Subgroups — C₉×#3266 #11767987

Order 1152.

741 conjugacy classes of subgroups.

The subgroup lattice has 615 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	C₂²×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#546	C₂	1	1	yes	maximal, characteristic
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×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#448	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×#3266	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	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
20	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₉×#137	—	2	4	no	—
22	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₉×SD₁₆	—	2	4	no	—
26	C₂×C₉×SD₁₆	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×SD₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
34	C₉×C₄⋊Q₈	—	2	1	no	—
35	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₉×#124	C₂²	1	1	yes	characteristic
37	C₉×#123	—	2	1	no	—
38	C₉×C₂²⋊Q₈	—	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, complemented
43	C₉×#121	—	2	1	no	—
44	C₉×#121	C₂²	1	1	yes	characteristic
45	C₉×#120	—	2	1	no	—
46	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
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×C₂²⋊C₄	—	2	1	no	—
51	C₉×#107	C₂²	1	1	yes	characteristic, complemented
52	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₉×#103	C₂²	1	1	yes	characteristic, complemented
54	C₉×#103	C₂²	1	1	yes	characteristic, complemented
55	C₉×#103	C₂²	1	1	yes	characteristic, complemented
56	C₉×#103	C₂²	1	1	yes	characteristic, complemented
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, complemented
61	C₉×#97	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
63	C₂²×C₃×SD₁₆	C₂×C₃	1	1	yes	characteristic
64	C₃×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
65	C₃×#546	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×#464	C₂×C₃	1	1	yes	characteristic
70	C₃×#461	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×#450	C₂×C₃	1	1	yes	characteristic
74	C₃×#448	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	C₂⁴×C₉	—	2	1	no	—
78	C₉×#41	—	2	2	no	—
79	C₉×#41	—	4	1	no	—
80	C₂×Q₈×C₉	—	2	1	no	—
81	C₂×Q₈×C₉	—	2	1	no	—
82	C₂×Q₈×C₉	—	2	2	no	—
83	C₂×Q₈×C₉	—	2	2	no	—
84	C₂×Q₈×C₉	—	4	1	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	2	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	—	4	1	no	—
95	C₂×D₄×C₉	D₄	1	1	yes	characteristic
96	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
97	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
107	C₉×SD₁₆	—	2	2	no	—
108	C₉×SD₁₆	—	2	2	no	—
109	C₉×SD₁₆	—	2	2	no	—
110	C₉×SD₁₆	—	2	2	no	—
111	C₉×SD₁₆	—	4	1	no	—
112	C₉×SD₁₆	D₄	1	4	yes	complemented
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	#3266	C₉	1	1	yes	characteristic, direct product factor, Sylow
140	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
141	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
143	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×#137	—	2	4	no	—
145	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×SD₁₆	—	2	4	no	—
149	C₂×C₃×SD₁₆	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×SD₁₆	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	—	2	1	no	—
158	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₃×#124	C₂²×C₃	1	1	yes	characteristic
160	C₃×#123	—	2	1	no	—
161	C₃×C₂²⋊Q₈	—	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	C₂²×C₃	1	1	yes	characteristic
168	C₃×#120	—	2	1	no	—
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×C₂²⋊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	—	4	2	no	—
188	C₂³×C₉	—	4	2	no	—
189	C₂³×C₉	—	8	1	no	—
190	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
197	Q₈×C₉	—	2	1	no	—
198	Q₈×C₉	—	2	1	no	—
199	Q₈×C₉	—	4	2	no	—
200	Q₈×C₉	—	4	2	no	—
201	Q₈×C₉	C₂×D₄	1	2	yes	—
202	D₄×C₉	—	2	2	no	—
203	D₄×C₉	—	2	1	no	—
204	D₄×C₉	—	2	1	no	—
205	D₄×C₉	—	2	1	no	—
206	D₄×C₉	—	4	2	no	—
207	D₄×C₉	—	4	2	no	—
208	D₄×C₉	—	8	1	no	—
209	D₄×C₉	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
218	C₂×C₄×C₉	—	2	1	no	—
219	C₂×C₄×C₉	—	2	1	no	—
220	C₂×C₄×C₉	—	4	2	no	—
221	C₂×C₄×C₉	—	4	2	no	—
222	C₂×C₄×C₉	—	4	2	no	—
223	C₂×C₄×C₉	—	8	1	no	—
224	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
225	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
226	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
227	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
228	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
229	C₈×C₉	—	2	1	no	—
230	C₈×C₉	—	2	1	no	—
231	C₈×C₉	—	2	1	no	—
232	C₈×C₉	C₂×D₄	1	2	yes	—
233	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
234	C₂²×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
235	D₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
236	#546	C₂×C₉	1	1	yes	characteristic
237	#497	C₂×C₉	1	1	yes	characteristic, complemented
238	#468	C₂×C₉	1	1	yes	characteristic, complemented
239	#467	C₂×C₉	1	1	yes	characteristic, complemented
240	#464	C₂×C₉	1	1	yes	characteristic, complemented
241	#461	C₂×C₉	1	1	yes	characteristic, complemented
242	#452	C₂×C₉	1	1	yes	characteristic, complemented
243	#451	C₂×C₉	1	1	yes	characteristic, complemented
244	#450	C₂×C₉	1	1	yes	characteristic, complemented
245	#448	C₂×C₉	1	1	yes	characteristic, complemented
246	#440	C₂×C₉	1	1	yes	characteristic, complemented
247	#435	C₂×C₉	1	1	yes	characteristic, complemented
248	C₂⁴×C₃	—	2	1	no	—
249	C₃×#41	—	2	2	no	—
250	C₃×#41	—	4	1	no	—
251	C₂×C₃×Q₈	—	2	1	no	—
252	C₂×C₃×Q₈	—	2	1	no	—
253	C₂×C₃×Q₈	—	2	2	no	—
254	C₂×C₃×Q₈	—	2	2	no	—
255	C₂×C₃×Q₈	—	4	1	no	—
256	C₂×C₃×Q₈	—	4	1	no	—
257	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₃×D₄	—	2	2	no	—
262	C₂×C₃×D₄	—	2	1	no	—
263	C₂×C₃×D₄	—	2	1	no	—
264	C₂×C₃×D₄	—	2	1	no	—
265	C₂×C₃×D₄	—	4	1	no	—
266	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
267	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
268	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₃×C₄	—	2	1	no	—
270	C₂²×C₃×C₄	—	2	1	no	—
271	C₂²×C₃×C₄	—	2	1	no	—
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
274	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
275	C₃×Q₁₆	—	2	2	no	—
276	C₃×Q₁₆	—	2	2	no	—
277	C₃×Q₁₆	—	4	1	no	—
278	C₃×SD₁₆	—	2	2	no	—
279	C₃×SD₁₆	—	2	2	no	—
280	C₃×SD₁₆	—	2	2	no	—
281	C₃×SD₁₆	—	2	2	no	—
282	C₃×SD₁₆	—	4	1	no	—
283	C₃×SD₁₆	C₃×D₄	1	4	yes	—
284	C₃×M₁₆	—	2	2	no	—
285	C₂×C₃×C₈	—	2	2	no	—
286	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
295	C₃×C₄⋊C₄	—	2	1	no	—
296	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
297	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
305	C₃×C₂²⋊C₄	—	2	1	no	—
306	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
307	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
308	C₃×C₄²	—	2	1	no	—
309	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
310	C₂²×C₉	—	2	1	no	—
311	C₂²×C₉	—	2	1	no	—
312	C₂²×C₉	—	2	1	no	—
313	C₂²×C₉	—	2	2	no	—
314	C₂²×C₉	—	2	1	no	—
315	C₂²×C₉	—	2	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	—	4	1	no	—
321	C₂²×C₉	—	8	4	no	—
322	C₂²×C₉	#137	1	2	yes	complemented
323	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
324	C₄×C₉	—	2	1	no	—
325	C₄×C₉	—	2	1	no	—
326	C₄×C₉	—	2	2	no	—
327	C₄×C₉	—	2	1	no	—
328	C₄×C₉	—	2	1	no	—
329	C₄×C₉	—	4	1	no	—
330	C₄×C₉	—	4	1	no	—
331	C₄×C₉	—	4	1	no	—
332	C₄×C₉	—	4	1	no	—
333	C₄×C₉	—	4	1	no	—
334	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
335	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×#41	C₂²×C₉	1	1	yes	characteristic
337	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
338	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
339	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
340	#137	—	2	4	no	—
341	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
342	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
343	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
344	C₂×SD₁₆	—	2	4	no	—
345	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
346	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
347	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
348	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
349	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
350	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
351	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
352	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
355	#124	C₂²×C₉	1	1	yes	characteristic
356	#123	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
360	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
361	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
362	#121	—	2	1	no	—
363	#121	C₂²×C₉	1	1	yes	characteristic
364	#120	—	2	1	no	—
365	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
368	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	#107	C₂²×C₉	1	1	yes	characteristic, complemented
371	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
372	#103	C₂²×C₉	1	1	yes	characteristic, complemented
373	#103	C₂²×C₉	1	1	yes	characteristic, complemented
374	#103	C₂²×C₉	1	1	yes	characteristic, complemented
375	#103	C₂²×C₉	1	1	yes	characteristic, complemented
376	#102	C₂²×C₉	1	1	yes	characteristic
377	#102	C₂²×C₉	1	1	yes	characteristic
378	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
379	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
380	#97	C₂²×C₉	1	1	yes	characteristic, complemented
381	C₂³×C₃	—	2	1	no	—
382	C₂³×C₃	—	2	1	no	—
383	C₂³×C₃	—	4	2	no	—
384	C₂³×C₃	—	4	2	no	—
385	C₂³×C₃	—	8	1	no	—
386	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
387	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
388	C₃×Q₈	—	2	1	no	—
389	C₃×Q₈	—	2	1	no	—
390	C₃×Q₈	—	2	1	no	—
391	C₃×Q₈	—	2	1	no	—
392	C₃×Q₈	—	2	1	no	—
393	C₃×Q₈	—	2	1	no	—
394	C₃×Q₈	—	2	1	no	—
395	C₃×Q₈	—	4	2	no	—
396	C₃×Q₈	—	4	2	no	—
397	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
398	C₃×D₄	—	2	2	no	—
399	C₃×D₄	—	2	1	no	—
400	C₃×D₄	—	2	1	no	—
401	C₃×D₄	—	2	1	no	—
402	C₃×D₄	—	4	2	no	—
403	C₃×D₄	—	4	2	no	—
404	C₃×D₄	—	8	1	no	—
405	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
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	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	4	2	no	—
417	C₂×C₃×C₄	—	4	2	no	—
418	C₂×C₃×C₄	—	4	2	no	—
419	C₂×C₃×C₄	—	8	1	no	—
420	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
421	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
422	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
423	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
425	C₃×C₈	—	2	1	no	—
426	C₃×C₈	—	2	1	no	—
427	C₃×C₈	—	2	1	no	—
428	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
429	C₂×C₉	—	2	2	no	—
430	C₂×C₉	—	4	1	no	—
431	C₂×C₉	—	4	2	no	—
432	C₂×C₉	—	8	1	no	—
433	C₂×C₉	D₄²	1	1	yes	characteristic
434	C₂×C₉	C₂×#137	1	1	yes	characteristic
435	C₂×C₉	#577	1	1	yes	characteristic
436	C₂⁴	—	2	1	no	—
437	#41	—	2	2	no	—
438	#41	—	4	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	—	4	1	no	—
445	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
446	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
447	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
448	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	4	1	no	—
454	C₂×D₄	D₄×C₉	1	1	yes	characteristic
455	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
456	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
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	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
462	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
463	Q₁₆	—	2	2	no	—
464	Q₁₆	—	2	2	no	—
465	Q₁₆	—	4	1	no	—
466	SD₁₆	—	2	2	no	—
467	SD₁₆	—	2	2	no	—
468	SD₁₆	—	2	2	no	—
469	SD₁₆	—	2	2	no	—
470	SD₁₆	—	4	1	no	—
471	SD₁₆	D₄×C₉	1	4	yes	complemented
472	M₁₆	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
475	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
476	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
477	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
485	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
495	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
496	C₄²	—	2	1	no	—
497	C₄²	C₂³×C₉	1	1	yes	characteristic
498	C₂²×C₃	—	2	1	no	—
499	C₂²×C₃	—	2	1	no	—
500	C₂²×C₃	—	2	1	no	—
501	C₂²×C₃	—	2	1	no	—
502	C₂²×C₃	—	2	1	no	—
503	C₂²×C₃	—	2	2	no	—
504	C₂²×C₃	—	4	1	no	—
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	4	1	no	—
507	C₂²×C₃	—	4	1	no	—
508	C₂²×C₃	—	4	1	no	—
509	C₂²×C₃	—	8	4	no	—
510	C₂²×C₃	C₃×#137	1	2	yes	—
511	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
512	C₃×C₄	—	2	1	no	—
513	C₃×C₄	—	2	1	no	—
514	C₃×C₄	—	2	1	no	—
515	C₃×C₄	—	2	1	no	—
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	4	1	no	—
518	C₃×C₄	—	4	1	no	—
519	C₃×C₄	—	4	1	no	—
520	C₃×C₄	—	4	1	no	—
521	C₃×C₄	—	4	1	no	—
522	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
523	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
524	C₉	#3266	1	1	yes	characteristic, direct product factor, Sylow
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	4	2	no	—
528	C₂³	—	4	2	no	—
529	C₂³	—	8	1	no	—
530	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
531	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
532	Q₈	—	2	1	no	—
533	Q₈	—	2	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	2	1	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	1	no	—
538	Q₈	—	2	1	no	—
539	Q₈	—	4	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	C₂×D₄×C₉	1	2	yes	—
542	D₄	—	2	2	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	8	1	no	—
549	D₄	C₂×D₄×C₉	1	2	yes	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	8	1	no	—
564	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
565	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
566	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
568	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
569	C₈	—	2	1	no	—
570	C₈	—	2	1	no	—
571	C₈	—	2	1	no	—
572	C₈	C₂×D₄×C₉	1	2	yes	—
573	C₂×C₃	—	2	2	no	—
574	C₂×C₃	—	4	1	no	—
575	C₂×C₃	—	4	2	no	—
576	C₂×C₃	—	8	1	no	—
577	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
578	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
579	C₂×C₃	C₃×#577	1	1	yes	characteristic
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	8	4	no	—
592	C₂²	C₉×#137	1	2	yes	complemented
593	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
605	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
606	C₃	C₃×#3266	1	1	yes	characteristic
607	C₂	—	2	2	no	—
608	C₂	—	4	1	no	—
609	C₂	—	4	2	no	—
610	C₂	—	8	1	no	—
611	C₂	D₄²×C₉	1	1	yes	characteristic
612	C₂	C₂×C₉×#137	1	1	yes	characteristic
613	C₂	C₉×#577	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×#546	C₂×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. C₂²×C₉×SD₁₆	C₂	semidirect
3. D₄×Q₈×C₉	C₂	semidirect
5. C₉×#497	C₂	semidirect
6. C₉×#468	C₂	semidirect
7. C₉×#467	C₂	semidirect
8. C₉×#464	C₂	semidirect
9. C₉×#461	C₂	semidirect
10. C₉×#452	C₂	semidirect
11. C₉×#451	C₂	semidirect
12. C₉×#450	C₂	semidirect
13. C₉×#448	C₂	semidirect
14. C₉×#440	C₂	semidirect
15. C₉×#435	C₂	semidirect
19. C₂²×Q₈×C₉	C₂²	semidirect
22. C₂×C₉×Q₁₆	C₂²	semidirect
23. C₂×C₉×Q₁₆	C₂²	semidirect
24. C₂×C₉×Q₁₆	C₂²	semidirect
32. C₂×C₉×M₁₆	C₂²	semidirect
35. C₉×C₄⋊Q₈	C₂²	semidirect
42. C₉×C₂²⋊Q₈	C₂²	semidirect
46. C₄×Q₈×C₉	C₂²	semidirect
51. C₉×#107	C₂²	semidirect
52. C₉×C₄⋊C₈	C₂²	semidirect
53. C₉×#103	C₂²	semidirect
54. C₉×#103	C₂²	semidirect
55. C₉×#103	C₂²	semidirect
56. C₉×#103	C₂²	semidirect
60. C₉×C₂²⋊C₈	C₂²	semidirect
61. C₉×#97	C₂²	semidirect
112. C₉×SD₁₆	D₄	semidirect
139. #3266	C₉	direct (N × H)
233. C₂×#137	C₂×C₉	semidirect
234. C₂²×SD₁₆	C₂×C₉	semidirect
235. D₄×Q₈	C₂×C₉	semidirect
237. #497	C₂×C₉	semidirect
238. #468	C₂×C₉	semidirect
239. #467	C₂×C₉	semidirect
240. #464	C₂×C₉	semidirect
241. #461	C₂×C₉	semidirect
242. #452	C₂×C₉	semidirect
243. #451	C₂×C₉	semidirect
244. #450	C₂×C₉	semidirect
245. #448	C₂×C₉	semidirect
246. #440	C₂×C₉	semidirect
247. #435	C₂×C₉	semidirect
322. C₂²×C₉	#137	semidirect
338. C₂²×Q₈	C₂²×C₉	semidirect
341. C₂×Q₁₆	C₂²×C₉	semidirect
342. C₂×Q₁₆	C₂²×C₉	semidirect
343. C₂×Q₁₆	C₂²×C₉	semidirect
351. C₂×M₁₆	C₂²×C₉	semidirect
354. C₄⋊Q₈	C₂²×C₉	semidirect
361. C₂²⋊Q₈	C₂²×C₉	semidirect
365. C₄×Q₈	C₂²×C₉	semidirect
370. #107	C₂²×C₉	semidirect
371. C₄⋊C₈	C₂²×C₉	semidirect
372. #103	C₂²×C₉	semidirect
373. #103	C₂²×C₉	semidirect
374. #103	C₂²×C₉	semidirect
375. #103	C₂²×C₉	semidirect
379. C₂²⋊C₈	C₂²×C₉	semidirect
380. #97	C₂²×C₉	semidirect
471. SD₁₆	D₄×C₉	semidirect
524. C₉	#3266	direct (N × H)
592. C₂²	C₉×#137	semidirect

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
C₂²×C₉×SD₁₆	2
D₄×Q₈×C₉	2
C₉×#546	2
C₉×#497	2
C₉×#468	2
C₉×#467	2
C₉×#464	2
C₉×#461	2
C₉×#452	2
C₉×#451	2
C₉×#450	2
C₉×#448	2
C₉×#440	2
C₉×#435	2
C₃×#3266	3

Subgroups — C9×#3266 #11767987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3266 #11767987