Subgroups — #10589662⋊C₃ #13152661

Order 1728.

797 conjugacy classes of subgroups.

The subgroup lattice has 738 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	#63501⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63499⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63492⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63491⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×(C₂×AGL(1,ℤ/9))⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#63444⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#63440⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#11721396	C₂	1	1	yes	maximal, characteristic, complemented
15	#63437⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5560	—	3	1	no	maximal
17	#10589662	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	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
25	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×3₋¹⁺²⋊C₄	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
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	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
33	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
34	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
35	#3676⋊C₃	C₂²	1	1	yes	characteristic
36	#3676⋊C₃	C₂²	1	1	yes	characteristic, complemented
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	(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	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	(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×C₄×D₄	D₃	1	1	yes	characteristic
54	C₃×#939	—	3	1	no	—
55	C₃×#937	—	3	1	no	—
56	C₃×#930	—	3	1	no	—
57	C₃×#929	—	3	1	no	—
58	C₃×C₄×#67	—	3	1	no	—
59	C₂×C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
60	C₃×#898	—	3	1	no	—
61	C₃×#894	—	3	1	no	—
62	C₃×#885	—	3	1	no	—
63	C₃×#884	—	3	1	no	—
64	C₃×#882	—	3	1	no	—
65	C₃×#878	—	3	1	no	—
66	C₃×#876	—	3	1	no	—
67	C₃×#875	—	3	1	no	—
68	C₄×D₄×C₉	—	2	1	no	—
69	C₄×D₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
70	#63501	C₂×C₃	1	1	yes	characteristic, complemented
71	#63499	C₂×C₃	1	1	yes	characteristic, complemented
72	#63492	C₂×C₃	1	1	yes	characteristic, complemented
73	#63491	C₂×C₃	1	1	yes	characteristic, complemented
74	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×(C₂×D₉)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
76	#63460	C₂×C₃	1	1	yes	characteristic, complemented
77	#63456	C₂×C₃	1	1	yes	characteristic, complemented
78	#63447	C₂×C₃	1	1	yes	characteristic, complemented
79	#63446	C₂×C₃	1	1	yes	characteristic, complemented
80	#63444	C₂×C₃	1	1	yes	characteristic, complemented
81	#63440	C₂×C₃	1	1	yes	characteristic, complemented
82	#63438	C₂×C₃	1	1	yes	characteristic, complemented
83	#63437	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)	—	4	1	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	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
92	D₄×3₋¹⁺²	—	2	2	no	—
93	C₂×C₄×3₋¹⁺²	—	4	1	no	—
94	C₂×C₄×3₋¹⁺²	—	4	1	no	—
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	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
100	#611⋊C₃	—	2	2	no	—
101	#611⋊C₃	—	4	1	no	—
102	#611⋊C₃	—	4	1	no	—
103	#611⋊C₃	—	4	1	no	—
104	C₂×3₋¹⁺²⋊C₄	—	4	1	no	—
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	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
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	#5560	—	3	1	no	—
116	C₂³×C₃×D₃	—	3	1	no	—
117	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
118	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
119	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
120	C₂×C₃×#67	—	3	1	no	—
121	C₂×C₃×#67	—	3	1	no	—
122	C₂×C₃×#67	—	3	1	no	—
123	C₂×C₃×#67	—	3	1	no	—
124	C₂²×C₃×Dic₃	—	3	1	no	—
125	C₂×C₃×D₁₂	—	3	1	no	—
126	C₂×C₃×D₁₂	—	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×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
132	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
134	C₃×#217	—	3	1	no	—
135	C₃×#217	—	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×(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×C₄⋊Dic₃	—	3	1	no	—
147	C₃×Dic₃⋊C₄	—	3	1	no	—
148	C₃×Dic₃⋊C₄	—	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×D₄×C₉	—	2	1	no	—
153	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
154	C₂²×C₄×C₉	—	2	1	no	—
155	C₂²×C₄×C₉	—	2	1	no	—
156	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
157	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂×#611	C₂²×C₃	1	1	yes	characteristic
159	C₂×#611	C₂²×C₃	1	1	yes	characteristic
160	C₂×#611	C₂²×C₃	1	1	yes	characteristic
161	C₂×#611	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
163	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₉×C₄⋊C₄	—	2	1	no	—
168	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₉×C₂²⋊C₄	—	2	1	no	—
170	C₉×C₂²⋊C₄	—	2	1	no	—
171	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₄²×C₉	—	2	1	no	—
174	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
175	#3676	C₂²×C₃	1	1	yes	characteristic
176	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
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	(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	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
188	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
189	Dic₉⋊C₄	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	—	2	1	no	—
197	C₂²×3₋¹⁺²	—	2	1	no	—
198	C₂²×3₋¹⁺²	#41	1	2	yes	—
199	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
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)	—	2	1	no	—
209	C₂×AGL(1,ℤ/9)	—	4	4	no	—
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	3₋¹⁺²⋊C₄	—	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	—	9	1	no	—
221	C₃×#126	—	9	1	no	—
222	C₃×#124	—	9	1	no	—
223	C₃×#124	—	9	1	no	—
224	C₃×#123	—	9	1	no	—
225	C₃×#123	—	9	1	no	—
226	C₃×C₂²⋊Q₈	—	9	1	no	—
227	C₃×#121	—	9	1	no	—
228	C₃×#121	—	9	1	no	—
229	C₃×#121	—	9	1	no	—
230	C₃×#120	—	9	1	no	—
231	C₃×#120	—	9	1	no	—
232	C₃×C₄×D₄	—	3	1	no	—
233	C₃×C₄×D₄	—	9	1	no	—
234	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
235	C₂×C₃×C₂²⋊C₄	—	9	1	no	—
236	#939	—	3	1	no	—
237	#937	—	3	1	no	—
238	#930	—	3	1	no	—
239	#929	—	3	1	no	—
240	C₄×#67	—	3	1	no	—
241	C₂×(C₂×D₃)⋊C₄	—	3	1	no	—
242	#898	—	3	1	no	—
243	#894	—	3	1	no	—
244	#885	—	3	1	no	—
245	#884	—	3	1	no	—
246	#882	—	3	1	no	—
247	#878	—	3	1	no	—
248	#876	—	3	1	no	—
249	#875	—	3	1	no	—
250	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
251	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
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	C₃²×D₄	—	2	2	no	—
259	C₂×C₃²×C₄	—	4	1	no	—
260	C₂×C₃²×C₄	—	4	1	no	—
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	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
265	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
266	C₃×#67	—	6	2	no	—
267	C₃×#67	—	12	1	no	—
268	C₃×#67	—	12	1	no	—
269	C₃×#67	—	12	1	no	—
270	C₂×C₃×Dic₃	—	3	1	no	—
271	C₂×C₃×Dic₃	—	3	1	no	—
272	C₂×C₃×Dic₃	—	3	1	no	—
273	C₂×C₃×Dic₃	—	3	1	no	—
274	C₂×C₃×Dic₃	—	3	1	no	—
275	C₂×C₃×Dic₃	—	12	1	no	—
276	C₃×D₁₂	—	12	1	no	—
277	C₃×D₁₂	—	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	—	2	1	no	—
282	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
283	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
284	C₂²×D₉	—	2	2	no	—
285	C₂²×D₉	—	4	1	no	—
286	C₂²×D₉	—	4	1	no	—
287	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
288	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
289	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
290	D₄×C₉	—	2	4	no	—
291	D₄×C₉	—	2	2	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	—	2	1	no	—
296	C₂×C₄×C₉	—	2	1	no	—
297	C₂×C₄×C₉	—	4	1	no	—
298	C₂×C₄×C₉	—	4	1	no	—
299	C₂×C₄×C₉	—	4	2	no	—
300	C₂×C₄×C₉	—	4	2	no	—
301	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
303	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
304	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
305	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
306	#611	—	2	2	no	—
307	#611	—	4	1	no	—
308	#611	—	4	1	no	—
309	#611	—	4	1	no	—
310	C₂×Dic₉	—	4	1	no	—
311	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
312	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
313	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
314	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
315	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
316	D₃₆	—	4	1	no	—
317	D₃₆	—	4	1	no	—
318	C₄×D₉	—	4	1	no	—
319	Dic₁₈	—	4	1	no	—
320	#538	—	9	1	no	Sylow
321	C₂×3₋¹⁺²	—	2	2	no	—
322	C₂×3₋¹⁺²	—	4	1	no	—
323	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
324	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
326	AGL(1,ℤ/9)	—	4	1	no	—
327	AGL(1,ℤ/9)	—	4	1	no	—
328	AGL(1,ℤ/9)	—	4	1	no	—
329	C₂⁴×C₃	—	9	1	no	—
330	C₂³×D₃	—	3	1	no	—
331	C₂×C₃×Q₈	—	9	1	no	—
332	C₂×C₃×D₄	—	3	1	no	—
333	C₂×C₃×D₄	—	9	1	no	—
334	C₂×C₃×D₄	—	9	1	no	—
335	C₂×C₃×D₄	—	9	1	no	—
336	C₂×C₃×D₄	—	9	1	no	—
337	C₂×C₃×D₄	—	9	1	no	—
338	C₂×C₃×D₄	—	9	1	no	—
339	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
340	C₂²×C₃×C₄	—	3	1	no	—
341	C₂²×C₃×C₄	—	3	1	no	—
342	C₂²×C₃×C₄	—	9	1	no	—
343	C₂²×C₃×C₄	—	9	1	no	—
344	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
346	C₂×#67	—	3	1	no	—
347	C₂×#67	—	3	1	no	—
348	C₂×#67	—	3	1	no	—
349	C₂×#67	—	3	1	no	—
350	C₂²×Dic₃	—	3	1	no	—
351	C₂×D₁₂	—	3	1	no	—
352	C₂×D₁₂	—	3	1	no	—
353	C₂×C₄×D₃	—	3	1	no	—
354	C₂×Dic₆	—	3	1	no	—
355	C₃×C₄⋊C₄	—	3	1	no	—
356	C₃×C₄⋊C₄	—	9	1	no	—
357	C₃×C₄⋊C₄	—	9	1	no	—
358	C₃×C₄⋊C₄	—	9	1	no	—
359	C₃×C₄⋊C₄	—	9	1	no	—
360	C₃×C₄⋊C₄	—	9	1	no	—
361	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
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	—	9	1	no	—
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	#217	—	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	(C₂×D₃)⋊C₄	—	3	1	no	—
393	C₄⋊Dic₃	—	3	1	no	—
394	Dic₃⋊C₄	—	3	1	no	—
395	Dic₃⋊C₄	—	3	1	no	—
396	Dic₃⋊C₄	—	3	1	no	—
397	Dic₃⋊C₄	—	3	1	no	—
398	C₄×Dic₃	—	3	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	#235	1	2	yes	—
405	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
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	—	6	1	no	—
413	C₂×C₃×D₃	—	6	1	no	—
414	C₂×C₃×D₃	—	6	1	no	—
415	C₂×C₃×D₃	—	12	4	no	—
416	C₃²×C₄	—	2	1	no	—
417	C₃²×C₄	—	2	1	no	—
418	C₃²×C₄	—	2	1	no	—
419	C₃²×C₄	—	2	1	no	—
420	C₃²×C₄	—	2	1	no	—
421	C₃×Dic₃	—	6	1	no	—
422	C₃×Dic₃	—	6	1	no	—
423	C₃×Dic₃	—	6	1	no	—
424	C₃×Dic₃	—	6	1	no	—
425	C₃×Dic₃	—	6	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	—	4	1	no	—
435	C₂²×C₉	—	4	1	no	—
436	C₂²×C₉	—	4	1	no	—
437	C₂²×C₉	—	4	1	no	—
438	C₂²×C₉	C₃×#41	1	2	yes	—
439	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
440	C₂×D₉	—	2	1	no	—
441	C₂×D₉	—	2	1	no	—
442	C₂×D₉	—	2	1	no	—
443	C₂×D₉	—	2	1	no	—
444	C₂×D₉	—	2	1	no	—
445	C₂×D₉	—	2	1	no	—
446	C₂×D₉	—	2	1	no	—
447	C₂×D₉	—	2	1	no	—
448	C₂×D₉	—	2	1	no	—
449	C₂×D₉	—	4	4	no	—
450	C₄×C₉	—	2	2	no	—
451	C₄×C₉	—	2	2	no	—
452	C₄×C₉	—	2	1	no	—
453	C₄×C₉	—	2	1	no	—
454	C₄×C₉	—	2	1	no	—
455	C₄×C₉	—	2	1	no	—
456	C₄×C₉	—	2	1	no	—
457	C₄×C₉	—	4	1	no	—
458	C₄×C₉	—	4	1	no	—
459	C₄×C₉	—	4	1	no	—
460	Dic₉	—	2	1	no	—
461	Dic₉	—	2	1	no	—
462	Dic₉	—	2	1	no	—
463	Dic₉	—	2	1	no	—
464	Dic₉	—	2	1	no	—
465	#126	—	9	1	no	—
466	#126	—	9	1	no	—
467	#124	—	9	1	no	—
468	#124	—	9	1	no	—
469	#123	—	9	1	no	—
470	#123	—	9	1	no	—
471	C₂²⋊Q₈	—	9	1	no	—
472	#121	—	9	1	no	—
473	#121	—	9	1	no	—
474	#121	—	9	1	no	—
475	#120	—	9	1	no	—
476	#120	—	9	1	no	—
477	C₄×D₄	—	9	1	no	—
478	C₄×D₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
479	C₂×C₂²⋊C₄	—	9	1	no	—
480	3₋¹⁺²	#538	1	1	yes	characteristic, complemented, Sylow
481	C₂³×C₃	—	3	1	no	—
482	C₂³×C₃	—	3	1	no	—
483	C₂³×C₃	—	9	1	no	—
484	C₂³×C₃	—	9	1	no	—
485	C₂³×C₃	—	9	1	no	—
486	C₂³×C₃	—	18	2	no	—
487	C₂³×C₃	—	36	1	no	—
488	C₂³×C₃	—	36	1	no	—
489	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
490	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
491	C₂²×D₃	—	3	1	no	—
492	C₂²×D₃	—	3	1	no	—
493	C₂²×D₃	—	3	1	no	—
494	C₂²×D₃	—	6	2	no	—
495	C₂²×D₃	—	12	1	no	—
496	C₂²×D₃	—	12	1	no	—
497	C₃×Q₈	—	36	1	no	—
498	C₃×D₄	—	2	2	no	—
499	C₃×D₄	—	6	2	no	—
500	C₃×D₄	—	18	2	no	—
501	C₃×D₄	—	36	1	no	—
502	C₃×D₄	—	36	1	no	—
503	C₃×D₄	—	36	1	no	—
504	C₃×D₄	—	36	1	no	—
505	C₃×D₄	—	36	1	no	—
506	C₂×C₃×C₄	—	3	1	no	—
507	C₂×C₃×C₄	—	3	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	—	4	1	no	—
512	C₂×C₃×C₄	—	4	1	no	—
513	C₂×C₃×C₄	—	9	1	no	—
514	C₂×C₃×C₄	—	9	1	no	—
515	C₂×C₃×C₄	—	9	1	no	—
516	C₂×C₃×C₄	—	9	1	no	—
517	C₂×C₃×C₄	—	9	1	no	—
518	C₂×C₃×C₄	—	12	1	no	—
519	C₂×C₃×C₄	—	12	1	no	—
520	C₂×C₃×C₄	—	36	1	no	—
521	C₂×C₃×C₄	—	36	1	no	—
522	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
523	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
524	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
525	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
526	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
527	#67	—	6	2	no	—
528	#67	—	12	1	no	—
529	#67	—	12	1	no	—
530	#67	—	12	1	no	—
531	C₂×Dic₃	—	3	1	no	—
532	C₂×Dic₃	—	3	1	no	—
533	C₂×Dic₃	—	3	1	no	—
534	C₂×Dic₃	—	3	1	no	—
535	C₂×Dic₃	—	3	1	no	—
536	C₂×Dic₃	—	12	1	no	—
537	D₁₂	—	12	1	no	—
538	D₁₂	—	12	1	no	—
539	C₄×D₃	—	12	1	no	—
540	Dic₆	—	12	1	no	—
541	C₂×C₃²	—	2	2	no	—
542	C₂×C₃²	—	4	1	no	—
543	C₂×C₃²	C₂×#235	1	1	yes	characteristic
544	C₂×C₃²	#1004	1	1	yes	characteristic
545	C₂×C₃²	#1009	1	1	yes	characteristic
546	C₃×D₃	—	12	1	no	—
547	C₃×D₃	—	12	1	no	—
548	C₃×D₃	—	12	1	no	—
549	C₂×C₉	—	2	2	no	—
550	C₂×C₉	—	2	1	no	—
551	C₂×C₉	—	2	1	no	—
552	C₂×C₉	—	2	1	no	—
553	C₂×C₉	—	4	2	no	—
554	C₂×C₉	—	4	2	no	—
555	C₂×C₉	—	4	1	no	—
556	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
557	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
559	D₉	—	4	1	no	—
560	D₉	—	4	1	no	—
561	D₉	—	4	1	no	—
562	C₂⁴	—	9	1	no	—
563	C₂×Q₈	—	9	1	no	—
564	C₂×D₄	—	9	1	no	—
565	C₂×D₄	—	9	1	no	—
566	C₂×D₄	—	9	1	no	—
567	C₂×D₄	—	9	1	no	—
568	C₂×D₄	—	9	1	no	—
569	C₂×D₄	—	9	1	no	—
570	C₂×D₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
571	C₂²×C₄	—	9	1	no	—
572	C₂²×C₄	—	9	1	no	—
573	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
574	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
575	C₄⋊C₄	—	9	1	no	—
576	C₄⋊C₄	—	9	1	no	—
577	C₄⋊C₄	—	9	1	no	—
578	C₄⋊C₄	—	9	1	no	—
579	C₄⋊C₄	—	9	1	no	—
580	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
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	—	9	1	no	—
587	C₂²⋊C₄	—	9	1	no	—
588	C₂²⋊C₄	—	9	1	no	—
589	C₂²⋊C₄	—	9	1	no	—
590	C₂²⋊C₄	—	9	1	no	—
591	C₂²⋊C₄	—	9	1	no	—
592	C₂²⋊C₄	—	9	1	no	—
593	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
594	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
595	C₄²	—	9	1	no	—
596	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
597	C₂²×C₃	—	2	1	no	—
598	C₂²×C₃	—	2	1	no	—
599	C₂²×C₃	—	2	1	no	—
600	C₂²×C₃	—	2	1	no	—
601	C₂²×C₃	—	2	1	no	—
602	C₂²×C₃	—	3	1	no	—
603	C₂²×C₃	—	3	2	no	—
604	C₂²×C₃	—	6	1	no	—
605	C₂²×C₃	—	6	1	no	—
606	C₂²×C₃	—	6	1	no	—
607	C₂²×C₃	—	6	1	no	—
608	C₂²×C₃	—	6	1	no	—
609	C₂²×C₃	—	18	1	no	—
610	C₂²×C₃	—	18	1	no	—
611	C₂²×C₃	—	18	1	no	—
612	C₂²×C₃	—	18	1	no	—
613	C₂²×C₃	—	18	1	no	—
614	C₂²×C₃	—	18	1	no	—
615	C₂²×C₃	—	18	1	no	—
616	C₂²×C₃	—	18	1	no	—
617	C₂²×C₃	—	18	1	no	—
618	C₂²×C₃	—	36	4	no	—
619	C₂²×C₃	C₃×#235	1	2	yes	—
620	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
621	C₂×D₃	—	6	1	no	—
622	C₂×D₃	—	6	1	no	—
623	C₂×D₃	—	6	1	no	—
624	C₂×D₃	—	6	1	no	—
625	C₂×D₃	—	6	1	no	—
626	C₂×D₃	—	6	1	no	—
627	C₂×D₃	—	6	1	no	—
628	C₂×D₃	—	6	1	no	—
629	C₂×D₃	—	6	1	no	—
630	C₂×D₃	—	12	4	no	—
631	C₃×C₄	—	2	1	no	—
632	C₃×C₄	—	2	1	no	—
633	C₃×C₄	—	2	1	no	—
634	C₃×C₄	—	2	1	no	—
635	C₃×C₄	—	2	1	no	—
636	C₃×C₄	—	6	1	no	—
637	C₃×C₄	—	6	1	no	—
638	C₃×C₄	—	6	1	no	—
639	C₃×C₄	—	6	1	no	—
640	C₃×C₄	—	6	1	no	—
641	C₃×C₄	—	18	1	no	—
642	C₃×C₄	—	18	1	no	—
643	C₃×C₄	—	18	1	no	—
644	C₃×C₄	—	18	1	no	—
645	C₃×C₄	—	18	1	no	—
646	Dic₃	—	6	1	no	—
647	Dic₃	—	6	1	no	—
648	Dic₃	—	6	1	no	—
649	Dic₃	—	6	1	no	—
650	Dic₃	—	6	1	no	—
651	C₃²	#5560	1	1	yes	characteristic
652	C₉	—	2	1	no	—
653	C₉	C₃×#538	1	1	yes	characteristic, complemented
654	C₂³	—	9	1	no	—
655	C₂³	—	9	1	no	—
656	C₂³	—	9	1	no	—
657	C₂³	—	18	2	no	—
658	C₂³	—	36	1	no	—
659	C₂³	—	36	1	no	—
660	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
661	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
662	Q₈	—	36	1	no	—
663	D₄	—	2	2	no	—
664	D₄	—	18	2	no	—
665	D₄	—	36	1	no	—
666	D₄	—	36	1	no	—
667	D₄	—	36	1	no	—
668	D₄	—	36	1	no	—
669	D₄	—	36	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	9	1	no	—
673	C₂×C₄	—	9	1	no	—
674	C₂×C₄	—	9	1	no	—
675	C₂×C₄	—	9	1	no	—
676	C₂×C₄	—	9	1	no	—
677	C₂×C₄	—	36	1	no	—
678	C₂×C₄	—	36	1	no	—
679	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
680	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
681	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
682	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
683	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
684	C₂×C₃	—	2	2	no	—
685	C₂×C₃	—	3	1	no	—
686	C₂×C₃	—	3	1	no	—
687	C₂×C₃	—	3	1	no	—
688	C₂×C₃	—	4	1	no	—
689	C₂×C₃	—	6	2	no	—
690	C₂×C₃	—	12	1	no	—
691	C₂×C₃	—	36	1	no	—
692	C₂×C₃	—	36	1	no	—
693	C₂×C₃	—	36	1	no	—
694	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
695	C₂×C₃	C₃×#1004	1	1	yes	characteristic
696	C₂×C₃	C₃×#1009	1	1	yes	characteristic
697	D₃	—	12	1	no	—
698	D₃	—	12	1	no	—
699	D₃	—	12	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	18	1	no	—
706	C₂²	—	18	1	no	—
707	C₂²	—	18	1	no	—
708	C₂²	—	18	1	no	—
709	C₂²	—	18	1	no	—
710	C₂²	—	18	1	no	—
711	C₂²	—	18	1	no	—
712	C₂²	—	18	1	no	—
713	C₂²	—	18	1	no	—
714	C₂²	—	36	4	no	—
715	C₂²	#3697⋊C₃	1	2	yes	—
716	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	18	1	no	—
723	C₄	—	18	1	no	—
724	C₄	—	18	1	no	—
725	C₄	—	18	1	no	—
726	C₄	—	18	1	no	—
727	C₃	—	3	1	no	—
728	C₃	C₃×#5560	1	1	yes	characteristic
729	C₂	—	2	2	no	—
730	C₂	—	4	1	no	—
731	C₂	—	36	1	no	—
732	C₂	—	36	1	no	—
733	C₂	—	36	1	no	—
734	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
735	C₂	#63710⋊C₃	1	1	yes	characteristic
736	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	C₄×D₄×3₋¹⁺²	C₂
hypercenter	C₄×D₄	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#538
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
2. #63501⋊C₃	C₂	semidirect
3. #63499⋊C₃	C₂	semidirect
4. #63492⋊C₃	C₂	semidirect
5. #63491⋊C₃	C₂	semidirect
6. C₄×#611⋊C₃	C₂	semidirect
7. C₂×(C₂×AGL(1,ℤ/9))⋊C₄	C₂	semidirect
8. #63460⋊C₃	C₂	semidirect
9. #63456⋊C₃	C₂	semidirect
10. #63447⋊C₃	C₂	semidirect
11. #63446⋊C₃	C₂	semidirect
12. #63444⋊C₃	C₂	semidirect
13. #63440⋊C₃	C₂	semidirect
14. #11721396	C₂	semidirect
15. #63437⋊C₃	C₂	semidirect
17. #10589662	C₃	semidirect
21. C₂²×C₄×3₋¹⁺²	C₂²	semidirect
25. C₂×#611⋊C₃	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
33. C₂²⋊C₄×3₋¹⁺²	C₂²	semidirect
34. C₄²×3₋¹⁺²	C₂²	semidirect
36. #3676⋊C₃	C₂²	semidirect
45. (C₂×AGL(1,ℤ/9))⋊C₄	C₂²	semidirect
46. (C₂×AGL(1,ℤ/9))⋊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. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
51. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
52. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
69. C₄×D₄×C₉	C₂×C₃	semidirect
70. #63501	C₂×C₃	semidirect
71. #63499	C₂×C₃	semidirect
72. #63492	C₂×C₃	semidirect
73. #63491	C₂×C₃	semidirect
74. C₄×#611	C₂×C₃	semidirect
75. C₂×(C₂×D₉)⋊C₄	C₂×C₃	semidirect
76. #63460	C₂×C₃	semidirect
77. #63456	C₂×C₃	semidirect
78. #63447	C₂×C₃	semidirect
79. #63446	C₂×C₃	semidirect
80. #63444	C₂×C₃	semidirect
81. #63440	C₂×C₃	semidirect
82. #63438	C₂×C₃	semidirect
83. #63437	C₂×C₃	semidirect
157. C₂²×C₄×C₉	C₂²×C₃	semidirect
161. C₂×#611	C₂²×C₃	semidirect
165. C₂×C₄×D₉	C₂²×C₃	semidirect
166. C₂×Dic₁₈	C₂²×C₃	semidirect
168. C₉×C₄⋊C₄	C₂²×C₃	semidirect
172. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
174. C₄²×C₉	C₂²×C₃	semidirect
176. #3676	C₂²×C₃	semidirect
185. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
186. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
187. C₄⋊Dic₉	C₂²×C₃	semidirect
188. Dic₉⋊C₄	C₂²×C₃	semidirect
189. Dic₉⋊C₄	C₂²×C₃	semidirect
190. Dic₉⋊C₄	C₂²×C₃	semidirect
191. Dic₉⋊C₄	C₂²×C₃	semidirect
192. C₄×Dic₉	C₂²×C₃	semidirect
478. C₄×D₄	AGL(1,ℤ/9)	semidirect
480. 3₋¹⁺²	#538	semidirect
574. C₂²×C₄	C₂×AGL(1,ℤ/9)	semidirect
580. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
594. C₂²⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
596. C₄²	C₂×AGL(1,ℤ/9)	semidirect
653. 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
C₄×D₄×3₋¹⁺²	2
#63501⋊C₃	2
#63499⋊C₃	2
#63492⋊C₃	2
#63491⋊C₃	2
C₄×#611⋊C₃	2
C₂×(C₂×AGL(1,ℤ/9))⋊C₄	2
#63460⋊C₃	2
#63456⋊C₃	2
#63447⋊C₃	2
#63446⋊C₃	2
#63444⋊C₃	2
#63440⋊C₃	2
#11721396	2
#63437⋊C₃	2
C₃×#5560	3
#10589662	3

Subgroups — #10589662⋊C3 #13152661

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589662⋊C₃ #13152661