Subgroups — C₃×#10595999 #13179282

Order 1728.

1708 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×#638	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64105	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64098	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#64094	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64093	C₂	1	1	yes	maximal, characteristic
10	C₃×#64092	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64088	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#64081	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
16	#10595999	C₃	1	1	yes	maximal, characteristic, direct product factor
17	C₃×#5528	—	3	4	no	maximal
18	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×#638	C₂²	1	1	yes	characteristic
20	C₂×C₃×#638	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
26	C₂×C₃×#634	C₂²	1	1	yes	characteristic
27	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃³×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃³×C₄²	C₂²	1	1	yes	characteristic
32	C₃³×C₄²	C₂²	1	1	yes	characteristic
33	C₃×#3757	C₂²	1	1	yes	characteristic
34	C₃×#3757	C₂²	1	1	yes	characteristic
35	C₃×#3752	C₂²	1	1	yes	characteristic
36	C₃×#3752	C₂²	1	1	yes	characteristic
37	C₃×#3752	C₂²	1	1	yes	characteristic
38	C₃×#3752	C₂²	1	1	yes	characteristic
39	C₃×#3752	C₂²	1	1	yes	characteristic
40	C₃×#3752	C₂²	1	1	yes	characteristic
41	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
42	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
43	C₃×#3750	C₂²	1	1	yes	characteristic
44	C₃×#3750	C₂²	1	1	yes	characteristic
45	C₃×#3750	C₂²	1	1	yes	characteristic
46	C₃×#3750	C₂²	1	1	yes	characteristic
47	C₃×#3750	C₂²	1	1	yes	characteristic
48	C₃×#3750	C₂²	1	1	yes	characteristic
49	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
50	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
51	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
52	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
53	C₃²×#117	—	2	4	no	—
54	C₃²×#117	D₃	1	4	yes	complemented
55	C₃²×#117	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
57	C₄×#638	C₂×C₃	1	1	yes	characteristic, complemented
58	#64107	C₂×C₃	1	1	yes	characteristic, complemented
59	#64105	C₂×C₃	1	1	yes	characteristic, complemented
60	#64103	C₂×C₃	1	1	yes	characteristic, complemented
61	#64098	C₂×C₃	1	1	yes	characteristic, complemented
62	#64094	C₂×C₃	1	1	yes	characteristic, complemented
63	#64093	C₂×C₃	1	1	yes	characteristic
64	#64092	C₂×C₃	1	1	yes	characteristic, complemented
65	#64088	C₂×C₃	1	1	yes	characteristic, complemented
66	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic, complemented
67	#64081	C₂×C₃	1	1	yes	characteristic, complemented
68	C₄²×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
69	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
70	C₃×C₄×#67	—	3	4	no	—
71	C₃×C₄×#67	—	3	4	no	—
72	C₃×#898	—	3	4	no	—
73	C₃×#896	—	3	4	no	—
74	C₃×#894	—	3	4	no	—
75	C₃×#889	—	3	4	no	—
76	C₃×#885	—	3	4	no	—
77	C₃×#884	—	3	4	no	—
78	C₃×#883	—	3	4	no	—
79	C₃×#879	—	3	4	no	—
80	C₃×C₄×D₁₂	—	3	4	no	—
81	C₃×#872	—	3	4	no	—
82	C₃×C₄²×D₃	—	3	4	no	—
83	C₃×C₄×Dic₆	—	3	4	no	—
84	C₂³×C₃³	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
87	C₂×C₃³×C₄	—	2	2	no	—
88	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
89	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
90	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
91	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
92	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
93	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
94	C₃×#638	—	2	2	no	—
95	C₃×#638	—	2	2	no	—
96	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₃⋊Dic₃	C₂³	1	1	yes	characteristic
102	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
103	C₃×C₄×C₃⋊D₃	—	2	2	no	—
104	C₃×C₄×C₃⋊D₃	—	2	2	no	—
105	C₃×C₄×C₃⋊D₃	—	2	2	no	—
106	C₃×C₄×C₃⋊D₃	—	2	2	no	—
107	C₃×#634	—	2	2	no	—
108	C₃×#529	—	9	1	no	—
109	#5528	—	3	4	no	—
110	C₂²×C₃²×C₄	—	2	4	no	—
111	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
112	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×#638	C₂²×C₃	1	1	yes	characteristic
114	C₂×#638	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
120	C₂×#634	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×#67	—	3	4	no	—
122	C₂×C₃×#67	—	3	4	no	—
123	C₂×C₃×D₁₂	—	3	4	no	—
124	C₂×C₃×C₄×D₃	—	3	4	no	—
125	C₂×C₃×C₄×D₃	—	3	4	no	—
126	C₂×C₃×C₄×D₃	—	3	4	no	—
127	C₂×C₃×C₄×D₃	—	3	4	no	—
128	C₂×C₃×Dic₆	—	3	4	no	—
129	C₃²×C₄⋊C₄	—	2	4	no	—
130	C₃²×C₄⋊C₄	—	2	4	no	—
131	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
132	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
133	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₃²×C₂²⋊C₄	—	2	4	no	—
136	C₃²×C₂²⋊C₄	—	2	4	no	—
137	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
138	C₃²×C₂²⋊C₄	C₂×D₃	1	4	yes	—
139	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₃²×C₄²	—	2	4	no	—
142	C₃²×C₄²	—	2	4	no	—
143	C₃²×C₄²	C₂×D₃	1	4	yes	—
144	C₃²×C₄²	C₂×D₃	1	4	yes	—
145	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
146	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
147	#3757	C₂²×C₃	1	1	yes	characteristic
148	#3757	C₂²×C₃	1	1	yes	characteristic
149	#3752	C₂²×C₃	1	1	yes	characteristic
150	#3752	C₂²×C₃	1	1	yes	characteristic
151	#3752	C₂²×C₃	1	1	yes	characteristic
152	#3752	C₂²×C₃	1	1	yes	characteristic
153	#3752	C₂²×C₃	1	1	yes	characteristic
154	#3752	C₂²×C₃	1	1	yes	characteristic
155	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
156	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
157	#3750	C₂²×C₃	1	1	yes	characteristic
158	#3750	C₂²×C₃	1	1	yes	characteristic
159	#3750	C₂²×C₃	1	1	yes	characteristic
160	#3750	C₂²×C₃	1	1	yes	characteristic
161	#3750	C₂²×C₃	1	1	yes	characteristic
162	#3750	C₂²×C₃	1	1	yes	characteristic
163	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
165	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
166	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
167	C₃×#217	—	3	4	no	—
168	C₃×#217	—	3	4	no	—
169	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
170	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
171	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
172	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
173	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
174	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
175	C₃×C₄⋊Dic₃	—	3	4	no	—
176	C₃×C₄⋊Dic₃	—	3	4	no	—
177	C₃×Dic₃⋊C₄	—	3	4	no	—
178	C₃×Dic₃⋊C₄	—	3	4	no	—
179	C₃×Dic₃⋊C₄	—	3	4	no	—
180	C₃×Dic₃⋊C₄	—	3	4	no	—
181	C₃×Dic₃⋊C₄	—	3	4	no	—
182	C₃×Dic₃⋊C₄	—	3	4	no	—
183	C₃×C₄×Dic₃	—	3	4	no	—
184	C₃×C₄×Dic₃	—	3	4	no	—
185	C₃×C₄×Dic₃	—	3	4	no	—
186	C₃×C₄×Dic₃	—	3	4	no	—
187	C₂²×C₃³	—	2	1	no	—
188	C₂²×C₃³	—	2	1	no	—
189	C₂²×C₃³	—	2	1	no	—
190	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
191	C₂×C₃×C₃⋊D₃	—	2	1	no	—
192	C₂×C₃×C₃⋊D₃	—	2	1	no	—
193	C₂×C₃×C₃⋊D₃	—	2	1	no	—
194	C₂×C₃×C₃⋊D₃	—	2	1	no	—
195	C₂×C₃×C₃⋊D₃	—	2	1	no	—
196	C₂×C₃×C₃⋊D₃	#41	1	2	yes	—
197	C₃³×C₄	—	2	1	no	—
198	C₃³×C₄	—	2	1	no	—
199	C₃³×C₄	—	2	1	no	—
200	C₃³×C₄	—	2	1	no	—
201	C₃³×C₄	—	2	1	no	—
202	C₃³×C₄	#41	1	2	yes	—
203	C₃×C₃⋊Dic₃	—	2	1	no	—
204	C₃×C₃⋊Dic₃	—	2	1	no	—
205	C₃×C₃⋊Dic₃	—	2	1	no	—
206	C₃×C₃⋊Dic₃	—	2	1	no	—
207	C₃×C₃⋊Dic₃	—	2	1	no	—
208	C₃×C₃⋊Dic₃	#41	1	2	yes	—
209	C₃×#126	—	9	1	no	—
210	C₃×#126	—	9	1	no	—
211	C₃×#125	—	9	1	no	—
212	C₃×#124	—	9	1	no	—
213	C₃×#123	—	9	1	no	—
214	C₃×#123	—	9	1	no	—
215	C₃×C₂²⋊Q₈	—	9	1	no	—
216	C₃×#121	—	9	1	no	—
217	C₃×C₄×Q₈	—	9	1	no	—
218	C₃×C₄×D₄	—	9	1	no	—
219	C₃×C₄×D₄	—	9	1	no	—
220	C₃×C₄×D₄	—	9	1	no	—
221	C₃×#117	—	2	4	no	—
222	C₃×#117	—	9	1	no	—
223	C₃×#117	C₃×D₃	1	4	yes	complemented
224	C₃×#117	C₃⋊D₃	1	1	yes	characteristic, complemented
225	C₂×C₃×C₄²	—	9	1	no	—
226	C₄×#67	—	3	4	no	—
227	C₄×#67	—	3	4	no	—
228	#898	—	3	4	no	—
229	#896	—	3	4	no	—
230	#894	—	3	4	no	—
231	#889	—	3	4	no	—
232	#885	—	3	4	no	—
233	#884	—	3	4	no	—
234	#883	—	3	4	no	—
235	#879	—	3	4	no	—
236	C₄×D₁₂	—	3	4	no	—
237	#872	—	3	4	no	—
238	C₄²×D₃	—	3	4	no	—
239	C₄×Dic₆	—	3	4	no	—
240	C₂³×C₃²	—	2	4	no	—
241	C₂³×C₃²	C₂²×D₃	1	4	yes	—
242	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
244	C₂²×C₃⋊D₃	C₂³×C₃	1	1	yes	characteristic
245	C₂²×C₃×D₃	—	3	4	no	—
246	C₂²×C₃×D₃	—	3	4	no	—
247	C₂×C₃²×C₄	—	2	16	no	—
248	C₂×C₃²×C₄	—	2	8	no	—
249	C₂×C₃²×C₄	—	2	2	no	—
250	C₂×C₃²×C₄	—	2	4	no	—
251	C₂×C₃²×C₄	—	2	4	no	—
252	C₂×C₃²×C₄	—	2	4	no	—
253	C₂×C₃²×C₄	—	2	4	no	—
254	C₂×C₃²×C₄	—	2	4	no	—
255	C₂×C₃²×C₄	—	2	4	no	—
256	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
257	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
258	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
259	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
260	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
261	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
262	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
267	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
268	#638	—	2	2	no	—
269	#638	—	2	2	no	—
270	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
271	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
272	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
273	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₃⋊Dic₃	C₂³×C₃	1	1	yes	characteristic
276	C₄⋊(C₃⋊D₃)	—	2	2	no	—
277	C₄×C₃⋊D₃	—	2	2	no	—
278	C₄×C₃⋊D₃	—	2	2	no	—
279	C₄×C₃⋊D₃	—	2	2	no	—
280	C₄×C₃⋊D₃	—	2	2	no	—
281	#634	—	2	2	no	—
282	C₃×#67	—	6	8	no	—
283	C₃×#67	—	6	8	no	—
284	C₂×C₃×Dic₃	—	3	4	no	—
285	C₂×C₃×Dic₃	—	3	4	no	—
286	C₂×C₃×Dic₃	—	3	4	no	—
287	C₂×C₃×Dic₃	—	3	4	no	—
288	C₂×C₃×Dic₃	—	3	4	no	—
289	C₂×C₃×Dic₃	—	3	4	no	—
290	C₃×D₁₂	—	6	8	no	—
291	C₃×C₄×D₃	—	6	8	no	—
292	C₃×C₄×D₃	—	6	8	no	—
293	C₃×C₄×D₃	—	6	8	no	—
294	C₃×C₄×D₃	—	6	8	no	—
295	C₃×Dic₆	—	6	8	no	—
296	#529	—	9	1	no	Sylow
297	C₂×C₃³	—	4	1	no	—
298	C₂×C₃³	C₂×#41	1	1	yes	characteristic
299	C₂×C₃³	C₂×#41	1	1	yes	characteristic
300	C₂×C₃³	C₂×#41	1	1	yes	characteristic
301	C₃×C₃⋊D₃	—	2	2	no	—
302	C₃×C₃⋊D₃	—	4	1	no	—
303	C₂×C₃×Q₈	—	9	1	no	—
304	C₂×C₃×D₄	—	9	1	no	—
305	C₂×C₃×D₄	—	9	1	no	—
306	C₂×C₃×D₄	—	9	1	no	—
307	C₂²×C₃×C₄	—	2	4	no	—
308	C₂²×C₃×C₄	—	9	1	no	—
309	C₂²×C₃×C₄	—	9	1	no	—
310	C₂²×C₃×C₄	—	9	1	no	—
311	C₂²×C₃×C₄	—	9	1	no	—
312	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
313	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
314	C₂×#67	—	3	4	no	—
315	C₂×#67	—	3	4	no	—
316	C₂×D₁₂	—	3	4	no	—
317	C₂×C₄×D₃	—	3	4	no	—
318	C₂×C₄×D₃	—	3	4	no	—
319	C₂×C₄×D₃	—	3	4	no	—
320	C₂×C₄×D₃	—	3	4	no	—
321	C₂×Dic₆	—	3	4	no	—
322	C₃×C₄⋊C₄	—	2	4	no	—
323	C₃×C₄⋊C₄	—	2	4	no	—
324	C₃×C₄⋊C₄	—	9	1	no	—
325	C₃×C₄⋊C₄	—	9	1	no	—
326	C₃×C₄⋊C₄	—	9	1	no	—
327	C₃×C₄⋊C₄	—	9	1	no	—
328	C₃×C₄⋊C₄	—	9	1	no	—
329	C₃×C₄⋊C₄	—	9	1	no	—
330	C₃×C₄⋊C₄	—	9	1	no	—
331	C₃×C₄⋊C₄	—	9	1	no	—
332	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
333	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
334	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
335	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
336	C₃×C₂²⋊C₄	—	2	4	no	—
337	C₃×C₂²⋊C₄	—	2	4	no	—
338	C₃×C₂²⋊C₄	—	9	1	no	—
339	C₃×C₂²⋊C₄	—	9	1	no	—
340	C₃×C₂²⋊C₄	—	9	1	no	—
341	C₃×C₂²⋊C₄	—	9	1	no	—
342	C₃×C₂²⋊C₄	—	9	1	no	—
343	C₃×C₂²⋊C₄	—	9	1	no	—
344	C₃×C₂²⋊C₄	—	9	1	no	—
345	C₃×C₂²⋊C₄	—	9	1	no	—
346	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
347	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
348	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
349	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
350	C₃×C₄²	—	2	4	no	—
351	C₃×C₄²	—	2	4	no	—
352	C₃×C₄²	—	9	1	no	—
353	C₃×C₄²	—	9	1	no	—
354	C₃×C₄²	—	9	1	no	—
355	C₃×C₄²	—	9	1	no	—
356	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
357	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
358	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
359	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
360	#217	—	3	4	no	—
361	#217	—	3	4	no	—
362	(C₂×D₃)⋊C₄	—	3	4	no	—
363	(C₂×D₃)⋊C₄	—	3	4	no	—
364	(C₂×D₃)⋊C₄	—	3	4	no	—
365	(C₂×D₃)⋊C₄	—	3	4	no	—
366	(C₂×D₃)⋊C₄	—	3	4	no	—
367	(C₂×D₃)⋊C₄	—	3	4	no	—
368	C₄⋊Dic₃	—	3	4	no	—
369	C₄⋊Dic₃	—	3	4	no	—
370	Dic₃⋊C₄	—	3	4	no	—
371	Dic₃⋊C₄	—	3	4	no	—
372	Dic₃⋊C₄	—	3	4	no	—
373	Dic₃⋊C₄	—	3	4	no	—
374	Dic₃⋊C₄	—	3	4	no	—
375	Dic₃⋊C₄	—	3	4	no	—
376	C₄×Dic₃	—	3	4	no	—
377	C₄×Dic₃	—	3	4	no	—
378	C₄×Dic₃	—	3	4	no	—
379	C₄×Dic₃	—	3	4	no	—
380	C₂²×C₃²	—	2	8	no	—
381	C₂²×C₃²	—	2	4	no	—
382	C₂²×C₃²	—	2	1	no	—
383	C₂²×C₃²	—	2	1	no	—
384	C₂²×C₃²	—	2	1	no	—
385	C₂²×C₃²	—	2	4	no	—
386	C₂²×C₃²	—	2	4	no	—
387	C₂²×C₃²	—	2	4	no	—
388	C₂²×C₃²	—	4	4	no	—
389	C₂²×C₃²	—	4	4	no	—
390	C₂²×C₃²	C₂³×D₃	1	4	yes	—
391	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
392	C₂×C₃⋊D₃	—	2	1	no	—
393	C₂×C₃⋊D₃	—	2	1	no	—
394	C₂×C₃⋊D₃	—	2	1	no	—
395	C₂×C₃⋊D₃	—	2	1	no	—
396	C₂×C₃⋊D₃	—	2	1	no	—
397	C₂×C₃⋊D₃	C₃×#41	1	2	yes	—
398	C₂×C₃×D₃	—	3	8	no	—
399	C₂×C₃×D₃	—	6	4	no	—
400	C₂×C₃×D₃	—	6	4	no	—
401	C₂×C₃×D₃	—	6	4	no	—
402	C₂×C₃×D₃	—	6	4	no	—
403	C₂×C₃×D₃	—	6	4	no	—
404	C₃²×C₄	—	2	8	no	—
405	C₃²×C₄	—	2	4	no	—
406	C₃²×C₄	—	2	1	no	—
407	C₃²×C₄	—	2	1	no	—
408	C₃²×C₄	—	2	1	no	—
409	C₃²×C₄	—	2	1	no	—
410	C₃²×C₄	—	2	1	no	—
411	C₃²×C₄	—	2	8	no	—
412	C₃²×C₄	—	2	4	no	—
413	C₃²×C₄	—	2	4	no	—
414	C₃²×C₄	—	2	4	no	—
415	C₃²×C₄	—	2	4	no	—
416	C₃²×C₄	—	4	4	no	—
417	C₃²×C₄	—	4	4	no	—
418	C₃²×C₄	—	4	4	no	—
419	C₃²×C₄	—	4	4	no	—
420	C₃²×C₄	#235	1	8	yes	—
421	C₃²×C₄	C₃×#41	1	2	yes	—
422	C₃⋊Dic₃	—	2	1	no	—
423	C₃⋊Dic₃	—	2	1	no	—
424	C₃⋊Dic₃	—	2	1	no	—
425	C₃⋊Dic₃	—	2	1	no	—
426	C₃⋊Dic₃	—	2	1	no	—
427	C₃⋊Dic₃	C₃×#41	1	2	yes	—
428	C₃×Dic₃	—	3	8	no	—
429	C₃×Dic₃	—	6	4	no	—
430	C₃×Dic₃	—	6	4	no	—
431	C₃×Dic₃	—	6	4	no	—
432	C₃×Dic₃	—	6	4	no	—
433	C₃×Dic₃	—	6	4	no	—
434	#126	—	9	1	no	—
435	#126	—	9	1	no	—
436	#125	—	9	1	no	—
437	#124	—	9	1	no	—
438	#123	—	9	1	no	—
439	#123	—	9	1	no	—
440	C₂²⋊Q₈	—	9	1	no	—
441	#121	—	9	1	no	—
442	C₄×Q₈	—	9	1	no	—
443	C₄×D₄	—	9	1	no	—
444	C₄×D₄	—	9	1	no	—
445	C₄×D₄	—	9	1	no	—
446	#117	—	9	1	no	—
447	#117	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
448	C₂×C₄²	—	9	1	no	—
449	C₃³	#529	1	1	yes	characteristic, complemented, Sylow
450	C₂³×C₃	—	2	4	no	—
451	C₂³×C₃	—	9	1	no	—
452	C₂³×C₃	—	9	1	no	—
453	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
454	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
455	C₂²×D₃	—	3	4	no	—
456	C₂²×D₃	—	3	4	no	—
457	C₃×Q₈	—	18	2	no	—
458	C₃×D₄	—	18	2	no	—
459	C₃×D₄	—	18	2	no	—
460	C₃×D₄	—	18	2	no	—
461	C₂×C₃×C₄	—	2	16	no	—
462	C₂×C₃×C₄	—	2	8	no	—
463	C₂×C₃×C₄	—	2	2	no	—
464	C₂×C₃×C₄	—	2	4	no	—
465	C₂×C₃×C₄	—	2	4	no	—
466	C₂×C₃×C₄	—	2	4	no	—
467	C₂×C₃×C₄	—	2	4	no	—
468	C₂×C₃×C₄	—	2	4	no	—
469	C₂×C₃×C₄	—	2	4	no	—
470	C₂×C₃×C₄	—	9	1	no	—
471	C₂×C₃×C₄	—	9	1	no	—
472	C₂×C₃×C₄	—	9	1	no	—
473	C₂×C₃×C₄	—	9	1	no	—
474	C₂×C₃×C₄	—	9	1	no	—
475	C₂×C₃×C₄	—	9	1	no	—
476	C₂×C₃×C₄	—	18	2	no	—
477	C₂×C₃×C₄	—	18	2	no	—
478	C₂×C₃×C₄	—	18	2	no	—
479	C₂×C₃×C₄	—	18	2	no	—
480	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
481	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
482	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
483	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
484	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
485	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
486	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
487	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
488	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
489	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
491	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
492	#67	—	6	8	no	—
493	#67	—	6	8	no	—
494	C₂×Dic₃	—	3	4	no	—
495	C₂×Dic₃	—	3	4	no	—
496	C₂×Dic₃	—	3	4	no	—
497	C₂×Dic₃	—	3	4	no	—
498	C₂×Dic₃	—	3	4	no	—
499	C₂×Dic₃	—	3	4	no	—
500	D₁₂	—	6	8	no	—
501	C₄×D₃	—	6	8	no	—
502	C₄×D₃	—	6	8	no	—
503	C₄×D₃	—	6	8	no	—
504	C₄×D₃	—	6	8	no	—
505	Dic₆	—	6	8	no	—
506	C₂×C₃²	—	2	4	no	—
507	C₂×C₃²	—	2	4	no	—
508	C₂×C₃²	—	2	4	no	—
509	C₂×C₃²	—	4	8	no	—
510	C₂×C₃²	—	4	4	no	—
511	C₂×C₃²	—	4	1	no	—
512	C₂×C₃²	C₂×#235	1	4	yes	—
513	C₂×C₃²	D₃×#41	1	4	yes	—
514	C₂×C₃²	D₃×#41	1	4	yes	—
515	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
516	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
517	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
518	C₃⋊D₃	—	2	2	no	—
519	C₃⋊D₃	—	4	1	no	—
520	C₃×D₃	—	6	8	no	—
521	C₃×D₃	—	12	4	no	—
522	C₂×Q₈	—	9	1	no	—
523	C₂×D₄	—	9	1	no	—
524	C₂×D₄	—	9	1	no	—
525	C₂×D₄	—	9	1	no	—
526	C₂²×C₄	—	9	1	no	—
527	C₂²×C₄	—	9	1	no	—
528	C₂²×C₄	—	9	1	no	—
529	C₂²×C₄	—	9	1	no	—
530	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
531	C₄⋊C₄	—	9	1	no	—
532	C₄⋊C₄	—	9	1	no	—
533	C₄⋊C₄	—	9	1	no	—
534	C₄⋊C₄	—	9	1	no	—
535	C₄⋊C₄	—	9	1	no	—
536	C₄⋊C₄	—	9	1	no	—
537	C₄⋊C₄	—	9	1	no	—
538	C₄⋊C₄	—	9	1	no	—
539	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
541	C₂²⋊C₄	—	9	1	no	—
542	C₂²⋊C₄	—	9	1	no	—
543	C₂²⋊C₄	—	9	1	no	—
544	C₂²⋊C₄	—	9	1	no	—
545	C₂²⋊C₄	—	9	1	no	—
546	C₂²⋊C₄	—	9	1	no	—
547	C₂²⋊C₄	—	9	1	no	—
548	C₂²⋊C₄	—	9	1	no	—
549	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
550	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
551	C₄²	—	9	1	no	—
552	C₄²	—	9	1	no	—
553	C₄²	—	9	1	no	—
554	C₄²	—	9	1	no	—
555	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
556	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
557	C₂²×C₃	—	2	8	no	—
558	C₂²×C₃	—	2	4	no	—
559	C₂²×C₃	—	2	4	no	—
560	C₂²×C₃	—	2	4	no	—
561	C₂²×C₃	—	2	1	no	—
562	C₂²×C₃	—	2	1	no	—
563	C₂²×C₃	—	2	1	no	—
564	C₂²×C₃	—	2	4	no	—
565	C₂²×C₃	—	4	4	no	—
566	C₂²×C₃	—	4	4	no	—
567	C₂²×C₃	—	9	2	no	—
568	C₂²×C₃	—	18	1	no	—
569	C₂²×C₃	—	18	1	no	—
570	C₂²×C₃	—	18	1	no	—
571	C₂²×C₃	—	18	1	no	—
572	C₂²×C₃	—	18	1	no	—
573	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
574	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
575	C₂×D₃	—	3	8	no	—
576	C₂×D₃	—	6	4	no	—
577	C₂×D₃	—	6	4	no	—
578	C₂×D₃	—	6	4	no	—
579	C₂×D₃	—	6	4	no	—
580	C₂×D₃	—	6	4	no	—
581	C₃×C₄	—	2	8	no	—
582	C₃×C₄	—	2	4	no	—
583	C₃×C₄	—	2	4	no	—
584	C₃×C₄	—	2	4	no	—
585	C₃×C₄	—	2	4	no	—
586	C₃×C₄	—	2	4	no	—
587	C₃×C₄	—	2	1	no	—
588	C₃×C₄	—	2	1	no	—
589	C₃×C₄	—	2	1	no	—
590	C₃×C₄	—	2	1	no	—
591	C₃×C₄	—	2	1	no	—
592	C₃×C₄	—	2	8	no	—
593	C₃×C₄	—	4	4	no	—
594	C₃×C₄	—	4	4	no	—
595	C₃×C₄	—	4	4	no	—
596	C₃×C₄	—	4	4	no	—
597	C₃×C₄	—	9	2	no	—
598	C₃×C₄	—	18	1	no	—
599	C₃×C₄	—	18	1	no	—
600	C₃×C₄	—	18	1	no	—
601	C₃×C₄	—	18	1	no	—
602	C₃×C₄	—	18	1	no	—
603	C₃×C₄	C₃×#235	1	8	yes	—
604	C₃×C₄	#3828	1	2	yes	—
605	Dic₃	—	3	8	no	—
606	Dic₃	—	6	4	no	—
607	Dic₃	—	6	4	no	—
608	Dic₃	—	6	4	no	—
609	Dic₃	—	6	4	no	—
610	Dic₃	—	6	4	no	—
611	C₃²	—	2	4	no	—
612	C₃²	#5528	1	4	yes	complemented
613	C₃²	C₃×#529	1	1	yes	characteristic, complemented
614	C₂³	—	9	1	no	—
615	C₂³	—	9	1	no	—
616	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
617	Q₈	—	18	2	no	—
618	D₄	—	18	2	no	—
619	D₄	—	18	2	no	—
620	D₄	—	18	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	9	1	no	—
623	C₂×C₄	—	9	1	no	—
624	C₂×C₄	—	9	1	no	—
625	C₂×C₄	—	9	1	no	—
626	C₂×C₄	—	9	1	no	—
627	C₂×C₄	—	9	1	no	—
628	C₂×C₄	—	18	2	no	—
629	C₂×C₄	—	18	2	no	—
630	C₂×C₄	—	18	2	no	—
631	C₂×C₄	—	18	2	no	—
632	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
633	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
634	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
635	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
636	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
637	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
638	C₂×C₃	—	2	4	no	—
639	C₂×C₃	—	2	4	no	—
640	C₂×C₃	—	2	4	no	—
641	C₂×C₃	—	4	8	no	—
642	C₂×C₃	—	4	4	no	—
643	C₂×C₃	—	4	1	no	—
644	C₂×C₃	—	18	2	no	—
645	C₂×C₃	—	36	1	no	—
646	C₂×C₃	C₂×C₃×#235	1	4	yes	—
647	C₂×C₃	C₃×D₃×#41	1	4	yes	—
648	C₂×C₃	C₃×D₃×#41	1	4	yes	—
649	C₂×C₃	C₂×#3828	1	1	yes	characteristic
650	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
651	C₂×C₃	#41×C₃⋊D₃	1	1	yes	characteristic
652	D₃	—	6	8	no	—
653	D₃	—	12	4	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	9	2	no	—
658	C₂²	—	18	1	no	—
659	C₂²	—	18	1	no	—
660	C₂²	—	18	1	no	—
661	C₂²	—	18	1	no	—
662	C₂²	—	18	1	no	—
663	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	9	2	no	—
670	C₄	—	18	1	no	—
671	C₄	—	18	1	no	—
672	C₄	—	18	1	no	—
673	C₄	—	18	1	no	—
674	C₄	—	18	1	no	—
675	C₄	C₃×#3828	1	2	yes	—
676	C₃	—	2	4	no	—
677	C₃	C₃×#5528	1	4	yes	complemented
678	C₃	#10595999	1	1	yes	characteristic, direct product factor
679	C₂	—	4	1	no	—
680	C₂	—	18	2	no	—
681	C₂	—	36	1	no	—
682	C₂	C₂×C₃×#3828	1	1	yes	characteristic
683	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic
684	C₂	C₃×#41×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×#117	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₃×#64093	C₂
hypercenter	C₃×#117	C₃⋊D₃
hypocenter	C₃²	C₃×#529
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
1. C₃³×#117	C₂	semidirect
2. C₃×C₄×#638	C₂	semidirect
3. C₃×C₄×#638	C₂	semidirect
4. C₃×#64107	C₂	semidirect
5. C₃×#64105	C₂	semidirect
6. C₃×#64103	C₂	semidirect
7. C₃×#64098	C₂	semidirect
8. C₃×#64094	C₂	semidirect
10. C₃×#64092	C₂	semidirect
11. C₃×#64088	C₂	semidirect
12. C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	semidirect
13. C₃×#64081	C₂	semidirect
14. C₃×C₄²×C₃⋊D₃	C₂	semidirect
15. C₃×C₄×#634	C₂	semidirect
16. #10595999	C₃	direct (N × H)
54. C₃²×#117	D₃	semidirect
55. C₃²×#117	C₂×C₃	semidirect
56. C₄×#638	C₂×C₃	semidirect
57. C₄×#638	C₂×C₃	semidirect
58. #64107	C₂×C₃	semidirect
59. #64105	C₂×C₃	semidirect
60. #64103	C₂×C₃	semidirect
61. #64098	C₂×C₃	semidirect
62. #64094	C₂×C₃	semidirect
64. #64092	C₂×C₃	semidirect
65. #64088	C₂×C₃	semidirect
66. C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
67. #64081	C₂×C₃	semidirect
68. C₄²×C₃⋊D₃	C₂×C₃	semidirect
69. C₄×#634	C₂×C₃	semidirect
223. C₃×#117	C₃×D₃	semidirect
224. C₃×#117	C₃⋊D₃	semidirect
447. #117	C₃×C₃⋊D₃	semidirect
449. C₃³	#529	semidirect
612. C₃²	#5528	semidirect
613. C₃²	C₃×#529	semidirect
677. C₃	C₃×#5528	semidirect
678. C₃	#10595999	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×#117	2
C₃×C₄×#638	2
C₃×#64107	2
C₃×#64105	2
C₃×#64103	2
C₃×#64098	2
C₃×#64094	2
C₃×#64093	2
C₃×#64092	2
C₃×#64088	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64081	2
C₃×C₄²×C₃⋊D₃	2
C₃×C₄×#634	2
#10595999	3
C₃×#5528	3

Subgroups — C3×#10595999 #13179282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10595999 #13179282