Subgroups — C₃×#80580 #11895506

Order 1152.

728 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5671	C₂	1	1	yes	maximal, characteristic
2	C₃×#5569	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#464	C₂	1	1	yes	maximal, characteristic
4	C₃×#5182	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5166	C₂	1	1	yes	maximal, characteristic
7	C₃×Dic₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
8	C₃×#5056	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×#216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4830	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4829	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4799	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4792	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4768	C₂	1	1	yes	maximal, characteristic
15	C₃×#4759	C₂	1	1	yes	maximal, characteristic
16	C₃×#3364	—	3	1	no	maximal
17	#80580	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃²×SD₁₆	C₂²	1	1	yes	characteristic
20	C₃²×#124	C₂²	1	1	yes	characteristic
21	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
22	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
23	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
24	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
25	C₃×#944	C₂²	1	1	yes	characteristic
26	C₂×C₃×#216	C₂²	1	1	yes	characteristic
27	C₃×#936	C₂²	1	1	yes	characteristic
28	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
29	C₃×#890	—	2	1	no	—
30	C₃×#890	C₂²	1	1	yes	characteristic
31	C₃×#888	—	2	1	no	—
32	C₃×#888	C₂²	1	1	yes	characteristic
33	C₃×#879	—	2	1	no	—
34	C₃×#879	—	2	1	no	—
35	C₃×#878	—	2	1	no	—
36	C₃×#877	—	2	1	no	—
37	C₃×#870	—	2	1	no	—
38	C₃×#870	C₂²	1	1	yes	characteristic
39	C₃×C₄×Dic₆	—	2	1	no	—
40	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
41	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
42	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₃²×#103	C₂²	1	1	yes	characteristic
44	C₃²×#102	C₂²	1	1	yes	characteristic
45	C₃×#835	C₂²	1	1	yes	characteristic
46	C₃×#835	C₂²	1	1	yes	characteristic
47	C₃×#835	C₂²	1	1	yes	characteristic
48	C₃×#832	C₂²	1	1	yes	characteristic
49	C₃×#832	C₂²	1	1	yes	characteristic
50	C₃×#818	C₂²	1	1	yes	characteristic
51	C₃×#817	C₂²	1	1	yes	characteristic
52	C₃×#816	C₂²	1	1	yes	characteristic
53	C₃×#816	C₂²	1	1	yes	characteristic
54	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
55	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
56	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
57	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
58	C₃×#810	C₂²	1	1	yes	characteristic
59	C₃×#807	C₂²	1	1	yes	characteristic
60	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
61	C₃×#557	—	3	1	no	—
62	C₃×#556	—	3	1	no	—
63	#5671	C₂×C₃	1	1	yes	characteristic
64	#5569	C₂×C₃	1	1	yes	characteristic, complemented
65	C₃×#488	—	3	1	no	—
66	C₃×#488	—	3	1	no	—
67	C₃×#487	—	3	1	no	—
68	C₃×#479	—	3	1	no	—
69	C₃×#479	—	3	1	no	—
70	C₃×#474	—	3	1	no	—
71	C₃×#464	—	2	1	no	—
72	C₃×#464	—	3	1	no	—
73	C₃×#464	D₃	1	1	yes	characteristic
74	C₃×#464	C₂×C₃	1	1	yes	characteristic
75	C₃×#462	—	3	1	no	—
76	C₃×C₈×Q₈	—	3	1	no	—
77	C₃×C₄×Q₁₆	—	3	1	no	—
78	C₃×C₄×Q₁₆	—	3	1	no	—
79	C₃×C₄×SD₁₆	—	3	1	no	—
80	#5182	C₂×C₃	1	1	yes	characteristic, complemented
81	Dic₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
82	#5166	C₂×C₃	1	1	yes	characteristic
83	Dic₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
84	#5056	C₂×C₃	1	1	yes	characteristic
85	C₄×#216	C₂×C₃	1	1	yes	characteristic, complemented
86	#4830	C₂×C₃	1	1	yes	characteristic, complemented
87	#4829	C₂×C₃	1	1	yes	characteristic, complemented
88	#4799	C₂×C₃	1	1	yes	characteristic, complemented
89	#4792	C₂×C₃	1	1	yes	characteristic, complemented
90	#4768	C₂×C₃	1	1	yes	characteristic
91	#4759	C₂×C₃	1	1	yes	characteristic
92	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
93	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
94	C₂×C₃²×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₃×Dic₃	—	2	1	no	—
96	C₂×C₃×Dic₆	—	2	1	no	—
97	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
98	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
99	C₃²×Q₁₆	—	2	2	no	—
100	C₃²×SD₁₆	—	2	2	no	—
101	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
102	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
103	C₃²×C₄⋊C₄	—	2	1	no	—
104	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
105	C₃²×C₂²⋊C₄	—	2	1	no	—
106	C₃²×C₂²⋊C₄	—	2	1	no	—
107	C₃²×C₄²	—	2	1	no	—
108	C₃²×C₄²	C₂³	1	1	yes	characteristic
109	C₃×#217	—	2	1	no	—
110	C₃×#217	—	2	1	no	—
111	C₃×#217	—	2	1	no	—
112	C₃×#216	—	2	2	no	—
113	C₃×C₄⋊Dic₃	—	2	1	no	—
114	C₃×C₄⋊Dic₃	—	2	1	no	—
115	C₃×C₄⋊Dic₃	—	2	1	no	—
116	C₃×C₄⋊Dic₃	—	2	1	no	—
117	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
118	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
119	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
120	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
121	C₃×Dic₃⋊C₄	—	2	1	no	—
122	C₃×Dic₃⋊C₄	—	2	1	no	—
123	C₃×Dic₃⋊C₄	—	2	1	no	—
124	C₃×Dic₃⋊C₄	—	2	1	no	—
125	C₃×Dic₃⋊C₄	—	2	1	no	—
126	C₃×Dic₃⋊C₄	—	2	1	no	—
127	C₃×Dic₃⋊C₄	—	2	1	no	—
128	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
129	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
130	C₃×C₄×Dic₃	—	2	1	no	—
131	C₃×C₄×Dic₃	—	2	1	no	—
132	C₃×C₄×Dic₃	—	2	1	no	—
133	C₃×C₄×Dic₃	—	2	1	no	—
134	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
135	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
136	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
137	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
138	#3364	—	3	1	no	Sylow
139	C₂×C₃×Q₁₆	—	2	1	no	—
140	C₂×C₃×Q₁₆	—	3	1	no	—
141	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
142	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₃×SD₁₆	—	2	1	no	—
144	C₂×C₃×SD₁₆	C₂×D₃	1	1	yes	characteristic
145	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
146	C₃×C₄⋊Q₈	—	3	1	no	—
147	C₃×C₄⋊Q₈	—	3	1	no	—
148	C₃×C₄⋊Q₈	—	6	1	no	—
149	C₃×#126	—	6	1	no	—
150	C₃×#126	—	6	1	no	—
151	C₃×#125	—	3	1	no	—
152	C₃×#125	—	3	1	no	—
153	C₃×#125	—	6	1	no	—
154	C₃×#125	—	6	1	no	—
155	C₃×#124	—	2	1	no	—
156	C₃×#124	—	3	1	no	—
157	C₃×#124	C₂×D₃	1	1	yes	characteristic
158	C₃×#124	C₂²×C₃	1	1	yes	characteristic
159	C₃×C₂²⋊Q₈	—	6	1	no	—
160	C₃×C₄×Q₈	—	2	1	no	—
161	C₃×C₄×Q₈	—	3	1	no	—
162	C₃×C₄×Q₈	—	3	1	no	—
163	C₃×C₄×Q₈	—	3	1	no	—
164	C₃×C₄×Q₈	—	3	1	no	—
165	C₃×C₄×Q₈	—	3	1	no	—
166	C₃×C₄×Q₈	—	6	1	no	—
167	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
168	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
169	C₃×C₄×D₄	—	3	1	no	—
170	C₃×#117	—	6	1	no	—
171	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
172	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
173	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
174	#944	C₂²×C₃	1	1	yes	characteristic
175	C₂×#216	C₂²×C₃	1	1	yes	characteristic
176	#936	C₂²×C₃	1	1	yes	characteristic
177	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
178	#890	—	2	1	no	—
179	#890	C₂²×C₃	1	1	yes	characteristic
180	#888	—	2	1	no	—
181	#888	C₂²×C₃	1	1	yes	characteristic
182	#879	—	2	1	no	—
183	#879	—	2	1	no	—
184	#878	—	2	1	no	—
185	#877	—	2	1	no	—
186	#870	—	2	1	no	—
187	#870	C₂²×C₃	1	1	yes	characteristic
188	C₄×Dic₆	—	2	1	no	—
189	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
190	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
191	C₃×#107	—	3	1	no	—
192	C₃×#107	—	3	1	no	—
193	C₃×#106	—	3	1	no	—
194	C₃×C₄⋊C₈	—	2	1	no	—
195	C₃×C₄⋊C₈	—	3	1	no	—
196	C₃×C₄⋊C₈	—	3	1	no	—
197	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
198	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
199	C₃×#103	—	2	1	no	—
200	C₃×#103	—	3	1	no	—
201	C₃×#103	—	3	1	no	—
202	C₃×#103	—	3	1	no	—
203	C₃×#103	—	3	1	no	—
204	C₃×#103	—	3	1	no	—
205	C₃×#103	—	3	1	no	—
206	C₃×#103	C₂×D₃	1	1	yes	characteristic
207	C₃×#103	C₂²×C₃	1	1	yes	characteristic
208	C₃×#102	—	2	1	no	—
209	C₃×#102	—	3	1	no	—
210	C₃×#102	—	3	1	no	—
211	C₃×#102	C₂×D₃	1	1	yes	characteristic
212	C₃×#102	C₂²×C₃	1	1	yes	characteristic
213	C₃×C₄×C₈	—	3	1	no	—
214	C₃×C₄×C₈	—	3	1	no	—
215	C₃×C₄×C₈	—	3	1	no	—
216	#835	C₂²×C₃	1	1	yes	characteristic
217	#835	C₂²×C₃	1	1	yes	characteristic
218	#835	C₂²×C₃	1	1	yes	characteristic
219	#832	C₂²×C₃	1	1	yes	characteristic
220	#832	C₂²×C₃	1	1	yes	characteristic
221	#818	C₂²×C₃	1	1	yes	characteristic
222	#817	C₂²×C₃	1	1	yes	characteristic
223	#816	C₂²×C₃	1	1	yes	characteristic
224	#816	C₂²×C₃	1	1	yes	characteristic
225	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
226	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
227	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
228	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
229	#810	C₂²×C₃	1	1	yes	characteristic
230	#807	C₂²×C₃	1	1	yes	characteristic
231	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
232	C₂³×C₃²	—	2	1	no	—
233	C₃²×Q₈	—	2	1	no	—
234	C₃²×Q₈	—	2	1	no	—
235	C₃²×Q₈	—	2	1	no	—
236	C₃²×Q₈	#41	1	2	yes	—
237	C₃²×D₄	—	2	1	no	—
238	C₃²×D₄	—	2	1	no	—
239	C₂×C₃²×C₄	—	2	1	no	—
240	C₂×C₃²×C₄	—	2	1	no	—
241	C₂×C₃²×C₄	—	2	1	no	—
242	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
244	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
245	C₂×C₃×Dic₃	—	2	1	no	—
246	C₂×C₃×Dic₃	—	2	1	no	—
247	C₂×C₃×Dic₃	—	2	1	no	—
248	C₂×C₃×Dic₃	—	2	1	no	—
249	C₂×C₃×Dic₃	—	4	2	no	—
250	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
251	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
252	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
253	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
254	C₃×Dic₆	—	2	2	no	—
255	C₃×Dic₆	—	2	1	no	—
256	C₃×Dic₆	—	2	1	no	—
257	C₃×Dic₆	—	4	2	no	—
258	C₃²×C₈	—	2	1	no	—
259	C₃²×C₈	—	2	1	no	—
260	C₃×C₃⋊C₈	—	2	1	no	—
261	C₃×C₃⋊C₈	—	2	1	no	—
262	#557	—	3	1	no	—
263	#556	—	3	1	no	—
264	#488	—	3	1	no	—
265	#488	—	3	1	no	—
266	#487	—	3	1	no	—
267	#479	—	3	1	no	—
268	#479	—	3	1	no	—
269	#474	—	3	1	no	—
270	#464	—	3	1	no	—
271	#464	C₃×D₃	1	1	yes	characteristic
272	#462	—	3	1	no	—
273	C₈×Q₈	—	3	1	no	—
274	C₄×Q₁₆	—	3	1	no	—
275	C₄×Q₁₆	—	3	1	no	—
276	C₄×SD₁₆	—	3	1	no	—
277	C₂×C₃×Q₈	—	2	1	no	—
278	C₂×C₃×Q₈	—	2	1	no	—
279	C₂×C₃×Q₈	—	3	1	no	—
280	C₂×C₃×Q₈	—	3	1	no	—
281	C₂×C₃×Q₈	—	6	1	no	—
282	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
284	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₃×D₄	—	2	1	no	—
287	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
288	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
289	C₂²×C₃×C₄	—	6	1	no	—
290	C₂²×Dic₃	—	2	1	no	—
291	C₂×Dic₆	—	2	1	no	—
292	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
293	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
294	C₃×Q₁₆	—	2	2	no	—
295	C₃×Q₁₆	—	2	2	no	—
296	C₃×Q₁₆	—	4	2	no	—
297	C₃×Q₁₆	—	6	2	no	—
298	C₃×SD₁₆	—	2	2	no	—
299	C₃×SD₁₆	—	2	2	no	—
300	C₃×SD₁₆	—	4	2	no	—
301	C₂×C₃×C₈	—	2	1	no	—
302	C₂×C₃×C₈	—	2	1	no	—
303	C₂×C₃×C₈	—	3	1	no	—
304	C₂×C₃×C₈	—	3	1	no	—
305	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
307	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
309	C₃×C₄⋊C₄	—	2	1	no	—
310	C₃×C₄⋊C₄	—	2	1	no	—
311	C₃×C₄⋊C₄	—	2	1	no	—
312	C₃×C₄⋊C₄	—	3	1	no	—
313	C₃×C₄⋊C₄	—	3	1	no	—
314	C₃×C₄⋊C₄	—	3	1	no	—
315	C₃×C₄⋊C₄	—	3	1	no	—
316	C₃×C₄⋊C₄	—	3	1	no	—
317	C₃×C₄⋊C₄	—	3	1	no	—
318	C₃×C₄⋊C₄	—	4	1	no	—
319	C₃×C₄⋊C₄	—	6	1	no	—
320	C₃×C₄⋊C₄	—	6	1	no	—
321	C₃×C₄⋊C₄	—	6	1	no	—
322	C₃×C₄⋊C₄	—	6	1	no	—
323	C₃×C₄⋊C₄	—	6	1	no	—
324	C₃×C₄⋊C₄	—	6	1	no	—
325	C₃×C₄⋊C₄	—	6	1	no	—
326	C₃×C₄⋊C₄	—	6	1	no	—
327	C₃×C₄⋊C₄	—	6	1	no	—
328	C₃×C₄⋊C₄	—	6	1	no	—
329	C₃×C₄⋊C₄	—	6	1	no	—
330	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
331	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
332	C₃×C₂²⋊C₄	—	2	1	no	—
333	C₃×C₂²⋊C₄	—	2	1	no	—
334	C₃×C₂²⋊C₄	—	2	1	no	—
335	C₃×C₂²⋊C₄	—	2	1	no	—
336	C₃×C₂²⋊C₄	—	4	1	no	—
337	C₃×C₂²⋊C₄	—	4	1	no	—
338	C₃×C₂²⋊C₄	—	6	1	no	—
339	C₃×C₂²⋊C₄	—	6	1	no	—
340	C₃×C₂²⋊C₄	—	6	1	no	—
341	C₃×C₄²	—	2	1	no	—
342	C₃×C₄²	—	2	1	no	—
343	C₃×C₄²	—	2	1	no	—
344	C₃×C₄²	—	3	1	no	—
345	C₃×C₄²	—	3	1	no	—
346	C₃×C₄²	—	4	1	no	—
347	C₃×C₄²	—	6	1	no	—
348	C₃×C₄²	—	6	1	no	—
349	C₃×C₄²	—	6	1	no	—
350	C₃×C₄²	—	6	1	no	—
351	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
352	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
353	#217	—	2	1	no	—
354	#217	—	2	1	no	—
355	#217	—	2	1	no	—
356	#216	—	2	2	no	—
357	C₄⋊Dic₃	—	2	1	no	—
358	C₄⋊Dic₃	—	2	1	no	—
359	C₄⋊Dic₃	—	2	1	no	—
360	C₄⋊Dic₃	—	2	1	no	—
361	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
362	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
363	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
364	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
365	Dic₃⋊C₄	—	2	1	no	—
366	Dic₃⋊C₄	—	2	1	no	—
367	Dic₃⋊C₄	—	2	1	no	—
368	Dic₃⋊C₄	—	2	1	no	—
369	Dic₃⋊C₄	—	2	1	no	—
370	Dic₃⋊C₄	—	2	1	no	—
371	Dic₃⋊C₄	—	2	1	no	—
372	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
373	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
374	C₄×Dic₃	—	2	1	no	—
375	C₄×Dic₃	—	2	1	no	—
376	C₄×Dic₃	—	2	1	no	—
377	C₄×Dic₃	—	2	1	no	—
378	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
379	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
380	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
381	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
382	C₂²×C₃²	—	4	1	no	—
383	C₂²×C₃²	—	4	1	no	—
384	C₂²×C₃²	—	4	1	no	—
385	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
386	C₃²×C₄	—	2	2	no	—
387	C₃²×C₄	—	2	1	no	—
388	C₃²×C₄	—	2	1	no	—
389	C₃²×C₄	—	4	1	no	—
390	C₃²×C₄	—	4	1	no	—
391	C₃²×C₄	C₂×#41	1	1	yes	characteristic
392	C₃²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
393	C₃×Dic₃	—	2	1	no	—
394	C₃×Dic₃	—	2	1	no	—
395	C₃×Dic₃	—	2	1	no	—
396	C₃×Dic₃	—	4	1	no	—
397	C₃×Dic₃	—	4	1	no	—
398	C₃×Dic₃	—	4	1	no	—
399	C₃×Dic₃	—	4	1	no	—
400	C₃×Dic₃	#135	1	2	yes	—
401	C₂×Q₁₆	—	3	1	no	—
402	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
403	C₂×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
404	C₄⋊Q₈	—	3	1	no	—
405	C₄⋊Q₈	—	3	1	no	—
406	C₄⋊Q₈	—	6	1	no	—
407	#126	—	6	1	no	—
408	#126	—	6	1	no	—
409	#125	—	3	1	no	—
410	#125	—	3	1	no	—
411	#125	—	6	1	no	—
412	#125	—	6	1	no	—
413	#124	—	3	1	no	—
414	#124	C₂×C₃×D₃	1	1	yes	characteristic
415	C₂²⋊Q₈	—	6	1	no	—
416	C₄×Q₈	—	3	1	no	—
417	C₄×Q₈	—	3	1	no	—
418	C₄×Q₈	—	3	1	no	—
419	C₄×Q₈	—	3	1	no	—
420	C₄×Q₈	—	3	1	no	—
421	C₄×Q₈	—	6	1	no	—
422	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
423	C₄×D₄	—	3	1	no	—
424	#117	—	6	1	no	—
425	#107	—	3	1	no	—
426	#107	—	3	1	no	—
427	#106	—	3	1	no	—
428	C₄⋊C₈	—	3	1	no	—
429	C₄⋊C₈	—	3	1	no	—
430	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
431	#103	—	3	1	no	—
432	#103	—	3	1	no	—
433	#103	—	3	1	no	—
434	#103	—	3	1	no	—
435	#103	—	3	1	no	—
436	#103	—	3	1	no	—
437	#103	C₂×C₃×D₃	1	1	yes	characteristic
438	#102	—	3	1	no	—
439	#102	—	3	1	no	—
440	#102	C₂×C₃×D₃	1	1	yes	characteristic
441	C₄×C₈	—	3	1	no	—
442	C₄×C₈	—	3	1	no	—
443	C₄×C₈	—	3	1	no	—
444	C₂³×C₃	—	2	1	no	—
445	C₂³×C₃	—	2	1	no	—
446	C₂³×C₃	—	4	1	no	—
447	C₃×Q₈	—	2	1	no	—
448	C₃×Q₈	—	2	1	no	—
449	C₃×Q₈	—	2	1	no	—
450	C₃×Q₈	—	2	1	no	—
451	C₃×Q₈	—	2	1	no	—
452	C₃×Q₈	—	2	1	no	—
453	C₃×Q₈	—	2	2	no	—
454	C₃×Q₈	—	4	1	no	—
455	C₃×Q₈	—	4	1	no	—
456	C₃×Q₈	—	4	1	no	—
457	C₃×Q₈	—	6	2	no	—
458	C₃×Q₈	—	6	1	no	—
459	C₃×Q₈	—	6	1	no	—
460	C₃×Q₈	—	12	2	no	—
461	C₃×Q₈	#237	1	2	yes	—
462	C₃×Q₈	C₃×#41	1	2	yes	—
463	C₃×D₄	—	2	1	no	—
464	C₃×D₄	—	2	1	no	—
465	C₃×D₄	—	2	1	no	—
466	C₃×D₄	—	2	1	no	—
467	C₃×D₄	—	4	1	no	—
468	C₃×D₄	—	4	1	no	—
469	C₂×C₃×C₄	—	2	1	no	—
470	C₂×C₃×C₄	—	2	1	no	—
471	C₂×C₃×C₄	—	2	1	no	—
472	C₂×C₃×C₄	—	2	1	no	—
473	C₂×C₃×C₄	—	2	1	no	—
474	C₂×C₃×C₄	—	2	1	no	—
475	C₂×C₃×C₄	—	2	1	no	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	3	1	no	—
479	C₂×C₃×C₄	—	3	1	no	—
480	C₂×C₃×C₄	—	3	1	no	—
481	C₂×C₃×C₄	—	3	1	no	—
482	C₂×C₃×C₄	—	4	1	no	—
483	C₂×C₃×C₄	—	4	1	no	—
484	C₂×C₃×C₄	—	4	1	no	—
485	C₂×C₃×C₄	—	6	1	no	—
486	C₂×C₃×C₄	—	6	1	no	—
487	C₂×C₃×C₄	—	6	1	no	—
488	C₂×C₃×C₄	—	6	1	no	—
489	C₂×C₃×C₄	—	12	2	no	—
490	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
491	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
492	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
493	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
494	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
496	C₂×Dic₃	—	2	1	no	—
497	C₂×Dic₃	—	2	1	no	—
498	C₂×Dic₃	—	2	1	no	—
499	C₂×Dic₃	—	2	1	no	—
500	C₂×Dic₃	—	4	2	no	—
501	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
502	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
503	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
504	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
505	Dic₆	—	2	2	no	—
506	Dic₆	—	2	1	no	—
507	Dic₆	—	2	1	no	—
508	Dic₆	—	4	2	no	—
509	C₃×C₈	—	2	1	no	—
510	C₃×C₈	—	2	1	no	—
511	C₃×C₈	—	2	1	no	—
512	C₃×C₈	—	2	1	no	—
513	C₃×C₈	—	4	1	no	—
514	C₃×C₈	—	4	1	no	—
515	C₃×C₈	—	6	1	no	—
516	C₃×C₈	—	6	1	no	—
517	C₃⋊C₈	—	2	1	no	—
518	C₃⋊C₈	—	2	1	no	—
519	C₂×C₃²	—	8	1	no	—
520	C₂×C₃²	#548	1	1	yes	characteristic
521	C₂×C₃²	C₂×#135	1	1	yes	characteristic
522	C₂×C₃²	#578	1	1	yes	characteristic
523	C₂×Q₈	—	3	1	no	—
524	C₂×Q₈	—	3	1	no	—
525	C₂×Q₈	—	6	1	no	—
526	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
527	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
528	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
529	C₂²×C₄	—	6	1	no	—
530	Q₁₆	—	2	2	no	—
531	Q₁₆	—	6	2	no	—
532	SD₁₆	—	2	2	no	—
533	C₂×C₈	—	3	1	no	—
534	C₂×C₈	—	3	1	no	—
535	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
536	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	3	1	no	—
539	C₄⋊C₄	—	3	1	no	—
540	C₄⋊C₄	—	3	1	no	—
541	C₄⋊C₄	—	3	1	no	—
542	C₄⋊C₄	—	3	1	no	—
543	C₄⋊C₄	—	3	1	no	—
544	C₄⋊C₄	—	6	1	no	—
545	C₄⋊C₄	—	6	1	no	—
546	C₄⋊C₄	—	6	1	no	—
547	C₄⋊C₄	—	6	1	no	—
548	C₄⋊C₄	—	6	1	no	—
549	C₄⋊C₄	—	6	1	no	—
550	C₄⋊C₄	—	6	1	no	—
551	C₄⋊C₄	—	6	1	no	—
552	C₄⋊C₄	—	6	1	no	—
553	C₄⋊C₄	—	6	1	no	—
554	C₄⋊C₄	—	6	1	no	—
555	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
556	C₂²⋊C₄	—	2	1	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	6	1	no	—
559	C₂²⋊C₄	—	6	1	no	—
560	C₂²⋊C₄	—	6	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	3	1	no	—
563	C₄²	—	3	1	no	—
564	C₄²	—	6	1	no	—
565	C₄²	—	6	1	no	—
566	C₄²	—	6	1	no	—
567	C₄²	—	6	1	no	—
568	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
569	C₂²×C₃	—	2	1	no	—
570	C₂²×C₃	—	4	1	no	—
571	C₂²×C₃	—	4	1	no	—
572	C₂²×C₃	—	4	1	no	—
573	C₂²×C₃	—	4	1	no	—
574	C₂²×C₃	—	4	1	no	—
575	C₂²×C₃	—	4	1	no	—
576	C₂²×C₃	—	8	1	no	—
577	C₂²×C₃	—	8	1	no	—
578	C₂²×C₃	—	8	1	no	—
579	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
580	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
581	C₃×C₄	—	2	1	no	—
582	C₃×C₄	—	2	1	no	—
583	C₃×C₄	—	2	1	no	—
584	C₃×C₄	—	2	1	no	—
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	2	no	—
587	C₃×C₄	—	2	1	no	—
588	C₃×C₄	—	2	1	no	—
589	C₃×C₄	—	3	2	no	—
590	C₃×C₄	—	4	1	no	—
591	C₃×C₄	—	4	1	no	—
592	C₃×C₄	—	4	2	no	—
593	C₃×C₄	—	4	1	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	—	4	1	no	—
596	C₃×C₄	—	4	1	no	—
597	C₃×C₄	—	6	1	no	—
598	C₃×C₄	—	6	1	no	—
599	C₃×C₄	—	6	1	no	—
600	C₃×C₄	—	8	1	no	—
601	C₃×C₄	—	8	1	no	—
602	C₃×C₄	—	12	1	no	—
603	C₃×C₄	—	12	1	no	—
604	C₃×C₄	—	12	1	no	—
605	C₃×C₄	—	12	1	no	—
606	C₃×C₄	C₂×#237	1	1	yes	characteristic
607	C₃×C₄	#1010	1	1	yes	characteristic
608	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
609	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
610	Dic₃	—	2	1	no	—
611	Dic₃	—	2	1	no	—
612	Dic₃	—	2	1	no	—
613	Dic₃	—	4	1	no	—
614	Dic₃	—	4	1	no	—
615	Dic₃	—	4	1	no	—
616	Dic₃	—	4	1	no	—
617	Dic₃	C₃×#135	1	2	yes	—
618	C₃²	#3364	1	1	yes	characteristic, complemented, Sylow
619	C₂³	—	2	1	no	—
620	Q₈	—	2	1	no	—
621	Q₈	—	2	1	no	—
622	Q₈	—	2	1	no	—
623	Q₈	—	6	2	no	—
624	Q₈	—	6	1	no	—
625	Q₈	—	6	1	no	—
626	Q₈	—	12	2	no	—
627	Q₈	C₃×#237	1	2	yes	—
628	D₄	—	2	1	no	—
629	D₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	3	1	no	—
634	C₂×C₄	—	3	1	no	—
635	C₂×C₄	—	3	1	no	—
636	C₂×C₄	—	3	1	no	—
637	C₂×C₄	—	6	1	no	—
638	C₂×C₄	—	6	1	no	—
639	C₂×C₄	—	6	1	no	—
640	C₂×C₄	—	6	1	no	—
641	C₂×C₄	—	12	2	no	—
642	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
643	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
644	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
645	C₈	—	2	1	no	—
646	C₈	—	2	1	no	—
647	C₈	—	6	1	no	—
648	C₈	—	6	1	no	—
649	C₂×C₃	—	2	1	no	—
650	C₂×C₃	—	2	1	no	—
651	C₂×C₃	—	2	1	no	—
652	C₂×C₃	—	8	1	no	—
653	C₂×C₃	—	8	1	no	—
654	C₂×C₃	—	16	1	no	—
655	C₂×C₃	#5598	1	1	yes	characteristic
656	C₂×C₃	D₃×#135	1	1	yes	characteristic
657	C₂×C₃	#5779	1	1	yes	characteristic
658	C₂×C₃	C₃×#548	1	1	yes	characteristic
659	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
660	C₂×C₃	C₃×#578	1	1	yes	characteristic
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	2	no	—
668	C₄	—	3	2	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	6	1	no	—
672	C₄	—	6	1	no	—
673	C₄	—	6	1	no	—
674	C₄	—	12	1	no	—
675	C₄	—	12	1	no	—
676	C₄	—	12	1	no	—
677	C₄	—	12	1	no	—
678	C₄	C₂×C₃×#237	1	1	yes	characteristic
679	C₄	C₃×#1010	1	1	yes	characteristic
680	C₃	—	2	1	no	—
681	C₃	#80580	1	1	yes	characteristic, direct product factor
682	C₃	C₃×#3364	1	1	yes	characteristic, complemented
683	C₂	—	8	1	no	—
684	C₂	C₃×#5598	1	1	yes	characteristic
685	C₂	C₃×D₃×#135	1	1	yes	characteristic
686	C₂	C₃×#5779	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#464	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃²×D₄	C₂³
hypercenter	C₃×#464	D₃
hypocenter	C₃	C₃×#3364
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#464

Complements

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

N	H ≅ G/N	type
2. C₃×#5569	C₂	semidirect
4. C₃×#5182	C₂	semidirect
5. C₃×Dic₃×Q₁₆	C₂	semidirect
9. C₃×C₄×#216	C₂	semidirect
10. C₃×#4830	C₂	semidirect
11. C₃×#4829	C₂	semidirect
12. C₃×#4799	C₂	semidirect
13. C₃×#4792	C₂	semidirect
17. #80580	C₃	direct (N × H)
64. #5569	C₂×C₃	semidirect
80. #5182	C₂×C₃	semidirect
81. Dic₃×Q₁₆	C₂×C₃	semidirect
85. C₄×#216	C₂×C₃	semidirect
86. #4830	C₂×C₃	semidirect
87. #4829	C₂×C₃	semidirect
88. #4799	C₂×C₃	semidirect
89. #4792	C₂×C₃	semidirect
618. C₃²	#3364	semidirect
681. C₃	#80580	direct (N × H)
682. 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×#5671	2
C₃×#5569	2
C₃²×#464	2
C₃×#5182	2
C₃×Dic₃×Q₁₆	2
C₃×#5166	2
C₃×Dic₃×SD₁₆	2
C₃×#5056	2
C₃×C₄×#216	2
C₃×#4830	2
C₃×#4829	2
C₃×#4799	2
C₃×#4792	2
C₃×#4768	2
C₃×#4759	2
C₃×#3364	3
#80580	3

Subgroups — C3×#80580 #11895506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#80580 #11895506