Subgroups — C₂×#14555440 #72244227

Order 4374.

12040 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14555440	C₂	1	1	yes	maximal, characteristic, direct product factor, Sylow
2	C₂×C₃×3₋¹⁺⁴	C₃	1	3	yes	maximal, complemented
3	C₂×C₃×3₋¹⁺⁴	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#10624936	C₃	1	27	yes	maximal, complemented
5	C₂×#10624935	C₃	1	27	yes	maximal, complemented
6	C₂×#10624934	C₃	1	27	yes	maximal, complemented
7	C₂×#10624929	C₃	1	27	yes	maximal, complemented
8	C₂×C₃×#6912	C₃	1	2	yes	maximal, complemented
9	C₂×C₃×#6911	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#6910	C₃	1	3	yes	maximal, complemented
11	C₂×C₃×#6909	C₃	1	3	yes	maximal, complemented
12	C₃×3₋¹⁺⁴	C₂×C₃	1	3	yes	complemented
13	C₃×3₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
14	#10624936	C₂×C₃	1	27	yes	complemented
15	#10624935	C₂×C₃	1	27	yes	complemented
16	#10624934	C₂×C₃	1	27	yes	complemented
17	#10624929	C₂×C₃	1	27	yes	complemented
18	C₃×#6912	C₂×C₃	1	2	yes	complemented
19	C₃×#6911	C₂×C₃	1	1	yes	characteristic, complemented
20	C₃×#6910	C₂×C₃	1	3	yes	complemented
21	C₃×#6909	C₂×C₃	1	3	yes	complemented
22	C₂×3₋¹⁺⁴	—	3	18	no	—
23	C₂×3₋¹⁺⁴	—	3	18	no	—
24	C₂×3₋¹⁺⁴	—	3	18	no	—
25	C₂×3₋¹⁺⁴	—	3	9	no	—
26	C₂×3₋¹⁺⁴	—	3	18	no	—
27	C₂×3₋¹⁺⁴	C₃²	1	27	yes	complemented
28	C₂×3₋¹⁺⁴	C₃²	1	27	yes	complemented
29	C₂×3₋¹⁺⁴	C₃²	1	27	yes	complemented
30	C₂×C₃×#737	—	3	18	no	—
31	C₂×C₃×#737	C₃²	1	27	yes	complemented
32	C₂×C₃×#737	C₃²	1	9	yes	complemented
33	C₂×C₃×#737	C₃²	1	9	yes	complemented
34	C₂×C₃×#737	C₃²	1	9	yes	complemented
35	C₂×C₃²×3₋¹⁺²	—	3	9	no	—
36	C₂×C₃²×3₋¹⁺²	C₃²	1	6	yes	—
37	C₂×C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
38	C₂×C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
39	C₂×C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
40	C₂×C₃²×3₋¹⁺²	C₃²	1	9	yes	complemented
41	C₂×C₃²×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
42	C₂×C₃²×H(3,𝔽₃)	C₃²	1	3	yes	—
43	C₂×#6913	C₃²	1	486	yes	complemented
44	C₂×#6912	C₃²	1	18	yes	complemented
45	C₂×#6912	C₃²	1	18	yes	complemented
46	C₂×#6912	C₃²	1	18	yes	complemented
47	C₂×#6911	C₃²	1	9	yes	—
48	C₂×#6911	C₃²	1	9	yes	complemented
49	C₂×#6911	C₃²	1	9	yes	complemented
50	C₂×#6910	C₃²	1	27	yes	complemented
51	C₂×#6910	C₃²	1	27	yes	complemented
52	C₂×#6910	C₃²	1	27	yes	complemented
53	C₂×#6909	C₃²	1	27	yes	complemented
54	C₂×#6909	C₃²	1	27	yes	complemented
55	C₂×#6909	C₃²	1	27	yes	complemented
56	C₂×#6908	C₃²	1	243	yes	complemented
57	C₂×C₃×#733	C₃²	1	18	yes	complemented
58	C₂×C₃×#732	C₃²	1	9	yes	complemented
59	C₂×C₃×#731	C₃²	1	27	yes	complemented
60	C₂×C₃×AΣL(1,𝔽₂₇)	C₃²	1	27	yes	complemented
61	3₋¹⁺⁴	—	3	18	no	—
62	3₋¹⁺⁴	—	3	18	no	—
63	3₋¹⁺⁴	—	3	18	no	—
64	3₋¹⁺⁴	—	3	9	no	—
65	3₋¹⁺⁴	—	3	18	no	—
66	3₋¹⁺⁴	C₂×C₃²	1	27	yes	complemented
67	3₋¹⁺⁴	C₂×C₃²	1	27	yes	complemented
68	3₋¹⁺⁴	C₂×C₃²	1	27	yes	complemented
69	C₃×#737	—	3	18	no	—
70	C₃×#737	C₂×C₃²	1	27	yes	complemented
71	C₃×#737	C₂×C₃²	1	9	yes	complemented
72	C₃×#737	C₂×C₃²	1	9	yes	complemented
73	C₃×#737	C₂×C₃²	1	9	yes	complemented
74	C₃²×3₋¹⁺²	—	3	9	no	—
75	C₃²×3₋¹⁺²	C₂×C₃²	1	6	yes	—
76	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
77	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
78	C₃²×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
79	C₃²×3₋¹⁺²	C₂×C₃²	1	9	yes	complemented
80	C₃²×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
81	C₃²×H(3,𝔽₃)	C₂×C₃²	1	3	yes	—
82	#6913	C₂×C₃²	1	486	yes	complemented
83	#6912	C₂×C₃²	1	18	yes	complemented
84	#6912	C₂×C₃²	1	18	yes	complemented
85	#6912	C₂×C₃²	1	18	yes	complemented
86	#6911	C₂×C₃²	1	9	yes	—
87	#6911	C₂×C₃²	1	9	yes	complemented
88	#6911	C₂×C₃²	1	9	yes	complemented
89	#6910	C₂×C₃²	1	27	yes	complemented
90	#6910	C₂×C₃²	1	27	yes	complemented
91	#6910	C₂×C₃²	1	27	yes	complemented
92	#6909	C₂×C₃²	1	27	yes	complemented
93	#6909	C₂×C₃²	1	27	yes	complemented
94	#6909	C₂×C₃²	1	27	yes	complemented
95	#6908	C₂×C₃²	1	243	yes	complemented
96	C₃×#733	C₂×C₃²	1	18	yes	complemented
97	C₃×#732	C₂×C₃²	1	9	yes	complemented
98	C₃×#731	C₂×C₃²	1	27	yes	complemented
99	C₃×AΣL(1,𝔽₂₇)	C₂×C₃²	1	27	yes	complemented
100	C₂×C₃⁴	—	3	3	no	—
101	C₂×C₃⁴	C₃³	1	3	yes	—
102	C₂×C₃⁴	C₃³	1	1	yes	characteristic
103	C₂×#737	—	3	162	no	—
104	C₂×#737	—	3	162	no	—
105	C₂×#737	—	3	162	no	—
106	C₂×#737	—	3	27	no	—
107	C₂×#737	—	3	81	no	—
108	C₂×#737	—	3	54	no	—
109	C₂×#737	—	3	162	no	—
110	C₂×#737	—	3	81	no	—
111	C₂×#737	C₃³	1	243	yes	complemented
112	C₂×C₃×3₋¹⁺²	—	3	6	no	—
113	C₂×C₃×3₋¹⁺²	—	3	6	no	—
114	C₂×C₃×3₋¹⁺²	—	3	6	no	—
115	C₂×C₃×3₋¹⁺²	—	3	6	no	—
116	C₂×C₃×3₋¹⁺²	—	3	6	no	—
117	C₂×C₃×3₋¹⁺²	—	3	6	no	—
118	C₂×C₃×3₋¹⁺²	—	3	6	no	—
119	C₂×C₃×3₋¹⁺²	—	3	6	no	—
120	C₂×C₃×3₋¹⁺²	—	3	6	no	—
121	C₂×C₃×3₋¹⁺²	—	3	6	no	—
122	C₂×C₃×3₋¹⁺²	—	3	3	no	—
123	C₂×C₃×3₋¹⁺²	—	3	3	no	—
124	C₂×C₃×3₋¹⁺²	—	3	81	no	—
125	C₂×C₃×3₋¹⁺²	—	3	81	no	—
126	C₂×C₃×3₋¹⁺²	—	3	81	no	—
127	C₂×C₃×3₋¹⁺²	—	3	81	no	—
128	C₂×C₃×3₋¹⁺²	—	3	54	no	—
129	C₂×C₃×3₋¹⁺²	H(3,𝔽₃)	1	9	yes	—
130	C₂×C₃×3₋¹⁺²	H(3,𝔽₃)	1	18	yes	—
131	C₂×C₃×3₋¹⁺²	C₃³	1	18	yes	—
132	C₂×C₃×3₋¹⁺²	C₃³	1	18	yes	—
133	C₂×C₃×3₋¹⁺²	C₃³	1	18	yes	—
134	C₂×C₃×3₋¹⁺²	C₃³	1	18	yes	—
135	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
136	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
137	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
138	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
139	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
140	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
141	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
142	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
143	C₂×C₃×3₋¹⁺²	C₃³	1	3	yes	—
144	C₂×C₃×3₋¹⁺²	C₃³	1	54	yes	complemented
145	C₂×C₃×H(3,𝔽₃)	—	3	6	no	—
146	C₂×C₃×H(3,𝔽₃)	—	3	6	no	—
147	C₂×C₃×H(3,𝔽₃)	—	3	3	no	—
148	C₂×C₃×H(3,𝔽₃)	—	3	6	no	—
149	C₂×C₃×H(3,𝔽₃)	—	3	6	no	—
150	C₂×C₃×H(3,𝔽₃)	—	3	6	no	—
151	C₂×C₃×H(3,𝔽₃)	C₃³	1	3	yes	—
152	C₂×C₃×H(3,𝔽₃)	C₃³	1	3	yes	—
153	C₂×C₃×H(3,𝔽₃)	C₃³	1	3	yes	—
154	C₂×C₃×H(3,𝔽₃)	C₃³	1	9	yes	—
155	C₂×C₃×H(3,𝔽₃)	C₃³	1	9	yes	—
156	C₂×C₃×H(3,𝔽₃)	C₃³	1	9	yes	—
157	C₂×C₃×H(3,𝔽₃)	C₃³	1	9	yes	—
158	C₂×C₃²×C₉	—	3	6	no	—
159	C₂×C₃²×C₉	—	3	27	no	—
160	C₂×C₃²×C₉	C₃³	1	3	yes	—
161	C₂×C₃²×C₉	C₃³	1	3	yes	—
162	C₂×C₃²×C₉	C₃³	1	3	yes	—
163	C₂×C₃²×C₉	C₃³	1	27	yes	complemented
164	C₂×#733	C₃³	1	162	yes	complemented
165	C₂×#732	C₃³	1	81	yes	—
166	C₂×#731	C₃³	1	243	yes	complemented
167	C₂×AΣL(1,𝔽₂₇)	C₃³	1	243	yes	complemented
168	C₃⁴	—	3	3	no	—
169	C₃⁴	C₂×C₃³	1	3	yes	—
170	C₃⁴	C₂×C₃³	1	1	yes	characteristic
171	#737	—	3	162	no	—
172	#737	—	3	162	no	—
173	#737	—	3	162	no	—
174	#737	—	3	27	no	—
175	#737	—	3	81	no	—
176	#737	—	3	54	no	—
177	#737	—	3	162	no	—
178	#737	—	3	81	no	—
179	#737	C₂×C₃³	1	243	yes	complemented
180	C₃×3₋¹⁺²	—	3	6	no	—
181	C₃×3₋¹⁺²	—	3	6	no	—
182	C₃×3₋¹⁺²	—	3	6	no	—
183	C₃×3₋¹⁺²	—	3	6	no	—
184	C₃×3₋¹⁺²	—	3	6	no	—
185	C₃×3₋¹⁺²	—	3	6	no	—
186	C₃×3₋¹⁺²	—	3	6	no	—
187	C₃×3₋¹⁺²	—	3	6	no	—
188	C₃×3₋¹⁺²	—	3	6	no	—
189	C₃×3₋¹⁺²	—	3	6	no	—
190	C₃×3₋¹⁺²	—	3	3	no	—
191	C₃×3₋¹⁺²	—	3	3	no	—
192	C₃×3₋¹⁺²	—	3	81	no	—
193	C₃×3₋¹⁺²	—	3	81	no	—
194	C₃×3₋¹⁺²	—	3	81	no	—
195	C₃×3₋¹⁺²	—	3	81	no	—
196	C₃×3₋¹⁺²	—	3	54	no	—
197	C₃×3₋¹⁺²	C₂×H(3,𝔽₃)	1	9	yes	—
198	C₃×3₋¹⁺²	C₂×H(3,𝔽₃)	1	18	yes	—
199	C₃×3₋¹⁺²	C₂×C₃³	1	18	yes	—
200	C₃×3₋¹⁺²	C₂×C₃³	1	18	yes	—
201	C₃×3₋¹⁺²	C₂×C₃³	1	18	yes	—
202	C₃×3₋¹⁺²	C₂×C₃³	1	18	yes	—
203	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
204	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
205	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
206	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
207	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
208	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
209	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
210	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
211	C₃×3₋¹⁺²	C₂×C₃³	1	3	yes	—
212	C₃×3₋¹⁺²	C₂×C₃³	1	54	yes	complemented
213	C₃×H(3,𝔽₃)	—	3	6	no	—
214	C₃×H(3,𝔽₃)	—	3	6	no	—
215	C₃×H(3,𝔽₃)	—	3	3	no	—
216	C₃×H(3,𝔽₃)	—	3	6	no	—
217	C₃×H(3,𝔽₃)	—	3	6	no	—
218	C₃×H(3,𝔽₃)	—	3	6	no	—
219	C₃×H(3,𝔽₃)	C₂×C₃³	1	3	yes	—
220	C₃×H(3,𝔽₃)	C₂×C₃³	1	3	yes	—
221	C₃×H(3,𝔽₃)	C₂×C₃³	1	3	yes	—
222	C₃×H(3,𝔽₃)	C₂×C₃³	1	9	yes	—
223	C₃×H(3,𝔽₃)	C₂×C₃³	1	9	yes	—
224	C₃×H(3,𝔽₃)	C₂×C₃³	1	9	yes	—
225	C₃×H(3,𝔽₃)	C₂×C₃³	1	9	yes	—
226	C₃²×C₉	—	3	6	no	—
227	C₃²×C₉	—	3	27	no	—
228	C₃²×C₉	C₂×C₃³	1	3	yes	—
229	C₃²×C₉	C₂×C₃³	1	3	yes	—
230	C₃²×C₉	C₂×C₃³	1	3	yes	—
231	C₃²×C₉	C₂×C₃³	1	27	yes	complemented
232	#733	C₂×C₃³	1	162	yes	complemented
233	#732	C₂×C₃³	1	81	yes	—
234	#731	C₂×C₃³	1	243	yes	complemented
235	AΣL(1,𝔽₂₇)	C₂×C₃³	1	243	yes	complemented
236	C₂×C₃³	—	3	9	no	—
237	C₂×C₃³	—	3	9	no	—
238	C₂×C₃³	—	3	9	no	—
239	C₂×C₃³	—	3	9	no	—
240	C₂×C₃³	—	3	9	no	—
241	C₂×C₃³	—	27	1	no	—
242	C₂×C₃³	—	27	9	no	—
243	C₂×C₃³	—	27	3	no	—
244	C₂×C₃³	C₃×H(3,𝔽₃)	1	6	yes	—
245	C₂×C₃³	C₃×H(3,𝔽₃)	1	3	yes	—
246	C₂×C₃³	C₃⁴	1	9	yes	—
247	C₂×C₃³	C₃⁴	1	1	yes	characteristic
248	C₂×C₃³	C₃⁴	1	1	yes	characteristic
249	C₂×C₃³	C₃⁴	1	1	yes	characteristic
250	C₂×C₃³	C₃⁴	1	1	yes	characteristic
251	C₂×3₋¹⁺²	—	3	18	no	—
252	C₂×3₋¹⁺²	—	3	18	no	—
253	C₂×3₋¹⁺²	—	3	18	no	—
254	C₂×3₋¹⁺²	—	3	9	no	—
255	C₂×3₋¹⁺²	—	3	9	no	—
256	C₂×3₋¹⁺²	—	3	18	no	—
257	C₂×3₋¹⁺²	—	3	18	no	—
258	C₂×3₋¹⁺²	—	3	18	no	—
259	C₂×3₋¹⁺²	—	3	18	no	—
260	C₂×3₋¹⁺²	—	3	18	no	—
261	C₂×3₋¹⁺²	—	3	6	no	—
262	C₂×3₋¹⁺²	—	3	9	no	—
263	C₂×3₋¹⁺²	—	3	9	no	—
264	C₂×3₋¹⁺²	—	3	9	no	—
265	C₂×3₋¹⁺²	—	3	3	no	—
266	C₂×3₋¹⁺²	—	3	486	no	—
267	C₂×3₋¹⁺²	—	3	162	no	—
268	C₂×3₋¹⁺²	C₃×H(3,𝔽₃)	1	9	yes	—
269	C₂×3₋¹⁺²	C₃×H(3,𝔽₃)	1	27	yes	—
270	C₂×3₋¹⁺²	C₃×H(3,𝔽₃)	1	27	yes	—
271	C₂×3₋¹⁺²	C₃×H(3,𝔽₃)	1	18	yes	—
272	C₂×3₋¹⁺²	C₃⁴	1	54	yes	—
273	C₂×H(3,𝔽₃)	—	3	6	no	—
274	C₂×H(3,𝔽₃)	—	3	9	no	—
275	C₂×H(3,𝔽₃)	—	3	9	no	—
276	C₂×H(3,𝔽₃)	—	3	3	no	—
277	C₂×H(3,𝔽₃)	—	3	18	no	—
278	C₂×H(3,𝔽₃)	—	3	18	no	—
279	C₂×H(3,𝔽₃)	—	3	18	no	—
280	C₂×H(3,𝔽₃)	—	3	18	no	—
281	C₂×H(3,𝔽₃)	C₃⁴	1	27	yes	—
282	C₂×C₃×C₉	—	3	18	no	—
283	C₂×C₃×C₉	—	3	18	no	—
284	C₂×C₃×C₉	—	3	18	no	—
285	C₂×C₃×C₉	—	3	18	no	—
286	C₂×C₃×C₉	—	3	6	no	—
287	C₂×C₃×C₉	—	3	9	no	—
288	C₂×C₃×C₉	—	3	3	no	—
289	C₂×C₃×C₉	—	3	243	no	—
290	C₂×C₃×C₉	—	3	81	no	—
291	C₂×C₃×C₉	C₃×H(3,𝔽₃)	1	27	yes	—
292	C₂×C₃×C₉	C₃⁴	1	9	yes	—
293	C₂×C₃×C₉	C₃⁴	1	9	yes	—
294	C₂×C₃×C₉	C₃⁴	1	9	yes	—
295	C₃³	—	3	9	no	—
296	C₃³	—	3	9	no	—
297	C₃³	—	3	9	no	—
298	C₃³	—	3	9	no	—
299	C₃³	—	3	9	no	—
300	C₃³	—	27	1	no	—
301	C₃³	—	27	3	no	—
302	C₃³	—	27	9	no	—
303	C₃³	C₂×C₃×H(3,𝔽₃)	1	6	yes	—
304	C₃³	C₂×C₃×H(3,𝔽₃)	1	3	yes	—
305	C₃³	C₂×C₃⁴	1	9	yes	—
306	C₃³	C₂×C₃⁴	1	1	yes	characteristic
307	C₃³	C₂×C₃⁴	1	1	yes	characteristic
308	C₃³	C₂×C₃⁴	1	1	yes	characteristic
309	C₃³	C₂×C₃⁴	1	1	yes	characteristic
310	3₋¹⁺²	—	3	18	no	—
311	3₋¹⁺²	—	3	18	no	—
312	3₋¹⁺²	—	3	18	no	—
313	3₋¹⁺²	—	3	9	no	—
314	3₋¹⁺²	—	3	9	no	—
315	3₋¹⁺²	—	3	18	no	—
316	3₋¹⁺²	—	3	18	no	—
317	3₋¹⁺²	—	3	18	no	—
318	3₋¹⁺²	—	3	18	no	—
319	3₋¹⁺²	—	3	18	no	—
320	3₋¹⁺²	—	3	6	no	—
321	3₋¹⁺²	—	3	9	no	—
322	3₋¹⁺²	—	3	9	no	—
323	3₋¹⁺²	—	3	9	no	—
324	3₋¹⁺²	—	3	3	no	—
325	3₋¹⁺²	—	3	486	no	—
326	3₋¹⁺²	—	3	162	no	—
327	3₋¹⁺²	C₂×C₃×H(3,𝔽₃)	1	9	yes	—
328	3₋¹⁺²	C₂×C₃×H(3,𝔽₃)	1	27	yes	—
329	3₋¹⁺²	C₂×C₃×H(3,𝔽₃)	1	27	yes	—
330	3₋¹⁺²	C₂×C₃×H(3,𝔽₃)	1	18	yes	—
331	3₋¹⁺²	C₂×C₃⁴	1	54	yes	—
332	H(3,𝔽₃)	—	3	6	no	—
333	H(3,𝔽₃)	—	3	9	no	—
334	H(3,𝔽₃)	—	3	9	no	—
335	H(3,𝔽₃)	—	3	3	no	—
336	H(3,𝔽₃)	—	3	18	no	—
337	H(3,𝔽₃)	—	3	18	no	—
338	H(3,𝔽₃)	—	3	18	no	—
339	H(3,𝔽₃)	—	3	18	no	—
340	H(3,𝔽₃)	C₂×C₃⁴	1	27	yes	—
341	C₃×C₉	—	3	18	no	—
342	C₃×C₉	—	3	18	no	—
343	C₃×C₉	—	3	18	no	—
344	C₃×C₉	—	3	18	no	—
345	C₃×C₉	—	3	6	no	—
346	C₃×C₉	—	3	9	no	—
347	C₃×C₉	—	3	3	no	—
348	C₃×C₉	—	3	243	no	—
349	C₃×C₉	—	3	81	no	—
350	C₃×C₉	C₂×C₃×H(3,𝔽₃)	1	27	yes	—
351	C₃×C₉	C₂×C₃⁴	1	9	yes	—
352	C₃×C₉	C₂×C₃⁴	1	9	yes	—
353	C₃×C₉	C₂×C₃⁴	1	9	yes	—
354	C₂×C₃²	—	3	9	no	—
355	C₂×C₃²	—	3	27	no	—
356	C₂×C₃²	—	9	3	no	—
357	C₂×C₃²	—	9	1	no	—
358	C₂×C₃²	—	9	6	no	—
359	C₂×C₃²	—	9	1	no	—
360	C₂×C₃²	—	9	1	no	—
361	C₂×C₃²	—	9	1	no	—
362	C₂×C₃²	—	9	27	no	—
363	C₂×C₃²	—	9	9	no	—
364	C₂×C₃²	—	27	9	no	—
365	C₂×C₃²	—	27	9	no	—
366	C₂×C₃²	—	27	9	no	—
367	C₂×C₃²	—	27	9	no	—
368	C₂×C₃²	C₃²×H(3,𝔽₃)	1	2	yes	—
369	C₂×C₃²	C₃²×H(3,𝔽₃)	1	3	yes	—
370	C₂×C₃²	C₃²×H(3,𝔽₃)	1	3	yes	—
371	C₂×C₃²	C₃²×H(3,𝔽₃)	1	3	yes	—
372	C₂×C₃²	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
373	C₂×C₃²	C₃⁵	1	1	yes	characteristic
374	C₂×C₉	—	3	54	no	—
375	C₂×C₉	—	3	9	no	—
376	C₂×C₉	—	3	9	no	—
377	C₂×C₉	C₃²×H(3,𝔽₃)	1	27	yes	—
378	C₃²	—	3	9	no	—
379	C₃²	—	3	27	no	—
380	C₃²	—	9	3	no	—
381	C₃²	—	9	1	no	—
382	C₃²	—	9	6	no	—
383	C₃²	—	9	1	no	—
384	C₃²	—	9	1	no	—
385	C₃²	—	9	1	no	—
386	C₃²	—	9	9	no	—
387	C₃²	—	9	27	no	—
388	C₃²	—	27	9	no	—
389	C₃²	—	27	9	no	—
390	C₃²	—	27	9	no	—
391	C₃²	—	27	9	no	—
392	C₃²	C₂×C₃²×H(3,𝔽₃)	1	2	yes	—
393	C₃²	C₂×C₃²×H(3,𝔽₃)	1	3	yes	—
394	C₃²	C₂×C₃²×H(3,𝔽₃)	1	3	yes	—
395	C₃²	C₂×C₃²×H(3,𝔽₃)	1	3	yes	—
396	C₃²	C₂×C₃²×H(3,𝔽₃)	1	1	yes	characteristic
397	C₃²	C₂×C₃⁵	1	1	yes	characteristic
398	C₉	—	3	54	no	—
399	C₉	—	3	9	no	—
400	C₉	—	3	9	no	—
401	C₉	C₂×C₃²×H(3,𝔽₃)	1	27	yes	—
402	C₂×C₃	—	3	3	no	—
403	C₂×C₃	—	3	1	no	—
404	C₂×C₃	—	3	1	no	—
405	C₂×C₃	—	3	3	no	—
406	C₂×C₃	—	3	3	no	—
407	C₂×C₃	—	3	2	no	—
408	C₂×C₃	—	9	27	no	—
409	C₂×C₃	—	9	9	no	—
410	C₂×C₃	C₃³×H(3,𝔽₃)	1	1	yes	characteristic
411	C₃	—	3	1	no	—
412	C₃	—	3	3	no	—
413	C₃	—	3	1	no	—
414	C₃	—	3	3	no	—
415	C₃	—	3	3	no	—
416	C₃	—	3	2	no	—
417	C₃	—	9	27	no	—
418	C₃	—	9	9	no	—
419	C₃	C₂×C₃³×H(3,𝔽₃)	1	1	yes	characteristic
420	C₂	#14555440	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, socle	C₂×C₃	C₃³×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃²	C₂×C₃⁵
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃²×3₋¹⁺² ◁ G

Complements

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

N	H ≅ G/N	type
1. #14555440	C₂	direct (N × H)
2. C₂×C₃×3₋¹⁺⁴	C₃	semidirect
3. C₂×C₃×3₋¹⁺⁴	C₃	semidirect
4. C₂×#10624936	C₃	semidirect
5. C₂×#10624935	C₃	semidirect
6. C₂×#10624934	C₃	semidirect
7. C₂×#10624929	C₃	semidirect
8. C₂×C₃×#6912	C₃	semidirect
9. C₂×C₃×#6911	C₃	semidirect
10. C₂×C₃×#6910	C₃	semidirect
11. C₂×C₃×#6909	C₃	semidirect
12. C₃×3₋¹⁺⁴	C₂×C₃	semidirect
13. C₃×3₋¹⁺⁴	C₂×C₃	semidirect
14. #10624936	C₂×C₃	semidirect
15. #10624935	C₂×C₃	semidirect
16. #10624934	C₂×C₃	semidirect
17. #10624929	C₂×C₃	semidirect
18. C₃×#6912	C₂×C₃	semidirect
19. C₃×#6911	C₂×C₃	semidirect
20. C₃×#6910	C₂×C₃	semidirect
21. C₃×#6909	C₂×C₃	semidirect
27. C₂×3₋¹⁺⁴	C₃²	semidirect
28. C₂×3₋¹⁺⁴	C₃²	semidirect
29. C₂×3₋¹⁺⁴	C₃²	semidirect
31. C₂×C₃×#737	C₃²	semidirect
32. C₂×C₃×#737	C₃²	semidirect
33. C₂×C₃×#737	C₃²	semidirect
34. C₂×C₃×#737	C₃²	semidirect
40. C₂×C₃²×3₋¹⁺²	C₃²	semidirect
43. C₂×#6913	C₃²	semidirect
44. C₂×#6912	C₃²	semidirect
45. C₂×#6912	C₃²	semidirect
46. C₂×#6912	C₃²	semidirect
48. C₂×#6911	C₃²	semidirect
49. C₂×#6911	C₃²	semidirect
50. C₂×#6910	C₃²	semidirect
51. C₂×#6910	C₃²	semidirect
52. C₂×#6910	C₃²	semidirect
53. C₂×#6909	C₃²	semidirect
54. C₂×#6909	C₃²	semidirect
55. C₂×#6909	C₃²	semidirect
56. C₂×#6908	C₃²	semidirect
57. C₂×C₃×#733	C₃²	semidirect
58. C₂×C₃×#732	C₃²	semidirect
59. C₂×C₃×#731	C₃²	semidirect
60. C₂×C₃×AΣL(1,𝔽₂₇)	C₃²	semidirect
66. 3₋¹⁺⁴	C₂×C₃²	semidirect
67. 3₋¹⁺⁴	C₂×C₃²	semidirect
68. 3₋¹⁺⁴	C₂×C₃²	semidirect
70. C₃×#737	C₂×C₃²	semidirect
71. C₃×#737	C₂×C₃²	semidirect
72. C₃×#737	C₂×C₃²	semidirect
73. C₃×#737	C₂×C₃²	semidirect
79. C₃²×3₋¹⁺²	C₂×C₃²	semidirect
82. #6913	C₂×C₃²	semidirect
83. #6912	C₂×C₃²	semidirect
84. #6912	C₂×C₃²	semidirect
85. #6912	C₂×C₃²	semidirect
87. #6911	C₂×C₃²	semidirect
88. #6911	C₂×C₃²	semidirect
89. #6910	C₂×C₃²	semidirect
90. #6910	C₂×C₃²	semidirect
91. #6910	C₂×C₃²	semidirect
92. #6909	C₂×C₃²	semidirect
93. #6909	C₂×C₃²	semidirect
94. #6909	C₂×C₃²	semidirect
95. #6908	C₂×C₃²	semidirect
96. C₃×#733	C₂×C₃²	semidirect
97. C₃×#732	C₂×C₃²	semidirect
98. C₃×#731	C₂×C₃²	semidirect
99. C₃×AΣL(1,𝔽₂₇)	C₂×C₃²	semidirect
111. C₂×#737	C₃³	semidirect
144. C₂×C₃×3₋¹⁺²	C₃³	semidirect
163. C₂×C₃²×C₉	C₃³	semidirect
164. C₂×#733	C₃³	semidirect
166. C₂×#731	C₃³	semidirect
167. C₂×AΣL(1,𝔽₂₇)	C₃³	semidirect
179. #737	C₂×C₃³	semidirect
212. C₃×3₋¹⁺²	C₂×C₃³	semidirect
231. C₃²×C₉	C₂×C₃³	semidirect
232. #733	C₂×C₃³	semidirect
234. #731	C₂×C₃³	semidirect
235. AΣL(1,𝔽₂₇)	C₂×C₃³	semidirect
420. C₂	#14555440	direct (N × H)

Maximal subgroups

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

subgroup	index
#14555440	2
C₂×C₃×3₋¹⁺⁴	3
C₂×#10624936	3
C₂×#10624935	3
C₂×#10624934	3
C₂×#10624929	3
C₂×C₃×#6912	3
C₂×C₃×#6911	3
C₂×C₃×#6910	3
C₂×C₃×#6909	3

Subgroups — C2×#14555440 #72244227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14555440 #72244227