Subgroups — C₃×#18012 #10636619

Order 768.

592 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3108	C₂	1	1	yes	maximal, characteristic
2	C₃×#2969	C₂	1	1	yes	maximal, characteristic
3	C₃×Q₈×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#1587	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1585	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#1583	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#1495	C₂	1	1	yes	maximal, characteristic
14	C₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	#18012	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×#529	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
19	C₃×#483	C₄	1	1	yes	characteristic
20	C₃×#480	C₄	1	1	yes	characteristic
21	C₃×#479	C₄	1	1	yes	characteristic
22	C₃×#479	C₄	1	1	yes	characteristic
23	C₃×#464	C₄	1	1	yes	characteristic
24	C₃×#464	C₄	1	1	yes	characteristic
25	C₃×#451	C₄	1	1	yes	characteristic
26	C₃×#448	C₄	1	1	yes	characteristic
27	C₃×#446	—	2	1	no	—
28	C₃×#446	—	2	1	no	—
29	C₃×#446	C₂²	1	1	yes	characteristic
30	C₃×#446	C₂²	1	1	yes	characteristic
31	C₃×#446	C₂²	1	1	yes	characteristic
32	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₈×Q₈	C₂²	1	1	yes	characteristic
35	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
36	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
37	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
38	C₃×C₄×SD₁₆	C₂²	1	1	yes	characteristic
39	C₃×#436	—	2	1	no	—
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×#431	C₂²	1	1	yes	characteristic
45	C₃×#431	C₂²	1	1	yes	characteristic
46	C₃×#431	C₂²	1	1	yes	characteristic
47	C₃×#423	—	2	1	no	—
48	C₃×#423	C₂²	1	1	yes	characteristic
49	C₃×#405	—	2	1	no	—
50	C₃×C₄×M₁₆	—	2	1	no	—
51	C₃×C₄×M₁₆	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×Q₈⋊C₈	C₂²	1	1	yes	characteristic
61	C₃×Q₈⋊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×C₈²	C₂²	1	1	yes	characteristic
68	#3108	C₂×C₃	1	1	yes	characteristic
69	#2969	C₂×C₃	1	1	yes	characteristic
70	Q₈×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
71	#1593	C₂×C₃	1	1	yes	characteristic, complemented
72	#1590	C₂×C₃	1	1	yes	characteristic, complemented
73	#1587	C₂×C₃	1	1	yes	characteristic, complemented
74	#1585	C₂×C₃	1	1	yes	characteristic, complemented
75	#1584	C₂×C₃	1	1	yes	characteristic, complemented
76	#1583	C₂×C₃	1	1	yes	characteristic, complemented
77	SD₁₆⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
78	C₈×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
79	#1574	C₂×C₃	1	1	yes	characteristic, complemented
80	#1495	C₂×C₃	1	1	yes	characteristic
81	#1479	C₂×C₃	1	1	yes	characteristic, complemented
82	#1453	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂²×C₃×Q₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
85	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
86	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
87	C₂×C₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
88	C₂×C₃×M₁₆	—	2	1	no	—
89	C₂×C₃×M₁₆	—	2	1	no	—
90	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
91	C₂×C₃×M₁₆	D₄	1	1	yes	characteristic
92	C₂²×C₃×C₈	—	2	1	no	—
93	C₃×#126	—	2	1	no	—
94	C₃×#125	C₂×C₄	1	1	yes	characteristic
95	C₃×#124	C₂×C₄	1	1	yes	characteristic
96	C₃×#123	—	2	1	no	—
97	C₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
98	C₃×#121	C₂×C₄	1	1	yes	characteristic
99	C₃×C₄×Q₈	—	2	1	no	—
100	C₃×C₄×Q₈	—	2	1	no	—
101	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
102	C₃×C₄×Q₈	C₂×C₄	1	1	yes	characteristic
103	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
104	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
105	C₃×C₄×Q₈	C₂³	1	1	yes	characteristic
106	C₃×C₄×D₄	—	2	1	no	—
107	C₃×C₄×D₄	C₂³	1	1	yes	characteristic
108	C₃×#117	—	2	1	no	—
109	C₂×C₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄²	—	2	1	no	—
112	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
113	C₃×#107	C₂×C₄	1	1	yes	characteristic
114	C₃×#107	C₂×C₄	1	1	yes	characteristic
115	C₃×#106	C₂×C₄	1	1	yes	characteristic
116	C₃×#106	C₂×C₄	1	1	yes	characteristic
117	C₃×C₄⋊C₈	—	2	1	no	—
118	C₃×C₄⋊C₈	—	2	1	no	—
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	—	2	1	no	—
124	C₃×C₄⋊C₈	—	2	1	no	—
125	C₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
126	C₃×C₄⋊C₈	C₂×C₄	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×#103	C₂×C₄	1	1	yes	characteristic
134	C₃×#103	C₂×C₄	1	1	yes	characteristic
135	C₃×#103	C₂×C₄	1	1	yes	characteristic
136	C₃×#103	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	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	—	2	1	no	—
148	C₃×#97	D₄	1	1	yes	characteristic
149	C₃×#97	D₄	1	1	yes	characteristic
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	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
162	#483	C₃×C₄	1	1	yes	characteristic
163	#480	C₃×C₄	1	1	yes	characteristic
164	#479	C₃×C₄	1	1	yes	characteristic
165	#479	C₃×C₄	1	1	yes	characteristic
166	#464	C₃×C₄	1	1	yes	characteristic
167	#464	C₃×C₄	1	1	yes	characteristic
168	#451	C₃×C₄	1	1	yes	characteristic
169	#448	C₃×C₄	1	1	yes	characteristic
170	#446	—	2	1	no	—
171	#446	—	2	1	no	—
172	#446	C₂²×C₃	1	1	yes	characteristic
173	#446	C₂²×C₃	1	1	yes	characteristic
174	#446	C₂²×C₃	1	1	yes	characteristic
175	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
176	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
177	C₈×Q₈	C₂²×C₃	1	1	yes	characteristic
178	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
179	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
180	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
181	C₄×SD₁₆	C₂²×C₃	1	1	yes	characteristic
182	#436	—	2	1	no	—
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	#431	C₂²×C₃	1	1	yes	characteristic
188	#431	C₂²×C₃	1	1	yes	characteristic
189	#431	C₂²×C₃	1	1	yes	characteristic
190	#423	—	2	1	no	—
191	#423	C₂²×C₃	1	1	yes	characteristic
192	#405	—	2	1	no	—
193	C₄×M₁₆	—	2	1	no	—
194	C₄×M₁₆	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	Q₈⋊C₈	C₂²×C₃	1	1	yes	characteristic
204	Q₈⋊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	C₈²	C₂²×C₃	1	1	yes	characteristic
211	C₂×C₃×Q₈	—	2	1	no	—
212	C₂×C₃×Q₈	—	2	2	no	—
213	C₂×C₃×Q₈	—	4	1	no	—
214	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₃×Q₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₃×D₄	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₃×C₄	#41	1	1	yes	characteristic
225	C₃×Q₁₆	—	2	2	no	—
226	C₃×Q₁₆	—	4	1	no	—
227	C₃×SD₁₆	—	2	2	no	—
228	C₃×SD₁₆	—	4	1	no	—
229	C₃×M₁₆	—	2	2	no	—
230	C₃×M₁₆	—	4	1	no	—
231	C₃×M₁₆	—	4	2	no	—
232	C₃×M₁₆	—	4	2	no	—
233	C₂×C₃×C₈	—	2	1	no	—
234	C₂×C₃×C₈	—	2	1	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	—	4	2	no	—
240	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
242	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
245	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
246	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
247	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
248	C₃×C₄⋊C₄	—	2	1	no	—
249	C₃×C₄⋊C₄	—	2	1	no	—
250	C₃×C₄⋊C₄	—	2	1	no	—
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×C₄²	—	2	1	no	—
267	C₃×C₄²	—	2	1	no	—
268	C₃×C₄²	—	2	1	no	—
269	C₃×C₄²	—	2	1	no	—
270	C₃×C₄²	—	2	1	no	—
271	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
272	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
273	C₃×C₄²	#41	1	1	yes	characteristic
274	C₃×C₄²	C₂⁴	1	1	yes	characteristic
275	C₂²×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
276	C₂×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
277	C₂×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
278	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
279	C₂×SD₁₆	C₂×C₃×C₄	1	1	yes	characteristic
280	C₂×M₁₆	—	2	1	no	—
281	C₂×M₁₆	—	2	1	no	—
282	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
283	C₂×M₁₆	C₃×D₄	1	1	yes	characteristic
284	C₂²×C₈	—	2	1	no	—
285	#126	—	2	1	no	—
286	#125	C₂×C₃×C₄	1	1	yes	characteristic
287	#124	C₂×C₃×C₄	1	1	yes	characteristic
288	#123	—	2	1	no	—
289	C₂²⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
290	#121	C₂×C₃×C₄	1	1	yes	characteristic
291	C₄×Q₈	—	2	1	no	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
294	C₄×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
295	C₄×Q₈	C₂³×C₃	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	C₂³×C₃	1	1	yes	characteristic
300	#117	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
305	#107	C₂×C₃×C₄	1	1	yes	characteristic
306	#107	C₂×C₃×C₄	1	1	yes	characteristic
307	#106	C₂×C₃×C₄	1	1	yes	characteristic
308	#106	C₂×C₃×C₄	1	1	yes	characteristic
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
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	#103	C₂×C₃×C₄	1	1	yes	characteristic
328	#103	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	C₂×C₃×C₄	1	1	yes	characteristic
336	C₂²⋊C₈	C₂×C₃×C₄	1	1	yes	characteristic
337	#97	—	2	1	no	—
338	#97	—	2	1	no	—
339	#97	—	2	1	no	—
340	#97	C₃×D₄	1	1	yes	characteristic
341	#97	C₃×D₄	1	1	yes	characteristic
342	C₄×C₈	—	2	1	no	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	2	1	no	—
345	C₄×C₈	—	2	1	no	—
346	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
347	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
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	C₂³×C₃	—	2	1	no	—
353	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
354	C₃×Q₈	—	2	1	no	—
355	C₃×Q₈	—	2	1	no	—
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	—	2	1	no	—
358	C₃×Q₈	—	2	1	no	—
359	C₃×Q₈	—	4	2	no	—
360	C₃×Q₈	#131	1	2	yes	—
361	C₃×D₄	—	2	1	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	8	1	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	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	—	4	1	no	—
376	C₂×C₃×C₄	—	4	2	no	—
377	C₂×C₃×C₄	—	4	1	no	—
378	C₂×C₃×C₄	—	4	1	no	—
379	C₂×C₃×C₄	—	8	1	no	—
380	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
381	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
386	C₃×C₈	—	2	1	no	—
387	C₃×C₈	—	2	1	no	—
388	C₃×C₈	—	2	1	no	—
389	C₃×C₈	—	2	1	no	—
390	C₃×C₈	—	2	1	no	—
391	C₃×C₈	—	2	1	no	—
392	C₃×C₈	—	2	1	no	—
393	C₃×C₈	—	4	1	no	—
394	C₃×C₈	—	4	1	no	—
395	C₃×C₈	—	4	1	no	—
396	C₃×C₈	—	4	1	no	—
397	C₃×C₈	—	4	1	no	—
398	C₃×C₈	—	4	1	no	—
399	C₃×C₈	#137	1	2	yes	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	4	1	no	—
403	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
404	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
405	C₂×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
412	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
413	C₂²×C₄	C₃×#41	1	1	yes	characteristic
414	Q₁₆	—	2	2	no	—
415	Q₁₆	—	4	1	no	—
416	SD₁₆	—	2	2	no	—
417	SD₁₆	—	4	1	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	4	1	no	—
420	M₁₆	—	4	2	no	—
421	M₁₆	—	4	2	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	4	2	no	—
429	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
430	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
431	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
432	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
433	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
434	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
435	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
436	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
447	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
449	C₄⋊C₄	C₂²×C₃×C₄	1	1	yes	characteristic
450	C₂²⋊C₄	—	2	1	no	—
451	C₂²⋊C₄	—	2	1	no	—
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
461	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
462	C₄²	C₃×#41	1	1	yes	characteristic
463	C₄²	C₂⁴×C₃	1	1	yes	characteristic
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	1	no	—
466	C₂²×C₃	—	2	1	no	—
467	C₂²×C₃	—	4	1	no	—
468	C₂²×C₃	—	4	1	no	—
469	C₂²×C₃	—	4	1	no	—
470	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	2	no	—
473	C₃×C₄	—	2	1	no	—
474	C₃×C₄	—	2	1	no	—
475	C₃×C₄	—	2	1	no	—
476	C₃×C₄	—	4	1	no	—
477	C₃×C₄	—	4	1	no	—
478	C₃×C₄	—	4	1	no	—
479	C₃×C₄	—	4	1	no	—
480	C₃×C₄	—	4	1	no	—
481	C₃×C₄	—	4	1	no	—
482	C₃×C₄	C₂×#131	1	1	yes	characteristic
483	C₃×C₄	#568	1	1	yes	characteristic
484	C₃×C₄	C₂×#137	1	1	yes	characteristic
485	C₃×C₄	#575	1	1	yes	characteristic
486	C₂³	—	2	1	no	—
487	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
488	Q₈	—	2	1	no	—
489	Q₈	—	2	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	2	1	no	—
493	Q₈	—	4	2	no	—
494	Q₈	C₃×#131	1	2	yes	—
495	D₄	—	2	1	no	—
496	D₄	—	2	1	no	—
497	D₄	—	8	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	8	1	no	—
514	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
515	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
516	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
517	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
519	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	2	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	1	no	—
533	C₈	C₃×#137	1	2	yes	—
534	C₂×C₃	—	4	1	no	—
535	C₂×C₃	—	8	1	no	—
536	C₂×C₃	#2933	1	1	yes	characteristic
537	C₂×C₃	C₄×#137	1	1	yes	characteristic
538	C₂×C₃	#2957	1	1	yes	characteristic
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	C₂×C₃×#131	1	1	yes	characteristic
558	C₄	C₃×#568	1	1	yes	characteristic
559	C₄	C₂×C₃×#137	1	1	yes	characteristic
560	C₄	C₃×#575	1	1	yes	characteristic
561	C₃	#18012	1	1	yes	characteristic, direct product factor, Sylow
562	C₂	—	4	1	no	—
563	C₂	—	8	1	no	—
564	C₂	C₃×#2933	1	1	yes	characteristic
565	C₂	C₃×C₄×#137	1	1	yes	characteristic
566	C₂	C₃×#2957	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×#121	C₂×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
3. C₃×Q₈×M₁₆	C₂	semidirect
4. C₃×#1593	C₂	semidirect
5. C₃×#1590	C₂	semidirect
6. C₃×#1587	C₂	semidirect
7. C₃×#1585	C₂	semidirect
8. C₃×#1584	C₂	semidirect
9. C₃×#1583	C₂	semidirect
10. C₃×SD₁₆⋊C₈	C₂	semidirect
11. C₃×C₈×Q₁₆	C₂	semidirect
12. C₃×#1574	C₂	semidirect
14. C₃×#1479	C₂	semidirect
15. C₃×#1453	C₂	semidirect
16. #18012	C₃	direct (N × H)
70. Q₈×M₁₆	C₂×C₃	semidirect
71. #1593	C₂×C₃	semidirect
72. #1590	C₂×C₃	semidirect
73. #1587	C₂×C₃	semidirect
74. #1585	C₂×C₃	semidirect
75. #1584	C₂×C₃	semidirect
76. #1583	C₂×C₃	semidirect
77. SD₁₆⋊C₈	C₂×C₃	semidirect
78. C₈×Q₁₆	C₂×C₃	semidirect
79. #1574	C₂×C₃	semidirect
81. #1479	C₂×C₃	semidirect
82. #1453	C₂×C₃	semidirect
561. C₃	#18012	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×#3108	2
C₃×#2969	2
C₃×Q₈×M₁₆	2
C₃×#1593	2
C₃×#1590	2
C₃×#1587	2
C₃×#1585	2
C₃×#1584	2
C₃×#1583	2
C₃×SD₁₆⋊C₈	2
C₃×C₈×Q₁₆	2
C₃×#1574	2
C₃×#1495	2
C₃×#1479	2
C₃×#1453	2
#18012	3

Subgroups — C3×#18012 #10636619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#18012 #10636619