Subgroups — #10589806⋊C₃ #13153247

Order 1728.

780 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63457⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63457⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63455⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63445⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63444⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#63444⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
14	#63437⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5704	—	3	1	no	maximal
17	#10589806	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂³×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
19	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
20	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
27	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
28	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic, complemented
30	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
32	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
34	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
35	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
36	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
37	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
38	#3676⋊C₃	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	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
45	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic, complemented
46	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic, complemented
50	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₃²×#126	D₃	1	1	yes	characteristic
54	C₃×#898	—	3	1	no	—
55	C₃×#896	—	3	1	no	—
56	C₃×#895	—	3	1	no	—
57	C₃×#895	—	3	1	no	—
58	C₃×#894	—	3	1	no	—
59	C₃×#893	—	3	1	no	—
60	C₃×#885	—	3	1	no	—
61	C₃×#884	—	3	1	no	—
62	C₃×#883	—	3	1	no	—
63	C₃×#882	—	3	1	no	—
64	C₃×#882	—	3	1	no	—
65	C₃×D₃×C₂²⋊C₄	—	3	1	no	—
66	C₃×#875	—	3	1	no	—
67	C₃×C₄×D₁₂	—	3	1	no	—
68	C₉×#126	—	2	1	no	—
69	C₉×#126	C₂×C₃	1	1	yes	characteristic, complemented
70	#63460	C₂×C₃	1	1	yes	characteristic, complemented
71	#63458	C₂×C₃	1	1	yes	characteristic, complemented
72	#63457	C₂×C₃	1	1	yes	characteristic, complemented
73	#63457	C₂×C₃	1	1	yes	characteristic, complemented
74	#63456	C₂×C₃	1	1	yes	characteristic, complemented
75	#63455	C₂×C₃	1	1	yes	characteristic, complemented
76	#63447	C₂×C₃	1	1	yes	characteristic, complemented
77	#63446	C₂×C₃	1	1	yes	characteristic, complemented
78	#63445	C₂×C₃	1	1	yes	characteristic, complemented
79	#63444	C₂×C₃	1	1	yes	characteristic, complemented
80	#63444	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂²⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
82	#63437	C₂×C₃	1	1	yes	characteristic, complemented
83	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
85	C₂²×AGL(1,ℤ/9)	—	2	2	no	—
86	C₂²×AGL(1,ℤ/9)	—	4	1	no	—
87	C₂²×AGL(1,ℤ/9)	—	4	1	no	—
88	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
89	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
90	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
91	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
92	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
99	#611⋊C₃	—	4	1	no	—
100	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
104	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
105	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
106	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
107	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
108	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
109	C₄×AGL(1,ℤ/9)	—	4	1	no	—
110	C₄×AGL(1,ℤ/9)	—	4	1	no	—
111	C₄×AGL(1,ℤ/9)	—	4	1	no	—
112	C₄×AGL(1,ℤ/9)	—	4	1	no	—
113	3₋¹⁺²⋊Q₈	—	4	1	no	—
114	C₃×#538	—	9	1	no	—
115	#5704	—	3	1	no	—
116	C₂³×C₃×D₃	—	3	1	no	—
117	C₂×C₃×#67	—	3	1	no	—
118	C₂×C₃×#67	—	3	1	no	—
119	C₂×C₃×D₁₂	—	3	1	no	—
120	C₂×C₃×D₁₂	—	3	1	no	—
121	C₂×C₃×D₁₂	—	3	1	no	—
122	C₂×C₃×D₁₂	—	3	1	no	—
123	C₂×C₃×D₁₂	—	3	1	no	—
124	C₂×C₃×C₄×D₃	—	3	1	no	—
125	C₂×C₃×C₄×D₃	—	3	1	no	—
126	C₂×C₃×C₄×D₃	—	3	1	no	—
127	C₂×C₃×C₄×D₃	—	3	1	no	—
128	C₂×C₃×Dic₆	—	3	1	no	—
129	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
130	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
131	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
134	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
135	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
136	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
137	C₃×#217	—	3	1	no	—
138	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
139	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
140	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
141	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
142	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
143	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
144	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
145	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
146	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
147	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
148	C₃×C₄⋊Dic₃	—	3	1	no	—
149	C₃×Dic₃⋊C₄	—	3	1	no	—
150	C₃×Dic₃⋊C₄	—	3	1	no	—
151	C₃×C₄×Dic₃	—	3	1	no	—
152	C₂×#611	C₂²×C₃	1	1	yes	characteristic
153	C₂×#611	C₂²×C₃	1	1	yes	characteristic
154	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
155	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
156	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
157	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
158	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₉×C₄⋊C₄	—	2	1	no	—
165	C₉×C₄⋊C₄	—	2	1	no	—
166	C₉×C₄⋊C₄	—	2	1	no	—
167	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₉×C₄⋊C₄	C₂²×C₃	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	C₂²×C₃	1	1	yes	characteristic
174	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₄²×C₉	—	2	1	no	—
177	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
178	#3676	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	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
185	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
186	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
187	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
188	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
190	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
191	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂²×3₋¹⁺²	—	2	1	no	—
194	C₂²×3₋¹⁺²	—	2	1	no	—
195	C₂²×3₋¹⁺²	—	2	1	no	—
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)	—	2	1	no	—
203	C₂×AGL(1,ℤ/9)	—	2	1	no	—
204	C₂×AGL(1,ℤ/9)	—	2	1	no	—
205	C₂×AGL(1,ℤ/9)	—	2	1	no	—
206	C₂×AGL(1,ℤ/9)	—	2	1	no	—
207	C₂×AGL(1,ℤ/9)	—	2	1	no	—
208	C₂×AGL(1,ℤ/9)	—	4	4	no	—
209	C₂×AGL(1,ℤ/9)	#41	1	2	yes	—
210	C₄×3₋¹⁺²	—	2	1	no	—
211	C₄×3₋¹⁺²	—	2	1	no	—
212	C₄×3₋¹⁺²	—	2	1	no	—
213	C₄×3₋¹⁺²	—	2	1	no	—
214	C₄×3₋¹⁺²	—	2	1	no	—
215	C₄×3₋¹⁺²	—	2	1	no	—
216	3₋¹⁺²⋊C₄	—	2	1	no	—
217	3₋¹⁺²⋊C₄	—	2	1	no	—
218	3₋¹⁺²⋊C₄	—	2	1	no	—
219	3₋¹⁺²⋊C₄	—	2	1	no	—
220	C₃×#126	—	3	1	no	—
221	C₃×#126	—	9	1	no	—
222	C₃×#126	C₃×D₃	1	1	yes	characteristic
223	C₃×#124	—	9	1	no	—
224	C₃×#124	—	9	1	no	—
225	C₃×#123	—	9	1	no	—
226	C₃×#123	—	9	1	no	—
227	C₃×C₂²⋊Q₈	—	9	1	no	—
228	C₃×#121	—	9	1	no	—
229	C₃×#121	—	9	1	no	—
230	C₃×#121	—	9	1	no	—
231	C₃×#120	—	9	1	no	—
232	C₃×#120	—	9	1	no	—
233	C₃×C₄×D₄	—	9	1	no	—
234	C₃×C₄×D₄	—	9	1	no	—
235	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
236	#898	—	3	1	no	—
237	#896	—	3	1	no	—
238	#895	—	3	1	no	—
239	#895	—	3	1	no	—
240	#894	—	3	1	no	—
241	#893	—	3	1	no	—
242	#885	—	3	1	no	—
243	#884	—	3	1	no	—
244	#883	—	3	1	no	—
245	#882	—	3	1	no	—
246	#882	—	3	1	no	—
247	D₃×C₂²⋊C₄	—	3	1	no	—
248	#875	—	3	1	no	—
249	C₄×D₁₂	—	3	1	no	—
250	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
251	C₂²×C₃×D₃	—	3	1	no	—
252	C₂²×C₃×D₃	—	3	1	no	—
253	C₂²×C₃×D₃	—	3	1	no	—
254	C₂²×C₃×D₃	—	3	1	no	—
255	C₂²×C₃×D₃	—	6	2	no	—
256	C₂²×C₃×D₃	—	12	1	no	—
257	C₂²×C₃×D₃	—	12	1	no	—
258	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
259	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
260	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
261	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
262	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
263	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
264	C₃×#67	—	12	1	no	—
265	C₃×#67	—	12	1	no	—
266	C₂×C₃×Dic₃	—	3	1	no	—
267	C₂×C₃×Dic₃	—	3	1	no	—
268	C₂×C₃×Dic₃	—	3	1	no	—
269	C₂×C₃×Dic₃	—	3	1	no	—
270	C₃×D₁₂	—	6	2	no	—
271	C₃×D₁₂	—	6	2	no	—
272	C₃×D₁₂	—	12	1	no	—
273	C₃×D₁₂	—	12	1	no	—
274	C₃×D₁₂	—	12	1	no	—
275	C₃×C₄×D₃	—	12	1	no	—
276	C₃×C₄×D₃	—	12	1	no	—
277	C₃×C₄×D₃	—	12	1	no	—
278	C₃×C₄×D₃	—	12	1	no	—
279	C₃×Dic₆	—	12	1	no	—
280	C₂³×C₉	—	2	1	no	—
281	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
282	C₂²×D₉	—	2	2	no	—
283	C₂²×D₉	—	4	1	no	—
284	C₂²×D₉	—	4	1	no	—
285	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
286	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
287	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
288	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
294	C₂×C₄×C₉	—	2	1	no	—
295	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
298	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
301	#611	—	4	1	no	—
302	#611	—	4	1	no	—
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	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
307	D₃₆	—	2	2	no	—
308	D₃₆	—	2	2	no	—
309	D₃₆	—	4	1	no	—
310	D₃₆	—	4	1	no	—
311	D₃₆	—	4	1	no	—
312	C₄×D₉	—	4	1	no	—
313	C₄×D₉	—	4	1	no	—
314	C₄×D₉	—	4	1	no	—
315	C₄×D₉	—	4	1	no	—
316	Dic₁₈	—	4	1	no	—
317	#538	—	9	1	no	Sylow
318	C₂×3₋¹⁺²	—	4	1	no	—
319	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
320	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
322	AGL(1,ℤ/9)	—	2	2	no	—
323	AGL(1,ℤ/9)	—	4	1	no	—
324	AGL(1,ℤ/9)	—	4	1	no	—
325	AGL(1,ℤ/9)	—	4	1	no	—
326	C₂⁴×C₃	—	9	1	no	—
327	C₂³×D₃	—	3	1	no	—
328	C₂×C₃×Q₈	—	9	1	no	—
329	C₂×C₃×D₄	—	9	1	no	—
330	C₂×C₃×D₄	—	9	1	no	—
331	C₂×C₃×D₄	—	9	1	no	—
332	C₂×C₃×D₄	—	9	1	no	—
333	C₂×C₃×D₄	—	9	1	no	—
334	C₂×C₃×D₄	—	9	1	no	—
335	C₂×C₃×D₄	—	9	1	no	—
336	C₂²×C₃×C₄	—	9	1	no	—
337	C₂²×C₃×C₄	—	9	1	no	—
338	C₂²×C₃×C₄	—	9	1	no	—
339	C₂²×C₃×C₄	—	9	1	no	—
340	C₂×#67	—	3	1	no	—
341	C₂×#67	—	3	1	no	—
342	C₂×D₁₂	—	3	1	no	—
343	C₂×D₁₂	—	3	1	no	—
344	C₂×D₁₂	—	3	1	no	—
345	C₂×D₁₂	—	3	1	no	—
346	C₂×D₁₂	—	3	1	no	—
347	C₂×C₄×D₃	—	3	1	no	—
348	C₂×C₄×D₃	—	3	1	no	—
349	C₂×C₄×D₃	—	3	1	no	—
350	C₂×C₄×D₃	—	3	1	no	—
351	C₂×Dic₆	—	3	1	no	—
352	C₃×C₄⋊C₄	—	3	1	no	—
353	C₃×C₄⋊C₄	—	3	1	no	—
354	C₃×C₄⋊C₄	—	3	1	no	—
355	C₃×C₄⋊C₄	—	9	1	no	—
356	C₃×C₄⋊C₄	—	9	1	no	—
357	C₃×C₄⋊C₄	—	9	1	no	—
358	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
359	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
360	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
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	—	9	1	no	—
365	C₃×C₂²⋊C₄	—	9	1	no	—
366	C₃×C₂²⋊C₄	—	9	1	no	—
367	C₃×C₂²⋊C₄	—	9	1	no	—
368	C₃×C₂²⋊C₄	—	9	1	no	—
369	C₃×C₂²⋊C₄	—	9	1	no	—
370	C₃×C₂²⋊C₄	—	9	1	no	—
371	C₃×C₂²⋊C₄	—	9	1	no	—
372	C₃×C₂²⋊C₄	—	9	1	no	—
373	C₃×C₂²⋊C₄	—	9	1	no	—
374	C₃×C₂²⋊C₄	—	9	1	no	—
375	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
376	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
377	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
378	C₃×C₄²	—	3	1	no	—
379	C₃×C₄²	—	9	1	no	—
380	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
381	#217	—	3	1	no	—
382	(C₂×D₃)⋊C₄	—	3	1	no	—
383	(C₂×D₃)⋊C₄	—	3	1	no	—
384	(C₂×D₃)⋊C₄	—	3	1	no	—
385	(C₂×D₃)⋊C₄	—	3	1	no	—
386	(C₂×D₃)⋊C₄	—	3	1	no	—
387	(C₂×D₃)⋊C₄	—	3	1	no	—
388	(C₂×D₃)⋊C₄	—	3	1	no	—
389	(C₂×D₃)⋊C₄	—	3	1	no	—
390	(C₂×D₃)⋊C₄	—	3	1	no	—
391	(C₂×D₃)⋊C₄	—	3	1	no	—
392	C₄⋊Dic₃	—	3	1	no	—
393	Dic₃⋊C₄	—	3	1	no	—
394	Dic₃⋊C₄	—	3	1	no	—
395	C₄×Dic₃	—	3	1	no	—
396	C₂²×C₃²	—	2	1	no	—
397	C₂²×C₃²	—	2	1	no	—
398	C₂²×C₃²	—	2	1	no	—
399	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
400	C₂×C₃×D₃	—	3	2	no	—
401	C₂×C₃×D₃	—	6	1	no	—
402	C₂×C₃×D₃	—	6	1	no	—
403	C₂×C₃×D₃	—	6	1	no	—
404	C₂×C₃×D₃	—	6	1	no	—
405	C₂×C₃×D₃	—	6	1	no	—
406	C₂×C₃×D₃	—	6	1	no	—
407	C₂×C₃×D₃	—	6	1	no	—
408	C₂×C₃×D₃	—	6	1	no	—
409	C₂×C₃×D₃	—	6	1	no	—
410	C₂×C₃×D₃	—	6	1	no	—
411	C₂×C₃×D₃	—	6	1	no	—
412	C₂×C₃×D₃	—	12	4	no	—
413	C₃²×C₄	—	2	1	no	—
414	C₃²×C₄	—	2	1	no	—
415	C₃²×C₄	—	2	1	no	—
416	C₃²×C₄	—	2	1	no	—
417	C₃²×C₄	—	2	1	no	—
418	C₃²×C₄	—	2	1	no	—
419	C₃×Dic₃	—	6	1	no	—
420	C₃×Dic₃	—	6	1	no	—
421	C₃×Dic₃	—	6	1	no	—
422	C₃×Dic₃	—	6	1	no	—
423	C₂²×C₉	—	2	1	no	—
424	C₂²×C₉	—	2	1	no	—
425	C₂²×C₉	—	2	1	no	—
426	C₂²×C₉	—	2	1	no	—
427	C₂²×C₉	—	4	1	no	—
428	C₂²×C₉	—	4	1	no	—
429	C₂²×C₉	—	4	1	no	—
430	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
431	C₂×D₉	—	2	1	no	—
432	C₂×D₉	—	2	1	no	—
433	C₂×D₉	—	2	1	no	—
434	C₂×D₉	—	2	1	no	—
435	C₂×D₉	—	2	1	no	—
436	C₂×D₉	—	2	1	no	—
437	C₂×D₉	—	2	1	no	—
438	C₂×D₉	—	2	1	no	—
439	C₂×D₉	—	2	1	no	—
440	C₂×D₉	—	2	1	no	—
441	C₂×D₉	—	2	1	no	—
442	C₂×D₉	—	4	4	no	—
443	C₂×D₉	C₃×#41	1	2	yes	—
444	C₄×C₉	—	2	1	no	—
445	C₄×C₉	—	2	1	no	—
446	C₄×C₉	—	2	1	no	—
447	C₄×C₉	—	2	1	no	—
448	C₄×C₉	—	2	1	no	—
449	C₄×C₉	—	2	1	no	—
450	C₄×C₉	—	4	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	—	4	1	no	—
456	Dic₉	—	2	1	no	—
457	Dic₉	—	2	1	no	—
458	Dic₉	—	2	1	no	—
459	Dic₉	—	2	1	no	—
460	#126	—	9	1	no	—
461	#126	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
462	#124	—	9	1	no	—
463	#124	—	9	1	no	—
464	#123	—	9	1	no	—
465	#123	—	9	1	no	—
466	C₂²⋊Q₈	—	9	1	no	—
467	#121	—	9	1	no	—
468	#121	—	9	1	no	—
469	#121	—	9	1	no	—
470	#120	—	9	1	no	—
471	#120	—	9	1	no	—
472	C₄×D₄	—	9	1	no	—
473	C₄×D₄	—	9	1	no	—
474	C₂×C₂²⋊C₄	—	9	1	no	—
475	3₋¹⁺²	#538	1	1	yes	characteristic, complemented, Sylow
476	C₂³×C₃	—	3	1	no	—
477	C₂³×C₃	—	9	1	no	—
478	C₂³×C₃	—	9	1	no	—
479	C₂³×C₃	—	9	1	no	—
480	C₂³×C₃	—	9	1	no	—
481	C₂³×C₃	—	18	2	no	—
482	C₂³×C₃	—	36	1	no	—
483	C₂³×C₃	—	36	1	no	—
484	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
485	C₂²×D₃	—	3	1	no	—
486	C₂²×D₃	—	3	1	no	—
487	C₂²×D₃	—	3	1	no	—
488	C₂²×D₃	—	3	1	no	—
489	C₂²×D₃	—	6	2	no	—
490	C₂²×D₃	—	12	1	no	—
491	C₂²×D₃	—	12	1	no	—
492	C₃×Q₈	—	36	1	no	—
493	C₃×D₄	—	18	2	no	—
494	C₃×D₄	—	18	2	no	—
495	C₃×D₄	—	36	1	no	—
496	C₃×D₄	—	36	1	no	—
497	C₃×D₄	—	36	1	no	—
498	C₃×D₄	—	36	1	no	—
499	C₃×D₄	—	36	1	no	—
500	C₂×C₃×C₄	—	3	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	—	9	1	no	—
507	C₂×C₃×C₄	—	9	1	no	—
508	C₂×C₃×C₄	—	9	1	no	—
509	C₂×C₃×C₄	—	9	1	no	—
510	C₂×C₃×C₄	—	36	1	no	—
511	C₂×C₃×C₄	—	36	1	no	—
512	C₂×C₃×C₄	—	36	1	no	—
513	C₂×C₃×C₄	—	36	1	no	—
514	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
515	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
516	C₂×C₃×C₄	C₂²×C₃×D₃	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	#67	—	12	1	no	—
521	#67	—	12	1	no	—
522	C₂×Dic₃	—	3	1	no	—
523	C₂×Dic₃	—	3	1	no	—
524	C₂×Dic₃	—	3	1	no	—
525	C₂×Dic₃	—	3	1	no	—
526	D₁₂	—	6	2	no	—
527	D₁₂	—	6	2	no	—
528	D₁₂	—	12	1	no	—
529	D₁₂	—	12	1	no	—
530	D₁₂	—	12	1	no	—
531	C₄×D₃	—	12	1	no	—
532	C₄×D₃	—	12	1	no	—
533	C₄×D₃	—	12	1	no	—
534	C₄×D₃	—	12	1	no	—
535	Dic₆	—	12	1	no	—
536	C₂×C₃²	—	4	1	no	—
537	C₂×C₃²	D₃×#41	1	1	yes	characteristic
538	C₂×C₃²	#1009	1	1	yes	characteristic
539	C₂×C₃²	#1009	1	1	yes	characteristic
540	C₃×D₃	—	6	2	no	—
541	C₃×D₃	—	12	1	no	—
542	C₃×D₃	—	12	1	no	—
543	C₃×D₃	—	12	1	no	—
544	C₂×C₉	—	2	1	no	—
545	C₂×C₉	—	2	1	no	—
546	C₂×C₉	—	2	1	no	—
547	C₂×C₉	—	4	1	no	—
548	C₂×C₉	—	8	1	no	—
549	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
550	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
552	D₉	—	2	2	no	—
553	D₉	—	4	1	no	—
554	D₉	—	4	1	no	—
555	D₉	—	4	1	no	—
556	C₂⁴	—	9	1	no	—
557	C₂×Q₈	—	9	1	no	—
558	C₂×D₄	—	9	1	no	—
559	C₂×D₄	—	9	1	no	—
560	C₂×D₄	—	9	1	no	—
561	C₂×D₄	—	9	1	no	—
562	C₂×D₄	—	9	1	no	—
563	C₂×D₄	—	9	1	no	—
564	C₂×D₄	—	9	1	no	—
565	C₂²×C₄	—	9	1	no	—
566	C₂²×C₄	—	9	1	no	—
567	C₂²×C₄	—	9	1	no	—
568	C₂²×C₄	—	9	1	no	—
569	C₄⋊C₄	—	9	1	no	—
570	C₄⋊C₄	—	9	1	no	—
571	C₄⋊C₄	—	9	1	no	—
572	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
573	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
574	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
575	C₂²⋊C₄	—	9	1	no	—
576	C₂²⋊C₄	—	9	1	no	—
577	C₂²⋊C₄	—	9	1	no	—
578	C₂²⋊C₄	—	9	1	no	—
579	C₂²⋊C₄	—	9	1	no	—
580	C₂²⋊C₄	—	9	1	no	—
581	C₂²⋊C₄	—	9	1	no	—
582	C₂²⋊C₄	—	9	1	no	—
583	C₂²⋊C₄	—	9	1	no	—
584	C₂²⋊C₄	—	9	1	no	—
585	C₂²⋊C₄	—	9	1	no	—
586	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
587	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
588	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
589	C₄²	—	9	1	no	—
590	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
591	C₂²×C₃	—	2	1	no	—
592	C₂²×C₃	—	2	1	no	—
593	C₂²×C₃	—	2	1	no	—
594	C₂²×C₃	—	3	1	no	—
595	C₂²×C₃	—	6	1	no	—
596	C₂²×C₃	—	6	1	no	—
597	C₂²×C₃	—	6	1	no	—
598	C₂²×C₃	—	9	2	no	—
599	C₂²×C₃	—	18	1	no	—
600	C₂²×C₃	—	18	1	no	—
601	C₂²×C₃	—	18	1	no	—
602	C₂²×C₃	—	18	1	no	—
603	C₂²×C₃	—	18	1	no	—
604	C₂²×C₃	—	18	1	no	—
605	C₂²×C₃	—	18	1	no	—
606	C₂²×C₃	—	18	1	no	—
607	C₂²×C₃	—	18	1	no	—
608	C₂²×C₃	—	18	1	no	—
609	C₂²×C₃	—	18	1	no	—
610	C₂²×C₃	—	36	4	no	—
611	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
612	C₂×D₃	—	3	2	no	—
613	C₂×D₃	—	6	1	no	—
614	C₂×D₃	—	6	1	no	—
615	C₂×D₃	—	6	1	no	—
616	C₂×D₃	—	6	1	no	—
617	C₂×D₃	—	6	1	no	—
618	C₂×D₃	—	6	1	no	—
619	C₂×D₃	—	6	1	no	—
620	C₂×D₃	—	6	1	no	—
621	C₂×D₃	—	6	1	no	—
622	C₂×D₃	—	6	1	no	—
623	C₂×D₃	—	6	1	no	—
624	C₂×D₃	—	12	4	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	—	6	1	no	—
632	C₃×C₄	—	6	1	no	—
633	C₃×C₄	—	6	1	no	—
634	C₃×C₄	—	6	1	no	—
635	C₃×C₄	—	6	1	no	—
636	C₃×C₄	—	6	1	no	—
637	C₃×C₄	—	18	1	no	—
638	C₃×C₄	—	18	1	no	—
639	C₃×C₄	—	18	1	no	—
640	C₃×C₄	—	18	1	no	—
641	Dic₃	—	6	1	no	—
642	Dic₃	—	6	1	no	—
643	Dic₃	—	6	1	no	—
644	Dic₃	—	6	1	no	—
645	C₃²	#5704	1	1	yes	characteristic
646	C₉	—	2	1	no	—
647	C₉	C₃×#538	1	1	yes	characteristic, complemented
648	C₂³	—	9	1	no	—
649	C₂³	—	9	1	no	—
650	C₂³	—	9	1	no	—
651	C₂³	—	9	1	no	—
652	C₂³	—	18	2	no	—
653	C₂³	—	36	1	no	—
654	C₂³	—	36	1	no	—
655	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
656	Q₈	—	36	1	no	—
657	D₄	—	18	2	no	—
658	D₄	—	18	2	no	—
659	D₄	—	36	1	no	—
660	D₄	—	36	1	no	—
661	D₄	—	36	1	no	—
662	D₄	—	36	1	no	—
663	D₄	—	36	1	no	—
664	C₂×C₄	—	9	1	no	—
665	C₂×C₄	—	9	1	no	—
666	C₂×C₄	—	9	1	no	—
667	C₂×C₄	—	9	1	no	—
668	C₂×C₄	—	36	1	no	—
669	C₂×C₄	—	36	1	no	—
670	C₂×C₄	—	36	1	no	—
671	C₂×C₄	—	36	1	no	—
672	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
673	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
674	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
675	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
676	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
677	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
678	C₂×C₃	—	3	1	no	—
679	C₂×C₃	—	3	1	no	—
680	C₂×C₃	—	3	1	no	—
681	C₂×C₃	—	4	1	no	—
682	C₂×C₃	—	12	1	no	—
683	C₂×C₃	—	18	2	no	—
684	C₂×C₃	—	36	1	no	—
685	C₂×C₃	—	36	1	no	—
686	C₂×C₃	—	36	1	no	—
687	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
688	C₂×C₃	C₃×#1009	1	1	yes	characteristic
689	C₂×C₃	C₃×#1009	1	1	yes	characteristic
690	D₃	—	6	2	no	—
691	D₃	—	12	1	no	—
692	D₃	—	12	1	no	—
693	D₃	—	12	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	9	2	no	—
698	C₂²	—	18	1	no	—
699	C₂²	—	18	1	no	—
700	C₂²	—	18	1	no	—
701	C₂²	—	18	1	no	—
702	C₂²	—	18	1	no	—
703	C₂²	—	18	1	no	—
704	C₂²	—	18	1	no	—
705	C₂²	—	18	1	no	—
706	C₂²	—	18	1	no	—
707	C₂²	—	18	1	no	—
708	C₂²	—	18	1	no	—
709	C₂²	—	36	4	no	—
710	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	18	1	no	—
718	C₄	—	18	1	no	—
719	C₄	—	18	1	no	—
720	C₄	—	18	1	no	—
721	C₃	—	3	1	no	—
722	C₃	C₃×#5704	1	1	yes	characteristic
723	C₂	—	4	1	no	—
724	C₂	—	18	2	no	—
725	C₂	—	36	1	no	—
726	C₂	—	36	1	no	—
727	C₂	—	36	1	no	—
728	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic
729	C₂	#11722641	1	1	yes	characteristic
730	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×#126	C₂
hypercenter	#126	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#538
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ #126

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×#126	C₂	semidirect
2. #63460⋊C₃	C₂	semidirect
3. #63458⋊C₃	C₂	semidirect
4. #63457⋊C₃	C₂	semidirect
5. #63457⋊C₃	C₂	semidirect
6. #63456⋊C₃	C₂	semidirect
7. #63455⋊C₃	C₂	semidirect
8. #63447⋊C₃	C₂	semidirect
9. #63446⋊C₃	C₂	semidirect
10. #63445⋊C₃	C₂	semidirect
11. #63444⋊C₃	C₂	semidirect
12. #63444⋊C₃	C₂	semidirect
13. C₂²⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
14. #63437⋊C₃	C₂	semidirect
15. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
17. #10589806	C₃	semidirect
25. C₂×C₄⋊AGL(1,ℤ/9)	C₂²	semidirect
28. C₂×C₄×AGL(1,ℤ/9)	C₂²	semidirect
29. C₂×C₄×AGL(1,ℤ/9)	C₂²	semidirect
30. C₂×3₋¹⁺²⋊Q₈	C₂²	semidirect
31. C₄⋊C₄×3₋¹⁺²	C₂²	semidirect
32. C₄⋊C₄×3₋¹⁺²	C₂²	semidirect
33. C₄⋊C₄×3₋¹⁺²	C₂²	semidirect
37. C₄²×3₋¹⁺²	C₂²	semidirect
45. (C₂×AGL(1,ℤ/9))⋊C₄	C₂²	semidirect
46. (C₂×AGL(1,ℤ/9))⋊C₄	C₂²	semidirect
47. (C₂×AGL(1,ℤ/9))⋊C₄	C₂²	semidirect
48. (C₂×AGL(1,ℤ/9))⋊C₄	C₂²	semidirect
49. C₄⋊(3₋¹⁺²⋊C₄)	C₂²	semidirect
50. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
51. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
52. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
69. C₉×#126	C₂×C₃	semidirect
70. #63460	C₂×C₃	semidirect
71. #63458	C₂×C₃	semidirect
72. #63457	C₂×C₃	semidirect
73. #63457	C₂×C₃	semidirect
74. #63456	C₂×C₃	semidirect
75. #63455	C₂×C₃	semidirect
76. #63447	C₂×C₃	semidirect
77. #63446	C₂×C₃	semidirect
78. #63445	C₂×C₃	semidirect
79. #63444	C₂×C₃	semidirect
80. #63444	C₂×C₃	semidirect
81. C₂²⋊C₄×D₉	C₂×C₃	semidirect
82. #63437	C₂×C₃	semidirect
83. C₄×D₃₆	C₂×C₃	semidirect
158. C₂×D₃₆	C₂²×C₃	semidirect
161. C₂×C₄×D₉	C₂²×C₃	semidirect
162. C₂×C₄×D₉	C₂²×C₃	semidirect
163. C₂×Dic₁₈	C₂²×C₃	semidirect
167. C₉×C₄⋊C₄	C₂²×C₃	semidirect
168. C₉×C₄⋊C₄	C₂²×C₃	semidirect
169. C₉×C₄⋊C₄	C₂²×C₃	semidirect
177. C₄²×C₉	C₂²×C₃	semidirect
185. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
186. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
187. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
188. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
189. C₄⋊Dic₉	C₂²×C₃	semidirect
190. Dic₉⋊C₄	C₂²×C₃	semidirect
191. Dic₉⋊C₄	C₂²×C₃	semidirect
192. C₄×Dic₉	C₂²×C₃	semidirect
461. #126	AGL(1,ℤ/9)	semidirect
475. 3₋¹⁺²	#538	semidirect
572. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
573. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
574. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
590. C₄²	C₂×AGL(1,ℤ/9)	semidirect
647. C₉	C₃×#538	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×#126	2
#63460⋊C₃	2
#63458⋊C₃	2
#63457⋊C₃	2
#63456⋊C₃	2
#63455⋊C₃	2
#63447⋊C₃	2
#63446⋊C₃	2
#63445⋊C₃	2
#63444⋊C₃	2
C₂²⋊C₄×AGL(1,ℤ/9)	2
#63437⋊C₃	2
C₄×C₄⋊AGL(1,ℤ/9)	2
C₃×#5704	3
#10589806	3

Subgroups — #10589806⋊C3 #13153247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589806⋊C₃ #13153247