Subgroups — C₃×#80589 #11898403

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5681	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×#5191	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#5182	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5175	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#5165	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×#215	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4844	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4830	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4788	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4786	C₂	1	1	yes	maximal, characteristic
15	C₃×#4758	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3394	—	3	1	no	maximal
17	#80589	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×#947	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	C₂×C₃×#215	C₂²	1	1	yes	characteristic
28	C₂×C₃×#215	C₂²	1	1	yes	characteristic
29	C₃×#940	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×D₂₄	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×#886	—	2	1	no	—
40	C₃×#885	—	2	1	no	—
41	C₃×#883	—	2	1	no	—
42	C₃×#67⋊C₄	—	2	1	no	—
43	C₃×#876	—	2	1	no	—
44	C₃×#875	C₂²	1	1	yes	characteristic
45	C₃×C₄×D₁₂	C₂²	1	1	yes	characteristic
46	C₃×#872	—	2	1	no	—
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×#809	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×#559	—	3	1	no	—
62	C₃×#556	—	3	1	no	—
63	#5681	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×#492	—	3	1	no	—
68	C₃×#464	—	2	1	no	—
69	C₃×#464	—	3	1	no	—
70	C₃×#464	D₃	1	1	yes	characteristic, complemented
71	C₃×#464	C₂×C₃	1	1	yes	characteristic, complemented
72	C₃×#463	—	3	1	no	—
73	C₃×#463	—	3	1	no	—
74	C₃×#462	—	3	1	no	—
75	C₃×#459	—	3	1	no	—
76	C₃×C₈×Q₈	—	3	1	no	—
77	C₃×C₄×SD₁₆	—	3	1	no	—
78	C₃×C₄×SD₁₆	—	3	1	no	—
79	C₃×C₄×SD₁₆	—	3	1	no	—
80	#5191	C₂×C₃	1	1	yes	characteristic, complemented
81	#5182	C₂×C₃	1	1	yes	characteristic, complemented
82	#5175	C₂×C₃	1	1	yes	characteristic, complemented
83	#5165	C₂×C₃	1	1	yes	characteristic, complemented
84	#5059	C₂×C₃	1	1	yes	characteristic, complemented
85	C₄×#215	C₂×C₃	1	1	yes	characteristic, complemented
86	#4844	C₂×C₃	1	1	yes	characteristic, complemented
87	#4830	C₂×C₃	1	1	yes	characteristic, complemented
88	#4798	C₂×C₃	1	1	yes	characteristic, complemented
89	#4788	C₂×C₃	1	1	yes	characteristic, complemented
90	#4786	C₂×C₃	1	1	yes	characteristic
91	#4758	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×C₃²×D₄	C₂³	1	1	yes	characteristic
95	C₂×C₃×#67	—	2	1	no	—
96	C₂×C₃×#67	—	2	1	no	—
97	C₂²×C₃×Dic₃	—	2	1	no	—
98	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
99	C₂×C₃×D₁₂	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₄×D₃	—	2	1	no	—
101	C₂×C₃×C₄×D₃	—	2	1	no	—
102	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
103	C₂×C₃×Dic₆	C₂³	1	1	yes	characteristic
104	C₃²×Q₁₆	—	4	1	no	—
105	C₃²×SD₁₆	—	4	1	no	—
106	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
108	C₃²×C₄⋊C₄	—	2	1	no	—
109	C₃²×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₃²×C₂²⋊C₄	—	2	1	no	—
111	C₃²×C₂²⋊C₄	—	2	1	no	—
112	C₃²×C₄²	—	2	1	no	—
113	C₃²×C₄²	C₂³	1	1	yes	characteristic
114	C₃×#217	—	2	1	no	—
115	C₃×#216	—	4	1	no	—
116	C₃×#215	—	2	2	no	—
117	C₃×#215	—	2	2	no	—
118	C₃×#214	—	2	2	no	—
119	C₃×#213	—	4	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×(C₂×D₃)⋊C₄	—	2	1	no	—
125	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
126	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
127	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
128	C₃×C₄⋊Dic₃	—	2	1	no	—
129	C₃×C₄⋊Dic₃	D₄	1	1	yes	characteristic
130	C₃×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
131	C₃×Dic₃⋊C₄	—	2	1	no	—
132	C₃×Dic₃⋊C₄	—	2	1	no	—
133	C₃×Dic₃⋊C₄	—	2	1	no	—
134	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
135	C₃×Dic₃⋊C₄	D₄	1	1	yes	characteristic
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×D₂₄	—	4	1	no	—
143	C₃×#204	—	4	1	no	—
144	#3394	—	3	1	no	Sylow
145	C₂×C₃×Q₁₆	—	2	1	no	—
146	C₂×C₃×Q₁₆	—	3	1	no	—
147	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
148	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×SD₁₆	—	2	1	no	—
150	C₂×C₃×SD₁₆	—	3	1	no	—
151	C₂×C₃×SD₁₆	—	3	1	no	—
152	C₂×C₃×SD₁₆	—	3	1	no	—
153	C₂×C₃×SD₁₆	—	3	1	no	—
154	C₂×C₃×SD₁₆	C₂×D₃	1	1	yes	characteristic
155	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₃×D₈	—	3	1	no	—
157	C₂×C₃×D₈	—	3	1	no	—
158	C₃×C₄⋊Q₈	—	3	1	no	—
159	C₃×#127	—	3	1	no	—
160	C₃×#126	—	6	1	no	—
161	C₃×#126	—	6	1	no	—
162	C₃×#124	—	2	1	no	—
163	C₃×#124	—	3	1	no	—
164	C₃×#124	—	3	1	no	—
165	C₃×#124	—	3	1	no	—
166	C₃×#124	—	6	1	no	—
167	C₃×#124	C₂×D₃	1	1	yes	characteristic
168	C₃×#124	C₂²×C₃	1	1	yes	characteristic
169	C₃×#123	—	6	1	no	—
170	C₃×#123	—	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	C₂×D₃	1	1	yes	characteristic
177	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
178	C₃×C₄×D₄	—	3	1	no	—
179	C₃×C₄×D₄	—	3	1	no	—
180	C₃×C₄×D₄	—	3	1	no	—
181	C₃×C₄×D₄	—	6	1	no	—
182	C₃×#117	—	6	1	no	—
183	#947	C₂²×C₃	1	1	yes	characteristic
184	#947	C₂²×C₃	1	1	yes	characteristic
185	Q₈×Dic₃	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×#215	C₂²×C₃	1	1	yes	characteristic
189	C₂×#215	C₂²×C₃	1	1	yes	characteristic
190	#940	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×D₂₄	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	#886	—	2	1	no	—
201	#885	—	2	1	no	—
202	#883	—	2	1	no	—
203	#67⋊C₄	—	2	1	no	—
204	#876	—	2	1	no	—
205	#875	C₂²×C₃	1	1	yes	characteristic
206	C₄×D₁₂	C₂²×C₃	1	1	yes	characteristic
207	#872	—	2	1	no	—
208	C₄×Dic₆	C₂²×C₃	1	1	yes	characteristic
209	C₃×#106	—	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	C₂×D₃	1	1	yes	characteristic
219	C₃×#103	C₂²×C₃	1	1	yes	characteristic
220	C₃×#102	—	2	1	no	—
221	C₃×#102	—	3	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	#809	C₂²×C₃	1	1	yes	characteristic
236	#808	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	C₂²×C₃×D₃	—	2	1	no	—
241	C₃²×Q₈	—	2	1	no	—
242	C₃²×Q₈	—	2	1	no	—
243	C₃²×Q₈	—	2	1	no	—
244	C₃²×Q₈	—	2	1	no	—
245	C₃²×D₄	—	2	1	no	—
246	C₃²×D₄	—	2	1	no	—
247	C₂×C₃²×C₄	—	2	1	no	—
248	C₂×C₃²×C₄	—	2	1	no	—
249	C₂×C₃²×C₄	—	2	1	no	—
250	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
251	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
252	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
253	C₃×#67	—	4	2	no	—
254	C₃×#67	—	8	1	no	—
255	C₂×C₃×Dic₃	—	2	1	no	—
256	C₂×C₃×Dic₃	—	2	1	no	—
257	C₂×C₃×Dic₃	—	8	1	no	—
258	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
259	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
260	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
261	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
262	C₃×D₁₂	—	2	1	no	—
263	C₃×D₁₂	—	2	1	no	—
264	C₃×D₁₂	—	2	1	no	—
265	C₃×D₁₂	—	2	1	no	—
266	C₃×C₄×D₃	—	4	2	no	—
267	C₃×C₄×D₃	—	8	1	no	—
268	C₃×Dic₆	—	2	2	no	—
269	C₃×Dic₆	—	2	1	no	—
270	C₃×Dic₆	—	2	1	no	—
271	C₃²×C₈	—	2	1	no	—
272	C₃²×C₈	—	2	1	no	—
273	C₃×C₃⋊C₈	—	2	1	no	—
274	C₃×C₃⋊C₈	#41	1	2	yes	—
275	#559	—	3	1	no	—
276	#556	—	3	1	no	—
277	#495	—	3	1	no	—
278	#495	—	3	1	no	—
279	#492	—	3	1	no	—
280	#464	—	3	1	no	—
281	#464	C₃×D₃	1	1	yes	characteristic, complemented
282	#463	—	3	1	no	—
283	#463	—	3	1	no	—
284	#462	—	3	1	no	—
285	#459	—	3	1	no	—
286	C₈×Q₈	—	3	1	no	—
287	C₄×SD₁₆	—	3	1	no	—
288	C₄×SD₁₆	—	3	1	no	—
289	C₄×SD₁₆	—	3	1	no	—
290	C₂×C₃×Q₈	—	2	1	no	—
291	C₂×C₃×Q₈	—	2	1	no	—
292	C₂×C₃×Q₈	—	3	1	no	—
293	C₂×C₃×Q₈	—	3	1	no	—
294	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
295	C₂×C₃×Q₈	C₂²×D₃	1	1	yes	characteristic
296	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₃×D₄	—	2	1	no	—
299	C₂×C₃×D₄	—	3	1	no	—
300	C₂×C₃×D₄	—	3	1	no	—
301	C₂×C₃×D₄	—	6	1	no	—
302	C₂×C₃×D₄	—	6	1	no	—
303	C₂×C₃×D₄	C₂²×D₃	1	1	yes	characteristic
304	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
305	C₂²×C₃×C₄	—	6	1	no	—
306	C₂²×C₃×C₄	—	6	1	no	—
307	C₂²×C₃×C₄	—	6	1	no	—
308	C₂×#67	—	2	1	no	—
309	C₂×#67	—	2	1	no	—
310	C₂²×Dic₃	—	2	1	no	—
311	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
312	C₂×D₁₂	C₂³×C₃	1	1	yes	characteristic
313	C₂×C₄×D₃	—	2	1	no	—
314	C₂×C₄×D₃	—	2	1	no	—
315	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
316	C₂×Dic₆	C₂³×C₃	1	1	yes	characteristic
317	C₃×Q₁₆	—	4	1	no	—
318	C₃×Q₁₆	—	4	1	no	—
319	C₃×Q₁₆	—	4	2	no	—
320	C₃×Q₁₆	—	12	1	no	—
321	C₃×SD₁₆	—	4	1	no	—
322	C₃×SD₁₆	—	4	1	no	—
323	C₃×SD₁₆	—	4	2	no	—
324	C₃×SD₁₆	—	6	2	no	—
325	C₃×SD₁₆	—	6	2	no	—
326	C₃×SD₁₆	—	6	2	no	—
327	C₃×SD₁₆	—	12	1	no	—
328	C₃×D₈	—	12	1	no	—
329	C₃×D₈	—	12	1	no	—
330	C₂×C₃×C₈	—	2	1	no	—
331	C₂×C₃×C₈	—	2	1	no	—
332	C₂×C₃×C₈	—	3	1	no	—
333	C₂×C₃×C₈	—	3	1	no	—
334	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
335	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
336	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
337	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
338	C₃×C₄⋊C₄	—	2	1	no	—
339	C₃×C₄⋊C₄	—	2	1	no	—
340	C₃×C₄⋊C₄	—	2	1	no	—
341	C₃×C₄⋊C₄	—	3	1	no	—
342	C₃×C₄⋊C₄	—	3	1	no	—
343	C₃×C₄⋊C₄	—	3	1	no	—
344	C₃×C₄⋊C₄	—	3	1	no	—
345	C₃×C₄⋊C₄	—	4	1	no	—
346	C₃×C₄⋊C₄	—	6	1	no	—
347	C₃×C₄⋊C₄	—	6	1	no	—
348	C₃×C₄⋊C₄	—	6	1	no	—
349	C₃×C₄⋊C₄	—	6	1	no	—
350	C₃×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
351	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
352	C₃×C₂²⋊C₄	—	2	1	no	—
353	C₃×C₂²⋊C₄	—	2	1	no	—
354	C₃×C₂²⋊C₄	—	2	1	no	—
355	C₃×C₂²⋊C₄	—	2	1	no	—
356	C₃×C₂²⋊C₄	—	4	1	no	—
357	C₃×C₂²⋊C₄	—	4	1	no	—
358	C₃×C₂²⋊C₄	—	6	1	no	—
359	C₃×C₂²⋊C₄	—	6	1	no	—
360	C₃×C₂²⋊C₄	—	6	1	no	—
361	C₃×C₂²⋊C₄	—	6	1	no	—
362	C₃×C₂²⋊C₄	—	6	1	no	—
363	C₃×C₂²⋊C₄	—	6	1	no	—
364	C₃×C₂²⋊C₄	—	6	1	no	—
365	C₃×C₂²⋊C₄	—	6	1	no	—
366	C₃×C₂²⋊C₄	—	6	1	no	—
367	C₃×C₄²	—	2	1	no	—
368	C₃×C₄²	—	2	1	no	—
369	C₃×C₄²	—	2	1	no	—
370	C₃×C₄²	—	3	1	no	—
371	C₃×C₄²	—	3	1	no	—
372	C₃×C₄²	—	4	1	no	—
373	C₃×C₄²	—	6	1	no	—
374	C₃×C₄²	—	6	1	no	—
375	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
376	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
377	#217	—	2	1	no	—
378	#216	—	4	1	no	—
379	#215	—	2	2	no	—
380	#215	—	2	2	no	—
381	#214	—	2	2	no	—
382	#213	—	4	1	no	—
383	(C₂×D₃)⋊C₄	—	2	1	no	—
384	(C₂×D₃)⋊C₄	—	2	1	no	—
385	(C₂×D₃)⋊C₄	—	2	1	no	—
386	(C₂×D₃)⋊C₄	—	2	1	no	—
387	(C₂×D₃)⋊C₄	—	2	1	no	—
388	(C₂×D₃)⋊C₄	—	2	1	no	—
389	(C₂×D₃)⋊C₄	—	2	1	no	—
390	(C₂×D₃)⋊C₄	—	2	1	no	—
391	C₄⋊Dic₃	—	2	1	no	—
392	C₄⋊Dic₃	C₃×D₄	1	1	yes	characteristic
393	C₄⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
394	Dic₃⋊C₄	—	2	1	no	—
395	Dic₃⋊C₄	—	2	1	no	—
396	Dic₃⋊C₄	—	2	1	no	—
397	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
398	Dic₃⋊C₄	C₃×D₄	1	1	yes	characteristic
399	C₄×Dic₃	—	2	1	no	—
400	C₄×Dic₃	—	2	1	no	—
401	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
402	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
403	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
404	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
405	D₂₄	—	4	1	no	—
406	#204	—	4	1	no	—
407	C₂²×C₃²	—	4	1	no	—
408	C₂²×C₃²	—	4	1	no	—
409	C₂²×C₃²	—	4	1	no	—
410	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₃×D₃	—	4	1	no	—
412	C₂×C₃×D₃	—	4	1	no	—
413	C₂×C₃×D₃	—	4	1	no	—
414	C₂×C₃×D₃	—	4	1	no	—
415	C₂×C₃×D₃	—	4	1	no	—
416	C₂×C₃×D₃	—	4	1	no	—
417	C₃²×C₄	—	2	1	no	—
418	C₃²×C₄	—	2	1	no	—
419	C₃²×C₄	—	4	1	no	—
420	C₃²×C₄	—	4	1	no	—
421	C₃²×C₄	—	4	1	no	—
422	C₃²×C₄	C₂×#41	1	1	yes	characteristic
423	C₃²×C₄	H(5,𝔽₂)	1	1	yes	characteristic
424	C₃×Dic₃	—	2	1	no	—
425	C₃×Dic₃	—	2	1	no	—
426	C₃×Dic₃	—	2	1	no	—
427	C₃×Dic₃	—	4	1	no	—
428	C₃×Dic₃	—	4	1	no	—
429	C₃×Dic₃	#135	1	2	yes	—
430	C₂×Q₁₆	—	3	1	no	—
431	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
432	C₂×SD₁₆	—	3	1	no	—
433	C₂×SD₁₆	—	3	1	no	—
434	C₂×SD₁₆	—	3	1	no	—
435	C₂×SD₁₆	—	3	1	no	—
436	C₂×SD₁₆	C₂×C₃×D₃	1	1	yes	characteristic
437	C₂×D₈	—	3	1	no	—
438	C₂×D₈	—	3	1	no	—
439	C₄⋊Q₈	—	3	1	no	—
440	#127	—	3	1	no	—
441	#126	—	6	1	no	—
442	#126	—	6	1	no	—
443	#124	—	3	1	no	—
444	#124	—	3	1	no	—
445	#124	—	3	1	no	—
446	#124	—	6	1	no	—
447	#124	C₂×C₃×D₃	1	1	yes	characteristic
448	#123	—	6	1	no	—
449	#123	—	6	1	no	—
450	C₂²⋊Q₈	—	6	1	no	—
451	C₄×Q₈	—	3	1	no	—
452	C₄×Q₈	—	3	1	no	—
453	C₄×Q₈	—	3	1	no	—
454	C₄×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
455	C₄×D₄	—	3	1	no	—
456	C₄×D₄	—	3	1	no	—
457	C₄×D₄	—	3	1	no	—
458	C₄×D₄	—	6	1	no	—
459	#117	—	6	1	no	—
460	#106	—	3	1	no	—
461	C₄⋊C₈	—	3	1	no	—
462	C₄⋊C₈	—	3	1	no	—
463	C₄⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
464	#103	—	3	1	no	—
465	#103	—	3	1	no	—
466	#103	C₂×C₃×D₃	1	1	yes	characteristic
467	#102	—	3	1	no	—
468	#102	—	3	1	no	—
469	#102	C₂×C₃×D₃	1	1	yes	characteristic
470	C₄×C₈	—	3	1	no	—
471	C₄×C₈	—	3	1	no	—
472	C₄×C₈	—	3	1	no	—
473	C₂³×C₃	—	2	1	no	—
474	C₂³×C₃	—	2	1	no	—
475	C₂³×C₃	—	4	1	no	—
476	C₂³×C₃	—	6	1	no	—
477	C₂³×C₃	—	6	1	no	—
478	C₂²×D₃	—	2	1	no	—
479	C₂²×D₃	—	2	1	no	—
480	C₃×Q₈	—	2	2	no	—
481	C₃×Q₈	—	2	1	no	—
482	C₃×Q₈	—	2	1	no	—
483	C₃×Q₈	—	2	1	no	—
484	C₃×Q₈	—	2	1	no	—
485	C₃×Q₈	—	2	1	no	—
486	C₃×Q₈	—	2	1	no	—
487	C₃×Q₈	—	2	1	no	—
488	C₃×Q₈	—	2	1	no	—
489	C₃×Q₈	—	4	1	no	—
490	C₃×Q₈	—	4	1	no	—
491	C₃×Q₈	—	4	1	no	—
492	C₃×Q₈	—	6	2	no	—
493	C₃×Q₈	—	6	1	no	—
494	C₃×Q₈	—	6	1	no	—
495	C₃×D₄	—	2	1	no	—
496	C₃×D₄	—	2	1	no	—
497	C₃×D₄	—	2	1	no	—
498	C₃×D₄	—	2	1	no	—
499	C₃×D₄	—	4	1	no	—
500	C₃×D₄	—	4	1	no	—
501	C₃×D₄	—	6	1	no	—
502	C₃×D₄	—	6	1	no	—
503	C₃×D₄	—	6	1	no	—
504	C₃×D₄	—	6	1	no	—
505	C₃×D₄	—	12	2	no	—
506	C₃×D₄	—	24	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	3	1	no	—
517	C₂×C₃×C₄	—	3	1	no	—
518	C₂×C₃×C₄	—	3	1	no	—
519	C₂×C₃×C₄	—	3	1	no	—
520	C₂×C₃×C₄	—	4	1	no	—
521	C₂×C₃×C₄	—	4	1	no	—
522	C₂×C₃×C₄	—	4	1	no	—
523	C₂×C₃×C₄	—	6	1	no	—
524	C₂×C₃×C₄	—	6	1	no	—
525	C₂×C₃×C₄	—	12	2	no	—
526	C₂×C₃×C₄	—	24	1	no	—
527	C₂×C₃×C₄	—	24	1	no	—
528	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
529	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
530	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
531	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
532	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
533	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
534	#67	—	4	2	no	—
535	#67	—	8	1	no	—
536	C₂×Dic₃	—	2	1	no	—
537	C₂×Dic₃	—	2	1	no	—
538	C₂×Dic₃	—	8	1	no	—
539	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
540	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
541	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
542	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
543	D₁₂	—	2	1	no	—
544	D₁₂	—	2	1	no	—
545	D₁₂	—	2	1	no	—
546	D₁₂	—	2	1	no	—
547	C₄×D₃	—	4	2	no	—
548	C₄×D₃	—	8	1	no	—
549	Dic₆	—	2	2	no	—
550	Dic₆	—	2	1	no	—
551	Dic₆	—	2	1	no	—
552	C₃×C₈	—	2	1	no	—
553	C₃×C₈	—	2	1	no	—
554	C₃×C₈	—	2	1	no	—
555	C₃×C₈	—	2	1	no	—
556	C₃×C₈	—	3	2	no	—
557	C₃×C₈	—	4	1	no	—
558	C₃×C₈	—	4	1	no	—
559	C₃×C₈	—	6	1	no	—
560	C₃⋊C₈	—	2	1	no	—
561	C₃⋊C₈	C₃×#41	1	2	yes	—
562	C₂×C₃²	—	8	1	no	—
563	C₂×C₃²	#550	1	1	yes	characteristic
564	C₂×C₃²	C₂×#135	1	1	yes	characteristic
565	C₂×C₃²	#577	1	1	yes	characteristic
566	C₃×D₃	—	8	1	no	—
567	C₃×D₃	—	8	1	no	—
568	C₂×Q₈	—	3	1	no	—
569	C₂×Q₈	—	3	1	no	—
570	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
571	C₂×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
572	C₂×D₄	—	3	1	no	—
573	C₂×D₄	—	3	1	no	—
574	C₂×D₄	—	6	1	no	—
575	C₂×D₄	—	6	1	no	—
576	C₂×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
577	C₂²×C₄	—	6	1	no	—
578	C₂²×C₄	—	6	1	no	—
579	C₂²×C₄	—	6	1	no	—
580	Q₁₆	—	4	1	no	—
581	Q₁₆	—	12	1	no	—
582	SD₁₆	—	4	1	no	—
583	SD₁₆	—	6	2	no	—
584	SD₁₆	—	6	2	no	—
585	SD₁₆	—	6	2	no	—
586	SD₁₆	—	12	1	no	—
587	D₈	—	12	1	no	—
588	D₈	—	12	1	no	—
589	C₂×C₈	—	3	1	no	—
590	C₂×C₈	—	3	1	no	—
591	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
592	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	3	1	no	—
595	C₄⋊C₄	—	3	1	no	—
596	C₄⋊C₄	—	3	1	no	—
597	C₄⋊C₄	—	3	1	no	—
598	C₄⋊C₄	—	6	1	no	—
599	C₄⋊C₄	—	6	1	no	—
600	C₄⋊C₄	—	6	1	no	—
601	C₄⋊C₄	—	6	1	no	—
602	C₄⋊C₄	C₂²×C₃×D₃	1	1	yes	characteristic
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	6	1	no	—
606	C₂²⋊C₄	—	6	1	no	—
607	C₂²⋊C₄	—	6	1	no	—
608	C₂²⋊C₄	—	6	1	no	—
609	C₂²⋊C₄	—	6	1	no	—
610	C₂²⋊C₄	—	6	1	no	—
611	C₂²⋊C₄	—	6	1	no	—
612	C₂²⋊C₄	—	6	1	no	—
613	C₂²⋊C₄	—	6	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	3	1	no	—
616	C₄²	—	3	1	no	—
617	C₄²	—	6	1	no	—
618	C₄²	—	6	1	no	—
619	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
620	C₂²×C₃	—	2	1	no	—
621	C₂²×C₃	—	4	1	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	—	4	1	no	—
625	C₂²×C₃	—	4	1	no	—
626	C₂²×C₃	—	4	1	no	—
627	C₂²×C₃	—	8	1	no	—
628	C₂²×C₃	—	8	1	no	—
629	C₂²×C₃	—	8	1	no	—
630	C₂²×C₃	—	12	1	no	—
631	C₂²×C₃	—	12	1	no	—
632	C₂²×C₃	—	12	1	no	—
633	C₂²×C₃	—	12	1	no	—
634	C₂²×C₃	—	12	1	no	—
635	C₂²×C₃	—	12	1	no	—
636	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
637	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
638	C₂×D₃	—	4	1	no	—
639	C₂×D₃	—	4	1	no	—
640	C₂×D₃	—	4	1	no	—
641	C₂×D₃	—	4	1	no	—
642	C₂×D₃	—	4	1	no	—
643	C₂×D₃	—	4	1	no	—
644	C₃×C₄	—	2	1	no	—
645	C₃×C₄	—	2	1	no	—
646	C₃×C₄	—	2	1	no	—
647	C₃×C₄	—	2	1	no	—
648	C₃×C₄	—	2	1	no	—
649	C₃×C₄	—	2	1	no	—
650	C₃×C₄	—	3	2	no	—
651	C₃×C₄	—	4	1	no	—
652	C₃×C₄	—	4	1	no	—
653	C₃×C₄	—	4	2	no	—
654	C₃×C₄	—	4	1	no	—
655	C₃×C₄	—	4	1	no	—
656	C₃×C₄	—	4	1	no	—
657	C₃×C₄	—	4	1	no	—
658	C₃×C₄	—	4	1	no	—
659	C₃×C₄	—	4	1	no	—
660	C₃×C₄	—	6	1	no	—
661	C₃×C₄	—	6	1	no	—
662	C₃×C₄	—	6	1	no	—
663	C₃×C₄	—	8	1	no	—
664	C₃×C₄	—	8	1	no	—
665	C₃×C₄	—	12	1	no	—
666	C₃×C₄	—	12	1	no	—
667	C₃×C₄	#1004	1	1	yes	characteristic
668	C₃×C₄	D₃×#41	1	1	yes	characteristic
669	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
670	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
671	Dic₃	—	2	1	no	—
672	Dic₃	—	2	1	no	—
673	Dic₃	—	2	1	no	—
674	Dic₃	—	4	1	no	—
675	Dic₃	—	4	1	no	—
676	Dic₃	C₃×#135	1	2	yes	—
677	C₃²	#3394	1	1	yes	characteristic, complemented, Sylow
678	C₂³	—	2	1	no	—
679	C₂³	—	6	1	no	—
680	C₂³	—	6	1	no	—
681	Q₈	—	2	1	no	—
682	Q₈	—	2	1	no	—
683	Q₈	—	2	1	no	—
684	Q₈	—	2	1	no	—
685	Q₈	—	6	2	no	—
686	Q₈	—	6	1	no	—
687	Q₈	—	6	1	no	—
688	D₄	—	2	1	no	—
689	D₄	—	2	1	no	—
690	D₄	—	6	1	no	—
691	D₄	—	6	1	no	—
692	D₄	—	6	1	no	—
693	D₄	—	6	1	no	—
694	D₄	—	12	2	no	—
695	D₄	—	24	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	3	1	no	—
700	C₂×C₄	—	3	1	no	—
701	C₂×C₄	—	3	1	no	—
702	C₂×C₄	—	3	1	no	—
703	C₂×C₄	—	6	1	no	—
704	C₂×C₄	—	6	1	no	—
705	C₂×C₄	—	12	2	no	—
706	C₂×C₄	—	24	1	no	—
707	C₂×C₄	—	24	1	no	—
708	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
709	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
710	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
711	C₈	—	2	1	no	—
712	C₈	—	2	1	no	—
713	C₈	—	3	2	no	—
714	C₈	—	6	1	no	—
715	C₂×C₃	—	2	1	no	—
716	C₂×C₃	—	2	1	no	—
717	C₂×C₃	—	2	1	no	—
718	C₂×C₃	—	8	1	no	—
719	C₂×C₃	—	8	1	no	—
720	C₂×C₃	—	16	1	no	—
721	C₂×C₃	—	24	1	no	—
722	C₂×C₃	—	24	1	no	—
723	C₂×C₃	#5599	1	1	yes	characteristic
724	C₂×C₃	D₃×#135	1	1	yes	characteristic
725	C₂×C₃	#5778	1	1	yes	characteristic
726	C₂×C₃	C₃×#550	1	1	yes	characteristic
727	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
728	C₂×C₃	C₃×#577	1	1	yes	characteristic
729	D₃	—	8	1	no	—
730	D₃	—	8	1	no	—
731	C₂²	—	4	1	no	—
732	C₂²	—	4	1	no	—
733	C₂²	—	4	1	no	—
734	C₂²	—	12	1	no	—
735	C₂²	—	12	1	no	—
736	C₂²	—	12	1	no	—
737	C₂²	—	12	1	no	—
738	C₂²	—	12	1	no	—
739	C₂²	—	12	1	no	—
740	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
741	C₄	—	2	1	no	—
742	C₄	—	2	1	no	—
743	C₄	—	3	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	6	1	no	—
748	C₄	—	6	1	no	—
749	C₄	—	6	1	no	—
750	C₄	—	12	1	no	—
751	C₄	—	12	1	no	—
752	C₄	C₃×#1004	1	1	yes	characteristic
753	C₄	C₃×D₃×#41	1	1	yes	characteristic
754	C₃	—	2	1	no	—
755	C₃	#80589	1	1	yes	characteristic, direct product factor
756	C₃	C₃×#3394	1	1	yes	characteristic, complemented
757	C₂	—	8	1	no	—
758	C₂	—	24	1	no	—
759	C₂	—	24	1	no	—
760	C₂	C₃×#5599	1	1	yes	characteristic
761	C₂	C₃×D₃×#135	1	1	yes	characteristic
762	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×#464	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₃×#4786	C₂
hypercenter	C₃×#464	D₃
hypocenter	C₃	C₃×#3394
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×#5681	C₂	semidirect
2. C₃×#5568	C₂	semidirect
3. C₃²×#464	C₂	semidirect
4. C₃×#5191	C₂	semidirect
5. C₃×#5182	C₂	semidirect
6. C₃×#5175	C₂	semidirect
7. C₃×#5165	C₂	semidirect
8. C₃×#5059	C₂	semidirect
9. C₃×C₄×#215	C₂	semidirect
10. C₃×#4844	C₂	semidirect
11. C₃×#4830	C₂	semidirect
12. C₃×#4798	C₂	semidirect
13. C₃×#4788	C₂	semidirect
15. C₃×#4758	C₂	semidirect
17. #80589	C₃	direct (N × H)
63. #5681	C₂×C₃	semidirect
64. #5568	C₂×C₃	semidirect
70. C₃×#464	D₃	semidirect
71. C₃×#464	C₂×C₃	semidirect
80. #5191	C₂×C₃	semidirect
81. #5182	C₂×C₃	semidirect
82. #5175	C₂×C₃	semidirect
83. #5165	C₂×C₃	semidirect
84. #5059	C₂×C₃	semidirect
85. C₄×#215	C₂×C₃	semidirect
86. #4844	C₂×C₃	semidirect
87. #4830	C₂×C₃	semidirect
88. #4798	C₂×C₃	semidirect
89. #4788	C₂×C₃	semidirect
91. #4758	C₂×C₃	semidirect
281. #464	C₃×D₃	semidirect
677. C₃²	#3394	semidirect
755. C₃	#80589	direct (N × H)
756. C₃	C₃×#3394	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5681	2
C₃×#5568	2
C₃²×#464	2
C₃×#5191	2
C₃×#5182	2
C₃×#5175	2
C₃×#5165	2
C₃×#5059	2
C₃×C₄×#215	2
C₃×#4844	2
C₃×#4830	2
C₃×#4798	2
C₃×#4788	2
C₃×#4786	2
C₃×#4758	2
C₃×#3394	3
#80589	3

Subgroups — C3×#80589 #11898403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#80589 #11898403