Finite Group Databasebeta

← C2×Dic3×C42⋊C3 #11921246

Subgroups — C2×Dic3×C42⋊C3 #11921246

Order 1152.

519 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 519 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C22×C3×C42⋊C3C211yesmaximal, characteristic
2Dic3×C42⋊C3C212yesmaximal, direct product factor
3C2×C42×Dic3C311yesmaximal, characteristic, complemented
4C2×C4×C42⋊C3—31nomaximal
5C2×Dic3×A4—41nomaximal
6C2×C3×C42⋊C3C412yescomplemented
7C2×C3×C42⋊C3C2211yescharacteristic
8C22×C3×C42C2×C311yescharacteristic
9C22×C4×Dic3—31no—
10C22×C4×Dic3—31no—
11C22×C42⋊C3—21no—
12C22×C42⋊C3D311yescharacteristic
13C42×Dic3—32no—
14C42×Dic3C2×C312yescomplemented
15C4×C42⋊C3—32no—
16C22×C3×A4—41no—
17Dic3×A4—42no—
18C3×C42⋊C3C2×C411yescharacteristic, complemented
19C2×C43—31noSylow
20C23×C3×C4—31no—
21C23×Dic3—31no—
22C23×Dic3A411yescharacteristic
23C2×C4×A4—121no—
24C2×C3×C42—31no—
25C2×C3×C42—32no—
26C2×C3×C42C3×C412yescomplemented
27C2×C3×C42C22×C311yescharacteristic
28C2×C4×Dic3—32no—
29C2×C4×Dic3—38no—
30C2×C4×Dic3—32no—
31C2×C4×Dic3—34no—
32C2×C4×Dic3—32no—
33C2×C4×Dic3—32no—
34C2×C4×Dic3—32no—
35C2×C4×Dic3—32no—
36C2×C42⋊C3—22no—
37C2×C42⋊C3—21no—
38C2×C42⋊C3Dic312yesdirect product factor
39C2×C42⋊C3C2×D311yescharacteristic
40C2×C3×A4—42no—
41C2×C3×A4—41no—
42C2×C3×Dic3—161no—
43C22×C42—91no—
44C22×C42—91no—
45C22×C42C3×D311yescharacteristic
46C43—32no—
47C43—92no—
48C24×C3C2×A411yescharacteristic
49C22×A4—41no—
50C22×A4—81no—
51C22×C3×C4—34no—
52C22×C3×C4—32no—
53C22×C3×C4—32no—
54C22×C3×C4—32no—
55C22×C3×C4—32no—
56C22×C3×C4—31no—
57C22×C3×C4—31no—
58C22×Dic3—38no—
59C22×Dic3—32no—
60C22×Dic3—32no—
61C22×Dic3—32no—
62C22×Dic3—31no—
63C22×Dic3—31no—
64C22×Dic3—32no—
65C22×Dic3C2×A412yes—
66C4×A4—122no—
67C3×C42—32no—
68C3×C42—31no—
69C3×C42—32no—
70C3×C42C2×C3×C411yescharacteristic, complemented
71C4×Dic3—38no—
72C4×Dic3—38no—
73C4×Dic3—34no—
74C4×Dic3—34no—
75C4×Dic3—34no—
76C4×Dic3—34no—
77C42⋊C3—21no—
78C42⋊C3C2×Dic311yescharacteristic, direct product factor
79C22×C32—161no—
80C3×A4—41no—
81C3×Dic3—162no—
82C23×C4—31no—
83C23×C4—31no—
84C23×C4—91no—
85C2×C42—31no—
86C2×C42—32no—
87C2×C42—92no—
88C2×C42—92no—
89C2×C42—92no—
90C2×C42—92no—
91C2×C42—92no—
92C2×C42—98no—
93C2×C42—94no—
94C2×C42—92no—
95C2×C42C3×Dic312yescomplemented
96C2×C42C2×C3×D311yescharacteristic
97C23×C3—32no—
98C23×C3—31no—
99C23×C3—31no—
100C23×C3C4×A412yes—
101C23×C3C22×A411yescharacteristic
102C2×A4—41no—
103C2×A4—42no—
104C2×A4—81no—
105C2×A4—82no—
106C2×C3×C4—32no—
107C2×C3×C4—32no—
108C2×C3×C4—32no—
109C2×C3×C4—32no—
110C2×C3×C4—34no—
111C2×C3×C4—34no—
112C2×C3×C4—34no—
113C2×C3×C4—34no—
114C2×C3×C4—31no—
115C2×C3×C4—32no—
116C2×C3×C4—31no—
117C2×C3×C4—481no—
118C2×Dic3—38no—
119C2×Dic3—34no—
120C2×Dic3—38no—
121C2×Dic3—38no—
122C2×Dic3—32no—
123C2×Dic3—31no—
124C2×Dic3—32no—
125C2×Dic3—32no—
126C2×Dic3—32no—
127C2×Dic3C42⋊C311yescharacteristic, direct product factor
128C2×C32—162no—
129C2×C32—161no—
130C24D3×A411yescharacteristic
131C22×C4—34no—
132C22×C4—32no—
133C22×C4—32no—
134C22×C4—31no—
135C22×C4—31no—
136C22×C4—32no—
137C22×C4—32no—
138C22×C4—32no—
139C22×C4—91no—
140C22×C4—98no—
141C22×C4—92no—
142C22×C4—92no—
143C22×C4—92no—
144C22×C4—92no—
145C22×C4—91no—
146C42—32no—
147C42—31no—
148C42—32no—
149C42—94no—
150C42—94no—
151C42—98no—
152C42—98no—
153C42—94no—
154C42—94no—
155C42C2×C3×Dic311yescharacteristic, complemented
156C22×C3—31no—
157C22×C3—32no—
158C22×C3—32no—
159C22×C3—32no—
160C22×C3—32no—
161C22×C3—31no—
162C22×C3—31no—
163C22×C3—161no—
164C22×C3—321no—
165C22×C3C2×C42⋊C311yescharacteristic
166C22×C3C2×C4×A411yescharacteristic
167A4—41no—
168A4—81no—
169C3×C4—32no—
170C3×C4—32no—
171C3×C4—34no—
172C3×C4—482no—
173Dic3—38no—
174Dic3—32no—
175Dic3C2×C42⋊C312yesdirect product factor
176C32—161noSylow
177C23—32no—
178C23—31no—
179C23—31no—
180C23Dic3×A412yes—
181C23C2×D3×A411yescharacteristic
182C2×C4—32no—
183C2×C4—32no—
184C2×C4—32no—
185C2×C4—32no—
186C2×C4—34no—
187C2×C4—34no—
188C2×C4—34no—
189C2×C4—34no—
190C2×C4—31no—
191C2×C4—31no—
192C2×C4—32no—
193C2×C4—31no—
194C2×C4—92no—
195C2×C4—92no—
196C2×C4—98no—
197C2×C4—94no—
198C2×C4—98no—
199C2×C4—98no—
200C2×C4—92no—
201C2×C4—91no—
202C2×C4—92no—
203C2×C3—31no—
204C2×C3—31no—
205C2×C3—32no—
206C2×C3—161no—
207C2×C3—162no—
208C2×C3—321no—
209C2×C3—322no—
210C2×C3C4×C42⋊C312yescomplemented
211C2×C3C22×C42⋊C311yescharacteristic
212C22—31no—
213C22—32no—
214C22—32no—
215C22—31no—
216C22—31no—
217C22—32no—
218C22—32no—
219C22D3×C42⋊C311yescharacteristic
220C22C2×Dic3×A411yescharacteristic
221C4—32no—
222C4—32no—
223C4—34no—
224C4—32no—
225C4—98no—
226C4—92no—
227C3—161no—
228C3—321no—
229C3C2×C4×C42⋊C311yescharacteristic, complemented
230C2—31no—
231C2—31no—
232C2—32no—
233C2Dic3×C42⋊C312yesdirect product factor
234C2C2×D3×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC22D3×C42⋊C3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC22×C3×C42C2×C3
socleC24×C3C2×A4
prime radicalC22×C3×C42⋊C3C2
cosocleC2×C3×C42C22×C3
LCSG ▷ C3×C42
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. Dic3×C42⋊C3C2direct (N × H)
3. C2×C42×Dic3C3semidirect
6. C2×C3×C42⋊C3C4semidirect
14. C42×Dic3C2×C3semidirect
18. C3×C42⋊C3C2×C4semidirect
26. C2×C3×C42C3×C4semidirect
38. C2×C42⋊C3Dic3direct (N × H)
70. C3×C42C2×C3×C4semidirect
78. C42⋊C3C2×Dic3direct (N × H)
95. C2×C42C3×Dic3semidirect
127. C2×Dic3C42⋊C3direct (N × H)
155. C42C2×C3×Dic3semidirect
175. Dic3C2×C42⋊C3direct (N × H)
210. C2×C3C4×C42⋊C3semidirect
229. C3C2×C4×C42⋊C3semidirect
233. C2Dic3×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C42⋊C32
Dic3×C42⋊C32
C2×C42×Dic33
C2×C4×C42⋊C33
C2×Dic3×A44