Subgroups — C₉×#5581 #13152702

Order 1728.

712 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#894	C₂	1	2	yes	maximal
5	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#889	C₂	1	2	yes	maximal, complemented
8	C₉×#876	C₂	1	2	yes	maximal, complemented
9	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
10	C₉×#872	C₂	1	2	yes	maximal, complemented
11	C₉×#870	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5581	C₃	1	1	yes	maximal, characteristic
13	C₉×#552	—	3	1	no	maximal
14	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
17	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
22	C₃×C₄²×C₉	C₂²	1	2	yes	—
23	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
24	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
27	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
28	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
30	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
32	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
33	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₄×C₉×Dic₃	C₂²	1	2	yes	—
37	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
38	C₃×#946	C₂×C₃	1	1	yes	characteristic
39	C₃×#946	C₂×C₃	1	1	yes	characteristic
40	C₃×#894	C₂×C₃	1	2	yes	—
41	C₃×#892	C₂×C₃	1	1	yes	characteristic
42	C₃×D₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
43	C₃×#889	C₂×C₃	1	2	yes	—
44	C₃×#876	C₂×C₃	1	2	yes	—
45	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
46	C₃×#872	C₂×C₃	1	2	yes	—
47	C₃×#870	C₂×C₃	1	1	yes	characteristic
48	C₉×#126	—	3	2	no	—
49	C₉×#125	—	3	2	no	—
50	C₉×#125	—	3	1	no	—
51	C₉×#123	—	3	2	no	—
52	C₉×C₂²⋊Q₈	—	3	1	no	—
53	C₉×C₂²⋊Q₈	—	3	1	no	—
54	C₄×Q₈×C₉	—	2	1	no	—
55	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
56	C₄×D₄×C₉	—	3	1	no	—
57	C₉×#117	—	3	1	no	—
58	C₉×#117	—	3	2	no	—
59	C₂×C₉×C₄⋊C₄	—	3	1	no	—
60	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
61	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
62	C₃×Q₈×C₉	—	2	2	no	—
63	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
64	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
66	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
68	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
69	C₂×C₉×Dic₃	C₂³	1	2	yes	—
70	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
71	C₂×C₉×Dic₃	C₂³	1	2	yes	—
72	C₉×D₁₂	—	2	2	no	—
73	C₄×D₃×C₉	—	2	4	no	—
74	C₄×D₃×C₉	—	2	2	no	—
75	C₄×D₃×C₉	—	2	2	no	—
76	C₃×#552	—	3	1	no	—
77	#5581	C₉	1	1	yes	characteristic, direct product factor
78	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
81	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
83	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
86	C₃²×C₄²	C₂²×C₃	1	2	yes	—
87	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
88	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
89	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
90	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
91	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
93	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
95	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
96	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
97	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
98	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
99	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
100	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
101	C₂×Q₈×C₉	—	2	1	no	—
102	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
103	C₂×D₄×C₉	—	3	1	no	—
104	C₂²×C₄×C₉	—	3	2	no	—
105	C₂²×C₄×C₉	—	3	1	no	—
106	C₂²×C₄×C₉	—	3	1	no	—
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	—	2	2	no	—
109	C₉×C₄⋊C₄	—	3	1	no	—
110	C₉×C₄⋊C₄	—	3	2	no	—
111	C₉×C₄⋊C₄	—	3	2	no	—
112	C₉×C₄⋊C₄	—	3	1	no	—
113	C₉×C₄⋊C₄	—	3	2	no	—
114	C₉×C₄⋊C₄	—	3	1	no	—
115	C₉×C₄⋊C₄	—	3	2	no	—
116	C₉×C₄⋊C₄	—	3	2	no	—
117	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
119	C₉×C₂²⋊C₄	—	3	1	no	—
120	C₉×C₂²⋊C₄	—	3	2	no	—
121	C₉×C₂²⋊C₄	—	3	2	no	—
122	C₉×C₂²⋊C₄	—	3	1	no	—
123	C₉×C₂²⋊C₄	—	3	2	no	—
124	C₄²×C₉	—	2	2	no	—
125	C₄²×C₉	—	2	1	no	—
126	C₄²×C₉	—	3	2	no	—
127	C₄²×C₉	C₂×D₃	1	2	yes	—
128	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
129	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
130	C₂×D₃×C₉	—	2	1	no	—
131	C₂×D₃×C₉	—	2	1	no	—
132	C₂×D₃×C₉	—	2	1	no	—
133	C₂×D₃×C₉	—	2	1	no	—
134	C₂×D₃×C₉	—	2	1	no	—
135	C₂×D₃×C₉	#41	1	2	yes	—
136	C₃×C₄×C₉	—	2	2	no	—
137	C₃×C₄×C₉	—	2	2	no	—
138	C₃×C₄×C₉	—	2	1	no	—
139	C₃×C₄×C₉	—	2	1	no	—
140	C₃×C₄×C₉	#41	1	2	yes	—
141	C₉×Dic₃	—	2	1	no	—
142	C₉×Dic₃	—	2	1	no	—
143	C₉×Dic₃	—	2	2	no	—
144	C₉×Dic₃	—	2	2	no	—
145	C₃×#126	—	3	2	no	—
146	C₃×#125	—	3	2	no	—
147	C₃×#125	—	3	1	no	—
148	C₃×#123	—	3	2	no	—
149	C₃×C₂²⋊Q₈	—	3	1	no	—
150	C₃×C₂²⋊Q₈	—	3	1	no	—
151	C₃×C₄×Q₈	—	2	1	no	—
152	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
153	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
154	C₃×C₄×D₄	—	3	1	no	—
155	C₃×#117	—	3	1	no	—
156	C₃×#117	—	3	2	no	—
157	C₂×C₃×C₄⋊C₄	—	3	1	no	—
158	#946	C₂×C₉	1	1	yes	characteristic, complemented
159	#946	C₂×C₉	1	1	yes	characteristic, complemented
160	#894	C₂×C₉	1	2	yes	—
161	#892	C₂×C₉	1	1	yes	characteristic, complemented
162	D₃×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
163	#889	C₂×C₉	1	2	yes	complemented
164	#876	C₂×C₉	1	2	yes	complemented
165	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
166	#872	C₂×C₉	1	2	yes	complemented
167	#870	C₂×C₉	1	1	yes	characteristic, complemented
168	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
170	C₃²×Q₈	—	2	2	no	—
171	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
172	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
174	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
175	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
177	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
178	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
179	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
180	C₃×D₁₂	—	2	2	no	—
181	C₃×C₄×D₃	—	2	4	no	—
182	C₃×C₄×D₃	—	2	2	no	—
183	C₃×C₄×D₃	—	2	2	no	—
184	C₂³×C₉	—	3	1	no	—
185	C₂³×C₉	—	3	1	no	—
186	Q₈×C₉	—	2	4	no	—
187	Q₈×C₉	—	2	2	no	—
188	D₄×C₉	—	6	2	no	—
189	C₂×C₄×C₉	—	2	1	no	—
190	C₂×C₄×C₉	—	2	2	no	—
191	C₂×C₄×C₉	—	2	1	no	—
192	C₂×C₄×C₉	—	2	2	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	3	1	no	—
195	C₂×C₄×C₉	—	3	2	no	—
196	C₂×C₄×C₉	—	3	1	no	—
197	C₂×C₄×C₉	—	3	2	no	—
198	C₂×C₄×C₉	—	6	4	no	—
199	C₂×C₄×C₉	—	6	2	no	—
200	C₂×C₄×C₉	—	6	2	no	—
201	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
202	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
203	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
204	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
205	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
206	#552	—	3	1	no	Sylow
207	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
210	D₃×C₉	—	2	2	no	—
211	D₃×C₉	—	4	1	no	—
212	C₂×C₃×Q₈	—	2	1	no	—
213	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
214	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
215	C₂×C₃×D₄	—	3	1	no	—
216	C₂²×C₃×C₄	—	3	2	no	—
217	C₂²×C₃×C₄	—	3	1	no	—
218	C₂²×C₃×C₄	—	3	1	no	—
219	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
220	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
221	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
222	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₄⋊C₄	—	3	2	no	—
226	C₃×C₄⋊C₄	—	3	2	no	—
227	C₃×C₄⋊C₄	—	3	2	no	—
228	C₃×C₄⋊C₄	—	3	2	no	—
229	C₃×C₄⋊C₄	—	3	2	no	—
230	C₃×C₄⋊C₄	—	3	1	no	—
231	C₃×C₄⋊C₄	—	3	1	no	—
232	C₃×C₄⋊C₄	—	3	1	no	—
233	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
234	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
235	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
236	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
237	C₃×C₂²⋊C₄	—	3	1	no	—
238	C₃×C₂²⋊C₄	—	3	2	no	—
239	C₃×C₂²⋊C₄	—	3	2	no	—
240	C₃×C₂²⋊C₄	—	3	1	no	—
241	C₃×C₂²⋊C₄	—	3	2	no	—
242	C₃×C₄²	—	2	2	no	—
243	C₃×C₄²	—	2	1	no	—
244	C₃×C₄²	—	3	2	no	—
245	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
246	C₃×C₄²	C₂²×C₉	1	2	yes	—
247	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
248	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
249	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
250	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
251	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
252	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
253	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
254	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
255	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
256	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
257	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
258	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
259	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
260	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
261	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
262	C₄×Dic₃	C₂²×C₉	1	2	yes	—
263	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
264	C₂×C₃×D₃	—	2	1	no	—
265	C₂×C₃×D₃	—	2	1	no	—
266	C₂×C₃×D₃	—	2	1	no	—
267	C₂×C₃×D₃	—	2	1	no	—
268	C₂×C₃×D₃	—	2	1	no	—
269	C₂×C₃×D₃	C₃×#41	1	2	yes	—
270	C₃²×C₄	—	2	2	no	—
271	C₃²×C₄	—	2	1	no	—
272	C₃²×C₄	—	2	2	no	—
273	C₃²×C₄	—	2	1	no	—
274	C₃²×C₄	C₃×#41	1	2	yes	—
275	C₃×Dic₃	—	2	1	no	—
276	C₃×Dic₃	—	2	1	no	—
277	C₃×Dic₃	—	2	2	no	—
278	C₃×Dic₃	—	2	2	no	—
279	C₂²×C₉	—	2	1	no	—
280	C₂²×C₉	—	3	2	no	—
281	C₂²×C₉	—	6	1	no	—
282	C₂²×C₉	—	6	1	no	—
283	C₂²×C₉	—	6	1	no	—
284	C₂²×C₉	—	6	1	no	—
285	C₂²×C₉	—	6	1	no	—
286	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
287	C₄×C₉	—	2	2	no	—
288	C₄×C₉	—	2	4	no	—
289	C₄×C₉	—	2	2	no	—
290	C₄×C₉	—	2	1	no	—
291	C₄×C₉	—	2	2	no	—
292	C₄×C₉	—	2	1	no	—
293	C₄×C₉	—	2	2	no	—
294	C₄×C₉	—	4	2	no	—
295	C₄×C₉	—	4	1	no	—
296	C₄×C₉	—	6	1	no	—
297	C₄×C₉	—	6	1	no	—
298	C₄×C₉	—	6	2	no	—
299	C₄×C₉	—	6	2	no	—
300	C₄×C₉	#235	1	2	yes	—
301	#126	—	3	2	no	—
302	#125	—	3	2	no	—
303	#125	—	3	1	no	—
304	#123	—	3	2	no	—
305	C₂²⋊Q₈	—	3	1	no	—
306	C₂²⋊Q₈	—	3	1	no	—
307	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
308	C₄×D₄	—	3	1	no	—
309	#117	—	3	1	no	—
310	#117	—	3	2	no	—
311	C₂×C₄⋊C₄	—	3	1	no	—
312	C₃×C₉	#552	1	1	yes	characteristic, complemented, Sylow
313	C₂³×C₃	—	3	1	no	—
314	C₂³×C₃	—	3	1	no	—
315	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
316	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
317	C₃×Q₈	—	2	4	no	—
318	C₃×Q₈	—	2	2	no	—
319	C₃×Q₈	—	2	2	no	—
320	C₃×D₄	—	6	2	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	3	1	no	—
327	C₂×C₃×C₄	—	3	2	no	—
328	C₂×C₃×C₄	—	3	1	no	—
329	C₂×C₃×C₄	—	3	2	no	—
330	C₂×C₃×C₄	—	6	4	no	—
331	C₂×C₃×C₄	—	6	2	no	—
332	C₂×C₃×C₄	—	6	2	no	—
333	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
334	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
336	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
337	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
338	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
339	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
341	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
343	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
344	C₂×Dic₃	C₂³×C₉	1	2	yes	—
345	C₂×Dic₃	C₂³×C₉	1	2	yes	—
346	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
347	D₁₂	—	2	2	no	—
348	C₄×D₃	—	2	4	no	—
349	C₄×D₃	—	2	2	no	—
350	C₄×D₃	—	2	2	no	—
351	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
352	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
353	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
354	C₃×D₃	—	2	2	no	—
355	C₃×D₃	—	4	1	no	—
356	C₂×C₉	—	2	1	no	—
357	C₂×C₉	—	2	1	no	—
358	C₂×C₉	—	2	1	no	—
359	C₂×C₉	—	6	2	no	—
360	C₂×C₉	—	12	1	no	—
361	C₂×C₉	C₂×#235	1	1	yes	characteristic
362	C₂×C₉	#1007	1	1	yes	characteristic
363	C₂×C₉	D₃×#41	1	1	yes	characteristic
364	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
365	C₂×D₄	—	3	1	no	—
366	C₂²×C₄	—	3	2	no	—
367	C₂²×C₄	—	3	1	no	—
368	C₂²×C₄	—	3	1	no	—
369	C₄⋊C₄	—	3	1	no	—
370	C₄⋊C₄	—	3	2	no	—
371	C₄⋊C₄	—	3	2	no	—
372	C₄⋊C₄	—	3	1	no	—
373	C₄⋊C₄	—	3	2	no	—
374	C₄⋊C₄	—	3	1	no	—
375	C₄⋊C₄	—	3	2	no	—
376	C₄⋊C₄	—	3	2	no	—
377	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
378	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
379	C₂²⋊C₄	—	3	1	no	—
380	C₂²⋊C₄	—	3	2	no	—
381	C₂²⋊C₄	—	3	2	no	—
382	C₂²⋊C₄	—	3	1	no	—
383	C₂²⋊C₄	—	3	2	no	—
384	C₄²	—	3	2	no	—
385	C₄²	C₂×D₃×C₉	1	2	yes	—
386	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
387	C₂²×C₃	—	2	1	no	—
388	C₂²×C₃	—	3	2	no	—
389	C₂²×C₃	—	6	1	no	—
390	C₂²×C₃	—	6	1	no	—
391	C₂²×C₃	—	6	1	no	—
392	C₂²×C₃	—	6	1	no	—
393	C₂²×C₃	—	6	1	no	—
394	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
395	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
396	C₂×D₃	—	2	1	no	—
397	C₂×D₃	—	2	1	no	—
398	C₂×D₃	—	2	1	no	—
399	C₂×D₃	—	2	1	no	—
400	C₂×D₃	—	2	1	no	—
401	C₂×D₃	C₉×#41	1	2	yes	—
402	C₃×C₄	—	2	4	no	—
403	C₃×C₄	—	2	2	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	1	no	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	2	1	no	—
408	C₃×C₄	—	2	2	no	—
409	C₃×C₄	—	2	1	no	—
410	C₃×C₄	—	2	2	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	2	no	—
413	C₃×C₄	—	4	2	no	—
414	C₃×C₄	—	4	1	no	—
415	C₃×C₄	—	6	1	no	—
416	C₃×C₄	—	6	1	no	—
417	C₃×C₄	—	6	2	no	—
418	C₃×C₄	—	6	2	no	—
419	C₃×C₄	C₉×#41	1	2	yes	—
420	C₃×C₄	C₃×#235	1	2	yes	—
421	Dic₃	—	2	1	no	—
422	Dic₃	—	2	1	no	—
423	Dic₃	—	2	2	no	—
424	Dic₃	—	2	2	no	—
425	C₃²	C₃×#552	1	1	yes	characteristic
426	C₉	—	2	1	no	—
427	C₉	#5581	1	1	yes	characteristic, direct product factor
428	C₂³	—	3	1	no	—
429	C₂³	—	3	1	no	—
430	Q₈	—	2	2	no	—
431	D₄	—	6	2	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	3	2	no	—
434	C₂×C₄	—	3	1	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	6	4	no	—
437	C₂×C₄	—	6	2	no	—
438	C₂×C₄	—	6	2	no	—
439	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
440	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
441	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
442	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	2	1	no	—
446	C₂×C₃	—	2	1	no	—
447	C₂×C₃	—	6	2	no	—
448	C₂×C₃	—	12	1	no	—
449	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
450	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
451	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
452	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
453	C₂×C₃	C₃×#1007	1	1	yes	characteristic
454	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
455	D₃	—	2	2	no	—
456	D₃	—	4	1	no	—
457	C₂²	—	3	2	no	—
458	C₂²	—	6	1	no	—
459	C₂²	—	6	1	no	—
460	C₂²	—	6	1	no	—
461	C₂²	—	6	1	no	—
462	C₂²	—	6	1	no	—
463	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	2	no	—
467	C₄	—	2	1	no	—
468	C₄	—	6	1	no	—
469	C₄	—	6	1	no	—
470	C₄	—	6	2	no	—
471	C₄	—	6	2	no	—
472	C₄	C₉×#235	1	2	yes	—
473	C₃	—	2	1	no	—
474	C₃	C₉×#552	1	1	yes	characteristic, complemented
475	C₃	C₃×#5581	1	1	yes	characteristic
476	C₂	—	6	2	no	—
477	C₂	—	12	1	no	—
478	C₂	C₂×C₉×#235	1	1	yes	characteristic
479	C₂	C₉×#1007	1	1	yes	characteristic
480	C₂	D₃×C₉×#41	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×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#552
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
2. C₉×#946	C₂	semidirect
3. C₉×#946	C₂	semidirect
5. C₉×#892	C₂	semidirect
6. D₃×C₉×C₄⋊C₄	C₂	semidirect
7. C₉×#889	C₂	semidirect
8. C₉×#876	C₂	semidirect
10. C₉×#872	C₂	semidirect
11. C₉×#870	C₂	semidirect
55. C₄×Q₈×C₉	D₃	semidirect
77. #5581	C₉	direct (N × H)
152. C₃×C₄×Q₈	C₂×C₉	semidirect
158. #946	C₂×C₉	semidirect
159. #946	C₂×C₉	semidirect
161. #892	C₂×C₉	semidirect
162. D₃×C₄⋊C₄	C₂×C₉	semidirect
163. #889	C₂×C₉	semidirect
164. #876	C₂×C₉	semidirect
166. #872	C₂×C₉	semidirect
167. #870	C₂×C₉	semidirect
307. C₄×Q₈	D₃×C₉	semidirect
312. C₃×C₉	#552	semidirect
427. C₉	#5581	direct (N × H)
474. C₃	C₉×#552	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×Q₈×C₉	2
C₉×#946	2
C₉×#894	2
C₉×#892	2
D₃×C₉×C₄⋊C₄	2
C₉×#889	2
C₉×#876	2
C₄×C₉×D₁₂	2
C₉×#872	2
C₉×#870	2
C₃×#5581	3
C₉×#552	3

Subgroups — C9×#5581 #13152702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5581 #13152702