Finite Group Databasebeta

← Dic3×#126⋊C3 #11921288

Subgroups — Dic3×#126⋊C3 #11921288

Order 1152.

267 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 267 conjugacy classes of subgroups — too many to draw. Only its 44 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⋊C3C211yesmaximal, characteristic
2Dic3×C42⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#383⋊C3)C211yesmaximal, characteristic, complemented
4Dic3×#126C311yesmaximal, characteristic, complemented
5C4×#126⋊C3—31nomaximal
6C2×Dic3×A4—41nomaximal
7C3×#126⋊C3C412yescomplemented
8C2×C3×C42⋊C3C2211yescharacteristic
9C2×C3×#126C2×C311yescharacteristic
10C2×#126⋊C3—21no—
11C2×#126⋊C3D311yescharacteristic
12#4980—31no—
13Dic3×C4⋊C4—31no—
14#4951—31no—
15Dic3×C22⋊C4—31no—
16#4937C2×C311yescharacteristic, complemented
17C42×Dic3C2×C311yescharacteristic, complemented
18#383⋊C3—31no—
19C4×C42⋊C3—31no—
20C22×C3×A4—41no—
21Dic3×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C4×#126—31noSylow
25C23×Dic3A411yescharacteristic
26C2×C4×A4—121no—
27C3×#126—32no—
28C3×#126C3×C412yescomplemented
29C2×C3×C4⋊C4—31no—
30C2×C3×C22⋊C4—31no—
31C2×C3×C42C22×C311yescharacteristic
32C2×#217—31no—
33C2×C4⋊Dic3—31no—
34C2×C4×Dic3—31no—
35C2×C4×Dic3—31no—
36C2×C4×Dic3—31no—
37#126⋊C3—22no—
38#126⋊C3Dic312yesdirect product factor
39C2×C42⋊C3—21no—
40C2×C42⋊C3C2×D311yescharacteristic
41C3⋊#95—31no—
42C3⋊#95—31no—
43C3⋊#95—31no—
44C3⋊#95—31no—
45C2×C3×A4—42no—
46C2×C3×A4—41no—
47C2×C3×Dic3—161no—
48C2×#126C3×D311yescharacteristic
49#388—91no—
50#387—91no—
51#383—31no—
52C4×C4⋊C4—91no—
53C4×C22⋊C4—91no—
54C43—31no—
55C24×C3C2×A411yescharacteristic
56C22×A4—41no—
57C22×A4—81no—
58C22×C3×C4—31no—
59C22×C3×C4—31no—
60C22×Dic3—31no—
61C22×Dic3—31no—
62C22×Dic3—61no—
63C22×Dic3—61no—
64C22×Dic3C2×A411yescharacteristic
65C22×Dic3C2×A411yescharacteristic
66C4×A4—121no—
67C4×A4—121no—
68C3×C4⋊C4—32no—
69C3×C4⋊C4—32no—
70C3×C22⋊C4—32no—
71C3×C22⋊C4—32no—
72C3×C42—31no—
73C3×C42C2×C3×C411yescharacteristic, complemented
74#217—62no—
75C4⋊Dic3—62no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C4×Dic3—61no—
80C4×Dic3—62no—
81C42⋊C3—21no—
82C42⋊C3C2×Dic311yescharacteristic, complemented
83C22×C32—161no—
84C3×A4—41no—
85C3×Dic3—161no—
86C3×Dic3—161no—
87C23×C4—31no—
88#126—32no—
89#126C3×Dic312yescomplemented
90C2×C4⋊C4—31no—
91C2×C4⋊C4—91no—
92C2×C22⋊C4—31no—
93C2×C22⋊C4—91no—
94C2×C42—91no—
95C2×C42—91no—
96C2×C42—91no—
97C2×C42C2×C3×D311yescharacteristic
98#95—91no—
99#95—91no—
100#95—91no—
101#95—91no—
102C23×C3—61no—
103C23×C3—61no—
104C23×C3C4×A412yes—
105C23×C3C22×A411yescharacteristic
106C2×A4—41no—
107C2×A4—42no—
108C2×A4—81no—
109C2×A4—82no—
110C2×C3×C4—31no—
111C2×C3×C4—31no—
112C2×C3×C4—32no—
113C2×C3×C4—61no—
114C2×C3×C4—61no—
115C2×C3×C4—61no—
116C2×C3×C4—61no—
117C2×C3×C4—481no—
118C2×Dic3—31no—
119C2×Dic3—31no—
120C2×Dic3—32no—
121C2×Dic3—41no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—121no—
129C2×C32—162no—
130C2×C32—161no—
131C24D3×A411yescharacteristic
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—31no—
135C22×C4—31no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4—181no—
139C22×C4—181no—
140C4⋊C4—32no—
141C4⋊C4—32no—
142C4⋊C4—182no—
143C22⋊C4—32no—
144C22⋊C4—32no—
145C22⋊C4—182no—
146C42—31no—
147C42—181no—
148C42—181no—
149C42—181no—
150C42—181no—
151C42—182no—
152C42C2×C3×Dic311yescharacteristic, complemented
153C22×C3—31no—
154C22×C3—31no—
155C22×C3—41no—
156C22×C3—62no—
157C22×C3—121no—
158C22×C3—161no—
159C22×C3—321no—
160C22×C3C2×C4×A411yescharacteristic
161A4—41no—
162A4—81no—
163C3×C4—61no—
164C3×C4—61no—
165C3×C4—62no—
166C3×C4—481no—
167C3×C4—481no—
168Dic3—31no—
169Dic3—41no—
170Dic3—62no—
171Dic3—121no—
172Dic3#126⋊C311yescharacteristic, direct product factor
173C32—161noSylow
174C23—61no—
175C23—61no—
176C23Dic3×A412yes—
177C23C2×D3×A411yescharacteristic
178C2×C4—31no—
179C2×C4—31no—
180C2×C4—32no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—61no—
184C2×C4—61no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—121no—
189C2×C4—181no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—181no—
193C2×C4—181no—
194C2×C4—181no—
195C2×C4—361no—
196C2×C3—31no—
197C2×C3—31no—
198C2×C3—42no—
199C2×C3—162no—
200C2×C3—161no—
201C2×C3—322no—
202C2×C3—321no—
203C2×C3C2×#126⋊C311yescharacteristic
204C22—31no—
205C22—31no—
206C22—41no—
207C22—62no—
208C22—121no—
209C22C2×Dic3×A411yescharacteristic
210C4—31no—
211C4—61no—
212C4—61no—
213C4—62no—
214C4—91no—
215C4—121no—
216C4—182no—
217C4—361no—
218C3—161no—
219C3—321no—
220C3C4×#126⋊C311yescharacteristic, complemented
221C2—31no—
222C2—31no—
223C2—42no—
224C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC2×C3×#126C2×C3
socleC23×C3C22×A4
prime radicalC2×C3×#126⋊C3C2
cosocleC2×C3×C42C22×C3
LCSG ▷ C3×C42
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic3×C42⋊C3C2semidirect
3. C3⋊(#383⋊C3)C2semidirect
4. Dic3×#126C3semidirect
7. C3×#126⋊C3C4semidirect
16. #4937C2×C3semidirect
17. C42×Dic3C2×C3semidirect
23. C3×C42⋊C3C2×C4semidirect
28. C3×#126C3×C4semidirect
38. #126⋊C3Dic3direct (N × H)
73. C3×C42C2×C3×C4semidirect
82. C42⋊C3C2×Dic3semidirect
89. #126C3×Dic3semidirect
152. C42C2×C3×Dic3semidirect
172. Dic3#126⋊C3direct (N × H)
220. C3C4×#126⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#126⋊C32
Dic3×C42⋊C32
C3⋊(#383⋊C3)2
Dic3×#1263
C4×#126⋊C33
C2×Dic3×A44