Subgroups — C₉×#3201 #11767922

Order 1152.

585 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#537	C₂	1	1	yes	maximal, characteristic
2	C₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#483	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#408	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3201	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic
18	C₂×C₉×#41	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
20	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
26	C₉×C₄⋊Q₈	—	2	1	no	—
27	C₉×#124	—	2	1	no	—
28	C₉×#123	—	2	1	no	—
29	C₉×#123	—	2	1	no	—
30	C₉×C₂²⋊Q₈	—	2	1	no	—
31	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₉×#121	—	2	1	no	—
38	C₉×#121	—	2	1	no	—
39	C₉×#121	—	2	1	no	—
40	C₉×#121	C₂²	1	1	yes	characteristic
41	C₉×#121	C₂²	1	1	yes	characteristic
42	C₉×#117	C₂²	1	1	yes	characteristic
43	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×#107	C₂²	1	1	yes	characteristic
45	C₉×#107	C₂²	1	1	yes	characteristic
46	C₉×#106	C₂²	1	1	yes	characteristic
47	C₉×#106	C₂²	1	1	yes	characteristic
48	C₉×#103	C₂²	1	1	yes	characteristic
49	C₉×#103	C₂²	1	1	yes	characteristic
50	C₉×#103	C₂²	1	1	yes	characteristic
51	C₉×#103	C₂²	1	1	yes	characteristic
52	C₉×#103	C₂²	1	1	yes	characteristic
53	C₉×#103	C₂²	1	1	yes	characteristic
54	C₉×#102	C₂²	1	1	yes	characteristic
55	C₉×#102	C₂²	1	1	yes	characteristic
56	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₃×#537	C₂×C₃	1	1	yes	characteristic
61	C₃×#536	C₂×C₃	1	1	yes	characteristic
62	C₃×#485	C₂×C₃	1	1	yes	characteristic
63	C₃×#484	C₂×C₃	1	1	yes	characteristic
64	C₃×#483	C₂×C₃	1	1	yes	characteristic
65	C₃×#482	C₂×C₃	1	1	yes	characteristic
66	C₃×#470	C₂×C₃	1	1	yes	characteristic
67	C₃×#468	C₂×C₃	1	1	yes	characteristic
68	C₃×#467	C₂×C₃	1	1	yes	characteristic
69	C₃×#465	C₂×C₃	1	1	yes	characteristic
70	C₃×#452	C₂×C₃	1	1	yes	characteristic
71	C₃×#452	C₂×C₃	1	1	yes	characteristic
72	C₃×#451	C₂×C₃	1	1	yes	characteristic
73	C₃×#448	C₂×C₃	1	1	yes	characteristic
74	C₃×#408	C₂×C₃	1	1	yes	characteristic
75	C₉×#41	—	4	1	no	—
76	C₉×#41	—	4	1	no	—
77	C₉×#41	—	4	1	no	—
78	C₉×#41	—	4	1	no	—
79	C₂×Q₈×C₉	—	2	1	no	—
80	C₂×Q₈×C₉	—	4	1	no	—
81	C₂×Q₈×C₉	—	4	1	no	—
82	C₂×Q₈×C₉	D₄	1	1	yes	characteristic
83	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₉	—	2	1	no	—
87	C₂×D₄×C₉	—	2	1	no	—
88	C₂×D₄×C₉	—	2	1	no	—
89	C₂×D₄×C₉	D₄	1	1	yes	characteristic
90	C₂×D₄×C₉	D₄	1	1	yes	characteristic
91	C₂×D₄×C₉	D₄	1	1	yes	characteristic
92	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₉	—	2	1	no	—
94	C₂²×C₄×C₉	—	2	1	no	—
95	C₂²×C₄×C₉	—	2	1	no	—
96	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
99	C₉×Q₁₆	—	4	1	no	—
100	C₉×Q₁₆	—	4	1	no	—
101	C₉×SD₁₆	—	4	1	no	—
102	C₉×SD₁₆	—	4	1	no	—
103	C₉×M₁₆	—	4	1	no	—
104	C₂×C₈×C₉	—	4	1	no	—
105	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
106	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
108	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
109	C₉×C₄⋊C₄	—	2	1	no	—
110	C₉×C₄⋊C₄	—	2	1	no	—
111	C₉×C₄⋊C₄	—	2	1	no	—
112	C₉×C₄⋊C₄	—	2	1	no	—
113	C₉×C₄⋊C₄	—	2	1	no	—
114	C₉×C₄⋊C₄	—	2	1	no	—
115	C₉×C₄⋊C₄	—	2	1	no	—
116	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₉×C₂²⋊C₄	—	2	1	no	—
121	C₉×C₂²⋊C₄	—	2	1	no	—
122	C₉×C₂²⋊C₄	—	2	1	no	—
123	C₉×C₂²⋊C₄	—	2	1	no	—
124	C₉×C₂²⋊C₄	—	2	1	no	—
125	C₉×C₂²⋊C₄	—	2	1	no	—
126	C₉×C₂²⋊C₄	—	2	1	no	—
127	C₉×C₂²⋊C₄	—	2	1	no	—
128	C₉×C₂²⋊C₄	—	2	1	no	—
129	C₄²×C₉	—	2	1	no	—
130	#3201	C₉	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
133	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
139	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
140	C₃×C₄⋊Q₈	—	2	1	no	—
141	C₃×#124	—	2	1	no	—
142	C₃×#123	—	2	1	no	—
143	C₃×#123	—	2	1	no	—
144	C₃×C₂²⋊Q₈	—	2	1	no	—
145	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
146	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
147	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
148	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
149	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
150	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
151	C₃×#121	—	2	1	no	—
152	C₃×#121	—	2	1	no	—
153	C₃×#121	—	2	1	no	—
154	C₃×#121	C₂²×C₃	1	1	yes	characteristic
155	C₃×#121	C₂²×C₃	1	1	yes	characteristic
156	C₃×#117	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₃×#107	C₂²×C₃	1	1	yes	characteristic
159	C₃×#107	C₂²×C₃	1	1	yes	characteristic
160	C₃×#106	C₂²×C₃	1	1	yes	characteristic
161	C₃×#106	C₂²×C₃	1	1	yes	characteristic
162	C₃×#103	C₂²×C₃	1	1	yes	characteristic
163	C₃×#103	C₂²×C₃	1	1	yes	characteristic
164	C₃×#103	C₂²×C₃	1	1	yes	characteristic
165	C₃×#103	C₂²×C₃	1	1	yes	characteristic
166	C₃×#103	C₂²×C₃	1	1	yes	characteristic
167	C₃×#103	C₂²×C₃	1	1	yes	characteristic
168	C₃×#102	C₂²×C₃	1	1	yes	characteristic
169	C₃×#102	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
171	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
172	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
173	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
174	C₂³×C₉	—	2	1	no	—
175	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
176	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
177	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
178	Q₈×C₉	—	2	1	no	—
179	Q₈×C₉	—	2	1	no	—
180	Q₈×C₉	—	2	1	no	—
181	Q₈×C₉	—	2	1	no	—
182	Q₈×C₉	—	2	1	no	—
183	Q₈×C₉	—	2	1	no	—
184	Q₈×C₉	—	4	1	no	—
185	Q₈×C₉	—	4	2	no	—
186	D₄×C₉	—	2	1	no	—
187	D₄×C₉	—	2	1	no	—
188	D₄×C₉	—	4	1	no	—
189	D₄×C₉	—	4	1	no	—
190	D₄×C₉	—	4	1	no	—
191	D₄×C₉	—	4	2	no	—
192	D₄×C₉	—	8	1	no	—
193	D₄×C₉	—	8	1	no	—
194	C₂×C₄×C₉	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	1	no	—
205	C₂×C₄×C₉	—	2	1	no	—
206	C₂×C₄×C₉	—	2	1	no	—
207	C₂×C₄×C₉	—	4	2	no	—
208	C₂×C₄×C₉	—	4	2	no	—
209	C₂×C₄×C₉	—	8	1	no	—
210	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
211	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
212	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
213	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
214	C₈×C₉	—	2	1	no	—
215	C₈×C₉	—	2	1	no	—
216	C₈×C₉	—	2	1	no	—
217	C₈×C₉	—	2	1	no	—
218	#537	C₂×C₉	1	1	yes	characteristic
219	#536	C₂×C₉	1	1	yes	characteristic, complemented
220	#485	C₂×C₉	1	1	yes	characteristic, complemented
221	#484	C₂×C₉	1	1	yes	characteristic, complemented
222	#483	C₂×C₉	1	1	yes	characteristic, complemented
223	#482	C₂×C₉	1	1	yes	characteristic, complemented
224	#470	C₂×C₉	1	1	yes	characteristic, complemented
225	#468	C₂×C₉	1	1	yes	characteristic, complemented
226	#467	C₂×C₉	1	1	yes	characteristic, complemented
227	#465	C₂×C₉	1	1	yes	characteristic, complemented
228	#452	C₂×C₉	1	1	yes	characteristic, complemented
229	#452	C₂×C₉	1	1	yes	characteristic, complemented
230	#451	C₂×C₉	1	1	yes	characteristic, complemented
231	#448	C₂×C₉	1	1	yes	characteristic, complemented
232	#408	C₂×C₉	1	1	yes	characteristic, complemented
233	C₃×#41	—	4	1	no	—
234	C₃×#41	—	4	1	no	—
235	C₃×#41	—	4	1	no	—
236	C₃×#41	—	4	1	no	—
237	C₂×C₃×Q₈	—	2	1	no	—
238	C₂×C₃×Q₈	—	4	1	no	—
239	C₂×C₃×Q₈	—	4	1	no	—
240	C₂×C₃×Q₈	C₃×D₄	1	1	yes	characteristic
241	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
243	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
244	C₂×C₃×D₄	—	2	1	no	—
245	C₂×C₃×D₄	—	2	1	no	—
246	C₂×C₃×D₄	—	2	1	no	—
247	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
248	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
249	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
250	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
251	C₂²×C₃×C₄	—	2	1	no	—
252	C₂²×C₃×C₄	—	2	1	no	—
253	C₂²×C₃×C₄	—	2	1	no	—
254	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
257	C₃×Q₁₆	—	4	1	no	—
258	C₃×Q₁₆	—	4	1	no	—
259	C₃×SD₁₆	—	4	1	no	—
260	C₃×SD₁₆	—	4	1	no	—
261	C₃×M₁₆	—	4	1	no	—
262	C₂×C₃×C₈	—	4	1	no	—
263	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
267	C₃×C₄⋊C₄	—	2	1	no	—
268	C₃×C₄⋊C₄	—	2	1	no	—
269	C₃×C₄⋊C₄	—	2	1	no	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	—	2	1	no	—
273	C₃×C₄⋊C₄	—	2	1	no	—
274	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
275	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
278	C₃×C₂²⋊C₄	—	2	1	no	—
279	C₃×C₂²⋊C₄	—	2	1	no	—
280	C₃×C₂²⋊C₄	—	2	1	no	—
281	C₃×C₂²⋊C₄	—	2	1	no	—
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×C₂²⋊C₄	—	2	1	no	—
285	C₃×C₂²⋊C₄	—	2	1	no	—
286	C₃×C₂²⋊C₄	—	2	1	no	—
287	C₃×C₄²	—	2	1	no	—
288	C₂²×C₉	—	2	1	no	—
289	C₂²×C₉	—	2	1	no	—
290	C₂²×C₉	—	2	1	no	—
291	C₂²×C₉	—	2	1	no	—
292	C₂²×C₉	—	2	1	no	—
293	C₂²×C₉	—	2	1	no	—
294	C₂²×C₉	—	2	1	no	—
295	C₂²×C₉	—	2	1	no	—
296	C₂²×C₉	—	2	1	no	—
297	C₂²×C₉	—	4	1	no	—
298	C₂²×C₉	—	4	1	no	—
299	C₂²×C₉	—	4	1	no	—
300	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
301	C₄×C₉	—	2	1	no	—
302	C₄×C₉	—	2	1	no	—
303	C₄×C₉	—	2	1	no	—
304	C₄×C₉	—	4	1	no	—
305	C₄×C₉	—	4	1	no	—
306	C₄×C₉	—	4	1	no	—
307	C₄×C₉	—	4	1	no	—
308	C₄×C₉	—	4	1	no	—
309	C₄×C₉	—	4	1	no	—
310	C₄×C₉	—	4	1	no	—
311	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
312	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×#41	C₂²×C₉	1	1	yes	characteristic
314	C₂×#41	C₂²×C₉	1	1	yes	characteristic
315	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
316	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
317	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
318	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
319	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
320	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
321	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
322	C₄⋊Q₈	—	2	1	no	—
323	#124	—	2	1	no	—
324	#123	—	2	1	no	—
325	#123	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
328	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
329	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
330	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
331	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
332	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
333	#121	—	2	1	no	—
334	#121	—	2	1	no	—
335	#121	—	2	1	no	—
336	#121	C₂²×C₉	1	1	yes	characteristic
337	#121	C₂²×C₉	1	1	yes	characteristic
338	#117	C₂²×C₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
340	#107	C₂²×C₉	1	1	yes	characteristic
341	#107	C₂²×C₉	1	1	yes	characteristic
342	#106	C₂²×C₉	1	1	yes	characteristic
343	#106	C₂²×C₉	1	1	yes	characteristic
344	#103	C₂²×C₉	1	1	yes	characteristic
345	#103	C₂²×C₉	1	1	yes	characteristic
346	#103	C₂²×C₉	1	1	yes	characteristic
347	#103	C₂²×C₉	1	1	yes	characteristic
348	#103	C₂²×C₉	1	1	yes	characteristic
349	#103	C₂²×C₉	1	1	yes	characteristic
350	#102	C₂²×C₉	1	1	yes	characteristic
351	#102	C₂²×C₉	1	1	yes	characteristic
352	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
353	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
354	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
355	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
358	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
359	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
360	C₃×Q₈	—	2	1	no	—
361	C₃×Q₈	—	2	1	no	—
362	C₃×Q₈	—	2	1	no	—
363	C₃×Q₈	—	2	1	no	—
364	C₃×Q₈	—	2	1	no	—
365	C₃×Q₈	—	2	1	no	—
366	C₃×Q₈	—	4	1	no	—
367	C₃×Q₈	—	4	2	no	—
368	C₃×D₄	—	2	1	no	—
369	C₃×D₄	—	2	1	no	—
370	C₃×D₄	—	4	1	no	—
371	C₃×D₄	—	4	1	no	—
372	C₃×D₄	—	4	1	no	—
373	C₃×D₄	—	4	2	no	—
374	C₃×D₄	—	8	1	no	—
375	C₃×D₄	—	8	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	4	2	no	—
390	C₂×C₃×C₄	—	4	2	no	—
391	C₂×C₃×C₄	—	8	1	no	—
392	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
395	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
396	C₃×C₈	—	2	1	no	—
397	C₃×C₈	—	2	1	no	—
398	C₃×C₈	—	2	1	no	—
399	C₃×C₈	—	2	1	no	—
400	C₂×C₉	—	4	1	no	—
401	C₂×C₉	—	4	1	no	—
402	C₂×C₉	—	4	1	no	—
403	C₂×C₉	—	8	1	no	—
404	C₂×C₉	#534	1	1	yes	characteristic
405	C₂×C₉	#577	1	1	yes	characteristic
406	C₂×C₉	#578	1	1	yes	characteristic
407	#41	—	4	1	no	—
408	#41	—	4	1	no	—
409	#41	—	4	1	no	—
410	#41	—	4	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	4	1	no	—
413	C₂×Q₈	—	4	1	no	—
414	C₂×Q₈	D₄×C₉	1	1	yes	characteristic
415	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
416	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
417	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	D₄×C₉	1	1	yes	characteristic
422	C₂×D₄	D₄×C₉	1	1	yes	characteristic
423	C₂×D₄	D₄×C₉	1	1	yes	characteristic
424	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
429	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
430	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
431	Q₁₆	—	4	1	no	—
432	Q₁₆	—	4	1	no	—
433	SD₁₆	—	4	1	no	—
434	SD₁₆	—	4	1	no	—
435	M₁₆	—	4	1	no	—
436	C₂×C₈	—	4	1	no	—
437	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
438	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
439	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
440	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
449	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
450	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
451	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
452	C₂²⋊C₄	—	2	1	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	2	1	no	—
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	2	1	no	—
464	C₂²×C₃	—	2	1	no	—
465	C₂²×C₃	—	2	1	no	—
466	C₂²×C₃	—	2	1	no	—
467	C₂²×C₃	—	2	1	no	—
468	C₂²×C₃	—	2	1	no	—
469	C₂²×C₃	—	2	1	no	—
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	4	1	no	—
472	C₂²×C₃	—	4	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
475	C₃×C₄	—	2	1	no	—
476	C₃×C₄	—	2	1	no	—
477	C₃×C₄	—	2	1	no	—
478	C₃×C₄	—	4	1	no	—
479	C₃×C₄	—	4	1	no	—
480	C₃×C₄	—	4	1	no	—
481	C₃×C₄	—	4	1	no	—
482	C₃×C₄	—	4	1	no	—
483	C₃×C₄	—	4	1	no	—
484	C₃×C₄	—	4	1	no	—
485	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
486	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
487	C₉	#3201	1	1	yes	characteristic, direct product factor, Sylow
488	C₂³	—	2	1	no	—
489	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
490	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
491	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
492	Q₈	—	2	1	no	—
493	Q₈	—	2	1	no	—
494	Q₈	—	2	1	no	—
495	Q₈	—	2	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	2	no	—
500	D₄	—	2	1	no	—
501	D₄	—	2	1	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	4	1	no	—
505	D₄	—	4	2	no	—
506	D₄	—	8	1	no	—
507	D₄	—	8	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	8	1	no	—
524	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
525	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
526	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
527	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
528	C₈	—	2	1	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₂×C₃	—	4	1	no	—
533	C₂×C₃	—	4	1	no	—
534	C₂×C₃	—	4	1	no	—
535	C₂×C₃	—	8	1	no	—
536	C₂×C₃	C₃×#534	1	1	yes	characteristic
537	C₂×C₃	C₃×#577	1	1	yes	characteristic
538	C₂×C₃	C₃×#578	1	1	yes	characteristic
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
552	C₄	—	2	1	no	—
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
563	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
564	C₃	C₃×#3201	1	1	yes	characteristic
565	C₂	—	4	1	no	—
566	C₂	—	4	1	no	—
567	C₂	—	4	1	no	—
568	C₂	—	8	1	no	—
569	C₂	C₉×#534	1	1	yes	characteristic
570	C₂	C₉×#577	1	1	yes	characteristic
571	C₂	C₉×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#537	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#536	C₂	semidirect
3. C₉×#485	C₂	semidirect
4. C₉×#484	C₂	semidirect
5. C₉×#483	C₂	semidirect
6. C₉×#482	C₂	semidirect
7. C₉×#470	C₂	semidirect
8. C₉×#468	C₂	semidirect
9. C₉×#467	C₂	semidirect
10. C₉×#465	C₂	semidirect
11. C₉×#452	C₂	semidirect
12. C₉×#452	C₂	semidirect
13. C₉×#451	C₂	semidirect
14. C₉×#448	C₂	semidirect
15. C₉×#408	C₂	semidirect
130. #3201	C₉	direct (N × H)
219. #536	C₂×C₉	semidirect
220. #485	C₂×C₉	semidirect
221. #484	C₂×C₉	semidirect
222. #483	C₂×C₉	semidirect
223. #482	C₂×C₉	semidirect
224. #470	C₂×C₉	semidirect
225. #468	C₂×C₉	semidirect
226. #467	C₂×C₉	semidirect
227. #465	C₂×C₉	semidirect
228. #452	C₂×C₉	semidirect
229. #452	C₂×C₉	semidirect
230. #451	C₂×C₉	semidirect
231. #448	C₂×C₉	semidirect
232. #408	C₂×C₉	semidirect
487. C₉	#3201	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#537	2
C₉×#536	2
C₉×#485	2
C₉×#484	2
C₉×#483	2
C₉×#482	2
C₉×#470	2
C₉×#468	2
C₉×#467	2
C₉×#465	2
C₉×#452	2
C₉×#451	2
C₉×#448	2
C₉×#408	2
C₃×#3201	3

Subgroups — C9×#3201 #11767922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3201 #11767922