Subgroups — C₂×C₃×#92283 #72254024

Order 2916.

1072 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#92283	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃×#6910	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#272	C₃	1	1	yes	maximal, characteristic
4	C₂×C₃×D₃×3₋¹⁺²	—	3	1	no	maximal
5	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
13	C₂×#92283	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×#4176	C₃	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#4176	C₃	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#4176	C₃	1	1	yes	maximal, characteristic, complemented
17	C₃×#6910	C₂²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃²×3₋¹⁺²	—	2	1	no	—
19	C₂×C₃²×3₋¹⁺²	D₃	1	1	yes	characteristic, complemented
20	C₂×C₃²×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
21	C₃²×#272	C₂×C₃	1	2	yes	—
22	C₃×D₃×3₋¹⁺²	—	3	2	no	—
23	C₂×#6910	—	2	1	no	—
24	C₂×#6910	—	2	1	no	—
25	C₂×#6910	—	2	1	no	—
26	C₂×#6910	—	2	1	no	—
27	C₂×#6910	—	2	1	no	—
28	C₂×#6910	—	2	1	no	—
29	C₂×#6910	—	2	1	no	—
30	C₂×#6910	—	2	1	no	—
31	C₂×#6910	—	2	1	no	—
32	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×#6910	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₃×#731	—	2	1	no	—
42	C₂×C₃×#731	—	2	1	no	—
43	C₂×C₃×#731	—	2	1	no	—
44	C₂×C₃×#731	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₃×#731	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₃×#731	C₂×C₃	1	1	yes	characteristic, complemented
47	#92283	C₂×C₃	1	2	yes	direct product factor
48	#92283	C₂×C₃	1	2	yes	direct product factor
49	#92283	C₂×C₃	1	2	yes	direct product factor
50	#92283	C₂×C₃	1	2	yes	direct product factor
51	#92283	C₂×C₃	1	2	yes	direct product factor
52	#92283	C₂×C₃	1	2	yes	direct product factor
53	#92283	C₂×C₃	1	2	yes	direct product factor
54	#92283	C₂×C₃	1	2	yes	direct product factor
55	#92283	C₂×C₃	1	2	yes	direct product factor
56	C₃×#4176	C₂×C₃	1	2	yes	complemented
57	C₃×#4176	C₂×C₃	1	2	yes	complemented
58	C₃×#4176	C₂×C₃	1	2	yes	complemented
59	C₂×C₃³×D₃	—	3	1	no	—
60	C₂×C₃³×D₃	—	9	1	no	—
61	C₂²×C₃×3₋¹⁺²	—	9	1	no	—
62	C₂×C₃×#272	C₃²	1	1	yes	characteristic
63	C₂×C₃×#272	C₃²	1	1	yes	characteristic
64	C₂×C₃×#272	C₃²	1	1	yes	characteristic
65	C₂×C₃×#272	C₃²	1	1	yes	characteristic
66	C₂×D₃×3₋¹⁺²	—	3	1	no	—
67	C₂×D₃×3₋¹⁺²	—	3	1	no	—
68	C₂×D₃×3₋¹⁺²	—	3	1	no	—
69	C₂×D₃×3₋¹⁺²	—	3	1	no	—
70	C₂×D₃×3₋¹⁺²	—	3	1	no	—
71	C₂×D₃×3₋¹⁺²	—	3	1	no	—
72	C₂×D₃×3₋¹⁺²	—	3	1	no	—
73	C₂×D₃×3₋¹⁺²	—	3	1	no	—
74	C₂×D₃×3₋¹⁺²	—	3	1	no	—
75	C₂×C₃×D₃×C₉	—	3	1	no	—
76	C₂×C₃×D₃×C₉	—	3	1	no	—
77	C₂×C₃×D₃×C₉	—	3	1	no	—
78	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
79	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
80	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
81	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
82	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
83	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
84	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
85	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
86	C₂×#4176	C₃²	1	1	yes	characteristic, complemented
87	C₃²×3₋¹⁺²	—	2	1	no	—
88	C₃²×3₋¹⁺²	C₂×D₃	1	1	yes	characteristic, complemented
89	C₃²×H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic
90	#6910	—	2	1	no	—
91	#6910	—	2	1	no	—
92	#6910	—	2	1	no	—
93	#6910	—	2	1	no	—
94	#6910	—	2	1	no	—
95	#6910	—	2	1	no	—
96	#6910	—	2	1	no	—
97	#6910	—	2	1	no	—
98	#6910	—	2	1	no	—
99	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
100	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
101	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
102	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
103	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
104	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
105	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
106	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
107	#6910	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₃×#731	—	2	1	no	—
109	C₃×#731	—	2	1	no	—
110	C₃×#731	—	2	1	no	—
111	C₃×#731	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₃×#731	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₃×#731	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₂×C₃⁴	—	3	1	no	—
115	C₂×C₃⁴	C₃×D₃	1	1	yes	characteristic
116	C₃³×D₃	—	3	2	no	—
117	C₃³×D₃	—	9	2	no	—
118	C₂×C₃×3₋¹⁺²	—	2	1	no	—
119	C₂×C₃×3₋¹⁺²	—	2	1	no	—
120	C₂×C₃×3₋¹⁺²	—	2	1	no	—
121	C₂×C₃×3₋¹⁺²	—	2	1	no	—
122	C₂×C₃×3₋¹⁺²	—	2	1	no	—
123	C₂×C₃×3₋¹⁺²	—	2	1	no	—
124	C₂×C₃×3₋¹⁺²	—	2	1	no	—
125	C₂×C₃×3₋¹⁺²	—	2	1	no	—
126	C₂×C₃×3₋¹⁺²	—	2	1	no	—
127	C₂×C₃×3₋¹⁺²	—	2	1	no	—
128	C₂×C₃×3₋¹⁺²	—	2	1	no	—
129	C₂×C₃×3₋¹⁺²	—	2	1	no	—
130	C₂×C₃×3₋¹⁺²	—	6	1	no	—
131	C₂×C₃×3₋¹⁺²	—	6	1	no	—
132	C₂×C₃×3₋¹⁺²	—	6	1	no	—
133	C₂×C₃×3₋¹⁺²	—	6	1	no	—
134	C₂×C₃×3₋¹⁺²	—	6	1	no	—
135	C₂×C₃×3₋¹⁺²	—	6	1	no	—
136	C₂×C₃×3₋¹⁺²	—	6	1	no	—
137	C₂×C₃×3₋¹⁺²	—	6	1	no	—
138	C₂×C₃×3₋¹⁺²	—	6	1	no	—
139	C₂×C₃×3₋¹⁺²	—	6	1	no	—
140	C₂×C₃×3₋¹⁺²	—	6	1	no	—
141	C₂×C₃×3₋¹⁺²	—	6	1	no	—
142	C₂×C₃×3₋¹⁺²	—	6	1	no	—
143	C₂×C₃×3₋¹⁺²	—	9	2	no	—
144	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
145	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
146	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
147	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
148	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
149	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
150	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
151	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
152	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
153	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
154	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
155	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
156	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
157	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
158	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
159	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
160	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
161	C₂×C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
162	C₂×C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
163	C₂×C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
164	C₂×C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
165	C₂×C₃²×C₉	—	6	1	no	—
166	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic, complemented
167	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic, complemented
168	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic, complemented
169	C₃×#272	C₂×C₃²	1	2	yes	—
170	C₃×#272	C₂×C₃²	1	2	yes	—
171	C₃×#272	C₂×C₃²	1	2	yes	—
172	C₃×#272	C₂×C₃²	1	2	yes	—
173	D₃×3₋¹⁺²	—	3	2	no	—
174	D₃×3₋¹⁺²	—	3	2	no	—
175	D₃×3₋¹⁺²	—	3	2	no	—
176	D₃×3₋¹⁺²	—	3	2	no	—
177	D₃×3₋¹⁺²	—	3	2	no	—
178	D₃×3₋¹⁺²	—	3	2	no	—
179	D₃×3₋¹⁺²	—	3	2	no	—
180	D₃×3₋¹⁺²	—	3	2	no	—
181	D₃×3₋¹⁺²	—	3	2	no	—
182	C₃×D₃×C₉	—	3	2	no	—
183	C₃×D₃×C₉	—	3	2	no	—
184	C₃×D₃×C₉	—	3	2	no	—
185	C₂×#731	—	2	1	no	—
186	C₂×#731	—	2	1	no	—
187	C₂×#731	—	2	1	no	—
188	C₂×#731	—	2	1	no	—
189	C₂×#731	—	2	1	no	—
190	C₂×#731	—	2	1	no	—
191	C₂×#731	—	2	1	no	—
192	C₂×#731	—	2	1	no	—
193	C₂×#731	—	2	1	no	—
194	C₂×#731	—	2	1	no	—
195	C₂×#731	—	2	1	no	—
196	C₂×#731	—	2	1	no	—
197	C₂×#731	—	2	1	no	—
198	C₂×#731	—	2	1	no	—
199	C₂×#731	—	2	1	no	—
200	C₂×#731	—	2	1	no	—
201	C₂×#731	—	2	1	no	—
202	C₂×#731	—	2	1	no	—
203	C₂×#731	—	2	1	no	—
204	C₂×#731	—	2	1	no	—
205	C₂×#731	—	2	1	no	—
206	C₂×#731	—	2	1	no	—
207	C₂×#731	—	2	1	no	—
208	C₂×#731	—	2	1	no	—
209	C₂×#731	—	2	1	no	—
210	C₂×#731	—	2	1	no	—
211	C₂×#731	—	2	1	no	—
212	C₂×#731	—	2	1	no	—
213	C₂×#731	—	2	1	no	—
214	C₂×#731	—	2	1	no	—
215	C₂×#731	—	2	1	no	—
216	C₂×#731	—	2	1	no	—
217	C₂×#731	—	2	1	no	—
218	C₂×#731	—	2	1	no	—
219	C₂×#731	—	2	1	no	—
220	C₂×#731	—	2	1	no	—
221	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
222	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
223	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
224	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
225	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
226	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
227	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
228	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
229	C₂×#731	C₂×C₃²	1	1	yes	characteristic, complemented
230	#4176	C₂×C₃²	1	2	yes	complemented
231	#4176	C₂×C₃²	1	2	yes	complemented
232	#4176	C₂×C₃²	1	2	yes	complemented
233	#4176	C₂×C₃²	1	2	yes	complemented
234	#4176	C₂×C₃²	1	2	yes	complemented
235	#4176	C₂×C₃²	1	2	yes	complemented
236	#4176	C₂×C₃²	1	2	yes	complemented
237	#4176	C₂×C₃²	1	2	yes	complemented
238	#4176	C₂×C₃²	1	2	yes	complemented
239	C₂²×C₃³	—	9	1	no	—
240	C₂×C₃²×D₃	—	3	1	no	—
241	C₂×C₃²×D₃	—	3	1	no	—
242	C₂×C₃²×D₃	—	3	1	no	—
243	C₂×C₃²×D₃	—	3	1	no	—
244	C₂×C₃²×D₃	—	9	1	no	—
245	C₂×C₃²×D₃	—	9	1	no	—
246	C₂×C₃²×D₃	—	9	1	no	—
247	C₂×C₃²×D₃	—	9	1	no	—
248	C₂×C₃²×D₃	—	9	1	no	—
249	C₂×C₃²×D₃	—	9	1	no	—
250	C₂×C₃²×D₃	—	9	1	no	—
251	C₂×C₃²×D₃	—	9	1	no	—
252	C₂×C₃²×D₃	—	9	1	no	—
253	C₂×C₃²×D₃	—	9	1	no	—
254	C₂×C₃²×D₃	—	9	1	no	—
255	C₂×C₃²×D₃	—	9	1	no	—
256	C₂×C₃²×D₃	—	9	1	no	—
257	C₂×C₃²×D₃	—	9	1	no	—
258	C₂×C₃²×D₃	—	9	1	no	—
259	C₂×C₃²×D₃	—	9	1	no	—
260	C₂²×3₋¹⁺²	—	9	1	no	—
261	C₂²×3₋¹⁺²	—	9	1	no	—
262	C₂²×3₋¹⁺²	—	9	1	no	—
263	C₂²×3₋¹⁺²	—	9	1	no	—
264	C₂²×3₋¹⁺²	—	9	1	no	—
265	C₂²×3₋¹⁺²	—	9	1	no	—
266	C₂²×3₋¹⁺²	—	9	1	no	—
267	C₂²×3₋¹⁺²	—	9	1	no	—
268	C₂²×3₋¹⁺²	—	9	1	no	—
269	C₂²×C₃×C₉	—	9	1	no	—
270	C₂²×C₃×C₉	—	9	1	no	—
271	C₂²×C₃×C₉	—	9	1	no	—
272	C₂×#272	C₃³	1	1	yes	characteristic
273	C₂×D₃×C₉	—	3	1	no	—
274	C₂×D₃×C₉	—	3	1	no	—
275	C₂×D₃×C₉	—	3	1	no	—
276	C₂×D₃×C₉	—	3	1	no	—
277	C₂×D₃×C₉	—	3	1	no	—
278	C₂×D₃×C₉	—	3	1	no	—
279	C₂×D₃×C₉	—	3	1	no	—
280	C₂×D₃×C₉	—	3	1	no	—
281	C₂×D₃×C₉	—	3	1	no	—
282	C₃⁴	—	3	1	no	—
283	C₃⁴	C₂×C₃×D₃	1	1	yes	characteristic
284	C₃×3₋¹⁺²	—	2	1	no	—
285	C₃×3₋¹⁺²	—	2	1	no	—
286	C₃×3₋¹⁺²	—	2	1	no	—
287	C₃×3₋¹⁺²	—	2	1	no	—
288	C₃×3₋¹⁺²	—	2	1	no	—
289	C₃×3₋¹⁺²	—	2	1	no	—
290	C₃×3₋¹⁺²	—	2	1	no	—
291	C₃×3₋¹⁺²	—	2	1	no	—
292	C₃×3₋¹⁺²	—	2	1	no	—
293	C₃×3₋¹⁺²	—	2	1	no	—
294	C₃×3₋¹⁺²	—	2	1	no	—
295	C₃×3₋¹⁺²	—	2	1	no	—
296	C₃×3₋¹⁺²	—	6	1	no	—
297	C₃×3₋¹⁺²	—	6	1	no	—
298	C₃×3₋¹⁺²	—	6	1	no	—
299	C₃×3₋¹⁺²	—	6	1	no	—
300	C₃×3₋¹⁺²	—	6	1	no	—
301	C₃×3₋¹⁺²	—	6	1	no	—
302	C₃×3₋¹⁺²	—	6	1	no	—
303	C₃×3₋¹⁺²	—	6	1	no	—
304	C₃×3₋¹⁺²	—	6	1	no	—
305	C₃×3₋¹⁺²	—	6	1	no	—
306	C₃×3₋¹⁺²	—	6	1	no	—
307	C₃×3₋¹⁺²	—	6	1	no	—
308	C₃×3₋¹⁺²	—	6	1	no	—
309	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
310	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
311	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
312	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
313	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
314	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
315	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
316	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
317	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
318	C₃×H(3,𝔽₃)	—	2	1	no	—
319	C₃×H(3,𝔽₃)	—	2	1	no	—
320	C₃×H(3,𝔽₃)	—	2	1	no	—
321	C₃×H(3,𝔽₃)	—	2	1	no	—
322	C₃×H(3,𝔽₃)	—	6	1	no	—
323	C₃×H(3,𝔽₃)	—	6	1	no	—
324	C₃×H(3,𝔽₃)	—	6	1	no	—
325	C₃×H(3,𝔽₃)	—	6	1	no	—
326	C₃×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
327	C₃×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
328	C₃×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
329	C₃×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
330	C₃²×C₉	—	6	1	no	—
331	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented
332	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented
333	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented
334	#731	—	2	1	no	—
335	#731	—	2	1	no	—
336	#731	—	2	1	no	—
337	#731	—	2	1	no	—
338	#731	—	2	1	no	—
339	#731	—	2	1	no	—
340	#731	—	2	1	no	—
341	#731	—	2	1	no	—
342	#731	—	2	1	no	—
343	#731	—	2	1	no	—
344	#731	—	2	1	no	—
345	#731	—	2	1	no	—
346	#731	—	2	1	no	—
347	#731	—	2	1	no	—
348	#731	—	2	1	no	—
349	#731	—	2	1	no	—
350	#731	—	2	1	no	—
351	#731	—	2	1	no	—
352	#731	—	2	1	no	—
353	#731	—	2	1	no	—
354	#731	—	2	1	no	—
355	#731	—	2	1	no	—
356	#731	—	2	1	no	—
357	#731	—	2	1	no	—
358	#731	—	2	1	no	—
359	#731	—	2	1	no	—
360	#731	—	2	1	no	—
361	#731	—	2	1	no	—
362	#731	—	2	1	no	—
363	#731	—	2	1	no	—
364	#731	—	2	1	no	—
365	#731	—	2	1	no	—
366	#731	—	2	1	no	—
367	#731	—	2	1	no	—
368	#731	—	2	1	no	—
369	#731	—	2	1	no	—
370	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
371	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
372	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
373	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
374	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
375	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
376	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
377	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
378	#731	C₂²×C₃²	1	1	yes	characteristic, complemented
379	C₂×C₃³	—	2	1	no	—
380	C₂×C₃³	—	2	1	no	—
381	C₂×C₃³	—	2	1	no	—
382	C₂×C₃³	—	2	1	no	—
383	C₂×C₃³	—	3	1	no	—
384	C₂×C₃³	—	3	1	no	—
385	C₂×C₃³	—	3	1	no	—
386	C₂×C₃³	—	3	1	no	—
387	C₂×C₃³	—	6	1	no	—
388	C₂×C₃³	—	6	1	no	—
389	C₂×C₃³	—	6	1	no	—
390	C₂×C₃³	—	6	1	no	—
391	C₂×C₃³	—	9	1	no	—
392	C₂×C₃³	—	9	1	no	—
393	C₂×C₃³	—	9	1	no	—
394	C₂×C₃³	—	9	1	no	—
395	C₂×C₃³	—	9	1	no	—
396	C₂×C₃³	—	9	1	no	—
397	C₂×C₃³	—	9	2	no	—
398	C₂×C₃³	—	18	1	no	—
399	C₂×C₃³	—	18	1	no	—
400	C₂×C₃³	—	18	1	no	—
401	C₂×C₃³	—	18	1	no	—
402	C₂×C₃³	—	18	1	no	—
403	C₂×C₃³	—	18	1	no	—
404	C₂×C₃³	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
405	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
406	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
407	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
408	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
409	C₃²×D₃	—	3	2	no	—
410	C₃²×D₃	—	3	2	no	—
411	C₃²×D₃	—	3	2	no	—
412	C₃²×D₃	—	3	2	no	—
413	C₃²×D₃	—	9	2	no	—
414	C₃²×D₃	—	9	2	no	—
415	C₃²×D₃	—	9	2	no	—
416	C₃²×D₃	—	9	2	no	—
417	C₃²×D₃	—	9	2	no	—
418	C₃²×D₃	—	9	2	no	—
419	C₃²×D₃	—	9	2	no	—
420	C₃²×D₃	—	9	2	no	—
421	C₃²×D₃	—	9	2	no	—
422	C₃²×D₃	—	9	2	no	—
423	C₃²×D₃	—	9	2	no	—
424	C₃²×D₃	—	9	2	no	—
425	C₃²×D₃	—	9	2	no	—
426	C₃²×D₃	—	9	2	no	—
427	C₃²×D₃	—	9	2	no	—
428	C₃²×D₃	—	9	2	no	—
429	C₂×3₋¹⁺²	—	2	1	no	—
430	C₂×3₋¹⁺²	—	2	1	no	—
431	C₂×3₋¹⁺²	—	2	1	no	—
432	C₂×3₋¹⁺²	—	2	1	no	—
433	C₂×3₋¹⁺²	—	2	1	no	—
434	C₂×3₋¹⁺²	—	2	1	no	—
435	C₂×3₋¹⁺²	—	2	1	no	—
436	C₂×3₋¹⁺²	—	2	1	no	—
437	C₂×3₋¹⁺²	—	2	1	no	—
438	C₂×3₋¹⁺²	—	3	1	no	—
439	C₂×3₋¹⁺²	—	6	1	no	—
440	C₂×3₋¹⁺²	—	6	1	no	—
441	C₂×3₋¹⁺²	—	6	1	no	—
442	C₂×3₋¹⁺²	—	6	1	no	—
443	C₂×3₋¹⁺²	—	6	1	no	—
444	C₂×3₋¹⁺²	—	6	1	no	—
445	C₂×3₋¹⁺²	—	6	1	no	—
446	C₂×3₋¹⁺²	—	6	1	no	—
447	C₂×3₋¹⁺²	—	6	1	no	—
448	C₂×3₋¹⁺²	—	6	1	no	—
449	C₂×3₋¹⁺²	—	6	1	no	—
450	C₂×3₋¹⁺²	—	6	1	no	—
451	C₂×3₋¹⁺²	—	6	1	no	—
452	C₂×3₋¹⁺²	—	6	1	no	—
453	C₂×3₋¹⁺²	—	6	1	no	—
454	C₂×3₋¹⁺²	—	6	1	no	—
455	C₂×3₋¹⁺²	—	6	1	no	—
456	C₂×3₋¹⁺²	—	6	1	no	—
457	C₂×3₋¹⁺²	—	6	1	no	—
458	C₂×3₋¹⁺²	—	6	1	no	—
459	C₂×3₋¹⁺²	—	6	1	no	—
460	C₂×3₋¹⁺²	—	6	1	no	—
461	C₂×3₋¹⁺²	—	6	1	no	—
462	C₂×3₋¹⁺²	—	6	1	no	—
463	C₂×3₋¹⁺²	—	6	1	no	—
464	C₂×3₋¹⁺²	—	6	1	no	—
465	C₂×3₋¹⁺²	—	6	1	no	—
466	C₂×3₋¹⁺²	—	6	1	no	—
467	C₂×3₋¹⁺²	—	6	1	no	—
468	C₂×3₋¹⁺²	—	6	1	no	—
469	C₂×3₋¹⁺²	—	6	1	no	—
470	C₂×3₋¹⁺²	—	6	1	no	—
471	C₂×3₋¹⁺²	—	6	1	no	—
472	C₂×3₋¹⁺²	—	6	1	no	—
473	C₂×3₋¹⁺²	—	6	1	no	—
474	C₂×3₋¹⁺²	—	6	1	no	—
475	C₂×3₋¹⁺²	—	6	1	no	—
476	C₂×3₋¹⁺²	—	6	1	no	—
477	C₂×3₋¹⁺²	—	6	1	no	—
478	C₂×3₋¹⁺²	—	6	1	no	—
479	C₂×3₋¹⁺²	—	6	1	no	—
480	C₂×3₋¹⁺²	—	9	2	no	—
481	C₂×3₋¹⁺²	—	9	2	no	—
482	C₂×3₋¹⁺²	—	9	2	no	—
483	C₂×3₋¹⁺²	—	9	2	no	—
484	C₂×3₋¹⁺²	—	9	2	no	—
485	C₂×3₋¹⁺²	—	9	2	no	—
486	C₂×3₋¹⁺²	—	9	2	no	—
487	C₂×3₋¹⁺²	—	9	2	no	—
488	C₂×3₋¹⁺²	—	9	2	no	—
489	C₂×H(3,𝔽₃)	—	2	1	no	—
490	C₂×H(3,𝔽₃)	—	2	1	no	—
491	C₂×H(3,𝔽₃)	—	2	1	no	—
492	C₂×H(3,𝔽₃)	—	2	1	no	—
493	C₂×H(3,𝔽₃)	—	6	1	no	—
494	C₂×H(3,𝔽₃)	—	6	1	no	—
495	C₂×H(3,𝔽₃)	—	6	1	no	—
496	C₂×H(3,𝔽₃)	—	6	1	no	—
497	C₂×H(3,𝔽₃)	—	6	2	no	—
498	C₂×H(3,𝔽₃)	—	6	2	no	—
499	C₂×H(3,𝔽₃)	—	6	2	no	—
500	C₂×H(3,𝔽₃)	—	6	2	no	—
501	C₂×H(3,𝔽₃)	C₂×C₃³	1	1	yes	characteristic
502	C₂×C₃×C₉	—	3	1	no	—
503	C₂×C₃×C₉	—	3	1	no	—
504	C₂×C₃×C₉	—	3	1	no	—
505	C₂×C₃×C₉	—	6	1	no	—
506	C₂×C₃×C₉	—	6	1	no	—
507	C₂×C₃×C₉	—	6	1	no	—
508	C₂×C₃×C₉	—	6	1	no	—
509	C₂×C₃×C₉	—	6	1	no	—
510	C₂×C₃×C₉	—	6	1	no	—
511	C₂×C₃×C₉	—	6	1	no	—
512	C₂×C₃×C₉	—	6	1	no	—
513	C₂×C₃×C₉	—	6	1	no	—
514	C₂×C₃×C₉	—	6	1	no	—
515	C₂×C₃×C₉	—	6	1	no	—
516	C₂×C₃×C₉	—	6	1	no	—
517	C₂×C₃×C₉	—	6	1	no	—
518	C₂×C₃×C₉	—	6	1	no	—
519	C₂×C₃×C₉	—	6	1	no	—
520	C₂×C₃×C₉	—	9	2	no	—
521	C₂×C₃×C₉	—	9	2	no	—
522	C₂×C₃×C₉	—	9	2	no	—
523	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
524	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
525	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
526	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
527	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
528	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
529	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
530	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
531	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic, complemented
532	#272	C₂×C₃³	1	2	yes	—
533	D₃×C₉	—	3	2	no	—
534	D₃×C₉	—	3	2	no	—
535	D₃×C₉	—	3	2	no	—
536	D₃×C₉	—	3	2	no	—
537	D₃×C₉	—	3	2	no	—
538	D₃×C₉	—	3	2	no	—
539	D₃×C₉	—	3	2	no	—
540	D₃×C₉	—	3	2	no	—
541	D₃×C₉	—	3	2	no	—
542	C₂²×C₃²	—	9	1	no	—
543	C₂²×C₃²	—	9	1	no	—
544	C₂²×C₃²	—	9	1	no	—
545	C₂²×C₃²	—	9	1	no	—
546	C₂²×C₃²	—	27	1	no	—
547	C₂²×C₃²	—	27	1	no	—
548	C₂²×C₃²	—	27	1	no	—
549	C₂×C₃×D₃	—	3	1	no	—
550	C₂×C₃×D₃	—	3	1	no	—
551	C₂×C₃×D₃	—	3	1	no	—
552	C₂×C₃×D₃	—	3	1	no	—
553	C₂×C₃×D₃	—	9	1	no	—
554	C₂×C₃×D₃	—	9	1	no	—
555	C₂×C₃×D₃	—	9	1	no	—
556	C₂×C₃×D₃	—	9	1	no	—
557	C₂×C₃×D₃	—	9	1	no	—
558	C₂×C₃×D₃	—	9	1	no	—
559	C₂×C₃×D₃	—	9	1	no	—
560	C₂×C₃×D₃	—	9	1	no	—
561	C₂×C₃×D₃	—	9	1	no	—
562	C₂×C₃×D₃	—	9	1	no	—
563	C₂×C₃×D₃	—	9	1	no	—
564	C₂×C₃×D₃	—	9	1	no	—
565	C₂×C₃×D₃	—	9	1	no	—
566	C₂×C₃×D₃	—	9	1	no	—
567	C₂×C₃×D₃	—	9	1	no	—
568	C₂×C₃×D₃	—	9	1	no	—
569	C₂²×C₉	—	9	1	no	—
570	C₂²×C₉	—	9	1	no	—
571	C₂²×C₉	—	9	1	no	—
572	C₂²×C₉	—	9	1	no	—
573	C₂²×C₉	—	9	1	no	—
574	C₂²×C₉	—	9	1	no	—
575	C₂²×C₉	—	9	1	no	—
576	C₂²×C₉	—	9	1	no	—
577	C₂²×C₉	—	9	1	no	—
578	C₃³	—	2	1	no	—
579	C₃³	—	2	1	no	—
580	C₃³	—	2	1	no	—
581	C₃³	—	2	1	no	—
582	C₃³	—	3	1	no	—
583	C₃³	—	3	1	no	—
584	C₃³	—	3	1	no	—
585	C₃³	—	3	1	no	—
586	C₃³	—	6	1	no	—
587	C₃³	—	6	1	no	—
588	C₃³	—	6	1	no	—
589	C₃³	—	6	1	no	—
590	C₃³	—	9	1	no	—
591	C₃³	—	9	1	no	—
592	C₃³	—	9	1	no	—
593	C₃³	—	9	1	no	—
594	C₃³	—	9	1	no	—
595	C₃³	—	9	1	no	—
596	C₃³	—	18	1	no	—
597	C₃³	—	18	1	no	—
598	C₃³	—	18	1	no	—
599	C₃³	—	18	1	no	—
600	C₃³	—	18	1	no	—
601	C₃³	—	18	1	no	—
602	C₃³	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
603	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
604	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
605	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
606	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
607	3₋¹⁺²	—	2	1	no	—
608	3₋¹⁺²	—	2	1	no	—
609	3₋¹⁺²	—	2	1	no	—
610	3₋¹⁺²	—	2	1	no	—
611	3₋¹⁺²	—	2	1	no	—
612	3₋¹⁺²	—	2	1	no	—
613	3₋¹⁺²	—	2	1	no	—
614	3₋¹⁺²	—	2	1	no	—
615	3₋¹⁺²	—	2	1	no	—
616	3₋¹⁺²	—	3	1	no	—
617	3₋¹⁺²	—	6	1	no	—
618	3₋¹⁺²	—	6	1	no	—
619	3₋¹⁺²	—	6	1	no	—
620	3₋¹⁺²	—	6	1	no	—
621	3₋¹⁺²	—	6	1	no	—
622	3₋¹⁺²	—	6	1	no	—
623	3₋¹⁺²	—	6	1	no	—
624	3₋¹⁺²	—	6	1	no	—
625	3₋¹⁺²	—	6	1	no	—
626	3₋¹⁺²	—	6	1	no	—
627	3₋¹⁺²	—	6	1	no	—
628	3₋¹⁺²	—	6	1	no	—
629	3₋¹⁺²	—	6	1	no	—
630	3₋¹⁺²	—	6	1	no	—
631	3₋¹⁺²	—	6	1	no	—
632	3₋¹⁺²	—	6	1	no	—
633	3₋¹⁺²	—	6	1	no	—
634	3₋¹⁺²	—	6	1	no	—
635	3₋¹⁺²	—	6	1	no	—
636	3₋¹⁺²	—	6	1	no	—
637	3₋¹⁺²	—	6	1	no	—
638	3₋¹⁺²	—	6	1	no	—
639	3₋¹⁺²	—	6	1	no	—
640	3₋¹⁺²	—	6	1	no	—
641	3₋¹⁺²	—	6	1	no	—
642	3₋¹⁺²	—	6	1	no	—
643	3₋¹⁺²	—	6	1	no	—
644	3₋¹⁺²	—	6	1	no	—
645	3₋¹⁺²	—	6	1	no	—
646	3₋¹⁺²	—	6	1	no	—
647	3₋¹⁺²	—	6	1	no	—
648	3₋¹⁺²	—	6	1	no	—
649	3₋¹⁺²	—	6	1	no	—
650	3₋¹⁺²	—	6	1	no	—
651	3₋¹⁺²	—	6	1	no	—
652	3₋¹⁺²	—	6	1	no	—
653	3₋¹⁺²	—	6	1	no	—
654	3₋¹⁺²	—	6	1	no	—
655	3₋¹⁺²	—	6	1	no	—
656	3₋¹⁺²	—	6	1	no	—
657	3₋¹⁺²	—	6	1	no	—
658	H(3,𝔽₃)	—	2	1	no	—
659	H(3,𝔽₃)	—	2	1	no	—
660	H(3,𝔽₃)	—	2	1	no	—
661	H(3,𝔽₃)	—	2	1	no	—
662	H(3,𝔽₃)	—	6	1	no	—
663	H(3,𝔽₃)	—	6	1	no	—
664	H(3,𝔽₃)	—	6	1	no	—
665	H(3,𝔽₃)	—	6	1	no	—
666	H(3,𝔽₃)	—	6	2	no	—
667	H(3,𝔽₃)	—	6	2	no	—
668	H(3,𝔽₃)	—	6	2	no	—
669	H(3,𝔽₃)	—	6	2	no	—
670	H(3,𝔽₃)	C₂²×C₃³	1	1	yes	characteristic
671	C₃×C₉	—	3	1	no	—
672	C₃×C₉	—	3	1	no	—
673	C₃×C₉	—	3	1	no	—
674	C₃×C₉	—	6	1	no	—
675	C₃×C₉	—	6	1	no	—
676	C₃×C₉	—	6	1	no	—
677	C₃×C₉	—	6	1	no	—
678	C₃×C₉	—	6	1	no	—
679	C₃×C₉	—	6	1	no	—
680	C₃×C₉	—	6	1	no	—
681	C₃×C₉	—	6	1	no	—
682	C₃×C₉	—	6	1	no	—
683	C₃×C₉	—	6	1	no	—
684	C₃×C₉	—	6	1	no	—
685	C₃×C₉	—	6	1	no	—
686	C₃×C₉	—	6	1	no	—
687	C₃×C₉	—	6	1	no	—
688	C₃×C₉	—	6	1	no	—
689	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
690	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
691	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
692	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
693	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
694	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
695	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
696	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
697	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
698	C₂×C₃²	—	2	1	no	—
699	C₂×C₃²	—	2	1	no	—
700	C₂×C₃²	—	2	1	no	—
701	C₂×C₃²	—	2	1	no	—
702	C₂×C₃²	—	3	1	no	—
703	C₂×C₃²	—	3	1	no	—
704	C₂×C₃²	—	3	1	no	—
705	C₂×C₃²	—	3	1	no	—
706	C₂×C₃²	—	3	1	no	—
707	C₂×C₃²	—	3	1	no	—
708	C₂×C₃²	—	6	1	no	—
709	C₂×C₃²	—	6	1	no	—
710	C₂×C₃²	—	6	1	no	—
711	C₂×C₃²	—	6	1	no	—
712	C₂×C₃²	—	6	1	no	—
713	C₂×C₃²	—	6	1	no	—
714	C₂×C₃²	—	6	1	no	—
715	C₂×C₃²	—	6	1	no	—
716	C₂×C₃²	—	9	1	no	—
717	C₂×C₃²	—	9	1	no	—
718	C₂×C₃²	—	9	1	no	—
719	C₂×C₃²	—	9	1	no	—
720	C₂×C₃²	—	9	2	no	—
721	C₂×C₃²	—	9	2	no	—
722	C₂×C₃²	—	9	2	no	—
723	C₂×C₃²	—	9	2	no	—
724	C₂×C₃²	—	9	1	no	—
725	C₂×C₃²	—	9	1	no	—
726	C₂×C₃²	—	18	1	no	—
727	C₂×C₃²	—	18	1	no	—
728	C₂×C₃²	—	18	1	no	—
729	C₂×C₃²	—	18	1	no	—
730	C₂×C₃²	—	18	1	no	—
731	C₂×C₃²	—	18	1	no	—
732	C₂×C₃²	—	18	1	no	—
733	C₂×C₃²	—	18	1	no	—
734	C₂×C₃²	—	18	1	no	—
735	C₂×C₃²	—	18	1	no	—
736	C₂×C₃²	—	18	1	no	—
737	C₂×C₃²	—	18	1	no	—
738	C₂×C₃²	—	18	1	no	—
739	C₂×C₃²	—	18	1	no	—
740	C₂×C₃²	—	18	1	no	—
741	C₂×C₃²	—	18	1	no	—
742	C₂×C₃²	—	18	1	no	—
743	C₂×C₃²	—	18	1	no	—
744	C₂×C₃²	—	18	1	no	—
745	C₂×C₃²	—	18	1	no	—
746	C₂×C₃²	—	18	1	no	—
747	C₂×C₃²	—	18	1	no	—
748	C₂×C₃²	—	18	1	no	—
749	C₂×C₃²	—	18	1	no	—
750	C₂×C₃²	—	27	2	no	—
751	C₂×C₃²	—	27	2	no	—
752	C₂×C₃²	—	27	2	no	—
753	C₂×C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
754	C₂×C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
755	C₂×C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
756	C₂×C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
757	C₂×C₃²	C₃³×D₃	1	1	yes	characteristic
758	C₃×D₃	—	3	2	no	—
759	C₃×D₃	—	3	2	no	—
760	C₃×D₃	—	3	2	no	—
761	C₃×D₃	—	3	2	no	—
762	C₃×D₃	—	9	2	no	—
763	C₃×D₃	—	9	2	no	—
764	C₃×D₃	—	9	2	no	—
765	C₃×D₃	—	9	2	no	—
766	C₃×D₃	—	9	2	no	—
767	C₃×D₃	—	9	2	no	—
768	C₃×D₃	—	9	2	no	—
769	C₃×D₃	—	9	2	no	—
770	C₃×D₃	—	9	2	no	—
771	C₃×D₃	—	9	2	no	—
772	C₃×D₃	—	9	2	no	—
773	C₃×D₃	—	9	2	no	—
774	C₃×D₃	—	9	2	no	—
775	C₃×D₃	—	9	2	no	—
776	C₃×D₃	—	9	2	no	—
777	C₃×D₃	—	9	2	no	—
778	C₂×C₉	—	3	1	no	—
779	C₂×C₉	—	3	1	no	—
780	C₂×C₉	—	3	1	no	—
781	C₂×C₉	—	3	1	no	—
782	C₂×C₉	—	6	1	no	—
783	C₂×C₉	—	6	1	no	—
784	C₂×C₉	—	6	1	no	—
785	C₂×C₉	—	6	1	no	—
786	C₂×C₉	—	6	1	no	—
787	C₂×C₉	—	6	1	no	—
788	C₂×C₉	—	6	1	no	—
789	C₂×C₉	—	6	1	no	—
790	C₂×C₉	—	6	1	no	—
791	C₂×C₉	—	6	1	no	—
792	C₂×C₉	—	6	1	no	—
793	C₂×C₉	—	6	1	no	—
794	C₂×C₉	—	6	1	no	—
795	C₂×C₉	—	6	1	no	—
796	C₂×C₉	—	9	2	no	—
797	C₂×C₉	—	9	2	no	—
798	C₂×C₉	—	9	2	no	—
799	C₂×C₉	—	9	2	no	—
800	C₂×C₉	—	9	2	no	—
801	C₂×C₉	—	9	2	no	—
802	C₂×C₉	—	9	2	no	—
803	C₂×C₉	—	9	2	no	—
804	C₂×C₉	—	9	2	no	—
805	C₂²×C₃	—	9	1	no	—
806	C₂²×C₃	—	9	1	no	—
807	C₂²×C₃	—	9	1	no	—
808	C₂²×C₃	—	9	1	no	—
809	C₂²×C₃	—	27	1	no	—
810	C₂²×C₃	—	27	1	no	—
811	C₂²×C₃	—	27	1	no	—
812	C₂×D₃	—	3	1	no	—
813	C₂×D₃	—	9	1	no	—
814	C₃²	—	2	1	no	—
815	C₃²	—	2	1	no	—
816	C₃²	—	2	1	no	—
817	C₃²	—	2	1	no	—
818	C₃²	—	3	1	no	—
819	C₃²	—	3	1	no	—
820	C₃²	—	3	1	no	—
821	C₃²	—	3	1	no	—
822	C₃²	—	3	1	no	—
823	C₃²	—	3	1	no	—
824	C₃²	—	6	1	no	—
825	C₃²	—	6	1	no	—
826	C₃²	—	6	1	no	—
827	C₃²	—	6	1	no	—
828	C₃²	—	6	1	no	—
829	C₃²	—	6	1	no	—
830	C₃²	—	6	1	no	—
831	C₃²	—	6	1	no	—
832	C₃²	—	9	1	no	—
833	C₃²	—	9	1	no	—
834	C₃²	—	9	1	no	—
835	C₃²	—	9	1	no	—
836	C₃²	—	9	1	no	—
837	C₃²	—	9	1	no	—
838	C₃²	—	18	1	no	—
839	C₃²	—	18	1	no	—
840	C₃²	—	18	1	no	—
841	C₃²	—	18	1	no	—
842	C₃²	—	18	1	no	—
843	C₃²	—	18	1	no	—
844	C₃²	—	18	1	no	—
845	C₃²	—	18	1	no	—
846	C₃²	—	18	1	no	—
847	C₃²	—	18	1	no	—
848	C₃²	—	18	1	no	—
849	C₃²	—	18	1	no	—
850	C₃²	—	18	1	no	—
851	C₃²	—	18	1	no	—
852	C₃²	—	18	1	no	—
853	C₃²	—	18	1	no	—
854	C₃²	—	18	1	no	—
855	C₃²	—	18	1	no	—
856	C₃²	—	18	1	no	—
857	C₃²	—	18	1	no	—
858	C₃²	—	18	1	no	—
859	C₃²	—	18	1	no	—
860	C₃²	—	18	1	no	—
861	C₃²	—	18	1	no	—
862	C₃²	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
863	C₃²	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
864	C₃²	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
865	C₃²	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
866	C₃²	C₂×C₃³×D₃	1	1	yes	characteristic
867	C₉	—	3	1	no	—
868	C₉	—	3	1	no	—
869	C₉	—	3	1	no	—
870	C₉	—	3	1	no	—
871	C₉	—	6	1	no	—
872	C₉	—	6	1	no	—
873	C₉	—	6	1	no	—
874	C₉	—	6	1	no	—
875	C₉	—	6	1	no	—
876	C₉	—	6	1	no	—
877	C₉	—	6	1	no	—
878	C₉	—	6	1	no	—
879	C₉	—	6	1	no	—
880	C₉	—	6	1	no	—
881	C₉	—	6	1	no	—
882	C₉	—	6	1	no	—
883	C₉	—	6	1	no	—
884	C₉	—	6	1	no	—
885	C₂×C₃	—	3	1	no	—
886	C₂×C₃	—	3	1	no	—
887	C₂×C₃	—	3	1	no	—
888	C₂×C₃	—	6	1	no	—
889	C₂×C₃	—	6	1	no	—
890	C₂×C₃	—	6	1	no	—
891	C₂×C₃	—	6	1	no	—
892	C₂×C₃	—	6	1	no	—
893	C₂×C₃	—	9	2	no	—
894	C₂×C₃	—	9	2	no	—
895	C₂×C₃	—	9	2	no	—
896	C₂×C₃	—	9	2	no	—
897	C₂×C₃	—	18	1	no	—
898	C₂×C₃	—	18	1	no	—
899	C₂×C₃	—	18	1	no	—
900	C₂×C₃	—	18	1	no	—
901	C₂×C₃	—	18	1	no	—
902	C₂×C₃	—	27	2	no	—
903	C₂×C₃	—	27	2	no	—
904	C₂×C₃	—	27	2	no	—
905	C₂×C₃	#92283	1	1	yes	characteristic, direct product factor
906	C₂×C₃	#92283	1	1	yes	characteristic, direct product factor
907	C₂×C₃	#92283	1	1	yes	characteristic, direct product factor
908	C₂×C₃	C₃²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
909	D₃	—	3	2	no	—
910	D₃	—	9	2	no	—
911	C₂²	—	9	1	no	Sylow
912	C₃	—	3	1	no	—
913	C₃	—	3	1	no	—
914	C₃	—	3	1	no	—
915	C₃	—	6	1	no	—
916	C₃	—	6	1	no	—
917	C₃	—	6	1	no	—
918	C₃	—	6	1	no	—
919	C₃	—	6	1	no	—
920	C₃	—	18	1	no	—
921	C₃	—	18	1	no	—
922	C₃	—	18	1	no	—
923	C₃	—	18	1	no	—
924	C₃	—	18	1	no	—
925	C₃	C₂×#92283	1	1	yes	characteristic, direct product factor
926	C₃	C₂×#92283	1	1	yes	characteristic, direct product factor
927	C₃	C₂×#92283	1	1	yes	characteristic, direct product factor
928	C₃	C₂×C₃²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
929	C₂	—	9	2	no	—
930	C₂	C₃×#92283	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, socle	C₂×C₃²	C₃×(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂²×C₃³
Frattini	C₃²	C₂×C₃³×D₃
Fitting	C₂×C₃×#6910	C₂
prime radical	C₂×C₃²×#272	C₃
hypercenter	C₂×C₃³	(C₃⋊D₃)⋊C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃² ◁ C₂×C₃³

Complements

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

N	H ≅ G/N	type
1. C₃×#92283	C₂	direct (N × H)
2. C₂×C₃×#6910	C₂	semidirect
5. C₂×#92283	C₃	direct (N × H)
6. C₂×#92283	C₃	direct (N × H)
7. C₂×#92283	C₃	direct (N × H)
8. C₂×#92283	C₃	direct (N × H)
9. C₂×#92283	C₃	direct (N × H)
10. C₂×#92283	C₃	direct (N × H)
11. C₂×#92283	C₃	direct (N × H)
12. C₂×#92283	C₃	direct (N × H)
13. C₂×#92283	C₃	direct (N × H)
14. C₂×C₃×#4176	C₃	semidirect
15. C₂×C₃×#4176	C₃	semidirect
16. C₂×C₃×#4176	C₃	semidirect
17. C₃×#6910	C₂²	semidirect
19. C₂×C₃²×3₋¹⁺²	D₃	semidirect
32. C₂×#6910	C₂×C₃	semidirect
33. C₂×#6910	C₂×C₃	semidirect
34. C₂×#6910	C₂×C₃	semidirect
35. C₂×#6910	C₂×C₃	semidirect
36. C₂×#6910	C₂×C₃	semidirect
37. C₂×#6910	C₂×C₃	semidirect
38. C₂×#6910	C₂×C₃	semidirect
39. C₂×#6910	C₂×C₃	semidirect
40. C₂×#6910	C₂×C₃	semidirect
44. C₂×C₃×#731	C₂×C₃	semidirect
45. C₂×C₃×#731	C₂×C₃	semidirect
46. C₂×C₃×#731	C₂×C₃	semidirect
47. #92283	C₂×C₃	direct (N × H)
48. #92283	C₂×C₃	direct (N × H)
49. #92283	C₂×C₃	direct (N × H)
50. #92283	C₂×C₃	direct (N × H)
51. #92283	C₂×C₃	direct (N × H)
52. #92283	C₂×C₃	direct (N × H)
53. #92283	C₂×C₃	direct (N × H)
54. #92283	C₂×C₃	direct (N × H)
55. #92283	C₂×C₃	direct (N × H)
56. C₃×#4176	C₂×C₃	semidirect
57. C₃×#4176	C₂×C₃	semidirect
58. C₃×#4176	C₂×C₃	semidirect
78. C₂×#4176	C₃²	semidirect
79. C₂×#4176	C₃²	semidirect
80. C₂×#4176	C₃²	semidirect
81. C₂×#4176	C₃²	semidirect
82. C₂×#4176	C₃²	semidirect
83. C₂×#4176	C₃²	semidirect
84. C₂×#4176	C₃²	semidirect
85. C₂×#4176	C₃²	semidirect
86. C₂×#4176	C₃²	semidirect
88. C₃²×3₋¹⁺²	C₂×D₃	semidirect
99. #6910	C₂²×C₃	semidirect
100. #6910	C₂²×C₃	semidirect
101. #6910	C₂²×C₃	semidirect
102. #6910	C₂²×C₃	semidirect
103. #6910	C₂²×C₃	semidirect
104. #6910	C₂²×C₃	semidirect
105. #6910	C₂²×C₃	semidirect
106. #6910	C₂²×C₃	semidirect
107. #6910	C₂²×C₃	semidirect
111. C₃×#731	C₂²×C₃	semidirect
112. C₃×#731	C₂²×C₃	semidirect
113. C₃×#731	C₂²×C₃	semidirect
144. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
145. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
146. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
147. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
148. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
149. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
150. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
151. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
152. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
166. C₂×C₃²×C₉	C₃×D₃	semidirect
167. C₂×C₃²×C₉	C₃×D₃	semidirect
168. C₂×C₃²×C₉	C₃×D₃	semidirect
221. C₂×#731	C₂×C₃²	semidirect
222. C₂×#731	C₂×C₃²	semidirect
223. C₂×#731	C₂×C₃²	semidirect
224. C₂×#731	C₂×C₃²	semidirect
225. C₂×#731	C₂×C₃²	semidirect
226. C₂×#731	C₂×C₃²	semidirect
227. C₂×#731	C₂×C₃²	semidirect
228. C₂×#731	C₂×C₃²	semidirect
229. C₂×#731	C₂×C₃²	semidirect
230. #4176	C₂×C₃²	semidirect
231. #4176	C₂×C₃²	semidirect
232. #4176	C₂×C₃²	semidirect
233. #4176	C₂×C₃²	semidirect
234. #4176	C₂×C₃²	semidirect
235. #4176	C₂×C₃²	semidirect
236. #4176	C₂×C₃²	semidirect
237. #4176	C₂×C₃²	semidirect
238. #4176	C₂×C₃²	semidirect
309. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
310. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
311. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
312. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
313. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
314. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
315. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
316. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
317. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
331. C₃²×C₉	C₂×C₃×D₃	semidirect
332. C₃²×C₉	C₂×C₃×D₃	semidirect
333. C₃²×C₉	C₂×C₃×D₃	semidirect
370. #731	C₂²×C₃²	semidirect
371. #731	C₂²×C₃²	semidirect
372. #731	C₂²×C₃²	semidirect
373. #731	C₂²×C₃²	semidirect
374. #731	C₂²×C₃²	semidirect
375. #731	C₂²×C₃²	semidirect
376. #731	C₂²×C₃²	semidirect
377. #731	C₂²×C₃²	semidirect
378. #731	C₂²×C₃²	semidirect
523. C₂×C₃×C₉	C₃²×D₃	semidirect
524. C₂×C₃×C₉	C₃²×D₃	semidirect
525. C₂×C₃×C₉	C₃²×D₃	semidirect
526. C₂×C₃×C₉	C₃²×D₃	semidirect
527. C₂×C₃×C₉	C₃²×D₃	semidirect
528. C₂×C₃×C₉	C₃²×D₃	semidirect
529. C₂×C₃×C₉	C₃²×D₃	semidirect
530. C₂×C₃×C₉	C₃²×D₃	semidirect
531. C₂×C₃×C₉	C₃²×D₃	semidirect
689. C₃×C₉	C₂×C₃²×D₃	semidirect
690. C₃×C₉	C₂×C₃²×D₃	semidirect
691. C₃×C₉	C₂×C₃²×D₃	semidirect
692. C₃×C₉	C₂×C₃²×D₃	semidirect
693. C₃×C₉	C₂×C₃²×D₃	semidirect
694. C₃×C₉	C₂×C₃²×D₃	semidirect
695. C₃×C₉	C₂×C₃²×D₃	semidirect
696. C₃×C₉	C₂×C₃²×D₃	semidirect
697. C₃×C₉	C₂×C₃²×D₃	semidirect
905. C₂×C₃	#92283	direct (N × H)
906. C₂×C₃	#92283	direct (N × H)
907. C₂×C₃	#92283	direct (N × H)
925. C₃	C₂×#92283	direct (N × H)
926. C₃	C₂×#92283	direct (N × H)
927. C₃	C₂×#92283	direct (N × H)
930. C₂	C₃×#92283	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#92283	2
C₂×C₃×#6910	2
C₂×C₃²×#272	3
C₂×C₃×D₃×3₋¹⁺²	3
C₂×#92283	3
C₂×C₃×#4176	3

Subgroups — C2×C3×#92283 #72254024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#92283 #72254024