—
72C22⋊Dic5—1512no—
73C22⋊Dic5—156no—
74C3×C52C2×C22⋊C411yescharacteristic, complemented, Hall
75C22×C3×C5—212no—
76C22×C3×C5C2×Dic5112yescomplemented
77C22×C3×C5C22×D516yes—
78C2×C5×D3—212no—
79C2×C5×D3—248no—
80C2×C5×D3C2×Dic5112yes—
81C2×C5×D3C2×Dic5112yescomplemented
82C2×C5×D3C22⋊D5124yes—
83Dic15—1012no—
84C3×Dic5—1012no—
85C2×C52—22no—
86C2×C52—34no—
87C2×C52—62no—
88C2×C52C2×C4×D311yescharacteristic
89C2×C52D3×D412yes—
90C23×D3C5⋊D511yescharacteristic
91C2×C4×D3—252no—
92C3×C22⋊C4—251no—
93#217—251no—
94(C2×D3)⋊C4—252no—
95C23×C5—36no—
96C23×C5—324no—
97C23×C5—36no—
98C23×C5—624no—
99C23×C5D3×D516yes—
100C2×Dic5—512no—
101C2×Dic5—1512no—
102C2×Dic5—3024no—
103C2×C22⋊C4—751noSylow
104C2×C3×C5—212no—
105C2×C3×C5C22×Dic516yes—
106C2×C3×C5C2×C22⋊D5112yes—
107C5×D3—212no—
108C5×D3C22⋊Dic5124yescomplemented
109C52D3×C22⋊C411yescharacteristic, complemented, Sylow
110C23×C3C2×C5⋊D511yescharacteristic
111C22×D3—24no—
112C22×D3#103914yescomplemented
113C22×D3C2×C5⋊D511yescharacteristic
114C22×D3C2×C5⋊D511yescharacteristic
115C2×C3×C4—252no—
116C2×Dic3—252no—
117C4×D3—504no—
118C22×C5—212no—
119C22×C5—312no—
120C22×C5—324no—
121C22×C5—312no—
122C22×C5—648no—
123C22×C5—612no—
124C22×C5D3×Dic5112yescomplemented
125C22×C5C2×D3×D516yes—
126Dic5—1012no—
127Dic5—3012no—
128C24—31no—
129C22×C4—752no—
130C22⋊C4—251no—
131C22⋊C4—752no—
132C22⋊C4—751no—
133C3×C5C2×C22⋊Dic516yescomplemented
134C22×C3—22no—
135C22×C3C2×#103912yescomplemented
136C22×C3C22×C5⋊D511yescharacteristic
137C2×D3—22no—
138C2×D3—28no—
139C2×D3C2×#103912yes—
140C2×D3C2×#103912yescomplemented
141C2×D3C22⋊(C5⋊D5)14yes—
142C3×C4—502no—
143Dic3—502no—
144C2×C5—212no—
145C2×C5—324no—
146C2×C5—612no—
147C2×C5C2×D3×Dic516yes—
148C2×C5D3×C22⋊D5112yes—
149C23—31no—
150C23—31no—
151C23—34no—
152C23—64no—
153C23D3×C5⋊D511yescharacteristic
154C2×C4—252no—
155C2×C4—752no—
156C2×C4—1504no—
157C2×C3—22no—
158C2×C3C22×#103911yescharacteristic
159C2×C3C2×C22⋊(C5⋊D5)12yes—
160D3—22no—
161D3C22⋊#103914yesdirect product factor
162C5D3×C22⋊Dic516yescomplemented
163C22—22no—
164C22—32no—
165C22—34no—
166C22—32no—
167C22—68no—
168C22—62no—
169C22D3×#103912yescomplemented
170C22C2×D3×C5⋊D511yescharacteristic
171C4—502no—
172C4—1502no—
173C3C2×C22⋊#103911yescharacteristic, complemented, Sylow
174C2—22no—
175C2—34no—
176C2—62no—
177C2C2×D3×#103911yescharacteristic
178C2D3×C22⋊(C5⋊D5)12yes—
subgroupG/H
center, FrattiniC22C2×D3×C5⋊D5
commutatorC2×C3×C52C22×C4
FittingC23×C3×C52C22
socle, cosocleC22×C3×C52C23
prime radicalC23×C52×D3C2
hypercenterC23D3×C5⋊D5
hypocenterC3×C52C2×C22⋊C4
LCSG ▷ C2×C3×C52 ▷ C3×C52
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C2×D3×#1039C2semidirect
3. #11925254C2semidirect
4. C3×C22⋊#1039C2semidirect
5. (C2×D3)⋊#1039C2semidirect
9. C22×C52×D3C4semidirect
12. C2×C3⋊#1039C22semidirect
13. C2×C3×#1039C22semidirect
20. C22⋊#1039D3direct (N × H)
22. C22×C3×C52C2×C4semidirect
27. C2×C52×D3C2×C4semidirect
43. C2×#1039C2×D3semidirect
49. C52×D3C22⋊C4semidirect
52. C22×C5×D3Dic5semidirect
64. C22×C52C4×D3semidirect
74. C3×C52C2×C22⋊C4semidirect
76. C22×C3×C5C2×Dic5semidirect
81. C2×C5×D3C2×Dic5semidirect
108. C5×D3C22⋊Dic5semidirect
109. C52D3×C22⋊C4semidirect
112. C22×D3#1039semidirect
124. C22×C5D3×Dic5semidirect
133. C3×C5C2×C22⋊Dic5semidirect
135. C22×C3C2×#1039semidirect
140. C2×D3C2×#1039semidirect
161. D3C22⋊#1039direct (N × H)
162. C5D3×C22⋊Dic5semidirect
169. C22D3×#1039semidirect
173. C3C2×C22⋊#1039semidirect

Maximal subgroups

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

subgroupindex
C23×C52×D32
C2×D3×#10392
#119252542
C3×C22⋊#10392
(C2×D3)⋊#10392
C2×C22⋊#10393
D3×C22⋊Dic55