Subgroups — C₉×#5598 #13152799

Order 1728.

964 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#939	C₂	1	2	yes	maximal, complemented
5	C₉×#936	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₉×Dic₃	C₂	1	2	yes	maximal, complemented
7	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#885	C₂	1	2	yes	maximal, complemented
11	C₉×#878	C₂	1	2	yes	maximal, complemented
12	C₃×#5598	C₃	1	1	yes	maximal, characteristic
13	C₉×#548	—	3	1	no	maximal
14	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₃×D₄×C₉	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₉×#67	C₂²	1	2	yes	—
18	C₂×C₉×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
20	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
21	C₉×#237	—	2	4	no	—
22	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
23	C₂×C₉×Dic₆	—	2	4	no	—
24	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
25	C₂×C₉×Dic₆	C₂²	1	2	yes	—
26	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
27	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×C₉×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₉×#217	C₂²	1	1	yes	characteristic
30	C₉×#217	C₂²	1	2	yes	—
31	C₉×#217	C₂²	1	2	yes	—
32	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
35	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
38	C₄×C₉×Dic₃	C₂²	1	2	yes	—
39	C₂×C₃×#237	C₂×C₃	1	1	yes	characteristic
40	C₂²×C₃×Dic₆	C₂×C₃	1	1	yes	characteristic
41	C₃²×#121	C₂×C₃	1	1	yes	characteristic
42	C₃×#939	C₂×C₃	1	2	yes	—
43	C₃×#936	C₂×C₃	1	1	yes	characteristic
44	C₃×D₄×Dic₃	C₂×C₃	1	2	yes	—
45	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
46	C₃×#897	C₂×C₃	1	1	yes	characteristic
47	C₃×#887	C₂×C₃	1	1	yes	characteristic
48	C₃×#885	C₂×C₃	1	2	yes	—
49	C₃×#878	C₂×C₃	1	2	yes	—
50	C₂×C₉×#41	—	3	1	no	—
51	C₂²×Q₈×C₉	—	3	1	no	—
52	C₉×#124	—	3	1	no	—
53	C₉×#124	—	3	2	no	—
54	C₉×C₂²⋊Q₈	—	3	1	no	—
55	C₉×C₂²⋊Q₈	—	3	2	no	—
56	C₉×#121	—	2	1	no	—
57	C₉×#121	—	3	2	no	—
58	C₉×#121	D₃	1	1	yes	characteristic, complemented
59	C₄×Q₈×C₉	—	3	1	no	—
60	C₄×D₄×C₉	—	3	2	no	—
61	C₄×D₄×C₉	—	3	1	no	—
62	C₂³×C₃×C₉	C₂³	1	2	yes	—
63	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
64	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
65	C₃×D₄×C₉	—	2	4	no	—
66	C₃×D₄×C₉	—	2	2	no	—
67	C₂×C₃×C₄×C₉	—	2	2	no	—
68	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
70	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
71	C₉×#67	—	2	2	no	—
72	C₉×#67	—	2	4	no	—
73	C₂×C₉×Dic₃	—	2	4	no	—
74	C₂×C₉×Dic₃	—	2	4	no	—
75	C₂×C₉×Dic₃	C₂³	1	2	yes	—
76	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
78	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₉×Dic₃	C₂³	1	2	yes	—
80	C₄×D₃×C₉	—	2	2	no	—
81	C₉×Dic₆	—	2	2	no	—
82	C₉×Dic₆	—	2	4	no	—
83	C₉×Dic₆	D₄	1	4	yes	complemented
84	C₃×#548	—	3	1	no	—
85	#5598	C₉	1	1	yes	characteristic, direct product factor
86	C₂×C₃²×D₄	C₂²×C₃	1	2	yes	—
87	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
88	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×#67	C₂²×C₃	1	2	yes	—
90	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
92	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
93	C₃×#237	—	2	4	no	—
94	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₃×Dic₆	—	2	4	no	—
96	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
97	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
99	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₃×#217	C₂²×C₃	1	2	yes	—
102	C₃×#217	C₂²×C₃	1	2	yes	—
103	C₃×#217	C₂²×C₃	1	1	yes	characteristic
104	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
106	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
107	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
108	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
109	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
110	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
111	C₉×#41	—	6	4	no	—
112	C₂×Q₈×C₉	—	3	1	no	—
113	C₂×Q₈×C₉	—	3	2	no	—
114	C₂×Q₈×C₉	—	3	1	no	—
115	C₂×Q₈×C₉	—	6	4	no	—
116	C₂×D₄×C₉	—	2	1	no	—
117	C₂×D₄×C₉	—	2	2	no	—
118	C₂×D₄×C₉	—	3	1	no	—
119	C₂×D₄×C₉	—	3	2	no	—
120	C₂×D₄×C₉	C₂×D₃	1	2	yes	—
121	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
122	C₂²×C₄×C₉	—	2	1	no	—
123	C₂²×C₄×C₉	—	3	2	no	—
124	C₂²×C₄×C₉	—	3	2	no	—
125	C₂²×C₄×C₉	—	3	1	no	—
126	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
127	C₉×C₄⋊C₄	—	2	1	no	—
128	C₉×C₄⋊C₄	—	3	1	no	—
129	C₉×C₄⋊C₄	—	3	2	no	—
130	C₉×C₄⋊C₄	—	3	2	no	—
131	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₉×C₂²⋊C₄	—	2	2	no	—
133	C₉×C₂²⋊C₄	—	3	1	no	—
134	C₉×C₂²⋊C₄	—	3	2	no	—
135	C₉×C₂²⋊C₄	—	3	2	no	—
136	C₉×C₂²⋊C₄	—	3	1	no	—
137	C₉×C₂²⋊C₄	—	3	2	no	—
138	C₉×C₂²⋊C₄	C₂×D₃	1	2	yes	—
139	C₄²×C₉	—	3	2	no	—
140	C₄²×C₉	—	3	1	no	—
141	C₂²×C₃×C₉	—	2	1	no	—
142	C₂²×C₃×C₉	—	2	1	no	—
143	C₂²×C₃×C₉	—	2	2	no	—
144	C₂²×C₃×C₉	—	2	2	no	—
145	C₂²×C₃×C₉	—	2	2	no	—
146	C₂²×C₃×C₉	#41	1	2	yes	complemented
147	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
148	C₂×D₃×C₉	—	2	1	no	—
149	C₂×D₃×C₉	—	2	1	no	—
150	C₂×D₃×C₉	—	2	1	no	—
151	C₃×C₄×C₉	—	2	1	no	—
152	C₃×C₄×C₉	—	2	2	no	—
153	C₃×C₄×C₉	C₂×D₄	1	2	yes	—
154	C₉×Dic₃	—	2	2	no	—
155	C₉×Dic₃	—	2	1	no	—
156	C₉×Dic₃	—	2	1	no	—
157	C₉×Dic₃	—	2	1	no	—
158	C₉×Dic₃	C₂×D₄	1	4	yes	—
159	C₂×C₃×#41	—	3	1	no	—
160	C₂²×C₃×Q₈	—	3	1	no	—
161	C₂×#237	C₂×C₉	1	1	yes	characteristic, complemented
162	C₂²×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
163	C₃×#124	—	3	1	no	—
164	C₃×#124	—	3	2	no	—
165	C₃×C₂²⋊Q₈	—	3	1	no	—
166	C₃×C₂²⋊Q₈	—	3	2	no	—
167	C₃×#121	—	2	1	no	—
168	C₃×#121	—	3	2	no	—
169	C₃×#121	C₂×C₉	1	1	yes	characteristic, complemented
170	C₃×#121	C₃×D₃	1	1	yes	characteristic
171	C₃×C₄×Q₈	—	3	1	no	—
172	C₃×C₄×D₄	—	3	2	no	—
173	C₃×C₄×D₄	—	3	1	no	—
174	#939	C₂×C₉	1	2	yes	complemented
175	#936	C₂×C₉	1	1	yes	characteristic, complemented
176	D₄×Dic₃	C₂×C₉	1	2	yes	complemented
177	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
178	#897	C₂×C₉	1	1	yes	characteristic, complemented
179	#887	C₂×C₉	1	1	yes	characteristic, complemented
180	#885	C₂×C₉	1	2	yes	complemented
181	#878	C₂×C₉	1	2	yes	complemented
182	C₂³×C₃²	C₂³×C₃	1	2	yes	—
183	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
185	C₃²×D₄	—	2	4	no	—
186	C₃²×D₄	—	2	2	no	—
187	C₂×C₃²×C₄	—	2	2	no	—
188	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
189	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
191	C₃×#67	—	2	2	no	—
192	C₃×#67	—	2	4	no	—
193	C₂×C₃×Dic₃	—	2	4	no	—
194	C₂×C₃×Dic₃	—	2	4	no	—
195	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
199	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
200	C₃×C₄×D₃	—	2	2	no	—
201	C₃×Dic₆	—	2	2	no	—
202	C₃×Dic₆	—	2	4	no	—
203	C₃×Dic₆	C₃×D₄	1	4	yes	—
204	C₂³×C₉	—	2	1	no	—
205	C₂³×C₉	—	2	2	no	—
206	C₂³×C₉	—	3	1	no	—
207	C₂³×C₉	C₂²×D₃	1	2	yes	—
208	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
209	Q₈×C₉	—	3	4	no	—
210	Q₈×C₉	—	6	4	no	—
211	Q₈×C₉	—	6	2	no	—
212	D₄×C₉	—	2	4	no	—
213	D₄×C₉	—	2	2	no	—
214	D₄×C₉	—	4	2	no	—
215	D₄×C₉	—	4	4	no	—
216	D₄×C₉	—	6	4	no	—
217	D₄×C₉	—	6	2	no	—
218	C₂×C₄×C₉	—	2	2	no	—
219	C₂×C₄×C₉	—	2	1	no	—
220	C₂×C₄×C₉	—	2	1	no	—
221	C₂×C₄×C₉	—	2	2	no	—
222	C₂×C₄×C₉	—	3	2	no	—
223	C₂×C₄×C₉	—	3	1	no	—
224	C₂×C₄×C₉	—	3	1	no	—
225	C₂×C₄×C₉	—	3	2	no	—
226	C₂×C₄×C₉	—	3	1	no	—
227	C₂×C₄×C₉	—	4	2	no	—
228	C₂×C₄×C₉	—	6	4	no	—
229	C₂×C₄×C₉	—	6	4	no	—
230	C₂×C₄×C₉	—	6	2	no	—
231	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
232	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
234	#548	—	3	1	no	Sylow
235	C₂×C₃×C₉	—	2	2	no	—
236	C₂×C₃×C₉	—	4	2	no	—
237	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
239	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
240	D₃×C₉	—	4	1	no	—
241	C₃×#41	—	6	4	no	—
242	C₂×C₃×Q₈	—	3	1	no	—
243	C₂×C₃×Q₈	—	3	2	no	—
244	C₂×C₃×Q₈	—	3	1	no	—
245	C₂×C₃×Q₈	—	6	4	no	—
246	C₂×C₃×D₄	—	2	2	no	—
247	C₂×C₃×D₄	—	2	1	no	—
248	C₂×C₃×D₄	—	3	1	no	—
249	C₂×C₃×D₄	—	3	2	no	—
250	C₂×C₃×D₄	C₂²×C₉	1	2	yes	—
251	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
252	C₂×C₃×D₄	C₂×C₃×D₃	1	2	yes	—
253	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
254	C₂²×C₃×C₄	—	2	1	no	—
255	C₂²×C₃×C₄	—	3	2	no	—
256	C₂²×C₃×C₄	—	3	2	no	—
257	C₂²×C₃×C₄	—	3	1	no	—
258	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
260	C₂×#67	C₂²×C₉	1	2	yes	—
261	C₂×#67	C₂²×C₉	1	1	yes	characteristic
262	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
263	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
264	#237	—	2	4	no	—
265	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
266	C₂×Dic₆	—	2	4	no	—
267	C₂×Dic₆	C₂²×C₉	1	2	yes	—
268	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
269	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	3	1	no	—
272	C₃×C₄⋊C₄	—	3	2	no	—
273	C₃×C₄⋊C₄	—	3	2	no	—
274	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
275	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	—	2	2	no	—
277	C₃×C₂²⋊C₄	—	3	1	no	—
278	C₃×C₂²⋊C₄	—	3	2	no	—
279	C₃×C₂²⋊C₄	—	3	2	no	—
280	C₃×C₂²⋊C₄	—	3	1	no	—
281	C₃×C₂²⋊C₄	—	3	2	no	—
282	C₃×C₂²⋊C₄	C₂²×C₉	1	2	yes	—
283	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
284	C₃×C₄²	—	3	2	no	—
285	C₃×C₄²	—	3	1	no	—
286	#217	C₂²×C₉	1	2	yes	—
287	#217	C₂²×C₉	1	2	yes	—
288	#217	C₂²×C₉	1	1	yes	characteristic
289	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
290	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
291	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
292	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic
293	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
294	C₄×Dic₃	C₂²×C₉	1	2	yes	—
295	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
296	C₂²×C₃²	—	2	1	no	—
297	C₂²×C₃²	—	2	1	no	—
298	C₂²×C₃²	—	2	2	no	—
299	C₂²×C₃²	—	2	2	no	—
300	C₂²×C₃²	—	2	2	no	—
301	C₂²×C₃²	C₃×#41	1	2	yes	—
302	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
303	C₂×C₃×D₃	—	2	1	no	—
304	C₂×C₃×D₃	—	2	1	no	—
305	C₂×C₃×D₃	—	2	1	no	—
306	C₃²×C₄	—	2	1	no	—
307	C₃²×C₄	—	2	2	no	—
308	C₃²×C₄	C₂×C₃×D₄	1	2	yes	—
309	C₃×Dic₃	—	2	2	no	—
310	C₃×Dic₃	—	2	1	no	—
311	C₃×Dic₃	—	2	1	no	—
312	C₃×Dic₃	—	2	1	no	—
313	C₃×Dic₃	C₂×C₃×D₄	1	4	yes	—
314	C₂²×C₉	—	2	1	no	—
315	C₂²×C₉	—	2	1	no	—
316	C₂²×C₉	—	2	2	no	—
317	C₂²×C₉	—	2	2	no	—
318	C₂²×C₉	—	2	2	no	—
319	C₂²×C₉	—	2	1	no	—
320	C₂²×C₉	—	2	2	no	—
321	C₂²×C₉	—	4	1	no	—
322	C₂²×C₉	—	4	1	no	—
323	C₂²×C₉	—	4	2	no	—
324	C₂²×C₉	—	4	2	no	—
325	C₂²×C₉	—	4	2	no	—
326	C₂²×C₉	—	6	1	no	—
327	C₂²×C₉	—	6	1	no	—
328	C₂²×C₉	—	6	1	no	—
329	C₂²×C₉	#237	1	2	yes	complemented
330	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
331	C₄×C₉	—	2	1	no	—
332	C₄×C₉	—	2	2	no	—
333	C₄×C₉	—	2	2	no	—
334	C₄×C₉	—	3	4	no	—
335	C₄×C₉	—	4	1	no	—
336	C₄×C₉	—	4	2	no	—
337	C₄×C₉	—	6	1	no	—
338	C₄×C₉	—	6	2	no	—
339	C₄×C₉	—	6	1	no	—
340	C₄×C₉	—	6	1	no	—
341	C₄×C₉	D₃×D₄	1	2	yes	—
342	C₂×#41	—	3	1	no	—
343	C₂²×Q₈	—	3	1	no	—
344	#124	—	3	1	no	—
345	#124	—	3	2	no	—
346	C₂²⋊Q₈	—	3	1	no	—
347	C₂²⋊Q₈	—	3	2	no	—
348	#121	—	3	2	no	—
349	#121	D₃×C₉	1	1	yes	characteristic, complemented
350	C₄×Q₈	—	3	1	no	—
351	C₄×D₄	—	3	2	no	—
352	C₄×D₄	—	3	1	no	—
353	C₃×C₉	#548	1	1	yes	characteristic, complemented, Sylow
354	C₂³×C₃	—	2	1	no	—
355	C₂³×C₃	—	2	2	no	—
356	C₂³×C₃	—	3	1	no	—
357	C₂³×C₃	C₂³×C₉	1	2	yes	—
358	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
359	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
360	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
361	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
362	C₃×Q₈	—	3	4	no	—
363	C₃×Q₈	—	6	4	no	—
364	C₃×Q₈	—	6	2	no	—
365	C₃×D₄	—	2	4	no	—
366	C₃×D₄	—	2	4	no	—
367	C₃×D₄	—	2	2	no	—
368	C₃×D₄	—	2	2	no	—
369	C₃×D₄	—	4	2	no	—
370	C₃×D₄	—	4	4	no	—
371	C₃×D₄	—	6	4	no	—
372	C₃×D₄	—	6	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	3	2	no	—
379	C₂×C₃×C₄	—	3	1	no	—
380	C₂×C₃×C₄	—	3	1	no	—
381	C₂×C₃×C₄	—	3	2	no	—
382	C₂×C₃×C₄	—	3	1	no	—
383	C₂×C₃×C₄	—	4	2	no	—
384	C₂×C₃×C₄	—	6	4	no	—
385	C₂×C₃×C₄	—	6	4	no	—
386	C₂×C₃×C₄	—	6	2	no	—
387	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
388	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
391	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
393	#67	—	2	2	no	—
394	#67	—	2	4	no	—
395	C₂×Dic₃	—	2	4	no	—
396	C₂×Dic₃	—	2	4	no	—
397	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
398	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
399	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
400	C₂×Dic₃	C₂³×C₉	1	2	yes	—
401	C₂×Dic₃	C₂³×C₉	1	2	yes	—
402	C₄×D₃	—	2	2	no	—
403	Dic₆	—	2	2	no	—
404	Dic₆	—	2	4	no	—
405	Dic₆	D₄×C₉	1	4	yes	complemented
406	C₂×C₃²	—	2	2	no	—
407	C₂×C₃²	—	4	2	no	—
408	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
409	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
410	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
411	C₃×D₃	—	4	1	no	—
412	C₂×C₉	—	2	2	no	—
413	C₂×C₉	—	2	1	no	—
414	C₂×C₉	—	2	1	no	—
415	C₂×C₉	—	2	1	no	—
416	C₂×C₉	—	4	2	no	—
417	C₂×C₉	—	4	2	no	—
418	C₂×C₉	—	8	2	no	—
419	C₂×C₉	—	12	1	no	—
420	C₂×C₉	C₂×D₃×D₄	1	1	yes	characteristic
421	C₂×C₉	C₂×#237	1	1	yes	characteristic
422	C₂×C₉	#1010	1	1	yes	characteristic
423	#41	—	6	4	no	—
424	C₂×Q₈	—	3	1	no	—
425	C₂×Q₈	—	3	2	no	—
426	C₂×Q₈	—	3	1	no	—
427	C₂×Q₈	—	6	4	no	—
428	C₂×D₄	—	3	1	no	—
429	C₂×D₄	—	3	2	no	—
430	C₂×D₄	C₂×D₃×C₉	1	2	yes	—
431	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
432	C₂²×C₄	—	3	2	no	—
433	C₂²×C₄	—	3	2	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
436	C₄⋊C₄	—	3	1	no	—
437	C₄⋊C₄	—	3	2	no	—
438	C₄⋊C₄	—	3	2	no	—
439	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
440	C₂²⋊C₄	—	3	1	no	—
441	C₂²⋊C₄	—	3	2	no	—
442	C₂²⋊C₄	—	3	2	no	—
443	C₂²⋊C₄	—	3	1	no	—
444	C₂²⋊C₄	—	3	2	no	—
445	C₂²⋊C₄	C₂×D₃×C₉	1	2	yes	—
446	C₄²	—	3	2	no	—
447	C₄²	—	3	1	no	—
448	C₂²×C₃	—	2	1	no	—
449	C₂²×C₃	—	2	1	no	—
450	C₂²×C₃	—	2	1	no	—
451	C₂²×C₃	—	2	1	no	—
452	C₂²×C₃	—	2	2	no	—
453	C₂²×C₃	—	2	2	no	—
454	C₂²×C₃	—	2	2	no	—
455	C₂²×C₃	—	2	2	no	—
456	C₂²×C₃	—	2	2	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	2	1	no	—
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	4	1	no	—
461	C₂²×C₃	—	4	1	no	—
462	C₂²×C₃	—	4	2	no	—
463	C₂²×C₃	—	4	2	no	—
464	C₂²×C₃	—	4	2	no	—
465	C₂²×C₃	—	6	1	no	—
466	C₂²×C₃	—	6	1	no	—
467	C₂²×C₃	—	6	1	no	—
468	C₂²×C₃	C₉×#41	1	2	yes	complemented
469	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
470	C₂²×C₃	C₃×#237	1	2	yes	—
471	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
472	C₂×D₃	—	2	1	no	—
473	C₂×D₃	—	2	1	no	—
474	C₂×D₃	—	2	1	no	—
475	C₃×C₄	—	2	1	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	2	1	no	—
478	C₃×C₄	—	2	2	no	—
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	3	4	no	—
481	C₃×C₄	—	4	1	no	—
482	C₃×C₄	—	4	2	no	—
483	C₃×C₄	—	6	1	no	—
484	C₃×C₄	—	6	2	no	—
485	C₃×C₄	—	6	1	no	—
486	C₃×C₄	—	6	1	no	—
487	C₃×C₄	C₂×D₄×C₉	1	2	yes	—
488	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
489	Dic₃	—	2	2	no	—
490	Dic₃	—	2	1	no	—
491	Dic₃	—	2	1	no	—
492	Dic₃	—	2	1	no	—
493	Dic₃	C₂×D₄×C₉	1	4	yes	—
494	C₃²	C₃×#548	1	1	yes	characteristic
495	C₉	—	2	1	no	—
496	C₉	#5598	1	1	yes	characteristic, direct product factor
497	C₂³	—	3	1	no	—
498	C₂³	C₂²×D₃×C₉	1	2	yes	—
499	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
500	Q₈	—	3	4	no	—
501	Q₈	—	6	4	no	—
502	Q₈	—	6	2	no	—
503	D₄	—	2	4	no	—
504	D₄	—	2	2	no	—
505	D₄	—	6	4	no	—
506	D₄	—	6	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	3	2	no	—
509	C₂×C₄	—	3	1	no	—
510	C₂×C₄	—	3	1	no	—
511	C₂×C₄	—	3	2	no	—
512	C₂×C₄	—	3	1	no	—
513	C₂×C₄	—	6	4	no	—
514	C₂×C₄	—	6	4	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
517	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
518	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
519	C₂×C₃	—	2	2	no	—
520	C₂×C₃	—	2	2	no	—
521	C₂×C₃	—	2	1	no	—
522	C₂×C₃	—	2	1	no	—
523	C₂×C₃	—	2	1	no	—
524	C₂×C₃	—	4	2	no	—
525	C₂×C₃	—	4	2	no	—
526	C₂×C₃	—	4	2	no	—
527	C₂×C₃	—	8	2	no	—
528	C₂×C₃	—	12	1	no	—
529	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
530	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
531	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
532	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
533	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
534	C₂×C₃	C₃×#1010	1	1	yes	characteristic
535	D₃	—	4	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	6	1	no	—
542	C₂²	—	6	1	no	—
543	C₂²	—	6	1	no	—
544	C₂²	C₉×#237	1	2	yes	complemented
545	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
546	C₄	—	2	1	no	—
547	C₄	—	2	2	no	—
548	C₄	—	3	4	no	—
549	C₄	—	6	1	no	—
550	C₄	—	6	2	no	—
551	C₄	—	6	1	no	—
552	C₄	—	6	1	no	—
553	C₄	D₃×D₄×C₉	1	2	yes	—
554	C₃	—	2	1	no	—
555	C₃	C₉×#548	1	1	yes	characteristic, complemented
556	C₃	C₃×#5598	1	1	yes	characteristic
557	C₂	—	2	2	no	—
558	C₂	—	4	2	no	—
559	C₂	—	12	1	no	—
560	C₂	C₂×D₃×D₄×C₉	1	1	yes	characteristic
561	C₂	C₂×C₉×#237	1	1	yes	characteristic
562	C₂	C₉×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#121	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5598	C₃
hypercenter	C₉×#121	D₃
hypocenter	C₃	C₉×#548
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×#237	C₂	semidirect
2. C₂²×C₉×Dic₆	C₂	semidirect
3. C₃×C₉×#121	C₂	semidirect
4. C₉×#939	C₂	semidirect
5. C₉×#936	C₂	semidirect
6. D₄×C₉×Dic₃	C₂	semidirect
7. C₄×C₉×#67	C₂	semidirect
8. C₉×#897	C₂	semidirect
9. C₉×#887	C₂	semidirect
10. C₉×#885	C₂	semidirect
11. C₉×#878	C₂	semidirect
58. C₉×#121	D₃	semidirect
83. C₉×Dic₆	D₄	semidirect
85. #5598	C₉	direct (N × H)
146. C₂²×C₃×C₉	#41	semidirect
161. C₂×#237	C₂×C₉	semidirect
162. C₂²×Dic₆	C₂×C₉	semidirect
169. C₃×#121	C₂×C₉	semidirect
174. #939	C₂×C₉	semidirect
175. #936	C₂×C₉	semidirect
176. D₄×Dic₃	C₂×C₉	semidirect
177. C₄×#67	C₂×C₉	semidirect
178. #897	C₂×C₉	semidirect
179. #887	C₂×C₉	semidirect
180. #885	C₂×C₉	semidirect
181. #878	C₂×C₉	semidirect
329. C₂²×C₉	#237	semidirect
349. #121	D₃×C₉	semidirect
353. C₃×C₉	#548	semidirect
405. Dic₆	D₄×C₉	semidirect
468. C₂²×C₃	C₉×#41	semidirect
496. C₉	#5598	direct (N × H)
544. C₂²	C₉×#237	semidirect
555. C₃	C₉×#548	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₉×#237	2
C₂²×C₉×Dic₆	2
C₃×C₉×#121	2
C₉×#939	2
C₉×#936	2
D₄×C₉×Dic₃	2
C₄×C₉×#67	2
C₉×#897	2
C₉×#887	2
C₉×#885	2
C₉×#878	2
C₃×#5598	3
C₉×#548	3

Subgroups — C9×#5598 #13152799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5598 #13152799