Finite Group Databasebeta

← C3×A4×#127 #11919710

Subgroups — C3×A4×#127 #11919710

Order 1152.

1576 conjugacy classes of subgroups; only the 208 normal subgroups are shown.

normal subgroups only

This group has 1576 conjugacy classes of subgroups — too many to draw. Only its 208 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×C3×D4×A4C216yesmaximal, complemented
2C3×C42×A4C211yesmaximal, characteristic, complemented
3C22×C3×#127C311yesmaximal, characteristic, complemented
4A4×#127C313yesmaximal, direct product factor
5C23×C3×A4C2214yes—
6C3×D4×A4—212no—
7C2×C3×C4×A4C2213yes—
8C32×#127—41nomaximal
9C23×C3×D4C2×C316yescomplemented
10C2×D4×A4C2×C3118yescomplemented
11C2×C3×#127—31no—
12C2×C3×#127—31no—
13C2×C3×#127—36no—
14C22×C3×C42C2×C311yescharacteristic, complemented
15C42×A4C2×C313yescomplemented
16C22×C3×A4—212no—
17C22×C3×A4C2311yescharacteristic
18C2×C32×D4—46no—
19C3×C4×A4D416yescomplemented
20C32×C42—41no—
21C22×#127C3211yescharacteristic, complemented, Sylow
22C25×C3C22×C314yes—
23C23×A4C22×C3112yes—
24C22×C3×D4—212no—
25C22×C3×D4—36no—
26C22×C3×D4—36no—
27C22×C3×D4—312no—
28C22×C3×D4—612no—
29C23×C3×C4C22×C313yes—
30D4×A4—236no—
31C2×C4×A4C22×C319yes—
32C3×#127—38no—
33C3×#127—36no—
34C3×#127—36no—
35C3×#127—31no—
36C3×#127—43no—
37C3×#127A411yescharacteristic, direct product factor
38C2×C3×C42—31no—
39C2×C3×C42—33no—
40C23×C32—44no—
41C2×C3×A4—44no—
42C2×C3×A4C2×D413yes—
43C32×D4—812no—
44C2×C32×C4—43no—
45C23×D4C2×C3216yescomplemented
46C2×#127—31no—
47C2×#127—31no—
48C2×#127—36no—
49C22×C42C2×C3211yescharacteristic, complemented
50C24×C3—212no—
51C24×C3—34no—
52C24×C3—34no—
53C24×C3—612no—
54C24×C3C23×C311yescharacteristic
55C22×A4—236no—
56C22×A4C23×C313yes—
57C2×C3×D4—312no—
58C2×C3×D4—312no—
59C2×C3×D4—36no—
60C2×C3×D4—418no—
61C2×C3×D4—612no—
62C2×C3×D4—612no—
63C2×C3×D4—624no—
64C2×C3×D4—612no—
65C2×C3×D4—624no—
66C2×C3×D4—612no—
67C2×C3×D4C2×A416yescomplemented
68C22×C3×C4—33no—
69C22×C3×C4—33no—
70C22×C3×C4—36no—
71C22×C3×C4C3×D416yescomplemented
72C4×A4C3×D4118yescomplemented
73C3×C42—32no—
74C3×C42—33no—
75C3×C42—43no—
76C3×C42C2×A411yescharacteristic, complemented
77C22×C32—41no—
78C22×C32—812no—
79C3×A4#12711yescharacteristic, direct product factor
80C32×C4—46no—
81C25C22×C3214yes—
82C22×D4—212no—
83C22×D4—36no—
84C22×D4—36no—
85C22×D4—312no—
86C22×D4—612no—
87C23×C4C22×C3213yes—
88#127—38no—
89#127—36no—
90#127—36no—
91#127—31no—
92#127C3×A411yescharacteristic, direct product factor
93C2×C42—31no—
94C2×C42—33no—
95C23×C3—33no—
96C23×C3—31no—
97C23×C3—34no—
98C23×C3—44no—
99C23×C3—412no—
100C23×C3—612no—
101C23×C3—612no—
102C23×C3—612no—
103C23×C3—612no—
104C23×C3—1212no—
105C23×C3—128no—
106C23×C3C2×C3×D413yes—
107C23×C3C22×A414yes—
108C2×A4—412no—
109C2×A4C2×C3×D419yes—
110C3×D4—212no—
111C3×D4—624no—
112C3×D4—624no—
113C3×D4—612no—
114C3×D4—836no—
115C2×C3×C4—36no—
116C2×C3×C4—33no—
117C2×C3×C4—36no—
118C2×C3×C4—36no—
119C2×C3×C4—36no—
120C2×C3×C4—49no—
121C2×C3×C4C22×A413yes—
122C2×C32—43no—
123C2×C32—164no—
124C24—212no—
125C24—34no—
126C24—34no—
127C24—612no—
128C24C23×C3211yescharacteristic
129C2×D4—312no—
130C2×D4—312no—
131C2×D4—36no—
132C2×D4—612no—
133C2×D4—612no—
134C2×D4—624no—
135C2×D4—612no—
136C2×D4—624no—
137C2×D4—612no—
138C2×D4C2×C3×A416yescomplemented
139C22×C4—33no—
140C22×C4—33no—
141C22×C4—36no—
142C22×C4C32×D416yescomplemented
143C42—32no—
144C42—33no—
145C42C2×C3×A411yescharacteristic, complemented
146C22×C3—212no—
147C22×C3—33no—
148C22×C3—32no—
149C22×C3—33no—
150C22×C3—33no—
151C22×C3—43no—
152C22×C3—612no—
153C22×C3—836no—
154C22×C3—124no—
155C22×C3—1212no—
156C22×C3—124no—
157C22×C3—1212no—
158C22×C3C3×#12711yescharacteristic, complemented
159C22×C3C23×A411yescharacteristic
160A4C3×#12713yesdirect product factor
161C3×C4—36no—
162C3×C4—418no—
163C3×C4D4×A416yescomplemented
164C32—41noSylow
165C23—33no—
166C23—31no—
167C23—34no—
168C23—44no—
169C23—612no—
170C23—612no—
171C23—612no—
172C23—612no—
173C23—1212no—
174C23—128no—
175C23C2×C32×D413yes—
176C23C22×C3×A414yes—
177D4—212no—
178D4—624no—
179D4—624no—
180D4—612no—
181C2×C4—36no—
182C2×C4—33no—
183C2×C4—36no—
184C2×C4—36no—
185C2×C4—36no—
186C2×C4C22×C3×A413yes—
187C2×C3—33no—
188C2×C3—31no—
189C2×C3—44no—
190C2×C3—49no—
191C2×C3—124no—
192C2×C3—1612no—
193C2×C3C2×D4×A413yes—
194C22—212no—
195C22—33no—
196C22—32no—
197C22—33no—
198C22—33no—
199C22—612no—
200C22—124no—
201C22—1212no—
202C22—124no—
203C22—1212no—
204C22C32×#12711yescharacteristic, complemented
205C22C23×C3×A411yescharacteristic
206C4—36no—
207C4C3×D4×A416yescomplemented
208C3—43no—
209C3A4×#12711yescharacteristic, direct product factor
210C2—31no—
211C2—33no—
212C2—44no—
213C2—124no—
214C2C2×C3×D4×A413yes—
subgroupG/H
centerC22×C3C23×A4
commutator, cosocleC24C23×C32
FrattiniC22C23×C3×A4
FittingC22×C3×#127C3
socleC24×C3C23×C3
hypercenterC3×#127A4
hypocenterC22C32×#127
LCSG ▷ C24 ▷ C22
UCSC1 ◁ C22×C3 ◁ C3×#127

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×A4C2semidirect
2. C3×C42×A4C2semidirect
3. C22×C3×#127C3semidirect
4. A4×#127C3direct (N × H)
9. C23×C3×D4C2×C3semidirect
10. C2×D4×A4C2×C3semidirect
14. C22×C3×C42C2×C3semidirect
15. C42×A4C2×C3semidirect
19. C3×C4×A4D4semidirect
21. C22×#127C32semidirect
37. C3×#127A4direct (N × H)
45. C23×D4C2×C32semidirect
49. C22×C42C2×C32semidirect
67. C2×C3×D4C2×A4semidirect
71. C22×C3×C4C3×D4semidirect
72. C4×A4C3×D4semidirect
76. C3×C42C2×A4semidirect
79. C3×A4#127direct (N × H)
92. #127C3×A4direct (N × H)
138. C2×D4C2×C3×A4semidirect
142. C22×C4C32×D4semidirect
145. C42C2×C3×A4semidirect
158. C22×C3C3×#127semidirect
160. A4C3×#127direct (N × H)
163. C3×C4D4×A4semidirect
204. C22C32×#127semidirect
207. C4C3×D4×A4semidirect
209. C3A4×#127direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×A42
C3×C42×A42
C22×C3×#1273
A4×#1273
C32×#1274