Subgroups — C₉×#3018 #11767739

Order 1152.

1086 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#575	C₂	1	2	yes	maximal, complemented
3	C₉×#532	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#456	C₂	1	2	yes	maximal, complemented
5	C₉×#455	C₂	1	2	yes	maximal, complemented
6	C₉×#454	C₂	1	2	yes	maximal, complemented
7	C₉×#453	C₂	1	2	yes	maximal, complemented
8	C₂×C₉×#104	C₂	1	2	yes	maximal, complemented
9	C₉×#413	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#3018	C₃	1	1	yes	maximal, characteristic
11	C₉×2₋¹⁺⁴	—	2	2	no	—
12	C₉×2₋¹⁺⁴	C₂²	1	2	yes	—
13	C₉×H(5,𝔽₂)	—	2	2	no	—
14	C₉×H(5,𝔽₂)	—	2	2	no	—
15	C₉×H(5,𝔽₂)	C₂²	1	2	yes	—
16	C₂×C₉×#41	—	2	4	no	—
17	C₂×C₉×#41	—	2	2	no	—
18	C₂×C₉×#41	C₂²	1	2	yes	—
19	C₂×C₉×#41	C₂²	1	1	yes	characteristic
20	C₂×C₉×#41	C₂²	1	1	yes	characteristic, complemented
21	C₉×#137	—	2	2	no	—
22	C₉×#137	C₂²	1	4	yes	complemented
23	C₉×AGL(1,ℤ/8)	—	2	2	no	—
24	C₉×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
25	C₉×#135	—	2	4	no	—
26	C₂×C₉×M₁₆	C₂²	1	2	yes	complemented
27	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₉×#127	C₂²	1	1	yes	characteristic, complemented
29	C₉×#124	C₂²	1	1	yes	characteristic, complemented
30	C₉×#124	C₂²	1	1	yes	characteristic, complemented
31	C₉×#121	—	2	2	no	—
32	C₄×D₄×C₉	—	2	2	no	—
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
34	C₉×#104	C₂²	1	4	yes	complemented
35	C₉×#104	C₂²	1	4	yes	complemented
36	C₉×#101	C₂²	1	2	yes	complemented
37	C₉×#100	C₂²	1	2	yes	complemented
38	C₃×#585	C₂×C₃	1	1	yes	characteristic
39	C₃×#575	C₂×C₃	1	2	yes	—
40	C₃×#532	C₂×C₃	1	1	yes	characteristic
41	C₃×#456	C₂×C₃	1	2	yes	—
42	C₃×#455	C₂×C₃	1	2	yes	—
43	C₃×#454	C₂×C₃	1	2	yes	—
44	C₃×#453	C₂×C₃	1	2	yes	—
45	C₂×C₃×#104	C₂×C₃	1	2	yes	—
46	C₃×#413	C₂×C₃	1	1	yes	characteristic
47	C₉×#41	—	2	4	no	—
48	C₉×#41	—	2	8	no	—
49	C₉×#41	—	2	4	no	—
50	C₉×#41	—	2	4	no	—
51	C₉×#41	—	2	4	no	—
52	C₉×#41	—	2	2	no	—
53	C₉×#41	—	2	2	no	—
54	C₉×#41	—	2	4	no	—
55	C₉×#41	—	2	2	no	—
56	C₉×#41	—	2	2	no	—
57	C₉×#41	—	2	2	no	—
58	C₉×#41	—	2	2	no	—
59	C₉×#41	D₄	1	4	yes	complemented
60	C₉×#41	C₂³	1	4	yes	—
61	C₂×Q₈×C₉	—	2	2	no	—
62	C₂×Q₈×C₉	—	2	4	no	—
63	C₂×Q₈×C₉	D₄	1	2	yes	complemented
64	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
65	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₉	—	2	8	no	—
67	C₂×D₄×C₉	—	2	2	no	—
68	C₂×D₄×C₉	—	2	4	no	—
69	C₂×D₄×C₉	—	2	2	no	—
70	C₂×D₄×C₉	—	2	4	no	—
71	C₂×D₄×C₉	—	2	2	no	—
72	C₂×D₄×C₉	—	2	1	no	—
73	C₂×D₄×C₉	D₄	1	2	yes	—
74	C₂×D₄×C₉	D₄	1	2	yes	complemented
75	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
76	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₉	—	2	4	no	—
78	C₂²×C₄×C₉	—	2	2	no	—
79	C₂²×C₄×C₉	—	2	1	no	—
80	C₂²×C₄×C₉	—	2	1	no	—
81	C₂²×C₄×C₉	D₄	1	2	yes	—
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₉×Q₁₆	—	2	4	no	—
84	C₉×SD₁₆	—	2	4	no	—
85	C₉×SD₁₆	—	2	4	no	—
86	C₉×D₈	—	2	4	no	—
87	C₉×M₁₆	—	2	2	no	—
88	C₉×M₁₆	C₂³	1	4	yes	—
89	C₂×C₈×C₉	—	2	2	no	—
90	C₉×C₄⋊C₄	—	2	2	no	—
91	C₉×C₂²⋊C₄	—	2	2	no	—
92	C₉×C₂²⋊C₄	—	2	2	no	—
93	C₄²×C₉	—	2	1	no	—
94	C₄²×C₉	C₂³	1	1	yes	characteristic
95	C₄²×C₉	C₂³	1	1	yes	characteristic
96	#3018	C₉	1	1	yes	characteristic, direct product factor, Sylow
97	C₃×2₋¹⁺⁴	—	2	2	no	—
98	C₃×2₋¹⁺⁴	C₂²×C₃	1	2	yes	—
99	C₃×H(5,𝔽₂)	—	2	2	no	—
100	C₃×H(5,𝔽₂)	—	2	2	no	—
101	C₃×H(5,𝔽₂)	C₂²×C₃	1	2	yes	—
102	C₂×C₃×#41	—	2	4	no	—
103	C₂×C₃×#41	—	2	2	no	—
104	C₂×C₃×#41	C₂²×C₃	1	2	yes	—
105	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
107	C₃×#137	—	2	2	no	—
108	C₃×#137	C₂²×C₃	1	4	yes	—
109	C₃×AGL(1,ℤ/8)	—	2	2	no	—
110	C₃×AGL(1,ℤ/8)	C₂²×C₃	1	4	yes	—
111	C₃×#135	—	2	4	no	—
112	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
113	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₃×#127	C₂²×C₃	1	1	yes	characteristic
115	C₃×#124	C₂²×C₃	1	1	yes	characteristic
116	C₃×#124	C₂²×C₃	1	1	yes	characteristic
117	C₃×#121	—	2	2	no	—
118	C₃×C₄×D₄	—	2	2	no	—
119	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
120	C₃×#104	C₂²×C₃	1	4	yes	—
121	C₃×#104	C₂²×C₃	1	4	yes	—
122	C₃×#101	C₂²×C₃	1	2	yes	—
123	C₃×#100	C₂²×C₃	1	2	yes	—
124	C₂³×C₉	—	2	4	no	—
125	C₂³×C₉	—	2	2	no	—
126	C₂³×C₉	—	2	1	no	—
127	C₂³×C₉	C₂×D₄	1	2	yes	—
128	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
129	Q₈×C₉	—	2	4	no	—
130	Q₈×C₉	—	2	2	no	—
131	Q₈×C₉	—	2	2	no	—
132	Q₈×C₉	—	2	2	no	—
133	Q₈×C₉	C₂×D₄	1	4	yes	—
134	D₄×C₉	—	2	8	no	—
135	D₄×C₉	—	2	4	no	—
136	D₄×C₉	—	2	4	no	—
137	D₄×C₉	—	2	4	no	—
138	D₄×C₉	—	2	4	no	—
139	D₄×C₉	—	2	2	no	—
140	D₄×C₉	—	2	2	no	—
141	D₄×C₉	—	2	2	no	—
142	D₄×C₉	—	4	4	no	—
143	D₄×C₉	—	4	2	no	—
144	D₄×C₉	C₂×D₄	1	4	yes	—
145	C₂×C₄×C₉	—	2	4	no	—
146	C₂×C₄×C₉	—	2	8	no	—
147	C₂×C₄×C₉	—	2	2	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	2	no	—
150	C₂×C₄×C₉	—	2	4	no	—
151	C₂×C₄×C₉	—	2	2	no	—
152	C₂×C₄×C₉	—	2	4	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	4	2	no	—
156	C₂×C₄×C₉	—	4	1	no	—
157	C₂×C₄×C₉	—	4	1	no	—
158	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
159	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
161	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
162	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
163	C₈×C₉	—	2	4	no	—
164	#585	C₂×C₉	1	1	yes	characteristic, complemented
165	#575	C₂×C₉	1	2	yes	complemented
166	#532	C₂×C₉	1	1	yes	characteristic, complemented
167	#456	C₂×C₉	1	2	yes	complemented
168	#455	C₂×C₉	1	2	yes	complemented
169	#454	C₂×C₉	1	2	yes	complemented
170	#453	C₂×C₉	1	2	yes	complemented
171	C₂×#104	C₂×C₉	1	2	yes	complemented
172	#413	C₂×C₉	1	1	yes	characteristic, complemented
173	C₃×#41	—	2	4	no	—
174	C₃×#41	—	2	8	no	—
175	C₃×#41	—	2	4	no	—
176	C₃×#41	—	2	4	no	—
177	C₃×#41	—	2	4	no	—
178	C₃×#41	—	2	2	no	—
179	C₃×#41	—	2	2	no	—
180	C₃×#41	—	2	4	no	—
181	C₃×#41	—	2	2	no	—
182	C₃×#41	—	2	2	no	—
183	C₃×#41	—	2	2	no	—
184	C₃×#41	—	2	2	no	—
185	C₃×#41	C₃×D₄	1	4	yes	—
186	C₃×#41	C₂³×C₃	1	4	yes	—
187	C₂×C₃×Q₈	—	2	2	no	—
188	C₂×C₃×Q₈	—	2	4	no	—
189	C₂×C₃×Q₈	C₃×D₄	1	2	yes	—
190	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₃×D₄	—	2	8	no	—
193	C₂×C₃×D₄	—	2	2	no	—
194	C₂×C₃×D₄	—	2	4	no	—
195	C₂×C₃×D₄	—	2	2	no	—
196	C₂×C₃×D₄	—	2	4	no	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	—	2	1	no	—
199	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
200	C₂×C₃×D₄	C₃×D₄	1	2	yes	—
201	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
203	C₂²×C₃×C₄	—	2	4	no	—
204	C₂²×C₃×C₄	—	2	2	no	—
205	C₂²×C₃×C₄	—	2	1	no	—
206	C₂²×C₃×C₄	—	2	1	no	—
207	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
208	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
209	C₃×Q₁₆	—	2	4	no	—
210	C₃×SD₁₆	—	2	4	no	—
211	C₃×SD₁₆	—	2	4	no	—
212	C₃×D₈	—	2	4	no	—
213	C₃×M₁₆	—	2	2	no	—
214	C₃×M₁₆	C₂³×C₃	1	4	yes	—
215	C₂×C₃×C₈	—	2	2	no	—
216	C₃×C₄⋊C₄	—	2	2	no	—
217	C₃×C₂²⋊C₄	—	2	2	no	—
218	C₃×C₂²⋊C₄	—	2	2	no	—
219	C₃×C₄²	—	2	1	no	—
220	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
221	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₉	—	2	2	no	—
223	C₂²×C₉	—	2	4	no	—
224	C₂²×C₉	—	4	1	no	—
225	C₂²×C₉	—	4	2	no	—
226	C₂²×C₉	—	4	2	no	—
227	C₂²×C₉	—	4	1	no	—
228	C₂²×C₉	—	8	2	no	—
229	C₂²×C₉	—	8	4	no	—
230	C₂²×C₉	#120	1	2	yes	—
231	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
232	C₄×C₉	—	2	2	no	—
233	C₄×C₉	—	2	4	no	—
234	C₄×C₉	—	2	2	no	—
235	C₄×C₉	—	4	1	no	—
236	C₄×C₉	—	4	1	no	—
237	C₄×C₉	#120	1	1	yes	characteristic
238	C₄×C₉	#120	1	1	yes	characteristic
239	C₄×C₉	C₂²×D₄	1	2	yes	—
240	2₋¹⁺⁴	—	2	2	no	—
241	2₋¹⁺⁴	C₂²×C₉	1	2	yes	—
242	H(5,𝔽₂)	—	2	2	no	—
243	H(5,𝔽₂)	—	2	2	no	—
244	H(5,𝔽₂)	C₂²×C₉	1	2	yes	—
245	C₂×#41	—	2	4	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	C₂²×C₉	1	2	yes	—
248	C₂×#41	C₂²×C₉	1	1	yes	characteristic
249	C₂×#41	C₂²×C₉	1	1	yes	characteristic, complemented
250	#137	—	2	2	no	—
251	#137	C₂²×C₉	1	4	yes	complemented
252	AGL(1,ℤ/8)	—	2	2	no	—
253	AGL(1,ℤ/8)	C₂²×C₉	1	4	yes	complemented
254	#135	—	2	4	no	—
255	C₂×M₁₆	C₂²×C₉	1	2	yes	complemented
256	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
257	#127	C₂²×C₉	1	1	yes	characteristic, complemented
258	#124	C₂²×C₉	1	1	yes	characteristic, complemented
259	#124	C₂²×C₉	1	1	yes	characteristic, complemented
260	#121	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
263	#104	C₂²×C₉	1	4	yes	complemented
264	#104	C₂²×C₉	1	4	yes	complemented
265	#101	C₂²×C₉	1	2	yes	complemented
266	#100	C₂²×C₉	1	2	yes	complemented
267	C₂³×C₃	—	2	4	no	—
268	C₂³×C₃	—	2	2	no	—
269	C₂³×C₃	—	2	1	no	—
270	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
271	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
272	C₃×Q₈	—	2	4	no	—
273	C₃×Q₈	—	2	2	no	—
274	C₃×Q₈	—	2	2	no	—
275	C₃×Q₈	—	2	2	no	—
276	C₃×Q₈	C₂×C₃×D₄	1	4	yes	—
277	C₃×D₄	—	2	8	no	—
278	C₃×D₄	—	2	4	no	—
279	C₃×D₄	—	2	4	no	—
280	C₃×D₄	—	2	4	no	—
281	C₃×D₄	—	2	4	no	—
282	C₃×D₄	—	2	2	no	—
283	C₃×D₄	—	2	2	no	—
284	C₃×D₄	—	2	2	no	—
285	C₃×D₄	—	4	4	no	—
286	C₃×D₄	—	4	2	no	—
287	C₃×D₄	C₂×C₃×D₄	1	4	yes	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	8	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	1	no	—
297	C₂×C₃×C₄	—	2	1	no	—
298	C₂×C₃×C₄	—	4	2	no	—
299	C₂×C₃×C₄	—	4	1	no	—
300	C₂×C₃×C₄	—	4	1	no	—
301	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
306	C₃×C₈	—	2	4	no	—
307	C₂×C₉	—	2	1	no	—
308	C₂×C₉	—	2	2	no	—
309	C₂×C₉	—	4	2	no	—
310	C₂×C₉	—	4	4	no	—
311	C₂×C₉	—	8	1	no	—
312	C₂×C₉	C₂×#120	1	1	yes	characteristic
313	#41	—	2	4	no	—
314	#41	—	2	8	no	—
315	#41	—	2	4	no	—
316	#41	—	2	4	no	—
317	#41	—	2	4	no	—
318	#41	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	4	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	D₄×C₉	1	4	yes	complemented
326	#41	C₂³×C₉	1	4	yes	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	D₄×C₉	1	2	yes	complemented
330	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
331	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	D₄×C₉	1	2	yes	—
340	C₂×D₄	D₄×C₉	1	2	yes	complemented
341	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
342	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	D₄×C₉	1	2	yes	—
348	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
349	Q₁₆	—	2	4	no	—
350	SD₁₆	—	2	4	no	—
351	SD₁₆	—	2	4	no	—
352	D₈	—	2	4	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	C₂³×C₉	1	4	yes	—
355	C₂×C₈	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	C₂³×C₉	1	1	yes	characteristic
361	C₄²	C₂³×C₉	1	1	yes	characteristic
362	C₂²×C₃	—	2	2	no	—
363	C₂²×C₃	—	2	4	no	—
364	C₂²×C₃	—	4	1	no	—
365	C₂²×C₃	—	4	2	no	—
366	C₂²×C₃	—	4	2	no	—
367	C₂²×C₃	—	4	1	no	—
368	C₂²×C₃	—	8	2	no	—
369	C₂²×C₃	—	8	4	no	—
370	C₂²×C₃	C₃×#120	1	2	yes	—
371	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
372	C₃×C₄	—	2	2	no	—
373	C₃×C₄	—	2	4	no	—
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	4	1	no	—
376	C₃×C₄	—	4	1	no	—
377	C₃×C₄	C₃×#120	1	1	yes	characteristic
378	C₃×C₄	C₃×#120	1	1	yes	characteristic
379	C₃×C₄	C₂²×C₃×D₄	1	2	yes	—
380	C₉	#3018	1	1	yes	characteristic, direct product factor, Sylow
381	C₂³	—	2	4	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	1	no	—
384	C₂³	C₂×D₄×C₉	1	2	yes	—
385	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
386	Q₈	—	2	4	no	—
387	Q₈	—	2	2	no	—
388	Q₈	—	2	2	no	—
389	Q₈	—	2	2	no	—
390	Q₈	C₂×D₄×C₉	1	4	yes	—
391	D₄	—	2	8	no	—
392	D₄	—	2	4	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	2	no	—
401	D₄	C₂×D₄×C₉	1	4	yes	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
416	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
418	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
419	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
420	C₈	—	2	4	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	2	2	no	—
423	C₂×C₃	—	4	2	no	—
424	C₂×C₃	—	4	4	no	—
425	C₂×C₃	—	8	1	no	—
426	C₂×C₃	C₂×C₃×#120	1	1	yes	characteristic
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	4	no	—
435	C₂²	C₉×#120	1	2	yes	—
436	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	C₉×#120	1	1	yes	characteristic
443	C₄	C₉×#120	1	1	yes	characteristic
444	C₄	C₂²×D₄×C₉	1	2	yes	—
445	C₃	C₃×#3018	1	1	yes	characteristic
446	C₂	—	2	1	no	—
447	C₂	—	2	2	no	—
448	C₂	—	4	2	no	—
449	C₂	—	4	4	no	—
450	C₂	—	8	1	no	—
451	C₂	C₂×C₉×#120	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	#120
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂×C₃	C₂×C₃×#120
prime radical	C₃×#3018	C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#585	C₂	semidirect
2. C₉×#575	C₂	semidirect
3. C₉×#532	C₂	semidirect
4. C₉×#456	C₂	semidirect
5. C₉×#455	C₂	semidirect
6. C₉×#454	C₂	semidirect
7. C₉×#453	C₂	semidirect
8. C₂×C₉×#104	C₂	semidirect
9. C₉×#413	C₂	semidirect
20. C₂×C₉×#41	C₂²	semidirect
22. C₉×#137	C₂²	semidirect
24. C₉×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₉×M₁₆	C₂²	semidirect
27. C₉×C₄⋊Q₈	C₂²	semidirect
28. C₉×#127	C₂²	semidirect
29. C₉×#124	C₂²	semidirect
30. C₉×#124	C₂²	semidirect
33. C₂×C₄²×C₉	C₂²	semidirect
34. C₉×#104	C₂²	semidirect
35. C₉×#104	C₂²	semidirect
36. C₉×#101	C₂²	semidirect
37. C₉×#100	C₂²	semidirect
59. C₉×#41	D₄	semidirect
63. C₂×Q₈×C₉	D₄	semidirect
74. C₂×D₄×C₉	D₄	semidirect
96. #3018	C₉	direct (N × H)
164. #585	C₂×C₉	semidirect
165. #575	C₂×C₉	semidirect
166. #532	C₂×C₉	semidirect
167. #456	C₂×C₉	semidirect
168. #455	C₂×C₉	semidirect
169. #454	C₂×C₉	semidirect
170. #453	C₂×C₉	semidirect
171. C₂×#104	C₂×C₉	semidirect
172. #413	C₂×C₉	semidirect
249. C₂×#41	C₂²×C₉	semidirect
251. #137	C₂²×C₉	semidirect
253. AGL(1,ℤ/8)	C₂²×C₉	semidirect
255. C₂×M₁₆	C₂²×C₉	semidirect
256. C₄⋊Q₈	C₂²×C₉	semidirect
257. #127	C₂²×C₉	semidirect
258. #124	C₂²×C₉	semidirect
259. #124	C₂²×C₉	semidirect
262. C₂×C₄²	C₂²×C₉	semidirect
263. #104	C₂²×C₉	semidirect
264. #104	C₂²×C₉	semidirect
265. #101	C₂²×C₉	semidirect
266. #100	C₂²×C₉	semidirect
325. #41	D₄×C₉	semidirect
329. C₂×Q₈	D₄×C₉	semidirect
340. C₂×D₄	D₄×C₉	semidirect
380. C₉	#3018	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×#585	2
C₉×#575	2
C₉×#532	2
C₉×#456	2
C₉×#455	2
C₉×#454	2
C₉×#453	2
C₂×C₉×#104	2
C₉×#413	2
C₃×#3018	3

Subgroups — C9×#3018 #11767739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3018 #11767739