Finite Group Databasebeta

← C3×C4⋊(#126⋊C3) #11919508

Subgroups — C3×C4⋊(#126⋊C3) #11919508

Order 1152.

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

normal subgroups only

This group has 300 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×#126⋊C3C212yesmaximal, complemented
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C3×#2860C311yesmaximal, characteristic, complemented
4C4⋊(#126⋊C3)C313yesmaximal, direct product factor
5C3×D4×A4—41nomaximal
6C3×#126⋊C3—22no—
7C2×C3×C42⋊C3C2211yescharacteristic
8C2×C3×#126C2×C312yescomplemented
9C2×#126⋊C3C2×C316yescomplemented
10C3×#390—31no—
11C3×#389—31no—
12C3×#388—32no—
13C3×C43C2×C311yescharacteristic, complemented
14C4×C42⋊C3C2×C313yescomplemented
15C22×C3×A4—42no—
16C3×C4×A4—41no—
17C3×C42⋊C3D411yescharacteristic, complemented
18#2860C3211yescharacteristic, complemented, Sylow
19C22×C3×D4A411yescharacteristic
20D4×A4—43no—
21C3×#126—22no—
22C3×#126—62no—
23C2×C3×C4⋊C4—32no—
24C2×C3×C4⋊C4—31no—
25C2×C3×C22⋊C4—32no—
26C2×C3×C22⋊C4—32no—
27C2×C3×C42—31no—
28C2×C3×C42—31no—
29C2×C3×C42C22×C311yescharacteristic
30#126⋊C3—26no—
31C2×C42⋊C3C22×C313yes—
32C3×#95—32no—
33C2×C3×A4—41no—
34C2×C3×A4—82no—
35C32×D4—161no—
36C2×#126C2×C3212yescomplemented
37#390—31no—
38#389—31no—
39#388—32no—
40C43C2×C3211yescharacteristic, complemented
41C24×C3C2×A412yes—
42C22×A4—46no—
43C2×C3×D4—61no—
44C2×C3×D4—61no—
45C22×C3×C4—31no—
46C22×C3×C4—31no—
47C22×C3×C4—32no—
48C22×C3×C4C2×A411yescharacteristic
49C4×A4—43no—
50C3×C4⋊C4—62no—
51C3×C4⋊C4—62no—
52C3×C4⋊C4—61no—
53C3×C4⋊C4—61no—
54C3×C22⋊C4—62no—
55C3×C22⋊C4—62no—
56C3×C22⋊C4—64no—
57C3×C42—31no—
58C3×C42—61no—
59C3×C42—61no—
60C3×C42—62no—
61C3×C42C3×D411yescharacteristic, complemented
62C42⋊C3C3×D413yescomplemented
63C22×C32—162no—
64C3×A4—41no—
65C32×C4—161no—
66C22×D4C3×A411yescharacteristic
67#126—22no—
68#126—62no—
69C2×C4⋊C4—32no—
70C2×C4⋊C4—31no—
71C2×C22⋊C4—32no—
72C2×C22⋊C4—32no—
73C2×C42—31no—
74C2×C42—31no—
75C2×C42C22×C3211yescharacteristic
76#95—32no—
77C23×C3—22no—
78C23×C3—62no—
79C23×C3—62no—
80C23×C3C22×A411yescharacteristic
81C2×A4—43no—
82C2×A4—86no—
83C3×D4—41no—
84C3×D4—121no—
85C3×D4—163no—
86C2×C3×C4—31no—
87C2×C3×C4—31no—
88C2×C3×C4—32no—
89C2×C3×C4—31no—
90C2×C3×C4—31no—
91C2×C3×C4—61no—
92C2×C3×C4—61no—
93C2×C3×C4—61no—
94C2×C3×C4—61no—
95C2×C3×C4—62no—
96C2×C3×C4—62no—
97C2×C3×C4—62no—
98C2×C32—161no—
99C2×C32—322no—
100C24C2×C3×A412yes—
101C2×D4—61no—
102C2×D4—61no—
103C22×C4—31no—
104C22×C4—31no—
105C22×C4—32no—
106C22×C4C2×C3×A411yescharacteristic
107C4⋊C4—62no—
108C4⋊C4—62no—
109C4⋊C4—61no—
110C4⋊C4—61no—
111C22⋊C4—62no—
112C22⋊C4—62no—
113C22⋊C4—64no—
114C42—31no—
115C42—61no—
116C42—61no—
117C42—62no—
118C42C32×D411yescharacteristic, complemented
119C22×C3—31no—
120C22×C3—31no—
121C22×C3—42no—
122C22×C3—122no—
123C22×C3—122no—
124C22×C3—166no—
125C22×C3D4×A411yescharacteristic
126A4—43no—
127C3×C4—31no—
128C3×C4—61no—
129C3×C4—61no—
130C3×C4—62no—
131C3×C4—122no—
132C3×C4—163no—
133C3×C4#126⋊C311yescharacteristic, complemented
134C32—161noSylow
135C23—22no—
136C23—62no—
137C23—62no—
138C23C22×C3×A411yescharacteristic
139D4—41no—
140D4—121no—
141C2×C4—31no—
142C2×C4—31no—
143C2×C4—32no—
144C2×C4—31no—
145C2×C4—31no—
146C2×C4—61no—
147C2×C4—61no—
148C2×C4—61no—
149C2×C4—61no—
150C2×C4—62no—
151C2×C4—62no—
152C2×C4—62no—
153C2×C3—31no—
154C2×C3—31no—
155C2×C3—82no—
156C2×C3—163no—
157C2×C3—326no—
158C2×C3C2×#126⋊C311yescharacteristic
159C22—31no—
160C22—31no—
161C22—42no—
162C22—122no—
163C22—122no—
164C22C3×D4×A411yescharacteristic
165C4—31no—
166C4—61no—
167C4—61no—
168C4—62no—
169C4—122no—
170C4C3×#126⋊C311yescharacteristic, complemented
171C3—163no—
172C3C4⋊(#126⋊C3)11yescharacteristic, direct product factor
173C2—31no—
174C2—31no—
175C2—82no—
176C2C2×C3×#126⋊C311yescharacteristic
subgroupG/H
centerC2×C3C2×#126⋊C3
commutator, cosocleC2×C42C22×C32
FrattiniC23C22×C3×A4
FittingC3×#2860C3
socleC23×C3C22×A4
hypercenterC3×C4#126⋊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×#126⋊C3C2semidirect
2. C3×C4×C42⋊C3C2semidirect
3. C3×#2860C3semidirect
4. C4⋊(#126⋊C3)C3direct (N × H)
8. C2×C3×#126C2×C3semidirect
9. C2×#126⋊C3C2×C3semidirect
13. C3×C43C2×C3semidirect
14. C4×C42⋊C3C2×C3semidirect
17. C3×C42⋊C3D4semidirect
18. #2860C32semidirect
36. C2×#126C2×C32semidirect
40. C43C2×C32semidirect
61. C3×C42C3×D4semidirect
62. C42⋊C3C3×D4semidirect
118. C42C32×D4semidirect
133. C3×C4#126⋊C3semidirect
170. C4C3×#126⋊C3semidirect
172. C3C4⋊(#126⋊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×#126⋊C32
C3×C4×C42⋊C32
C3×#28603
C4⋊(#126⋊C3)3
C3×D4×A44