Finite Group Databasebeta

← D3×#383⋊C3 #11921150

Subgroups — D3×#383⋊C3 #11921150

Order 1152.

297 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 297 conjugacy classes of subgroups — too many to draw. Only its 40 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⋊C3C211yesmaximal, characteristic
2C3×#383⋊C3C211yesmaximal, characteristic, complemented
3C3⋊(#383⋊C3)C211yesmaximal, characteristic, complemented
4D3×#383C311yesmaximal, characteristic, complemented
5C2×#383⋊C3—31nomaximal
6C4×D3×A4—41nomaximal
7C2×C3×C42⋊C3C2211yescharacteristic
8D3×C42⋊C3C412yescomplemented
9C2×C42×D3C2×C311yescharacteristic
10C22×C42⋊C3—31no—
11C3×#383C2×C311yescharacteristic, complemented
12#4937C2×C311yescharacteristic, complemented
13D3×#95—31no—
14D3×#95—31no—
15#4651—31no—
16#4651—31no—
17#383⋊C3—21no—
18#383⋊C3—31no—
19#383⋊C3D311yescharacteristic, direct product factor
20C2×D3×A4—41no—
21C3×C4×A4—41no—
22Dic3×A4—41no—
23C3×C42⋊C3C2×C411yescharacteristic, complemented
24C2×#383—31noSylow
25C22×C4×D3—31no—
26C22×C4×D3—31no—
27C22×C4×D3A411yescharacteristic
28C2×C4×A4—121no—
29C2×C3×C42C22×C311yescharacteristic
30C2×C4×Dic3—31no—
31C42×D3—32no—
32C42×D3C3×C412yescomplemented
33C2×C42⋊C3—21no—
34C2×C42⋊C3—32no—
35C2×C42⋊C3C2×D311yescharacteristic
36C3×#95—31no—
37C3×#95—31no—
38C3⋊#95—32no—
39C3⋊#95—31no—
40C3⋊#95—31no—
41C3⋊#95—31no—
42C3⋊#95—31no—
43C2×C3×A4—41no—
44D3×A4—42no—
45C3×C4×D3—161no—
46C22×C42—31no—
47#383—31no—
48#383—91no—
49#383—91no—
50#383C3×D311yescharacteristic, complemented
51C2×#95—91no—
52C2×#95—91no—
53C23×D3C2×A411yescharacteristic
54C22×A4—121no—
55C22×C3×C4—31no—
56C22×C3×C4—31no—
57C22×C3×C4C2×A411yescharacteristic
58C22×Dic3—31no—
59C22×Dic3—31no—
60C22×Dic3C2×A411yescharacteristic
61C2×C4×D3—32no—
62C2×C4×D3—32no—
63C2×C4×D3—61no—
64C2×C4×D3—61no—
65C2×C4×D3—62no—
66C2×C4×D3—61no—
67C2×C4×D3—61no—
68C2×C4×D3—61no—
69C2×C4×D3—64no—
70C2×C4×D3—61no—
71C4×A4—41no—
72C4×A4—81no—
73C4×A4—121no—
74C3×C42—31no—
75C3×C42C2×C3×C411yescharacteristic, complemented
76C4×Dic3—32no—
77C4×Dic3—32no—
78C42⋊C3—21no—
79C42⋊C3C4×D311yescharacteristic, complemented
80C2×C3×D3—161no—
81C3×A4—41no—
82C32×C4—161no—
83C3×Dic3—161no—
84C23×C4—31no—
85C23×C4—91no—
86C23×C4—91no—
87C2×C42—32no—
88C2×C42—92no—
89C2×C42—91no—
90C2×C42C2×C3×D311yescharacteristic
91#95—31no—
92#95—31no—
93#95—91no—
94#95—91no—
95#95—91no—
96#95—92no—
97#95—91no—
98C23×C3C22×A411yescharacteristic
99C22×D3—31no—
100C22×D3—31no—
101C22×D3—32no—
102C22×D3C4×A412yes—
103C2×A4—41no—
104C2×A4—81no—
105C2×A4—122no—
106C2×C3×C4—31no—
107C2×C3×C4—31no—
108C2×C3×C4—61no—
109C2×C3×C4—61no—
110C2×C3×C4—61no—
111C2×C3×C4—62no—
112C2×C3×C4—61no—
113C2×C3×C4—481no—
114C2×Dic3—32no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—62no—
119C2×Dic3—61no—
120C4×D3—41no—
121C4×D3—62no—
122C4×D3—62no—
123C4×D3—62no—
124C4×D3—62no—
125C4×D3—121no—
126C4×D3—122no—
127C4×D3—122no—
128C2×C32—161no—
129C3×D3—162no—
130C24—31no—
131C22×C4—31no—
132C22×C4—31no—
133C22×C4—31no—
134C22×C4—92no—
135C22×C4—92no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4—181no—
139C22×C4—181no—
140C22×C4—182no—
141C22×C4—181no—
142C22×C4—181no—
143C22×C4—184no—
144C22×C4—181no—
145C22×C4—181no—
146C22×C4D3×A411yescharacteristic
147C42—31no—
148C42—92no—
149C42—92no—
150C42C3×C4×D311yescharacteristic, complemented
151C22×C3—31no—
152C22×C3—31no—
153C22×C3—481no—
154C22×C3C2×C4×A411yescharacteristic
155C2×D3—32no—
156C2×D3—31no—
157C2×D3—32no—
158C2×D3—32no—
159C2×D3—32no—
160C2×D3#126⋊C311yescharacteristic
161A4—41no—
162A4—81no—
163C3×C4—41no—
164C3×C4—61no—
165C3×C4—61no—
166C3×C4—121no—
167C3×C4—161no—
168C3×C4—321no—
169C3×C4—481no—
170Dic3—41no—
171Dic3—62no—
172Dic3—121no—
173C32—161noSylow
174C23—32no—
175C23—91no—
176C23—92no—
177C23—91no—
178C23C2×D3×A411yescharacteristic
179C2×C4—31no—
180C2×C4—31no—
181C2×C4—61no—
182C2×C4—61no—
183C2×C4—61no—
184C2×C4—62no—
185C2×C4—61no—
186C2×C4—92no—
187C2×C4—121no—
188C2×C4—182no—
189C2×C4—182no—
190C2×C4—182no—
191C2×C4—182no—
192C2×C4—181no—
193C2×C4—181no—
194C2×C4—181no—
195C2×C4—182no—
196C2×C4—181no—
197C2×C4—361no—
198C2×C4—362no—
199C2×C4—362no—
200C2×C3—31no—
201C2×C3—31no—
202C2×C3—161no—
203C2×C3—321no—
204C2×C3—482no—
205C2×C3C2×#126⋊C311yescharacteristic
206D3—32no—
207D3#383⋊C312yesdirect product factor
208C22—31no—
209C22—31no—
210C22—31no—
211C22—92no—
212C22—92no—
213C22—92no—
214C22—92no—
215C22—91no—
216C22C4×D3×A411yescharacteristic
217C4—41no—
218C4—61no—
219C4—61no—
220C4—121no—
221C4—121no—
222C4—182no—
223C4—361no—
224C3—161no—
225C3—321no—
226C3C2×#383⋊C311yescharacteristic, complemented
227C2—31no—
228C2—31no—
229C2—32no—
230C2—92no—
231C2D3×#126⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2D3×#126⋊C3
commutator, hypocenterC3×C42C2×C3×C4
FrattiniC23C2×D3×A4
FittingC3×#383C2×C3
socleC23×C3C22×A4
prime radicalC2×D3×C42⋊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. C3×#383⋊C3C2semidirect
3. C3⋊(#383⋊C3)C2semidirect
4. D3×#383C3semidirect
8. D3×C42⋊C3C4semidirect
11. C3×#383C2×C3semidirect
12. #4937C2×C3semidirect
19. #383⋊C3D3direct (N × H)
23. C3×C42⋊C3C2×C4semidirect
32. C42×D3C3×C4semidirect
50. #383C3×D3semidirect
75. C3×C42C2×C3×C4semidirect
79. C42⋊C3C4×D3semidirect
150. C42C3×C4×D3semidirect
207. D3#383⋊C3direct (N × H)
226. C3C2×#383⋊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×#383⋊C32
C3⋊(#383⋊C3)2
D3×#3833
C2×#383⋊C33
C4×D3×A44