Subgroups — C₉×#3264 #11767985

Order 1152.

852 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#442	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3264	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₄×C₉	—	2	1	no	—
19	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
22	C₉×AGL(1,ℤ/8)	—	2	4	no	—
23	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₉×D₈	—	2	4	no	—
27	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
28	C₂×C₉×D₈	C₂²	1	1	yes	characteristic
29	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₉×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic, complemented
35	C₉×#127	C₂²	1	1	yes	characteristic, complemented
36	C₉×#124	C₂²	1	1	yes	characteristic, complemented
37	C₉×#123	—	2	1	no	—
38	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₉×#121	—	2	1	no	—
40	C₉×#121	—	2	1	no	—
41	C₉×#121	C₂²	1	1	yes	characteristic
42	C₉×#121	C₂²	1	1	yes	characteristic, complemented
43	C₉×#121	C₂²	1	1	yes	characteristic, complemented
44	C₉×#120	—	2	1	no	—
45	C₉×#120	—	2	1	no	—
46	C₉×#120	—	2	1	no	—
47	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
48	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
49	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
51	C₉×#106	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×#102	C₂²	1	1	yes	characteristic, complemented
55	C₉×#102	C₂²	1	1	yes	characteristic, complemented
56	C₉×#102	C₂²	1	1	yes	characteristic, complemented
57	C₉×#102	C₂²	1	1	yes	characteristic, complemented
58	C₉×#102	C₂²	1	1	yes	characteristic, complemented
59	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₉×#97	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
63	C₂²×C₃×D₈	C₂×C₃	1	1	yes	characteristic
64	C₃×#546	C₂×C₃	1	1	yes	characteristic
65	C₃×D₄²	C₂×C₃	1	1	yes	characteristic
66	C₃×#496	C₂×C₃	1	1	yes	characteristic
67	C₃×#469	C₂×C₃	1	1	yes	characteristic
68	C₃×#465	C₂×C₃	1	1	yes	characteristic
69	C₃×#463	C₂×C₃	1	1	yes	characteristic
70	C₃×#459	C₂×C₃	1	1	yes	characteristic
71	C₃×#450	C₂×C₃	1	1	yes	characteristic
72	C₃×#449	C₂×C₃	1	1	yes	characteristic
73	C₃×#447	C₂×C₃	1	1	yes	characteristic
74	C₃×#447	C₂×C₃	1	1	yes	characteristic
75	C₃×#442	C₂×C₃	1	1	yes	characteristic
76	C₃×#435	C₂×C₃	1	1	yes	characteristic
77	C₂⁴×C₉	—	2	1	no	—
78	C₂⁴×C₉	—	2	1	no	—
79	C₂⁴×C₉	—	2	1	no	—
80	C₉×#41	—	2	2	no	—
81	C₉×#41	—	4	1	no	—
82	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₉	—	2	2	no	—
84	C₂×D₄×C₉	—	2	2	no	—
85	C₂×D₄×C₉	—	2	2	no	—
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	—	2	1	no	—
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	—	2	1	no	—
95	C₂×D₄×C₉	—	4	1	no	—
96	C₂×D₄×C₉	—	4	1	no	—
97	C₂×D₄×C₉	—	4	1	no	—
98	C₂×D₄×C₉	—	4	4	no	—
99	C₂×D₄×C₉	D₄	1	1	yes	characteristic
100	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
104	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₉	—	2	1	no	—
106	C₂²×C₄×C₉	—	2	1	no	—
107	C₂²×C₄×C₉	—	2	1	no	—
108	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
109	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
110	C₉×SD₁₆	—	2	2	no	—
111	C₉×SD₁₆	—	2	2	no	—
112	C₉×SD₁₆	—	4	1	no	—
113	C₉×D₈	—	2	2	no	—
114	C₉×D₈	—	2	2	no	—
115	C₉×D₈	—	2	2	no	—
116	C₉×D₈	—	2	2	no	—
117	C₉×D₈	—	4	1	no	—
118	C₉×D₈	D₄	1	4	yes	complemented
119	C₉×M₁₆	—	2	2	no	—
120	C₂×C₈×C₉	—	2	2	no	—
121	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
122	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
124	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
125	C₉×C₄⋊C₄	—	2	1	no	—
126	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
127	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
136	C₉×C₂²⋊C₄	—	2	1	no	—
137	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
138	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
139	C₄²×C₉	C₂³	1	1	yes	characteristic
140	#3264	C₉	1	1	yes	characteristic, direct product factor, Sylow
141	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₃×D₄	—	2	1	no	—
143	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
146	C₃×AGL(1,ℤ/8)	—	2	4	no	—
147	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×D₈	—	2	4	no	—
151	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₃×D₈	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
158	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
159	C₃×#127	C₂²×C₃	1	1	yes	characteristic
160	C₃×#124	C₂²×C₃	1	1	yes	characteristic
161	C₃×#123	—	2	1	no	—
162	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
163	C₃×#121	—	2	1	no	—
164	C₃×#121	—	2	1	no	—
165	C₃×#121	C₂²×C₃	1	1	yes	characteristic
166	C₃×#121	C₂²×C₃	1	1	yes	characteristic
167	C₃×#121	C₂²×C₃	1	1	yes	characteristic
168	C₃×#120	—	2	1	no	—
169	C₃×#120	—	2	1	no	—
170	C₃×#120	—	2	1	no	—
171	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
172	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
173	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
175	C₃×#106	C₂²×C₃	1	1	yes	characteristic
176	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
177	C₃×#103	C₂²×C₃	1	1	yes	characteristic
178	C₃×#102	C₂²×C₃	1	1	yes	characteristic
179	C₃×#102	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×#102	C₂²×C₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
185	C₃×#97	C₂²×C₃	1	1	yes	characteristic
186	C₂³×C₉	—	2	1	no	—
187	C₂³×C₉	—	2	1	no	—
188	C₂³×C₉	—	2	1	no	—
189	C₂³×C₉	—	2	1	no	—
190	C₂³×C₉	—	2	1	no	—
191	C₂³×C₉	—	4	2	no	—
192	C₂³×C₉	—	4	2	no	—
193	C₂³×C₉	—	4	2	no	—
194	C₂³×C₉	—	4	2	no	—
195	C₂³×C₉	—	4	2	no	—
196	C₂³×C₉	—	4	2	no	—
197	C₂³×C₉	—	8	1	no	—
198	C₂³×C₉	—	8	1	no	—
199	C₂³×C₉	—	8	1	no	—
200	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
201	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
202	Q₈×C₉	—	2	1	no	—
203	Q₈×C₉	—	2	1	no	—
204	D₄×C₉	—	2	2	no	—
205	D₄×C₉	—	2	1	no	—
206	D₄×C₉	—	2	1	no	—
207	D₄×C₉	—	2	1	no	—
208	D₄×C₉	—	2	1	no	—
209	D₄×C₉	—	2	1	no	—
210	D₄×C₉	—	2	1	no	—
211	D₄×C₉	—	2	1	no	—
212	D₄×C₉	—	2	1	no	—
213	D₄×C₉	—	4	2	no	—
214	D₄×C₉	—	4	2	no	—
215	D₄×C₉	—	4	2	no	—
216	D₄×C₉	—	4	2	no	—
217	D₄×C₉	—	4	2	no	—
218	D₄×C₉	—	4	2	no	—
219	D₄×C₉	—	4	2	no	—
220	D₄×C₉	—	8	1	no	—
221	D₄×C₉	—	8	1	no	—
222	D₄×C₉	C₂×D₄	1	2	yes	—
223	D₄×C₉	C₂×D₄	1	2	yes	complemented
224	C₂×C₄×C₉	—	2	1	no	—
225	C₂×C₄×C₉	—	2	1	no	—
226	C₂×C₄×C₉	—	2	1	no	—
227	C₂×C₄×C₉	—	2	1	no	—
228	C₂×C₄×C₉	—	2	1	no	—
229	C₂×C₄×C₉	—	2	1	no	—
230	C₂×C₄×C₉	—	2	1	no	—
231	C₂×C₄×C₉	—	4	2	no	—
232	C₂×C₄×C₉	—	4	2	no	—
233	C₂×C₄×C₉	—	8	1	no	—
234	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
235	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
236	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
237	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
238	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
239	C₈×C₉	—	2	1	no	—
240	C₈×C₉	—	2	1	no	—
241	C₈×C₉	—	2	1	no	—
242	C₈×C₉	C₂×D₄	1	2	yes	complemented
243	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
244	C₂²×D₈	C₂×C₉	1	1	yes	characteristic, complemented
245	#546	C₂×C₉	1	1	yes	characteristic, complemented
246	D₄²	C₂×C₉	1	1	yes	characteristic, complemented
247	#496	C₂×C₉	1	1	yes	characteristic, complemented
248	#469	C₂×C₉	1	1	yes	characteristic, complemented
249	#465	C₂×C₉	1	1	yes	characteristic, complemented
250	#463	C₂×C₉	1	1	yes	characteristic, complemented
251	#459	C₂×C₉	1	1	yes	characteristic, complemented
252	#450	C₂×C₉	1	1	yes	characteristic, complemented
253	#449	C₂×C₉	1	1	yes	characteristic, complemented
254	#447	C₂×C₉	1	1	yes	characteristic, complemented
255	#447	C₂×C₉	1	1	yes	characteristic, complemented
256	#442	C₂×C₉	1	1	yes	characteristic, complemented
257	#435	C₂×C₉	1	1	yes	characteristic, complemented
258	C₂⁴×C₃	—	2	1	no	—
259	C₂⁴×C₃	—	2	1	no	—
260	C₂⁴×C₃	—	2	1	no	—
261	C₃×#41	—	2	2	no	—
262	C₃×#41	—	4	1	no	—
263	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₃×D₄	—	2	2	no	—
265	C₂×C₃×D₄	—	2	2	no	—
266	C₂×C₃×D₄	—	2	2	no	—
267	C₂×C₃×D₄	—	2	1	no	—
268	C₂×C₃×D₄	—	2	1	no	—
269	C₂×C₃×D₄	—	2	1	no	—
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	—	2	1	no	—
272	C₂×C₃×D₄	—	2	1	no	—
273	C₂×C₃×D₄	—	2	1	no	—
274	C₂×C₃×D₄	—	2	1	no	—
275	C₂×C₃×D₄	—	2	1	no	—
276	C₂×C₃×D₄	—	4	1	no	—
277	C₂×C₃×D₄	—	4	1	no	—
278	C₂×C₃×D₄	—	4	1	no	—
279	C₂×C₃×D₄	—	4	4	no	—
280	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
281	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
282	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
286	C₂²×C₃×C₄	—	2	1	no	—
287	C₂²×C₃×C₄	—	2	1	no	—
288	C₂²×C₃×C₄	—	2	1	no	—
289	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
290	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
291	C₃×SD₁₆	—	2	2	no	—
292	C₃×SD₁₆	—	2	2	no	—
293	C₃×SD₁₆	—	4	1	no	—
294	C₃×D₈	—	2	2	no	—
295	C₃×D₈	—	2	2	no	—
296	C₃×D₈	—	2	2	no	—
297	C₃×D₈	—	2	2	no	—
298	C₃×D₈	—	4	1	no	—
299	C₃×D₈	C₃×D₄	1	4	yes	—
300	C₃×M₁₆	—	2	2	no	—
301	C₂×C₃×C₈	—	2	2	no	—
302	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
306	C₃×C₄⋊C₄	—	2	1	no	—
307	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
308	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
309	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
310	C₃×C₂²⋊C₄	—	2	1	no	—
311	C₃×C₂²⋊C₄	—	2	1	no	—
312	C₃×C₂²⋊C₄	—	2	1	no	—
313	C₃×C₂²⋊C₄	—	2	1	no	—
314	C₃×C₂²⋊C₄	—	2	1	no	—
315	C₃×C₂²⋊C₄	—	2	1	no	—
316	C₃×C₂²⋊C₄	—	2	1	no	—
317	C₃×C₂²⋊C₄	—	2	1	no	—
318	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
319	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
320	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
321	C₂²×C₉	—	2	1	no	—
322	C₂²×C₉	—	2	1	no	—
323	C₂²×C₉	—	2	1	no	—
324	C₂²×C₉	—	2	2	no	—
325	C₂²×C₉	—	2	2	no	—
326	C₂²×C₉	—	2	1	no	—
327	C₂²×C₉	—	2	1	no	—
328	C₂²×C₉	—	4	1	no	—
329	C₂²×C₉	—	4	1	no	—
330	C₂²×C₉	—	4	1	no	—
331	C₂²×C₉	—	4	1	no	—
332	C₂²×C₉	—	4	1	no	—
333	C₂²×C₉	—	4	1	no	—
334	C₂²×C₉	—	4	1	no	—
335	C₂²×C₉	—	4	1	no	—
336	C₂²×C₉	—	4	1	no	—
337	C₂²×C₉	—	4	1	no	—
338	C₂²×C₉	—	4	1	no	—
339	C₂²×C₉	—	4	1	no	—
340	C₂²×C₉	—	4	1	no	—
341	C₂²×C₉	—	8	4	no	—
342	C₂²×C₉	—	8	4	no	—
343	C₂²×C₉	—	8	4	no	—
344	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	complemented
345	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
346	C₄×C₉	—	2	1	no	—
347	C₄×C₉	—	2	1	no	—
348	C₄×C₉	—	2	1	no	—
349	C₄×C₉	—	2	1	no	—
350	C₄×C₉	—	4	1	no	—
351	C₄×C₉	—	4	1	no	—
352	C₄×C₉	—	4	1	no	—
353	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
354	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
355	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
358	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
359	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
360	AGL(1,ℤ/8)	—	2	4	no	—
361	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
362	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
363	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
364	C₂×D₈	—	2	4	no	—
365	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
366	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
367	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
368	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
369	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
370	C₂×D₈	C₂²×C₉	1	1	yes	characteristic, complemented
371	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
372	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
373	#127	C₂²×C₉	1	1	yes	characteristic, complemented
374	#124	C₂²×C₉	1	1	yes	characteristic, complemented
375	#123	—	2	1	no	—
376	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
377	#121	—	2	1	no	—
378	#121	—	2	1	no	—
379	#121	C₂²×C₉	1	1	yes	characteristic
380	#121	C₂²×C₉	1	1	yes	characteristic, complemented
381	#121	C₂²×C₉	1	1	yes	characteristic, complemented
382	#120	—	2	1	no	—
383	#120	—	2	1	no	—
384	#120	—	2	1	no	—
385	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
386	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
387	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	#106	C₂²×C₉	1	1	yes	characteristic, complemented
390	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
391	#103	C₂²×C₉	1	1	yes	characteristic, complemented
392	#102	C₂²×C₉	1	1	yes	characteristic, complemented
393	#102	C₂²×C₉	1	1	yes	characteristic, complemented
394	#102	C₂²×C₉	1	1	yes	characteristic, complemented
395	#102	C₂²×C₉	1	1	yes	characteristic, complemented
396	#102	C₂²×C₉	1	1	yes	characteristic, complemented
397	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
398	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
399	#97	C₂²×C₉	1	1	yes	characteristic, complemented
400	C₂³×C₃	—	2	1	no	—
401	C₂³×C₃	—	2	1	no	—
402	C₂³×C₃	—	2	1	no	—
403	C₂³×C₃	—	2	1	no	—
404	C₂³×C₃	—	2	1	no	—
405	C₂³×C₃	—	4	2	no	—
406	C₂³×C₃	—	4	2	no	—
407	C₂³×C₃	—	4	2	no	—
408	C₂³×C₃	—	4	2	no	—
409	C₂³×C₃	—	4	2	no	—
410	C₂³×C₃	—	4	2	no	—
411	C₂³×C₃	—	8	1	no	—
412	C₂³×C₃	—	8	1	no	—
413	C₂³×C₃	—	8	1	no	—
414	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
415	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
416	C₃×Q₈	—	2	1	no	—
417	C₃×Q₈	—	2	1	no	—
418	C₃×D₄	—	2	2	no	—
419	C₃×D₄	—	2	1	no	—
420	C₃×D₄	—	2	1	no	—
421	C₃×D₄	—	2	1	no	—
422	C₃×D₄	—	2	1	no	—
423	C₃×D₄	—	2	1	no	—
424	C₃×D₄	—	2	1	no	—
425	C₃×D₄	—	2	1	no	—
426	C₃×D₄	—	2	1	no	—
427	C₃×D₄	—	4	2	no	—
428	C₃×D₄	—	4	2	no	—
429	C₃×D₄	—	4	2	no	—
430	C₃×D₄	—	4	2	no	—
431	C₃×D₄	—	4	2	no	—
432	C₃×D₄	—	4	2	no	—
433	C₃×D₄	—	4	2	no	—
434	C₃×D₄	—	8	1	no	—
435	C₃×D₄	—	8	1	no	—
436	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
437	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
438	C₂×C₃×C₄	—	2	1	no	—
439	C₂×C₃×C₄	—	2	1	no	—
440	C₂×C₃×C₄	—	2	1	no	—
441	C₂×C₃×C₄	—	2	1	no	—
442	C₂×C₃×C₄	—	2	1	no	—
443	C₂×C₃×C₄	—	2	1	no	—
444	C₂×C₃×C₄	—	2	1	no	—
445	C₂×C₃×C₄	—	4	2	no	—
446	C₂×C₃×C₄	—	4	2	no	—
447	C₂×C₃×C₄	—	8	1	no	—
448	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
449	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
450	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
451	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
452	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
453	C₃×C₈	—	2	1	no	—
454	C₃×C₈	—	2	1	no	—
455	C₃×C₈	—	2	1	no	—
456	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
457	C₂×C₉	—	2	2	no	—
458	C₂×C₉	—	4	1	no	—
459	C₂×C₉	—	4	2	no	—
460	C₂×C₉	—	4	2	no	—
461	C₂×C₉	—	8	1	no	—
462	C₂×C₉	—	8	1	no	—
463	C₂×C₉	—	8	1	no	—
464	C₂×C₉	D₄²	1	1	yes	characteristic
465	C₂×C₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
466	C₂×C₉	#576	1	1	yes	characteristic
467	C₂⁴	—	2	1	no	—
468	C₂⁴	—	2	1	no	—
469	C₂⁴	—	2	1	no	—
470	#41	—	2	2	no	—
471	#41	—	4	1	no	—
472	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
473	C₂×D₄	—	2	2	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	4	1	no	—
488	C₂×D₄	—	4	4	no	—
489	C₂×D₄	D₄×C₉	1	1	yes	characteristic
490	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
491	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
492	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
493	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
494	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
499	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
500	SD₁₆	—	2	2	no	—
501	SD₁₆	—	2	2	no	—
502	SD₁₆	—	4	1	no	—
503	D₈	—	2	2	no	—
504	D₈	—	2	2	no	—
505	D₈	—	2	2	no	—
506	D₈	—	2	2	no	—
507	D₈	—	4	1	no	—
508	D₈	D₄×C₉	1	4	yes	complemented
509	M₁₆	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
512	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
513	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
514	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
517	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
518	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
519	C₂²⋊C₄	—	2	1	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	1	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
528	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
529	C₄²	C₂³×C₉	1	1	yes	characteristic
530	C₂²×C₃	—	2	1	no	—
531	C₂²×C₃	—	2	1	no	—
532	C₂²×C₃	—	2	1	no	—
533	C₂²×C₃	—	2	1	no	—
534	C₂²×C₃	—	2	1	no	—
535	C₂²×C₃	—	2	2	no	—
536	C₂²×C₃	—	2	2	no	—
537	C₂²×C₃	—	4	1	no	—
538	C₂²×C₃	—	4	1	no	—
539	C₂²×C₃	—	4	1	no	—
540	C₂²×C₃	—	4	1	no	—
541	C₂²×C₃	—	4	1	no	—
542	C₂²×C₃	—	4	1	no	—
543	C₂²×C₃	—	4	1	no	—
544	C₂²×C₃	—	4	1	no	—
545	C₂²×C₃	—	4	1	no	—
546	C₂²×C₃	—	4	1	no	—
547	C₂²×C₃	—	4	1	no	—
548	C₂²×C₃	—	4	1	no	—
549	C₂²×C₃	—	4	1	no	—
550	C₂²×C₃	—	8	4	no	—
551	C₂²×C₃	—	8	4	no	—
552	C₂²×C₃	—	8	4	no	—
553	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	2	yes	—
554	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
555	C₃×C₄	—	2	1	no	—
556	C₃×C₄	—	2	1	no	—
557	C₃×C₄	—	2	1	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	4	1	no	—
560	C₃×C₄	—	4	1	no	—
561	C₃×C₄	—	4	1	no	—
562	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
563	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
564	C₉	#3264	1	1	yes	characteristic, direct product factor, Sylow
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	—	2	1	no	—
570	C₂³	—	4	2	no	—
571	C₂³	—	4	2	no	—
572	C₂³	—	4	2	no	—
573	C₂³	—	4	2	no	—
574	C₂³	—	4	2	no	—
575	C₂³	—	4	2	no	—
576	C₂³	—	8	1	no	—
577	C₂³	—	8	1	no	—
578	C₂³	—	8	1	no	—
579	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
580	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
581	Q₈	—	2	1	no	—
582	Q₈	—	2	1	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	1	no	—
585	D₄	—	2	1	no	—
586	D₄	—	2	1	no	—
587	D₄	—	2	1	no	—
588	D₄	—	2	1	no	—
589	D₄	—	2	1	no	—
590	D₄	—	2	1	no	—
591	D₄	—	2	1	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	2	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	2	no	—
599	D₄	—	8	1	no	—
600	D₄	—	8	1	no	—
601	D₄	C₂×D₄×C₉	1	2	yes	—
602	D₄	C₂×D₄×C₉	1	2	yes	complemented
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	8	1	no	—
613	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
614	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
615	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
616	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
617	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
618	C₈	—	2	1	no	—
619	C₈	—	2	1	no	—
620	C₈	—	2	1	no	—
621	C₈	C₂×D₄×C₉	1	2	yes	complemented
622	C₂×C₃	—	2	2	no	—
623	C₂×C₃	—	4	1	no	—
624	C₂×C₃	—	4	2	no	—
625	C₂×C₃	—	4	2	no	—
626	C₂×C₃	—	8	1	no	—
627	C₂×C₃	—	8	1	no	—
628	C₂×C₃	—	8	1	no	—
629	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
630	C₂×C₃	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
631	C₂×C₃	C₃×#576	1	1	yes	characteristic
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	1	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	8	4	no	—
653	C₂²	—	8	4	no	—
654	C₂²	—	8	4	no	—
655	C₂²	C₉×AGL(1,ℤ/8)	1	2	yes	complemented
656	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
665	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
666	C₃	C₃×#3264	1	1	yes	characteristic
667	C₂	—	2	2	no	—
668	C₂	—	4	1	no	—
669	C₂	—	4	2	no	—
670	C₂	—	4	2	no	—
671	C₂	—	8	1	no	—
672	C₂	—	8	1	no	—
673	C₂	—	8	1	no	—
674	C₂	D₄²×C₉	1	1	yes	characteristic
675	C₂	C₂×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
676	C₂	C₉×#576	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×#3264	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×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₉×D₈	C₂	semidirect
3. C₉×#546	C₂	semidirect
4. D₄²×C₉	C₂	semidirect
5. C₉×#496	C₂	semidirect
6. C₉×#469	C₂	semidirect
7. C₉×#465	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#459	C₂	semidirect
10. C₉×#450	C₂	semidirect
11. C₉×#449	C₂	semidirect
12. C₉×#447	C₂	semidirect
13. C₉×#447	C₂	semidirect
14. C₉×#442	C₂	semidirect
15. C₉×#435	C₂	semidirect
17. C₂×C₉×#41	C₂²	semidirect
20. C₂²×D₄×C₉	C₂²	semidirect
21. C₂²×D₄×C₉	C₂²	semidirect
23. C₂×C₉×SD₁₆	C₂²	semidirect
24. C₂×C₉×SD₁₆	C₂²	semidirect
25. C₂×C₉×SD₁₆	C₂²	semidirect
29. C₂×C₉×D₈	C₂²	semidirect
30. C₂×C₉×D₈	C₂²	semidirect
31. C₂×C₉×D₈	C₂²	semidirect
32. C₂×C₉×D₈	C₂²	semidirect
33. C₂×C₉×M₁₆	C₂²	semidirect
34. C₂²×C₈×C₉	C₂²	semidirect
35. C₉×#127	C₂²	semidirect
36. C₉×#124	C₂²	semidirect
38. C₉×C₂²⋊Q₈	C₂²	semidirect
42. C₉×#121	C₂²	semidirect
43. C₉×#121	C₂²	semidirect
48. C₄×D₄×C₉	C₂²	semidirect
49. C₄×D₄×C₉	C₂²	semidirect
51. C₉×#106	C₂²	semidirect
52. C₉×C₄⋊C₈	C₂²	semidirect
53. C₉×#103	C₂²	semidirect
54. C₉×#102	C₂²	semidirect
55. C₉×#102	C₂²	semidirect
56. C₉×#102	C₂²	semidirect
57. C₉×#102	C₂²	semidirect
58. C₉×#102	C₂²	semidirect
59. C₉×C₂²⋊C₈	C₂²	semidirect
60. C₉×C₂²⋊C₈	C₂²	semidirect
61. C₉×#97	C₂²	semidirect
118. C₉×D₈	D₄	semidirect
140. #3264	C₉	direct (N × H)
223. D₄×C₉	C₂×D₄	semidirect
242. C₈×C₉	C₂×D₄	semidirect
243. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
244. C₂²×D₈	C₂×C₉	semidirect
245. #546	C₂×C₉	semidirect
246. D₄²	C₂×C₉	semidirect
247. #496	C₂×C₉	semidirect
248. #469	C₂×C₉	semidirect
249. #465	C₂×C₉	semidirect
250. #463	C₂×C₉	semidirect
251. #459	C₂×C₉	semidirect
252. #450	C₂×C₉	semidirect
253. #449	C₂×C₉	semidirect
254. #447	C₂×C₉	semidirect
255. #447	C₂×C₉	semidirect
256. #442	C₂×C₉	semidirect
257. #435	C₂×C₉	semidirect
344. C₂²×C₉	AGL(1,ℤ/8)	semidirect
355. C₂×#41	C₂²×C₉	semidirect
358. C₂²×D₄	C₂²×C₉	semidirect
359. C₂²×D₄	C₂²×C₉	semidirect
361. C₂×SD₁₆	C₂²×C₉	semidirect
362. C₂×SD₁₆	C₂²×C₉	semidirect
363. C₂×SD₁₆	C₂²×C₉	semidirect
367. C₂×D₈	C₂²×C₉	semidirect
368. C₂×D₈	C₂²×C₉	semidirect
369. C₂×D₈	C₂²×C₉	semidirect
370. C₂×D₈	C₂²×C₉	semidirect
371. C₂×M₁₆	C₂²×C₉	semidirect
372. C₂²×C₈	C₂²×C₉	semidirect
373. #127	C₂²×C₉	semidirect
374. #124	C₂²×C₉	semidirect
376. C₂²⋊Q₈	C₂²×C₉	semidirect
380. #121	C₂²×C₉	semidirect
381. #121	C₂²×C₉	semidirect
386. C₄×D₄	C₂²×C₉	semidirect
387. C₄×D₄	C₂²×C₉	semidirect
389. #106	C₂²×C₉	semidirect
390. C₄⋊C₈	C₂²×C₉	semidirect
391. #103	C₂²×C₉	semidirect
392. #102	C₂²×C₉	semidirect
393. #102	C₂²×C₉	semidirect
394. #102	C₂²×C₉	semidirect
395. #102	C₂²×C₉	semidirect
396. #102	C₂²×C₉	semidirect
397. C₂²⋊C₈	C₂²×C₉	semidirect
398. C₂²⋊C₈	C₂²×C₉	semidirect
399. #97	C₂²×C₉	semidirect
508. D₈	D₄×C₉	semidirect
564. C₉	#3264	direct (N × H)
602. D₄	C₂×D₄×C₉	semidirect
621. C₈	C₂×D₄×C₉	semidirect
655. C₂²	C₉×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×AGL(1,ℤ/8)	2
C₂²×C₉×D₈	2
C₉×#546	2
D₄²×C₉	2
C₉×#496	2
C₉×#469	2
C₉×#465	2
C₉×#463	2
C₉×#459	2
C₉×#450	2
C₉×#449	2
C₉×#447	2
C₉×#442	2
C₉×#435	2
C₃×#3264	3

Subgroups — C9×#3264 #11767985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3264 #11767985