Subgroups — C₃×#79935 #11895628

Order 1152.

747 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5585	C₂	1	1	yes	maximal, characteristic
2	C₃×#5567	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4851	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4848	C₂	1	1	yes	maximal, characteristic
6	C₃×#4847	C₂	1	2	yes	maximal, complemented
7	C₃×#4845	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4697	C₂	1	2	yes	maximal, complemented
10	C₃×#4694	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×#204	C₂	1	2	yes	maximal, complemented
12	C₃×#3365	—	3	1	no	maximal
13	#79935	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
15	C₃×#947	—	2	1	no	—
16	C₃×#944	—	2	1	no	—
17	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
18	C₂×C₃×#204	C₂²	1	2	yes	—
19	C₃×#894	—	2	2	no	—
20	C₃×#893	—	2	1	no	—
21	C₃×#889	—	2	2	no	—
22	C₃×#887	—	2	1	no	—
23	C₃×#875	C₂²	1	2	yes	—
24	C₃×#874	C₂²	1	1	yes	characteristic
25	C₃×C₄×D₁₂	C₂²	1	2	yes	—
26	C₃×#870	C₂²	1	2	yes	—
27	C₃×#869	C₂²	1	1	yes	characteristic
28	C₃×C₄×Dic₆	C₂²	1	2	yes	—
29	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
30	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
31	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃²×C₄×C₈	C₂²	1	2	yes	—
34	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
35	C₃×#821	C₂²	1	2	yes	—
36	C₃×#821	C₂²	1	2	yes	—
37	C₃×#821	C₂²	1	2	yes	—
38	C₃×#818	C₂²	1	1	yes	characteristic
39	C₃×#817	C₂²	1	2	yes	—
40	C₃×#816	C₂²	1	1	yes	characteristic
41	C₃×#816	C₂²	1	1	yes	characteristic
42	C₃×#816	C₂²	1	2	yes	—
43	C₃×#559	—	3	1	no	—
44	C₃×#557	—	3	1	no	—
45	#5585	C₂×C₃	1	1	yes	characteristic
46	#5567	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#488	—	3	2	no	—
48	C₃×#486	—	3	1	no	—
49	C₃×#478	—	3	2	no	—
50	C₃×#475	—	3	1	no	—
51	C₃×#464	—	3	2	no	—
52	C₃×#460	—	3	1	no	—
53	C₃×C₈×Q₈	—	2	1	no	—
54	C₃×C₈×Q₈	D₃	1	1	yes	characteristic, complemented
55	C₃×C₈×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₄×Q₁₆	—	3	1	no	—
57	C₃×C₄×SD₁₆	—	3	2	no	—
58	#4851	C₂×C₃	1	1	yes	characteristic, complemented
59	#4848	C₂×C₃	1	1	yes	characteristic
60	#4847	C₂×C₃	1	2	yes	complemented
61	#4845	C₂×C₃	1	2	yes	complemented
62	C₄×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
63	#4697	C₂×C₃	1	2	yes	complemented
64	#4694	C₂×C₃	1	1	yes	characteristic
65	C₄×#204	C₂×C₃	1	2	yes	complemented
66	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
67	C₂×C₃×D₁₂	—	2	1	no	—
68	C₂×C₃×D₁₂	—	2	1	no	—
69	C₂×C₃×D₁₂	C₂³	1	2	yes	—
70	C₂×C₃×C₄×D₃	—	2	2	no	—
71	C₂×C₃×Dic₆	—	2	1	no	—
72	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
74	C₂×C₃²×C₈	C₂³	1	2	yes	—
75	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
76	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
77	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	D₄	1	2	yes	—
79	C₃²×C₄²	C₂³	1	1	yes	characteristic
80	C₃²×C₄²	C₂³	1	2	yes	—
81	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
83	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
84	C₃×C₄⋊Dic₃	—	2	1	no	—
85	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
86	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
87	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
88	C₃×Dic₃⋊C₄	—	2	2	no	—
89	C₃×Dic₃⋊C₄	—	2	1	no	—
90	C₃×Dic₃⋊C₄	—	2	2	no	—
91	C₃×Dic₃⋊C₄	—	2	2	no	—
92	C₃×Dic₃⋊C₄	—	2	1	no	—
93	C₃×C₄×Dic₃	—	2	2	no	—
94	C₃×C₄×Dic₃	—	2	1	no	—
95	C₃×C₄×Dic₃	—	2	1	no	—
96	C₃×Dic₁₂	—	2	2	no	—
97	C₃×#204	—	2	4	no	—
98	#3365	—	3	1	no	Sylow
99	C₂×C₃×Q₁₆	—	3	1	no	—
100	C₂×C₃×SD₁₆	—	3	2	no	—
101	C₃×C₄⋊Q₈	—	3	1	no	—
102	C₃×C₄⋊Q₈	—	6	1	no	—
103	C₃×#127	—	3	1	no	—
104	C₃×#125	—	3	2	no	—
105	C₃×#125	—	6	2	no	—
106	C₃×#124	—	3	2	no	—
107	C₃×#124	—	6	1	no	—
108	C₃×#123	—	6	2	no	—
109	C₃×C₄×Q₈	—	2	1	no	—
110	C₃×C₄×Q₈	—	3	1	no	—
111	C₃×C₄×Q₈	—	3	2	no	—
112	C₃×C₄×Q₈	—	3	1	no	—
113	C₃×C₄×Q₈	—	6	1	no	—
114	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
115	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
116	C₃×C₄×D₄	—	3	2	no	—
117	C₃×C₄×D₄	—	6	1	no	—
118	#947	—	2	1	no	—
119	#944	—	2	1	no	—
120	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
121	C₂×#204	C₂²×C₃	1	2	yes	—
122	#894	—	2	2	no	—
123	#893	—	2	1	no	—
124	#889	—	2	2	no	—
125	#887	—	2	1	no	—
126	#875	C₂²×C₃	1	2	yes	—
127	#874	C₂²×C₃	1	1	yes	characteristic
128	C₄×D₁₂	C₂²×C₃	1	2	yes	—
129	#870	C₂²×C₃	1	2	yes	—
130	#869	C₂²×C₃	1	1	yes	characteristic
131	C₄×Dic₆	C₂²×C₃	1	2	yes	—
132	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
133	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
134	C₃×#107	—	3	1	no	—
135	C₃×#106	—	3	2	no	—
136	C₃×C₄⋊C₈	—	2	1	no	—
137	C₃×C₄⋊C₈	—	2	2	no	—
138	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
139	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
140	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
141	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
142	C₃×#103	—	3	1	no	—
143	C₃×#103	—	3	1	no	—
144	C₃×#103	—	3	2	no	—
145	C₃×#102	—	3	2	no	—
146	C₃×#102	—	3	2	no	—
147	C₃×#102	—	3	2	no	—
148	C₃×C₄×C₈	—	2	2	no	—
149	C₃×C₄×C₈	—	2	1	no	—
150	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
151	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
152	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
153	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
154	#821	C₂²×C₃	1	2	yes	—
155	#821	C₂²×C₃	1	2	yes	—
156	#821	C₂²×C₃	1	2	yes	—
157	#818	C₂²×C₃	1	1	yes	characteristic
158	#817	C₂²×C₃	1	2	yes	—
159	#816	C₂²×C₃	1	1	yes	characteristic
160	#816	C₂²×C₃	1	1	yes	characteristic
161	#816	C₂²×C₃	1	2	yes	—
162	C₂²×C₃×D₃	—	2	2	no	—
163	C₃²×Q₈	—	2	2	no	—
164	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
165	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
166	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
167	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
169	C₂×C₃×Dic₃	—	2	1	no	—
170	C₂×C₃×Dic₃	—	2	1	no	—
171	C₂×C₃×Dic₃	—	2	2	no	—
172	C₂×C₃×Dic₃	—	2	1	no	—
173	C₂×C₃×Dic₃	—	2	1	no	—
174	C₃×D₁₂	—	2	2	no	—
175	C₃×D₁₂	—	2	2	no	—
176	C₃×D₁₂	—	4	2	no	—
177	C₃×D₁₂	—	8	1	no	—
178	C₃×C₄×D₃	—	8	2	no	—
179	C₃×Dic₆	—	2	1	no	—
180	C₃×Dic₆	—	2	1	no	—
181	C₃×Dic₆	—	2	1	no	—
182	C₃×Dic₆	—	4	2	no	—
183	C₃×Dic₆	#41	1	2	yes	—
184	C₃²×C₈	—	2	1	no	—
185	C₃²×C₈	—	2	2	no	—
186	C₃²×C₈	—	2	1	no	—
187	#559	—	3	1	no	—
188	#557	—	3	1	no	—
189	#488	—	3	2	no	—
190	#486	—	3	1	no	—
191	#478	—	3	2	no	—
192	#475	—	3	1	no	—
193	#464	—	3	2	no	—
194	#460	—	3	1	no	—
195	C₈×Q₈	C₃×D₃	1	1	yes	characteristic, complemented
196	C₄×Q₁₆	—	3	1	no	—
197	C₄×SD₁₆	—	3	2	no	—
198	C₂×C₃×Q₈	—	2	1	no	—
199	C₂×C₃×Q₈	—	3	1	no	—
200	C₂×C₃×Q₈	—	3	1	no	—
201	C₂×C₃×Q₈	—	6	1	no	—
202	C₂×C₃×Q₈	D₁₂	1	1	yes	characteristic
203	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
204	C₂×C₃×D₄	—	3	2	no	—
205	C₂×C₃×D₄	—	6	1	no	—
206	C₂×C₃×D₄	—	6	1	no	—
207	C₂²×C₃×C₄	—	6	2	no	—
208	C₂×D₁₂	—	2	1	no	—
209	C₂×D₁₂	—	2	1	no	—
210	C₂×D₁₂	C₂³×C₃	1	2	yes	—
211	C₂×C₄×D₃	—	2	2	no	—
212	C₂×Dic₆	—	2	1	no	—
213	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
214	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
215	C₃×Q₁₆	—	6	2	no	—
216	C₃×SD₁₆	—	6	4	no	—
217	C₂×C₃×C₈	—	2	1	no	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	2	2	no	—
220	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
221	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
222	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
223	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
225	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	3	2	no	—
229	C₃×C₄⋊C₄	—	3	1	no	—
230	C₃×C₄⋊C₄	—	3	1	no	—
231	C₃×C₄⋊C₄	—	6	1	no	—
232	C₃×C₄⋊C₄	—	6	1	no	—
233	C₃×C₄⋊C₄	—	6	2	no	—
234	C₃×C₄⋊C₄	—	6	2	no	—
235	C₃×C₄⋊C₄	—	6	2	no	—
236	C₃×C₄⋊C₄	—	6	1	no	—
237	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
238	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
239	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
240	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
241	C₃×C₂²⋊C₄	—	6	2	no	—
242	C₃×C₂²⋊C₄	—	6	2	no	—
243	C₃×C₂²⋊C₄	—	6	2	no	—
244	C₃×C₄²	—	2	2	no	—
245	C₃×C₄²	—	2	1	no	—
246	C₃×C₄²	—	6	1	no	—
247	C₃×C₄²	—	6	2	no	—
248	C₃×C₄²	—	6	1	no	—
249	C₃×C₄²	C₂²×D₃	1	2	yes	—
250	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
251	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
252	C₃×C₄²	C₂³×C₃	1	2	yes	—
253	(C₂×D₃)⋊C₄	—	2	2	no	—
254	(C₂×D₃)⋊C₄	—	2	2	no	—
255	(C₂×D₃)⋊C₄	—	2	2	no	—
256	C₄⋊Dic₃	—	2	1	no	—
257	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
258	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
259	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
260	Dic₃⋊C₄	—	2	1	no	—
261	Dic₃⋊C₄	—	2	2	no	—
262	Dic₃⋊C₄	—	2	1	no	—
263	Dic₃⋊C₄	—	2	2	no	—
264	Dic₃⋊C₄	—	2	2	no	—
265	C₄×Dic₃	—	2	2	no	—
266	C₄×Dic₃	—	2	1	no	—
267	C₄×Dic₃	—	2	1	no	—
268	Dic₁₂	—	2	2	no	—
269	#204	—	2	4	no	—
270	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₃×D₃	—	4	2	no	—
272	C₂×C₃×D₃	—	4	2	no	—
273	C₂×C₃×D₃	—	4	2	no	—
274	C₃²×C₄	—	2	2	no	—
275	C₃²×C₄	—	2	2	no	—
276	C₃²×C₄	—	2	1	no	—
277	C₃²×C₄	#135	1	2	yes	—
278	C₃²×C₄	C₂×#41	1	1	yes	characteristic
279	C₃²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
280	C₃×Dic₃	—	2	2	no	—
281	C₃×Dic₃	—	4	1	no	—
282	C₃×Dic₃	—	4	2	no	—
283	C₃×Dic₃	—	4	1	no	—
284	C₃×Dic₃	—	4	1	no	—
285	C₂×Q₁₆	—	3	1	no	—
286	C₂×SD₁₆	—	3	2	no	—
287	C₄⋊Q₈	—	3	1	no	—
288	C₄⋊Q₈	—	6	1	no	—
289	#127	—	3	1	no	—
290	#125	—	3	2	no	—
291	#125	—	6	2	no	—
292	#124	—	3	2	no	—
293	#124	—	6	1	no	—
294	#123	—	6	2	no	—
295	C₄×Q₈	—	3	2	no	—
296	C₄×Q₈	—	3	1	no	—
297	C₄×Q₈	—	3	1	no	—
298	C₄×Q₈	—	6	1	no	—
299	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
300	C₄×D₄	—	3	2	no	—
301	C₄×D₄	—	6	1	no	—
302	#107	—	3	1	no	—
303	#106	—	3	2	no	—
304	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
305	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
306	#103	—	3	1	no	—
307	#103	—	3	1	no	—
308	#103	—	3	2	no	—
309	#102	—	3	2	no	—
310	#102	—	3	2	no	—
311	#102	—	3	2	no	—
312	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
313	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
314	C₂³×C₃	—	6	2	no	—
315	C₂²×D₃	—	2	2	no	—
316	C₃×Q₈	—	2	4	no	—
317	C₃×Q₈	—	2	2	no	—
318	C₃×Q₈	—	2	2	no	—
319	C₃×Q₈	—	3	2	no	—
320	C₃×Q₈	—	6	1	no	—
321	C₃×Q₈	—	6	1	no	—
322	C₃×Q₈	—	6	1	no	—
323	C₃×Q₈	—	12	2	no	—
324	C₃×D₄	—	6	2	no	—
325	C₃×D₄	—	6	2	no	—
326	C₃×D₄	—	12	2	no	—
327	C₃×D₄	—	24	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	6	1	no	—
334	C₂×C₃×C₄	—	6	1	no	—
335	C₂×C₃×C₄	—	6	1	no	—
336	C₂×C₃×C₄	—	6	1	no	—
337	C₂×C₃×C₄	—	6	2	no	—
338	C₂×C₃×C₄	—	24	2	no	—
339	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
340	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
341	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
344	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
346	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
349	C₂×Dic₃	—	2	1	no	—
350	C₂×Dic₃	—	2	1	no	—
351	C₂×Dic₃	—	2	2	no	—
352	C₂×Dic₃	—	2	1	no	—
353	C₂×Dic₃	—	2	1	no	—
354	D₁₂	—	2	2	no	—
355	D₁₂	—	2	2	no	—
356	D₁₂	—	4	2	no	—
357	D₁₂	—	8	1	no	—
358	C₄×D₃	—	8	2	no	—
359	Dic₆	—	2	1	no	—
360	Dic₆	—	2	1	no	—
361	Dic₆	—	2	1	no	—
362	Dic₆	—	4	2	no	—
363	Dic₆	C₃×#41	1	2	yes	—
364	C₃×C₈	—	2	2	no	—
365	C₃×C₈	—	2	1	no	—
366	C₃×C₈	—	2	2	no	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	—	2	2	no	—
369	C₃×C₈	—	2	1	no	—
370	C₃×C₈	—	2	1	no	—
371	C₃×C₈	—	4	2	no	—
372	C₃×C₈	—	4	1	no	—
373	C₂×C₃²	#548	1	1	yes	characteristic
374	C₂×C₃²	C₂×#135	1	1	yes	characteristic
375	C₂×C₃²	#577	1	1	yes	characteristic
376	C₃×D₃	—	8	2	no	—
377	C₂×Q₈	—	3	1	no	—
378	C₂×Q₈	—	3	1	no	—
379	C₂×Q₈	—	6	1	no	—
380	C₂×Q₈	C₃×D₁₂	1	1	yes	characteristic
381	C₂×D₄	—	3	2	no	—
382	C₂×D₄	—	6	1	no	—
383	C₂×D₄	—	6	1	no	—
384	C₂²×C₄	—	6	2	no	—
385	Q₁₆	—	6	2	no	—
386	SD₁₆	—	6	4	no	—
387	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
388	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
389	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
390	C₄⋊C₄	—	3	2	no	—
391	C₄⋊C₄	—	3	1	no	—
392	C₄⋊C₄	—	3	1	no	—
393	C₄⋊C₄	—	6	1	no	—
394	C₄⋊C₄	—	6	1	no	—
395	C₄⋊C₄	—	6	2	no	—
396	C₄⋊C₄	—	6	2	no	—
397	C₄⋊C₄	—	6	2	no	—
398	C₄⋊C₄	—	6	1	no	—
399	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
400	C₄⋊C₄	C₃×D₁₂	1	2	yes	—
401	C₂²⋊C₄	—	6	2	no	—
402	C₂²⋊C₄	—	6	2	no	—
403	C₂²⋊C₄	—	6	2	no	—
404	C₄²	—	6	1	no	—
405	C₄²	—	6	2	no	—
406	C₄²	—	6	1	no	—
407	C₄²	C₂²×C₃×D₃	1	2	yes	—
408	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
409	C₂²×C₃	—	2	1	no	—
410	C₂²×C₃	—	12	2	no	—
411	C₂²×C₃	—	12	2	no	—
412	C₂²×C₃	—	12	2	no	—
413	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
414	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
415	C₂×D₃	—	4	2	no	—
416	C₂×D₃	—	4	2	no	—
417	C₂×D₃	—	4	2	no	—
418	C₃×C₄	—	2	4	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	2	2	no	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	2	no	—
423	C₃×C₄	—	2	2	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	1	no	—
428	C₃×C₄	—	4	2	no	—
429	C₃×C₄	—	4	1	no	—
430	C₃×C₄	—	6	2	no	—
431	C₃×C₄	—	12	2	no	—
432	C₃×C₄	—	12	1	no	—
433	C₃×C₄	—	12	1	no	—
434	C₃×C₄	—	12	1	no	—
435	C₃×C₄	#904	1	2	yes	—
436	C₃×C₄	C₃×#135	1	2	yes	—
437	C₃×C₄	#1007	1	1	yes	characteristic
438	C₃×C₄	D₃×#41	1	1	yes	characteristic
439	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
440	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
441	Dic₃	—	2	2	no	—
442	Dic₃	—	4	2	no	—
443	Dic₃	—	4	1	no	—
444	Dic₃	—	4	1	no	—
445	Dic₃	—	4	1	no	—
446	C₃²	#3365	1	1	yes	characteristic, complemented, Sylow
447	C₂³	—	6	2	no	—
448	Q₈	—	2	2	no	—
449	Q₈	—	3	2	no	—
450	Q₈	—	6	1	no	—
451	Q₈	—	6	1	no	—
452	Q₈	—	6	1	no	—
453	Q₈	—	12	2	no	—
454	D₄	—	6	2	no	—
455	D₄	—	6	2	no	—
456	D₄	—	12	2	no	—
457	D₄	—	24	1	no	—
458	C₂×C₄	—	6	1	no	—
459	C₂×C₄	—	6	1	no	—
460	C₂×C₄	—	6	1	no	—
461	C₂×C₄	—	6	1	no	—
462	C₂×C₄	—	6	2	no	—
463	C₂×C₄	—	24	2	no	—
464	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
465	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
466	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
467	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
468	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
469	C₈	—	2	1	no	—
470	C₈	—	2	2	no	—
471	C₈	—	2	1	no	—
472	C₂×C₃	—	2	1	no	—
473	C₂×C₃	—	2	1	no	—
474	C₂×C₃	—	2	1	no	—
475	C₂×C₃	—	24	2	no	—
476	C₂×C₃	#5576	1	1	yes	characteristic
477	C₂×C₃	C₂×#904	1	1	yes	characteristic
478	C₂×C₃	#5751	1	1	yes	characteristic
479	C₂×C₃	C₃×#548	1	1	yes	characteristic
480	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
481	C₂×C₃	C₃×#577	1	1	yes	characteristic
482	D₃	—	8	2	no	—
483	C₂²	—	12	2	no	—
484	C₂²	—	12	2	no	—
485	C₂²	—	12	2	no	—
486	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
487	C₄	—	2	2	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	2	no	—
490	C₄	—	6	2	no	—
491	C₄	—	12	1	no	—
492	C₄	—	12	1	no	—
493	C₄	—	12	1	no	—
494	C₄	—	12	2	no	—
495	C₄	C₃×#904	1	2	yes	—
496	C₄	C₃×#1007	1	1	yes	characteristic
497	C₄	C₃×D₃×#41	1	1	yes	characteristic
498	C₃	—	2	1	no	—
499	C₃	#79935	1	1	yes	characteristic, direct product factor
500	C₃	C₃×#3365	1	1	yes	characteristic, complemented
501	C₂	—	24	2	no	—
502	C₂	C₃×#5576	1	1	yes	characteristic
503	C₂	C₂×C₃×#904	1	1	yes	characteristic
504	C₂	C₃×#5751	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₈×Q₈	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₃×#874	C₂²
hypercenter	C₃×C₈×Q₈	D₃
hypocenter	C₃	C₃×#3365
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈ ◁ C₃×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. C₃×#5567	C₂	semidirect
3. C₃²×C₈×Q₈	C₂	semidirect
4. C₃×#4851	C₂	semidirect
6. C₃×#4847	C₂	semidirect
7. C₃×#4845	C₂	semidirect
8. C₃×C₄×Dic₁₂	C₂	semidirect
9. C₃×#4697	C₂	semidirect
11. C₃×C₄×#204	C₂	semidirect
13. #79935	C₃	direct (N × H)
46. #5567	C₂×C₃	semidirect
54. C₃×C₈×Q₈	D₃	semidirect
55. C₃×C₈×Q₈	C₂×C₃	semidirect
58. #4851	C₂×C₃	semidirect
60. #4847	C₂×C₃	semidirect
61. #4845	C₂×C₃	semidirect
62. C₄×Dic₁₂	C₂×C₃	semidirect
63. #4697	C₂×C₃	semidirect
65. C₄×#204	C₂×C₃	semidirect
195. C₈×Q₈	C₃×D₃	semidirect
446. C₃²	#3365	semidirect
499. C₃	#79935	direct (N × H)
500. C₃	C₃×#3365	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5585	2
C₃×#5567	2
C₃²×C₈×Q₈	2
C₃×#4851	2
C₃×#4848	2
C₃×#4847	2
C₃×#4845	2
C₃×C₄×Dic₁₂	2
C₃×#4697	2
C₃×#4694	2
C₃×C₄×#204	2
C₃×#3365	3
#79935	3

Subgroups — C3×#79935 #11895628

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79935 #11895628