Subgroups — C₃×#10590785 #13157774

Order 1728.

518 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×#627	C₂	1	1	yes	maximal, characteristic
2	C₃×#63641	C₂	1	1	yes	maximal, characteristic
3	C₃²×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃²×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₃×Dic₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
6	C₃×#63555	C₂	1	1	yes	maximal, characteristic
7	C₃×#63554	C₂	1	1	yes	maximal, characteristic
8	C₃×#4828	—	3	1	no	maximal
9	C₃×#4679	—	3	1	no	maximal
10	#10590785	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×#627	C₄	1	1	yes	characteristic
12	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
16	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₃×#3724	C₄	1	1	yes	characteristic
20	C₃×Dic₃⋊Dic₃	C₄	1	1	yes	characteristic
21	C₃×Dic₃⋊Dic₃	C₄	1	1	yes	characteristic
22	C₃×C₄×Dic₆	—	3	1	no	—
23	C₃×C₄×Dic₆	—	3	1	no	—
24	C₄×#627	C₂×C₃	1	1	yes	characteristic
25	C₃²×C₄⋊C₈	—	3	1	no	—
26	C₃²×C₄×C₈	—	3	1	no	—
27	#63641	C₂×C₃	1	1	yes	characteristic
28	C₃×#815	—	3	1	no	—
29	C₃×#815	—	3	1	no	—
30	C₃×#815	—	3	1	no	—
31	C₃×Dic₃⋊C₈	—	2	1	no	—
32	C₃×Dic₃⋊C₈	—	3	1	no	—
33	C₃×Dic₃⋊C₈	—	3	1	no	—
34	C₃×Dic₃⋊C₈	—	3	1	no	—
35	C₃×Dic₃⋊C₈	—	6	1	no	—
36	C₃×Dic₃⋊C₈	D₃	1	1	yes	characteristic
37	C₃×Dic₃⋊C₈	C₂×C₃	1	1	yes	characteristic
38	C₃×C₈×Dic₃	—	2	1	no	—
39	C₃×C₈×Dic₃	D₃	1	1	yes	characteristic
40	C₃×C₈×Dic₃	C₂×C₃	1	1	yes	characteristic
41	C₃×C₄⋊(C₃⋊C₈)	—	3	1	no	—
42	C₃×#803	—	3	1	no	—
43	Dic₃⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic
44	#63555	C₂×C₃	1	1	yes	characteristic
45	#63554	C₂×C₃	1	1	yes	characteristic
46	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₃×#627	—	2	2	no	—
54	C₃³×C₈	—	2	1	no	—
55	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
56	C₃²×C₃⋊C₈	—	2	1	no	—
57	C₃²×C₃⋊C₈	Q₈	1	2	yes	complemented
58	C₃×#446	—	9	1	no	—
59	#4828	—	3	1	no	—
60	#4679	—	3	1	no	—
61	C₂×C₃×Dic₆	—	3	1	no	—
62	C₂×C₃×Dic₆	—	3	1	no	—
63	C₂×#627	C₃×C₄	1	1	yes	characteristic
64	C₂×C₃²×C₈	—	2	1	no	—
65	C₂×C₃²×C₈	—	2	1	no	—
66	C₂×C₃²×C₈	—	2	1	no	—
67	C₂×C₃²×C₈	—	3	1	no	—
68	C₂×C₃²×C₈	—	3	1	no	—
69	C₂×C₃²×C₈	—	4	1	no	—
70	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
71	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₃²×C₄²	—	3	1	no	—
74	C₃²×C₄²	—	3	1	no	—
75	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
77	C₃×C₄⋊Dic₃	—	3	1	no	—
78	C₃×C₄⋊Dic₃	—	3	1	no	—
79	C₃×Dic₃⋊C₄	—	3	1	no	—
80	C₃×Dic₃⋊C₄	—	3	1	no	—
81	C₃×Dic₃⋊C₄	—	3	1	no	—
82	C₃×Dic₃⋊C₄	—	3	1	no	—
83	C₃×C₄×Dic₃	—	2	1	no	—
84	C₃×C₄×Dic₃	—	2	1	no	—
85	C₃×C₄×Dic₃	—	3	1	no	—
86	C₃×C₄×Dic₃	—	3	1	no	—
87	C₃×C₄×Dic₃	—	6	1	no	—
88	C₃×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
89	C₃×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
90	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
91	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×C₃⋊C₈	—	2	1	no	—
93	C₂×C₃×C₃⋊C₈	—	2	1	no	—
94	C₂×C₃×C₃⋊C₈	—	3	1	no	—
95	C₂×C₃×C₃⋊C₈	—	3	1	no	—
96	C₂×C₃×C₃⋊C₈	—	6	1	no	—
97	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
98	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
99	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
101	#3724	C₃×C₄	1	1	yes	characteristic
102	Dic₃⋊Dic₃	C₃×C₄	1	1	yes	characteristic
103	Dic₃⋊Dic₃	C₃×C₄	1	1	yes	characteristic
104	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
105	C₃³×C₄	C₂×Q₈	1	1	yes	characteristic
106	C₃³×C₄	#41	1	1	yes	characteristic
107	C₃×C₃⋊Dic₃	—	2	1	no	—
108	C₃×C₃⋊Dic₃	—	2	1	no	—
109	C₃²×Dic₃	—	2	1	no	—
110	C₃²×Dic₃	—	2	1	no	—
111	C₃²×Dic₃	—	2	1	no	—
112	C₃²×Dic₃	M₁₆	1	2	yes	—
113	C₃×C₄×Q₈	—	9	1	no	—
114	C₄×Dic₆	—	3	1	no	—
115	C₄×Dic₆	—	3	1	no	—
116	C₃×C₄⋊C₈	—	3	1	no	—
117	C₃×C₄⋊C₈	—	3	1	no	—
118	C₃×C₄⋊C₈	—	6	1	no	—
119	C₃×C₄⋊C₈	—	9	1	no	—
120	C₃×C₄⋊C₈	—	9	1	no	—
121	C₃×#97	—	9	1	no	—
122	C₃×#97	—	9	1	no	—
123	C₃×C₄×C₈	—	3	1	no	—
124	C₃×C₄×C₈	—	3	1	no	—
125	C₃×C₄×C₈	—	6	1	no	—
126	#815	—	3	1	no	—
127	#815	—	3	1	no	—
128	#815	—	3	1	no	—
129	Dic₃⋊C₈	—	3	1	no	—
130	Dic₃⋊C₈	—	3	1	no	—
131	Dic₃⋊C₈	—	3	1	no	—
132	Dic₃⋊C₈	—	6	1	no	—
133	Dic₃⋊C₈	C₃×D₃	1	1	yes	characteristic
134	C₈×Dic₃	C₃×D₃	1	1	yes	characteristic
135	C₄⋊(C₃⋊C₈)	—	3	1	no	—
136	#803	—	3	1	no	—
137	C₂×C₃²×C₄	—	2	1	no	—
138	C₂×C₃²×C₄	—	2	1	no	—
139	C₂×C₃²×C₄	—	2	1	no	—
140	C₂×C₃²×C₄	—	3	1	no	—
141	C₂×C₃²×C₄	—	3	1	no	—
142	C₂×C₃²×C₄	—	3	1	no	—
143	C₂×C₃²×C₄	—	3	1	no	—
144	C₂×C₃²×C₄	—	4	1	no	—
145	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
146	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
147	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
148	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂×C₃⋊Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂×C₃×Dic₃	—	2	1	no	—
151	C₂×C₃×Dic₃	—	2	1	no	—
152	C₂×C₃×Dic₃	—	2	1	no	—
153	C₂×C₃×Dic₃	—	2	1	no	—
154	C₂×C₃×Dic₃	—	3	1	no	—
155	C₂×C₃×Dic₃	—	3	1	no	—
156	C₂×C₃×Dic₃	—	3	1	no	—
157	C₂×C₃×Dic₃	—	3	1	no	—
158	C₂×C₃×Dic₃	—	6	1	no	—
159	C₂×C₃×Dic₃	—	6	1	no	—
160	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
161	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
162	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
163	C₂×C₃×Dic₃	C₄×D₃	1	1	yes	characteristic
164	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
165	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
168	C₃×Dic₆	—	6	2	no	—
169	C₃×Dic₆	—	6	2	no	—
170	#627	—	2	2	no	—
171	C₃²×C₈	—	2	1	no	—
172	C₃²×C₈	—	2	2	no	—
173	C₃²×C₈	—	2	1	no	—
174	C₃²×C₈	—	2	1	no	—
175	C₃²×C₈	—	3	2	no	—
176	C₃²×C₈	—	4	1	no	—
177	C₃²×C₈	—	4	1	no	—
178	C₃²×C₈	—	4	2	no	—
179	C₃²×C₈	—	6	1	no	—
180	C₃⋊(C₃⋊C₈)	—	2	1	no	—
181	C₃×C₃⋊C₈	—	2	1	no	—
182	C₃×C₃⋊C₈	—	2	1	no	—
183	C₃×C₃⋊C₈	—	2	2	no	—
184	C₃×C₃⋊C₈	—	4	1	no	—
185	C₃×C₃⋊C₈	—	6	1	no	—
186	C₃×C₃⋊C₈	—	6	1	no	—
187	C₃×C₃⋊C₈	—	12	1	no	—
188	C₃×C₃⋊C₈	Dic₆	1	2	yes	complemented
189	C₃×C₃⋊C₈	C₃×Q₈	1	2	yes	complemented
190	#446	—	9	1	no	Sylow
191	C₂×C₃³	C₄×Q₈	1	1	yes	characteristic
192	C₂×C₃³	C₂×M₁₆	1	1	yes	characteristic
193	C₂×C₃³	#131	1	1	yes	characteristic
194	C₂×C₃×Q₈	—	9	1	no	—
195	C₂×Dic₆	—	3	1	no	—
196	C₂×Dic₆	—	3	1	no	—
197	C₂×C₃×C₈	—	2	1	no	—
198	C₂×C₃×C₈	—	2	1	no	—
199	C₂×C₃×C₈	—	2	1	no	—
200	C₂×C₃×C₈	—	3	1	no	—
201	C₂×C₃×C₈	—	3	1	no	—
202	C₂×C₃×C₈	—	3	1	no	—
203	C₂×C₃×C₈	—	3	1	no	—
204	C₂×C₃×C₈	—	4	1	no	—
205	C₂×C₃×C₈	—	6	1	no	—
206	C₂×C₃×C₈	—	6	1	no	—
207	C₂×C₃×C₈	—	9	1	no	—
208	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
210	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
211	C₃×C₄⋊C₄	—	9	1	no	—
212	C₃×C₄⋊C₄	—	9	1	no	—
213	C₃×C₄⋊C₄	—	9	1	no	—
214	C₃×C₄²	—	3	1	no	—
215	C₃×C₄²	—	3	1	no	—
216	C₃×C₄²	—	3	1	no	—
217	C₃×C₄²	—	3	1	no	—
218	C₃×C₄²	—	6	1	no	—
219	C₃×C₄²	—	6	1	no	—
220	C₃×C₄²	—	9	1	no	—
221	C₄⋊Dic₃	—	3	1	no	—
222	C₄⋊Dic₃	—	3	1	no	—
223	Dic₃⋊C₄	—	3	1	no	—
224	Dic₃⋊C₄	—	3	1	no	—
225	Dic₃⋊C₄	—	3	1	no	—
226	Dic₃⋊C₄	—	3	1	no	—
227	C₄×Dic₃	—	3	1	no	—
228	C₄×Dic₃	—	3	1	no	—
229	C₄×Dic₃	—	6	1	no	—
230	C₄×Dic₃	C₂×C₃×D₃	1	1	yes	characteristic
231	C₄×Dic₃	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂×C₃⋊C₈	—	3	1	no	—
233	C₂×C₃⋊C₈	—	3	1	no	—
234	C₂×C₃⋊C₈	—	6	1	no	—
235	C₂×C₃⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
236	C₂×C₃⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
237	C₂²×C₃²	—	2	1	no	—
238	C₂²×C₃²	—	2	1	no	—
239	C₂²×C₃²	—	2	1	no	—
240	C₂²×C₃²	—	4	1	no	—
241	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
242	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
243	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
244	C₃²×C₄	—	2	1	no	—
245	C₃²×C₄	—	2	1	no	—
246	C₃²×C₄	—	2	1	no	—
247	C₃²×C₄	—	2	1	no	—
248	C₃²×C₄	—	2	1	no	—
249	C₃²×C₄	—	2	1	no	—
250	C₃²×C₄	—	3	2	no	—
251	C₃²×C₄	—	4	1	no	—
252	C₃²×C₄	—	4	1	no	—
253	C₃²×C₄	—	6	1	no	—
254	C₃²×C₄	—	6	1	no	—
255	C₃²×C₄	—	6	1	no	—
256	C₃²×C₄	C₂×Dic₆	1	1	yes	characteristic
257	C₃²×C₄	#235	1	1	yes	characteristic
258	C₃²×C₄	#237	1	1	yes	characteristic
259	C₃²×C₄	D₃×Q₈	1	1	yes	characteristic
260	C₃²×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
261	C₃²×C₄	C₃×#41	1	1	yes	characteristic
262	C₃⋊Dic₃	—	2	1	no	—
263	C₃⋊Dic₃	—	2	1	no	—
264	C₃×Dic₃	—	2	2	no	—
265	C₃×Dic₃	—	2	2	no	—
266	C₃×Dic₃	—	2	1	no	—
267	C₃×Dic₃	—	2	1	no	—
268	C₃×Dic₃	—	2	1	no	—
269	C₃×Dic₃	—	2	1	no	—
270	C₃×Dic₃	—	2	1	no	—
271	C₃×Dic₃	—	2	1	no	—
272	C₃×Dic₃	—	2	2	no	—
273	C₃×Dic₃	—	4	1	no	—
274	C₃×Dic₃	—	6	2	no	—
275	C₃×Dic₃	—	6	1	no	—
276	C₃×Dic₃	—	6	1	no	—
277	C₃×Dic₃	—	6	1	no	—
278	C₃×Dic₃	—	6	1	no	—
279	C₃×Dic₃	—	12	1	no	—
280	C₃×Dic₃	ΓL(1,𝔽₂₅)	1	2	yes	—
281	C₃×Dic₃	C₃×M₁₆	1	2	yes	—
282	C₄×Q₈	—	9	1	no	—
283	C₄⋊C₈	—	3	1	no	—
284	C₄⋊C₈	—	9	1	no	—
285	C₄⋊C₈	—	9	1	no	—
286	#97	—	9	1	no	—
287	#97	—	9	1	no	—
288	C₄×C₈	—	3	1	no	—
289	C₃³	#446	1	1	yes	characteristic, complemented, Sylow
290	C₃×Q₈	—	18	2	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	3	1	no	—
295	C₂×C₃×C₄	—	3	1	no	—
296	C₂×C₃×C₄	—	3	1	no	—
297	C₂×C₃×C₄	—	3	1	no	—
298	C₂×C₃×C₄	—	3	1	no	—
299	C₂×C₃×C₄	—	3	1	no	—
300	C₂×C₃×C₄	—	3	1	no	—
301	C₂×C₃×C₄	—	3	1	no	—
302	C₂×C₃×C₄	—	4	1	no	—
303	C₂×C₃×C₄	—	6	1	no	—
304	C₂×C₃×C₄	—	6	1	no	—
305	C₂×C₃×C₄	—	6	1	no	—
306	C₂×C₃×C₄	—	6	1	no	—
307	C₂×C₃×C₄	—	9	1	no	—
308	C₂×C₃×C₄	—	9	1	no	—
309	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
310	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
312	C₂×Dic₃	—	3	1	no	—
313	C₂×Dic₃	—	3	1	no	—
314	C₂×Dic₃	—	3	1	no	—
315	C₂×Dic₃	—	3	1	no	—
316	C₂×Dic₃	—	6	1	no	—
317	C₂×Dic₃	—	6	1	no	—
318	C₂×Dic₃	C₃×C₄×D₃	1	1	yes	characteristic
319	C₂×Dic₃	C₃×C₄×D₃	1	1	yes	characteristic
320	C₂×Dic₃	C₃×C₄×D₃	1	1	yes	characteristic
321	C₂×Dic₃	C₃×C₄×D₃	1	1	yes	characteristic
322	Dic₆	—	6	2	no	—
323	Dic₆	—	6	2	no	—
324	C₃×C₈	—	2	2	no	—
325	C₃×C₈	—	2	1	no	—
326	C₃×C₈	—	2	1	no	—
327	C₃×C₈	—	2	1	no	—
328	C₃×C₈	—	3	2	no	—
329	C₃×C₈	—	3	2	no	—
330	C₃×C₈	—	4	1	no	—
331	C₃×C₈	—	4	1	no	—
332	C₃×C₈	—	4	2	no	—
333	C₃×C₈	—	6	2	no	—
334	C₃×C₈	—	6	1	no	—
335	C₃×C₈	—	6	1	no	—
336	C₃×C₈	—	12	1	no	—
337	C₃×C₈	—	18	1	no	—
338	C₃⋊C₈	—	2	1	no	—
339	C₃⋊C₈	—	6	1	no	—
340	C₃⋊C₈	—	6	1	no	—
341	C₃⋊C₈	—	12	1	no	—
342	C₃⋊C₈	C₃×Dic₆	1	2	yes	complemented
343	C₂×C₃²	—	2	1	no	—
344	C₂×C₃²	—	2	1	no	—
345	C₂×C₃²	—	2	1	no	—
346	C₂×C₃²	—	2	1	no	—
347	C₂×C₃²	—	2	1	no	—
348	C₂×C₃²	—	2	1	no	—
349	C₂×C₃²	—	2	1	no	—
350	C₂×C₃²	—	2	1	no	—
351	C₂×C₃²	—	2	1	no	—
352	C₂×C₃²	—	4	1	no	—
353	C₂×C₃²	—	4	1	no	—
354	C₂×C₃²	—	4	1	no	—
355	C₂×C₃²	C₄×Dic₆	1	1	yes	characteristic
356	C₂×C₃²	#887	1	1	yes	characteristic
357	C₂×C₃²	C₂×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
358	C₂×C₃²	#901	1	1	yes	characteristic
359	C₂×C₃²	#901	1	1	yes	characteristic
360	C₂×C₃²	D₃×M₁₆	1	1	yes	characteristic
361	C₂×C₃²	C₃×C₄×Q₈	1	1	yes	characteristic
362	C₂×C₃²	C₂×C₃×M₁₆	1	1	yes	characteristic
363	C₂×C₃²	C₃×#131	1	1	yes	characteristic
364	C₂×Q₈	—	9	1	no	—
365	C₂×C₈	—	3	1	no	—
366	C₂×C₈	—	3	1	no	—
367	C₂×C₈	—	9	1	no	—
368	C₂×C₈	C₃×D₃²	1	1	yes	characteristic
369	C₄⋊C₄	—	9	1	no	—
370	C₄⋊C₄	—	9	1	no	—
371	C₄⋊C₄	—	9	1	no	—
372	C₄²	—	3	1	no	—
373	C₄²	—	3	1	no	—
374	C₄²	—	9	1	no	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	2	1	no	—
378	C₂²×C₃	—	4	1	no	—
379	C₂²×C₃	C₄×D₃²	1	1	yes	characteristic
380	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
381	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	3	2	no	—
389	C₃×C₄	—	3	2	no	—
390	C₃×C₄	—	4	1	no	—
391	C₃×C₄	—	4	1	no	—
392	C₃×C₄	—	6	2	no	—
393	C₃×C₄	—	6	2	no	—
394	C₃×C₄	—	6	2	no	—
395	C₃×C₄	—	6	1	no	—
396	C₃×C₄	—	6	1	no	—
397	C₃×C₄	—	6	1	no	—
398	C₃×C₄	—	6	1	no	—
399	C₃×C₄	—	6	1	no	—
400	C₃×C₄	—	6	1	no	—
401	C₃×C₄	—	12	1	no	—
402	C₃×C₄	—	18	1	no	—
403	C₃×C₄	—	18	1	no	—
404	C₃×C₄	D₃×Dic₆	1	1	yes	characteristic
405	C₃×C₄	#3804	1	1	yes	characteristic
406	C₃×C₄	C₂×C₃×Dic₆	1	1	yes	characteristic
407	C₃×C₄	C₃×#235	1	1	yes	characteristic
408	C₃×C₄	C₃×#237	1	1	yes	characteristic
409	C₃×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
410	Dic₃	—	2	1	no	—
411	Dic₃	—	2	1	no	—
412	Dic₃	—	2	1	no	—
413	Dic₃	—	6	2	no	—
414	Dic₃	—	6	1	no	—
415	Dic₃	—	6	1	no	—
416	Dic₃	—	6	1	no	—
417	Dic₃	—	6	1	no	—
418	Dic₃	—	12	1	no	—
419	Dic₃	C₃×ΓL(1,𝔽₂₅)	1	2	yes	—
420	C₃²	—	2	1	no	—
421	C₃²	—	2	1	no	—
422	C₃²	—	2	1	no	—
423	C₃²	—	4	1	no	—
424	C₃²	#4679	1	1	yes	characteristic, complemented
425	C₃²	#4828	1	1	yes	characteristic, complemented
426	C₃²	C₃×#446	1	1	yes	characteristic, complemented
427	Q₈	—	18	2	no	—
428	C₂×C₄	—	3	1	no	—
429	C₂×C₄	—	3	1	no	—
430	C₂×C₄	—	3	1	no	—
431	C₂×C₄	—	3	1	no	—
432	C₂×C₄	—	9	1	no	—
433	C₂×C₄	—	9	1	no	—
434	C₂×C₄	C₂×C₃×D₃²	1	1	yes	characteristic
435	C₈	—	2	1	no	—
436	C₈	—	3	2	no	—
437	C₈	—	6	1	no	—
438	C₈	—	18	1	no	—
439	C₂×C₃	—	2	1	no	—
440	C₂×C₃	—	2	1	no	—
441	C₂×C₃	—	2	1	no	—
442	C₂×C₃	—	2	1	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	2	1	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	2	1	no	—
448	C₂×C₃	—	4	1	no	—
449	C₂×C₃	—	4	1	no	—
450	C₂×C₃	—	4	1	no	—
451	C₂×C₃	D₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
452	C₂×C₃	#63803	1	1	yes	characteristic
453	C₂×C₃	#63837	1	1	yes	characteristic
454	C₂×C₃	C₃×C₄×Dic₆	1	1	yes	characteristic
455	C₂×C₃	C₃×#887	1	1	yes	characteristic
456	C₂×C₃	C₂×C₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
457	C₂×C₃	C₃×#901	1	1	yes	characteristic
458	C₂×C₃	C₃×#901	1	1	yes	characteristic
459	C₂×C₃	C₃×D₃×M₁₆	1	1	yes	characteristic
460	C₂²	C₃×C₄×D₃²	1	1	yes	characteristic
461	C₄	—	3	2	no	—
462	C₄	—	6	1	no	—
463	C₄	—	6	1	no	—
464	C₄	—	6	1	no	—
465	C₄	—	18	1	no	—
466	C₄	—	18	1	no	—
467	C₄	C₃×D₃×Dic₆	1	1	yes	characteristic
468	C₄	C₃×#3804	1	1	yes	characteristic
469	C₃	—	2	1	no	—
470	C₃	—	2	1	no	—
471	C₃	—	2	1	no	—
472	C₃	—	4	1	no	—
473	C₃	#10590785	1	1	yes	characteristic, direct product factor
474	C₃	C₃×#4679	1	1	yes	characteristic, complemented
475	C₃	C₃×#4828	1	1	yes	characteristic, complemented
476	C₂	C₃×D₃×ΓL(1,𝔽₂₅)	1	1	yes	characteristic
477	C₂	C₃×#63803	1	1	yes	characteristic
478	C₂	C₃×#63837	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₃²
commutator	C₂²×C₃²	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃²
Fitting	C₂×C₃³×C₈	C₂²
socle, prime radical	C₂²×C₃³	C₂²×C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₈	D₃²
hypocenter	C₃²	C₃×#446
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
10. #10590785	C₃	direct (N × H)
57. C₃²×C₃⋊C₈	Q₈	semidirect
188. C₃×C₃⋊C₈	Dic₆	semidirect
189. C₃×C₃⋊C₈	C₃×Q₈	semidirect
289. C₃³	#446	semidirect
342. C₃⋊C₈	C₃×Dic₆	semidirect
424. C₃²	#4679	semidirect
425. C₃²	#4828	semidirect
426. C₃²	C₃×#446	semidirect
473. C₃	#10590785	direct (N × H)
474. C₃	C₃×#4679	semidirect
475. C₃	C₃×#4828	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×#627	2
C₃×#63641	2
C₃²×Dic₃⋊C₈	2
C₃²×C₈×Dic₃	2
C₃×Dic₃⋊(C₃⋊C₈)	2
C₃×#63555	2
C₃×#63554	2
C₃×#4828	3
C₃×#4679	3
#10590785	3

Subgroups — C3×#10590785 #13157774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10590785 #13157774