Subgroups — C₉×#2527 #11767248

Order 1152.

630 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#401	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#397	C₂	1	1	yes	maximal, characteristic
4	C₉×#393	C₂	1	1	yes	maximal, characteristic
5	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#388	C₂	1	1	yes	maximal, characteristic
8	C₉×#388	C₂	1	1	yes	maximal, characteristic
9	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#385	C₂	1	1	yes	maximal, characteristic
13	C₉×#381	C₂	1	1	yes	maximal, characteristic
14	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
15	C₉×#376	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2527	C₃	1	1	yes	maximal, characteristic
17	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
31	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
33	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
34	C₉×#95	C₂²	1	1	yes	characteristic
35	C₉×#95	C₂²	1	1	yes	characteristic
36	C₉×#95	C₂²	1	1	yes	characteristic
37	C₉×#95	C₂²	1	1	yes	characteristic
38	C₉×#95	C₂²	1	1	yes	characteristic
39	C₉×#95	C₂²	1	1	yes	characteristic
40	C₉×#95	C₂²	1	1	yes	characteristic
41	C₉×#95	C₂²	1	1	yes	characteristic
42	C₉×#95	C₂²	1	1	yes	characteristic
43	C₉×#95	C₂²	1	1	yes	characteristic
44	C₉×#95	C₂²	1	1	yes	characteristic
45	C₉×#95	C₂²	1	1	yes	characteristic
46	C₉×#95	C₂²	1	1	yes	characteristic
47	C₉×#95	C₂²	1	1	yes	characteristic
48	C₉×#95	C₂²	1	1	yes	characteristic
49	C₉×#95	C₂²	1	1	yes	characteristic
50	C₉×#95	C₂²	1	1	yes	characteristic
51	C₉×#95	C₂²	1	1	yes	characteristic
52	C₃×#401	C₂×C₃	1	1	yes	characteristic
53	C₃×#400	C₂×C₃	1	1	yes	characteristic
54	C₃×#397	C₂×C₃	1	1	yes	characteristic
55	C₃×#393	C₂×C₃	1	1	yes	characteristic
56	C₃×#391	C₂×C₃	1	1	yes	characteristic
57	C₃×#391	C₂×C₃	1	1	yes	characteristic
58	C₃×#388	C₂×C₃	1	1	yes	characteristic
59	C₃×#388	C₂×C₃	1	1	yes	characteristic
60	C₃×#387	C₂×C₃	1	1	yes	characteristic
61	C₃×#387	C₂×C₃	1	1	yes	characteristic
62	C₃×#387	C₂×C₃	1	1	yes	characteristic
63	C₃×#385	C₂×C₃	1	1	yes	characteristic
64	C₃×#381	C₂×C₃	1	1	yes	characteristic
65	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
66	C₃×#376	C₂×C₃	1	1	yes	characteristic
67	C₂⁴×C₉	C₂³	1	1	yes	characteristic
68	C₂×Q₈×C₉	—	2	2	no	—
69	C₂×Q₈×C₉	—	2	2	no	—
70	C₂×Q₈×C₉	—	4	1	no	—
71	C₂²×C₄×C₉	—	2	2	no	—
72	C₂²×C₄×C₉	—	2	2	no	—
73	C₂²×C₄×C₉	—	4	1	no	—
74	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
88	C₉×C₄⋊C₄	—	2	2	no	—
89	C₉×C₄⋊C₄	—	2	2	no	—
90	C₉×C₄⋊C₄	—	2	2	no	—
91	C₉×C₄⋊C₄	—	4	1	no	—
92	C₉×C₄⋊C₄	—	4	1	no	—
93	C₉×C₂²⋊C₄	—	2	2	no	—
94	C₉×C₂²⋊C₄	—	2	2	no	—
95	C₉×C₂²⋊C₄	—	2	2	no	—
96	C₉×C₂²⋊C₄	—	2	2	no	—
97	C₉×C₂²⋊C₄	—	2	2	no	—
98	C₉×C₂²⋊C₄	—	4	1	no	—
99	C₄²×C₉	—	2	2	no	—
100	C₄²×C₉	—	2	2	no	—
101	C₄²×C₉	—	2	2	no	—
102	C₄²×C₉	—	4	1	no	—
103	#2527	C₉	1	1	yes	characteristic, direct product factor, Sylow
104	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
121	C₃×#95	C₂²×C₃	1	1	yes	characteristic
122	C₃×#95	C₂²×C₃	1	1	yes	characteristic
123	C₃×#95	C₂²×C₃	1	1	yes	characteristic
124	C₃×#95	C₂²×C₃	1	1	yes	characteristic
125	C₃×#95	C₂²×C₃	1	1	yes	characteristic
126	C₃×#95	C₂²×C₃	1	1	yes	characteristic
127	C₃×#95	C₂²×C₃	1	1	yes	characteristic
128	C₃×#95	C₂²×C₃	1	1	yes	characteristic
129	C₃×#95	C₂²×C₃	1	1	yes	characteristic
130	C₃×#95	C₂²×C₃	1	1	yes	characteristic
131	C₃×#95	C₂²×C₃	1	1	yes	characteristic
132	C₃×#95	C₂²×C₃	1	1	yes	characteristic
133	C₃×#95	C₂²×C₃	1	1	yes	characteristic
134	C₃×#95	C₂²×C₃	1	1	yes	characteristic
135	C₃×#95	C₂²×C₃	1	1	yes	characteristic
136	C₃×#95	C₂²×C₃	1	1	yes	characteristic
137	C₃×#95	C₂²×C₃	1	1	yes	characteristic
138	C₃×#95	C₂²×C₃	1	1	yes	characteristic
139	C₂³×C₉	—	2	1	no	—
140	C₂³×C₉	—	2	1	no	—
141	C₂³×C₉	—	2	1	no	—
142	C₂³×C₉	—	2	1	no	—
143	C₂³×C₉	—	2	1	no	—
144	C₂³×C₉	—	2	1	no	—
145	C₂³×C₉	#41	1	2	yes	—
146	C₂³×C₉	C₂⁴	1	1	yes	characteristic
147	Q₈×C₉	—	4	4	no	—
148	C₂×C₄×C₉	—	2	1	no	—
149	C₂×C₄×C₉	—	2	1	no	—
150	C₂×C₄×C₉	—	2	1	no	—
151	C₂×C₄×C₉	—	2	1	no	—
152	C₂×C₄×C₉	—	2	1	no	—
153	C₂×C₄×C₉	—	2	1	no	—
154	C₂×C₄×C₉	—	2	1	no	—
155	C₂×C₄×C₉	—	2	1	no	—
156	C₂×C₄×C₉	—	2	1	no	—
157	C₂×C₄×C₉	—	2	1	no	—
158	C₂×C₄×C₉	—	2	1	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	2	1	no	—
161	C₂×C₄×C₉	—	2	1	no	—
162	C₂×C₄×C₉	—	2	1	no	—
163	C₂×C₄×C₉	—	2	1	no	—
164	C₂×C₄×C₉	—	2	1	no	—
165	C₂×C₄×C₉	—	2	1	no	—
166	C₂×C₄×C₉	—	2	1	no	—
167	C₂×C₄×C₉	—	2	1	no	—
168	C₂×C₄×C₉	—	2	1	no	—
169	C₂×C₄×C₉	—	2	1	no	—
170	C₂×C₄×C₉	—	2	1	no	—
171	C₂×C₄×C₉	—	2	1	no	—
172	C₂×C₄×C₉	—	2	1	no	—
173	C₂×C₄×C₉	—	2	1	no	—
174	C₂×C₄×C₉	—	2	1	no	—
175	C₂×C₄×C₉	—	2	1	no	—
176	C₂×C₄×C₉	—	2	1	no	—
177	C₂×C₄×C₉	—	2	1	no	—
178	C₂×C₄×C₉	—	2	1	no	—
179	C₂×C₄×C₉	—	2	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	—	4	4	no	—
187	C₂×C₄×C₉	#41	1	2	yes	—
188	C₂×C₄×C₉	#41	1	2	yes	—
189	C₂×C₄×C₉	#41	1	2	yes	—
190	C₂×C₄×C₉	#41	1	2	yes	—
191	#401	C₂×C₉	1	1	yes	characteristic, complemented
192	#400	C₂×C₉	1	1	yes	characteristic, complemented
193	#397	C₂×C₉	1	1	yes	characteristic
194	#393	C₂×C₉	1	1	yes	characteristic
195	#391	C₂×C₉	1	1	yes	characteristic, complemented
196	#391	C₂×C₉	1	1	yes	characteristic, complemented
197	#388	C₂×C₉	1	1	yes	characteristic
198	#388	C₂×C₉	1	1	yes	characteristic
199	#387	C₂×C₉	1	1	yes	characteristic, complemented
200	#387	C₂×C₉	1	1	yes	characteristic, complemented
201	#387	C₂×C₉	1	1	yes	characteristic, complemented
202	#385	C₂×C₉	1	1	yes	characteristic
203	#381	C₂×C₉	1	1	yes	characteristic
204	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
205	#376	C₂×C₉	1	1	yes	characteristic, complemented
206	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₃×Q₈	—	2	2	no	—
208	C₂×C₃×Q₈	—	2	2	no	—
209	C₂×C₃×Q₈	—	4	1	no	—
210	C₂²×C₃×C₄	—	2	2	no	—
211	C₂²×C₃×C₄	—	2	2	no	—
212	C₂²×C₃×C₄	—	4	1	no	—
213	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
215	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
227	C₃×C₄⋊C₄	—	2	2	no	—
228	C₃×C₄⋊C₄	—	2	2	no	—
229	C₃×C₄⋊C₄	—	2	2	no	—
230	C₃×C₄⋊C₄	—	4	1	no	—
231	C₃×C₄⋊C₄	—	4	1	no	—
232	C₃×C₂²⋊C₄	—	2	2	no	—
233	C₃×C₂²⋊C₄	—	2	2	no	—
234	C₃×C₂²⋊C₄	—	2	2	no	—
235	C₃×C₂²⋊C₄	—	2	2	no	—
236	C₃×C₂²⋊C₄	—	2	2	no	—
237	C₃×C₂²⋊C₄	—	4	1	no	—
238	C₃×C₄²	—	2	2	no	—
239	C₃×C₄²	—	2	2	no	—
240	C₃×C₄²	—	2	2	no	—
241	C₃×C₄²	—	4	1	no	—
242	C₂²×C₉	—	2	2	no	—
243	C₂²×C₉	—	2	2	no	—
244	C₂²×C₉	—	2	2	no	—
245	C₂²×C₉	—	4	1	no	—
246	C₂²×C₉	—	4	1	no	—
247	C₂²×C₉	—	4	1	no	—
248	C₂²×C₉	—	4	1	no	—
249	C₂²×C₉	C₂×#41	1	1	yes	characteristic
250	C₂²×C₉	C₂×#41	1	1	yes	characteristic
251	C₂²×C₉	C₂×#41	1	1	yes	characteristic
252	C₂²×C₉	C₂×#41	1	1	yes	characteristic
253	C₂²×C₉	C₂×#41	1	1	yes	characteristic
254	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
256	C₄×C₉	—	2	2	no	—
257	C₄×C₉	—	2	2	no	—
258	C₄×C₉	—	2	2	no	—
259	C₄×C₉	—	2	2	no	—
260	C₄×C₉	—	4	1	no	—
261	C₄×C₉	—	4	1	no	—
262	C₄×C₉	—	4	1	no	—
263	C₄×C₉	—	4	1	no	—
264	C₄×C₉	—	4	1	no	—
265	C₄×C₉	—	4	1	no	—
266	C₄×C₉	—	4	1	no	—
267	C₄×C₉	—	4	1	no	—
268	C₄×C₉	—	4	1	no	—
269	C₄×C₉	—	4	1	no	—
270	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
271	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
283	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
284	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
285	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
286	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
287	#95	C₂²×C₉	1	1	yes	characteristic
288	#95	C₂²×C₉	1	1	yes	characteristic
289	#95	C₂²×C₉	1	1	yes	characteristic
290	#95	C₂²×C₉	1	1	yes	characteristic
291	#95	C₂²×C₉	1	1	yes	characteristic
292	#95	C₂²×C₉	1	1	yes	characteristic
293	#95	C₂²×C₉	1	1	yes	characteristic
294	#95	C₂²×C₉	1	1	yes	characteristic
295	#95	C₂²×C₉	1	1	yes	characteristic
296	#95	C₂²×C₉	1	1	yes	characteristic
297	#95	C₂²×C₉	1	1	yes	characteristic
298	#95	C₂²×C₉	1	1	yes	characteristic
299	#95	C₂²×C₉	1	1	yes	characteristic
300	#95	C₂²×C₉	1	1	yes	characteristic
301	#95	C₂²×C₉	1	1	yes	characteristic
302	#95	C₂²×C₉	1	1	yes	characteristic
303	#95	C₂²×C₉	1	1	yes	characteristic
304	#95	C₂²×C₉	1	1	yes	characteristic
305	C₂³×C₃	—	2	1	no	—
306	C₂³×C₃	—	2	1	no	—
307	C₂³×C₃	—	2	1	no	—
308	C₂³×C₃	—	2	1	no	—
309	C₂³×C₃	—	2	1	no	—
310	C₂³×C₃	—	2	1	no	—
311	C₂³×C₃	C₃×#41	1	2	yes	—
312	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
313	C₃×Q₈	—	4	4	no	—
314	C₂×C₃×C₄	—	2	1	no	—
315	C₂×C₃×C₄	—	2	1	no	—
316	C₂×C₃×C₄	—	2	1	no	—
317	C₂×C₃×C₄	—	2	1	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	1	no	—
320	C₂×C₃×C₄	—	2	1	no	—
321	C₂×C₃×C₄	—	2	1	no	—
322	C₂×C₃×C₄	—	2	1	no	—
323	C₂×C₃×C₄	—	2	1	no	—
324	C₂×C₃×C₄	—	2	1	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	1	no	—
327	C₂×C₃×C₄	—	2	1	no	—
328	C₂×C₃×C₄	—	2	1	no	—
329	C₂×C₃×C₄	—	2	1	no	—
330	C₂×C₃×C₄	—	2	1	no	—
331	C₂×C₃×C₄	—	2	1	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	2	1	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	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	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	1	no	—
352	C₂×C₃×C₄	—	4	4	no	—
353	C₂×C₃×C₄	C₃×#41	1	2	yes	—
354	C₂×C₃×C₄	C₃×#41	1	2	yes	—
355	C₂×C₃×C₄	C₃×#41	1	2	yes	—
356	C₂×C₃×C₄	C₃×#41	1	2	yes	—
357	C₂×C₉	—	4	2	no	—
358	C₂×C₉	#529	1	1	yes	characteristic
359	C₂×C₉	#529	1	1	yes	characteristic
360	C₂×C₉	#542	1	1	yes	characteristic
361	C₂×C₉	#551	1	1	yes	characteristic
362	C₂×C₉	#551	1	1	yes	characteristic
363	C₂×C₉	#552	1	1	yes	characteristic
364	C₂×C₉	#556	1	1	yes	characteristic
365	C₂⁴	C₂³×C₉	1	1	yes	characteristic
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	4	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
373	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
374	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
375	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
376	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
377	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
378	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
379	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
380	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
381	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
382	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
383	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
384	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
385	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	4	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	4	1	no	—
401	C₂²×C₃	—	2	2	no	—
402	C₂²×C₃	—	2	2	no	—
403	C₂²×C₃	—	2	2	no	—
404	C₂²×C₃	—	4	1	no	—
405	C₂²×C₃	—	4	1	no	—
406	C₂²×C₃	—	4	1	no	—
407	C₂²×C₃	—	4	1	no	—
408	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
409	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
410	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
411	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
412	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
413	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	2	no	—
417	C₃×C₄	—	2	2	no	—
418	C₃×C₄	—	2	2	no	—
419	C₃×C₄	—	4	1	no	—
420	C₃×C₄	—	4	1	no	—
421	C₃×C₄	—	4	1	no	—
422	C₃×C₄	—	4	1	no	—
423	C₃×C₄	—	4	1	no	—
424	C₃×C₄	—	4	1	no	—
425	C₃×C₄	—	4	1	no	—
426	C₃×C₄	—	4	1	no	—
427	C₃×C₄	—	4	1	no	—
428	C₃×C₄	—	4	1	no	—
429	C₉	#2527	1	1	yes	characteristic, direct product factor, Sylow
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	C₉×#41	1	2	yes	—
437	C₂³	C₂⁴×C₉	1	1	yes	characteristic
438	Q₈	—	4	4	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	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	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	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	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	C₉×#41	1	2	yes	—
479	C₂×C₄	C₉×#41	1	2	yes	—
480	C₂×C₄	C₉×#41	1	2	yes	—
481	C₂×C₄	C₉×#41	1	2	yes	—
482	C₂×C₃	—	4	2	no	—
483	C₂×C₃	C₃×#529	1	1	yes	characteristic
484	C₂×C₃	C₃×#529	1	1	yes	characteristic
485	C₂×C₃	C₃×#542	1	1	yes	characteristic
486	C₂×C₃	C₃×#551	1	1	yes	characteristic
487	C₂×C₃	C₃×#551	1	1	yes	characteristic
488	C₂×C₃	C₃×#552	1	1	yes	characteristic
489	C₂×C₃	C₃×#556	1	1	yes	characteristic
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	C₂×C₉×#41	1	1	yes	characteristic
498	C₂²	C₂×C₉×#41	1	1	yes	characteristic
499	C₂²	C₂×C₉×#41	1	1	yes	characteristic
500	C₂²	C₂×C₉×#41	1	1	yes	characteristic
501	C₂²	C₂×C₉×#41	1	1	yes	characteristic
502	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
503	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	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	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	4	1	no	—
518	C₃	C₃×#2527	1	1	yes	characteristic
519	C₂	—	4	2	no	—
520	C₂	C₉×#529	1	1	yes	characteristic
521	C₂	C₉×#529	1	1	yes	characteristic
522	C₂	C₉×#542	1	1	yes	characteristic
523	C₂	C₉×#551	1	1	yes	characteristic
524	C₂	C₉×#551	1	1	yes	characteristic
525	C₂	C₉×#552	1	1	yes	characteristic
526	C₂	C₉×#556	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂⁴
commutator	C₂³	C₂⁴×C₉
Frattini, socle, cosocle	C₂³×C₃	C₂⁴×C₃
prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#401	C₂	semidirect
2. C₉×#400	C₂	semidirect
5. C₉×#391	C₂	semidirect
6. C₉×#391	C₂	semidirect
9. C₉×#387	C₂	semidirect
10. C₉×#387	C₂	semidirect
11. C₉×#387	C₂	semidirect
15. C₉×#376	C₂	semidirect
103. #2527	C₉	direct (N × H)
191. #401	C₂×C₉	semidirect
192. #400	C₂×C₉	semidirect
195. #391	C₂×C₉	semidirect
196. #391	C₂×C₉	semidirect
199. #387	C₂×C₉	semidirect
200. #387	C₂×C₉	semidirect
201. #387	C₂×C₉	semidirect
205. #376	C₂×C₉	semidirect
429. C₉	#2527	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×#401	2
C₉×#400	2
C₉×#397	2
C₉×#393	2
C₉×#391	2
C₉×#388	2
C₉×#387	2
C₉×#385	2
C₉×#381	2
C₄×C₉×C₂²⋊C₄	2
C₉×#376	2
C₃×#2527	3

Subgroups — C9×#2527 #11767248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2527 #11767248