Subgroups — C₉×#3270 #11767991

Order 1152.

708 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#548	C₂	1	1	yes	maximal, characteristic
5	C₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#465	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#451	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#448	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#441	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#3270	C₃	1	1	yes	maximal, characteristic
17	C₂×C₉×#41	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
19	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
20	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
21	C₉×#137	—	2	4	no	—
22	C₂×C₉×Q₁₆	—	2	4	no	—
23	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
24	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₉×Q₁₆	C₂²	1	1	yes	characteristic
29	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₉×SD₁₆	C₂²	1	1	yes	characteristic
32	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
34	C₉×C₄⋊Q₈	—	2	1	no	—
35	C₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
36	C₉×#124	—	2	1	no	—
37	C₉×#124	C₂²	1	1	yes	characteristic
38	C₉×C₂²⋊Q₈	—	2	1	no	—
39	C₉×C₂²⋊Q₈	—	2	1	no	—
40	C₉×C₂²⋊Q₈	—	2	1	no	—
41	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₉×#121	—	2	1	no	—
45	C₉×#121	C₂²	1	1	yes	characteristic
46	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
47	C₄×Q₈×C₉	C₂²	1	1	yes	characteristic
48	C₄×D₄×C₉	—	2	1	no	—
49	C₄×D₄×C₉	—	2	1	no	—
50	C₄×D₄×C₉	C₂²	1	1	yes	characteristic
51	C₉×#106	C₂²	1	1	yes	characteristic
52	C₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
53	C₉×#103	C₂²	1	1	yes	characteristic
54	C₉×#103	C₂²	1	1	yes	characteristic
55	C₉×#103	C₂²	1	1	yes	characteristic
56	C₉×#103	C₂²	1	1	yes	characteristic
57	C₉×#103	C₂²	1	1	yes	characteristic
58	C₉×#102	C₂²	1	1	yes	characteristic
59	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₉×#97	C₂²	1	1	yes	characteristic
62	C₂×C₃×#137	C₂×C₃	1	1	yes	characteristic
63	C₂²×C₃×Q₁₆	C₂×C₃	1	1	yes	characteristic
64	C₃×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
65	C₃×#548	C₂×C₃	1	1	yes	characteristic
66	C₃×#497	C₂×C₃	1	1	yes	characteristic
67	C₃×#470	C₂×C₃	1	1	yes	characteristic
68	C₃×#465	C₂×C₃	1	1	yes	characteristic
69	C₃×#464	C₂×C₃	1	1	yes	characteristic
70	C₃×#462	C₂×C₃	1	1	yes	characteristic
71	C₃×#452	C₂×C₃	1	1	yes	characteristic
72	C₃×#451	C₂×C₃	1	1	yes	characteristic
73	C₃×#451	C₂×C₃	1	1	yes	characteristic
74	C₃×#448	C₂×C₃	1	1	yes	characteristic
75	C₃×#441	C₂×C₃	1	1	yes	characteristic
76	C₃×#435	C₂×C₃	1	1	yes	characteristic
77	C₉×#41	—	2	2	no	—
78	C₉×#41	—	4	1	no	—
79	C₂×Q₈×C₉	—	2	1	no	—
80	C₂×Q₈×C₉	—	2	1	no	—
81	C₂×Q₈×C₉	—	2	1	no	—
82	C₂×Q₈×C₉	—	2	2	no	—
83	C₂×Q₈×C₉	—	2	2	no	—
84	C₂×Q₈×C₉	—	2	2	no	—
85	C₂×Q₈×C₉	—	4	1	no	—
86	C₂×Q₈×C₉	—	4	1	no	—
87	C₂×Q₈×C₉	—	4	1	no	—
88	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
90	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
91	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
92	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
93	C₂×D₄×C₉	—	2	1	no	—
94	C₂×D₄×C₉	—	2	1	no	—
95	C₂×D₄×C₉	D₄	1	1	yes	characteristic
96	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
97	C₂²×C₄×C₉	—	2	1	no	—
98	C₂²×C₄×C₉	—	2	1	no	—
99	C₂²×C₄×C₉	—	2	1	no	—
100	C₂²×C₄×C₉	—	2	1	no	—
101	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
103	C₉×Q₁₆	—	2	2	no	—
104	C₉×Q₁₆	—	2	2	no	—
105	C₉×Q₁₆	—	2	2	no	—
106	C₉×Q₁₆	—	2	2	no	—
107	C₉×Q₁₆	—	4	1	no	—
108	C₉×Q₁₆	D₄	1	4	yes	complemented
109	C₉×SD₁₆	—	2	2	no	—
110	C₉×SD₁₆	—	2	2	no	—
111	C₉×SD₁₆	—	4	1	no	—
112	C₉×M₁₆	—	2	2	no	—
113	C₂×C₈×C₉	—	2	2	no	—
114	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
117	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
118	C₉×C₄⋊C₄	—	2	1	no	—
119	C₉×C₄⋊C₄	—	2	1	no	—
120	C₉×C₄⋊C₄	—	2	1	no	—
121	C₉×C₄⋊C₄	—	2	1	no	—
122	C₉×C₄⋊C₄	—	2	1	no	—
123	C₉×C₄⋊C₄	—	2	1	no	—
124	C₉×C₄⋊C₄	—	2	1	no	—
125	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
126	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
127	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₉×C₂²⋊C₄	—	2	1	no	—
129	C₉×C₂²⋊C₄	—	2	1	no	—
130	C₉×C₂²⋊C₄	—	2	1	no	—
131	C₉×C₂²⋊C₄	—	2	1	no	—
132	C₉×C₂²⋊C₄	—	2	1	no	—
133	C₉×C₂²⋊C₄	—	2	1	no	—
134	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
135	C₉×C₂²⋊C₄	D₄	1	1	yes	characteristic
136	C₄²×C₉	—	2	1	no	—
137	C₄²×C₉	—	2	1	no	—
138	C₄²×C₉	C₂³	1	1	yes	characteristic
139	#3270	C₉	1	1	yes	characteristic, direct product factor, Sylow
140	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
141	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
143	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
144	C₃×#137	—	2	4	no	—
145	C₂×C₃×Q₁₆	—	2	4	no	—
146	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₃×SD₁₆	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
156	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
157	C₃×C₄⋊Q₈	—	2	1	no	—
158	C₃×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₃×#124	—	2	1	no	—
160	C₃×#124	C₂²×C₃	1	1	yes	characteristic
161	C₃×C₂²⋊Q₈	—	2	1	no	—
162	C₃×C₂²⋊Q₈	—	2	1	no	—
163	C₃×C₂²⋊Q₈	—	2	1	no	—
164	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
165	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
166	C₃×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
167	C₃×#121	—	2	1	no	—
168	C₃×#121	C₂²×C₃	1	1	yes	characteristic
169	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
170	C₃×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
171	C₃×C₄×D₄	—	2	1	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	C₂²×C₃	1	1	yes	characteristic
174	C₃×#106	C₂²×C₃	1	1	yes	characteristic
175	C₃×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
176	C₃×#103	C₂²×C₃	1	1	yes	characteristic
177	C₃×#103	C₂²×C₃	1	1	yes	characteristic
178	C₃×#103	C₂²×C₃	1	1	yes	characteristic
179	C₃×#103	C₂²×C₃	1	1	yes	characteristic
180	C₃×#103	C₂²×C₃	1	1	yes	characteristic
181	C₃×#102	C₂²×C₃	1	1	yes	characteristic
182	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
183	C₃×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₃×#97	C₂²×C₃	1	1	yes	characteristic
185	C₂³×C₉	—	2	1	no	—
186	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
187	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
188	Q₈×C₉	—	2	1	no	—
189	Q₈×C₉	—	2	1	no	—
190	Q₈×C₉	—	2	1	no	—
191	Q₈×C₉	—	2	1	no	—
192	Q₈×C₉	—	2	1	no	—
193	Q₈×C₉	—	2	1	no	—
194	Q₈×C₉	—	2	1	no	—
195	Q₈×C₉	—	2	1	no	—
196	Q₈×C₉	—	4	2	no	—
197	Q₈×C₉	—	4	2	no	—
198	Q₈×C₉	—	4	2	no	—
199	Q₈×C₉	C₂×D₄	1	2	yes	—
200	Q₈×C₉	C₂×D₄	1	2	yes	—
201	D₄×C₉	—	2	2	no	—
202	D₄×C₉	—	2	1	no	—
203	D₄×C₉	—	2	1	no	—
204	D₄×C₉	—	4	2	no	—
205	D₄×C₉	—	4	2	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	—	2	1	no	—
216	C₂×C₄×C₉	—	2	1	no	—
217	C₂×C₄×C₉	—	4	2	no	—
218	C₂×C₄×C₉	—	4	2	no	—
219	C₂×C₄×C₉	—	4	2	no	—
220	C₂×C₄×C₉	—	4	2	no	—
221	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
222	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
223	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
224	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
225	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
226	C₈×C₉	—	2	1	no	—
227	C₈×C₉	—	2	1	no	—
228	C₈×C₉	—	2	1	no	—
229	C₈×C₉	C₂×D₄	1	2	yes	—
230	C₂×#137	C₂×C₉	1	1	yes	characteristic, complemented
231	C₂²×Q₁₆	C₂×C₉	1	1	yes	characteristic, complemented
232	D₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
233	#548	C₂×C₉	1	1	yes	characteristic
234	#497	C₂×C₉	1	1	yes	characteristic, complemented
235	#470	C₂×C₉	1	1	yes	characteristic, complemented
236	#465	C₂×C₉	1	1	yes	characteristic, complemented
237	#464	C₂×C₉	1	1	yes	characteristic, complemented
238	#462	C₂×C₉	1	1	yes	characteristic, complemented
239	#452	C₂×C₉	1	1	yes	characteristic, complemented
240	#451	C₂×C₉	1	1	yes	characteristic, complemented
241	#451	C₂×C₉	1	1	yes	characteristic, complemented
242	#448	C₂×C₉	1	1	yes	characteristic, complemented
243	#441	C₂×C₉	1	1	yes	characteristic, complemented
244	#435	C₂×C₉	1	1	yes	characteristic, complemented
245	C₃×#41	—	2	2	no	—
246	C₃×#41	—	4	1	no	—
247	C₂×C₃×Q₈	—	2	1	no	—
248	C₂×C₃×Q₈	—	2	1	no	—
249	C₂×C₃×Q₈	—	2	1	no	—
250	C₂×C₃×Q₈	—	2	2	no	—
251	C₂×C₃×Q₈	—	2	2	no	—
252	C₂×C₃×Q₈	—	2	2	no	—
253	C₂×C₃×Q₈	—	4	1	no	—
254	C₂×C₃×Q₈	—	4	1	no	—
255	C₂×C₃×Q₈	—	4	1	no	—
256	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
261	C₂×C₃×D₄	—	2	1	no	—
262	C₂×C₃×D₄	—	2	1	no	—
263	C₂×C₃×D₄	C₃×D₄	1	1	yes	characteristic
264	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₃×C₄	—	2	1	no	—
266	C₂²×C₃×C₄	—	2	1	no	—
267	C₂²×C₃×C₄	—	2	1	no	—
268	C₂²×C₃×C₄	—	2	1	no	—
269	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
271	C₃×Q₁₆	—	2	2	no	—
272	C₃×Q₁₆	—	2	2	no	—
273	C₃×Q₁₆	—	2	2	no	—
274	C₃×Q₁₆	—	2	2	no	—
275	C₃×Q₁₆	—	4	1	no	—
276	C₃×Q₁₆	C₃×D₄	1	4	yes	—
277	C₃×SD₁₆	—	2	2	no	—
278	C₃×SD₁₆	—	2	2	no	—
279	C₃×SD₁₆	—	4	1	no	—
280	C₃×M₁₆	—	2	2	no	—
281	C₂×C₃×C₈	—	2	2	no	—
282	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
283	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	—	2	1	no	—
288	C₃×C₄⋊C₄	—	2	1	no	—
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	—	2	1	no	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₄⋊C₄	—	2	1	no	—
293	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
294	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
295	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
296	C₃×C₂²⋊C₄	—	2	1	no	—
297	C₃×C₂²⋊C₄	—	2	1	no	—
298	C₃×C₂²⋊C₄	—	2	1	no	—
299	C₃×C₂²⋊C₄	—	2	1	no	—
300	C₃×C₂²⋊C₄	—	2	1	no	—
301	C₃×C₂²⋊C₄	—	2	1	no	—
302	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
303	C₃×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
304	C₃×C₄²	—	2	1	no	—
305	C₃×C₄²	—	2	1	no	—
306	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
307	C₂²×C₉	—	2	1	no	—
308	C₂²×C₉	—	2	1	no	—
309	C₂²×C₉	—	2	1	no	—
310	C₂²×C₉	—	2	1	no	—
311	C₂²×C₉	—	2	1	no	—
312	C₂²×C₉	—	4	1	no	—
313	C₂²×C₉	—	4	1	no	—
314	C₂²×C₉	—	4	1	no	—
315	C₂²×C₉	#137	1	2	yes	complemented
316	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
317	C₄×C₉	—	2	1	no	—
318	C₄×C₉	—	2	1	no	—
319	C₄×C₉	—	2	2	no	—
320	C₄×C₉	—	2	2	no	—
321	C₄×C₉	—	2	1	no	—
322	C₄×C₉	—	2	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	C₄×C₉	C₂²×D₄	1	1	yes	characteristic
329	C₄×C₉	H(5,𝔽₂)	1	1	yes	characteristic
330	C₂×#41	C₂²×C₉	1	1	yes	characteristic
331	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
332	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
333	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
334	#137	—	2	4	no	—
335	C₂×Q₁₆	—	2	4	no	—
336	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
337	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
338	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
339	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
340	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
341	C₂×Q₁₆	C₂²×C₉	1	1	yes	characteristic
342	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
343	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
344	C₂×SD₁₆	C₂²×C₉	1	1	yes	characteristic
345	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
346	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	C₂²×C₉	1	1	yes	characteristic
349	#124	—	2	1	no	—
350	#124	C₂²×C₉	1	1	yes	characteristic
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
355	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
356	C₂²⋊Q₈	C₂²×C₉	1	1	yes	characteristic
357	#121	—	2	1	no	—
358	#121	C₂²×C₉	1	1	yes	characteristic
359	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
360	C₄×Q₈	C₂²×C₉	1	1	yes	characteristic
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	C₂²×C₉	1	1	yes	characteristic
364	#106	C₂²×C₉	1	1	yes	characteristic
365	C₄⋊C₈	C₂²×C₉	1	1	yes	characteristic
366	#103	C₂²×C₉	1	1	yes	characteristic
367	#103	C₂²×C₉	1	1	yes	characteristic
368	#103	C₂²×C₉	1	1	yes	characteristic
369	#103	C₂²×C₉	1	1	yes	characteristic
370	#103	C₂²×C₉	1	1	yes	characteristic
371	#102	C₂²×C₉	1	1	yes	characteristic
372	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
373	C₂²⋊C₈	C₂²×C₉	1	1	yes	characteristic
374	#97	C₂²×C₉	1	1	yes	characteristic
375	C₂³×C₃	—	2	1	no	—
376	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
377	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
378	C₃×Q₈	—	2	1	no	—
379	C₃×Q₈	—	2	1	no	—
380	C₃×Q₈	—	2	1	no	—
381	C₃×Q₈	—	2	1	no	—
382	C₃×Q₈	—	2	1	no	—
383	C₃×Q₈	—	2	1	no	—
384	C₃×Q₈	—	2	1	no	—
385	C₃×Q₈	—	2	1	no	—
386	C₃×Q₈	—	4	2	no	—
387	C₃×Q₈	—	4	2	no	—
388	C₃×Q₈	—	4	2	no	—
389	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
390	C₃×Q₈	C₂×C₃×D₄	1	2	yes	—
391	C₃×D₄	—	2	2	no	—
392	C₃×D₄	—	2	1	no	—
393	C₃×D₄	—	2	1	no	—
394	C₃×D₄	—	4	2	no	—
395	C₃×D₄	—	4	2	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	—	4	2	no	—
408	C₂×C₃×C₄	—	4	2	no	—
409	C₂×C₃×C₄	—	4	2	no	—
410	C₂×C₃×C₄	—	4	2	no	—
411	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
412	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
413	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
415	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
416	C₃×C₈	—	2	1	no	—
417	C₃×C₈	—	2	1	no	—
418	C₃×C₈	—	2	1	no	—
419	C₃×C₈	C₂×C₃×D₄	1	2	yes	—
420	C₂×C₉	—	2	2	no	—
421	C₂×C₉	—	4	1	no	—
422	C₂×C₉	—	8	1	no	—
423	C₂×C₉	D₄²	1	1	yes	characteristic
424	C₂×C₉	C₂×#137	1	1	yes	characteristic
425	C₂×C₉	#578	1	1	yes	characteristic
426	#41	—	2	2	no	—
427	#41	—	4	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	4	1	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	—	4	1	no	—
437	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
438	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
439	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
440	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
441	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	D₄×C₉	1	1	yes	characteristic
445	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
451	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
452	Q₁₆	—	2	2	no	—
453	Q₁₆	—	2	2	no	—
454	Q₁₆	—	2	2	no	—
455	Q₁₆	—	2	2	no	—
456	Q₁₆	—	4	1	no	—
457	Q₁₆	D₄×C₉	1	4	yes	complemented
458	SD₁₆	—	2	2	no	—
459	SD₁₆	—	2	2	no	—
460	SD₁₆	—	4	1	no	—
461	M₁₆	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
464	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
465	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
466	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
476	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
477	C₂²⋊C₄	—	2	1	no	—
478	C₂²⋊C₄	—	2	1	no	—
479	C₂²⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
484	C₂²⋊C₄	D₄×C₉	1	1	yes	characteristic
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	C₂³×C₉	1	1	yes	characteristic
488	C₂²×C₃	—	2	1	no	—
489	C₂²×C₃	—	2	1	no	—
490	C₂²×C₃	—	2	1	no	—
491	C₂²×C₃	—	2	1	no	—
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	4	1	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	1	no	—
496	C₂²×C₃	C₃×#137	1	2	yes	—
497	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
498	C₃×C₄	—	2	1	no	—
499	C₃×C₄	—	2	1	no	—
500	C₃×C₄	—	2	1	no	—
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	2	no	—
503	C₃×C₄	—	2	2	no	—
504	C₃×C₄	—	4	1	no	—
505	C₃×C₄	—	4	1	no	—
506	C₃×C₄	—	4	1	no	—
507	C₃×C₄	—	4	1	no	—
508	C₃×C₄	—	4	1	no	—
509	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
510	C₃×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
511	C₉	#3270	1	1	yes	characteristic, direct product factor, Sylow
512	C₂³	—	2	1	no	—
513	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
514	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
515	Q₈	—	2	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	2	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	1	no	—
522	Q₈	—	2	1	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	Q₈	C₂×D₄×C₉	1	2	yes	—
527	Q₈	C₂×D₄×C₉	1	2	yes	—
528	D₄	—	2	2	no	—
529	D₄	—	2	1	no	—
530	D₄	—	2	1	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	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	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
549	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
550	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
552	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	C₂×D₄×C₉	1	2	yes	—
557	C₂×C₃	—	2	2	no	—
558	C₂×C₃	—	4	1	no	—
559	C₂×C₃	—	8	1	no	—
560	C₂×C₃	C₃×D₄²	1	1	yes	characteristic
561	C₂×C₃	C₂×C₃×#137	1	1	yes	characteristic
562	C₂×C₃	C₃×#578	1	1	yes	characteristic
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	C₉×#137	1	2	yes	complemented
572	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	C₂²×D₄×C₉	1	1	yes	characteristic
585	C₄	C₉×H(5,𝔽₂)	1	1	yes	characteristic
586	C₃	C₃×#3270	1	1	yes	characteristic
587	C₂	—	2	2	no	—
588	C₂	—	4	1	no	—
589	C₂	—	8	1	no	—
590	C₂	D₄²×C₉	1	1	yes	characteristic
591	C₂	C₂×C₉×#137	1	1	yes	characteristic
592	C₂	C₉×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₃×#548	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×D₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#137	C₂	semidirect
2. C₂²×C₉×Q₁₆	C₂	semidirect
3. D₄×Q₈×C₉	C₂	semidirect
5. C₉×#497	C₂	semidirect
6. C₉×#470	C₂	semidirect
7. C₉×#465	C₂	semidirect
8. C₉×#464	C₂	semidirect
9. C₉×#462	C₂	semidirect
10. C₉×#452	C₂	semidirect
11. C₉×#451	C₂	semidirect
12. C₉×#451	C₂	semidirect
13. C₉×#448	C₂	semidirect
14. C₉×#441	C₂	semidirect
15. C₉×#435	C₂	semidirect
108. C₉×Q₁₆	D₄	semidirect
139. #3270	C₉	direct (N × H)
230. C₂×#137	C₂×C₉	semidirect
231. C₂²×Q₁₆	C₂×C₉	semidirect
232. D₄×Q₈	C₂×C₉	semidirect
234. #497	C₂×C₉	semidirect
235. #470	C₂×C₉	semidirect
236. #465	C₂×C₉	semidirect
237. #464	C₂×C₉	semidirect
238. #462	C₂×C₉	semidirect
239. #452	C₂×C₉	semidirect
240. #451	C₂×C₉	semidirect
241. #451	C₂×C₉	semidirect
242. #448	C₂×C₉	semidirect
243. #441	C₂×C₉	semidirect
244. #435	C₂×C₉	semidirect
315. C₂²×C₉	#137	semidirect
457. Q₁₆	D₄×C₉	semidirect
511. C₉	#3270	direct (N × H)
571. C₂²	C₉×#137	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₉×#137	2
C₂²×C₉×Q₁₆	2
D₄×Q₈×C₉	2
C₉×#548	2
C₉×#497	2
C₉×#470	2
C₉×#465	2
C₉×#464	2
C₉×#462	2
C₉×#452	2
C₉×#451	2
C₉×#448	2
C₉×#441	2
C₉×#435	2
C₃×#3270	3

Subgroups — C9×#3270 #11767991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3270 #11767991