Subgroups — C₄×Dic₃×C₃⋊C₈ #11783013

Order 1152.

897 conjugacy classes of subgroups.

The subgroup lattice has 207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃×C₃⋊C₈	C₂	1	4	yes	maximal
5	C₄×C₈×Dic₃	—	3	1	no	maximal
6	C₄²×C₃⋊C₈	—	3	1	no	maximal
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₃×C₄×Dic₃	C₄	1	4	yes	—
10	C₂×C₃×C₄×Dic₃	C₂²	1	2	yes	—
11	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
12	C₄×C₃⋊(C₃⋊C₈)	C₄	1	4	yes	complemented
13	C₃×C₄×C₃⋊C₈	C₄	1	4	yes	complemented
14	Dic₃×C₃⋊C₈	C₄	1	16	yes	direct product factor
15	C₂×C₃×C₄×C₈	—	3	1	no	—
16	C₃×C₄³	—	3	1	no	—
17	C₂×C₈×Dic₃	—	3	4	no	—
18	C₄²×Dic₃	D₃	1	1	yes	characteristic
19	C₂×C₄×C₃⋊C₈	—	3	1	no	—
20	C₂×C₄×C₃⋊C₈	—	3	1	no	—
21	C₂×C₄×C₃⋊C₈	—	3	4	no	—
22	C₂×C₄×C₃⋊C₈	—	6	1	no	—
23	C₂×C₄×C₃⋊C₈	D₃	1	1	yes	characteristic
24	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
25	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
26	C₂²×C₃×Dic₃	C₂×C₄	1	4	yes	—
27	C₃²×C₄²	C₂×C₄	1	2	yes	—
28	C₃²×C₄²	C₂×C₄	1	2	yes	—
29	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	8	yes	—
30	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	—
31	C₃×C₄×Dic₃	C₈	1	16	yes	complemented
32	C₃×C₄×Dic₃	C₂×C₄	1	8	yes	—
33	C₂×C₃×C₃⋊C₈	C₂×C₄	1	8	yes	—
34	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
35	C₄²×C₈	—	9	1	no	Sylow
36	C₂²×C₃×C₈	—	3	2	no	—
37	C₂×C₃×C₄²	—	2	1	no	—
38	C₂×C₃×C₄²	—	3	4	no	—
39	C₂×C₃×C₄²	—	3	2	no	—
40	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
42	C₂×C₄×Dic₃	Dic₃	1	4	yes	—
43	C₂×C₄×Dic₃	C₂×D₃	1	2	yes	—
44	C₂²×C₃⋊C₈	—	3	2	no	—
45	C₂²×C₃⋊C₈	—	3	2	no	—
46	C₂²×C₃⋊C₈	—	6	2	no	—
47	C₂²×C₃⋊C₈	C₂×D₃	1	2	yes	—
48	C₃×C₄×C₈	—	3	4	no	—
49	C₈×Dic₃	—	3	16	no	—
50	C₄×C₃⋊C₈	—	3	4	no	—
51	C₄×C₃⋊C₈	—	3	4	no	—
52	C₄×C₃⋊C₈	—	3	16	no	—
53	C₄×C₃⋊C₈	—	6	4	no	—
54	C₄×C₃⋊C₈	Dic₃	1	4	yes	direct product factor
55	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₃²×C₄	C₄²	1	4	yes	—
57	C₂×C₃²×C₄	C₂×C₈	1	8	yes	—
58	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
59	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₃×Dic₃	C₄²	1	8	yes	—
62	C₂×C₃×Dic₃	C₂×C₈	1	16	yes	—
63	C₃⋊(C₃⋊C₈)	C₄²	1	8	yes	complemented
64	C₃×C₃⋊C₈	C₄²	1	8	yes	complemented
65	C₂×C₄×C₈	—	3	1	no	—
66	C₂×C₄×C₈	—	9	4	no	—
67	C₂×C₄×C₈	—	9	1	no	—
68	C₄³	—	3	1	no	—
69	C₂²×C₃×C₄	—	2	2	no	—
70	C₂²×C₃×C₄	—	2	1	no	—
71	C₂²×C₃×C₄	—	3	4	no	—
72	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
73	C₂²×C₃×C₄	C₂×Dic₃	1	2	yes	—
74	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
75	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
76	C₂²×Dic₃	C₂×Dic₃	1	4	yes	—
77	C₂×C₃×C₈	—	3	8	no	—
78	C₂×C₃×C₈	—	3	4	no	—
79	C₃×C₄²	—	2	2	no	—
80	C₃×C₄²	—	2	2	no	—
81	C₃×C₄²	—	3	16	no	—
82	C₃×C₄²	—	3	8	no	—
83	C₃×C₄²	C₄×D₃	1	2	yes	—
84	C₃×C₄²	C₄×D₃	1	2	yes	—
85	C₃×C₄²	C₄×D₃	1	2	yes	—
86	C₃×C₄²	C₂×Dic₃	1	2	yes	—
87	C₄×Dic₃	C₃⋊C₈	1	16	yes	direct product factor
88	C₄×Dic₃	C₄×D₃	1	8	yes	—
89	C₂×C₃⋊C₈	—	3	8	no	—
90	C₂×C₃⋊C₈	—	3	4	no	—
91	C₂×C₃⋊C₈	—	3	4	no	—
92	C₂×C₃⋊C₈	—	3	8	no	—
93	C₂×C₃⋊C₈	—	6	4	no	—
94	C₂×C₃⋊C₈	—	6	8	no	—
95	C₂×C₃⋊C₈	C₄×D₃	1	8	yes	—
96	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	—
97	C₂²×C₃²	C₂×C₄²	1	2	yes	—
98	C₂²×C₃²	C₂×C₄²	1	1	yes	characteristic
99	C₂²×C₃²	C₂²×C₈	1	4	yes	—
100	C₃²×C₄	C₄×C₈	1	8	yes	complemented
101	C₃²×C₄	C₂×C₄²	1	2	yes	—
102	C₃²×C₄	C₂×C₄²	1	2	yes	—
103	C₃×Dic₃	C₄×C₈	1	16	yes	complemented
104	C₂²×C₈	—	3	2	no	—
105	C₂²×C₈	—	9	2	no	—
106	C₂×C₄²	—	3	4	no	—
107	C₂×C₄²	—	3	2	no	—
108	C₂×C₄²	D₃²	1	1	yes	characteristic
109	C₄×C₈	—	3	4	no	—
110	C₄×C₈	—	9	16	no	—
111	C₄×C₈	—	9	4	no	—
112	C₂³×C₃	—	2	1	no	—
113	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
114	C₂³×C₃	C₂²×Dic₃	1	1	yes	characteristic
115	C₂×C₃×C₄	—	2	8	no	—
116	C₂×C₃×C₄	—	2	4	no	—
117	C₂×C₃×C₄	—	2	4	no	—
118	C₂×C₃×C₄	—	2	1	no	—
119	C₂×C₃×C₄	—	2	1	no	—
120	C₂×C₃×C₄	—	3	8	no	—
121	C₂×C₃×C₄	—	3	16	no	—
122	C₂×C₃×C₄	D₃×C₈	1	8	yes	—
123	C₂×C₃×C₄	C₂×C₃⋊C₈	1	8	yes	—
124	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
125	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
126	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
127	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
128	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
129	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
130	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
131	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
132	C₂×Dic₃	C₂×C₃⋊C₈	1	16	yes	—
133	C₂×Dic₃	C₄×Dic₃	1	8	yes	—
134	C₃×C₈	—	3	8	no	—
135	C₃⋊C₈	—	3	8	no	—
136	C₃⋊C₈	—	3	8	no	—
137	C₃⋊C₈	—	6	8	no	—
138	C₃⋊C₈	C₄×Dic₃	1	8	yes	direct product factor
139	C₂×C₃²	C₄³	1	1	yes	characteristic
140	C₂×C₃²	C₂×C₄×C₈	1	4	yes	—
141	C₂×C₃²	C₂×C₄×C₈	1	2	yes	—
142	C₂²×C₄	—	3	4	no	—
143	C₂²×C₄	D₃×Dic₃	1	2	yes	—
144	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
145	C₂×C₈	—	3	8	no	—
146	C₂×C₈	—	3	4	no	—
147	C₂×C₈	—	9	8	no	—
148	C₂×C₈	—	9	4	no	—
149	C₄²	—	3	16	no	—
150	C₄²	—	3	8	no	—
151	C₄²	D₃×Dic₃	1	2	yes	—
152	C₄²	#624	1	2	yes	—
153	C₂²×C₃	—	2	4	no	—
154	C₂²×C₃	—	2	2	no	—
155	C₂²×C₃	—	2	1	no	—
156	C₂²×C₃	C₄²×D₃	1	2	yes	—
157	C₂²×C₃	C₂×D₃×C₈	1	4	yes	—
158	C₂²×C₃	C₂²×C₃⋊C₈	1	4	yes	—
159	C₂²×C₃	C₂×C₄×Dic₃	1	2	yes	—
160	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
161	C₂²×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
162	C₃×C₄	—	2	8	no	—
163	C₃×C₄	—	2	2	no	—
164	C₃×C₄	—	2	2	no	—
165	C₃×C₄	—	3	16	no	—
166	C₃×C₄	C₄×C₃⋊C₈	1	8	yes	complemented
167	C₃×C₄	C₈×Dic₃	1	8	yes	complemented
168	C₃×C₄	C₄²×D₃	1	2	yes	—
169	C₃×C₄	C₄²×D₃	1	2	yes	—
170	C₃×C₄	C₄²×D₃	1	2	yes	—
171	C₃×C₄	C₂×C₄×Dic₃	1	2	yes	—
172	Dic₃	C₄×C₃⋊C₈	1	16	yes	direct product factor
173	C₃²	C₄²×C₈	1	1	yes	characteristic, complemented, Sylow
174	C₂³	C₂×D₃×Dic₃	1	1	yes	characteristic
175	C₂×C₄	—	3	16	no	—
176	C₂×C₄	—	3	8	no	—
177	C₂×C₄	D₃×C₃⋊C₈	1	8	yes	—
178	C₂×C₄	Dic₃²	1	4	yes	—
179	C₂×C₄	C₄×D₃²	1	4	yes	—
180	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
181	C₂×C₄	C₂×#624	1	1	yes	characteristic
182	C₈	—	3	8	no	—
183	C₈	—	9	8	no	—
184	C₂×C₃	—	2	1	no	—
185	C₂×C₃	—	2	2	no	—
186	C₂×C₃	—	2	4	no	—
187	C₂×C₃	C₄×D₃×C₈	1	4	yes	—
188	C₂×C₃	C₂×C₄×C₃⋊C₈	1	2	yes	—
189	C₂×C₃	C₂×C₄×C₃⋊C₈	1	4	yes	—
190	C₂×C₃	C₄²×Dic₃	1	1	yes	characteristic
191	C₂×C₃	C₄²×Dic₃	1	1	yes	characteristic
192	C₂×C₃	C₂×C₈×Dic₃	1	2	yes	—
193	C₂²	C₂×D₃×C₃⋊C₈	1	4	yes	—
194	C₂²	C₄×D₃×Dic₃	1	2	yes	—
195	C₂²	C₂×Dic₃²	1	1	yes	characteristic
196	C₄	—	3	16	no	—
197	C₄	Dic₃×C₃⋊C₈	1	8	yes	direct product factor
198	C₄	C₄×D₃×Dic₃	1	2	yes	—
199	C₄	C₄×#624	1	2	yes	—
200	C₃	—	2	1	no	—
201	C₃	C₄²×C₃⋊C₈	1	1	yes	characteristic, complemented
202	C₃	C₄×C₈×Dic₃	1	1	yes	characteristic, complemented
203	C₂	C₄×D₃×C₃⋊C₈	1	4	yes	—
204	C₂	C₂×Dic₃×C₃⋊C₈	1	2	yes	—
205	C₂	C₄×Dic₃²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄²	D₃²
commutator, hypocenter	C₃²	C₄²×C₈
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂²×C₄
cosocle	C₂²×C₃²×C₄	C₂³
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
12. C₄×C₃⋊(C₃⋊C₈)	C₄	semidirect
13. C₃×C₄×C₃⋊C₈	C₄	semidirect
14. Dic₃×C₃⋊C₈	C₄	direct (N × H)
31. C₃×C₄×Dic₃	C₈	semidirect
54. C₄×C₃⋊C₈	Dic₃	direct (N × H)
63. C₃⋊(C₃⋊C₈)	C₄²	semidirect
64. C₃×C₃⋊C₈	C₄²	semidirect
87. C₄×Dic₃	C₃⋊C₈	direct (N × H)
100. C₃²×C₄	C₄×C₈	semidirect
103. C₃×Dic₃	C₄×C₈	semidirect
138. C₃⋊C₈	C₄×Dic₃	direct (N × H)
166. C₃×C₄	C₄×C₃⋊C₈	semidirect
167. C₃×C₄	C₈×Dic₃	semidirect
172. Dic₃	C₄×C₃⋊C₈	direct (N × H)
173. C₃²	C₄²×C₈	semidirect
197. C₄	Dic₃×C₃⋊C₈	direct (N × H)
201. C₃	C₄²×C₃⋊C₈	semidirect
202. C₃	C₄×C₈×Dic₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₃⋊(C₃⋊C₈)	2
C₃×C₄²×Dic₃	2
C₂×C₃×C₄×C₃⋊C₈	2
C₂×Dic₃×C₃⋊C₈	2
C₄×C₈×Dic₃	3
C₄²×C₃⋊C₈	3

Subgroups — C4×Dic3×C3⋊C8 #11783013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Dic₃×C₃⋊C₈ #11783013