Subgroups — C₃×#79934 #11895527

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5584	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×#4849	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4846	C₂	1	1	yes	maximal, characteristic
6	C₃×#4845	C₂	1	2	yes	maximal
7	C₃×#4829	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×Dic₁₂	C₂	1	2	yes	maximal, complemented
9	C₃×#4697	C₂	1	2	yes	maximal
10	C₃×C₄×#204	C₂	1	1	yes	maximal, characteristic
11	C₃×#4681	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3364	—	3	1	no	maximal
13	#79934	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
15	C₃×#946	—	2	1	no	—
16	C₃×#944	—	2	1	no	—
17	C₂×C₃×Dic₁₂	C₂²	1	2	yes	—
18	C₂×C₃×#204	C₂²	1	1	yes	characteristic
19	C₃×#898	—	2	2	no	—
20	C₃×#892	—	2	1	no	—
21	C₃×#889	—	2	2	no	—
22	C₃×#887	—	2	1	no	—
23	C₃×#875	C₂²	1	2	yes	—
24	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
25	C₃×#870	C₂²	1	2	yes	—
26	C₃×#869	C₂²	1	1	yes	characteristic
27	C₃×#869	C₂²	1	1	yes	characteristic
28	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₆	C₂²	1	2	yes	—
30	C₃×C₄×Dic₆	C₂²	1	2	yes	—
31	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₃²×C₄×C₈	C₂²	1	2	yes	—
35	C₃×#821	C₂²	1	1	yes	characteristic
36	C₃×#821	C₂²	1	2	yes	—
37	C₃×#818	C₂²	1	2	yes	—
38	C₃×#817	C₂²	1	1	yes	characteristic
39	C₃×#816	C₂²	1	2	yes	—
40	C₃×#816	C₂²	1	2	yes	—
41	C₃×#816	C₂²	1	1	yes	characteristic
42	C₃×#816	C₂²	1	2	yes	—
43	C₃×#557	—	3	1	no	—
44	C₃×#556	—	3	1	no	—
45	#5584	C₂×C₃	1	1	yes	characteristic
46	#5567	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×#488	—	3	2	no	—
48	C₃×#487	—	3	1	no	—
49	C₃×#479	—	3	2	no	—
50	C₃×#474	—	3	1	no	—
51	C₃×#464	—	3	2	no	—
52	C₃×#462	—	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	2	no	—
57	C₃×C₄×SD₁₆	—	3	1	no	—
58	#4849	C₂×C₃	1	1	yes	characteristic, complemented
59	#4846	C₂×C₃	1	1	yes	characteristic
60	#4845	C₂×C₃	1	2	yes	—
61	#4829	C₂×C₃	1	2	yes	complemented
62	C₄×Dic₁₂	C₂×C₃	1	2	yes	complemented
63	#4697	C₂×C₃	1	2	yes	—
64	C₄×#204	C₂×C₃	1	1	yes	characteristic
65	#4681	C₂×C₃	1	1	yes	characteristic, complemented
66	C₂×C₃²×Q₈	D₄	1	1	yes	characteristic
67	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₄×D₃	—	2	1	no	—
69	C₂×C₃×Dic₆	—	2	1	no	—
70	C₂×C₃×Dic₆	C₂³	1	2	yes	—
71	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂³	1	2	yes	—
74	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
75	C₃²×C₄⋊C₄	D₄	1	1	yes	characteristic
76	C₃²×C₄⋊C₄	D₄	1	2	yes	—
77	C₃²×C₄²	C₂³	1	2	yes	—
78	C₃²×C₄²	C₂³	1	1	yes	characteristic
79	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
80	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
81	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
82	C₃×C₄⋊Dic₃	—	2	1	no	—
83	C₃×C₄⋊Dic₃	—	2	1	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	2	no	—
93	C₃×C₄×Dic₃	—	2	2	no	—
94	C₃×C₄×Dic₃	—	2	1	no	—
95	C₃×C₄×Dic₃	—	2	2	no	—
96	C₃×Dic₁₂	—	2	4	no	—
97	C₃×#204	—	2	2	no	—
98	#3364	—	3	1	no	Sylow
99	C₂×C₃×Q₁₆	—	3	2	no	—
100	C₂×C₃×SD₁₆	—	3	1	no	—
101	C₃×C₄⋊Q₈	—	3	1	no	—
102	C₃×C₄⋊Q₈	—	3	1	no	—
103	C₃×C₄⋊Q₈	—	6	1	no	—
104	C₃×#126	—	6	2	no	—
105	C₃×#125	—	3	2	no	—
106	C₃×#125	—	6	2	no	—
107	C₃×#124	—	3	2	no	—
108	C₃×C₂²⋊Q₈	—	6	1	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	2	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	1	no	—
117	C₃×#117	—	6	1	no	—
118	#946	—	2	1	no	—
119	#944	—	2	1	no	—
120	C₂×Dic₁₂	C₂²×C₃	1	2	yes	—
121	C₂×#204	C₂²×C₃	1	1	yes	characteristic
122	#898	—	2	2	no	—
123	#892	—	2	1	no	—
124	#889	—	2	2	no	—
125	#887	—	2	1	no	—
126	#875	C₂²×C₃	1	2	yes	—
127	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
128	#870	C₂²×C₃	1	2	yes	—
129	#869	C₂²×C₃	1	1	yes	characteristic
130	#869	C₂²×C₃	1	1	yes	characteristic
131	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
132	C₄×Dic₆	C₂²×C₃	1	2	yes	—
133	C₄×Dic₆	C₂²×C₃	1	2	yes	—
134	C₃×#107	—	3	2	no	—
135	C₃×#106	—	3	1	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	2	no	—
144	C₃×#103	—	3	2	no	—
145	C₃×#103	—	3	2	no	—
146	C₃×#102	—	3	1	no	—
147	C₃×#102	—	3	2	no	—
148	C₃×C₄×C₈	—	2	1	no	—
149	C₃×C₄×C₈	—	2	2	no	—
150	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
151	C₃×C₄×C₈	C₂×D₃	1	2	yes	—
152	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
153	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
154	#821	C₂²×C₃	1	1	yes	characteristic
155	#821	C₂²×C₃	1	2	yes	—
156	#818	C₂²×C₃	1	2	yes	—
157	#817	C₂²×C₃	1	1	yes	characteristic
158	#816	C₂²×C₃	1	2	yes	—
159	#816	C₂²×C₃	1	2	yes	—
160	#816	C₂²×C₃	1	1	yes	characteristic
161	#816	C₂²×C₃	1	2	yes	—
162	C₂²×C₃×D₃	—	2	1	no	—
163	C₃²×Q₈	—	2	2	no	—
164	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
165	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
166	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
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	1	no	—
172	C₂×C₃×Dic₃	—	2	2	no	—
173	C₂×C₃×Dic₃	—	2	2	no	—
174	C₃×D₁₂	—	2	1	no	—
175	C₃×D₁₂	—	2	1	no	—
176	C₃×C₄×D₃	—	4	2	no	—
177	C₃×Dic₆	—	2	1	no	—
178	C₃×Dic₆	—	2	2	no	—
179	C₃×Dic₆	—	2	2	no	—
180	C₃×Dic₆	—	4	2	no	—
181	C₃×Dic₆	#41	1	2	yes	—
182	C₃²×C₈	—	2	1	no	—
183	C₃²×C₈	—	2	1	no	—
184	C₃²×C₈	—	2	2	no	—
185	#557	—	3	1	no	—
186	#556	—	3	1	no	—
187	#488	—	3	2	no	—
188	#487	—	3	1	no	—
189	#479	—	3	2	no	—
190	#474	—	3	1	no	—
191	#464	—	3	2	no	—
192	#462	—	3	1	no	—
193	C₈×Q₈	C₃×D₃	1	1	yes	characteristic, complemented
194	C₄×Q₁₆	—	3	2	no	—
195	C₄×SD₁₆	—	3	1	no	—
196	C₂×C₃×Q₈	—	2	1	no	—
197	C₂×C₃×Q₈	—	3	1	no	—
198	C₂×C₃×Q₈	—	3	2	no	—
199	C₂×C₃×Q₈	—	6	1	no	—
200	C₂×C₃×Q₈	D₁₂	1	1	yes	characteristic
201	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
202	C₂×C₃×D₄	—	3	1	no	—
203	C₂²×C₃×C₄	—	6	1	no	—
204	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₄×D₃	—	2	1	no	—
206	C₂×Dic₆	—	2	1	no	—
207	C₂×Dic₆	C₂³×C₃	1	2	yes	—
208	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
209	C₃×Q₁₆	—	6	4	no	—
210	C₃×SD₁₆	—	6	2	no	—
211	C₂×C₃×C₈	—	2	1	no	—
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	—	2	1	no	—
214	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
215	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
216	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	—	3	1	no	—
223	C₃×C₄⋊C₄	—	3	2	no	—
224	C₃×C₄⋊C₄	—	3	1	no	—
225	C₃×C₄⋊C₄	—	6	2	no	—
226	C₃×C₄⋊C₄	—	6	1	no	—
227	C₃×C₄⋊C₄	—	6	2	no	—
228	C₃×C₄⋊C₄	—	6	2	no	—
229	C₃×C₄⋊C₄	—	6	2	no	—
230	C₃×C₄⋊C₄	—	6	1	no	—
231	C₃×C₄⋊C₄	—	6	1	no	—
232	C₃×C₄⋊C₄	—	6	1	no	—
233	C₃×C₄⋊C₄	D₁₂	1	1	yes	characteristic
234	C₃×C₄⋊C₄	D₁₂	1	2	yes	—
235	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₃×D₄	1	2	yes	—
237	C₃×C₂²⋊C₄	—	6	2	no	—
238	C₃×C₂²⋊C₄	—	6	1	no	—
239	C₃×C₂²⋊C₄	—	6	2	no	—
240	C₃×C₄²	—	2	1	no	—
241	C₃×C₄²	—	2	2	no	—
242	C₃×C₄²	—	6	2	no	—
243	C₃×C₄²	—	6	2	no	—
244	C₃×C₄²	—	6	1	no	—
245	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
246	C₃×C₄²	C₂²×D₃	1	2	yes	—
247	C₃×C₄²	C₂³×C₃	1	2	yes	—
248	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
249	(C₂×D₃)⋊C₄	—	2	1	no	—
250	(C₂×D₃)⋊C₄	—	2	2	no	—
251	(C₂×D₃)⋊C₄	—	2	2	no	—
252	C₄⋊Dic₃	—	2	1	no	—
253	C₄⋊Dic₃	—	2	1	no	—
254	C₄⋊Dic₃	—	2	1	no	—
255	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
256	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
257	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
258	Dic₃⋊C₄	—	2	1	no	—
259	Dic₃⋊C₄	—	2	2	no	—
260	Dic₃⋊C₄	—	2	2	no	—
261	Dic₃⋊C₄	—	2	2	no	—
262	Dic₃⋊C₄	—	2	2	no	—
263	C₄×Dic₃	—	2	2	no	—
264	C₄×Dic₃	—	2	1	no	—
265	C₄×Dic₃	—	2	2	no	—
266	Dic₁₂	—	2	4	no	—
267	#204	—	2	2	no	—
268	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₃×D₃	—	4	1	no	—
270	C₂×C₃×D₃	—	4	1	no	—
271	C₂×C₃×D₃	—	4	1	no	—
272	C₃²×C₄	—	2	2	no	—
273	C₃²×C₄	—	2	2	no	—
274	C₃²×C₄	—	2	1	no	—
275	C₃²×C₄	#135	1	2	yes	—
276	C₃²×C₄	C₂×#41	1	1	yes	characteristic
277	C₃²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
278	C₃×Dic₃	—	2	2	no	—
279	C₃×Dic₃	—	4	2	no	—
280	C₃×Dic₃	—	4	2	no	—
281	C₃×Dic₃	—	4	1	no	—
282	C₃×Dic₃	—	4	1	no	—
283	C₂×Q₁₆	—	3	2	no	—
284	C₂×SD₁₆	—	3	1	no	—
285	C₄⋊Q₈	—	3	1	no	—
286	C₄⋊Q₈	—	3	1	no	—
287	C₄⋊Q₈	—	6	1	no	—
288	#126	—	6	2	no	—
289	#125	—	3	2	no	—
290	#125	—	6	2	no	—
291	#124	—	3	2	no	—
292	C₂²⋊Q₈	—	6	1	no	—
293	C₄×Q₈	—	3	2	no	—
294	C₄×Q₈	—	3	1	no	—
295	C₄×Q₈	—	3	2	no	—
296	C₄×Q₈	—	6	1	no	—
297	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
298	C₄×D₄	—	3	1	no	—
299	#117	—	6	1	no	—
300	#107	—	3	2	no	—
301	#106	—	3	1	no	—
302	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
303	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
304	#103	—	3	1	no	—
305	#103	—	3	2	no	—
306	#103	—	3	2	no	—
307	#103	—	3	2	no	—
308	#102	—	3	1	no	—
309	#102	—	3	2	no	—
310	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
311	C₄×C₈	C₂×C₃×D₃	1	2	yes	—
312	C₂³×C₃	—	6	1	no	—
313	C₂²×D₃	—	2	1	no	—
314	C₃×Q₈	—	2	4	no	—
315	C₃×Q₈	—	2	2	no	—
316	C₃×Q₈	—	2	2	no	—
317	C₃×Q₈	—	3	2	no	—
318	C₃×Q₈	—	6	1	no	—
319	C₃×Q₈	—	6	2	no	—
320	C₃×Q₈	—	6	2	no	—
321	C₃×Q₈	—	12	2	no	—
322	C₃×D₄	—	6	1	no	—
323	C₃×D₄	—	6	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	6	1	no	—
330	C₂×C₃×C₄	—	6	1	no	—
331	C₂×C₃×C₄	—	6	2	no	—
332	C₂×C₃×C₄	—	6	1	no	—
333	C₂×C₃×C₄	—	6	2	no	—
334	C₂×C₃×C₄	—	12	2	no	—
335	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
336	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
338	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
339	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
340	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
341	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
345	C₂×Dic₃	—	2	1	no	—
346	C₂×Dic₃	—	2	1	no	—
347	C₂×Dic₃	—	2	1	no	—
348	C₂×Dic₃	—	2	2	no	—
349	C₂×Dic₃	—	2	2	no	—
350	D₁₂	—	2	1	no	—
351	D₁₂	—	2	1	no	—
352	C₄×D₃	—	4	2	no	—
353	Dic₆	—	2	1	no	—
354	Dic₆	—	2	2	no	—
355	Dic₆	—	2	2	no	—
356	Dic₆	—	4	2	no	—
357	Dic₆	C₃×#41	1	2	yes	—
358	C₃×C₈	—	2	2	no	—
359	C₃×C₈	—	2	1	no	—
360	C₃×C₈	—	2	1	no	—
361	C₃×C₈	—	2	2	no	—
362	C₃×C₈	—	2	1	no	—
363	C₃×C₈	—	2	2	no	—
364	C₃×C₈	—	2	1	no	—
365	C₃×C₈	—	4	1	no	—
366	C₃×C₈	—	4	2	no	—
367	C₂×C₃²	#548	1	1	yes	characteristic
368	C₂×C₃²	C₂×#135	1	1	yes	characteristic
369	C₂×C₃²	#578	1	1	yes	characteristic
370	C₃×D₃	—	8	1	no	—
371	C₂×Q₈	—	3	1	no	—
372	C₂×Q₈	—	3	2	no	—
373	C₂×Q₈	—	6	1	no	—
374	C₂×Q₈	C₃×D₁₂	1	1	yes	characteristic
375	C₂×D₄	—	3	1	no	—
376	C₂²×C₄	—	6	1	no	—
377	Q₁₆	—	6	4	no	—
378	SD₁₆	—	6	2	no	—
379	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
380	C₂×C₈	C₂²×C₃×D₃	1	2	yes	—
381	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
382	C₄⋊C₄	—	3	1	no	—
383	C₄⋊C₄	—	3	2	no	—
384	C₄⋊C₄	—	3	1	no	—
385	C₄⋊C₄	—	6	1	no	—
386	C₄⋊C₄	—	6	2	no	—
387	C₄⋊C₄	—	6	1	no	—
388	C₄⋊C₄	—	6	2	no	—
389	C₄⋊C₄	—	6	2	no	—
390	C₄⋊C₄	—	6	2	no	—
391	C₄⋊C₄	—	6	1	no	—
392	C₄⋊C₄	—	6	1	no	—
393	C₄⋊C₄	C₃×D₁₂	1	1	yes	characteristic
394	C₄⋊C₄	C₃×D₁₂	1	2	yes	—
395	C₂²⋊C₄	—	6	2	no	—
396	C₂²⋊C₄	—	6	1	no	—
397	C₂²⋊C₄	—	6	2	no	—
398	C₄²	—	6	2	no	—
399	C₄²	—	6	2	no	—
400	C₄²	—	6	1	no	—
401	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
402	C₄²	C₂²×C₃×D₃	1	2	yes	—
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	12	1	no	—
405	C₂²×C₃	—	12	1	no	—
406	C₂²×C₃	—	12	1	no	—
407	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
408	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
409	C₂×D₃	—	4	1	no	—
410	C₂×D₃	—	4	1	no	—
411	C₂×D₃	—	4	1	no	—
412	C₃×C₄	—	2	4	no	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	1	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	1	no	—
419	C₃×C₄	—	2	2	no	—
420	C₃×C₄	—	2	1	no	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	4	2	no	—
423	C₃×C₄	—	4	1	no	—
424	C₃×C₄	—	6	2	no	—
425	C₃×C₄	—	12	1	no	—
426	C₃×C₄	—	12	2	no	—
427	C₃×C₄	—	12	1	no	—
428	C₃×C₄	—	12	2	no	—
429	C₃×C₄	#904	1	2	yes	—
430	C₃×C₄	C₃×#135	1	2	yes	—
431	C₃×C₄	#1007	1	1	yes	characteristic
432	C₃×C₄	D₃×#41	1	1	yes	characteristic
433	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
434	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
435	Dic₃	—	2	2	no	—
436	Dic₃	—	4	2	no	—
437	Dic₃	—	4	1	no	—
438	Dic₃	—	4	1	no	—
439	Dic₃	—	4	2	no	—
440	C₃²	#3364	1	1	yes	characteristic, complemented, Sylow
441	C₂³	—	6	1	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	3	2	no	—
444	Q₈	—	6	1	no	—
445	Q₈	—	6	2	no	—
446	Q₈	—	6	2	no	—
447	Q₈	—	12	2	no	—
448	D₄	—	6	1	no	—
449	D₄	—	6	1	no	—
450	C₂×C₄	—	6	1	no	—
451	C₂×C₄	—	6	1	no	—
452	C₂×C₄	—	6	2	no	—
453	C₂×C₄	—	6	1	no	—
454	C₂×C₄	—	6	2	no	—
455	C₂×C₄	—	12	2	no	—
456	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
457	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
458	C₂×C₄	C₂×C₃×D₁₂	1	2	yes	—
459	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
460	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	2	no	—
464	C₂×C₃	—	2	1	no	—
465	C₂×C₃	—	2	1	no	—
466	C₂×C₃	—	2	1	no	—
467	C₂×C₃	—	24	1	no	—
468	C₂×C₃	#5576	1	1	yes	characteristic
469	C₂×C₃	C₂×#904	1	1	yes	characteristic
470	C₂×C₃	#5753	1	1	yes	characteristic
471	C₂×C₃	C₃×#548	1	1	yes	characteristic
472	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
473	C₂×C₃	C₃×#578	1	1	yes	characteristic
474	D₃	—	8	1	no	—
475	C₂²	—	12	1	no	—
476	C₂²	—	12	1	no	—
477	C₂²	—	12	1	no	—
478	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
479	C₄	—	2	2	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	6	2	no	—
483	C₄	—	12	1	no	—
484	C₄	—	12	2	no	—
485	C₄	—	12	1	no	—
486	C₄	—	12	2	no	—
487	C₄	C₃×#904	1	2	yes	—
488	C₄	C₃×#1007	1	1	yes	characteristic
489	C₄	C₃×D₃×#41	1	1	yes	characteristic
490	C₃	—	2	1	no	—
491	C₃	#79934	1	1	yes	characteristic, direct product factor
492	C₃	C₃×#3364	1	1	yes	characteristic, complemented
493	C₂	—	24	1	no	—
494	C₂	C₃×#5576	1	1	yes	characteristic
495	C₂	C₂×C₃×#904	1	1	yes	characteristic
496	C₂	C₃×#5753	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	C₂×C₃×D₁₂	C₂³
hypercenter	C₃×C₈×Q₈	D₃
hypocenter	C₃	C₃×#3364
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×#4849	C₂	semidirect
7. C₃×#4829	C₂	semidirect
8. C₃×C₄×Dic₁₂	C₂	semidirect
11. C₃×#4681	C₂	semidirect
13. #79934	C₃	direct (N × H)
46. #5567	C₂×C₃	semidirect
54. C₃×C₈×Q₈	D₃	semidirect
55. C₃×C₈×Q₈	C₂×C₃	semidirect
58. #4849	C₂×C₃	semidirect
61. #4829	C₂×C₃	semidirect
62. C₄×Dic₁₂	C₂×C₃	semidirect
65. #4681	C₂×C₃	semidirect
193. C₈×Q₈	C₃×D₃	semidirect
440. C₃²	#3364	semidirect
491. C₃	#79934	direct (N × H)
492. C₃	C₃×#3364	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5584	2
C₃×#5567	2
C₃²×C₈×Q₈	2
C₃×#4849	2
C₃×#4846	2
C₃×#4845	2
C₃×#4829	2
C₃×C₄×Dic₁₂	2
C₃×#4697	2
C₃×C₄×#204	2
C₃×#4681	2
C₃×#3364	3
#79934	3

Subgroups — C3×#79934 #11895527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79934 #11895527