Subgroups — C₉×#2450 #11767171

Order 1152.

876 conjugacy classes of subgroups.

The subgroup lattice has 621 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
3	C₉×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#393	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#391	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#386	C₂	1	1	yes	maximal, characteristic
10	C₉×#386	C₂	1	1	yes	maximal, characteristic
11	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#380	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₉×#95	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2450	C₃	1	1	yes	maximal, characteristic
17	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
20	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
21	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₉	C₂²	1	1	yes	characteristic
23	C₉×C₂²⋊Q₈	—	2	4	no	—
24	C₄×D₄×C₉	—	2	4	no	—
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×C₂²⋊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×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₄²×C₉	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	C₉×#95	C₂²	1	1	yes	characteristic
53	C₉×#95	C₂²	1	1	yes	characteristic
54	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
56	C₃×#400	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×#393	C₂×C₃	1	1	yes	characteristic
60	C₃×#391	C₂×C₃	1	1	yes	characteristic
61	C₃×#387	C₂×C₃	1	1	yes	characteristic
62	C₃×#386	C₂×C₃	1	1	yes	characteristic
63	C₃×#386	C₂×C₃	1	1	yes	characteristic
64	C₃×#385	C₂×C₃	1	1	yes	characteristic
65	C₃×#385	C₂×C₃	1	1	yes	characteristic
66	C₃×#385	C₂×C₃	1	1	yes	characteristic
67	C₃×#380	C₂×C₃	1	1	yes	characteristic
68	C₂×C₃×#95	C₂×C₃	1	1	yes	characteristic
69	C₂⁴×C₉	C₂³	1	1	yes	characteristic
70	C₂⁴×C₉	C₂³	1	1	yes	characteristic
71	C₂×Q₈×C₉	—	2	2	no	—
72	C₂×Q₈×C₉	—	2	2	no	—
73	C₂×Q₈×C₉	—	4	1	no	—
74	C₂×D₄×C₉	—	2	2	no	—
75	C₂×D₄×C₉	—	2	2	no	—
76	C₂×D₄×C₉	Q₈	1	4	yes	complemented
77	C₂²×C₄×C₉	—	2	2	no	—
78	C₂²×C₄×C₉	—	2	2	no	—
79	C₂²×C₄×C₉	—	2	2	no	—
80	C₂²×C₄×C₉	—	2	2	no	—
81	C₂²×C₄×C₉	—	2	2	no	—
82	C₂²×C₄×C₉	—	2	2	no	—
83	C₂²×C₄×C₉	—	2	2	no	—
84	C₂²×C₄×C₉	—	4	1	no	—
85	C₂²×C₄×C₉	—	4	1	no	—
86	C₂²×C₄×C₉	—	4	1	no	—
87	C₂²×C₄×C₉	—	4	1	no	—
88	C₂²×C₄×C₉	—	4	1	no	—
89	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
90	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
92	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
102	C₉×C₄⋊C₄	—	2	2	no	—
103	C₉×C₄⋊C₄	—	2	2	no	—
104	C₉×C₄⋊C₄	—	2	2	no	—
105	C₉×C₄⋊C₄	—	2	2	no	—
106	C₉×C₄⋊C₄	—	2	2	no	—
107	C₉×C₄⋊C₄	—	4	1	no	—
108	C₉×C₄⋊C₄	—	4	1	no	—
109	C₉×C₄⋊C₄	—	4	1	no	—
110	C₉×C₂²⋊C₄	—	2	2	no	—
111	C₉×C₂²⋊C₄	—	2	2	no	—
112	C₉×C₂²⋊C₄	—	2	2	no	—
113	C₉×C₂²⋊C₄	—	2	2	no	—
114	C₉×C₂²⋊C₄	—	4	1	no	—
115	C₉×C₂²⋊C₄	—	4	1	no	—
116	C₉×C₂²⋊C₄	—	4	1	no	—
117	C₉×C₂²⋊C₄	D₄	1	4	yes	—
118	C₄²×C₉	—	2	2	no	—
119	#2450	C₉	1	1	yes	characteristic, direct product factor, Sylow
120	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
122	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
124	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
126	C₃×C₂²⋊Q₈	—	2	4	no	—
127	C₃×C₄×D₄	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₃×C₄²	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	C₃×#95	C₂²×C₃	1	1	yes	characteristic
152	C₃×#95	C₂²×C₃	1	1	yes	characteristic
153	C₃×#95	C₂²×C₃	1	1	yes	characteristic
154	C₃×#95	C₂²×C₃	1	1	yes	characteristic
155	C₃×#95	C₂²×C₃	1	1	yes	characteristic
156	C₃×#95	C₂²×C₃	1	1	yes	characteristic
157	C₂³×C₉	—	2	1	no	—
158	C₂³×C₉	—	2	1	no	—
159	C₂³×C₉	—	2	1	no	—
160	C₂³×C₉	—	2	1	no	—
161	C₂³×C₉	—	2	1	no	—
162	C₂³×C₉	—	2	1	no	—
163	C₂³×C₉	—	2	1	no	—
164	C₂³×C₉	—	2	1	no	—
165	C₂³×C₉	—	2	1	no	—
166	C₂³×C₉	—	2	1	no	—
167	C₂³×C₉	C₂×D₄	1	2	yes	—
168	C₂³×C₉	C₂×Q₈	1	2	yes	—
169	C₂³×C₉	C₂×Q₈	1	2	yes	—
170	C₂³×C₉	#41	1	2	yes	—
171	C₂³×C₉	C₂⁴	1	1	yes	characteristic
172	Q₈×C₉	—	4	4	no	—
173	D₄×C₉	—	2	8	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	—	2	1	no	—
195	C₂×C₄×C₉	—	2	1	no	—
196	C₂×C₄×C₉	—	2	1	no	—
197	C₂×C₄×C₉	—	2	1	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	—	2	1	no	—
205	C₂×C₄×C₉	—	2	1	no	—
206	C₂×C₄×C₉	—	2	1	no	—
207	C₂×C₄×C₉	—	2	1	no	—
208	C₂×C₄×C₉	—	4	4	no	—
209	C₂×C₄×C₉	—	4	4	no	—
210	C₂×C₄×C₉	—	4	4	no	—
211	C₂×C₄×C₉	—	4	4	no	—
212	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
213	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
214	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
215	C₂×C₄×C₉	#41	1	2	yes	—
216	C₂×C₄×C₉	#41	1	2	yes	—
217	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
218	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
219	#400	C₂×C₉	1	1	yes	characteristic, complemented
220	#398	C₂×C₉	1	1	yes	characteristic, complemented
221	#396	C₂×C₉	1	1	yes	characteristic, complemented
222	#393	C₂×C₉	1	1	yes	characteristic, complemented
223	#391	C₂×C₉	1	1	yes	characteristic, complemented
224	#387	C₂×C₉	1	1	yes	characteristic, complemented
225	#386	C₂×C₉	1	1	yes	characteristic
226	#386	C₂×C₉	1	1	yes	characteristic
227	#385	C₂×C₉	1	1	yes	characteristic, complemented
228	#385	C₂×C₉	1	1	yes	characteristic, complemented
229	#385	C₂×C₉	1	1	yes	characteristic, complemented
230	#380	C₂×C₉	1	1	yes	characteristic, complemented
231	C₂×#95	C₂×C₉	1	1	yes	characteristic, complemented
232	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
233	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
234	C₂×C₃×Q₈	—	2	2	no	—
235	C₂×C₃×Q₈	—	2	2	no	—
236	C₂×C₃×Q₈	—	4	1	no	—
237	C₂×C₃×D₄	—	2	2	no	—
238	C₂×C₃×D₄	—	2	2	no	—
239	C₂×C₃×D₄	C₃×Q₈	1	4	yes	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	—	2	2	no	—
242	C₂²×C₃×C₄	—	2	2	no	—
243	C₂²×C₃×C₄	—	2	2	no	—
244	C₂²×C₃×C₄	—	2	2	no	—
245	C₂²×C₃×C₄	—	2	2	no	—
246	C₂²×C₃×C₄	—	2	2	no	—
247	C₂²×C₃×C₄	—	4	1	no	—
248	C₂²×C₃×C₄	—	4	1	no	—
249	C₂²×C₃×C₄	—	4	1	no	—
250	C₂²×C₃×C₄	—	4	1	no	—
251	C₂²×C₃×C₄	—	4	1	no	—
252	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
254	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
255	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
256	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
263	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
265	C₃×C₄⋊C₄	—	2	2	no	—
266	C₃×C₄⋊C₄	—	2	2	no	—
267	C₃×C₄⋊C₄	—	2	2	no	—
268	C₃×C₄⋊C₄	—	2	2	no	—
269	C₃×C₄⋊C₄	—	2	2	no	—
270	C₃×C₄⋊C₄	—	4	1	no	—
271	C₃×C₄⋊C₄	—	4	1	no	—
272	C₃×C₄⋊C₄	—	4	1	no	—
273	C₃×C₂²⋊C₄	—	2	2	no	—
274	C₃×C₂²⋊C₄	—	2	2	no	—
275	C₃×C₂²⋊C₄	—	2	2	no	—
276	C₃×C₂²⋊C₄	—	2	2	no	—
277	C₃×C₂²⋊C₄	—	4	1	no	—
278	C₃×C₂²⋊C₄	—	4	1	no	—
279	C₃×C₂²⋊C₄	—	4	1	no	—
280	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
281	C₃×C₄²	—	2	2	no	—
282	C₂²×C₉	—	2	2	no	—
283	C₂²×C₉	—	2	2	no	—
284	C₂²×C₉	—	2	2	no	—
285	C₂²×C₉	—	2	2	no	—
286	C₂²×C₉	—	2	2	no	—
287	C₂²×C₉	—	2	2	no	—
288	C₂²×C₉	—	2	2	no	—
289	C₂²×C₉	—	2	2	no	—
290	C₂²×C₉	—	2	2	no	—
291	C₂²×C₉	—	4	1	no	—
292	C₂²×C₉	—	4	1	no	—
293	C₂²×C₉	—	4	1	no	—
294	C₂²×C₉	—	4	1	no	—
295	C₂²×C₉	C₂²⋊Q₈	1	4	yes	—
296	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
297	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
298	C₂²×C₉	C₂×#41	1	1	yes	characteristic
299	C₂²×C₉	C₂×#41	1	1	yes	characteristic
300	C₂²×C₉	C₂×#41	1	1	yes	characteristic
301	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
302	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
303	C₄×C₉	—	2	2	no	—
304	C₄×C₉	—	2	2	no	—
305	C₄×C₉	—	2	2	no	—
306	C₄×C₉	—	2	2	no	—
307	C₄×C₉	—	2	2	no	—
308	C₄×C₉	—	4	1	no	—
309	C₄×C₉	—	4	1	no	—
310	C₄×C₉	—	4	1	no	—
311	C₄×C₉	—	4	1	no	—
312	C₄×C₉	—	4	1	no	—
313	C₄×C₉	—	4	1	no	—
314	C₄×C₉	—	4	1	no	—
315	C₄×C₉	—	4	1	no	—
316	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
317	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
318	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
319	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
320	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
321	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
322	C₂²⋊Q₈	—	2	4	no	—
323	C₄×D₄	—	2	4	no	—
324	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
337	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
340	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
341	#95	C₂²×C₉	1	1	yes	characteristic
342	#95	C₂²×C₉	1	1	yes	characteristic
343	#95	C₂²×C₉	1	1	yes	characteristic
344	#95	C₂²×C₉	1	1	yes	characteristic
345	#95	C₂²×C₉	1	1	yes	characteristic
346	#95	C₂²×C₉	1	1	yes	characteristic
347	#95	C₂²×C₉	1	1	yes	characteristic
348	#95	C₂²×C₉	1	1	yes	characteristic
349	#95	C₂²×C₉	1	1	yes	characteristic
350	#95	C₂²×C₉	1	1	yes	characteristic
351	#95	C₂²×C₉	1	1	yes	characteristic
352	#95	C₂²×C₉	1	1	yes	characteristic
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	—	2	1	no	—
357	C₂³×C₃	—	2	1	no	—
358	C₂³×C₃	—	2	1	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	2	1	no	—
363	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
364	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
365	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
366	C₂³×C₃	C₃×#41	1	2	yes	—
367	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
368	C₃×Q₈	—	4	4	no	—
369	C₃×D₄	—	2	8	no	—
370	C₂×C₃×C₄	—	2	1	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	1	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	1	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	1	no	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	1	no	—
402	C₂×C₃×C₄	—	2	1	no	—
403	C₂×C₃×C₄	—	2	1	no	—
404	C₂×C₃×C₄	—	4	4	no	—
405	C₂×C₃×C₄	—	4	4	no	—
406	C₂×C₃×C₄	—	4	4	no	—
407	C₂×C₃×C₄	—	4	4	no	—
408	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
409	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
410	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
411	C₂×C₃×C₄	C₃×#41	1	2	yes	—
412	C₂×C₃×C₄	C₃×#41	1	2	yes	—
413	C₂×C₉	—	2	4	no	—
414	C₂×C₉	—	4	2	no	—
415	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
416	C₂×C₉	#529	1	1	yes	characteristic
417	C₂×C₉	#538	1	1	yes	characteristic
418	C₂×C₉	#546	1	1	yes	characteristic
419	C₂×C₉	#546	1	1	yes	characteristic
420	C₂×C₉	#554	1	1	yes	characteristic
421	C₂×C₉	#554	1	1	yes	characteristic
422	C₂⁴	C₂³×C₉	1	1	yes	characteristic
423	C₂⁴	C₂³×C₉	1	1	yes	characteristic
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	—	2	2	no	—
426	C₂×Q₈	—	4	1	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	Q₈×C₉	1	4	yes	complemented
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
443	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
444	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
445	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
446	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
447	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
448	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
449	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
450	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
451	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
452	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
453	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
454	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	D₄×C₉	1	4	yes	—
471	C₄²	—	2	2	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	—	2	2	no	—
479	C₂²×C₃	—	2	2	no	—
480	C₂²×C₃	—	2	2	no	—
481	C₂²×C₃	—	4	1	no	—
482	C₂²×C₃	—	4	1	no	—
483	C₂²×C₃	—	4	1	no	—
484	C₂²×C₃	—	4	1	no	—
485	C₂²×C₃	C₃×C₂²⋊Q₈	1	4	yes	—
486	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
487	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
488	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
489	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
490	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
491	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
492	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
493	C₃×C₄	—	2	2	no	—
494	C₃×C₄	—	2	2	no	—
495	C₃×C₄	—	2	2	no	—
496	C₃×C₄	—	2	2	no	—
497	C₃×C₄	—	2	2	no	—
498	C₃×C₄	—	4	1	no	—
499	C₃×C₄	—	4	1	no	—
500	C₃×C₄	—	4	1	no	—
501	C₃×C₄	—	4	1	no	—
502	C₃×C₄	—	4	1	no	—
503	C₃×C₄	—	4	1	no	—
504	C₃×C₄	—	4	1	no	—
505	C₃×C₄	—	4	1	no	—
506	C₉	#2450	1	1	yes	characteristic, direct product factor, Sylow
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	—	2	1	no	—
512	C₂³	—	2	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	2	1	no	—
515	C₂³	—	2	1	no	—
516	C₂³	—	2	1	no	—
517	C₂³	C₂×D₄×C₉	1	2	yes	—
518	C₂³	C₂×Q₈×C₉	1	2	yes	—
519	C₂³	C₂×Q₈×C₉	1	2	yes	—
520	C₂³	C₉×#41	1	2	yes	—
521	C₂³	C₂⁴×C₉	1	1	yes	characteristic
522	Q₈	—	4	4	no	—
523	D₄	—	2	8	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
563	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
564	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
565	C₂×C₄	C₉×#41	1	2	yes	—
566	C₂×C₄	C₉×#41	1	2	yes	—
567	C₂×C₃	—	2	4	no	—
568	C₂×C₃	—	4	2	no	—
569	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
570	C₂×C₃	C₃×#529	1	1	yes	characteristic
571	C₂×C₃	C₃×#538	1	1	yes	characteristic
572	C₂×C₃	C₃×#546	1	1	yes	characteristic
573	C₂×C₃	C₃×#546	1	1	yes	characteristic
574	C₂×C₃	C₃×#554	1	1	yes	characteristic
575	C₂×C₃	C₃×#554	1	1	yes	characteristic
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	C₉×C₂²⋊Q₈	1	4	yes	—
590	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
591	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
592	C₂²	C₂×C₉×#41	1	1	yes	characteristic
593	C₂²	C₂×C₉×#41	1	1	yes	characteristic
594	C₂²	C₂×C₉×#41	1	1	yes	characteristic
595	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
596	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	1	no	—
609	C₄	—	4	1	no	—
610	C₃	C₃×#2450	1	1	yes	characteristic
611	C₂	—	2	4	no	—
612	C₂	—	4	2	no	—
613	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
614	C₂	C₉×#529	1	1	yes	characteristic
615	C₂	C₉×#538	1	1	yes	characteristic
616	C₂	C₉×#546	1	1	yes	characteristic
617	C₂	C₉×#546	1	1	yes	characteristic
618	C₂	C₉×#554	1	1	yes	characteristic
619	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	C₂²×C₃×D₄	C₂²×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×C₂²⋊Q₈	C₂	semidirect
3. C₉×#400	C₂	semidirect
4. C₉×#398	C₂	semidirect
5. C₉×#396	C₂	semidirect
6. C₉×#393	C₂	semidirect
7. C₉×#391	C₂	semidirect
8. C₉×#387	C₂	semidirect
11. C₉×#385	C₂	semidirect
12. C₉×#385	C₂	semidirect
13. C₉×#385	C₂	semidirect
14. C₉×#380	C₂	semidirect
15. C₂×C₉×#95	C₂	semidirect
76. C₂×D₄×C₉	Q₈	semidirect
119. #2450	C₉	direct (N × H)
217. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
219. #400	C₂×C₉	semidirect
220. #398	C₂×C₉	semidirect
221. #396	C₂×C₉	semidirect
222. #393	C₂×C₉	semidirect
223. #391	C₂×C₉	semidirect
224. #387	C₂×C₉	semidirect
227. #385	C₂×C₉	semidirect
228. #385	C₂×C₉	semidirect
229. #385	C₂×C₉	semidirect
230. #380	C₂×C₉	semidirect
231. C₂×#95	C₂×C₉	semidirect
429. C₂×D₄	Q₈×C₉	semidirect
506. C₉	#2450	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×C₂²⋊Q₈	2
C₂×C₄×D₄×C₉	2
C₉×#400	2
C₉×#398	2
C₉×#396	2
C₉×#393	2
C₉×#391	2
C₉×#387	2
C₉×#386	2
C₉×#385	2
C₉×#380	2
C₂×C₉×#95	2
C₃×#2450	3

Subgroups — C9×#2450 #11767171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2450 #11767171