Finite Group Databasebeta

← C32×D3×C22⋊A4 #72220587

Subgroups — C32×D3×C22⋊A4 #72220587

Order 2592.

2930 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 2930 conjugacy classes of subgroups — too many to draw. Only its 192 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
1C33×C22⋊A4C211yesmaximal, characteristic, complemented
2C24×C32×D3C311yesmaximal, characteristic, complemented
3C2×C32×C22⋊A4—31nomaximal
4C3×D3×C22⋊A4C3112yesmaximal, direct product factor
5C32×D3×A4—45nomaximal
6C24×C33C2×C311yescharacteristic, complemented
7C23×C32×D3—35no—
8C23×C32×D3—35no—
9C32×C22⋊A4—21no—
10C32×C22⋊A4—212no—
11C32×C22⋊A4D311yescharacteristic, direct product factor
12C32×C22⋊A4C2×C3112yescomplemented
13C33×A4—45no—
14C25×C32—31no—
15C24×C3×D3C3214yescomplemented
16C2×C3×C22⋊A4—312no—
17D3×C22⋊A4C3219yesdirect product factor
18C23×C33—35no—
19C22×C32×D3—330no—
20C22×C32×D3—310no—
21C22×C32×D3—35no—
22C22×C32×D3A415yescomplemented
23C2×C32×A4—125no—
24C3×D3×A4—460no—
25C33×D3—161no—
26C24×C32—24no—
27C24×C32—95no—
28C24×C32—95no—
29C24×C32C3×D311yescharacteristic, complemented
30C24×C32C2×C3214yescomplemented
31C23×C3×D3—320no—
32C23×C3×D3—320no—
33C3×C22⋊A4—212no—
34C3×C22⋊A4—236no—
35C3×C22⋊A4C3×D3112yesdirect product factor
36C3×C22⋊A4C2×C3219yescomplemented
37C22×C33—310no—
38C22×C33C2×A415yescomplemented
39C2×C32×D3—330no—
40C2×C32×D3—35no—
41C2×C32×D3—35no—
42C32×A4—45no—
43C32×A4—460no—
44C32×A4—860no—
45C32×A4—85no—
46C25×C3—34no—
47C24×D3C3311yescharacteristic, complemented
48C2×C22⋊A4—39no—
49C34—161noSylow
50C23×C32—35no—
51C23×C32—35no—
52C23×C32—320no—
53C23×C32—620no—
54C23×C32—910no—
55C23×C32—930no—
56C23×C32—95no—
57C22×C3×D3—3120no—
58C22×C3×D3—340no—
59C22×C3×D3—320no—
60C22×C3×D3C3×A4120yescomplemented
61C2×C3×A4—1260no—
62D3×A4—445no—
63C2×C33—35no—
64C2×C33—481no—
65C32×D3—35no—
66C32×D3—1612no—
67C32×D3C22⋊A411yescharacteristic, direct product factor
68C24×C3—24no—
69C24×C3—920no—
70C24×C3—920no—
71C24×C3C32×D314yescomplemented
72C24×C3C2×C3311yescharacteristic, complemented
73C23×D3—35no—
74C23×D3—35no—
75C22⋊A4—29no—
76C22⋊A4C32×D319yesdirect product factor
77C22×C32—220no—
78C22×C32—310no—
79C22×C32—340no—
80C22×C32—640no—
81C22×C32—95no—
82C22×C32—95no—
83C22×C32—930no—
84C22×C32D3×A415yescomplemented
85C22×C32C2×C3×A4120yescomplemented
86C2×C3×D3—3120no—
87C2×C3×D3—320no—
88C2×C3×D3—320no—
89C3×A4—460no—
90C3×A4—445no—
91C3×A4—8180no—
92C3×A4—860no—
93C25—31noSylow
94C33—161no—
95C33—1612no—
96C33—3212no—
97C33—321no—
98C33C2×C22⋊A411yescharacteristic, complemented
99C23×C3—320no—
100C23×C3—35no—
101C23×C3—320no—
102C23×C3—620no—
103C23×C3—940no—
104C23×C3—9120no—
105C23×C3—920no—
106C22×D3—330no—
107C22×D3—310no—
108C22×D3—35no—
109C22×D3C32×A415yescomplemented
110C2×A4—1245no—
111C2×C32—31no—
112C2×C32—35no—
113C2×C32—320no—
114C2×C32—620no—
115C2×C32—95no—
116C2×C32—4812no—
117C3×D3—320no—
118C3×D3—169no—
119C3×D3C3×C22⋊A414yesdirect product factor
120C24—95no—
121C24—95no—
122C24C33×D311yescharacteristic, complemented
123C22×C3—220no—
124C22×C3—310no—
125C22×C3—340no—
126C22×C3—640no—
127C22×C3—920no—
128C22×C3—920no—
129C22×C3—9120no—
130C22×C3C3×D3×A4120yescomplemented
131C22×C3C2×C32×A415yescomplemented
132C2×D3—330no—
133C2×D3—35no—
134C2×D3—35no—
135A4—445no—
136A4—845no—
137C32—24no—
138C32—1612no—
139C32—169no—
140C32—3236no—
141C32—3212no—
142C32D3×C22⋊A411yescharacteristic, direct product factor
143C32C2×C3×C22⋊A414yescomplemented
144C23—35no—
145C23—35no—
146C23—910no—
147C23—930no—
148C23—95no—
149C2×C3—320no—
150C2×C3—34no—
151C2×C3—35no—
152C2×C3—620no—
153C2×C3—920no—
154C2×C3—489no—
155D3—35no—
156D3C32×C22⋊A411yescharacteristic, direct product factor
157C22—310no—
158C22—95no—
159C22—95no—
160C22—930no—
161C22C32×D3×A415yescomplemented
162C3—24no—
163C3—169no—
164C3—329no—
165C3C3×D3×C22⋊A414yesdirect product factor
166C3C2×C32×C22⋊A411yescharacteristic, complemented
167C2—35no—
168C2—31no—
169C2—95no—
subgroupG/H
center, hypercenterC32D3×C22⋊A4
commutator, cosocle, hypocenterC24×C3C2×C33
FrattiniC1G
Fitting, socleC24×C33C2×C3
LCSG ▷ C24×C3
UCSC1 ◁ C32

Complements

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

NH ≅ G/Ntype
1. C33×C22⋊A4C2semidirect
2. C24×C32×D3C3semidirect
4. C3×D3×C22⋊A4C3direct (N × H)
6. C24×C33C2×C3semidirect
11. C32×C22⋊A4D3direct (N × H)
12. C32×C22⋊A4C2×C3semidirect
15. C24×C3×D3C32semidirect
17. D3×C22⋊A4C32direct (N × H)
22. C22×C32×D3A4semidirect
29. C24×C32C3×D3semidirect
30. C24×C32C2×C32semidirect
35. C3×C22⋊A4C3×D3direct (N × H)
36. C3×C22⋊A4C2×C32semidirect
38. C22×C33C2×A4semidirect
47. C24×D3C33semidirect
60. C22×C3×D3C3×A4semidirect
67. C32×D3C22⋊A4direct (N × H)
71. C24×C3C32×D3semidirect
72. C24×C3C2×C33semidirect
76. C22⋊A4C32×D3direct (N × H)
84. C22×C32D3×A4semidirect
85. C22×C32C2×C3×A4semidirect
98. C33C2×C22⋊A4semidirect
109. C22×D3C32×A4semidirect
119. C3×D3C3×C22⋊A4direct (N × H)
122. C24C33×D3semidirect
130. C22×C3C3×D3×A4semidirect
131. C22×C3C2×C32×A4semidirect
142. C32D3×C22⋊A4direct (N × H)
143. C32C2×C3×C22⋊A4semidirect
156. D3C32×C22⋊A4direct (N × H)
161. C22C32×D3×A4semidirect
165. C3C3×D3×C22⋊A4direct (N × H)
166. C3C2×C32×C22⋊A4semidirect

Maximal subgroups

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

subgroupindex
C33×C22⋊A42
C24×C32×D33
C2×C32×C22⋊A43
C3×D3×C22⋊A43
C32×D3×A44