Subgroups — C₂×#72221823 #72243967

Order 8748.

4521 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13091435	—	3	2	no	maximal
2	C₂×#10624891⋊C₂	—	3	6	no	maximal
3	C₂×#13091425	—	3	1	no	maximal
4	C₂×#10624904⋊C₂	C₃	1	2	yes	maximal, complemented
5	C₂×#13091524	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×#4207⋊C₉	—	3	3	no	maximal
7	C₂×C₃×C₃⋊(D₉⋊C₉)	—	3	1	no	maximal
8	C₂×#13091424	C₃	1	1	yes	maximal, characteristic
9	C₂×#14555333	C₂	1	1	yes	maximal, characteristic, complemented
10	#72221823	C₂	1	2	yes	maximal, direct product factor
11	#14555333	C₂²	1	1	yes	characteristic, complemented, Sylow
12	#10624904⋊C₂	C₂×C₃	1	4	yes	complemented
13	#13091524	C₂×C₃	1	2	yes	complemented
14	#10624891⋊C₂	—	3	12	no	—
15	#13091435	—	3	4	no	—
16	#13091425	—	3	2	no	—
17	#13091424	C₂×C₃	1	2	yes	—
18	#4207⋊C₉	—	3	6	no	—
19	C₃×C₃⋊(D₉⋊C₉)	—	3	2	no	—
20	C₂×#10624907	—	2	6	no	—
21	C₂×#10624907	—	2	2	no	—
22	C₂×#10624907	—	2	6	no	—
23	C₂×#10624907	—	2	2	no	—
24	C₂×#10624907	—	2	2	no	—
25	C₂×#10624904	—	2	6	no	—
26	C₂×#10624904	—	2	2	no	—
27	C₂×#10624904	C₂×C₃	1	2	yes	complemented
28	C₂×#10624901	—	2	1	no	—
29	C₂×#10624901	—	2	6	no	—
30	C₂×#10624901	—	2	2	no	—
31	C₂×#10624900	—	2	1	no	—
32	C₂×#10624900	—	2	3	no	—
33	C₂×#10624900	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#10624891	—	2	6	no	—
35	C₂×#10624891	D₃	1	6	yes	complemented
36	C₂×#10624887	—	2	3	no	—
37	C₂×#10624872	—	2	1	no	—
38	C₂×#10624872	—	2	2	no	—
39	C₂×#10624872	D₃	1	2	yes	complemented
40	C₂×#10624869	—	2	1	no	—
41	C₂×#10624869	D₃	1	1	yes	characteristic
42	C₂×#10624869	C₂×C₃	1	1	yes	characteristic
43	C₂×#10624864	D₃	1	3	yes	complemented
44	C₂×C₃²×C₉⋊C₉	D₃	1	1	yes	characteristic, complemented
45	C₂×C₃⋊#4208	—	3	1	no	—
46	C₂×C₃×#4207	—	3	3	no	—
47	C₂×C₃×C₉×C₃⋊D₃	—	9	1	no	—
48	C₂×C₃²×C₃⋊D₉	—	3	1	no	—
49	C₂×C₉⋊#272	C₃²	1	1	yes	characteristic
50	C₂×#92311	—	3	6	no	—
51	C₂×#92308	—	3	6	no	—
52	C₂×#6895⋊C₂	—	3	2	no	—
53	C₂×#6895⋊C₂	—	3	2	no	—
54	C₂×#6895⋊C₂	—	3	6	no	—
55	C₂×#92305	—	3	2	no	—
56	C₂×#92304	—	3	6	no	—
57	C₂×#92302	—	3	2	no	—
58	C₂×#92300	—	3	1	no	—
59	C₂×#92295	—	3	2	no	—
60	C₂×#92294	—	3	6	no	—
61	C₂×C₃⋊(D₉⋊C₉)	—	3	1	no	—
62	C₂×C₃⋊(D₉⋊C₉)	—	3	2	no	—
63	C₂×C₃⋊(D₉⋊C₉)	—	3	3	no	—
64	C₂×C₉×AGL(1,ℤ/9)	—	9	6	no	—
65	C₂×C₉×(C₃⋊D₃)⋊C₃	—	9	3	no	—
66	C₂×C₃×D₉⋊C₉	—	9	1	no	—
67	C₂×C₃×D₉⋊C₉	—	9	2	no	—
68	#10624907	—	2	6	no	—
69	#10624907	—	2	2	no	—
70	#10624907	—	2	6	no	—
71	#10624907	—	2	2	no	—
72	#10624907	—	2	2	no	—
73	#10624904	—	2	6	no	—
74	#10624904	—	2	2	no	—
75	#10624904	C₂²×C₃	1	2	yes	complemented
76	#10624901	—	2	6	no	—
77	#10624901	—	2	2	no	—
78	#10624901	—	2	1	no	—
79	#10624900	—	2	1	no	—
80	#10624900	—	2	3	no	—
81	#10624900	C₂²×C₃	1	1	yes	characteristic, complemented
82	#10624891	—	2	6	no	—
83	#10624891	C₂×D₃	1	6	yes	complemented
84	#10624887	—	2	3	no	—
85	#10624872	—	2	2	no	—
86	#10624872	—	2	1	no	—
87	#10624872	C₂×D₃	1	2	yes	complemented
88	#10624869	—	2	1	no	—
89	#10624869	C₂×D₃	1	1	yes	characteristic
90	#10624869	C₂²×C₃	1	1	yes	characteristic
91	#10624864	C₂×D₃	1	3	yes	complemented
92	C₃²×C₉⋊C₉	C₂×D₃	1	1	yes	characteristic, complemented
93	C₂×C₃×#737	—	2	3	no	—
94	C₂×C₃×#737	—	2	1	no	—
95	C₂×C₃×#737	C₃×D₃	1	3	yes	—
96	C₂×C₃×#737	C₃×D₃	1	1	yes	characteristic
97	C₂×C₃³×C₉	—	2	1	no	—
98	C₂×C₃³×C₉	C₃×D₃	1	1	yes	characteristic
99	C₂×C₃³×C₉	C₃⋊D₃	1	1	yes	characteristic
100	C₃⋊#4208	—	3	2	no	—
101	C₃×#4207	—	3	6	no	—
102	C₃×C₉×C₃⋊D₃	—	9	2	no	—
103	C₃²×C₃⋊D₉	—	3	2	no	—
104	C₂×#6900	—	2	3	no	—
105	C₂×#6900	—	2	6	no	—
106	C₂×#6899	—	2	6	no	—
107	C₂×#6899	—	2	6	no	—
108	C₂×#6899	—	2	6	no	—
109	C₂×#6899	—	2	6	no	—
110	C₂×#6899	—	2	6	no	—
111	C₂×#6899	—	2	6	no	—
112	C₂×#6899	—	2	6	no	—
113	C₂×#6899	—	2	6	no	—
114	C₂×#6899	—	2	6	no	—
115	C₂×#6899	—	2	6	no	—
116	C₂×#6899	—	2	6	no	—
117	C₂×#6899	—	2	6	no	—
118	C₂×#6898	—	2	6	no	—
119	C₂×#6898	—	2	6	no	—
120	C₂×#6898	—	2	6	no	—
121	C₂×#6898	—	2	6	no	—
122	C₂×#6898	C₃×D₃	1	6	yes	complemented
123	C₂×#6897	—	2	6	no	—
124	C₂×#6897	—	2	6	no	—
125	C₂×#6897	—	2	6	no	—
126	C₂×#6897	—	2	6	no	—
127	C₂×#6897	—	2	6	no	—
128	C₂×#6897	—	2	6	no	—
129	C₂×#6897	—	2	6	no	—
130	C₂×#6897	—	2	6	no	—
131	C₂×#6897	—	2	6	no	—
132	C₂×#6896	—	2	6	no	—
133	C₂×#6896	—	2	6	no	—
134	C₂×#6896	—	2	6	no	—
135	C₂×#6896	—	2	3	no	—
136	C₂×#6896	—	2	6	no	—
137	C₂×#6896	—	2	6	no	—
138	C₂×#6896	—	2	6	no	—
139	C₂×#6896	—	2	6	no	—
140	C₂×#6896	—	2	6	no	—
141	C₂×#6896	C₃×D₃	1	6	yes	complemented
142	C₂×#6895	—	2	6	no	—
143	C₂×#6895	—	2	6	no	—
144	C₂×#6895	—	2	6	no	—
145	C₂×#6895	—	2	6	no	—
146	C₂×#6895	—	2	6	no	—
147	C₂×#6895	—	2	6	no	—
148	C₂×#6895	—	2	2	no	—
149	C₂×#6895	—	2	2	no	—
150	C₂×#6895	—	2	6	no	—
151	C₂×#6895	C₃×D₃	1	2	yes	—
152	C₂×#6895	C₃×D₃	1	2	yes	—
153	C₂×#6895	C₃×D₃	1	6	yes	complemented
154	C₂×#6894	—	2	6	no	—
155	C₂×#6894	—	2	6	no	—
156	C₂×#6894	—	2	2	no	—
157	C₂×#6894	—	2	2	no	—
158	C₂×#6894	—	2	6	no	—
159	C₂×#6894	—	2	2	no	—
160	C₂×#6894	—	2	2	no	—
161	C₂×#6894	—	2	6	no	—
162	C₂×#6894	—	2	2	no	—
163	C₂×#6894	—	2	1	no	—
164	C₂×#6894	—	2	6	no	—
165	C₂×#6894	—	2	6	no	—
166	C₂×#6894	—	2	6	no	—
167	C₂×#6894	—	2	6	no	—
168	C₂×#6894	—	2	6	no	—
169	C₂×#6894	—	2	6	no	—
170	C₂×#6894	—	2	6	no	—
171	C₂×#6894	—	2	6	no	—
172	C₂×#6894	—	2	6	no	—
173	C₂×#6894	—	2	6	no	—
174	C₂×#6894	—	2	6	no	—
175	C₂×#6894	—	2	2	no	—
176	C₂×#6894	—	2	1	no	—
177	C₂×#6894	—	2	6	no	—
178	C₂×#6894	—	2	3	no	—
179	C₂×#6894	—	2	6	no	—
180	C₂×#6894	—	2	6	no	—
181	C₂×#6894	—	2	6	no	—
182	C₂×#6894	—	2	6	no	—
183	C₂×#6894	—	2	6	no	—
184	C₂×#6894	—	2	2	no	—
185	C₂×#6894	—	2	2	no	—
186	C₂×#6894	—	2	6	no	—
187	C₂×#6893	—	2	6	no	—
188	C₂×#6893	—	2	2	no	—
189	C₂×#6893	C₃×D₃	1	6	yes	—
190	C₂×#6893	C₃×D₃	1	2	yes	—
191	C₂×C₉⋊H(3,𝔽₃)	—	2	6	no	—
192	C₂×C₉⋊H(3,𝔽₃)	—	2	2	no	—
193	C₂×C₉⋊H(3,𝔽₃)	—	2	2	no	—
194	C₂×C₉⋊H(3,𝔽₃)	—	2	2	no	—
195	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
196	C₂×C₉⋊H(3,𝔽₃)	—	2	6	no	—
197	C₂×C₉⋊H(3,𝔽₃)	—	2	3	no	—
198	C₂×C₉⋊H(3,𝔽₃)	—	2	2	no	—
199	C₂×C₉⋊H(3,𝔽₃)	—	2	6	no	—
200	C₂×C₉⋊H(3,𝔽₃)	—	2	6	no	—
201	C₂×#6891	—	2	2	no	—
202	C₂×#6891	—	2	1	no	—
203	C₂×#6891	C₃×D₃	1	2	yes	—
204	C₂×C₃²⋊H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
205	C₂×C₉×3₋¹⁺²	—	2	2	no	—
206	C₂×C₉×3₋¹⁺²	—	2	2	no	—
207	C₂×C₉×3₋¹⁺²	—	2	6	no	—
208	C₂×C₉×3₋¹⁺²	—	2	6	no	—
209	C₂×C₉×3₋¹⁺²	—	2	1	no	—
210	C₂×C₉×3₋¹⁺²	—	2	2	no	—
211	C₂×C₉×3₋¹⁺²	—	2	6	no	—
212	C₂×C₉×3₋¹⁺²	—	2	3	no	—
213	C₂×C₉×3₋¹⁺²	—	2	6	no	—
214	C₂×C₉×3₋¹⁺²	—	2	6	no	—
215	C₂×C₉×3₋¹⁺²	—	2	2	no	—
216	C₂×C₉×3₋¹⁺²	—	2	6	no	—
217	C₂×C₉×3₋¹⁺²	—	2	6	no	—
218	C₂×C₉×3₋¹⁺²	—	2	6	no	—
219	C₂×C₉×3₋¹⁺²	C₃⋊D₃	1	6	yes	—
220	C₂×C₉×H(3,𝔽₃)	—	2	3	no	—
221	C₂×C₉×H(3,𝔽₃)	—	2	1	no	—
222	C₂×C₉×H(3,𝔽₃)	—	2	1	no	—
223	C₂×C₉×H(3,𝔽₃)	—	2	1	no	—
224	C₂×C₉×H(3,𝔽₃)	—	2	3	no	—
225	C₂×C₉×H(3,𝔽₃)	—	2	1	no	—
226	C₂×C₉×H(3,𝔽₃)	—	2	3	no	—
227	C₂×C₉×H(3,𝔽₃)	—	2	3	no	—
228	C₂×C₉×H(3,𝔽₃)	C₃⋊D₃	1	3	yes	—
229	C₂×C₉×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
230	C₂×#6887	—	2	6	no	—
231	C₂×#6887	—	2	3	no	—
232	C₂×#6887	—	2	2	no	—
233	C₂×#6887	—	2	6	no	—
234	C₂×#6887	C₃×D₃	1	2	yes	—
235	C₂×#6887	C₃×D₃	1	6	yes	complemented
236	C₂×C₃×C₉⋊C₉	—	2	1	no	—
237	C₂×C₃×C₉⋊C₉	—	2	2	no	—
238	C₂×C₃×C₉⋊C₉	—	2	1	no	—
239	C₂×C₃×C₉⋊C₉	—	2	2	no	—
240	C₂×C₃×C₉⋊C₉	—	2	1	no	—
241	C₂×C₃×C₉⋊C₉	—	2	2	no	—
242	C₂×C₃×C₉⋊C₉	—	2	2	no	—
243	C₂×C₃×C₉⋊C₉	—	2	2	no	—
244	C₂×C₃×C₉⋊C₉	—	2	2	no	—
245	C₂×C₃×C₉⋊C₉	—	2	3	no	—
246	C₂×C₃×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
247	C₂×C₃×C₉⋊C₉	C₃×D₃	1	2	yes	—
248	C₂×C₃×C₉⋊C₉	C₃×D₃	1	3	yes	complemented
249	C₂×C₃×C₉⋊C₉	C₃⋊D₃	1	1	yes	characteristic
250	C₂×C₃×C₉⋊C₉	C₃⋊D₃	1	2	yes	—
251	C₉⋊#272	C₂×C₃²	1	2	yes	—
252	#92311	—	3	12	no	—
253	#92308	—	3	12	no	—
254	#6895⋊C₂	—	3	4	no	—
255	#6895⋊C₂	—	3	4	no	—
256	#6895⋊C₂	—	3	12	no	—
257	#92305	—	3	4	no	—
258	#92304	—	3	12	no	—
259	#92302	—	3	4	no	—
260	#92300	—	3	2	no	—
261	#92295	—	3	4	no	—
262	#92294	—	3	12	no	—
263	C₃⋊(D₉⋊C₉)	—	3	2	no	—
264	C₃⋊(D₉⋊C₉)	—	3	4	no	—
265	C₃⋊(D₉⋊C₉)	—	3	6	no	—
266	C₉×AGL(1,ℤ/9)	—	9	12	no	—
267	C₉×(C₃⋊D₃)⋊C₃	—	9	6	no	—
268	C₃×D₉⋊C₉	—	9	2	no	—
269	C₃×D₉⋊C₉	—	9	4	no	—
270	C₂×C₃²×C₃⋊D₃	—	9	1	no	—
271	C₂×C₃⋊#272	—	3	1	no	—
272	C₂×#4208	—	27	3	no	—
273	C₂×#4207	—	3	9	no	—
274	C₂×C₉×C₃⋊D₃	—	9	1	no	—
275	C₂×C₉×C₃⋊D₃	—	9	2	no	—
276	C₂×C₉×C₃⋊D₃	—	9	3	no	—
277	C₂×C₃×C₃⋊D₉	—	3	3	no	—
278	C₂×C₃×C₃⋊D₉	—	3	1	no	—
279	C₂×C₃×C₃⋊D₉	—	3	3	no	—
280	C₂×C₃×AGL(1,ℤ/9)	—	9	6	no	—
281	C₂×C₃×(C₃⋊D₃)⋊C₃	—	9	3	no	—
282	C₂×C₃×D₃×C₉	—	27	3	no	—
283	C₂×C₃×D₃×C₉	—	27	1	no	—
284	C₂×C₃²×D₉	—	9	1	no	—
285	C₂×C₃²×D₉	—	9	2	no	—
286	C₂×#4181	—	3	2	no	—
287	C₂×#4181	—	3	6	no	—
288	C₂×D₉⋊C₉	—	9	1	no	—
289	C₂×D₉⋊C₉	—	9	2	no	—
290	C₂×D₉⋊C₉	—	9	2	no	—
291	C₂×D₉⋊C₉	—	9	2	no	—
292	C₂×D₉⋊C₉	—	9	2	no	—
293	C₂×D₉⋊C₉	—	9	6	no	—
294	C₂×D₉⋊C₉	—	9	6	no	—
295	C₂×(C₃⋊D₃)⋊C₉	—	9	6	no	—
296	C₂×C₉×D₉	—	9	6	no	—
297	C₃×#737	—	2	3	no	—
298	C₃×#737	—	2	1	no	—
299	C₃×#737	C₂×C₃×D₃	1	3	yes	—
300	C₃×#737	C₂×C₃×D₃	1	1	yes	characteristic
301	C₃³×C₉	—	2	1	no	—
302	C₃³×C₉	C₂×C₃×D₃	1	1	yes	characteristic
303	C₃³×C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
304	#6900	—	2	3	no	—
305	#6900	—	2	6	no	—
306	#6899	—	2	6	no	—
307	#6899	—	2	6	no	—
308	#6899	—	2	6	no	—
309	#6899	—	2	6	no	—
310	#6899	—	2	6	no	—
311	#6899	—	2	6	no	—
312	#6899	—	2	6	no	—
313	#6899	—	2	6	no	—
314	#6899	—	2	6	no	—
315	#6899	—	2	6	no	—
316	#6899	—	2	6	no	—
317	#6899	—	2	6	no	—
318	#6898	—	2	6	no	—
319	#6898	—	2	6	no	—
320	#6898	—	2	6	no	—
321	#6898	—	2	6	no	—
322	#6898	C₂×C₃×D₃	1	6	yes	complemented
323	#6897	—	2	6	no	—
324	#6897	—	2	6	no	—
325	#6897	—	2	6	no	—
326	#6897	—	2	6	no	—
327	#6897	—	2	6	no	—
328	#6897	—	2	6	no	—
329	#6897	—	2	6	no	—
330	#6897	—	2	6	no	—
331	#6897	—	2	6	no	—
332	#6896	—	2	6	no	—
333	#6896	—	2	6	no	—
334	#6896	—	2	6	no	—
335	#6896	—	2	3	no	—
336	#6896	—	2	6	no	—
337	#6896	—	2	6	no	—
338	#6896	—	2	6	no	—
339	#6896	—	2	6	no	—
340	#6896	—	2	6	no	—
341	#6896	C₂×C₃×D₃	1	6	yes	complemented
342	#6895	—	2	6	no	—
343	#6895	—	2	6	no	—
344	#6895	—	2	6	no	—
345	#6895	—	2	6	no	—
346	#6895	—	2	6	no	—
347	#6895	—	2	6	no	—
348	#6895	—	2	2	no	—
349	#6895	—	2	2	no	—
350	#6895	—	2	6	no	—
351	#6895	C₂×C₃×D₃	1	2	yes	—
352	#6895	C₂×C₃×D₃	1	2	yes	—
353	#6895	C₂×C₃×D₃	1	6	yes	complemented
354	#6894	—	2	6	no	—
355	#6894	—	2	6	no	—
356	#6894	—	2	2	no	—
357	#6894	—	2	2	no	—
358	#6894	—	2	6	no	—
359	#6894	—	2	2	no	—
360	#6894	—	2	2	no	—
361	#6894	—	2	6	no	—
362	#6894	—	2	2	no	—
363	#6894	—	2	1	no	—
364	#6894	—	2	6	no	—
365	#6894	—	2	6	no	—
366	#6894	—	2	6	no	—
367	#6894	—	2	6	no	—
368	#6894	—	2	6	no	—
369	#6894	—	2	6	no	—
370	#6894	—	2	6	no	—
371	#6894	—	2	6	no	—
372	#6894	—	2	6	no	—
373	#6894	—	2	6	no	—
374	#6894	—	2	6	no	—
375	#6894	—	2	2	no	—
376	#6894	—	2	1	no	—
377	#6894	—	2	6	no	—
378	#6894	—	2	3	no	—
379	#6894	—	2	6	no	—
380	#6894	—	2	6	no	—
381	#6894	—	2	6	no	—
382	#6894	—	2	6	no	—
383	#6894	—	2	6	no	—
384	#6894	—	2	2	no	—
385	#6894	—	2	2	no	—
386	#6894	—	2	6	no	—
387	#6893	—	2	6	no	—
388	#6893	—	2	2	no	—
389	#6893	C₂×C₃×D₃	1	6	yes	—
390	#6893	C₂×C₃×D₃	1	2	yes	—
391	C₉⋊H(3,𝔽₃)	—	2	6	no	—
392	C₉⋊H(3,𝔽₃)	—	2	2	no	—
393	C₉⋊H(3,𝔽₃)	—	2	2	no	—
394	C₉⋊H(3,𝔽₃)	—	2	2	no	—
395	C₉⋊H(3,𝔽₃)	—	2	1	no	—
396	C₉⋊H(3,𝔽₃)	—	2	6	no	—
397	C₉⋊H(3,𝔽₃)	—	2	3	no	—
398	C₉⋊H(3,𝔽₃)	—	2	2	no	—
399	C₉⋊H(3,𝔽₃)	—	2	6	no	—
400	C₉⋊H(3,𝔽₃)	—	2	6	no	—
401	#6891	—	2	2	no	—
402	#6891	—	2	1	no	—
403	#6891	C₂×C₃×D₃	1	2	yes	—
404	C₃²⋊H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
405	C₉×3₋¹⁺²	—	2	2	no	—
406	C₉×3₋¹⁺²	—	2	2	no	—
407	C₉×3₋¹⁺²	—	2	6	no	—
408	C₉×3₋¹⁺²	—	2	6	no	—
409	C₉×3₋¹⁺²	—	2	1	no	—
410	C₉×3₋¹⁺²	—	2	2	no	—
411	C₉×3₋¹⁺²	—	2	6	no	—
412	C₉×3₋¹⁺²	—	2	3	no	—
413	C₉×3₋¹⁺²	—	2	6	no	—
414	C₉×3₋¹⁺²	—	2	6	no	—
415	C₉×3₋¹⁺²	—	2	2	no	—
416	C₉×3₋¹⁺²	—	2	6	no	—
417	C₉×3₋¹⁺²	—	2	6	no	—
418	C₉×3₋¹⁺²	—	2	6	no	—
419	C₉×3₋¹⁺²	C₂×C₃⋊D₃	1	6	yes	—
420	C₉×H(3,𝔽₃)	—	2	3	no	—
421	C₉×H(3,𝔽₃)	—	2	1	no	—
422	C₉×H(3,𝔽₃)	—	2	1	no	—
423	C₉×H(3,𝔽₃)	—	2	1	no	—
424	C₉×H(3,𝔽₃)	—	2	3	no	—
425	C₉×H(3,𝔽₃)	—	2	1	no	—
426	C₉×H(3,𝔽₃)	—	2	3	no	—
427	C₉×H(3,𝔽₃)	—	2	3	no	—
428	C₉×H(3,𝔽₃)	C₂×C₃⋊D₃	1	3	yes	—
429	C₉×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
430	#6887	—	2	6	no	—
431	#6887	—	2	3	no	—
432	#6887	—	2	2	no	—
433	#6887	—	2	6	no	—
434	#6887	C₂×C₃×D₃	1	2	yes	—
435	#6887	C₂×C₃×D₃	1	6	yes	complemented
436	C₃×C₉⋊C₉	—	2	1	no	—
437	C₃×C₉⋊C₉	—	2	2	no	—
438	C₃×C₉⋊C₉	—	2	1	no	—
439	C₃×C₉⋊C₉	—	2	2	no	—
440	C₃×C₉⋊C₉	—	2	1	no	—
441	C₃×C₉⋊C₉	—	2	2	no	—
442	C₃×C₉⋊C₉	—	2	2	no	—
443	C₃×C₉⋊C₉	—	2	2	no	—
444	C₃×C₉⋊C₉	—	2	2	no	—
445	C₃×C₉⋊C₉	—	2	3	no	—
446	C₃×C₉⋊C₉	C₂×C₃×D₃	1	1	yes	characteristic
447	C₃×C₉⋊C₉	C₂×C₃×D₃	1	2	yes	—
448	C₃×C₉⋊C₉	C₂×C₃×D₃	1	3	yes	complemented
449	C₃×C₉⋊C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
450	C₃×C₉⋊C₉	C₂×C₃⋊D₃	1	2	yes	—
451	C₂×C₃⁴	C₃×C₃⋊D₃	1	1	yes	characteristic
452	C₃²×C₃⋊D₃	—	9	2	no	—
453	C₂×#737	—	3	9	no	—
454	C₂×#737	—	6	9	no	—
455	C₂×#737	—	9	3	no	—
456	C₂×#737	—	18	3	no	—
457	C₂×#737	—	18	9	no	—
458	C₂×C₃×3₋¹⁺²	—	2	6	no	—
459	C₂×C₃×3₋¹⁺²	—	2	1	no	—
460	C₂×C₃×3₋¹⁺²	—	2	2	no	—
461	C₂×C₃×3₋¹⁺²	—	2	3	no	—
462	C₂×C₃×3₋¹⁺²	—	2	6	no	—
463	C₂×C₃×3₋¹⁺²	—	2	6	no	—
464	C₂×C₃×3₋¹⁺²	—	2	6	no	—
465	C₂×C₃×3₋¹⁺²	—	2	3	no	—
466	C₂×C₃×3₋¹⁺²	—	2	6	no	—
467	C₂×C₃×3₋¹⁺²	—	2	6	no	—
468	C₂×C₃×3₋¹⁺²	C₃×C₃⋊D₃	1	6	yes	—
469	C₂×C₃×H(3,𝔽₃)	—	2	3	no	—
470	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
471	C₂×C₃×H(3,𝔽₃)	C₃²×D₃	1	1	yes	characteristic
472	C₂×C₃×H(3,𝔽₃)	C₃×C₃⋊D₃	1	3	yes	—
473	C₂×C₃²×C₉	—	2	2	no	—
474	C₂×C₃²×C₉	—	2	1	no	—
475	C₂×C₃²×C₉	—	2	1	no	—
476	C₂×C₃²×C₉	—	2	1	no	—
477	C₂×C₃²×C₉	—	2	2	no	—
478	C₂×C₃²×C₉	—	2	3	no	—
479	C₂×C₃²×C₉	—	2	3	no	—
480	C₂×C₃²×C₉	—	2	1	no	—
481	C₂×C₃²×C₉	—	2	2	no	—
482	C₂×C₃²×C₉	—	2	3	no	—
483	C₂×C₃²×C₉	—	2	1	no	—
484	C₂×C₃²×C₉	—	2	1	no	—
485	C₂×C₃²×C₉	—	2	2	no	—
486	C₂×C₃²×C₉	—	2	1	no	—
487	C₂×C₃²×C₉	—	2	2	no	—
488	C₂×C₃²×C₉	—	2	3	no	—
489	C₂×C₃²×C₉	—	2	1	no	—
490	C₂×C₃²×C₉	—	2	2	no	—
491	C₂×C₃²×C₉	—	2	3	no	—
492	C₂×C₃²×C₉	—	3	3	no	—
493	C₂×C₃²×C₉	—	6	3	no	—
494	C₂×C₃²×C₉	—	9	3	no	—
495	C₂×C₃²×C₉	—	18	3	no	—
496	C₂×C₃²×C₉	C₃²×D₃	1	1	yes	characteristic
497	C₂×C₃²×C₉	C₃²×D₃	1	3	yes	—
498	C₂×C₃²×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
499	C₂×C₃²×C₉	C₃×C₃⋊D₃	1	2	yes	—
500	C₂×C₃²×C₉	C₃×C₃⋊D₃	1	2	yes	—
501	C₂×C₃²×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
502	C₂×C₃²×C₉	C₃×C₃⋊D₃	1	3	yes	—
503	C₂×C₃²×C₉	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
504	C₃⋊#272	—	3	2	no	—
505	#4208	—	27	6	no	—
506	#4207	—	3	18	no	—
507	C₉×C₃⋊D₃	—	9	4	no	—
508	C₉×C₃⋊D₃	—	9	2	no	—
509	C₉×C₃⋊D₃	—	9	6	no	—
510	C₃×C₃⋊D₉	—	3	6	no	—
511	C₃×C₃⋊D₉	—	3	2	no	—
512	C₃×C₃⋊D₉	—	3	6	no	—
513	C₃×AGL(1,ℤ/9)	—	9	12	no	—
514	C₃×(C₃⋊D₃)⋊C₃	—	9	6	no	—
515	C₃×D₃×C₉	—	27	6	no	—
516	C₃×D₃×C₉	—	27	2	no	—
517	C₃²×D₉	—	9	4	no	—
518	C₃²×D₉	—	9	2	no	—
519	C₂×C₉⋊C₉	—	2	2	no	—
520	C₂×C₉⋊C₉	—	2	2	no	—
521	C₂×C₉⋊C₉	—	2	2	no	—
522	C₂×C₉⋊C₉	—	2	1	no	—
523	C₂×C₉⋊C₉	—	2	2	no	—
524	C₂×C₉⋊C₉	—	2	2	no	—
525	C₂×C₉⋊C₉	—	2	2	no	—
526	C₂×C₉⋊C₉	—	2	2	no	—
527	C₂×C₉⋊C₉	—	2	2	no	—
528	C₂×C₉⋊C₉	—	2	1	no	—
529	C₂×C₉⋊C₉	—	2	6	no	—
530	C₂×C₉⋊C₉	—	2	6	no	—
531	C₂×C₉⋊C₉	—	2	3	no	—
532	C₂×C₉⋊C₉	—	2	6	no	—
533	C₂×C₉⋊C₉	—	2	6	no	—
534	C₂×C₉⋊C₉	—	2	6	no	—
535	C₂×C₉⋊C₉	—	2	6	no	—
536	C₂×C₉⋊C₉	—	2	6	no	—
537	C₂×C₉⋊C₉	—	2	6	no	—
538	C₂×C₉⋊C₉	—	2	6	no	—
539	C₂×C₉⋊C₉	—	2	6	no	—
540	C₂×C₉⋊C₉	—	2	6	no	—
541	C₂×C₉⋊C₉	—	2	6	no	—
542	C₂×C₉⋊C₉	—	2	6	no	—
543	C₂×C₉⋊C₉	—	2	6	no	—
544	C₂×C₉⋊C₉	—	2	6	no	—
545	C₂×C₉⋊C₉	—	2	6	no	—
546	C₂×C₉⋊C₉	—	2	6	no	—
547	C₂×C₉⋊C₉	—	2	6	no	—
548	C₂×C₉⋊C₉	—	2	6	no	—
549	C₂×C₉⋊C₉	—	2	6	no	—
550	C₂×C₉⋊C₉	—	2	6	no	—
551	C₂×C₉⋊C₉	—	2	6	no	—
552	C₂×C₉⋊C₉	—	2	6	no	—
553	C₂×C₉⋊C₉	—	2	6	no	—
554	C₂×C₉⋊C₉	—	2	6	no	—
555	C₂×C₉⋊C₉	—	2	6	no	—
556	C₂×C₉⋊C₉	—	2	6	no	—
557	C₂×C₉⋊C₉	—	2	6	no	—
558	C₂×C₉⋊C₉	—	2	6	no	—
559	C₂×C₉⋊C₉	—	2	2	no	—
560	C₂×C₉⋊C₉	—	2	1	no	—
561	C₂×C₉⋊C₉	—	2	2	no	—
562	C₂×C₉⋊C₉	—	2	2	no	—
563	C₂×C₉⋊C₉	—	2	2	no	—
564	C₂×C₉⋊C₉	—	2	6	no	—
565	C₂×C₉⋊C₉	—	2	3	no	—
566	C₂×C₉⋊C₉	—	2	6	no	—
567	C₂×C₉⋊C₉	—	2	6	no	—
568	C₂×C₉⋊C₉	—	2	6	no	—
569	C₂×C₉⋊C₉	—	2	6	no	—
570	C₂×C₉⋊C₉	—	2	6	no	—
571	C₂×C₉⋊C₉	—	2	6	no	—
572	C₂×C₉⋊C₉	—	2	6	no	—
573	C₂×C₉⋊C₉	—	2	6	no	—
574	C₂×C₉⋊C₉	—	2	6	no	—
575	C₂×C₉⋊C₉	—	2	6	no	—
576	C₂×C₉⋊C₉	—	2	6	no	—
577	C₂×C₉⋊C₉	—	2	6	no	—
578	C₂×C₉⋊C₉	—	2	6	no	—
579	C₂×C₉⋊C₉	—	2	6	no	—
580	C₂×C₉⋊C₉	—	2	1	no	—
581	C₂×C₉⋊C₉	—	2	2	no	—
582	C₂×C₉⋊C₉	—	2	2	no	—
583	C₂×C₉⋊C₉	—	2	2	no	—
584	C₂×C₉⋊C₉	—	2	2	no	—
585	C₂×C₉⋊C₉	—	2	6	no	—
586	C₂×C₉⋊C₉	—	2	6	no	—
587	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
588	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	2	yes	—
589	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	2	yes	—
590	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	2	yes	—
591	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	2	yes	—
592	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	6	yes	—
593	C₂×C₉⋊C₉	C₃×C₃⋊D₃	1	6	yes	—
594	C₂×C₃²⋊C₉	—	2	6	no	—
595	C₂×C₃²⋊C₉	—	2	6	no	—
596	C₂×C₃²⋊C₉	—	2	6	no	—
597	C₂×C₃²⋊C₉	—	2	6	no	—
598	C₂×C₃²⋊C₉	—	2	6	no	—
599	C₂×C₃²⋊C₉	—	2	6	no	—
600	C₂×C₃²⋊C₉	—	2	6	no	—
601	C₂×C₃²⋊C₉	—	2	6	no	—
602	C₂×C₃²⋊C₉	—	2	6	no	—
603	C₂×C₃²⋊C₉	—	2	6	no	—
604	C₂×C₃²⋊C₉	—	2	2	no	—
605	C₂×C₃²⋊C₉	—	2	2	no	—
606	C₂×C₃²⋊C₉	—	2	2	no	—
607	C₂×C₃²⋊C₉	—	2	2	no	—
608	C₂×C₃²⋊C₉	—	2	6	no	—
609	C₂×C₃²⋊C₉	—	2	6	no	—
610	C₂×C₃²⋊C₉	—	2	6	no	—
611	C₂×C₃²⋊C₉	—	2	6	no	—
612	C₂×C₃²⋊C₉	—	2	6	no	—
613	C₂×C₃²⋊C₉	—	2	6	no	—
614	C₂×C₃²⋊C₉	—	2	3	no	—
615	C₂×C₃²⋊C₉	—	2	6	no	—
616	C₂×C₃²⋊C₉	—	2	6	no	—
617	C₂×C₃²⋊C₉	—	2	6	no	—
618	C₂×C₃²⋊C₉	—	2	6	no	—
619	C₂×C₃²⋊C₉	—	2	6	no	—
620	C₂×C₃²⋊C₉	C₃²×D₃	1	2	yes	—
621	C₂×C₃²⋊C₉	C₃²×D₃	1	6	yes	—
622	C₂×C₃²⋊C₉	C₃×C₃⋊D₃	1	6	yes	—
623	C₂×C₉²	—	2	6	no	—
624	C₂×C₉²	—	2	6	no	—
625	C₂×C₉²	—	2	3	no	—
626	C₂×C₉²	—	2	6	no	—
627	C₂×C₉²	—	2	6	no	—
628	C₂×C₉²	—	2	6	no	—
629	C₂×C₉²	C₃×C₃⋊D₃	1	6	yes	—
630	#4181	—	3	4	no	—
631	#4181	—	3	12	no	—
632	D₉⋊C₉	—	9	2	no	—
633	D₉⋊C₉	—	9	4	no	—
634	D₉⋊C₉	—	9	4	no	—
635	D₉⋊C₉	—	9	4	no	—
636	D₉⋊C₉	—	9	4	no	—
637	D₉⋊C₉	—	9	12	no	—
638	D₉⋊C₉	—	9	12	no	—
639	(C₃⋊D₃)⋊C₉	—	9	12	no	—
640	C₉×D₉	—	9	12	no	—
641	C₂×C₃×C₃⋊D₃	—	9	3	no	—
642	C₂×C₃×C₃⋊D₃	—	9	1	no	—
643	C₂×C₃×C₃⋊D₃	—	9	3	no	—
644	C₂×C₃²×D₃	—	27	3	no	—
645	C₂×C₃²×D₃	—	27	1	no	—
646	C₂²×C₃×C₉	—	81	1	no	—
647	C₂×#272	—	27	3	no	—
648	C₂×C₃⋊D₉	—	3	1	no	—
649	C₂×C₃⋊D₉	—	3	3	no	—
650	C₂×AGL(1,ℤ/9)	—	9	18	no	—
651	C₂×(C₃⋊D₃)⋊C₃	—	9	9	no	—
652	C₂×D₃×C₉	—	27	6	no	—
653	C₂×D₃×C₉	—	27	3	no	—
654	C₂×D₃×C₉	—	27	2	no	—
655	C₂×D₃×C₉	—	27	1	no	—
656	C₂×D₃×C₉	—	81	3	no	—
657	C₂×C₃×D₉	—	9	6	no	—
658	C₂×C₃×D₉	—	9	3	no	—
659	C₂×C₃×D₉	—	9	6	no	—
660	C₂×C₃×D₉	—	9	2	no	—
661	C₂×C₃×D₉	—	9	1	no	—
662	C₃⁴	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
663	#737	—	3	9	no	—
664	#737	—	6	9	no	—
665	#737	—	9	3	no	—
666	#737	—	18	3	no	—
667	#737	—	18	9	no	—
668	C₃×3₋¹⁺²	—	2	6	no	—
669	C₃×3₋¹⁺²	—	2	2	no	—
670	C₃×3₋¹⁺²	—	2	1	no	—
671	C₃×3₋¹⁺²	—	2	3	no	—
672	C₃×3₋¹⁺²	—	2	6	no	—
673	C₃×3₋¹⁺²	—	2	6	no	—
674	C₃×3₋¹⁺²	—	2	6	no	—
675	C₃×3₋¹⁺²	—	2	6	no	—
676	C₃×3₋¹⁺²	—	2	3	no	—
677	C₃×3₋¹⁺²	—	2	6	no	—
678	C₃×3₋¹⁺²	C₂×C₃×C₃⋊D₃	1	6	yes	—
679	C₃×H(3,𝔽₃)	—	2	3	no	—
680	C₃×H(3,𝔽₃)	—	2	1	no	—
681	C₃×H(3,𝔽₃)	C₂×C₃²×D₃	1	1	yes	characteristic
682	C₃×H(3,𝔽₃)	C₂×C₃×C₃⋊D₃	1	3	yes	—
683	C₃²×C₉	—	2	1	no	—
684	C₃²×C₉	—	2	2	no	—
685	C₃²×C₉	—	2	1	no	—
686	C₃²×C₉	—	2	1	no	—
687	C₃²×C₉	—	2	2	no	—
688	C₃²×C₉	—	2	3	no	—
689	C₃²×C₉	—	2	3	no	—
690	C₃²×C₉	—	2	1	no	—
691	C₃²×C₉	—	2	2	no	—
692	C₃²×C₉	—	2	3	no	—
693	C₃²×C₉	—	2	1	no	—
694	C₃²×C₉	—	2	2	no	—
695	C₃²×C₉	—	2	1	no	—
696	C₃²×C₉	—	2	1	no	—
697	C₃²×C₉	—	2	2	no	—
698	C₃²×C₉	—	2	3	no	—
699	C₃²×C₉	—	2	1	no	—
700	C₃²×C₉	—	2	2	no	—
701	C₃²×C₉	—	2	3	no	—
702	C₃²×C₉	—	3	3	no	—
703	C₃²×C₉	—	6	3	no	—
704	C₃²×C₉	—	9	3	no	—
705	C₃²×C₉	—	18	3	no	—
706	C₃²×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
707	C₃²×C₉	C₂×C₃²×D₃	1	3	yes	—
708	C₃²×C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
709	C₃²×C₉	C₂×C₃×C₃⋊D₃	1	2	yes	—
710	C₃²×C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
711	C₃²×C₉	C₂×C₃×C₃⋊D₃	1	2	yes	—
712	C₃²×C₉	C₂×C₃×C₃⋊D₃	1	3	yes	—
713	C₃²×C₉	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
714	C₉⋊C₉	—	2	2	no	—
715	C₉⋊C₉	—	2	2	no	—
716	C₉⋊C₉	—	2	2	no	—
717	C₉⋊C₉	—	2	1	no	—
718	C₉⋊C₉	—	2	2	no	—
719	C₉⋊C₉	—	2	2	no	—
720	C₉⋊C₉	—	2	2	no	—
721	C₉⋊C₉	—	2	2	no	—
722	C₉⋊C₉	—	2	2	no	—
723	C₉⋊C₉	—	2	1	no	—
724	C₉⋊C₉	—	2	6	no	—
725	C₉⋊C₉	—	2	6	no	—
726	C₉⋊C₉	—	2	3	no	—
727	C₉⋊C₉	—	2	6	no	—
728	C₉⋊C₉	—	2	6	no	—
729	C₉⋊C₉	—	2	6	no	—
730	C₉⋊C₉	—	2	6	no	—
731	C₉⋊C₉	—	2	6	no	—
732	C₉⋊C₉	—	2	6	no	—
733	C₉⋊C₉	—	2	6	no	—
734	C₉⋊C₉	—	2	6	no	—
735	C₉⋊C₉	—	2	6	no	—
736	C₉⋊C₉	—	2	6	no	—
737	C₉⋊C₉	—	2	6	no	—
738	C₉⋊C₉	—	2	6	no	—
739	C₉⋊C₉	—	2	6	no	—
740	C₉⋊C₉	—	2	6	no	—
741	C₉⋊C₉	—	2	6	no	—
742	C₉⋊C₉	—	2	6	no	—
743	C₉⋊C₉	—	2	6	no	—
744	C₉⋊C₉	—	2	6	no	—
745	C₉⋊C₉	—	2	6	no	—
746	C₉⋊C₉	—	2	6	no	—
747	C₉⋊C₉	—	2	6	no	—
748	C₉⋊C₉	—	2	6	no	—
749	C₉⋊C₉	—	2	6	no	—
750	C₉⋊C₉	—	2	6	no	—
751	C₉⋊C₉	—	2	6	no	—
752	C₉⋊C₉	—	2	6	no	—
753	C₉⋊C₉	—	2	6	no	—
754	C₉⋊C₉	—	2	2	no	—
755	C₉⋊C₉	—	2	1	no	—
756	C₉⋊C₉	—	2	2	no	—
757	C₉⋊C₉	—	2	2	no	—
758	C₉⋊C₉	—	2	2	no	—
759	C₉⋊C₉	—	2	6	no	—
760	C₉⋊C₉	—	2	3	no	—
761	C₉⋊C₉	—	2	6	no	—
762	C₉⋊C₉	—	2	6	no	—
763	C₉⋊C₉	—	2	6	no	—
764	C₉⋊C₉	—	2	6	no	—
765	C₉⋊C₉	—	2	6	no	—
766	C₉⋊C₉	—	2	6	no	—
767	C₉⋊C₉	—	2	6	no	—
768	C₉⋊C₉	—	2	6	no	—
769	C₉⋊C₉	—	2	6	no	—
770	C₉⋊C₉	—	2	6	no	—
771	C₉⋊C₉	—	2	6	no	—
772	C₉⋊C₉	—	2	6	no	—
773	C₉⋊C₉	—	2	6	no	—
774	C₉⋊C₉	—	2	6	no	—
775	C₉⋊C₉	—	2	1	no	—
776	C₉⋊C₉	—	2	2	no	—
777	C₉⋊C₉	—	2	2	no	—
778	C₉⋊C₉	—	2	2	no	—
779	C₉⋊C₉	—	2	2	no	—
780	C₉⋊C₉	—	2	6	no	—
781	C₉⋊C₉	—	2	6	no	—
782	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
783	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	2	yes	—
784	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	2	yes	—
785	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	2	yes	—
786	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	2	yes	—
787	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	6	yes	—
788	C₉⋊C₉	C₂×C₃×C₃⋊D₃	1	6	yes	—
789	C₃²⋊C₉	—	2	6	no	—
790	C₃²⋊C₉	—	2	6	no	—
791	C₃²⋊C₉	—	2	6	no	—
792	C₃²⋊C₉	—	2	6	no	—
793	C₃²⋊C₉	—	2	6	no	—
794	C₃²⋊C₉	—	2	6	no	—
795	C₃²⋊C₉	—	2	6	no	—
796	C₃²⋊C₉	—	2	6	no	—
797	C₃²⋊C₉	—	2	6	no	—
798	C₃²⋊C₉	—	2	6	no	—
799	C₃²⋊C₉	—	2	2	no	—
800	C₃²⋊C₉	—	2	2	no	—
801	C₃²⋊C₉	—	2	2	no	—
802	C₃²⋊C₉	—	2	2	no	—
803	C₃²⋊C₉	—	2	6	no	—
804	C₃²⋊C₉	—	2	6	no	—
805	C₃²⋊C₉	—	2	6	no	—
806	C₃²⋊C₉	—	2	6	no	—
807	C₃²⋊C₉	—	2	6	no	—
808	C₃²⋊C₉	—	2	6	no	—
809	C₃²⋊C₉	—	2	3	no	—
810	C₃²⋊C₉	—	2	6	no	—
811	C₃²⋊C₉	—	2	6	no	—
812	C₃²⋊C₉	—	2	6	no	—
813	C₃²⋊C₉	—	2	6	no	—
814	C₃²⋊C₉	—	2	6	no	—
815	C₃²⋊C₉	C₂×C₃²×D₃	1	2	yes	—
816	C₃²⋊C₉	C₂×C₃²×D₃	1	6	yes	—
817	C₃²⋊C₉	C₂×C₃×C₃⋊D₃	1	6	yes	—
818	C₉²	—	2	6	no	—
819	C₉²	—	2	6	no	—
820	C₉²	—	2	3	no	—
821	C₉²	—	2	6	no	—
822	C₉²	—	2	6	no	—
823	C₉²	—	2	6	no	—
824	C₉²	C₂×C₃×C₃⋊D₃	1	6	yes	—
825	C₂×C₃³	—	2	1	no	—
826	C₂×C₃³	—	2	3	no	—
827	C₂×C₃³	—	3	3	no	—
828	C₂×C₃³	—	3	3	no	—
829	C₂×C₃³	—	6	3	no	—
830	C₂×C₃³	C₃²×C₃⋊D₃	1	3	yes	—
831	C₂×C₃³	C₃²×C₃⋊D₃	1	1	yes	characteristic
832	C₂×C₃³	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
833	C₃×C₃⋊D₃	—	9	6	no	—
834	C₃×C₃⋊D₃	—	9	2	no	—
835	C₃×C₃⋊D₃	—	9	6	no	—
836	C₃²×D₃	—	27	6	no	—
837	C₃²×D₃	—	27	2	no	—
838	C₂×3₋¹⁺²	—	3	18	no	—
839	C₂×3₋¹⁺²	—	6	18	no	—
840	C₂×3₋¹⁺²	—	6	9	no	—
841	C₂×3₋¹⁺²	—	6	18	no	—
842	C₂×3₋¹⁺²	—	6	3	no	—
843	C₂×3₋¹⁺²	—	6	6	no	—
844	C₂×3₋¹⁺²	—	18	3	no	—
845	C₂×3₋¹⁺²	—	18	6	no	—
846	C₂×3₋¹⁺²	—	18	6	no	—
847	C₂×3₋¹⁺²	—	18	6	no	—
848	C₂×3₋¹⁺²	—	18	6	no	—
849	C₂×H(3,𝔽₃)	—	3	3	no	—
850	C₂×H(3,𝔽₃)	—	3	9	no	—
851	C₂×H(3,𝔽₃)	—	6	9	no	—
852	C₂×H(3,𝔽₃)	—	6	3	no	—
853	C₂×C₃×C₉	—	2	3	no	—
854	C₂×C₃×C₉	—	2	1	no	—
855	C₂×C₃×C₉	—	2	2	no	—
856	C₂×C₃×C₉	—	2	6	no	—
857	C₂×C₃×C₉	—	2	3	no	—
858	C₂×C₃×C₉	—	2	6	no	—
859	C₂×C₃×C₉	—	2	6	no	—
860	C₂×C₃×C₉	—	2	6	no	—
861	C₂×C₃×C₉	—	2	6	no	—
862	C₂×C₃×C₉	—	2	2	no	—
863	C₂×C₃×C₉	—	2	2	no	—
864	C₂×C₃×C₉	—	2	2	no	—
865	C₂×C₃×C₉	—	2	2	no	—
866	C₂×C₃×C₉	—	2	1	no	—
867	C₂×C₃×C₉	—	2	1	no	—
868	C₂×C₃×C₉	—	2	2	no	—
869	C₂×C₃×C₉	—	3	1	no	—
870	C₂×C₃×C₉	—	3	3	no	—
871	C₂×C₃×C₉	—	3	6	no	—
872	C₂×C₃×C₉	—	3	3	no	—
873	C₂×C₃×C₉	—	3	6	no	—
874	C₂×C₃×C₉	—	6	1	no	—
875	C₂×C₃×C₉	—	6	3	no	—
876	C₂×C₃×C₉	—	6	6	no	—
877	C₂×C₃×C₉	—	6	3	no	—
878	C₂×C₃×C₉	—	6	2	no	—
879	C₂×C₃×C₉	—	6	6	no	—
880	C₂×C₃×C₉	—	6	6	no	—
881	C₂×C₃×C₉	—	6	3	no	—
882	C₂×C₃×C₉	—	6	1	no	—
883	C₂×C₃×C₉	—	6	3	no	—
884	C₂×C₃×C₉	—	9	1	no	—
885	C₂×C₃×C₉	—	9	3	no	—
886	C₂×C₃×C₉	—	18	1	no	—
887	C₂×C₃×C₉	—	18	2	no	—
888	C₂×C₃×C₉	—	18	3	no	—
889	C₂×C₃×C₉	—	18	1	no	—
890	C₂×C₃×C₉	—	18	1	no	—
891	C₂×C₃×C₉	—	18	1	no	—
892	C₂×C₃×C₉	—	18	1	no	—
893	C₂×C₃×C₉	—	18	2	no	—
894	C₂×C₃×C₉	—	18	2	no	—
895	C₂×C₃×C₉	—	18	2	no	—
896	C₂×C₃×C₉	—	18	3	no	—
897	C₂×C₃×C₉	—	18	3	no	—
898	C₂×C₃×C₉	—	18	3	no	—
899	C₂×C₃×C₉	—	81	2	no	—
900	C₂×C₃×C₉	#4208	1	3	yes	complemented
901	C₂×C₃×C₉	C₃²×C₃⋊D₃	1	1	yes	characteristic
902	C₂×C₃×C₉	C₃²×C₃⋊D₃	1	6	yes	—
903	C₂×C₃×C₉	C₃²×C₃⋊D₃	1	2	yes	—
904	C₂×C₃×C₉	C₃×C₃⋊(C₃⋊D₃)	1	2	yes	—
905	C₂×C₃×C₉	C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
906	#272	—	27	6	no	—
907	C₃⋊D₉	—	3	2	no	—
908	C₃⋊D₉	—	3	6	no	—
909	AGL(1,ℤ/9)	—	9	36	no	—
910	(C₃⋊D₃)⋊C₃	—	9	18	no	—
911	D₃×C₉	—	27	12	no	—
912	D₃×C₉	—	27	6	no	—
913	D₃×C₉	—	27	4	no	—
914	D₃×C₉	—	27	2	no	—
915	D₃×C₉	—	81	6	no	—
916	C₃×D₉	—	9	12	no	—
917	C₃×D₉	—	9	6	no	—
918	C₃×D₉	—	9	12	no	—
919	C₃×D₉	—	9	4	no	—
920	C₃×D₉	—	9	2	no	—
921	C₂²×C₃²	—	81	1	no	—
922	C₂×C₃⋊D₃	—	9	1	no	—
923	C₂×C₃⋊D₃	—	9	3	no	—
924	C₂×C₃×D₃	—	27	9	no	—
925	C₂×C₃×D₃	—	27	3	no	—
926	C₂×C₃×D₃	—	27	3	no	—
927	C₂×C₃×D₃	—	27	1	no	—
928	C₂×C₃×D₃	—	81	3	no	—
929	C₂²×C₉	—	81	1	no	—
930	C₂²×C₉	—	81	2	no	—
931	C₂×D₉	—	9	2	no	—
932	C₂×D₉	—	9	6	no	—
933	C₂×D₉	—	9	1	no	—
934	C₃³	—	2	1	no	—
935	C₃³	—	2	3	no	—
936	C₃³	—	3	3	no	—
937	C₃³	—	3	3	no	—
938	C₃³	—	6	3	no	—
939	C₃³	C₂×C₃²×C₃⋊D₃	1	3	yes	—
940	C₃³	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic
941	C₃³	C₂×C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
942	3₋¹⁺²	—	3	18	no	—
943	3₋¹⁺²	—	6	18	no	—
944	3₋¹⁺²	—	6	9	no	—
945	3₋¹⁺²	—	6	18	no	—
946	3₋¹⁺²	—	6	3	no	—
947	3₋¹⁺²	—	6	6	no	—
948	3₋¹⁺²	—	18	3	no	—
949	3₋¹⁺²	—	18	6	no	—
950	3₋¹⁺²	—	18	6	no	—
951	3₋¹⁺²	—	18	6	no	—
952	3₋¹⁺²	—	18	6	no	—
953	H(3,𝔽₃)	—	3	3	no	—
954	H(3,𝔽₃)	—	3	9	no	—
955	H(3,𝔽₃)	—	6	9	no	—
956	H(3,𝔽₃)	—	6	3	no	—
957	C₃×C₉	—	2	3	no	—
958	C₃×C₉	—	2	1	no	—
959	C₃×C₉	—	2	2	no	—
960	C₃×C₉	—	2	6	no	—
961	C₃×C₉	—	2	3	no	—
962	C₃×C₉	—	2	6	no	—
963	C₃×C₉	—	2	6	no	—
964	C₃×C₉	—	2	6	no	—
965	C₃×C₉	—	2	6	no	—
966	C₃×C₉	—	2	2	no	—
967	C₃×C₉	—	2	2	no	—
968	C₃×C₉	—	2	2	no	—
969	C₃×C₉	—	2	2	no	—
970	C₃×C₉	—	2	1	no	—
971	C₃×C₉	—	2	1	no	—
972	C₃×C₉	—	2	2	no	—
973	C₃×C₉	—	3	1	no	—
974	C₃×C₉	—	3	3	no	—
975	C₃×C₉	—	3	6	no	—
976	C₃×C₉	—	3	3	no	—
977	C₃×C₉	—	3	6	no	—
978	C₃×C₉	—	6	1	no	—
979	C₃×C₉	—	6	3	no	—
980	C₃×C₉	—	6	6	no	—
981	C₃×C₉	—	6	3	no	—
982	C₃×C₉	—	6	2	no	—
983	C₃×C₉	—	6	6	no	—
984	C₃×C₉	—	6	6	no	—
985	C₃×C₉	—	6	3	no	—
986	C₃×C₉	—	6	1	no	—
987	C₃×C₉	—	6	3	no	—
988	C₃×C₉	—	9	1	no	—
989	C₃×C₉	—	9	3	no	—
990	C₃×C₉	—	18	1	no	—
991	C₃×C₉	—	18	2	no	—
992	C₃×C₉	—	18	3	no	—
993	C₃×C₉	—	18	1	no	—
994	C₃×C₉	—	18	1	no	—
995	C₃×C₉	—	18	1	no	—
996	C₃×C₉	—	18	1	no	—
997	C₃×C₉	—	18	2	no	—
998	C₃×C₉	—	18	2	no	—
999	C₃×C₉	—	18	2	no	—
1000	C₃×C₉	—	18	3	no	—
1001	C₃×C₉	—	18	3	no	—
1002	C₃×C₉	—	18	3	no	—
1003	C₃×C₉	C₂×#4208	1	3	yes	complemented
1004	C₃×C₉	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic
1005	C₃×C₉	C₂×C₃²×C₃⋊D₃	1	6	yes	—
1006	C₃×C₉	C₂×C₃²×C₃⋊D₃	1	2	yes	—
1007	C₃×C₉	C₂×C₃×C₃⋊(C₃⋊D₃)	1	2	yes	—
1008	C₃×C₉	C₂×C₃×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
1009	C₂×C₃²	—	2	3	no	—
1010	C₂×C₃²	—	3	1	no	—
1011	C₂×C₃²	—	3	1	no	—
1012	C₂×C₃²	—	3	9	no	—
1013	C₂×C₃²	—	3	3	no	—
1014	C₂×C₃²	—	3	3	no	—
1015	C₂×C₃²	—	6	1	no	—
1016	C₂×C₃²	—	6	1	no	—
1017	C₂×C₃²	—	6	1	no	—
1018	C₂×C₃²	—	6	3	no	—
1019	C₂×C₃²	—	6	3	no	—
1020	C₂×C₃²	—	6	3	no	—
1021	C₂×C₃²	—	6	9	no	—
1022	C₂×C₃²	—	6	1	no	—
1023	C₂×C₃²	—	6	1	no	—
1024	C₂×C₃²	—	6	3	no	—
1025	C₂×C₃²	—	6	3	no	—
1026	C₂×C₃²	—	81	2	no	—
1027	C₂×C₃²	#4207⋊C₃	1	3	yes	—
1028	C₂×C₃²	C₃⋊#4208	1	3	yes	—
1029	C₂×C₃²	C₃²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
1030	C₃⋊D₃	—	9	2	no	—
1031	C₃⋊D₃	—	9	6	no	—
1032	C₃×D₃	—	27	18	no	—
1033	C₃×D₃	—	27	6	no	—
1034	C₃×D₃	—	27	6	no	—
1035	C₃×D₃	—	27	2	no	—
1036	C₃×D₃	—	81	6	no	—
1037	C₂×C₉	—	2	1	no	—
1038	C₂×C₉	—	2	3	no	—
1039	C₂×C₉	—	3	2	no	—
1040	C₂×C₉	—	3	6	no	—
1041	C₂×C₉	—	3	1	no	—
1042	C₂×C₉	—	3	2	no	—
1043	C₂×C₉	—	6	2	no	—
1044	C₂×C₉	—	6	2	no	—
1045	C₂×C₉	—	6	2	no	—
1046	C₂×C₉	—	6	1	no	—
1047	C₂×C₉	—	6	2	no	—
1048	C₂×C₉	—	6	6	no	—
1049	C₂×C₉	—	6	6	no	—
1050	C₂×C₉	—	6	6	no	—
1051	C₂×C₉	—	6	2	no	—
1052	C₂×C₉	—	6	6	no	—
1053	C₂×C₉	—	6	2	no	—
1054	C₂×C₉	—	6	1	no	—
1055	C₂×C₉	—	6	3	no	—
1056	C₂×C₉	—	6	6	no	—
1057	C₂×C₉	—	81	2	no	—
1058	C₂×C₉	—	81	4	no	—
1059	C₂×C₉	C₃×#4208	1	1	yes	characteristic
1060	D₉	—	9	4	no	—
1061	D₉	—	9	12	no	—
1062	D₉	—	9	2	no	—
1063	C₂²×C₃	—	81	3	no	—
1064	C₂²×C₃	—	81	1	no	—
1065	C₂×D₃	—	27	3	no	—
1066	C₂×D₃	—	27	1	no	—
1067	C₂×D₃	—	81	3	no	—
1068	C₃²	—	2	3	no	—
1069	C₃²	—	3	1	no	—
1070	C₃²	—	3	1	no	—
1071	C₃²	—	3	9	no	—
1072	C₃²	—	3	3	no	—
1073	C₃²	—	3	3	no	—
1074	C₃²	—	6	1	no	—
1075	C₃²	—	6	1	no	—
1076	C₃²	—	6	1	no	—
1077	C₃²	—	6	3	no	—
1078	C₃²	—	6	3	no	—
1079	C₃²	—	6	3	no	—
1080	C₃²	—	6	9	no	—
1081	C₃²	—	6	1	no	—
1082	C₃²	—	6	1	no	—
1083	C₃²	—	6	3	no	—
1084	C₃²	—	6	3	no	—
1085	C₃²	C₂×#4207⋊C₃	1	3	yes	—
1086	C₃²	C₂×C₃⋊#4208	1	3	yes	—
1087	C₃²	C₂×C₃²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
1088	C₉	—	2	1	no	—
1089	C₉	—	2	3	no	—
1090	C₉	—	3	1	no	—
1091	C₉	—	3	2	no	—
1092	C₉	—	3	2	no	—
1093	C₉	—	3	6	no	—
1094	C₉	—	6	2	no	—
1095	C₉	—	6	2	no	—
1096	C₉	—	6	2	no	—
1097	C₉	—	6	1	no	—
1098	C₉	—	6	2	no	—
1099	C₉	—	6	6	no	—
1100	C₉	—	6	6	no	—
1101	C₉	—	6	6	no	—
1102	C₉	—	6	2	no	—
1103	C₉	—	6	1	no	—
1104	C₉	—	6	3	no	—
1105	C₉	—	6	6	no	—
1106	C₉	—	6	2	no	—
1107	C₉	—	6	6	no	—
1108	C₉	C₂×C₃×#4208	1	1	yes	characteristic
1109	C₂×C₃	—	2	1	no	—
1110	C₂×C₃	—	3	3	no	—
1111	C₂×C₃	—	3	3	no	—
1112	C₂×C₃	—	6	3	no	—
1113	C₂×C₃	—	9	3	no	—
1114	C₂×C₃	—	18	3	no	—
1115	C₂×C₃	—	81	6	no	—
1116	C₂×C₃	—	81	2	no	—
1117	C₂×C₃	C₃×C₃⋊#4208	1	1	yes	characteristic
1118	C₂×C₃	C₃⋊(#4207⋊C₃)	1	1	yes	characteristic
1119	D₃	—	27	6	no	—
1120	D₃	—	27	2	no	—
1121	D₃	—	81	6	no	—
1122	C₂²	—	81	1	no	Sylow
1123	C₃	—	2	1	no	—
1124	C₃	—	3	3	no	—
1125	C₃	—	3	3	no	—
1126	C₃	—	6	3	no	—
1127	C₃	—	9	3	no	—
1128	C₃	—	18	3	no	—
1129	C₃	C₂×C₃⋊(#4207⋊C₃)	1	1	yes	characteristic
1130	C₃	C₂×C₃×C₃⋊#4208	1	1	yes	characteristic
1131	C₂	—	81	2	no	—
1132	C₂	#72221823	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(#4207⋊C₃)
commutator, cosocle, hypocenter	C₉×H(3,𝔽₃)	C₂²×C₃²
Frattini	C₃²	C₂×C₃²×C₃⋊(C₃⋊D₃)
Fitting	C₂×#14555333	C₂
socle	C₂×C₃²	C₃²×C₃⋊(C₃⋊D₃)
prime radical	C₂×#13091424	C₃
LCS	G ▷ C₉×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
4. C₂×#10624904⋊C₂	C₃	semidirect
5. C₂×#13091524	C₃	semidirect
9. C₂×#14555333	C₂	semidirect
10. #72221823	C₂	direct (N × H)
11. #14555333	C₂²	semidirect
12. #10624904⋊C₂	C₂×C₃	semidirect
13. #13091524	C₂×C₃	semidirect
27. C₂×#10624904	C₂×C₃	semidirect
33. C₂×#10624900	C₂×C₃	semidirect
35. C₂×#10624891	D₃	semidirect
39. C₂×#10624872	D₃	semidirect
43. C₂×#10624864	D₃	semidirect
44. C₂×C₃²×C₉⋊C₉	D₃	semidirect
75. #10624904	C₂²×C₃	semidirect
81. #10624900	C₂²×C₃	semidirect
83. #10624891	C₂×D₃	semidirect
87. #10624872	C₂×D₃	semidirect
91. #10624864	C₂×D₃	semidirect
92. C₃²×C₉⋊C₉	C₂×D₃	semidirect
122. C₂×#6898	C₃×D₃	semidirect
141. C₂×#6896	C₃×D₃	semidirect
153. C₂×#6895	C₃×D₃	semidirect
235. C₂×#6887	C₃×D₃	semidirect
248. C₂×C₃×C₉⋊C₉	C₃×D₃	semidirect
322. #6898	C₂×C₃×D₃	semidirect
341. #6896	C₂×C₃×D₃	semidirect
353. #6895	C₂×C₃×D₃	semidirect
435. #6887	C₂×C₃×D₃	semidirect
448. C₃×C₉⋊C₉	C₂×C₃×D₃	semidirect
900. C₂×C₃×C₉	#4208	semidirect
1003. C₃×C₉	C₂×#4208	semidirect
1132. C₂	#72221823	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#13091435	3
C₂×#10624891⋊C₂	3
C₂×#13091425	3
C₂×#10624904⋊C₂	3
C₂×#13091524	3
C₂×#4207⋊C₉	3
C₂×C₃×C₃⋊(D₉⋊C₉)	3
C₂×#13091424	3
C₂×#14555333	2
#72221823	2

Subgroups — C2×#72221823 #72243967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#72221823 #72243967