Subgroups — C₉×#2556 #11767277

Order 1152.

738 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₉×#399	C₂	1	1	yes	maximal, characteristic
4	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#396	C₂	1	1	yes	maximal, characteristic
6	C₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#388	C₂	1	1	yes	maximal, characteristic
11	C₉×#388	C₂	1	1	yes	maximal, characteristic
12	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#385	C₂	1	1	yes	maximal, characteristic
14	C₄×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₃×#2556	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	C₉×#125	—	2	4	no	—
20	C₉×C₂²⋊Q₈	—	2	4	no	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
42	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
43	C₂×C₄²×C₉	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	C₉×#95	C₂²	1	1	yes	characteristic
53	C₉×#95	C₂²	1	1	yes	characteristic
54	C₂×C₃×#125	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
56	C₃×#399	C₂×C₃	1	1	yes	characteristic
57	C₃×#398	C₂×C₃	1	1	yes	characteristic
58	C₃×#396	C₂×C₃	1	1	yes	characteristic
59	C₃×#395	C₂×C₃	1	1	yes	characteristic
60	C₃×#391	C₂×C₃	1	1	yes	characteristic
61	C₃×#389	C₂×C₃	1	1	yes	characteristic
62	C₃×#389	C₂×C₃	1	1	yes	characteristic
63	C₃×#388	C₂×C₃	1	1	yes	characteristic
64	C₃×#388	C₂×C₃	1	1	yes	characteristic
65	C₃×#387	C₂×C₃	1	1	yes	characteristic
66	C₃×#385	C₂×C₃	1	1	yes	characteristic
67	C₃×C₄×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
68	C₃×C₄×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
69	C₂⁴×C₉	C₂³	1	1	yes	characteristic
70	C₂×Q₈×C₉	—	2	2	no	—
71	C₂×Q₈×C₉	—	2	2	no	—
72	C₂×Q₈×C₉	—	4	1	no	—
73	C₂²×C₄×C₉	—	2	2	no	—
74	C₂²×C₄×C₉	—	2	2	no	—
75	C₂²×C₄×C₉	—	4	1	no	—
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	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₉×C₄⋊C₄	—	2	2	no	—
91	C₉×C₄⋊C₄	—	2	2	no	—
92	C₉×C₄⋊C₄	—	2	2	no	—
93	C₉×C₄⋊C₄	—	2	2	no	—
94	C₉×C₄⋊C₄	—	2	2	no	—
95	C₉×C₄⋊C₄	—	2	2	no	—
96	C₉×C₄⋊C₄	—	2	2	no	—
97	C₉×C₄⋊C₄	—	2	2	no	—
98	C₉×C₄⋊C₄	—	2	2	no	—
99	C₉×C₄⋊C₄	—	2	2	no	—
100	C₉×C₄⋊C₄	—	2	2	no	—
101	C₉×C₄⋊C₄	—	4	1	no	—
102	C₉×C₄⋊C₄	D₄	1	4	yes	—
103	C₉×C₂²⋊C₄	—	2	2	no	—
104	C₉×C₂²⋊C₄	—	2	2	no	—
105	C₉×C₂²⋊C₄	—	2	2	no	—
106	C₉×C₂²⋊C₄	—	2	2	no	—
107	C₉×C₂²⋊C₄	—	4	1	no	—
108	C₉×C₂²⋊C₄	Q₈	1	4	yes	complemented
109	C₄²×C₉	—	2	2	no	—
110	C₄²×C₉	—	2	2	no	—
111	C₄²×C₉	—	4	1	no	—
112	C₄²×C₉	—	4	1	no	—
113	#2556	C₉	1	1	yes	characteristic, direct product factor, Sylow
114	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
116	C₃×#125	—	2	4	no	—
117	C₃×C₂²⋊Q₈	—	2	4	no	—
118	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
141	C₃×#95	C₂²×C₃	1	1	yes	characteristic
142	C₃×#95	C₂²×C₃	1	1	yes	characteristic
143	C₃×#95	C₂²×C₃	1	1	yes	characteristic
144	C₃×#95	C₂²×C₃	1	1	yes	characteristic
145	C₃×#95	C₂²×C₃	1	1	yes	characteristic
146	C₃×#95	C₂²×C₃	1	1	yes	characteristic
147	C₃×#95	C₂²×C₃	1	1	yes	characteristic
148	C₃×#95	C₂²×C₃	1	1	yes	characteristic
149	C₃×#95	C₂²×C₃	1	1	yes	characteristic
150	C₃×#95	C₂²×C₃	1	1	yes	characteristic
151	C₂³×C₉	—	2	1	no	—
152	C₂³×C₉	—	2	1	no	—
153	C₂³×C₉	—	2	1	no	—
154	C₂³×C₉	—	2	1	no	—
155	C₂³×C₉	—	2	1	no	—
156	C₂³×C₉	—	2	1	no	—
157	C₂³×C₉	C₂×Q₈	1	2	yes	—
158	C₂³×C₉	C₂⁴	1	1	yes	characteristic
159	Q₈×C₉	—	4	4	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	—	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	—	2	1	no	—
192	C₂×C₄×C₉	—	2	1	no	—
193	C₂×C₄×C₉	—	2	1	no	—
194	C₂×C₄×C₉	—	4	4	no	—
195	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
196	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
197	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
198	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
199	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
200	C₂×C₄×C₉	#41	1	2	yes	—
201	C₂×C₄×C₉	#41	1	2	yes	—
202	C₂×C₄×C₉	#41	1	2	yes	—
203	C₂×#125	C₂×C₉	1	1	yes	characteristic, complemented
204	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic
205	#399	C₂×C₉	1	1	yes	characteristic
206	#398	C₂×C₉	1	1	yes	characteristic, complemented
207	#396	C₂×C₉	1	1	yes	characteristic
208	#395	C₂×C₉	1	1	yes	characteristic, complemented
209	#391	C₂×C₉	1	1	yes	characteristic, complemented
210	#389	C₂×C₉	1	1	yes	characteristic, complemented
211	#389	C₂×C₉	1	1	yes	characteristic, complemented
212	#388	C₂×C₉	1	1	yes	characteristic
213	#388	C₂×C₉	1	1	yes	characteristic
214	#387	C₂×C₉	1	1	yes	characteristic, complemented
215	#385	C₂×C₉	1	1	yes	characteristic
216	C₄×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
217	C₄×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic
218	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	2	2	no	—
221	C₂×C₃×Q₈	—	4	1	no	—
222	C₂²×C₃×C₄	—	2	2	no	—
223	C₂²×C₃×C₄	—	2	2	no	—
224	C₂²×C₃×C₄	—	4	1	no	—
225	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
229	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
230	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
233	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
234	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
235	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
236	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
237	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
238	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
239	C₃×C₄⋊C₄	—	2	2	no	—
240	C₃×C₄⋊C₄	—	2	2	no	—
241	C₃×C₄⋊C₄	—	2	2	no	—
242	C₃×C₄⋊C₄	—	2	2	no	—
243	C₃×C₄⋊C₄	—	2	2	no	—
244	C₃×C₄⋊C₄	—	2	2	no	—
245	C₃×C₄⋊C₄	—	2	2	no	—
246	C₃×C₄⋊C₄	—	2	2	no	—
247	C₃×C₄⋊C₄	—	2	2	no	—
248	C₃×C₄⋊C₄	—	2	2	no	—
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	4	1	no	—
251	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
252	C₃×C₂²⋊C₄	—	2	2	no	—
253	C₃×C₂²⋊C₄	—	2	2	no	—
254	C₃×C₂²⋊C₄	—	2	2	no	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₂²⋊C₄	—	4	1	no	—
257	C₃×C₂²⋊C₄	C₃×Q₈	1	4	yes	—
258	C₃×C₄²	—	2	2	no	—
259	C₃×C₄²	—	2	2	no	—
260	C₃×C₄²	—	4	1	no	—
261	C₃×C₄²	—	4	1	no	—
262	C₂²×C₉	—	2	2	no	—
263	C₂²×C₉	—	2	2	no	—
264	C₂²×C₉	—	2	2	no	—
265	C₂²×C₉	—	4	1	no	—
266	C₂²×C₉	—	4	1	no	—
267	C₂²×C₉	—	4	1	no	—
268	C₂²×C₉	—	4	1	no	—
269	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
270	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
271	C₂²×C₉	C₂×#41	1	1	yes	characteristic
272	C₂²×C₉	C₂×#41	1	1	yes	characteristic
273	C₂²×C₉	C₂×#41	1	1	yes	characteristic
274	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
275	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
276	C₄×C₉	—	2	2	no	—
277	C₄×C₉	—	2	2	no	—
278	C₄×C₉	—	2	2	no	—
279	C₄×C₉	—	2	2	no	—
280	C₄×C₉	—	2	2	no	—
281	C₄×C₉	—	2	2	no	—
282	C₄×C₉	—	2	2	no	—
283	C₄×C₉	—	2	2	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	—	4	1	no	—
290	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
291	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
292	#125	—	2	4	no	—
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
308	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
313	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
314	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
315	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
316	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
317	#95	C₂²×C₉	1	1	yes	characteristic
318	#95	C₂²×C₉	1	1	yes	characteristic
319	#95	C₂²×C₉	1	1	yes	characteristic
320	#95	C₂²×C₉	1	1	yes	characteristic
321	#95	C₂²×C₉	1	1	yes	characteristic
322	#95	C₂²×C₉	1	1	yes	characteristic
323	#95	C₂²×C₉	1	1	yes	characteristic
324	#95	C₂²×C₉	1	1	yes	characteristic
325	#95	C₂²×C₉	1	1	yes	characteristic
326	#95	C₂²×C₉	1	1	yes	characteristic
327	C₂³×C₃	—	2	1	no	—
328	C₂³×C₃	—	2	1	no	—
329	C₂³×C₃	—	2	1	no	—
330	C₂³×C₃	—	2	1	no	—
331	C₂³×C₃	—	2	1	no	—
332	C₂³×C₃	—	2	1	no	—
333	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
334	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
335	C₃×Q₈	—	4	4	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	—	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	—	2	1	no	—
359	C₂×C₃×C₄	—	2	1	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	4	4	no	—
371	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
372	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
373	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
374	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
375	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
376	C₂×C₃×C₄	C₃×#41	1	2	yes	—
377	C₂×C₃×C₄	C₃×#41	1	2	yes	—
378	C₂×C₃×C₄	C₃×#41	1	2	yes	—
379	C₂×C₉	—	4	2	no	—
380	C₂×C₉	#532	1	1	yes	characteristic
381	C₂×C₉	#533	1	1	yes	characteristic
382	C₂×C₉	#539	1	1	yes	characteristic
383	C₂×C₉	#546	1	1	yes	characteristic
384	C₂×C₉	D₄×Q₈	1	1	yes	characteristic
385	C₂×C₉	#552	1	1	yes	characteristic
386	C₂×C₉	#554	1	1	yes	characteristic
387	C₂⁴	C₂³×C₉	1	1	yes	characteristic
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	4	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
395	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
396	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
397	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
398	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
399	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
400	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
401	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
402	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
403	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
404	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
405	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
406	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
407	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	D₄×C₉	1	4	yes	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	4	1	no	—
426	C₂²⋊C₄	Q₈×C₉	1	4	yes	complemented
427	C₄²	—	2	2	no	—
428	C₄²	—	2	2	no	—
429	C₄²	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	—	4	1	no	—
436	C₂²×C₃	—	4	1	no	—
437	C₂²×C₃	—	4	1	no	—
438	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
439	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
440	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
441	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
442	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
443	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
445	C₃×C₄	—	2	2	no	—
446	C₃×C₄	—	2	2	no	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	2	2	no	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	2	2	no	—
452	C₃×C₄	—	2	2	no	—
453	C₃×C₄	—	4	1	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	4	1	no	—
457	C₃×C₄	—	4	1	no	—
458	C₃×C₄	—	4	1	no	—
459	C₉	#2556	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	1	no	—
466	C₂³	C₂×Q₈×C₉	1	2	yes	—
467	C₂³	C₂⁴×C₉	1	1	yes	characteristic
468	Q₈	—	4	4	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	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
505	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
506	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
507	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
508	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
509	C₂×C₄	C₉×#41	1	2	yes	—
510	C₂×C₄	C₉×#41	1	2	yes	—
511	C₂×C₄	C₉×#41	1	2	yes	—
512	C₂×C₃	—	4	2	no	—
513	C₂×C₃	C₃×#532	1	1	yes	characteristic
514	C₂×C₃	C₃×#533	1	1	yes	characteristic
515	C₂×C₃	C₃×#539	1	1	yes	characteristic
516	C₂×C₃	C₃×#546	1	1	yes	characteristic
517	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
518	C₂×C₃	C₃×#552	1	1	yes	characteristic
519	C₂×C₃	C₃×#554	1	1	yes	characteristic
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
528	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
529	C₂²	C₂×C₉×#41	1	1	yes	characteristic
530	C₂²	C₂×C₉×#41	1	1	yes	characteristic
531	C₂²	C₂×C₉×#41	1	1	yes	characteristic
532	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	4	1	no	—
548	C₃	C₃×#2556	1	1	yes	characteristic
549	C₂	—	4	2	no	—
550	C₂	C₉×#532	1	1	yes	characteristic
551	C₂	C₉×#533	1	1	yes	characteristic
552	C₂	C₉×#539	1	1	yes	characteristic
553	C₂	C₉×#546	1	1	yes	characteristic
554	C₂	D₄×Q₈×C₉	1	1	yes	characteristic
555	C₂	C₉×#552	1	1	yes	characteristic
556	C₂	C₉×#554	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. C₂×C₉×#125	C₂	semidirect
4. C₉×#398	C₂	semidirect
6. C₉×#395	C₂	semidirect
7. C₉×#391	C₂	semidirect
8. C₉×#389	C₂	semidirect
9. C₉×#389	C₂	semidirect
12. C₉×#387	C₂	semidirect
14. C₄×C₉×C₄⋊C₄	C₂	semidirect
108. C₉×C₂²⋊C₄	Q₈	semidirect
113. #2556	C₉	direct (N × H)
203. C₂×#125	C₂×C₉	semidirect
206. #398	C₂×C₉	semidirect
208. #395	C₂×C₉	semidirect
209. #391	C₂×C₉	semidirect
210. #389	C₂×C₉	semidirect
211. #389	C₂×C₉	semidirect
214. #387	C₂×C₉	semidirect
216. C₄×C₄⋊C₄	C₂×C₉	semidirect
426. C₂²⋊C₄	Q₈×C₉	semidirect
459. C₉	#2556	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×#125	2
C₂×C₉×C₂²⋊Q₈	2
C₉×#399	2
C₉×#398	2
C₉×#396	2
C₉×#395	2
C₉×#391	2
C₉×#389	2
C₉×#388	2
C₉×#387	2
C₉×#385	2
C₄×C₉×C₄⋊C₄	2
C₄×C₉×C₂²⋊C₄	2
C₃×#2556	3

Subgroups — C9×#2556 #11767277

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2556 #11767277