Subgroups — C₃×D₃×#819 #13157877

Order 1728.

582 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×D₃×#208	C₂	1	2	yes	maximal
3	C₃×#63646	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#819	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63577	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#819	—	3	1	no	maximal
7	C₃×D₃×#108	—	3	1	no	maximal
8	D₃×#819	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
11	C₃×#3748	C₂²	1	2	yes	—
12	C₃²×#208	C₂²	1	2	yes	—
13	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₃²×D₃×C₈	C₄	1	2	yes	—
15	C₃²×D₃×C₈	C₄	1	2	yes	—
16	C₃×#3711	—	2	2	no	—
17	C₃×D₃×C₃⋊C₈	—	2	2	no	—
18	C₂²×C₃²×C₈	—	3	1	no	—
19	C₂×C₃×#208	—	3	2	no	—
20	C₃×D₃×M₁₆	—	3	2	no	—
21	C₂×C₃×D₃×C₈	—	2	1	no	—
22	C₂×C₃×D₃×C₈	D₃	1	1	yes	characteristic
23	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
24	D₃×#208	C₂×C₃	1	2	yes	—
25	C₃²×#108	—	3	1	no	—
26	#63646	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×#822	—	3	2	no	—
28	C₃×#819	—	2	1	no	—
29	C₃×#819	—	3	1	no	—
30	C₃×#819	—	3	1	no	—
31	C₃×#819	—	3	2	no	—
32	C₃×#819	—	6	1	no	—
33	C₃×#819	D₃	1	1	yes	characteristic, direct product factor
34	C₃×#819	C₂×C₃	1	1	yes	characteristic, complemented
35	#63577	C₂×C₃	1	2	yes	complemented
36	C₂²×C₃²×D₃	Q₈	1	1	yes	characteristic
37	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
38	C₂×C₃²×Dic₃	Q₈	1	1	yes	characteristic
39	C₃²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
40	C₃²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
41	C₃²×C₄×D₃	D₄	1	1	yes	characteristic
42	C₃²×C₄×D₃	D₄	1	1	yes	characteristic
43	C₃³×C₈	C₂×C₄	1	2	yes	—
44	C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
45	C₃²×C₃⋊C₈	—	2	2	no	—
46	C₃²×C₃⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×C₃×#108	—	9	1	no	—
48	C₂×#819	—	3	1	no	—
49	D₃×#108	—	3	1	no	—
50	C₂²×C₃²×C₄	—	3	1	no	—
51	C₂×C₃×C₄×D₃	—	2	1	no	—
52	C₂×C₃×C₄×D₃	C₂×D₃	1	1	yes	characteristic
53	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
54	C₃²×M₁₆	—	3	2	no	—
55	C₂×C₃²×C₈	—	2	1	no	—
56	C₂×C₃²×C₈	—	2	1	no	—
57	C₂×C₃²×C₈	—	2	1	no	—
58	C₂×C₃²×C₈	—	3	1	no	—
59	C₂×C₃²×C₈	—	3	2	no	—
60	C₂×C₃²×C₈	—	3	2	no	—
61	C₂×C₃²×C₈	—	4	1	no	—
62	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
64	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
65	#3748	C₂²×C₃	1	2	yes	—
66	C₃×#208	—	2	2	no	—
67	C₃×#208	—	3	2	no	—
68	C₃×#208	—	3	2	no	—
69	C₃×#208	—	6	2	no	—
70	C₃×#208	—	6	2	no	—
71	C₃×#208	C₂×D₃	1	2	yes	—
72	C₃×#208	C₂²×C₃	1	2	yes	—
73	C₂×C₃×C₃⋊C₈	—	2	1	no	—
74	C₂×C₃×C₃⋊C₈	—	6	2	no	—
75	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
77	C₃×ΓL(1,𝔽₂₅)	—	6	2	no	—
78	C₃×D₃×C₈	—	2	2	no	—
79	C₃×D₃×C₈	—	2	2	no	—
80	C₃×D₃×C₈	—	6	2	no	—
81	C₃×D₃×C₈	Dic₃	1	2	yes	—
82	C₃×D₃×C₈	Dic₃	1	2	yes	—
83	C₃×D₃×C₈	C₃×C₄	1	2	yes	—
84	C₃×D₃×C₈	C₃×C₄	1	2	yes	—
85	#3711	—	2	2	no	—
86	D₃×C₃⋊C₈	—	2	2	no	—
87	C₂²×C₃³	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₃²×D₃	—	2	2	no	—
89	C₂×C₃²×D₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₃²×D₃	C₄⋊C₄	1	1	yes	characteristic
91	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
92	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
93	C₃²×Dic₃	C₄⋊C₄	1	1	yes	characteristic
94	C₃²×Dic₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₃×M₁₆	—	9	2	no	—
96	C₂²×C₃×C₈	—	3	1	no	—
97	C₂²×C₃×C₈	—	3	1	no	—
98	C₂²×C₃×C₈	—	6	1	no	—
99	C₂×#208	—	3	2	no	—
100	D₃×M₁₆	—	3	2	no	—
101	C₂×D₃×C₈	C₃×D₃	1	1	yes	characteristic
102	C₃×#108	—	3	1	no	—
103	C₃×#108	—	3	1	no	—
104	C₃×#108	—	6	1	no	—
105	C₃×#108	—	9	2	no	—
106	C₃×#108	—	9	1	no	—
107	#822	—	3	2	no	—
108	#819	—	3	1	no	—
109	#819	—	3	1	no	—
110	#819	—	3	2	no	—
111	#819	—	6	1	no	—
112	#819	C₃×D₃	1	1	yes	characteristic, direct product factor
113	C₂³×C₃²	—	3	1	no	—
114	C₂²×C₃×D₃	—	2	1	no	—
115	C₂²×C₃×D₃	Dic₆	1	1	yes	characteristic
116	C₂²×C₃×D₃	C₃×Q₈	1	1	yes	characteristic
117	C₂×C₃²×C₄	—	2	1	no	—
118	C₂×C₃²×C₄	—	2	1	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	—	3	1	no	—
121	C₂×C₃²×C₄	—	3	1	no	—
122	C₂×C₃²×C₄	—	3	1	no	—
123	C₂×C₃²×C₄	—	3	1	no	—
124	C₂×C₃²×C₄	—	3	1	no	—
125	C₂×C₃²×C₄	—	4	1	no	—
126	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₃×Dic₃	—	2	1	no	—
130	C₂×C₃×Dic₃	Dic₆	1	1	yes	characteristic
131	C₂×C₃×Dic₃	C₃×Q₈	1	1	yes	characteristic
132	C₃×C₄×D₃	—	2	1	no	—
133	C₃×C₄×D₃	—	2	1	no	—
134	C₃×C₄×D₃	—	2	1	no	—
135	C₃×C₄×D₃	—	2	1	no	—
136	C₃×C₄×D₃	D₁₂	1	1	yes	characteristic
137	C₃×C₄×D₃	D₁₂	1	1	yes	characteristic
138	C₃×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
139	C₃×C₄×D₃	C₂×Dic₃	1	1	yes	characteristic
140	C₃×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
141	C₃×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
142	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
143	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
144	C₃²×C₈	—	2	2	no	—
145	C₃²×C₈	—	2	2	no	—
146	C₃²×C₈	—	2	2	no	—
147	C₃²×C₈	—	3	2	no	—
148	C₃²×C₈	—	4	2	no	—
149	C₃²×C₈	—	6	2	no	—
150	C₃²×C₈	C₄×D₃	1	2	yes	—
151	C₃²×C₈	C₂×Dic₃	1	2	yes	—
152	C₃²×C₈	C₂×C₃×C₄	1	2	yes	—
153	C₃⋊(C₃⋊C₈)	—	2	2	no	—
154	C₃×C₃⋊C₈	—	2	2	no	—
155	C₃×C₃⋊C₈	—	2	2	no	—
156	C₃×C₃⋊C₈	—	2	2	no	—
157	C₃×C₃⋊C₈	—	4	2	no	—
158	C₃×C₃⋊C₈	—	6	2	no	—
159	C₃×C₃⋊C₈	—	6	2	no	—
160	C₃×C₃⋊C₈	—	12	2	no	—
161	C₃×C₃⋊C₈	C₂×Dic₃	1	2	yes	—
162	C₃×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
163	C₂×#108	—	9	1	no	Sylow
164	C₂×C₃³	—	2	1	no	—
165	C₂×C₃³	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₃²×D₃	—	2	1	no	—
167	C₃²×D₃	#108	1	2	yes	complemented
168	C₂²×C₃×C₄	—	3	1	no	—
169	C₂²×C₃×C₄	—	3	1	no	—
170	C₂²×C₃×C₄	—	6	1	no	—
171	C₂×C₄×D₃	C₂×C₃×D₃	1	1	yes	characteristic
172	C₃×M₁₆	—	3	2	no	—
173	C₃×M₁₆	—	3	2	no	—
174	C₃×M₁₆	—	6	2	no	—
175	C₃×M₁₆	—	9	2	no	—
176	C₃×M₁₆	—	18	2	no	—
177	C₂×C₃×C₈	—	2	1	no	—
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₂×C₃×C₈	—	3	1	no	—
181	C₂×C₃×C₈	—	3	1	no	—
182	C₂×C₃×C₈	—	3	2	no	—
183	C₂×C₃×C₈	—	3	2	no	—
184	C₂×C₃×C₈	—	3	2	no	—
185	C₂×C₃×C₈	—	3	2	no	—
186	C₂×C₃×C₈	—	4	1	no	—
187	C₂×C₃×C₈	—	6	2	no	—
188	C₂×C₃×C₈	—	6	2	no	—
189	C₂×C₃×C₈	—	6	1	no	—
190	C₂×C₃×C₈	—	18	2	no	—
191	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
192	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
193	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
194	#208	—	3	2	no	—
195	#208	—	3	2	no	—
196	#208	—	6	2	no	—
197	#208	—	6	2	no	—
198	#208	C₂×C₃×D₃	1	2	yes	—
199	C₂×C₃⋊C₈	—	6	2	no	—
200	C₂×C₃⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
201	ΓL(1,𝔽₂₅)	—	6	2	no	—
202	D₃×C₈	—	6	2	no	—
203	D₃×C₈	C₃×Dic₃	1	2	yes	—
204	D₃×C₈	C₃×Dic₃	1	2	yes	—
205	C₂²×C₃²	—	2	1	no	—
206	C₂²×C₃²	—	2	1	no	—
207	C₂²×C₃²	—	2	1	no	—
208	C₂²×C₃²	—	3	1	no	—
209	C₂²×C₃²	—	3	1	no	—
210	C₂²×C₃²	—	4	1	no	—
211	C₂²×C₃²	—	6	2	no	—
212	C₂²×C₃²	C₂×Dic₆	1	1	yes	characteristic
213	C₂²×C₃²	D₃×Q₈	1	1	yes	characteristic
214	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
215	C₂×C₃×D₃	—	2	4	no	—
216	C₂×C₃×D₃	—	2	2	no	—
217	C₂×C₃×D₃	—	2	2	no	—
218	C₂×C₃×D₃	—	2	1	no	—
219	C₂×C₃×D₃	—	2	1	no	—
220	C₂×C₃×D₃	C₄⋊Dic₃	1	1	yes	characteristic
221	C₂×C₃×D₃	C₄⋊Dic₃	1	1	yes	characteristic
222	C₂×C₃×D₃	C₃×C₄⋊C₄	1	1	yes	characteristic
223	C₂×C₃×D₃	C₃×C₄⋊C₄	1	1	yes	characteristic
224	C₃²×C₄	—	2	1	no	—
225	C₃²×C₄	—	2	1	no	—
226	C₃²×C₄	—	2	1	no	—
227	C₃²×C₄	—	2	1	no	—
228	C₃²×C₄	—	2	1	no	—
229	C₃²×C₄	—	2	1	no	—
230	C₃²×C₄	—	3	1	no	—
231	C₃²×C₄	—	3	1	no	—
232	C₃²×C₄	—	4	1	no	—
233	C₃²×C₄	—	4	1	no	—
234	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
235	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
236	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
237	C₃²×C₄	C₂²×Dic₃	1	1	yes	characteristic
238	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
240	C₃×Dic₃	—	2	1	no	—
241	C₃×Dic₃	—	2	1	no	—
242	C₃×Dic₃	C₄⋊Dic₃	1	1	yes	characteristic
243	C₃×Dic₃	C₄⋊Dic₃	1	1	yes	characteristic
244	C₃×Dic₃	C₃×C₄⋊C₄	1	1	yes	characteristic
245	C₃×Dic₃	C₃×C₄⋊C₄	1	1	yes	characteristic
246	C₂×M₁₆	—	9	2	no	—
247	C₂²×C₈	—	3	1	no	—
248	#108	—	3	1	no	—
249	#108	—	9	2	no	—
250	#108	—	9	1	no	—
251	C₃³	C₂×#108	1	1	yes	characteristic, complemented, Sylow
252	C₂³×C₃	—	3	1	no	—
253	C₂³×C₃	—	3	1	no	—
254	C₂³×C₃	—	6	1	no	—
255	C₂²×D₃	C₃×Dic₆	1	1	yes	characteristic
256	C₂×C₃×C₄	—	2	1	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	3	1	no	—
260	C₂×C₃×C₄	—	3	1	no	—
261	C₂×C₃×C₄	—	3	1	no	—
262	C₂×C₃×C₄	—	3	1	no	—
263	C₂×C₃×C₄	—	3	1	no	—
264	C₂×C₃×C₄	—	3	1	no	—
265	C₂×C₃×C₄	—	3	1	no	—
266	C₂×C₃×C₄	—	3	1	no	—
267	C₂×C₃×C₄	—	3	1	no	—
268	C₂×C₃×C₄	—	3	1	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	—	6	1	no	—
271	C₂×C₃×C₄	—	6	1	no	—
272	C₂×C₃×C₄	—	6	1	no	—
273	C₂×C₃×C₄	—	6	1	no	—
274	C₂×C₃×C₄	—	6	1	no	—
275	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
278	C₂×Dic₃	C₃×Dic₆	1	1	yes	characteristic
279	C₄×D₃	C₃×D₁₂	1	1	yes	characteristic
280	C₄×D₃	C₃×D₁₂	1	1	yes	characteristic
281	C₄×D₃	C₂×C₃×Dic₃	1	1	yes	characteristic
282	C₄×D₃	C₂×C₃×Dic₃	1	1	yes	characteristic
283	C₃×C₈	—	2	2	no	—
284	C₃×C₈	—	2	2	no	—
285	C₃×C₈	—	2	2	no	—
286	C₃×C₈	—	3	2	no	—
287	C₃×C₈	—	3	2	no	—
288	C₃×C₈	—	4	2	no	—
289	C₃×C₈	—	6	2	no	—
290	C₃×C₈	—	6	2	no	—
291	C₃×C₈	—	6	2	no	—
292	C₃×C₈	—	12	2	no	—
293	C₃×C₈	—	18	2	no	—
294	C₃×C₈	D₃×Dic₃	1	2	yes	—
295	C₃×C₈	C₃×C₄×D₃	1	2	yes	—
296	C₃×C₈	C₂×C₃×Dic₃	1	2	yes	—
297	C₃⋊C₈	—	2	2	no	—
298	C₃⋊C₈	—	6	2	no	—
299	C₃⋊C₈	—	6	2	no	—
300	C₃⋊C₈	—	12	2	no	—
301	C₃⋊C₈	C₂×C₃×Dic₃	1	2	yes	—
302	C₂×C₃²	—	2	1	no	—
303	C₂×C₃²	—	2	2	no	—
304	C₂×C₃²	—	2	1	no	—
305	C₂×C₃²	—	2	1	no	—
306	C₂×C₃²	—	2	1	no	—
307	C₂×C₃²	—	2	1	no	—
308	C₂×C₃²	—	2	1	no	—
309	C₂×C₃²	—	3	2	no	—
310	C₂×C₃²	—	4	1	no	—
311	C₂×C₃²	—	4	1	no	—
312	C₂×C₃²	—	4	1	no	—
313	C₂×C₃²	—	4	2	no	—
314	C₂×C₃²	—	6	1	no	—
315	C₂×C₃²	D₃×C₄⋊C₄	1	1	yes	characteristic
316	C₂×C₃²	C₂×C₄⋊Dic₃	1	1	yes	characteristic
317	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
318	C₃×D₃	—	2	2	no	—
319	C₃×D₃	—	2	1	no	—
320	C₃×D₃	—	2	1	no	—
321	C₃×D₃	—	2	2	no	—
322	C₃×D₃	#819	1	2	yes	direct product factor
323	C₃×D₃	C₃×#108	1	2	yes	complemented
324	C₂²×C₄	—	3	1	no	—
325	M₁₆	—	3	2	no	—
326	M₁₆	—	9	2	no	—
327	M₁₆	—	18	2	no	—
328	C₂×C₈	—	3	1	no	—
329	C₂×C₈	—	3	2	no	—
330	C₂×C₈	—	3	2	no	—
331	C₂×C₈	—	18	2	no	—
332	C₂×C₈	C₃×D₃²	1	1	yes	characteristic
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	2	1	no	—
335	C₂²×C₃	—	2	1	no	—
336	C₂²×C₃	—	3	1	no	—
337	C₂²×C₃	—	3	1	no	—
338	C₂²×C₃	—	3	1	no	—
339	C₂²×C₃	—	3	1	no	—
340	C₂²×C₃	—	4	1	no	—
341	C₂²×C₃	—	6	1	no	—
342	C₂²×C₃	—	6	1	no	—
343	C₂²×C₃	—	6	2	no	—
344	C₂²×C₃	—	6	2	no	—
345	C₂²×C₃	—	6	4	no	—
346	C₂²×C₃	D₃×Dic₆	1	1	yes	characteristic
347	C₂²×C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
348	C₂²×C₃	C₃×D₃×Q₈	1	1	yes	characteristic
349	C₂×D₃	—	2	2	no	—
350	C₂×D₃	C₃×C₄⋊Dic₃	1	1	yes	characteristic
351	C₂×D₃	C₃×C₄⋊Dic₃	1	1	yes	characteristic
352	C₃×C₄	—	2	1	no	—
353	C₃×C₄	—	2	1	no	—
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	3	1	no	—
359	C₃×C₄	—	3	1	no	—
360	C₃×C₄	—	3	1	no	—
361	C₃×C₄	—	3	1	no	—
362	C₃×C₄	—	4	1	no	—
363	C₃×C₄	—	4	1	no	—
364	C₃×C₄	—	6	1	no	—
365	C₃×C₄	—	6	1	no	—
366	C₃×C₄	D₃×D₁₂	1	1	yes	characteristic
367	C₃×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
368	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
369	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
370	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
371	C₃×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
372	Dic₃	C₃×C₄⋊Dic₃	1	1	yes	characteristic
373	Dic₃	C₃×C₄⋊Dic₃	1	1	yes	characteristic
374	C₃²	—	2	1	no	—
375	C₃²	—	2	1	no	—
376	C₃²	—	2	1	no	—
377	C₃²	—	4	1	no	—
378	C₃²	D₃×#108	1	1	yes	characteristic, complemented
379	C₃²	C₂×#819	1	1	yes	characteristic, complemented
380	C₃²	C₂×C₃×#108	1	1	yes	characteristic, complemented
381	C₂³	—	3	1	no	—
382	C₂×C₄	—	3	1	no	—
383	C₂×C₄	—	3	1	no	—
384	C₂×C₄	—	3	1	no	—
385	C₂×C₄	—	3	1	no	—
386	C₂×C₄	—	3	1	no	—
387	C₂×C₄	C₂×C₃×D₃²	1	1	yes	characteristic
388	C₈	—	3	2	no	—
389	C₈	—	6	2	no	—
390	C₈	—	18	2	no	—
391	C₈	C₃×D₃×Dic₃	1	2	yes	—
392	C₂×C₃	—	2	2	no	—
393	C₂×C₃	—	2	1	no	—
394	C₂×C₃	—	2	1	no	—
395	C₂×C₃	—	2	1	no	—
396	C₂×C₃	—	2	1	no	—
397	C₂×C₃	—	2	1	no	—
398	C₂×C₃	—	2	1	no	—
399	C₂×C₃	—	3	2	no	—
400	C₂×C₃	—	3	2	no	—
401	C₂×C₃	—	4	1	no	—
402	C₂×C₃	—	4	1	no	—
403	C₂×C₃	—	4	2	no	—
404	C₂×C₃	—	4	1	no	—
405	C₂×C₃	—	6	2	no	—
406	C₂×C₃	—	6	2	no	—
407	C₂×C₃	—	6	1	no	—
408	C₂×C₃	—	6	1	no	—
409	C₂×C₃	D₃×C₄⋊Dic₃	1	1	yes	characteristic
410	C₂×C₃	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
411	C₂×C₃	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
412	D₃	—	2	1	no	—
413	D₃	C₃×#819	1	2	yes	direct product factor
414	C₂²	—	3	1	no	—
415	C₂²	—	3	1	no	—
416	C₂²	—	6	2	no	—
417	C₂²	C₃×D₃×Dic₆	1	1	yes	characteristic
418	C₄	—	3	1	no	—
419	C₄	—	3	1	no	—
420	C₄	C₃×D₃×D₁₂	1	1	yes	characteristic
421	C₄	C₂×C₃×D₃×Dic₃	1	1	yes	characteristic
422	C₃	—	2	1	no	—
423	C₃	—	2	1	no	—
424	C₃	—	2	1	no	—
425	C₃	—	4	1	no	—
426	C₃	D₃×#819	1	1	yes	characteristic, direct product factor
427	C₃	C₃×D₃×#108	1	1	yes	characteristic, complemented
428	C₃	C₂×C₃×#819	1	1	yes	characteristic, complemented
429	C₂	—	2	1	no	—
430	C₂	—	3	2	no	—
431	C₂	—	6	1	no	—
432	C₂	C₃×D₃×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	D₃×D₁₂
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃²
Fitting	C₂×C₃³×C₈	C₂²
socle	C₂×C₃³	C₂×C₄⋊C₄
prime radical	C₂²×C₃²×D₃	Q₈
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₈	D₃²
hypocenter	C₃²	C₂×C₃×#108
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₃×C₄ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
3. C₃×#63646	C₂	semidirect
4. C₃²×#819	C₂	semidirect
5. C₃×#63577	C₂	semidirect
8. D₃×#819	C₃	direct (N × H)
26. #63646	C₂×C₃	semidirect
33. C₃×#819	D₃	direct (N × H)
34. C₃×#819	C₂×C₃	semidirect
35. #63577	C₂×C₃	semidirect
112. #819	C₃×D₃	direct (N × H)
167. C₃²×D₃	#108	semidirect
251. C₃³	C₂×#108	semidirect
322. C₃×D₃	#819	direct (N × H)
323. C₃×D₃	C₃×#108	semidirect
378. C₃²	D₃×#108	semidirect
379. C₃²	C₂×#819	semidirect
380. C₃²	C₂×C₃×#108	semidirect
413. D₃	C₃×#819	direct (N × H)
426. C₃	D₃×#819	direct (N × H)
427. C₃	C₃×D₃×#108	semidirect
428. C₃	C₂×C₃×#819	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₃×C₈	2
C₃×D₃×#208	2
C₃×#63646	2
C₃²×#819	2
C₃×#63577	2
C₂×C₃×#819	3
C₃×D₃×#108	3
D₃×#819	3

Subgroups — C3×D3×#819 #13157877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#819 #13157877