Subgroups — C₉×#3269 #11767990

Order 1152.

717 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#468	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#467	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×#452	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, complemented
14	C₉×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3269	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	C₂×C₉×#41	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
21	C₉×#137	—	2	4	no	—
22	C₉×#135	—	2	4	no	—
23	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
32	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
34	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
35	C₉×#124	—	2	1	no	—
36	C₉×#124	C₂²	1	1	yes	characteristic
37	C₉×#123	—	2	1	no	—
38	C₉×#123	—	2	1	no	—
39	C₉×C₂²⋊Q₈	—	2	1	no	—
40	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₉×#121	—	2	1	no	—
44	C₉×#121	—	2	1	no	—
45	C₉×#121	C₂²	1	1	yes	characteristic
46	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
47	C₄×D₄×C₉	—	2	1	no	—
48	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
49	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
50	C₂×C₉×C₄⋊C₄	—	2	1	no	—
51	C₉×#107	C₂²	1	1	yes	characteristic
52	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₉×#103	C₂²	1	1	yes	characteristic
54	C₉×#103	C₂²	1	1	yes	characteristic
55	C₉×#103	C₂²	1	1	yes	characteristic
56	C₉×#103	C₂²	1	1	yes	characteristic
57	C₉×#102	C₂²	1	1	yes	characteristic
58	C₉×#102	C₂²	1	1	yes	characteristic
59	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₉×#97	C₂²	1	1	yes	characteristic
62	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
63	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
64	C₃×#548	C₂×C₃	1	1	yes	characteristic
65	C₃×#547	C₂×C₃	1	1	yes	characteristic
66	C₃×#497	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×#463	C₂×C₃	1	1	yes	characteristic
70	C₃×#462	C₂×C₃	1	1	yes	characteristic
71	C₃×#452	C₂×C₃	1	1	yes	characteristic
72	C₃×#452	C₂×C₃	1	1	yes	characteristic
73	C₃×#451	C₂×C₃	1	1	yes	characteristic
74	C₃×#449	C₂×C₃	1	1	yes	characteristic
75	C₃×#440	C₂×C₃	1	1	yes	characteristic
76	C₃×#435	C₂×C₃	1	1	yes	characteristic
77	C₉×#41	—	2	2	no	—
78	C₉×#41	—	2	2	no	—
79	C₉×#41	—	2	2	no	—
80	C₉×#41	—	4	1	no	—
81	C₉×#41	—	4	1	no	—
82	C₉×#41	—	4	1	no	—
83	C₂×Q₈×C₉	—	2	1	no	—
84	C₂×Q₈×C₉	—	2	2	no	—
85	C₂×Q₈×C₉	—	4	1	no	—
86	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
87	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
90	C₂×D₄×C₉	—	2	1	no	—
91	C₂×D₄×C₉	—	2	1	no	—
92	C₂×D₄×C₉	—	2	1	no	—
93	C₂×D₄×C₉	—	2	1	no	—
94	C₂×D₄×C₉	D₄	1	1	yes	characteristic
95	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
96	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₉	—	2	1	no	—
98	C₂²×C₄×C₉	—	2	1	no	—
99	C₂²×C₄×C₉	—	2	1	no	—
100	C₂²×C₄×C₉	—	2	1	no	—
101	C₂²×C₄×C₉	—	2	1	no	—
102	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
104	C₉×Q₁₆	—	2	2	no	—
105	C₉×Q₁₆	—	2	2	no	—
106	C₉×Q₁₆	—	2	2	no	—
107	C₉×Q₁₆	—	4	1	no	—
108	C₉×SD₁₆	—	2	2	no	—
109	C₉×SD₁₆	—	2	2	no	—
110	C₉×SD₁₆	—	4	1	no	—
111	C₉×SD₁₆	D₄	1	4	yes	complemented
112	C₉×D₈	—	2	2	no	—
113	C₉×M₁₆	—	2	2	no	—
114	C₂×C₈×C₉	—	2	2	no	—
115	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
117	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
118	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
119	C₉×C₄⋊C₄	—	2	1	no	—
120	C₉×C₄⋊C₄	—	2	1	no	—
121	C₉×C₄⋊C₄	—	2	1	no	—
122	C₉×C₄⋊C₄	—	2	1	no	—
123	C₉×C₄⋊C₄	—	2	1	no	—
124	C₉×C₄⋊C₄	—	2	1	no	—
125	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
126	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₉×C₂²⋊C₄	—	2	1	no	—
129	C₉×C₂²⋊C₄	—	2	1	no	—
130	C₉×C₂²⋊C₄	—	2	1	no	—
131	C₉×C₂²⋊C₄	—	2	1	no	—
132	C₉×C₂²⋊C₄	—	2	1	no	—
133	C₉×C₂²⋊C₄	—	2	1	no	—
134	C₉×C₂²⋊C₄	—	2	1	no	—
135	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
136	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₄²×C₉	—	2	1	no	—
138	C₄²×C₉	C₂³	1	1	yes	characteristic
139	#3269	C₉	1	1	yes	characteristic, direct product factor, Sylow
140	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
143	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
144	C₃×#137	—	2	4	no	—
145	C₃×#135	—	2	4	no	—
146	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
156	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
157	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₃×#124	—	2	1	no	—
159	C₃×#124	C₂²×C₃	1	1	yes	characteristic
160	C₃×#123	—	2	1	no	—
161	C₃×#123	—	2	1	no	—
162	C₃×C₂²⋊Q₈	—	2	1	no	—
163	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
165	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
166	C₃×#121	—	2	1	no	—
167	C₃×#121	—	2	1	no	—
168	C₃×#121	C₂²×C₃	1	1	yes	characteristic
169	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₄×D₄	—	2	1	no	—
171	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	—	2	1	no	—
174	C₃×#107	C₂²×C₃	1	1	yes	characteristic
175	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
176	C₃×#103	C₂²×C₃	1	1	yes	characteristic
177	C₃×#103	C₂²×C₃	1	1	yes	characteristic
178	C₃×#103	C₂²×C₃	1	1	yes	characteristic
179	C₃×#103	C₂²×C₃	1	1	yes	characteristic
180	C₃×#102	C₂²×C₃	1	1	yes	characteristic
181	C₃×#102	C₂²×C₃	1	1	yes	characteristic
182	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₃×#97	C₂²×C₃	1	1	yes	characteristic
185	C₂³×C₉	—	2	1	no	—
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
188	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
189	Q₈×C₉	—	2	1	no	—
190	Q₈×C₉	—	2	1	no	—
191	Q₈×C₉	—	2	1	no	—
192	Q₈×C₉	—	2	1	no	—
193	Q₈×C₉	—	2	1	no	—
194	Q₈×C₉	—	2	1	no	—
195	Q₈×C₉	—	2	1	no	—
196	Q₈×C₉	—	4	2	no	—
197	Q₈×C₉	C₂×D₄	1	2	yes	—
198	D₄×C₉	—	2	1	no	—
199	D₄×C₉	—	2	1	no	—
200	D₄×C₉	—	2	1	no	—
201	D₄×C₉	—	4	1	no	—
202	D₄×C₉	—	4	2	no	—
203	D₄×C₉	—	4	2	no	—
204	D₄×C₉	—	4	2	no	—
205	D₄×C₉	—	4	2	no	—
206	D₄×C₉	C₂×D₄	1	2	yes	—
207	C₂×C₄×C₉	—	2	1	no	—
208	C₂×C₄×C₉	—	2	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	2	1	no	—
215	C₂×C₄×C₉	—	2	1	no	—
216	C₂×C₄×C₉	—	2	1	no	—
217	C₂×C₄×C₉	—	4	2	no	—
218	C₂×C₄×C₉	—	4	2	no	—
219	C₂×C₄×C₉	—	4	2	no	—
220	C₂×C₄×C₉	—	4	2	no	—
221	C₂×C₄×C₉	—	4	2	no	—
222	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
223	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
224	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
225	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
226	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
227	C₈×C₉	—	2	1	no	—
228	C₈×C₉	—	2	1	no	—
229	C₈×C₉	—	2	1	no	—
230	C₈×C₉	C₂×D₄	1	2	yes	—
231	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
232	C₂×#135	C₂×C₉	1	1	yes	characteristic, complemented
233	#548	C₂×C₉	1	1	yes	characteristic, complemented
234	#547	C₂×C₉	1	1	yes	characteristic, complemented
235	#497	C₂×C₉	1	1	yes	characteristic, complemented
236	#468	C₂×C₉	1	1	yes	characteristic, complemented
237	#467	C₂×C₉	1	1	yes	characteristic, complemented
238	#463	C₂×C₉	1	1	yes	characteristic, complemented
239	#462	C₂×C₉	1	1	yes	characteristic, complemented
240	#452	C₂×C₉	1	1	yes	characteristic, complemented
241	#452	C₂×C₉	1	1	yes	characteristic, complemented
242	#451	C₂×C₉	1	1	yes	characteristic, complemented
243	#449	C₂×C₉	1	1	yes	characteristic, complemented
244	#440	C₂×C₉	1	1	yes	characteristic, complemented
245	#435	C₂×C₉	1	1	yes	characteristic, complemented
246	C₃×#41	—	2	2	no	—
247	C₃×#41	—	2	2	no	—
248	C₃×#41	—	2	2	no	—
249	C₃×#41	—	4	1	no	—
250	C₃×#41	—	4	1	no	—
251	C₃×#41	—	4	1	no	—
252	C₂×C₃×Q₈	—	2	1	no	—
253	C₂×C₃×Q₈	—	2	2	no	—
254	C₂×C₃×Q₈	—	4	1	no	—
255	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
256	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₃×D₄	—	2	1	no	—
260	C₂×C₃×D₄	—	2	1	no	—
261	C₂×C₃×D₄	—	2	1	no	—
262	C₂×C₃×D₄	—	2	1	no	—
263	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
264	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
266	C₂²×C₃×C₄	—	2	1	no	—
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	—	2	1	no	—
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
273	C₃×Q₁₆	—	2	2	no	—
274	C₃×Q₁₆	—	2	2	no	—
275	C₃×Q₁₆	—	2	2	no	—
276	C₃×Q₁₆	—	4	1	no	—
277	C₃×SD₁₆	—	2	2	no	—
278	C₃×SD₁₆	—	2	2	no	—
279	C₃×SD₁₆	—	4	1	no	—
280	C₃×SD₁₆	C₃×D₄	1	4	yes	—
281	C₃×D₈	—	2	2	no	—
282	C₃×M₁₆	—	2	2	no	—
283	C₂×C₃×C₈	—	2	2	no	—
284	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
286	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	—	2	1	no	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₄⋊C₄	—	2	1	no	—
293	C₃×C₄⋊C₄	—	2	1	no	—
294	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
295	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
296	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
297	C₃×C₂²⋊C₄	—	2	1	no	—
298	C₃×C₂²⋊C₄	—	2	1	no	—
299	C₃×C₂²⋊C₄	—	2	1	no	—
300	C₃×C₂²⋊C₄	—	2	1	no	—
301	C₃×C₂²⋊C₄	—	2	1	no	—
302	C₃×C₂²⋊C₄	—	2	1	no	—
303	C₃×C₂²⋊C₄	—	2	1	no	—
304	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
305	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
306	C₃×C₄²	—	2	1	no	—
307	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
308	C₂²×C₉	—	2	1	no	—
309	C₂²×C₉	—	2	1	no	—
310	C₂²×C₉	—	2	2	no	—
311	C₂²×C₉	—	2	1	no	—
312	C₂²×C₉	—	2	1	no	—
313	C₂²×C₉	—	2	1	no	—
314	C₂²×C₉	—	2	1	no	—
315	C₂²×C₉	—	4	1	no	—
316	C₂²×C₉	—	4	1	no	—
317	C₂²×C₉	—	4	1	no	—
318	C₂²×C₉	—	4	1	no	—
319	C₂²×C₉	—	4	1	no	—
320	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
321	C₄×C₉	—	2	1	no	—
322	C₄×C₉	—	2	1	no	—
323	C₄×C₉	—	2	2	no	—
324	C₄×C₉	—	2	1	no	—
325	C₄×C₉	—	2	1	no	—
326	C₄×C₉	—	4	1	no	—
327	C₄×C₉	—	4	1	no	—
328	C₄×C₉	—	4	1	no	—
329	C₄×C₉	—	4	1	no	—
330	C₄×C₉	—	4	1	no	—
331	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
332	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂×#41	C₂²×C₉	1	1	yes	characteristic
334	C₂×#41	C₂²×C₉	1	1	yes	characteristic
335	C₂×#41	C₂²×C₉	1	1	yes	characteristic
336	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
337	#137	—	2	4	no	—
338	#135	—	2	4	no	—
339	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
340	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
341	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
342	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
343	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
344	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
345	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
346	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
347	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
348	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
349	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
350	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
351	#124	—	2	1	no	—
352	#124	C₂²×C₉	1	1	yes	characteristic
353	#123	—	2	1	no	—
354	#123	—	2	1	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
357	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
358	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
359	#121	—	2	1	no	—
360	#121	—	2	1	no	—
361	#121	C₂²×C₉	1	1	yes	characteristic
362	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
365	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
366	C₂×C₄⋊C₄	—	2	1	no	—
367	#107	C₂²×C₉	1	1	yes	characteristic
368	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
369	#103	C₂²×C₉	1	1	yes	characteristic
370	#103	C₂²×C₉	1	1	yes	characteristic
371	#103	C₂²×C₉	1	1	yes	characteristic
372	#103	C₂²×C₉	1	1	yes	characteristic
373	#102	C₂²×C₉	1	1	yes	characteristic
374	#102	C₂²×C₉	1	1	yes	characteristic
375	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
376	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
377	#97	C₂²×C₉	1	1	yes	characteristic
378	C₂³×C₃	—	2	1	no	—
379	C₂³×C₃	—	2	1	no	—
380	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
381	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
382	C₃×Q₈	—	2	1	no	—
383	C₃×Q₈	—	2	1	no	—
384	C₃×Q₈	—	2	1	no	—
385	C₃×Q₈	—	2	1	no	—
386	C₃×Q₈	—	2	1	no	—
387	C₃×Q₈	—	2	1	no	—
388	C₃×Q₈	—	2	1	no	—
389	C₃×Q₈	—	4	2	no	—
390	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
391	C₃×D₄	—	2	1	no	—
392	C₃×D₄	—	2	1	no	—
393	C₃×D₄	—	2	1	no	—
394	C₃×D₄	—	4	1	no	—
395	C₃×D₄	—	4	2	no	—
396	C₃×D₄	—	4	2	no	—
397	C₃×D₄	—	4	2	no	—
398	C₃×D₄	—	4	2	no	—
399	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	2	1	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	—	4	2	no	—
412	C₂×C₃×C₄	—	4	2	no	—
413	C₂×C₃×C₄	—	4	2	no	—
414	C₂×C₃×C₄	—	4	2	no	—
415	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
416	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
417	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
418	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
419	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
420	C₃×C₈	—	2	1	no	—
421	C₃×C₈	—	2	1	no	—
422	C₃×C₈	—	2	1	no	—
423	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
424	C₂×C₉	—	4	1	no	—
425	C₂×C₉	—	4	1	no	—
426	C₂×C₉	—	4	2	no	—
427	C₂×C₉	—	8	1	no	—
428	C₂×C₉	D₄²	1	1	yes	characteristic
429	C₂×C₉	#575	1	1	yes	characteristic
430	C₂×C₉	#578	1	1	yes	characteristic
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	4	1	no	—
440	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
441	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
442	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
443	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	D₄×C₉	1	1	yes	characteristic
449	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
450	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
451	C₂²×C₄	—	2	1	no	—
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	C₂³×C₉	1	1	yes	characteristic
457	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
458	Q₁₆	—	2	2	no	—
459	Q₁₆	—	2	2	no	—
460	Q₁₆	—	2	2	no	—
461	Q₁₆	—	4	1	no	—
462	SD₁₆	—	2	2	no	—
463	SD₁₆	—	2	2	no	—
464	SD₁₆	—	4	1	no	—
465	SD₁₆	D₄×C₉	1	4	yes	complemented
466	D₈	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
470	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
471	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
472	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
480	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
481	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
490	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
491	C₄²	—	2	1	no	—
492	C₄²	C₂³×C₉	1	1	yes	characteristic
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	1	no	—
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	2	no	—
500	C₂²×C₃	—	4	1	no	—
501	C₂²×C₃	—	4	1	no	—
502	C₂²×C₃	—	4	1	no	—
503	C₂²×C₃	—	4	1	no	—
504	C₂²×C₃	—	4	1	no	—
505	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
506	C₃×C₄	—	2	1	no	—
507	C₃×C₄	—	2	1	no	—
508	C₃×C₄	—	2	1	no	—
509	C₃×C₄	—	2	1	no	—
510	C₃×C₄	—	2	2	no	—
511	C₃×C₄	—	4	1	no	—
512	C₃×C₄	—	4	1	no	—
513	C₃×C₄	—	4	1	no	—
514	C₃×C₄	—	4	1	no	—
515	C₃×C₄	—	4	1	no	—
516	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
517	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
518	C₉	#3269	1	1	yes	characteristic, direct product factor, Sylow
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
522	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	2	1	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	2	1	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	2	1	no	—
529	Q₈	—	2	1	no	—
530	Q₈	—	4	2	no	—
531	Q₈	C₂×D₄×C₉	1	2	yes	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	2	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	C₂×D₄×C₉	1	2	yes	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
557	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
558	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
559	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
560	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
561	C₈	—	2	1	no	—
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	C₂×D₄×C₉	1	2	yes	—
565	C₂×C₃	—	4	1	no	—
566	C₂×C₃	—	4	1	no	—
567	C₂×C₃	—	4	2	no	—
568	C₂×C₃	—	8	1	no	—
569	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
570	C₂×C₃	C₃×#575	1	1	yes	characteristic
571	C₂×C₃	C₃×#578	1	1	yes	characteristic
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	2	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	4	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
596	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
597	C₃	C₃×#3269	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	1	no	—
600	C₂	—	4	2	no	—
601	C₂	—	8	1	no	—
602	C₂	D₄²×C₉	1	1	yes	characteristic
603	C₂	C₉×#575	1	1	yes	characteristic
604	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×#3269	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×D₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#137	C₂	semidirect
2. C₂×C₉×#135	C₂	semidirect
3. C₉×#548	C₂	semidirect
4. C₉×#547	C₂	semidirect
5. C₉×#497	C₂	semidirect
6. C₉×#468	C₂	semidirect
7. C₉×#467	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#462	C₂	semidirect
10. C₉×#452	C₂	semidirect
11. C₉×#452	C₂	semidirect
12. C₉×#451	C₂	semidirect
13. C₉×#449	C₂	semidirect
14. C₉×#440	C₂	semidirect
15. C₉×#435	C₂	semidirect
111. C₉×SD₁₆	D₄	semidirect
139. #3269	C₉	direct (N × H)
231. C₂×#137	C₂×C₉	semidirect
232. C₂×#135	C₂×C₉	semidirect
233. #548	C₂×C₉	semidirect
234. #547	C₂×C₉	semidirect
235. #497	C₂×C₉	semidirect
236. #468	C₂×C₉	semidirect
237. #467	C₂×C₉	semidirect
238. #463	C₂×C₉	semidirect
239. #462	C₂×C₉	semidirect
240. #452	C₂×C₉	semidirect
241. #452	C₂×C₉	semidirect
242. #451	C₂×C₉	semidirect
243. #449	C₂×C₉	semidirect
244. #440	C₂×C₉	semidirect
245. #435	C₂×C₉	semidirect
465. SD₁₆	D₄×C₉	semidirect
518. C₉	#3269	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×#137	2
C₂×C₉×#135	2
C₉×#548	2
C₉×#547	2
C₉×#497	2
C₉×#468	2
C₉×#467	2
C₉×#463	2
C₉×#462	2
C₉×#452	2
C₉×#451	2
C₉×#449	2
C₉×#440	2
C₉×#435	2
C₃×#3269	3

Subgroups — C9×#3269 #11767990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3269 #11767990