Subgroups — C₂×C₃×#63650 #13163167

Order 1728.

1388 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63650	C₂	1	4	yes	maximal, direct product factor
5	C₂×#63650	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃×#823	—	3	4	no	maximal
7	C₂³×C₃×C₃⋊D₃	C₄	1	2	yes	—
8	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
10	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
11	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
12	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	1	2	yes	—
14	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
15	C₃³×M₁₆	—	2	1	no	—
16	C₃³×M₁₆	C₂²	1	2	yes	complemented
17	C₂×C₃³×C₈	—	2	1	no	—
18	C₃×#3748	—	2	1	no	—
19	C₃×#3748	C₂²	1	2	yes	complemented
20	C₂×C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
21	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
22	C₂²×C₃×D₁₂	—	3	4	no	—
23	C₂×C₃²×M₁₆	—	2	4	no	—
24	C₂×C₃²×M₁₆	D₃	1	4	yes	complemented
25	C₂×C₃²×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#3748	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#208	—	3	4	no	—
28	#63650	C₂×C₃	1	4	yes	direct product factor
29	C₃×#823	—	3	16	no	—
30	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
32	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
33	C₂²×C₃×C₃⋊D₃	—	4	4	no	—
34	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	4	yes	—
35	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
38	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
39	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
42	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
43	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
44	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
45	C₃³×C₈	—	2	2	no	—
46	C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
47	C₂×C₃×#100	—	9	1	no	—
48	C₂×#823	—	3	4	no	—
49	C₂³×C₃⋊D₃	C₃×C₄	1	2	yes	—
50	C₂³×C₃×D₃	—	3	8	no	—
51	C₂²×C₃²×C₄	—	2	4	no	—
52	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
53	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
55	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
56	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
57	C₂×C₄⋊(C₃⋊D₃)	—	2	1	no	—
58	C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	1	2	yes	—
59	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
60	C₂×C₃×D₁₂	—	3	8	no	—
61	C₂×C₃×D₁₂	—	3	8	no	—
62	C₂×C₃×D₁₂	—	6	4	no	—
63	C₂×C₃×D₁₂	—	6	4	no	—
64	C₂×C₃×D₁₂	—	6	4	no	—
65	C₂×C₃×D₁₂	—	6	4	no	—
66	C₃²×M₁₆	—	2	8	no	—
67	C₃²×M₁₆	—	2	8	no	—
68	C₃²×M₁₆	—	2	4	no	—
69	C₃²×M₁₆	—	2	1	no	—
70	C₃²×M₁₆	C₂×D₃	1	8	yes	complemented
71	C₃²×M₁₆	C₂²×C₃	1	2	yes	complemented
72	C₂×C₃²×C₈	—	2	8	no	—
73	C₂×C₃²×C₈	—	2	4	no	—
74	C₂×C₃²×C₈	—	2	1	no	—
75	#3748	—	2	1	no	—
76	#3748	C₂²×C₃	1	2	yes	complemented
77	C₂×C₃⋊(C₃⋊C₈)	—	2	1	no	—
78	C₃×#208	—	3	8	no	—
79	C₃×#208	—	6	4	no	—
80	C₂×C₃×C₃⋊C₈	—	6	4	no	—
81	C₂²×C₃³	—	2	2	no	—
82	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₃³	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₃×C₃⋊D₃	—	2	4	no	—
86	C₂×C₃×C₃⋊D₃	—	4	4	no	—
87	C₂×C₃×C₃⋊D₃	—	4	4	no	—
88	C₂×C₃×C₃⋊D₃	—	4	4	no	—
89	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
90	C₃³×C₄	C₂²⋊C₄	1	1	yes	characteristic
91	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
92	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₃×D₄	—	9	1	no	—
94	C₂²×D₁₂	—	3	4	no	—
95	C₂×C₃×M₁₆	—	2	4	no	—
96	C₂×C₃×M₁₆	—	9	1	no	—
97	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
98	C₂×C₃×M₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
99	C₂×#208	—	3	4	no	—
100	C₃×#100	—	9	4	no	—
101	#823	—	3	16	no	—
102	C₂³×C₃²	—	2	4	no	—
103	C₂³×C₃²	C₄×D₃	1	4	yes	—
104	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
105	C₂²×C₃⋊D₃	—	2	2	no	—
106	C₂²×C₃⋊D₃	—	2	2	no	—
107	C₂²×C₃⋊D₃	—	4	4	no	—
108	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	4	yes	—
109	C₂²×C₃×D₃	—	3	16	no	—
110	C₂²×C₃×D₃	—	6	8	no	—
111	C₂²×C₃×D₃	—	6	8	no	—
112	C₂²×C₃×D₃	—	12	16	no	—
113	C₂×C₃²×C₄	—	2	4	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	—	2	4	no	—
116	C₂×C₃²×C₄	—	2	4	no	—
117	C₂×C₃²×C₄	—	2	4	no	—
118	C₂×C₃²×C₄	—	2	4	no	—
119	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
120	C₂×C₃²×C₄	D₁₂	1	4	yes	—
121	C₂×C₃²×C₄	D₁₂	1	4	yes	—
122	C₂×C₃²×C₄	#67	1	4	yes	—
123	C₂×C₃²×C₄	#67	1	4	yes	—
124	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
125	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
130	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
131	C₄⋊(C₃⋊D₃)	—	2	2	no	—
132	C₄⋊(C₃⋊D₃)	—	2	2	no	—
133	C₄⋊(C₃⋊D₃)	—	2	2	no	—
134	C₄⋊(C₃⋊D₃)	—	2	2	no	—
135	C₃×D₁₂	—	6	8	no	—
136	C₃×D₁₂	—	6	8	no	—
137	C₃×D₁₂	—	6	8	no	—
138	C₃×D₁₂	—	6	8	no	—
139	C₃²×C₈	—	2	16	no	—
140	C₃²×C₈	—	2	8	no	—
141	C₃²×C₈	—	2	2	no	—
142	C₃⋊(C₃⋊C₈)	—	2	2	no	—
143	C₃×C₃⋊C₈	—	6	8	no	—
144	C₂×#100	—	9	1	no	Sylow
145	C₂×C₃³	—	2	1	no	—
146	C₂×C₃³	—	2	1	no	—
147	C₂×C₃³	#100	1	2	yes	complemented
148	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₃×C₃⋊D₃	—	4	4	no	—
150	C₂⁴×C₃	—	9	2	no	—
151	C₂³×D₃	—	3	8	no	—
152	C₂×C₃×D₄	—	9	2	no	—
153	C₂×C₃×D₄	—	9	2	no	—
154	C₂×C₃×D₄	—	18	1	no	—
155	C₂×C₃×D₄	—	18	1	no	—
156	C₂×C₃×D₄	—	18	1	no	—
157	C₂×C₃×D₄	—	18	1	no	—
158	C₂²×C₃×C₄	—	2	4	no	—
159	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
160	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
161	C₂×D₁₂	—	3	8	no	—
162	C₂×D₁₂	—	3	8	no	—
163	C₂×D₁₂	—	6	4	no	—
164	C₂×D₁₂	—	6	4	no	—
165	C₂×D₁₂	—	6	4	no	—
166	C₂×D₁₂	—	6	4	no	—
167	C₃×M₁₆	—	2	8	no	—
168	C₃×M₁₆	—	2	4	no	—
169	C₃×M₁₆	—	2	1	no	—
170	C₃×M₁₆	—	2	8	no	—
171	C₃×M₁₆	—	9	2	no	—
172	C₃×M₁₆	—	18	1	no	—
173	C₃×M₁₆	C₂×C₃×D₃	1	8	yes	complemented
174	C₃×M₁₆	C₂×C₃⋊D₃	1	2	yes	complemented
175	C₂×C₃×C₈	—	2	8	no	—
176	C₂×C₃×C₈	—	2	4	no	—
177	C₂×C₃×C₈	—	2	1	no	—
178	C₂×C₃×C₈	—	18	1	no	—
179	#208	—	3	8	no	—
180	#208	—	6	4	no	—
181	C₂×C₃⋊C₈	—	6	4	no	—
182	C₂²×C₃²	—	2	2	no	—
183	C₂²×C₃²	—	2	4	no	—
184	C₂²×C₃²	—	2	4	no	—
185	C₂²×C₃²	—	2	4	no	—
186	C₂²×C₃²	—	2	8	no	—
187	C₂²×C₃²	—	4	8	no	—
188	C₂²×C₃²	(C₂×D₃)⋊C₄	1	4	yes	—
189	C₂²×C₃²	(C₂×D₃)⋊C₄	1	4	yes	—
190	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×C₃²	C₃×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
193	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
194	C₂×C₃⋊D₃	—	2	4	no	—
195	C₂×C₃⋊D₃	—	4	4	no	—
196	C₂×C₃⋊D₃	—	4	4	no	—
197	C₂×C₃⋊D₃	—	4	4	no	—
198	C₂×C₃×D₃	—	6	16	no	—
199	C₂×C₃×D₃	—	12	16	no	—
200	C₂×C₃×D₃	—	12	16	no	—
201	C₂×C₃×D₃	—	12	16	no	—
202	C₃²×C₄	—	2	4	no	—
203	C₃²×C₄	—	2	4	no	—
204	C₃²×C₄	—	2	4	no	—
205	C₃²×C₄	—	2	4	no	—
206	C₃²×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
207	C₃²×C₄	(C₂×D₃)⋊C₄	1	4	yes	—
208	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
209	C₃²×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
210	C₃²×C₄	C₂×D₁₂	1	4	yes	—
211	C₃²×C₄	C₂×#67	1	4	yes	—
212	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
213	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
214	C₂²×D₄	—	9	1	no	—
215	C₂×M₁₆	—	9	1	no	—
216	C₂×M₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
217	#100	—	9	4	no	—
218	C₃³	C₂×#100	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₃	—	2	4	no	—
220	C₂³×C₃	—	9	4	no	—
221	C₂³×C₃	—	18	2	no	—
222	C₂³×C₃	—	18	2	no	—
223	C₂³×C₃	—	36	4	no	—
224	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
225	C₂³×C₃	C₄×C₃⋊D₃	1	1	yes	characteristic
226	C₂²×D₃	—	3	16	no	—
227	C₂²×D₃	—	6	8	no	—
228	C₂²×D₃	—	6	8	no	—
229	C₂²×D₃	—	12	16	no	—
230	C₃×D₄	—	18	2	no	—
231	C₃×D₄	—	18	2	no	—
232	C₃×D₄	—	18	2	no	—
233	C₃×D₄	—	18	2	no	—
234	C₂×C₃×C₄	—	2	4	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
241	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
242	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
243	C₂×C₃×C₄	C₃×#67	1	4	yes	—
244	C₂×C₃×C₄	C₃×#67	1	4	yes	—
245	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
246	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
247	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
248	C₂×C₃×C₄	#638	1	1	yes	characteristic
249	C₂×C₃×C₄	#638	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
251	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
252	D₁₂	—	6	8	no	—
253	D₁₂	—	6	8	no	—
254	D₁₂	—	6	8	no	—
255	D₁₂	—	6	8	no	—
256	C₃×C₈	—	2	16	no	—
257	C₃×C₈	—	2	8	no	—
258	C₃×C₈	—	2	2	no	—
259	C₃×C₈	—	18	2	no	—
260	C₃⋊C₈	—	6	8	no	—
261	C₂×C₃²	—	2	1	no	—
262	C₂×C₃²	—	2	1	no	—
263	C₂×C₃²	—	2	4	no	—
264	C₂×C₃²	—	2	8	no	—
265	C₂×C₃²	—	2	4	no	—
266	C₂×C₃²	—	2	4	no	—
267	C₂×C₃²	—	4	4	no	—
268	C₂×C₃²	—	4	4	no	—
269	C₂×C₃²	#823	1	8	yes	complemented
270	C₂×C₃²	C₃×#100	1	2	yes	complemented
271	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
272	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
273	C₃⋊D₃	—	4	4	no	—
274	C₃×D₃	—	12	16	no	—
275	C₂⁴	—	9	2	no	—
276	C₂×D₄	—	9	2	no	—
277	C₂×D₄	—	9	2	no	—
278	C₂×D₄	—	18	1	no	—
279	C₂×D₄	—	18	1	no	—
280	C₂×D₄	—	18	1	no	—
281	C₂×D₄	—	18	1	no	—
282	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
283	M₁₆	—	2	1	no	—
284	M₁₆	—	9	2	no	—
285	M₁₆	—	18	1	no	—
286	M₁₆	C₂×C₃×C₃⋊D₃	1	2	yes	complemented
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	18	1	no	—
289	C₂²×C₃	—	2	8	no	—
290	C₂²×C₃	—	2	2	no	—
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	2	4	no	—
293	C₂²×C₃	—	2	4	no	—
294	C₂²×C₃	—	4	8	no	—
295	C₂²×C₃	—	18	4	no	—
296	C₂²×C₃	—	36	4	no	—
297	C₂²×C₃	—	36	4	no	—
298	C₂²×C₃	—	36	4	no	—
299	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
300	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
301	C₂²×C₃	#3752	1	1	yes	characteristic
302	C₂²×C₃	#3752	1	1	yes	characteristic
303	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
304	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
305	C₂×D₃	—	6	16	no	—
306	C₂×D₃	—	12	16	no	—
307	C₂×D₃	—	12	16	no	—
308	C₂×D₃	—	12	16	no	—
309	C₃×C₄	—	2	4	no	—
310	C₃×C₄	—	2	4	no	—
311	C₃×C₄	—	2	4	no	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
314	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	4	yes	—
315	C₃×C₄	#3752	1	1	yes	characteristic
316	C₃×C₄	#3752	1	1	yes	characteristic
317	C₃×C₄	C₂×C₃×D₁₂	1	4	yes	—
318	C₃×C₄	C₂×C₃×#67	1	4	yes	—
319	C₃×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
320	C₃×C₄	C₂×#638	1	1	yes	characteristic
321	C₃²	—	2	4	no	—
322	C₃²	C₂×#823	1	4	yes	complemented
323	C₃²	C₂×C₃×#100	1	1	yes	characteristic, complemented
324	C₂³	—	9	4	no	—
325	C₂³	—	18	2	no	—
326	C₂³	—	18	2	no	—
327	C₂³	—	36	4	no	—
328	C₂³	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
329	D₄	—	18	2	no	—
330	D₄	—	18	2	no	—
331	D₄	—	18	2	no	—
332	D₄	—	18	2	no	—
333	C₂×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
334	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
335	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
336	C₂×C₄	C₃×#638	1	1	yes	characteristic
337	C₂×C₄	C₃×#638	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
339	C₈	—	2	2	no	—
340	C₈	—	18	2	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	2	4	no	—
344	C₂×C₃	—	2	4	no	—
345	C₂×C₃	—	2	4	no	—
346	C₂×C₃	—	2	8	no	—
347	C₂×C₃	—	4	4	no	—
348	C₂×C₃	—	4	4	no	—
349	C₂×C₃	—	36	4	no	—
350	C₂×C₃	C₃×#823	1	8	yes	complemented
351	C₂×C₃	#63650	1	2	yes	direct product factor
352	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
353	C₂×C₃	C₂×#3752	1	1	yes	characteristic
354	D₃	—	12	16	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	18	4	no	—
357	C₂²	—	36	4	no	—
358	C₂²	—	36	4	no	—
359	C₂²	—	36	4	no	—
360	C₂²	C₃×#3752	1	1	yes	characteristic
361	C₂²	C₃×#3752	1	1	yes	characteristic
362	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
363	C₄	C₃×#3752	1	1	yes	characteristic
364	C₄	C₃×#3752	1	1	yes	characteristic
365	C₄	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
366	C₄	C₂×C₃×#638	1	1	yes	characteristic
367	C₃	—	2	4	no	—
368	C₃	C₂×C₃×#823	1	4	yes	complemented
369	C₃	C₂×#63650	1	1	yes	characteristic, direct product factor
370	C₂	—	2	1	no	—
371	C₂	—	2	1	no	—
372	C₂	—	36	4	no	—
373	C₂	C₃×#63650	1	2	yes	direct product factor
374	C₂	C₂×C₃×#3752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#3752
commutator	C₂²×C₃²	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂²×C₃³	C₂²⋊C₄
prime radical	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×M₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#100
LCS	G ▷ C₂²×C₃² ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×M₁₆	C₂	semidirect
3. C₂×C₃×#3748	C₂	semidirect
4. C₃×#63650	C₂	direct (N × H)
5. C₂×#63650	C₃	direct (N × H)
16. C₃³×M₁₆	C₂²	semidirect
19. C₃×#3748	C₂²	semidirect
24. C₂×C₃²×M₁₆	D₃	semidirect
25. C₂×C₃²×M₁₆	C₂×C₃	semidirect
26. C₂×#3748	C₂×C₃	semidirect
28. #63650	C₂×C₃	direct (N × H)
70. C₃²×M₁₆	C₂×D₃	semidirect
71. C₃²×M₁₆	C₂²×C₃	semidirect
76. #3748	C₂²×C₃	semidirect
97. C₂×C₃×M₁₆	C₃×D₃	semidirect
98. C₂×C₃×M₁₆	C₃⋊D₃	semidirect
147. C₂×C₃³	#100	semidirect
173. C₃×M₁₆	C₂×C₃×D₃	semidirect
174. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
216. C₂×M₁₆	C₃×C₃⋊D₃	semidirect
218. C₃³	C₂×#100	semidirect
269. C₂×C₃²	#823	semidirect
270. C₂×C₃²	C₃×#100	semidirect
286. M₁₆	C₂×C₃×C₃⋊D₃	semidirect
322. C₃²	C₂×#823	semidirect
323. C₃²	C₂×C₃×#100	semidirect
350. C₂×C₃	C₃×#823	semidirect
351. C₂×C₃	#63650	direct (N × H)
368. C₃	C₂×C₃×#823	semidirect
369. C₃	C₂×#63650	direct (N × H)
373. C₂	C₃×#63650	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₂×C₃³×M₁₆	2
C₂×C₃×#3748	2
C₃×#63650	2
C₂×#63650	3
C₂×C₃×#823	3

Subgroups — C2×C3×#63650 #13163167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#63650 #13163167