Finite Group Databasebeta

← C3×C4⋊(#127⋊C3) #11919512

Subgroups — C3×C4⋊(#127⋊C3) #11919512

Order 1152.

552 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 54 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×#127⋊C3C212yesmaximal, complemented
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C3×#2867C311yesmaximal, characteristic, complemented
4C4⋊(#127⋊C3)C313yesmaximal, direct product factor
5C3×D4×A4—41nomaximal
6C3×#127⋊C3—22no—
7C2×C3×C42⋊C3C2211yescharacteristic
8C2×C3×#127—32no—
9C2×C3×#127—31no—
10C2×C3×#127—31no—
11C2×C3×#127C2×C312yescomplemented
12C2×#127⋊C3C2×C316yescomplemented
13C3×C43C2×C311yescharacteristic, complemented
14C4×C42⋊C3C2×C313yescomplemented
15C22×C3×A4—42no—
16C3×C4×A4—41no—
17C3×C42⋊C3D411yescharacteristic, complemented
18#2867C3211yescharacteristic, complemented, Sylow
19C22×C3×D4—32no—
20C22×C3×D4—32no—
21C22×C3×D4—32no—
22C22×C3×D4—32no—
23C22×C3×D4—31no—
24C22×C3×D4A411yescharacteristic
25D4×A4—43no—
26C3×#127—22no—
27C3×#127—62no—
28C3×#127—62no—
29C3×#127—68no—
30C3×#127—62no—
31C3×#127—62no—
32C3×#127—62no—
33C2×C3×C42—31no—
34C2×C3×C42—31no—
35C2×C3×C42C22×C311yescharacteristic
36#127⋊C3—26no—
37C2×C42⋊C3C22×C313yes—
38C2×C3×A4—41no—
39C2×C3×A4—82no—
40C32×D4—161no—
41C2×#127—32no—
42C2×#127—31no—
43C2×#127—31no—
44C2×#127C2×C3212yescomplemented
45C43C2×C3211yescharacteristic, complemented
46C24×C3—32no—
47C24×C3C2×A412yes—
48C22×A4—46no—
49C2×C3×D4—61no—
50C2×C3×D4—62no—
51C2×C3×D4—62no—
52C2×C3×D4—62no—
53C2×C3×D4—62no—
54C2×C3×D4—64no—
55C2×C3×D4—64no—
56C2×C3×D4—68no—
57C2×C3×D4—64no—
58C2×C3×D4—64no—
59C2×C3×D4—64no—
60C2×C3×D4—68no—
61C2×C3×D4—64no—
62C2×C3×D4—61no—
63C2×C3×D4—62no—
64C2×C3×D4—62no—
65C2×C3×D4—61no—
66C2×C3×D4—61no—
67C22×C3×C4—31no—
68C22×C3×C4—31no—
69C22×C3×C4C2×A411yescharacteristic
70C4×A4—43no—
71C3×C42—31no—
72C3×C42—34no—
73C3×C42—32no—
74C3×C42—32no—
75C3×C42C3×D411yescharacteristic, complemented
76C42⋊C3C3×D413yescomplemented
77C22×C32—162no—
78C3×A4—41no—
79C32×C4—161no—
80C22×D4—32no—
81C22×D4—32no—
82C22×D4—32no—
83C22×D4—32no—
84C22×D4—31no—
85C22×D4C3×A411yescharacteristic
86#127—22no—
87#127—62no—
88#127—62no—
89#127—68no—
90#127—62no—
91#127—62no—
92#127—62no—
93C2×C42—31no—
94C2×C42—31no—
95C2×C42C22×C3211yescharacteristic
96C23×C3—22no—
97C23×C3—62no—
98C23×C3—62no—
99C23×C3—64no—
100C23×C3—62no—
101C23×C3—62no—
102C23×C3—64no—
103C23×C3—62no—
104C23×C3C22×A411yescharacteristic
105C2×A4—43no—
106C2×A4—86no—
107C3×D4—41no—
108C3×D4—121no—
109C3×D4—124no—
110C3×D4—124no—
111C3×D4—128no—
112C3×D4—124no—
113C3×D4—124no—
114C3×D4—128no—
115C3×D4—121no—
116C3×D4—122no—
117C3×D4—121no—
118C3×D4—163no—
119C2×C3×C4—32no—
120C2×C3×C4—34no—
121C2×C3×C4—32no—
122C2×C3×C4—32no—
123C2×C3×C4—31no—
124C2×C3×C4—31no—
125C2×C3×C4—31no—
126C2×C3×C4—31no—
127C2×C32—161no—
128C2×C32—322no—
129C24—32no—
130C24C2×C3×A412yes—
131C2×D4—61no—
132C2×D4—62no—
133C2×D4—62no—
134C2×D4—62no—
135C2×D4—62no—
136C2×D4—64no—
137C2×D4—64no—
138C2×D4—64no—
139C2×D4—68no—
140C2×D4—64no—
141C2×D4—64no—
142C2×D4—68no—
143C2×D4—64no—
144C2×D4—61no—
145C2×D4—62no—
146C2×D4—62no—
147C2×D4—61no—
148C2×D4—61no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4C2×C3×A411yescharacteristic
152C42—31no—
153C42—34no—
154C42—32no—
155C42—32no—
156C42C32×D411yescharacteristic, complemented
157C22×C3—31no—
158C22×C3—31no—
159C22×C3—42no—
160C22×C3—122no—
161C22×C3—122no—
162C22×C3—122no—
163C22×C3—124no—
164C22×C3—122no—
165C22×C3—124no—
166C22×C3—122no—
167C22×C3—166no—
168C22×C3D4×A411yescharacteristic
169A4—43no—
170C3×C4—34no—
171C3×C4—32no—
172C3×C4—32no—
173C3×C4—31no—
174C3×C4—163no—
175C3×C4#127⋊C311yescharacteristic, complemented
176C32—161noSylow
177C23—22no—
178C23—62no—
179C23—62no—
180C23—62no—
181C23—64no—
182C23—62no—
183C23—64no—
184C23—62no—
185C23C22×C3×A411yescharacteristic
186D4—41no—
187D4—121no—
188D4—124no—
189D4—124no—
190D4—128no—
191D4—124no—
192D4—124no—
193D4—128no—
194D4—121no—
195D4—122no—
196D4—121no—
197C2×C4—32no—
198C2×C4—34no—
199C2×C4—32no—
200C2×C4—32no—
201C2×C4—31no—
202C2×C4—31no—
203C2×C4—31no—
204C2×C4—31no—
205C2×C3—31no—
206C2×C3—31no—
207C2×C3—82no—
208C2×C3—163no—
209C2×C3—242no—
210C2×C3—326no—
211C2×C3C2×#127⋊C311yescharacteristic
212C22—31no—
213C22—31no—
214C22—42no—
215C22—122no—
216C22—122no—
217C22—122no—
218C22—124no—
219C22—122no—
220C22—124no—
221C22—122no—
222C22C3×D4×A411yescharacteristic
223C4—32no—
224C4—32no—
225C4—34no—
226C4—31no—
227C4C3×#127⋊C311yescharacteristic, complemented
228C3—163no—
229C3C4⋊(#127⋊C3)11yescharacteristic, direct product factor
230C2—31no—
231C2—31no—
232C2—82no—
233C2—242no—
234C2C2×C3×#127⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×#127⋊C3
commutator, cosocleC2×C42C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2867C3
socleC23×C3C22×A4
hypercenterC3×C4#127⋊C3
hypocenterC42C32×D4
LCSG ▷ C2×C42 ▷ C42
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#127⋊C3C2semidirect
2. C3×C4×C42⋊C3C2semidirect
3. C3×#2867C3semidirect
4. C4⋊(#127⋊C3)C3direct (N × H)
11. C2×C3×#127C2×C3semidirect
12. C2×#127⋊C3C2×C3semidirect
13. C3×C43C2×C3semidirect
14. C4×C42⋊C3C2×C3semidirect
17. C3×C42⋊C3D4semidirect
18. #2867C32semidirect
44. C2×#127C2×C32semidirect
45. C43C2×C32semidirect
75. C3×C42C3×D4semidirect
76. C42⋊C3C3×D4semidirect
156. C42C32×D4semidirect
175. C3×C4#127⋊C3semidirect
227. C4C3×#127⋊C3semidirect
229. C3C4⋊(#127⋊C3)direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#127⋊C32
C3×C4×C42⋊C32
C3×#28673
C4⋊(#127⋊C3)3
C3×D4×A44