Subgroups — C₃×#18005 #10636612

Order 768.

608 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3102	C₂	1	1	yes	maximal, characteristic
2	C₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1594	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1592	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
16	#18005	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#529	C₂²	1	1	yes	characteristic
18	C₃×C₄×#41	C₂²	1	1	yes	characteristic
19	C₃×#485	C₄	1	1	yes	characteristic
20	C₃×#482	C₄	1	1	yes	characteristic
21	C₃×#479	C₄	1	1	yes	characteristic
22	C₃×#478	C₄	1	1	yes	characteristic
23	C₃×#464	C₄	1	1	yes	characteristic
24	C₃×#463	C₄	1	1	yes	characteristic
25	C₃×#452	C₄	1	1	yes	characteristic
26	C₃×#449	C₄	1	1	yes	characteristic
27	C₃×#446	C₂²	1	1	yes	characteristic
28	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
30	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
32	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
33	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
34	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
35	C₃×#436	—	2	1	no	—
36	C₃×#436	—	2	1	no	—
37	C₃×#436	—	2	1	no	—
38	C₃×#436	C₂²	1	1	yes	characteristic
39	C₃×#436	C₂²	1	1	yes	characteristic
40	C₃×#436	C₂²	1	1	yes	characteristic
41	C₃×#435	—	2	1	no	—
42	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
43	C₃×#433	—	2	1	no	—
44	C₃×#432	—	2	1	no	—
45	C₃×#432	C₂²	1	1	yes	characteristic
46	C₃×#431	C₂²	1	1	yes	characteristic
47	C₃×#431	C₂²	1	1	yes	characteristic
48	C₃×#405	—	2	1	no	—
49	C₃×C₄×M₁₆	—	2	1	no	—
50	C₃×C₄×M₁₆	C₂²	1	1	yes	characteristic
51	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
52	C₃×#335	C₂²	1	1	yes	characteristic
53	C₃×#335	C₂²	1	1	yes	characteristic
54	C₃×#334	C₂²	1	1	yes	characteristic
55	C₃×#334	C₂²	1	1	yes	characteristic
56	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
60	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
64	C₃×#322	C₂²	1	1	yes	characteristic
65	C₃×#322	C₂²	1	1	yes	characteristic
66	C₃×#322	C₂²	1	1	yes	characteristic
67	C₃×#322	C₂²	1	1	yes	characteristic
68	#3102	C₂×C₃	1	1	yes	characteristic
69	#2971	C₂×C₃	1	1	yes	characteristic, complemented
70	#2969	C₂×C₃	1	1	yes	characteristic, complemented
71	#1594	C₂×C₃	1	1	yes	characteristic, complemented
72	#1592	C₂×C₃	1	1	yes	characteristic, complemented
73	#1588	C₂×C₃	1	1	yes	characteristic, complemented
74	#1588	C₂×C₃	1	1	yes	characteristic, complemented
75	#1587	C₂×C₃	1	1	yes	characteristic, complemented
76	#1586	C₂×C₃	1	1	yes	characteristic, complemented
77	#1579	C₂×C₃	1	1	yes	characteristic, complemented
78	SD₁₆⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
79	#1572	C₂×C₃	1	1	yes	characteristic, complemented
80	#1494	C₂×C₃	1	1	yes	characteristic, complemented
81	#1476	C₂×C₃	1	1	yes	characteristic, complemented
82	#1451	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×C₃×#41	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
86	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
87	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
88	C₂×C₃×M₁₆	—	2	1	no	—
89	C₂×C₃×M₁₆	—	2	1	no	—
90	C₂×C₃×M₁₆	—	2	1	no	—
91	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
92	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
93	C₂²×C₃×C₈	—	2	1	no	—
94	C₂²×C₃×C₈	—	2	1	no	—
95	C₃×#126	—	2	1	no	—
96	C₃×#125	C₂×C₄	1	1	yes	characteristic
97	C₃×#124	C₂×C₄	1	1	yes	characteristic
98	C₃×#123	—	2	1	no	—
99	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
100	C₃×#121	C₂×C₄	1	1	yes	characteristic
101	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
102	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
103	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
104	C₃×C₄×D₄	—	2	1	no	—
105	C₃×C₄×D₄	—	2	1	no	—
106	C₃×C₄×D₄	—	2	1	no	—
107	C₃×C₄×D₄	C₂×C₄	1	1	yes	characteristic
108	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
109	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
110	C₃×#117	—	2	1	no	—
111	C₃×#117	—	2	1	no	—
112	C₃×#117	C₂×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄²	—	2	1	no	—
114	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
115	C₃×#107	C₂×C₄	1	1	yes	characteristic
116	C₃×#107	C₂×C₄	1	1	yes	characteristic
117	C₃×#106	C₂×C₄	1	1	yes	characteristic
118	C₃×#106	C₂×C₄	1	1	yes	characteristic
119	C₃×C₄⋊C₈	—	2	1	no	—
120	C₃×C₄⋊C₈	—	2	1	no	—
121	C₃×C₄⋊C₈	—	2	1	no	—
122	C₃×C₄⋊C₈	—	2	1	no	—
123	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
125	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
126	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
127	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
128	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
129	C₃×#103	C₂×C₄	1	1	yes	characteristic
130	C₃×#103	C₂×C₄	1	1	yes	characteristic
131	C₃×#103	C₂×C₄	1	1	yes	characteristic
132	C₃×#103	C₂×C₄	1	1	yes	characteristic
133	C₃×#102	C₂×C₄	1	1	yes	characteristic
134	C₃×#102	C₂×C₄	1	1	yes	characteristic
135	C₃×#102	C₂×C₄	1	1	yes	characteristic
136	C₃×#102	C₂×C₄	1	1	yes	characteristic
137	C₃×C₂²⋊C₈	—	2	1	no	—
138	C₃×C₂²⋊C₈	—	2	1	no	—
139	C₃×C₂²⋊C₈	—	2	1	no	—
140	C₃×C₂²⋊C₈	—	2	1	no	—
141	C₃×C₂²⋊C₈	—	2	1	no	—
142	C₃×C₂²⋊C₈	—	2	1	no	—
143	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
144	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
145	C₃×#97	—	2	1	no	—
146	C₃×#97	—	2	1	no	—
147	C₃×#97	D₄	1	1	yes	characteristic
148	C₃×#97	D₄	1	1	yes	characteristic
149	C₃×C₄×C₈	—	2	1	no	—
150	C₃×C₄×C₈	—	2	1	no	—
151	C₃×C₄×C₈	—	2	1	no	—
152	C₃×C₄×C₈	—	2	1	no	—
153	C₃×C₄×C₈	—	2	1	no	—
154	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
155	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
156	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
157	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
158	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
159	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
160	#529	C₂²×C₃	1	1	yes	characteristic
161	C₄×#41	C₂²×C₃	1	1	yes	characteristic
162	#485	C₃×C₄	1	1	yes	characteristic
163	#482	C₃×C₄	1	1	yes	characteristic
164	#479	C₃×C₄	1	1	yes	characteristic
165	#478	C₃×C₄	1	1	yes	characteristic
166	#464	C₃×C₄	1	1	yes	characteristic
167	#463	C₃×C₄	1	1	yes	characteristic
168	#452	C₃×C₄	1	1	yes	characteristic
169	#449	C₃×C₄	1	1	yes	characteristic
170	#446	C₂²×C₃	1	1	yes	characteristic
171	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
172	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
173	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
174	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
175	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
176	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
177	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
178	#436	—	2	1	no	—
179	#436	—	2	1	no	—
180	#436	—	2	1	no	—
181	#436	C₂²×C₃	1	1	yes	characteristic
182	#436	C₂²×C₃	1	1	yes	characteristic
183	#436	C₂²×C₃	1	1	yes	characteristic
184	#435	—	2	1	no	—
185	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
186	#433	—	2	1	no	—
187	#432	—	2	1	no	—
188	#432	C₂²×C₃	1	1	yes	characteristic
189	#431	C₂²×C₃	1	1	yes	characteristic
190	#431	C₂²×C₃	1	1	yes	characteristic
191	#405	—	2	1	no	—
192	C₄×M₁₆	—	2	1	no	—
193	C₄×M₁₆	C₂²×C₃	1	1	yes	characteristic
194	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
195	#335	C₂²×C₃	1	1	yes	characteristic
196	#335	C₂²×C₃	1	1	yes	characteristic
197	#334	C₂²×C₃	1	1	yes	characteristic
198	#334	C₂²×C₃	1	1	yes	characteristic
199	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
200	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
201	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
202	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
203	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
204	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
205	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
206	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
207	#322	C₂²×C₃	1	1	yes	characteristic
208	#322	C₂²×C₃	1	1	yes	characteristic
209	#322	C₂²×C₃	1	1	yes	characteristic
210	#322	C₂²×C₃	1	1	yes	characteristic
211	C₃×#41	—	2	2	no	—
212	C₃×#41	—	4	1	no	—
213	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₃×D₄	—	2	1	no	—
216	C₂×C₃×D₄	—	2	1	no	—
217	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
219	C₂²×C₃×C₄	—	2	1	no	—
220	C₂²×C₃×C₄	—	2	1	no	—
221	C₂²×C₃×C₄	—	2	1	no	—
222	C₂²×C₃×C₄	—	2	1	no	—
223	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₃×C₄	#41	1	1	yes	characteristic
226	C₃×Q₁₆	—	2	2	no	—
227	C₃×SD₁₆	—	2	2	no	—
228	C₃×SD₁₆	—	4	1	no	—
229	C₃×D₈	—	4	1	no	—
230	C₃×M₁₆	—	4	1	no	—
231	C₃×M₁₆	—	4	1	no	—
232	C₃×M₁₆	—	4	2	no	—
233	C₃×M₁₆	—	4	2	no	—
234	C₃×M₁₆	—	4	2	no	—
235	C₂×C₃×C₈	—	2	1	no	—
236	C₂×C₃×C₈	—	2	1	no	—
237	C₂×C₃×C₈	—	2	1	no	—
238	C₂×C₃×C₈	—	2	1	no	—
239	C₂×C₃×C₈	—	2	1	no	—
240	C₂×C₃×C₈	—	2	1	no	—
241	C₂×C₃×C₈	—	4	2	no	—
242	C₂×C₃×C₈	—	4	2	no	—
243	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
246	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
248	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
249	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
250	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
251	C₃×C₄⋊C₄	—	2	1	no	—
252	C₃×C₄⋊C₄	—	2	1	no	—
253	C₃×C₄⋊C₄	—	2	1	no	—
254	C₃×C₄⋊C₄	—	2	1	no	—
255	C₃×C₄⋊C₄	—	2	1	no	—
256	C₃×C₄⋊C₄	—	2	1	no	—
257	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
258	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
259	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
260	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
261	C₃×C₂²⋊C₄	—	2	1	no	—
262	C₃×C₂²⋊C₄	—	2	1	no	—
263	C₃×C₂²⋊C₄	—	2	1	no	—
264	C₃×C₂²⋊C₄	—	2	1	no	—
265	C₃×C₂²⋊C₄	—	2	1	no	—
266	C₃×C₂²⋊C₄	—	2	1	no	—
267	C₃×C₂²⋊C₄	—	2	1	no	—
268	C₃×C₂²⋊C₄	—	2	1	no	—
269	C₃×C₄²	—	2	1	no	—
270	C₃×C₄²	—	2	1	no	—
271	C₃×C₄²	—	2	1	no	—
272	C₃×C₄²	—	2	1	no	—
273	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
274	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
275	C₃×C₄²	#41	1	1	yes	characteristic
276	C₃×C₄²	C₂⁴	1	1	yes	characteristic
277	C₂×#41	C₂×C₃×C₄	1	1	yes	characteristic
278	C₂×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
279	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
280	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
281	C₂×D₈	C₂×C₃×C₄	1	1	yes	characteristic
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
286	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	2	1	no	—
289	#126	—	2	1	no	—
290	#125	C₂×C₃×C₄	1	1	yes	characteristic
291	#124	C₂×C₃×C₄	1	1	yes	characteristic
292	#123	—	2	1	no	—
293	C₂²⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
294	#121	C₂×C₃×C₄	1	1	yes	characteristic
295	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
302	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
303	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	#117	—	2	1	no	—
306	#117	C₂×C₃×C₄	1	1	yes	characteristic
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
309	#107	C₂×C₃×C₄	1	1	yes	characteristic
310	#107	C₂×C₃×C₄	1	1	yes	characteristic
311	#106	C₂×C₃×C₄	1	1	yes	characteristic
312	#106	C₂×C₃×C₄	1	1	yes	characteristic
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
318	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
319	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
320	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
321	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
322	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
323	#103	C₂×C₃×C₄	1	1	yes	characteristic
324	#103	C₂×C₃×C₄	1	1	yes	characteristic
325	#103	C₂×C₃×C₄	1	1	yes	characteristic
326	#103	C₂×C₃×C₄	1	1	yes	characteristic
327	#102	C₂×C₃×C₄	1	1	yes	characteristic
328	#102	C₂×C₃×C₄	1	1	yes	characteristic
329	#102	C₂×C₃×C₄	1	1	yes	characteristic
330	#102	C₂×C₃×C₄	1	1	yes	characteristic
331	C₂²⋊C₈	—	2	1	no	—
332	C₂²⋊C₈	—	2	1	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	1	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₂²⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
338	C₂²⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
339	#97	—	2	1	no	—
340	#97	—	2	1	no	—
341	#97	C₃×D₄	1	1	yes	characteristic
342	#97	C₃×D₄	1	1	yes	characteristic
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	—	2	1	no	—
347	C₄×C₈	—	2	1	no	—
348	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
349	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
350	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
351	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
352	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
353	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
357	C₃×Q₈	—	2	1	no	—
358	C₃×Q₈	—	2	1	no	—
359	C₃×Q₈	—	2	1	no	—
360	C₃×Q₈	#131	1	2	yes	—
361	C₃×D₄	—	2	1	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	2	1	no	—
364	C₃×D₄	—	2	1	no	—
365	C₃×D₄	—	4	2	no	—
366	C₃×D₄	—	8	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	4	1	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	4	1	no	—
380	C₂×C₃×C₄	—	4	1	no	—
381	C₂×C₃×C₄	—	4	1	no	—
382	C₂×C₃×C₄	—	4	1	no	—
383	C₂×C₃×C₄	—	8	1	no	—
384	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
386	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
390	C₃×C₈	—	2	2	no	—
391	C₃×C₈	—	2	1	no	—
392	C₃×C₈	—	2	1	no	—
393	C₃×C₈	—	2	1	no	—
394	C₃×C₈	—	2	1	no	—
395	C₃×C₈	—	2	1	no	—
396	C₃×C₈	—	2	1	no	—
397	C₃×C₈	—	2	1	no	—
398	C₃×C₈	—	2	1	no	—
399	C₃×C₈	—	4	1	no	—
400	C₃×C₈	—	4	1	no	—
401	C₃×C₈	—	4	1	no	—
402	C₃×C₈	—	4	1	no	—
403	C₃×C₈	—	4	1	no	—
404	#41	—	2	2	no	—
405	#41	—	4	1	no	—
406	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
407	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
411	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
418	C₂²×C₄	C₃×#41	1	1	yes	characteristic
419	Q₁₆	—	2	2	no	—
420	SD₁₆	—	2	2	no	—
421	SD₁₆	—	4	1	no	—
422	D₈	—	4	1	no	—
423	M₁₆	—	4	1	no	—
424	M₁₆	—	4	1	no	—
425	M₁₆	—	4	2	no	—
426	M₁₆	—	4	2	no	—
427	M₁₆	—	4	2	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	4	2	no	—
435	C₂×C₈	—	4	2	no	—
436	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
437	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
438	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
439	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
440	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
441	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
442	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
443	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
451	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
452	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
453	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
467	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
468	C₄²	C₃×#41	1	1	yes	characteristic
469	C₄²	C₂⁴×C₃	1	1	yes	characteristic
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	—	4	1	no	—
475	C₂²×C₃	—	4	1	no	—
476	C₂²×C₃	—	4	1	no	—
477	C₂²×C₃	—	4	1	no	—
478	C₂²×C₃	—	4	1	no	—
479	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
480	C₃×C₄	—	2	1	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	2	1	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	2	1	no	—
485	C₃×C₄	—	4	1	no	—
486	C₃×C₄	—	4	1	no	—
487	C₃×C₄	—	4	1	no	—
488	C₃×C₄	—	4	1	no	—
489	C₃×C₄	—	4	1	no	—
490	C₃×C₄	C₂×#131	1	1	yes	characteristic
491	C₃×C₄	#568	1	1	yes	characteristic
492	C₃×C₄	#575	1	1	yes	characteristic
493	C₃×C₄	#575	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	C₃×#131	1	2	yes	—
501	D₄	—	2	1	no	—
502	D₄	—	2	1	no	—
503	D₄	—	2	1	no	—
504	D₄	—	2	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
525	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
526	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
527	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
528	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
530	C₈	—	2	2	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₂×C₃	—	4	1	no	—
545	C₂×C₃	—	8	1	no	—
546	C₂×C₃	—	8	1	no	—
547	C₂×C₃	#2933	1	1	yes	characteristic
548	C₂×C₃	#2943	1	1	yes	characteristic
549	C₂×C₃	#2956	1	1	yes	characteristic
550	C₂²	—	2	1	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	1	no	—
559	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
560	C₄	—	2	1	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	C₂×C₃×#131	1	1	yes	characteristic
571	C₄	C₃×#568	1	1	yes	characteristic
572	C₄	C₃×#575	1	1	yes	characteristic
573	C₄	C₃×#575	1	1	yes	characteristic
574	C₃	#18005	1	1	yes	characteristic, direct product factor, Sylow
575	C₂	—	4	1	no	—
576	C₂	—	8	1	no	—
577	C₂	—	8	1	no	—
578	C₂	C₃×#2933	1	1	yes	characteristic
579	C₂	C₃×#2943	1	1	yes	characteristic
580	C₂	C₃×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₄²	C₂⁴×C₃
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₃×#449	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2971	C₂	semidirect
3. C₃×#2969	C₂	semidirect
4. C₃×#1594	C₂	semidirect
5. C₃×#1592	C₂	semidirect
6. C₃×#1588	C₂	semidirect
7. C₃×#1588	C₂	semidirect
8. C₃×#1587	C₂	semidirect
9. C₃×#1586	C₂	semidirect
10. C₃×#1579	C₂	semidirect
11. C₃×SD₁₆⋊C₈	C₂	semidirect
12. C₃×#1572	C₂	semidirect
13. C₃×#1494	C₂	semidirect
14. C₃×#1476	C₂	semidirect
15. C₃×#1451	C₂	semidirect
16. #18005	C₃	direct (N × H)
69. #2971	C₂×C₃	semidirect
70. #2969	C₂×C₃	semidirect
71. #1594	C₂×C₃	semidirect
72. #1592	C₂×C₃	semidirect
73. #1588	C₂×C₃	semidirect
74. #1588	C₂×C₃	semidirect
75. #1587	C₂×C₃	semidirect
76. #1586	C₂×C₃	semidirect
77. #1579	C₂×C₃	semidirect
78. SD₁₆⋊C₈	C₂×C₃	semidirect
79. #1572	C₂×C₃	semidirect
80. #1494	C₂×C₃	semidirect
81. #1476	C₂×C₃	semidirect
82. #1451	C₂×C₃	semidirect
574. C₃	#18005	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3102	2
C₃×#2971	2
C₃×#2969	2
C₃×#1594	2
C₃×#1592	2
C₃×#1588	2
C₃×#1587	2
C₃×#1586	2
C₃×#1579	2
C₃×SD₁₆⋊C₈	2
C₃×#1572	2
C₃×#1494	2
C₃×#1476	2
C₃×#1451	2
#18005	3

Subgroups — C3×#18005 #10636612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#18005 #10636612