Subgroups — C₉×#3489 #11768210

Order 1152.

2283 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₉	C₂	1	2	yes	maximal, complemented
4	C₉×#548	C₂	1	2	yes	maximal, complemented
5	C₉×#547	C₂	1	6	yes	maximal, complemented
6	C₉×#546	C₂	1	6	yes	maximal, complemented
7	C₉×#537	C₂	1	3	yes	maximal, complemented
8	C₉×#536	C₂	1	3	yes	maximal, complemented
9	C₉×#525	C₂	1	3	yes	maximal, complemented
10	C₂×C₉×C₂²⋊Q₈	C₂	1	3	yes	maximal, complemented
11	C₉×#520	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3489	C₃	1	1	yes	maximal, characteristic
13	C₉×2₋¹⁺⁴	—	2	8	no	—
14	C₂×C₉×#41	—	2	8	no	—
15	C₂×C₉×#41	C₂²	1	3	yes	—
16	C₂×C₉×#41	C₂²	1	3	yes	—
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic
18	C₂×C₉×#41	C₂²	1	1	yes	characteristic
19	C₂×C₉×#41	C₂²	1	3	yes	complemented
20	C₂×C₉×#41	C₂²	1	6	yes	complemented
21	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
22	C₂²×Q₈×C₉	C₂²	1	3	yes	complemented
23	C₂²×Q₈×C₉	C₂²	1	2	yes	complemented
24	C₂²×D₄×C₉	C₂²	1	3	yes	—
25	C₂³×C₄×C₉	C₂²	1	3	yes	—
26	C₉×C₄⋊Q₈	C₂²	1	6	yes	complemented
27	C₉×#124	C₂²	1	6	yes	complemented
28	C₉×#123	C₂²	1	6	yes	complemented
29	C₉×#123	C₂²	1	12	yes	complemented
30	C₉×C₂²⋊Q₈	C₂²	1	3	yes	—
31	C₉×C₂²⋊Q₈	C₂²	1	6	yes	—
32	C₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
33	C₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
34	C₉×C₂²⋊Q₈	C₂²	1	3	yes	complemented
35	C₉×C₂²⋊Q₈	C₂²	1	6	yes	complemented
36	C₉×#121	C₂²	1	1	yes	characteristic
37	C₉×#121	C₂²	1	3	yes	complemented
38	C₉×#121	C₂²	1	12	yes	complemented
39	C₉×#121	C₂²	1	6	yes	complemented
40	C₉×#120	C₂²	1	6	yes	—
41	C₄×Q₈×C₉	C₂²	1	2	yes	complemented
42	C₄×D₄×C₉	C₂²	1	6	yes	—
43	C₄×D₄×C₉	C₂²	1	6	yes	complemented
44	C₄×D₄×C₉	C₂²	1	6	yes	complemented
45	C₉×#117	C₂²	1	3	yes	complemented
46	C₂×C₉×C₄⋊C₄	C₂²	1	3	yes	complemented
47	C₂×C₉×C₄⋊C₄	C₂²	1	6	yes	complemented
48	C₂×C₉×C₂²⋊C₄	C₂²	1	6	yes	—
49	C₂×C₃×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic
50	C₂²×C₃×#41	C₂×C₃	1	1	yes	characteristic
51	C₃×D₄×Q₈	C₂×C₃	1	2	yes	—
52	C₃×#548	C₂×C₃	1	2	yes	—
53	C₃×#547	C₂×C₃	1	6	yes	—
54	C₃×#546	C₂×C₃	1	6	yes	—
55	C₃×#537	C₂×C₃	1	3	yes	—
56	C₃×#536	C₂×C₃	1	3	yes	—
57	C₃×#525	C₂×C₃	1	3	yes	—
58	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	3	yes	—
59	C₃×#520	C₂×C₃	1	1	yes	characteristic
60	C₂⁴×C₉	C₂³	1	3	yes	—
61	C₉×#41	—	2	4	no	—
62	C₉×#41	—	2	12	no	—
63	C₉×#41	—	2	24	no	—
64	C₉×#41	—	2	12	no	—
65	C₉×#41	—	2	12	no	—
66	C₉×#41	D₄	1	8	yes	complemented
67	C₂×Q₈×C₉	—	2	4	no	—
68	C₂×Q₈×C₉	—	2	8	no	—
69	C₂×Q₈×C₉	—	2	12	no	—
70	C₂×Q₈×C₉	C₂³	1	3	yes	—
71	C₂×Q₈×C₉	C₂³	1	6	yes	—
72	C₂×Q₈×C₉	C₂³	1	3	yes	—
73	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₉	—	2	12	no	—
75	C₂×D₄×C₉	C₂³	1	2	yes	—
76	C₂×D₄×C₉	C₂³	1	6	yes	—
77	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
78	C₂×D₄×C₉	C₂³	1	6	yes	—
79	C₂×D₄×C₉	C₂³	1	3	yes	—
80	C₂×D₄×C₉	C₂³	1	6	yes	—
81	C₂×D₄×C₉	C₂³	1	3	yes	—
82	C₂²×C₄×C₉	—	2	12	no	—
83	C₂²×C₄×C₉	C₂³	1	6	yes	—
84	C₂²×C₄×C₉	C₂³	1	3	yes	—
85	C₂²×C₄×C₉	C₂³	1	3	yes	—
86	C₂²×C₄×C₉	C₂³	1	6	yes	—
87	C₂²×C₄×C₉	C₂³	1	3	yes	—
88	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₉	C₂³	1	3	yes	—
90	C₂²×C₄×C₉	C₂³	1	6	yes	—
91	C₂²×C₄×C₉	C₂³	1	3	yes	—
92	C₉×C₄⋊C₄	C₂³	1	3	yes	—
93	C₉×C₄⋊C₄	C₂³	1	6	yes	—
94	C₉×C₄⋊C₄	C₂³	1	6	yes	—
95	C₉×C₄⋊C₄	C₂³	1	12	yes	—
96	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₉×C₄⋊C₄	C₂³	1	6	yes	—
98	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
99	C₉×C₂²⋊C₄	C₂³	1	12	yes	—
100	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
101	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
102	C₉×C₂²⋊C₄	C₂³	1	2	yes	—
103	C₉×C₂²⋊C₄	C₂³	1	6	yes	—
104	C₄²×C₉	C₂³	1	6	yes	—
105	#3489	C₉	1	1	yes	characteristic, direct product factor, Sylow
106	C₃×2₋¹⁺⁴	—	2	8	no	—
107	C₂×C₃×#41	—	2	8	no	—
108	C₂×C₃×#41	C₂²×C₃	1	3	yes	—
109	C₂×C₃×#41	C₂²×C₃	1	3	yes	—
110	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×#41	C₂²×C₃	1	3	yes	—
113	C₂×C₃×#41	C₂²×C₃	1	6	yes	—
114	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₃×Q₈	C₂²×C₃	1	3	yes	—
116	C₂²×C₃×Q₈	C₂²×C₃	1	2	yes	—
117	C₂²×C₃×D₄	C₂²×C₃	1	3	yes	—
118	C₂³×C₃×C₄	C₂²×C₃	1	3	yes	—
119	C₃×C₄⋊Q₈	C₂²×C₃	1	6	yes	—
120	C₃×#124	C₂²×C₃	1	6	yes	—
121	C₃×#123	C₂²×C₃	1	6	yes	—
122	C₃×#123	C₂²×C₃	1	12	yes	—
123	C₃×C₂²⋊Q₈	C₂²×C₃	1	3	yes	—
124	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
125	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
126	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
127	C₃×C₂²⋊Q₈	C₂²×C₃	1	3	yes	—
128	C₃×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
129	C₃×#121	C₂²×C₃	1	1	yes	characteristic
130	C₃×#121	C₂²×C₃	1	3	yes	—
131	C₃×#121	C₂²×C₃	1	12	yes	—
132	C₃×#121	C₂²×C₃	1	6	yes	—
133	C₃×#120	C₂²×C₃	1	6	yes	—
134	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
135	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
136	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
137	C₃×C₄×D₄	C₂²×C₃	1	6	yes	—
138	C₃×#117	C₂²×C₃	1	3	yes	—
139	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	3	yes	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	6	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	6	yes	—
142	C₂³×C₉	—	2	6	no	—
143	C₂³×C₉	—	2	6	no	—
144	C₂³×C₉	—	4	3	no	—
145	C₂³×C₉	C₂⁴	1	3	yes	—
146	C₂³×C₉	C₂⁴	1	2	yes	—
147	C₂³×C₉	C₂⁴	1	3	yes	—
148	C₂³×C₉	C₂⁴	1	1	yes	characteristic
149	Q₈×C₉	—	2	6	no	—
150	Q₈×C₉	—	2	12	no	—
151	Q₈×C₉	—	2	6	no	—
152	Q₈×C₉	C₂×D₄	1	4	yes	—
153	D₄×C₉	—	2	12	no	—
154	D₄×C₉	—	2	12	no	—
155	D₄×C₉	—	2	4	no	—
156	D₄×C₉	—	2	6	no	—
157	D₄×C₉	—	2	2	no	—
158	D₄×C₉	—	4	6	no	—
159	D₄×C₉	C₂×D₄	1	12	yes	—
160	C₂×C₄×C₉	—	2	6	no	—
161	C₂×C₄×C₉	—	2	12	no	—
162	C₂×C₄×C₉	—	2	2	no	—
163	C₂×C₄×C₉	—	2	6	no	—
164	C₂×C₄×C₉	—	2	6	no	—
165	C₂×C₄×C₉	—	2	6	no	—
166	C₂×C₄×C₉	—	2	12	no	—
167	C₂×C₄×C₉	—	4	6	no	—
168	C₂×C₄×C₉	C₂×D₄	1	12	yes	—
169	C₂×C₄×C₉	C₂⁴	1	2	yes	—
170	C₂×C₄×C₉	C₂⁴	1	6	yes	—
171	C₂×C₄×C₉	C₂⁴	1	6	yes	—
172	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₉	C₂⁴	1	3	yes	—
174	C₂×C₄×C₉	C₂⁴	1	3	yes	—
175	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
176	C₂×2₋¹⁺⁴	C₂×C₉	1	1	yes	characteristic, complemented
177	C₂²×#41	C₂×C₉	1	1	yes	characteristic, complemented
178	D₄×Q₈	C₂×C₉	1	2	yes	complemented
179	#548	C₂×C₉	1	2	yes	complemented
180	#547	C₂×C₉	1	6	yes	complemented
181	#546	C₂×C₉	1	6	yes	complemented
182	#537	C₂×C₉	1	3	yes	complemented
183	#536	C₂×C₉	1	3	yes	complemented
184	#525	C₂×C₉	1	3	yes	complemented
185	C₂×C₂²⋊Q₈	C₂×C₉	1	3	yes	complemented
186	#520	C₂×C₉	1	1	yes	characteristic, complemented
187	C₂⁴×C₃	C₂³×C₃	1	3	yes	—
188	C₃×#41	—	2	4	no	—
189	C₃×#41	—	2	12	no	—
190	C₃×#41	—	2	24	no	—
191	C₃×#41	—	2	12	no	—
192	C₃×#41	—	2	12	no	—
193	C₃×#41	C₃×D₄	1	8	yes	—
194	C₂×C₃×Q₈	—	2	4	no	—
195	C₂×C₃×Q₈	—	2	8	no	—
196	C₂×C₃×Q₈	—	2	12	no	—
197	C₂×C₃×Q₈	C₂³×C₃	1	3	yes	—
198	C₂×C₃×Q₈	C₂³×C₃	1	6	yes	—
199	C₂×C₃×Q₈	C₂³×C₃	1	3	yes	—
200	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₃×D₄	—	2	12	no	—
202	C₂×C₃×D₄	C₂³×C₃	1	2	yes	—
203	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
204	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
206	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
207	C₂×C₃×D₄	C₂³×C₃	1	6	yes	—
208	C₂×C₃×D₄	C₂³×C₃	1	3	yes	—
209	C₂²×C₃×C₄	—	2	12	no	—
210	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
211	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
212	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
213	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
214	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
215	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
217	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
218	C₂²×C₃×C₄	C₂³×C₃	1	3	yes	—
219	C₃×C₄⋊C₄	C₂³×C₃	1	3	yes	—
220	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
221	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
222	C₃×C₄⋊C₄	C₂³×C₃	1	12	yes	—
223	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
224	C₃×C₄⋊C₄	C₂³×C₃	1	6	yes	—
225	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
226	C₃×C₂²⋊C₄	C₂³×C₃	1	12	yes	—
227	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
228	C₃×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
229	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
230	C₃×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
231	C₃×C₄²	C₂³×C₃	1	6	yes	—
232	C₂²×C₉	—	2	1	no	—
233	C₂²×C₉	—	2	3	no	—
234	C₂²×C₉	—	2	3	no	—
235	C₂²×C₉	—	2	1	no	—
236	C₂²×C₉	—	2	2	no	—
237	C₂²×C₉	—	2	3	no	—
238	C₂²×C₉	—	2	2	no	—
239	C₂²×C₉	—	2	3	no	—
240	C₂²×C₉	—	2	2	no	—
241	C₂²×C₉	—	2	3	no	—
242	C₂²×C₉	—	4	12	no	—
243	C₂²×C₉	C₂²×D₄	1	6	yes	—
244	C₂²×C₉	2₋¹⁺⁴	1	2	yes	complemented
245	C₂²×C₉	C₂⁵	1	1	yes	characteristic
246	C₄×C₉	—	2	1	no	—
247	C₄×C₉	—	2	3	no	—
248	C₄×C₉	—	2	6	no	—
249	C₄×C₉	—	2	2	no	—
250	C₄×C₉	—	2	6	no	—
251	C₄×C₉	C₂²×D₄	1	2	yes	—
252	C₄×C₉	C₂²×D₄	1	6	yes	—
253	2₋¹⁺⁴	—	2	8	no	—
254	C₂×#41	—	2	8	no	—
255	C₂×#41	C₂²×C₉	1	3	yes	—
256	C₂×#41	C₂²×C₉	1	3	yes	—
257	C₂×#41	C₂²×C₉	1	1	yes	characteristic
258	C₂×#41	C₂²×C₉	1	1	yes	characteristic
259	C₂×#41	C₂²×C₉	1	3	yes	complemented
260	C₂×#41	C₂²×C₉	1	6	yes	complemented
261	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
262	C₂²×Q₈	C₂²×C₉	1	3	yes	complemented
263	C₂²×Q₈	C₂²×C₉	1	2	yes	complemented
264	C₂²×D₄	C₂²×C₉	1	3	yes	—
265	C₂³×C₄	C₂²×C₉	1	3	yes	—
266	C₄⋊Q₈	C₂²×C₉	1	6	yes	complemented
267	#124	C₂²×C₉	1	6	yes	complemented
268	#123	C₂²×C₉	1	6	yes	complemented
269	#123	C₂²×C₉	1	12	yes	complemented
270	C₂²⋊Q₈	C₂²×C₉	1	3	yes	—
271	C₂²⋊Q₈	C₂²×C₉	1	6	yes	—
272	C₂²⋊Q₈	C₂²×C₉	1	6	yes	complemented
273	C₂²⋊Q₈	C₂²×C₉	1	6	yes	complemented
274	C₂²⋊Q₈	C₂²×C₉	1	3	yes	complemented
275	C₂²⋊Q₈	C₂²×C₉	1	6	yes	complemented
276	#121	C₂²×C₉	1	1	yes	characteristic
277	#121	C₂²×C₉	1	3	yes	complemented
278	#121	C₂²×C₉	1	12	yes	complemented
279	#121	C₂²×C₉	1	6	yes	complemented
280	#120	C₂²×C₉	1	6	yes	—
281	C₄×Q₈	C₂²×C₉	1	2	yes	complemented
282	C₄×D₄	C₂²×C₉	1	6	yes	—
283	C₄×D₄	C₂²×C₉	1	6	yes	complemented
284	C₄×D₄	C₂²×C₉	1	6	yes	complemented
285	#117	C₂²×C₉	1	3	yes	complemented
286	C₂×C₄⋊C₄	C₂²×C₉	1	3	yes	complemented
287	C₂×C₄⋊C₄	C₂²×C₉	1	6	yes	complemented
288	C₂×C₂²⋊C₄	C₂²×C₉	1	6	yes	—
289	C₂³×C₃	—	2	6	no	—
290	C₂³×C₃	—	2	6	no	—
291	C₂³×C₃	—	4	3	no	—
292	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
293	C₂³×C₃	C₂⁴×C₃	1	2	yes	—
294	C₂³×C₃	C₂⁴×C₃	1	3	yes	—
295	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
296	C₃×Q₈	—	2	6	no	—
297	C₃×Q₈	—	2	12	no	—
298	C₃×Q₈	—	2	6	no	—
299	C₃×Q₈	C₂×C₃×D₄	1	4	yes	—
300	C₃×D₄	—	2	12	no	—
301	C₃×D₄	—	2	12	no	—
302	C₃×D₄	—	2	4	no	—
303	C₃×D₄	—	2	6	no	—
304	C₃×D₄	—	2	2	no	—
305	C₃×D₄	—	4	6	no	—
306	C₃×D₄	C₂×C₃×D₄	1	12	yes	—
307	C₂×C₃×C₄	—	2	6	no	—
308	C₂×C₃×C₄	—	2	12	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	6	no	—
311	C₂×C₃×C₄	—	2	6	no	—
312	C₂×C₃×C₄	—	2	6	no	—
313	C₂×C₃×C₄	—	2	12	no	—
314	C₂×C₃×C₄	—	4	6	no	—
315	C₂×C₃×C₄	C₂×C₃×D₄	1	12	yes	—
316	C₂×C₃×C₄	C₂⁴×C₃	1	2	yes	—
317	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
318	C₂×C₃×C₄	C₂⁴×C₃	1	6	yes	—
319	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
321	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
322	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
323	C₂×C₉	—	2	2	no	—
324	C₂×C₉	—	2	6	no	—
325	C₂×C₉	—	4	2	no	—
326	C₂×C₉	—	4	3	no	—
327	C₂×C₉	C₂³×D₄	1	1	yes	characteristic
328	C₂×C₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	C₂×C₉	#585	1	1	yes	characteristic
330	C₂⁴	C₂³×C₉	1	3	yes	—
331	#41	—	2	4	no	—
332	#41	—	2	12	no	—
333	#41	—	2	24	no	—
334	#41	—	2	12	no	—
335	#41	—	2	12	no	—
336	#41	D₄×C₉	1	8	yes	complemented
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	8	no	—
339	C₂×Q₈	—	2	12	no	—
340	C₂×Q₈	C₂³×C₉	1	3	yes	—
341	C₂×Q₈	C₂³×C₉	1	6	yes	—
342	C₂×Q₈	C₂³×C₉	1	3	yes	—
343	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
344	C₂×D₄	—	2	12	no	—
345	C₂×D₄	C₂³×C₉	1	2	yes	—
346	C₂×D₄	C₂³×C₉	1	6	yes	—
347	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
348	C₂×D₄	C₂³×C₉	1	6	yes	—
349	C₂×D₄	C₂³×C₉	1	3	yes	—
350	C₂×D₄	C₂³×C₉	1	6	yes	—
351	C₂×D₄	C₂³×C₉	1	3	yes	—
352	C₂²×C₄	—	2	12	no	—
353	C₂²×C₄	C₂³×C₉	1	6	yes	—
354	C₂²×C₄	C₂³×C₉	1	3	yes	—
355	C₂²×C₄	C₂³×C₉	1	3	yes	—
356	C₂²×C₄	C₂³×C₉	1	6	yes	—
357	C₂²×C₄	C₂³×C₉	1	3	yes	—
358	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
359	C₂²×C₄	C₂³×C₉	1	3	yes	—
360	C₂²×C₄	C₂³×C₉	1	6	yes	—
361	C₂²×C₄	C₂³×C₉	1	3	yes	—
362	C₄⋊C₄	C₂³×C₉	1	3	yes	—
363	C₄⋊C₄	C₂³×C₉	1	6	yes	—
364	C₄⋊C₄	C₂³×C₉	1	6	yes	—
365	C₄⋊C₄	C₂³×C₉	1	12	yes	—
366	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
367	C₄⋊C₄	C₂³×C₉	1	6	yes	—
368	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
369	C₂²⋊C₄	C₂³×C₉	1	12	yes	—
370	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
371	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
372	C₂²⋊C₄	C₂³×C₉	1	2	yes	—
373	C₂²⋊C₄	C₂³×C₉	1	6	yes	—
374	C₄²	C₂³×C₉	1	6	yes	—
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	3	no	—
377	C₂²×C₃	—	2	3	no	—
378	C₂²×C₃	—	2	1	no	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	2	3	no	—
381	C₂²×C₃	—	2	2	no	—
382	C₂²×C₃	—	2	3	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	3	no	—
385	C₂²×C₃	—	4	12	no	—
386	C₂²×C₃	C₂²×C₃×D₄	1	6	yes	—
387	C₂²×C₃	C₃×2₋¹⁺⁴	1	2	yes	—
388	C₂²×C₃	C₂⁵×C₃	1	1	yes	characteristic
389	C₃×C₄	—	2	1	no	—
390	C₃×C₄	—	2	3	no	—
391	C₃×C₄	—	2	6	no	—
392	C₃×C₄	—	2	2	no	—
393	C₃×C₄	—	2	6	no	—
394	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
395	C₃×C₄	C₂²×C₃×D₄	1	6	yes	—
396	C₉	#3489	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³	—	2	6	no	—
398	C₂³	—	2	6	no	—
399	C₂³	—	4	3	no	—
400	C₂³	C₂⁴×C₉	1	3	yes	—
401	C₂³	C₂⁴×C₉	1	2	yes	—
402	C₂³	C₂⁴×C₉	1	3	yes	—
403	C₂³	C₂⁴×C₉	1	1	yes	characteristic
404	Q₈	—	2	6	no	—
405	Q₈	—	2	12	no	—
406	Q₈	—	2	6	no	—
407	Q₈	C₂×D₄×C₉	1	4	yes	—
408	D₄	—	2	12	no	—
409	D₄	—	2	12	no	—
410	D₄	—	2	4	no	—
411	D₄	—	2	6	no	—
412	D₄	—	2	2	no	—
413	D₄	—	4	6	no	—
414	D₄	C₂×D₄×C₉	1	12	yes	—
415	C₂×C₄	—	2	6	no	—
416	C₂×C₄	—	2	12	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	6	no	—
419	C₂×C₄	—	2	6	no	—
420	C₂×C₄	—	2	6	no	—
421	C₂×C₄	—	2	12	no	—
422	C₂×C₄	—	4	6	no	—
423	C₂×C₄	C₂×D₄×C₉	1	12	yes	—
424	C₂×C₄	C₂⁴×C₉	1	2	yes	—
425	C₂×C₄	C₂⁴×C₉	1	6	yes	—
426	C₂×C₄	C₂⁴×C₉	1	6	yes	—
427	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
428	C₂×C₄	C₂⁴×C₉	1	3	yes	—
429	C₂×C₄	C₂⁴×C₉	1	3	yes	—
430	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
431	C₂×C₃	—	2	2	no	—
432	C₂×C₃	—	2	6	no	—
433	C₂×C₃	—	4	3	no	—
434	C₂×C₃	—	4	2	no	—
435	C₂×C₃	C₂³×C₃×D₄	1	1	yes	characteristic
436	C₂×C₃	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
437	C₂×C₃	C₃×#585	1	1	yes	characteristic
438	C₂²	—	2	1	no	—
439	C₂²	—	2	3	no	—
440	C₂²	—	2	3	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	3	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	3	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	3	no	—
448	C₂²	—	4	12	no	—
449	C₂²	C₂²×D₄×C₉	1	6	yes	—
450	C₂²	C₉×2₋¹⁺⁴	1	2	yes	complemented
451	C₂²	C₂⁵×C₉	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	3	no	—
454	C₄	—	2	6	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	6	no	—
457	C₄	C₂²×D₄×C₉	1	2	yes	—
458	C₄	C₂²×D₄×C₉	1	6	yes	—
459	C₃	C₃×#3489	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	2	6	no	—
462	C₂	—	4	3	no	—
463	C₂	—	4	2	no	—
464	C₂	C₂³×D₄×C₉	1	1	yes	characteristic
465	C₂	C₂×C₉×2₋¹⁺⁴	1	1	yes	characteristic
466	C₂	C₉×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂⁵
commutator	C₂²	C₂⁵×C₉
Frattini, socle, cosocle	C₂²×C₃	C₂⁵×C₃
prime radical	C₃×#3489	C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×2₋¹⁺⁴	C₂	semidirect
2. C₂²×C₉×#41	C₂	semidirect
3. D₄×Q₈×C₉	C₂	semidirect
4. C₉×#548	C₂	semidirect
5. C₉×#547	C₂	semidirect
6. C₉×#546	C₂	semidirect
7. C₉×#537	C₂	semidirect
8. C₉×#536	C₂	semidirect
9. C₉×#525	C₂	semidirect
10. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
11. C₉×#520	C₂	semidirect
19. C₂×C₉×#41	C₂²	semidirect
20. C₂×C₉×#41	C₂²	semidirect
22. C₂²×Q₈×C₉	C₂²	semidirect
23. C₂²×Q₈×C₉	C₂²	semidirect
26. C₉×C₄⋊Q₈	C₂²	semidirect
27. C₉×#124	C₂²	semidirect
28. C₉×#123	C₂²	semidirect
29. C₉×#123	C₂²	semidirect
32. C₉×C₂²⋊Q₈	C₂²	semidirect
33. C₉×C₂²⋊Q₈	C₂²	semidirect
34. C₉×C₂²⋊Q₈	C₂²	semidirect
35. C₉×C₂²⋊Q₈	C₂²	semidirect
37. C₉×#121	C₂²	semidirect
38. C₉×#121	C₂²	semidirect
39. C₉×#121	C₂²	semidirect
41. C₄×Q₈×C₉	C₂²	semidirect
43. C₄×D₄×C₉	C₂²	semidirect
44. C₄×D₄×C₉	C₂²	semidirect
45. C₉×#117	C₂²	semidirect
46. C₂×C₉×C₄⋊C₄	C₂²	semidirect
47. C₂×C₉×C₄⋊C₄	C₂²	semidirect
66. C₉×#41	D₄	semidirect
105. #3489	C₉	direct (N × H)
176. C₂×2₋¹⁺⁴	C₂×C₉	semidirect
177. C₂²×#41	C₂×C₉	semidirect
178. D₄×Q₈	C₂×C₉	semidirect
179. #548	C₂×C₉	semidirect
180. #547	C₂×C₉	semidirect
181. #546	C₂×C₉	semidirect
182. #537	C₂×C₉	semidirect
183. #536	C₂×C₉	semidirect
184. #525	C₂×C₉	semidirect
185. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
186. #520	C₂×C₉	semidirect
244. C₂²×C₉	2₋¹⁺⁴	semidirect
259. C₂×#41	C₂²×C₉	semidirect
260. C₂×#41	C₂²×C₉	semidirect
262. C₂²×Q₈	C₂²×C₉	semidirect
263. C₂²×Q₈	C₂²×C₉	semidirect
266. C₄⋊Q₈	C₂²×C₉	semidirect
267. #124	C₂²×C₉	semidirect
268. #123	C₂²×C₉	semidirect
269. #123	C₂²×C₉	semidirect
272. C₂²⋊Q₈	C₂²×C₉	semidirect
273. C₂²⋊Q₈	C₂²×C₉	semidirect
274. C₂²⋊Q₈	C₂²×C₉	semidirect
275. C₂²⋊Q₈	C₂²×C₉	semidirect
277. #121	C₂²×C₉	semidirect
278. #121	C₂²×C₉	semidirect
279. #121	C₂²×C₉	semidirect
281. C₄×Q₈	C₂²×C₉	semidirect
283. C₄×D₄	C₂²×C₉	semidirect
284. C₄×D₄	C₂²×C₉	semidirect
285. #117	C₂²×C₉	semidirect
286. C₂×C₄⋊C₄	C₂²×C₉	semidirect
287. C₂×C₄⋊C₄	C₂²×C₉	semidirect
336. #41	D₄×C₉	semidirect
396. C₉	#3489	direct (N × H)
450. C₂²	C₉×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×2₋¹⁺⁴	2
C₂²×C₉×#41	2
D₄×Q₈×C₉	2
C₉×#548	2
C₉×#547	2
C₉×#546	2
C₉×#537	2
C₉×#536	2
C₉×#525	2
C₂×C₉×C₂²⋊Q₈	2
C₉×#520	2
C₃×#3489	3

Subgroups — C9×#3489 #11768210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3489 #11768210