Subgroups — C₉×#3267 #11767988

Order 1152.

750 conjugacy classes of subgroups.

The subgroup lattice has 627 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	C₂×C₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#470	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×#461	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×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#449	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×#3267	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, complemented
20	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
21	C₉×AGL(1,ℤ/8)	—	2	4	no	—
22	C₉×#135	—	2	4	no	—
23	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
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, complemented
30	C₂×C₉×D₈	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, complemented
34	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₉×#124	C₂²	1	1	yes	characteristic
36	C₉×#123	—	2	1	no	—
37	C₉×#123	—	2	1	no	—
38	C₉×#123	—	2	1	no	—
39	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₉×#121	—	2	1	no	—
43	C₉×#121	—	2	1	no	—
44	C₉×#121	C₂²	1	1	yes	characteristic
45	C₉×#120	—	2	1	no	—
46	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
47	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
48	C₄×D₄×C₉	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₉×C₄⋊C₄	—	2	1	no	—
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×#103	C₂²	1	1	yes	characteristic, complemented
55	C₉×#103	C₂²	1	1	yes	characteristic, complemented
56	C₉×#102	C₂²	1	1	yes	characteristic
57	C₉×#102	C₂²	1	1	yes	characteristic
58	C₉×#102	C₂²	1	1	yes	characteristic, complemented
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×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic
63	C₂×C₃×#135	C₂×C₃	1	1	yes	characteristic
64	C₃×#547	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×#470	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×#461	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×#450	C₂×C₃	1	1	yes	characteristic
74	C₃×#449	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	C₉×#41	—	2	2	no	—
79	C₉×#41	—	2	2	no	—
80	C₉×#41	—	2	2	no	—
81	C₉×#41	—	4	1	no	—
82	C₉×#41	—	4	1	no	—
83	C₉×#41	—	4	1	no	—
84	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₉	—	2	2	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	—	4	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	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	—	2	1	no	—
103	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
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×D₈	—	2	2	no	—
113	C₉×D₈	D₄	1	4	yes	complemented
114	C₉×M₁₆	—	2	2	no	—
115	C₂×C₈×C₉	—	2	2	no	—
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	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
136	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
138	C₄²×C₉	C₂³	1	1	yes	characteristic
139	#3267	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×D₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×AGL(1,ℤ/8)	—	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×SD₁₆	C₂²×C₃	1	1	yes	characteristic
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×D₈	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	C₂²×C₃	1	1	yes	characteristic
159	C₃×#123	—	2	1	no	—
160	C₃×#123	—	2	1	no	—
161	C₃×#123	—	2	1	no	—
162	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
163	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
165	C₃×#121	—	2	1	no	—
166	C₃×#121	—	2	1	no	—
167	C₃×#121	C₂²×C₃	1	1	yes	characteristic
168	C₃×#120	—	2	1	no	—
169	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
171	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	—	2	1	no	—
173	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
174	C₃×#106	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×#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×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	—	2	1	no	—
188	C₂³×C₉	—	4	2	no	—
189	C₂³×C₉	—	4	2	no	—
190	C₂³×C₉	—	8	1	no	—
191	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
192	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
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	D₄×C₉	—	2	1	no	—
200	D₄×C₉	—	2	1	no	—
201	D₄×C₉	—	2	1	no	—
202	D₄×C₉	—	2	1	no	—
203	D₄×C₉	—	4	1	no	—
204	D₄×C₉	—	4	2	no	—
205	D₄×C₉	—	4	2	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	D₄×C₉	C₂×D₄	1	2	yes	—
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	—	4	2	no	—
224	C₂×C₄×C₉	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
229	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
230	C₈×C₉	—	2	1	no	—
231	C₈×C₉	—	2	1	no	—
232	C₈×C₉	—	2	1	no	—
233	C₈×C₉	C₂×D₄	1	2	yes	—
234	C₂×AGL(1,ℤ/8)	C₂×C₉	1	1	yes	characteristic, complemented
235	C₂×#135	C₂×C₉	1	1	yes	characteristic, complemented
236	#547	C₂×C₉	1	1	yes	characteristic, complemented
237	#546	C₂×C₉	1	1	yes	characteristic, complemented
238	#497	C₂×C₉	1	1	yes	characteristic, complemented
239	#470	C₂×C₉	1	1	yes	characteristic, complemented
240	#465	C₂×C₉	1	1	yes	characteristic, complemented
241	#463	C₂×C₉	1	1	yes	characteristic, complemented
242	#461	C₂×C₉	1	1	yes	characteristic, complemented
243	#452	C₂×C₉	1	1	yes	characteristic, complemented
244	#452	C₂×C₉	1	1	yes	characteristic, complemented
245	#450	C₂×C₉	1	1	yes	characteristic, complemented
246	#449	C₂×C₉	1	1	yes	characteristic, complemented
247	#442	C₂×C₉	1	1	yes	characteristic, complemented
248	#435	C₂×C₉	1	1	yes	characteristic, complemented
249	C₂⁴×C₃	—	2	1	no	—
250	C₃×#41	—	2	2	no	—
251	C₃×#41	—	2	2	no	—
252	C₃×#41	—	2	2	no	—
253	C₃×#41	—	4	1	no	—
254	C₃×#41	—	4	1	no	—
255	C₃×#41	—	4	1	no	—
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	2	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	—	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	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
274	C₂²×C₃×C₄	—	2	1	no	—
275	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
277	C₃×Q₁₆	—	2	2	no	—
278	C₃×Q₁₆	—	4	1	no	—
279	C₃×SD₁₆	—	2	2	no	—
280	C₃×SD₁₆	—	2	2	no	—
281	C₃×SD₁₆	—	2	2	no	—
282	C₃×SD₁₆	—	2	2	no	—
283	C₃×SD₁₆	—	4	1	no	—
284	C₃×D₈	—	2	2	no	—
285	C₃×D₈	C₃×D₄	1	4	yes	—
286	C₃×M₁₆	—	2	2	no	—
287	C₂×C₃×C₈	—	2	2	no	—
288	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
297	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
299	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
307	C₃×C₂²⋊C₄	—	2	1	no	—
308	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
309	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
310	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
311	C₂²×C₉	—	2	1	no	—
312	C₂²×C₉	—	2	1	no	—
313	C₂²×C₉	—	2	2	no	—
314	C₂²×C₉	—	2	2	no	—
315	C₂²×C₉	—	2	1	no	—
316	C₂²×C₉	—	2	1	no	—
317	C₂²×C₉	—	2	1	no	—
318	C₂²×C₉	—	2	1	no	—
319	C₂²×C₉	—	4	1	no	—
320	C₂²×C₉	—	4	1	no	—
321	C₂²×C₉	—	4	1	no	—
322	C₂²×C₉	—	4	1	no	—
323	C₂²×C₉	—	4	1	no	—
324	C₂²×C₉	—	4	1	no	—
325	C₂²×C₉	—	4	1	no	—
326	C₂²×C₉	—	8	4	no	—
327	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
328	C₄×C₉	—	2	1	no	—
329	C₄×C₉	—	2	1	no	—
330	C₄×C₉	—	2	1	no	—
331	C₄×C₉	—	2	1	no	—
332	C₄×C₉	—	4	1	no	—
333	C₄×C₉	—	4	1	no	—
334	C₄×C₉	—	4	1	no	—
335	C₄×C₉	—	4	1	no	—
336	C₄×C₉	—	4	1	no	—
337	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
338	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×#41	C₂²×C₉	1	1	yes	characteristic
340	C₂×#41	C₂²×C₉	1	1	yes	characteristic
341	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
342	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
343	AGL(1,ℤ/8)	—	2	4	no	—
344	#135	—	2	4	no	—
345	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
346	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
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×SD₁₆	C₂²×C₉	1	1	yes	characteristic, complemented
352	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
353	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
354	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
355	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic, complemented
356	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
357	#124	C₂²×C₉	1	1	yes	characteristic
358	#123	—	2	1	no	—
359	#123	—	2	1	no	—
360	#123	—	2	1	no	—
361	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
362	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
363	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
364	#121	—	2	1	no	—
365	#121	—	2	1	no	—
366	#121	C₂²×C₉	1	1	yes	characteristic
367	#120	—	2	1	no	—
368	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
369	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
370	C₄×D₄	C₂²×C₉	1	1	yes	characteristic, complemented
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	#106	C₂²×C₉	1	1	yes	characteristic, complemented
374	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
375	#103	C₂²×C₉	1	1	yes	characteristic, complemented
376	#103	C₂²×C₉	1	1	yes	characteristic, complemented
377	#103	C₂²×C₉	1	1	yes	characteristic, complemented
378	#102	C₂²×C₉	1	1	yes	characteristic
379	#102	C₂²×C₉	1	1	yes	characteristic
380	#102	C₂²×C₉	1	1	yes	characteristic, complemented
381	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
382	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic, complemented
383	#97	C₂²×C₉	1	1	yes	characteristic, complemented
384	C₂³×C₃	—	2	1	no	—
385	C₂³×C₃	—	2	1	no	—
386	C₂³×C₃	—	2	1	no	—
387	C₂³×C₃	—	4	2	no	—
388	C₂³×C₃	—	4	2	no	—
389	C₂³×C₃	—	8	1	no	—
390	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
391	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
392	C₃×Q₈	—	2	1	no	—
393	C₃×Q₈	—	2	1	no	—
394	C₃×Q₈	—	2	1	no	—
395	C₃×Q₈	—	2	1	no	—
396	C₃×Q₈	—	2	1	no	—
397	C₃×Q₈	—	2	1	no	—
398	C₃×D₄	—	2	1	no	—
399	C₃×D₄	—	2	1	no	—
400	C₃×D₄	—	2	1	no	—
401	C₃×D₄	—	2	1	no	—
402	C₃×D₄	—	4	1	no	—
403	C₃×D₄	—	4	2	no	—
404	C₃×D₄	—	4	2	no	—
405	C₃×D₄	—	4	2	no	—
406	C₃×D₄	—	4	2	no	—
407	C₃×D₄	—	8	1	no	—
408	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
409	C₃×D₄	C₂×C₃×D₄	1	2	yes	—
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	—	2	1	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	2	1	no	—
419	C₂×C₃×C₄	—	4	2	no	—
420	C₂×C₃×C₄	—	4	2	no	—
421	C₂×C₃×C₄	—	4	2	no	—
422	C₂×C₃×C₄	—	4	2	no	—
423	C₂×C₃×C₄	—	8	1	no	—
424	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
426	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
427	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
429	C₃×C₈	—	2	1	no	—
430	C₃×C₈	—	2	1	no	—
431	C₃×C₈	—	2	1	no	—
432	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
433	C₂×C₉	—	4	1	no	—
434	C₂×C₉	—	4	1	no	—
435	C₂×C₉	—	4	2	no	—
436	C₂×C₉	—	4	2	no	—
437	C₂×C₉	—	8	1	no	—
438	C₂×C₉	D₄²	1	1	yes	characteristic
439	C₂×C₉	#575	1	1	yes	characteristic
440	C₂×C₉	#577	1	1	yes	characteristic
441	C₂⁴	—	2	1	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	4	1	no	—
446	#41	—	4	1	no	—
447	#41	—	4	1	no	—
448	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
449	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
450	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	4	1	no	—
458	C₂×D₄	D₄×C₉	1	1	yes	characteristic
459	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
460	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
461	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
469	Q₁₆	—	2	2	no	—
470	Q₁₆	—	4	1	no	—
471	SD₁₆	—	2	2	no	—
472	SD₁₆	—	2	2	no	—
473	SD₁₆	—	2	2	no	—
474	SD₁₆	—	2	2	no	—
475	SD₁₆	—	4	1	no	—
476	D₈	—	2	2	no	—
477	D₈	D₄×C₉	1	4	yes	complemented
478	M₁₆	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
481	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
482	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
483	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
490	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
491	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	1	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
501	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
502	C₄²	C₂³×C₉	1	1	yes	characteristic
503	C₂²×C₃	—	2	1	no	—
504	C₂²×C₃	—	2	1	no	—
505	C₂²×C₃	—	2	1	no	—
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	1	no	—
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	2	2	no	—
511	C₂²×C₃	—	4	1	no	—
512	C₂²×C₃	—	4	1	no	—
513	C₂²×C₃	—	4	1	no	—
514	C₂²×C₃	—	4	1	no	—
515	C₂²×C₃	—	4	1	no	—
516	C₂²×C₃	—	4	1	no	—
517	C₂²×C₃	—	4	1	no	—
518	C₂²×C₃	—	8	4	no	—
519	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
520	C₃×C₄	—	2	1	no	—
521	C₃×C₄	—	2	1	no	—
522	C₃×C₄	—	2	1	no	—
523	C₃×C₄	—	2	1	no	—
524	C₃×C₄	—	4	1	no	—
525	C₃×C₄	—	4	1	no	—
526	C₃×C₄	—	4	1	no	—
527	C₃×C₄	—	4	1	no	—
528	C₃×C₄	—	4	1	no	—
529	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
530	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
531	C₉	#3267	1	1	yes	characteristic, direct product factor, Sylow
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	4	2	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	8	1	no	—
538	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
539	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
540	Q₈	—	2	1	no	—
541	Q₈	—	2	1	no	—
542	Q₈	—	2	1	no	—
543	Q₈	—	2	1	no	—
544	Q₈	—	2	1	no	—
545	Q₈	—	2	1	no	—
546	D₄	—	2	1	no	—
547	D₄	—	2	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	8	1	no	—
556	D₄	C₂×D₄×C₉	1	2	yes	—
557	D₄	C₂×D₄×C₉	1	2	yes	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	8	1	no	—
572	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
573	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
574	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
575	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
576	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
577	C₈	—	2	1	no	—
578	C₈	—	2	1	no	—
579	C₈	—	2	1	no	—
580	C₈	C₂×D₄×C₉	1	2	yes	—
581	C₂×C₃	—	4	1	no	—
582	C₂×C₃	—	4	1	no	—
583	C₂×C₃	—	4	2	no	—
584	C₂×C₃	—	4	2	no	—
585	C₂×C₃	—	8	1	no	—
586	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
587	C₂×C₃	C₃×#575	1	1	yes	characteristic
588	C₂×C₃	C₃×#577	1	1	yes	characteristic
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	8	4	no	—
605	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	1	no	—
609	C₄	—	2	1	no	—
610	C₄	—	4	1	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	1	no	—
614	C₄	—	4	1	no	—
615	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
616	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
617	C₃	C₃×#3267	1	1	yes	characteristic
618	C₂	—	4	1	no	—
619	C₂	—	4	1	no	—
620	C₂	—	4	2	no	—
621	C₂	—	4	2	no	—
622	C₂	—	8	1	no	—
623	C₂	D₄²×C₉	1	1	yes	characteristic
624	C₂	C₉×#575	1	1	yes	characteristic
625	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×#3267	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. C₂×C₉×#135	C₂	semidirect
3. C₉×#547	C₂	semidirect
4. C₉×#546	C₂	semidirect
5. C₉×#497	C₂	semidirect
6. C₉×#470	C₂	semidirect
7. C₉×#465	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#461	C₂	semidirect
10. C₉×#452	C₂	semidirect
11. C₉×#452	C₂	semidirect
12. C₉×#450	C₂	semidirect
13. C₉×#449	C₂	semidirect
14. C₉×#442	C₂	semidirect
15. C₉×#435	C₂	semidirect
19. C₂×C₉×#41	C₂²	semidirect
23. C₂×C₉×Q₁₆	C₂²	semidirect
24. C₂×C₉×Q₁₆	C₂²	semidirect
29. C₂×C₉×SD₁₆	C₂²	semidirect
33. C₂²×C₈×C₉	C₂²	semidirect
34. C₉×C₄⋊Q₈	C₂²	semidirect
41. C₉×C₂²⋊Q₈	C₂²	semidirect
48. C₄×D₄×C₉	C₂²	semidirect
51. C₉×#106	C₂²	semidirect
52. C₉×C₄⋊C₈	C₂²	semidirect
53. C₉×#103	C₂²	semidirect
54. C₉×#103	C₂²	semidirect
55. C₉×#103	C₂²	semidirect
58. C₉×#102	C₂²	semidirect
60. C₉×C₂²⋊C₈	C₂²	semidirect
61. C₉×#97	C₂²	semidirect
113. C₉×D₈	D₄	semidirect
139. #3267	C₉	direct (N × H)
234. C₂×AGL(1,ℤ/8)	C₂×C₉	semidirect
235. C₂×#135	C₂×C₉	semidirect
236. #547	C₂×C₉	semidirect
237. #546	C₂×C₉	semidirect
238. #497	C₂×C₉	semidirect
239. #470	C₂×C₉	semidirect
240. #465	C₂×C₉	semidirect
241. #463	C₂×C₉	semidirect
242. #461	C₂×C₉	semidirect
243. #452	C₂×C₉	semidirect
244. #452	C₂×C₉	semidirect
245. #450	C₂×C₉	semidirect
246. #449	C₂×C₉	semidirect
247. #442	C₂×C₉	semidirect
248. #435	C₂×C₉	semidirect
341. C₂×#41	C₂²×C₉	semidirect
345. C₂×Q₁₆	C₂²×C₉	semidirect
346. C₂×Q₁₆	C₂²×C₉	semidirect
351. C₂×SD₁₆	C₂²×C₉	semidirect
355. C₂²×C₈	C₂²×C₉	semidirect
356. C₄⋊Q₈	C₂²×C₉	semidirect
363. C₂²⋊Q₈	C₂²×C₉	semidirect
370. C₄×D₄	C₂²×C₉	semidirect
373. #106	C₂²×C₉	semidirect
374. C₄⋊C₈	C₂²×C₉	semidirect
375. #103	C₂²×C₉	semidirect
376. #103	C₂²×C₉	semidirect
377. #103	C₂²×C₉	semidirect
380. #102	C₂²×C₉	semidirect
382. C₂²⋊C₈	C₂²×C₉	semidirect
383. #97	C₂²×C₉	semidirect
477. D₈	D₄×C₉	semidirect
531. C₉	#3267	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×AGL(1,ℤ/8)	2
C₂×C₉×#135	2
C₉×#547	2
C₉×#546	2
C₉×#497	2
C₉×#470	2
C₉×#465	2
C₉×#463	2
C₉×#461	2
C₉×#452	2
C₉×#450	2
C₉×#449	2
C₉×#442	2
C₉×#435	2
C₃×#3267	3

Subgroups — C9×#3267 #11767988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3267 #11767988