Subgroups — C₃×#80588 #11898335

Order 1152.

776 conjugacy classes of subgroups.

The subgroup lattice has 740 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, complemented
2	C₃×#5568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#464	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5185	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5183	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5168	C₂	1	1	yes	maximal, characteristic
7	C₃×#5162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5059	C₂	1	1	yes	maximal, characteristic
9	C₃×C₄×#216	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4830	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4818	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4790	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4767	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#4756	C₂	1	1	yes	maximal, characteristic
16	C₃×#3393	—	3	1	no	maximal
17	#80588	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×#947	C₂²	1	1	yes	characteristic
23	C₃×Q₈×Dic₃	C₂²	1	1	yes	characteristic
24	C₃×#944	C₂²	1	1	yes	characteristic
25	C₃×#944	C₂²	1	1	yes	characteristic
26	C₂×C₃×#216	C₂²	1	1	yes	characteristic
27	C₂×C₃×#216	C₂²	1	1	yes	characteristic
28	C₂×C₃×#215	C₂²	1	1	yes	characteristic
29	C₃×#936	C₂²	1	1	yes	characteristic
30	C₃×D₄×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₃×#214	C₂²	1	1	yes	characteristic
32	C₂×C₃×#213	C₂²	1	1	yes	characteristic
33	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
34	C₂×C₃×#204	C₂²	1	1	yes	characteristic
35	C₃×#898	—	2	1	no	—
36	C₃×#896	—	2	1	no	—
37	C₃×#893	C₂²	1	1	yes	characteristic
38	C₃×#887	C₂²	1	1	yes	characteristic
39	C₃×#879	—	2	1	no	—
40	C₃×#879	—	2	1	no	—
41	C₃×#878	—	2	1	no	—
42	C₃×#877	—	2	1	no	—
43	C₃×#876	—	2	1	no	—
44	C₃×#875	C₂²	1	1	yes	characteristic
45	C₃×#872	—	2	1	no	—
46	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
47	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
48	C₃²×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₃²×#103	C₂²	1	1	yes	characteristic
50	C₃²×#102	C₂²	1	1	yes	characteristic
51	C₃×#835	C₂²	1	1	yes	characteristic
52	C₃×#821	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×#556	—	3	1	no	—
62	C₃×#556	—	3	1	no	—
63	#5671	C₂×C₃	1	1	yes	characteristic, complemented
64	#5568	C₂×C₃	1	1	yes	characteristic, complemented
65	C₃×#495	—	3	1	no	—
66	C₃×#495	—	3	1	no	—
67	C₃×#494	—	3	1	no	—
68	C₃×#464	—	2	1	no	—
69	C₃×#464	—	3	1	no	—
70	C₃×#464	—	3	1	no	—
71	C₃×#464	—	3	1	no	—
72	C₃×#464	D₃	1	1	yes	characteristic, complemented
73	C₃×#464	C₂×C₃	1	1	yes	characteristic, complemented
74	C₃×#461	—	3	1	no	—
75	C₃×#461	—	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×D₈	—	3	1	no	—
80	#5185	C₂×C₃	1	1	yes	characteristic, complemented
81	#5183	C₂×C₃	1	1	yes	characteristic, complemented
82	#5168	C₂×C₃	1	1	yes	characteristic
83	#5162	C₂×C₃	1	1	yes	characteristic, complemented
84	#5059	C₂×C₃	1	1	yes	characteristic
85	C₄×#216	C₂×C₃	1	1	yes	characteristic, complemented
86	#4845	C₂×C₃	1	1	yes	characteristic, complemented
87	#4830	C₂×C₃	1	1	yes	characteristic, complemented
88	#4818	C₂×C₃	1	1	yes	characteristic, complemented
89	#4790	C₂×C₃	1	1	yes	characteristic, complemented
90	#4767	C₂×C₃	1	1	yes	characteristic, complemented
91	#4756	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×D₁₂	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄×D₃	—	2	1	no	—
98	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
99	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
100	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
101	C₃²×Q₁₆	—	4	1	no	—
102	C₃²×SD₁₆	—	4	1	no	—
103	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
105	C₃²×C₄⋊C₄	—	2	1	no	—
106	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₃²×C₂²⋊C₄	—	2	1	no	—
108	C₃²×C₂²⋊C₄	—	2	1	no	—
109	C₃²×C₄²	—	2	1	no	—
110	C₃²×C₄²	C₂³	1	1	yes	characteristic
111	C₃×#217	—	2	1	no	—
112	C₃×#217	—	2	1	no	—
113	C₃×#217	—	2	1	no	—
114	C₃×#216	—	2	2	no	—
115	C₃×#216	—	2	2	no	—
116	C₃×#215	—	4	1	no	—
117	C₃×#214	—	4	1	no	—
118	C₃×#213	—	2	2	no	—
119	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
122	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
123	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
124	C₃×C₄⋊Dic₃	—	2	1	no	—
125	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
126	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
127	C₃×Dic₃⋊C₄	—	2	1	no	—
128	C₃×Dic₃⋊C₄	—	2	1	no	—
129	C₃×Dic₃⋊C₄	—	2	1	no	—
130	C₃×Dic₃⋊C₄	—	2	1	no	—
131	C₃×Dic₃⋊C₄	—	2	1	no	—
132	C₃×Dic₃⋊C₄	—	2	1	no	—
133	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
134	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
135	C₃×C₄×Dic₃	—	2	1	no	—
136	C₃×C₄×Dic₃	—	2	1	no	—
137	C₃×C₄×Dic₃	—	2	1	no	—
138	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
139	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
140	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
141	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
142	C₃×Dic₁₂	—	4	1	no	—
143	C₃×#204	—	4	1	no	—
144	#3393	—	3	1	no	Sylow
145	C₂×C₃×Q₁₆	—	2	1	no	—
146	C₂×C₃×Q₁₆	—	3	1	no	—
147	C₂×C₃×Q₁₆	—	3	1	no	—
148	C₂×C₃×Q₁₆	—	3	1	no	—
149	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
150	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×SD₁₆	—	2	1	no	—
152	C₂×C₃×SD₁₆	—	3	1	no	—
153	C₂×C₃×SD₁₆	—	3	1	no	—
154	C₂×C₃×SD₁₆	—	3	1	no	—
155	C₂×C₃×SD₁₆	C₂×D₃	1	1	yes	characteristic
156	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₃×D₈	—	3	1	no	—
158	C₃×C₄⋊Q₈	—	3	1	no	—
159	C₃×C₄⋊Q₈	—	3	1	no	—
160	C₃×#126	—	6	1	no	—
161	C₃×#126	—	6	1	no	—
162	C₃×#126	—	6	1	no	—
163	C₃×#126	—	6	1	no	—
164	C₃×#124	—	2	1	no	—
165	C₃×#124	—	3	1	no	—
166	C₃×#124	—	3	1	no	—
167	C₃×#124	—	3	1	no	—
168	C₃×#124	C₂×D₃	1	1	yes	characteristic
169	C₃×#124	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₂²⋊Q₈	—	6	1	no	—
171	C₃×C₂²⋊Q₈	—	6	1	no	—
172	C₃×C₄×Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	—	3	1	no	—
174	C₃×C₄×Q₈	—	3	1	no	—
175	C₃×C₄×Q₈	—	3	1	no	—
176	C₃×C₄×Q₈	—	3	1	no	—
177	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
178	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
179	C₃×C₄×D₄	—	3	1	no	—
180	C₃×C₄×D₄	—	3	1	no	—
181	C₃×#117	—	6	1	no	—
182	C₃×#117	—	6	1	no	—
183	#947	C₂²×C₃	1	1	yes	characteristic
184	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
185	#944	C₂²×C₃	1	1	yes	characteristic
186	#944	C₂²×C₃	1	1	yes	characteristic
187	C₂×#216	C₂²×C₃	1	1	yes	characteristic
188	C₂×#216	C₂²×C₃	1	1	yes	characteristic
189	C₂×#215	C₂²×C₃	1	1	yes	characteristic
190	#936	C₂²×C₃	1	1	yes	characteristic
191	D₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
192	C₂×#214	C₂²×C₃	1	1	yes	characteristic
193	C₂×#213	C₂²×C₃	1	1	yes	characteristic
194	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
195	C₂×#204	C₂²×C₃	1	1	yes	characteristic
196	#898	—	2	1	no	—
197	#896	—	2	1	no	—
198	#893	C₂²×C₃	1	1	yes	characteristic
199	#887	C₂²×C₃	1	1	yes	characteristic
200	#879	—	2	1	no	—
201	#879	—	2	1	no	—
202	#878	—	2	1	no	—
203	#877	—	2	1	no	—
204	#876	—	2	1	no	—
205	#875	C₂²×C₃	1	1	yes	characteristic
206	#872	—	2	1	no	—
207	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
208	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
209	C₃×#107	—	3	1	no	—
210	C₃×C₄⋊C₈	—	2	1	no	—
211	C₃×C₄⋊C₈	—	3	1	no	—
212	C₃×C₄⋊C₈	—	3	1	no	—
213	C₃×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
214	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
215	C₃×#103	—	2	1	no	—
216	C₃×#103	—	3	1	no	—
217	C₃×#103	—	3	1	no	—
218	C₃×#103	—	3	1	no	—
219	C₃×#103	C₂×D₃	1	1	yes	characteristic
220	C₃×#103	C₂²×C₃	1	1	yes	characteristic
221	C₃×#102	—	2	1	no	—
222	C₃×#102	—	3	1	no	—
223	C₃×#102	C₂×D₃	1	1	yes	characteristic
224	C₃×#102	C₂²×C₃	1	1	yes	characteristic
225	C₃×C₄×C₈	—	3	1	no	—
226	C₃×C₄×C₈	—	3	1	no	—
227	C₃×C₄×C₈	—	3	1	no	—
228	#835	C₂²×C₃	1	1	yes	characteristic
229	#821	C₂²×C₃	1	1	yes	characteristic
230	#816	C₂²×C₃	1	1	yes	characteristic
231	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
232	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
233	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
234	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
235	#810	C₂²×C₃	1	1	yes	characteristic
236	#807	C₂²×C₃	1	1	yes	characteristic
237	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
238	C₂³×C₃²	—	2	1	no	—
239	C₂²×C₃×D₃	—	2	1	no	—
240	C₃²×Q₈	—	2	1	no	—
241	C₃²×Q₈	—	2	1	no	—
242	C₃²×Q₈	—	2	1	no	—
243	C₃²×Q₈	—	2	1	no	—
244	C₃²×D₄	—	2	1	no	—
245	C₃²×D₄	—	2	1	no	—
246	C₂×C₃²×C₄	—	2	1	no	—
247	C₂×C₃²×C₄	—	2	1	no	—
248	C₂×C₃²×C₄	—	2	1	no	—
249	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
250	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
251	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
252	C₂×C₃×Dic₃	—	2	1	no	—
253	C₂×C₃×Dic₃	—	2	1	no	—
254	C₂×C₃×Dic₃	—	2	1	no	—
255	C₂×C₃×Dic₃	—	4	2	no	—
256	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
257	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
258	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
259	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
260	C₃×D₁₂	—	2	1	no	—
261	C₃×D₁₂	—	2	1	no	—
262	C₃×C₄×D₃	—	4	2	no	—
263	C₃×Dic₆	—	2	2	no	—
264	C₃×Dic₆	—	2	1	no	—
265	C₃×Dic₆	—	2	1	no	—
266	C₃×Dic₆	—	2	1	no	—
267	C₃×Dic₆	—	2	1	no	—
268	C₃²×C₈	—	2	1	no	—
269	C₃²×C₈	—	2	1	no	—
270	C₃×C₃⋊C₈	—	2	1	no	—
271	C₃×C₃⋊C₈	#41	1	2	yes	—
272	#556	—	3	1	no	—
273	#556	—	3	1	no	—
274	#495	—	3	1	no	—
275	#495	—	3	1	no	—
276	#494	—	3	1	no	—
277	#464	—	3	1	no	—
278	#464	—	3	1	no	—
279	#464	—	3	1	no	—
280	#464	C₃×D₃	1	1	yes	characteristic, complemented
281	#461	—	3	1	no	—
282	#461	—	3	1	no	—
283	C₈×Q₈	—	3	1	no	—
284	C₄×Q₁₆	—	3	1	no	—
285	C₄×Q₁₆	—	3	1	no	—
286	C₄×D₈	—	3	1	no	—
287	C₂×C₃×Q₈	—	2	1	no	—
288	C₂×C₃×Q₈	—	2	1	no	—
289	C₂×C₃×Q₈	—	3	1	no	—
290	C₂×C₃×Q₈	—	3	1	no	—
291	C₂×C₃×Q₈	—	3	1	no	—
292	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
293	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
294	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₃×D₄	—	2	1	no	—
297	C₂×C₃×D₄	—	3	1	no	—
298	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
299	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
300	C₂²×C₃×C₄	—	6	1	no	—
301	C₂²×C₃×C₄	—	6	1	no	—
302	C₂²×Dic₃	—	2	1	no	—
303	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₄×D₃	—	2	1	no	—
305	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
306	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
307	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
308	C₃×Q₁₆	—	4	1	no	—
309	C₃×Q₁₆	—	4	1	no	—
310	C₃×Q₁₆	—	4	2	no	—
311	C₃×Q₁₆	—	6	2	no	—
312	C₃×Q₁₆	—	6	2	no	—
313	C₃×Q₁₆	—	12	1	no	—
314	C₃×SD₁₆	—	4	1	no	—
315	C₃×SD₁₆	—	4	1	no	—
316	C₃×SD₁₆	—	4	2	no	—
317	C₃×SD₁₆	—	12	1	no	—
318	C₃×SD₁₆	—	12	1	no	—
319	C₃×SD₁₆	—	12	1	no	—
320	C₃×D₈	—	6	2	no	—
321	C₂×C₃×C₈	—	2	1	no	—
322	C₂×C₃×C₈	—	2	1	no	—
323	C₂×C₃×C₈	—	3	1	no	—
324	C₂×C₃×C₈	—	3	1	no	—
325	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
326	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
327	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
329	C₃×C₄⋊C₄	—	2	1	no	—
330	C₃×C₄⋊C₄	—	2	1	no	—
331	C₃×C₄⋊C₄	—	2	1	no	—
332	C₃×C₄⋊C₄	—	3	1	no	—
333	C₃×C₄⋊C₄	—	3	1	no	—
334	C₃×C₄⋊C₄	—	3	1	no	—
335	C₃×C₄⋊C₄	—	3	1	no	—
336	C₃×C₄⋊C₄	—	4	1	no	—
337	C₃×C₄⋊C₄	—	6	1	no	—
338	C₃×C₄⋊C₄	—	6	1	no	—
339	C₃×C₄⋊C₄	—	6	1	no	—
340	C₃×C₄⋊C₄	—	6	1	no	—
341	C₃×C₄⋊C₄	—	6	1	no	—
342	C₃×C₄⋊C₄	—	6	1	no	—
343	C₃×C₄⋊C₄	—	6	1	no	—
344	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
345	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
346	C₃×C₂²⋊C₄	—	2	1	no	—
347	C₃×C₂²⋊C₄	—	2	1	no	—
348	C₃×C₂²⋊C₄	—	2	1	no	—
349	C₃×C₂²⋊C₄	—	2	1	no	—
350	C₃×C₂²⋊C₄	—	4	1	no	—
351	C₃×C₂²⋊C₄	—	4	1	no	—
352	C₃×C₂²⋊C₄	—	6	1	no	—
353	C₃×C₂²⋊C₄	—	6	1	no	—
354	C₃×C₂²⋊C₄	—	6	1	no	—
355	C₃×C₂²⋊C₄	—	6	1	no	—
356	C₃×C₂²⋊C₄	—	6	1	no	—
357	C₃×C₂²⋊C₄	—	6	1	no	—
358	C₃×C₂²⋊C₄	—	6	1	no	—
359	C₃×C₂²⋊C₄	—	6	1	no	—
360	C₃×C₄²	—	2	1	no	—
361	C₃×C₄²	—	2	1	no	—
362	C₃×C₄²	—	2	1	no	—
363	C₃×C₄²	—	3	1	no	—
364	C₃×C₄²	—	3	1	no	—
365	C₃×C₄²	—	4	1	no	—
366	C₃×C₄²	—	6	1	no	—
367	C₃×C₄²	—	6	1	no	—
368	C₃×C₄²	—	6	1	no	—
369	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
370	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
371	#217	—	2	1	no	—
372	#217	—	2	1	no	—
373	#217	—	2	1	no	—
374	#216	—	2	2	no	—
375	#216	—	2	2	no	—
376	#215	—	4	1	no	—
377	#214	—	4	1	no	—
378	#213	—	2	2	no	—
379	(C₂×D₃)⋊C₄	—	2	1	no	—
380	(C₂×D₃)⋊C₄	—	2	1	no	—
381	(C₂×D₃)⋊C₄	—	2	1	no	—
382	(C₂×D₃)⋊C₄	—	2	1	no	—
383	(C₂×D₃)⋊C₄	—	2	1	no	—
384	C₄⋊Dic₃	—	2	1	no	—
385	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
386	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
387	Dic₃⋊C₄	—	2	1	no	—
388	Dic₃⋊C₄	—	2	1	no	—
389	Dic₃⋊C₄	—	2	1	no	—
390	Dic₃⋊C₄	—	2	1	no	—
391	Dic₃⋊C₄	—	2	1	no	—
392	Dic₃⋊C₄	—	2	1	no	—
393	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
394	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
395	C₄×Dic₃	—	2	1	no	—
396	C₄×Dic₃	—	2	1	no	—
397	C₄×Dic₃	—	2	1	no	—
398	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
399	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
400	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
401	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
402	Dic₁₂	—	4	1	no	—
403	#204	—	4	1	no	—
404	C₂²×C₃²	—	4	1	no	—
405	C₂²×C₃²	—	4	1	no	—
406	C₂²×C₃²	—	4	1	no	—
407	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₃×D₃	—	4	1	no	—
409	C₂×C₃×D₃	—	4	1	no	—
410	C₂×C₃×D₃	—	4	1	no	—
411	C₃²×C₄	—	2	1	no	—
412	C₃²×C₄	—	2	1	no	—
413	C₃²×C₄	—	4	1	no	—
414	C₃²×C₄	—	4	1	no	—
415	C₃²×C₄	—	4	1	no	—
416	C₃²×C₄	C₂×#41	1	1	yes	characteristic
417	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
418	C₃×Dic₃	—	2	1	no	—
419	C₃×Dic₃	—	2	1	no	—
420	C₃×Dic₃	—	2	1	no	—
421	C₃×Dic₃	—	4	1	no	—
422	C₃×Dic₃	—	4	1	no	—
423	C₃×Dic₃	—	4	1	no	—
424	C₃×Dic₃	#135	1	2	yes	—
425	C₂×Q₁₆	—	3	1	no	—
426	C₂×Q₁₆	—	3	1	no	—
427	C₂×Q₁₆	—	3	1	no	—
428	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
429	C₂×SD₁₆	—	3	1	no	—
430	C₂×SD₁₆	—	3	1	no	—
431	C₂×SD₁₆	—	3	1	no	—
432	C₂×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
433	C₂×D₈	—	3	1	no	—
434	C₄⋊Q₈	—	3	1	no	—
435	C₄⋊Q₈	—	3	1	no	—
436	#126	—	6	1	no	—
437	#126	—	6	1	no	—
438	#126	—	6	1	no	—
439	#126	—	6	1	no	—
440	#124	—	3	1	no	—
441	#124	—	3	1	no	—
442	#124	—	3	1	no	—
443	#124	C₂×C₃×D₃	1	1	yes	characteristic
444	C₂²⋊Q₈	—	6	1	no	—
445	C₂²⋊Q₈	—	6	1	no	—
446	C₄×Q₈	—	3	1	no	—
447	C₄×Q₈	—	3	1	no	—
448	C₄×Q₈	—	3	1	no	—
449	C₄×Q₈	—	3	1	no	—
450	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
451	C₄×D₄	—	3	1	no	—
452	C₄×D₄	—	3	1	no	—
453	#117	—	6	1	no	—
454	#117	—	6	1	no	—
455	#107	—	3	1	no	—
456	C₄⋊C₈	—	3	1	no	—
457	C₄⋊C₈	—	3	1	no	—
458	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
459	#103	—	3	1	no	—
460	#103	—	3	1	no	—
461	#103	—	3	1	no	—
462	#103	C₂×C₃×D₃	1	1	yes	characteristic
463	#102	—	3	1	no	—
464	#102	C₂×C₃×D₃	1	1	yes	characteristic
465	C₄×C₈	—	3	1	no	—
466	C₄×C₈	—	3	1	no	—
467	C₄×C₈	—	3	1	no	—
468	C₂³×C₃	—	2	1	no	—
469	C₂³×C₃	—	2	1	no	—
470	C₂³×C₃	—	4	1	no	—
471	C₂³×C₃	—	6	1	no	—
472	C₂²×D₃	—	2	1	no	—
473	C₃×Q₈	—	2	2	no	—
474	C₃×Q₈	—	2	1	no	—
475	C₃×Q₈	—	2	1	no	—
476	C₃×Q₈	—	2	1	no	—
477	C₃×Q₈	—	2	1	no	—
478	C₃×Q₈	—	2	1	no	—
479	C₃×Q₈	—	2	1	no	—
480	C₃×Q₈	—	2	1	no	—
481	C₃×Q₈	—	2	1	no	—
482	C₃×Q₈	—	4	1	no	—
483	C₃×Q₈	—	4	1	no	—
484	C₃×Q₈	—	4	1	no	—
485	C₃×Q₈	—	6	2	no	—
486	C₃×Q₈	—	6	1	no	—
487	C₃×Q₈	—	6	1	no	—
488	C₃×Q₈	—	6	1	no	—
489	C₃×Q₈	—	6	1	no	—
490	C₃×D₄	—	2	1	no	—
491	C₃×D₄	—	2	1	no	—
492	C₃×D₄	—	2	1	no	—
493	C₃×D₄	—	2	1	no	—
494	C₃×D₄	—	4	1	no	—
495	C₃×D₄	—	4	1	no	—
496	C₃×D₄	—	6	1	no	—
497	C₃×D₄	—	6	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	3	1	no	—
508	C₂×C₃×C₄	—	3	1	no	—
509	C₂×C₃×C₄	—	3	1	no	—
510	C₂×C₃×C₄	—	3	1	no	—
511	C₂×C₃×C₄	—	4	1	no	—
512	C₂×C₃×C₄	—	4	1	no	—
513	C₂×C₃×C₄	—	4	1	no	—
514	C₂×C₃×C₄	—	6	1	no	—
515	C₂×C₃×C₄	—	6	1	no	—
516	C₂×C₃×C₄	—	6	1	no	—
517	C₂×C₃×C₄	—	12	2	no	—
518	C₂×C₃×C₄	—	12	2	no	—
519	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
520	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
522	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
525	C₂×Dic₃	—	2	1	no	—
526	C₂×Dic₃	—	2	1	no	—
527	C₂×Dic₃	—	2	1	no	—
528	C₂×Dic₃	—	4	2	no	—
529	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
530	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
531	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
532	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
533	D₁₂	—	2	1	no	—
534	D₁₂	—	2	1	no	—
535	C₄×D₃	—	4	2	no	—
536	Dic₆	—	2	2	no	—
537	Dic₆	—	2	1	no	—
538	Dic₆	—	2	1	no	—
539	Dic₆	—	2	1	no	—
540	Dic₆	—	2	1	no	—
541	C₃×C₈	—	2	1	no	—
542	C₃×C₈	—	2	1	no	—
543	C₃×C₈	—	2	1	no	—
544	C₃×C₈	—	2	1	no	—
545	C₃×C₈	—	3	2	no	—
546	C₃×C₈	—	4	1	no	—
547	C₃×C₈	—	4	1	no	—
548	C₃×C₈	—	6	1	no	—
549	C₃⋊C₈	—	2	1	no	—
550	C₃⋊C₈	C₃×#41	1	2	yes	—
551	C₂×C₃²	—	8	1	no	—
552	C₂×C₃²	#550	1	1	yes	characteristic
553	C₂×C₃²	C₂×#135	1	1	yes	characteristic
554	C₂×C₃²	#578	1	1	yes	characteristic
555	C₃×D₃	—	8	1	no	—
556	C₂×Q₈	—	3	1	no	—
557	C₂×Q₈	—	3	1	no	—
558	C₂×Q₈	—	3	1	no	—
559	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
560	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
561	C₂×D₄	—	3	1	no	—
562	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
563	C₂²×C₄	—	6	1	no	—
564	C₂²×C₄	—	6	1	no	—
565	Q₁₆	—	4	1	no	—
566	Q₁₆	—	6	2	no	—
567	Q₁₆	—	6	2	no	—
568	Q₁₆	—	12	1	no	—
569	SD₁₆	—	4	1	no	—
570	SD₁₆	—	12	1	no	—
571	SD₁₆	—	12	1	no	—
572	SD₁₆	—	12	1	no	—
573	D₈	—	6	2	no	—
574	C₂×C₈	—	3	1	no	—
575	C₂×C₈	—	3	1	no	—
576	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
577	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	3	1	no	—
580	C₄⋊C₄	—	3	1	no	—
581	C₄⋊C₄	—	3	1	no	—
582	C₄⋊C₄	—	3	1	no	—
583	C₄⋊C₄	—	6	1	no	—
584	C₄⋊C₄	—	6	1	no	—
585	C₄⋊C₄	—	6	1	no	—
586	C₄⋊C₄	—	6	1	no	—
587	C₄⋊C₄	—	6	1	no	—
588	C₄⋊C₄	—	6	1	no	—
589	C₄⋊C₄	—	6	1	no	—
590	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
591	C₂²⋊C₄	—	2	1	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	6	1	no	—
594	C₂²⋊C₄	—	6	1	no	—
595	C₂²⋊C₄	—	6	1	no	—
596	C₂²⋊C₄	—	6	1	no	—
597	C₂²⋊C₄	—	6	1	no	—
598	C₂²⋊C₄	—	6	1	no	—
599	C₂²⋊C₄	—	6	1	no	—
600	C₂²⋊C₄	—	6	1	no	—
601	C₄²	—	2	1	no	—
602	C₄²	—	3	1	no	—
603	C₄²	—	3	1	no	—
604	C₄²	—	6	1	no	—
605	C₄²	—	6	1	no	—
606	C₄²	—	6	1	no	—
607	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
608	C₂²×C₃	—	2	1	no	—
609	C₂²×C₃	—	4	1	no	—
610	C₂²×C₃	—	4	1	no	—
611	C₂²×C₃	—	4	1	no	—
612	C₂²×C₃	—	4	1	no	—
613	C₂²×C₃	—	4	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	8	1	no	—
616	C₂²×C₃	—	8	1	no	—
617	C₂²×C₃	—	8	1	no	—
618	C₂²×C₃	—	12	1	no	—
619	C₂²×C₃	—	12	1	no	—
620	C₂²×C₃	—	12	1	no	—
621	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
622	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
623	C₂×D₃	—	4	1	no	—
624	C₂×D₃	—	4	1	no	—
625	C₂×D₃	—	4	1	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	2	1	no	—
630	C₃×C₄	—	2	1	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	3	2	no	—
633	C₃×C₄	—	4	1	no	—
634	C₃×C₄	—	4	1	no	—
635	C₃×C₄	—	4	2	no	—
636	C₃×C₄	—	4	1	no	—
637	C₃×C₄	—	4	1	no	—
638	C₃×C₄	—	4	1	no	—
639	C₃×C₄	—	4	1	no	—
640	C₃×C₄	—	4	1	no	—
641	C₃×C₄	—	4	1	no	—
642	C₃×C₄	—	6	1	no	—
643	C₃×C₄	—	6	1	no	—
644	C₃×C₄	—	6	1	no	—
645	C₃×C₄	—	8	1	no	—
646	C₃×C₄	—	8	1	no	—
647	C₃×C₄	—	12	1	no	—
648	C₃×C₄	—	12	1	no	—
649	C₃×C₄	—	12	1	no	—
650	C₃×C₄	#1004	1	1	yes	characteristic
651	C₃×C₄	D₃×#41	1	1	yes	characteristic
652	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
653	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
654	Dic₃	—	2	1	no	—
655	Dic₃	—	2	1	no	—
656	Dic₃	—	2	1	no	—
657	Dic₃	—	4	1	no	—
658	Dic₃	—	4	1	no	—
659	Dic₃	—	4	1	no	—
660	Dic₃	C₃×#135	1	2	yes	—
661	C₃²	#3393	1	1	yes	characteristic, complemented, Sylow
662	C₂³	—	2	1	no	—
663	C₂³	—	6	1	no	—
664	Q₈	—	2	1	no	—
665	Q₈	—	2	1	no	—
666	Q₈	—	2	1	no	—
667	Q₈	—	2	1	no	—
668	Q₈	—	6	2	no	—
669	Q₈	—	6	1	no	—
670	Q₈	—	6	1	no	—
671	Q₈	—	6	1	no	—
672	Q₈	—	6	1	no	—
673	D₄	—	2	1	no	—
674	D₄	—	2	1	no	—
675	D₄	—	6	1	no	—
676	D₄	—	6	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	3	1	no	—
681	C₂×C₄	—	3	1	no	—
682	C₂×C₄	—	3	1	no	—
683	C₂×C₄	—	3	1	no	—
684	C₂×C₄	—	6	1	no	—
685	C₂×C₄	—	6	1	no	—
686	C₂×C₄	—	6	1	no	—
687	C₂×C₄	—	12	2	no	—
688	C₂×C₄	—	12	2	no	—
689	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
690	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
691	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
692	C₈	—	2	1	no	—
693	C₈	—	2	1	no	—
694	C₈	—	3	2	no	—
695	C₈	—	6	1	no	—
696	C₂×C₃	—	2	1	no	—
697	C₂×C₃	—	2	1	no	—
698	C₂×C₃	—	2	1	no	—
699	C₂×C₃	—	8	1	no	—
700	C₂×C₃	—	8	1	no	—
701	C₂×C₃	—	16	1	no	—
702	C₂×C₃	—	24	1	no	—
703	C₂×C₃	#5599	1	1	yes	characteristic
704	C₂×C₃	D₃×#135	1	1	yes	characteristic
705	C₂×C₃	#5779	1	1	yes	characteristic
706	C₂×C₃	C₃×#550	1	1	yes	characteristic
707	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
708	C₂×C₃	C₃×#578	1	1	yes	characteristic
709	D₃	—	8	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	—	12	1	no	—
714	C₂²	—	12	1	no	—
715	C₂²	—	12	1	no	—
716	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	3	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	1	no	—
723	C₄	—	6	1	no	—
724	C₄	—	6	1	no	—
725	C₄	—	6	1	no	—
726	C₄	—	12	1	no	—
727	C₄	—	12	1	no	—
728	C₄	—	12	1	no	—
729	C₄	C₃×#1004	1	1	yes	characteristic
730	C₄	C₃×D₃×#41	1	1	yes	characteristic
731	C₃	—	2	1	no	—
732	C₃	#80588	1	1	yes	characteristic, direct product factor
733	C₃	C₃×#3393	1	1	yes	characteristic, complemented
734	C₂	—	8	1	no	—
735	C₂	—	24	1	no	—
736	C₂	C₃×#5599	1	1	yes	characteristic
737	C₂	C₃×D₃×#135	1	1	yes	characteristic
738	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×C₃×#213	C₂²
hypercenter	C₃×#464	D₃
hypocenter	C₃	C₃×#3393
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
1. C₃×#5671	C₂	semidirect
2. C₃×#5568	C₂	semidirect
3. C₃²×#464	C₂	semidirect
4. C₃×#5185	C₂	semidirect
5. C₃×#5183	C₂	semidirect
7. C₃×#5162	C₂	semidirect
9. C₃×C₄×#216	C₂	semidirect
10. C₃×#4845	C₂	semidirect
11. C₃×#4830	C₂	semidirect
12. C₃×#4818	C₂	semidirect
13. C₃×#4790	C₂	semidirect
14. C₃×#4767	C₂	semidirect
17. #80588	C₃	direct (N × H)
63. #5671	C₂×C₃	semidirect
64. #5568	C₂×C₃	semidirect
72. C₃×#464	D₃	semidirect
73. C₃×#464	C₂×C₃	semidirect
80. #5185	C₂×C₃	semidirect
81. #5183	C₂×C₃	semidirect
83. #5162	C₂×C₃	semidirect
85. C₄×#216	C₂×C₃	semidirect
86. #4845	C₂×C₃	semidirect
87. #4830	C₂×C₃	semidirect
88. #4818	C₂×C₃	semidirect
89. #4790	C₂×C₃	semidirect
90. #4767	C₂×C₃	semidirect
280. #464	C₃×D₃	semidirect
661. C₃²	#3393	semidirect
732. C₃	#80588	direct (N × H)
733. C₃	C₃×#3393	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×#5568	2
C₃²×#464	2
C₃×#5185	2
C₃×#5183	2
C₃×#5168	2
C₃×#5162	2
C₃×#5059	2
C₃×C₄×#216	2
C₃×#4845	2
C₃×#4830	2
C₃×#4818	2
C₃×#4790	2
C₃×#4767	2
C₃×#4756	2
C₃×#3393	3
#80588	3

Subgroups — C3×#80588 #11898335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#80588 #11898335