Subgroups — C₉×#5777 #13153512

Order 1728.

846 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#949	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#942	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#919	C₂	1	2	yes	maximal, complemented
7	C₉×#918	C₂	1	2	yes	maximal, complemented
8	C₉×#916	C₂	1	2	yes	maximal, complemented
9	C₉×#914	C₂	1	2	yes	maximal, complemented
10	C₉×#908	C₂	1	1	yes	maximal, characteristic, complemented
11	D₃×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5777	C₃	1	1	yes	maximal, characteristic
13	C₉×#575	—	3	1	no	maximal
14	C₃×C₉×#41	C₂²	1	1	yes	characteristic
15	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
16	C₉×#239	—	2	1	no	—
17	C₉×#239	—	2	1	no	—
18	C₉×#239	C₂²	1	2	yes	—
19	C₉×#239	C₂²	1	2	yes	complemented
20	C₉×#239	C₂²	1	1	yes	characteristic, complemented
21	D₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₉×#237	—	2	1	no	—
23	C₉×#237	C₂²	1	1	yes	characteristic, complemented
24	D₃×D₄×C₉	—	2	1	no	—
25	D₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
26	C₉×#235	—	2	1	no	—
27	C₉×#235	C₂²	1	1	yes	characteristic
28	C₂×C₉×D₁₂	—	2	1	no	—
29	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₄×D₃×C₉	—	2	1	no	—
31	C₂×C₄×D₃×C₉	—	2	1	no	—
32	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
33	C₃×C₉×Q₁₆	C₂²	1	2	yes	complemented
34	C₃×C₉×SD₁₆	C₂²	1	2	yes	complemented
35	C₃×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₉×#216	C₂²	1	2	yes	complemented
37	C₉×#215	C₂²	1	2	yes	complemented
38	C₉×#215	C₂²	1	2	yes	complemented
39	C₉×#213	C₂²	1	2	yes	complemented
40	C₉×#208	C₂²	1	1	yes	characteristic, complemented
41	C₉×D₂₄	C₂²	1	2	yes	complemented
42	C₉×#204	C₂²	1	2	yes	complemented
43	C₉×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
44	D₃×C₈×C₉	C₂²	1	2	yes	complemented
45	C₃×D₃×#41	C₂×C₃	1	1	yes	characteristic
46	C₂×C₃×#239	C₂×C₃	1	1	yes	characteristic
47	C₃²×#137	C₂×C₃	1	1	yes	characteristic
48	C₃×#949	C₂×C₃	1	1	yes	characteristic
49	C₃×#942	C₂×C₃	1	1	yes	characteristic
50	C₃×#919	C₂×C₃	1	2	yes	—
51	C₃×#918	C₂×C₃	1	2	yes	—
52	C₃×#916	C₂×C₃	1	2	yes	—
53	C₃×#914	C₂×C₃	1	2	yes	—
54	C₃×#908	C₂×C₃	1	1	yes	characteristic
55	C₃×D₃×M₁₆	C₂×C₃	1	1	yes	characteristic
56	C₂×C₉×#41	—	3	1	no	—
57	C₂×C₉×#41	—	3	1	no	—
58	C₉×#137	—	2	1	no	—
59	C₉×#137	—	3	1	no	—
60	C₉×#137	—	3	2	no	—
61	C₉×#137	D₃	1	1	yes	characteristic, complemented
62	C₉×AGL(1,ℤ/8)	—	3	1	no	—
63	C₉×AGL(1,ℤ/8)	—	3	2	no	—
64	C₉×AGL(1,ℤ/8)	—	3	1	no	—
65	C₉×#135	—	3	2	no	—
66	C₉×#135	—	3	2	no	—
67	C₂×C₉×M₁₆	—	3	1	no	—
68	C₂²×D₃×C₉	—	2	1	no	—
69	C₂²×D₃×C₉	—	2	1	no	—
70	C₂²×D₃×C₉	D₄	1	1	yes	characteristic
71	C₃×Q₈×C₉	—	2	1	no	—
72	C₃×Q₈×C₉	C₂³	1	1	yes	characteristic
73	C₃×Q₈×C₉	C₂³	1	2	yes	—
74	C₃×D₄×C₉	—	2	1	no	—
75	C₃×D₄×C₉	C₂³	1	1	yes	characteristic
76	C₂×C₃×C₄×C₉	—	2	1	no	—
77	C₂×C₃×C₄×C₉	—	2	1	no	—
78	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₉×#67	—	2	1	no	—
80	C₉×#67	—	2	1	no	—
81	C₉×#67	—	2	1	no	—
82	C₂×C₉×Dic₃	—	2	1	no	—
83	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
84	C₉×D₁₂	—	2	2	no	—
85	C₉×D₁₂	—	2	2	no	—
86	C₉×D₁₂	—	2	1	no	—
87	C₉×D₁₂	—	2	1	no	—
88	C₉×D₁₂	C₂³	1	2	yes	—
89	C₉×D₁₂	C₂³	1	1	yes	characteristic
90	C₄×D₃×C₉	—	2	1	no	—
91	C₄×D₃×C₉	—	2	1	no	—
92	C₄×D₃×C₉	—	2	1	no	—
93	C₄×D₃×C₉	—	2	2	no	—
94	C₄×D₃×C₉	—	2	2	no	—
95	C₄×D₃×C₉	D₄	1	1	yes	characteristic
96	C₄×D₃×C₉	D₄	1	1	yes	characteristic
97	C₄×D₃×C₉	C₂³	1	1	yes	characteristic
98	C₄×D₃×C₉	C₂³	1	1	yes	characteristic
99	C₉×Dic₆	—	2	1	no	—
100	C₉×Dic₆	C₂³	1	1	yes	characteristic
101	C₃×C₈×C₉	C₂³	1	2	yes	—
102	C₉×C₃⋊C₈	C₂³	1	2	yes	—
103	C₃×#575	—	3	1	no	—
104	#5777	C₉	1	1	yes	characteristic, direct product factor
105	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₃×#239	—	2	1	no	—
108	C₃×#239	—	2	1	no	—
109	C₃×#239	C₂²×C₃	1	2	yes	—
110	C₃×#239	C₂²×C₃	1	2	yes	—
111	C₃×#239	C₂²×C₃	1	1	yes	characteristic
112	C₃×D₃×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₃×#237	—	2	1	no	—
114	C₃×#237	C₂²×C₃	1	1	yes	characteristic
115	C₃×D₃×D₄	—	2	1	no	—
116	C₃×D₃×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₃×#235	—	2	1	no	—
118	C₃×#235	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×D₁₂	—	2	1	no	—
120	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₄×D₃	—	2	1	no	—
122	C₂×C₃×C₄×D₃	—	2	1	no	—
123	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
124	C₃²×Q₁₆	C₂²×C₃	1	2	yes	—
125	C₃²×SD₁₆	C₂²×C₃	1	2	yes	—
126	C₃²×M₁₆	C₂²×C₃	1	1	yes	characteristic
127	C₃×#216	C₂²×C₃	1	2	yes	—
128	C₃×#215	C₂²×C₃	1	2	yes	—
129	C₃×#215	C₂²×C₃	1	2	yes	—
130	C₃×#213	C₂²×C₃	1	2	yes	—
131	C₃×#208	C₂²×C₃	1	1	yes	characteristic
132	C₃×D₂₄	C₂²×C₃	1	2	yes	—
133	C₃×#204	C₂²×C₃	1	2	yes	—
134	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	2	yes	—
135	C₃×D₃×C₈	C₂²×C₃	1	2	yes	—
136	C₉×#41	—	2	1	no	—
137	C₉×#41	—	3	1	no	—
138	C₉×#41	—	3	2	no	—
139	C₉×#41	—	3	2	no	—
140	C₉×#41	—	3	1	no	—
141	C₉×#41	—	3	1	no	—
142	C₉×#41	—	6	1	no	—
143	C₉×#41	—	6	1	no	—
144	C₉×#41	—	6	1	no	—
145	C₉×#41	—	6	1	no	—
146	C₉×#41	C₂×D₃	1	1	yes	characteristic
147	C₂×Q₈×C₉	—	2	1	no	—
148	C₂×Q₈×C₉	—	3	1	no	—
149	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
150	C₂×D₄×C₉	—	3	1	no	—
151	C₂×D₄×C₉	—	3	1	no	—
152	C₂×D₄×C₉	—	6	1	no	—
153	C₂×D₄×C₉	—	6	1	no	—
154	C₂²×C₄×C₉	—	3	1	no	—
155	C₂²×C₄×C₉	—	6	1	no	—
156	C₂²×C₄×C₉	—	6	1	no	—
157	C₉×Q₁₆	—	2	2	no	—
158	C₉×Q₁₆	—	3	2	no	—
159	C₉×Q₁₆	C₂×D₃	1	2	yes	complemented
160	C₉×SD₁₆	—	2	2	no	—
161	C₉×SD₁₆	—	3	2	no	—
162	C₉×SD₁₆	—	3	2	no	—
163	C₉×SD₁₆	—	3	2	no	—
164	C₉×SD₁₆	C₂×D₃	1	2	yes	complemented
165	C₉×D₈	—	3	2	no	—
166	C₉×D₈	—	3	2	no	—
167	C₉×M₁₆	—	2	1	no	—
168	C₉×M₁₆	—	3	1	no	—
169	C₉×M₁₆	—	3	2	no	—
170	C₉×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
171	C₂×C₈×C₉	—	3	2	no	—
172	C₂²×C₃×C₉	—	2	1	no	—
173	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
174	C₂×D₃×C₉	—	2	2	no	—
175	C₂×D₃×C₉	—	2	1	no	—
176	C₂×D₃×C₉	—	4	1	no	—
177	C₂×D₃×C₉	—	4	2	no	—
178	C₂×D₃×C₉	—	4	2	no	—
179	C₂×D₃×C₉	C₂×D₄	1	1	yes	characteristic
180	C₂×D₃×C₉	C₂×D₄	1	1	yes	characteristic
181	C₃×C₄×C₉	—	2	1	no	—
182	C₃×C₄×C₉	—	2	2	no	—
183	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
184	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
185	C₉×Dic₃	—	2	1	no	—
186	C₉×Dic₃	C₂×D₄	1	1	yes	characteristic
187	C₉×Dic₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₃×#41	—	3	1	no	—
189	C₂×C₃×#41	—	3	1	no	—
190	D₃×#41	C₂×C₉	1	1	yes	characteristic, complemented
191	C₂×#239	C₂×C₉	1	1	yes	characteristic, complemented
192	C₃×#137	—	2	1	no	—
193	C₃×#137	—	3	1	no	—
194	C₃×#137	—	3	2	no	—
195	C₃×#137	C₂×C₉	1	1	yes	characteristic, complemented
196	C₃×#137	C₃×D₃	1	1	yes	characteristic
197	C₃×AGL(1,ℤ/8)	—	3	1	no	—
198	C₃×AGL(1,ℤ/8)	—	3	2	no	—
199	C₃×AGL(1,ℤ/8)	—	3	1	no	—
200	C₃×#135	—	3	2	no	—
201	C₃×#135	—	3	2	no	—
202	C₂×C₃×M₁₆	—	3	1	no	—
203	#949	C₂×C₉	1	1	yes	characteristic, complemented
204	#942	C₂×C₉	1	1	yes	characteristic, complemented
205	#919	C₂×C₉	1	2	yes	complemented
206	#918	C₂×C₉	1	2	yes	complemented
207	#916	C₂×C₉	1	2	yes	complemented
208	#914	C₂×C₉	1	2	yes	complemented
209	#908	C₂×C₉	1	1	yes	characteristic, complemented
210	D₃×M₁₆	C₂×C₉	1	1	yes	characteristic, complemented
211	C₂²×C₃×D₃	—	2	1	no	—
212	C₂²×C₃×D₃	—	2	1	no	—
213	C₂²×C₃×D₃	C₃×D₄	1	1	yes	characteristic
214	C₃²×Q₈	—	2	1	no	—
215	C₃²×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₃²×Q₈	C₂³×C₃	1	2	yes	—
217	C₃²×D₄	—	2	1	no	—
218	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₃²×C₄	—	2	1	no	—
220	C₂×C₃²×C₄	—	2	1	no	—
221	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₃×#67	—	2	1	no	—
223	C₃×#67	—	2	1	no	—
224	C₃×#67	—	2	1	no	—
225	C₂×C₃×Dic₃	—	2	1	no	—
226	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
227	C₃×D₁₂	—	2	2	no	—
228	C₃×D₁₂	—	2	2	no	—
229	C₃×D₁₂	—	2	1	no	—
230	C₃×D₁₂	—	2	1	no	—
231	C₃×D₁₂	C₂³×C₃	1	2	yes	—
232	C₃×D₁₂	C₂³×C₃	1	1	yes	characteristic
233	C₃×C₄×D₃	—	2	1	no	—
234	C₃×C₄×D₃	—	2	1	no	—
235	C₃×C₄×D₃	—	2	1	no	—
236	C₃×C₄×D₃	—	2	2	no	—
237	C₃×C₄×D₃	—	2	2	no	—
238	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
239	C₃×C₄×D₃	C₃×D₄	1	1	yes	characteristic
240	C₃×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
241	C₃×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
242	C₃×Dic₆	—	2	1	no	—
243	C₃×Dic₆	C₂³×C₃	1	1	yes	characteristic
244	C₂³×C₉	—	3	1	no	—
245	C₂³×C₉	—	6	1	no	—
246	C₂³×C₉	—	6	1	no	—
247	C₃²×C₈	C₂³×C₃	1	2	yes	—
248	C₃×C₃⋊C₈	C₂³×C₃	1	2	yes	—
249	Q₈×C₉	—	2	1	no	—
250	Q₈×C₉	—	2	2	no	—
251	Q₈×C₉	—	2	1	no	—
252	Q₈×C₉	—	3	1	no	—
253	Q₈×C₉	—	4	1	no	—
254	Q₈×C₉	—	6	1	no	—
255	Q₈×C₉	C₂²×D₃	1	1	yes	characteristic
256	Q₈×C₉	C₂²×D₃	1	2	yes	—
257	D₄×C₉	—	2	1	no	—
258	D₄×C₉	—	2	1	no	—
259	D₄×C₉	—	3	2	no	—
260	D₄×C₉	—	3	1	no	—
261	D₄×C₉	—	4	1	no	—
262	D₄×C₉	—	6	1	no	—
263	D₄×C₉	—	6	2	no	—
264	D₄×C₉	—	6	2	no	—
265	D₄×C₉	—	6	1	no	—
266	D₄×C₉	—	6	1	no	—
267	D₄×C₉	—	6	1	no	—
268	D₄×C₉	—	6	1	no	—
269	D₄×C₉	C₂²×D₃	1	1	yes	characteristic
270	C₂×C₄×C₉	—	2	1	no	—
271	C₂×C₄×C₉	—	2	1	no	—
272	C₂×C₄×C₉	—	2	1	no	—
273	C₂×C₄×C₉	—	3	1	no	—
274	C₂×C₄×C₉	—	3	1	no	—
275	C₂×C₄×C₉	—	3	1	no	—
276	C₂×C₄×C₉	—	3	1	no	—
277	C₂×C₄×C₉	—	3	1	no	—
278	C₂×C₄×C₉	—	4	1	no	—
279	C₂×C₄×C₉	—	4	1	no	—
280	C₂×C₄×C₉	—	6	1	no	—
281	C₂×C₄×C₉	—	6	2	no	—
282	C₂×C₄×C₉	—	6	2	no	—
283	C₂×C₄×C₉	—	6	1	no	—
284	C₂×C₄×C₉	—	6	1	no	—
285	C₂×C₄×C₉	—	6	1	no	—
286	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
287	C₈×C₉	—	2	2	no	—
288	C₈×C₉	—	3	2	no	—
289	C₈×C₉	C₂²×D₃	1	2	yes	—
290	#575	—	3	1	no	Sylow
291	C₂×C₃×C₉	—	2	1	no	—
292	C₂×C₃×C₉	—	4	1	no	—
293	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
294	D₃×C₉	—	2	1	no	—
295	D₃×C₉	—	2	1	no	—
296	D₃×C₉	—	4	2	no	—
297	D₃×C₉	—	4	1	no	—
298	C₃×#41	—	2	1	no	—
299	C₃×#41	—	3	1	no	—
300	C₃×#41	—	3	2	no	—
301	C₃×#41	—	3	2	no	—
302	C₃×#41	—	3	1	no	—
303	C₃×#41	—	3	1	no	—
304	C₃×#41	—	6	1	no	—
305	C₃×#41	—	6	1	no	—
306	C₃×#41	—	6	1	no	—
307	C₃×#41	—	6	1	no	—
308	C₃×#41	C₂²×C₉	1	1	yes	characteristic
309	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
310	C₂×C₃×Q₈	—	2	1	no	—
311	C₂×C₃×Q₈	—	3	1	no	—
312	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
313	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
314	C₂×C₃×D₄	—	3	1	no	—
315	C₂×C₃×D₄	—	3	1	no	—
316	C₂×C₃×D₄	—	6	1	no	—
317	C₂×C₃×D₄	—	6	1	no	—
318	C₂²×C₃×C₄	—	3	1	no	—
319	C₂²×C₃×C₄	—	6	1	no	—
320	C₂²×C₃×C₄	—	6	1	no	—
321	#239	—	2	1	no	—
322	#239	—	2	1	no	—
323	#239	C₂²×C₉	1	2	yes	—
324	#239	C₂²×C₉	1	2	yes	complemented
325	#239	C₂²×C₉	1	1	yes	characteristic, complemented
326	D₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
327	#237	—	2	1	no	—
328	#237	C₂²×C₉	1	1	yes	characteristic, complemented
329	D₃×D₄	—	2	1	no	—
330	D₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
331	#235	—	2	1	no	—
332	#235	C₂²×C₉	1	1	yes	characteristic
333	C₂×D₁₂	—	2	1	no	—
334	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
335	C₂×C₄×D₃	—	2	1	no	—
336	C₂×C₄×D₃	—	2	1	no	—
337	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
338	C₃×Q₁₆	—	2	2	no	—
339	C₃×Q₁₆	—	3	2	no	—
340	C₃×Q₁₆	C₂²×C₉	1	2	yes	complemented
341	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
342	C₃×SD₁₆	—	2	2	no	—
343	C₃×SD₁₆	—	3	2	no	—
344	C₃×SD₁₆	—	3	2	no	—
345	C₃×SD₁₆	—	3	2	no	—
346	C₃×SD₁₆	C₂²×C₉	1	2	yes	complemented
347	C₃×SD₁₆	C₂×C₃×D₃	1	2	yes	—
348	C₃×D₈	—	3	2	no	—
349	C₃×D₈	—	3	2	no	—
350	C₃×M₁₆	—	2	1	no	—
351	C₃×M₁₆	—	3	1	no	—
352	C₃×M₁₆	—	3	2	no	—
353	C₃×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
354	C₃×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
355	C₂×C₃×C₈	—	3	2	no	—
356	#216	C₂²×C₉	1	2	yes	complemented
357	#215	C₂²×C₉	1	2	yes	complemented
358	#215	C₂²×C₉	1	2	yes	complemented
359	#213	C₂²×C₉	1	2	yes	complemented
360	#208	C₂²×C₉	1	1	yes	characteristic, complemented
361	D₂₄	C₂²×C₉	1	2	yes	complemented
362	#204	C₂²×C₉	1	2	yes	complemented
363	ΓL(1,𝔽₂₅)	C₂²×C₉	1	2	yes	complemented
364	D₃×C₈	C₂²×C₉	1	2	yes	complemented
365	C₂²×C₃²	—	2	1	no	—
366	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
367	C₂×C₃×D₃	—	2	2	no	—
368	C₂×C₃×D₃	—	2	1	no	—
369	C₂×C₃×D₃	—	4	1	no	—
370	C₂×C₃×D₃	—	4	2	no	—
371	C₂×C₃×D₃	—	4	2	no	—
372	C₂×C₃×D₃	C₂×C₃×D₄	1	1	yes	characteristic
373	C₂×C₃×D₃	C₂×C₃×D₄	1	1	yes	characteristic
374	C₃²×C₄	—	2	1	no	—
375	C₃²×C₄	—	2	2	no	—
376	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
377	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
378	C₃×Dic₃	—	2	1	no	—
379	C₃×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
380	C₃×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
381	C₂²×C₉	—	2	1	no	—
382	C₂²×C₉	—	2	1	no	—
383	C₂²×C₉	—	3	1	no	—
384	C₂²×C₉	—	3	1	no	—
385	C₂²×C₉	—	4	1	no	—
386	C₂²×C₉	—	6	2	no	—
387	C₂²×C₉	—	6	1	no	—
388	C₂²×C₉	—	12	1	no	—
389	C₂²×C₉	—	12	2	no	—
390	C₂²×C₉	—	12	2	no	—
391	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
392	C₄×C₉	—	2	1	no	—
393	C₄×C₉	—	2	2	no	—
394	C₄×C₉	—	2	1	no	—
395	C₄×C₉	—	2	1	no	—
396	C₄×C₉	—	3	1	no	—
397	C₄×C₉	—	3	1	no	—
398	C₄×C₉	—	4	1	no	—
399	C₄×C₉	—	4	2	no	—
400	C₄×C₉	—	6	1	no	—
401	C₄×C₉	D₃×D₄	1	1	yes	characteristic
402	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
403	C₂×#41	—	3	1	no	—
404	C₂×#41	—	3	1	no	—
405	#137	—	3	1	no	—
406	#137	—	3	2	no	—
407	#137	D₃×C₉	1	1	yes	characteristic, complemented
408	AGL(1,ℤ/8)	—	3	1	no	—
409	AGL(1,ℤ/8)	—	3	2	no	—
410	AGL(1,ℤ/8)	—	3	1	no	—
411	#135	—	3	2	no	—
412	#135	—	3	2	no	—
413	C₂×M₁₆	—	3	1	no	—
414	C₃×C₉	#575	1	1	yes	characteristic, complemented, Sylow
415	C₂³×C₃	—	3	1	no	—
416	C₂³×C₃	—	6	1	no	—
417	C₂³×C₃	—	6	1	no	—
418	C₂²×D₃	—	2	1	no	—
419	C₂²×D₃	—	2	1	no	—
420	C₂²×D₃	D₄×C₉	1	1	yes	characteristic
421	C₃×Q₈	—	2	1	no	—
422	C₃×Q₈	—	2	1	no	—
423	C₃×Q₈	—	2	2	no	—
424	C₃×Q₈	—	2	1	no	—
425	C₃×Q₈	—	3	1	no	—
426	C₃×Q₈	—	4	1	no	—
427	C₃×Q₈	—	6	1	no	—
428	C₃×Q₈	C₂³×C₉	1	1	yes	characteristic
429	C₃×Q₈	C₂³×C₉	1	2	yes	—
430	C₃×Q₈	C₂²×C₃×D₃	1	1	yes	characteristic
431	C₃×Q₈	C₂²×C₃×D₃	1	2	yes	—
432	C₃×D₄	—	2	1	no	—
433	C₃×D₄	—	2	1	no	—
434	C₃×D₄	—	2	1	no	—
435	C₃×D₄	—	3	2	no	—
436	C₃×D₄	—	3	1	no	—
437	C₃×D₄	—	4	1	no	—
438	C₃×D₄	—	6	1	no	—
439	C₃×D₄	—	6	2	no	—
440	C₃×D₄	—	6	2	no	—
441	C₃×D₄	—	6	1	no	—
442	C₃×D₄	—	6	1	no	—
443	C₃×D₄	—	6	1	no	—
444	C₃×D₄	—	6	1	no	—
445	C₃×D₄	C₂³×C₉	1	1	yes	characteristic
446	C₃×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
447	C₂×C₃×C₄	—	2	1	no	—
448	C₂×C₃×C₄	—	2	1	no	—
449	C₂×C₃×C₄	—	2	1	no	—
450	C₂×C₃×C₄	—	2	1	no	—
451	C₂×C₃×C₄	—	2	1	no	—
452	C₂×C₃×C₄	—	3	1	no	—
453	C₂×C₃×C₄	—	3	1	no	—
454	C₂×C₃×C₄	—	3	1	no	—
455	C₂×C₃×C₄	—	3	1	no	—
456	C₂×C₃×C₄	—	3	1	no	—
457	C₂×C₃×C₄	—	4	1	no	—
458	C₂×C₃×C₄	—	4	1	no	—
459	C₂×C₃×C₄	—	6	1	no	—
460	C₂×C₃×C₄	—	6	2	no	—
461	C₂×C₃×C₄	—	6	2	no	—
462	C₂×C₃×C₄	—	6	1	no	—
463	C₂×C₃×C₄	—	6	1	no	—
464	C₂×C₃×C₄	—	6	1	no	—
465	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
466	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
467	#67	—	2	1	no	—
468	#67	—	2	1	no	—
469	#67	—	2	1	no	—
470	C₂×Dic₃	—	2	1	no	—
471	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
472	D₁₂	—	2	2	no	—
473	D₁₂	—	2	2	no	—
474	D₁₂	—	2	1	no	—
475	D₁₂	—	2	1	no	—
476	D₁₂	C₂³×C₉	1	2	yes	—
477	D₁₂	C₂³×C₉	1	1	yes	characteristic
478	C₄×D₃	—	2	1	no	—
479	C₄×D₃	—	2	1	no	—
480	C₄×D₃	—	2	1	no	—
481	C₄×D₃	—	2	2	no	—
482	C₄×D₃	—	2	2	no	—
483	C₄×D₃	D₄×C₉	1	1	yes	characteristic
484	C₄×D₃	D₄×C₉	1	1	yes	characteristic
485	C₄×D₃	C₂³×C₉	1	1	yes	characteristic
486	C₄×D₃	C₂³×C₉	1	1	yes	characteristic
487	Dic₆	—	2	1	no	—
488	Dic₆	C₂³×C₉	1	1	yes	characteristic
489	C₃×C₈	—	2	2	no	—
490	C₃×C₈	—	3	2	no	—
491	C₃×C₈	C₂³×C₉	1	2	yes	—
492	C₃×C₈	C₂²×C₃×D₃	1	2	yes	—
493	C₃⋊C₈	C₂³×C₉	1	2	yes	—
494	C₂×C₃²	—	2	1	no	—
495	C₂×C₃²	—	4	1	no	—
496	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
497	C₃×D₃	—	2	1	no	—
498	C₃×D₃	—	2	1	no	—
499	C₃×D₃	—	4	2	no	—
500	C₃×D₃	—	4	1	no	—
501	C₂×C₉	—	2	1	no	—
502	C₂×C₉	—	2	1	no	—
503	C₂×C₉	—	4	1	no	—
504	C₂×C₉	—	4	1	no	—
505	C₂×C₉	—	6	1	no	—
506	C₂×C₉	—	6	1	no	—
507	C₂×C₉	—	8	1	no	—
508	C₂×C₉	—	12	2	no	—
509	C₂×C₉	—	12	1	no	—
510	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
511	#41	—	3	1	no	—
512	#41	—	3	2	no	—
513	#41	—	3	2	no	—
514	#41	—	3	1	no	—
515	#41	—	3	1	no	—
516	#41	—	6	1	no	—
517	#41	—	6	1	no	—
518	#41	—	6	1	no	—
519	#41	—	6	1	no	—
520	#41	C₂×D₃×C₉	1	1	yes	characteristic
521	C₂×Q₈	—	3	1	no	—
522	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
523	C₂×D₄	—	3	1	no	—
524	C₂×D₄	—	3	1	no	—
525	C₂×D₄	—	6	1	no	—
526	C₂×D₄	—	6	1	no	—
527	C₂²×C₄	—	3	1	no	—
528	C₂²×C₄	—	6	1	no	—
529	C₂²×C₄	—	6	1	no	—
530	Q₁₆	—	3	2	no	—
531	Q₁₆	C₂×D₃×C₉	1	2	yes	complemented
532	SD₁₆	—	3	2	no	—
533	SD₁₆	—	3	2	no	—
534	SD₁₆	—	3	2	no	—
535	SD₁₆	C₂×D₃×C₉	1	2	yes	complemented
536	D₈	—	3	2	no	—
537	D₈	—	3	2	no	—
538	M₁₆	—	3	1	no	—
539	M₁₆	—	3	2	no	—
540	M₁₆	C₂×D₃×C₉	1	1	yes	characteristic, complemented
541	C₂×C₈	—	3	2	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	1	no	—
544	C₂²×C₃	—	2	1	no	—
545	C₂²×C₃	—	3	1	no	—
546	C₂²×C₃	—	3	1	no	—
547	C₂²×C₃	—	4	1	no	—
548	C₂²×C₃	—	6	2	no	—
549	C₂²×C₃	—	6	1	no	—
550	C₂²×C₃	—	12	1	no	—
551	C₂²×C₃	—	12	2	no	—
552	C₂²×C₃	—	12	2	no	—
553	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
554	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
555	C₂×D₃	—	2	2	no	—
556	C₂×D₃	—	2	1	no	—
557	C₂×D₃	—	4	1	no	—
558	C₂×D₃	—	4	2	no	—
559	C₂×D₃	—	4	2	no	—
560	C₂×D₃	C₂×D₄×C₉	1	1	yes	characteristic
561	C₂×D₃	C₂×D₄×C₉	1	1	yes	characteristic
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	2	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	2	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	3	1	no	—
569	C₃×C₄	—	3	1	no	—
570	C₃×C₄	—	4	1	no	—
571	C₃×C₄	—	4	2	no	—
572	C₃×C₄	—	6	1	no	—
573	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
574	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
575	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
576	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
577	Dic₃	—	2	1	no	—
578	Dic₃	C₂×D₄×C₉	1	1	yes	characteristic
579	Dic₃	C₂×D₄×C₉	1	1	yes	characteristic
580	C₃²	C₃×#575	1	1	yes	characteristic
581	C₉	—	2	1	no	—
582	C₉	#5777	1	1	yes	characteristic, direct product factor
583	C₂³	—	3	1	no	—
584	C₂³	—	6	1	no	—
585	C₂³	—	6	1	no	—
586	Q₈	—	2	1	no	—
587	Q₈	—	3	1	no	—
588	Q₈	—	6	1	no	—
589	Q₈	C₂²×D₃×C₉	1	1	yes	characteristic
590	Q₈	C₂²×D₃×C₉	1	2	yes	—
591	D₄	—	2	1	no	—
592	D₄	—	3	2	no	—
593	D₄	—	3	1	no	—
594	D₄	—	6	1	no	—
595	D₄	—	6	2	no	—
596	D₄	—	6	2	no	—
597	D₄	—	6	1	no	—
598	D₄	—	6	1	no	—
599	D₄	—	6	1	no	—
600	D₄	—	6	1	no	—
601	D₄	C₂²×D₃×C₉	1	1	yes	characteristic
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	3	1	no	—
605	C₂×C₄	—	3	1	no	—
606	C₂×C₄	—	3	1	no	—
607	C₂×C₄	—	3	1	no	—
608	C₂×C₄	—	3	1	no	—
609	C₂×C₄	—	6	1	no	—
610	C₂×C₄	—	6	2	no	—
611	C₂×C₄	—	6	2	no	—
612	C₂×C₄	—	6	1	no	—
613	C₂×C₄	—	6	1	no	—
614	C₂×C₄	—	6	1	no	—
615	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
616	C₈	—	3	2	no	—
617	C₈	C₂²×D₃×C₉	1	2	yes	—
618	C₂×C₃	—	2	1	no	—
619	C₂×C₃	—	2	1	no	—
620	C₂×C₃	—	2	1	no	—
621	C₂×C₃	—	4	1	no	—
622	C₂×C₃	—	4	1	no	—
623	C₂×C₃	—	4	1	no	—
624	C₂×C₃	—	6	1	no	—
625	C₂×C₃	—	6	1	no	—
626	C₂×C₃	—	8	1	no	—
627	C₂×C₃	—	12	2	no	—
628	C₂×C₃	—	12	1	no	—
629	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
630	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
631	D₃	—	2	1	no	—
632	D₃	—	2	1	no	—
633	D₃	—	4	2	no	—
634	D₃	—	4	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	3	1	no	—
637	C₂²	—	3	1	no	—
638	C₂²	—	6	2	no	—
639	C₂²	—	6	1	no	—
640	C₂²	—	12	1	no	—
641	C₂²	—	12	2	no	—
642	C₂²	—	12	2	no	—
643	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
644	C₄	—	2	1	no	—
645	C₄	—	2	2	no	—
646	C₄	—	3	1	no	—
647	C₄	—	3	1	no	—
648	C₄	—	6	1	no	—
649	C₄	D₃×D₄×C₉	1	1	yes	characteristic
650	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
651	C₃	—	2	1	no	—
652	C₃	C₉×#575	1	1	yes	characteristic, complemented
653	C₃	C₃×#5777	1	1	yes	characteristic
654	C₂	—	2	1	no	—
655	C₂	—	4	1	no	—
656	C₂	—	6	1	no	—
657	C₂	—	6	1	no	—
658	C₂	—	12	2	no	—
659	C₂	—	12	1	no	—
660	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂×D₃×D₄
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×#137	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5777	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₉×#137	D₃
hypocenter	C₃	C₉×#575
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#137

Complements

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

N	H ≅ G/N	type
1. D₃×C₉×#41	C₂	semidirect
2. C₂×C₉×#239	C₂	semidirect
3. C₃×C₉×#137	C₂	semidirect
4. C₉×#949	C₂	semidirect
5. C₉×#942	C₂	semidirect
6. C₉×#919	C₂	semidirect
7. C₉×#918	C₂	semidirect
8. C₉×#916	C₂	semidirect
9. C₉×#914	C₂	semidirect
10. C₉×#908	C₂	semidirect
11. D₃×C₉×M₁₆	C₂	semidirect
15. C₂×C₃×Q₈×C₉	C₂²	semidirect
19. C₉×#239	C₂²	semidirect
20. C₉×#239	C₂²	semidirect
21. D₃×Q₈×C₉	C₂²	semidirect
23. C₉×#237	C₂²	semidirect
25. D₃×D₄×C₉	C₂²	semidirect
29. C₂×C₉×D₁₂	C₂²	semidirect
33. C₃×C₉×Q₁₆	C₂²	semidirect
34. C₃×C₉×SD₁₆	C₂²	semidirect
35. C₃×C₉×M₁₆	C₂²	semidirect
36. C₉×#216	C₂²	semidirect
37. C₉×#215	C₂²	semidirect
38. C₉×#215	C₂²	semidirect
39. C₉×#213	C₂²	semidirect
40. C₉×#208	C₂²	semidirect
41. C₉×D₂₄	C₂²	semidirect
42. C₉×#204	C₂²	semidirect
43. C₉×ΓL(1,𝔽₂₅)	C₂²	semidirect
44. D₃×C₈×C₉	C₂²	semidirect
61. C₉×#137	D₃	semidirect
104. #5777	C₉	direct (N × H)
149. C₂×Q₈×C₉	C₂×D₃	semidirect
159. C₉×Q₁₆	C₂×D₃	semidirect
164. C₉×SD₁₆	C₂×D₃	semidirect
170. C₉×M₁₆	C₂×D₃	semidirect
190. D₃×#41	C₂×C₉	semidirect
191. C₂×#239	C₂×C₉	semidirect
195. C₃×#137	C₂×C₉	semidirect
203. #949	C₂×C₉	semidirect
204. #942	C₂×C₉	semidirect
205. #919	C₂×C₉	semidirect
206. #918	C₂×C₉	semidirect
207. #916	C₂×C₉	semidirect
208. #914	C₂×C₉	semidirect
209. #908	C₂×C₉	semidirect
210. D₃×M₁₆	C₂×C₉	semidirect
312. C₂×C₃×Q₈	C₂²×C₉	semidirect
324. #239	C₂²×C₉	semidirect
325. #239	C₂²×C₉	semidirect
326. D₃×Q₈	C₂²×C₉	semidirect
328. #237	C₂²×C₉	semidirect
330. D₃×D₄	C₂²×C₉	semidirect
334. C₂×D₁₂	C₂²×C₉	semidirect
340. C₃×Q₁₆	C₂²×C₉	semidirect
346. C₃×SD₁₆	C₂²×C₉	semidirect
353. C₃×M₁₆	C₂²×C₉	semidirect
356. #216	C₂²×C₉	semidirect
357. #215	C₂²×C₉	semidirect
358. #215	C₂²×C₉	semidirect
359. #213	C₂²×C₉	semidirect
360. #208	C₂²×C₉	semidirect
361. D₂₄	C₂²×C₉	semidirect
362. #204	C₂²×C₉	semidirect
363. ΓL(1,𝔽₂₅)	C₂²×C₉	semidirect
364. D₃×C₈	C₂²×C₉	semidirect
407. #137	D₃×C₉	semidirect
414. C₃×C₉	#575	semidirect
522. C₂×Q₈	C₂×D₃×C₉	semidirect
531. Q₁₆	C₂×D₃×C₉	semidirect
535. SD₁₆	C₂×D₃×C₉	semidirect
540. M₁₆	C₂×D₃×C₉	semidirect
582. C₉	#5777	direct (N × H)
652. C₃	C₉×#575	semidirect

Maximal subgroups

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

subgroup	index
D₃×C₉×#41	2
C₂×C₉×#239	2
C₃×C₉×#137	2
C₉×#949	2
C₉×#942	2
C₉×#919	2
C₉×#918	2
C₉×#916	2
C₉×#914	2
C₉×#908	2
D₃×C₉×M₁₆	2
C₃×#5777	3
C₉×#575	3

Subgroups — C9×#5777 #13153512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5777 #13153512