Subgroups — #72243691

Order 4374.

1024 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14552080	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×#92262	C₃	1	1	yes	maximal, characteristic
3	D₃×C₉×3₋¹⁺²	—	3	1	no	maximal
4	C₃×C₉×(C₃⋊D₃)⋊C₃	C₃	1	1	yes	maximal, characteristic
5	C₃⋊D₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	((C₃⋊D₃)⋊C₉)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
11	(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	C₃	1	1	yes	maximal, characteristic
12	#13090622	C₃	1	1	yes	maximal, characteristic, complemented
13	C₉×(C₃⋊D₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
14	C₉×(C₃⋊D₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
15	C₉×(C₃⋊D₃)⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
16	C₃×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
17	C₃×C₉×3₋¹⁺²	—	2	1	no	—
18	C₃×C₉×3₋¹⁺²	D₃	1	1	yes	characteristic, complemented
19	C₃×C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
20	C₃²×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
21	#10624560	—	2	1	no	—
22	#10624560	—	2	1	no	—
23	#10624560	—	2	1	no	—
24	#10624557	—	2	1	no	—
25	#10624557	—	2	1	no	—
26	#10624557	—	2	1	no	—
27	#10624557	—	2	1	no	—
28	#10624557	—	2	1	no	—
29	#10624557	—	2	1	no	—
30	#10624556	—	2	1	no	—
31	#10624556	—	2	1	no	—
32	#10624556	—	2	1	no	—
33	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
34	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
35	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
36	#10624556	C₂×C₃	1	1	yes	characteristic, complemented
37	#10624555	C₂×C₃	1	1	yes	characteristic
38	#10624555	C₂×C₃	1	1	yes	characteristic
39	#10624548	C₂×C₃	1	1	yes	characteristic, complemented
40	C₉×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
41	C₉×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
42	C₉×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
44	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
45	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
46	C₃×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic
47	C₃×D₃×3₋¹⁺²	—	3	1	no	—
48	C₃²×(C₃⋊D₃)⋊C₃	C₃²	1	1	yes	characteristic
49	C₃²×D₃×C₉	—	3	1	no	—
50	C₂×C₉×3₋¹⁺²	—	9	1	no	—
51	#92262	C₉	1	1	yes	characteristic, complemented
52	#92262	C₉	1	1	yes	characteristic, complemented
53	#92262	C₉	1	1	yes	characteristic, complemented
54	#92262	C₉	1	1	yes	characteristic, complemented
55	#92262	C₉	1	1	yes	characteristic, complemented
56	#92262	C₉	1	1	yes	characteristic, complemented
57	#92262	C₉	1	1	yes	characteristic, complemented
58	#92262	C₉	1	1	yes	characteristic, complemented
59	#92262	C₉	1	1	yes	characteristic, complemented
60	C₉×(C₃⋊D₃)⋊C₃	—	3	1	no	—
61	C₉×(C₃⋊D₃)⋊C₃	—	3	2	no	—
62	D₃×C₉⋊C₉	—	3	1	no	—
63	D₃×C₉⋊C₉	—	3	1	no	—
64	D₃×C₉⋊C₉	—	3	1	no	—
65	D₃×C₉⋊C₉	—	3	1	no	—
66	D₃×C₉⋊C₉	—	3	1	no	—
67	D₃×C₉⋊C₉	—	3	1	no	—
68	D₃×C₉⋊C₉	—	9	1	no	—
69	D₃×C₃²⋊C₉	—	3	1	no	—
70	D₃×C₃²⋊C₉	—	3	1	no	—
71	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
73	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
74	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
75	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
76	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
77	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
78	C₃×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic
79	D₃×C₉²	—	3	1	no	—
80	D₃×C₉²	—	3	1	no	—
81	D₃×C₉²	—	3	1	no	—
82	C₃²×3₋¹⁺²	—	2	1	no	—
83	C₃²×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
84	C₃²×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
85	C₃³×C₉	—	2	1	no	—
86	C₃³×C₉	C₃×D₃	1	1	yes	characteristic
87	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
88	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
89	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
90	C₃³×C₉	C₂×C₃²	1	1	yes	characteristic
91	C₉⋊H(3,𝔽₃)	—	2	1	no	—
92	C₉⋊H(3,𝔽₃)	—	2	1	no	—
93	C₉⋊H(3,𝔽₃)	—	2	1	no	—
94	C₉⋊H(3,𝔽₃)	—	2	1	no	—
95	C₉⋊H(3,𝔽₃)	—	2	1	no	—
96	C₉⋊H(3,𝔽₃)	—	2	1	no	—
97	C₉⋊H(3,𝔽₃)	—	2	1	no	—
98	C₉⋊H(3,𝔽₃)	—	2	1	no	—
99	C₉⋊H(3,𝔽₃)	—	2	1	no	—
100	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
101	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
102	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
103	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
104	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
105	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
106	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
107	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
108	C₉⋊H(3,𝔽₃)	C₂×C₉	1	1	yes	characteristic, complemented
109	C₉×3₋¹⁺²	—	3	1	no	—
110	C₉×3₋¹⁺²	—	6	1	no	—
111	C₉×3₋¹⁺²	—	6	1	no	—
112	C₉×3₋¹⁺²	—	6	1	no	—
113	C₉×3₋¹⁺²	—	6	1	no	—
114	C₉×3₋¹⁺²	—	6	1	no	—
115	C₉×3₋¹⁺²	—	6	1	no	—
116	C₉×3₋¹⁺²	—	6	1	no	—
117	C₉×3₋¹⁺²	—	6	1	no	—
118	C₉×3₋¹⁺²	—	6	1	no	—
119	C₉×3₋¹⁺²	—	6	1	no	—
120	C₉×3₋¹⁺²	—	6	1	no	—
121	C₉×3₋¹⁺²	—	6	1	no	—
122	C₉×3₋¹⁺²	—	6	1	no	—
123	C₉×H(3,𝔽₃)	—	3	1	no	—
124	C₉×H(3,𝔽₃)	—	3	2	no	—
125	C₉×H(3,𝔽₃)	—	6	1	no	—
126	C₉×H(3,𝔽₃)	—	6	2	no	—
127	C₃×C₉⋊C₉	—	2	1	no	—
128	C₃×C₉⋊C₉	—	2	1	no	—
129	C₃×C₉⋊C₉	—	2	1	no	—
130	C₃×C₉⋊C₉	—	2	1	no	—
131	C₃×C₉⋊C₉	—	2	1	no	—
132	C₃×C₉⋊C₉	—	2	1	no	—
133	C₃×C₉⋊C₉	—	2	1	no	—
134	C₃×C₉⋊C₉	—	2	1	no	—
135	C₃×C₉⋊C₉	—	2	1	no	—
136	C₃×C₉⋊C₉	—	3	1	no	—
137	C₃×C₉⋊C₉	—	6	1	no	—
138	C₃×C₉⋊C₉	—	6	1	no	—
139	C₃×C₉⋊C₉	—	6	1	no	—
140	C₃×C₉⋊C₉	—	6	1	no	—
141	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
142	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
143	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
144	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
145	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
146	C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
147	C₃×C₃²⋊C₉	—	2	1	no	—
148	C₃×C₃²⋊C₉	—	2	1	no	—
149	C₃×C₃²⋊C₉	—	2	1	no	—
150	C₃×C₃²⋊C₉	—	2	1	no	—
151	C₃×C₃²⋊C₉	—	2	1	no	—
152	C₃×C₃²⋊C₉	—	2	1	no	—
153	C₃×C₃²⋊C₉	—	2	1	no	—
154	C₃×C₃²⋊C₉	—	2	1	no	—
155	C₃×C₃²⋊C₉	—	2	1	no	—
156	C₃×C₃²⋊C₉	—	2	1	no	—
157	C₃×C₃²⋊C₉	—	2	1	no	—
158	C₃×C₃²⋊C₉	—	2	1	no	—
159	C₃×C₃²⋊C₉	—	2	1	no	—
160	C₃×C₃²⋊C₉	—	2	1	no	—
161	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
162	C₃×C₃²⋊C₉	C₃×D₃	1	1	yes	characteristic
163	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
164	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
165	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
166	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
167	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
168	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
169	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
170	C₃×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic
171	C₃×C₉²	—	2	1	no	—
172	C₃×C₉²	—	2	1	no	—
173	C₃×C₉²	—	2	1	no	—
174	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
175	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
176	C₃×C₉²	C₃×D₃	1	1	yes	characteristic
177	#6855	—	2	1	no	—
178	#6855	—	2	1	no	—
179	#6855	—	2	1	no	—
180	#6855	—	2	1	no	—
181	#6855	—	2	1	no	—
182	#6855	—	2	1	no	—
183	#6855	—	2	1	no	—
184	#6855	—	2	1	no	—
185	#6855	—	2	1	no	—
186	#6855	—	2	1	no	—
187	#6855	—	2	1	no	—
188	#6855	—	2	1	no	—
189	#6855	—	2	1	no	—
190	#6855	—	2	1	no	—
191	#6855	—	2	1	no	—
192	#6855	—	2	1	no	—
193	#6855	—	2	1	no	—
194	#6855	—	2	1	no	—
195	#6855	—	2	1	no	—
196	#6855	—	2	1	no	—
197	#6855	—	2	1	no	—
198	#6855	—	2	1	no	—
199	#6855	—	2	1	no	—
200	#6855	—	2	1	no	—
201	C₃²×C₃⋊D₃	C₃³	1	1	yes	characteristic
202	C₃³×D₃	—	3	1	no	—
203	C₂×C₃×3₋¹⁺²	—	9	1	no	—
204	C₂×C₃²×C₉	—	9	1	no	—
205	C₉×C₃⋊D₃	—	3	1	no	—
206	C₉×C₃⋊D₃	—	3	1	no	—
207	C₉×C₃⋊D₃	—	3	1	no	—
208	C₉×C₃⋊D₃	C₃×C₉	1	1	yes	characteristic, complemented
209	C₉×C₃⋊D₃	C₃×C₉	1	1	yes	characteristic, complemented
210	C₉×C₃⋊D₃	C₃×C₉	1	1	yes	characteristic, complemented
211	D₃×3₋¹⁺²	—	3	1	no	—
212	D₃×3₋¹⁺²	—	3	1	no	—
213	D₃×3₋¹⁺²	—	3	1	no	—
214	D₃×3₋¹⁺²	—	3	1	no	—
215	D₃×3₋¹⁺²	—	3	1	no	—
216	D₃×3₋¹⁺²	—	3	1	no	—
217	D₃×3₋¹⁺²	—	3	1	no	—
218	D₃×3₋¹⁺²	—	3	1	no	—
219	D₃×3₋¹⁺²	—	3	1	no	—
220	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
221	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
222	C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
223	C₃×(C₃⋊D₃)⋊C₃	C₃×C₉	1	1	yes	characteristic
224	C₃×(C₃⋊D₃)⋊C₃	C₃×C₉	1	1	yes	characteristic
225	C₃×(C₃⋊D₃)⋊C₃	C₃×C₉	1	1	yes	characteristic
226	C₃×D₃×C₉	—	3	1	no	—
227	C₃×D₃×C₉	—	3	1	no	—
228	C₃×D₃×C₉	—	3	1	no	—
229	C₃×D₃×C₉	—	3	1	no	—
230	C₃×D₃×C₉	—	3	1	no	—
231	C₃×D₃×C₉	—	3	1	no	—
232	C₃×D₃×C₉	—	3	1	no	—
233	C₃×D₃×C₉	—	3	1	no	—
234	C₃×D₃×C₉	—	3	1	no	—
235	C₃×D₃×C₉	—	3	1	no	—
236	C₃×D₃×C₉	—	3	1	no	—
237	C₃×D₃×C₉	—	3	1	no	—
238	C₃×D₃×C₉	—	9	1	no	—
239	C₃×D₃×C₉	—	9	2	no	—
240	C₃×D₃×C₉	—	9	1	no	—
241	C₃×D₃×C₉	—	9	1	no	—
242	C₃×D₃×C₉	—	9	1	no	—
243	C₃×D₃×C₉	—	9	1	no	—
244	C₂×C₉⋊C₉	—	9	1	no	—
245	C₂×C₉⋊C₉	—	9	1	no	—
246	C₂×C₉⋊C₉	—	9	1	no	—
247	C₂×C₉⋊C₉	—	9	1	no	—
248	C₂×C₉⋊C₉	—	9	1	no	—
249	C₂×C₉⋊C₉	—	9	1	no	—
250	C₂×C₃²⋊C₉	—	9	1	no	—
251	C₂×C₃²⋊C₉	—	9	1	no	—
252	C₂×C₉²	—	9	1	no	—
253	C₂×C₉²	—	9	1	no	—
254	C₂×C₉²	—	9	1	no	—
255	(C₃⋊D₃)⋊C₉	—	3	1	no	—
256	(C₃⋊D₃)⋊C₉	—	3	1	no	—
257	(C₃⋊D₃)⋊C₉	—	3	1	no	—
258	(C₃⋊D₃)⋊C₉	—	3	1	no	—
259	(C₃⋊D₃)⋊C₉	—	3	1	no	—
260	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
261	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
262	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
263	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
264	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
265	(C₃⋊D₃)⋊C₉	C₃×C₉	1	1	yes	characteristic, complemented
266	(C₃⋊D₃)⋊C₉	3₋¹⁺²	1	2	yes	complemented
267	(C₃⋊D₃)⋊C₉	3₋¹⁺²	1	1	yes	characteristic, complemented
268	C₃⁴	—	2	1	no	—
269	C₃⁴	C₃²×D₃	1	1	yes	characteristic
270	C₃⁴	C₂×C₃³	1	1	yes	characteristic
271	C₃×3₋¹⁺²	—	2	1	no	—
272	C₃×3₋¹⁺²	—	2	1	no	—
273	C₃×3₋¹⁺²	—	2	1	no	—
274	C₃×3₋¹⁺²	—	2	1	no	—
275	C₃×3₋¹⁺²	—	2	1	no	—
276	C₃×3₋¹⁺²	—	2	1	no	—
277	C₃×3₋¹⁺²	—	2	1	no	—
278	C₃×3₋¹⁺²	—	2	1	no	—
279	C₃×3₋¹⁺²	—	2	1	no	—
280	C₃×3₋¹⁺²	—	3	1	no	—
281	C₃×3₋¹⁺²	—	6	1	no	—
282	C₃×3₋¹⁺²	—	6	1	no	—
283	C₃×3₋¹⁺²	—	6	1	no	—
284	C₃×3₋¹⁺²	—	6	1	no	—
285	C₃×3₋¹⁺²	—	6	1	no	—
286	C₃×3₋¹⁺²	—	6	1	no	—
287	C₃×3₋¹⁺²	—	6	1	no	—
288	C₃×3₋¹⁺²	—	6	1	no	—
289	C₃×3₋¹⁺²	—	6	1	no	—
290	C₃×3₋¹⁺²	—	6	1	no	—
291	C₃×3₋¹⁺²	—	6	1	no	—
292	C₃×3₋¹⁺²	—	6	1	no	—
293	C₃×3₋¹⁺²	—	6	1	no	—
294	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
295	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
296	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
297	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
298	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
299	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
300	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
301	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
302	C₃×3₋¹⁺²	D₃×C₉	1	1	yes	characteristic, complemented
303	C₃×H(3,𝔽₃)	—	2	1	no	—
304	C₃×H(3,𝔽₃)	—	2	1	no	—
305	C₃×H(3,𝔽₃)	—	2	1	no	—
306	C₃×H(3,𝔽₃)	—	3	1	no	—
307	C₃×H(3,𝔽₃)	—	3	1	no	—
308	C₃×H(3,𝔽₃)	—	3	1	no	—
309	C₃×H(3,𝔽₃)	—	6	1	no	—
310	C₃×H(3,𝔽₃)	—	6	1	no	—
311	C₃×H(3,𝔽₃)	—	6	1	no	—
312	C₃×H(3,𝔽₃)	C₂×C₃×C₉	1	1	yes	characteristic
313	C₃×H(3,𝔽₃)	C₂×C₃×C₉	1	1	yes	characteristic
314	C₃×H(3,𝔽₃)	C₂×C₃×C₉	1	1	yes	characteristic
315	C₃²×C₉	—	2	1	no	—
316	C₃²×C₉	—	2	1	no	—
317	C₃²×C₉	—	2	1	no	—
318	C₃²×C₉	—	2	1	no	—
319	C₃²×C₉	—	2	1	no	—
320	C₃²×C₉	—	2	1	no	—
321	C₃²×C₉	—	2	1	no	—
322	C₃²×C₉	—	2	1	no	—
323	C₃²×C₉	—	2	1	no	—
324	C₃²×C₉	—	2	1	no	—
325	C₃²×C₉	—	2	1	no	—
326	C₃²×C₉	—	2	1	no	—
327	C₃²×C₉	—	2	1	no	—
328	C₃²×C₉	—	2	1	no	—
329	C₃²×C₉	—	2	1	no	—
330	C₃²×C₉	—	3	1	no	—
331	C₃²×C₉	—	3	1	no	—
332	C₃²×C₉	—	3	2	no	—
333	C₃²×C₉	—	3	1	no	—
334	C₃²×C₉	—	3	1	no	—
335	C₃²×C₉	—	3	1	no	—
336	C₃²×C₉	—	3	1	no	—
337	C₃²×C₉	—	3	1	no	—
338	C₃²×C₉	—	3	1	no	—
339	C₃²×C₉	—	6	1	no	—
340	C₃²×C₉	—	6	1	no	—
341	C₃²×C₉	—	6	1	no	—
342	C₃²×C₉	—	6	1	no	—
343	C₃²×C₉	—	6	1	no	—
344	C₃²×C₉	—	6	2	no	—
345	C₃²×C₉	—	6	1	no	—
346	C₃²×C₉	—	6	1	no	—
347	C₃²×C₉	—	6	1	no	—
348	C₃²×C₉	—	6	1	no	—
349	C₃²×C₉	—	6	1	no	—
350	C₃²×C₉	—	6	1	no	—
351	C₃²×C₉	—	6	1	no	—
352	C₃²×C₉	—	6	1	no	—
353	C₃²×C₉	—	6	1	no	—
354	C₃²×C₉	—	6	1	no	—
355	C₃²×C₉	—	6	1	no	—
356	C₃²×C₉	—	18	1	no	—
357	C₃²×C₉	—	18	1	no	—
358	C₃²×C₉	—	18	1	no	—
359	C₃²×C₉	—	18	1	no	—
360	C₃²×C₉	—	18	1	no	—
361	C₃²×C₉	—	18	1	no	—
362	C₃²×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
363	C₃²×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
364	C₃²×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
365	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
366	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
367	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
368	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
369	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
370	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
371	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
372	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
373	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
374	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
375	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
376	C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
377	C₉⋊C₉	—	2	1	no	—
378	C₉⋊C₉	—	2	1	no	—
379	C₉⋊C₉	—	2	1	no	—
380	C₉⋊C₉	—	2	1	no	—
381	C₉⋊C₉	—	3	1	no	—
382	C₉⋊C₉	—	3	1	no	—
383	C₉⋊C₉	—	6	1	no	—
384	C₉⋊C₉	—	6	1	no	—
385	C₉⋊C₉	—	6	1	no	—
386	C₉⋊C₉	—	6	1	no	—
387	C₉⋊C₉	—	6	1	no	—
388	C₉⋊C₉	—	6	2	no	—
389	C₉⋊C₉	—	6	2	no	—
390	C₉⋊C₉	—	6	2	no	—
391	C₉⋊C₉	—	6	2	no	—
392	C₉⋊C₉	—	6	1	no	—
393	C₉⋊C₉	—	6	1	no	—
394	C₉⋊C₉	—	6	1	no	—
395	C₉⋊C₉	—	6	1	no	—
396	C₉⋊C₉	—	6	1	no	—
397	C₉⋊C₉	—	6	1	no	—
398	C₉⋊C₉	—	6	1	no	—
399	C₉⋊C₉	—	6	1	no	—
400	C₉⋊C₉	—	6	1	no	—
401	C₉⋊C₉	—	6	1	no	—
402	C₉⋊C₉	—	6	1	no	—
403	C₉⋊C₉	—	6	1	no	—
404	C₉⋊C₉	—	6	1	no	—
405	C₉⋊C₉	—	6	1	no	—
406	C₉⋊C₉	—	6	1	no	—
407	C₉⋊C₉	—	6	1	no	—
408	C₉⋊C₉	—	6	1	no	—
409	C₉⋊C₉	—	6	1	no	—
410	C₉⋊C₉	—	6	1	no	—
411	C₉⋊C₉	—	6	1	no	—
412	C₉⋊C₉	—	6	1	no	—
413	C₉⋊C₉	—	6	1	no	—
414	C₉⋊C₉	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
415	C₃²⋊C₉	—	2	1	no	—
416	C₃²⋊C₉	—	2	1	no	—
417	C₃²⋊C₉	—	2	1	no	—
418	C₃²⋊C₉	—	2	1	no	—
419	C₃²⋊C₉	—	2	1	no	—
420	C₃²⋊C₉	—	2	1	no	—
421	C₃²⋊C₉	—	2	1	no	—
422	C₃²⋊C₉	—	2	1	no	—
423	C₃²⋊C₉	—	2	1	no	—
424	C₃²⋊C₉	—	2	1	no	—
425	C₃²⋊C₉	—	2	1	no	—
426	C₃²⋊C₉	—	2	1	no	—
427	C₃²⋊C₉	—	2	1	no	—
428	C₃²⋊C₉	—	2	1	no	—
429	C₃²⋊C₉	—	2	1	no	—
430	C₃²⋊C₉	—	2	1	no	—
431	C₃²⋊C₉	—	2	1	no	—
432	C₃²⋊C₉	—	2	1	no	—
433	C₃²⋊C₉	—	2	1	no	—
434	C₃²⋊C₉	—	2	1	no	—
435	C₃²⋊C₉	—	2	1	no	—
436	C₃²⋊C₉	—	2	1	no	—
437	C₃²⋊C₉	—	2	1	no	—
438	C₃²⋊C₉	—	2	1	no	—
439	C₃²⋊C₉	—	2	1	no	—
440	C₃²⋊C₉	—	2	1	no	—
441	C₃²⋊C₉	—	2	1	no	—
442	C₃²⋊C₉	—	2	1	no	—
443	C₃²⋊C₉	—	2	1	no	—
444	C₃²⋊C₉	—	2	1	no	—
445	C₃²⋊C₉	—	2	1	no	—
446	C₃²⋊C₉	—	2	1	no	—
447	C₃²⋊C₉	—	2	1	no	—
448	C₃²⋊C₉	—	2	2	no	—
449	C₃²⋊C₉	—	2	1	no	—
450	C₃²⋊C₉	—	3	1	no	—
451	C₃²⋊C₉	—	3	1	no	—
452	C₃²⋊C₉	—	3	1	no	—
453	C₃²⋊C₉	—	3	1	no	—
454	C₃²⋊C₉	—	3	1	no	—
455	C₃²⋊C₉	—	3	1	no	—
456	C₃²⋊C₉	—	3	1	no	—
457	C₃²⋊C₉	—	6	1	no	—
458	C₃²⋊C₉	—	6	1	no	—
459	C₃²⋊C₉	—	6	1	no	—
460	C₃²⋊C₉	—	6	2	no	—
461	C₃²⋊C₉	—	6	1	no	—
462	C₃²⋊C₉	—	6	2	no	—
463	C₃²⋊C₉	—	6	1	no	—
464	C₃²⋊C₉	—	6	1	no	—
465	C₃²⋊C₉	—	6	1	no	—
466	C₃²⋊C₉	—	6	1	no	—
467	C₃²⋊C₉	—	6	1	no	—
468	C₃²⋊C₉	—	6	1	no	—
469	C₃²⋊C₉	—	6	1	no	—
470	C₃²⋊C₉	—	6	1	no	—
471	C₃²⋊C₉	—	6	1	no	—
472	C₃²⋊C₉	—	6	1	no	—
473	C₃²⋊C₉	—	6	1	no	—
474	C₃²⋊C₉	—	6	2	no	—
475	C₃²⋊C₉	—	6	1	no	—
476	C₃²⋊C₉	—	18	1	no	—
477	C₃²⋊C₉	—	18	1	no	—
478	C₃²⋊C₉	—	18	1	no	—
479	C₃²⋊C₉	—	18	1	no	—
480	C₃²⋊C₉	—	18	1	no	—
481	C₃²⋊C₉	—	18	1	no	—
482	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
483	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
484	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
485	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
486	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
487	C₃²⋊C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
488	C₃²⋊C₉	C₂×3₋¹⁺²	1	2	yes	complemented
489	C₃²⋊C₉	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
490	C₉²	—	3	1	no	—
491	C₉²	—	6	1	no	—
492	C₉²	—	6	1	no	—
493	C₉²	—	6	1	no	—
494	C₉²	—	6	1	no	—
495	C₉²	—	6	1	no	—
496	C₉²	—	6	1	no	—
497	C₉²	—	6	1	no	—
498	C₉²	—	6	1	no	—
499	C₉²	—	6	1	no	—
500	C₉²	—	6	1	no	—
501	C₉²	—	6	1	no	—
502	C₉²	—	6	1	no	—
503	C₉²	—	6	1	no	—
504	C₉²	—	6	1	no	—
505	C₂×C₃³	—	9	1	no	—
506	C₃×C₃⋊D₃	C₃²×C₉	1	1	yes	characteristic
507	C₃×C₃⋊D₃	C₃×3₋¹⁺²	1	1	yes	characteristic
508	C₃×C₃⋊D₃	#737	1	1	yes	characteristic
509	C₃×C₃⋊D₃	#737	1	1	yes	characteristic
510	C₃²×D₃	—	3	1	no	—
511	C₃²×D₃	—	3	1	no	—
512	C₃²×D₃	—	3	1	no	—
513	C₃²×D₃	—	3	1	no	—
514	C₃²×D₃	—	9	1	no	—
515	C₃²×D₃	—	9	1	no	—
516	C₃²×D₃	—	9	1	no	—
517	C₃²×D₃	—	9	1	no	—
518	C₂×3₋¹⁺²	—	9	1	no	—
519	C₂×3₋¹⁺²	—	9	1	no	—
520	C₂×3₋¹⁺²	—	9	1	no	—
521	C₂×3₋¹⁺²	—	9	1	no	—
522	C₂×3₋¹⁺²	—	9	1	no	—
523	C₂×3₋¹⁺²	—	9	1	no	—
524	C₂×3₋¹⁺²	—	9	1	no	—
525	C₂×3₋¹⁺²	—	9	1	no	—
526	C₂×3₋¹⁺²	—	9	1	no	—
527	C₂×C₃×C₉	—	9	1	no	—
528	C₂×C₃×C₉	—	9	1	no	—
529	C₂×C₃×C₉	—	9	1	no	—
530	C₂×C₃×C₉	—	9	1	no	—
531	C₂×C₃×C₉	—	9	1	no	—
532	C₂×C₃×C₉	—	9	1	no	—
533	C₂×C₃×C₉	—	9	1	no	—
534	C₂×C₃×C₉	—	9	1	no	—
535	C₂×C₃×C₉	—	9	1	no	—
536	C₂×C₃×C₉	—	9	1	no	—
537	C₂×C₃×C₉	—	9	1	no	—
538	C₂×C₃×C₉	—	9	1	no	—
539	C₂×C₃×C₉	—	27	1	no	—
540	C₂×C₃×C₉	—	27	2	no	—
541	(C₃⋊D₃)⋊C₃	—	3	1	no	—
542	(C₃⋊D₃)⋊C₃	—	3	1	no	—
543	(C₃⋊D₃)⋊C₃	—	3	1	no	—
544	D₃×C₉	—	3	1	no	—
545	D₃×C₉	—	3	1	no	—
546	D₃×C₉	—	3	1	no	—
547	D₃×C₉	—	3	1	no	—
548	D₃×C₉	—	3	1	no	—
549	D₃×C₉	—	3	1	no	—
550	D₃×C₉	—	3	1	no	—
551	D₃×C₉	—	3	1	no	—
552	D₃×C₉	—	3	1	no	—
553	D₃×C₉	—	3	2	no	—
554	D₃×C₉	—	3	1	no	—
555	D₃×C₉	—	9	1	no	—
556	D₃×C₉	—	9	1	no	—
557	D₃×C₉	—	9	1	no	—
558	D₃×C₉	—	9	1	no	—
559	D₃×C₉	—	9	1	no	—
560	D₃×C₉	—	9	1	no	—
561	D₃×C₉	—	9	1	no	—
562	D₃×C₉	—	9	1	no	—
563	D₃×C₉	—	9	1	no	—
564	D₃×C₉	—	9	1	no	—
565	D₃×C₉	—	9	1	no	—
566	D₃×C₉	—	27	1	no	—
567	D₃×C₉	—	27	1	no	—
568	D₃×C₉	—	27	1	no	—
569	C₃³	—	2	1	no	—
570	C₃³	—	2	1	no	—
571	C₃³	—	2	1	no	—
572	C₃³	—	2	1	no	—
573	C₃³	—	2	1	no	—
574	C₃³	—	2	1	no	—
575	C₃³	—	2	1	no	—
576	C₃³	—	3	1	no	—
577	C₃³	—	3	1	no	—
578	C₃³	—	3	1	no	—
579	C₃³	—	3	1	no	—
580	C₃³	—	3	1	no	—
581	C₃³	—	6	1	no	—
582	C₃³	—	6	1	no	—
583	C₃³	—	6	1	no	—
584	C₃³	—	6	1	no	—
585	C₃³	—	6	1	no	—
586	C₃³	—	6	1	no	—
587	C₃³	—	6	1	no	—
588	C₃³	—	6	1	no	—
589	C₃³	—	6	1	no	—
590	C₃³	—	6	1	no	—
591	C₃³	—	6	1	no	—
592	C₃³	—	6	1	no	—
593	C₃³	—	6	1	no	—
594	C₃³	—	6	1	no	—
595	C₃³	—	6	1	no	—
596	C₃³	—	6	1	no	—
597	C₃³	—	6	1	no	—
598	C₃³	—	6	1	no	—
599	C₃³	—	6	1	no	—
600	C₃³	—	6	1	no	—
601	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
602	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
603	C₃³	C₃×D₃×C₉	1	1	yes	characteristic
604	C₃³	C₂×C₃²×C₉	1	1	yes	characteristic
605	C₃³	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic
606	C₃³	C₂×#737	1	1	yes	characteristic
607	C₃³	C₂×#737	1	1	yes	characteristic
608	C₃³	C₃³×D₃	1	1	yes	characteristic
609	3₋¹⁺²	—	3	1	no	—
610	3₋¹⁺²	—	3	1	no	—
611	3₋¹⁺²	—	3	1	no	—
612	3₋¹⁺²	—	6	1	no	—
613	3₋¹⁺²	—	6	1	no	—
614	3₋¹⁺²	—	6	1	no	—
615	3₋¹⁺²	—	6	1	no	—
616	3₋¹⁺²	—	6	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	H(3,𝔽₃)	—	3	1	no	—
655	H(3,𝔽₃)	—	3	1	no	—
656	H(3,𝔽₃)	—	3	1	no	—
657	H(3,𝔽₃)	—	6	1	no	—
658	H(3,𝔽₃)	—	6	1	no	—
659	H(3,𝔽₃)	—	6	1	no	—
660	H(3,𝔽₃)	—	6	1	no	—
661	H(3,𝔽₃)	—	6	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	1	no	—
667	H(3,𝔽₃)	—	6	1	no	—
668	H(3,𝔽₃)	—	6	1	no	—
669	C₃×C₉	—	2	1	no	—
670	C₃×C₉	—	2	1	no	—
671	C₃×C₉	—	2	1	no	—
672	C₃×C₉	—	2	1	no	—
673	C₃×C₉	—	2	1	no	—
674	C₃×C₉	—	2	1	no	—
675	C₃×C₉	—	2	1	no	—
676	C₃×C₉	—	2	1	no	—
677	C₃×C₉	—	2	1	no	—
678	C₃×C₉	—	2	1	no	—
679	C₃×C₉	—	2	1	no	—
680	C₃×C₉	—	2	1	no	—
681	C₃×C₉	—	2	1	no	—
682	C₃×C₉	—	2	1	no	—
683	C₃×C₉	—	2	1	no	—
684	C₃×C₉	—	2	1	no	—
685	C₃×C₉	—	2	1	no	—
686	C₃×C₉	—	2	2	no	—
687	C₃×C₉	—	3	1	no	—
688	C₃×C₉	—	3	1	no	—
689	C₃×C₉	—	3	1	no	—
690	C₃×C₉	—	3	1	no	—
691	C₃×C₉	—	3	1	no	—
692	C₃×C₉	—	3	1	no	—
693	C₃×C₉	—	3	1	no	—
694	C₃×C₉	—	3	1	no	—
695	C₃×C₉	—	3	1	no	—
696	C₃×C₉	—	3	1	no	—
697	C₃×C₉	—	3	1	no	—
698	C₃×C₉	—	3	1	no	—
699	C₃×C₉	—	3	1	no	—
700	C₃×C₉	—	3	1	no	—
701	C₃×C₉	—	3	1	no	—
702	C₃×C₉	—	3	1	no	—
703	C₃×C₉	—	3	1	no	—
704	C₃×C₉	—	6	2	no	—
705	C₃×C₉	—	6	2	no	—
706	C₃×C₉	—	6	2	no	—
707	C₃×C₉	—	6	1	no	—
708	C₃×C₉	—	6	1	no	—
709	C₃×C₉	—	6	1	no	—
710	C₃×C₉	—	6	1	no	—
711	C₃×C₉	—	6	1	no	—
712	C₃×C₉	—	6	1	no	—
713	C₃×C₉	—	6	1	no	—
714	C₃×C₉	—	6	1	no	—
715	C₃×C₉	—	6	1	no	—
716	C₃×C₉	—	6	1	no	—
717	C₃×C₉	—	6	2	no	—
718	C₃×C₉	—	6	1	no	—
719	C₃×C₉	—	6	1	no	—
720	C₃×C₉	—	6	1	no	—
721	C₃×C₉	—	6	1	no	—
722	C₃×C₉	—	6	1	no	—
723	C₃×C₉	—	6	1	no	—
724	C₃×C₉	—	6	1	no	—
725	C₃×C₉	—	6	1	no	—
726	C₃×C₉	—	6	1	no	—
727	C₃×C₉	—	6	1	no	—
728	C₃×C₉	—	6	1	no	—
729	C₃×C₉	—	6	1	no	—
730	C₃×C₉	—	6	1	no	—
731	C₃×C₉	—	6	1	no	—
732	C₃×C₉	—	6	1	no	—
733	C₃×C₉	—	6	1	no	—
734	C₃×C₉	—	6	1	no	—
735	C₃×C₉	—	6	1	no	—
736	C₃×C₉	—	6	1	no	—
737	C₃×C₉	—	6	1	no	—
738	C₃×C₉	—	6	1	no	—
739	C₃×C₉	—	6	1	no	—
740	C₃×C₉	—	6	1	no	—
741	C₃×C₉	—	6	1	no	—
742	C₃×C₉	—	6	1	no	—
743	C₃×C₉	—	6	1	no	—
744	C₃×C₉	—	6	1	no	—
745	C₃×C₉	—	6	1	no	—
746	C₃×C₉	—	6	1	no	—
747	C₃×C₉	—	6	2	no	—
748	C₃×C₉	—	6	1	no	—
749	C₃×C₉	—	6	1	no	—
750	C₃×C₉	—	6	1	no	—
751	C₃×C₉	—	6	1	no	—
752	C₃×C₉	—	6	1	no	—
753	C₃×C₉	—	6	1	no	—
754	C₃×C₉	—	6	1	no	—
755	C₃×C₉	—	6	1	no	—
756	C₃×C₉	—	6	1	no	—
757	C₃×C₉	—	6	1	no	—
758	C₃×C₉	—	6	1	no	—
759	C₃×C₉	—	6	1	no	—
760	C₃×C₉	—	6	1	no	—
761	C₃×C₉	—	6	1	no	—
762	C₃×C₉	—	6	1	no	—
763	C₃×C₉	—	6	1	no	—
764	C₃×C₉	—	6	1	no	—
765	C₃×C₉	—	6	1	no	—
766	C₃×C₉	—	6	1	no	—
767	C₃×C₉	—	6	1	no	—
768	C₃×C₉	—	9	1	no	—
769	C₃×C₉	—	9	1	no	—
770	C₃×C₉	—	9	1	no	—
771	C₃×C₉	—	9	1	no	—
772	C₃×C₉	—	18	2	no	—
773	C₃×C₉	—	18	2	no	—
774	C₃×C₉	—	18	1	no	—
775	C₃×C₉	—	18	2	no	—
776	C₃×C₉	—	18	1	no	—
777	C₃×C₉	—	18	1	no	—
778	C₃×C₉	—	18	1	no	—
779	C₃×C₉	—	18	1	no	—
780	C₃×C₉	—	18	1	no	—
781	C₃×C₉	—	18	1	no	—
782	C₃×C₉	—	18	2	no	—
783	C₃×C₉	—	18	2	no	—
784	C₃×C₉	—	18	1	no	—
785	C₃×C₉	—	18	1	no	—
786	C₃×C₉	—	18	1	no	—
787	C₃×C₉	—	18	2	no	—
788	C₃×C₉	—	18	2	no	—
789	C₃×C₉	—	18	2	no	—
790	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
791	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
792	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
793	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
794	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
795	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
796	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
797	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
798	C₃×C₉	C₃×D₃×C₉	1	1	yes	characteristic
799	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
800	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
801	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
802	C₃×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
803	C₃×C₉	D₃×3₋¹⁺²	1	2	yes	—
804	C₃×C₉	D₃×3₋¹⁺²	1	1	yes	characteristic
805	C₂×C₃²	—	9	1	no	—
806	C₂×C₃²	—	9	1	no	—
807	C₂×C₃²	—	9	1	no	—
808	C₂×C₃²	—	9	1	no	—
809	C₂×C₃²	—	27	1	no	—
810	C₂×C₃²	—	27	1	no	—
811	C₂×C₃²	—	27	1	no	—
812	C₃⋊D₃	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented
813	C₃×D₃	—	3	1	no	—
814	C₃×D₃	—	3	1	no	—
815	C₃×D₃	—	3	1	no	—
816	C₃×D₃	—	3	1	no	—
817	C₃×D₃	—	9	1	no	—
818	C₃×D₃	—	9	1	no	—
819	C₃×D₃	—	9	1	no	—
820	C₃×D₃	—	9	1	no	—
821	C₃×D₃	—	9	1	no	—
822	C₃×D₃	—	9	1	no	—
823	C₃×D₃	—	9	1	no	—
824	C₂×C₉	—	9	2	no	—
825	C₂×C₉	—	9	1	no	—
826	C₂×C₉	—	9	1	no	—
827	C₂×C₉	—	9	1	no	—
828	C₂×C₉	—	9	1	no	—
829	C₂×C₉	—	9	1	no	—
830	C₂×C₉	—	9	1	no	—
831	C₂×C₉	—	9	1	no	—
832	C₂×C₉	—	9	1	no	—
833	C₂×C₉	—	9	1	no	—
834	C₂×C₉	—	9	1	no	—
835	C₂×C₉	—	27	1	no	—
836	C₂×C₉	—	27	1	no	—
837	C₂×C₉	—	27	1	no	—
838	C₂×C₉	—	27	1	no	—
839	C₂×C₉	—	27	1	no	—
840	C₂×C₉	—	27	1	no	—
841	C₂×C₉	—	27	1	no	—
842	C₂×C₉	—	27	1	no	—
843	C₃²	—	2	1	no	—
844	C₃²	—	2	1	no	—
845	C₃²	—	2	1	no	—
846	C₃²	—	2	1	no	—
847	C₃²	—	2	1	no	—
848	C₃²	—	2	1	no	—
849	C₃²	—	2	1	no	—
850	C₃²	—	2	1	no	—
851	C₃²	—	3	1	no	—
852	C₃²	—	3	1	no	—
853	C₃²	—	3	1	no	—
854	C₃²	—	3	1	no	—
855	C₃²	—	3	1	no	—
856	C₃²	—	3	1	no	—
857	C₃²	—	3	1	no	—
858	C₃²	—	3	1	no	—
859	C₃²	—	3	1	no	—
860	C₃²	—	6	1	no	—
861	C₃²	—	6	1	no	—
862	C₃²	—	6	1	no	—
863	C₃²	—	6	1	no	—
864	C₃²	—	6	2	no	—
865	C₃²	—	6	2	no	—
866	C₃²	—	6	2	no	—
867	C₃²	—	6	2	no	—
868	C₃²	—	6	1	no	—
869	C₃²	—	6	1	no	—
870	C₃²	—	6	1	no	—
871	C₃²	—	6	1	no	—
872	C₃²	—	6	1	no	—
873	C₃²	—	6	1	no	—
874	C₃²	—	6	1	no	—
875	C₃²	—	6	1	no	—
876	C₃²	—	6	1	no	—
877	C₃²	—	6	1	no	—
878	C₃²	—	6	1	no	—
879	C₃²	—	6	1	no	—
880	C₃²	—	6	1	no	—
881	C₃²	—	6	1	no	—
882	C₃²	—	6	1	no	—
883	C₃²	—	6	1	no	—
884	C₃²	—	6	1	no	—
885	C₃²	—	6	1	no	—
886	C₃²	—	6	1	no	—
887	C₃²	—	6	1	no	—
888	C₃²	—	9	1	no	—
889	C₃²	—	9	1	no	—
890	C₃²	—	18	1	no	—
891	C₃²	—	18	1	no	—
892	C₃²	—	18	1	no	—
893	C₃²	—	18	1	no	—
894	C₃²	—	18	1	no	—
895	C₃²	—	18	1	no	—
896	C₃²	—	18	1	no	—
897	C₃²	—	18	1	no	—
898	C₃²	—	18	1	no	—
899	C₃²	—	18	1	no	—
900	C₃²	—	18	1	no	—
901	C₃²	—	18	1	no	—
902	C₃²	—	18	1	no	—
903	C₃²	C₂×C₉×3₋¹⁺²	1	1	yes	characteristic, complemented
904	C₃²	C₃²×D₃×C₉	1	1	yes	characteristic
905	C₃²	C₃²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
906	C₃²	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
907	C₃²	D₃×#737	1	1	yes	characteristic
908	C₃²	D₃×#737	1	1	yes	characteristic
909	C₉	—	2	1	no	—
910	C₉	—	2	1	no	—
911	C₉	—	2	1	no	—
912	C₉	—	3	1	no	—
913	C₉	—	3	1	no	—
914	C₉	—	3	2	no	—
915	C₉	—	3	1	no	—
916	C₉	—	3	1	no	—
917	C₉	—	3	1	no	—
918	C₉	—	6	1	no	—
919	C₉	—	6	1	no	—
920	C₉	—	6	1	no	—
921	C₉	—	6	1	no	—
922	C₉	—	6	1	no	—
923	C₉	—	6	1	no	—
924	C₉	—	6	1	no	—
925	C₉	—	6	1	no	—
926	C₉	—	6	1	no	—
927	C₉	—	6	1	no	—
928	C₉	—	6	1	no	—
929	C₉	—	6	1	no	—
930	C₉	—	6	1	no	—
931	C₉	—	6	1	no	—
932	C₉	—	6	1	no	—
933	C₉	—	6	1	no	—
934	C₉	—	6	2	no	—
935	C₉	—	6	1	no	—
936	C₉	—	6	1	no	—
937	C₉	—	9	1	no	—
938	C₉	—	9	1	no	—
939	C₉	—	9	1	no	—
940	C₉	—	18	1	no	—
941	C₉	—	18	1	no	—
942	C₉	—	18	1	no	—
943	C₉	—	18	1	no	—
944	C₉	—	18	1	no	—
945	C₉	—	18	1	no	—
946	C₉	—	18	1	no	—
947	C₉	—	18	1	no	—
948	C₉	—	18	1	no	—
949	C₉	—	18	1	no	—
950	C₉	C₉×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
951	C₉	C₉×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
952	C₉	C₉×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
953	C₂×C₃	—	9	1	no	—
954	C₂×C₃	—	9	1	no	—
955	C₂×C₃	—	9	1	no	—
956	C₂×C₃	—	9	1	no	—
957	C₂×C₃	—	27	1	no	—
958	C₂×C₃	—	27	1	no	—
959	C₂×C₃	—	27	1	no	—
960	D₃	—	3	1	no	—
961	D₃	—	9	1	no	—
962	C₃	—	2	1	no	—
963	C₃	—	2	1	no	—
964	C₃	—	2	1	no	—
965	C₃	—	2	1	no	—
966	C₃	—	3	1	no	—
967	C₃	—	6	1	no	—
968	C₃	—	6	1	no	—
969	C₃	—	6	1	no	—
970	C₃	—	6	1	no	—
971	C₃	—	18	1	no	—
972	C₃	—	18	1	no	—
973	C₃	—	18	1	no	—
974	C₃	—	18	1	no	—
975	C₃	—	18	1	no	—
976	C₃	—	18	1	no	—
977	C₃	C₃×C₉×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
978	C₃	D₃×C₉×3₋¹⁺²	1	1	yes	characteristic
979	C₃	3₋¹⁺²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
980	C₃	#13091514	1	1	yes	characteristic
981	C₃	#13091514	1	1	yes	characteristic
982	C₂	—	9	1	no	Sylow

	subgroup	G/H
center	C₃²	C₃²×(C₃⋊D₃)⋊C₃
commutator	C₃³	C₂×C₃²×C₉
Frattini, socle	C₃³	C₃³×D₃
Fitting	#14552080	C₂
prime radical	C₃²×(C₃⋊D₃)⋊C₃	C₃²
cosocle	C₃⁴	C₂×C₃³
hypercenter	C₉⋊C₉	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₂×C₉×3₋¹⁺²
LCS	G ▷ C₃³ ▷ C₃²
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
1. #14552080	C₂	semidirect
5. C₃⋊D₃×C₉⋊C₉	C₃	semidirect
6. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
7. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
8. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
9. ((C₃⋊D₃)⋊C₉)⋊C₉	C₃	semidirect
12. #13090622	C₃	semidirect
13. C₉×(C₃⋊D₃)⋊C₉	C₃	semidirect
14. C₉×(C₃⋊D₃)⋊C₉	C₃	semidirect
15. C₉×(C₃⋊D₃)⋊C₉	C₃	semidirect
18. C₃×C₉×3₋¹⁺²	D₃	semidirect
20. C₃²×C₉⋊C₉	C₂×C₃	semidirect
33. #10624556	C₂×C₃	semidirect
34. #10624556	C₂×C₃	semidirect
35. #10624556	C₂×C₃	semidirect
36. #10624556	C₂×C₃	semidirect
39. #10624548	C₂×C₃	semidirect
40. C₉×C₃²⋊C₉	C₂×C₃	semidirect
41. C₉×C₃²⋊C₉	C₂×C₃	semidirect
42. C₉×C₃²⋊C₉	C₂×C₃	semidirect
51. #92262	C₉	semidirect
52. #92262	C₉	semidirect
53. #92262	C₉	semidirect
54. #92262	C₉	semidirect
55. #92262	C₉	semidirect
56. #92262	C₉	semidirect
57. #92262	C₉	semidirect
58. #92262	C₉	semidirect
59. #92262	C₉	semidirect
100. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
101. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
102. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
103. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
104. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
105. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
106. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
107. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
108. C₉⋊H(3,𝔽₃)	C₂×C₉	semidirect
208. C₉×C₃⋊D₃	C₃×C₉	semidirect
209. C₉×C₃⋊D₃	C₃×C₉	semidirect
210. C₉×C₃⋊D₃	C₃×C₉	semidirect
260. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
261. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
262. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
263. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
264. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
265. (C₃⋊D₃)⋊C₉	C₃×C₉	semidirect
266. (C₃⋊D₃)⋊C₉	3₋¹⁺²	semidirect
267. (C₃⋊D₃)⋊C₉	3₋¹⁺²	semidirect
294. C₃×3₋¹⁺²	D₃×C₉	semidirect
295. C₃×3₋¹⁺²	D₃×C₉	semidirect
296. C₃×3₋¹⁺²	D₃×C₉	semidirect
297. C₃×3₋¹⁺²	D₃×C₉	semidirect
298. C₃×3₋¹⁺²	D₃×C₉	semidirect
299. C₃×3₋¹⁺²	D₃×C₉	semidirect
300. C₃×3₋¹⁺²	D₃×C₉	semidirect
301. C₃×3₋¹⁺²	D₃×C₉	semidirect
302. C₃×3₋¹⁺²	D₃×C₉	semidirect
362. C₃²×C₉	C₂×C₃×C₉	semidirect
363. C₃²×C₉	C₂×C₃×C₉	semidirect
364. C₃²×C₉	C₂×C₃×C₉	semidirect
414. C₉⋊C₉	(C₃⋊D₃)⋊C₃	semidirect
482. C₃²⋊C₉	C₂×C₃×C₉	semidirect
483. C₃²⋊C₉	C₂×C₃×C₉	semidirect
484. C₃²⋊C₉	C₂×C₃×C₉	semidirect
485. C₃²⋊C₉	C₂×C₃×C₉	semidirect
486. C₃²⋊C₉	C₂×C₃×C₉	semidirect
487. C₃²⋊C₉	C₂×C₃×C₉	semidirect
488. C₃²⋊C₉	C₂×3₋¹⁺²	semidirect
489. C₃²⋊C₉	C₂×3₋¹⁺²	semidirect
812. C₃⋊D₃	C₉×3₋¹⁺²	semidirect
903. C₃²	C₂×C₉×3₋¹⁺²	semidirect
950. C₉	C₉×(C₃⋊D₃)⋊C₃	semidirect
951. C₉	C₉×(C₃⋊D₃)⋊C₃	semidirect
952. C₉	C₉×(C₃⋊D₃)⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#14552080	2
C₃×#92262	3
D₃×C₉×3₋¹⁺²	3
C₃×C₉×(C₃⋊D₃)⋊C₃	3
C₃⋊D₃×C₉⋊C₉	3
((C₃⋊D₃)⋊C₉)⋊C₉	3
(C₃×(C₃⋊D₃)⋊C₃)⋊C₉	3
#13090622	3
C₉×(C₃⋊D₃)⋊C₉	3