Subgroups — C₉×#2449 #11767170

Order 1152.

972 conjugacy classes of subgroups.

The subgroup lattice has 639 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×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×D₄×C₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₉×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#399	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#398	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#396	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#395	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#387	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#386	C₂	1	1	yes	maximal, characteristic
12	C₉×#386	C₂	1	1	yes	maximal, characteristic
13	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#2449	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	C₉×C₂²⋊Q₈	—	2	4	no	—
25	C₄×D₄×C₉	—	2	4	no	—
26	C₂×C₉×C₄⋊C₄	—	2	4	no	—
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₉×C₄⋊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×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₄²×C₉	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	C₉×#95	C₂²	1	1	yes	characteristic
55	C₉×#95	C₂²	1	1	yes	characteristic
56	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
58	C₂×C₃×C₄×D₄	C₂×C₃	1	1	yes	characteristic
59	C₂²×C₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
60	C₃×#399	C₂×C₃	1	1	yes	characteristic
61	C₃×#398	C₂×C₃	1	1	yes	characteristic
62	C₃×#396	C₂×C₃	1	1	yes	characteristic
63	C₃×#395	C₂×C₃	1	1	yes	characteristic
64	C₃×#389	C₂×C₃	1	1	yes	characteristic
65	C₃×#387	C₂×C₃	1	1	yes	characteristic
66	C₃×#386	C₂×C₃	1	1	yes	characteristic
67	C₃×#386	C₂×C₃	1	1	yes	characteristic
68	C₃×#385	C₂×C₃	1	1	yes	characteristic
69	C₃×#385	C₂×C₃	1	1	yes	characteristic
70	C₃×#385	C₂×C₃	1	1	yes	characteristic
71	C₂⁴×C₉	C₂³	1	1	yes	characteristic
72	C₂⁴×C₉	C₂³	1	1	yes	characteristic
73	C₂×Q₈×C₉	—	2	2	no	—
74	C₂×Q₈×C₉	—	2	2	no	—
75	C₂×Q₈×C₉	—	4	1	no	—
76	C₂×D₄×C₉	—	2	2	no	—
77	C₂×D₄×C₉	—	2	2	no	—
78	C₂×D₄×C₉	Q₈	1	4	yes	complemented
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	—	2	2	no	—
85	C₂²×C₄×C₉	—	2	2	no	—
86	C₂²×C₄×C₉	—	2	2	no	—
87	C₂²×C₄×C₉	—	2	2	no	—
88	C₂²×C₄×C₉	—	4	1	no	—
89	C₂²×C₄×C₉	—	4	1	no	—
90	C₂²×C₄×C₉	—	4	1	no	—
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	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
108	C₉×C₄⋊C₄	—	2	2	no	—
109	C₉×C₄⋊C₄	—	2	2	no	—
110	C₉×C₄⋊C₄	—	2	2	no	—
111	C₉×C₄⋊C₄	—	2	2	no	—
112	C₉×C₄⋊C₄	—	2	2	no	—
113	C₉×C₄⋊C₄	—	2	2	no	—
114	C₉×C₄⋊C₄	—	4	1	no	—
115	C₉×C₄⋊C₄	D₄	1	4	yes	complemented
116	C₉×C₂²⋊C₄	—	2	2	no	—
117	C₉×C₂²⋊C₄	—	2	2	no	—
118	C₉×C₂²⋊C₄	—	2	2	no	—
119	C₉×C₂²⋊C₄	—	2	2	no	—
120	C₉×C₂²⋊C₄	—	2	2	no	—
121	C₉×C₂²⋊C₄	—	2	2	no	—
122	C₉×C₂²⋊C₄	—	4	1	no	—
123	C₉×C₂²⋊C₄	D₄	1	4	yes	—
124	C₄²×C₉	—	2	2	no	—
125	#2449	C₉	1	1	yes	characteristic, direct product factor, Sylow
126	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
127	C₂²×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
128	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
129	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
132	C₃×C₂²⋊Q₈	—	2	4	no	—
133	C₃×C₂²⋊Q₈	—	2	4	no	—
134	C₃×C₄×D₄	—	2	4	no	—
135	C₂×C₃×C₄⋊C₄	—	2	4	no	—
136	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
157	C₃×#95	C₂²×C₃	1	1	yes	characteristic
158	C₃×#95	C₂²×C₃	1	1	yes	characteristic
159	C₃×#95	C₂²×C₃	1	1	yes	characteristic
160	C₃×#95	C₂²×C₃	1	1	yes	characteristic
161	C₃×#95	C₂²×C₃	1	1	yes	characteristic
162	C₃×#95	C₂²×C₃	1	1	yes	characteristic
163	C₃×#95	C₂²×C₃	1	1	yes	characteristic
164	C₃×#95	C₂²×C₃	1	1	yes	characteristic
165	C₂³×C₉	—	2	1	no	—
166	C₂³×C₉	—	2	1	no	—
167	C₂³×C₉	—	2	1	no	—
168	C₂³×C₉	—	2	1	no	—
169	C₂³×C₉	—	2	1	no	—
170	C₂³×C₉	—	2	1	no	—
171	C₂³×C₉	—	2	1	no	—
172	C₂³×C₉	—	2	1	no	—
173	C₂³×C₉	—	2	1	no	—
174	C₂³×C₉	—	2	1	no	—
175	C₂³×C₉	C₂×D₄	1	2	yes	—
176	C₂³×C₉	C₂×Q₈	1	2	yes	—
177	C₂³×C₉	C₂×Q₈	1	2	yes	—
178	C₂³×C₉	#41	1	2	yes	—
179	C₂³×C₉	C₂⁴	1	1	yes	characteristic
180	Q₈×C₉	—	4	4	no	—
181	D₄×C₉	—	2	8	no	—
182	C₂×C₄×C₉	—	2	8	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	—	2	1	no	—
209	C₂×C₄×C₉	—	2	1	no	—
210	C₂×C₄×C₉	—	2	1	no	—
211	C₂×C₄×C₉	—	2	1	no	—
212	C₂×C₄×C₉	—	2	1	no	—
213	C₂×C₄×C₉	—	2	1	no	—
214	C₂×C₄×C₉	—	2	1	no	—
215	C₂×C₄×C₉	—	4	4	no	—
216	C₂×C₄×C₉	—	4	4	no	—
217	C₂×C₄×C₉	—	4	4	no	—
218	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
219	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
220	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
221	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
222	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
223	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
224	C₂×C₄×C₉	#41	1	2	yes	—
225	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
226	C₂×C₂²⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
227	C₂×C₄×D₄	C₂×C₉	1	1	yes	characteristic
228	C₂²×C₄⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
229	#399	C₂×C₉	1	1	yes	characteristic, complemented
230	#398	C₂×C₉	1	1	yes	characteristic, complemented
231	#396	C₂×C₉	1	1	yes	characteristic, complemented
232	#395	C₂×C₉	1	1	yes	characteristic, complemented
233	#389	C₂×C₉	1	1	yes	characteristic, complemented
234	#387	C₂×C₉	1	1	yes	characteristic, complemented
235	#386	C₂×C₉	1	1	yes	characteristic
236	#386	C₂×C₉	1	1	yes	characteristic
237	#385	C₂×C₉	1	1	yes	characteristic, complemented
238	#385	C₂×C₉	1	1	yes	characteristic, complemented
239	#385	C₂×C₉	1	1	yes	characteristic, complemented
240	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
241	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
242	C₂×C₃×Q₈	—	2	2	no	—
243	C₂×C₃×Q₈	—	2	2	no	—
244	C₂×C₃×Q₈	—	4	1	no	—
245	C₂×C₃×D₄	—	2	2	no	—
246	C₂×C₃×D₄	—	2	2	no	—
247	C₂×C₃×D₄	C₃×Q₈	1	4	yes	—
248	C₂²×C₃×C₄	—	2	2	no	—
249	C₂²×C₃×C₄	—	2	2	no	—
250	C₂²×C₃×C₄	—	2	2	no	—
251	C₂²×C₃×C₄	—	2	2	no	—
252	C₂²×C₃×C₄	—	2	2	no	—
253	C₂²×C₃×C₄	—	2	2	no	—
254	C₂²×C₃×C₄	—	2	2	no	—
255	C₂²×C₃×C₄	—	2	2	no	—
256	C₂²×C₃×C₄	—	2	2	no	—
257	C₂²×C₃×C₄	—	4	1	no	—
258	C₂²×C₃×C₄	—	4	1	no	—
259	C₂²×C₃×C₄	—	4	1	no	—
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	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
266	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
271	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
273	C₃×C₄⋊C₄	—	2	2	no	—
274	C₃×C₄⋊C₄	—	2	2	no	—
275	C₃×C₄⋊C₄	—	2	2	no	—
276	C₃×C₄⋊C₄	—	2	2	no	—
277	C₃×C₄⋊C₄	—	2	2	no	—
278	C₃×C₄⋊C₄	—	2	2	no	—
279	C₃×C₄⋊C₄	—	2	2	no	—
280	C₃×C₄⋊C₄	—	2	2	no	—
281	C₃×C₄⋊C₄	—	2	2	no	—
282	C₃×C₄⋊C₄	—	2	2	no	—
283	C₃×C₄⋊C₄	—	4	1	no	—
284	C₃×C₄⋊C₄	C₃×D₄	1	4	yes	—
285	C₃×C₂²⋊C₄	—	2	2	no	—
286	C₃×C₂²⋊C₄	—	2	2	no	—
287	C₃×C₂²⋊C₄	—	2	2	no	—
288	C₃×C₂²⋊C₄	—	2	2	no	—
289	C₃×C₂²⋊C₄	—	2	2	no	—
290	C₃×C₂²⋊C₄	—	2	2	no	—
291	C₃×C₂²⋊C₄	—	4	1	no	—
292	C₃×C₂²⋊C₄	C₃×D₄	1	4	yes	—
293	C₃×C₄²	—	2	2	no	—
294	C₂²×C₉	—	2	2	no	—
295	C₂²×C₉	—	2	2	no	—
296	C₂²×C₉	—	2	2	no	—
297	C₂²×C₉	—	2	2	no	—
298	C₂²×C₉	—	2	2	no	—
299	C₂²×C₉	—	2	2	no	—
300	C₂²×C₉	—	2	2	no	—
301	C₂²×C₉	—	2	2	no	—
302	C₂²×C₉	—	2	2	no	—
303	C₂²×C₉	—	4	1	no	—
304	C₂²×C₉	—	4	1	no	—
305	C₂²×C₉	—	4	1	no	—
306	C₂²×C₉	—	4	1	no	—
307	C₂²×C₉	C₂²⋊Q₈	1	4	yes	complemented
308	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
309	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
310	C₂²×C₉	C₂²×Q₈	1	1	yes	characteristic
311	C₂²×C₉	C₂×#41	1	1	yes	characteristic
312	C₂²×C₉	C₂×#41	1	1	yes	characteristic
313	C₂²×C₉	H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₉	2₋¹⁺⁴	1	1	yes	characteristic
315	C₄×C₉	—	2	2	no	—
316	C₄×C₉	—	2	2	no	—
317	C₄×C₉	—	2	2	no	—
318	C₄×C₉	—	2	2	no	—
319	C₄×C₉	—	2	2	no	—
320	C₄×C₉	—	2	2	no	—
321	C₄×C₉	—	2	2	no	—
322	C₄×C₉	—	4	1	no	—
323	C₄×C₉	—	4	1	no	—
324	C₄×C₉	—	4	1	no	—
325	C₄×C₉	—	4	1	no	—
326	C₄×C₉	—	4	1	no	—
327	C₄×C₉	—	4	1	no	—
328	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
329	C₂²×D₄	C₂²×C₉	1	1	yes	characteristic
330	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
331	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
332	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
333	C₂³×C₄	C₂²×C₉	1	1	yes	characteristic
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	C₄×D₄	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
346	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
356	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
358	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
359	#95	C₂²×C₉	1	1	yes	characteristic
360	#95	C₂²×C₉	1	1	yes	characteristic
361	#95	C₂²×C₉	1	1	yes	characteristic
362	#95	C₂²×C₉	1	1	yes	characteristic
363	#95	C₂²×C₉	1	1	yes	characteristic
364	#95	C₂²×C₉	1	1	yes	characteristic
365	#95	C₂²×C₉	1	1	yes	characteristic
366	#95	C₂²×C₉	1	1	yes	characteristic
367	C₂³×C₃	—	2	1	no	—
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	—	2	1	no	—
370	C₂³×C₃	—	2	1	no	—
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	—	2	1	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂³×C₃	—	2	1	no	—
376	C₂³×C₃	—	2	1	no	—
377	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
378	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
379	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
380	C₂³×C₃	C₃×#41	1	2	yes	—
381	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
382	C₃×Q₈	—	4	4	no	—
383	C₃×D₄	—	2	8	no	—
384	C₂×C₃×C₄	—	2	8	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	—	2	1	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	1	no	—
407	C₂×C₃×C₄	—	2	1	no	—
408	C₂×C₃×C₄	—	2	1	no	—
409	C₂×C₃×C₄	—	2	1	no	—
410	C₂×C₃×C₄	—	2	1	no	—
411	C₂×C₃×C₄	—	2	1	no	—
412	C₂×C₃×C₄	—	2	1	no	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	1	no	—
415	C₂×C₃×C₄	—	2	1	no	—
416	C₂×C₃×C₄	—	2	1	no	—
417	C₂×C₃×C₄	—	4	4	no	—
418	C₂×C₃×C₄	—	4	4	no	—
419	C₂×C₃×C₄	—	4	4	no	—
420	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
421	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
422	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
423	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
424	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
425	C₂×C₃×C₄	C₂×C₃×Q₈	1	2	yes	—
426	C₂×C₃×C₄	C₃×#41	1	2	yes	—
427	C₂×C₉	—	2	4	no	—
428	C₂×C₉	—	4	2	no	—
429	C₂×C₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
430	C₂×C₉	#525	1	1	yes	characteristic
431	C₂×C₉	#539	1	1	yes	characteristic
432	C₂×C₉	D₄²	1	1	yes	characteristic
433	C₂×C₉	#547	1	1	yes	characteristic
434	C₂×C₉	D₄×Q₈	1	1	yes	characteristic
435	C₂×C₉	#554	1	1	yes	characteristic
436	C₂⁴	C₂³×C₉	1	1	yes	characteristic
437	C₂⁴	C₂³×C₉	1	1	yes	characteristic
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	2	no	—
440	C₂×Q₈	—	4	1	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	Q₈×C₉	1	4	yes	complemented
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
457	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
458	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
459	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
460	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
461	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
462	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
463	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
464	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
465	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
466	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
467	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
468	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	4	1	no	—
480	C₄⋊C₄	D₄×C₉	1	4	yes	complemented
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	D₄×C₉	1	4	yes	—
489	C₄²	—	2	2	no	—
490	C₂²×C₃	—	2	2	no	—
491	C₂²×C₃	—	2	2	no	—
492	C₂²×C₃	—	2	2	no	—
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	2	2	no	—
495	C₂²×C₃	—	2	2	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	2	2	no	—
499	C₂²×C₃	—	4	1	no	—
500	C₂²×C₃	—	4	1	no	—
501	C₂²×C₃	—	4	1	no	—
502	C₂²×C₃	—	4	1	no	—
503	C₂²×C₃	C₃×C₂²⋊Q₈	1	4	yes	—
504	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
505	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
506	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
507	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
508	C₂²×C₃	C₂×C₃×#41	1	1	yes	characteristic
509	C₂²×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂²×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	2	no	—
513	C₃×C₄	—	2	2	no	—
514	C₃×C₄	—	2	2	no	—
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	—	4	1	no	—
519	C₃×C₄	—	4	1	no	—
520	C₃×C₄	—	4	1	no	—
521	C₃×C₄	—	4	1	no	—
522	C₃×C₄	—	4	1	no	—
523	C₃×C₄	—	4	1	no	—
524	C₉	#2449	1	1	yes	characteristic, direct product factor, Sylow
525	C₂³	—	2	1	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	1	no	—
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	C₂×D₄×C₉	1	2	yes	—
536	C₂³	C₂×Q₈×C₉	1	2	yes	—
537	C₂³	C₂×Q₈×C₉	1	2	yes	—
538	C₂³	C₉×#41	1	2	yes	—
539	C₂³	C₂⁴×C₉	1	1	yes	characteristic
540	Q₈	—	4	4	no	—
541	D₄	—	2	8	no	—
542	C₂×C₄	—	2	8	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	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	4	4	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
579	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
580	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
581	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
582	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
583	C₂×C₄	C₂×Q₈×C₉	1	2	yes	—
584	C₂×C₄	C₉×#41	1	2	yes	—
585	C₂×C₃	—	2	4	no	—
586	C₂×C₃	—	4	2	no	—
587	C₂×C₃	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
588	C₂×C₃	C₃×#525	1	1	yes	characteristic
589	C₂×C₃	C₃×#539	1	1	yes	characteristic
590	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
591	C₂×C₃	C₃×#547	1	1	yes	characteristic
592	C₂×C₃	C₃×D₄×Q₈	1	1	yes	characteristic
593	C₂×C₃	C₃×#554	1	1	yes	characteristic
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	C₉×C₂²⋊Q₈	1	4	yes	complemented
608	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
609	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
610	C₂²	C₂²×Q₈×C₉	1	1	yes	characteristic
611	C₂²	C₂×C₉×#41	1	1	yes	characteristic
612	C₂²	C₂×C₉×#41	1	1	yes	characteristic
613	C₂²	C₉×H(5,𝔽₂)	1	1	yes	characteristic
614	C₂²	C₉×2₋¹⁺⁴	1	1	yes	characteristic
615	C₄	—	2	2	no	—
616	C₄	—	2	2	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	4	1	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₃	C₃×#2449	1	1	yes	characteristic
629	C₂	—	2	4	no	—
630	C₂	—	4	2	no	—
631	C₂	C₂×C₉×C₂²⋊Q₈	1	1	yes	characteristic
632	C₂	C₉×#525	1	1	yes	characteristic
633	C₂	C₉×#539	1	1	yes	characteristic
634	C₂	D₄²×C₉	1	1	yes	characteristic
635	C₂	C₉×#547	1	1	yes	characteristic
636	C₂	D₄×Q₈×C₉	1	1	yes	characteristic
637	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
2. C₂×C₉×C₂²⋊Q₈	C₂	semidirect
4. C₂²×C₉×C₄⋊C₄	C₂	semidirect
5. C₉×#399	C₂	semidirect
6. C₉×#398	C₂	semidirect
7. C₉×#396	C₂	semidirect
8. C₉×#395	C₂	semidirect
9. C₉×#389	C₂	semidirect
10. C₉×#387	C₂	semidirect
13. C₉×#385	C₂	semidirect
14. C₉×#385	C₂	semidirect
15. C₉×#385	C₂	semidirect
78. C₂×D₄×C₉	Q₈	semidirect
115. C₉×C₄⋊C₄	D₄	semidirect
125. #2449	C₉	direct (N × H)
225. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
226. C₂×C₂²⋊Q₈	C₂×C₉	semidirect
228. C₂²×C₄⋊C₄	C₂×C₉	semidirect
229. #399	C₂×C₉	semidirect
230. #398	C₂×C₉	semidirect
231. #396	C₂×C₉	semidirect
232. #395	C₂×C₉	semidirect
233. #389	C₂×C₉	semidirect
234. #387	C₂×C₉	semidirect
237. #385	C₂×C₉	semidirect
238. #385	C₂×C₉	semidirect
239. #385	C₂×C₉	semidirect
307. C₂²×C₉	C₂²⋊Q₈	semidirect
443. C₂×D₄	Q₈×C₉	semidirect
480. C₄⋊C₄	D₄×C₉	semidirect
524. C₉	#2449	direct (N × H)
607. C₂²	C₉×C₂²⋊Q₈	semidirect

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
C₂²×C₉×C₄⋊C₄	2
C₉×#399	2
C₉×#398	2
C₉×#396	2
C₉×#395	2
C₉×#389	2
C₉×#387	2
C₉×#386	2
C₉×#385	2
C₃×#2449	3

Subgroups — C9×#2449 #11767170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#2449 #11767170