Subgroups — C₃×#10590844 #13157816

Order 1728.

746 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63916	C₂	1	2	yes	maximal, complemented
4	C₃²×#818	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63562	C₂	1	2	yes	maximal, complemented
6	C₃×#5157	—	3	1	no	maximal
7	C₃×#4883	—	3	1	no	maximal
8	#10590844	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
11	C₂×C₃×#626	—	2	2	no	—
12	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₃×C₈×C₃⋊D₃	—	2	2	no	—
15	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
16	C₃²×D₂₄	—	2	2	no	—
17	C₃×(C₂×D₃)⋊Dic₃	—	2	2	no	—
18	C₂×C₃²×D₈	—	3	1	no	—
19	C₂×C₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
20	C₃×#938	—	3	2	no	—
21	C₂×C₃×D₂₄	—	2	1	no	—
22	C₂×C₃×D₂₄	D₃	1	1	yes	characteristic, complemented
23	C₂×C₃×D₂₄	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₃×D₃×C₈	—	3	1	no	—
25	C₂×C₃×D₃×C₈	—	3	1	no	—
26	C₂×C₃×D₃×C₈	—	6	1	no	—
27	C₃×#895	—	3	2	no	—
28	#63916	C₂×C₃	1	2	yes	complemented
29	C₃²×#107	—	3	1	no	—
30	C₃×#832	—	3	2	no	—
31	C₃×#818	—	2	1	no	—
32	C₃×#818	D₃	1	1	yes	characteristic, complemented
33	C₃×#818	C₂×C₃	1	1	yes	characteristic, complemented
34	C₃×#809	—	3	2	no	—
35	#63562	C₂×C₃	1	2	yes	complemented
36	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
37	C₂²×C₃²×D₃	—	2	2	no	—
38	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
39	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
40	C₃×C₄×C₃⋊D₃	—	2	1	no	—
41	C₃×C₄×C₃⋊D₃	—	2	1	no	—
42	C₂×C₃²×Dic₃	—	2	2	no	—
43	C₃²×D₁₂	—	2	2	no	—
44	C₃²×D₁₂	—	2	2	no	—
45	C₃×#626	—	4	4	no	—
46	C₃³×C₈	D₄	1	2	yes	complemented
47	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
48	C₃×#466	—	9	1	no	—
49	#5157	—	3	1	no	—
50	#4883	—	3	1	no	—
51	C₂×C₃²×D₄	—	3	2	no	—
52	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
53	C₂×C₃×#67	—	6	2	no	—
54	C₂×C₃×D₁₂	—	2	2	no	—
55	C₂×C₃×D₁₂	—	6	2	no	—
56	C₂×C₃×D₁₂	C₂×D₃	1	2	yes	—
57	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
58	C₂×C₃×C₄×D₃	—	3	1	no	—
59	C₂×C₃×C₄×D₃	—	3	1	no	—
60	C₂×C₃×C₄×D₃	—	6	1	no	—
61	C₂×#626	—	2	2	no	—
62	C₃²×D₈	—	6	2	no	—
63	C₂×C₃²×C₈	—	2	1	no	—
64	C₂×C₃²×C₈	—	2	1	no	—
65	C₂×C₃²×C₈	—	2	1	no	—
66	C₂×C₃²×C₈	—	4	1	no	—
67	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
68	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
69	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
70	C₃²×C₄⋊C₄	—	3	2	no	—
71	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
72	C₈×C₃⋊D₃	—	2	2	no	—
73	C₃×#217	—	6	2	no	—
74	C₃×(C₂×D₃)⋊C₄	—	6	2	no	—
75	C₃×C₄⋊Dic₃	—	2	2	no	—
76	C₃×C₄⋊Dic₃	C₂×D₃	1	2	yes	—
77	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
78	C₂×C₃×C₃⋊C₈	—	3	1	no	—
79	C₂×C₃×C₃⋊C₈	—	3	1	no	—
80	C₂×C₃×C₃⋊C₈	—	6	1	no	—
81	C₃×D₂₄	—	2	4	no	—
82	C₃×D₂₄	—	2	2	no	—
83	C₃×D₂₄	—	2	2	no	—
84	C₃×D₃×C₈	—	6	4	no	—
85	C₃×D₃×C₈	—	6	2	no	—
86	C₃×D₃×C₈	—	6	2	no	—
87	(C₂×D₃)⋊Dic₃	—	2	2	no	—
88	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₃⋊D₃	—	2	1	no	—
90	C₂×C₃×C₃⋊D₃	—	2	1	no	—
91	C₂×C₃×C₃⋊D₃	D₈	1	2	yes	complemented
92	C₂×C₃²×D₃	—	4	2	no	—
93	C₂×C₃²×D₃	—	4	2	no	—
94	C₂×C₃²×D₃	—	4	2	no	—
95	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
96	C₃³×C₄	#41	1	1	yes	characteristic
97	C₃×C₃⋊Dic₃	—	2	1	no	—
98	C₃²×Dic₃	—	4	2	no	—
99	C₂×C₃×D₈	—	3	1	no	—
100	C₂×C₃×D₈	—	3	1	no	—
101	C₂×C₃×D₈	—	6	1	no	—
102	C₂²×C₃×C₈	—	9	1	no	—
103	C₃×#121	—	9	2	no	—
104	#938	—	3	2	no	—
105	C₂×D₂₄	C₃×D₃	1	1	yes	characteristic, complemented
106	C₂×D₃×C₈	—	3	1	no	—
107	C₂×D₃×C₈	—	3	1	no	—
108	C₂×D₃×C₈	—	6	1	no	—
109	#895	—	3	2	no	—
110	C₃×#107	—	3	1	no	—
111	C₃×#107	—	3	1	no	—
112	C₃×#107	—	6	1	no	—
113	C₃×#102	—	9	2	no	—
114	#832	—	3	2	no	—
115	#818	C₃×D₃	1	1	yes	characteristic, complemented
116	#809	—	3	2	no	—
117	C₂³×C₃²	—	6	2	no	—
118	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
119	C₂²×C₃×D₃	—	2	2	no	—
120	C₂²×C₃×D₃	—	2	2	no	—
121	C₂²×C₃×D₃	—	3	1	no	—
122	C₂²×C₃×D₃	—	3	1	no	—
123	C₂²×C₃×D₃	—	4	2	no	—
124	C₂²×C₃×D₃	—	6	1	no	—
125	C₃²×D₄	—	6	2	no	—
126	C₃²×D₄	—	6	2	no	—
127	C₂×C₃²×C₄	—	2	1	no	—
128	C₂×C₃²×C₄	—	2	1	no	—
129	C₂×C₃²×C₄	—	2	1	no	—
130	C₂×C₃²×C₄	—	4	1	no	—
131	C₂×C₃²×C₄	—	6	2	no	—
132	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
133	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
134	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
135	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
136	C₄×C₃⋊D₃	—	2	1	no	—
137	C₄×C₃⋊D₃	—	2	1	no	—
138	C₃×#67	—	12	4	no	—
139	C₂×C₃×Dic₃	—	2	2	no	—
140	C₂×C₃×Dic₃	—	2	2	no	—
141	C₂×C₃×Dic₃	—	3	1	no	—
142	C₂×C₃×Dic₃	—	3	1	no	—
143	C₂×C₃×Dic₃	—	4	2	no	—
144	C₂×C₃×Dic₃	—	6	1	no	—
145	C₃×D₁₂	—	2	4	no	—
146	C₃×D₁₂	—	2	2	no	—
147	C₃×D₁₂	—	2	2	no	—
148	C₃×D₁₂	—	2	2	no	—
149	C₃×D₁₂	—	2	2	no	—
150	C₃×D₁₂	—	4	2	no	—
151	C₃×D₁₂	—	12	4	no	—
152	C₃×C₄×D₃	—	6	2	no	—
153	C₃×C₄×D₃	—	6	2	no	—
154	C₃×C₄×D₃	—	6	1	no	—
155	C₃×C₄×D₃	—	6	1	no	—
156	C₃×C₄×D₃	—	6	1	no	—
157	C₃×C₄×D₃	—	6	1	no	—
158	#626	—	4	4	no	—
159	C₃²×C₈	—	2	2	no	—
160	C₃²×C₈	—	2	2	no	—
161	C₃²×C₈	—	2	2	no	—
162	C₃²×C₈	—	4	2	no	—
163	C₃²×C₈	D₁₂	1	2	yes	complemented
164	C₃²×C₈	#67	1	2	yes	complemented
165	C₃²×C₈	C₃×D₄	1	2	yes	complemented
166	C₃⋊(C₃⋊C₈)	—	2	1	no	—
167	C₃×C₃⋊C₈	—	6	2	no	—
168	C₃×C₃⋊C₈	—	6	1	no	—
169	C₃×C₃⋊C₈	—	6	1	no	—
170	#466	—	9	1	no	Sylow
171	C₂×C₃³	#121	1	1	yes	characteristic
172	C₂×C₃³	C₂×D₈	1	1	yes	characteristic
173	C₂×C₃³	#135	1	1	yes	characteristic
174	C₃×C₃⋊D₃	—	2	2	no	—
175	C₃²×D₃	—	8	2	no	—
176	C₂×C₃×D₄	—	3	2	no	—
177	C₂×C₃×D₄	—	3	2	no	—
178	C₂×C₃×D₄	—	6	2	no	—
179	C₂×C₃×D₄	—	18	2	no	—
180	C₂²×C₃×C₄	—	9	1	no	—
181	C₂×#67	—	6	2	no	—
182	C₂×D₁₂	—	6	2	no	—
183	C₂×D₁₂	C₂×C₃×D₃	1	2	yes	—
184	C₂×C₄×D₃	—	3	1	no	—
185	C₂×C₄×D₃	—	3	1	no	—
186	C₂×C₄×D₃	—	6	1	no	—
187	C₃×D₈	—	6	4	no	—
188	C₃×D₈	—	6	2	no	—
189	C₃×D₈	—	6	2	no	—
190	C₂×C₃×C₈	—	2	1	no	—
191	C₂×C₃×C₈	—	2	1	no	—
192	C₂×C₃×C₈	—	2	1	no	—
193	C₂×C₃×C₈	—	4	1	no	—
194	C₂×C₃×C₈	—	9	1	no	—
195	C₂×C₃×C₈	—	18	2	no	—
196	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
197	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
198	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
199	C₃×C₄⋊C₄	—	3	2	no	—
200	C₃×C₄⋊C₄	—	3	2	no	—
201	C₃×C₄⋊C₄	—	6	2	no	—
202	C₃×C₂²⋊C₄	—	18	2	no	—
203	#217	—	6	2	no	—
204	(C₂×D₃)⋊C₄	—	6	2	no	—
205	C₄⋊Dic₃	C₂×C₃×D₃	1	2	yes	—
206	C₂×C₃⋊C₈	—	3	1	no	—
207	C₂×C₃⋊C₈	—	3	1	no	—
208	C₂×C₃⋊C₈	—	6	1	no	—
209	D₂₄	—	2	2	no	—
210	D₃×C₈	—	6	4	no	—
211	D₃×C₈	—	6	2	no	—
212	D₃×C₈	—	6	2	no	—
213	C₂²×C₃²	—	2	1	no	—
214	C₂²×C₃²	—	2	1	no	—
215	C₂²×C₃²	—	2	1	no	—
216	C₂²×C₃²	—	4	1	no	—
217	C₂²×C₃²	—	12	2	no	—
218	C₂²×C₃²	—	12	2	no	—
219	C₂²×C₃²	—	12	2	no	—
220	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
221	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
222	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
223	C₂×C₃⋊D₃	—	2	1	no	—
224	C₂×C₃⋊D₃	—	2	1	no	—
225	C₂×C₃⋊D₃	C₃×D₈	1	2	yes	complemented
226	C₂×C₃×D₃	—	3	2	no	—
227	C₂×C₃×D₃	—	3	2	no	—
228	C₂×C₃×D₃	—	4	4	no	—
229	C₂×C₃×D₃	—	4	2	no	—
230	C₂×C₃×D₃	—	4	2	no	—
231	C₂×C₃×D₃	—	4	2	no	—
232	C₂×C₃×D₃	—	4	2	no	—
233	C₂×C₃×D₃	—	4	2	no	—
234	C₂×C₃×D₃	—	4	2	no	—
235	C₂×C₃×D₃	—	6	2	no	—
236	C₂×C₃×D₃	—	6	2	no	—
237	C₂×C₃×D₃	—	6	2	no	—
238	C₂×C₃×D₃	—	6	1	no	—
239	C₂×C₃×D₃	—	6	1	no	—
240	C₂×C₃×D₃	—	6	1	no	—
241	C₂×C₃×D₃	—	6	1	no	—
242	C₂×C₃×D₃	—	8	2	no	—
243	C₂×C₃×D₃	—	8	2	no	—
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	—	4	1	no	—
251	C₃²×C₄	—	4	1	no	—
252	C₃²×C₄	—	12	2	no	—
253	C₃²×C₄	C₂×D₁₂	1	1	yes	characteristic
254	C₃²×C₄	#237	1	1	yes	characteristic
255	C₃²×C₄	#239	1	1	yes	characteristic
256	C₃²×C₄	C₂×#67	1	1	yes	characteristic
257	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
258	C₃²×C₄	C₃×#41	1	1	yes	characteristic
259	C₃⋊Dic₃	—	2	1	no	—
260	C₃×Dic₃	—	4	2	no	—
261	C₃×Dic₃	—	4	2	no	—
262	C₃×Dic₃	—	6	2	no	—
263	C₃×Dic₃	—	6	1	no	—
264	C₃×Dic₃	—	6	1	no	—
265	C₃×Dic₃	—	8	2	no	—
266	C₂×D₈	—	3	1	no	—
267	C₂²×C₈	—	9	1	no	—
268	#121	—	9	2	no	—
269	#107	—	3	1	no	—
270	#102	—	9	2	no	—
271	C₃³	#466	1	1	yes	characteristic, complemented, Sylow
272	C₂³×C₃	—	6	2	no	—
273	C₂³×C₃	—	6	2	no	—
274	C₂³×C₃	—	9	1	no	—
275	C₂³×C₃	—	12	2	no	—
276	C₂²×D₃	—	2	2	no	—
277	C₂²×D₃	—	3	1	no	—
278	C₂²×D₃	—	3	1	no	—
279	C₂²×D₃	—	6	1	no	—
280	C₃×D₄	—	6	4	no	—
281	C₃×D₄	—	6	2	no	—
282	C₃×D₄	—	6	2	no	—
283	C₃×D₄	—	6	2	no	—
284	C₃×D₄	—	6	2	no	—
285	C₃×D₄	—	12	2	no	—
286	C₃×D₄	—	36	4	no	—
287	C₂×C₃×C₄	—	2	1	no	—
288	C₂×C₃×C₄	—	2	1	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	4	1	no	—
291	C₂×C₃×C₄	—	6	2	no	—
292	C₂×C₃×C₄	—	6	2	no	—
293	C₂×C₃×C₄	—	9	1	no	—
294	C₂×C₃×C₄	—	12	2	no	—
295	C₂×C₃×C₄	—	18	1	no	—
296	C₂×C₃×C₄	—	18	1	no	—
297	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
300	#67	—	12	4	no	—
301	C₂×Dic₃	—	2	2	no	—
302	C₂×Dic₃	—	3	1	no	—
303	C₂×Dic₃	—	3	1	no	—
304	C₂×Dic₃	—	6	1	no	—
305	D₁₂	—	2	2	no	—
306	D₁₂	—	2	2	no	—
307	D₁₂	—	12	4	no	—
308	C₄×D₃	—	6	2	no	—
309	C₄×D₃	—	6	2	no	—
310	C₄×D₃	—	6	1	no	—
311	C₄×D₃	—	6	1	no	—
312	C₄×D₃	—	6	1	no	—
313	C₄×D₃	—	6	1	no	—
314	C₃×C₈	—	2	2	no	—
315	C₃×C₈	—	2	2	no	—
316	C₃×C₈	—	2	2	no	—
317	C₃×C₈	—	4	2	no	—
318	C₃×C₈	—	18	1	no	—
319	C₃×C₈	#626	1	2	yes	complemented
320	C₃×C₈	C₃×D₁₂	1	2	yes	complemented
321	C₃×C₈	C₃×#67	1	2	yes	complemented
322	C₃⋊C₈	—	6	2	no	—
323	C₃⋊C₈	—	6	1	no	—
324	C₃⋊C₈	—	6	1	no	—
325	C₂×C₃²	—	2	1	no	—
326	C₂×C₃²	—	2	1	no	—
327	C₂×C₃²	—	2	1	no	—
328	C₂×C₃²	—	2	1	no	—
329	C₂×C₃²	—	2	1	no	—
330	C₂×C₃²	—	2	1	no	—
331	C₂×C₃²	—	2	1	no	—
332	C₂×C₃²	—	2	1	no	—
333	C₂×C₃²	—	2	1	no	—
334	C₂×C₃²	—	4	1	no	—
335	C₂×C₃²	—	4	1	no	—
336	C₂×C₃²	—	4	1	no	—
337	C₂×C₃²	—	24	2	no	—
338	C₂×C₃²	#895	1	1	yes	characteristic
339	C₂×C₃²	D₃×D₈	1	1	yes	characteristic
340	C₂×C₃²	D₃×D₈	1	1	yes	characteristic
341	C₂×C₃²	#912	1	1	yes	characteristic
342	C₂×C₃²	#919	1	1	yes	characteristic
343	C₂×C₃²	#938	1	1	yes	characteristic
344	C₂×C₃²	C₃×#121	1	1	yes	characteristic
345	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
346	C₂×C₃²	C₃×#135	1	1	yes	characteristic
347	C₃⋊D₃	—	2	2	no	—
348	C₃×D₃	—	6	4	no	—
349	C₃×D₃	—	6	2	no	—
350	C₃×D₃	—	6	2	no	—
351	C₃×D₃	—	8	4	no	—
352	C₃×D₃	—	8	2	no	—
353	C₃×D₃	—	8	2	no	—
354	C₂×D₄	—	3	2	no	—
355	C₂×D₄	—	18	2	no	—
356	C₂²×C₄	—	9	1	no	—
357	D₈	—	6	2	no	—
358	C₂×C₈	—	9	1	no	—
359	C₂×C₈	—	18	2	no	—
360	C₂×C₈	C₃×D₃²	1	1	yes	characteristic
361	C₄⋊C₄	—	3	2	no	—
362	C₂²⋊C₄	—	18	2	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	4	1	no	—
367	C₂²×C₃	—	9	2	no	—
368	C₂²×C₃	—	12	4	no	—
369	C₂²×C₃	—	12	2	no	—
370	C₂²×C₃	—	12	2	no	—
371	C₂²×C₃	—	12	2	no	—
372	C₂²×C₃	—	12	2	no	—
373	C₂²×C₃	—	12	2	no	—
374	C₂²×C₃	—	12	2	no	—
375	C₂²×C₃	—	18	1	no	—
376	C₂²×C₃	—	18	1	no	—
377	C₂²×C₃	—	24	2	no	—
378	C₂²×C₃	—	24	2	no	—
379	C₂²×C₃	#3802	1	1	yes	characteristic
380	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
381	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
382	C₂×D₃	—	3	2	no	—
383	C₂×D₃	—	3	2	no	—
384	C₂×D₃	—	4	2	no	—
385	C₂×D₃	—	4	2	no	—
386	C₂×D₃	—	4	2	no	—
387	C₂×D₃	—	6	2	no	—
388	C₂×D₃	—	6	2	no	—
389	C₂×D₃	—	6	2	no	—
390	C₂×D₃	—	6	1	no	—
391	C₂×D₃	—	6	1	no	—
392	C₂×D₃	—	6	1	no	—
393	C₂×D₃	—	6	1	no	—
394	C₃×C₄	—	2	1	no	—
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	2	1	no	—
397	C₃×C₄	—	2	1	no	—
398	C₃×C₄	—	2	1	no	—
399	C₃×C₄	—	2	1	no	—
400	C₃×C₄	—	4	1	no	—
401	C₃×C₄	—	4	1	no	—
402	C₃×C₄	—	12	2	no	—
403	C₃×C₄	—	12	2	no	—
404	C₃×C₄	—	18	1	no	—
405	C₃×C₄	—	24	2	no	—
406	C₃×C₄	#3796	1	1	yes	characteristic
407	C₃×C₄	C₂×#626	1	1	yes	characteristic
408	C₃×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
409	C₃×C₄	C₃×#237	1	1	yes	characteristic
410	C₃×C₄	C₃×#239	1	1	yes	characteristic
411	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
412	Dic₃	—	4	2	no	—
413	Dic₃	—	6	2	no	—
414	Dic₃	—	6	1	no	—
415	Dic₃	—	6	1	no	—
416	C₃²	—	2	1	no	—
417	C₃²	—	2	1	no	—
418	C₃²	—	2	1	no	—
419	C₃²	—	4	1	no	—
420	C₃²	#4883	1	1	yes	characteristic, complemented
421	C₃²	#5157	1	1	yes	characteristic, complemented
422	C₃²	C₃×#466	1	1	yes	characteristic, complemented
423	C₂³	—	6	2	no	—
424	C₂³	—	9	1	no	—
425	D₄	—	6	2	no	—
426	D₄	—	6	2	no	—
427	D₄	—	36	4	no	—
428	C₂×C₄	—	6	2	no	—
429	C₂×C₄	—	9	1	no	—
430	C₂×C₄	—	18	1	no	—
431	C₂×C₄	—	18	1	no	—
432	C₂×C₄	C₂×C₃×D₃²	1	1	yes	characteristic
433	C₈	—	18	1	no	—
434	C₈	C₃×#626	1	2	yes	complemented
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	1	no	—
438	C₂×C₃	—	2	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	—	4	1	no	—
445	C₂×C₃	—	4	1	no	—
446	C₂×C₃	—	4	1	no	—
447	C₂×C₃	—	18	2	no	—
448	C₂×C₃	—	24	4	no	—
449	C₂×C₃	—	24	2	no	—
450	C₂×C₃	—	24	2	no	—
451	C₂×C₃	#63797	1	1	yes	characteristic
452	C₂×C₃	#63810	1	1	yes	characteristic
453	C₂×C₃	#63916	1	1	yes	characteristic
454	C₂×C₃	C₃×#895	1	1	yes	characteristic
455	C₂×C₃	C₃×D₃×D₈	1	1	yes	characteristic
456	C₂×C₃	C₃×D₃×D₈	1	1	yes	characteristic
457	C₂×C₃	C₃×#912	1	1	yes	characteristic
458	C₂×C₃	C₃×#919	1	1	yes	characteristic
459	C₂×C₃	C₃×#938	1	1	yes	characteristic
460	D₃	—	6	4	no	—
461	D₃	—	6	2	no	—
462	D₃	—	6	2	no	—
463	D₃	—	8	2	no	—
464	C₂²	—	9	2	no	—
465	C₂²	—	12	2	no	—
466	C₂²	—	12	2	no	—
467	C₂²	—	12	2	no	—
468	C₂²	—	18	1	no	—
469	C₂²	—	18	1	no	—
470	C₂²	C₃×#3802	1	1	yes	characteristic
471	C₄	—	12	2	no	—
472	C₄	—	18	1	no	—
473	C₄	C₃×#3796	1	1	yes	characteristic
474	C₄	C₂×C₃×#626	1	1	yes	characteristic
475	C₃	—	2	1	no	—
476	C₃	—	2	1	no	—
477	C₃	—	2	1	no	—
478	C₃	—	4	1	no	—
479	C₃	#10590844	1	1	yes	characteristic, direct product factor
480	C₃	C₃×#4883	1	1	yes	characteristic, complemented
481	C₃	C₃×#5157	1	1	yes	characteristic, complemented
482	C₂	—	18	2	no	—
483	C₂	—	24	2	no	—
484	C₂	C₃×#63797	1	1	yes	characteristic
485	C₂	C₃×#63810	1	1	yes	characteristic
486	C₂	C₃×#63916	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#3802
commutator, cosocle	C₂×C₃²×C₄	C₂³×C₃
Frattini	C₂×C₄	C₂×C₃×D₃²
Fitting	C₂×C₃³×C₈	C₂²
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂×C₃×C₈	D₃²
hypocenter	C₃²	C₃×#466
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₈×C₃⋊D₃	C₂	semidirect
2. C₂×C₃²×D₂₄	C₂	semidirect
3. C₃×#63916	C₂	semidirect
4. C₃²×#818	C₂	semidirect
5. C₃×#63562	C₂	semidirect
8. #10590844	C₃	direct (N × H)
19. C₂×C₈×C₃⋊D₃	C₂×C₃	semidirect
22. C₂×C₃×D₂₄	D₃	semidirect
23. C₂×C₃×D₂₄	C₂×C₃	semidirect
28. #63916	C₂×C₃	semidirect
32. C₃×#818	D₃	semidirect
33. C₃×#818	C₂×C₃	semidirect
35. #63562	C₂×C₃	semidirect
46. C₃³×C₈	D₄	semidirect
91. C₂×C₃×C₃⋊D₃	D₈	semidirect
105. C₂×D₂₄	C₃×D₃	semidirect
115. #818	C₃×D₃	semidirect
163. C₃²×C₈	D₁₂	semidirect
164. C₃²×C₈	#67	semidirect
165. C₃²×C₈	C₃×D₄	semidirect
225. C₂×C₃⋊D₃	C₃×D₈	semidirect
271. C₃³	#466	semidirect
319. C₃×C₈	#626	semidirect
320. C₃×C₈	C₃×D₁₂	semidirect
321. C₃×C₈	C₃×#67	semidirect
420. C₃²	#4883	semidirect
421. C₃²	#5157	semidirect
422. C₃²	C₃×#466	semidirect
434. C₈	C₃×#626	semidirect
479. C₃	#10590844	direct (N × H)
480. C₃	C₃×#4883	semidirect
481. C₃	C₃×#5157	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₈×C₃⋊D₃	2
C₂×C₃²×D₂₄	2
C₃×#63916	2
C₃²×#818	2
C₃×#63562	2
C₃×#5157	3
C₃×#4883	3
#10590844	3

Subgroups — C3×#10590844 #13157816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10590844 #13157816