Subgroups — C₂×#4207⋊C₉ #72243924

Order 2916.

755 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#4207⋊C₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×#10624864	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4207	C₃	1	1	yes	maximal, characteristic
4	C₂×#92294	C₃	1	2	yes	maximal, complemented
5	C₂×C₃⋊(D₉⋊C₉)	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×C₉×AGL(1,ℤ/9)	—	3	2	no	maximal
7	C₂×C₉×(C₃⋊D₃)⋊C₃	—	3	1	no	maximal
8	C₂×C₃×D₉⋊C₉	—	3	1	no	maximal
9	#10624864	C₂²	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₃×#737	C₂×C₃	1	1	yes	characteristic
11	C₃×#4207	C₂×C₃	1	2	yes	—
12	C₂×C₉×3₋¹⁺²	—	2	2	no	—
13	C₂×C₉×3₋¹⁺²	—	2	1	no	—
14	C₂×C₉×3₋¹⁺²	—	2	2	no	—
15	C₂×C₉×3₋¹⁺²	—	2	2	no	—
16	C₂×C₉×3₋¹⁺²	—	2	2	no	—
17	C₂×C₉×3₋¹⁺²	—	2	2	no	—
18	C₂×C₉×3₋¹⁺²	D₃	1	2	yes	complemented
19	C₂×C₉×H(3,𝔽₃)	—	2	1	no	—
20	C₂×C₉×H(3,𝔽₃)	D₃	1	1	yes	characteristic
21	C₂×#6887	—	2	1	no	—
22	C₂×#6887	—	2	2	no	—
23	C₂×#6887	C₂×C₃	1	2	yes	complemented
24	C₂×C₃×C₉⋊C₉	—	2	1	no	—
25	C₂×C₃×C₉⋊C₉	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃×C₉⋊C₉	C₂×C₃	1	1	yes	characteristic, complemented
27	#92294	C₂×C₃	1	4	yes	complemented
28	C₃⋊(D₉⋊C₉)	C₂×C₃	1	2	yes	complemented
29	C₉×AGL(1,ℤ/9)	—	3	4	no	—
30	C₉×(C₃⋊D₃)⋊C₃	—	3	2	no	—
31	C₃×D₉⋊C₉	—	3	2	no	—
32	C₂×#4207	C₉	1	1	yes	characteristic, complemented
33	C₂×#4207	C₉	1	2	yes	complemented
34	C₂×C₉×C₃⋊D₃	—	3	1	no	—
35	C₂×C₃×C₃⋊D₉	C₃²	1	1	yes	characteristic
36	C₂×C₃×AGL(1,ℤ/9)	—	3	2	no	—
37	C₂×C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
38	C₂×C₃×D₃×C₉	—	9	1	no	—
39	C₂×C₃²×D₉	—	3	1	no	—
40	C₂×D₉⋊C₉	—	3	1	no	—
41	C₂×D₉⋊C₉	—	3	2	no	—
42	C₂×D₉⋊C₉	—	3	2	no	—
43	C₂×D₉⋊C₉	—	3	2	no	—
44	C₂×(C₃⋊D₃)⋊C₉	—	3	2	no	—
45	C₂×C₉×D₉	—	3	2	no	—
46	C₃×#737	C₂²×C₃	1	1	yes	characteristic
47	C₉×3₋¹⁺²	—	2	2	no	—
48	C₉×3₋¹⁺²	—	2	1	no	—
49	C₉×3₋¹⁺²	—	2	2	no	—
50	C₉×3₋¹⁺²	—	2	2	no	—
51	C₉×3₋¹⁺²	—	2	2	no	—
52	C₉×3₋¹⁺²	—	2	2	no	—
53	C₉×3₋¹⁺²	C₂×D₃	1	2	yes	complemented
54	C₉×H(3,𝔽₃)	—	2	1	no	—
55	C₉×H(3,𝔽₃)	C₂×D₃	1	1	yes	characteristic
56	#6887	—	2	1	no	—
57	#6887	—	2	2	no	—
58	#6887	C₂²×C₃	1	2	yes	complemented
59	C₃×C₉⋊C₉	—	2	1	no	—
60	C₃×C₉⋊C₉	C₂×D₃	1	1	yes	characteristic, complemented
61	C₃×C₉⋊C₉	C₂²×C₃	1	1	yes	characteristic, complemented
62	C₂×#737	—	2	2	no	—
63	C₂×#737	—	2	4	no	—
64	C₂×#737	—	2	1	no	—
65	C₂×#737	—	2	2	no	—
66	C₂×#737	—	2	1	no	—
67	C₂×#737	—	2	2	no	—
68	C₂×#737	C₂×C₉	1	1	yes	characteristic, complemented
69	C₂×#737	C₂×C₉	1	2	yes	complemented
70	C₂×C₃×3₋¹⁺²	—	2	1	no	—
71	C₂×C₃×3₋¹⁺²	—	2	2	no	—
72	C₂×C₃×3₋¹⁺²	C₃×D₃	1	2	yes	—
73	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
74	C₂×C₃²×C₉	—	2	1	no	—
75	C₂×C₃²×C₉	—	2	1	no	—
76	C₂×C₃²×C₉	—	2	1	no	—
77	C₂×C₃²×C₉	—	2	1	no	—
78	C₂×C₃²×C₉	—	2	1	no	—
79	C₂×C₃²×C₉	—	2	1	no	—
80	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
81	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic
82	C₂×C₃²×C₉	C₃⋊D₃	1	1	yes	characteristic
83	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
84	#4207	C₂×C₉	1	2	yes	complemented
85	#4207	C₂×C₉	1	4	yes	complemented
86	C₉×C₃⋊D₃	—	3	2	no	—
87	C₃×C₃⋊D₉	C₂×C₃²	1	2	yes	—
88	C₃×AGL(1,ℤ/9)	—	3	4	no	—
89	C₃×(C₃⋊D₃)⋊C₃	—	3	2	no	—
90	C₃×D₃×C₉	—	9	2	no	—
91	C₃²×D₉	—	3	2	no	—
92	C₂×C₉⋊C₉	—	2	2	no	—
93	C₂×C₉⋊C₉	—	2	2	no	—
94	C₂×C₉⋊C₉	—	2	2	no	—
95	C₂×C₉⋊C₉	—	2	2	no	—
96	C₂×C₉⋊C₉	—	2	1	no	—
97	C₂×C₉⋊C₉	—	2	2	no	—
98	C₂×C₉⋊C₉	—	2	2	no	—
99	C₂×C₉⋊C₉	—	2	1	no	—
100	C₂×C₉⋊C₉	—	2	2	no	—
101	C₂×C₉⋊C₉	—	2	2	no	—
102	C₂×C₉⋊C₉	—	2	2	no	—
103	C₂×C₉⋊C₉	—	2	1	no	—
104	C₂×C₉⋊C₉	—	2	2	no	—
105	C₂×C₉⋊C₉	—	2	2	no	—
106	C₂×C₉⋊C₉	C₃×D₃	1	1	yes	characteristic
107	C₂×C₉⋊C₉	C₃×D₃	1	2	yes	—
108	C₂×C₉⋊C₉	C₃×D₃	1	2	yes	—
109	C₂×C₉⋊C₉	C₃×D₃	1	2	yes	—
110	C₂×C₃²⋊C₉	—	2	2	no	—
111	C₂×C₃²⋊C₉	—	2	2	no	—
112	C₂×C₃²⋊C₉	—	2	2	no	—
113	C₂×C₃²⋊C₉	—	2	2	no	—
114	C₂×C₃²⋊C₉	—	2	1	no	—
115	C₂×C₃²⋊C₉	—	2	2	no	—
116	C₂×C₃²⋊C₉	C₃×D₃	1	2	yes	—
117	C₂×C₉²	—	2	2	no	—
118	C₂×C₉²	—	2	2	no	—
119	C₂×C₉²	—	2	1	no	—
120	C₂×C₉²	—	2	2	no	—
121	C₂×C₉²	—	2	2	no	—
122	C₂×C₉²	—	2	2	no	—
123	C₂×C₉²	C₃×D₃	1	2	yes	—
124	D₉⋊C₉	—	3	2	no	—
125	D₉⋊C₉	—	3	4	no	—
126	D₉⋊C₉	—	3	4	no	—
127	D₉⋊C₉	—	3	4	no	—
128	(C₃⋊D₃)⋊C₉	—	3	4	no	—
129	C₉×D₉	—	3	4	no	—
130	C₂×C₃×C₃⋊D₃	—	3	1	no	—
131	C₂×C₃²×D₃	—	9	1	no	—
132	C₂²×C₃×C₉	—	27	1	no	—
133	C₂×C₃⋊D₉	C₃×C₉	1	1	yes	characteristic, complemented
134	C₂×AGL(1,ℤ/9)	—	3	2	no	—
135	C₂×AGL(1,ℤ/9)	—	3	4	no	—
136	C₂×(C₃⋊D₃)⋊C₃	—	3	1	no	—
137	C₂×(C₃⋊D₃)⋊C₃	—	3	2	no	—
138	C₂×D₃×C₉	—	9	2	no	—
139	C₂×D₃×C₉	—	9	1	no	—
140	C₂×D₃×C₉	—	27	1	no	—
141	C₂×C₃×D₉	—	3	1	no	—
142	C₂×C₃×D₉	—	3	2	no	—
143	C₂×C₃×D₉	—	3	2	no	—
144	C₂×C₃×D₉	—	3	1	no	—
145	#737	—	2	2	no	—
146	#737	—	2	4	no	—
147	#737	—	2	1	no	—
148	#737	—	2	2	no	—
149	#737	—	2	1	no	—
150	#737	—	2	2	no	—
151	#737	C₂²×C₉	1	1	yes	characteristic, complemented
152	#737	C₂²×C₉	1	2	yes	complemented
153	C₃×3₋¹⁺²	—	2	1	no	—
154	C₃×3₋¹⁺²	—	2	2	no	—
155	C₃×3₋¹⁺²	C₂×C₃×D₃	1	2	yes	—
156	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
157	C₃²×C₉	—	2	1	no	—
158	C₃²×C₉	—	2	1	no	—
159	C₃²×C₉	—	2	1	no	—
160	C₃²×C₉	—	2	1	no	—
161	C₃²×C₉	—	2	1	no	—
162	C₃²×C₉	—	2	1	no	—
163	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
164	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic
165	C₃²×C₉	C₂×C₃⋊D₃	1	1	yes	characteristic
166	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic
167	C₉⋊C₉	—	2	2	no	—
168	C₉⋊C₉	—	2	2	no	—
169	C₉⋊C₉	—	2	2	no	—
170	C₉⋊C₉	—	2	2	no	—
171	C₉⋊C₉	—	2	1	no	—
172	C₉⋊C₉	—	2	2	no	—
173	C₉⋊C₉	—	2	2	no	—
174	C₉⋊C₉	—	2	1	no	—
175	C₉⋊C₉	—	2	2	no	—
176	C₉⋊C₉	—	2	2	no	—
177	C₉⋊C₉	—	2	2	no	—
178	C₉⋊C₉	—	2	1	no	—
179	C₉⋊C₉	—	2	2	no	—
180	C₉⋊C₉	—	2	2	no	—
181	C₉⋊C₉	C₂×C₃×D₃	1	1	yes	characteristic
182	C₉⋊C₉	C₂×C₃×D₃	1	2	yes	—
183	C₉⋊C₉	C₂×C₃×D₃	1	2	yes	—
184	C₉⋊C₉	C₂×C₃×D₃	1	2	yes	—
185	C₃²⋊C₉	—	2	2	no	—
186	C₃²⋊C₉	—	2	2	no	—
187	C₃²⋊C₉	—	2	2	no	—
188	C₃²⋊C₉	—	2	2	no	—
189	C₃²⋊C₉	—	2	1	no	—
190	C₃²⋊C₉	—	2	2	no	—
191	C₃²⋊C₉	C₂×C₃×D₃	1	2	yes	—
192	C₉²	—	2	2	no	—
193	C₉²	—	2	2	no	—
194	C₉²	—	2	1	no	—
195	C₉²	—	2	2	no	—
196	C₉²	—	2	2	no	—
197	C₉²	—	2	2	no	—
198	C₉²	C₂×C₃×D₃	1	2	yes	—
199	C₂×C₃³	—	2	1	no	—
200	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
201	C₂×C₃³	C₃×C₃⋊D₃	1	1	yes	characteristic
202	C₃×C₃⋊D₃	—	3	2	no	—
203	C₃²×D₃	—	9	2	no	—
204	C₂×3₋¹⁺²	—	2	2	no	—
205	C₂×3₋¹⁺²	—	2	4	no	—
206	C₂×3₋¹⁺²	—	2	4	no	—
207	C₂×3₋¹⁺²	—	2	4	no	—
208	C₂×3₋¹⁺²	—	2	4	no	—
209	C₂×3₋¹⁺²	—	2	2	no	—
210	C₂×3₋¹⁺²	—	2	1	no	—
211	C₂×3₋¹⁺²	—	2	2	no	—
212	C₂×3₋¹⁺²	—	2	4	no	—
213	C₂×3₋¹⁺²	—	2	4	no	—
214	C₂×3₋¹⁺²	—	2	2	no	—
215	C₂×3₋¹⁺²	D₃×C₉	1	2	yes	complemented
216	C₂×3₋¹⁺²	D₃×C₉	1	4	yes	complemented
217	C₂×H(3,𝔽₃)	—	2	1	no	—
218	C₂×H(3,𝔽₃)	—	2	2	no	—
219	C₂×H(3,𝔽₃)	D₃×C₉	1	1	yes	characteristic
220	C₂×H(3,𝔽₃)	D₃×C₉	1	2	yes	—
221	C₂×C₃×C₉	—	2	2	no	—
222	C₂×C₃×C₉	—	2	4	no	—
223	C₂×C₃×C₉	—	2	1	no	—
224	C₂×C₃×C₉	—	2	1	no	—
225	C₂×C₃×C₉	—	2	2	no	—
226	C₂×C₃×C₉	—	2	2	no	—
227	C₂×C₃×C₉	—	2	1	no	—
228	C₂×C₃×C₉	—	2	2	no	—
229	C₂×C₃×C₉	—	2	1	no	—
230	C₂×C₃×C₉	—	2	2	no	—
231	C₂×C₃×C₉	—	2	1	no	—
232	C₂×C₃×C₉	—	2	1	no	—
233	C₂×C₃×C₉	—	2	2	no	—
234	C₂×C₃×C₉	—	2	2	no	—
235	C₂×C₃×C₉	—	2	2	no	—
236	C₂×C₃×C₉	—	2	2	no	—
237	C₂×C₃×C₉	—	2	2	no	—
238	C₂×C₃×C₉	—	2	1	no	—
239	C₂×C₃×C₉	—	18	1	no	—
240	C₂×C₃×C₉	—	18	1	no	—
241	C₂×C₃×C₉	—	18	1	no	—
242	C₂×C₃×C₉	—	18	1	no	—
243	C₂×C₃×C₉	—	18	1	no	—
244	C₂×C₃×C₉	—	18	1	no	—
245	C₂×C₃×C₉	—	18	1	no	—
246	C₂×C₃×C₉	—	27	2	no	—
247	C₂×C₃×C₉	D₃×C₉	1	1	yes	characteristic, complemented
248	C₂×C₃×C₉	D₃×C₉	1	2	yes	complemented
249	C₂×C₃×C₉	C₂×C₃×C₉	1	1	yes	characteristic, complemented
250	C₂×C₃×C₉	C₃²×D₃	1	2	yes	—
251	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
252	C₂×C₃×C₉	C₃×C₃⋊D₃	1	2	yes	—
253	C₂×C₃×C₉	C₃×C₃⋊D₃	1	1	yes	characteristic
254	C₃⋊D₉	C₂×C₃×C₉	1	2	yes	complemented
255	AGL(1,ℤ/9)	—	3	4	no	—
256	AGL(1,ℤ/9)	—	3	8	no	—
257	(C₃⋊D₃)⋊C₃	—	3	2	no	—
258	(C₃⋊D₃)⋊C₃	—	3	4	no	—
259	D₃×C₉	—	9	4	no	—
260	D₃×C₉	—	9	2	no	—
261	D₃×C₉	—	27	2	no	—
262	C₃×D₉	—	3	2	no	—
263	C₃×D₉	—	3	4	no	—
264	C₃×D₉	—	3	4	no	—
265	C₃×D₉	—	3	2	no	—
266	C₂²×C₃²	—	27	1	no	—
267	C₂×C₃⋊D₃	—	3	1	no	—
268	C₂×C₃×D₃	—	9	1	no	—
269	C₂×C₃×D₃	—	9	2	no	—
270	C₂×C₃×D₃	—	9	1	no	—
271	C₂×C₃×D₃	—	27	1	no	—
272	C₂²×C₉	—	27	1	no	—
273	C₂²×C₉	—	27	2	no	—
274	C₂×D₉	—	3	1	no	—
275	C₂×D₉	—	3	2	no	—
276	C₃³	—	2	1	no	—
277	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
278	C₃³	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
279	3₋¹⁺²	—	2	2	no	—
280	3₋¹⁺²	—	2	4	no	—
281	3₋¹⁺²	—	2	4	no	—
282	3₋¹⁺²	—	2	4	no	—
283	3₋¹⁺²	—	2	4	no	—
284	3₋¹⁺²	—	2	2	no	—
285	3₋¹⁺²	—	2	1	no	—
286	3₋¹⁺²	—	2	2	no	—
287	3₋¹⁺²	—	2	4	no	—
288	3₋¹⁺²	—	2	4	no	—
289	3₋¹⁺²	—	2	2	no	—
290	3₋¹⁺²	C₂×D₃×C₉	1	2	yes	complemented
291	3₋¹⁺²	C₂×D₃×C₉	1	4	yes	complemented
292	H(3,𝔽₃)	—	2	1	no	—
293	H(3,𝔽₃)	—	2	2	no	—
294	H(3,𝔽₃)	C₂×D₃×C₉	1	1	yes	characteristic
295	H(3,𝔽₃)	C₂×D₃×C₉	1	2	yes	—
296	C₃×C₉	—	2	2	no	—
297	C₃×C₉	—	2	4	no	—
298	C₃×C₉	—	2	1	no	—
299	C₃×C₉	—	2	1	no	—
300	C₃×C₉	—	2	2	no	—
301	C₃×C₉	—	2	2	no	—
302	C₃×C₉	—	2	1	no	—
303	C₃×C₉	—	2	2	no	—
304	C₃×C₉	—	2	1	no	—
305	C₃×C₉	—	2	2	no	—
306	C₃×C₉	—	2	1	no	—
307	C₃×C₉	—	2	1	no	—
308	C₃×C₉	—	2	2	no	—
309	C₃×C₉	—	2	2	no	—
310	C₃×C₉	—	2	2	no	—
311	C₃×C₉	—	2	2	no	—
312	C₃×C₉	—	2	2	no	—
313	C₃×C₉	—	2	1	no	—
314	C₃×C₉	—	18	1	no	—
315	C₃×C₉	—	18	1	no	—
316	C₃×C₉	—	18	1	no	—
317	C₃×C₉	—	18	1	no	—
318	C₃×C₉	—	18	1	no	—
319	C₃×C₉	—	18	1	no	—
320	C₃×C₉	—	18	1	no	—
321	C₃×C₉	C₂×D₃×C₉	1	1	yes	characteristic, complemented
322	C₃×C₉	C₂×D₃×C₉	1	2	yes	complemented
323	C₃×C₉	C₂²×C₃×C₉	1	1	yes	characteristic, complemented
324	C₃×C₉	C₂×C₃²×D₃	1	2	yes	—
325	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
326	C₃×C₉	C₂×C₃×C₃⋊D₃	1	2	yes	—
327	C₃×C₉	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
328	C₂×C₃²	—	2	1	no	—
329	C₂×C₃²	—	2	2	no	—
330	C₂×C₃²	—	2	1	no	—
331	C₂×C₃²	—	3	1	no	—
332	C₂×C₃²	—	6	1	no	—
333	C₂×C₃²	—	6	1	no	—
334	C₂×C₃²	—	6	1	no	—
335	C₂×C₃²	—	6	1	no	—
336	C₂×C₃²	—	6	1	no	—
337	C₂×C₃²	—	6	1	no	—
338	C₂×C₃²	—	27	2	no	—
339	C₂×C₃²	C₃×D₃×C₉	1	1	yes	characteristic
340	C₂×C₃²	C₉×C₃⋊D₃	1	1	yes	characteristic
341	C₂×C₃²	C₉×C₃⋊D₃	1	2	yes	—
342	C₂×C₃²	C₃²×C₃⋊D₃	1	1	yes	characteristic
343	C₃⋊D₃	—	3	2	no	—
344	C₃×D₃	—	9	2	no	—
345	C₃×D₃	—	9	4	no	—
346	C₃×D₃	—	9	2	no	—
347	C₃×D₃	—	27	2	no	—
348	C₂×C₉	—	2	1	no	—
349	C₂×C₉	—	2	4	no	—
350	C₂×C₉	—	2	2	no	—
351	C₂×C₉	—	2	2	no	—
352	C₂×C₉	—	2	1	no	—
353	C₂×C₉	—	2	2	no	—
354	C₂×C₉	—	6	2	no	—
355	C₂×C₉	—	6	2	no	—
356	C₂×C₉	—	6	2	no	—
357	C₂×C₉	—	6	2	no	—
358	C₂×C₉	—	6	1	no	—
359	C₂×C₉	—	6	1	no	—
360	C₂×C₉	—	6	2	no	—
361	C₂×C₉	—	6	1	no	—
362	C₂×C₉	—	6	2	no	—
363	C₂×C₉	—	27	2	no	—
364	C₂×C₉	—	27	4	no	—
365	C₂×C₉	C₃×D₃×C₉	1	1	yes	characteristic
366	C₂×C₉	C₃×D₃×C₉	1	2	yes	—
367	D₉	—	3	2	no	—
368	D₉	—	3	4	no	—
369	C₂²×C₃	—	27	1	no	—
370	C₂²×C₃	—	27	2	no	—
371	C₂²×C₃	—	27	1	no	—
372	C₂×D₃	—	9	1	no	—
373	C₂×D₃	—	27	1	no	—
374	C₃²	—	2	1	no	—
375	C₃²	—	2	2	no	—
376	C₃²	—	2	1	no	—
377	C₃²	—	3	1	no	—
378	C₃²	—	6	1	no	—
379	C₃²	—	6	1	no	—
380	C₃²	—	6	1	no	—
381	C₃²	—	6	1	no	—
382	C₃²	—	6	1	no	—
383	C₃²	—	6	1	no	—
384	C₃²	C₂×C₃×D₃×C₉	1	1	yes	characteristic
385	C₃²	C₂×C₉×C₃⋊D₃	1	1	yes	characteristic
386	C₃²	C₂×C₉×C₃⋊D₃	1	2	yes	—
387	C₃²	C₂×C₃²×C₃⋊D₃	1	1	yes	characteristic
388	C₉	—	2	1	no	—
389	C₉	—	2	4	no	—
390	C₉	—	2	2	no	—
391	C₉	—	2	2	no	—
392	C₉	—	2	1	no	—
393	C₉	—	2	2	no	—
394	C₉	—	6	2	no	—
395	C₉	—	6	2	no	—
396	C₉	—	6	2	no	—
397	C₉	—	6	2	no	—
398	C₉	—	6	1	no	—
399	C₉	—	6	1	no	—
400	C₉	—	6	2	no	—
401	C₉	—	6	1	no	—
402	C₉	—	6	2	no	—
403	C₉	C₂×C₃×D₃×C₉	1	1	yes	characteristic
404	C₉	C₂×C₃×D₃×C₉	1	2	yes	—
405	C₂×C₃	—	2	1	no	—
406	C₂×C₃	—	3	1	no	—
407	C₂×C₃	—	3	1	no	—
408	C₂×C₃	—	6	2	no	—
409	C₂×C₃	—	6	1	no	—
410	C₂×C₃	—	6	2	no	—
411	C₂×C₃	—	6	1	no	—
412	C₂×C₃	—	27	2	no	—
413	C₂×C₃	—	27	4	no	—
414	C₂×C₃	—	27	2	no	—
415	C₂×C₃	C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
416	C₂×C₃	#4207⋊C₃	1	1	yes	characteristic
417	D₃	—	9	2	no	—
418	D₃	—	27	2	no	—
419	C₂²	—	27	1	no	Sylow
420	C₃	—	2	1	no	—
421	C₃	—	3	1	no	—
422	C₃	—	3	1	no	—
423	C₃	—	6	2	no	—
424	C₃	—	6	1	no	—
425	C₃	—	6	2	no	—
426	C₃	—	6	1	no	—
427	C₃	C₂×C₃×C₉×C₃⋊D₃	1	1	yes	characteristic
428	C₃	C₂×#4207⋊C₃	1	1	yes	characteristic
429	C₂	—	27	2	no	—
430	C₂	#4207⋊C₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	#4207⋊C₃
commutator, hypocenter	C₃×C₉	C₂²×C₃×C₉
Frattini	C₃²	C₂×C₃²×C₃⋊D₃
Fitting	C₂×#10624864	C₂
socle	C₂×C₃²	C₃²×C₃⋊D₃
prime radical	C₂×C₃×#4207	C₃
cosocle	C₃²×C₉	C₂²×C₃²
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. #4207⋊C₉	C₂	direct (N × H)
2. C₂×#10624864	C₂	semidirect
4. C₂×#92294	C₃	semidirect
5. C₂×C₃⋊(D₉⋊C₉)	C₃	semidirect
9. #10624864	C₂²	semidirect
18. C₂×C₉×3₋¹⁺²	D₃	semidirect
23. C₂×#6887	C₂×C₃	semidirect
25. C₂×C₃×C₉⋊C₉	D₃	semidirect
26. C₂×C₃×C₉⋊C₉	C₂×C₃	semidirect
27. #92294	C₂×C₃	semidirect
28. C₃⋊(D₉⋊C₉)	C₂×C₃	semidirect
32. C₂×#4207	C₉	semidirect
33. C₂×#4207	C₉	semidirect
53. C₉×3₋¹⁺²	C₂×D₃	semidirect
58. #6887	C₂²×C₃	semidirect
60. C₃×C₉⋊C₉	C₂×D₃	semidirect
61. C₃×C₉⋊C₉	C₂²×C₃	semidirect
68. C₂×#737	C₂×C₉	semidirect
69. C₂×#737	C₂×C₉	semidirect
84. #4207	C₂×C₉	semidirect
85. #4207	C₂×C₉	semidirect
133. C₂×C₃⋊D₉	C₃×C₉	semidirect
151. #737	C₂²×C₉	semidirect
152. #737	C₂²×C₉	semidirect
215. C₂×3₋¹⁺²	D₃×C₉	semidirect
216. C₂×3₋¹⁺²	D₃×C₉	semidirect
247. C₂×C₃×C₉	D₃×C₉	semidirect
248. C₂×C₃×C₉	D₃×C₉	semidirect
249. C₂×C₃×C₉	C₂×C₃×C₉	semidirect
254. C₃⋊D₉	C₂×C₃×C₉	semidirect
290. 3₋¹⁺²	C₂×D₃×C₉	semidirect
291. 3₋¹⁺²	C₂×D₃×C₉	semidirect
321. C₃×C₉	C₂×D₃×C₉	semidirect
322. C₃×C₉	C₂×D₃×C₉	semidirect
323. C₃×C₉	C₂²×C₃×C₉	semidirect
430. C₂	#4207⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
#4207⋊C₉	2
C₂×#10624864	2
C₂×C₃×#4207	3
C₂×#92294	3
C₂×C₃⋊(D₉⋊C₉)	3
C₂×C₉×AGL(1,ℤ/9)	3
C₂×C₉×(C₃⋊D₃)⋊C₃	3
C₂×C₃×D₉⋊C₉	3

Subgroups — C2×#4207⋊C9 #72243924

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4207⋊C₉ #72243924