Subgroups — C₃×D₃×#490 #11873562

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₃×D₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#490	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5071	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×D₃×#102	C₂	1	4	yes	maximal, complemented
7	C₃×#4764	C₂	1	4	yes	maximal, complemented
8	C₃×#4713	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#490	—	3	1	no	maximal
11	D₃×#490	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₃×D₃×D₄	—	2	2	no	—
13	C₂×C₃×D₃×D₄	C₂²	1	2	yes	—
14	C₃²×#127	C₂²	1	1	yes	characteristic
15	C₃²×#125	C₂²	1	1	yes	characteristic, complemented
16	C₃×#940	—	2	2	no	—
17	C₃×#940	C₂²	1	2	yes	—
18	C₂×C₃×D₃×C₈	C₂²	1	2	yes	—
19	C₃×D₃×C₄⋊C₄	—	2	2	no	—
20	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×#890	C₂²	1	2	yes	complemented
22	C₃×#889	—	2	2	no	—
23	C₃×#874	C₂²	1	1	yes	characteristic
24	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
25	C₃×#870	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#102	C₂²	1	4	yes	complemented
27	C₃²×#97	C₂²	1	1	yes	characteristic, complemented
28	C₃×#832	C₂²	1	4	yes	complemented
29	C₃×#821	C₂²	1	4	yes	complemented
30	C₃×#815	C₂²	1	2	yes	complemented
31	C₃×#809	C₂²	1	4	yes	complemented
32	C₃×#803	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×#127	—	3	1	no	—
34	C₂×C₃×#125	—	3	1	no	—
35	D₃×#127	C₂×C₃	1	1	yes	characteristic
36	D₃×#125	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×#490	—	2	1	no	—
38	C₃×#490	—	3	1	no	—
39	C₃×#490	—	3	1	no	—
40	C₃×#490	—	3	4	no	—
41	C₃×#490	—	3	1	no	—
42	C₃×#490	D₃	1	1	yes	characteristic, direct product factor
43	C₃×#490	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×C₃×#102	—	3	4	no	—
45	C₂×C₃×#97	—	3	1	no	—
46	#5071	C₂×C₃	1	1	yes	characteristic, complemented
47	#5067	C₂×C₃	1	1	yes	characteristic, complemented
48	D₃×#102	C₂×C₃	1	4	yes	complemented
49	#4764	C₂×C₃	1	4	yes	complemented
50	#4713	C₂×C₃	1	1	yes	characteristic, complemented
51	D₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂³×C₃×D₃	—	2	2	no	—
53	C₂×C₃²×D₄	—	2	2	no	—
54	C₂×C₃²×D₄	C₂³	1	2	yes	—
55	C₂×C₃×#67	—	2	2	no	—
56	C₂×C₃×#67	—	2	4	no	—
57	C₃×D₃×D₄	—	2	8	no	—
58	C₃×D₃×D₄	—	4	8	no	—
59	C₂×C₃×D₁₂	—	2	2	no	—
60	C₂×C₃×D₁₂	C₂³	1	2	yes	—
61	C₂×C₃×C₄×D₃	—	2	2	no	—
62	C₂×C₃×C₄×D₃	D₄	1	2	yes	—
63	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
64	C₂×C₃²×C₈	C₂³	1	2	yes	—
65	C₃²×C₄⋊C₄	—	2	2	no	—
66	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
67	C₃²×C₄²	C₂³	1	1	yes	characteristic
68	C₃×C₄⋊Dic₃	—	2	2	no	—
69	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
70	C₃×Dic₃⋊C₄	—	2	2	no	—
71	C₃×Dic₃⋊C₄	—	2	2	no	—
72	C₃×Dic₃⋊C₄	—	2	2	no	—
73	C₃×C₄×Dic₃	D₄	1	2	yes	—
74	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
76	C₃×D₃×C₈	—	2	4	no	—
77	C₂×#490	—	3	1	no	Sylow
78	C₂²×C₃×D₄	—	3	2	no	—
79	C₂²×C₃×D₄	—	6	2	no	—
80	C₂×D₃×D₄	—	2	2	no	—
81	C₂×D₃×D₄	C₂²×C₃	1	2	yes	—
82	C₂²×C₃×C₈	—	3	2	no	—
83	C₃×#127	—	2	1	no	—
84	C₃×#127	—	3	2	no	—
85	C₃×#127	—	3	1	no	—
86	C₃×#127	—	6	2	no	—
87	C₃×#127	C₂×D₃	1	1	yes	characteristic
88	C₃×#127	C₂²×C₃	1	1	yes	characteristic
89	C₃×#125	—	2	1	no	—
90	C₃×#125	—	3	2	no	—
91	C₃×#125	—	3	1	no	—
92	C₃×#125	—	6	2	no	—
93	C₃×#125	C₂×D₃	1	1	yes	characteristic, complemented
94	C₃×#125	C₂²×C₃	1	1	yes	characteristic, complemented
95	C₂×C₃×C₄⋊C₄	—	3	2	no	—
96	C₂×C₃×C₄⋊C₄	—	6	2	no	—
97	C₂×C₃×C₄²	—	3	1	no	—
98	#940	—	2	2	no	—
99	#940	C₂²×C₃	1	2	yes	—
100	C₂×D₃×C₈	C₂²×C₃	1	2	yes	—
101	D₃×C₄⋊C₄	—	2	2	no	—
102	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
103	#890	C₂²×C₃	1	2	yes	complemented
104	#889	—	2	2	no	—
105	#874	C₂²×C₃	1	1	yes	characteristic
106	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
107	#870	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₃×#102	—	2	4	no	—
109	C₃×#102	—	3	4	no	—
110	C₃×#102	—	3	4	no	—
111	C₃×#102	—	3	4	no	—
112	C₃×#102	C₂×D₃	1	4	yes	complemented
113	C₃×#102	C₂²×C₃	1	4	yes	complemented
114	C₃×#97	—	2	1	no	—
115	C₃×#97	—	3	2	no	—
116	C₃×#97	—	3	1	no	—
117	C₃×#97	C₂×D₃	1	1	yes	characteristic, complemented
118	C₃×#97	C₂²×C₃	1	1	yes	characteristic, complemented
119	#832	C₂²×C₃	1	4	yes	complemented
120	#821	C₂²×C₃	1	4	yes	complemented
121	#815	C₂²×C₃	1	2	yes	complemented
122	#809	C₂²×C₃	1	4	yes	complemented
123	#803	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂³×C₃²	—	2	2	no	—
125	C₂²×C₃×D₃	—	2	2	no	—
126	C₂²×C₃×D₃	—	4	4	no	—
127	C₂²×C₃×D₃	—	4	8	no	—
128	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
129	C₃²×D₄	—	2	4	no	—
130	C₃²×D₄	—	4	4	no	—
131	C₂×C₃²×C₄	—	2	2	no	—
132	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
133	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
134	C₃×#67	—	4	8	no	—
135	C₃×#67	—	4	4	no	—
136	C₂×C₃×Dic₃	—	2	2	no	—
137	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
138	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
139	C₃×D₁₂	—	2	4	no	—
140	C₃×D₁₂	—	4	4	no	—
141	C₃×C₄×D₃	—	2	4	no	—
142	C₃×C₄×D₃	—	4	4	no	—
143	C₃×C₄×D₃	#41	1	4	yes	—
144	C₃²×C₈	—	2	2	no	—
145	C₃×C₃⋊C₈	—	2	2	no	—
146	C₂×#127	—	3	1	no	—
147	C₂×#125	—	3	1	no	—
148	#490	—	3	1	no	—
149	#490	—	3	1	no	—
150	#490	—	3	4	no	—
151	#490	—	3	1	no	—
152	#490	C₃×D₃	1	1	yes	characteristic, direct product factor
153	C₂×#102	—	3	4	no	—
154	C₂×#97	—	3	1	no	—
155	C₂⁴×C₃	—	6	2	no	—
156	C₂³×D₃	—	2	2	no	—
157	C₂×C₃×D₄	—	2	2	no	—
158	C₂×C₃×D₄	—	2	2	no	—
159	C₂×C₃×D₄	—	2	2	no	—
160	C₂×C₃×D₄	—	3	2	no	—
161	C₂×C₃×D₄	—	4	2	no	—
162	C₂×C₃×D₄	—	6	8	no	—
163	C₂×C₃×D₄	—	6	4	no	—
164	C₂×C₃×D₄	—	6	2	no	—
165	C₂×C₃×D₄	—	6	2	no	—
166	C₂×C₃×D₄	—	12	8	no	—
167	C₂×C₃×D₄	C₂²×D₃	1	2	yes	—
168	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
169	C₂²×C₃×C₄	—	3	1	no	—
170	C₂²×C₃×C₄	—	3	2	no	—
171	C₂²×C₃×C₄	—	6	2	no	—
172	C₂×#67	—	2	2	no	—
173	C₂×#67	—	2	4	no	—
174	D₃×D₄	—	2	8	no	—
175	D₃×D₄	—	4	8	no	—
176	C₂×D₁₂	—	2	2	no	—
177	C₂×D₁₂	C₂³×C₃	1	2	yes	—
178	C₂×C₄×D₃	—	2	2	no	—
179	C₂×C₄×D₃	C₃×D₄	1	2	yes	—
180	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	3	2	no	—
183	C₂×C₃×C₈	—	6	4	no	—
184	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
185	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
186	C₃×C₄⋊C₄	—	2	2	no	—
187	C₃×C₄⋊C₄	—	2	2	no	—
188	C₃×C₄⋊C₄	—	2	2	no	—
189	C₃×C₄⋊C₄	—	3	2	no	—
190	C₃×C₄⋊C₄	—	4	2	no	—
191	C₃×C₄⋊C₄	—	6	2	no	—
192	C₃×C₄⋊C₄	—	6	2	no	—
193	C₃×C₄⋊C₄	—	6	2	no	—
194	C₃×C₄⋊C₄	—	6	2	no	—
195	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
196	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
197	C₃×C₄²	—	2	1	no	—
198	C₃×C₄²	—	3	2	no	—
199	C₃×C₄²	—	3	1	no	—
200	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
201	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
202	C₄⋊Dic₃	—	2	2	no	—
203	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
204	Dic₃⋊C₄	—	2	2	no	—
205	Dic₃⋊C₄	—	2	2	no	—
206	Dic₃⋊C₄	—	2	2	no	—
207	C₄×Dic₃	C₃×D₄	1	2	yes	—
208	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
210	D₃×C₈	—	2	4	no	—
211	C₂²×C₃²	—	4	2	no	—
212	C₂²×C₃²	—	4	4	no	—
213	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₃×D₃	—	4	2	no	—
215	C₂×C₃×D₃	—	4	4	no	—
216	C₂×C₃×D₃	—	8	8	no	—
217	C₂×C₃×D₃	#124	1	2	yes	—
218	C₂×C₃×D₃	AGL(1,ℤ/8)	1	4	yes	—
219	C₃²×C₄	—	2	2	no	—
220	C₃²×C₄	—	4	2	no	—
221	C₃²×C₄	C₂×#41	1	2	yes	—
222	C₃×Dic₃	—	2	2	no	—
223	C₃×Dic₃	—	4	2	no	—
224	C₃×Dic₃	#124	1	2	yes	—
225	C₂²×D₄	—	3	2	no	—
226	C₂²×D₄	—	6	2	no	—
227	C₂²×C₈	—	3	2	no	—
228	#127	—	3	2	no	—
229	#127	—	3	1	no	—
230	#127	—	6	2	no	—
231	#127	C₂×C₃×D₃	1	1	yes	characteristic
232	#125	—	3	2	no	—
233	#125	—	3	1	no	—
234	#125	—	6	2	no	—
235	#125	C₂×C₃×D₃	1	1	yes	characteristic, complemented
236	C₂×C₄⋊C₄	—	3	2	no	—
237	C₂×C₄⋊C₄	—	6	2	no	—
238	C₂×C₄²	—	3	1	no	—
239	#102	—	3	4	no	—
240	#102	—	3	4	no	—
241	#102	—	3	4	no	—
242	#102	C₂×C₃×D₃	1	4	yes	complemented
243	#97	—	3	2	no	—
244	#97	—	3	1	no	—
245	#97	C₂×C₃×D₃	1	1	yes	characteristic, complemented
246	C₂³×C₃	—	2	2	no	—
247	C₂³×C₃	—	2	2	no	—
248	C₂³×C₃	—	3	1	no	—
249	C₂³×C₃	—	4	2	no	—
250	C₂³×C₃	—	6	2	no	—
251	C₂³×C₃	—	12	4	no	—
252	C₂³×C₃	—	12	8	no	—
253	C₂²×D₃	—	2	2	no	—
254	C₂²×D₃	—	4	4	no	—
255	C₂²×D₃	—	4	8	no	—
256	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
257	C₃×D₄	—	2	4	no	—
258	C₃×D₄	—	2	4	no	—
259	C₃×D₄	—	4	4	no	—
260	C₃×D₄	—	4	4	no	—
261	C₃×D₄	—	4	4	no	—
262	C₃×D₄	—	6	4	no	—
263	C₃×D₄	—	8	4	no	—
264	C₃×D₄	—	12	4	no	—
265	C₃×D₄	—	12	4	no	—
266	C₃×D₄	—	12	8	no	—
267	C₂×C₃×C₄	—	2	2	no	—
268	C₂×C₃×C₄	—	2	2	no	—
269	C₂×C₃×C₄	—	2	1	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	3	1	no	—
272	C₂×C₃×C₄	—	3	4	no	—
273	C₂×C₃×C₄	—	3	2	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	6	4	no	—
276	C₂×C₃×C₄	—	6	2	no	—
277	C₂×C₃×C₄	—	12	4	no	—
278	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
279	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
280	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
282	#67	—	4	8	no	—
283	#67	—	4	4	no	—
284	C₂×Dic₃	—	2	2	no	—
285	C₂×Dic₃	C₂×C₃×D₄	1	2	yes	—
286	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
287	D₁₂	—	2	4	no	—
288	D₁₂	—	4	4	no	—
289	C₄×D₃	—	2	4	no	—
290	C₄×D₃	—	4	4	no	—
291	C₄×D₃	C₃×#41	1	4	yes	—
292	C₃×C₈	—	2	2	no	—
293	C₃×C₈	—	2	2	no	—
294	C₃×C₈	—	4	2	no	—
295	C₃×C₈	—	6	2	no	—
296	C₃⋊C₈	—	2	2	no	—
297	C₂×C₃²	—	8	2	no	—
298	C₂×C₃²	C₂×#124	1	1	yes	characteristic
299	C₂×C₃²	C₂×AGL(1,ℤ/8)	1	2	yes	—
300	C₃×D₃	—	8	2	no	—
301	C₃×D₃	#490	1	4	yes	direct product factor
302	C₂⁴	—	6	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	3	2	no	—
305	C₂×D₄	—	6	8	no	—
306	C₂×D₄	—	6	4	no	—
307	C₂×D₄	—	6	2	no	—
308	C₂×D₄	—	6	2	no	—
309	C₂×D₄	—	12	8	no	—
310	C₂×D₄	C₂²×C₃×D₃	1	2	yes	—
311	C₂²×C₄	—	3	1	no	—
312	C₂²×C₄	—	3	2	no	—
313	C₂²×C₄	—	6	2	no	—
314	C₂×C₈	—	3	2	no	—
315	C₂×C₈	—	6	4	no	—
316	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	3	2	no	—
319	C₄⋊C₄	—	6	2	no	—
320	C₄⋊C₄	—	6	2	no	—
321	C₄⋊C₄	—	6	2	no	—
322	C₄⋊C₄	—	6	2	no	—
323	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
324	C₄²	—	3	1	no	—
325	C₄²	—	3	2	no	—
326	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
327	C₂²×C₃	—	2	1	no	—
328	C₂²×C₃	—	3	2	no	—
329	C₂²×C₃	—	3	4	no	—
330	C₂²×C₃	—	4	4	no	—
331	C₂²×C₃	—	4	2	no	—
332	C₂²×C₃	—	4	4	no	—
333	C₂²×C₃	—	4	2	no	—
334	C₂²×C₃	—	8	2	no	—
335	C₂²×C₃	—	8	4	no	—
336	C₂²×C₃	—	12	2	no	—
337	C₂²×C₃	—	12	4	no	—
338	C₂²×C₃	—	24	8	no	—
339	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
340	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
341	C₂×D₃	—	4	4	no	—
342	C₂×D₃	—	4	2	no	—
343	C₂×D₃	—	8	8	no	—
344	C₂×D₃	C₃×#124	1	2	yes	—
345	C₂×D₃	C₃×AGL(1,ℤ/8)	1	4	yes	—
346	C₃×C₄	—	2	2	no	—
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	2	2	no	—
349	C₃×C₄	—	3	2	no	—
350	C₃×C₄	—	4	2	no	—
351	C₃×C₄	—	4	2	no	—
352	C₃×C₄	—	4	2	no	—
353	C₃×C₄	—	6	2	no	—
354	C₃×C₄	—	8	2	no	—
355	C₃×C₄	—	12	2	no	—
356	C₃×C₄	D₃×#41	1	2	yes	—
357	C₃×C₄	C₂×C₃×#41	1	2	yes	—
358	Dic₃	—	2	2	no	—
359	Dic₃	—	4	2	no	—
360	Dic₃	C₃×#124	1	2	yes	—
361	C₃²	C₂×#490	1	1	yes	characteristic, complemented, Sylow
362	C₂³	—	2	2	no	—
363	C₂³	—	3	1	no	—
364	C₂³	—	6	2	no	—
365	C₂³	—	12	4	no	—
366	C₂³	—	12	8	no	—
367	D₄	—	2	4	no	—
368	D₄	—	4	4	no	—
369	D₄	—	6	4	no	—
370	D₄	—	12	4	no	—
371	D₄	—	12	4	no	—
372	D₄	—	12	8	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	3	1	no	—
375	C₂×C₄	—	3	4	no	—
376	C₂×C₄	—	3	2	no	—
377	C₂×C₄	—	6	4	no	—
378	C₂×C₄	—	6	2	no	—
379	C₂×C₄	—	12	4	no	—
380	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
381	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	6	2	no	—
384	C₂×C₃	—	2	2	no	—
385	C₂×C₃	—	2	1	no	—
386	C₂×C₃	—	3	4	no	—
387	C₂×C₃	—	8	2	no	—
388	C₂×C₃	—	8	2	no	—
389	C₂×C₃	—	16	2	no	—
390	C₂×C₃	—	24	2	no	—
391	C₂×C₃	D₃×#124	1	1	yes	characteristic
392	C₂×C₃	D₃×AGL(1,ℤ/8)	1	2	yes	—
393	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
394	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	2	yes	—
395	D₃	—	8	2	no	—
396	D₃	C₃×#490	1	4	yes	direct product factor
397	C₂²	—	3	4	no	—
398	C₂²	—	3	2	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	12	4	no	—
402	C₂²	—	12	2	no	—
403	C₂²	—	24	8	no	—
404	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
405	C₄	—	2	2	no	—
406	C₄	—	3	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	6	2	no	—
409	C₄	—	12	2	no	—
410	C₄	C₃×D₃×#41	1	2	yes	—
411	C₃	—	2	1	no	—
412	C₃	D₃×#490	1	1	yes	characteristic, direct product factor
413	C₃	C₂×C₃×#490	1	1	yes	characteristic, complemented
414	C₂	—	3	4	no	—
415	C₂	—	8	2	no	—
416	C₂	—	24	2	no	—
417	C₂	C₃×D₃×#124	1	1	yes	characteristic
418	C₂	C₃×D₃×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#490	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₃×D₃×#127	C₂
hypercenter	C₃×#490	D₃
hypocenter	C₃	C₂×C₃×#490
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#490

Complements

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

N	H ≅ G/N	type
2. C₃×D₃×#125	C₂	semidirect
3. C₃²×#490	C₂	semidirect
4. C₃×#5071	C₂	semidirect
5. C₃×#5067	C₂	semidirect
6. C₃×D₃×#102	C₂	semidirect
7. C₃×#4764	C₂	semidirect
8. C₃×#4713	C₂	semidirect
9. C₃×D₃×#97	C₂	semidirect
11. D₃×#490	C₃	direct (N × H)
15. C₃²×#125	C₂²	semidirect
21. C₃×#890	C₂²	semidirect
25. C₃×#870	C₂²	semidirect
26. C₃²×#102	C₂²	semidirect
27. C₃²×#97	C₂²	semidirect
28. C₃×#832	C₂²	semidirect
29. C₃×#821	C₂²	semidirect
30. C₃×#815	C₂²	semidirect
31. C₃×#809	C₂²	semidirect
32. C₃×#803	C₂²	semidirect
36. D₃×#125	C₂×C₃	semidirect
42. C₃×#490	D₃	direct (N × H)
43. C₃×#490	C₂×C₃	semidirect
46. #5071	C₂×C₃	semidirect
47. #5067	C₂×C₃	semidirect
48. D₃×#102	C₂×C₃	semidirect
49. #4764	C₂×C₃	semidirect
50. #4713	C₂×C₃	semidirect
51. D₃×#97	C₂×C₃	semidirect
93. C₃×#125	C₂×D₃	semidirect
94. C₃×#125	C₂²×C₃	semidirect
103. #890	C₂²×C₃	semidirect
107. #870	C₂²×C₃	semidirect
112. C₃×#102	C₂×D₃	semidirect
113. C₃×#102	C₂²×C₃	semidirect
117. C₃×#97	C₂×D₃	semidirect
118. C₃×#97	C₂²×C₃	semidirect
119. #832	C₂²×C₃	semidirect
120. #821	C₂²×C₃	semidirect
121. #815	C₂²×C₃	semidirect
122. #809	C₂²×C₃	semidirect
123. #803	C₂²×C₃	semidirect
152. #490	C₃×D₃	direct (N × H)
235. #125	C₂×C₃×D₃	semidirect
242. #102	C₂×C₃×D₃	semidirect
245. #97	C₂×C₃×D₃	semidirect
301. C₃×D₃	#490	direct (N × H)
361. C₃²	C₂×#490	semidirect
396. D₃	C₃×#490	direct (N × H)
412. C₃	D₃×#490	direct (N × H)
413. C₃	C₂×C₃×#490	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×#127	2
C₃×D₃×#125	2
C₃²×#490	2
C₃×#5071	2
C₃×#5067	2
C₃×D₃×#102	2
C₃×#4764	2
C₃×#4713	2
C₃×D₃×#97	2
C₂×C₃×#490	3
D₃×#490	3

Subgroups — C3×D3×#490 #11873562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#490 #11873562