Subgroups — C₃²×#64330 #72220352

Order 2592.

3466 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#638	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃³×#67	C₂	1	2	yes	maximal, complemented
3	C₃²×#3811	C₂	1	2	yes	maximal, complemented
4	C₃²×D₃×#67	C₂	1	4	yes	maximal, complemented
5	C₃²×#3805	C₂	1	2	yes	maximal, complemented
6	C₃²×#3804	C₂	1	4	yes	maximal, complemented
7	C₃²×#1004	—	3	2	no	maximal
8	C₃×#64330	C₃	1	4	yes	maximal, direct product factor
9	C₂³×C₃⁴	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₃²×C₃⋊D₃	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₃³×D₃	C₂²	1	2	yes	complemented
12	C₂×C₃²×D₃²	C₂²	1	2	yes	complemented
13	C₃²×#638	C₂²	1	4	yes	complemented
14	C₂×C₃²×C₃⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
15	C₃³×#67	C₂²	1	4	yes	complemented
16	C₃³×#67	C₂²	1	4	yes	complemented
17	C₂×C₃³×Dic₃	C₂²	1	2	yes	complemented
18	C₃²×#627	C₂²	1	2	yes	complemented
19	C₃²×#626	C₂²	1	4	yes	complemented
20	C₃²×#625	C₂²	1	2	yes	complemented
21	C₃²×#624	C₂²	1	2	yes	complemented
22	C₃²×D₃×Dic₃	C₂²	1	4	yes	complemented
23	C₂×C₃³×D₄	—	3	2	no	—
24	C₂×C₃×#638	C₂×C₃	1	4	yes	complemented
25	C₂×C₃²×#67	—	2	8	no	—
26	C₂×C₃²×#67	—	3	2	no	—
27	C₂×C₃²×#67	—	3	4	no	—
28	C₂×C₃²×#67	—	6	1	no	—
29	C₂×C₃²×#67	D₃	1	2	yes	complemented
30	C₂×C₃²×#67	C₂×C₃	1	8	yes	complemented
31	C₃²×#237	—	3	4	no	—
32	C₃²×#237	—	3	4	no	—
33	C₃²×D₃×D₄	—	3	4	no	—
34	C₃²×D₃×D₄	—	3	4	no	—
35	C₃²×#235	—	3	4	no	—
36	C₃×#3811	C₂×C₃	1	8	yes	complemented
37	C₃×D₃×#67	C₂×C₃	1	16	yes	complemented
38	C₃×#3805	C₂×C₃	1	8	yes	complemented
39	C₃×#3804	C₂×C₃	1	16	yes	complemented
40	C₂²×C₃⁴	—	4	1	no	—
41	C₂²×C₃⁴	C₂³	1	2	yes	—
42	C₂²×C₃⁴	C₂³	1	1	yes	characteristic
43	C₂×C₃²×C₃⋊D₃	—	4	1	no	—
44	C₂×C₃²×C₃⋊D₃	C₂³	1	2	yes	—
45	C₂×C₃³×D₃	—	4	2	no	—
46	C₂×C₃³×D₃	C₂³	1	4	yes	—
47	C₃²×D₃²	—	4	2	no	—
48	C₃²×C₃⋊Dic₃	C₂³	1	2	yes	—
49	C₃³×Dic₃	C₂³	1	4	yes	—
50	C₃²×H(5,𝔽₂)	—	9	1	no	—
51	C₃×#1004	—	3	8	no	—
52	#64330	C₃²	1	1	yes	characteristic, direct product factor
53	C₂³×C₃³	—	2	1	no	—
54	C₂³×C₃³	—	2	8	no	—
55	C₂³×C₃³	—	3	2	no	—
56	C₂³×C₃³	—	4	4	no	—
57	C₂³×C₃³	C₂×D₃	1	2	yes	complemented
58	C₂³×C₃³	C₂²×C₃	1	4	yes	complemented
59	C₂²×C₃×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
60	C₂²×C₃²×D₃	—	2	8	no	—
61	C₂²×C₃²×D₃	—	3	2	no	—
62	C₂²×C₃²×D₃	—	3	4	no	—
63	C₂²×C₃²×D₃	—	6	1	no	—
64	C₂²×C₃²×D₃	C₂×D₃	1	2	yes	complemented
65	C₂²×C₃²×D₃	C₂²×C₃	1	8	yes	complemented
66	C₂×C₃×D₃²	C₂²×C₃	1	8	yes	complemented
67	C₃³×D₄	—	3	4	no	—
68	C₃³×D₄	—	3	4	no	—
69	C₂×C₃³×C₄	—	3	2	no	—
70	C₃×#638	C₂²×C₃	1	16	yes	complemented
71	C₂×C₃×C₃⋊Dic₃	C₂²×C₃	1	4	yes	complemented
72	C₃²×#67	—	2	16	no	—
73	C₃²×#67	—	2	16	no	—
74	C₃²×#67	—	3	4	no	—
75	C₃²×#67	—	3	4	no	—
76	C₃²×#67	—	3	4	no	—
77	C₃²×#67	—	3	4	no	—
78	C₃²×#67	—	6	4	no	—
79	C₃²×#67	C₂×D₃	1	4	yes	complemented
80	C₃²×#67	C₂×D₃	1	4	yes	complemented
81	C₃²×#67	C₂²×C₃	1	16	yes	complemented
82	C₃²×#67	C₂²×C₃	1	16	yes	complemented
83	C₂×C₃²×Dic₃	—	2	8	no	—
84	C₂×C₃²×Dic₃	—	3	2	no	—
85	C₂×C₃²×Dic₃	—	3	4	no	—
86	C₂×C₃²×Dic₃	—	6	1	no	—
87	C₂×C₃²×Dic₃	C₂×D₃	1	2	yes	complemented
88	C₂×C₃²×Dic₃	C₂²×C₃	1	8	yes	complemented
89	C₃²×D₁₂	—	3	4	no	—
90	C₃²×C₄×D₃	—	3	4	no	—
91	C₃²×C₄×D₃	—	3	4	no	—
92	C₃²×Dic₆	—	3	4	no	—
93	C₃×#627	C₂²×C₃	1	8	yes	complemented
94	C₃×#626	C₂²×C₃	1	16	yes	complemented
95	C₃×#625	C₂²×C₃	1	8	yes	complemented
96	C₃×#624	C₂²×C₃	1	8	yes	complemented
97	C₃×D₃×Dic₃	C₂²×C₃	1	16	yes	complemented
98	C₂×C₃⁴	—	2	2	no	—
99	C₂×C₃⁴	—	2	1	no	—
100	C₂×C₃⁴	C₂⁴	1	1	yes	characteristic
101	C₃²×C₃⋊D₃	—	2	2	no	—
102	C₃³×D₃	—	2	4	no	—
103	C₃²×#41	—	9	4	no	—
104	C₃²×#41	—	9	2	no	—
105	C₂×C₃²×D₄	—	3	2	no	—
106	C₂×C₃²×D₄	—	3	8	no	—
107	C₂×C₃²×D₄	—	6	8	no	—
108	C₂×C₃²×D₄	—	9	2	no	—
109	C₂×C₃²×D₄	—	9	4	no	—
110	C₂×C₃²×D₄	—	9	1	no	—
111	C₂×#638	C₂×C₃²	1	1	yes	characteristic, complemented
112	C₂×C₃×#67	—	2	8	no	—
113	C₂×C₃×#67	—	3	8	no	—
114	C₂×C₃×#67	—	3	16	no	—
115	C₂×C₃×#67	—	6	4	no	—
116	C₂×C₃×#67	C₃×D₃	1	8	yes	complemented
117	C₂×C₃×#67	C₂×C₃²	1	2	yes	complemented
118	C₃×#237	—	3	16	no	—
119	C₃×#237	—	3	16	no	—
120	C₃×D₃×D₄	—	3	16	no	—
121	C₃×D₃×D₄	—	3	16	no	—
122	C₃×#235	—	3	16	no	—
123	#3811	C₂×C₃²	1	2	yes	complemented
124	D₃×#67	C₂×C₃²	1	4	yes	complemented
125	#3805	C₂×C₃²	1	2	yes	complemented
126	#3804	C₂×C₃²	1	4	yes	complemented
127	C₂²×C₃³	—	2	1	no	—
128	C₂²×C₃³	—	2	8	no	—
129	C₂²×C₃³	—	2	2	no	—
130	C₂²×C₃³	—	2	8	no	—
131	C₂²×C₃³	—	2	8	no	—
132	C₂²×C₃³	—	3	4	no	—
133	C₂²×C₃³	—	4	2	no	—
134	C₂²×C₃³	—	4	4	no	—
135	C₂²×C₃³	—	4	16	no	—
136	C₂²×C₃³	—	4	2	no	—
137	C₂²×C₃³	—	4	8	no	—
138	C₂²×C₃³	—	4	4	no	—
139	C₂²×C₃³	—	4	16	no	—
140	C₂²×C₃³	—	12	2	no	—
141	C₂²×C₃³	C₂²×D₃	1	2	yes	—
142	C₂²×C₃³	C₂²×D₃	1	2	yes	—
143	C₂²×C₃³	C₂²×D₃	1	2	yes	—
144	C₂²×C₃³	C₂³×C₃	1	8	yes	—
145	C₂²×C₃³	C₂³×C₃	1	4	yes	—
146	C₂×C₃×C₃⋊D₃	—	4	4	no	—
147	C₂×C₃×C₃⋊D₃	C₂³×C₃	1	8	yes	—
148	C₂×C₃²×D₃	—	2	16	no	—
149	C₂×C₃²×D₃	—	3	4	no	—
150	C₂×C₃²×D₃	—	4	2	no	—
151	C₂×C₃²×D₃	—	4	8	no	—
152	C₂×C₃²×D₃	—	4	16	no	—
153	C₂×C₃²×D₃	—	6	2	no	—
154	C₂×C₃²×D₃	—	12	4	no	—
155	C₂×C₃²×D₃	—	12	2	no	—
156	C₂×C₃²×D₃	—	12	2	no	—
157	C₂×C₃²×D₃	C₂²×D₃	1	4	yes	—
158	C₂×C₃²×D₃	C₂³×C₃	1	16	yes	—
159	C₃×D₃²	—	4	8	no	—
160	C₃³×C₄	—	3	4	no	—
161	C₃×C₃⋊Dic₃	C₂³×C₃	1	8	yes	—
162	C₃²×Dic₃	—	2	16	no	—
163	C₃²×Dic₃	—	3	4	no	—
164	C₃²×Dic₃	—	6	2	no	—
165	C₃²×Dic₃	C₂²×D₃	1	4	yes	—
166	C₃²×Dic₃	C₂³×C₃	1	16	yes	—
167	C₃×H(5,𝔽₂)	—	9	4	no	—
168	#1004	—	3	2	no	—
169	C₃⁴	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
170	C₂³×C₃²	—	2	8	no	—
171	C₂³×C₃²	—	2	4	no	—
172	C₂³×C₃²	—	2	8	no	—
173	C₂³×C₃²	—	3	2	no	—
174	C₂³×C₃²	—	3	8	no	—
175	C₂³×C₃²	—	4	4	no	—
176	C₂³×C₃²	—	4	12	no	—
177	C₂³×C₃²	—	4	4	no	—
178	C₂³×C₃²	—	6	8	no	—
179	C₂³×C₃²	—	9	2	no	—
180	C₂³×C₃²	—	9	1	no	—
181	C₂³×C₃²	D₃²	1	1	yes	characteristic, complemented
182	C₂³×C₃²	C₂×C₃×D₃	1	8	yes	complemented
183	C₂³×C₃²	C₂²×C₃²	1	1	yes	characteristic, complemented
184	C₂²×C₃⋊D₃	C₂²×C₃²	1	1	yes	characteristic, complemented
185	C₂²×C₃×D₃	—	2	8	no	—
186	C₂²×C₃×D₃	—	3	8	no	—
187	C₂²×C₃×D₃	—	3	16	no	—
188	C₂²×C₃×D₃	—	6	4	no	—
189	C₂²×C₃×D₃	C₂×C₃×D₃	1	8	yes	complemented
190	C₂²×C₃×D₃	C₂²×C₃²	1	2	yes	complemented
191	C₂×D₃²	C₂²×C₃²	1	2	yes	complemented
192	C₃²×Q₈	—	9	2	no	—
193	C₃²×D₄	—	3	4	no	—
194	C₃²×D₄	—	3	4	no	—
195	C₃²×D₄	—	3	16	no	—
196	C₃²×D₄	—	3	16	no	—
197	C₃²×D₄	—	6	16	no	—
198	C₃²×D₄	—	6	16	no	—
199	C₃²×D₄	—	9	4	no	—
200	C₃²×D₄	—	9	2	no	—
201	C₃²×D₄	—	9	4	no	—
202	C₂×C₃²×C₄	—	3	2	no	—
203	C₂×C₃²×C₄	—	3	8	no	—
204	C₂×C₃²×C₄	—	6	8	no	—
205	C₂×C₃²×C₄	—	9	2	no	—
206	C₂×C₃²×C₄	—	9	4	no	—
207	C₂×C₃²×C₄	—	9	1	no	—
208	#638	C₂²×C₃²	1	4	yes	complemented
209	C₂×C₃⋊Dic₃	C₂²×C₃²	1	1	yes	characteristic, complemented
210	C₃×#67	—	2	16	no	—
211	C₃×#67	—	2	16	no	—
212	C₃×#67	—	3	16	no	—
213	C₃×#67	—	3	16	no	—
214	C₃×#67	—	3	16	no	—
215	C₃×#67	—	3	16	no	—
216	C₃×#67	—	6	16	no	—
217	C₃×#67	C₂×C₃×D₃	1	16	yes	complemented
218	C₃×#67	C₂×C₃×D₃	1	16	yes	complemented
219	C₃×#67	C₂²×C₃²	1	4	yes	complemented
220	C₃×#67	C₂²×C₃²	1	4	yes	complemented
221	C₂×C₃×Dic₃	—	2	8	no	—
222	C₂×C₃×Dic₃	—	3	8	no	—
223	C₂×C₃×Dic₃	—	3	16	no	—
224	C₂×C₃×Dic₃	—	6	4	no	—
225	C₂×C₃×Dic₃	C₂×C₃×D₃	1	8	yes	complemented
226	C₂×C₃×Dic₃	C₂²×C₃²	1	2	yes	complemented
227	C₃×D₁₂	—	3	16	no	—
228	C₃×C₄×D₃	—	3	16	no	—
229	C₃×C₄×D₃	—	3	16	no	—
230	C₃×Dic₆	—	3	16	no	—
231	#627	C₂²×C₃²	1	2	yes	complemented
232	#626	C₂²×C₃²	1	4	yes	complemented
233	#625	C₂²×C₃²	1	2	yes	complemented
234	#624	C₂²×C₃²	1	2	yes	complemented
235	D₃×Dic₃	C₂²×C₃²	1	4	yes	complemented
236	C₂×C₃³	—	2	2	no	—
237	C₂×C₃³	—	2	16	no	—
238	C₂×C₃³	—	2	2	no	—
239	C₂×C₃³	—	2	2	no	—
240	C₂×C₃³	—	2	2	no	—
241	C₂×C₃³	—	2	8	no	—
242	C₂×C₃³	—	2	4	no	—
243	C₂×C₃³	—	2	1	no	—
244	C₂×C₃³	—	2	8	no	—
245	C₂×C₃³	—	4	4	no	—
246	C₂×C₃³	—	4	2	no	—
247	C₂×C₃³	—	4	8	no	—
248	C₂×C₃³	—	4	8	no	—
249	C₂×C₃³	—	4	16	no	—
250	C₂×C₃³	—	4	8	no	—
251	C₂×C₃³	—	6	4	no	—
252	C₂×C₃³	C₂³×D₃	1	2	yes	—
253	C₂×C₃³	C₂⁴×C₃	1	4	yes	—
254	C₃×C₃⋊D₃	—	2	8	no	—
255	C₃²×D₃	—	2	4	no	—
256	C₃²×D₃	—	2	16	no	—
257	C₃²×D₃	—	4	16	no	—
258	C₃²×D₃	—	6	4	no	—
259	C₃²×D₃	—	12	2	no	—
260	C₃×#41	—	9	16	no	—
261	C₃×#41	—	9	8	no	—
262	C₂×C₃×D₄	—	3	8	no	—
263	C₂×C₃×D₄	—	3	2	no	—
264	C₂×C₃×D₄	—	6	8	no	—
265	C₂×C₃×D₄	—	9	8	no	—
266	C₂×C₃×D₄	—	9	16	no	—
267	C₂×C₃×D₄	—	9	4	no	—
268	C₂×#67	—	3	2	no	—
269	C₂×#67	—	3	4	no	—
270	C₂×#67	—	6	1	no	—
271	C₂×#67	C₃²×D₃	1	2	yes	complemented
272	#237	—	3	4	no	—
273	#237	—	3	4	no	—
274	D₃×D₄	—	3	4	no	—
275	D₃×D₄	—	3	4	no	—
276	#235	—	3	4	no	—
277	C₂²×C₃²	—	2	8	no	—
278	C₂²×C₃²	—	2	8	no	—
279	C₂²×C₃²	—	2	8	no	—
280	C₂²×C₃²	—	2	4	no	—
281	C₂²×C₃²	—	2	8	no	—
282	C₂²×C₃²	—	2	8	no	—
283	C₂²×C₃²	—	2	8	no	—
284	C₂²×C₃²	—	2	8	no	—
285	C₂²×C₃²	—	3	4	no	—
286	C₂²×C₃²	—	3	16	no	—
287	C₂²×C₃²	—	4	4	no	—
288	C₂²×C₃²	—	4	8	no	—
289	C₂²×C₃²	—	4	24	no	—
290	C₂²×C₃²	—	4	12	no	—
291	C₂²×C₃²	—	4	1	no	—
292	C₂²×C₃²	—	4	8	no	—
293	C₂²×C₃²	—	4	1	no	—
294	C₂²×C₃²	—	4	16	no	—
295	C₂²×C₃²	—	4	8	no	—
296	C₂²×C₃²	—	4	16	no	—
297	C₂²×C₃²	—	4	16	no	—
298	C₂²×C₃²	—	4	16	no	—
299	C₂²×C₃²	—	4	48	no	—
300	C₂²×C₃²	—	4	8	no	—
301	C₂²×C₃²	—	4	4	no	—
302	C₂²×C₃²	—	6	16	no	—
303	C₂²×C₃²	—	9	2	no	—
304	C₂²×C₃²	—	12	2	no	—
305	C₂²×C₃²	—	12	8	no	—
306	C₂²×C₃²	—	12	16	no	—
307	C₂²×C₃²	—	36	1	no	—
308	C₂²×C₃²	—	36	2	no	—
309	C₂²×C₃²	C₂×D₃²	1	2	yes	—
310	C₂²×C₃²	C₂×D₃²	1	1	yes	characteristic
311	C₂²×C₃²	C₂²×C₃×D₃	1	8	yes	—
312	C₂²×C₃²	C₂²×C₃×D₃	1	8	yes	—
313	C₂²×C₃²	C₂²×C₃×D₃	1	8	yes	—
314	C₂²×C₃²	C₂³×C₃²	1	2	yes	—
315	C₂²×C₃²	C₂³×C₃²	1	1	yes	characteristic
316	C₂×C₃⋊D₃	—	4	1	no	—
317	C₂×C₃⋊D₃	C₂³×C₃²	1	2	yes	—
318	C₂×C₃×D₃	—	2	16	no	—
319	C₂×C₃×D₃	—	3	16	no	—
320	C₂×C₃×D₃	—	4	8	no	—
321	C₂×C₃×D₃	—	4	2	no	—
322	C₂×C₃×D₃	—	4	16	no	—
323	C₂×C₃×D₃	—	6	8	no	—
324	C₂×C₃×D₃	—	12	16	no	—
325	C₂×C₃×D₃	—	12	8	no	—
326	C₂×C₃×D₃	—	12	8	no	—
327	C₂×C₃×D₃	C₂²×C₃×D₃	1	16	yes	—
328	C₂×C₃×D₃	C₂³×C₃²	1	4	yes	—
329	D₃²	—	4	2	no	—
330	C₃²×C₄	—	3	4	no	—
331	C₃²×C₄	—	3	16	no	—
332	C₃²×C₄	—	6	16	no	—
333	C₃²×C₄	—	9	2	no	—
334	C₃⋊Dic₃	C₂³×C₃²	1	2	yes	—
335	C₃×Dic₃	—	2	16	no	—
336	C₃×Dic₃	—	3	16	no	—
337	C₃×Dic₃	—	6	8	no	—
338	C₃×Dic₃	C₂²×C₃×D₃	1	16	yes	—
339	C₃×Dic₃	C₂³×C₃²	1	4	yes	—
340	H(5,𝔽₂)	—	9	1	no	Sylow
341	C₃³	—	2	1	no	—
342	C₃³	—	2	8	no	—
343	C₃³	—	4	4	no	—
344	C₃³	#1004	1	2	yes	complemented
345	C₃³	C₃×H(5,𝔽₂)	1	4	yes	complemented
346	C₂³×C₃	—	2	8	no	—
347	C₂³×C₃	—	2	1	no	—
348	C₂³×C₃	—	3	8	no	—
349	C₂³×C₃	—	3	2	no	—
350	C₂³×C₃	—	4	4	no	—
351	C₂³×C₃	—	6	8	no	—
352	C₂³×C₃	—	9	8	no	—
353	C₂³×C₃	—	9	4	no	—
354	C₂³×C₃	C₃×D₃²	1	4	yes	complemented
355	C₂³×C₃	C₂×C₃²×D₃	1	2	yes	complemented
356	C₂²×D₃	—	3	2	no	—
357	C₂²×D₃	—	3	4	no	—
358	C₂²×D₃	—	6	1	no	—
359	C₂²×D₃	C₂×C₃²×D₃	1	2	yes	complemented
360	C₃×Q₈	—	9	8	no	—
361	C₃×D₄	—	3	16	no	—
362	C₃×D₄	—	3	16	no	—
363	C₃×D₄	—	3	4	no	—
364	C₃×D₄	—	3	4	no	—
365	C₃×D₄	—	6	16	no	—
366	C₃×D₄	—	6	16	no	—
367	C₃×D₄	—	9	16	no	—
368	C₃×D₄	—	9	8	no	—
369	C₃×D₄	—	9	16	no	—
370	C₂×C₃×C₄	—	3	8	no	—
371	C₂×C₃×C₄	—	3	2	no	—
372	C₂×C₃×C₄	—	6	8	no	—
373	C₂×C₃×C₄	—	9	8	no	—
374	C₂×C₃×C₄	—	9	16	no	—
375	C₂×C₃×C₄	—	9	4	no	—
376	#67	—	3	4	no	—
377	#67	—	3	4	no	—
378	#67	—	3	4	no	—
379	#67	—	3	4	no	—
380	#67	—	6	4	no	—
381	#67	C₂×C₃²×D₃	1	4	yes	complemented
382	#67	C₂×C₃²×D₃	1	4	yes	complemented
383	C₂×Dic₃	—	3	2	no	—
384	C₂×Dic₃	—	3	4	no	—
385	C₂×Dic₃	—	6	1	no	—
386	C₂×Dic₃	C₂×C₃²×D₃	1	2	yes	complemented
387	D₁₂	—	3	4	no	—
388	C₄×D₃	—	3	4	no	—
389	C₄×D₃	—	3	4	no	—
390	Dic₆	—	3	4	no	—
391	C₂×C₃²	—	2	16	no	—
392	C₂×C₃²	—	2	1	no	—
393	C₂×C₃²	—	2	2	no	—
394	C₂×C₃²	—	2	8	no	—
395	C₂×C₃²	—	2	1	no	—
396	C₂×C₃²	—	2	8	no	—
397	C₂×C₃²	—	2	16	no	—
398	C₂×C₃²	—	2	8	no	—
399	C₂×C₃²	—	2	8	no	—
400	C₂×C₃²	—	2	8	no	—
401	C₂×C₃²	—	2	2	no	—
402	C₂×C₃²	—	2	4	no	—
403	C₂×C₃²	—	2	8	no	—
404	C₂×C₃²	—	4	4	no	—
405	C₂×C₃²	—	4	12	no	—
406	C₂×C₃²	—	4	8	no	—
407	C₂×C₃²	—	4	8	no	—
408	C₂×C₃²	—	4	8	no	—
409	C₂×C₃²	—	4	8	no	—
410	C₂×C₃²	—	4	8	no	—
411	C₂×C₃²	—	4	8	no	—
412	C₂×C₃²	—	4	16	no	—
413	C₂×C₃²	—	4	48	no	—
414	C₂×C₃²	—	4	16	no	—
415	C₂×C₃²	—	4	8	no	—
416	C₂×C₃²	—	4	24	no	—
417	C₂×C₃²	—	4	4	no	—
418	C₂×C₃²	—	6	4	no	—
419	C₂×C₃²	—	6	16	no	—
420	C₂×C₃²	—	12	16	no	—
421	C₂×C₃²	—	18	2	no	—
422	C₂×C₃²	C₂²×D₃²	1	1	yes	characteristic
423	C₂×C₃²	C₂³×C₃×D₃	1	8	yes	—
424	C₂×C₃²	C₂⁴×C₃²	1	1	yes	characteristic
425	C₃⋊D₃	—	2	2	no	—
426	C₃×D₃	—	2	16	no	—
427	C₃×D₃	—	2	4	no	—
428	C₃×D₃	—	4	16	no	—
429	C₃×D₃	—	6	16	no	—
430	C₃×D₃	—	12	8	no	—
431	#41	—	9	4	no	—
432	#41	—	9	2	no	—
433	C₂×D₄	—	3	2	no	—
434	C₂×D₄	—	9	2	no	—
435	C₂×D₄	—	9	4	no	—
436	C₂×D₄	—	9	1	no	—
437	C₂²×C₃	—	2	1	no	—
438	C₂²×C₃	—	2	8	no	—
439	C₂²×C₃	—	2	2	no	—
440	C₂²×C₃	—	2	8	no	—
441	C₂²×C₃	—	2	8	no	—
442	C₂²×C₃	—	3	16	no	—
443	C₂²×C₃	—	3	4	no	—
444	C₂²×C₃	—	4	4	no	—
445	C₂²×C₃	—	4	2	no	—
446	C₂²×C₃	—	4	2	no	—
447	C₂²×C₃	—	4	16	no	—
448	C₂²×C₃	—	4	16	no	—
449	C₂²×C₃	—	4	8	no	—
450	C₂²×C₃	—	4	4	no	—
451	C₂²×C₃	—	6	16	no	—
452	C₂²×C₃	—	9	8	no	—
453	C₂²×C₃	—	12	8	no	—
454	C₂²×C₃	—	12	2	no	—
455	C₂²×C₃	—	12	16	no	—
456	C₂²×C₃	—	36	4	no	—
457	C₂²×C₃	—	36	8	no	—
458	C₂²×C₃	C₂×C₃×D₃²	1	8	yes	—
459	C₂²×C₃	C₂×C₃×D₃²	1	4	yes	—
460	C₂²×C₃	C₂²×C₃²×D₃	1	2	yes	—
461	C₂²×C₃	C₂²×C₃²×D₃	1	2	yes	—
462	C₂²×C₃	C₂²×C₃²×D₃	1	2	yes	—
463	C₂×D₃	—	3	4	no	—
464	C₂×D₃	—	4	2	no	—
465	C₂×D₃	—	6	2	no	—
466	C₂×D₃	—	12	4	no	—
467	C₂×D₃	—	12	2	no	—
468	C₂×D₃	—	12	2	no	—
469	C₂×D₃	C₂²×C₃²×D₃	1	4	yes	—
470	C₃×C₄	—	3	16	no	—
471	C₃×C₄	—	3	4	no	—
472	C₃×C₄	—	6	16	no	—
473	C₃×C₄	—	9	8	no	—
474	Dic₃	—	3	4	no	—
475	Dic₃	—	6	2	no	—
476	Dic₃	C₂²×C₃²×D₃	1	4	yes	—
477	C₃²	—	2	8	no	—
478	C₃²	—	2	4	no	—
479	C₃²	—	2	8	no	—
480	C₃²	—	4	4	no	—
481	C₃²	—	4	12	no	—
482	C₃²	—	4	4	no	—
483	C₃²	#64330	1	1	yes	characteristic, direct product factor
484	C₃²	C₃×#1004	1	8	yes	complemented
485	C₃²	C₃²×H(5,𝔽₂)	1	1	yes	characteristic, complemented
486	C₂³	—	3	2	no	—
487	C₂³	—	9	2	no	—
488	C₂³	—	9	1	no	—
489	C₂³	C₃²×D₃²	1	1	yes	characteristic, complemented
490	Q₈	—	9	2	no	—
491	D₄	—	3	4	no	—
492	D₄	—	3	4	no	—
493	D₄	—	9	4	no	—
494	D₄	—	9	2	no	—
495	D₄	—	9	4	no	—
496	C₂×C₄	—	3	2	no	—
497	C₂×C₄	—	9	2	no	—
498	C₂×C₄	—	9	4	no	—
499	C₂×C₄	—	9	1	no	—
500	C₂×C₃	—	2	2	no	—
501	C₂×C₃	—	2	16	no	—
502	C₂×C₃	—	2	8	no	—
503	C₂×C₃	—	2	4	no	—
504	C₂×C₃	—	2	2	no	—
505	C₂×C₃	—	2	2	no	—
506	C₂×C₃	—	2	2	no	—
507	C₂×C₃	—	2	1	no	—
508	C₂×C₃	—	2	8	no	—
509	C₂×C₃	—	4	2	no	—
510	C₂×C₃	—	4	8	no	—
511	C₂×C₃	—	4	8	no	—
512	C₂×C₃	—	4	16	no	—
513	C₂×C₃	—	4	8	no	—
514	C₂×C₃	—	4	4	no	—
515	C₂×C₃	—	6	16	no	—
516	C₂×C₃	—	6	4	no	—
517	C₂×C₃	—	12	16	no	—
518	C₂×C₃	—	18	8	no	—
519	C₂×C₃	C₂²×C₃×D₃²	1	4	yes	—
520	C₂×C₃	C₂³×C₃²×D₃	1	2	yes	—
521	D₃	—	2	4	no	—
522	D₃	—	6	4	no	—
523	D₃	—	12	2	no	—
524	C₂²	—	3	4	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	9	2	no	—
527	C₂²	—	12	2	no	—
528	C₂²	—	36	1	no	—
529	C₂²	—	36	2	no	—
530	C₂²	C₂×C₃²×D₃²	1	2	yes	—
531	C₂²	C₂×C₃²×D₃²	1	1	yes	characteristic
532	C₄	—	3	4	no	—
533	C₄	—	9	2	no	—
534	C₃	—	2	1	no	—
535	C₃	—	2	8	no	—
536	C₃	—	4	4	no	—
537	C₃	C₃×#64330	1	4	yes	direct product factor
538	C₃	C₃²×#1004	1	2	yes	complemented
539	C₂	—	2	2	no	—
540	C₂	—	2	1	no	—
541	C₂	—	6	4	no	—
542	C₂	—	18	2	no	—
543	C₂	C₂²×C₃²×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²	C₂²×D₃²
commutator, cosocle	C₂×C₃²	C₂⁴×C₃²
Frattini	C₂	C₂²×C₃²×D₃²
Fitting	C₂³×C₃⁴	C₂²
socle	C₂×C₃⁴	C₂⁴
hypercenter	C₂³×C₃²	D₃²
hypocenter	C₃²	C₃²×H(5,𝔽₂)
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃² ◁ C₂³×C₃²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×#638	C₂	semidirect
2. C₂×C₃³×#67	C₂	semidirect
3. C₃²×#3811	C₂	semidirect
4. C₃²×D₃×#67	C₂	semidirect
5. C₃²×#3805	C₂	semidirect
6. C₃²×#3804	C₂	semidirect
8. C₃×#64330	C₃	direct (N × H)
9. C₂³×C₃⁴	C₂²	semidirect
10. C₂²×C₃²×C₃⋊D₃	C₂²	semidirect
11. C₂²×C₃³×D₃	C₂²	semidirect
12. C₂×C₃²×D₃²	C₂²	semidirect
13. C₃²×#638	C₂²	semidirect
14. C₂×C₃²×C₃⋊Dic₃	C₂²	semidirect
15. C₃³×#67	C₂²	semidirect
16. C₃³×#67	C₂²	semidirect
17. C₂×C₃³×Dic₃	C₂²	semidirect
18. C₃²×#627	C₂²	semidirect
19. C₃²×#626	C₂²	semidirect
20. C₃²×#625	C₂²	semidirect
21. C₃²×#624	C₂²	semidirect
22. C₃²×D₃×Dic₃	C₂²	semidirect
24. C₂×C₃×#638	C₂×C₃	semidirect
29. C₂×C₃²×#67	D₃	semidirect
30. C₂×C₃²×#67	C₂×C₃	semidirect
36. C₃×#3811	C₂×C₃	semidirect
37. C₃×D₃×#67	C₂×C₃	semidirect
38. C₃×#3805	C₂×C₃	semidirect
39. C₃×#3804	C₂×C₃	semidirect
52. #64330	C₃²	direct (N × H)
57. C₂³×C₃³	C₂×D₃	semidirect
58. C₂³×C₃³	C₂²×C₃	semidirect
59. C₂²×C₃×C₃⋊D₃	C₂²×C₃	semidirect
64. C₂²×C₃²×D₃	C₂×D₃	semidirect
65. C₂²×C₃²×D₃	C₂²×C₃	semidirect
66. C₂×C₃×D₃²	C₂²×C₃	semidirect
70. C₃×#638	C₂²×C₃	semidirect
71. C₂×C₃×C₃⋊Dic₃	C₂²×C₃	semidirect
79. C₃²×#67	C₂×D₃	semidirect
80. C₃²×#67	C₂×D₃	semidirect
81. C₃²×#67	C₂²×C₃	semidirect
82. C₃²×#67	C₂²×C₃	semidirect
87. C₂×C₃²×Dic₃	C₂×D₃	semidirect
88. C₂×C₃²×Dic₃	C₂²×C₃	semidirect
93. C₃×#627	C₂²×C₃	semidirect
94. C₃×#626	C₂²×C₃	semidirect
95. C₃×#625	C₂²×C₃	semidirect
96. C₃×#624	C₂²×C₃	semidirect
97. C₃×D₃×Dic₃	C₂²×C₃	semidirect
111. C₂×#638	C₂×C₃²	semidirect
116. C₂×C₃×#67	C₃×D₃	semidirect
117. C₂×C₃×#67	C₂×C₃²	semidirect
123. #3811	C₂×C₃²	semidirect
124. D₃×#67	C₂×C₃²	semidirect
125. #3805	C₂×C₃²	semidirect
126. #3804	C₂×C₃²	semidirect
169. C₃⁴	H(5,𝔽₂)	semidirect
181. C₂³×C₃²	D₃²	semidirect
182. C₂³×C₃²	C₂×C₃×D₃	semidirect
183. C₂³×C₃²	C₂²×C₃²	semidirect
184. C₂²×C₃⋊D₃	C₂²×C₃²	semidirect
189. C₂²×C₃×D₃	C₂×C₃×D₃	semidirect
190. C₂²×C₃×D₃	C₂²×C₃²	semidirect
191. C₂×D₃²	C₂²×C₃²	semidirect
208. #638	C₂²×C₃²	semidirect
209. C₂×C₃⋊Dic₃	C₂²×C₃²	semidirect
217. C₃×#67	C₂×C₃×D₃	semidirect
218. C₃×#67	C₂×C₃×D₃	semidirect
219. C₃×#67	C₂²×C₃²	semidirect
220. C₃×#67	C₂²×C₃²	semidirect
225. C₂×C₃×Dic₃	C₂×C₃×D₃	semidirect
226. C₂×C₃×Dic₃	C₂²×C₃²	semidirect
231. #627	C₂²×C₃²	semidirect
232. #626	C₂²×C₃²	semidirect
233. #625	C₂²×C₃²	semidirect
234. #624	C₂²×C₃²	semidirect
235. D₃×Dic₃	C₂²×C₃²	semidirect
271. C₂×#67	C₃²×D₃	semidirect
344. C₃³	#1004	semidirect
345. C₃³	C₃×H(5,𝔽₂)	semidirect
354. C₂³×C₃	C₃×D₃²	semidirect
355. C₂³×C₃	C₂×C₃²×D₃	semidirect
359. C₂²×D₃	C₂×C₃²×D₃	semidirect
381. #67	C₂×C₃²×D₃	semidirect
382. #67	C₂×C₃²×D₃	semidirect
386. C₂×Dic₃	C₂×C₃²×D₃	semidirect
483. C₃²	#64330	direct (N × H)
484. C₃²	C₃×#1004	semidirect
485. C₃²	C₃²×H(5,𝔽₂)	semidirect
489. C₂³	C₃²×D₃²	semidirect
537. C₃	C₃×#64330	direct (N × H)
538. C₃	C₃²×#1004	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×#638	2
C₂×C₃³×#67	2
C₃²×#3811	2
C₃²×D₃×#67	2
C₃²×#3805	2
C₃²×#3804	2
C₃²×#1004	3
C₃×#64330	3

Subgroups — C32×#64330 #72220352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#64330 #72220352