Subgroups — C₉×#5609 #13152828

Order 1728.

1378 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃×D₄×C₉	C₂	1	2	yes	maximal, complemented
3	C₂²×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#937	C₂	1	2	yes	maximal, complemented
7	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#884	C₂	1	2	yes	maximal, complemented
11	C₉×#882	C₂	1	2	yes	maximal, complemented
12	C₃×#5609	C₃	1	1	yes	maximal, characteristic
13	D₄²×C₉	—	3	1	no	maximal
14	C₂³×D₃×C₉	C₂²	1	2	yes	complemented
15	C₂³×D₃×C₉	C₂²	1	2	yes	complemented
16	C₂×C₃×D₄×C₉	C₂²	1	2	yes	complemented
17	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₉×#67	C₂²	1	1	yes	characteristic
20	C₂×C₉×#67	C₂²	1	2	yes	complemented
21	C₂×C₉×#67	C₂²	1	2	yes	complemented
22	C₂×C₉×#67	C₂²	1	2	yes	complemented
23	D₃×D₄×C₉	—	2	8	no	—
24	D₃×D₄×C₉	—	2	4	no	—
25	C₂×C₉×D₁₂	—	2	4	no	—
26	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
27	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
29	C₂×C₉×D₁₂	C₂²	1	2	yes	complemented
30	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₄×D₃×C₉	C₂²	1	2	yes	complemented
32	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	complemented
34	C₉×#217	C₂²	1	1	yes	characteristic, complemented
35	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
37	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	complemented
38	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃×D₃×D₄	C₂×C₃	1	1	yes	characteristic
41	C₂×C₃×D₃×D₄	C₂×C₃	1	2	yes	—
42	C₂²×C₃×D₁₂	C₂×C₃	1	1	yes	characteristic
43	C₃²×#121	C₂×C₃	1	1	yes	characteristic
44	C₃×#940	C₂×C₃	1	1	yes	characteristic
45	C₃×#937	C₂×C₃	1	2	yes	—
46	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
47	C₃×#895	C₂×C₃	1	1	yes	characteristic
48	C₃×#893	C₂×C₃	1	1	yes	characteristic
49	C₃×#884	C₂×C₃	1	2	yes	—
50	C₃×#882	C₂×C₃	1	2	yes	—
51	C₂²×D₄×C₉	—	3	2	no	—
52	C₂²×D₄×C₉	—	3	1	no	—
53	C₂²×D₄×C₉	—	3	1	no	—
54	C₉×#127	—	3	1	no	—
55	C₉×#121	—	2	1	no	—
56	C₉×#121	—	3	1	no	—
57	C₉×#121	—	3	2	no	—
58	C₉×#121	D₃	1	1	yes	characteristic, complemented
59	C₉×#120	—	3	2	no	—
60	C₉×#120	—	3	2	no	—
61	C₄×D₄×C₉	—	3	1	no	—
62	C₄×D₄×C₉	—	3	1	no	—
63	C₂³×C₃×C₉	C₂³	1	2	yes	—
64	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
65	C₂²×D₃×C₉	—	2	4	no	—
66	C₂²×D₃×C₉	—	2	4	no	—
67	C₂²×D₃×C₉	—	2	4	no	—
68	C₂²×D₃×C₉	—	2	4	no	—
69	C₂²×D₃×C₉	—	4	2	no	—
70	C₂²×D₃×C₉	—	4	2	no	—
71	C₂²×D₃×C₉	C₂³	1	2	yes	—
72	C₂²×D₃×C₉	C₂³	1	2	yes	—
73	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
74	C₃×D₄×C₉	—	2	4	no	—
75	C₃×D₄×C₉	—	2	2	no	—
76	C₂×C₃×C₄×C₉	—	2	2	no	—
77	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
78	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₉×#67	—	2	4	no	—
81	C₉×#67	—	2	4	no	—
82	C₉×#67	—	4	2	no	—
83	C₉×#67	D₄	1	4	yes	complemented
84	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
85	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
86	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
87	C₉×D₁₂	—	2	4	no	—
88	C₉×D₁₂	—	2	4	no	—
89	C₉×D₁₂	—	2	2	no	—
90	C₉×D₁₂	D₄	1	4	yes	complemented
91	C₄×D₃×C₉	—	2	2	no	—
92	C₄×D₃×C₉	—	2	4	no	—
93	C₃×D₄²	—	3	1	no	—
94	#5609	C₉	1	1	yes	characteristic, direct product factor
95	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
96	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
97	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
98	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
101	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
102	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
103	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
104	C₃×D₃×D₄	—	2	8	no	—
105	C₃×D₃×D₄	—	2	4	no	—
106	C₂×C₃×D₁₂	—	2	4	no	—
107	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
108	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
109	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
112	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
113	C₂⁴×C₉	—	3	2	no	—
114	C₂⁴×C₉	—	3	2	no	—
115	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
117	C₃×#217	C₂²×C₃	1	1	yes	characteristic
118	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
120	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
121	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
123	C₂×D₄×C₉	—	2	1	no	—
124	C₂×D₄×C₉	—	2	2	no	—
125	C₂×D₄×C₉	—	3	1	no	—
126	C₂×D₄×C₉	—	3	2	no	—
127	C₂×D₄×C₉	—	3	2	no	—
128	C₂×D₄×C₉	—	3	2	no	—
129	C₂×D₄×C₉	—	3	1	no	—
130	C₂×D₄×C₉	—	3	2	no	—
131	C₂×D₄×C₉	—	3	2	no	—
132	C₂×D₄×C₉	—	3	1	no	—
133	C₂×D₄×C₉	—	6	4	no	—
134	C₂×D₄×C₉	—	6	8	no	—
135	C₂×D₄×C₉	—	6	4	no	—
136	C₂×D₄×C₉	C₂×D₃	1	2	yes	complemented
137	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
138	C₂²×C₄×C₉	—	2	1	no	—
139	C₂²×C₄×C₉	—	3	2	no	—
140	C₂²×C₄×C₉	—	3	1	no	—
141	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic, complemented
142	C₉×C₄⋊C₄	—	2	1	no	—
143	C₉×C₄⋊C₄	—	3	1	no	—
144	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
145	C₉×C₂²⋊C₄	—	2	2	no	—
146	C₉×C₂²⋊C₄	—	3	1	no	—
147	C₉×C₂²⋊C₄	—	3	2	no	—
148	C₉×C₂²⋊C₄	—	3	1	no	—
149	C₉×C₂²⋊C₄	—	3	2	no	—
150	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	complemented
151	C₄²×C₉	—	3	1	no	—
152	C₂²×C₃×C₉	—	2	1	no	—
153	C₂²×C₃×C₉	—	2	1	no	—
154	C₂²×C₃×C₉	—	2	2	no	—
155	C₂²×C₃×C₉	—	2	2	no	—
156	C₂²×C₃×C₉	—	2	2	no	—
157	C₂²×C₃×C₉	C₂×D₄	1	2	yes	complemented
158	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
159	C₂×D₃×C₉	—	2	1	no	—
160	C₂×D₃×C₉	—	2	2	no	—
161	C₂×D₃×C₉	—	2	2	no	—
162	C₂×D₃×C₉	—	2	1	no	—
163	C₂×D₃×C₉	—	2	2	no	—
164	C₂×D₃×C₉	—	2	2	no	—
165	C₂×D₃×C₉	—	2	2	no	—
166	C₂×D₃×C₉	—	4	8	no	—
167	C₂×D₃×C₉	—	4	8	no	—
168	C₂×D₃×C₉	C₂×D₄	1	2	yes	complemented
169	C₂×D₃×C₉	C₂×D₄	1	4	yes	complemented
170	C₃×C₄×C₉	—	2	2	no	—
171	C₃×C₄×C₉	—	2	1	no	—
172	C₃×C₄×C₉	C₂×D₄	1	2	yes	complemented
173	C₉×Dic₃	—	2	1	no	—
174	C₉×Dic₃	—	2	1	no	—
175	C₉×Dic₃	C₂×D₄	1	2	yes	complemented
176	C₂²×C₃×D₄	—	3	2	no	—
177	C₂²×C₃×D₄	—	3	1	no	—
178	C₂²×C₃×D₄	—	3	1	no	—
179	C₂×D₃×D₄	C₂×C₉	1	1	yes	characteristic, complemented
180	C₂×D₃×D₄	C₂×C₉	1	2	yes	complemented
181	C₂²×D₁₂	C₂×C₉	1	1	yes	characteristic, complemented
182	C₃×#127	—	3	1	no	—
183	C₃×#121	—	2	1	no	—
184	C₃×#121	—	3	1	no	—
185	C₃×#121	—	3	2	no	—
186	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
187	C₃×#121	C₃×D₃	1	1	yes	characteristic
188	C₃×#120	—	3	2	no	—
189	C₃×#120	—	3	2	no	—
190	C₃×C₄×D₄	—	3	1	no	—
191	C₃×C₄×D₄	—	3	1	no	—
192	#940	C₂×C₉	1	1	yes	characteristic, complemented
193	#937	C₂×C₉	1	2	yes	complemented
194	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
195	#895	C₂×C₉	1	1	yes	characteristic, complemented
196	#893	C₂×C₉	1	1	yes	characteristic, complemented
197	#884	C₂×C₉	1	2	yes	complemented
198	#882	C₂×C₉	1	2	yes	complemented
199	C₂³×C₃²	C₂³×C₃	1	2	yes	—
200	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₃×D₃	—	2	4	no	—
202	C₂²×C₃×D₃	—	2	4	no	—
203	C₂²×C₃×D₃	—	2	4	no	—
204	C₂²×C₃×D₃	—	2	4	no	—
205	C₂²×C₃×D₃	—	4	2	no	—
206	C₂²×C₃×D₃	—	4	2	no	—
207	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
208	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
209	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
210	C₃²×D₄	—	2	4	no	—
211	C₃²×D₄	—	2	2	no	—
212	C₂×C₃²×C₄	—	2	2	no	—
213	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
215	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₃×#67	—	2	4	no	—
217	C₃×#67	—	2	4	no	—
218	C₃×#67	—	4	2	no	—
219	C₃×#67	C₃×D₄	1	4	yes	—
220	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
223	C₃×D₁₂	—	2	4	no	—
224	C₃×D₁₂	—	2	4	no	—
225	C₃×D₁₂	—	2	2	no	—
226	C₃×D₁₂	C₃×D₄	1	4	yes	—
227	C₃×C₄×D₃	—	2	2	no	—
228	C₃×C₄×D₃	—	2	4	no	—
229	C₂³×C₉	—	2	1	no	—
230	C₂³×C₉	—	2	2	no	—
231	C₂³×C₉	—	3	1	no	—
232	C₂³×C₉	—	3	2	no	—
233	C₂³×C₉	—	3	2	no	—
234	C₂³×C₉	—	6	4	no	—
235	C₂³×C₉	—	6	4	no	—
236	C₂³×C₉	—	6	4	no	—
237	C₂³×C₉	—	6	4	no	—
238	C₂³×C₉	—	12	2	no	—
239	C₂³×C₉	—	12	2	no	—
240	C₂³×C₉	C₂²×D₃	1	2	yes	—
241	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
242	D₄×C₉	—	2	4	no	—
243	D₄×C₉	—	2	2	no	—
244	D₄×C₉	—	3	4	no	—
245	D₄×C₉	—	3	4	no	—
246	D₄×C₉	—	4	2	no	—
247	D₄×C₉	—	4	4	no	—
248	D₄×C₉	—	6	4	no	—
249	D₄×C₉	—	6	4	no	—
250	D₄×C₉	—	6	4	no	—
251	D₄×C₉	—	6	4	no	—
252	D₄×C₉	—	6	2	no	—
253	D₄×C₉	—	12	2	no	—
254	C₂×C₄×C₉	—	2	2	no	—
255	C₂×C₄×C₉	—	2	1	no	—
256	C₂×C₄×C₉	—	2	1	no	—
257	C₂×C₄×C₉	—	2	2	no	—
258	C₂×C₄×C₉	—	3	1	no	—
259	C₂×C₄×C₉	—	3	1	no	—
260	C₂×C₄×C₉	—	3	1	no	—
261	C₂×C₄×C₉	—	4	2	no	—
262	C₂×C₄×C₉	—	6	4	no	—
263	C₂×C₄×C₉	—	6	2	no	—
264	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
265	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
266	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
267	D₄²	—	3	1	no	Sylow
268	C₂×C₃×C₉	—	2	2	no	—
269	C₂×C₃×C₉	—	4	2	no	—
270	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
273	D₃×C₉	—	2	2	no	—
274	D₃×C₉	—	2	4	no	—
275	D₃×C₉	—	4	2	no	—
276	C₂⁴×C₃	—	3	2	no	—
277	C₂⁴×C₃	—	3	2	no	—
278	C₂³×D₃	C₂²×C₉	1	2	yes	complemented
279	C₂³×D₃	C₂²×C₉	1	2	yes	complemented
280	C₂×C₃×D₄	—	2	2	no	—
281	C₂×C₃×D₄	—	2	1	no	—
282	C₂×C₃×D₄	—	3	1	no	—
283	C₂×C₃×D₄	—	3	2	no	—
284	C₂×C₃×D₄	—	3	2	no	—
285	C₂×C₃×D₄	—	3	2	no	—
286	C₂×C₃×D₄	—	3	1	no	—
287	C₂×C₃×D₄	—	3	2	no	—
288	C₂×C₃×D₄	—	3	2	no	—
289	C₂×C₃×D₄	—	3	1	no	—
290	C₂×C₃×D₄	—	6	4	no	—
291	C₂×C₃×D₄	—	6	8	no	—
292	C₂×C₃×D₄	—	6	4	no	—
293	C₂×C₃×D₄	C₂²×C₉	1	2	yes	complemented
294	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
295	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
296	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂²×C₃×C₄	—	3	2	no	—
299	C₂²×C₃×C₄	—	3	1	no	—
300	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic, complemented
301	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
302	C₂×#67	C₂²×C₉	1	1	yes	characteristic
303	C₂×#67	C₂²×C₉	1	2	yes	complemented
304	C₂×#67	C₂²×C₉	1	2	yes	complemented
305	C₂×#67	C₂²×C₉	1	2	yes	complemented
306	D₃×D₄	—	2	8	no	—
307	D₃×D₄	—	2	4	no	—
308	C₂×D₁₂	—	2	4	no	—
309	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
310	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
311	C₂×D₁₂	C₂²×C₉	1	2	yes	complemented
312	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic, complemented
313	C₂×C₄×D₃	C₂²×C₉	1	2	yes	complemented
314	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
315	C₃×C₄⋊C₄	—	2	1	no	—
316	C₃×C₄⋊C₄	—	3	1	no	—
317	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
318	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
319	C₃×C₂²⋊C₄	—	2	2	no	—
320	C₃×C₂²⋊C₄	—	3	1	no	—
321	C₃×C₂²⋊C₄	—	3	2	no	—
322	C₃×C₂²⋊C₄	—	3	1	no	—
323	C₃×C₂²⋊C₄	—	3	2	no	—
324	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	complemented
325	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
326	C₃×C₄²	—	3	1	no	—
327	#217	C₂²×C₉	1	1	yes	characteristic, complemented
328	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
329	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
330	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	complemented
331	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
332	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
333	C₂²×C₃²	—	2	1	no	—
334	C₂²×C₃²	—	2	1	no	—
335	C₂²×C₃²	—	2	2	no	—
336	C₂²×C₃²	—	2	2	no	—
337	C₂²×C₃²	—	2	2	no	—
338	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
339	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
340	C₂×C₃×D₃	—	2	1	no	—
341	C₂×C₃×D₃	—	2	2	no	—
342	C₂×C₃×D₃	—	2	2	no	—
343	C₂×C₃×D₃	—	2	1	no	—
344	C₂×C₃×D₃	—	2	2	no	—
345	C₂×C₃×D₃	—	2	2	no	—
346	C₂×C₃×D₃	—	2	2	no	—
347	C₂×C₃×D₃	—	4	8	no	—
348	C₂×C₃×D₃	—	4	8	no	—
349	C₂×C₃×D₃	C₂×C₃×D₄	1	2	yes	—
350	C₂×C₃×D₃	C₂×C₃×D₄	1	4	yes	—
351	C₃²×C₄	—	2	2	no	—
352	C₃²×C₄	—	2	1	no	—
353	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
354	C₃×Dic₃	—	2	1	no	—
355	C₃×Dic₃	—	2	1	no	—
356	C₃×Dic₃	C₂×C₃×D₄	1	2	yes	—
357	C₂²×C₉	—	2	1	no	—
358	C₂²×C₉	—	2	1	no	—
359	C₂²×C₉	—	2	2	no	—
360	C₂²×C₉	—	2	2	no	—
361	C₂²×C₉	—	2	2	no	—
362	C₂²×C₉	—	2	1	no	—
363	C₂²×C₉	—	2	2	no	—
364	C₂²×C₉	—	3	2	no	—
365	C₂²×C₉	—	3	4	no	—
366	C₂²×C₉	—	4	1	no	—
367	C₂²×C₉	—	4	1	no	—
368	C₂²×C₉	—	4	2	no	—
369	C₂²×C₉	—	4	2	no	—
370	C₂²×C₉	—	4	2	no	—
371	C₂²×C₉	—	6	2	no	—
372	C₂²×C₉	—	6	1	no	—
373	C₂²×C₉	—	6	2	no	—
374	C₂²×C₉	—	6	1	no	—
375	C₂²×C₉	—	6	2	no	—
376	C₂²×C₉	—	6	2	no	—
377	C₂²×C₉	—	6	2	no	—
378	C₂²×C₉	—	12	8	no	—
379	C₂²×C₉	—	12	8	no	—
380	C₂²×C₉	D₃×D₄	1	2	yes	complemented
381	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
382	C₄×C₉	—	2	1	no	—
383	C₄×C₉	—	2	2	no	—
384	C₄×C₉	—	2	2	no	—
385	C₄×C₉	—	3	2	no	—
386	C₄×C₉	—	4	1	no	—
387	C₄×C₉	—	4	2	no	—
388	C₄×C₉	—	6	1	no	—
389	C₄×C₉	—	6	1	no	—
390	C₄×C₉	D₃×D₄	1	2	yes	complemented
391	C₂²×D₄	—	3	2	no	—
392	C₂²×D₄	—	3	1	no	—
393	C₂²×D₄	—	3	1	no	—
394	#127	—	3	1	no	—
395	#121	—	3	1	no	—
396	#121	—	3	2	no	—
397	#121	D₃×C₉	1	1	yes	characteristic, complemented
398	#120	—	3	2	no	—
399	#120	—	3	2	no	—
400	C₄×D₄	—	3	1	no	—
401	C₄×D₄	—	3	1	no	—
402	C₃×C₉	D₄²	1	1	yes	characteristic, complemented, Sylow
403	C₂³×C₃	—	2	1	no	—
404	C₂³×C₃	—	2	2	no	—
405	C₂³×C₃	—	3	1	no	—
406	C₂³×C₃	—	3	2	no	—
407	C₂³×C₃	—	3	2	no	—
408	C₂³×C₃	—	6	4	no	—
409	C₂³×C₃	—	6	4	no	—
410	C₂³×C₃	—	6	4	no	—
411	C₂³×C₃	—	6	4	no	—
412	C₂³×C₃	—	12	2	no	—
413	C₂³×C₃	—	12	2	no	—
414	C₂³×C₃	C₂³×C₉	1	2	yes	—
415	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
416	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
417	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
418	C₂²×D₃	—	2	4	no	—
419	C₂²×D₃	—	2	4	no	—
420	C₂²×D₃	—	2	4	no	—
421	C₂²×D₃	—	2	4	no	—
422	C₂²×D₃	—	4	2	no	—
423	C₂²×D₃	—	4	2	no	—
424	C₂²×D₃	C₂³×C₉	1	2	yes	—
425	C₂²×D₃	C₂³×C₉	1	2	yes	—
426	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
427	C₃×D₄	—	2	4	no	—
428	C₃×D₄	—	2	4	no	—
429	C₃×D₄	—	2	2	no	—
430	C₃×D₄	—	2	2	no	—
431	C₃×D₄	—	3	4	no	—
432	C₃×D₄	—	3	4	no	—
433	C₃×D₄	—	4	2	no	—
434	C₃×D₄	—	4	4	no	—
435	C₃×D₄	—	6	4	no	—
436	C₃×D₄	—	6	4	no	—
437	C₃×D₄	—	6	4	no	—
438	C₃×D₄	—	6	4	no	—
439	C₃×D₄	—	6	2	no	—
440	C₃×D₄	—	12	2	no	—
441	C₂×C₃×C₄	—	2	2	no	—
442	C₂×C₃×C₄	—	2	2	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	3	1	no	—
447	C₂×C₃×C₄	—	3	1	no	—
448	C₂×C₃×C₄	—	3	1	no	—
449	C₂×C₃×C₄	—	4	2	no	—
450	C₂×C₃×C₄	—	6	4	no	—
451	C₂×C₃×C₄	—	6	2	no	—
452	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
453	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
454	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
455	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
456	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
457	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
458	#67	—	2	4	no	—
459	#67	—	2	4	no	—
460	#67	—	4	2	no	—
461	#67	D₄×C₉	1	4	yes	complemented
462	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
463	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
464	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
465	D₁₂	—	2	4	no	—
466	D₁₂	—	2	4	no	—
467	D₁₂	—	2	2	no	—
468	D₁₂	D₄×C₉	1	4	yes	complemented
469	C₄×D₃	—	2	2	no	—
470	C₄×D₃	—	2	4	no	—
471	C₂×C₃²	—	2	2	no	—
472	C₂×C₃²	—	4	2	no	—
473	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
474	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
475	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
476	C₃×D₃	—	2	2	no	—
477	C₃×D₃	—	2	4	no	—
478	C₃×D₃	—	4	2	no	—
479	C₂×C₉	—	2	2	no	—
480	C₂×C₉	—	2	1	no	—
481	C₂×C₉	—	2	1	no	—
482	C₂×C₉	—	2	1	no	—
483	C₂×C₉	—	4	2	no	—
484	C₂×C₉	—	4	2	no	—
485	C₂×C₉	—	6	4	no	—
486	C₂×C₉	—	6	2	no	—
487	C₂×C₉	—	8	2	no	—
488	C₂×C₉	—	12	2	no	—
489	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
490	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
491	C₂×C₉	#1009	1	1	yes	characteristic
492	C₂⁴	—	3	2	no	—
493	C₂⁴	—	3	2	no	—
494	C₂×D₄	—	3	1	no	—
495	C₂×D₄	—	3	2	no	—
496	C₂×D₄	—	3	2	no	—
497	C₂×D₄	—	3	2	no	—
498	C₂×D₄	—	3	1	no	—
499	C₂×D₄	—	3	2	no	—
500	C₂×D₄	—	3	2	no	—
501	C₂×D₄	—	3	1	no	—
502	C₂×D₄	—	6	4	no	—
503	C₂×D₄	—	6	8	no	—
504	C₂×D₄	—	6	4	no	—
505	C₂×D₄	C₂×D₃×C₉	1	2	yes	complemented
506	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
507	C₂²×C₄	—	3	2	no	—
508	C₂²×C₄	—	3	1	no	—
509	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
510	C₄⋊C₄	—	3	1	no	—
511	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
512	C₂²⋊C₄	—	3	1	no	—
513	C₂²⋊C₄	—	3	2	no	—
514	C₂²⋊C₄	—	3	1	no	—
515	C₂²⋊C₄	—	3	2	no	—
516	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	complemented
517	C₄²	—	3	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	2	1	no	—
520	C₂²×C₃	—	2	1	no	—
521	C₂²×C₃	—	2	1	no	—
522	C₂²×C₃	—	2	2	no	—
523	C₂²×C₃	—	2	2	no	—
524	C₂²×C₃	—	2	2	no	—
525	C₂²×C₃	—	2	2	no	—
526	C₂²×C₃	—	2	2	no	—
527	C₂²×C₃	—	2	2	no	—
528	C₂²×C₃	—	2	1	no	—
529	C₂²×C₃	—	2	2	no	—
530	C₂²×C₃	—	3	2	no	—
531	C₂²×C₃	—	3	4	no	—
532	C₂²×C₃	—	4	1	no	—
533	C₂²×C₃	—	4	1	no	—
534	C₂²×C₃	—	4	2	no	—
535	C₂²×C₃	—	4	2	no	—
536	C₂²×C₃	—	4	2	no	—
537	C₂²×C₃	—	6	2	no	—
538	C₂²×C₃	—	6	1	no	—
539	C₂²×C₃	—	6	2	no	—
540	C₂²×C₃	—	6	1	no	—
541	C₂²×C₃	—	6	2	no	—
542	C₂²×C₃	—	6	2	no	—
543	C₂²×C₃	—	6	2	no	—
544	C₂²×C₃	—	12	8	no	—
545	C₂²×C₃	—	12	8	no	—
546	C₂²×C₃	C₂×D₄×C₉	1	2	yes	complemented
547	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
548	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
549	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
550	C₂×D₃	—	2	1	no	—
551	C₂×D₃	—	2	2	no	—
552	C₂×D₃	—	2	2	no	—
553	C₂×D₃	—	2	1	no	—
554	C₂×D₃	—	2	2	no	—
555	C₂×D₃	—	2	2	no	—
556	C₂×D₃	—	2	2	no	—
557	C₂×D₃	—	4	8	no	—
558	C₂×D₃	—	4	8	no	—
559	C₂×D₃	C₂×D₄×C₉	1	2	yes	complemented
560	C₂×D₃	C₂×D₄×C₉	1	4	yes	complemented
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	2	no	—
563	C₃×C₄	—	2	2	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	2	no	—
566	C₃×C₄	—	3	2	no	—
567	C₃×C₄	—	4	1	no	—
568	C₃×C₄	—	4	2	no	—
569	C₃×C₄	—	6	1	no	—
570	C₃×C₄	—	6	1	no	—
571	C₃×C₄	C₂×D₄×C₉	1	2	yes	complemented
572	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
573	Dic₃	—	2	1	no	—
574	Dic₃	—	2	1	no	—
575	Dic₃	C₂×D₄×C₉	1	2	yes	complemented
576	C₃²	C₃×D₄²	1	1	yes	characteristic
577	C₉	—	2	1	no	—
578	C₉	#5609	1	1	yes	characteristic, direct product factor
579	C₂³	—	3	1	no	—
580	C₂³	—	3	2	no	—
581	C₂³	—	3	2	no	—
582	C₂³	—	6	4	no	—
583	C₂³	—	6	4	no	—
584	C₂³	—	6	4	no	—
585	C₂³	—	6	4	no	—
586	C₂³	—	12	2	no	—
587	C₂³	—	12	2	no	—
588	C₂³	C₂²×D₃×C₉	1	2	yes	—
589	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
590	D₄	—	2	4	no	—
591	D₄	—	2	2	no	—
592	D₄	—	3	4	no	—
593	D₄	—	3	4	no	—
594	D₄	—	6	4	no	—
595	D₄	—	6	4	no	—
596	D₄	—	6	4	no	—
597	D₄	—	6	4	no	—
598	D₄	—	6	2	no	—
599	D₄	—	12	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	3	1	no	—
602	C₂×C₄	—	3	1	no	—
603	C₂×C₄	—	3	1	no	—
604	C₂×C₄	—	6	4	no	—
605	C₂×C₄	—	6	2	no	—
606	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
607	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
609	C₂×C₃	—	2	2	no	—
610	C₂×C₃	—	2	2	no	—
611	C₂×C₃	—	2	1	no	—
612	C₂×C₃	—	2	1	no	—
613	C₂×C₃	—	2	1	no	—
614	C₂×C₃	—	4	2	no	—
615	C₂×C₃	—	4	2	no	—
616	C₂×C₃	—	4	2	no	—
617	C₂×C₃	—	6	4	no	—
618	C₂×C₃	—	6	2	no	—
619	C₂×C₃	—	8	2	no	—
620	C₂×C₃	—	12	2	no	—
621	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
622	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
623	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
625	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
626	C₂×C₃	C₃×#1009	1	1	yes	characteristic
627	D₃	—	2	2	no	—
628	D₃	—	2	4	no	—
629	D₃	—	4	2	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	3	2	no	—
636	C₂²	—	3	4	no	—
637	C₂²	—	6	2	no	—
638	C₂²	—	6	1	no	—
639	C₂²	—	6	2	no	—
640	C₂²	—	6	1	no	—
641	C₂²	—	6	2	no	—
642	C₂²	—	6	2	no	—
643	C₂²	—	6	2	no	—
644	C₂²	—	12	8	no	—
645	C₂²	—	12	8	no	—
646	C₂²	D₃×D₄×C₉	1	2	yes	complemented
647	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	3	2	no	—
651	C₄	—	6	1	no	—
652	C₄	—	6	1	no	—
653	C₄	D₃×D₄×C₉	1	2	yes	complemented
654	C₃	—	2	1	no	—
655	C₃	D₄²×C₉	1	1	yes	characteristic, complemented
656	C₃	C₃×#5609	1	1	yes	characteristic
657	C₂	—	2	2	no	—
658	C₂	—	4	2	no	—
659	C₂	—	6	4	no	—
660	C₂	—	6	2	no	—
661	C₂	—	12	2	no	—
662	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
663	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
664	C₂	C₉×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5609	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	D₄²×C₉
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₂×D₃×D₄×C₉	C₂	semidirect
2. C₂×D₃×D₄×C₉	C₂	semidirect
3. C₂²×C₉×D₁₂	C₂	semidirect
4. C₃×C₉×#121	C₂	semidirect
5. C₉×#940	C₂	semidirect
6. C₉×#937	C₂	semidirect
7. C₄×C₉×#67	C₂	semidirect
8. C₉×#895	C₂	semidirect
9. C₉×#893	C₂	semidirect
10. C₉×#884	C₂	semidirect
11. C₉×#882	C₂	semidirect
14. C₂³×D₃×C₉	C₂²	semidirect
15. C₂³×D₃×C₉	C₂²	semidirect
16. C₂×C₃×D₄×C₉	C₂²	semidirect
17. C₂×C₃×D₄×C₉	C₂²	semidirect
18. C₂²×C₃×C₄×C₉	C₂²	semidirect
20. C₂×C₉×#67	C₂²	semidirect
21. C₂×C₉×#67	C₂²	semidirect
22. C₂×C₉×#67	C₂²	semidirect
27. C₂×C₉×D₁₂	C₂²	semidirect
28. C₂×C₉×D₁₂	C₂²	semidirect
29. C₂×C₉×D₁₂	C₂²	semidirect
30. C₂×C₄×D₃×C₉	C₂²	semidirect
31. C₂×C₄×D₃×C₉	C₂²	semidirect
32. C₃×C₉×C₄⋊C₄	C₂²	semidirect
33. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
34. C₉×#217	C₂²	semidirect
35. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
36. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
37. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
38. C₉×Dic₃⋊C₄	C₂²	semidirect
39. C₄×C₉×Dic₃	C₂²	semidirect
58. C₉×#121	D₃	semidirect
83. C₉×#67	D₄	semidirect
90. C₉×D₁₂	D₄	semidirect
94. #5609	C₉	direct (N × H)
136. C₂×D₄×C₉	C₂×D₃	semidirect
137. C₂×D₄×C₉	C₂×D₃	semidirect
141. C₂²×C₄×C₉	C₂×D₃	semidirect
144. C₉×C₄⋊C₄	C₂×D₃	semidirect
150. C₉×C₂²⋊C₄	C₂×D₃	semidirect
157. C₂²×C₃×C₉	C₂×D₄	semidirect
168. C₂×D₃×C₉	C₂×D₄	semidirect
169. C₂×D₃×C₉	C₂×D₄	semidirect
172. C₃×C₄×C₉	C₂×D₄	semidirect
175. C₉×Dic₃	C₂×D₄	semidirect
179. C₂×D₃×D₄	C₂×C₉	semidirect
180. C₂×D₃×D₄	C₂×C₉	semidirect
181. C₂²×D₁₂	C₂×C₉	semidirect
186. C₃×#121	C₂×C₉	semidirect
192. #940	C₂×C₉	semidirect
193. #937	C₂×C₉	semidirect
194. C₄×#67	C₂×C₉	semidirect
195. #895	C₂×C₉	semidirect
196. #893	C₂×C₉	semidirect
197. #884	C₂×C₉	semidirect
198. #882	C₂×C₉	semidirect
278. C₂³×D₃	C₂²×C₉	semidirect
279. C₂³×D₃	C₂²×C₉	semidirect
293. C₂×C₃×D₄	C₂²×C₉	semidirect
294. C₂×C₃×D₄	C₂²×C₉	semidirect
300. C₂²×C₃×C₄	C₂²×C₉	semidirect
303. C₂×#67	C₂²×C₉	semidirect
304. C₂×#67	C₂²×C₉	semidirect
305. C₂×#67	C₂²×C₉	semidirect
310. C₂×D₁₂	C₂²×C₉	semidirect
311. C₂×D₁₂	C₂²×C₉	semidirect
312. C₂×D₁₂	C₂²×C₉	semidirect
313. C₂×C₄×D₃	C₂²×C₉	semidirect
314. C₂×C₄×D₃	C₂²×C₉	semidirect
317. C₃×C₄⋊C₄	C₂²×C₉	semidirect
324. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
327. #217	C₂²×C₉	semidirect
328. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
329. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
330. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
331. Dic₃⋊C₄	C₂²×C₉	semidirect
332. C₄×Dic₃	C₂²×C₉	semidirect
380. C₂²×C₉	D₃×D₄	semidirect
390. C₄×C₉	D₃×D₄	semidirect
397. #121	D₃×C₉	semidirect
402. C₃×C₉	D₄²	semidirect
461. #67	D₄×C₉	semidirect
468. D₁₂	D₄×C₉	semidirect
505. C₂×D₄	C₂×D₃×C₉	semidirect
506. C₂×D₄	C₂×D₃×C₉	semidirect
509. C₂²×C₄	C₂×D₃×C₉	semidirect
511. C₄⋊C₄	C₂×D₃×C₉	semidirect
516. C₂²⋊C₄	C₂×D₃×C₉	semidirect
546. C₂²×C₃	C₂×D₄×C₉	semidirect
559. C₂×D₃	C₂×D₄×C₉	semidirect
560. C₂×D₃	C₂×D₄×C₉	semidirect
571. C₃×C₄	C₂×D₄×C₉	semidirect
575. Dic₃	C₂×D₄×C₉	semidirect
578. C₉	#5609	direct (N × H)
646. C₂²	D₃×D₄×C₉	semidirect
653. C₄	D₃×D₄×C₉	semidirect
655. C₃	D₄²×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₄×C₉	2
C₂²×C₉×D₁₂	2
C₃×C₉×#121	2
C₉×#940	2
C₉×#937	2
C₄×C₉×#67	2
C₉×#895	2
C₉×#893	2
C₉×#884	2
C₉×#882	2
C₃×#5609	3
D₄²×C₉	3

Subgroups — C9×#5609 #13152828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5609 #13152828