Subgroups — C₉×#3225 #11767946

Order 1152.

564 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#449	C₂	1	1	yes	maximal, characteristic
14	C₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3225	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₉×Q₁₆	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×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
27	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₉×#126	—	2	1	no	—
31	C₉×#124	—	2	1	no	—
32	C₉×#124	C₂²	1	1	yes	characteristic
33	C₉×#124	C₂²	1	1	yes	characteristic
34	C₉×#124	C₂²	1	1	yes	characteristic
35	C₉×#123	—	2	1	no	—
36	C₉×#123	—	2	1	no	—
37	C₉×#123	—	2	1	no	—
38	C₉×C₂²⋊Q₈	—	2	1	no	—
39	C₉×C₂²⋊Q₈	—	2	1	no	—
40	C₉×C₂²⋊Q₈	—	2	1	no	—
41	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₉×#121	C₂²	1	1	yes	characteristic
43	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
44	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
45	C₉×#117	C₂²	1	1	yes	characteristic
46	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₉×C₄⋊C₈	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×#97	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
60	C₃×#542	C₂×C₃	1	1	yes	characteristic
61	C₃×#536	C₂×C₃	1	1	yes	characteristic
62	C₃×#497	C₂×C₃	1	1	yes	characteristic
63	C₃×#495	C₂×C₃	1	1	yes	characteristic
64	C₃×#489	C₂×C₃	1	1	yes	characteristic
65	C₃×#487	C₂×C₃	1	1	yes	characteristic
66	C₃×#464	C₂×C₃	1	1	yes	characteristic
67	C₃×#463	C₂×C₃	1	1	yes	characteristic
68	C₃×#462	C₂×C₃	1	1	yes	characteristic
69	C₃×#461	C₂×C₃	1	1	yes	characteristic
70	C₃×#452	C₂×C₃	1	1	yes	characteristic
71	C₃×#451	C₂×C₃	1	1	yes	characteristic
72	C₃×#449	C₂×C₃	1	1	yes	characteristic
73	C₃×#448	C₂×C₃	1	1	yes	characteristic
74	C₃×#433	C₂×C₃	1	1	yes	characteristic
75	C₉×#41	—	4	1	no	—
76	C₉×#41	—	4	1	no	—
77	C₂×Q₈×C₉	—	2	1	no	—
78	C₂×Q₈×C₉	—	2	1	no	—
79	C₂×Q₈×C₉	—	4	1	no	—
80	C₂×Q₈×C₉	—	4	1	no	—
81	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
82	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
83	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₉	—	2	1	no	—
86	C₂×D₄×C₉	—	2	1	no	—
87	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₉	—	2	1	no	—
90	C₂²×C₄×C₉	—	2	1	no	—
91	C₂²×C₄×C₉	—	2	1	no	—
92	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₉×Q₁₆	—	4	1	no	—
94	C₉×Q₁₆	—	4	1	no	—
95	C₉×Q₁₆	—	4	1	no	—
96	C₉×SD₁₆	—	4	1	no	—
97	C₉×SD₁₆	—	4	1	no	—
98	C₉×SD₁₆	—	4	1	no	—
99	C₉×SD₁₆	—	4	1	no	—
100	C₉×D₈	—	4	1	no	—
101	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
103	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
104	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
105	C₉×C₄⋊C₄	—	2	1	no	—
106	C₉×C₄⋊C₄	—	2	1	no	—
107	C₉×C₄⋊C₄	—	2	1	no	—
108	C₉×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
113	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₉×C₂²⋊C₄	—	2	1	no	—
117	C₉×C₂²⋊C₄	—	2	1	no	—
118	C₉×C₂²⋊C₄	—	2	1	no	—
119	C₉×C₂²⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
126	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₄²×C₉	—	2	1	no	—
128	C₄²×C₉	C₂³	1	1	yes	characteristic
129	C₄²×C₉	C₂³	1	1	yes	characteristic
130	#3225	C₉	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
132	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×Q₁₆	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×SD₁₆	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
141	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
142	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
143	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
144	C₃×#126	—	2	1	no	—
145	C₃×#124	—	2	1	no	—
146	C₃×#124	C₂²×C₃	1	1	yes	characteristic
147	C₃×#124	C₂²×C₃	1	1	yes	characteristic
148	C₃×#124	C₂²×C₃	1	1	yes	characteristic
149	C₃×#123	—	2	1	no	—
150	C₃×#123	—	2	1	no	—
151	C₃×#123	—	2	1	no	—
152	C₃×C₂²⋊Q₈	—	2	1	no	—
153	C₃×C₂²⋊Q₈	—	2	1	no	—
154	C₃×C₂²⋊Q₈	—	2	1	no	—
155	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
156	C₃×#121	C₂²×C₃	1	1	yes	characteristic
157	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₃×#117	C₂²×C₃	1	1	yes	characteristic
160	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
161	C₃×C₄⋊C₈	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×#97	C₂²×C₃	1	1	yes	characteristic
173	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
174	C₂³×C₉	—	2	1	no	—
175	C₂³×C₉	—	2	1	no	—
176	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
177	Q₈×C₉	—	2	1	no	—
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	—	2	1	no	—
185	Q₈×C₉	—	4	2	no	—
186	Q₈×C₉	—	8	1	no	—
187	D₄×C₉	—	2	1	no	—
188	D₄×C₉	—	2	1	no	—
189	D₄×C₉	—	2	1	no	—
190	D₄×C₉	—	2	1	no	—
191	D₄×C₉	—	4	2	no	—
192	D₄×C₉	—	8	1	no	—
193	C₂×C₄×C₉	—	2	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	—	4	2	no	—
202	C₂×C₄×C₉	—	4	2	no	—
203	C₂×C₄×C₉	—	8	1	no	—
204	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
205	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
206	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
208	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
209	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
210	C₈×C₉	—	2	1	no	—
211	C₈×C₉	—	2	1	no	—
212	C₈×C₉	—	2	1	no	—
213	C₈×C₉	—	2	1	no	—
214	#542	C₂×C₉	1	1	yes	characteristic, complemented
215	#536	C₂×C₉	1	1	yes	characteristic, complemented
216	#497	C₂×C₉	1	1	yes	characteristic, complemented
217	#495	C₂×C₉	1	1	yes	characteristic, complemented
218	#489	C₂×C₉	1	1	yes	characteristic, complemented
219	#487	C₂×C₉	1	1	yes	characteristic, complemented
220	#464	C₂×C₉	1	1	yes	characteristic, complemented
221	#463	C₂×C₉	1	1	yes	characteristic, complemented
222	#462	C₂×C₉	1	1	yes	characteristic, complemented
223	#461	C₂×C₉	1	1	yes	characteristic, complemented
224	#452	C₂×C₉	1	1	yes	characteristic, complemented
225	#451	C₂×C₉	1	1	yes	characteristic, complemented
226	#449	C₂×C₉	1	1	yes	characteristic
227	#448	C₂×C₉	1	1	yes	characteristic, complemented
228	#433	C₂×C₉	1	1	yes	characteristic, complemented
229	C₃×#41	—	4	1	no	—
230	C₃×#41	—	4	1	no	—
231	C₂×C₃×Q₈	—	2	1	no	—
232	C₂×C₃×Q₈	—	2	1	no	—
233	C₂×C₃×Q₈	—	4	1	no	—
234	C₂×C₃×Q₈	—	4	1	no	—
235	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
236	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₃×D₄	—	2	1	no	—
240	C₂×C₃×D₄	—	2	1	no	—
241	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
243	C₂²×C₃×C₄	—	2	1	no	—
244	C₂²×C₃×C₄	—	2	1	no	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
247	C₃×Q₁₆	—	4	1	no	—
248	C₃×Q₁₆	—	4	1	no	—
249	C₃×Q₁₆	—	4	1	no	—
250	C₃×SD₁₆	—	4	1	no	—
251	C₃×SD₁₆	—	4	1	no	—
252	C₃×SD₁₆	—	4	1	no	—
253	C₃×SD₁₆	—	4	1	no	—
254	C₃×D₈	—	4	1	no	—
255	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
256	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
259	C₃×C₄⋊C₄	—	2	1	no	—
260	C₃×C₄⋊C₄	—	2	1	no	—
261	C₃×C₄⋊C₄	—	2	1	no	—
262	C₃×C₄⋊C₄	—	2	1	no	—
263	C₃×C₄⋊C₄	—	2	1	no	—
264	C₃×C₄⋊C₄	—	2	1	no	—
265	C₃×C₄⋊C₄	—	2	1	no	—
266	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
267	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
268	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
269	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
270	C₃×C₂²⋊C₄	—	2	1	no	—
271	C₃×C₂²⋊C₄	—	2	1	no	—
272	C₃×C₂²⋊C₄	—	2	1	no	—
273	C₃×C₂²⋊C₄	—	2	1	no	—
274	C₃×C₂²⋊C₄	—	2	1	no	—
275	C₃×C₂²⋊C₄	—	2	1	no	—
276	C₃×C₂²⋊C₄	—	2	1	no	—
277	C₃×C₂²⋊C₄	—	2	1	no	—
278	C₃×C₂²⋊C₄	—	2	1	no	—
279	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
281	C₃×C₄²	—	2	1	no	—
282	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
283	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
284	C₂²×C₉	—	2	1	no	—
285	C₂²×C₉	—	2	1	no	—
286	C₂²×C₉	—	2	1	no	—
287	C₂²×C₉	—	4	1	no	—
288	C₂²×C₉	—	4	1	no	—
289	C₂²×C₉	—	4	1	no	—
290	C₂²×C₉	—	4	1	no	—
291	C₂²×C₉	—	4	1	no	—
292	C₂²×C₉	—	4	1	no	—
293	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
294	C₄×C₉	—	2	1	no	—
295	C₄×C₉	—	2	1	no	—
296	C₄×C₉	—	2	1	no	—
297	C₄×C₉	—	2	1	no	—
298	C₄×C₉	—	2	1	no	—
299	C₄×C₉	—	4	1	no	—
300	C₄×C₉	—	4	1	no	—
301	C₄×C₉	—	4	1	no	—
302	C₄×C₉	—	4	1	no	—
303	C₄×C₉	—	4	1	no	—
304	C₄×C₉	—	4	1	no	—
305	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
306	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂×#41	C₂²×C₉	1	1	yes	characteristic
308	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
309	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
310	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
311	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
312	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
313	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
314	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
315	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
316	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
317	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
318	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
319	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
320	#126	—	2	1	no	—
321	#124	—	2	1	no	—
322	#124	C₂²×C₉	1	1	yes	characteristic
323	#124	C₂²×C₉	1	1	yes	characteristic
324	#124	C₂²×C₉	1	1	yes	characteristic
325	#123	—	2	1	no	—
326	#123	—	2	1	no	—
327	#123	—	2	1	no	—
328	C₂²⋊Q₈	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
332	#121	C₂²×C₉	1	1	yes	characteristic
333	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
334	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
335	#117	C₂²×C₉	1	1	yes	characteristic
336	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
337	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
338	#103	C₂²×C₉	1	1	yes	characteristic
339	#103	C₂²×C₉	1	1	yes	characteristic
340	#103	C₂²×C₉	1	1	yes	characteristic
341	#103	C₂²×C₉	1	1	yes	characteristic
342	#103	C₂²×C₉	1	1	yes	characteristic
343	#103	C₂²×C₉	1	1	yes	characteristic
344	#102	C₂²×C₉	1	1	yes	characteristic
345	#102	C₂²×C₉	1	1	yes	characteristic
346	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
347	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
348	#97	C₂²×C₉	1	1	yes	characteristic
349	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
350	C₂³×C₃	—	2	1	no	—
351	C₂³×C₃	—	2	1	no	—
352	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
353	C₃×Q₈	—	2	1	no	—
354	C₃×Q₈	—	2	1	no	—
355	C₃×Q₈	—	2	1	no	—
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	—	2	1	no	—
358	C₃×Q₈	—	2	1	no	—
359	C₃×Q₈	—	2	1	no	—
360	C₃×Q₈	—	2	1	no	—
361	C₃×Q₈	—	4	2	no	—
362	C₃×Q₈	—	8	1	no	—
363	C₃×D₄	—	2	1	no	—
364	C₃×D₄	—	2	1	no	—
365	C₃×D₄	—	2	1	no	—
366	C₃×D₄	—	2	1	no	—
367	C₃×D₄	—	4	2	no	—
368	C₃×D₄	—	8	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	4	2	no	—
378	C₂×C₃×C₄	—	4	2	no	—
379	C₂×C₃×C₄	—	8	1	no	—
380	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
386	C₃×C₈	—	2	1	no	—
387	C₃×C₈	—	2	1	no	—
388	C₃×C₈	—	2	1	no	—
389	C₃×C₈	—	2	1	no	—
390	C₂×C₉	—	4	1	no	—
391	C₂×C₉	—	8	1	no	—
392	C₂×C₉	—	8	1	no	—
393	C₂×C₉	#535	1	1	yes	characteristic
394	C₂×C₉	#577	1	1	yes	characteristic
395	C₂×C₉	#578	1	1	yes	characteristic
396	#41	—	4	1	no	—
397	#41	—	4	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	4	1	no	—
401	C₂×Q₈	—	4	1	no	—
402	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
403	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
404	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
405	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
409	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
414	Q₁₆	—	4	1	no	—
415	Q₁₆	—	4	1	no	—
416	Q₁₆	—	4	1	no	—
417	SD₁₆	—	4	1	no	—
418	SD₁₆	—	4	1	no	—
419	SD₁₆	—	4	1	no	—
420	SD₁₆	—	4	1	no	—
421	D₈	—	4	1	no	—
422	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
423	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
424	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
425	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
434	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
435	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
436	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	1	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
447	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
448	C₄²	—	2	1	no	—
449	C₄²	C₂³×C₉	1	1	yes	characteristic
450	C₄²	C₂³×C₉	1	1	yes	characteristic
451	C₂²×C₃	—	2	1	no	—
452	C₂²×C₃	—	2	1	no	—
453	C₂²×C₃	—	2	1	no	—
454	C₂²×C₃	—	4	1	no	—
455	C₂²×C₃	—	4	1	no	—
456	C₂²×C₃	—	4	1	no	—
457	C₂²×C₃	—	4	1	no	—
458	C₂²×C₃	—	4	1	no	—
459	C₂²×C₃	—	4	1	no	—
460	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
461	C₃×C₄	—	2	1	no	—
462	C₃×C₄	—	2	1	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	—	4	1	no	—
468	C₃×C₄	—	4	1	no	—
469	C₃×C₄	—	4	1	no	—
470	C₃×C₄	—	4	1	no	—
471	C₃×C₄	—	4	1	no	—
472	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
473	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
474	C₉	#3225	1	1	yes	characteristic, direct product factor, Sylow
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	4	2	no	—
487	Q₈	—	8	1	no	—
488	D₄	—	2	1	no	—
489	D₄	—	2	1	no	—
490	D₄	—	2	1	no	—
491	D₄	—	2	1	no	—
492	D₄	—	4	2	no	—
493	D₄	—	8	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	8	1	no	—
505	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
506	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
507	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
508	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
509	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
510	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₂×C₃	—	4	1	no	—
516	C₂×C₃	—	8	1	no	—
517	C₂×C₃	—	8	1	no	—
518	C₂×C₃	C₃×#535	1	1	yes	characteristic
519	C₂×C₃	C₃×#577	1	1	yes	characteristic
520	C₂×C₃	C₃×#578	1	1	yes	characteristic
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
543	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
544	C₃	C₃×#3225	1	1	yes	characteristic
545	C₂	—	4	1	no	—
546	C₂	—	8	1	no	—
547	C₂	—	8	1	no	—
548	C₂	C₉×#535	1	1	yes	characteristic
549	C₂	C₉×#577	1	1	yes	characteristic
550	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×#449	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#542	C₂	semidirect
2. C₉×#536	C₂	semidirect
3. C₉×#497	C₂	semidirect
4. C₉×#495	C₂	semidirect
5. C₉×#489	C₂	semidirect
6. C₉×#487	C₂	semidirect
7. C₉×#464	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#462	C₂	semidirect
10. C₉×#461	C₂	semidirect
11. C₉×#452	C₂	semidirect
12. C₉×#451	C₂	semidirect
14. C₉×#448	C₂	semidirect
15. C₉×#433	C₂	semidirect
130. #3225	C₉	direct (N × H)
214. #542	C₂×C₉	semidirect
215. #536	C₂×C₉	semidirect
216. #497	C₂×C₉	semidirect
217. #495	C₂×C₉	semidirect
218. #489	C₂×C₉	semidirect
219. #487	C₂×C₉	semidirect
220. #464	C₂×C₉	semidirect
221. #463	C₂×C₉	semidirect
222. #462	C₂×C₉	semidirect
223. #461	C₂×C₉	semidirect
224. #452	C₂×C₉	semidirect
225. #451	C₂×C₉	semidirect
227. #448	C₂×C₉	semidirect
228. #433	C₂×C₉	semidirect
474. C₉	#3225	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×#542	2
C₉×#536	2
C₉×#497	2
C₉×#495	2
C₉×#489	2
C₉×#487	2
C₉×#464	2
C₉×#463	2
C₉×#462	2
C₉×#461	2
C₉×#452	2
C₉×#451	2
C₉×#449	2
C₉×#448	2
C₉×#433	2
C₃×#3225	3

Subgroups — C9×#3225 #11767946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3225 #11767946