Finite Group Databasebeta

← C3×A43 #72252856

Subgroups — C3×A43 #72252856

Order 5184.

2806 conjugacy classes of subgroups; only the 316 normal subgroups are shown.

normal subgroups only

This group has 2806 conjugacy classes of subgroups — too many to draw. Only its 316 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
1C3×#10596782C314yesmaximal, complemented
2C3×A4×C22⋊A4C316yesmaximal, complemented
3C22×C3×A42C313yesmaximal, complemented
4A43C3127yesmaximal, direct product factor
5C32×A42—43nomaximal
6C2×C3×A42—33no—
7C3×C22⋊(C22⋊A4)C3214yescomplemented
8C22×C3×C22⋊A4C3216yescomplemented
9C24×C3×A4C3213yescomplemented
10#10596782C32136yescomplemented
11A4×C22⋊A4C32154yescomplemented
12C22×A42C32127yescomplemented
13C32×C22⋊A4—46no—
14C22×C32×A4—46no—
15C3×A42—412no—
16C3×A42—412no—
17C3×A42—481no—
18C3×A42—126no—
19C3×A42A413yesdirect product factor
20C33×A4—163no—
21C2×C3×C22⋊A4—36no—
22C23×C3×A4—36no—
23C23×C3×A4—93no—
24C2×A42—327no—
25C2×C32×A4—126no—
26C26×C3C3311yescharacteristic, complemented
27C22⋊(C22⋊A4)C33112yescomplemented
28C22×C22⋊A4C33118yescomplemented
29C24×A4C3319yescomplemented
30C24×C32—43no—
31C3×C22⋊A4—412no—
32C3×C22⋊A4—454no—
33C3×C22⋊A4—1212no—
34C3×C22⋊A4—364no—
35C3×C22⋊A4C3×A416yescomplemented
36C22×C3×A4—36no—
37C22×C3×A4—412no—
38C22×C3×A4—454no—
39C22×C3×A4—93no—
40C22×C3×A4—96no—
41C22×C3×A4—126no—
42C22×C3×A4C3×A416yescomplemented
43A42—4108no—
44A42—4108no—
45A42—1254no—
46A42C3×A4127yesdirect product factor
47C22×C33—163no—
48C32×A4—46no—
49C32×A4—1612no—
50C32×A4—1681no—
51C32×A4—1612no—
52C32×A4—166no—
53C32×A4—486no—
54C25×C3—33no—
55C25×C3—93no—
56C25×C3—271no—
57C2×C22⋊A4—318no—
58C23×A4—318no—
59C23×A4—99no—
60C34—641noSylow
61C23×C32—126no—
62C23×C32—363no—
63C2×C3×A4—36no—
64C2×C3×A4—93no—
65C2×C3×A4—1254no—
66C2×C3×A4—1212no—
67C2×C3×A4—366no—
68C26C3411yescharacteristic, complemented, Sylow
69C2×C33—483no—
70C24×C3—36no—
71C24×C3—49no—
72C24×C3—93no—
73C24×C3—96no—
74C24×C3—94no—
75C24×C3—273no—
76C24×C3—273no—
77C24×C3—276no—
78C24×C3—271no—
79C24×C3—276no—
80C24×C3C32×A413yescomplemented
81C22⋊A4—436no—
82C22⋊A4—1236no—
83C22⋊A4—3612no—
84C22⋊A4C32×A4118yescomplemented
85C22×A4—318no—
86C22×A4—436no—
87C22×A4—99no—
88C22×A4—918no—
89C22×A4—1218no—
90C22×A4C32×A4118yescomplemented
91C22×C32—46no—
92C22×C32—126no—
93C22×C32—1627no—
94C22×C32—166no—
95C22×C32—363no—
96C22×C32—366no—
97C3×A4—412no—
98C3×A4—454no—
99C3×A4—126no—
100C3×A4—16108no—
101C3×A4—16108no—
102C3×A4—1612no—
103C3×A4—1654no—
104C3×A4—4854no—
105C3×A4—4812no—
106C3×A4—1444no—
107C3×A4A4213yesdirect product factor
108C25—33no—
109C25—93no—
110C25—271no—
111C33—163no—
112C33—646no—
113C33—6427no—
114C33—644no—
115C23×C3—36no—
116C23×C3—93no—
117C23×C3—96no—
118C23×C3—93no—
119C23×C3—1218no—
120C23×C3—276no—
121C23×C3—271no—
122C23×C3—276no—
123C23×C3—276no—
124C23×C3—273no—
125C23×C3—273no—
126C23×C3—2712no—
127C23×C3—278no—
128C23×C3—272no—
129C23×C3—369no—
130C2×A4—318no—
131C2×A4—99no—
132C2×A4—1236no—
133C2×A4—3618no—
134C2×C32—126no—
135C2×C32—363no—
136C2×C32—486no—
137C2×C32—4827no—
138C24—36no—
139C24—93no—
140C24—96no—
141C24—94no—
142C24—273no—
143C24—273no—
144C24—276no—
145C24—271no—
146C24—276no—
147C24C33×A413yescomplemented
148C22×C3—36no—
149C22×C3—418no—
150C22×C3—93no—
151C22×C3—96no—
152C22×C3—94no—
153C22×C3—1218no—
154C22×C3—1618no—
155C22×C3—273no—
156C22×C3—273no—
157C22×C3—271no—
158C22×C3—276no—
159C22×C3—276no—
160C22×C3—369no—
161C22×C3—3618no—
162C22×C3C3×A4213yescomplemented
163A4—436no—
164A4—1218no—
165A4—1636no—
166A4—4836no—
167A4—14412no—
168A4C3×A4219yesdirect product factor
169C32—43no—
170C32—1627no—
171C32—166no—
172C32—6454no—
173C32—6436no—
174C32—644no—
175C23—36no—
176C23—93no—
177C23—96no—
178C23—93no—
179C23—276no—
180C23—271no—
181C23—276no—
182C23—276no—
183C23—273no—
184C23—273no—
185C23—2712no—
186C23—278no—
187C23—272no—
188C2×C3—33no—
189C2×C3—93no—
190C2×C3—1218no—
191C2×C3—271no—
192C2×C3—369no—
193C2×C3—4818no—
194C22—36no—
195C22—93no—
196C22—96no—
197C22—94no—
198C22—273no—
199C22—273no—
200C22—271no—
201C22—276no—
202C22—276no—
203C22C32×A4213yescomplemented
204C3—49no—
205C3—1618no—
206C3—6412no—
207C3A4311yescharacteristic, direct product factor
208C2—33no—
209C2—93no—
210C2—271no—
subgroupG/H
center, hypercenterC3A43
commutator, cosocle, hypocenterC26C34
FrattiniC1G
Fitting, socleC26×C3C33
LCSG ▷ C26
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×#10596782C3semidirect
2. C3×A4×C22⋊A4C3semidirect
3. C22×C3×A42C3semidirect
4. A43C3direct (N × H)
7. C3×C22⋊(C22⋊A4)C32semidirect
8. C22×C3×C22⋊A4C32semidirect
9. C24×C3×A4C32semidirect
10. #10596782C32semidirect
11. A4×C22⋊A4C32semidirect
12. C22×A42C32semidirect
19. C3×A42A4direct (N × H)
26. C26×C3C33semidirect
27. C22⋊(C22⋊A4)C33semidirect
28. C22×C22⋊A4C33semidirect
29. C24×A4C33semidirect
35. C3×C22⋊A4C3×A4semidirect
42. C22×C3×A4C3×A4semidirect
46. A42C3×A4direct (N × H)
68. C26C34semidirect
80. C24×C3C32×A4semidirect
84. C22⋊A4C32×A4semidirect
90. C22×A4C32×A4semidirect
107. C3×A4A42direct (N × H)
147. C24C33×A4semidirect
162. C22×C3C3×A42semidirect
168. A4C3×A42direct (N × H)
203. C22C32×A42semidirect
207. C3A43direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#105967823
C3×A4×C22⋊A43
C22×C3×A423
A433
C32×A424