Subgroups — C₉×#3258 #11767979

Order 1152.

501 conjugacy classes of subgroups.

The subgroup lattice has 501 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#542	C₂	1	1	yes	maximal, characteristic
2	C₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#468	C₂	1	1	yes	maximal, characteristic
9	C₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#465	C₂	1	1	yes	maximal, characteristic
11	C₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#461	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3258	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
23	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₉×#126	—	2	1	no	—
26	C₉×#126	—	2	1	no	—
27	C₉×#126	—	2	1	no	—
28	C₉×#125	—	2	1	no	—
29	C₉×#125	—	2	1	no	—
30	C₉×#125	C₂²	1	1	yes	characteristic
31	C₉×#124	—	2	1	no	—
32	C₉×#124	C₂²	1	1	yes	characteristic
33	C₉×#123	—	2	1	no	—
34	C₉×C₂²⋊Q₈	—	2	1	no	—
35	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
37	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₉×#121	C₂²	1	1	yes	characteristic
39	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
40	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
42	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
43	C₉×#117	C₂²	1	1	yes	characteristic
44	C₉×#107	C₂²	1	1	yes	characteristic
45	C₉×#107	C₂²	1	1	yes	characteristic
46	C₉×#106	C₂²	1	1	yes	characteristic
47	C₉×#106	C₂²	1	1	yes	characteristic
48	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₉×#103	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×#103	C₂²	1	1	yes	characteristic
58	C₉×#102	C₂²	1	1	yes	characteristic
59	C₉×#102	C₂²	1	1	yes	characteristic
60	C₃×#542	C₂×C₃	1	1	yes	characteristic
61	C₃×#541	C₂×C₃	1	1	yes	characteristic
62	C₃×#479	C₂×C₃	1	1	yes	characteristic
63	C₃×#478	C₂×C₃	1	1	yes	characteristic
64	C₃×#477	C₂×C₃	1	1	yes	characteristic
65	C₃×#475	C₂×C₃	1	1	yes	characteristic
66	C₃×#470	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×#465	C₂×C₃	1	1	yes	characteristic
70	C₃×#464	C₂×C₃	1	1	yes	characteristic
71	C₃×#464	C₂×C₃	1	1	yes	characteristic
72	C₃×#462	C₂×C₃	1	1	yes	characteristic
73	C₃×#461	C₂×C₃	1	1	yes	characteristic
74	C₃×#424	C₂×C₃	1	1	yes	characteristic
75	C₂×Q₈×C₉	—	2	1	no	—
76	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
77	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
78	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
79	C₂×D₄×C₉	—	2	1	no	—
80	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₉	—	2	1	no	—
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₉×Q₁₆	—	4	1	no	—
84	C₉×Q₁₆	—	4	1	no	—
85	C₉×SD₁₆	—	4	1	no	—
86	C₉×SD₁₆	—	4	1	no	—
87	C₉×M₁₆	—	4	1	no	—
88	C₂×C₈×C₉	—	4	1	no	—
89	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
93	C₉×C₄⋊C₄	—	2	1	no	—
94	C₉×C₄⋊C₄	—	2	1	no	—
95	C₉×C₄⋊C₄	—	2	1	no	—
96	C₉×C₄⋊C₄	—	2	1	no	—
97	C₉×C₄⋊C₄	—	2	1	no	—
98	C₉×C₄⋊C₄	—	2	1	no	—
99	C₉×C₄⋊C₄	—	2	1	no	—
100	C₉×C₄⋊C₄	—	2	1	no	—
101	C₉×C₄⋊C₄	—	2	1	no	—
102	C₉×C₄⋊C₄	—	2	1	no	—
103	C₉×C₄⋊C₄	—	2	1	no	—
104	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₉×C₂²⋊C₄	—	2	1	no	—
111	C₉×C₂²⋊C₄	—	2	1	no	—
112	C₉×C₂²⋊C₄	—	2	1	no	—
113	C₉×C₂²⋊C₄	—	2	1	no	—
114	C₉×C₂²⋊C₄	—	2	1	no	—
115	C₉×C₂²⋊C₄	—	2	1	no	—
116	C₉×C₂²⋊C₄	—	2	1	no	—
117	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
118	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
119	C₄²×C₉	—	2	1	no	—
120	C₄²×C₉	—	2	1	no	—
121	C₄²×C₉	—	2	1	no	—
122	C₄²×C₉	C₂³	1	1	yes	characteristic
123	C₄²×C₉	C₂³	1	1	yes	characteristic
124	#3258	C₉	1	1	yes	characteristic, direct product factor, Sylow
125	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
131	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
132	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
133	C₃×#126	—	2	1	no	—
134	C₃×#126	—	2	1	no	—
135	C₃×#126	—	2	1	no	—
136	C₃×#125	—	2	1	no	—
137	C₃×#125	—	2	1	no	—
138	C₃×#125	C₂²×C₃	1	1	yes	characteristic
139	C₃×#124	—	2	1	no	—
140	C₃×#124	C₂²×C₃	1	1	yes	characteristic
141	C₃×#123	—	2	1	no	—
142	C₃×C₂²⋊Q₈	—	2	1	no	—
143	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
144	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
145	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
146	C₃×#121	C₂²×C₃	1	1	yes	characteristic
147	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
148	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
149	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
150	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
151	C₃×#117	C₂²×C₃	1	1	yes	characteristic
152	C₃×#107	C₂²×C₃	1	1	yes	characteristic
153	C₃×#107	C₂²×C₃	1	1	yes	characteristic
154	C₃×#106	C₂²×C₃	1	1	yes	characteristic
155	C₃×#106	C₂²×C₃	1	1	yes	characteristic
156	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
157	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
158	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
159	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
160	C₃×#103	C₂²×C₃	1	1	yes	characteristic
161	C₃×#103	C₂²×C₃	1	1	yes	characteristic
162	C₃×#103	C₂²×C₃	1	1	yes	characteristic
163	C₃×#103	C₂²×C₃	1	1	yes	characteristic
164	C₃×#103	C₂²×C₃	1	1	yes	characteristic
165	C₃×#103	C₂²×C₃	1	1	yes	characteristic
166	C₃×#102	C₂²×C₃	1	1	yes	characteristic
167	C₃×#102	C₂²×C₃	1	1	yes	characteristic
168	C₂³×C₉	—	2	1	no	—
169	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
170	Q₈×C₉	—	2	1	no	—
171	Q₈×C₉	—	2	1	no	—
172	Q₈×C₉	—	2	1	no	—
173	Q₈×C₉	—	2	1	no	—
174	Q₈×C₉	—	2	1	no	—
175	Q₈×C₉	—	2	1	no	—
176	Q₈×C₉	—	8	1	no	—
177	D₄×C₉	—	2	1	no	—
178	D₄×C₉	—	2	1	no	—
179	D₄×C₉	—	8	1	no	—
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	1	no	—
184	C₂×C₄×C₉	—	2	1	no	—
185	C₂×C₄×C₉	—	2	1	no	—
186	C₂×C₄×C₉	—	2	1	no	—
187	C₂×C₄×C₉	—	2	1	no	—
188	C₂×C₄×C₉	—	2	1	no	—
189	C₂×C₄×C₉	—	8	1	no	—
190	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
196	C₈×C₉	—	2	1	no	—
197	C₈×C₉	—	2	1	no	—
198	C₈×C₉	—	2	1	no	—
199	C₈×C₉	—	2	1	no	—
200	#542	C₂×C₉	1	1	yes	characteristic
201	#541	C₂×C₉	1	1	yes	characteristic, complemented
202	#479	C₂×C₉	1	1	yes	characteristic, complemented
203	#478	C₂×C₉	1	1	yes	characteristic, complemented
204	#477	C₂×C₉	1	1	yes	characteristic, complemented
205	#475	C₂×C₉	1	1	yes	characteristic, complemented
206	#470	C₂×C₉	1	1	yes	characteristic, complemented
207	#468	C₂×C₉	1	1	yes	characteristic
208	#467	C₂×C₉	1	1	yes	characteristic, complemented
209	#465	C₂×C₉	1	1	yes	characteristic
210	#464	C₂×C₉	1	1	yes	characteristic, complemented
211	#464	C₂×C₉	1	1	yes	characteristic, complemented
212	#462	C₂×C₉	1	1	yes	characteristic, complemented
213	#461	C₂×C₉	1	1	yes	characteristic, complemented
214	#424	C₂×C₉	1	1	yes	characteristic, complemented
215	C₂×C₃×Q₈	—	2	1	no	—
216	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₃×D₄	—	2	1	no	—
220	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₃×C₄	—	2	1	no	—
222	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
223	C₃×Q₁₆	—	4	1	no	—
224	C₃×Q₁₆	—	4	1	no	—
225	C₃×SD₁₆	—	4	1	no	—
226	C₃×SD₁₆	—	4	1	no	—
227	C₃×M₁₆	—	4	1	no	—
228	C₂×C₃×C₈	—	4	1	no	—
229	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
232	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
233	C₃×C₄⋊C₄	—	2	1	no	—
234	C₃×C₄⋊C₄	—	2	1	no	—
235	C₃×C₄⋊C₄	—	2	1	no	—
236	C₃×C₄⋊C₄	—	2	1	no	—
237	C₃×C₄⋊C₄	—	2	1	no	—
238	C₃×C₄⋊C₄	—	2	1	no	—
239	C₃×C₄⋊C₄	—	2	1	no	—
240	C₃×C₄⋊C₄	—	2	1	no	—
241	C₃×C₄⋊C₄	—	2	1	no	—
242	C₃×C₄⋊C₄	—	2	1	no	—
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
245	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
246	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
247	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
248	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
249	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
250	C₃×C₂²⋊C₄	—	2	1	no	—
251	C₃×C₂²⋊C₄	—	2	1	no	—
252	C₃×C₂²⋊C₄	—	2	1	no	—
253	C₃×C₂²⋊C₄	—	2	1	no	—
254	C₃×C₂²⋊C₄	—	2	1	no	—
255	C₃×C₂²⋊C₄	—	2	1	no	—
256	C₃×C₂²⋊C₄	—	2	1	no	—
257	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
258	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
259	C₃×C₄²	—	2	1	no	—
260	C₃×C₄²	—	2	1	no	—
261	C₃×C₄²	—	2	1	no	—
262	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
263	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₉	—	2	1	no	—
265	C₂²×C₉	—	2	1	no	—
266	C₂²×C₉	—	2	1	no	—
267	C₂²×C₉	—	4	1	no	—
268	C₂²×C₉	—	4	1	no	—
269	C₂²×C₉	—	4	1	no	—
270	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
271	C₄×C₉	—	2	1	no	—
272	C₄×C₉	—	2	1	no	—
273	C₄×C₉	—	2	1	no	—
274	C₄×C₉	—	2	1	no	—
275	C₄×C₉	—	2	1	no	—
276	C₄×C₉	—	4	1	no	—
277	C₄×C₉	—	4	1	no	—
278	C₄×C₉	—	4	1	no	—
279	C₄×C₉	—	4	1	no	—
280	C₄×C₉	—	4	1	no	—
281	C₄×C₉	—	4	1	no	—
282	C₄×C₉	—	4	1	no	—
283	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
284	C₄×C₉	2₋¹⁺⁴	1	1	yes	characteristic
285	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
286	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
287	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
288	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
289	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
290	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
291	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
292	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
293	#126	—	2	1	no	—
294	#126	—	2	1	no	—
295	#126	—	2	1	no	—
296	#125	—	2	1	no	—
297	#125	—	2	1	no	—
298	#125	C₂²×C₉	1	1	yes	characteristic
299	#124	—	2	1	no	—
300	#124	C₂²×C₉	1	1	yes	characteristic
301	#123	—	2	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
304	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
305	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
306	#121	C₂²×C₉	1	1	yes	characteristic
307	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
308	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
309	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
310	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
311	#117	C₂²×C₉	1	1	yes	characteristic
312	#107	C₂²×C₉	1	1	yes	characteristic
313	#107	C₂²×C₉	1	1	yes	characteristic
314	#106	C₂²×C₉	1	1	yes	characteristic
315	#106	C₂²×C₉	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
317	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
320	#103	C₂²×C₉	1	1	yes	characteristic
321	#103	C₂²×C₉	1	1	yes	characteristic
322	#103	C₂²×C₉	1	1	yes	characteristic
323	#103	C₂²×C₉	1	1	yes	characteristic
324	#103	C₂²×C₉	1	1	yes	characteristic
325	#103	C₂²×C₉	1	1	yes	characteristic
326	#102	C₂²×C₉	1	1	yes	characteristic
327	#102	C₂²×C₉	1	1	yes	characteristic
328	C₂³×C₃	—	2	1	no	—
329	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
330	C₃×Q₈	—	2	1	no	—
331	C₃×Q₈	—	2	1	no	—
332	C₃×Q₈	—	2	1	no	—
333	C₃×Q₈	—	2	1	no	—
334	C₃×Q₈	—	2	1	no	—
335	C₃×Q₈	—	2	1	no	—
336	C₃×Q₈	—	8	1	no	—
337	C₃×D₄	—	2	1	no	—
338	C₃×D₄	—	2	1	no	—
339	C₃×D₄	—	8	1	no	—
340	C₂×C₃×C₄	—	2	1	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	1	no	—
345	C₂×C₃×C₄	—	2	1	no	—
346	C₂×C₃×C₄	—	2	1	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	8	1	no	—
350	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
354	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
355	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
356	C₃×C₈	—	2	1	no	—
357	C₃×C₈	—	2	1	no	—
358	C₃×C₈	—	2	1	no	—
359	C₃×C₈	—	2	1	no	—
360	C₂×C₉	—	4	1	no	—
361	C₂×C₉	—	8	1	no	—
362	C₂×C₉	#537	1	1	yes	characteristic
363	C₂×C₉	#577	1	1	yes	characteristic
364	C₂×C₉	#578	1	1	yes	characteristic
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
367	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
368	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
373	Q₁₆	—	4	1	no	—
374	Q₁₆	—	4	1	no	—
375	SD₁₆	—	4	1	no	—
376	SD₁₆	—	4	1	no	—
377	M₁₆	—	4	1	no	—
378	C₂×C₈	—	4	1	no	—
379	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
380	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
381	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
382	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
395	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
396	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
397	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
398	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
399	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
408	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	C₂³×C₉	1	1	yes	characteristic
413	C₄²	C₂³×C₉	1	1	yes	characteristic
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	—	2	1	no	—
417	C₂²×C₃	—	4	1	no	—
418	C₂²×C₃	—	4	1	no	—
419	C₂²×C₃	—	4	1	no	—
420	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	4	1	no	—
427	C₃×C₄	—	4	1	no	—
428	C₃×C₄	—	4	1	no	—
429	C₃×C₄	—	4	1	no	—
430	C₃×C₄	—	4	1	no	—
431	C₃×C₄	—	4	1	no	—
432	C₃×C₄	—	4	1	no	—
433	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
434	C₃×C₄	C₃×2₋¹⁺⁴	1	1	yes	characteristic
435	C₉	#3258	1	1	yes	characteristic, direct product factor, Sylow
436	C₂³	—	2	1	no	—
437	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
438	Q₈	—	2	1	no	—
439	Q₈	—	2	1	no	—
440	Q₈	—	2	1	no	—
441	Q₈	—	2	1	no	—
442	Q₈	—	2	1	no	—
443	Q₈	—	2	1	no	—
444	Q₈	—	8	1	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	8	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
459	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
460	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
461	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
462	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
463	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
464	C₈	—	2	1	no	—
465	C₈	—	2	1	no	—
466	C₈	—	2	1	no	—
467	C₈	—	2	1	no	—
468	C₂×C₃	—	4	1	no	—
469	C₂×C₃	—	8	1	no	—
470	C₂×C₃	C₃×#537	1	1	yes	characteristic
471	C₂×C₃	C₃×#577	1	1	yes	characteristic
472	C₂×C₃	C₃×#578	1	1	yes	characteristic
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	4	1	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	4	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
493	C₄	C₉×2₋¹⁺⁴	1	1	yes	characteristic
494	C₃	C₃×#3258	1	1	yes	characteristic
495	C₂	—	4	1	no	—
496	C₂	—	8	1	no	—
497	C₂	C₉×#537	1	1	yes	characteristic
498	C₂	C₉×#577	1	1	yes	characteristic
499	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×#121	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#541	C₂	semidirect
3. C₉×#479	C₂	semidirect
4. C₉×#478	C₂	semidirect
5. C₉×#477	C₂	semidirect
6. C₉×#475	C₂	semidirect
7. C₉×#470	C₂	semidirect
9. C₉×#467	C₂	semidirect
11. C₉×#464	C₂	semidirect
12. C₉×#464	C₂	semidirect
13. C₉×#462	C₂	semidirect
14. C₉×#461	C₂	semidirect
15. C₉×#424	C₂	semidirect
124. #3258	C₉	direct (N × H)
201. #541	C₂×C₉	semidirect
202. #479	C₂×C₉	semidirect
203. #478	C₂×C₉	semidirect
204. #477	C₂×C₉	semidirect
205. #475	C₂×C₉	semidirect
206. #470	C₂×C₉	semidirect
208. #467	C₂×C₉	semidirect
210. #464	C₂×C₉	semidirect
211. #464	C₂×C₉	semidirect
212. #462	C₂×C₉	semidirect
213. #461	C₂×C₉	semidirect
214. #424	C₂×C₉	semidirect
435. C₉	#3258	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×#542	2
C₉×#541	2
C₉×#479	2
C₉×#478	2
C₉×#477	2
C₉×#475	2
C₉×#470	2
C₉×#468	2
C₉×#467	2
C₉×#465	2
C₉×#464	2
C₉×#462	2
C₉×#461	2
C₉×#424	2
C₃×#3258	3

Subgroups — C9×#3258 #11767979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3258 #11767979