Subgroups — C₃×#18014 #10636621

Order 768.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3105	C₂	1	1	yes	maximal, characteristic
2	C₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1585	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₈×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1573	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1494	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
16	#18014	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#529	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×D₄	C₂²	1	1	yes	characteristic
19	C₃×#484	C₄	1	1	yes	characteristic
20	C₃×#481	C₄	1	1	yes	characteristic
21	C₃×#478	C₄	1	1	yes	characteristic
22	C₃×#478	C₄	1	1	yes	characteristic
23	C₃×#463	C₄	1	1	yes	characteristic
24	C₃×#463	C₄	1	1	yes	characteristic
25	C₃×#450	C₄	1	1	yes	characteristic
26	C₃×#447	C₄	1	1	yes	characteristic
27	C₃×#446	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
30	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
31	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
32	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
33	C₃×#436	C₂²	1	1	yes	characteristic
34	C₃×#436	C₂²	1	1	yes	characteristic
35	C₃×#436	C₂²	1	1	yes	characteristic, complemented
36	C₃×#435	—	2	1	no	—
37	C₃×#435	—	2	1	no	—
38	C₃×#435	—	2	1	no	—
39	C₃×C₈×D₄	—	2	1	no	—
40	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
41	C₃×C₈×D₄	C₂²	1	1	yes	characteristic
42	C₃×C₈×D₄	C₂²	1	1	yes	characteristic, complemented
43	C₃×#433	—	2	1	no	—
44	C₃×#432	C₂²	1	1	yes	characteristic
45	C₃×#431	C₂²	1	1	yes	characteristic
46	C₃×#431	C₂²	1	1	yes	characteristic
47	C₃×#424	—	2	1	no	—
48	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₃×#407	—	2	1	no	—
50	C₂×C₃×C₂²⋊C₈	—	2	1	no	—
51	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
52	C₃×#335	C₂²	1	1	yes	characteristic, complemented
53	C₃×#335	C₂²	1	1	yes	characteristic, complemented
54	C₃×#334	C₂²	1	1	yes	characteristic, complemented
55	C₃×#334	C₂²	1	1	yes	characteristic, complemented
56	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	C₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
59	C₃×D₄⋊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, complemented
63	C₃×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
64	C₃×#322	C₂²	1	1	yes	characteristic, complemented
65	C₃×#322	C₂²	1	1	yes	characteristic, complemented
66	C₃×C₈²	C₂²	1	1	yes	characteristic, complemented
67	C₃×C₈²	C₂²	1	1	yes	characteristic, complemented
68	#3105	C₂×C₃	1	1	yes	characteristic
69	#2994	C₂×C₃	1	1	yes	characteristic, complemented
70	#2974	C₂×C₃	1	1	yes	characteristic, complemented
71	#1590	C₂×C₃	1	1	yes	characteristic, complemented
72	#1589	C₂×C₃	1	1	yes	characteristic, complemented
73	#1588	C₂×C₃	1	1	yes	characteristic, complemented
74	#1586	C₂×C₃	1	1	yes	characteristic, complemented
75	#1586	C₂×C₃	1	1	yes	characteristic, complemented
76	#1585	C₂×C₃	1	1	yes	characteristic, complemented
77	C₈×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
78	C₈×D₈	C₂×C₃	1	1	yes	characteristic, complemented
79	#1573	C₂×C₃	1	1	yes	characteristic, complemented
80	#1494	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×D₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
82	#1450	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂²×C₃×D₄	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₃×C₄	—	2	1	no	—
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×D₈	C₂×C₄	1	1	yes	characteristic
89	C₂×C₃×M₁₆	—	2	1	no	—
90	C₂×C₃×M₁₆	—	2	1	no	—
91	C₂×C₃×M₁₆	—	2	1	no	—
92	C₂²×C₃×C₈	—	2	1	no	—
93	C₂²×C₃×C₈	—	2	1	no	—
94	C₂²×C₃×C₈	—	2	1	no	—
95	C₂²×C₃×C₈	—	2	1	no	—
96	C₂²×C₃×C₈	—	2	1	no	—
97	C₃×#126	—	2	1	no	—
98	C₃×#125	C₂×C₄	1	1	yes	characteristic
99	C₃×#124	C₂×C₄	1	1	yes	characteristic
100	C₃×#123	—	2	1	no	—
101	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
102	C₃×#121	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
109	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
110	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
111	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
112	C₃×#117	—	2	1	no	—
113	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
116	C₃×#107	C₂×C₄	1	1	yes	characteristic
117	C₃×#107	C₂×C₄	1	1	yes	characteristic
118	C₃×#106	C₂×C₄	1	1	yes	characteristic
119	C₃×#106	C₂×C₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
126	C₃×C₄⋊C₈	D₄	1	1	yes	characteristic
127	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
128	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
129	C₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
130	C₃×C₄⋊C₈	C₂³	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×#102	C₂×C₄	1	1	yes	characteristic
138	C₃×#102	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
144	C₃×C₂²⋊C₈	—	2	1	no	—
145	C₃×C₂²⋊C₈	—	2	1	no	—
146	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
147	C₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
148	C₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
149	C₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
150	C₃×#97	—	2	1	no	—
151	C₃×#97	—	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	C₂×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
162	#484	C₃×C₄	1	1	yes	characteristic
163	#481	C₃×C₄	1	1	yes	characteristic
164	#478	C₃×C₄	1	1	yes	characteristic
165	#478	C₃×C₄	1	1	yes	characteristic
166	#463	C₃×C₄	1	1	yes	characteristic
167	#463	C₃×C₄	1	1	yes	characteristic
168	#450	C₃×C₄	1	1	yes	characteristic
169	#447	C₃×C₄	1	1	yes	characteristic
170	#446	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
173	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
174	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
175	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
176	#436	C₂²×C₃	1	1	yes	characteristic
177	#436	C₂²×C₃	1	1	yes	characteristic
178	#436	C₂²×C₃	1	1	yes	characteristic, complemented
179	#435	—	2	1	no	—
180	#435	—	2	1	no	—
181	#435	—	2	1	no	—
182	C₈×D₄	—	2	1	no	—
183	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
184	C₈×D₄	C₂²×C₃	1	1	yes	characteristic
185	C₈×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
186	#433	—	2	1	no	—
187	#432	C₂²×C₃	1	1	yes	characteristic
188	#431	C₂²×C₃	1	1	yes	characteristic
189	#431	C₂²×C₃	1	1	yes	characteristic
190	#424	—	2	1	no	—
191	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
192	#407	—	2	1	no	—
193	C₂×C₂²⋊C₈	—	2	1	no	—
194	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
195	#335	C₂²×C₃	1	1	yes	characteristic, complemented
196	#335	C₂²×C₃	1	1	yes	characteristic, complemented
197	#334	C₂²×C₃	1	1	yes	characteristic, complemented
198	#334	C₂²×C₃	1	1	yes	characteristic, complemented
199	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
200	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
201	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
202	D₄⋊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, complemented
206	D₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
207	#322	C₂²×C₃	1	1	yes	characteristic, complemented
208	#322	C₂²×C₃	1	1	yes	characteristic, complemented
209	C₈²	C₂²×C₃	1	1	yes	characteristic, complemented
210	C₈²	C₂²×C₃	1	1	yes	characteristic, complemented
211	C₂⁴×C₃	—	2	1	no	—
212	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
213	C₂×C₃×D₄	—	2	2	no	—
214	C₂×C₃×D₄	—	2	1	no	—
215	C₂×C₃×D₄	—	2	1	no	—
216	C₂×C₃×D₄	—	4	1	no	—
217	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₃×D₄	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
224	C₂²×C₃×C₄	—	2	1	no	—
225	C₂²×C₃×C₄	—	2	1	no	—
226	C₂²×C₃×C₄	—	8	1	no	—
227	C₂²×C₃×C₄	—	8	1	no	—
228	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₃×C₄	#41	1	1	yes	characteristic
231	C₃×SD₁₆	—	2	2	no	—
232	C₃×SD₁₆	—	4	1	no	—
233	C₃×D₈	—	2	2	no	—
234	C₃×D₈	—	4	1	no	—
235	C₃×M₁₆	—	8	1	no	—
236	C₃×M₁₆	—	8	1	no	—
237	C₃×M₁₆	—	8	1	no	—
238	C₂×C₃×C₈	—	2	4	no	—
239	C₂×C₃×C₈	—	2	1	no	—
240	C₂×C₃×C₈	—	2	1	no	—
241	C₂×C₃×C₈	—	2	1	no	—
242	C₂×C₃×C₈	—	2	1	no	—
243	C₂×C₃×C₈	—	2	1	no	—
244	C₂×C₃×C₈	—	2	1	no	—
245	C₂×C₃×C₈	—	8	1	no	—
246	C₂×C₃×C₈	—	8	1	no	—
247	C₂×C₃×C₈	—	8	1	no	—
248	C₂×C₃×C₈	—	8	1	no	—
249	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
250	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
251	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
252	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
253	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
254	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
255	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
256	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
257	C₃×C₄⋊C₄	—	2	1	no	—
258	C₃×C₄⋊C₄	—	2	1	no	—
259	C₃×C₄⋊C₄	—	2	1	no	—
260	C₃×C₄⋊C₄	—	2	1	no	—
261	C₃×C₄⋊C₄	—	2	1	no	—
262	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
265	C₃×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
266	C₃×C₂²⋊C₄	—	2	1	no	—
267	C₃×C₂²⋊C₄	—	2	1	no	—
268	C₃×C₂²⋊C₄	—	2	1	no	—
269	C₃×C₂²⋊C₄	—	2	1	no	—
270	C₃×C₂²⋊C₄	—	2	1	no	—
271	C₃×C₂²⋊C₄	—	2	1	no	—
272	C₃×C₂²⋊C₄	—	2	1	no	—
273	C₃×C₂²⋊C₄	—	2	1	no	—
274	C₃×C₂²⋊C₄	—	2	1	no	—
275	C₃×C₄²	—	2	1	no	—
276	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
277	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
278	C₃×C₄²	#41	1	1	yes	characteristic
279	C₃×C₄²	C₂⁴	1	1	yes	characteristic
280	C₂²×D₄	C₂×C₃×C₄	1	1	yes	characteristic
281	C₂³×C₄	—	2	1	no	—
282	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
283	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
284	C₂×D₈	C₂×C₃×C₄	1	1	yes	characteristic
285	C₂×D₈	C₂×C₃×C₄	1	1	yes	characteristic
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	2	1	no	—
294	#126	—	2	1	no	—
295	#125	C₂×C₃×C₄	1	1	yes	characteristic
296	#124	C₂×C₃×C₄	1	1	yes	characteristic
297	#123	—	2	1	no	—
298	C₂²⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
299	#121	C₂×C₃×C₄	1	1	yes	characteristic
300	C₄×Q₈	C₂³×C₃	1	1	yes	characteristic
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
305	C₄×D₄	C₂×C₃×C₄	1	1	yes	characteristic
306	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
307	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
308	C₄×D₄	C₂³×C₃	1	1	yes	characteristic
309	#117	—	2	1	no	—
310	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
313	#107	C₂×C₃×C₄	1	1	yes	characteristic
314	#107	C₂×C₃×C₄	1	1	yes	characteristic
315	#106	C₂×C₃×C₄	1	1	yes	characteristic
316	#106	C₂×C₃×C₄	1	1	yes	characteristic
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
321	C₄⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
322	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
323	C₄⋊C₈	C₃×D₄	1	1	yes	characteristic
324	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
325	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
326	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
327	C₄⋊C₈	C₂³×C₃	1	1	yes	characteristic
328	#103	C₂×C₃×C₄	1	1	yes	characteristic
329	#103	C₂×C₃×C₄	1	1	yes	characteristic
330	#102	C₂×C₃×C₄	1	1	yes	characteristic
331	#102	C₂×C₃×C₄	1	1	yes	characteristic
332	#102	C₂×C₃×C₄	1	1	yes	characteristic
333	#102	C₂×C₃×C₄	1	1	yes	characteristic
334	#102	C₂×C₃×C₄	1	1	yes	characteristic
335	#102	C₂×C₃×C₄	1	1	yes	characteristic
336	C₂²⋊C₈	—	2	1	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	C₂²⋊C₈	—	2	1	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
344	C₂²⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
345	C₂²⋊C₈	C₃×D₄	1	1	yes	characteristic
346	C₂²⋊C₈	C₃×D₄	1	1	yes	characteristic
347	#97	—	2	1	no	—
348	#97	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
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	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
355	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
356	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	4	2	no	—
361	C₂³×C₃	—	4	2	no	—
362	C₂³×C₃	—	8	1	no	—
363	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
364	C₃×Q₈	—	2	1	no	—
365	C₃×Q₈	—	2	1	no	—
366	C₃×D₄	—	2	1	no	—
367	C₃×D₄	—	2	1	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	—	2	1	no	—
370	C₃×D₄	—	2	1	no	—
371	C₃×D₄	—	4	2	no	—
372	C₃×D₄	—	4	2	no	—
373	C₃×D₄	#131	1	2	yes	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	4	1	no	—
385	C₂×C₃×C₄	—	4	1	no	—
386	C₂×C₃×C₄	—	4	1	no	—
387	C₂×C₃×C₄	—	4	1	no	—
388	C₂×C₃×C₄	—	4	1	no	—
389	C₂×C₃×C₄	—	4	1	no	—
390	C₂×C₃×C₄	—	8	1	no	—
391	C₂×C₃×C₄	—	8	1	no	—
392	C₂×C₃×C₄	—	8	1	no	—
393	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
394	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
397	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
399	C₃×C₈	—	2	2	no	—
400	C₃×C₈	—	2	2	no	—
401	C₃×C₈	—	2	1	no	—
402	C₃×C₈	—	2	1	no	—
403	C₃×C₈	—	2	1	no	—
404	C₃×C₈	—	2	1	no	—
405	C₃×C₈	—	2	1	no	—
406	C₃×C₈	—	2	1	no	—
407	C₃×C₈	—	2	1	no	—
408	C₃×C₈	—	2	1	no	—
409	C₃×C₈	—	4	1	no	—
410	C₃×C₈	—	4	1	no	—
411	C₃×C₈	—	4	1	no	—
412	C₃×C₈	—	4	1	no	—
413	C₂⁴	—	2	1	no	—
414	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
420	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
421	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	8	1	no	—
429	C₂²×C₄	—	8	1	no	—
430	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₃×#41	1	1	yes	characteristic
433	SD₁₆	—	2	2	no	—
434	SD₁₆	—	4	1	no	—
435	D₈	—	2	2	no	—
436	D₈	—	4	1	no	—
437	M₁₆	—	8	1	no	—
438	M₁₆	—	8	1	no	—
439	M₁₆	—	8	1	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	8	1	no	—
448	C₂×C₈	—	8	1	no	—
449	C₂×C₈	—	8	1	no	—
450	C₂×C₈	—	8	1	no	—
451	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
452	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
453	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
454	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
455	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
456	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
457	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
458	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
465	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
466	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
467	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	2	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
479	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
480	C₄²	C₃×#41	1	1	yes	characteristic
481	C₄²	C₂⁴×C₃	1	1	yes	characteristic
482	C₂²×C₃	—	2	1	no	—
483	C₂²×C₃	—	2	1	no	—
484	C₂²×C₃	—	2	2	no	—
485	C₂²×C₃	—	4	1	no	—
486	C₂²×C₃	—	4	1	no	—
487	C₂²×C₃	—	4	1	no	—
488	C₂²×C₃	—	4	1	no	—
489	C₂²×C₃	—	4	1	no	—
490	C₂²×C₃	—	4	1	no	—
491	C₂²×C₃	—	4	1	no	—
492	C₂²×C₃	—	4	1	no	—
493	C₂²×C₃	—	8	4	no	—
494	C₂²×C₃	#443	1	2	yes	—
495	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
496	C₃×C₄	—	2	1	no	—
497	C₃×C₄	—	2	1	no	—
498	C₃×C₄	—	2	1	no	—
499	C₃×C₄	—	2	1	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	—	4	1	no	—
502	C₃×C₄	—	4	1	no	—
503	C₃×C₄	—	4	1	no	—
504	C₃×C₄	—	4	1	no	—
505	C₃×C₄	C₂×#131	1	1	yes	characteristic
506	C₃×C₄	#568	1	1	yes	characteristic
507	C₃×C₄	#576	1	1	yes	characteristic
508	C₃×C₄	#577	1	1	yes	characteristic
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	8	1	no	—
515	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
516	Q₈	—	2	1	no	—
517	Q₈	—	2	1	no	—
518	D₄	—	2	1	no	—
519	D₄	—	2	1	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	C₃×#131	1	2	yes	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	—	8	1	no	—
544	C₂×C₄	—	8	1	no	—
545	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
546	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
547	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
548	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
549	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
550	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	2	no	—
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	2	1	no	—
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	1	no	—
565	C₂×C₃	—	2	2	no	—
566	C₂×C₃	—	4	2	no	—
567	C₂×C₃	—	8	1	no	—
568	C₂×C₃	—	8	1	no	—
569	C₂×C₃	#2933	1	1	yes	characteristic
570	C₂×C₃	#2946	1	1	yes	characteristic
571	C₂×C₃	C₂×#443	1	1	yes	characteristic
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	8	4	no	—
584	C₂²	C₃×#443	1	2	yes	—
585	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	C₂×C₃×#131	1	1	yes	characteristic
596	C₄	C₃×#568	1	1	yes	characteristic
597	C₄	C₃×#576	1	1	yes	characteristic
598	C₄	C₃×#577	1	1	yes	characteristic
599	C₃	#18014	1	1	yes	characteristic, direct product factor, Sylow
600	C₂	—	2	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	1	no	—
603	C₂	—	8	1	no	—
604	C₂	C₃×#2933	1	1	yes	characteristic
605	C₂	C₃×#2946	1	1	yes	characteristic
606	C₂	C₂×C₃×#443	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×#447	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2994	C₂	semidirect
3. C₃×#2974	C₂	semidirect
4. C₃×#1590	C₂	semidirect
5. C₃×#1589	C₂	semidirect
6. C₃×#1588	C₂	semidirect
7. C₃×#1586	C₂	semidirect
8. C₃×#1586	C₂	semidirect
9. C₃×#1585	C₂	semidirect
10. C₃×C₈×SD₁₆	C₂	semidirect
11. C₃×C₈×D₈	C₂	semidirect
12. C₃×#1573	C₂	semidirect
13. C₃×#1494	C₂	semidirect
14. C₂×C₃×D₄⋊C₈	C₂	semidirect
15. C₃×#1450	C₂	semidirect
16. #18014	C₃	direct (N × H)
27. C₃×#446	C₂²	semidirect
28. C₃×C₈×Q₈	C₂²	semidirect
35. C₃×#436	C₂²	semidirect
42. C₃×C₈×D₄	C₂²	semidirect
52. C₃×#335	C₂²	semidirect
53. C₃×#335	C₂²	semidirect
54. C₃×#334	C₂²	semidirect
55. C₃×#334	C₂²	semidirect
56. C₃×Q₈⋊C₈	C₂²	semidirect
57. C₃×Q₈⋊C₈	C₂²	semidirect
62. C₃×D₄⋊C₈	C₂²	semidirect
63. C₃×D₄⋊C₈	C₂²	semidirect
64. C₃×#322	C₂²	semidirect
65. C₃×#322	C₂²	semidirect
66. C₃×C₈²	C₂²	semidirect
67. C₃×C₈²	C₂²	semidirect
69. #2994	C₂×C₃	semidirect
70. #2974	C₂×C₃	semidirect
71. #1590	C₂×C₃	semidirect
72. #1589	C₂×C₃	semidirect
73. #1588	C₂×C₃	semidirect
74. #1586	C₂×C₃	semidirect
75. #1586	C₂×C₃	semidirect
76. #1585	C₂×C₃	semidirect
77. C₈×SD₁₆	C₂×C₃	semidirect
78. C₈×D₈	C₂×C₃	semidirect
79. #1573	C₂×C₃	semidirect
80. #1494	C₂×C₃	semidirect
81. C₂×D₄⋊C₈	C₂×C₃	semidirect
82. #1450	C₂×C₃	semidirect
170. #446	C₂²×C₃	semidirect
171. C₈×Q₈	C₂²×C₃	semidirect
178. #436	C₂²×C₃	semidirect
185. C₈×D₄	C₂²×C₃	semidirect
195. #335	C₂²×C₃	semidirect
196. #335	C₂²×C₃	semidirect
197. #334	C₂²×C₃	semidirect
198. #334	C₂²×C₃	semidirect
199. Q₈⋊C₈	C₂²×C₃	semidirect
200. Q₈⋊C₈	C₂²×C₃	semidirect
205. D₄⋊C₈	C₂²×C₃	semidirect
206. D₄⋊C₈	C₂²×C₃	semidirect
207. #322	C₂²×C₃	semidirect
208. #322	C₂²×C₃	semidirect
209. C₈²	C₂²×C₃	semidirect
210. C₈²	C₂²×C₃	semidirect
599. C₃	#18014	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×#3105	2
C₃×#2994	2
C₃×#2974	2
C₃×#1590	2
C₃×#1589	2
C₃×#1588	2
C₃×#1586	2
C₃×#1585	2
C₃×C₈×SD₁₆	2
C₃×C₈×D₈	2
C₃×#1573	2
C₃×#1494	2
C₂×C₃×D₄⋊C₈	2
C₃×#1450	2
#18014	3

Subgroups — C3×#18014 #10636621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#18014 #10636621