Subgroups — C₉×#3102 #11767823

Order 1152.

594 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₉×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#479	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#478	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#449	C₂	1	1	yes	maximal, characteristic
11	C₄×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₉×D₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3102	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	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×D₈	C₂²	1	1	yes	characteristic
22	C₉×#126	—	2	1	no	—
23	C₉×#125	C₂²	1	1	yes	characteristic
24	C₉×#124	C₂²	1	1	yes	characteristic
25	C₉×#123	—	2	1	no	—
26	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₉×#121	C₂²	1	1	yes	characteristic
28	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
29	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
30	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
31	C₄×D₄×C₉	—	2	1	no	—
32	C₄×D₄×C₉	—	2	1	no	—
33	C₄×D₄×C₉	—	2	1	no	—
34	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
37	C₉×#117	—	2	1	no	—
38	C₉×#117	—	2	1	no	—
39	C₉×#117	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₉	—	2	1	no	—
41	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
42	C₉×#107	C₂²	1	1	yes	characteristic
43	C₉×#107	C₂²	1	1	yes	characteristic
44	C₉×#106	C₂²	1	1	yes	characteristic
45	C₉×#106	C₂²	1	1	yes	characteristic
46	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
48	C₉×#103	C₂²	1	1	yes	characteristic
49	C₉×#103	C₂²	1	1	yes	characteristic
50	C₉×#103	C₂²	1	1	yes	characteristic
51	C₉×#103	C₂²	1	1	yes	characteristic
52	C₉×#102	C₂²	1	1	yes	characteristic
53	C₉×#102	C₂²	1	1	yes	characteristic
54	C₉×#102	C₂²	1	1	yes	characteristic
55	C₉×#102	C₂²	1	1	yes	characteristic
56	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
60	C₃×#529	C₂×C₃	1	1	yes	characteristic
61	C₃×C₄×#41	C₂×C₃	1	1	yes	characteristic
62	C₃×#485	C₂×C₃	1	1	yes	characteristic
63	C₃×#482	C₂×C₃	1	1	yes	characteristic
64	C₃×#479	C₂×C₃	1	1	yes	characteristic
65	C₃×#478	C₂×C₃	1	1	yes	characteristic
66	C₃×#464	C₂×C₃	1	1	yes	characteristic
67	C₃×#463	C₂×C₃	1	1	yes	characteristic
68	C₃×#452	C₂×C₃	1	1	yes	characteristic
69	C₃×#449	C₂×C₃	1	1	yes	characteristic
70	C₃×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic
71	C₃×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic
72	C₃×C₄×SD₁₆	C₂×C₃	1	1	yes	characteristic
73	C₃×C₄×D₈	C₂×C₃	1	1	yes	characteristic
74	C₃×#431	C₂×C₃	1	1	yes	characteristic
75	C₉×#41	—	2	2	no	—
76	C₉×#41	—	2	2	no	—
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	—	2	1	no	—
81	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₉	—	2	1	no	—
84	C₂²×C₄×C₉	—	2	1	no	—
85	C₂²×C₄×C₉	—	2	1	no	—
86	C₂²×C₄×C₉	—	2	1	no	—
87	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
88	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
89	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₉×Q₁₆	—	2	2	no	—
91	C₉×SD₁₆	—	2	2	no	—
92	C₉×SD₁₆	—	2	2	no	—
93	C₉×D₈	—	2	2	no	—
94	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
95	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
96	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
97	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
105	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₉×C₂²⋊C₄	—	2	1	no	—
109	C₉×C₂²⋊C₄	—	2	1	no	—
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	C₄²×C₉	—	2	1	no	—
117	C₄²×C₉	—	2	1	no	—
118	C₄²×C₉	—	2	1	no	—
119	C₄²×C₉	—	2	1	no	—
120	C₄²×C₉	D₄	1	1	yes	characteristic
121	C₄²×C₉	D₄	1	1	yes	characteristic
122	C₄²×C₉	C₂³	1	1	yes	characteristic
123	C₄²×C₉	C₂³	1	1	yes	characteristic
124	#3102	C₉	1	1	yes	characteristic, direct product factor, Sylow
125	C₂×C₃×#41	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×D₈	C₂²×C₃	1	1	yes	characteristic
130	C₃×#126	—	2	1	no	—
131	C₃×#125	C₂²×C₃	1	1	yes	characteristic
132	C₃×#124	C₂²×C₃	1	1	yes	characteristic
133	C₃×#123	—	2	1	no	—
134	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
135	C₃×#121	C₂²×C₃	1	1	yes	characteristic
136	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
137	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
138	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
139	C₃×C₄×D₄	—	2	1	no	—
140	C₃×C₄×D₄	—	2	1	no	—
141	C₃×C₄×D₄	—	2	1	no	—
142	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
143	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
144	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
145	C₃×#117	—	2	1	no	—
146	C₃×#117	—	2	1	no	—
147	C₃×#117	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×C₄²	—	2	1	no	—
149	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
150	C₃×#107	C₂²×C₃	1	1	yes	characteristic
151	C₃×#107	C₂²×C₃	1	1	yes	characteristic
152	C₃×#106	C₂²×C₃	1	1	yes	characteristic
153	C₃×#106	C₂²×C₃	1	1	yes	characteristic
154	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
155	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
156	C₃×#103	C₂²×C₃	1	1	yes	characteristic
157	C₃×#103	C₂²×C₃	1	1	yes	characteristic
158	C₃×#103	C₂²×C₃	1	1	yes	characteristic
159	C₃×#103	C₂²×C₃	1	1	yes	characteristic
160	C₃×#102	C₂²×C₃	1	1	yes	characteristic
161	C₃×#102	C₂²×C₃	1	1	yes	characteristic
162	C₃×#102	C₂²×C₃	1	1	yes	characteristic
163	C₃×#102	C₂²×C₃	1	1	yes	characteristic
164	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
165	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
166	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
167	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
168	C₂³×C₉	—	2	1	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
171	Q₈×C₉	—	2	1	no	—
172	Q₈×C₉	—	2	1	no	—
173	Q₈×C₉	—	2	1	no	—
174	Q₈×C₉	#41	1	2	yes	—
175	D₄×C₉	—	2	4	no	—
176	D₄×C₉	—	2	1	no	—
177	D₄×C₉	—	2	1	no	—
178	D₄×C₉	—	2	1	no	—
179	D₄×C₉	—	4	2	no	—
180	D₄×C₉	#41	1	2	yes	—
181	C₂×C₄×C₉	—	2	4	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	2	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	—	2	1	no	—
190	C₂×C₄×C₉	—	2	1	no	—
191	C₂×C₄×C₉	—	4	1	no	—
192	C₂×C₄×C₉	—	4	2	no	—
193	C₂×C₄×C₉	—	4	2	no	—
194	C₂×C₄×C₉	—	4	2	no	—
195	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
201	C₈×C₉	—	2	1	no	—
202	C₈×C₉	—	2	1	no	—
203	C₈×C₉	—	2	1	no	—
204	C₈×C₉	—	2	1	no	—
205	#529	C₂×C₉	1	1	yes	characteristic, complemented
206	C₄×#41	C₂×C₉	1	1	yes	characteristic, complemented
207	#485	C₂×C₉	1	1	yes	characteristic, complemented
208	#482	C₂×C₉	1	1	yes	characteristic, complemented
209	#479	C₂×C₉	1	1	yes	characteristic, complemented
210	#478	C₂×C₉	1	1	yes	characteristic, complemented
211	#464	C₂×C₉	1	1	yes	characteristic, complemented
212	#463	C₂×C₉	1	1	yes	characteristic, complemented
213	#452	C₂×C₉	1	1	yes	characteristic, complemented
214	#449	C₂×C₉	1	1	yes	characteristic
215	C₄×Q₁₆	C₂×C₉	1	1	yes	characteristic, complemented
216	C₄×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
217	C₄×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
218	C₄×D₈	C₂×C₉	1	1	yes	characteristic, complemented
219	#431	C₂×C₉	1	1	yes	characteristic, complemented
220	C₃×#41	—	2	2	no	—
221	C₃×#41	—	2	2	no	—
222	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₃×D₄	—	2	1	no	—
225	C₂×C₃×D₄	—	2	1	no	—
226	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₃×C₄	—	2	1	no	—
229	C₂²×C₃×C₄	—	2	1	no	—
230	C₂²×C₃×C₄	—	2	1	no	—
231	C₂²×C₃×C₄	—	2	1	no	—
232	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
235	C₃×Q₁₆	—	2	2	no	—
236	C₃×SD₁₆	—	2	2	no	—
237	C₃×SD₁₆	—	2	2	no	—
238	C₃×D₈	—	2	2	no	—
239	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
240	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
241	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
243	C₃×C₄⋊C₄	—	2	1	no	—
244	C₃×C₄⋊C₄	—	2	1	no	—
245	C₃×C₄⋊C₄	—	2	1	no	—
246	C₃×C₄⋊C₄	—	2	1	no	—
247	C₃×C₄⋊C₄	—	2	1	no	—
248	C₃×C₄⋊C₄	—	2	1	no	—
249	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
250	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
251	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
252	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
258	C₃×C₂²⋊C₄	—	2	1	no	—
259	C₃×C₂²⋊C₄	—	2	1	no	—
260	C₃×C₂²⋊C₄	—	2	1	no	—
261	C₃×C₄²	—	2	1	no	—
262	C₃×C₄²	—	2	1	no	—
263	C₃×C₄²	—	2	1	no	—
264	C₃×C₄²	—	2	1	no	—
265	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
266	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
267	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
268	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₉	—	2	1	no	—
270	C₂²×C₉	—	2	2	no	—
271	C₂²×C₉	—	2	1	no	—
272	C₂²×C₉	—	2	1	no	—
273	C₂²×C₉	—	4	1	no	—
274	C₂²×C₉	—	4	1	no	—
275	C₂²×C₉	—	4	1	no	—
276	C₂²×C₉	—	4	1	no	—
277	C₂²×C₉	—	4	1	no	—
278	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
279	C₄×C₉	—	2	1	no	—
280	C₄×C₉	—	2	2	no	—
281	C₄×C₉	—	2	1	no	—
282	C₄×C₉	—	2	1	no	—
283	C₄×C₉	—	2	1	no	—
284	C₄×C₉	—	4	1	no	—
285	C₄×C₉	—	4	1	no	—
286	C₄×C₉	—	4	1	no	—
287	C₄×C₉	—	4	1	no	—
288	C₄×C₉	—	4	1	no	—
289	C₄×C₉	#135	1	2	yes	—
290	C₄×C₉	C₂×#41	1	1	yes	characteristic
291	C₄×C₉	C₂×#41	1	1	yes	characteristic
292	C₂×#41	C₂²×C₉	1	1	yes	characteristic
293	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
294	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
295	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
296	C₂×D₈	C₂²×C₉	1	1	yes	characteristic
297	#126	—	2	1	no	—
298	#125	C₂²×C₉	1	1	yes	characteristic
299	#124	C₂²×C₉	1	1	yes	characteristic
300	#123	—	2	1	no	—
301	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
302	#121	C₂²×C₉	1	1	yes	characteristic
303	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
304	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
305	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
310	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
311	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
312	#117	—	2	1	no	—
313	#117	—	2	1	no	—
314	#117	C₂²×C₉	1	1	yes	characteristic
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
317	#107	C₂²×C₉	1	1	yes	characteristic
318	#107	C₂²×C₉	1	1	yes	characteristic
319	#106	C₂²×C₉	1	1	yes	characteristic
320	#106	C₂²×C₉	1	1	yes	characteristic
321	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
322	C₄⋊C₈	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	#103	C₂²×C₉	1	1	yes	characteristic
327	#102	C₂²×C₉	1	1	yes	characteristic
328	#102	C₂²×C₉	1	1	yes	characteristic
329	#102	C₂²×C₉	1	1	yes	characteristic
330	#102	C₂²×C₉	1	1	yes	characteristic
331	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
332	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
333	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
334	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
335	C₂³×C₃	—	2	1	no	—
336	C₂³×C₃	—	2	1	no	—
337	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
338	C₃×Q₈	—	2	1	no	—
339	C₃×Q₈	—	2	1	no	—
340	C₃×Q₈	—	2	1	no	—
341	C₃×Q₈	C₃×#41	1	2	yes	—
342	C₃×D₄	—	2	4	no	—
343	C₃×D₄	—	2	1	no	—
344	C₃×D₄	—	2	1	no	—
345	C₃×D₄	—	2	1	no	—
346	C₃×D₄	—	4	2	no	—
347	C₃×D₄	C₃×#41	1	2	yes	—
348	C₂×C₃×C₄	—	2	4	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	2	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	1	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	4	1	no	—
359	C₂×C₃×C₄	—	4	2	no	—
360	C₂×C₃×C₄	—	4	2	no	—
361	C₂×C₃×C₄	—	4	2	no	—
362	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
364	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
366	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
367	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
368	C₃×C₈	—	2	1	no	—
369	C₃×C₈	—	2	1	no	—
370	C₃×C₈	—	2	1	no	—
371	C₃×C₈	—	2	1	no	—
372	C₂×C₉	—	4	1	no	—
373	C₂×C₉	—	4	2	no	—
374	C₂×C₉	—	8	1	no	—
375	C₂×C₉	#525	1	1	yes	characteristic
376	C₂×C₉	C₂×#135	1	1	yes	characteristic
377	C₂×C₉	#575	1	1	yes	characteristic
378	#41	—	2	2	no	—
379	#41	—	2	2	no	—
380	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
381	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
385	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
391	C₂²×C₄	D₄×C₉	1	1	yes	characteristic
392	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
393	Q₁₆	—	2	2	no	—
394	SD₁₆	—	2	2	no	—
395	SD₁₆	—	2	2	no	—
396	D₈	—	2	2	no	—
397	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
398	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
399	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
400	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
408	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
409	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
410	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	2	1	no	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	D₄×C₉	1	1	yes	characteristic
424	C₄²	D₄×C₉	1	1	yes	characteristic
425	C₄²	C₂³×C₉	1	1	yes	characteristic
426	C₄²	C₂³×C₉	1	1	yes	characteristic
427	C₂²×C₃	—	2	1	no	—
428	C₂²×C₃	—	2	1	no	—
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	2	no	—
431	C₂²×C₃	—	4	1	no	—
432	C₂²×C₃	—	4	1	no	—
433	C₂²×C₃	—	4	1	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	—	4	1	no	—
436	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
437	C₃×C₄	—	2	1	no	—
438	C₃×C₄	—	2	1	no	—
439	C₃×C₄	—	2	1	no	—
440	C₃×C₄	—	2	1	no	—
441	C₃×C₄	—	2	2	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	—	4	1	no	—
444	C₃×C₄	—	4	1	no	—
445	C₃×C₄	—	4	1	no	—
446	C₃×C₄	—	4	1	no	—
447	C₃×C₄	C₃×#135	1	2	yes	—
448	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
449	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
450	C₉	#3102	1	1	yes	characteristic, direct product factor, Sylow
451	C₂³	—	2	1	no	—
452	C₂³	—	2	1	no	—
453	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
454	Q₈	—	2	1	no	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	1	no	—
457	Q₈	C₉×#41	1	2	yes	—
458	D₄	—	2	4	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	2	1	no	—
462	D₄	—	4	2	no	—
463	D₄	C₉×#41	1	2	yes	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
479	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
480	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
481	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
482	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
483	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
484	C₈	—	2	1	no	—
485	C₈	—	2	1	no	—
486	C₈	—	2	1	no	—
487	C₈	—	2	1	no	—
488	C₂×C₃	—	4	1	no	—
489	C₂×C₃	—	4	2	no	—
490	C₂×C₃	—	8	1	no	—
491	C₂×C₃	C₃×#525	1	1	yes	characteristic
492	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
493	C₂×C₃	C₃×#575	1	1	yes	characteristic
494	C₂²	—	2	1	no	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	2	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
504	C₄	—	2	1	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	C₉×#135	1	2	yes	—
515	C₄	C₂×C₉×#41	1	1	yes	characteristic
516	C₄	C₂×C₉×#41	1	1	yes	characteristic
517	C₃	C₃×#3102	1	1	yes	characteristic
518	C₂	—	4	1	no	—
519	C₂	—	4	2	no	—
520	C₂	—	8	1	no	—
521	C₂	C₉×#525	1	1	yes	characteristic
522	C₂	C₂×C₉×#135	1	1	yes	characteristic
523	C₂	C₉×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₉	C₂×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#449	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#529	C₂	semidirect
2. C₄×C₉×#41	C₂	semidirect
3. C₉×#485	C₂	semidirect
4. C₉×#482	C₂	semidirect
5. C₉×#479	C₂	semidirect
6. C₉×#478	C₂	semidirect
7. C₉×#464	C₂	semidirect
8. C₉×#463	C₂	semidirect
9. C₉×#452	C₂	semidirect
11. C₄×C₉×Q₁₆	C₂	semidirect
12. C₄×C₉×SD₁₆	C₂	semidirect
13. C₄×C₉×SD₁₆	C₂	semidirect
14. C₄×C₉×D₈	C₂	semidirect
15. C₉×#431	C₂	semidirect
124. #3102	C₉	direct (N × H)
205. #529	C₂×C₉	semidirect
206. C₄×#41	C₂×C₉	semidirect
207. #485	C₂×C₉	semidirect
208. #482	C₂×C₉	semidirect
209. #479	C₂×C₉	semidirect
210. #478	C₂×C₉	semidirect
211. #464	C₂×C₉	semidirect
212. #463	C₂×C₉	semidirect
213. #452	C₂×C₉	semidirect
215. C₄×Q₁₆	C₂×C₉	semidirect
216. C₄×SD₁₆	C₂×C₉	semidirect
217. C₄×SD₁₆	C₂×C₉	semidirect
218. C₄×D₈	C₂×C₉	semidirect
219. #431	C₂×C₉	semidirect
450. C₉	#3102	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×#529	2
C₄×C₉×#41	2
C₉×#485	2
C₉×#482	2
C₉×#479	2
C₉×#478	2
C₉×#464	2
C₉×#463	2
C₉×#452	2
C₉×#449	2
C₄×C₉×Q₁₆	2
C₄×C₉×SD₁₆	2
C₄×C₉×D₈	2
C₉×#431	2
C₃×#3102	3

Subgroups — C9×#3102 #11767823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3102 #11767823