Subgroups — #10589760⋊C₃ #13153068

Order 1728.

783 conjugacy classes of subgroups.

The subgroup lattice has 701 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	#63499⋊C₃	C₂	1	1	yes	maximal, characteristic
3	D₄×3₋¹⁺²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₂×AGL(1,ℤ/9))⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#63488⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63459⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63454⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63448⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#63445⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	(#611⋊C₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
15	#63440⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5658	—	3	1	no	maximal
17	#10589760	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂³×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
19	C₂×D₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
21	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
22	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
23	C₂²×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
26	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
27	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
29	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
30	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
31	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
32	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
33	#3676⋊C₃	C₂²	1	1	yes	characteristic
34	#3676⋊C₃	C₂²	1	1	yes	characteristic
35	#3676⋊C₃	C₂²	1	1	yes	characteristic, complemented
36	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
38	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
41	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
42	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
44	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic, complemented
45	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic, complemented
46	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic, complemented
47	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic, complemented
48	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₃²×#123	D₃	1	1	yes	characteristic
54	C₃×#937	—	3	1	no	—
55	C₃×D₄×Dic₃	—	3	1	no	—
56	C₂×C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
57	C₃×#926	—	3	1	no	—
58	C₃×#898	—	3	1	no	—
59	C₃×#898	—	3	1	no	—
60	C₃×#897	—	3	1	no	—
61	C₃×#892	—	3	1	no	—
62	C₃×#886	—	3	1	no	—
63	C₃×#885	—	3	1	no	—
64	C₃×#883	—	3	1	no	—
65	C₃×#67⋊C₄	—	3	1	no	—
66	C₃×D₃×C₂²⋊C₄	—	3	1	no	—
67	C₃×#878	—	3	1	no	—
68	C₉×#123	—	2	1	no	—
69	C₉×#123	C₂×C₃	1	1	yes	characteristic, complemented
70	#63499	C₂×C₃	1	1	yes	characteristic
71	D₄×Dic₉	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×(C₂×D₉)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
73	#63488	C₂×C₃	1	1	yes	characteristic, complemented
74	#63460	C₂×C₃	1	1	yes	characteristic, complemented
75	#63460	C₂×C₃	1	1	yes	characteristic, complemented
76	#63459	C₂×C₃	1	1	yes	characteristic, complemented
77	#63454	C₂×C₃	1	1	yes	characteristic, complemented
78	#63448	C₂×C₃	1	1	yes	characteristic, complemented
79	#63447	C₂×C₃	1	1	yes	characteristic, complemented
80	#63445	C₂×C₃	1	1	yes	characteristic, complemented
81	#611⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂²⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
83	#63440	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
85	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
86	C₂²×AGL(1,ℤ/9)	—	2	2	no	—
87	C₂²×AGL(1,ℤ/9)	—	2	2	no	—
88	C₂²×AGL(1,ℤ/9)	—	4	1	no	—
89	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
90	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
91	D₄×3₋¹⁺²	—	2	2	no	—
92	C₂×C₄×3₋¹⁺²	—	2	2	no	—
93	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
94	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
95	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
96	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
97	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
98	#611⋊C₃	—	2	2	no	—
99	#611⋊C₃	—	4	1	no	—
100	C₂×3₋¹⁺²⋊C₄	—	4	1	no	—
101	C₂×3₋¹⁺²⋊C₄	—	4	1	no	—
102	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
106	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
108	C₄×AGL(1,ℤ/9)	—	2	2	no	—
109	C₄×AGL(1,ℤ/9)	—	4	1	no	—
110	3₋¹⁺²⋊Q₈	—	4	1	no	—
111	C₃×#551	—	9	1	no	—
112	#5658	—	3	1	no	—
113	C₂³×C₃×D₃	—	3	1	no	—
114	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
115	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
116	C₂×C₃×#67	—	3	1	no	—
117	C₂×C₃×#67	—	3	1	no	—
118	C₂²×C₃×Dic₃	—	3	1	no	—
119	C₂²×C₃×Dic₃	—	3	1	no	—
120	C₂×C₃×C₄×D₃	—	3	1	no	—
121	C₂×C₃×C₄×D₃	—	3	1	no	—
122	C₂×C₃×Dic₆	—	3	1	no	—
123	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
124	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
125	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
127	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
128	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
129	C₃×#217	—	3	1	no	—
130	C₃×#217	—	3	1	no	—
131	C₃×#217	—	3	1	no	—
132	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
133	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
134	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
135	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
136	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
137	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
138	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
139	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
140	C₃×C₄⋊Dic₃	—	3	1	no	—
141	C₃×C₄⋊Dic₃	—	3	1	no	—
142	C₃×C₄⋊Dic₃	—	3	1	no	—
143	C₃×C₄⋊Dic₃	—	3	1	no	—
144	C₃×Dic₃⋊C₄	—	3	1	no	—
145	C₃×Dic₃⋊C₄	—	3	1	no	—
146	C₃×C₄×Dic₃	—	3	1	no	—
147	C₃×C₄×Dic₃	—	3	1	no	—
148	C₃×C₄×Dic₃	—	3	1	no	—
149	C₂×D₄×C₉	—	2	1	no	—
150	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
151	C₂²×C₄×C₉	—	2	1	no	—
152	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
153	C₂×#611	C₂²×C₃	1	1	yes	characteristic
154	C₂×#611	C₂²×C₃	1	1	yes	characteristic
155	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
156	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
159	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
160	C₉×C₄⋊C₄	—	2	1	no	—
161	C₉×C₄⋊C₄	—	2	1	no	—
162	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₉×C₂²⋊C₄	—	2	1	no	—
165	C₉×C₂²⋊C₄	—	2	1	no	—
166	C₉×C₂²⋊C₄	—	2	1	no	—
167	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
170	#3676	C₂²×C₃	1	1	yes	characteristic
171	#3676	C₂²×C₃	1	1	yes	characteristic
172	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
173	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
185	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
186	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₂²×3₋¹⁺²	—	2	1	no	—
191	C₂²×3₋¹⁺²	—	2	1	no	—
192	C₂²×3₋¹⁺²	—	2	1	no	—
193	C₂²×3₋¹⁺²	—	2	1	no	—
194	C₂²×3₋¹⁺²	—	2	1	no	—
195	C₂²×3₋¹⁺²	#41	1	2	yes	—
196	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
197	C₂×AGL(1,ℤ/9)	—	2	1	no	—
198	C₂×AGL(1,ℤ/9)	—	2	1	no	—
199	C₂×AGL(1,ℤ/9)	—	2	1	no	—
200	C₂×AGL(1,ℤ/9)	—	2	1	no	—
201	C₂×AGL(1,ℤ/9)	—	2	1	no	—
202	C₂×AGL(1,ℤ/9)	—	4	4	no	—
203	C₂×AGL(1,ℤ/9)	#41	1	2	yes	—
204	C₄×3₋¹⁺²	—	2	1	no	—
205	C₄×3₋¹⁺²	—	2	1	no	—
206	C₄×3₋¹⁺²	—	2	1	no	—
207	C₄×3₋¹⁺²	—	2	1	no	—
208	C₄×3₋¹⁺²	—	2	1	no	—
209	3₋¹⁺²⋊C₄	—	2	1	no	—
210	3₋¹⁺²⋊C₄	—	2	1	no	—
211	3₋¹⁺²⋊C₄	—	2	1	no	—
212	3₋¹⁺²⋊C₄	—	2	1	no	—
213	3₋¹⁺²⋊C₄	—	2	1	no	—
214	3₋¹⁺²⋊C₄	—	2	1	no	—
215	C₃×#126	—	9	1	no	—
216	C₃×#126	—	9	1	no	—
217	C₃×#124	—	9	1	no	—
218	C₃×#123	—	3	1	no	—
219	C₃×#123	—	9	1	no	—
220	C₃×#123	—	9	1	no	—
221	C₃×#123	C₃×D₃	1	1	yes	characteristic
222	C₃×C₂²⋊Q₈	—	9	1	no	—
223	C₃×C₂²⋊Q₈	—	9	1	no	—
224	C₃×#120	—	9	1	no	—
225	C₃×C₄×D₄	—	9	1	no	—
226	C₃×C₄×D₄	—	9	1	no	—
227	C₃×#117	—	9	1	no	—
228	C₃×#117	—	9	1	no	—
229	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
230	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
231	#937	—	3	1	no	—
232	D₄×Dic₃	—	3	1	no	—
233	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
234	#926	—	3	1	no	—
235	#898	—	3	1	no	—
236	#898	—	3	1	no	—
237	#897	—	3	1	no	—
238	#892	—	3	1	no	—
239	#886	—	3	1	no	—
240	#885	—	3	1	no	—
241	#883	—	3	1	no	—
242	#67⋊C₄	—	3	1	no	—
243	D₃×C₂²⋊C₄	—	3	1	no	—
244	#878	—	3	1	no	—
245	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
246	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
247	C₂²×C₃×D₃	—	3	1	no	—
248	C₂²×C₃×D₃	—	3	1	no	—
249	C₂²×C₃×D₃	—	6	2	no	—
250	C₂²×C₃×D₃	—	6	2	no	—
251	C₂²×C₃×D₃	—	12	1	no	—
252	C₃²×D₄	—	2	2	no	—
253	C₂×C₃²×C₄	—	2	2	no	—
254	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
255	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
256	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
257	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
258	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
259	C₃×#67	—	6	2	no	—
260	C₃×#67	—	12	1	no	—
261	C₂×C₃×Dic₃	—	3	1	no	—
262	C₂×C₃×Dic₃	—	3	1	no	—
263	C₂×C₃×Dic₃	—	3	1	no	—
264	C₂×C₃×Dic₃	—	3	1	no	—
265	C₂×C₃×Dic₃	—	3	1	no	—
266	C₂×C₃×Dic₃	—	3	1	no	—
267	C₂×C₃×Dic₃	—	12	1	no	—
268	C₂×C₃×Dic₃	—	12	1	no	—
269	C₃×C₄×D₃	—	6	2	no	—
270	C₃×C₄×D₃	—	12	1	no	—
271	C₃×Dic₆	—	12	1	no	—
272	C₂³×C₉	—	2	1	no	—
273	C₂³×C₉	—	2	1	no	—
274	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
275	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
276	C₂²×D₉	—	2	2	no	—
277	C₂²×D₉	—	2	2	no	—
278	C₂²×D₉	—	4	1	no	—
279	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
280	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
281	D₄×C₉	—	2	2	no	—
282	D₄×C₉	—	4	2	no	—
283	C₂×C₄×C₉	—	2	2	no	—
284	C₂×C₄×C₉	—	2	1	no	—
285	C₂×C₄×C₉	—	2	1	no	—
286	C₂×C₄×C₉	—	2	1	no	—
287	C₂×C₄×C₉	—	2	1	no	—
288	C₂×C₄×C₉	—	2	1	no	—
289	C₂×C₄×C₉	—	4	2	no	—
290	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
294	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
295	#611	—	2	2	no	—
296	#611	—	4	1	no	—
297	C₂×Dic₉	—	4	1	no	—
298	C₂×Dic₉	—	4	1	no	—
299	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
300	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
301	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
302	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
303	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
304	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
305	C₄×D₉	—	2	2	no	—
306	C₄×D₉	—	4	1	no	—
307	Dic₁₈	—	4	1	no	—
308	#551	—	9	1	no	Sylow
309	C₂×3₋¹⁺²	—	2	2	no	—
310	C₂×3₋¹⁺²	—	4	1	no	—
311	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
312	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
313	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
314	AGL(1,ℤ/9)	—	2	2	no	—
315	AGL(1,ℤ/9)	—	4	1	no	—
316	C₂⁴×C₃	—	9	1	no	—
317	C₂³×D₃	—	3	1	no	—
318	C₂×C₃×Q₈	—	9	1	no	—
319	C₂×C₃×D₄	—	3	1	no	—
320	C₂×C₃×D₄	—	9	1	no	—
321	C₂×C₃×D₄	—	9	1	no	—
322	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
323	C₂²×C₃×C₄	—	3	1	no	—
324	C₂²×C₃×C₄	—	9	1	no	—
325	C₂²×C₃×C₄	—	9	1	no	—
326	C₂²×C₃×C₄	—	9	1	no	—
327	C₂²×C₃×C₄	—	9	1	no	—
328	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
329	C₂×#67	—	3	1	no	—
330	C₂×#67	—	3	1	no	—
331	C₂²×Dic₃	—	3	1	no	—
332	C₂²×Dic₃	—	3	1	no	—
333	C₂×C₄×D₃	—	3	1	no	—
334	C₂×C₄×D₃	—	3	1	no	—
335	C₂×Dic₆	—	3	1	no	—
336	C₃×C₄⋊C₄	—	3	1	no	—
337	C₃×C₄⋊C₄	—	3	1	no	—
338	C₃×C₄⋊C₄	—	9	1	no	—
339	C₃×C₄⋊C₄	—	9	1	no	—
340	C₃×C₄⋊C₄	—	9	1	no	—
341	C₃×C₄⋊C₄	—	9	1	no	—
342	C₃×C₄⋊C₄	—	9	1	no	—
343	C₃×C₄⋊C₄	—	9	1	no	—
344	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
345	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
346	C₃×C₂²⋊C₄	—	3	1	no	—
347	C₃×C₂²⋊C₄	—	3	1	no	—
348	C₃×C₂²⋊C₄	—	3	1	no	—
349	C₃×C₂²⋊C₄	—	9	1	no	—
350	C₃×C₂²⋊C₄	—	9	1	no	—
351	C₃×C₂²⋊C₄	—	9	1	no	—
352	C₃×C₂²⋊C₄	—	9	1	no	—
353	C₃×C₂²⋊C₄	—	9	1	no	—
354	C₃×C₂²⋊C₄	—	9	1	no	—
355	C₃×C₂²⋊C₄	—	9	1	no	—
356	C₃×C₂²⋊C₄	—	9	1	no	—
357	C₃×C₂²⋊C₄	—	9	1	no	—
358	C₃×C₂²⋊C₄	—	9	1	no	—
359	C₃×C₂²⋊C₄	—	9	1	no	—
360	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
361	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
362	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
363	C₃×C₄²	—	9	1	no	—
364	C₃×C₄²	—	9	1	no	—
365	C₃×C₄²	—	9	1	no	—
366	#217	—	3	1	no	—
367	#217	—	3	1	no	—
368	#217	—	3	1	no	—
369	(C₂×D₃)⋊C₄	—	3	1	no	—
370	(C₂×D₃)⋊C₄	—	3	1	no	—
371	(C₂×D₃)⋊C₄	—	3	1	no	—
372	(C₂×D₃)⋊C₄	—	3	1	no	—
373	(C₂×D₃)⋊C₄	—	3	1	no	—
374	(C₂×D₃)⋊C₄	—	3	1	no	—
375	(C₂×D₃)⋊C₄	—	3	1	no	—
376	(C₂×D₃)⋊C₄	—	3	1	no	—
377	C₄⋊Dic₃	—	3	1	no	—
378	C₄⋊Dic₃	—	3	1	no	—
379	C₄⋊Dic₃	—	3	1	no	—
380	C₄⋊Dic₃	—	3	1	no	—
381	Dic₃⋊C₄	—	3	1	no	—
382	Dic₃⋊C₄	—	3	1	no	—
383	C₄×Dic₃	—	3	1	no	—
384	C₄×Dic₃	—	3	1	no	—
385	C₄×Dic₃	—	3	1	no	—
386	C₂²×C₃²	—	2	1	no	—
387	C₂²×C₃²	—	2	1	no	—
388	C₂²×C₃²	—	2	1	no	—
389	C₂²×C₃²	—	2	1	no	—
390	C₂²×C₃²	—	2	1	no	—
391	C₂²×C₃²	#237	1	2	yes	—
392	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
393	C₂×C₃×D₃	—	3	2	no	—
394	C₂×C₃×D₃	—	6	1	no	—
395	C₂×C₃×D₃	—	6	1	no	—
396	C₂×C₃×D₃	—	6	1	no	—
397	C₂×C₃×D₃	—	6	1	no	—
398	C₂×C₃×D₃	—	6	1	no	—
399	C₂×C₃×D₃	—	12	4	no	—
400	C₃²×C₄	—	2	1	no	—
401	C₃²×C₄	—	2	1	no	—
402	C₃²×C₄	—	2	1	no	—
403	C₃²×C₄	—	2	1	no	—
404	C₃²×C₄	—	2	1	no	—
405	C₃×Dic₃	—	6	1	no	—
406	C₃×Dic₃	—	6	1	no	—
407	C₃×Dic₃	—	6	1	no	—
408	C₃×Dic₃	—	6	1	no	—
409	C₃×Dic₃	—	6	1	no	—
410	C₃×Dic₃	—	6	1	no	—
411	C₂²×C₉	—	2	1	no	—
412	C₂²×C₉	—	2	1	no	—
413	C₂²×C₉	—	2	1	no	—
414	C₂²×C₉	—	2	1	no	—
415	C₂²×C₉	—	2	1	no	—
416	C₂²×C₉	—	2	1	no	—
417	C₂²×C₉	—	2	2	no	—
418	C₂²×C₉	—	4	1	no	—
419	C₂²×C₉	—	4	1	no	—
420	C₂²×C₉	—	4	1	no	—
421	C₂²×C₉	—	4	1	no	—
422	C₂²×C₉	—	4	1	no	—
423	C₂²×C₉	C₃×#41	1	2	yes	—
424	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
425	C₂×D₉	—	2	1	no	—
426	C₂×D₉	—	2	1	no	—
427	C₂×D₉	—	2	1	no	—
428	C₂×D₉	—	2	1	no	—
429	C₂×D₉	—	2	1	no	—
430	C₂×D₉	—	4	4	no	—
431	C₂×D₉	C₃×#41	1	2	yes	—
432	C₄×C₉	—	2	1	no	—
433	C₄×C₉	—	2	1	no	—
434	C₄×C₉	—	2	1	no	—
435	C₄×C₉	—	2	1	no	—
436	C₄×C₉	—	2	1	no	—
437	C₄×C₉	—	4	1	no	—
438	C₄×C₉	—	4	1	no	—
439	C₄×C₉	—	4	1	no	—
440	C₄×C₉	—	4	1	no	—
441	C₄×C₉	—	4	1	no	—
442	Dic₉	—	2	1	no	—
443	Dic₉	—	2	1	no	—
444	Dic₉	—	2	1	no	—
445	Dic₉	—	2	1	no	—
446	Dic₉	—	2	1	no	—
447	Dic₉	—	2	1	no	—
448	#126	—	9	1	no	—
449	#126	—	9	1	no	—
450	#124	—	9	1	no	—
451	#123	—	9	1	no	—
452	#123	—	9	1	no	—
453	#123	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
454	C₂²⋊Q₈	—	9	1	no	—
455	C₂²⋊Q₈	—	9	1	no	—
456	#120	—	9	1	no	—
457	C₄×D₄	—	9	1	no	—
458	C₄×D₄	—	9	1	no	—
459	#117	—	9	1	no	—
460	#117	—	9	1	no	—
461	C₂×C₂²⋊C₄	—	9	1	no	—
462	C₂×C₂²⋊C₄	—	9	1	no	—
463	3₋¹⁺²	#551	1	1	yes	characteristic, complemented, Sylow
464	C₂³×C₃	—	3	1	no	—
465	C₂³×C₃	—	3	1	no	—
466	C₂³×C₃	—	9	1	no	—
467	C₂³×C₃	—	9	1	no	—
468	C₂³×C₃	—	18	2	no	—
469	C₂³×C₃	—	18	2	no	—
470	C₂³×C₃	—	36	1	no	—
471	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
472	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
473	C₂²×D₃	—	3	1	no	—
474	C₂²×D₃	—	3	1	no	—
475	C₂²×D₃	—	6	2	no	—
476	C₂²×D₃	—	6	2	no	—
477	C₂²×D₃	—	12	1	no	—
478	C₃×Q₈	—	36	1	no	—
479	C₃×D₄	—	2	2	no	—
480	C₃×D₄	—	6	2	no	—
481	C₃×D₄	—	18	2	no	—
482	C₃×D₄	—	36	1	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	3	1	no	—
485	C₂×C₃×C₄	—	3	1	no	—
486	C₂×C₃×C₄	—	3	1	no	—
487	C₂×C₃×C₄	—	3	1	no	—
488	C₂×C₃×C₄	—	3	1	no	—
489	C₂×C₃×C₄	—	6	2	no	—
490	C₂×C₃×C₄	—	9	1	no	—
491	C₂×C₃×C₄	—	9	1	no	—
492	C₂×C₃×C₄	—	9	1	no	—
493	C₂×C₃×C₄	—	9	1	no	—
494	C₂×C₃×C₄	—	9	1	no	—
495	C₂×C₃×C₄	—	9	1	no	—
496	C₂×C₃×C₄	—	18	2	no	—
497	C₂×C₃×C₄	—	36	1	no	—
498	C₂×C₃×C₄	—	36	1	no	—
499	C₂×C₃×C₄	—	36	1	no	—
500	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
501	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
502	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
503	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
504	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
505	#67	—	6	2	no	—
506	#67	—	12	1	no	—
507	C₂×Dic₃	—	3	1	no	—
508	C₂×Dic₃	—	3	1	no	—
509	C₂×Dic₃	—	3	1	no	—
510	C₂×Dic₃	—	3	1	no	—
511	C₂×Dic₃	—	3	1	no	—
512	C₂×Dic₃	—	3	1	no	—
513	C₂×Dic₃	—	12	1	no	—
514	C₂×Dic₃	—	12	1	no	—
515	C₄×D₃	—	6	2	no	—
516	C₄×D₃	—	12	1	no	—
517	Dic₆	—	12	1	no	—
518	C₂×C₃²	—	2	2	no	—
519	C₂×C₃²	—	4	1	no	—
520	C₂×C₃²	C₂×#237	1	1	yes	characteristic
521	C₂×C₃²	D₃×#41	1	1	yes	characteristic
522	C₂×C₃²	#1009	1	1	yes	characteristic
523	C₃×D₃	—	6	2	no	—
524	C₃×D₃	—	12	1	no	—
525	C₂×C₉	—	2	2	no	—
526	C₂×C₉	—	2	1	no	—
527	C₂×C₉	—	2	1	no	—
528	C₂×C₉	—	2	1	no	—
529	C₂×C₉	—	4	2	no	—
530	C₂×C₉	—	4	1	no	—
531	C₂×C₉	—	8	1	no	—
532	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
533	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
534	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
535	D₉	—	2	2	no	—
536	D₉	—	4	1	no	—
537	C₂⁴	—	9	1	no	—
538	C₂×Q₈	—	9	1	no	—
539	C₂×D₄	—	9	1	no	—
540	C₂×D₄	—	9	1	no	—
541	C₂×D₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
542	C₂²×C₄	—	9	1	no	—
543	C₂²×C₄	—	9	1	no	—
544	C₂²×C₄	—	9	1	no	—
545	C₂²×C₄	—	9	1	no	—
546	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
547	C₄⋊C₄	—	9	1	no	—
548	C₄⋊C₄	—	9	1	no	—
549	C₄⋊C₄	—	9	1	no	—
550	C₄⋊C₄	—	9	1	no	—
551	C₄⋊C₄	—	9	1	no	—
552	C₄⋊C₄	—	9	1	no	—
553	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
554	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
555	C₂²⋊C₄	—	9	1	no	—
556	C₂²⋊C₄	—	9	1	no	—
557	C₂²⋊C₄	—	9	1	no	—
558	C₂²⋊C₄	—	9	1	no	—
559	C₂²⋊C₄	—	9	1	no	—
560	C₂²⋊C₄	—	9	1	no	—
561	C₂²⋊C₄	—	9	1	no	—
562	C₂²⋊C₄	—	9	1	no	—
563	C₂²⋊C₄	—	9	1	no	—
564	C₂²⋊C₄	—	9	1	no	—
565	C₂²⋊C₄	—	9	1	no	—
566	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
567	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
568	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
569	C₄²	—	9	1	no	—
570	C₄²	—	9	1	no	—
571	C₄²	—	9	1	no	—
572	C₂²×C₃	—	2	1	no	—
573	C₂²×C₃	—	2	1	no	—
574	C₂²×C₃	—	2	1	no	—
575	C₂²×C₃	—	2	1	no	—
576	C₂²×C₃	—	2	1	no	—
577	C₂²×C₃	—	3	1	no	—
578	C₂²×C₃	—	3	2	no	—
579	C₂²×C₃	—	6	1	no	—
580	C₂²×C₃	—	6	1	no	—
581	C₂²×C₃	—	6	1	no	—
582	C₂²×C₃	—	6	1	no	—
583	C₂²×C₃	—	6	1	no	—
584	C₂²×C₃	—	9	2	no	—
585	C₂²×C₃	—	18	1	no	—
586	C₂²×C₃	—	18	1	no	—
587	C₂²×C₃	—	18	1	no	—
588	C₂²×C₃	—	18	1	no	—
589	C₂²×C₃	—	18	1	no	—
590	C₂²×C₃	—	36	4	no	—
591	C₂²×C₃	C₃×#237	1	2	yes	—
592	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
593	C₂×D₃	—	3	2	no	—
594	C₂×D₃	—	6	1	no	—
595	C₂×D₃	—	6	1	no	—
596	C₂×D₃	—	6	1	no	—
597	C₂×D₃	—	6	1	no	—
598	C₂×D₃	—	6	1	no	—
599	C₂×D₃	—	12	4	no	—
600	C₃×C₄	—	2	1	no	—
601	C₃×C₄	—	2	1	no	—
602	C₃×C₄	—	2	1	no	—
603	C₃×C₄	—	2	1	no	—
604	C₃×C₄	—	2	1	no	—
605	C₃×C₄	—	6	1	no	—
606	C₃×C₄	—	6	1	no	—
607	C₃×C₄	—	6	1	no	—
608	C₃×C₄	—	6	1	no	—
609	C₃×C₄	—	6	1	no	—
610	C₃×C₄	—	18	1	no	—
611	C₃×C₄	—	18	1	no	—
612	C₃×C₄	—	18	1	no	—
613	C₃×C₄	—	18	1	no	—
614	C₃×C₄	—	18	1	no	—
615	C₃×C₄	—	18	1	no	—
616	Dic₃	—	6	1	no	—
617	Dic₃	—	6	1	no	—
618	Dic₃	—	6	1	no	—
619	Dic₃	—	6	1	no	—
620	Dic₃	—	6	1	no	—
621	Dic₃	—	6	1	no	—
622	C₃²	#5658	1	1	yes	characteristic
623	C₉	—	2	1	no	—
624	C₉	C₃×#551	1	1	yes	characteristic, complemented
625	C₂³	—	9	1	no	—
626	C₂³	—	9	1	no	—
627	C₂³	—	18	2	no	—
628	C₂³	—	18	2	no	—
629	C₂³	—	36	1	no	—
630	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
631	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
632	Q₈	—	36	1	no	—
633	D₄	—	2	2	no	—
634	D₄	—	18	2	no	—
635	D₄	—	36	1	no	—
636	C₂×C₄	—	2	2	no	—
637	C₂×C₄	—	9	1	no	—
638	C₂×C₄	—	9	1	no	—
639	C₂×C₄	—	9	1	no	—
640	C₂×C₄	—	9	1	no	—
641	C₂×C₄	—	9	1	no	—
642	C₂×C₄	—	9	1	no	—
643	C₂×C₄	—	18	2	no	—
644	C₂×C₄	—	36	1	no	—
645	C₂×C₄	—	36	1	no	—
646	C₂×C₄	—	36	1	no	—
647	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
648	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
649	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
650	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
651	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
652	C₂×C₃	—	2	2	no	—
653	C₂×C₃	—	3	1	no	—
654	C₂×C₃	—	3	1	no	—
655	C₂×C₃	—	3	1	no	—
656	C₂×C₃	—	4	1	no	—
657	C₂×C₃	—	6	2	no	—
658	C₂×C₃	—	12	1	no	—
659	C₂×C₃	—	18	2	no	—
660	C₂×C₃	—	36	1	no	—
661	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
662	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
663	C₂×C₃	C₃×#1009	1	1	yes	characteristic
664	D₃	—	6	2	no	—
665	D₃	—	12	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	9	2	no	—
672	C₂²	—	18	1	no	—
673	C₂²	—	18	1	no	—
674	C₂²	—	18	1	no	—
675	C₂²	—	18	1	no	—
676	C₂²	—	18	1	no	—
677	C₂²	—	36	4	no	—
678	C₂²	#3699⋊C₃	1	2	yes	—
679	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
680	C₄	—	2	1	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	18	1	no	—
686	C₄	—	18	1	no	—
687	C₄	—	18	1	no	—
688	C₄	—	18	1	no	—
689	C₄	—	18	1	no	—
690	C₄	—	18	1	no	—
691	C₃	—	3	1	no	—
692	C₃	C₃×#5658	1	1	yes	characteristic
693	C₂	—	2	2	no	—
694	C₂	—	4	1	no	—
695	C₂	—	18	2	no	—
696	C₂	—	36	1	no	—
697	C₂	C₂×#3699⋊C₃	1	1	yes	characteristic
698	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic
699	C₂	#11722641	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×AGL(1,ℤ/9)
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini, socle	C₂²×C₃	C₂³×C₃×D₃
Fitting	3₋¹⁺²×#123	C₂
prime radical	#63499⋊C₃	C₂
hypercenter	#123	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#551
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ #123

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×#123	C₂	semidirect
3. D₄×3₋¹⁺²⋊C₄	C₂	semidirect
4. C₂×(C₂×AGL(1,ℤ/9))⋊C₄	C₂	semidirect
5. #63488⋊C₃	C₂	semidirect
6. #63460⋊C₃	C₂	semidirect
7. #63460⋊C₃	C₂	semidirect
8. #63459⋊C₃	C₂	semidirect
9. #63454⋊C₃	C₂	semidirect
10. #63448⋊C₃	C₂	semidirect
11. #63447⋊C₃	C₂	semidirect
12. #63445⋊C₃	C₂	semidirect
13. (#611⋊C₃)⋊C₄	C₂	semidirect
14. C₂²⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
15. #63440⋊C₃	C₂	semidirect
17. #10589760	C₃	semidirect
24. C₂²×3₋¹⁺²⋊C₄	C₂²	semidirect
27. C₂×3₋¹⁺²⋊Q₈	C₂²	semidirect
28. C₄⋊C₄×3₋¹⁺²	C₂²	semidirect
29. C₄⋊C₄×3₋¹⁺²	C₂²	semidirect
31. C₂²⋊C₄×3₋¹⁺²	C₂²	semidirect
32. C₂²⋊C₄×3₋¹⁺²	C₂²	semidirect
35. #3676⋊C₃	C₂²	semidirect
44. C₄⋊(3₋¹⁺²⋊C₄)	C₂²	semidirect
45. C₄⋊(3₋¹⁺²⋊C₄)	C₂²	semidirect
46. C₄⋊(3₋¹⁺²⋊C₄)	C₂²	semidirect
47. C₄⋊(3₋¹⁺²⋊C₄)	C₂²	semidirect
48. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
49. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
50. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
51. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
52. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
69. C₉×#123	C₂×C₃	semidirect
71. D₄×Dic₉	C₂×C₃	semidirect
72. C₂×(C₂×D₉)⋊C₄	C₂×C₃	semidirect
73. #63488	C₂×C₃	semidirect
74. #63460	C₂×C₃	semidirect
75. #63460	C₂×C₃	semidirect
76. #63459	C₂×C₃	semidirect
77. #63454	C₂×C₃	semidirect
78. #63448	C₂×C₃	semidirect
79. #63447	C₂×C₃	semidirect
80. #63445	C₂×C₃	semidirect
81. #611⋊C₄	C₂×C₃	semidirect
82. C₂²⋊C₄×D₉	C₂×C₃	semidirect
83. #63440	C₂×C₃	semidirect
156. C₂²×Dic₉	C₂²×C₃	semidirect
159. C₂×Dic₁₈	C₂²×C₃	semidirect
162. C₉×C₄⋊C₄	C₂²×C₃	semidirect
163. C₉×C₄⋊C₄	C₂²×C₃	semidirect
168. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
169. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
172. #3676	C₂²×C₃	semidirect
181. C₄⋊Dic₉	C₂²×C₃	semidirect
182. C₄⋊Dic₉	C₂²×C₃	semidirect
183. C₄⋊Dic₉	C₂²×C₃	semidirect
184. C₄⋊Dic₉	C₂²×C₃	semidirect
185. Dic₉⋊C₄	C₂²×C₃	semidirect
186. Dic₉⋊C₄	C₂²×C₃	semidirect
187. C₄×Dic₉	C₂²×C₃	semidirect
188. C₄×Dic₉	C₂²×C₃	semidirect
189. C₄×Dic₉	C₂²×C₃	semidirect
453. #123	AGL(1,ℤ/9)	semidirect
463. 3₋¹⁺²	#551	semidirect
553. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
554. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
567. C₂²⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
568. C₂²⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
624. C₉	C₃×#551	semidirect

Maximal subgroups

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

subgroup	index
3₋¹⁺²×#123	2
#63499⋊C₃	2
D₄×3₋¹⁺²⋊C₄	2
C₂×(C₂×AGL(1,ℤ/9))⋊C₄	2
#63488⋊C₃	2
#63460⋊C₃	2
#63459⋊C₃	2
#63454⋊C₃	2
#63448⋊C₃	2
#63447⋊C₃	2
#63445⋊C₃	2
(#611⋊C₃)⋊C₄	2
C₂²⋊C₄×AGL(1,ℤ/9)	2
#63440⋊C₃	2
C₃×#5658	3
#10589760	3

Subgroups — #10589760⋊C3 #13153068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589760⋊C₃ #13153068