Subgroups — C₃×#72013 #11785543

Order 1152.

645 conjugacy classes of subgroups.

The subgroup lattice has 439 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#131	C₂	1	1	yes	maximal, characteristic
2	C₃×#5236	C₂	1	2	yes	maximal
3	C₂×C₃×#819	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4559	C₂	1	2	yes	maximal, complemented
6	C₃×#1814	—	3	1	no	maximal
7	#72013	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃²×#41	C₂²	1	1	yes	characteristic
9	C₃²×#131	—	2	1	no	—
10	C₃²×#131	—	2	1	no	—
11	C₃²×#131	C₄	1	2	yes	complemented
12	C₃²×#131	C₄	1	2	yes	complemented
13	C₂×C₃²×M₁₆	—	2	1	no	—
14	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₈	—	2	1	no	—
16	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
17	C₃×#926	C₂²	1	2	yes	—
18	C₂×C₃×#208	C₂²	1	2	yes	—
19	C₃×#837	—	2	4	no	—
20	C₃×#819	—	2	1	no	—
21	C₃×#819	—	2	1	no	—
22	C₃×#818	—	2	1	no	—
23	C₃×#817	—	2	1	no	—
24	C₂×C₃×#131	—	2	1	no	—
25	C₂×C₃×#131	D₃	1	1	yes	characteristic
26	C₂×C₃×#131	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×#108	—	3	1	no	—
28	C₃×#427	—	3	1	no	—
29	C₃×#421	—	3	2	no	—
30	#5236	C₂×C₃	1	2	yes	—
31	C₂×#819	C₂×C₃	1	1	yes	characteristic, complemented
32	#5106	C₂×C₃	1	1	yes	characteristic, complemented
33	C₃×#344	—	3	2	no	—
34	#4559	C₂×C₃	1	2	yes	complemented
35	C₃²×#41	—	2	1	no	—
36	C₃²×#41	—	2	1	no	—
37	C₃²×#41	C₂×C₄	1	2	yes	—
38	C₃²×#41	D₄	1	2	yes	—
39	C₂×C₃²×Q₈	Q₈	1	1	yes	characteristic
40	C₂×C₃²×D₄	—	2	1	no	—
41	C₂×C₃²×D₄	Q₈	1	1	yes	characteristic
42	C₂²×C₃²×C₄	—	2	1	no	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₃²×M₁₆	—	2	1	no	—
45	C₃²×M₁₆	—	2	2	no	—
46	C₃²×M₁₆	—	2	2	no	—
47	C₃²×M₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₃²×C₈	—	2	1	no	—
49	C₂×C₃²×C₈	—	2	2	no	—
50	C₂×C₃²×C₈	—	2	2	no	—
51	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
54	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
55	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
56	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
57	C₃×#217	—	2	2	no	—
58	C₃×C₄⋊Dic₃	—	2	2	no	—
59	C₃×C₄×Dic₃	—	2	2	no	—
60	C₃×#208	—	2	2	no	—
61	C₃×#208	—	2	2	no	—
62	C₂×C₃×C₃⋊C₈	—	2	2	no	—
63	#1814	—	3	1	no	Sylow
64	C₂×C₃×#41	—	2	1	no	—
65	C₂×C₃×#41	C₂×D₃	1	1	yes	characteristic
66	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
67	C₃×#131	—	2	2	no	—
68	C₃×#131	—	2	2	no	—
69	C₃×#131	—	2	1	no	—
70	C₃×#131	—	2	1	no	—
71	C₃×#131	—	2	1	no	—
72	C₃×#131	—	2	1	no	—
73	C₃×#131	—	2	2	no	—
74	C₃×#131	—	2	2	no	—
75	C₃×#131	Dic₃	1	2	yes	complemented
76	C₃×#131	Dic₃	1	2	yes	complemented
77	C₃×#131	C₃×C₄	1	2	yes	complemented
78	C₃×#131	C₃×C₄	1	2	yes	complemented
79	C₂×C₃×M₁₆	—	2	2	no	—
80	C₂×C₃×M₁₆	—	2	1	no	—
81	C₂×C₃×M₁₆	—	2	1	no	—
82	C₂×C₃×M₁₆	—	2	1	no	—
83	C₂×C₃×M₁₆	—	3	2	no	—
84	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
85	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃×C₈	—	2	2	no	—
87	C₂²×C₃×C₈	—	2	1	no	—
88	C₂²×C₃×C₈	—	2	1	no	—
89	C₂²×C₃×C₈	—	2	1	no	—
90	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
91	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
92	C₃×#117	—	3	2	no	—
93	#926	C₂²×C₃	1	2	yes	—
94	C₂×#208	C₂²×C₃	1	2	yes	—
95	C₃×#108	—	6	1	no	—
96	C₃×#108	—	6	1	no	—
97	C₃×#107	—	6	1	no	—
98	C₃×#106	—	6	1	no	—
99	C₃×#104	—	6	4	no	—
100	#837	—	2	4	no	—
101	#819	—	2	1	no	—
102	#819	—	2	1	no	—
103	#818	—	2	1	no	—
104	#817	—	2	1	no	—
105	C₂³×C₃²	—	2	1	no	—
106	C₂³×C₃²	#41	1	1	yes	characteristic
107	C₃²×Q₈	—	2	1	no	—
108	C₃²×Q₈	C₄⋊C₄	1	2	yes	—
109	C₃²×D₄	—	2	2	no	—
110	C₃²×D₄	—	2	2	no	—
111	C₃²×D₄	—	2	1	no	—
112	C₃²×D₄	C₄⋊C₄	1	2	yes	—
113	C₂×C₃²×C₄	—	2	1	no	—
114	C₂×C₃²×C₄	—	2	2	no	—
115	C₂×C₃²×C₄	—	2	2	no	—
116	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
121	C₂×C₃²×C₄	#41	1	1	yes	characteristic
122	C₂×C₃×Dic₃	—	4	2	no	—
123	C₃²×C₈	—	2	2	no	—
124	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
125	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
126	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
127	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
128	C₃×C₃⋊C₈	—	4	2	no	—
129	C₂×#131	C₃×D₃	1	1	yes	characteristic
130	C₂×#108	—	3	1	no	—
131	#427	—	3	1	no	—
132	#421	—	3	2	no	—
133	#344	—	3	2	no	—
134	C₃×#41	—	2	2	no	—
135	C₃×#41	—	2	2	no	—
136	C₃×#41	—	2	1	no	—
137	C₃×#41	—	2	1	no	—
138	C₃×#41	—	2	1	no	—
139	C₃×#41	—	2	1	no	—
140	C₃×#41	—	2	2	no	—
141	C₃×#41	—	2	2	no	—
142	C₃×#41	D₁₂	1	2	yes	—
143	C₃×#41	C₂×Dic₃	1	2	yes	—
144	C₃×#41	C₂×C₃×C₄	1	2	yes	—
145	C₃×#41	C₃×D₄	1	2	yes	—
146	C₂×C₃×Q₈	—	2	1	no	—
147	C₂×C₃×Q₈	Dic₆	1	1	yes	characteristic
148	C₂×C₃×Q₈	C₃×Q₈	1	1	yes	characteristic
149	C₂×C₃×D₄	—	2	2	no	—
150	C₂×C₃×D₄	—	2	1	no	—
151	C₂×C₃×D₄	—	2	1	no	—
152	C₂×C₃×D₄	—	2	1	no	—
153	C₂×C₃×D₄	Dic₆	1	1	yes	characteristic
154	C₂×C₃×D₄	C₃×Q₈	1	1	yes	characteristic
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	—	2	1	no	—
157	C₂²×C₃×C₄	—	2	1	no	—
158	C₂²×C₃×C₄	—	2	1	no	—
159	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
160	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
161	C₃×M₁₆	—	2	2	no	—
162	C₃×M₁₆	—	2	4	no	—
163	C₃×M₁₆	—	2	4	no	—
164	C₃×M₁₆	—	2	1	no	—
165	C₃×M₁₆	—	2	1	no	—
166	C₃×M₁₆	—	2	2	no	—
167	C₃×M₁₆	—	2	2	no	—
168	C₃×M₁₆	—	2	2	no	—
169	C₃×M₁₆	—	2	2	no	—
170	C₃×M₁₆	—	2	2	no	—
171	C₃×M₁₆	—	6	2	no	—
172	C₃×M₁₆	—	6	2	no	—
173	C₃×M₁₆	C₂×Dic₃	1	2	yes	—
174	C₃×M₁₆	C₂×C₃×C₄	1	2	yes	—
175	C₂×C₃×C₈	—	2	2	no	—
176	C₂×C₃×C₈	—	2	4	no	—
177	C₂×C₃×C₈	—	2	4	no	—
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₂×C₃×C₈	—	2	2	no	—
181	C₂×C₃×C₈	—	2	2	no	—
182	C₂×C₃×C₈	—	2	2	no	—
183	C₂×C₃×C₈	—	2	2	no	—
184	C₂×C₃×C₈	—	2	1	no	—
185	C₂×C₃×C₈	—	2	1	no	—
186	C₂×C₃×C₈	—	2	1	no	—
187	C₂×C₃×C₈	—	2	1	no	—
188	C₂×C₃×C₈	—	2	1	no	—
189	C₂×C₃×C₈	—	2	1	no	—
190	C₂×C₃×C₈	—	6	2	no	—
191	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
192	C₂×C₃×C₈	C₂×Dic₃	1	1	yes	characteristic
193	C₂×C₃×C₈	#67	1	1	yes	characteristic
194	C₂×C₃×C₈	#67	1	1	yes	characteristic
195	C₂×C₃×C₈	#67	1	1	yes	characteristic
196	C₂×C₃×C₈	#67	1	1	yes	characteristic
197	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
198	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
199	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
200	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
201	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
202	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
203	C₃×C₄⋊C₄	—	6	2	no	—
204	C₃×C₂²⋊C₄	—	6	2	no	—
205	C₃×C₄²	—	6	2	no	—
206	#217	—	2	2	no	—
207	C₄⋊Dic₃	—	2	2	no	—
208	C₄×Dic₃	—	2	2	no	—
209	#208	—	2	2	no	—
210	#208	—	2	2	no	—
211	C₂×C₃⋊C₈	—	2	2	no	—
212	C₂²×C₃²	—	2	2	no	—
213	C₂²×C₃²	—	4	1	no	—
214	C₂²×C₃²	—	4	2	no	—
215	C₂²×C₃²	#117	1	1	yes	characteristic
216	C₂²×C₃²	#121	1	1	yes	characteristic
217	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
218	C₃²×C₄	—	2	2	no	—
219	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
221	C₃²×C₄	#121	1	1	yes	characteristic
222	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
223	C₃×Dic₃	—	8	2	no	—
224	C₂×#41	C₂×C₃×D₃	1	1	yes	characteristic
225	#131	—	2	1	no	—
226	#131	—	2	1	no	—
227	#131	C₃×Dic₃	1	2	yes	complemented
228	#131	C₃×Dic₃	1	2	yes	complemented
229	C₂×M₁₆	—	2	1	no	—
230	C₂×M₁₆	—	3	2	no	—
231	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
234	#117	—	3	2	no	—
235	#108	—	6	1	no	—
236	#108	—	6	1	no	—
237	#107	—	6	1	no	—
238	#106	—	6	1	no	—
239	#104	—	6	4	no	—
240	C₂³×C₃	—	2	2	no	—
241	C₂³×C₃	—	2	1	no	—
242	C₂³×C₃	—	2	1	no	—
243	C₂³×C₃	—	2	1	no	—
244	C₂³×C₃	#235	1	1	yes	characteristic
245	C₂³×C₃	C₃×#41	1	1	yes	characteristic
246	C₃×Q₈	—	2	2	no	—
247	C₃×Q₈	—	2	1	no	—
248	C₃×Q₈	—	2	1	no	—
249	C₃×Q₈	—	2	2	no	—
250	C₃×Q₈	C₄⋊Dic₃	1	2	yes	—
251	C₃×Q₈	C₃×C₄⋊C₄	1	2	yes	—
252	C₃×D₄	—	2	4	no	—
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	2	no	—
255	C₃×D₄	—	2	2	no	—
256	C₃×D₄	—	2	2	no	—
257	C₃×D₄	—	2	2	no	—
258	C₃×D₄	—	2	2	no	—
259	C₃×D₄	—	2	1	no	—
260	C₃×D₄	—	2	1	no	—
261	C₃×D₄	—	2	2	no	—
262	C₃×D₄	C₄⋊Dic₃	1	2	yes	—
263	C₃×D₄	C₃×C₄⋊C₄	1	2	yes	—
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	2	4	no	—
267	C₂×C₃×C₄	—	2	1	no	—
268	C₂×C₃×C₄	—	2	1	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	2	no	—
272	C₂×C₃×C₄	—	2	2	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	2	1	no	—
278	C₂×C₃×C₄	—	2	1	no	—
279	C₂×C₃×C₄	—	12	2	no	—
280	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
282	C₂×C₃×C₄	#235	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
291	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
292	C₂×Dic₃	—	4	2	no	—
293	C₃×C₈	—	2	4	no	—
294	C₃×C₈	—	2	2	no	—
295	C₃×C₈	—	2	2	no	—
296	C₃×C₈	—	2	1	no	—
297	C₃×C₈	—	2	1	no	—
298	C₃×C₈	—	2	1	no	—
299	C₃×C₈	—	2	1	no	—
300	C₃×C₈	—	12	2	no	—
301	C₃×C₈	#217	1	1	yes	characteristic
302	C₃×C₈	#217	1	1	yes	characteristic
303	C₃×C₈	#217	1	1	yes	characteristic
304	C₃×C₈	#217	1	1	yes	characteristic
305	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
306	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
307	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
308	C₃×C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
309	C₃⋊C₈	—	4	2	no	—
310	C₂×C₃²	—	2	1	no	—
311	C₂×C₃²	—	2	1	no	—
312	C₂×C₃²	—	2	1	no	—
313	C₂×C₃²	—	4	2	no	—
314	C₂×C₃²	#380	1	1	yes	characteristic
315	#41	—	2	1	no	—
316	#41	—	2	1	no	—
317	#41	C₃×D₁₂	1	2	yes	—
318	#41	C₂×C₃×Dic₃	1	2	yes	—
319	C₂×Q₈	C₃×Dic₆	1	1	yes	characteristic
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	C₃×Dic₆	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	6	2	no	—
328	M₁₆	—	6	2	no	—
329	M₁₆	C₂×C₃×Dic₃	1	2	yes	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	6	2	no	—
334	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
335	C₂×C₈	C₂×C₃×Dic₃	1	1	yes	characteristic
336	C₂×C₈	C₃×#67	1	1	yes	characteristic
337	C₂×C₈	C₃×#67	1	1	yes	characteristic
338	C₂×C₈	C₃×#67	1	1	yes	characteristic
339	C₂×C₈	C₃×#67	1	1	yes	characteristic
340	C₄⋊C₄	—	6	2	no	—
341	C₂²⋊C₄	—	6	2	no	—
342	C₄²	—	6	2	no	—
343	C₂²×C₃	—	2	4	no	—
344	C₂²×C₃	—	2	2	no	—
345	C₂²×C₃	—	2	2	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	4	1	no	—
351	C₂²×C₃	—	4	2	no	—
352	C₂²×C₃	—	4	4	no	—
353	C₂²×C₃	—	4	2	no	—
354	C₂²×C₃	—	4	2	no	—
355	C₂²×C₃	#924	1	1	yes	characteristic
356	C₂²×C₃	#926	1	1	yes	characteristic
357	C₂²×C₃	#930	1	1	yes	characteristic
358	C₂²×C₃	C₃×#117	1	1	yes	characteristic
359	C₂²×C₃	C₃×#121	1	1	yes	characteristic
360	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
361	C₃×C₄	—	2	4	no	—
362	C₃×C₄	—	2	2	no	—
363	C₃×C₄	—	2	2	no	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	24	2	no	—
369	C₃×C₄	#924	1	1	yes	characteristic
370	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
371	C₃×C₄	#930	1	1	yes	characteristic
372	C₃×C₄	C₂×#217	1	1	yes	characteristic
373	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
374	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
375	C₃×C₄	C₃×#121	1	1	yes	characteristic
376	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
377	Dic₃	—	8	2	no	—
378	C₃²	#1814	1	1	yes	characteristic, complemented, Sylow
379	C₂³	—	2	1	no	—
380	C₂³	C₃×#235	1	1	yes	characteristic
381	Q₈	—	2	1	no	—
382	Q₈	C₃×C₄⋊Dic₃	1	2	yes	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	1	no	—
386	D₄	C₃×C₄⋊Dic₃	1	2	yes	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	12	2	no	—
391	C₂×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
392	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
393	C₂×C₄	C₃×#235	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
395	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
396	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
397	C₈	—	2	2	no	—
398	C₈	—	12	2	no	—
399	C₈	C₃×#217	1	1	yes	characteristic
400	C₈	C₃×#217	1	1	yes	characteristic
401	C₈	C₃×#217	1	1	yes	characteristic
402	C₈	C₃×#217	1	1	yes	characteristic
403	C₂×C₃	—	2	2	no	—
404	C₂×C₃	—	2	1	no	—
405	C₂×C₃	—	2	1	no	—
406	C₂×C₃	—	2	1	no	—
407	C₂×C₃	—	2	1	no	—
408	C₂×C₃	—	2	1	no	—
409	C₂×C₃	—	2	1	no	—
410	C₂×C₃	—	2	1	no	—
411	C₂×C₃	—	4	1	no	—
412	C₂×C₃	—	4	1	no	—
413	C₂×C₃	—	4	4	no	—
414	C₂×C₃	—	4	2	no	—
415	C₂×C₃	—	4	2	no	—
416	C₂×C₃	#5212	1	1	yes	characteristic
417	C₂×C₃	C₃×#380	1	1	yes	characteristic
418	C₂²	—	2	2	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	C₃×#924	1	1	yes	characteristic
422	C₂²	C₃×#926	1	1	yes	characteristic
423	C₂²	C₃×#930	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	24	2	no	—
426	C₄	C₃×#924	1	1	yes	characteristic
427	C₄	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
428	C₄	C₃×#930	1	1	yes	characteristic
429	C₄	C₂×C₃×#217	1	1	yes	characteristic
430	C₃	—	2	1	no	—
431	C₃	#72013	1	1	yes	characteristic, direct product factor
432	C₃	C₃×#1814	1	1	yes	characteristic, complemented
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	1	no	—
436	C₂	—	4	2	no	—
437	C₂	C₃×#5212	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#930
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#131	C₂
socle	C₂×C₃²	#380
prime radical	C₂×C₃²×#41	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×#131	D₃
hypocenter	C₃	C₃×#1814
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#819	C₂	semidirect
4. C₃×#5106	C₂	semidirect
5. C₃×#4559	C₂	semidirect
7. #72013	C₃	direct (N × H)
11. C₃²×#131	C₄	semidirect
12. C₃²×#131	C₄	semidirect
31. C₂×#819	C₂×C₃	semidirect
32. #5106	C₂×C₃	semidirect
34. #4559	C₂×C₃	semidirect
75. C₃×#131	Dic₃	semidirect
76. C₃×#131	Dic₃	semidirect
77. C₃×#131	C₃×C₄	semidirect
78. C₃×#131	C₃×C₄	semidirect
227. #131	C₃×Dic₃	semidirect
228. #131	C₃×Dic₃	semidirect
378. C₃²	#1814	semidirect
431. C₃	#72013	direct (N × H)
432. C₃	C₃×#1814	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#131	2
C₃×#5236	2
C₂×C₃×#819	2
C₃×#5106	2
C₃×#4559	2
C₃×#1814	3
#72013	3

Subgroups — C3×#72013 #11785543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#72013 #11785543