Subgroups — C₉×#5495 #13152354

Order 1728.

876 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#953	C₂	1	1	yes	maximal, characteristic
3	C₂×C₉×#217	C₂	1	1	yes	maximal, characteristic, complemented
4	C₉×#929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₉×#67	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#926	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#924	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#886	C₂	1	1	yes	maximal, characteristic, complemented
9	C₉×#885	C₂	1	1	yes	maximal, characteristic, complemented
10	C₉×#883	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₉×#879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₉×#879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₉×#878	C₂	1	1	yes	maximal, characteristic, complemented
15	C₉×#877	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5495	C₃	1	1	yes	maximal, characteristic
17	C₉×#551	—	3	1	no	maximal
18	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×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	C₂×C₉×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
25	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₃×C₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₃×C₉×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₉×#217	C₂²	1	1	yes	characteristic
33	C₉×#217	C₂²	1	1	yes	characteristic
34	C₉×#217	C₂²	1	1	yes	characteristic
35	C₉×#217	C₂²	1	1	yes	characteristic
36	C₉×#217	C₂²	1	1	yes	characteristic
37	C₉×#217	C₂²	1	1	yes	characteristic
38	C₉×#217	C₂²	1	1	yes	characteristic
39	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	C₉×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
43	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
44	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
45	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	C₉×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₉×Dic₃⋊C₄	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	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
54	C₃×#953	C₂×C₃	1	1	yes	characteristic
55	C₂×C₃×#217	C₂×C₃	1	1	yes	characteristic
56	C₃×#929	C₂×C₃	1	1	yes	characteristic
57	C₃×C₄×#67	C₂×C₃	1	1	yes	characteristic
58	C₃×#926	C₂×C₃	1	1	yes	characteristic
59	C₃×#924	C₂×C₃	1	1	yes	characteristic
60	C₃×#886	C₂×C₃	1	1	yes	characteristic
61	C₃×#885	C₂×C₃	1	1	yes	characteristic
62	C₃×#883	C₂×C₃	1	1	yes	characteristic
63	C₃×#67⋊C₄	C₂×C₃	1	1	yes	characteristic
64	C₃×#879	C₂×C₃	1	1	yes	characteristic
65	C₃×#879	C₂×C₃	1	1	yes	characteristic
66	C₃×#878	C₂×C₃	1	1	yes	characteristic
67	C₃×#877	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	—	3	1	no	—
72	C₉×#123	—	3	1	no	—
73	C₉×#123	—	3	1	no	—
74	C₉×C₂²⋊Q₈	—	3	1	no	—
75	C₉×C₂²⋊Q₈	—	3	1	no	—
76	C₉×#120	—	3	1	no	—
77	C₄×D₄×C₉	—	3	1	no	—
78	C₄×D₄×C₉	—	3	1	no	—
79	C₉×#117	—	3	1	no	—
80	C₉×#117	—	3	1	no	—
81	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₉×C₂²⋊C₄	—	3	1	no	—
83	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
84	C₂³×C₃×C₉	—	2	2	no	—
85	C₂³×C₃×C₉	—	2	2	no	—
86	C₂³×C₃×C₉	—	4	1	no	—
87	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
88	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
89	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
90	C₂²×D₃×C₉	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄×C₉	—	2	2	no	—
92	C₂×C₃×C₄×C₉	—	4	1	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	C₉×#67	—	2	2	no	—
98	C₉×#67	—	2	2	no	—
99	C₉×#67	—	4	1	no	—
100	C₂×C₉×Dic₃	—	2	2	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	C₂×C₉×Dic₃	C₂³	1	1	yes	characteristic
109	C₄×D₃×C₉	—	4	1	no	—
110	C₉×Dic₆	—	4	1	no	—
111	C₃×#551	—	3	1	no	—
112	#5495	C₉	1	1	yes	characteristic, direct product factor
113	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₃²×C₄	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	C₂×C₃×#67	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
120	C₂²×C₃×Dic₃	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	—	2	1	no	—
124	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
125	C₃²×C₂²⋊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×#217	C₂²×C₃	1	1	yes	characteristic
133	C₃×#217	C₂²×C₃	1	1	yes	characteristic
134	C₃×#217	C₂²×C₃	1	1	yes	characteristic
135	C₃×#217	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×C₄⋊Dic₃	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×Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₃×Dic₃⋊C₄	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×Dic₃⋊C₄	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	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
150	C₂×Q₈×C₉	—	3	1	no	—
151	C₂×D₄×C₉	—	3	1	no	—
152	C₂×D₄×C₉	—	3	1	no	—
153	C₂×D₄×C₉	—	3	1	no	—
154	C₂²×C₄×C₉	—	2	1	no	—
155	C₂²×C₄×C₉	—	2	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	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
161	C₉×C₄⋊C₄	—	3	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	—	3	1	no	—
169	C₉×C₂²⋊C₄	—	2	1	no	—
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	C₂×D₃	1	1	yes	characteristic
184	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
185	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
186	C₉×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
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	—	2	1	no	—
196	C₂²×C₃×C₉	—	2	1	no	—
197	C₂²×C₃×C₉	—	4	4	no	—
198	C₂²×C₃×C₉	#41	1	2	yes	—
199	C₂²×C₃×C₉	#41	1	2	yes	—
200	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
201	C₂×D₃×C₉	—	2	1	no	—
202	C₂×D₃×C₉	—	2	1	no	—
203	C₂×D₃×C₉	—	2	1	no	—
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	C₉×Dic₃	—	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	—	3	1	no	—
219	C₃×#123	—	3	1	no	—
220	C₃×#123	—	3	1	no	—
221	C₃×C₂²⋊Q₈	—	3	1	no	—
222	C₃×C₂²⋊Q₈	—	3	1	no	—
223	C₃×#120	—	3	1	no	—
224	C₃×C₄×D₄	—	3	1	no	—
225	C₃×C₄×D₄	—	3	1	no	—
226	C₃×#117	—	3	1	no	—
227	C₃×#117	—	3	1	no	—
228	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₃×C₂²⋊C₄	—	3	1	no	—
230	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
231	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
232	#953	C₂×C₉	1	1	yes	characteristic
233	C₂×#217	C₂×C₉	1	1	yes	characteristic, complemented
234	#929	C₂×C₉	1	1	yes	characteristic, complemented
235	C₄×#67	C₂×C₉	1	1	yes	characteristic, complemented
236	#926	C₂×C₉	1	1	yes	characteristic, complemented
237	#924	C₂×C₉	1	1	yes	characteristic, complemented
238	#886	C₂×C₉	1	1	yes	characteristic, complemented
239	#885	C₂×C₉	1	1	yes	characteristic, complemented
240	#883	C₂×C₉	1	1	yes	characteristic, complemented
241	#67⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
242	#879	C₂×C₉	1	1	yes	characteristic, complemented
243	#879	C₂×C₉	1	1	yes	characteristic, complemented
244	#878	C₂×C₉	1	1	yes	characteristic, complemented
245	#877	C₂×C₉	1	1	yes	characteristic, complemented
246	C₂³×C₃²	—	2	2	no	—
247	C₂³×C₃²	—	2	2	no	—
248	C₂³×C₃²	—	4	1	no	—
249	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
250	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
251	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
252	C₂²×C₃×D₃	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₃²×C₄	—	2	2	no	—
254	C₂×C₃²×C₄	—	4	1	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	C₃×#67	—	2	2	no	—
260	C₃×#67	—	2	2	no	—
261	C₃×#67	—	4	1	no	—
262	C₂×C₃×Dic₃	—	2	2	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	C₂×C₃×Dic₃	C₂³×C₃	1	1	yes	characteristic
271	C₃×C₄×D₃	—	4	1	no	—
272	C₃×Dic₆	—	4	1	no	—
273	C₂³×C₉	—	2	4	no	—
274	C₂³×C₉	—	2	2	no	—
275	C₂³×C₉	—	2	2	no	—
276	C₂³×C₉	—	2	1	no	—
277	C₂³×C₉	—	2	1	no	—
278	C₂³×C₉	—	2	1	no	—
279	C₂³×C₉	—	3	1	no	—
280	C₂³×C₉	—	4	2	no	—
281	C₂³×C₉	—	4	1	no	—
282	C₂³×C₉	—	4	2	no	—
283	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
284	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
285	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
286	Q₈×C₉	—	12	1	no	—
287	D₄×C₉	—	6	2	no	—
288	D₄×C₉	—	6	2	no	—
289	D₄×C₉	—	12	1	no	—
290	C₂×C₄×C₉	—	2	2	no	—
291	C₂×C₄×C₉	—	2	1	no	—
292	C₂×C₄×C₉	—	2	1	no	—
293	C₂×C₄×C₉	—	2	1	no	—
294	C₂×C₄×C₉	—	2	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	—	3	1	no	—
300	C₂×C₄×C₉	—	3	1	no	—
301	C₂×C₄×C₉	—	3	1	no	—
302	C₂×C₄×C₉	—	4	2	no	—
303	C₂×C₄×C₉	—	4	1	no	—
304	C₂×C₄×C₉	—	4	2	no	—
305	C₂×C₄×C₉	—	6	2	no	—
306	C₂×C₄×C₉	—	12	1	no	—
307	C₂×C₄×C₉	—	12	1	no	—
308	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
309	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
310	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
311	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
312	#551	—	3	1	no	Sylow
313	C₂×C₃×C₉	—	2	2	no	—
314	C₂×C₃×C₉	—	2	2	no	—
315	C₂×C₃×C₉	—	4	1	no	—
316	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
317	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
318	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
319	D₃×C₉	—	4	1	no	—
320	C₂⁴×C₃	—	2	1	no	—
321	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
322	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
323	C₂×C₃×Q₈	—	3	1	no	—
324	C₂×C₃×D₄	—	3	1	no	—
325	C₂×C₃×D₄	—	3	1	no	—
326	C₂×C₃×D₄	—	3	1	no	—
327	C₂²×C₃×C₄	—	2	1	no	—
328	C₂²×C₃×C₄	—	2	1	no	—
329	C₂²×C₃×C₄	—	3	1	no	—
330	C₂²×C₃×C₄	—	3	1	no	—
331	C₂²×C₃×C₄	—	3	1	no	—
332	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
336	C₂×#67	C₂²×C₉	1	1	yes	characteristic
337	C₂×#67	C₂²×C₉	1	1	yes	characteristic
338	C₂×#67	C₂²×C₉	1	1	yes	characteristic
339	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
340	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
341	C₂×C₄×D₃	C₂²×C₉	1	1	yes	characteristic, complemented
342	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic, complemented
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	—	3	1	no	—
348	C₃×C₄⋊C₄	—	3	1	no	—
349	C₃×C₄⋊C₄	—	3	1	no	—
350	C₃×C₄⋊C₄	—	3	1	no	—
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	—	2	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
367	C₃×C₂²⋊C₄	C₂²×C₉	1	1	yes	characteristic
368	C₃×C₂²⋊C₄	C₂²×C₉	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×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
372	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
373	C₃×C₄²	—	3	1	no	—
374	C₃×C₄²	—	3	1	no	—
375	C₃×C₄²	—	3	1	no	—
376	#217	C₂²×C₉	1	1	yes	characteristic
377	#217	C₂²×C₉	1	1	yes	characteristic
378	#217	C₂²×C₉	1	1	yes	characteristic
379	#217	C₂²×C₉	1	1	yes	characteristic
380	#217	C₂²×C₉	1	1	yes	characteristic
381	#217	C₂²×C₉	1	1	yes	characteristic
382	#217	C₂²×C₉	1	1	yes	characteristic
383	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
384	(C₂×D₃)⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
385	(C₂×D₃)⋊C₄	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	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
392	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
393	Dic₃⋊C₄	C₂²×C₉	1	1	yes	characteristic, complemented
394	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
395	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
396	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic, complemented
397	C₂²×C₃²	—	2	1	no	—
398	C₂²×C₃²	—	2	1	no	—
399	C₂²×C₃²	—	2	1	no	—
400	C₂²×C₃²	—	2	1	no	—
401	C₂²×C₃²	—	2	1	no	—
402	C₂²×C₃²	—	2	1	no	—
403	C₂²×C₃²	—	2	1	no	—
404	C₂²×C₃²	—	4	4	no	—
405	C₂²×C₃²	C₃×#41	1	2	yes	—
406	C₂²×C₃²	C₃×#41	1	2	yes	—
407	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
408	C₂×C₃×D₃	—	2	1	no	—
409	C₂×C₃×D₃	—	2	1	no	—
410	C₂×C₃×D₃	—	2	1	no	—
411	C₃²×C₄	—	2	1	no	—
412	C₃²×C₄	—	2	1	no	—
413	C₃²×C₄	—	2	1	no	—
414	C₃²×C₄	—	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	C₃×Dic₃	—	2	1	no	—
420	C₃×Dic₃	—	2	1	no	—
421	C₃×Dic₃	—	2	1	no	—
422	C₂²×C₉	—	2	2	no	—
423	C₂²×C₉	—	2	2	no	—
424	C₂²×C₉	—	2	1	no	—
425	C₂²×C₉	—	2	1	no	—
426	C₂²×C₉	—	2	1	no	—
427	C₂²×C₉	—	2	1	no	—
428	C₂²×C₉	—	2	2	no	—
429	C₂²×C₉	—	2	1	no	—
430	C₂²×C₉	—	2	1	no	—
431	C₂²×C₉	—	2	1	no	—
432	C₂²×C₉	—	2	1	no	—
433	C₂²×C₉	—	2	2	no	—
434	C₂²×C₉	—	2	2	no	—
435	C₂²×C₉	—	4	1	no	—
436	C₂²×C₉	—	4	1	no	—
437	C₂²×C₉	—	4	1	no	—
438	C₂²×C₉	—	4	1	no	—
439	C₂²×C₉	—	4	4	no	—
440	C₂²×C₉	—	4	8	no	—
441	C₂²×C₉	—	6	1	no	—
442	C₂²×C₉	—	6	1	no	—
443	C₂²×C₉	—	6	1	no	—
444	C₂²×C₉	#235	1	2	yes	—
445	C₂²×C₉	#237	1	2	yes	—
446	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
447	C₄×C₉	—	2	1	no	—
448	C₄×C₉	—	2	1	no	—
449	C₄×C₉	—	2	1	no	—
450	C₄×C₉	—	2	1	no	—
451	C₄×C₉	—	4	1	no	—
452	C₄×C₉	—	4	1	no	—
453	C₄×C₉	—	4	1	no	—
454	C₄×C₉	—	4	1	no	—
455	C₄×C₉	—	6	1	no	—
456	C₄×C₉	—	6	1	no	—
457	C₄×C₉	—	6	1	no	—
458	C₄×C₉	—	6	1	no	—
459	C₄×C₉	—	6	1	no	—
460	C₄×C₉	—	6	1	no	—
461	C₄×C₉	—	6	1	no	—
462	#126	—	3	1	no	—
463	#126	—	3	1	no	—
464	#124	—	3	1	no	—
465	#123	—	3	1	no	—
466	#123	—	3	1	no	—
467	#123	—	3	1	no	—
468	C₂²⋊Q₈	—	3	1	no	—
469	C₂²⋊Q₈	—	3	1	no	—
470	#120	—	3	1	no	—
471	C₄×D₄	—	3	1	no	—
472	C₄×D₄	—	3	1	no	—
473	#117	—	3	1	no	—
474	#117	—	3	1	no	—
475	C₂×C₂²⋊C₄	—	3	1	no	—
476	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
477	C₃×C₉	#551	1	1	yes	characteristic, complemented, Sylow
478	C₂³×C₃	—	2	4	no	—
479	C₂³×C₃	—	2	2	no	—
480	C₂³×C₃	—	2	2	no	—
481	C₂³×C₃	—	2	2	no	—
482	C₂³×C₃	—	2	2	no	—
483	C₂³×C₃	—	2	1	no	—
484	C₂³×C₃	—	2	1	no	—
485	C₂³×C₃	—	2	1	no	—
486	C₂³×C₃	—	3	1	no	—
487	C₂³×C₃	—	4	2	no	—
488	C₂³×C₃	—	4	1	no	—
489	C₂³×C₃	—	4	1	no	—
490	C₂³×C₃	—	4	2	no	—
491	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
492	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
493	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
494	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
495	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
496	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
497	C₂²×D₃	C₂³×C₉	1	1	yes	characteristic
498	C₃×Q₈	—	12	1	no	—
499	C₃×D₄	—	6	2	no	—
500	C₃×D₄	—	6	2	no	—
501	C₃×D₄	—	12	1	no	—
502	C₂×C₃×C₄	—	2	2	no	—
503	C₂×C₃×C₄	—	2	2	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	3	1	no	—
509	C₂×C₃×C₄	—	3	1	no	—
510	C₂×C₃×C₄	—	3	1	no	—
511	C₂×C₃×C₄	—	3	1	no	—
512	C₂×C₃×C₄	—	3	1	no	—
513	C₂×C₃×C₄	—	3	1	no	—
514	C₂×C₃×C₄	—	3	1	no	—
515	C₂×C₃×C₄	—	4	2	no	—
516	C₂×C₃×C₄	—	4	1	no	—
517	C₂×C₃×C₄	—	4	1	no	—
518	C₂×C₃×C₄	—	4	2	no	—
519	C₂×C₃×C₄	—	6	2	no	—
520	C₂×C₃×C₄	—	12	1	no	—
521	C₂×C₃×C₄	—	12	1	no	—
522	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
525	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
528	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
529	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
530	#67	—	2	2	no	—
531	#67	—	2	2	no	—
532	#67	—	4	1	no	—
533	C₂×Dic₃	—	2	2	no	—
534	C₂×Dic₃	—	4	1	no	—
535	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
536	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
537	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
538	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
539	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
540	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
541	C₂×Dic₃	C₂³×C₉	1	1	yes	characteristic
542	C₄×D₃	—	4	1	no	—
543	Dic₆	—	4	1	no	—
544	C₂×C₃²	—	2	2	no	—
545	C₂×C₃²	—	2	2	no	—
546	C₂×C₃²	—	4	1	no	—
547	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
548	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
549	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
550	C₃×D₃	—	4	1	no	—
551	C₂×C₉	—	2	4	no	—
552	C₂×C₉	—	2	2	no	—
553	C₂×C₉	—	2	2	no	—
554	C₂×C₉	—	2	1	no	—
555	C₂×C₉	—	2	1	no	—
556	C₂×C₉	—	2	1	no	—
557	C₂×C₉	—	4	2	no	—
558	C₂×C₉	—	4	2	no	—
559	C₂×C₉	—	4	1	no	—
560	C₂×C₉	—	12	1	no	—
561	C₂×C₉	C₂×#235	1	1	yes	characteristic
562	C₂×C₉	C₂×#237	1	1	yes	characteristic
563	C₂×C₉	#1004	1	1	yes	characteristic
564	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
565	C₂×Q₈	—	3	1	no	—
566	C₂×D₄	—	3	1	no	—
567	C₂×D₄	—	3	1	no	—
568	C₂×D₄	—	3	1	no	—
569	C₂²×C₄	—	3	1	no	—
570	C₂²×C₄	—	3	1	no	—
571	C₂²×C₄	—	3	1	no	—
572	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
574	C₄⋊C₄	—	3	1	no	—
575	C₄⋊C₄	—	3	1	no	—
576	C₄⋊C₄	—	3	1	no	—
577	C₄⋊C₄	—	3	1	no	—
578	C₄⋊C₄	—	3	1	no	—
579	C₄⋊C₄	—	3	1	no	—
580	C₄⋊C₄	—	3	1	no	—
581	C₄⋊C₄	—	3	1	no	—
582	C₂²⋊C₄	—	3	1	no	—
583	C₂²⋊C₄	—	3	1	no	—
584	C₂²⋊C₄	—	3	1	no	—
585	C₂²⋊C₄	—	3	1	no	—
586	C₂²⋊C₄	—	3	1	no	—
587	C₂²⋊C₄	—	3	1	no	—
588	C₂²⋊C₄	—	3	1	no	—
589	C₂²⋊C₄	—	3	1	no	—
590	C₂²⋊C₄	—	3	1	no	—
591	C₂²⋊C₄	—	3	1	no	—
592	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
593	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
594	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
595	C₂²⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
596	C₄²	—	3	1	no	—
597	C₄²	—	3	1	no	—
598	C₄²	—	3	1	no	—
599	C₂²×C₃	—	2	2	no	—
600	C₂²×C₃	—	2	2	no	—
601	C₂²×C₃	—	2	1	no	—
602	C₂²×C₃	—	2	1	no	—
603	C₂²×C₃	—	2	1	no	—
604	C₂²×C₃	—	2	1	no	—
605	C₂²×C₃	—	2	1	no	—
606	C₂²×C₃	—	2	1	no	—
607	C₂²×C₃	—	2	1	no	—
608	C₂²×C₃	—	2	1	no	—
609	C₂²×C₃	—	2	2	no	—
610	C₂²×C₃	—	2	1	no	—
611	C₂²×C₃	—	2	1	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	2	1	no	—
617	C₂²×C₃	—	2	2	no	—
618	C₂²×C₃	—	2	2	no	—
619	C₂²×C₃	—	4	1	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	4	1	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	4	no	—
624	C₂²×C₃	—	4	4	no	—
625	C₂²×C₃	—	4	8	no	—
626	C₂²×C₃	—	6	1	no	—
627	C₂²×C₃	—	6	1	no	—
628	C₂²×C₃	—	6	1	no	—
629	C₂²×C₃	C₉×#41	1	2	yes	—
630	C₂²×C₃	C₉×#41	1	2	yes	—
631	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
632	C₂²×C₃	C₃×#235	1	2	yes	—
633	C₂²×C₃	C₃×#237	1	2	yes	—
634	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
635	C₂×D₃	—	2	1	no	—
636	C₂×D₃	—	2	1	no	—
637	C₂×D₃	—	2	1	no	—
638	C₃×C₄	—	2	1	no	—
639	C₃×C₄	—	2	1	no	—
640	C₃×C₄	—	2	1	no	—
641	C₃×C₄	—	2	1	no	—
642	C₃×C₄	—	2	1	no	—
643	C₃×C₄	—	2	1	no	—
644	C₃×C₄	—	2	1	no	—
645	C₃×C₄	—	2	1	no	—
646	C₃×C₄	—	4	1	no	—
647	C₃×C₄	—	4	1	no	—
648	C₃×C₄	—	4	1	no	—
649	C₃×C₄	—	4	1	no	—
650	C₃×C₄	—	6	1	no	—
651	C₃×C₄	—	6	1	no	—
652	C₃×C₄	—	6	1	no	—
653	C₃×C₄	—	6	1	no	—
654	C₃×C₄	—	6	1	no	—
655	C₃×C₄	—	6	1	no	—
656	C₃×C₄	—	6	1	no	—
657	Dic₃	—	2	1	no	—
658	Dic₃	—	2	1	no	—
659	Dic₃	—	2	1	no	—
660	Dic₃	—	2	1	no	—
661	Dic₃	—	2	1	no	—
662	Dic₃	—	2	1	no	—
663	Dic₃	—	2	1	no	—
664	C₃²	C₃×#551	1	1	yes	characteristic
665	C₉	—	2	1	no	—
666	C₉	#5495	1	1	yes	characteristic, direct product factor
667	C₂³	—	2	2	no	—
668	C₂³	—	2	2	no	—
669	C₂³	—	3	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
672	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
673	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
674	Q₈	—	12	1	no	—
675	D₄	—	6	2	no	—
676	D₄	—	6	2	no	—
677	D₄	—	12	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	3	1	no	—
680	C₂×C₄	—	3	1	no	—
681	C₂×C₄	—	3	1	no	—
682	C₂×C₄	—	3	1	no	—
683	C₂×C₄	—	3	1	no	—
684	C₂×C₄	—	3	1	no	—
685	C₂×C₄	—	3	1	no	—
686	C₂×C₄	—	4	1	no	—
687	C₂×C₄	—	6	2	no	—
688	C₂×C₄	—	12	1	no	—
689	C₂×C₄	—	12	1	no	—
690	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
693	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
694	C₂×C₃	—	2	4	no	—
695	C₂×C₃	—	2	2	no	—
696	C₂×C₃	—	2	2	no	—
697	C₂×C₃	—	2	2	no	—
698	C₂×C₃	—	2	2	no	—
699	C₂×C₃	—	2	1	no	—
700	C₂×C₃	—	2	1	no	—
701	C₂×C₃	—	2	1	no	—
702	C₂×C₃	—	4	2	no	—
703	C₂×C₃	—	4	2	no	—
704	C₂×C₃	—	4	1	no	—
705	C₂×C₃	—	4	1	no	—
706	C₂×C₃	—	12	1	no	—
707	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
708	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
709	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
710	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
711	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
712	C₂×C₃	C₃×#1004	1	1	yes	characteristic
713	D₃	—	4	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	4	4	no	—
722	C₂²	—	6	1	no	—
723	C₂²	—	6	1	no	—
724	C₂²	—	6	1	no	—
725	C₂²	C₉×#235	1	2	yes	—
726	C₂²	C₉×#237	1	2	yes	—
727	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	1	no	—
732	C₄	—	6	1	no	—
733	C₄	—	6	1	no	—
734	C₄	—	6	1	no	—
735	C₄	—	6	1	no	—
736	C₄	—	6	1	no	—
737	C₄	—	6	1	no	—
738	C₄	—	6	1	no	—
739	C₃	—	2	1	no	—
740	C₃	C₉×#551	1	1	yes	characteristic, complemented
741	C₃	C₃×#5495	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	2	2	no	—
744	C₂	—	4	1	no	—
745	C₂	—	12	1	no	—
746	C₂	C₂×C₉×#235	1	1	yes	characteristic
747	C₂	C₂×C₉×#237	1	1	yes	characteristic
748	C₂	C₉×#1004	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#953	C₂×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₉×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
3. C₂×C₉×#217	C₂	semidirect
4. C₉×#929	C₂	semidirect
5. C₄×C₉×#67	C₂	semidirect
6. C₉×#926	C₂	semidirect
7. C₉×#924	C₂	semidirect
8. C₉×#886	C₂	semidirect
9. C₉×#885	C₂	semidirect
10. C₉×#883	C₂	semidirect
11. C₉×#67⋊C₄	C₂	semidirect
12. C₉×#879	C₂	semidirect
13. C₉×#879	C₂	semidirect
14. C₉×#878	C₂	semidirect
15. C₉×#877	C₂	semidirect
26. C₂×C₄×D₃×C₉	C₂²	semidirect
27. C₂×C₉×Dic₆	C₂²	semidirect
39. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
40. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
41. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
42. C₉×C₄⋊Dic₃	C₂²	semidirect
43. C₉×C₄⋊Dic₃	C₂²	semidirect
44. C₉×C₄⋊Dic₃	C₂²	semidirect
45. C₉×Dic₃⋊C₄	C₂²	semidirect
46. C₉×Dic₃⋊C₄	C₂²	semidirect
47. C₉×Dic₃⋊C₄	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
83. C₂×C₉×C₂²⋊C₄	D₃	semidirect
112. #5495	C₉	direct (N × H)
230. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
233. C₂×#217	C₂×C₉	semidirect
234. #929	C₂×C₉	semidirect
235. C₄×#67	C₂×C₉	semidirect
236. #926	C₂×C₉	semidirect
237. #924	C₂×C₉	semidirect
238. #886	C₂×C₉	semidirect
239. #885	C₂×C₉	semidirect
240. #883	C₂×C₉	semidirect
241. #67⋊C₄	C₂×C₉	semidirect
242. #879	C₂×C₉	semidirect
243. #879	C₂×C₉	semidirect
244. #878	C₂×C₉	semidirect
245. #877	C₂×C₉	semidirect
341. C₂×C₄×D₃	C₂²×C₉	semidirect
342. C₂×Dic₆	C₂²×C₉	semidirect
383. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
384. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
385. (C₂×D₃)⋊C₄	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. Dic₃⋊C₄	C₂²×C₉	semidirect
392. Dic₃⋊C₄	C₂²×C₉	semidirect
393. Dic₃⋊C₄	C₂²×C₉	semidirect
394. C₄×Dic₃	C₂²×C₉	semidirect
395. C₄×Dic₃	C₂²×C₉	semidirect
396. C₄×Dic₃	C₂²×C₉	semidirect
476. C₂×C₂²⋊C₄	D₃×C₉	semidirect
477. C₃×C₉	#551	semidirect
666. C₉	#5495	direct (N × H)
740. 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
C₂×C₃×C₉×C₂²⋊C₄	2
C₉×#953	2
C₂×C₉×#217	2
C₉×#929	2
C₄×C₉×#67	2
C₉×#926	2
C₉×#924	2
C₉×#886	2
C₉×#885	2
C₉×#883	2
C₉×#67⋊C₄	2
C₉×#879	2
C₉×#878	2
C₉×#877	2
C₃×#5495	3
C₉×#551	3

Subgroups — C9×#5495 #13152354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5495 #13152354