Subgroups — D₃×#12011 #72226257

Order 1536.

1032 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×#364	C₂	1	2	yes	maximal
2	C₄×D₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	#10706783	C₂	1	1	yes	maximal, characteristic, complemented
4	#10706782	C₂	1	2	yes	maximal, complemented
5	#10706781	C₂	1	4	yes	maximal, complemented
6	D₃×#1373	C₂	1	4	yes	maximal, complemented
7	C₃×#12011	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#12011	—	3	1	no	maximal, Sylow
9	C₂×D₃×M₃₂	—	2	2	no	—
10	C₂×D₃×M₃₂	C₄	1	1	yes	characteristic
11	C₂×D₃×M₃₂	C₄	1	1	yes	characteristic
12	C₂×C₄×D₃×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×#364	C₂²	1	2	yes	—
14	C₃×C₄×M₃₂	C₂²	1	1	yes	characteristic
15	C₂×#4511	—	2	2	no	—
16	Dic₃×M₃₂	C₄	1	1	yes	characteristic
17	Dic₃×M₃₂	C₄	1	1	yes	characteristic
18	C₂×#4463	C₂²	1	2	yes	—
19	C₄×#812	C₂²	1	1	yes	characteristic
20	D₃×#364	—	2	2	no	—
21	D₃×#364	—	2	2	no	—
22	D₃×#364	C₂²	1	4	yes	—
23	D₃×#364	C₂²	1	4	yes	—
24	#69071	C₄	1	2	yes	—
25	D₃×#346	C₄	1	2	yes	—
26	C₄×#798	C₂²	1	2	yes	—
27	C₄×D₃×C₁₆	C₂²	1	2	yes	—
28	C₃×#1373	C₂²	1	4	yes	complemented
29	#67566	C₂²	1	8	yes	complemented
30	#67502	C₂²	1	4	yes	complemented
31	C₂²×#364	—	3	2	no	—
32	C₂×C₄×M₃₂	—	3	1	no	—
33	#12011	—	3	2	no	—
34	#12011	—	3	4	no	—
35	#12011	—	3	1	no	—
36	#12011	D₃	1	1	yes	characteristic, direct product factor
37	C₂×#1373	—	3	4	no	—
38	C₂²×D₃×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₃×C₈	D₄	1	1	yes	characteristic
40	C₂×C₄²×D₃	Q₈	1	1	yes	characteristic
41	C₂×C₃×M₃₂	—	2	2	no	—
42	C₂×C₃×M₃₂	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×M₃₂	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×C₈	C₂³	1	1	yes	characteristic
45	C₂×C₈×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×Dic₃	D₄	1	1	yes	characteristic
47	C₂×#812	—	2	2	no	—
48	C₂×#812	C₂×C₄	1	1	yes	characteristic
49	C₂×#812	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×C₃⋊C₈	Q₈	1	1	yes	characteristic
51	D₃×M₃₂	—	2	2	no	—
52	D₃×M₃₂	—	2	2	no	—
53	D₃×M₃₂	—	2	4	no	—
54	D₃×M₃₂	—	2	4	no	—
55	D₃×M₃₂	—	4	2	no	—
56	D₃×M₃₂	—	4	2	no	—
57	D₃×M₃₂	C₈	1	4	yes	—
58	D₃×M₃₂	C₈	1	4	yes	—
59	C₂×#798	—	4	2	no	—
60	C₂×#798	C₂×C₄	1	2	yes	—
61	C₂×#798	C₂×C₄	1	2	yes	—
62	C₂×D₃×C₁₆	—	4	2	no	—
63	C₂×D₃×C₁₆	C₂×C₄	1	2	yes	—
64	C₂×D₃×C₁₆	C₂×C₄	1	2	yes	—
65	C₄×D₃×C₈	C₂×C₄	1	1	yes	characteristic
66	C₄×D₃×C₈	C₂×C₄	1	1	yes	characteristic
67	C₄×D₃×C₈	D₄	1	1	yes	characteristic
68	C₄×D₃×C₈	D₄	1	1	yes	characteristic
69	C₄×D₃×C₈	Q₈	1	1	yes	characteristic
70	C₄×D₃×C₈	Q₈	1	1	yes	characteristic
71	C₄×D₃×C₈	C₂³	1	1	yes	characteristic
72	C₄×D₃×C₈	C₂³	1	1	yes	characteristic
73	C₃×#364	—	2	2	no	—
74	C₃×#364	C₂³	1	4	yes	—
75	C₃×#346	C₂×C₄	1	2	yes	—
76	C₃×C₄×C₁₆	C₂³	1	2	yes	—
77	#4511	—	2	4	no	—
78	#4511	—	2	4	no	—
79	#4502	C₂×C₄	1	2	yes	—
80	#4502	C₂×C₄	1	2	yes	—
81	Dic₃×C₁₆	C₂×C₄	1	2	yes	—
82	Dic₃×C₁₆	C₂×C₄	1	2	yes	—
83	#4463	—	2	2	no	—
84	#4463	C₂³	1	4	yes	—
85	#4461	C₂×C₄	1	2	yes	—
86	C₄×C₃⋊C₁₆	C₂³	1	2	yes	—
87	C₂²×M₃₂	—	3	1	no	—
88	C₂²×M₃₂	—	3	1	no	—
89	C₂²×M₃₂	—	6	2	no	—
90	C₂²×C₄×C₈	—	3	1	no	—
91	C₂×#364	—	3	2	no	—
92	C₂×#364	—	3	4	no	—
93	C₂×#364	—	3	4	no	—
94	C₂×#364	—	6	2	no	—
95	C₂×#364	—	6	2	no	—
96	C₂×#364	—	6	2	no	—
97	C₂×#364	C₂×D₃	1	2	yes	—
98	C₄×M₃₂	—	3	1	no	—
99	C₄×M₃₂	—	3	1	no	—
100	C₄×M₃₂	—	3	1	no	—
101	C₄×M₃₂	—	3	2	no	—
102	C₄×M₃₂	—	3	2	no	—
103	C₄×M₃₂	C₂×D₃	1	1	yes	characteristic
104	C₂×#346	—	3	2	no	—
105	C₂×C₄×C₁₆	—	3	2	no	—
106	#1373	—	3	8	no	—
107	#1373	—	3	4	no	—
108	#1373	C₂×D₃	1	4	yes	complemented
109	C₂²×C₄×D₃	—	2	1	no	—
110	C₂²×C₄×D₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₃×C₈	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄²	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₄×Dic₃	—	2	1	no	—
115	C₂×C₄×Dic₃	C₄⋊C₄	1	1	yes	characteristic
116	C₂²×C₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
118	C₂×D₃×C₈	C₄⋊C₄	1	1	yes	characteristic
119	C₂×D₃×C₈	C₄⋊C₄	1	1	yes	characteristic
120	C₂×D₃×C₈	C₄⋊C₄	1	1	yes	characteristic
121	C₂×D₃×C₈	C₄⋊C₄	1	1	yes	characteristic
122	C₂×D₃×C₈	C₂×C₈	1	2	yes	—
123	C₂×D₃×C₈	C₂×C₈	1	2	yes	—
124	C₂×D₃×C₈	M₁₆	1	2	yes	—
125	C₂×D₃×C₈	M₁₆	1	2	yes	—
126	C₂×D₃×C₈	D₈	1	2	yes	—
127	C₂×D₃×C₈	D₈	1	2	yes	—
128	C₂×D₃×C₈	Q₁₆	1	2	yes	—
129	C₂×D₃×C₈	Q₁₆	1	2	yes	—
130	C₂×D₃×C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×D₃×C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×D₃×C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×D₃×C₈	C₂×D₄	1	1	yes	characteristic
134	C₄²×D₃	—	2	1	no	—
135	C₄²×D₃	—	2	1	no	—
136	C₄²×D₃	C₄⋊C₄	1	1	yes	characteristic
137	C₄²×D₃	C₄⋊C₄	1	1	yes	characteristic
138	C₄²×D₃	C₂×Q₈	1	1	yes	characteristic
139	C₄²×D₃	C₂×Q₈	1	1	yes	characteristic
140	C₃×M₃₂	—	2	2	no	—
141	C₃×M₃₂	—	2	4	no	—
142	C₃×M₃₂	—	4	2	no	—
143	C₃×M₃₂	C₂×C₈	1	4	yes	—
144	C₂×C₃×C₁₆	—	4	2	no	—
145	C₂×C₃×C₁₆	C₂²×C₄	1	2	yes	—
146	C₂×C₃×C₁₆	C₂²×C₄	1	2	yes	—
147	C₃×C₄×C₈	C₂²×C₄	1	1	yes	characteristic
148	C₃×C₄×C₈	C₂×D₄	1	1	yes	characteristic
149	C₃×C₄×C₈	C₂×Q₈	1	1	yes	characteristic
150	C₃×C₄×C₈	C₂⁴	1	1	yes	characteristic
151	C₈×Dic₃	C₄⋊C₄	1	1	yes	characteristic
152	C₈×Dic₃	C₄⋊C₄	1	1	yes	characteristic
153	C₈×Dic₃	C₄⋊C₄	1	1	yes	characteristic
154	C₈×Dic₃	C₄⋊C₄	1	1	yes	characteristic
155	C₈×Dic₃	C₂²×C₄	1	1	yes	characteristic
156	C₈×Dic₃	C₂²×C₄	1	1	yes	characteristic
157	C₈×Dic₃	C₂×D₄	1	1	yes	characteristic
158	C₈×Dic₃	C₂×D₄	1	1	yes	characteristic
159	#812	—	2	2	no	—
160	#812	—	2	4	no	—
161	#812	—	4	2	no	—
162	#812	C₂×C₈	1	4	yes	—
163	C₂×C₃⋊C₁₆	—	4	2	no	—
164	C₂×C₃⋊C₁₆	C₂²×C₄	1	2	yes	—
165	C₂×C₃⋊C₁₆	C₂²×C₄	1	2	yes	—
166	C₄×C₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
167	C₄×C₃⋊C₈	C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₃⋊C₈	C₂×Q₈	1	1	yes	characteristic
169	C₄×C₃⋊C₈	C₂×Q₈	1	1	yes	characteristic
170	#798	—	2	4	no	—
171	#798	—	4	4	no	—
172	#798	—	4	4	no	—
173	#798	C₂×C₈	1	8	yes	—
174	D₃×C₁₆	—	2	2	no	—
175	D₃×C₁₆	—	2	2	no	—
176	D₃×C₁₆	—	4	4	no	—
177	D₃×C₁₆	—	4	4	no	—
178	D₃×C₁₆	C₂×C₈	1	4	yes	—
179	D₃×C₁₆	C₂×C₈	1	4	yes	—
180	C₂³×C₈	—	3	1	no	—
181	C₂³×C₈	—	3	1	no	—
182	C₂²×C₄²	—	3	1	no	—
183	C₂×M₃₂	—	2	2	no	—
184	C₂×M₃₂	—	3	1	no	—
185	C₂×M₃₂	—	3	4	no	—
186	C₂×M₃₂	—	3	4	no	—
187	C₂×M₃₂	—	3	1	no	—
188	C₂×M₃₂	—	3	2	no	—
189	C₂×M₃₂	—	3	2	no	—
190	C₂×M₃₂	—	6	2	no	—
191	C₂×M₃₂	—	6	2	no	—
192	C₂×M₃₂	—	6	4	no	—
193	C₂×M₃₂	—	6	4	no	—
194	C₂×M₃₂	—	6	2	no	—
195	C₂×M₃₂	—	12	2	no	—
196	C₂×M₃₂	—	12	2	no	—
197	C₂×M₃₂	—	12	2	no	—
198	C₂×M₃₂	C₄×D₃	1	1	yes	characteristic
199	C₂×M₃₂	C₄×D₃	1	1	yes	characteristic
200	C₂²×C₁₆	—	3	2	no	—
201	C₂²×C₁₆	—	3	2	no	—
202	C₂²×C₁₆	—	12	2	no	—
203	C₂×C₄×C₈	—	3	1	no	—
204	C₂×C₄×C₈	—	3	1	no	—
205	C₂×C₄×C₈	—	3	1	no	—
206	C₂×C₄×C₈	—	3	1	no	—
207	C₂×C₄×C₈	—	3	1	no	—
208	C₂×C₄×C₈	—	3	1	no	—
209	C₂×C₄×C₈	—	3	1	no	—
210	C₂×C₄×C₈	—	3	1	no	—
211	C₂×C₄×C₈	—	3	1	no	—
212	C₂×C₄×C₈	—	3	1	no	—
213	C₂×C₄×C₈	—	3	1	no	—
214	C₂×C₄×C₈	C₂²×D₃	1	1	yes	characteristic
215	#364	—	2	2	no	—
216	#364	—	3	4	no	—
217	#364	—	6	4	no	—
218	#364	—	6	4	no	—
219	#364	—	6	2	no	—
220	#364	C₂²×D₃	1	4	yes	—
221	#346	—	3	2	no	—
222	#346	—	3	2	no	—
223	#346	—	3	2	no	—
224	#346	C₄×D₃	1	2	yes	—
225	C₄×C₁₆	—	3	2	no	—
226	C₄×C₁₆	—	3	2	no	—
227	C₄×C₁₆	—	3	2	no	—
228	C₄×C₁₆	C₂²×D₃	1	2	yes	—
229	C₂³×D₃	#108	1	1	yes	characteristic
230	C₂²×C₃×C₄	—	2	1	no	—
231	C₂²×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂²×Dic₃	—	2	1	no	—
233	C₂²×Dic₃	#108	1	1	yes	characteristic
234	C₂×C₄×D₃	—	2	1	no	—
235	C₂×C₄×D₃	—	2	1	no	—
236	C₂×C₄×D₃	—	2	1	no	—
237	C₂×C₄×D₃	—	2	1	no	—
238	C₂×C₄×D₃	—	4	4	no	—
239	C₂×C₄×D₃	C₄⋊C₈	1	2	yes	—
240	C₂×C₄×D₃	C₄⋊C₈	1	2	yes	—
241	C₂×C₄×D₃	#107	1	2	yes	—
242	C₂×C₄×D₃	#107	1	2	yes	—
243	C₂×C₄×D₃	#108	1	1	yes	characteristic
244	C₂×C₄×D₃	#108	1	1	yes	characteristic
245	C₂×C₄×D₃	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×C₄×D₃	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂×C₃×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×C₃×C₈	C₂²×C₈	1	2	yes	—
250	C₂×C₃×C₈	C₂×M₁₆	1	2	yes	—
251	C₂×C₃×C₈	C₂×D₈	1	2	yes	—
252	C₂×C₃×C₈	C₂×Q₁₆	1	2	yes	—
253	C₂×C₃×C₈	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₃×C₈	C₂²×D₄	1	1	yes	characteristic
255	C₃×C₄²	—	2	1	no	—
256	C₃×C₄²	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₃×C₄²	C₂²×Q₈	1	1	yes	characteristic
258	C₄×Dic₃	—	2	1	no	—
259	C₄×Dic₃	—	2	1	no	—
260	C₄×Dic₃	—	2	1	no	—
261	C₄×Dic₃	—	2	1	no	—
262	C₄×Dic₃	—	2	1	no	—
263	C₄×Dic₃	C₂×C₄⋊C₄	1	1	yes	characteristic
264	C₄×Dic₃	C₂×C₄⋊C₄	1	1	yes	characteristic
265	C₂×C₃⋊C₈	C₄⋊C₈	1	2	yes	—
266	C₂×C₃⋊C₈	C₄⋊C₈	1	2	yes	—
267	C₂×C₃⋊C₈	#107	1	2	yes	—
268	C₂×C₃⋊C₈	#107	1	2	yes	—
269	C₂×C₃⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
270	C₂×C₃⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
271	C₂×C₃⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
273	D₃×C₈	C₄⋊C₈	1	2	yes	—
274	D₃×C₈	C₄⋊C₈	1	2	yes	—
275	D₃×C₈	C₄⋊C₈	1	2	yes	—
276	D₃×C₈	C₄⋊C₈	1	2	yes	—
277	D₃×C₈	#107	1	2	yes	—
278	D₃×C₈	#107	1	2	yes	—
279	D₃×C₈	#107	1	2	yes	—
280	D₃×C₈	#107	1	2	yes	—
281	D₃×C₈	C₂²×C₈	1	1	yes	characteristic
282	D₃×C₈	C₂²×C₈	1	1	yes	characteristic
283	D₃×C₈	C₂²×C₈	1	2	yes	—
284	D₃×C₈	C₂×M₁₆	1	1	yes	characteristic
285	D₃×C₈	C₂×M₁₆	1	1	yes	characteristic
286	D₃×C₈	C₂×M₁₆	1	2	yes	—
287	D₃×C₈	C₂×D₈	1	1	yes	characteristic
288	D₃×C₈	C₂×D₈	1	2	yes	—
289	D₃×C₈	C₂×D₈	1	1	yes	characteristic
290	D₃×C₈	C₂×Q₁₆	1	1	yes	characteristic
291	D₃×C₈	C₂×Q₁₆	1	2	yes	—
292	D₃×C₈	C₂×Q₁₆	1	1	yes	characteristic
293	C₃×C₁₆	—	2	2	no	—
294	C₃×C₁₆	—	4	4	no	—
295	C₃×C₁₆	C₂²×C₈	1	4	yes	—
296	C₃⋊C₁₆	—	2	2	no	—
297	C₃⋊C₁₆	—	4	4	no	—
298	C₃⋊C₁₆	C₂²×C₈	1	4	yes	—
299	C₂³×C₄	—	3	1	no	—
300	C₂³×C₄	—	6	1	no	—
301	C₂²×C₈	—	3	1	no	—
302	C₂²×C₈	—	3	1	no	—
303	C₂²×C₈	—	3	1	no	—
304	C₂²×C₈	—	3	1	no	—
305	C₂²×C₈	—	3	1	no	—
306	C₂²×C₈	—	3	1	no	—
307	C₂²×C₈	—	3	2	no	—
308	C₂²×C₈	—	3	2	no	—
309	C₂²×C₈	—	3	2	no	—
310	C₂²×C₈	—	3	2	no	—
311	C₂²×C₈	—	3	2	no	—
312	C₂²×C₈	—	3	2	no	—
313	C₂²×C₈	—	3	2	no	—
314	C₂²×C₈	—	3	2	no	—
315	C₂²×C₈	—	3	1	no	—
316	C₂²×C₈	—	3	1	no	—
317	C₂²×C₈	—	3	1	no	—
318	C₂²×C₈	—	3	1	no	—
319	C₂²×C₈	C₂×C₄×D₃	1	1	yes	characteristic
320	C₂²×C₈	D₃×D₄	1	1	yes	characteristic
321	C₂×C₄²	—	3	1	no	—
322	C₂×C₄²	—	3	1	no	—
323	C₂×C₄²	—	3	1	no	—
324	C₂×C₄²	—	3	1	no	—
325	C₂×C₄²	—	3	1	no	—
326	C₂×C₄²	—	6	1	no	—
327	C₂×C₄²	—	6	1	no	—
328	C₂×C₄²	—	6	1	no	—
329	C₂×C₄²	D₃×Q₈	1	1	yes	characteristic
330	M₃₂	—	2	2	no	—
331	M₃₂	—	2	4	no	—
332	M₃₂	—	3	4	no	—
333	M₃₂	—	3	8	no	—
334	M₃₂	—	4	2	no	—
335	M₃₂	—	6	4	no	—
336	M₃₂	—	6	2	no	—
337	M₃₂	—	6	4	no	—
338	M₃₂	—	12	4	no	—
339	M₃₂	—	12	4	no	—
340	M₃₂	—	12	2	no	—
341	M₃₂	D₃×C₈	1	4	yes	—
342	C₂×C₁₆	—	3	2	no	—
343	C₂×C₁₆	—	3	4	no	—
344	C₂×C₁₆	—	3	4	no	—
345	C₂×C₁₆	—	3	2	no	—
346	C₂×C₁₆	—	4	2	no	—
347	C₂×C₁₆	—	6	2	no	—
348	C₂×C₁₆	—	6	2	no	—
349	C₂×C₁₆	—	12	4	no	—
350	C₂×C₁₆	—	12	4	no	—
351	C₂×C₁₆	—	12	2	no	—
352	C₂×C₁₆	C₂×C₄×D₃	1	2	yes	—
353	C₂×C₁₆	C₂×C₄×D₃	1	2	yes	—
354	C₄×C₈	—	3	1	no	—
355	C₄×C₈	—	3	1	no	—
356	C₄×C₈	—	3	1	no	—
357	C₄×C₈	—	3	1	no	—
358	C₄×C₈	—	3	1	no	—
359	C₄×C₈	—	3	1	no	—
360	C₄×C₈	—	3	1	no	—
361	C₄×C₈	—	3	1	no	—
362	C₄×C₈	—	3	1	no	—
363	C₄×C₈	—	3	1	no	—
364	C₄×C₈	—	3	1	no	—
365	C₄×C₈	—	3	1	no	—
366	C₄×C₈	C₂×C₄×D₃	1	1	yes	characteristic
367	C₄×C₈	D₃×D₄	1	1	yes	characteristic
368	C₄×C₈	D₃×Q₈	1	1	yes	characteristic
369	C₄×C₈	C₂³×D₃	1	1	yes	characteristic
370	C₂³×C₃	C₂×#108	1	1	yes	characteristic
371	C₂²×D₃	—	4	2	no	—
372	C₂²×D₃	#335	1	2	yes	—
373	C₂²×D₃	#335	1	2	yes	—
374	C₂²×D₃	C₂×#108	1	1	yes	characteristic
375	C₂²×D₃	C₂×#108	1	1	yes	characteristic
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	C₂×C₄⋊C₈	1	2	yes	—
380	C₂×C₃×C₄	C₂×#107	1	2	yes	—
381	C₂×C₃×C₄	C₂×#108	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
383	C₂×Dic₃	—	2	1	no	—
384	C₂×Dic₃	—	2	1	no	—
385	C₂×Dic₃	—	4	2	no	—
386	C₂×Dic₃	#335	1	2	yes	—
387	C₂×Dic₃	#335	1	2	yes	—
388	C₂×Dic₃	C₂×#108	1	1	yes	characteristic
389	C₂×Dic₃	C₂×#108	1	1	yes	characteristic
390	C₄×D₃	—	2	4	no	—
391	C₄×D₃	—	4	2	no	—
392	C₄×D₃	—	4	2	no	—
393	C₄×D₃	—	4	2	no	—
394	C₄×D₃	#335	1	2	yes	—
395	C₄×D₃	#335	1	2	yes	—
396	C₄×D₃	#335	1	2	yes	—
397	C₄×D₃	#335	1	2	yes	—
398	C₄×D₃	C₂×C₄⋊C₈	1	1	yes	characteristic
399	C₄×D₃	C₂×C₄⋊C₈	1	2	yes	—
400	C₄×D₃	C₂×C₄⋊C₈	1	1	yes	characteristic
401	C₄×D₃	C₂×#107	1	2	yes	—
402	C₄×D₃	C₂×#107	1	1	yes	characteristic
403	C₄×D₃	C₂×#107	1	1	yes	characteristic
404	C₃×C₈	C₂×C₄⋊C₈	1	2	yes	—
405	C₃×C₈	C₂×#107	1	2	yes	—
406	C₃×C₈	C₂³×C₈	1	1	yes	characteristic
407	C₃×C₈	C₂²×M₁₆	1	1	yes	characteristic
408	C₃×C₈	C₂²×D₈	1	1	yes	characteristic
409	C₃×C₈	C₂²×Q₁₆	1	1	yes	characteristic
410	C₃⋊C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
411	C₃⋊C₈	C₂×C₄⋊C₈	1	1	yes	characteristic
412	C₃⋊C₈	C₂×C₄⋊C₈	1	2	yes	—
413	C₃⋊C₈	C₂×#107	1	1	yes	characteristic
414	C₃⋊C₈	C₂×#107	1	2	yes	—
415	C₃⋊C₈	C₂×#107	1	1	yes	characteristic
416	C₂⁴	—	3	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	3	1	no	—
419	C₂²×C₄	—	3	2	no	—
420	C₂²×C₄	—	3	2	no	—
421	C₂²×C₄	—	3	1	no	—
422	C₂²×C₄	—	3	1	no	—
423	C₂²×C₄	—	3	1	no	—
424	C₂²×C₄	—	3	1	no	—
425	C₂²×C₄	—	3	2	no	—
426	C₂²×C₄	—	3	2	no	—
427	C₂²×C₄	—	6	1	no	—
428	C₂²×C₄	—	6	1	no	—
429	C₂²×C₄	—	6	1	no	—
430	C₂²×C₄	—	6	1	no	—
431	C₂²×C₄	—	6	1	no	—
432	C₂²×C₄	—	12	4	no	—
433	C₂²×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
434	C₂×C₈	—	3	2	no	—
435	C₂×C₈	—	3	2	no	—
436	C₂×C₈	—	3	1	no	—
437	C₂×C₈	—	3	1	no	—
438	C₂×C₈	—	3	1	no	—
439	C₂×C₈	—	3	1	no	—
440	C₂×C₈	—	3	2	no	—
441	C₂×C₈	—	3	2	no	—
442	C₂×C₈	—	3	2	no	—
443	C₂×C₈	—	3	2	no	—
444	C₂×C₈	—	3	2	no	—
445	C₂×C₈	—	3	2	no	—
446	C₂×C₈	—	3	1	no	—
447	C₂×C₈	—	3	1	no	—
448	C₂×C₈	—	3	2	no	—
449	C₂×C₈	—	3	1	no	—
450	C₂×C₈	—	3	1	no	—
451	C₂×C₈	—	3	2	no	—
452	C₂×C₈	—	3	1	no	—
453	C₂×C₈	—	3	2	no	—
454	C₂×C₈	—	3	1	no	—
455	C₂×C₈	—	3	1	no	—
456	C₂×C₈	—	3	2	no	—
457	C₂×C₈	—	3	1	no	—
458	C₂×C₈	—	3	2	no	—
459	C₂×C₈	—	3	2	no	—
460	C₂×C₈	—	3	2	no	—
461	C₂×C₈	—	3	2	no	—
462	C₂×C₈	D₃×C₄⋊C₄	1	1	yes	characteristic
463	C₂×C₈	D₃×C₄⋊C₄	1	1	yes	characteristic
464	C₂×C₈	C₂×D₃×C₈	1	2	yes	—
465	C₂×C₈	D₃×M₁₆	1	2	yes	—
466	C₂×C₈	D₃×D₈	1	2	yes	—
467	C₂×C₈	D₃×Q₁₆	1	2	yes	—
468	C₂×C₈	C₂²×C₄×D₃	1	1	yes	characteristic
469	C₂×C₈	C₂×D₃×D₄	1	1	yes	characteristic
470	C₄²	—	2	1	no	—
471	C₄²	—	3	1	no	—
472	C₄²	—	3	1	no	—
473	C₄²	—	6	1	no	—
474	C₄²	—	6	1	no	—
475	C₄²	—	6	1	no	—
476	C₄²	—	6	1	no	—
477	C₄²	—	6	1	no	—
478	C₄²	D₃×C₄⋊C₄	1	1	yes	characteristic
479	C₄²	C₂×D₃×Q₈	1	1	yes	characteristic
480	C₁₆	—	2	2	no	—
481	C₁₆	—	3	4	no	—
482	C₁₆	—	4	4	no	—
483	C₁₆	—	6	2	no	—
484	C₁₆	—	12	4	no	—
485	C₁₆	C₂×D₃×C₈	1	4	yes	—
486	C₂²×C₃	—	4	1	no	—
487	C₂²×C₃	C₂×#335	1	2	yes	—
488	C₂²×C₃	C₂²×#108	1	1	yes	characteristic
489	C₂×D₃	—	2	2	no	—
490	C₂×D₃	—	2	4	no	—
491	C₂×D₃	—	4	1	no	—
492	C₂×D₃	—	4	2	no	—
493	C₂×D₃	C₂×#335	1	2	yes	—
494	C₂×D₃	C₂×#335	1	1	yes	characteristic
495	C₂×D₃	C₂×#335	1	1	yes	characteristic
496	C₃×C₄	—	2	2	no	—
497	C₃×C₄	—	4	1	no	—
498	C₃×C₄	C₂×#335	1	2	yes	—
499	C₃×C₄	C₂²×C₄⋊C₈	1	1	yes	characteristic
500	C₃×C₄	C₂²×#107	1	1	yes	characteristic
501	Dic₃	—	2	2	no	—
502	Dic₃	—	4	1	no	—
503	Dic₃	C₂×#335	1	1	yes	characteristic
504	Dic₃	C₂×#335	1	1	yes	characteristic
505	Dic₃	C₂×#335	1	2	yes	—
506	C₂³	—	3	1	no	—
507	C₂³	—	3	2	no	—
508	C₂³	—	3	1	no	—
509	C₂³	—	3	2	no	—
510	C₂³	—	12	2	no	—
511	C₂³	D₃×#108	1	1	yes	characteristic
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	3	1	no	—
515	C₂×C₄	—	3	1	no	—
516	C₂×C₄	—	3	2	no	—
517	C₂×C₄	—	3	2	no	—
518	C₂×C₄	—	3	1	no	—
519	C₂×C₄	—	3	2	no	—
520	C₂×C₄	—	3	1	no	—
521	C₂×C₄	—	3	1	no	—
522	C₂×C₄	—	3	1	no	—
523	C₂×C₄	—	3	2	no	—
524	C₂×C₄	—	3	2	no	—
525	C₂×C₄	—	3	2	no	—
526	C₂×C₄	—	3	2	no	—
527	C₂×C₄	—	3	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	6	4	no	—
530	C₂×C₄	—	6	1	no	—
531	C₂×C₄	—	6	1	no	—
532	C₂×C₄	—	12	2	no	—
533	C₂×C₄	—	12	2	no	—
534	C₂×C₄	—	12	2	no	—
535	C₂×C₄	—	12	2	no	—
536	C₂×C₄	D₃×C₄⋊C₈	1	2	yes	—
537	C₂×C₄	D₃×#107	1	2	yes	—
538	C₂×C₄	D₃×#108	1	1	yes	characteristic
539	C₂×C₄	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
540	C₈	—	3	1	no	—
541	C₈	—	3	2	no	—
542	C₈	—	3	1	no	—
543	C₈	—	3	1	no	—
544	C₈	—	3	1	no	—
545	C₈	—	3	2	no	—
546	C₈	D₃×C₄⋊C₈	1	2	yes	—
547	C₈	D₃×#107	1	2	yes	—
548	C₈	C₂²×D₃×C₈	1	1	yes	characteristic
549	C₈	C₂×D₃×M₁₆	1	1	yes	characteristic
550	C₈	C₂×D₃×D₈	1	1	yes	characteristic
551	C₈	C₂×D₃×Q₁₆	1	1	yes	characteristic
552	C₂×C₃	—	2	1	no	—
553	C₂×C₃	—	2	2	no	—
554	C₂×C₃	C₂²×#335	1	1	yes	characteristic
555	D₃	—	2	1	no	—
556	D₃	—	2	2	no	—
557	D₃	#12011	1	2	yes	direct product factor
558	C₂²	—	3	1	no	—
559	C₂²	—	3	1	no	—
560	C₂²	—	3	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	6	2	no	—
563	C₂²	—	6	4	no	—
564	C₂²	—	12	1	no	—
565	C₂²	—	12	2	no	—
566	C₂²	D₃×#335	1	2	yes	—
567	C₂²	C₂×D₃×#108	1	1	yes	characteristic
568	C₄	—	2	2	no	—
569	C₄	—	3	1	no	—
570	C₄	—	3	2	no	—
571	C₄	—	3	1	no	—
572	C₄	—	4	1	no	—
573	C₄	—	6	2	no	—
574	C₄	—	12	1	no	—
575	C₄	D₃×#335	1	2	yes	—
576	C₄	C₂×D₃×C₄⋊C₈	1	1	yes	characteristic
577	C₄	C₂×D₃×#107	1	1	yes	characteristic
578	C₃	C₂×#12011	1	1	yes	characteristic, complemented, Sylow
579	C₂	—	2	1	no	—
580	C₂	—	2	2	no	—
581	C₂	—	3	2	no	—
582	C₂	—	6	1	no	—
583	C₂	—	6	2	no	—
584	C₂	C₂×D₃×#335	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₃×D₈
commutator	C₃×C₈	C₂³×C₈
Frattini	C₄×C₈	C₂³×D₃
Fitting	C₃×#12011	C₂
socle	C₂×C₃	C₂²×#335
prime radical	C₂³×D₃	#108
cosocle	C₃×C₄×C₈	C₂⁴
hypercenter	#12011	D₃
hypocenter	C₃	C₂×#12011
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ #12011

Complements

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

N	H ≅ G/N	type
3. #10706783	C₂	semidirect
4. #10706782	C₂	semidirect
5. #10706781	C₂	semidirect
6. D₃×#1373	C₂	semidirect
7. C₃×#12011	C₂	semidirect
28. C₃×#1373	C₂²	semidirect
29. #67566	C₂²	semidirect
30. #67502	C₂²	semidirect
36. #12011	D₃	direct (N × H)
108. #1373	C₂×D₃	semidirect
557. D₃	#12011	direct (N × H)
578. C₃	C₂×#12011	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×#364	2
C₄×D₃×M₃₂	2
#10706783	2
#10706782	2
#10706781	2
D₃×#1373	2
C₃×#12011	2
C₂×#12011	3

Subgroups — D3×#12011 #72226257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#12011 #72226257