Subgroups — C₉×#4727 #13141588

Order 1728.

524 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×ΓL(1,𝔽₂₅)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#830	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×(C₂×D₃)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4727	C₃	1	1	yes	maximal, characteristic
9	C₉×#408	—	3	1	no	maximal
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₉×#67	C₄	1	1	yes	characteristic
12	C₂×C₉×#67	C₄	1	1	yes	characteristic
13	C₉×#235	—	2	2	no	—
14	C₉×#235	—	2	2	no	—
15	C₂×C₉×D₁₂	C₄	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₉×Dic₆	C₄	1	1	yes	characteristic
19	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₉×ΓL(1,𝔽₂₅)	—	2	2	no	—
24	D₃×C₈×C₉	—	2	2	no	—
25	C₂×C₃×#235	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	1	yes	characteristic
27	C₂×C₃×D₃×C₈	C₂×C₃	1	1	yes	characteristic
28	C₂×C₉×#41	—	3	1	no	—
29	C₃²×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
30	C₃×#830	C₂×C₃	1	1	yes	characteristic
31	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
32	C₃×(C₂×D₃)⋊C₈	C₂×C₃	1	1	yes	characteristic
33	C₂×C₉×M₁₆	—	3	1	no	—
34	C₂²×C₈×C₉	—	3	1	no	—
35	C₉×C₂²⋊C₈	—	2	1	no	—
36	C₉×C₂²⋊C₈	—	3	1	no	—
37	C₉×C₂²⋊C₈	—	3	1	no	—
38	C₉×C₂²⋊C₈	—	3	1	no	—
39	C₉×C₂²⋊C₈	D₃	1	1	yes	characteristic, complemented
40	C₂³×C₃×C₉	C₂×C₄	1	1	yes	characteristic
41	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₃×C₉	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×C₉	—	2	1	no	—
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
47	C₉×#67	—	2	2	no	—
48	C₉×#67	—	2	2	no	—
49	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₉×Dic₃	C₂×C₄	1	1	yes	characteristic
51	C₉×D₁₂	—	2	2	no	—
52	C₄×D₃×C₉	—	2	1	no	—
53	C₄×D₃×C₉	—	2	1	no	—
54	C₄×D₃×C₉	D₄	1	2	yes	—
55	C₄×D₃×C₉	D₄	1	2	yes	—
56	C₉×Dic₆	—	2	2	no	—
57	C₃×C₈×C₉	—	2	1	no	—
58	C₃×C₈×C₉	—	2	1	no	—
59	C₉×C₃⋊C₈	—	2	1	no	—
60	C₉×C₃⋊C₈	—	2	1	no	—
61	C₃×#408	—	3	1	no	—
62	#4727	C₉	1	1	yes	characteristic, direct product factor
63	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₃×#67	C₃×C₄	1	1	yes	characteristic
65	C₂×C₃×#67	C₃×C₄	1	1	yes	characteristic
66	C₃×#235	—	2	2	no	—
67	C₃×#235	—	2	2	no	—
68	C₂×C₃×D₁₂	C₃×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
70	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃×Dic₆	C₃×C₄	1	1	yes	characteristic
72	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
75	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
76	C₃×ΓL(1,𝔽₂₅)	—	2	2	no	—
77	C₃×D₃×C₈	—	2	2	no	—
78	C₉×#41	—	6	2	no	—
79	C₉×#41	—	6	2	no	—
80	C₂×Q₈×C₉	—	3	1	no	—
81	C₂×D₄×C₉	—	3	1	no	—
82	C₂×D₄×C₉	—	3	1	no	—
83	C₂×D₄×C₉	—	3	1	no	—
84	C₂²×C₄×C₉	—	2	1	no	—
85	C₂²×C₄×C₉	—	3	1	no	—
86	C₂²×C₄×C₉	—	3	1	no	—
87	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
88	C₉×M₁₆	—	6	2	no	—
89	C₂×C₈×C₉	—	2	1	no	—
90	C₂×C₈×C₉	—	2	1	no	—
91	C₂×C₈×C₉	—	3	1	no	—
92	C₂×C₈×C₉	—	3	1	no	—
93	C₂×C₈×C₉	—	6	2	no	—
94	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
95	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
96	C₂²×C₃×C₉	—	2	1	no	—
97	C₂²×C₃×C₉	—	2	1	no	—
98	C₂²×C₃×C₉	—	2	1	no	—
99	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×D₃×C₉	—	2	1	no	—
101	C₂×D₃×C₉	—	2	1	no	—
102	C₂×D₃×C₉	—	2	1	no	—
103	C₂×D₃×C₉	—	2	1	no	—
104	C₂×D₃×C₉	—	2	1	no	—
105	C₂×D₃×C₉	C₂²⋊C₄	1	2	yes	—
106	C₃×C₄×C₉	—	2	1	no	—
107	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
108	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
109	C₉×Dic₃	—	2	1	no	—
110	C₉×Dic₃	C₂²⋊C₄	1	2	yes	—
111	C₂×C₃×#41	—	3	1	no	—
112	C₂×#235	C₂×C₉	1	1	yes	characteristic
113	C₂×C₃×M₁₆	—	3	1	no	—
114	C₂²×C₃×C₈	—	3	1	no	—
115	C₂×ΓL(1,𝔽₂₅)	C₂×C₉	1	1	yes	characteristic, complemented
116	C₂×D₃×C₈	C₂×C₉	1	1	yes	characteristic, complemented
117	C₃×C₂²⋊C₈	—	2	1	no	—
118	C₃×C₂²⋊C₈	—	3	1	no	—
119	C₃×C₂²⋊C₈	—	3	1	no	—
120	C₃×C₂²⋊C₈	—	3	1	no	—
121	C₃×C₂²⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
122	C₃×C₂²⋊C₈	C₃×D₃	1	1	yes	characteristic
123	#830	C₂×C₉	1	1	yes	characteristic, complemented
124	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
125	(C₂×D₃)⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
126	C₂³×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
128	C₂²×C₃×D₃	C₂×C₃×C₄	1	1	yes	characteristic
129	C₂×C₃²×C₄	—	2	1	no	—
130	C₂×C₃²×C₄	—	2	1	no	—
131	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
132	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
133	C₃×#67	—	2	2	no	—
134	C₃×#67	—	2	2	no	—
135	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
136	C₂×C₃×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
137	C₃×D₁₂	—	2	2	no	—
138	C₃×C₄×D₃	—	2	1	no	—
139	C₃×C₄×D₃	—	2	1	no	—
140	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
141	C₃×C₄×D₃	C₃×D₄	1	2	yes	—
142	C₃×Dic₆	—	2	2	no	—
143	C₂³×C₉	—	2	1	no	—
144	C₂³×C₉	—	3	1	no	—
145	C₂³×C₉	—	3	1	no	—
146	C₂³×C₉	C₄×D₃	1	1	yes	characteristic
147	C₃²×C₈	—	2	1	no	—
148	C₃²×C₈	—	2	1	no	—
149	C₃×C₃⋊C₈	—	2	1	no	—
150	C₃×C₃⋊C₈	—	2	1	no	—
151	Q₈×C₉	—	6	2	no	—
152	D₄×C₉	—	6	2	no	—
153	D₄×C₉	—	6	2	no	—
154	D₄×C₉	—	6	2	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	3	1	no	—
160	C₂×C₄×C₉	—	3	2	no	—
161	C₂×C₄×C₉	—	3	2	no	—
162	C₂×C₄×C₉	—	3	1	no	—
163	C₂×C₄×C₉	—	4	1	no	—
164	C₂×C₄×C₉	—	4	1	no	—
165	C₂×C₄×C₉	—	6	1	no	—
166	C₂×C₄×C₉	—	6	1	no	—
167	C₂×C₄×C₉	C₄×D₃	1	1	yes	characteristic
168	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
169	C₈×C₉	—	2	1	no	—
170	C₈×C₉	—	2	1	no	—
171	C₈×C₉	—	4	1	no	—
172	C₈×C₉	—	4	1	no	—
173	C₈×C₉	—	6	1	no	—
174	C₈×C₉	—	6	1	no	—
175	#408	—	3	1	no	Sylow
176	C₂×C₃×C₉	—	4	1	no	—
177	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₃×C₉	#131	1	1	yes	characteristic
179	C₂×C₃×C₉	#131	1	1	yes	characteristic
180	D₃×C₉	—	2	2	no	—
181	D₃×C₉	—	4	1	no	—
182	C₃×#41	—	6	2	no	—
183	C₃×#41	—	6	2	no	—
184	C₂×C₃×Q₈	—	3	1	no	—
185	C₂×C₃×D₄	—	3	1	no	—
186	C₂×C₃×D₄	—	3	1	no	—
187	C₂×C₃×D₄	—	3	1	no	—
188	C₂²×C₃×C₄	—	2	1	no	—
189	C₂²×C₃×C₄	—	3	1	no	—
190	C₂²×C₃×C₄	—	3	1	no	—
191	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
192	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
193	C₂×#67	C₄×C₉	1	1	yes	characteristic
194	C₂×#67	C₄×C₉	1	1	yes	characteristic
195	#235	—	2	2	no	—
196	#235	—	2	2	no	—
197	C₂×D₁₂	C₄×C₉	1	1	yes	characteristic
198	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
199	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
200	C₂×Dic₆	C₄×C₉	1	1	yes	characteristic
201	C₃×M₁₆	—	6	2	no	—
202	C₂×C₃×C₈	—	2	1	no	—
203	C₂×C₃×C₈	—	2	1	no	—
204	C₂×C₃×C₈	—	3	1	no	—
205	C₂×C₃×C₈	—	3	1	no	—
206	C₂×C₃×C₈	—	6	2	no	—
207	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
208	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
209	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
210	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
211	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
212	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
213	ΓL(1,𝔽₂₅)	—	2	2	no	—
214	D₃×C₈	—	2	2	no	—
215	C₂²×C₃²	—	2	1	no	—
216	C₂²×C₃²	—	2	1	no	—
217	C₂²×C₃²	—	2	1	no	—
218	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
219	C₂×C₃×D₃	—	2	1	no	—
220	C₂×C₃×D₃	—	2	1	no	—
221	C₂×C₃×D₃	—	2	1	no	—
222	C₂×C₃×D₃	—	2	1	no	—
223	C₂×C₃×D₃	—	2	1	no	—
224	C₂×C₃×D₃	C₃×C₂²⋊C₄	1	2	yes	—
225	C₃²×C₄	—	2	1	no	—
226	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
227	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
228	C₃×Dic₃	—	2	1	no	—
229	C₃×Dic₃	C₃×C₂²⋊C₄	1	2	yes	—
230	C₂²×C₉	—	2	2	no	—
231	C₂²×C₉	—	2	1	no	—
232	C₂²×C₉	—	2	1	no	—
233	C₂²×C₉	—	2	1	no	—
234	C₂²×C₉	—	2	1	no	—
235	C₂²×C₉	—	3	2	no	—
236	C₂²×C₉	—	4	1	no	—
237	C₂²×C₉	—	4	1	no	—
238	C₂²×C₉	—	6	1	no	—
239	C₂²×C₉	—	6	1	no	—
240	C₂²×C₉	—	6	1	no	—
241	C₂²×C₉	—	6	1	no	—
242	C₂²×C₉	—	6	1	no	—
243	C₂²×C₉	C₂×C₄×D₃	1	1	yes	characteristic
244	C₄×C₉	—	2	1	no	—
245	C₄×C₉	—	2	1	no	—
246	C₄×C₉	—	2	1	no	—
247	C₄×C₉	—	3	2	no	—
248	C₄×C₉	—	4	1	no	—
249	C₄×C₉	—	6	1	no	—
250	C₄×C₉	D₃×D₄	1	1	yes	characteristic
251	C₄×C₉	D₃×D₄	1	1	yes	characteristic
252	C₂×#41	—	3	1	no	—
253	C₂×M₁₆	—	3	1	no	—
254	C₂²×C₈	—	3	1	no	—
255	C₂²⋊C₈	—	3	1	no	—
256	C₂²⋊C₈	—	3	1	no	—
257	C₂²⋊C₈	—	3	1	no	—
258	C₂²⋊C₈	D₃×C₉	1	1	yes	characteristic, complemented
259	C₃×C₉	#408	1	1	yes	characteristic, complemented, Sylow
260	C₂³×C₃	—	2	1	no	—
261	C₂³×C₃	—	3	1	no	—
262	C₂³×C₃	—	3	1	no	—
263	C₂³×C₃	C₂×C₄×C₉	1	1	yes	characteristic
264	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
265	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
266	C₂²×D₃	C₂×C₄×C₉	1	1	yes	characteristic
267	C₃×Q₈	—	6	2	no	—
268	C₃×D₄	—	6	2	no	—
269	C₃×D₄	—	6	2	no	—
270	C₃×D₄	—	6	2	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	2	1	no	—
275	C₂×C₃×C₄	—	2	1	no	—
276	C₂×C₃×C₄	—	2	1	no	—
277	C₂×C₃×C₄	—	3	1	no	—
278	C₂×C₃×C₄	—	3	2	no	—
279	C₂×C₃×C₄	—	3	2	no	—
280	C₂×C₃×C₄	—	3	1	no	—
281	C₂×C₃×C₄	—	4	1	no	—
282	C₂×C₃×C₄	—	4	1	no	—
283	C₂×C₃×C₄	—	6	1	no	—
284	C₂×C₃×C₄	—	6	1	no	—
285	C₂×C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
287	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
289	#67	—	2	2	no	—
290	#67	—	2	2	no	—
291	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
292	C₂×Dic₃	C₂×C₄×C₉	1	1	yes	characteristic
293	D₁₂	—	2	2	no	—
294	C₄×D₃	—	2	1	no	—
295	C₄×D₃	—	2	1	no	—
296	C₄×D₃	D₄×C₉	1	2	yes	—
297	C₄×D₃	D₄×C₉	1	2	yes	—
298	Dic₆	—	2	2	no	—
299	C₃×C₈	—	2	1	no	—
300	C₃×C₈	—	2	1	no	—
301	C₃×C₈	—	2	1	no	—
302	C₃×C₈	—	2	1	no	—
303	C₃×C₈	—	4	1	no	—
304	C₃×C₈	—	4	1	no	—
305	C₃×C₈	—	6	1	no	—
306	C₃×C₈	—	6	1	no	—
307	C₃⋊C₈	—	2	1	no	—
308	C₃⋊C₈	—	2	1	no	—
309	C₂×C₃²	—	4	1	no	—
310	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₃²	C₃×#131	1	1	yes	characteristic
312	C₂×C₃²	C₃×#131	1	1	yes	characteristic
313	C₃×D₃	—	2	2	no	—
314	C₃×D₃	—	4	1	no	—
315	C₂×C₉	—	2	1	no	—
316	C₂×C₉	—	2	1	no	—
317	C₂×C₉	—	2	1	no	—
318	C₂×C₉	—	4	2	no	—
319	C₂×C₉	—	4	1	no	—
320	C₂×C₉	—	6	2	no	—
321	C₂×C₉	—	12	1	no	—
322	C₂×C₉	D₃×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×C₉	#901	1	1	yes	characteristic
324	C₂×C₉	#907	1	1	yes	characteristic
325	#41	—	6	2	no	—
326	#41	—	6	2	no	—
327	C₂×Q₈	—	3	1	no	—
328	C₂×D₄	—	3	1	no	—
329	C₂×D₄	—	3	1	no	—
330	C₂×D₄	—	3	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
334	M₁₆	—	6	2	no	—
335	C₂×C₈	—	3	1	no	—
336	C₂×C₈	—	3	1	no	—
337	C₂×C₈	—	6	2	no	—
338	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
339	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
340	C₂²×C₃	—	2	2	no	—
341	C₂²×C₃	—	2	1	no	—
342	C₂²×C₃	—	2	1	no	—
343	C₂²×C₃	—	2	1	no	—
344	C₂²×C₃	—	2	1	no	—
345	C₂²×C₃	—	2	1	no	—
346	C₂²×C₃	—	2	1	no	—
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	3	2	no	—
349	C₂²×C₃	—	4	1	no	—
350	C₂²×C₃	—	4	1	no	—
351	C₂²×C₃	—	6	1	no	—
352	C₂²×C₃	—	6	1	no	—
353	C₂²×C₃	—	6	1	no	—
354	C₂²×C₃	—	6	1	no	—
355	C₂²×C₃	—	6	1	no	—
356	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
357	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
358	C₂×D₃	—	2	1	no	—
359	C₂×D₃	—	2	1	no	—
360	C₂×D₃	—	2	1	no	—
361	C₂×D₃	—	2	1	no	—
362	C₂×D₃	—	2	1	no	—
363	C₂×D₃	C₉×C₂²⋊C₄	1	2	yes	—
364	C₃×C₄	—	2	1	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	3	2	no	—
369	C₃×C₄	—	4	1	no	—
370	C₃×C₄	—	6	1	no	—
371	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
372	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
373	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
374	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
375	Dic₃	—	2	1	no	—
376	Dic₃	C₉×C₂²⋊C₄	1	2	yes	—
377	C₃²	C₃×#408	1	1	yes	characteristic
378	C₉	—	2	1	no	—
379	C₉	#4727	1	1	yes	characteristic, direct product factor
380	C₂³	—	3	1	no	—
381	C₂³	—	3	1	no	—
382	C₂³	C₄×D₃×C₉	1	1	yes	characteristic
383	Q₈	—	6	2	no	—
384	D₄	—	6	2	no	—
385	D₄	—	6	2	no	—
386	D₄	—	6	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	3	1	no	—
390	C₂×C₄	—	3	2	no	—
391	C₂×C₄	—	3	2	no	—
392	C₂×C₄	—	3	1	no	—
393	C₂×C₄	—	6	1	no	—
394	C₂×C₄	—	6	1	no	—
395	C₂×C₄	C₄×D₃×C₉	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
397	C₈	—	2	1	no	—
398	C₈	—	2	1	no	—
399	C₈	—	6	1	no	—
400	C₈	—	6	1	no	—
401	C₂×C₃	—	2	1	no	—
402	C₂×C₃	—	2	1	no	—
403	C₂×C₃	—	2	1	no	—
404	C₂×C₃	—	4	2	no	—
405	C₂×C₃	—	4	1	no	—
406	C₂×C₃	—	4	1	no	—
407	C₂×C₃	—	6	2	no	—
408	C₂×C₃	—	12	1	no	—
409	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
410	C₂×C₃	C₉×#131	1	1	yes	characteristic
411	C₂×C₃	C₉×#131	1	1	yes	characteristic
412	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
413	C₂×C₃	C₃×#901	1	1	yes	characteristic
414	C₂×C₃	C₃×#907	1	1	yes	characteristic
415	D₃	—	2	2	no	—
416	D₃	—	4	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	3	2	no	—
421	C₂²	—	6	1	no	—
422	C₂²	—	6	1	no	—
423	C₂²	—	6	1	no	—
424	C₂²	—	6	1	no	—
425	C₂²	—	6	1	no	—
426	C₂²	C₂×C₄×D₃×C₉	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	3	2	no	—
429	C₄	—	6	1	no	—
430	C₄	D₃×D₄×C₉	1	1	yes	characteristic
431	C₄	D₃×D₄×C₉	1	1	yes	characteristic
432	C₃	—	2	1	no	—
433	C₃	C₉×#408	1	1	yes	characteristic, complemented
434	C₃	C₃×#4727	1	1	yes	characteristic
435	C₂	—	4	1	no	—
436	C₂	—	6	2	no	—
437	C₂	—	12	1	no	—
438	C₂	D₃×C₉×C₂²⋊C₄	1	1	yes	characteristic
439	C₂	C₉×#901	1	1	yes	characteristic
440	C₂	C₉×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×C₂²⋊C₈	C₂
socle	C₂²×C₃²	C₂²×C₃×C₄
prime radical	C₂×C₃×#235	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×C₂²⋊C₈	D₃
hypocenter	C₃	C₉×#408
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₉×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×ΓL(1,𝔽₂₅)	C₂	semidirect
3. C₂×D₃×C₈×C₉	C₂	semidirect
4. C₃×C₉×C₂²⋊C₈	C₂	semidirect
5. C₉×#830	C₂	semidirect
6. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
7. C₉×(C₂×D₃)⋊C₈	C₂	semidirect
39. C₉×C₂²⋊C₈	D₃	semidirect
62. #4727	C₉	direct (N × H)
115. C₂×ΓL(1,𝔽₂₅)	C₂×C₉	semidirect
116. C₂×D₃×C₈	C₂×C₉	semidirect
121. C₃×C₂²⋊C₈	C₂×C₉	semidirect
123. #830	C₂×C₉	semidirect
124. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
125. (C₂×D₃)⋊C₈	C₂×C₉	semidirect
258. C₂²⋊C₈	D₃×C₉	semidirect
259. C₃×C₉	#408	semidirect
379. C₉	#4727	direct (N × H)
433. C₃	C₉×#408	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#235	2
C₂×C₉×ΓL(1,𝔽₂₅)	2
C₂×D₃×C₈×C₉	2
C₃×C₉×C₂²⋊C₈	2
C₉×#830	2
C₉×(C₂×D₃)⋊C₈	2
C₃×#4727	3
C₉×#408	3

Subgroups — C9×#4727 #13141588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4727 #13141588