Subgroups — C₃×#10596303 #13179582

Order 1728.

2516 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#64156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#64153	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64149	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#64148	C₂	1	4	yes	maximal, complemented
7	C₃×#64145	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#638	C₂	1	4	yes	maximal, complemented
9	C₂×C₃×C₄×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#10596303	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₃×#5832	—	3	4	no	maximal
12	C₃³×#41	—	2	4	no	—
13	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃³×D₄	C₂²	1	2	yes	—
16	C₂²×C₃³×C₄	C₂²	1	2	yes	—
17	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×#638	C₂²	1	4	yes	—
19	C₂×C₃×#638	C₂²	1	2	yes	—
20	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
21	C₃×#3828	—	2	4	no	—
22	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
24	C₂×C₃×#634	C₂²	1	1	yes	characteristic
25	C₃×#3757	C₂²	1	4	yes	—
26	C₃×#3752	C₂²	1	4	yes	—
27	C₃×#3750	C₂²	1	4	yes	—
28	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
29	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₃²×#41	—	2	4	no	—
32	C₂×C₃²×#41	D₃	1	4	yes	complemented
33	C₂×C₃²×#41	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#3828	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₃×#235	—	3	4	no	—
36	#64156	C₂×C₃	1	1	yes	characteristic, complemented
37	#64153	C₂×C₃	1	1	yes	characteristic, complemented
38	#64149	C₂×C₃	1	1	yes	characteristic, complemented
39	#64148	C₂×C₃	1	4	yes	complemented
40	#64145	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×#638	C₂×C₃	1	4	yes	complemented
42	C₂×C₄×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×#947	—	3	4	no	—
44	C₃×#944	—	3	4	no	—
45	C₃×#940	—	3	4	no	—
46	C₃×#939	—	3	16	no	—
47	C₃×#936	—	3	4	no	—
48	C₃×C₄×#67	—	3	16	no	—
49	C₂×C₃×C₄×Dic₃	—	3	4	no	—
50	C₂³×C₃³	C₂³	1	2	yes	—
51	C₂³×C₃³	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
53	C₃³×Q₈	—	2	2	no	—
54	C₃³×D₄	—	2	4	no	—
55	C₃³×D₄	—	2	2	no	—
56	C₂×C₃³×C₄	—	2	4	no	—
57	C₂×C₃³×C₄	D₄	1	4	yes	complemented
58	C₂×C₃³×C₄	C₂³	1	2	yes	—
59	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
60	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
61	C₃×#638	—	2	4	no	—
62	C₃×#638	—	2	8	no	—
63	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
64	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
65	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
66	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
67	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
68	C₃×C₄×C₃⋊D₃	—	2	4	no	—
69	C₃×#634	—	2	2	no	—
70	C₃×#532	—	9	1	no	—
71	#5832	—	3	4	no	—
72	C₃²×#41	—	2	32	no	—
73	C₃²×#41	—	2	16	no	—
74	C₃²×#41	—	2	4	no	—
75	C₂×C₃²×Q₈	—	2	4	no	—
76	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
77	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₃²×D₄	—	2	4	no	—
79	C₂×C₃²×D₄	—	2	8	no	—
80	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
81	C₂×C₃²×D₄	C₂×D₃	1	8	yes	—
82	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
84	C₂²×C₃²×C₄	—	2	8	no	—
85	C₂²×C₃²×C₄	—	2	4	no	—
86	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
87	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
88	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
89	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×#638	C₂²×C₃	1	2	yes	—
91	C₂×#638	C₂²×C₃	1	4	yes	—
92	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
93	#3828	—	2	4	no	—
94	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
96	C₂×#634	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₃×#67	—	3	16	no	—
98	C₂×C₃×#67	—	3	8	no	—
99	C₂²×C₃×Dic₃	—	3	8	no	—
100	C₃×#235	—	6	16	no	—
101	C₂×C₃×D₁₂	—	3	4	no	—
102	C₂×C₃×C₄×D₃	—	3	8	no	—
103	C₂×C₃×Dic₆	—	3	4	no	—
104	#3757	C₂²×C₃	1	4	yes	—
105	#3752	C₂²×C₃	1	4	yes	—
106	#3750	C₂²×C₃	1	4	yes	—
107	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
108	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
109	C₄×C₃⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
110	C₃×#217	—	3	16	no	—
111	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
112	C₃×Dic₃⋊C₄	—	3	16	no	—
113	C₃×C₄×Dic₃	—	3	8	no	—
114	C₃×C₄×Dic₃	—	3	4	no	—
115	C₃×C₄×Dic₃	—	3	4	no	—
116	C₂²×C₃³	—	2	2	no	—
117	C₂²×C₃³	—	2	2	no	—
118	C₂²×C₃³	—	2	4	no	—
119	C₂²×C₃³	C₂×D₄	1	2	yes	—
120	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
121	C₂×C₃×C₃⋊D₃	—	2	2	no	—
122	C₂×C₃×C₃⋊D₃	—	2	4	no	—
123	C₃³×C₄	—	2	2	no	—
124	C₃³×C₄	C₂×D₄	1	2	yes	—
125	C₃³×C₄	C₂×D₄	1	2	yes	—
126	C₃×C₃⋊Dic₃	—	2	2	no	—
127	C₃×C₃⋊Dic₃	—	2	2	no	—
128	C₃×C₃⋊Dic₃	#41	1	4	yes	complemented
129	C₂×C₃×#41	—	2	4	no	—
130	C₂×C₃×#41	—	9	1	no	—
131	C₂×C₃×#41	C₃×D₃	1	4	yes	complemented
132	C₂×C₃×#41	C₃⋊D₃	1	1	yes	characteristic, complemented
133	C₂×#235	—	3	4	no	—
134	C₃×C₄⋊Q₈	—	9	1	no	—
135	C₃×#127	—	9	1	no	—
136	C₃×#124	—	9	1	no	—
137	C₃×#124	—	9	1	no	—
138	C₃×#121	—	9	4	no	—
139	C₃×C₄×D₄	—	9	4	no	—
140	C₂×C₃×C₄²	—	9	1	no	—
141	#947	—	3	4	no	—
142	#944	—	3	4	no	—
143	#940	—	3	4	no	—
144	#939	—	3	16	no	—
145	#936	—	3	4	no	—
146	C₄×#67	—	3	16	no	—
147	C₂×C₄×Dic₃	—	3	4	no	—
148	C₂³×C₃²	—	2	8	no	—
149	C₂³×C₃²	—	2	4	no	—
150	C₂³×C₃²	C₂²×D₃	1	8	yes	—
151	C₂³×C₃²	C₂²×D₃	1	4	yes	—
152	C₂³×C₃²	C₂³×C₃	1	2	yes	—
153	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
154	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
155	C₂²×C₃×D₃	—	3	8	no	—
156	C₃²×Q₈	—	2	16	no	—
157	C₃²×Q₈	—	2	8	no	—
158	C₃²×Q₈	—	2	2	no	—
159	C₃²×D₄	—	2	32	no	—
160	C₃²×D₄	—	2	16	no	—
161	C₃²×D₄	—	2	16	no	—
162	C₃²×D₄	—	2	4	no	—
163	C₃²×D₄	—	2	8	no	—
164	C₃²×D₄	—	2	2	no	—
165	C₂×C₃²×C₄	—	2	32	no	—
166	C₂×C₃²×C₄	—	2	16	no	—
167	C₂×C₃²×C₄	—	2	4	no	—
168	C₂×C₃²×C₄	—	2	16	no	—
169	C₂×C₃²×C₄	—	2	4	no	—
170	C₂×C₃²×C₄	—	2	8	no	—
171	C₂×C₃²×C₄	—	2	4	no	—
172	C₂×C₃²×C₄	#67	1	16	yes	complemented
173	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
174	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
175	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
176	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
177	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
178	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
180	#638	—	2	4	no	—
181	#638	—	2	8	no	—
182	C₂×C₃⋊Dic₃	—	2	4	no	—
183	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
184	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
185	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
186	C₄⋊(C₃⋊D₃)	—	2	2	no	—
187	C₄×C₃⋊D₃	—	2	4	no	—
188	#634	—	2	2	no	—
189	C₃×#67	—	6	32	no	—
190	C₃×#67	—	6	16	no	—
191	C₂×C₃×Dic₃	—	3	8	no	—
192	C₂×C₃×Dic₃	—	3	8	no	—
193	C₂×C₃×Dic₃	—	3	8	no	—
194	C₂×C₃×Dic₃	—	6	16	no	—
195	C₃×D₁₂	—	6	8	no	—
196	C₃×C₄×D₃	—	6	16	no	—
197	C₃×Dic₆	—	6	8	no	—
198	#532	—	9	1	no	Sylow
199	C₂×C₃³	—	2	2	no	—
200	C₂×C₃³	—	4	2	no	—
201	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₃³	C₂×#41	1	2	yes	—
203	C₃×C₃⋊D₃	—	4	2	no	—
204	C₃×#41	—	2	32	no	—
205	C₃×#41	—	2	16	no	—
206	C₃×#41	—	2	4	no	—
207	C₃×#41	—	18	4	no	—
208	C₂×C₃×Q₈	—	2	4	no	—
209	C₂×C₃×Q₈	—	9	1	no	—
210	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
211	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
212	C₂×C₃×D₄	—	2	8	no	—
213	C₂×C₃×D₄	—	2	4	no	—
214	C₂×C₃×D₄	—	9	4	no	—
215	C₂×C₃×D₄	—	9	2	no	—
216	C₂×C₃×D₄	—	9	1	no	—
217	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
218	C₂×C₃×D₄	C₂×C₃×D₃	1	8	yes	—
219	C₂×C₃×D₄	C₂×C₃⋊D₃	1	2	yes	—
220	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
221	C₂²×C₃×C₄	—	2	8	no	—
222	C₂²×C₃×C₄	—	2	4	no	—
223	C₂²×C₃×C₄	—	9	2	no	—
224	C₂²×C₃×C₄	—	9	2	no	—
225	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
226	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
227	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
228	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
229	C₂×#67	—	3	16	no	—
230	C₂×#67	—	3	8	no	—
231	C₂²×Dic₃	—	3	8	no	—
232	#235	—	6	16	no	—
233	C₂×D₁₂	—	3	4	no	—
234	C₂×C₄×D₃	—	3	8	no	—
235	C₂×Dic₆	—	3	4	no	—
236	C₃×C₄⋊C₄	—	9	4	no	—
237	C₃×C₂²⋊C₄	—	9	4	no	—
238	C₃×C₂²⋊C₄	—	9	4	no	—
239	C₃×C₄²	—	9	1	no	—
240	C₃×C₄²	—	9	1	no	—
241	C₃×C₄²	—	9	2	no	—
242	#217	—	3	16	no	—
243	(C₂×D₃)⋊C₄	—	3	16	no	—
244	Dic₃⋊C₄	—	3	16	no	—
245	C₄×Dic₃	—	3	8	no	—
246	C₄×Dic₃	—	3	4	no	—
247	C₄×Dic₃	—	3	4	no	—
248	C₂²×C₃²	—	2	2	no	—
249	C₂²×C₃²	—	2	16	no	—
250	C₂²×C₃²	—	2	8	no	—
251	C₂²×C₃²	—	2	2	no	—
252	C₂²×C₃²	—	2	4	no	—
253	C₂²×C₃²	—	2	4	no	—
254	C₂²×C₃²	—	2	8	no	—
255	C₂²×C₃²	—	2	8	no	—
256	C₂²×C₃²	—	2	16	no	—
257	C₂²×C₃²	—	4	8	no	—
258	C₂²×C₃²	—	4	16	no	—
259	C₂²×C₃²	C₂×#67	1	8	yes	—
260	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
261	C₂²×C₃²	C₂³×D₃	1	4	yes	—
262	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
263	C₂×C₃⋊D₃	—	2	2	no	—
264	C₂×C₃⋊D₃	—	2	4	no	—
265	C₂×C₃×D₃	—	6	16	no	—
266	C₂×C₃×D₃	—	6	8	no	—
267	C₃²×C₄	—	2	16	no	—
268	C₃²×C₄	—	2	8	no	—
269	C₃²×C₄	—	2	2	no	—
270	C₃²×C₄	—	2	8	no	—
271	C₃²×C₄	—	2	8	no	—
272	C₃²×C₄	C₂×#67	1	8	yes	—
273	C₃²×C₄	C₂×#67	1	8	yes	—
274	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
275	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
276	C₃⋊Dic₃	—	2	2	no	—
277	C₃⋊Dic₃	—	2	2	no	—
278	C₃⋊Dic₃	C₃×#41	1	4	yes	complemented
279	C₃×Dic₃	—	3	16	no	—
280	C₃×Dic₃	—	6	8	no	—
281	C₃×Dic₃	—	6	8	no	—
282	C₂×#41	—	9	1	no	—
283	C₂×#41	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
284	C₄⋊Q₈	—	9	1	no	—
285	#127	—	9	1	no	—
286	#124	—	9	1	no	—
287	#124	—	9	1	no	—
288	#121	—	9	4	no	—
289	C₄×D₄	—	9	4	no	—
290	C₂×C₄²	—	9	1	no	—
291	C₃³	#532	1	1	yes	characteristic, complemented, Sylow
292	C₂³×C₃	—	2	8	no	—
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	9	2	no	—
295	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
296	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
297	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
298	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
299	C₂²×D₃	—	3	8	no	—
300	C₃×Q₈	—	2	16	no	—
301	C₃×Q₈	—	2	8	no	—
302	C₃×Q₈	—	2	2	no	—
303	C₃×Q₈	—	18	2	no	—
304	C₃×D₄	—	2	32	no	—
305	C₃×D₄	—	2	16	no	—
306	C₃×D₄	—	2	16	no	—
307	C₃×D₄	—	2	4	no	—
308	C₃×D₄	—	2	8	no	—
309	C₃×D₄	—	2	2	no	—
310	C₃×D₄	—	18	8	no	—
311	C₃×D₄	—	18	4	no	—
312	C₃×D₄	—	18	2	no	—
313	C₂×C₃×C₄	—	2	32	no	—
314	C₂×C₃×C₄	—	2	16	no	—
315	C₂×C₃×C₄	—	2	4	no	—
316	C₂×C₃×C₄	—	2	16	no	—
317	C₂×C₃×C₄	—	2	4	no	—
318	C₂×C₃×C₄	—	2	8	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	—	9	2	no	—
321	C₂×C₃×C₄	—	9	2	no	—
322	C₂×C₃×C₄	—	9	2	no	—
323	C₂×C₃×C₄	—	18	4	no	—
324	C₂×C₃×C₄	—	18	4	no	—
325	C₂×C₃×C₄	C₃×#67	1	16	yes	complemented
326	C₂×C₃×C₄	#638	1	4	yes	complemented
327	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
328	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
329	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
330	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
333	#67	—	6	32	no	—
334	#67	—	6	16	no	—
335	C₂×Dic₃	—	3	8	no	—
336	C₂×Dic₃	—	3	8	no	—
337	C₂×Dic₃	—	3	8	no	—
338	C₂×Dic₃	—	6	16	no	—
339	D₁₂	—	6	8	no	—
340	C₄×D₃	—	6	16	no	—
341	Dic₆	—	6	8	no	—
342	C₂×C₃²	—	2	2	no	—
343	C₂×C₃²	—	2	8	no	—
344	C₂×C₃²	—	2	4	no	—
345	C₂×C₃²	—	2	8	no	—
346	C₂×C₃²	—	4	8	no	—
347	C₂×C₃²	—	4	16	no	—
348	C₂×C₃²	—	4	8	no	—
349	C₂×C₃²	—	4	2	no	—
350	C₂×C₃²	D₃×#41	1	8	yes	—
351	C₂×C₃²	C₂²×#67	1	4	yes	—
352	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
353	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
354	C₃⋊D₃	—	4	2	no	—
355	C₃×D₃	—	12	8	no	—
356	#41	—	2	4	no	—
357	#41	—	18	4	no	—
358	C₂×Q₈	—	9	1	no	—
359	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
360	C₂×D₄	—	9	4	no	—
361	C₂×D₄	—	9	2	no	—
362	C₂×D₄	—	9	1	no	—
363	C₂×D₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
364	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
365	C₂²×C₄	—	9	2	no	—
366	C₂²×C₄	—	9	2	no	—
367	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
368	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
369	C₄⋊C₄	—	9	4	no	—
370	C₂²⋊C₄	—	9	4	no	—
371	C₂²⋊C₄	—	9	4	no	—
372	C₄²	—	9	2	no	—
373	C₄²	—	9	1	no	—
374	C₄²	—	9	1	no	—
375	C₂²×C₃	—	2	8	no	—
376	C₂²×C₃	—	2	2	no	—
377	C₂²×C₃	—	2	16	no	—
378	C₂²×C₃	—	2	16	no	—
379	C₂²×C₃	—	2	8	no	—
380	C₂²×C₃	—	2	4	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	4	no	—
383	C₂²×C₃	—	2	8	no	—
384	C₂²×C₃	—	4	8	no	—
385	C₂²×C₃	—	4	16	no	—
386	C₂²×C₃	—	18	4	no	—
387	C₂²×C₃	—	18	2	no	—
388	C₂²×C₃	C₂×C₃×#67	1	8	yes	—
389	C₂²×C₃	C₂×#638	1	2	yes	—
390	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
391	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
392	C₂×D₃	—	6	16	no	—
393	C₂×D₃	—	6	8	no	—
394	C₃×C₄	—	2	16	no	—
395	C₃×C₄	—	2	8	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	8	no	—
398	C₃×C₄	—	2	8	no	—
399	C₃×C₄	—	9	4	no	—
400	C₃×C₄	—	18	2	no	—
401	C₃×C₄	—	18	2	no	—
402	C₃×C₄	C₂×C₃×#67	1	8	yes	—
403	C₃×C₄	C₂×C₃×#67	1	8	yes	—
404	C₃×C₄	C₂×#638	1	2	yes	—
405	C₃×C₄	C₂×#638	1	2	yes	—
406	Dic₃	—	3	16	no	—
407	Dic₃	—	6	8	no	—
408	Dic₃	—	6	8	no	—
409	C₃²	—	2	4	no	—
410	C₃²	#5832	1	4	yes	complemented
411	C₃²	C₃×#532	1	1	yes	characteristic, complemented
412	C₂³	—	9	2	no	—
413	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
414	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	18	2	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	2	no	—
419	D₄	—	18	8	no	—
420	D₄	—	18	4	no	—
421	D₄	—	18	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	9	2	no	—
424	C₂×C₄	—	9	2	no	—
425	C₂×C₄	—	9	2	no	—
426	C₂×C₄	—	18	4	no	—
427	C₂×C₄	—	18	4	no	—
428	C₂×C₄	C₃×#638	1	4	yes	complemented
429	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
430	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
431	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
432	C₂×C₃	—	2	8	no	—
433	C₂×C₃	—	2	2	no	—
434	C₂×C₃	—	2	8	no	—
435	C₂×C₃	—	2	4	no	—
436	C₂×C₃	—	4	8	no	—
437	C₂×C₃	—	4	16	no	—
438	C₂×C₃	—	4	8	no	—
439	C₂×C₃	—	4	2	no	—
440	C₂×C₃	—	36	2	no	—
441	C₂×C₃	C₃×D₃×#41	1	8	yes	—
442	C₂×C₃	C₂²×C₃×#67	1	4	yes	—
443	C₂×C₃	#41×C₃⋊D₃	1	2	yes	—
444	C₂×C₃	C₂²×#638	1	1	yes	characteristic
445	D₃	—	12	8	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	18	4	no	—
450	C₂²	—	18	2	no	—
451	C₂²	C₂×C₃×#638	1	2	yes	—
452	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
453	C₄	—	2	2	no	—
454	C₄	—	9	4	no	—
455	C₄	—	18	2	no	—
456	C₄	—	18	2	no	—
457	C₄	C₂×C₃×#638	1	2	yes	—
458	C₄	C₂×C₃×#638	1	2	yes	—
459	C₃	—	2	4	no	—
460	C₃	C₃×#5832	1	4	yes	complemented
461	C₃	#10596303	1	1	yes	characteristic, direct product factor
462	C₂	—	2	2	no	—
463	C₂	—	4	2	no	—
464	C₂	—	36	2	no	—
465	C₂	C₃×#41×C₃⋊D₃	1	2	yes	—
466	C₂	C₂²×C₃×#638	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	C₂×C₃³×#41	C₂
socle	C₂²×C₃³	C₂⁴
hypercenter	C₂×C₃×#41	C₃⋊D₃
hypocenter	C₃²	C₃×#532
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×#41

Complements

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

N	H ≅ G/N	type
1. C₂×C₃³×#41	C₂	semidirect
2. C₂×C₃×#3828	C₂	semidirect
3. C₃×#64156	C₂	semidirect
4. C₃×#64153	C₂	semidirect
5. C₃×#64149	C₂	semidirect
6. C₃×#64148	C₂	semidirect
7. C₃×#64145	C₂	semidirect
8. C₃×C₄×#638	C₂	semidirect
9. C₂×C₃×C₄×C₃⋊Dic₃	C₂	semidirect
10. #10596303	C₃	direct (N × H)
32. C₂×C₃²×#41	D₃	semidirect
33. C₂×C₃²×#41	C₂×C₃	semidirect
34. C₂×#3828	C₂×C₃	semidirect
36. #64156	C₂×C₃	semidirect
37. #64153	C₂×C₃	semidirect
38. #64149	C₂×C₃	semidirect
39. #64148	C₂×C₃	semidirect
40. #64145	C₂×C₃	semidirect
41. C₄×#638	C₂×C₃	semidirect
42. C₂×C₄×C₃⋊Dic₃	C₂×C₃	semidirect
57. C₂×C₃³×C₄	D₄	semidirect
128. C₃×C₃⋊Dic₃	#41	semidirect
131. C₂×C₃×#41	C₃×D₃	semidirect
132. C₂×C₃×#41	C₃⋊D₃	semidirect
172. C₂×C₃²×C₄	#67	semidirect
173. C₂×C₃²×C₄	C₃×D₄	semidirect
278. C₃⋊Dic₃	C₃×#41	semidirect
283. C₂×#41	C₃×C₃⋊D₃	semidirect
291. C₃³	#532	semidirect
325. C₂×C₃×C₄	C₃×#67	semidirect
326. C₂×C₃×C₄	#638	semidirect
410. C₃²	#5832	semidirect
411. C₃²	C₃×#532	semidirect
428. C₂×C₄	C₃×#638	semidirect
460. C₃	C₃×#5832	semidirect
461. C₃	#10596303	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃³×#41	2
C₂×C₃×#3828	2
C₃×#64156	2
C₃×#64153	2
C₃×#64149	2
C₃×#64148	2
C₃×#64145	2
C₃×C₄×#638	2
C₂×C₃×C₄×C₃⋊Dic₃	2
#10596303	3
C₃×#5832	3

Subgroups — C3×#10596303 #13179582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596303 #13179582