Subgroups — C₂×C₃×#4466 #11795916

Order 1152.

409 conjugacy classes of subgroups.

The subgroup lattice has 243 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#812	C₂	1	2	yes	maximal
3	C₃×#4466	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×#347	—	3	1	no	maximal
5	C₂×#4466	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²×C₈	C₄	1	1	yes	characteristic
7	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
9	C₃²×#97	C₄	1	2	yes	—
10	C₃²×#97	C₂²	1	2	yes	—
11	C₃×#812	C₄	1	4	yes	complemented
12	C₃×#812	C₂²	1	4	yes	—
13	C₂×C₃×C₃⋊C₁₆	C₄	1	4	yes	complemented
14	C₂×C₃×M₃₂	—	3	2	no	—
15	C₂×C₃×#97	—	2	1	no	—
16	C₂×C₃×#97	D₃	1	1	yes	characteristic
17	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic
18	C₂×#812	C₂×C₃	1	2	yes	—
19	C₃×#347	—	3	4	no	—
20	#4466	C₂×C₃	1	4	yes	direct product factor
21	C₂²×C₃²×C₄	—	2	1	no	—
22	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
23	C₂×C₃²×C₈	—	2	1	no	—
24	C₂×C₃²×C₈	—	2	1	no	—
25	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
26	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
28	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
29	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
30	C₃²×C₄²	—	2	1	no	—
31	C₃²×C₄²	C₂×C₄	1	2	yes	—
32	C₃×C₃⋊C₁₆	C₂×C₄	1	8	yes	complemented
33	C₂×#347	—	3	1	no	Sylow
34	C₂²×C₃×C₈	—	2	1	no	—
35	C₂²×C₃×C₈	—	2	1	no	—
36	C₂²×C₃×C₈	Dic₃	1	1	yes	characteristic
37	C₂²×C₃×C₈	C₃×C₄	1	1	yes	characteristic
38	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
39	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
40	C₂×C₃×C₄²	—	2	1	no	—
41	C₂×C₃×C₄²	Dic₃	1	1	yes	characteristic
42	C₂×C₃×C₄²	C₃×C₄	1	1	yes	characteristic
43	C₃×M₃₂	—	3	4	no	—
44	C₃×M₃₂	—	3	4	no	—
45	C₂×C₃×C₁₆	—	3	4	no	—
46	C₃×#97	—	2	2	no	—
47	C₃×#97	—	2	2	no	—
48	C₃×#97	Dic₃	1	2	yes	—
49	C₃×#97	C₃×C₄	1	2	yes	—
50	C₃×#97	C₂×D₃	1	2	yes	—
51	C₃×#97	C₂²×C₃	1	2	yes	—
52	#812	C₃×C₄	1	4	yes	complemented
53	#812	C₂²×C₃	1	4	yes	—
54	C₂×C₃⋊C₁₆	C₃×C₄	1	4	yes	complemented
55	C₂³×C₃²	M₁₆	1	1	yes	characteristic
56	C₂×C₃²×C₄	—	2	2	no	—
57	C₂×C₃²×C₄	—	4	2	no	—
58	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
59	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
60	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
61	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
62	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
63	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
64	C₃²×C₈	—	2	2	no	—
65	C₃²×C₈	C₄²	1	2	yes	—
66	C₃²×C₈	C₂²×C₄	1	2	yes	—
67	C₂×M₃₂	—	3	2	no	—
68	C₂×#97	C₃×D₃	1	1	yes	characteristic
69	#347	—	3	4	no	—
70	C₂²×C₃×C₄	—	2	2	no	—
71	C₂²×C₃×C₄	—	2	1	no	—
72	C₂²×C₃×C₄	—	2	1	no	—
73	C₂²×C₃×C₄	—	2	1	no	—
74	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
75	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
76	C₂×C₃×C₈	—	2	2	no	—
77	C₂×C₃×C₈	—	2	2	no	—
78	C₂×C₃×C₈	—	2	1	no	—
79	C₂×C₃×C₈	—	2	1	no	—
80	C₂×C₃×C₈	—	2	1	no	—
81	C₂×C₃×C₈	—	2	1	no	—
82	C₂×C₃×C₈	—	2	2	no	—
83	C₂×C₃×C₈	—	2	2	no	—
84	C₂×C₃×C₈	—	2	2	no	—
85	C₂×C₃×C₈	—	2	1	no	—
86	C₂×C₃×C₈	—	2	1	no	—
87	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
88	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
89	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
90	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
91	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
92	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
93	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
94	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
95	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
96	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
97	C₃×C₄²	—	2	2	no	—
98	C₃×C₄²	—	2	1	no	—
99	C₃×C₄²	—	2	1	no	—
100	C₃×C₄²	—	2	2	no	—
101	C₃×C₄²	C₂×Dic₃	1	2	yes	—
102	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
103	C₃×C₁₆	—	3	8	no	—
104	C₃⋊C₁₆	C₂×C₃×C₄	1	8	yes	complemented
105	C₂²×C₃²	—	2	2	no	—
106	C₂²×C₃²	#97	1	1	yes	characteristic
107	C₂²×C₃²	#97	1	1	yes	characteristic
108	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
109	C₃²×C₄	—	4	2	no	—
110	C₃²×C₄	#97	1	1	yes	characteristic
111	C₃²×C₄	#97	1	1	yes	characteristic
112	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
113	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
114	C₂²×C₈	C₃×Dic₃	1	1	yes	characteristic
115	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
116	C₂×C₄²	C₃×Dic₃	1	1	yes	characteristic
117	M₃₂	—	3	4	no	—
118	M₃₂	—	3	4	no	—
119	C₂×C₁₆	—	3	4	no	—
120	#97	C₃×Dic₃	1	2	yes	—
121	#97	C₂×C₃×D₃	1	2	yes	—
122	C₂³×C₃	—	2	1	no	—
123	C₂³×C₃	#208	1	1	yes	characteristic
124	C₂³×C₃	C₃×M₁₆	1	1	yes	characteristic
125	C₂×C₃×C₄	—	2	4	no	—
126	C₂×C₃×C₄	—	2	2	no	—
127	C₂×C₃×C₄	—	2	2	no	—
128	C₂×C₃×C₄	—	2	1	no	—
129	C₂×C₃×C₄	—	2	1	no	—
130	C₂×C₃×C₄	—	2	1	no	—
131	C₂×C₃×C₄	—	2	1	no	—
132	C₂×C₃×C₄	—	2	1	no	—
133	C₂×C₃×C₄	—	2	1	no	—
134	C₂×C₃×C₄	—	4	4	no	—
135	C₂×C₃×C₄	—	4	2	no	—
136	C₂×C₃×C₄	—	4	2	no	—
137	C₂×C₃×C₄	#208	1	1	yes	characteristic
138	C₂×C₃×C₄	#208	1	1	yes	characteristic
139	C₂×C₃×C₄	#208	1	1	yes	characteristic
140	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
141	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
142	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
143	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
144	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
145	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
146	C₂×C₃×C₄	C₃×M₁₆	1	1	yes	characteristic
147	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
148	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
149	C₃×C₈	—	2	4	no	—
150	C₃×C₈	—	2	2	no	—
151	C₃×C₈	—	2	2	no	—
152	C₃×C₈	—	2	2	no	—
153	C₃×C₈	—	2	2	no	—
154	C₃×C₈	C₄×Dic₃	1	2	yes	—
155	C₃×C₈	C₃×C₄²	1	2	yes	—
156	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
157	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
158	C₂×C₃²	—	2	1	no	—
159	C₂×C₃²	—	2	1	no	—
160	C₂×C₃²	#347	1	2	yes	complemented
161	C₂×C₃²	C₂×#97	1	1	yes	characteristic
162	C₂²×C₄	—	2	1	no	—
163	C₂²×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	1	no	—
166	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
167	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
168	C₂×C₈	C₂×C₃×Dic₃	1	2	yes	—
169	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
170	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
171	C₄²	—	2	1	no	—
172	C₄²	C₂×C₃×Dic₃	1	2	yes	—
173	C₁₆	—	3	8	no	—
174	C₂²×C₃	—	2	4	no	—
175	C₂²×C₃	—	2	2	no	—
176	C₂²×C₃	—	2	2	no	—
177	C₂²×C₃	—	2	1	no	—
178	C₂²×C₃	—	2	1	no	—
179	C₂²×C₃	—	2	1	no	—
180	C₂²×C₃	#803	1	1	yes	characteristic
181	C₂²×C₃	#803	1	1	yes	characteristic
182	C₂²×C₃	C₃×#97	1	1	yes	characteristic
183	C₂²×C₃	C₃×#97	1	1	yes	characteristic
184	C₂²×C₃	C₂×#208	1	1	yes	characteristic
185	C₂²×C₃	C₂×C₃×M₁₆	1	1	yes	characteristic
186	C₃×C₄	—	2	1	no	—
187	C₃×C₄	—	2	1	no	—
188	C₃×C₄	—	2	1	no	—
189	C₃×C₄	—	2	1	no	—
190	C₃×C₄	—	4	4	no	—
191	C₃×C₄	—	4	2	no	—
192	C₃×C₄	—	4	2	no	—
193	C₃×C₄	#803	1	1	yes	characteristic
194	C₃×C₄	#803	1	1	yes	characteristic
195	C₃×C₄	C₃×#97	1	1	yes	characteristic
196	C₃×C₄	C₃×#97	1	1	yes	characteristic
197	C₃×C₄	C₂×#208	1	1	yes	characteristic
198	C₃×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
199	C₃×C₄	C₂×C₃×C₄²	1	1	yes	characteristic
200	C₃×C₄	C₂×C₃×M₁₆	1	1	yes	characteristic
201	C₃²	C₂×#347	1	1	yes	characteristic, complemented, Sylow
202	C₂³	C₃×#208	1	1	yes	characteristic
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	C₃×#208	1	1	yes	characteristic
206	C₂×C₄	C₃×#208	1	1	yes	characteristic
207	C₂×C₄	C₃×#208	1	1	yes	characteristic
208	C₂×C₄	C₃×C₄×Dic₃	1	1	yes	characteristic
209	C₂×C₄	C₃×C₄×Dic₃	1	1	yes	characteristic
210	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
211	C₈	—	2	2	no	—
212	C₈	C₃×C₄×Dic₃	1	2	yes	—
213	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
214	C₂×C₃	—	2	2	no	—
215	C₂×C₃	—	2	2	no	—
216	C₂×C₃	—	2	1	no	—
217	C₂×C₃	—	2	1	no	—
218	C₂×C₃	—	2	1	no	—
219	C₂×C₃	—	2	1	no	—
220	C₂×C₃	—	2	1	no	—
221	C₂×C₃	—	2	2	no	—
222	C₂×C₃	#4466	1	2	yes	direct product factor
223	C₂×C₃	C₃×#347	1	2	yes	complemented
224	C₂×C₃	C₂×#803	1	1	yes	characteristic
225	C₂×C₃	C₂×C₃×#97	1	1	yes	characteristic
226	C₂²	—	2	2	no	—
227	C₂²	C₃×#803	1	1	yes	characteristic
228	C₂²	C₃×#803	1	1	yes	characteristic
229	C₂²	C₂×C₃×#208	1	1	yes	characteristic
230	C₄	—	4	2	no	—
231	C₄	C₃×#803	1	1	yes	characteristic
232	C₄	C₃×#803	1	1	yes	characteristic
233	C₄	C₂×C₃×#208	1	1	yes	characteristic
234	C₄	C₂×C₃×C₄×Dic₃	1	1	yes	characteristic
235	C₃	—	2	1	no	—
236	C₃	C₂×#4466	1	1	yes	characteristic, direct product factor
237	C₃	C₂×C₃×#347	1	1	yes	characteristic, complemented
238	C₂	—	2	1	no	—
239	C₂	—	2	1	no	—
240	C₂	C₃×#4466	1	2	yes	direct product factor
241	C₂	C₂×C₃×#803	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₄×Dic₃
commutator	C₃×C₄	C₂×C₃×C₄²
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂²×C₃²	#97
prime radical	C₂³×C₃²	M₁₆
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₂×C₃×#347
LCS	G ▷ C₃×C₄ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
3. C₃×#4466	C₂	direct (N × H)
5. C₂×#4466	C₃	direct (N × H)
11. C₃×#812	C₄	semidirect
13. C₂×C₃×C₃⋊C₁₆	C₄	semidirect
20. #4466	C₂×C₃	direct (N × H)
32. C₃×C₃⋊C₁₆	C₂×C₄	semidirect
52. #812	C₃×C₄	semidirect
54. C₂×C₃⋊C₁₆	C₃×C₄	semidirect
104. C₃⋊C₁₆	C₂×C₃×C₄	semidirect
160. C₂×C₃²	#347	semidirect
201. C₃²	C₂×#347	semidirect
222. C₂×C₃	#4466	direct (N × H)
223. C₂×C₃	C₃×#347	semidirect
236. C₃	C₂×#4466	direct (N × H)
237. C₃	C₂×C₃×#347	semidirect
240. C₂	C₃×#4466	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×#97	2
C₂×C₃×#812	2
C₃×#4466	2
C₂×C₃×#347	3
C₂×#4466	3

Subgroups — C2×C3×#4466 #11795916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4466 #11795916