Subgroups — C₉×#5658 #13153028

Order 1728.

822 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#937	C₂	1	1	yes	maximal, characteristic
3	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#898	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#897	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#892	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	D₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5658	C₃	1	1	yes	maximal, characteristic
17	C₉×#551	—	3	1	no	maximal
18	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
21	C₂×C₉×#67	C₂²	1	1	yes	characteristic
22	C₂×C₉×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
24	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic
27	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₉×#217	C₂²	1	1	yes	characteristic
34	C₉×#217	C₂²	1	1	yes	characteristic
35	C₉×#217	C₂²	1	1	yes	characteristic, complemented
36	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
48	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
51	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic, complemented
53	C₃²×#123	C₂×C₃	1	1	yes	characteristic
54	C₃×#937	C₂×C₃	1	1	yes	characteristic
55	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
56	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic
57	C₃×#926	C₂×C₃	1	1	yes	characteristic
58	C₃×#898	C₂×C₃	1	1	yes	characteristic
59	C₃×#898	C₂×C₃	1	1	yes	characteristic
60	C₃×#897	C₂×C₃	1	1	yes	characteristic
61	C₃×#892	C₂×C₃	1	1	yes	characteristic
62	C₃×#886	C₂×C₃	1	1	yes	characteristic
63	C₃×#885	C₂×C₃	1	1	yes	characteristic
64	C₃×#883	C₂×C₃	1	1	yes	characteristic
65	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
66	C₃×D₃×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
67	C₃×#878	C₂×C₃	1	1	yes	characteristic
68	C₉×#126	—	3	1	no	—
69	C₉×#126	—	3	1	no	—
70	C₉×#124	—	3	1	no	—
71	C₉×#123	—	2	1	no	—
72	C₉×#123	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×#123	D₃	1	1	yes	characteristic, complemented
75	C₉×C₂²⋊Q₈	—	3	1	no	—
76	C₉×C₂²⋊Q₈	—	3	1	no	—
77	C₉×#120	—	3	1	no	—
78	C₄×D₄×C₉	—	3	1	no	—
79	C₄×D₄×C₉	—	3	1	no	—
80	C₉×#117	—	3	1	no	—
81	C₉×#117	—	3	1	no	—
82	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
83	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
84	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
85	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
86	C₂²×D₃×C₉	—	2	2	no	—
87	C₂²×D₃×C₉	—	2	2	no	—
88	C₂²×D₃×C₉	—	4	1	no	—
89	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
90	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
91	C₃×D₄×C₉	—	2	2	no	—
92	C₂×C₃×C₄×C₉	—	2	2	no	—
93	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
98	C₉×#67	—	2	2	no	—
99	C₉×#67	—	4	1	no	—
100	C₂×C₉×Dic₃	—	4	1	no	—
101	C₂×C₉×Dic₃	—	4	1	no	—
102	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
103	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
104	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
106	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
107	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
108	C₄×D₃×C₉	—	2	2	no	—
109	C₄×D₃×C₉	—	4	1	no	—
110	C₉×Dic₆	—	4	1	no	—
111	C₃×#551	—	3	1	no	—
112	#5658	C₉	1	1	yes	characteristic, direct product factor
113	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
118	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₃×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
123	C₂⁴×C₉	—	3	1	no	—
124	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₃²×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	C₃×#217	C₂²×C₃	1	1	yes	characteristic
130	C₃×#217	C₂²×C₃	1	1	yes	characteristic
131	C₃×#217	C₂²×C₃	1	1	yes	characteristic
132	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
141	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
142	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
143	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
144	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₃×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
147	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
148	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
149	C₂×Q₈×C₉	—	3	1	no	—
150	C₂×D₄×C₉	—	2	1	no	—
151	C₂×D₄×C₉	—	3	1	no	—
152	C₂×D₄×C₉	—	3	1	no	—
153	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
154	C₂²×C₄×C₉	—	2	1	no	—
155	C₂²×C₄×C₉	—	3	1	no	—
156	C₂²×C₄×C₉	—	3	1	no	—
157	C₂²×C₄×C₉	—	3	1	no	—
158	C₂²×C₄×C₉	—	3	1	no	—
159	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
160	C₉×C₄⋊C₄	—	2	1	no	—
161	C₉×C₄⋊C₄	—	2	1	no	—
162	C₉×C₄⋊C₄	—	3	1	no	—
163	C₉×C₄⋊C₄	—	3	1	no	—
164	C₉×C₄⋊C₄	—	3	1	no	—
165	C₉×C₄⋊C₄	—	3	1	no	—
166	C₉×C₄⋊C₄	—	3	1	no	—
167	C₉×C₄⋊C₄	—	3	1	no	—
168	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
169	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
170	C₉×C₂²⋊C₄	—	2	1	no	—
171	C₉×C₂²⋊C₄	—	2	1	no	—
172	C₉×C₂²⋊C₄	—	2	1	no	—
173	C₉×C₂²⋊C₄	—	3	1	no	—
174	C₉×C₂²⋊C₄	—	3	1	no	—
175	C₉×C₂²⋊C₄	—	3	1	no	—
176	C₉×C₂²⋊C₄	—	3	1	no	—
177	C₉×C₂²⋊C₄	—	3	1	no	—
178	C₉×C₂²⋊C₄	—	3	1	no	—
179	C₉×C₂²⋊C₄	—	3	1	no	—
180	C₉×C₂²⋊C₄	—	3	1	no	—
181	C₉×C₂²⋊C₄	—	3	1	no	—
182	C₉×C₂²⋊C₄	—	3	1	no	—
183	C₉×C₂²⋊C₄	—	3	1	no	—
184	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
185	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
186	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
187	C₄²×C₉	—	3	1	no	—
188	C₄²×C₉	—	3	1	no	—
189	C₄²×C₉	—	3	1	no	—
190	C₂²×C₃×C₉	—	2	1	no	—
191	C₂²×C₃×C₉	—	2	1	no	—
192	C₂²×C₃×C₉	—	2	1	no	—
193	C₂²×C₃×C₉	—	2	1	no	—
194	C₂²×C₃×C₉	—	2	1	no	—
195	C₂²×C₃×C₉	#41	1	2	yes	—
196	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
197	C₂×D₃×C₉	—	2	1	no	—
198	C₂×D₃×C₉	—	2	1	no	—
199	C₂×D₃×C₉	—	2	1	no	—
200	C₂×D₃×C₉	—	2	1	no	—
201	C₂×D₃×C₉	—	2	1	no	—
202	C₂×D₃×C₉	—	4	4	no	—
203	C₂×D₃×C₉	#41	1	2	yes	—
204	C₃×C₄×C₉	—	2	1	no	—
205	C₃×C₄×C₉	—	2	1	no	—
206	C₃×C₄×C₉	—	2	1	no	—
207	C₃×C₄×C₉	—	2	1	no	—
208	C₃×C₄×C₉	—	2	1	no	—
209	C₉×Dic₃	—	2	1	no	—
210	C₉×Dic₃	—	2	1	no	—
211	C₉×Dic₃	—	2	1	no	—
212	C₉×Dic₃	—	2	1	no	—
213	C₉×Dic₃	—	2	1	no	—
214	C₉×Dic₃	—	2	1	no	—
215	C₃×#126	—	3	1	no	—
216	C₃×#126	—	3	1	no	—
217	C₃×#124	—	3	1	no	—
218	C₃×#123	—	2	1	no	—
219	C₃×#123	—	3	1	no	—
220	C₃×#123	—	3	1	no	—
221	C₃×#123	C₂×C₉	1	1	yes	characteristic, complemented
222	C₃×#123	C₃×D₃	1	1	yes	characteristic
223	C₃×C₂²⋊Q₈	—	3	1	no	—
224	C₃×C₂²⋊Q₈	—	3	1	no	—
225	C₃×#120	—	3	1	no	—
226	C₃×C₄×D₄	—	3	1	no	—
227	C₃×C₄×D₄	—	3	1	no	—
228	C₃×#117	—	3	1	no	—
229	C₃×#117	—	3	1	no	—
230	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
231	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
232	#937	C₂×C₉	1	1	yes	characteristic
233	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
234	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
235	#926	C₂×C₉	1	1	yes	characteristic, complemented
236	#898	C₂×C₉	1	1	yes	characteristic, complemented
237	#898	C₂×C₉	1	1	yes	characteristic, complemented
238	#897	C₂×C₉	1	1	yes	characteristic, complemented
239	#892	C₂×C₉	1	1	yes	characteristic, complemented
240	#886	C₂×C₉	1	1	yes	characteristic, complemented
241	#885	C₂×C₉	1	1	yes	characteristic, complemented
242	#883	C₂×C₉	1	1	yes	characteristic, complemented
243	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
244	D₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
245	#878	C₂×C₉	1	1	yes	characteristic, complemented
246	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
247	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
248	C₂²×C₃×D₃	—	2	2	no	—
249	C₂²×C₃×D₃	—	2	2	no	—
250	C₂²×C₃×D₃	—	4	1	no	—
251	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
253	C₃²×D₄	—	2	2	no	—
254	C₂×C₃²×C₄	—	2	2	no	—
255	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
256	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
260	C₃×#67	—	2	2	no	—
261	C₃×#67	—	4	1	no	—
262	C₂×C₃×Dic₃	—	4	1	no	—
263	C₂×C₃×Dic₃	—	4	1	no	—
264	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
267	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
268	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
270	C₃×C₄×D₃	—	2	2	no	—
271	C₃×C₄×D₃	—	4	1	no	—
272	C₃×Dic₆	—	4	1	no	—
273	C₂³×C₉	—	2	1	no	—
274	C₂³×C₉	—	2	1	no	—
275	C₂³×C₉	—	3	1	no	—
276	C₂³×C₉	—	3	1	no	—
277	C₂³×C₉	—	6	2	no	—
278	C₂³×C₉	—	6	2	no	—
279	C₂³×C₉	—	12	1	no	—
280	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
281	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
282	Q₈×C₉	—	12	1	no	—
283	D₄×C₉	—	2	2	no	—
284	D₄×C₉	—	4	2	no	—
285	D₄×C₉	—	6	2	no	—
286	D₄×C₉	—	12	1	no	—
287	C₂×C₄×C₉	—	2	2	no	—
288	C₂×C₄×C₉	—	2	1	no	—
289	C₂×C₄×C₉	—	2	1	no	—
290	C₂×C₄×C₉	—	2	1	no	—
291	C₂×C₄×C₉	—	2	1	no	—
292	C₂×C₄×C₉	—	2	1	no	—
293	C₂×C₄×C₉	—	3	1	no	—
294	C₂×C₄×C₉	—	3	1	no	—
295	C₂×C₄×C₉	—	3	1	no	—
296	C₂×C₄×C₉	—	3	1	no	—
297	C₂×C₄×C₉	—	3	1	no	—
298	C₂×C₄×C₉	—	3	1	no	—
299	C₂×C₄×C₉	—	4	2	no	—
300	C₂×C₄×C₉	—	6	2	no	—
301	C₂×C₄×C₉	—	12	1	no	—
302	C₂×C₄×C₉	—	12	1	no	—
303	C₂×C₄×C₉	—	12	1	no	—
304	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
305	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
306	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
307	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
308	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
309	#551	—	3	1	no	Sylow
310	C₂×C₃×C₉	—	2	2	no	—
311	C₂×C₃×C₉	—	4	1	no	—
312	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
313	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
314	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
315	D₃×C₉	—	2	2	no	—
316	D₃×C₉	—	4	1	no	—
317	C₂⁴×C₃	—	3	1	no	—
318	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
319	C₂×C₃×Q₈	—	3	1	no	—
320	C₂×C₃×D₄	—	2	1	no	—
321	C₂×C₃×D₄	—	3	1	no	—
322	C₂×C₃×D₄	—	3	1	no	—
323	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
324	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
325	C₂²×C₃×C₄	—	2	1	no	—
326	C₂²×C₃×C₄	—	3	1	no	—
327	C₂²×C₃×C₄	—	3	1	no	—
328	C₂²×C₃×C₄	—	3	1	no	—
329	C₂²×C₃×C₄	—	3	1	no	—
330	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
331	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
332	C₂×#67	C₂²×C₉	1	1	yes	characteristic
333	C₂×#67	C₂²×C₉	1	1	yes	characteristic
334	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
335	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
336	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
337	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic
338	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
339	C₃×C₄⋊C₄	—	2	1	no	—
340	C₃×C₄⋊C₄	—	2	1	no	—
341	C₃×C₄⋊C₄	—	3	1	no	—
342	C₃×C₄⋊C₄	—	3	1	no	—
343	C₃×C₄⋊C₄	—	3	1	no	—
344	C₃×C₄⋊C₄	—	3	1	no	—
345	C₃×C₄⋊C₄	—	3	1	no	—
346	C₃×C₄⋊C₄	—	3	1	no	—
347	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
348	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
349	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
350	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
351	C₃×C₂²⋊C₄	—	2	1	no	—
352	C₃×C₂²⋊C₄	—	2	1	no	—
353	C₃×C₂²⋊C₄	—	2	1	no	—
354	C₃×C₂²⋊C₄	—	3	1	no	—
355	C₃×C₂²⋊C₄	—	3	1	no	—
356	C₃×C₂²⋊C₄	—	3	1	no	—
357	C₃×C₂²⋊C₄	—	3	1	no	—
358	C₃×C₂²⋊C₄	—	3	1	no	—
359	C₃×C₂²⋊C₄	—	3	1	no	—
360	C₃×C₂²⋊C₄	—	3	1	no	—
361	C₃×C₂²⋊C₄	—	3	1	no	—
362	C₃×C₂²⋊C₄	—	3	1	no	—
363	C₃×C₂²⋊C₄	—	3	1	no	—
364	C₃×C₂²⋊C₄	—	3	1	no	—
365	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
366	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
367	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
368	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
369	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
370	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
371	C₃×C₄²	—	3	1	no	—
372	C₃×C₄²	—	3	1	no	—
373	C₃×C₄²	—	3	1	no	—
374	#217	C₂²×C₉	1	1	yes	characteristic
375	#217	C₂²×C₉	1	1	yes	characteristic
376	#217	C₂²×C₉	1	1	yes	characteristic, complemented
377	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
378	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
379	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
380	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
381	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
382	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
383	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
384	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic
385	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
386	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
387	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
388	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
389	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
390	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
391	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
392	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
393	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
394	C₂²×C₃²	—	2	1	no	—
395	C₂²×C₃²	—	2	1	no	—
396	C₂²×C₃²	—	2	1	no	—
397	C₂²×C₃²	—	2	1	no	—
398	C₂²×C₃²	—	2	1	no	—
399	C₂²×C₃²	C₃×#41	1	2	yes	—
400	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
401	C₂×C₃×D₃	—	2	1	no	—
402	C₂×C₃×D₃	—	2	1	no	—
403	C₂×C₃×D₃	—	2	1	no	—
404	C₂×C₃×D₃	—	2	1	no	—
405	C₂×C₃×D₃	—	2	1	no	—
406	C₂×C₃×D₃	—	4	4	no	—
407	C₂×C₃×D₃	C₃×#41	1	2	yes	—
408	C₃²×C₄	—	2	1	no	—
409	C₃²×C₄	—	2	1	no	—
410	C₃²×C₄	—	2	1	no	—
411	C₃²×C₄	—	2	1	no	—
412	C₃²×C₄	—	2	1	no	—
413	C₃×Dic₃	—	2	1	no	—
414	C₃×Dic₃	—	2	1	no	—
415	C₃×Dic₃	—	2	1	no	—
416	C₃×Dic₃	—	2	1	no	—
417	C₃×Dic₃	—	2	1	no	—
418	C₃×Dic₃	—	2	1	no	—
419	C₂²×C₉	—	2	1	no	—
420	C₂²×C₉	—	2	1	no	—
421	C₂²×C₉	—	2	1	no	—
422	C₂²×C₉	—	2	1	no	—
423	C₂²×C₉	—	2	1	no	—
424	C₂²×C₉	—	2	1	no	—
425	C₂²×C₉	—	2	2	no	—
426	C₂²×C₉	—	3	2	no	—
427	C₂²×C₉	—	4	1	no	—
428	C₂²×C₉	—	4	1	no	—
429	C₂²×C₉	—	4	1	no	—
430	C₂²×C₉	—	4	1	no	—
431	C₂²×C₉	—	4	1	no	—
432	C₂²×C₉	—	6	1	no	—
433	C₂²×C₉	—	6	1	no	—
434	C₂²×C₉	—	6	1	no	—
435	C₂²×C₉	—	6	1	no	—
436	C₂²×C₉	—	6	1	no	—
437	C₂²×C₉	—	12	4	no	—
438	C₂²×C₉	#237	1	2	yes	—
439	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
440	C₄×C₉	—	2	1	no	—
441	C₄×C₉	—	2	1	no	—
442	C₄×C₉	—	2	1	no	—
443	C₄×C₉	—	2	1	no	—
444	C₄×C₉	—	2	1	no	—
445	C₄×C₉	—	4	1	no	—
446	C₄×C₉	—	4	1	no	—
447	C₄×C₉	—	4	1	no	—
448	C₄×C₉	—	4	1	no	—
449	C₄×C₉	—	4	1	no	—
450	C₄×C₉	—	6	1	no	—
451	C₄×C₉	—	6	1	no	—
452	C₄×C₉	—	6	1	no	—
453	C₄×C₉	—	6	1	no	—
454	C₄×C₉	—	6	1	no	—
455	C₄×C₉	—	6	1	no	—
456	#126	—	3	1	no	—
457	#126	—	3	1	no	—
458	#124	—	3	1	no	—
459	#123	—	3	1	no	—
460	#123	—	3	1	no	—
461	#123	D₃×C₉	1	1	yes	characteristic, complemented
462	C₂²⋊Q₈	—	3	1	no	—
463	C₂²⋊Q₈	—	3	1	no	—
464	#120	—	3	1	no	—
465	C₄×D₄	—	3	1	no	—
466	C₄×D₄	—	3	1	no	—
467	#117	—	3	1	no	—
468	#117	—	3	1	no	—
469	C₂×C₂²⋊C₄	—	3	1	no	—
470	C₂×C₂²⋊C₄	—	3	1	no	—
471	C₃×C₉	#551	1	1	yes	characteristic, complemented, Sylow
472	C₂³×C₃	—	2	1	no	—
473	C₂³×C₃	—	2	1	no	—
474	C₂³×C₃	—	3	1	no	—
475	C₂³×C₃	—	3	1	no	—
476	C₂³×C₃	—	6	2	no	—
477	C₂³×C₃	—	6	2	no	—
478	C₂³×C₃	—	12	1	no	—
479	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
480	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
481	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
482	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
483	C₂²×D₃	—	2	2	no	—
484	C₂²×D₃	—	2	2	no	—
485	C₂²×D₃	—	4	1	no	—
486	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
487	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
488	C₃×Q₈	—	12	1	no	—
489	C₃×D₄	—	2	2	no	—
490	C₃×D₄	—	2	2	no	—
491	C₃×D₄	—	4	2	no	—
492	C₃×D₄	—	6	2	no	—
493	C₃×D₄	—	12	1	no	—
494	C₂×C₃×C₄	—	2	2	no	—
495	C₂×C₃×C₄	—	2	2	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	3	1	no	—
502	C₂×C₃×C₄	—	3	1	no	—
503	C₂×C₃×C₄	—	3	1	no	—
504	C₂×C₃×C₄	—	3	1	no	—
505	C₂×C₃×C₄	—	3	1	no	—
506	C₂×C₃×C₄	—	3	1	no	—
507	C₂×C₃×C₄	—	4	2	no	—
508	C₂×C₃×C₄	—	6	2	no	—
509	C₂×C₃×C₄	—	12	1	no	—
510	C₂×C₃×C₄	—	12	1	no	—
511	C₂×C₃×C₄	—	12	1	no	—
512	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
513	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
514	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
515	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
516	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
517	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
518	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
519	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
520	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
521	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
522	#67	—	2	2	no	—
523	#67	—	4	1	no	—
524	C₂×Dic₃	—	4	1	no	—
525	C₂×Dic₃	—	4	1	no	—
526	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
527	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
528	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
529	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
530	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
531	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
532	C₄×D₃	—	2	2	no	—
533	C₄×D₃	—	4	1	no	—
534	Dic₆	—	4	1	no	—
535	C₂×C₃²	—	2	2	no	—
536	C₂×C₃²	—	4	1	no	—
537	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
538	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
539	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
540	C₃×D₃	—	2	2	no	—
541	C₃×D₃	—	4	1	no	—
542	C₂×C₉	—	2	2	no	—
543	C₂×C₉	—	2	1	no	—
544	C₂×C₉	—	2	1	no	—
545	C₂×C₉	—	2	1	no	—
546	C₂×C₉	—	4	2	no	—
547	C₂×C₉	—	4	1	no	—
548	C₂×C₉	—	6	2	no	—
549	C₂×C₉	—	8	1	no	—
550	C₂×C₉	—	12	1	no	—
551	C₂×C₉	C₂×#237	1	1	yes	characteristic
552	C₂×C₉	D₃×#41	1	1	yes	characteristic
553	C₂×C₉	#1009	1	1	yes	characteristic
554	C₂⁴	—	3	1	no	—
555	C₂×Q₈	—	3	1	no	—
556	C₂×D₄	—	3	1	no	—
557	C₂×D₄	—	3	1	no	—
558	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
559	C₂²×C₄	—	3	1	no	—
560	C₂²×C₄	—	3	1	no	—
561	C₂²×C₄	—	3	1	no	—
562	C₂²×C₄	—	3	1	no	—
563	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
564	C₄⋊C₄	—	3	1	no	—
565	C₄⋊C₄	—	3	1	no	—
566	C₄⋊C₄	—	3	1	no	—
567	C₄⋊C₄	—	3	1	no	—
568	C₄⋊C₄	—	3	1	no	—
569	C₄⋊C₄	—	3	1	no	—
570	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
571	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
572	C₂²⋊C₄	—	3	1	no	—
573	C₂²⋊C₄	—	3	1	no	—
574	C₂²⋊C₄	—	3	1	no	—
575	C₂²⋊C₄	—	3	1	no	—
576	C₂²⋊C₄	—	3	1	no	—
577	C₂²⋊C₄	—	3	1	no	—
578	C₂²⋊C₄	—	3	1	no	—
579	C₂²⋊C₄	—	3	1	no	—
580	C₂²⋊C₄	—	3	1	no	—
581	C₂²⋊C₄	—	3	1	no	—
582	C₂²⋊C₄	—	3	1	no	—
583	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
584	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
585	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic, complemented
586	C₄²	—	3	1	no	—
587	C₄²	—	3	1	no	—
588	C₄²	—	3	1	no	—
589	C₂²×C₃	—	2	1	no	—
590	C₂²×C₃	—	2	1	no	—
591	C₂²×C₃	—	2	1	no	—
592	C₂²×C₃	—	2	1	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	2	1	no	—
595	C₂²×C₃	—	2	1	no	—
596	C₂²×C₃	—	2	1	no	—
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	2	no	—
601	C₂²×C₃	—	3	2	no	—
602	C₂²×C₃	—	4	1	no	—
603	C₂²×C₃	—	4	1	no	—
604	C₂²×C₃	—	4	1	no	—
605	C₂²×C₃	—	4	1	no	—
606	C₂²×C₃	—	4	1	no	—
607	C₂²×C₃	—	6	1	no	—
608	C₂²×C₃	—	6	1	no	—
609	C₂²×C₃	—	6	1	no	—
610	C₂²×C₃	—	6	1	no	—
611	C₂²×C₃	—	6	1	no	—
612	C₂²×C₃	—	12	4	no	—
613	C₂²×C₃	C₉×#41	1	2	yes	—
614	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
615	C₂²×C₃	C₃×#237	1	2	yes	—
616	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
617	C₂×D₃	—	2	1	no	—
618	C₂×D₃	—	2	1	no	—
619	C₂×D₃	—	2	1	no	—
620	C₂×D₃	—	2	1	no	—
621	C₂×D₃	—	2	1	no	—
622	C₂×D₃	—	4	4	no	—
623	C₂×D₃	C₉×#41	1	2	yes	—
624	C₃×C₄	—	2	1	no	—
625	C₃×C₄	—	2	1	no	—
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	2	1	no	—
630	C₃×C₄	—	2	1	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	2	1	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	4	1	no	—
635	C₃×C₄	—	4	1	no	—
636	C₃×C₄	—	4	1	no	—
637	C₃×C₄	—	4	1	no	—
638	C₃×C₄	—	4	1	no	—
639	C₃×C₄	—	6	1	no	—
640	C₃×C₄	—	6	1	no	—
641	C₃×C₄	—	6	1	no	—
642	C₃×C₄	—	6	1	no	—
643	C₃×C₄	—	6	1	no	—
644	C₃×C₄	—	6	1	no	—
645	Dic₃	—	2	1	no	—
646	Dic₃	—	2	1	no	—
647	Dic₃	—	2	1	no	—
648	Dic₃	—	2	1	no	—
649	Dic₃	—	2	1	no	—
650	Dic₃	—	2	1	no	—
651	C₃²	C₃×#551	1	1	yes	characteristic
652	C₉	—	2	1	no	—
653	C₉	#5658	1	1	yes	characteristic, direct product factor
654	C₂³	—	3	1	no	—
655	C₂³	—	3	1	no	—
656	C₂³	—	6	2	no	—
657	C₂³	—	6	2	no	—
658	C₂³	—	12	1	no	—
659	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
660	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
661	Q₈	—	12	1	no	—
662	D₄	—	2	2	no	—
663	D₄	—	6	2	no	—
664	D₄	—	12	1	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	3	1	no	—
667	C₂×C₄	—	3	1	no	—
668	C₂×C₄	—	3	1	no	—
669	C₂×C₄	—	3	1	no	—
670	C₂×C₄	—	3	1	no	—
671	C₂×C₄	—	3	1	no	—
672	C₂×C₄	—	6	2	no	—
673	C₂×C₄	—	12	1	no	—
674	C₂×C₄	—	12	1	no	—
675	C₂×C₄	—	12	1	no	—
676	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
681	C₂×C₃	—	2	2	no	—
682	C₂×C₃	—	2	2	no	—
683	C₂×C₃	—	2	1	no	—
684	C₂×C₃	—	2	1	no	—
685	C₂×C₃	—	2	1	no	—
686	C₂×C₃	—	4	2	no	—
687	C₂×C₃	—	4	1	no	—
688	C₂×C₃	—	4	1	no	—
689	C₂×C₃	—	6	2	no	—
690	C₂×C₃	—	8	1	no	—
691	C₂×C₃	—	12	1	no	—
692	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
693	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
694	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
695	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
696	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
697	C₂×C₃	C₃×#1009	1	1	yes	characteristic
698	D₃	—	2	2	no	—
699	D₃	—	4	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	3	2	no	—
706	C₂²	—	6	1	no	—
707	C₂²	—	6	1	no	—
708	C₂²	—	6	1	no	—
709	C₂²	—	6	1	no	—
710	C₂²	—	6	1	no	—
711	C₂²	—	12	4	no	—
712	C₂²	C₉×#237	1	2	yes	—
713	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	6	1	no	—
720	C₄	—	6	1	no	—
721	C₄	—	6	1	no	—
722	C₄	—	6	1	no	—
723	C₄	—	6	1	no	—
724	C₄	—	6	1	no	—
725	C₃	—	2	1	no	—
726	C₃	C₉×#551	1	1	yes	characteristic, complemented
727	C₃	C₃×#5658	1	1	yes	characteristic
728	C₂	—	2	2	no	—
729	C₂	—	4	1	no	—
730	C₂	—	6	2	no	—
731	C₂	—	12	1	no	—
732	C₂	C₂×C₉×#237	1	1	yes	characteristic
733	C₂	D₃×C₉×#41	1	1	yes	characteristic
734	C₂	C₉×#1009	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×#123	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#937	C₂×C₃
hypercenter	C₉×#123	D₃
hypocenter	C₃	C₉×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#123

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#123	C₂	semidirect
3. D₄×C₉×Dic₃	C₂	semidirect
4. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₉×#926	C₂	semidirect
6. C₉×#898	C₂	semidirect
7. C₉×#898	C₂	semidirect
8. C₉×#897	C₂	semidirect
9. C₉×#892	C₂	semidirect
10. C₉×#886	C₂	semidirect
11. C₉×#885	C₂	semidirect
12. C₉×#883	C₂	semidirect
13. C₉×#67⋊C₄	C₂	semidirect
14. D₃×C₉×C₂²⋊C₄	C₂	semidirect
15. C₉×#878	C₂	semidirect
24. C₂²×C₉×Dic₃	C₂²	semidirect
27. C₂×C₉×Dic₆	C₂²	semidirect
28. C₃×C₉×C₄⋊C₄	C₂²	semidirect
29. C₃×C₉×C₄⋊C₄	C₂²	semidirect
31. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
32. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
35. C₉×#217	C₂²	semidirect
44. C₉×C₄⋊Dic₃	C₂²	semidirect
45. C₉×C₄⋊Dic₃	C₂²	semidirect
46. C₉×C₄⋊Dic₃	C₂²	semidirect
47. C₉×C₄⋊Dic₃	C₂²	semidirect
48. C₉×Dic₃⋊C₄	C₂²	semidirect
49. C₉×Dic₃⋊C₄	C₂²	semidirect
50. C₄×C₉×Dic₃	C₂²	semidirect
51. C₄×C₉×Dic₃	C₂²	semidirect
52. C₄×C₉×Dic₃	C₂²	semidirect
74. C₉×#123	D₃	semidirect
112. #5658	C₉	direct (N × H)
168. C₉×C₄⋊C₄	C₂×D₃	semidirect
169. C₉×C₄⋊C₄	C₂×D₃	semidirect
185. C₉×C₂²⋊C₄	C₂×D₃	semidirect
186. C₉×C₂²⋊C₄	C₂×D₃	semidirect
221. C₃×#123	C₂×C₉	semidirect
233. D₄×Dic₃	C₂×C₉	semidirect
234. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
235. #926	C₂×C₉	semidirect
236. #898	C₂×C₉	semidirect
237. #898	C₂×C₉	semidirect
238. #897	C₂×C₉	semidirect
239. #892	C₂×C₉	semidirect
240. #886	C₂×C₉	semidirect
241. #885	C₂×C₉	semidirect
242. #883	C₂×C₉	semidirect
243. #67⋊C₄	C₂×C₉	semidirect
244. D₃×C₂²⋊C₄	C₂×C₉	semidirect
245. #878	C₂×C₉	semidirect
335. C₂²×Dic₃	C₂²×C₉	semidirect
338. C₂×Dic₆	C₂²×C₉	semidirect
347. C₃×C₄⋊C₄	C₂²×C₉	semidirect
348. C₃×C₄⋊C₄	C₂²×C₉	semidirect
366. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
367. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
376. #217	C₂²×C₉	semidirect
385. C₄⋊Dic₃	C₂²×C₉	semidirect
386. C₄⋊Dic₃	C₂²×C₉	semidirect
387. C₄⋊Dic₃	C₂²×C₉	semidirect
388. C₄⋊Dic₃	C₂²×C₉	semidirect
389. Dic₃⋊C₄	C₂²×C₉	semidirect
390. Dic₃⋊C₄	C₂²×C₉	semidirect
391. C₄×Dic₃	C₂²×C₉	semidirect
392. C₄×Dic₃	C₂²×C₉	semidirect
393. C₄×Dic₃	C₂²×C₉	semidirect
461. #123	D₃×C₉	semidirect
471. C₃×C₉	#551	semidirect
570. C₄⋊C₄	C₂×D₃×C₉	semidirect
571. C₄⋊C₄	C₂×D₃×C₉	semidirect
584. C₂²⋊C₄	C₂×D₃×C₉	semidirect
585. C₂²⋊C₄	C₂×D₃×C₉	semidirect
653. C₉	#5658	direct (N × H)
726. C₃	C₉×#551	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#123	2
C₉×#937	2
D₄×C₉×Dic₃	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₉×#926	2
C₉×#898	2
C₉×#897	2
C₉×#892	2
C₉×#886	2
C₉×#885	2
C₉×#883	2
C₉×#67⋊C₄	2
D₃×C₉×C₂²⋊C₄	2
C₉×#878	2
C₃×#5658	3
C₉×#551	3

Subgroups — C9×#5658 #13153028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5658 #13153028