Subgroups — C₃×#79815 #11896029

Order 1152.

730 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5568	C₂	1	1	yes	maximal, characteristic
2	C₃×Q₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5185	C₂	1	1	yes	maximal, characteristic
5	C₃×#5182	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5028	C₂	1	1	yes	maximal, characteristic
7	C₃×#5020	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4870	C₂	1	1	yes	maximal, characteristic
9	C₃×#4854	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4794	C₂	1	1	yes	maximal, characteristic
11	C₃×#4792	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4789	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4788	C₂	1	1	yes	maximal, characteristic
14	C₃×#4714	C₂	1	1	yes	maximal, characteristic
15	C₃×#4701	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3369	—	3	1	no	maximal
17	#79815	C₃	1	1	yes	maximal, characteristic, direct product factor
18	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
19	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
20	C₃²×C₄×Q₈	C₂²	1	1	yes	characteristic
21	C₃×#947	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×#944	C₂²	1	1	yes	characteristic
25	C₂×C₃×#216	C₂²	1	1	yes	characteristic
26	C₂×C₃×#215	C₂²	1	1	yes	characteristic
27	C₃×#898	—	2	1	no	—
28	C₃×#896	—	2	1	no	—
29	C₃×#893	C₂²	1	1	yes	characteristic
30	C₃×#888	—	2	1	no	—
31	C₃×#888	—	2	1	no	—
32	C₃×#888	C₂²	1	1	yes	characteristic
33	C₃×#888	C₂²	1	1	yes	characteristic
34	C₃×#887	C₂²	1	1	yes	characteristic
35	C₃×#876	—	2	1	no	—
36	C₃×#875	C₂²	1	1	yes	characteristic
37	C₃×#872	—	2	1	no	—
38	C₃×#869	—	2	1	no	—
39	C₃×#869	C₂²	1	1	yes	characteristic
40	C₃×C₄×Dic₆	—	2	1	no	—
41	C₃×C₄×Dic₆	C₂²	1	1	yes	characteristic
42	C₃²×#106	C₂²	1	1	yes	characteristic
43	C₃²×#103	C₂²	1	1	yes	characteristic
44	C₃²×#103	C₂²	1	1	yes	characteristic
45	C₃²×#97	C₂²	1	1	yes	characteristic
46	C₃×#835	C₂²	1	1	yes	characteristic
47	C₃×#835	C₂²	1	1	yes	characteristic
48	C₃×#821	C₂²	1	1	yes	characteristic
49	C₃×#821	C₂²	1	1	yes	characteristic
50	C₃×#816	C₂²	1	1	yes	characteristic
51	C₃×#816	C₂²	1	1	yes	characteristic
52	C₃×#815	C₂²	1	1	yes	characteristic
53	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
54	C₃×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
55	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
56	C₃×#810	C₂²	1	1	yes	characteristic
57	C₃×#809	C₂²	1	1	yes	characteristic
58	C₃×#808	C₂²	1	1	yes	characteristic
59	C₃×#808	C₂²	1	1	yes	characteristic
60	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
61	C₃×Q₈²	—	3	1	no	—
62	C₃×#556	—	3	1	no	—
63	#5568	C₂×C₃	1	1	yes	characteristic
64	Q₈×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
65	C₃×#489	—	3	1	no	—
66	C₃×#489	—	3	1	no	—
67	C₃×#487	—	3	1	no	—
68	C₃×#476	—	3	1	no	—
69	C₃×#475	—	3	1	no	—
70	C₃×#475	—	3	1	no	—
71	C₃×#464	—	3	1	no	—
72	C₃×#464	—	3	1	no	—
73	C₃×#462	—	3	1	no	—
74	C₃×#446	—	3	1	no	—
75	C₃×#441	—	2	1	no	—
76	C₃×#441	—	3	1	no	—
77	C₃×#441	D₃	1	1	yes	characteristic, complemented
78	C₃×#441	C₂×C₃	1	1	yes	characteristic, complemented
79	C₃×C₄×SD₁₆	—	3	1	no	—
80	#5185	C₂×C₃	1	1	yes	characteristic
81	#5182	C₂×C₃	1	1	yes	characteristic, complemented
82	#5028	C₂×C₃	1	1	yes	characteristic
83	#5020	C₂×C₃	1	1	yes	characteristic, complemented
84	#4870	C₂×C₃	1	1	yes	characteristic
85	#4854	C₂×C₃	1	1	yes	characteristic, complemented
86	#4794	C₂×C₃	1	1	yes	characteristic
87	#4792	C₂×C₃	1	1	yes	characteristic, complemented
88	#4789	C₂×C₃	1	1	yes	characteristic, complemented
89	#4788	C₂×C₃	1	1	yes	characteristic
90	#4714	C₂×C₃	1	1	yes	characteristic
91	#4701	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
93	C₂×C₃²×Q₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×D₃	—	2	1	no	—
96	C₂×C₃×Dic₆	—	2	1	no	—
97	C₂×C₃×Dic₆	—	2	1	no	—
98	C₂×C₃×Dic₆	—	2	1	no	—
99	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
100	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
101	C₃²×Q₁₆	—	2	2	no	—
102	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
104	C₃²×C₄⋊C₄	—	2	1	no	—
105	C₃²×C₄⋊C₄	—	2	1	no	—
106	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₃²×C₄²	—	2	1	no	—
109	C₃²×C₄²	—	2	1	no	—
110	C₃²×C₄²	C₂³	1	1	yes	characteristic
111	C₃×#216	—	2	2	no	—
112	C₃×#215	—	2	2	no	—
113	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
114	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
115	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
116	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
117	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
118	C₃×C₄⋊Dic₃	—	2	1	no	—
119	C₃×C₄⋊Dic₃	—	2	1	no	—
120	C₃×C₄⋊Dic₃	—	2	1	no	—
121	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
122	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
123	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
129	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
130	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
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	#3369	—	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	—	3	1	no	—
144	C₃×C₄⋊Q₈	—	3	1	no	—
145	C₃×C₄⋊Q₈	—	3	1	no	—
146	C₃×C₄⋊Q₈	—	3	1	no	—
147	C₃×C₄⋊Q₈	—	3	1	no	—
148	C₃×C₄⋊Q₈	—	6	1	no	—
149	C₃×C₄⋊Q₈	—	6	1	no	—
150	C₃×C₄⋊Q₈	—	6	1	no	—
151	C₃×#126	—	6	1	no	—
152	C₃×#126	—	6	1	no	—
153	C₃×#124	—	3	1	no	—
154	C₃×#124	—	3	1	no	—
155	C₃×C₂²⋊Q₈	—	6	1	no	—
156	C₃×C₄×Q₈	—	2	1	no	—
157	C₃×C₄×Q₈	—	2	1	no	—
158	C₃×C₄×Q₈	—	3	1	no	—
159	C₃×C₄×Q₈	—	3	1	no	—
160	C₃×C₄×Q₈	—	3	1	no	—
161	C₃×C₄×Q₈	—	3	1	no	—
162	C₃×C₄×Q₈	—	6	1	no	—
163	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
164	C₃×C₄×Q₈	C₂×D₃	1	1	yes	characteristic
165	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
166	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
167	C₃×C₄×D₄	—	3	1	no	—
168	C₃×#117	—	6	1	no	—
169	#947	C₂²×C₃	1	1	yes	characteristic
170	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
171	Q₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
172	#944	C₂²×C₃	1	1	yes	characteristic
173	C₂×#216	C₂²×C₃	1	1	yes	characteristic
174	C₂×#215	C₂²×C₃	1	1	yes	characteristic
175	#898	—	2	1	no	—
176	#896	—	2	1	no	—
177	#893	C₂²×C₃	1	1	yes	characteristic
178	#888	—	2	1	no	—
179	#888	—	2	1	no	—
180	#888	C₂²×C₃	1	1	yes	characteristic
181	#888	C₂²×C₃	1	1	yes	characteristic
182	#887	C₂²×C₃	1	1	yes	characteristic
183	#876	—	2	1	no	—
184	#875	C₂²×C₃	1	1	yes	characteristic
185	#872	—	2	1	no	—
186	#869	—	2	1	no	—
187	#869	C₂²×C₃	1	1	yes	characteristic
188	C₄×Dic₆	—	2	1	no	—
189	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
190	C₃×#106	—	2	1	no	—
191	C₃×#106	—	3	1	no	—
192	C₃×#106	—	3	1	no	—
193	C₃×#106	C₂×D₃	1	1	yes	characteristic
194	C₃×#106	C₂²×C₃	1	1	yes	characteristic
195	C₃×C₄⋊C₈	—	3	1	no	—
196	C₃×C₄⋊C₈	—	3	1	no	—
197	C₃×C₄⋊C₈	—	3	1	no	—
198	C₃×#103	—	2	1	no	—
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	C₂×D₃	1	1	yes	characteristic
206	C₃×#103	C₂×D₃	1	1	yes	characteristic
207	C₃×#103	C₂²×C₃	1	1	yes	characteristic
208	C₃×#103	C₂²×C₃	1	1	yes	characteristic
209	C₃×#102	—	3	1	no	—
210	C₃×#102	—	3	1	no	—
211	C₃×#102	—	3	1	no	—
212	C₃×#97	—	2	1	no	—
213	C₃×#97	—	3	1	no	—
214	C₃×#97	C₂×D₃	1	1	yes	characteristic
215	C₃×#97	C₂²×C₃	1	1	yes	characteristic
216	C₃×C₄×C₈	—	3	1	no	—
217	#835	C₂²×C₃	1	1	yes	characteristic
218	#835	C₂²×C₃	1	1	yes	characteristic
219	#821	C₂²×C₃	1	1	yes	characteristic
220	#821	C₂²×C₃	1	1	yes	characteristic
221	#816	C₂²×C₃	1	1	yes	characteristic
222	#816	C₂²×C₃	1	1	yes	characteristic
223	#815	C₂²×C₃	1	1	yes	characteristic
224	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
225	Dic₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
226	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
227	#810	C₂²×C₃	1	1	yes	characteristic
228	#809	C₂²×C₃	1	1	yes	characteristic
229	#808	C₂²×C₃	1	1	yes	characteristic
230	#808	C₂²×C₃	1	1	yes	characteristic
231	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
232	C₂²×C₃×D₃	—	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	C₂×C₃²×C₄	—	2	1	no	—
238	C₂×C₃²×C₄	—	2	1	no	—
239	C₂×C₃²×C₄	—	2	1	no	—
240	C₂×C₃²×C₄	—	2	1	no	—
241	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
242	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
244	C₂×C₃×Dic₃	—	2	1	no	—
245	C₂×C₃×Dic₃	—	2	1	no	—
246	C₂×C₃×Dic₃	—	2	1	no	—
247	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
248	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
249	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
250	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
251	C₃×D₁₂	—	2	1	no	—
252	C₃×D₁₂	—	2	1	no	—
253	C₃×C₄×D₃	—	4	2	no	—
254	C₃×Dic₆	—	2	2	no	—
255	C₃×Dic₆	—	2	1	no	—
256	C₃×Dic₆	—	2	1	no	—
257	C₃×Dic₆	—	8	1	no	—
258	C₃×Dic₆	—	8	1	no	—
259	C₃×Dic₆	—	8	1	no	—
260	C₃²×C₈	—	2	1	no	—
261	C₃²×C₈	—	2	1	no	—
262	C₃×C₃⋊C₈	—	2	1	no	—
263	C₃×C₃⋊C₈	—	2	1	no	—
264	Q₈²	—	3	1	no	—
265	#556	—	3	1	no	—
266	#489	—	3	1	no	—
267	#489	—	3	1	no	—
268	#487	—	3	1	no	—
269	#476	—	3	1	no	—
270	#475	—	3	1	no	—
271	#475	—	3	1	no	—
272	#464	—	3	1	no	—
273	#464	—	3	1	no	—
274	#462	—	3	1	no	—
275	#446	—	3	1	no	—
276	#441	—	3	1	no	—
277	#441	C₃×D₃	1	1	yes	characteristic, complemented
278	C₄×SD₁₆	—	3	1	no	—
279	C₂×C₃×Q₈	—	2	1	no	—
280	C₂×C₃×Q₈	—	2	1	no	—
281	C₂×C₃×Q₈	—	3	1	no	—
282	C₂×C₃×Q₈	—	3	1	no	—
283	C₂×C₃×Q₈	—	6	1	no	—
284	C₂×C₃×Q₈	—	6	1	no	—
285	C₂×C₃×Q₈	—	6	1	no	—
286	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
287	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
288	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₃×D₄	—	3	1	no	—
291	C₂²×C₃×C₄	—	6	1	no	—
292	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₄×D₃	—	2	1	no	—
294	C₂×Dic₆	—	2	1	no	—
295	C₂×Dic₆	—	2	1	no	—
296	C₂×Dic₆	—	2	1	no	—
297	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
298	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
299	C₃×Q₁₆	—	2	4	no	—
300	C₃×Q₁₆	—	2	2	no	—
301	C₃×Q₁₆	—	2	2	no	—
302	C₃×Q₁₆	—	6	2	no	—
303	C₃×SD₁₆	—	6	2	no	—
304	C₂×C₃×C₈	—	2	1	no	—
305	C₂×C₃×C₈	—	2	1	no	—
306	C₂×C₃×C₈	—	3	1	no	—
307	C₂×C₃×C₈	—	3	1	no	—
308	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
312	C₃×C₄⋊C₄	—	2	1	no	—
313	C₃×C₄⋊C₄	—	2	1	no	—
314	C₃×C₄⋊C₄	—	2	1	no	—
315	C₃×C₄⋊C₄	—	2	1	no	—
316	C₃×C₄⋊C₄	—	2	1	no	—
317	C₃×C₄⋊C₄	—	2	1	no	—
318	C₃×C₄⋊C₄	—	3	1	no	—
319	C₃×C₄⋊C₄	—	3	1	no	—
320	C₃×C₄⋊C₄	—	3	1	no	—
321	C₃×C₄⋊C₄	—	3	1	no	—
322	C₃×C₄⋊C₄	—	3	1	no	—
323	C₃×C₄⋊C₄	—	4	1	no	—
324	C₃×C₄⋊C₄	—	4	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	—	6	1	no	—
331	C₃×C₄⋊C₄	—	6	1	no	—
332	C₃×C₄⋊C₄	—	6	1	no	—
333	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
334	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
335	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
336	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
337	C₃×C₂²⋊C₄	—	6	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×C₂²⋊C₄	—	6	1	no	—
342	C₃×C₄²	—	2	1	no	—
343	C₃×C₄²	—	2	1	no	—
344	C₃×C₄²	—	2	1	no	—
345	C₃×C₄²	—	2	1	no	—
346	C₃×C₄²	—	2	1	no	—
347	C₃×C₄²	—	3	1	no	—
348	C₃×C₄²	—	3	1	no	—
349	C₃×C₄²	—	4	1	no	—
350	C₃×C₄²	—	4	1	no	—
351	C₃×C₄²	—	6	1	no	—
352	C₃×C₄²	—	6	1	no	—
353	C₃×C₄²	—	6	1	no	—
354	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
355	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
356	#216	—	2	2	no	—
357	#215	—	2	2	no	—
358	(C₂×D₃)⋊C₄	—	2	1	no	—
359	(C₂×D₃)⋊C₄	—	2	1	no	—
360	(C₂×D₃)⋊C₄	—	2	1	no	—
361	(C₂×D₃)⋊C₄	—	2	1	no	—
362	(C₂×D₃)⋊C₄	—	2	1	no	—
363	C₄⋊Dic₃	—	2	1	no	—
364	C₄⋊Dic₃	—	2	1	no	—
365	C₄⋊Dic₃	—	2	1	no	—
366	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
367	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
368	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
369	Dic₃⋊C₄	—	2	1	no	—
370	Dic₃⋊C₄	—	2	1	no	—
371	Dic₃⋊C₄	—	2	1	no	—
372	Dic₃⋊C₄	—	2	1	no	—
373	Dic₃⋊C₄	—	2	1	no	—
374	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
375	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
376	C₄×Dic₃	—	2	1	no	—
377	C₄×Dic₃	—	2	1	no	—
378	C₄×Dic₃	—	2	1	no	—
379	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
380	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
381	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
382	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
383	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₃×D₃	—	4	1	no	—
385	C₂×C₃×D₃	—	4	1	no	—
386	C₂×C₃×D₃	—	4	1	no	—
387	C₃²×C₄	—	2	2	no	—
388	C₃²×C₄	—	2	1	no	—
389	C₃²×C₄	—	2	1	no	—
390	C₃²×C₄	—	4	1	no	—
391	C₃²×C₄	—	4	1	no	—
392	C₃²×C₄	—	4	1	no	—
393	C₃²×C₄	C₂×#41	1	1	yes	characteristic
394	C₃²×C₄	2₋¹⁺⁴	1	1	yes	characteristic
395	C₃×Dic₃	—	2	1	no	—
396	C₃×Dic₃	—	2	1	no	—
397	C₃×Dic₃	—	2	1	no	—
398	C₃×Dic₃	—	4	1	no	—
399	C₃×Dic₃	—	4	1	no	—
400	C₃×Dic₃	—	4	1	no	—
401	C₃×Dic₃	#137	1	2	yes	—
402	C₂×Q₁₆	—	3	1	no	—
403	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
404	C₂×SD₁₆	—	3	1	no	—
405	C₄⋊Q₈	—	3	1	no	—
406	C₄⋊Q₈	—	3	1	no	—
407	C₄⋊Q₈	—	3	1	no	—
408	C₄⋊Q₈	—	3	1	no	—
409	C₄⋊Q₈	—	6	1	no	—
410	C₄⋊Q₈	—	6	1	no	—
411	C₄⋊Q₈	—	6	1	no	—
412	#126	—	6	1	no	—
413	#126	—	6	1	no	—
414	#124	—	3	1	no	—
415	#124	—	3	1	no	—
416	C₂²⋊Q₈	—	6	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×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
424	C₄×D₄	—	3	1	no	—
425	#117	—	6	1	no	—
426	#106	—	3	1	no	—
427	#106	—	3	1	no	—
428	#106	C₂×C₃×D₃	1	1	yes	characteristic
429	C₄⋊C₈	—	3	1	no	—
430	C₄⋊C₈	—	3	1	no	—
431	C₄⋊C₈	—	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	#103	C₂×C₃×D₃	1	1	yes	characteristic
439	#102	—	3	1	no	—
440	#102	—	3	1	no	—
441	#102	—	3	1	no	—
442	#97	—	3	1	no	—
443	#97	C₂×C₃×D₃	1	1	yes	characteristic
444	C₄×C₈	—	3	1	no	—
445	C₂³×C₃	—	6	1	no	—
446	C₂²×D₃	—	2	1	no	—
447	C₃×Q₈	—	2	1	no	—
448	C₃×Q₈	—	2	1	no	—
449	C₃×Q₈	—	2	2	no	—
450	C₃×Q₈	—	2	1	no	—
451	C₃×Q₈	—	2	1	no	—
452	C₃×Q₈	—	2	1	no	—
453	C₃×Q₈	—	2	1	no	—
454	C₃×Q₈	—	2	2	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	—	24	1	no	—
461	C₃×Q₈	—	24	1	no	—
462	C₃×Q₈	—	24	1	no	—
463	C₃×Q₈	#235	1	2	yes	—
464	C₃×Q₈	C₃×#41	1	2	yes	—
465	C₃×D₄	—	6	1	no	—
466	C₃×D₄	—	6	1	no	—
467	C₂×C₃×C₄	—	2	1	no	—
468	C₂×C₃×C₄	—	2	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	—	4	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	C₂×C₃×D₄	1	1	yes	characteristic
500	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
501	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
502	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
503	D₁₂	—	2	1	no	—
504	D₁₂	—	2	1	no	—
505	C₄×D₃	—	4	2	no	—
506	Dic₆	—	2	2	no	—
507	Dic₆	—	2	1	no	—
508	Dic₆	—	2	1	no	—
509	Dic₆	—	8	1	no	—
510	Dic₆	—	8	1	no	—
511	Dic₆	—	8	1	no	—
512	C₃×C₈	—	2	2	no	—
513	C₃×C₈	—	2	1	no	—
514	C₃×C₈	—	2	1	no	—
515	C₃×C₈	—	2	1	no	—
516	C₃×C₈	—	2	1	no	—
517	C₃×C₈	—	4	1	no	—
518	C₃×C₈	—	6	1	no	—
519	C₃×C₈	—	6	1	no	—
520	C₃⋊C₈	—	2	1	no	—
521	C₃⋊C₈	—	2	1	no	—
522	C₂×C₃²	#548	1	1	yes	characteristic
523	C₂×C₃²	C₂×#137	1	1	yes	characteristic
524	C₂×C₃²	#577	1	1	yes	characteristic
525	C₃×D₃	—	8	1	no	—
526	C₂×Q₈	—	3	1	no	—
527	C₂×Q₈	—	3	1	no	—
528	C₂×Q₈	—	6	1	no	—
529	C₂×Q₈	—	6	1	no	—
530	C₂×Q₈	—	6	1	no	—
531	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
532	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
533	C₂×D₄	—	3	1	no	—
534	C₂²×C₄	—	6	1	no	—
535	Q₁₆	—	2	2	no	—
536	Q₁₆	—	6	2	no	—
537	SD₁₆	—	6	2	no	—
538	C₂×C₈	—	3	1	no	—
539	C₂×C₈	—	3	1	no	—
540	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
541	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	3	1	no	—
545	C₄⋊C₄	—	3	1	no	—
546	C₄⋊C₄	—	3	1	no	—
547	C₄⋊C₄	—	3	1	no	—
548	C₄⋊C₄	—	3	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	—	6	1	no	—
556	C₄⋊C₄	—	6	1	no	—
557	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
558	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
559	C₂²⋊C₄	—	6	1	no	—
560	C₂²⋊C₄	—	6	1	no	—
561	C₂²⋊C₄	—	6	1	no	—
562	C₂²⋊C₄	—	6	1	no	—
563	C₂²⋊C₄	—	6	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	3	1	no	—
567	C₄²	—	3	1	no	—
568	C₄²	—	6	1	no	—
569	C₄²	—	6	1	no	—
570	C₄²	—	6	1	no	—
571	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
572	C₂²×C₃	—	2	1	no	—
573	C₂²×C₃	—	12	1	no	—
574	C₂²×C₃	—	12	1	no	—
575	C₂²×C₃	—	12	1	no	—
576	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
577	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
578	C₂×D₃	—	4	1	no	—
579	C₂×D₃	—	4	1	no	—
580	C₂×D₃	—	4	1	no	—
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	2	no	—
594	C₃×C₄	—	4	1	no	—
595	C₃×C₄	—	4	1	no	—
596	C₃×C₄	—	4	1	no	—
597	C₃×C₄	—	4	1	no	—
598	C₃×C₄	—	4	1	no	—
599	C₃×C₄	—	4	1	no	—
600	C₃×C₄	—	6	1	no	—
601	C₃×C₄	—	6	1	no	—
602	C₃×C₄	—	6	1	no	—
603	C₃×C₄	—	8	1	no	—
604	C₃×C₄	—	8	1	no	—
605	C₃×C₄	—	12	1	no	—
606	C₃×C₄	—	12	1	no	—
607	C₃×C₄	—	12	1	no	—
608	C₃×C₄	C₂×#235	1	1	yes	characteristic
609	C₃×C₄	#1010	1	1	yes	characteristic
610	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
611	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
612	Dic₃	—	2	1	no	—
613	Dic₃	—	2	1	no	—
614	Dic₃	—	2	1	no	—
615	Dic₃	—	4	1	no	—
616	Dic₃	—	4	1	no	—
617	Dic₃	—	4	1	no	—
618	Dic₃	C₃×#137	1	2	yes	—
619	C₃²	#3369	1	1	yes	characteristic, complemented, Sylow
620	C₂³	—	6	1	no	—
621	Q₈	—	2	1	no	—
622	Q₈	—	2	1	no	—
623	Q₈	—	2	1	no	—
624	Q₈	—	6	2	no	—
625	Q₈	—	6	1	no	—
626	Q₈	—	6	1	no	—
627	Q₈	—	24	1	no	—
628	Q₈	—	24	1	no	—
629	Q₈	—	24	1	no	—
630	Q₈	C₃×#235	1	2	yes	—
631	D₄	—	6	1	no	—
632	D₄	—	6	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	3	1	no	—
638	C₂×C₄	—	3	1	no	—
639	C₂×C₄	—	3	1	no	—
640	C₂×C₄	—	3	1	no	—
641	C₂×C₄	—	6	1	no	—
642	C₂×C₄	—	6	1	no	—
643	C₂×C₄	—	6	1	no	—
644	C₂×C₄	—	12	2	no	—
645	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
646	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
647	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
648	C₈	—	2	1	no	—
649	C₈	—	2	1	no	—
650	C₈	—	6	1	no	—
651	C₈	—	6	1	no	—
652	C₂×C₃	—	2	1	no	—
653	C₂×C₃	—	2	1	no	—
654	C₂×C₃	—	2	1	no	—
655	C₂×C₃	—	24	1	no	—
656	C₂×C₃	#5552	1	1	yes	characteristic
657	C₂×C₃	D₃×#137	1	1	yes	characteristic
658	C₂×C₃	#5778	1	1	yes	characteristic
659	C₂×C₃	C₃×#548	1	1	yes	characteristic
660	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
661	C₂×C₃	C₃×#577	1	1	yes	characteristic
662	D₃	—	8	1	no	—
663	C₂²	—	12	1	no	—
664	C₂²	—	12	1	no	—
665	C₂²	—	12	1	no	—
666	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	3	2	no	—
671	C₄	—	4	1	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	6	1	no	—
675	C₄	—	6	1	no	—
676	C₄	—	6	1	no	—
677	C₄	—	12	1	no	—
678	C₄	—	12	1	no	—
679	C₄	—	12	1	no	—
680	C₄	C₂×C₃×#235	1	1	yes	characteristic
681	C₄	C₃×#1010	1	1	yes	characteristic
682	C₃	—	2	1	no	—
683	C₃	#79815	1	1	yes	characteristic, direct product factor
684	C₃	C₃×#3369	1	1	yes	characteristic, complemented
685	C₂	—	24	1	no	—
686	C₂	C₃×#5552	1	1	yes	characteristic
687	C₂	C₃×D₃×#137	1	1	yes	characteristic
688	C₂	C₃×#5778	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×#441	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂×C₃×D₁₂	C₂³
hypercenter	C₃×#441	D₃
hypocenter	C₃	C₃×#3369
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#441

Complements

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

N	H ≅ G/N	type
2. C₃×Q₈×Dic₆	C₂	semidirect
3. C₃²×#441	C₂	semidirect
5. C₃×#5182	C₂	semidirect
7. C₃×#5020	C₂	semidirect
9. C₃×#4854	C₂	semidirect
11. C₃×#4792	C₂	semidirect
12. C₃×#4789	C₂	semidirect
15. C₃×#4701	C₂	semidirect
17. #79815	C₃	direct (N × H)
64. Q₈×Dic₆	C₂×C₃	semidirect
77. C₃×#441	D₃	semidirect
78. C₃×#441	C₂×C₃	semidirect
81. #5182	C₂×C₃	semidirect
83. #5020	C₂×C₃	semidirect
85. #4854	C₂×C₃	semidirect
87. #4792	C₂×C₃	semidirect
88. #4789	C₂×C₃	semidirect
91. #4701	C₂×C₃	semidirect
277. #441	C₃×D₃	semidirect
619. C₃²	#3369	semidirect
683. C₃	#79815	direct (N × H)
684. C₃	C₃×#3369	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5568	2
C₃×Q₈×Dic₆	2
C₃²×#441	2
C₃×#5185	2
C₃×#5182	2
C₃×#5028	2
C₃×#5020	2
C₃×#4870	2
C₃×#4854	2
C₃×#4794	2
C₃×#4792	2
C₃×#4789	2
C₃×#4788	2
C₃×#4714	2
C₃×#4701	2
C₃×#3369	3
#79815	3

Subgroups — C3×#79815 #11896029

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79815 #11896029