Finite Group Databasebeta

← D12×C42⋊C3 #11921120

Subgroups — D12×C42⋊C3 #11921120

Order 1152.

397 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 397 conjugacy classes of subgroups — too many to draw. Only its 36 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×D3×C42⋊C3C212yesmaximal, complemented
2C3×C4×C42⋊C3C211yesmaximal, characteristic, complemented
3C42×D12C311yesmaximal, characteristic, complemented
4D4×C42⋊C3—31nomaximal
5A4×D12—41nomaximal
6C2×C3×C42⋊C3C2211yescharacteristic
7D3×C42⋊C3—22no—
8C2×C4×D12—31no—
9C2×C42×D3C2×C312yescomplemented
10C22×C42⋊C3—32no—
11C3×C43C2×C311yescharacteristic, complemented
12C4×(C2×D3)⋊C4—32no—
13C4×C4⋊Dic3—31no—
14C4×C42⋊C3—21no—
15C4×C42⋊C3D311yescharacteristic, complemented
16C2×D3×A4—42no—
17C3×C4×A4—41no—
18C3×C42⋊C3D411yescharacteristic, complemented
19C42×D4—31noSylow
20C22×D12A411yescharacteristic
21C22×C4×D3—32no—
22D4×A4—121no—
23C2×C3×C42—31no—
24C2×C3×C42—31no—
25C2×C3×C42C22×C311yescharacteristic
26C2×(C2×D3)⋊C4—32no—
27C2×C4⋊Dic3—31no—
28C2×C4×Dic3—32no—
29C4×D12—32no—
30C4×D12—32no—
31C4×D12—34no—
32C42×D3—22no—
33C42×D3—62no—
34C2×C42⋊C3—21no—
35C2×C42⋊C3—62no—
36C2×C42⋊C3C2×D311yescharacteristic
37C3⋊#95—32no—
38C2×C3×A4—41no—
39D3×A4—82no—
40C3×D12—161no—
41C2×C4×D4—91no—
42C22×C42—32no—
43C4×C4⋊C4—91no—
44C4×C22⋊C4—92no—
45C43C3×D311yescharacteristic, complemented
46C23×D3C2×A412yes—
47C22×A4—122no—
48C22×C3×C4—31no—
49C22×C3×C4—31no—
50C22×C3×C4C2×A411yescharacteristic
51C22×Dic3—32no—
52C2×D12—31no—
53C2×D12—32no—
54C2×D12—31no—
55C2×C4×D3—34no—
56C2×C4×D3—34no—
57C2×C4×D3—62no—
58C2×C4×D3—62no—
59C2×C4×D3—64no—
60C4×A4—41no—
61C4×A4—81no—
62C3×C42—31no—
63C3×C42—32no—
64C3×C42—32no—
65C3×C42—62no—
66C3×C42C3×D411yescharacteristic, complemented
67(C2×D3)⋊C4—34no—
68(C2×D3)⋊C4—34no—
69C4⋊Dic3—32no—
70C4⋊Dic3—32no—
71C4×Dic3—62no—
72C4×Dic3—62no—
73C42⋊C3—21no—
74C42⋊C3D1211yescharacteristic, direct product factor
75C2×C3×D3—162no—
76C3×A4—41no—
77C32×C4—161no—
78C22×D4—31no—
79C23×C4—92no—
80C4×D4—92no—
81C4×D4—92no—
82C4×D4—94no—
83C2×C4⋊C4—91no—
84C2×C22⋊C4—92no—
85C2×C42—31no—
86C2×C42—31no—
87C2×C42—62no—
88C2×C42—92no—
89C2×C42—182no—
90C2×C42C2×C3×D311yescharacteristic
91#95—92no—
92C23×C3C22×A411yescharacteristic
93C22×D3—22no—
94C22×D3—32no—
95C22×D3—32no—
96C22×D3—62no—
97C2×A4—41no—
98C2×A4—81no—
99C2×A4—242no—
100C3×D4—481no—
101C2×C3×C4—32no—
102C2×C3×C4—32no—
103C2×C3×C4—31no—
104C2×C3×C4—31no—
105C2×C3×C4—31no—
106C2×C3×C4—31no—
107C2×C3×C4—32no—
108C2×C3×C4—62no—
109C2×Dic3—34no—
110C2×Dic3—62no—
111C2×Dic3—62no—
112D12—32no—
113D12—32no—
114D12—31no—
115D12C42⋊C311yescharacteristic, direct product factor
116C4×D3—64no—
117C4×D3—64no—
118C4×D3—64no—
119C4×D3—64no—
120C2×C32—161no—
121C3×D3—322no—
122C24—32no—
123C2×D4—91no—
124C2×D4—91no—
125C2×D4—92no—
126C22×C4—31no—
127C22×C4—31no—
128C22×C4—94no—
129C22×C4—94no—
130C22×C4—92no—
131C22×C4—182no—
132C22×C4—182no—
133C22×C4—184no—
134C22×C4D3×A411yescharacteristic
135C4⋊C4—92no—
136C4⋊C4—92no—
137C22⋊C4—94no—
138C22⋊C4—94no—
139C42—31no—
140C42—32no—
141C42—32no—
142C42—62no—
143C42—182no—
144C42—182no—
145C42C3×D1211yescharacteristic, complemented
146C22×C3—31no—
147C22×C3—31no—
148C22×C3—482no—
149C22×C3D4×A411yescharacteristic
150C2×D3—32no—
151C2×D3—62no—
152C2×D3—62no—
153C2×D3—62no—
154C2×D3—62no—
155C2×D3C2×C42⋊C312yescomplemented
156A4—41no—
157A4—81no—
158C3×C4—32no—
159C3×C4—32no—
160C3×C4—31no—
161C3×C4—62no—
162C3×C4—161no—
163C3×C4—321no—
164C3×C4C2×C42⋊C311yescharacteristic, complemented
165Dic3—64no—
166C32—161noSylow
167C23—62no—
168C23—92no—
169C23—92no—
170C23—182no—
171C23C2×D3×A411yescharacteristic
172D4—31no—
173D4—92no—
174D4—92no—
175D4—91no—
176C2×C4—32no—
177C2×C4—32no—
178C2×C4—31no—
179C2×C4—31no—
180C2×C4—31no—
181C2×C4—31no—
182C2×C4—32no—
183C2×C4—62no—
184C2×C4—94no—
185C2×C4—184no—
186C2×C4—184no—
187C2×C4—184no—
188C2×C4—184no—
189C2×C4—182no—
190C2×C4—182no—
191C2×C3—31no—
192C2×C3—31no—
193C2×C3—161no—
194C2×C3—321no—
195C2×C3—962no—
196C2×C3C22×C42⋊C311yescharacteristic
197D3—22no—
198D3—62no—
199C22—31no—
200C22—31no—
201C22—32no—
202C22—92no—
203C22—182no—
204C22—182no—
205C22—182no—
206C22—182no—
207C22A4×D1211yescharacteristic
208C4—32no—
209C4—32no—
210C4—31no—
211C4—62no—
212C4—184no—
213C4D3×C42⋊C311yescharacteristic, complemented
214C3—161no—
215C3—321no—
216C3D4×C42⋊C311yescharacteristic, complemented
217C2—31no—
218C2—31no—
219C2—62no—
220C2—182no—
221C2C2×D3×C42⋊C311yescharacteristic
subgroupG/H
centerC2C2×D3×C42⋊C3
commutator, cosocleC2×C3×C42C22×C3
FrattiniC23C2×D3×A4
FittingC3×C43C2×C3
socleC23×C3C22×A4
hypercenterC4D3×C42⋊C3
hypocenterC3×C42C3×D4
LCSG ▷ C2×C3×C42 ▷ C3×C42
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×C42⋊C3C2semidirect
2. C3×C4×C42⋊C3C2semidirect
3. C42×D12C3semidirect
9. C2×C42×D3C2×C3semidirect
11. C3×C43C2×C3semidirect
15. C4×C42⋊C3D3semidirect
18. C3×C42⋊C3D4semidirect
45. C43C3×D3semidirect
66. C3×C42C3×D4semidirect
74. C42⋊C3D12direct (N × H)
115. D12C42⋊C3direct (N × H)
145. C42C3×D12semidirect
155. C2×D3C2×C42⋊C3semidirect
164. C3×C4C2×C42⋊C3semidirect
213. C4D3×C42⋊C3semidirect
216. C3D4×C42⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C42⋊C32
C3×C4×C42⋊C32
C42×D123
D4×C42⋊C33
A4×D124