Subgroups — #10589658⋊C₃ #13152658

Order 1728.

791 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	#63499⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#63497⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63491⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×(C₂×AGL(1,ℤ/9))⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#63486⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63445⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
13	#63439⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#11721396	C₂	1	1	yes	maximal, characteristic, complemented
15	#63434⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5556	—	3	1	no	maximal
17	#10589658	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	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
22	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
23	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
24	C₂²×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
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	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
30	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
31	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
32	#3676⋊C₃	C₂²	1	1	yes	characteristic
33	#3676⋊C₃	C₂²	1	1	yes	characteristic
34	#3676⋊C₃	C₂²	1	1	yes	characteristic, complemented
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	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	(3₋¹⁺²⋊C₄)⋊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	(3₋¹⁺²⋊C₄)⋊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×C₄×D₄	D₃	1	1	yes	characteristic
54	C₃×#937	—	3	1	no	—
55	C₃×#935	—	3	1	no	—
56	C₃×#929	—	3	1	no	—
57	C₃×C₄×#67	—	3	1	no	—
58	C₂×C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
59	C₃×#924	—	3	1	no	—
60	C₃×#898	—	3	1	no	—
61	C₃×#896	—	3	1	no	—
62	C₃×#885	—	3	1	no	—
63	C₃×#883	—	3	1	no	—
64	C₃×D₃×C₂²⋊C₄	—	3	1	no	—
65	C₃×#877	—	3	1	no	—
66	C₃×#876	—	3	1	no	—
67	C₃×#872	—	3	1	no	—
68	C₄×D₄×C₉	—	2	1	no	—
69	C₄×D₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
70	#63499	C₂×C₃	1	1	yes	characteristic
71	#63497	C₂×C₃	1	1	yes	characteristic, complemented
72	#63491	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×(C₂×D₉)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
75	#63486	C₂×C₃	1	1	yes	characteristic, complemented
76	#63460	C₂×C₃	1	1	yes	characteristic, complemented
77	#63458	C₂×C₃	1	1	yes	characteristic, complemented
78	#63447	C₂×C₃	1	1	yes	characteristic, complemented
79	#63445	C₂×C₃	1	1	yes	characteristic, complemented
80	C₂²⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
81	#63439	C₂×C₃	1	1	yes	characteristic, complemented
82	#63438	C₂×C₃	1	1	yes	characteristic, complemented
83	#63434	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	—	4	1	no	—
93	C₂×C₄×3₋¹⁺²	—	4	1	no	—
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	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
99	#611⋊C₃	—	2	2	no	—
100	#611⋊C₃	—	4	1	no	—
101	C₂×3₋¹⁺²⋊C₄	—	2	2	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	#5556	—	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	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
117	C₂×C₃×#67	—	3	1	no	—
118	C₂×C₃×#67	—	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×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
127	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
128	C₃×#217	—	3	1	no	—
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×Dic₃⋊C₄	—	3	1	no	—
142	C₃×Dic₃⋊C₄	—	3	1	no	—
143	C₃×Dic₃⋊C₄	—	3	1	no	—
144	C₃×Dic₃⋊C₄	—	3	1	no	—
145	C₃×Dic₃⋊C₄	—	3	1	no	—
146	C₃×Dic₃⋊C₄	—	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	—	2	1	no	—
153	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₂×#611	C₂²×C₃	1	1	yes	characteristic
156	C₂×#611	C₂²×C₃	1	1	yes	characteristic
157	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
160	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₉×C₄⋊C₄	—	2	1	no	—
162	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₉×C₂²⋊C₄	—	2	1	no	—
164	C₉×C₂²⋊C₄	—	2	1	no	—
165	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₄²×C₉	—	2	1	no	—
168	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
169	#3676	C₂²×C₃	1	1	yes	characteristic
170	#3676	C₂²×C₃	1	1	yes	characteristic
171	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
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	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
183	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
184	Dic₉⋊C₄	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	Dic₉⋊C₄	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	—	9	1	no	—
219	C₃×#123	—	9	1	no	—
220	C₃×#123	—	9	1	no	—
221	C₃×C₂²⋊Q₈	—	9	1	no	—
222	C₃×C₂²⋊Q₈	—	9	1	no	—
223	C₃×#120	—	9	1	no	—
224	C₃×C₄×D₄	—	3	1	no	—
225	C₃×C₄×D₄	—	9	1	no	—
226	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
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	#935	—	3	1	no	—
233	#929	—	3	1	no	—
234	C₄×#67	—	3	1	no	—
235	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
236	#924	—	3	1	no	—
237	#898	—	3	1	no	—
238	#896	—	3	1	no	—
239	#885	—	3	1	no	—
240	#883	—	3	1	no	—
241	D₃×C₂²⋊C₄	—	3	1	no	—
242	#877	—	3	1	no	—
243	#876	—	3	1	no	—
244	#872	—	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	—	4	1	no	—
254	C₂×C₃²×C₄	—	4	1	no	—
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	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
260	C₃×#67	—	6	2	no	—
261	C₃×#67	—	12	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	—	3	1	no	—
268	C₂×C₃×Dic₃	—	6	2	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	4	no	—
282	D₄×C₉	—	2	2	no	—
283	C₂×C₄×C₉	—	2	1	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	—	4	1	no	—
289	C₂×C₄×C₉	—	4	1	no	—
290	C₂×C₄×C₉	—	4	2	no	—
291	C₂×C₄×C₉	—	4	2	no	—
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	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
297	#611	—	2	2	no	—
298	#611	—	4	1	no	—
299	C₂×Dic₉	—	2	2	no	—
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	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
306	C₄×D₉	—	2	2	no	—
307	C₄×D₉	—	4	1	no	—
308	Dic₁₈	—	4	1	no	—
309	#551	—	9	1	no	Sylow
310	C₂×3₋¹⁺²	—	2	2	no	—
311	C₂×3₋¹⁺²	—	4	1	no	—
312	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
313	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
314	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
315	AGL(1,ℤ/9)	—	2	2	no	—
316	AGL(1,ℤ/9)	—	4	1	no	—
317	C₂⁴×C₃	—	9	1	no	—
318	C₂³×D₃	—	3	1	no	—
319	C₂×C₃×Q₈	—	9	1	no	—
320	C₂×C₃×D₄	—	3	1	no	—
321	C₂×C₃×D₄	—	9	1	no	—
322	C₂×C₃×D₄	—	9	1	no	—
323	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
324	C₂²×C₃×C₄	—	3	1	no	—
325	C₂²×C₃×C₄	—	3	1	no	—
326	C₂²×C₃×C₄	—	9	1	no	—
327	C₂²×C₃×C₄	—	9	1	no	—
328	C₂²×C₃×C₄	—	9	1	no	—
329	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
330	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
331	C₂×#67	—	3	1	no	—
332	C₂×#67	—	3	1	no	—
333	C₂²×Dic₃	—	3	1	no	—
334	C₂×C₄×D₃	—	3	1	no	—
335	C₂×C₄×D₃	—	3	1	no	—
336	C₂×Dic₆	—	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	—	9	1	no	—
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	—	9	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×C₄²	—	3	1	no	—
363	C₃×C₄²	—	9	1	no	—
364	C₃×C₄²	—	9	1	no	—
365	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
366	#217	—	3	1	no	—
367	#217	—	3	1	no	—
368	#217	—	3	1	no	—
369	#217	—	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	(C₂×D₃)⋊C₄	—	3	1	no	—
378	C₄⋊Dic₃	—	3	1	no	—
379	Dic₃⋊C₄	—	3	1	no	—
380	Dic₃⋊C₄	—	3	1	no	—
381	Dic₃⋊C₄	—	3	1	no	—
382	Dic₃⋊C₄	—	3	1	no	—
383	Dic₃⋊C₄	—	3	1	no	—
384	Dic₃⋊C₄	—	3	1	no	—
385	C₄×Dic₃	—	3	1	no	—
386	C₄×Dic₃	—	3	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	—	2	1	no	—
392	C₂²×C₃²	#235	1	2	yes	—
393	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
394	C₂×C₃×D₃	—	3	2	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	—	6	1	no	—
400	C₂×C₃×D₃	—	12	4	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	C₃²×C₄	—	2	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	C₃×Dic₃	—	6	1	no	—
412	C₂²×C₉	—	2	1	no	—
413	C₂²×C₉	—	2	1	no	—
414	C₂²×C₉	—	2	2	no	—
415	C₂²×C₉	—	2	1	no	—
416	C₂²×C₉	—	2	1	no	—
417	C₂²×C₉	—	2	1	no	—
418	C₂²×C₉	—	2	1	no	—
419	C₂²×C₉	—	2	2	no	—
420	C₂²×C₉	—	4	1	no	—
421	C₂²×C₉	—	4	1	no	—
422	C₂²×C₉	—	4	1	no	—
423	C₂²×C₉	—	4	1	no	—
424	C₂²×C₉	C₃×#41	1	2	yes	—
425	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
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	—	2	1	no	—
431	C₂×D₉	—	4	4	no	—
432	C₂×D₉	C₃×#41	1	2	yes	—
433	C₄×C₉	—	2	2	no	—
434	C₄×C₉	—	2	2	no	—
435	C₄×C₉	—	2	1	no	—
436	C₄×C₉	—	2	1	no	—
437	C₄×C₉	—	2	1	no	—
438	C₄×C₉	—	2	1	no	—
439	C₄×C₉	—	2	1	no	—
440	C₄×C₉	—	4	1	no	—
441	C₄×C₉	—	4	1	no	—
442	C₄×C₉	—	4	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	Dic₉	—	2	1	no	—
449	#126	—	9	1	no	—
450	#126	—	9	1	no	—
451	#124	—	9	1	no	—
452	#123	—	9	1	no	—
453	#123	—	9	1	no	—
454	#123	—	9	1	no	—
455	C₂²⋊Q₈	—	9	1	no	—
456	C₂²⋊Q₈	—	9	1	no	—
457	#120	—	9	1	no	—
458	C₄×D₄	—	9	1	no	—
459	C₄×D₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
460	#117	—	9	1	no	—
461	#117	—	9	1	no	—
462	C₂×C₂²⋊C₄	—	9	1	no	—
463	C₂×C₂²⋊C₄	—	9	1	no	—
464	3₋¹⁺²	#551	1	1	yes	characteristic, complemented, Sylow
465	C₂³×C₃	—	3	1	no	—
466	C₂³×C₃	—	3	1	no	—
467	C₂³×C₃	—	9	1	no	—
468	C₂³×C₃	—	9	1	no	—
469	C₂³×C₃	—	18	2	no	—
470	C₂³×C₃	—	18	2	no	—
471	C₂³×C₃	—	36	1	no	—
472	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
473	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
474	C₂²×D₃	—	3	1	no	—
475	C₂²×D₃	—	3	1	no	—
476	C₂²×D₃	—	6	2	no	—
477	C₂²×D₃	—	6	2	no	—
478	C₂²×D₃	—	12	1	no	—
479	C₃×Q₈	—	36	1	no	—
480	C₃×D₄	—	2	2	no	—
481	C₃×D₄	—	6	2	no	—
482	C₃×D₄	—	18	2	no	—
483	C₃×D₄	—	36	1	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	—	4	1	no	—
490	C₂×C₃×C₄	—	4	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	—	9	1	no	—
497	C₂×C₃×C₄	—	12	1	no	—
498	C₂×C₃×C₄	—	12	1	no	—
499	C₂×C₃×C₄	—	18	2	no	—
500	C₂×C₃×C₄	—	18	2	no	—
501	C₂×C₃×C₄	—	36	1	no	—
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	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
506	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
507	#67	—	6	2	no	—
508	#67	—	12	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	—	3	1	no	—
514	C₂×Dic₃	—	3	1	no	—
515	C₂×Dic₃	—	6	2	no	—
516	C₄×D₃	—	6	2	no	—
517	C₄×D₃	—	12	1	no	—
518	Dic₆	—	12	1	no	—
519	C₂×C₃²	—	2	2	no	—
520	C₂×C₃²	—	4	1	no	—
521	C₂×C₃²	C₂×#235	1	1	yes	characteristic
522	C₂×C₃²	#1004	1	1	yes	characteristic
523	C₂×C₃²	D₃×#41	1	1	yes	characteristic
524	C₃×D₃	—	6	2	no	—
525	C₃×D₃	—	12	1	no	—
526	C₂×C₉	—	2	2	no	—
527	C₂×C₉	—	2	1	no	—
528	C₂×C₉	—	2	1	no	—
529	C₂×C₉	—	2	1	no	—
530	C₂×C₉	—	4	2	no	—
531	C₂×C₉	—	4	2	no	—
532	C₂×C₉	—	4	1	no	—
533	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
534	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
535	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
536	D₉	—	2	2	no	—
537	D₉	—	4	1	no	—
538	C₂⁴	—	9	1	no	—
539	C₂×Q₈	—	9	1	no	—
540	C₂×D₄	—	9	1	no	—
541	C₂×D₄	—	9	1	no	—
542	C₂×D₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
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	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
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	—	9	1	no	—
554	C₄⋊C₄	—	9	1	no	—
555	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
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	—	9	1	no	—
567	C₂²⋊C₄	—	9	1	no	—
568	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
569	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
570	C₄²	—	9	1	no	—
571	C₄²	—	9	1	no	—
572	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
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	—	2	1	no	—
578	C₂²×C₃	—	3	1	no	—
579	C₂²×C₃	—	3	2	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	—	6	1	no	—
585	C₂²×C₃	—	9	2	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	—	18	1	no	—
591	C₂²×C₃	—	36	4	no	—
592	C₂²×C₃	C₃×#235	1	2	yes	—
593	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
594	C₂×D₃	—	3	2	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	—	6	1	no	—
600	C₂×D₃	—	12	4	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	—	2	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	—	6	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	C₃×C₄	—	18	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	Dic₃	—	6	1	no	—
623	C₃²	#5556	1	1	yes	characteristic
624	C₉	—	2	1	no	—
625	C₉	C₃×#551	1	1	yes	characteristic, complemented
626	C₂³	—	9	1	no	—
627	C₂³	—	9	1	no	—
628	C₂³	—	18	2	no	—
629	C₂³	—	18	2	no	—
630	C₂³	—	36	1	no	—
631	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
632	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
633	Q₈	—	36	1	no	—
634	D₄	—	2	2	no	—
635	D₄	—	18	2	no	—
636	D₄	—	36	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	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	—	9	1	no	—
644	C₂×C₄	—	9	1	no	—
645	C₂×C₄	—	18	2	no	—
646	C₂×C₄	—	18	2	no	—
647	C₂×C₄	—	36	1	no	—
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×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
653	C₂×C₃	—	2	2	no	—
654	C₂×C₃	—	3	1	no	—
655	C₂×C₃	—	3	1	no	—
656	C₂×C₃	—	3	1	no	—
657	C₂×C₃	—	4	1	no	—
658	C₂×C₃	—	6	2	no	—
659	C₂×C₃	—	12	1	no	—
660	C₂×C₃	—	18	2	no	—
661	C₂×C₃	—	36	1	no	—
662	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
663	C₂×C₃	C₃×#1004	1	1	yes	characteristic
664	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
665	D₃	—	6	2	no	—
666	D₃	—	12	1	no	—
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	1	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	1	no	—
672	C₂²	—	9	2	no	—
673	C₂²	—	18	1	no	—
674	C₂²	—	18	1	no	—
675	C₂²	—	18	1	no	—
676	C₂²	—	18	1	no	—
677	C₂²	—	18	1	no	—
678	C₂²	—	36	4	no	—
679	C₂²	#3697⋊C₃	1	2	yes	—
680	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	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	C₄	—	18	1	no	—
692	C₃	—	3	1	no	—
693	C₃	C₃×#5556	1	1	yes	characteristic
694	C₂	—	2	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	18	2	no	—
697	C₂	—	36	1	no	—
698	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
699	C₂	#63710⋊C₃	1	1	yes	characteristic
700	C₂	#41×AGL(1,ℤ/9)	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	C₄×D₄×3₋¹⁺²	C₂
prime radical	#63499⋊C₃	C₂
hypercenter	C₄×D₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#551
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₄×D₄×3₋¹⁺²	C₂	semidirect
3. #63497⋊C₃	C₂	semidirect
4. #63491⋊C₃	C₂	semidirect
5. C₄×#611⋊C₃	C₂	semidirect
6. C₂×(C₂×AGL(1,ℤ/9))⋊C₄	C₂	semidirect
7. #63486⋊C₃	C₂	semidirect
8. #63460⋊C₃	C₂	semidirect
9. #63458⋊C₃	C₂	semidirect
10. #63447⋊C₃	C₂	semidirect
11. #63445⋊C₃	C₂	semidirect
12. C₂²⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
13. #63439⋊C₃	C₂	semidirect
14. #11721396	C₂	semidirect
15. #63434⋊C₃	C₂	semidirect
17. #10589658	C₃	semidirect
21. C₂²×C₄×3₋¹⁺²	C₂²	semidirect
27. C₂×3₋¹⁺²⋊Q₈	C₂²	semidirect
28. C₄⋊C₄×3₋¹⁺²	C₂²	semidirect
30. C₂²⋊C₄×3₋¹⁺²	C₂²	semidirect
31. C₄²×3₋¹⁺²	C₂²	semidirect
34. #3676⋊C₃	C₂²	semidirect
35. #3676⋊C₃	C₂²	semidirect
44. C₄⋊(3₋¹⁺²⋊C₄)	C₂²	semidirect
45. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
46. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
47. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
48. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
49. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
50. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
51. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
52. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
69. C₄×D₄×C₉	C₂×C₃	semidirect
71. #63497	C₂×C₃	semidirect
72. #63491	C₂×C₃	semidirect
73. C₄×#611	C₂×C₃	semidirect
74. C₂×(C₂×D₉)⋊C₄	C₂×C₃	semidirect
75. #63486	C₂×C₃	semidirect
76. #63460	C₂×C₃	semidirect
77. #63458	C₂×C₃	semidirect
78. #63447	C₂×C₃	semidirect
79. #63445	C₂×C₃	semidirect
80. C₂²⋊C₄×D₉	C₂×C₃	semidirect
81. #63439	C₂×C₃	semidirect
82. #63438	C₂×C₃	semidirect
83. #63434	C₂×C₃	semidirect
154. C₂²×C₄×C₉	C₂²×C₃	semidirect
160. C₂×Dic₁₈	C₂²×C₃	semidirect
162. C₉×C₄⋊C₄	C₂²×C₃	semidirect
166. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
168. C₄²×C₉	C₂²×C₃	semidirect
171. #3676	C₂²×C₃	semidirect
172. #3676	C₂²×C₃	semidirect
181. C₄⋊Dic₉	C₂²×C₃	semidirect
182. Dic₉⋊C₄	C₂²×C₃	semidirect
183. Dic₉⋊C₄	C₂²×C₃	semidirect
184. Dic₉⋊C₄	C₂²×C₃	semidirect
185. Dic₉⋊C₄	C₂²×C₃	semidirect
186. Dic₉⋊C₄	C₂²×C₃	semidirect
187. Dic₉⋊C₄	C₂²×C₃	semidirect
188. C₄×Dic₉	C₂²×C₃	semidirect
189. C₄×Dic₉	C₂²×C₃	semidirect
459. C₄×D₄	AGL(1,ℤ/9)	semidirect
464. 3₋¹⁺²	#551	semidirect
547. C₂²×C₄	C₂×AGL(1,ℤ/9)	semidirect
555. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
569. C₂²⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
572. C₄²	C₂×AGL(1,ℤ/9)	semidirect
625. 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
C₄×D₄×3₋¹⁺²	2
#63499⋊C₃	2
#63497⋊C₃	2
#63491⋊C₃	2
C₄×#611⋊C₃	2
C₂×(C₂×AGL(1,ℤ/9))⋊C₄	2
#63486⋊C₃	2
#63460⋊C₃	2
#63458⋊C₃	2
#63447⋊C₃	2
#63445⋊C₃	2
C₂²⋊C₄×AGL(1,ℤ/9)	2
#63439⋊C₃	2
#11721396	2
#63434⋊C₃	2
C₃×#5556	3
#10589658	3

Subgroups — #10589658⋊C3 #13152658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589658⋊C₃ #13152658