Subgroups — #10589649⋊C₃ #13152651

Order 1728.

1037 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#3697⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
4	#63501⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63499⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63445⋊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	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
15	#63434⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5547	—	3	1	no	maximal
17	#10589649	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	#3697⋊C₃	—	2	4	no	—
28	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
30	C₂×C₄×AGL(1,ℤ/9)	—	2	4	no	—
31	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
32	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
33	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
34	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
35	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic, complemented
36	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
38	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
39	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
40	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented
41	#3676⋊C₃	C₂²	1	1	yes	characteristic
42	#3676⋊C₃	C₂²	1	1	yes	characteristic, complemented
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
46	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
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	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₃×#235	—	3	1	no	—
56	C₂²×C₃×C₄×D₃	—	3	1	no	—
57	C₃²×C₄×D₄	D₃	1	1	yes	characteristic
58	C₃×#939	—	3	1	no	—
59	C₃×#937	—	3	1	no	—
60	C₃×C₄×#67	—	3	1	no	—
61	C₃×C₄×#67	—	3	1	no	—
62	C₃×#896	—	3	1	no	—
63	C₃×#894	—	3	1	no	—
64	C₃×#884	—	3	1	no	—
65	C₃×#883	—	3	1	no	—
66	C₃×#882	—	3	1	no	—
67	C₃×#878	—	3	1	no	—
68	C₃×C₄×D₁₂	—	3	1	no	—
69	C₃×#872	—	3	1	no	—
70	C₂×#3697	C₂×C₃	1	1	yes	characteristic, complemented
71	C₂²×C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
72	C₄×D₄×C₉	—	2	1	no	—
73	C₄×D₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
74	#63501	C₂×C₃	1	1	yes	characteristic, complemented
75	#63499	C₂×C₃	1	1	yes	characteristic, complemented
76	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
77	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
78	#63458	C₂×C₃	1	1	yes	characteristic, complemented
79	#63456	C₂×C₃	1	1	yes	characteristic, complemented
80	#63446	C₂×C₃	1	1	yes	characteristic, complemented
81	#63445	C₂×C₃	1	1	yes	characteristic, complemented
82	#63444	C₂×C₃	1	1	yes	characteristic, complemented
83	#63440	C₂×C₃	1	1	yes	characteristic, complemented
84	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
85	#63434	C₂×C₃	1	1	yes	characteristic, complemented
86	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
87	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
88	C₂²×AGL(1,ℤ/9)	—	2	2	no	—
89	C₂²×AGL(1,ℤ/9)	—	2	2	no	—
90	C₂²×AGL(1,ℤ/9)	—	2	2	no	—
91	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
92	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
93	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
94	D₄×3₋¹⁺²	—	2	2	no	—
95	C₂×C₄×3₋¹⁺²	—	2	2	no	—
96	C₂×C₄×3₋¹⁺²	—	2	2	no	—
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	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
101	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
102	#611⋊C₃	—	2	2	no	—
103	#611⋊C₃	—	2	2	no	—
104	#611⋊C₃	—	2	2	no	—
105	#611⋊C₃	—	2	2	no	—
106	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
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	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
112	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
113	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
114	C₄×AGL(1,ℤ/9)	—	2	2	no	—
115	C₄×AGL(1,ℤ/9)	—	2	2	no	—
116	C₄×AGL(1,ℤ/9)	—	2	2	no	—
117	C₄×AGL(1,ℤ/9)	—	2	2	no	—
118	C₄×AGL(1,ℤ/9)	D₄	1	4	yes	complemented
119	3₋¹⁺²⋊Q₈	—	2	2	no	—
120	C₃×#525	—	9	1	no	—
121	#5547	—	3	1	no	—
122	C₂³×C₃×D₃	—	3	1	no	—
123	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
124	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
125	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
126	C₂×C₃×#67	—	3	1	no	—
127	C₂×C₃×#67	—	3	1	no	—
128	C₂×C₃×#67	—	3	1	no	—
129	C₂×C₃×#67	—	3	1	no	—
130	C₂²×C₃×Dic₃	—	3	1	no	—
131	C₃×#235	—	6	4	no	—
132	C₂×C₃×D₁₂	—	3	1	no	—
133	C₂×C₃×D₁₂	—	3	1	no	—
134	C₂×C₃×C₄×D₃	—	3	1	no	—
135	C₂×C₃×C₄×D₃	—	3	1	no	—
136	C₂×C₃×C₄×D₃	—	3	1	no	—
137	C₂×C₃×C₄×D₃	—	3	1	no	—
138	C₂×C₃×C₄×D₃	—	3	1	no	—
139	C₂×C₃×C₄×D₃	—	6	4	no	—
140	C₂×C₃×Dic₆	—	3	1	no	—
141	C₂³×D₉	C₂²×C₃	1	1	yes	characteristic
142	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
143	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
144	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
145	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
146	C₃×#217	—	3	1	no	—
147	C₃×#217	—	3	1	no	—
148	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
149	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
150	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
151	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
152	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
153	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
154	C₃×C₄⋊Dic₃	—	3	1	no	—
155	C₃×Dic₃⋊C₄	—	3	1	no	—
156	C₃×Dic₃⋊C₄	—	3	1	no	—
157	C₃×Dic₃⋊C₄	—	3	1	no	—
158	C₃×Dic₃⋊C₄	—	3	1	no	—
159	C₃×C₄×Dic₃	—	3	1	no	—
160	C₂×D₄×C₉	—	2	1	no	—
161	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
162	C₂²×C₄×C₉	—	2	1	no	—
163	C₂²×C₄×C₉	—	2	1	no	—
164	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
165	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×#611	C₂²×C₃	1	1	yes	characteristic
167	C₂×#611	C₂²×C₃	1	1	yes	characteristic
168	C₂×#611	C₂²×C₃	1	1	yes	characteristic
169	C₂×#611	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
171	#3697	—	2	4	no	—
172	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
173	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₄×D₉	—	2	4	no	—
175	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
176	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
177	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
178	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic, complemented
180	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₉×C₄⋊C₄	—	2	1	no	—
182	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₉×C₂²⋊C₄	—	2	1	no	—
184	C₉×C₂²⋊C₄	—	2	1	no	—
185	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₄²×C₉	—	2	1	no	—
188	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic, complemented
189	#3676	C₂²×C₃	1	1	yes	characteristic
190	#3676	C₂²×C₃	1	1	yes	characteristic, complemented
191	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
192	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
193	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
194	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
195	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
196	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
198	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
199	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
200	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
201	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
202	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic, complemented
203	C₂²×3₋¹⁺²	—	2	1	no	—
204	C₂²×3₋¹⁺²	—	2	1	no	—
205	C₂²×3₋¹⁺²	—	2	1	no	—
206	C₂²×3₋¹⁺²	—	2	1	no	—
207	C₂²×3₋¹⁺²	—	2	1	no	—
208	C₂²×3₋¹⁺²	#41	1	2	yes	complemented
209	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
210	C₂×AGL(1,ℤ/9)	—	2	8	no	—
211	C₂×AGL(1,ℤ/9)	—	2	1	no	—
212	C₂×AGL(1,ℤ/9)	—	2	1	no	—
213	C₂×AGL(1,ℤ/9)	—	2	1	no	—
214	C₂×AGL(1,ℤ/9)	—	2	1	no	—
215	C₂×AGL(1,ℤ/9)	—	2	1	no	—
216	C₂×AGL(1,ℤ/9)	—	2	1	no	—
217	C₂×AGL(1,ℤ/9)	—	2	1	no	—
218	C₂×AGL(1,ℤ/9)	C₂×D₄	1	2	yes	—
219	C₂×AGL(1,ℤ/9)	#41	1	2	yes	complemented
220	C₄×3₋¹⁺²	—	2	1	no	—
221	C₄×3₋¹⁺²	—	2	1	no	—
222	C₄×3₋¹⁺²	—	2	1	no	—
223	C₄×3₋¹⁺²	—	2	1	no	—
224	C₄×3₋¹⁺²	C₂×D₄	1	2	yes	—
225	3₋¹⁺²⋊C₄	—	2	1	no	—
226	3₋¹⁺²⋊C₄	—	2	1	no	—
227	3₋¹⁺²⋊C₄	—	2	1	no	—
228	3₋¹⁺²⋊C₄	—	2	1	no	—
229	3₋¹⁺²⋊C₄	C₂×D₄	1	2	yes	—
230	C₂×C₃×#41	—	9	1	no	—
231	C₂³×C₃×C₄	—	9	1	no	—
232	C₂×#235	—	3	1	no	—
233	C₂²×C₄×D₃	—	3	1	no	—
234	C₃×#123	—	9	1	no	—
235	C₃×#123	—	9	1	no	—
236	C₃×C₂²⋊Q₈	—	9	1	no	—
237	C₃×C₂²⋊Q₈	—	9	1	no	—
238	C₃×#121	—	9	1	no	—
239	C₃×#121	—	9	1	no	—
240	C₃×#120	—	9	1	no	—
241	C₃×#120	—	9	1	no	—
242	C₃×C₄×D₄	—	3	1	no	—
243	C₃×C₄×D₄	—	9	1	no	—
244	C₃×C₄×D₄	—	9	1	no	—
245	C₃×C₄×D₄	—	9	1	no	—
246	C₃×C₄×D₄	C₃×D₃	1	1	yes	characteristic
247	C₃×#117	—	9	1	no	—
248	#939	—	3	1	no	—
249	#937	—	3	1	no	—
250	C₄×#67	—	3	1	no	—
251	C₄×#67	—	3	1	no	—
252	#896	—	3	1	no	—
253	#894	—	3	1	no	—
254	#884	—	3	1	no	—
255	#883	—	3	1	no	—
256	#882	—	3	1	no	—
257	#878	—	3	1	no	—
258	C₄×D₁₂	—	3	1	no	—
259	#872	—	3	1	no	—
260	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
261	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
262	C₂²×C₃×D₃	—	3	1	no	—
263	C₂²×C₃×D₃	—	3	1	no	—
264	C₂²×C₃×D₃	—	3	1	no	—
265	C₂²×C₃×D₃	—	6	2	no	—
266	C₂²×C₃×D₃	—	6	2	no	—
267	C₂²×C₃×D₃	—	6	2	no	—
268	C₃²×D₄	—	2	2	no	—
269	C₂×C₃²×C₄	—	2	2	no	—
270	C₂×C₃²×C₄	—	2	2	no	—
271	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
272	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
273	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
274	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
275	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
276	C₃×#67	—	6	2	no	—
277	C₃×#67	—	6	2	no	—
278	C₃×#67	—	6	2	no	—
279	C₃×#67	—	6	2	no	—
280	C₂×C₃×Dic₃	—	3	1	no	—
281	C₂×C₃×Dic₃	—	3	1	no	—
282	C₂×C₃×Dic₃	—	3	1	no	—
283	C₂×C₃×Dic₃	—	3	1	no	—
284	C₂×C₃×Dic₃	—	3	1	no	—
285	C₂×C₃×Dic₃	—	6	2	no	—
286	C₃×D₁₂	—	6	2	no	—
287	C₃×D₁₂	—	6	2	no	—
288	C₃×C₄×D₃	—	3	4	no	—
289	C₃×C₄×D₃	—	6	2	no	—
290	C₃×C₄×D₃	—	6	2	no	—
291	C₃×C₄×D₃	—	6	2	no	—
292	C₃×C₄×D₃	—	6	2	no	—
293	C₃×Dic₆	—	6	2	no	—
294	C₂³×C₉	—	2	1	no	—
295	C₂³×C₉	—	2	1	no	—
296	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
297	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
298	C₂²×D₉	—	2	2	no	—
299	C₂²×D₉	—	2	2	no	—
300	C₂²×D₉	—	2	2	no	—
301	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
302	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
303	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
304	D₄×C₉	—	2	4	no	—
305	D₄×C₉	—	2	2	no	—
306	C₂×C₄×C₉	—	2	2	no	—
307	C₂×C₄×C₉	—	2	2	no	—
308	C₂×C₄×C₉	—	2	1	no	—
309	C₂×C₄×C₉	—	2	1	no	—
310	C₂×C₄×C₉	—	2	1	no	—
311	C₂×C₄×C₉	—	2	1	no	—
312	C₂×C₄×C₉	—	2	1	no	—
313	C₂×C₄×C₉	—	4	2	no	—
314	C₂×C₄×C₉	—	4	2	no	—
315	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
316	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
317	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
318	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
319	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
320	#611	—	2	2	no	—
321	#611	—	2	2	no	—
322	#611	—	2	2	no	—
323	#611	—	2	2	no	—
324	C₂×Dic₉	—	2	2	no	—
325	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
326	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
327	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
328	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
329	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
330	D₃₆	—	2	2	no	—
331	D₃₆	—	2	2	no	—
332	C₄×D₉	—	2	2	no	—
333	C₄×D₉	—	2	2	no	—
334	C₄×D₉	—	2	2	no	—
335	C₄×D₉	—	2	2	no	—
336	C₄×D₉	C₃×D₄	1	4	yes	complemented
337	Dic₁₈	—	2	2	no	—
338	#525	—	9	1	no	Sylow
339	C₂×3₋¹⁺²	—	2	2	no	—
340	C₂×3₋¹⁺²	—	4	1	no	—
341	C₂×3₋¹⁺²	C₂²×D₄	1	1	yes	characteristic
342	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
343	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
344	AGL(1,ℤ/9)	—	2	2	no	—
345	AGL(1,ℤ/9)	—	2	2	no	—
346	AGL(1,ℤ/9)	—	4	1	no	—
347	C₂⁴×C₃	—	9	1	no	—
348	C₂³×D₃	—	3	1	no	—
349	C₃×#41	—	18	4	no	—
350	C₂×C₃×Q₈	—	9	1	no	—
351	C₂×C₃×D₄	—	3	1	no	—
352	C₂×C₃×D₄	—	9	1	no	—
353	C₂×C₃×D₄	—	9	1	no	—
354	C₂×C₃×D₄	—	9	1	no	—
355	C₂×C₃×D₄	—	9	1	no	—
356	C₂×C₃×D₄	—	9	1	no	—
357	C₂×C₃×D₄	—	9	1	no	—
358	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
359	C₂²×C₃×C₄	—	3	1	no	—
360	C₂²×C₃×C₄	—	3	1	no	—
361	C₂²×C₃×C₄	—	9	1	no	—
362	C₂²×C₃×C₄	—	9	1	no	—
363	C₂²×C₃×C₄	—	9	1	no	—
364	C₂²×C₃×C₄	—	9	1	no	—
365	C₂²×C₃×C₄	—	9	1	no	—
366	C₂²×C₃×C₄	—	9	1	no	—
367	C₂²×C₃×C₄	—	18	4	no	—
368	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
369	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
370	C₂×#67	—	3	1	no	—
371	C₂×#67	—	3	1	no	—
372	C₂×#67	—	3	1	no	—
373	C₂×#67	—	3	1	no	—
374	C₂²×Dic₃	—	3	1	no	—
375	#235	—	6	4	no	—
376	C₂×D₁₂	—	3	1	no	—
377	C₂×D₁₂	—	3	1	no	—
378	C₂×C₄×D₃	—	3	1	no	—
379	C₂×C₄×D₃	—	3	1	no	—
380	C₂×C₄×D₃	—	3	1	no	—
381	C₂×C₄×D₃	—	3	1	no	—
382	C₂×C₄×D₃	—	3	1	no	—
383	C₂×C₄×D₃	—	6	4	no	—
384	C₂×Dic₆	—	3	1	no	—
385	C₃×C₄⋊C₄	—	3	1	no	—
386	C₃×C₄⋊C₄	—	9	1	no	—
387	C₃×C₄⋊C₄	—	9	1	no	—
388	C₃×C₄⋊C₄	—	9	1	no	—
389	C₃×C₄⋊C₄	—	9	1	no	—
390	C₃×C₄⋊C₄	—	9	1	no	—
391	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
392	C₃×C₂²⋊C₄	—	3	1	no	—
393	C₃×C₂²⋊C₄	—	3	1	no	—
394	C₃×C₂²⋊C₄	—	9	1	no	—
395	C₃×C₂²⋊C₄	—	9	1	no	—
396	C₃×C₂²⋊C₄	—	9	1	no	—
397	C₃×C₂²⋊C₄	—	9	1	no	—
398	C₃×C₂²⋊C₄	—	9	1	no	—
399	C₃×C₂²⋊C₄	—	9	1	no	—
400	C₃×C₂²⋊C₄	—	9	1	no	—
401	C₃×C₂²⋊C₄	—	9	1	no	—
402	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
403	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
404	C₃×C₄²	—	3	1	no	—
405	C₃×C₄²	—	9	1	no	—
406	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
407	#217	—	3	1	no	—
408	#217	—	3	1	no	—
409	(C₂×D₃)⋊C₄	—	3	1	no	—
410	(C₂×D₃)⋊C₄	—	3	1	no	—
411	(C₂×D₃)⋊C₄	—	3	1	no	—
412	(C₂×D₃)⋊C₄	—	3	1	no	—
413	(C₂×D₃)⋊C₄	—	3	1	no	—
414	(C₂×D₃)⋊C₄	—	3	1	no	—
415	C₄⋊Dic₃	—	3	1	no	—
416	Dic₃⋊C₄	—	3	1	no	—
417	Dic₃⋊C₄	—	3	1	no	—
418	Dic₃⋊C₄	—	3	1	no	—
419	Dic₃⋊C₄	—	3	1	no	—
420	C₄×Dic₃	—	3	1	no	—
421	C₂²×C₃²	—	2	1	no	—
422	C₂²×C₃²	—	2	1	no	—
423	C₂²×C₃²	—	2	1	no	—
424	C₂²×C₃²	—	2	1	no	—
425	C₂²×C₃²	—	2	1	no	—
426	C₂²×C₃²	#235	1	2	yes	—
427	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
428	C₂×C₃×D₃	—	3	2	no	—
429	C₂×C₃×D₃	—	3	2	no	—
430	C₂×C₃×D₃	—	6	8	no	—
431	C₂×C₃×D₃	—	6	1	no	—
432	C₂×C₃×D₃	—	6	1	no	—
433	C₂×C₃×D₃	—	6	1	no	—
434	C₂×C₃×D₃	—	6	1	no	—
435	C₂×C₃×D₃	—	6	1	no	—
436	C₂×C₃×D₃	—	6	1	no	—
437	C₂×C₃×D₃	—	6	1	no	—
438	C₃²×C₄	—	2	1	no	—
439	C₃²×C₄	—	2	1	no	—
440	C₃²×C₄	—	2	1	no	—
441	C₃²×C₄	—	2	1	no	—
442	C₃²×C₄	D₃×D₄	1	2	yes	—
443	C₃×Dic₃	—	3	2	no	—
444	C₃×Dic₃	—	6	1	no	—
445	C₃×Dic₃	—	6	1	no	—
446	C₃×Dic₃	—	6	1	no	—
447	C₃×Dic₃	—	6	1	no	—
448	C₂²×C₉	—	2	1	no	—
449	C₂²×C₉	—	2	1	no	—
450	C₂²×C₉	—	2	2	no	—
451	C₂²×C₉	—	2	1	no	—
452	C₂²×C₉	—	2	1	no	—
453	C₂²×C₉	—	2	1	no	—
454	C₂²×C₉	—	2	1	no	—
455	C₂²×C₉	—	2	2	no	—
456	C₂²×C₉	—	4	1	no	—
457	C₂²×C₉	—	4	1	no	—
458	C₂²×C₉	—	4	1	no	—
459	C₂²×C₉	—	4	1	no	—
460	C₂²×C₉	C₃×#41	1	2	yes	complemented
461	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
462	C₂×D₉	—	2	8	no	—
463	C₂×D₉	—	2	1	no	—
464	C₂×D₉	—	2	1	no	—
465	C₂×D₉	—	2	1	no	—
466	C₂×D₉	—	2	1	no	—
467	C₂×D₉	—	2	1	no	—
468	C₂×D₉	—	2	1	no	—
469	C₂×D₉	—	2	1	no	—
470	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
471	C₂×D₉	C₃×#41	1	2	yes	complemented
472	C₄×C₉	—	2	2	no	—
473	C₄×C₉	—	2	1	no	—
474	C₄×C₉	—	2	1	no	—
475	C₄×C₉	—	2	1	no	—
476	C₄×C₉	—	2	1	no	—
477	C₄×C₉	—	2	2	no	—
478	C₄×C₉	—	4	1	no	—
479	C₄×C₉	—	4	1	no	—
480	C₄×C₉	—	4	1	no	—
481	C₄×C₉	C₂×C₃×D₄	1	2	yes	—
482	Dic₉	—	2	1	no	—
483	Dic₉	—	2	1	no	—
484	Dic₉	—	2	1	no	—
485	Dic₉	—	2	1	no	—
486	Dic₉	C₂×C₃×D₄	1	2	yes	—
487	C₂×#41	—	9	1	no	—
488	C₂³×C₄	—	9	1	no	—
489	#123	—	9	1	no	—
490	#123	—	9	1	no	—
491	C₂²⋊Q₈	—	9	1	no	—
492	C₂²⋊Q₈	—	9	1	no	—
493	#121	—	9	1	no	—
494	#121	—	9	1	no	—
495	#120	—	9	1	no	—
496	#120	—	9	1	no	—
497	C₄×D₄	—	9	1	no	—
498	C₄×D₄	—	9	1	no	—
499	C₄×D₄	—	9	1	no	—
500	C₄×D₄	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
501	#117	—	9	1	no	—
502	3₋¹⁺²	#525	1	1	yes	characteristic, complemented, Sylow
503	C₂³×C₃	—	3	1	no	—
504	C₂³×C₃	—	3	1	no	—
505	C₂³×C₃	—	9	1	no	—
506	C₂³×C₃	—	9	1	no	—
507	C₂³×C₃	—	9	1	no	—
508	C₂³×C₃	—	18	2	no	—
509	C₂³×C₃	—	18	2	no	—
510	C₂³×C₃	—	18	2	no	—
511	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
512	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
513	C₂²×D₃	—	3	1	no	—
514	C₂²×D₃	—	3	1	no	—
515	C₂²×D₃	—	3	1	no	—
516	C₂²×D₃	—	6	2	no	—
517	C₂²×D₃	—	6	2	no	—
518	C₂²×D₃	—	6	2	no	—
519	C₃×Q₈	—	18	2	no	—
520	C₃×D₄	—	2	2	no	—
521	C₃×D₄	—	6	2	no	—
522	C₃×D₄	—	18	2	no	—
523	C₃×D₄	—	18	2	no	—
524	C₃×D₄	—	18	2	no	—
525	C₃×D₄	—	18	2	no	—
526	C₃×D₄	—	18	2	no	—
527	C₃×D₄	—	18	2	no	—
528	C₂×C₃×C₄	—	2	2	no	—
529	C₂×C₃×C₄	—	2	2	no	—
530	C₂×C₃×C₄	—	3	1	no	—
531	C₂×C₃×C₄	—	3	1	no	—
532	C₂×C₃×C₄	—	3	1	no	—
533	C₂×C₃×C₄	—	3	1	no	—
534	C₂×C₃×C₄	—	3	1	no	—
535	C₂×C₃×C₄	—	6	2	no	—
536	C₂×C₃×C₄	—	6	2	no	—
537	C₂×C₃×C₄	—	9	4	no	—
538	C₂×C₃×C₄	—	9	1	no	—
539	C₂×C₃×C₄	—	9	1	no	—
540	C₂×C₃×C₄	—	9	1	no	—
541	C₂×C₃×C₄	—	9	1	no	—
542	C₂×C₃×C₄	—	9	1	no	—
543	C₂×C₃×C₄	—	18	2	no	—
544	C₂×C₃×C₄	—	18	2	no	—
545	C₂×C₃×C₄	—	18	2	no	—
546	C₂×C₃×C₄	—	18	2	no	—
547	C₂×C₃×C₄	—	18	2	no	—
548	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
549	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
550	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
551	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
552	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
553	#67	—	6	2	no	—
554	#67	—	6	2	no	—
555	#67	—	6	2	no	—
556	#67	—	6	2	no	—
557	C₂×Dic₃	—	3	1	no	—
558	C₂×Dic₃	—	3	1	no	—
559	C₂×Dic₃	—	3	1	no	—
560	C₂×Dic₃	—	3	1	no	—
561	C₂×Dic₃	—	3	1	no	—
562	C₂×Dic₃	—	6	2	no	—
563	D₁₂	—	6	2	no	—
564	D₁₂	—	6	2	no	—
565	C₄×D₃	—	3	4	no	—
566	C₄×D₃	—	6	2	no	—
567	C₄×D₃	—	6	2	no	—
568	C₄×D₃	—	6	2	no	—
569	C₄×D₃	—	6	2	no	—
570	Dic₆	—	6	2	no	—
571	C₂×C₃²	—	2	2	no	—
572	C₂×C₃²	—	4	1	no	—
573	C₂×C₃²	C₂×#235	1	1	yes	characteristic
574	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
575	C₂×C₃²	D₃×#41	1	1	yes	characteristic
576	C₃×D₃	—	6	2	no	—
577	C₃×D₃	—	6	2	no	—
578	C₃×D₃	—	12	1	no	—
579	C₂×C₉	—	2	2	no	—
580	C₂×C₉	—	2	1	no	—
581	C₂×C₉	—	2	1	no	—
582	C₂×C₉	—	2	1	no	—
583	C₂×C₉	—	4	2	no	—
584	C₂×C₉	—	4	2	no	—
585	C₂×C₉	—	4	1	no	—
586	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
587	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
588	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
589	D₉	—	2	2	no	—
590	D₉	—	2	2	no	—
591	D₉	—	4	1	no	—
592	C₂⁴	—	9	1	no	—
593	#41	—	18	4	no	—
594	C₂×Q₈	—	9	1	no	—
595	C₂×D₄	—	9	1	no	—
596	C₂×D₄	—	9	1	no	—
597	C₂×D₄	—	9	1	no	—
598	C₂×D₄	—	9	1	no	—
599	C₂×D₄	—	9	1	no	—
600	C₂×D₄	—	9	1	no	—
601	C₂×D₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
602	C₂²×C₄	—	9	1	no	—
603	C₂²×C₄	—	9	1	no	—
604	C₂²×C₄	—	9	1	no	—
605	C₂²×C₄	—	9	1	no	—
606	C₂²×C₄	—	9	1	no	—
607	C₂²×C₄	—	9	1	no	—
608	C₂²×C₄	—	18	4	no	—
609	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
610	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
611	C₄⋊C₄	—	9	1	no	—
612	C₄⋊C₄	—	9	1	no	—
613	C₄⋊C₄	—	9	1	no	—
614	C₄⋊C₄	—	9	1	no	—
615	C₄⋊C₄	—	9	1	no	—
616	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
617	C₂²⋊C₄	—	9	1	no	—
618	C₂²⋊C₄	—	9	1	no	—
619	C₂²⋊C₄	—	9	1	no	—
620	C₂²⋊C₄	—	9	1	no	—
621	C₂²⋊C₄	—	9	1	no	—
622	C₂²⋊C₄	—	9	1	no	—
623	C₂²⋊C₄	—	9	1	no	—
624	C₂²⋊C₄	—	9	1	no	—
625	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
626	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
627	C₄²	—	9	1	no	—
628	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
629	C₂²×C₃	—	2	1	no	—
630	C₂²×C₃	—	2	1	no	—
631	C₂²×C₃	—	2	1	no	—
632	C₂²×C₃	—	2	1	no	—
633	C₂²×C₃	—	2	1	no	—
634	C₂²×C₃	—	3	1	no	—
635	C₂²×C₃	—	3	2	no	—
636	C₂²×C₃	—	6	1	no	—
637	C₂²×C₃	—	6	1	no	—
638	C₂²×C₃	—	6	1	no	—
639	C₂²×C₃	—	6	1	no	—
640	C₂²×C₃	—	6	1	no	—
641	C₂²×C₃	—	9	2	no	—
642	C₂²×C₃	—	9	2	no	—
643	C₂²×C₃	—	18	1	no	—
644	C₂²×C₃	—	18	1	no	—
645	C₂²×C₃	—	18	1	no	—
646	C₂²×C₃	—	18	1	no	—
647	C₂²×C₃	—	18	1	no	—
648	C₂²×C₃	—	18	1	no	—
649	C₂²×C₃	—	18	1	no	—
650	C₂²×C₃	—	18	8	no	—
651	C₂²×C₃	C₃×#235	1	2	yes	—
652	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
653	C₂×D₃	—	3	2	no	—
654	C₂×D₃	—	3	2	no	—
655	C₂×D₃	—	6	8	no	—
656	C₂×D₃	—	6	1	no	—
657	C₂×D₃	—	6	1	no	—
658	C₂×D₃	—	6	1	no	—
659	C₂×D₃	—	6	1	no	—
660	C₂×D₃	—	6	1	no	—
661	C₂×D₃	—	6	1	no	—
662	C₂×D₃	—	6	1	no	—
663	C₃×C₄	—	2	1	no	—
664	C₃×C₄	—	2	1	no	—
665	C₃×C₄	—	2	1	no	—
666	C₃×C₄	—	2	1	no	—
667	C₃×C₄	—	3	2	no	—
668	C₃×C₄	—	6	1	no	—
669	C₃×C₄	—	6	1	no	—
670	C₃×C₄	—	6	1	no	—
671	C₃×C₄	—	6	1	no	—
672	C₃×C₄	—	9	2	no	—
673	C₃×C₄	—	18	1	no	—
674	C₃×C₄	—	18	1	no	—
675	C₃×C₄	—	18	1	no	—
676	C₃×C₄	—	18	1	no	—
677	C₃×C₄	C₃×D₃×D₄	1	2	yes	—
678	Dic₃	—	3	2	no	—
679	Dic₃	—	6	1	no	—
680	Dic₃	—	6	1	no	—
681	Dic₃	—	6	1	no	—
682	Dic₃	—	6	1	no	—
683	C₃²	#5547	1	1	yes	characteristic
684	C₉	—	2	1	no	—
685	C₉	C₃×#525	1	1	yes	characteristic, complemented
686	C₂³	—	9	1	no	—
687	C₂³	—	9	1	no	—
688	C₂³	—	9	1	no	—
689	C₂³	—	18	2	no	—
690	C₂³	—	18	2	no	—
691	C₂³	—	18	2	no	—
692	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
693	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
694	Q₈	—	18	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	18	2	no	—
697	D₄	—	18	2	no	—
698	D₄	—	18	2	no	—
699	D₄	—	18	2	no	—
700	D₄	—	18	2	no	—
701	D₄	—	18	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	9	1	no	—
705	C₂×C₄	—	9	4	no	—
706	C₂×C₄	—	9	1	no	—
707	C₂×C₄	—	9	1	no	—
708	C₂×C₄	—	9	1	no	—
709	C₂×C₄	—	9	1	no	—
710	C₂×C₄	—	18	2	no	—
711	C₂×C₄	—	18	2	no	—
712	C₂×C₄	—	18	2	no	—
713	C₂×C₄	—	18	2	no	—
714	C₂×C₄	—	18	2	no	—
715	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
716	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
717	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
718	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
719	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
720	C₂×C₃	—	2	2	no	—
721	C₂×C₃	—	3	1	no	—
722	C₂×C₃	—	3	1	no	—
723	C₂×C₃	—	3	1	no	—
724	C₂×C₃	—	4	1	no	—
725	C₂×C₃	—	6	2	no	—
726	C₂×C₃	—	12	1	no	—
727	C₂×C₃	—	18	2	no	—
728	C₂×C₃	—	18	2	no	—
729	C₂×C₃	—	36	1	no	—
730	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
731	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
732	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
733	D₃	—	6	2	no	—
734	D₃	—	6	2	no	—
735	D₃	—	12	1	no	—
736	C₂²	—	2	1	no	—
737	C₂²	—	2	1	no	—
738	C₂²	—	2	1	no	—
739	C₂²	—	2	1	no	—
740	C₂²	—	2	1	no	—
741	C₂²	—	9	2	no	—
742	C₂²	—	9	2	no	—
743	C₂²	—	18	8	no	—
744	C₂²	—	18	1	no	—
745	C₂²	—	18	1	no	—
746	C₂²	—	18	1	no	—
747	C₂²	—	18	1	no	—
748	C₂²	—	18	1	no	—
749	C₂²	—	18	1	no	—
750	C₂²	—	18	1	no	—
751	C₂²	#3697⋊C₃	1	2	yes	complemented
752	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
753	C₄	—	2	1	no	—
754	C₄	—	2	1	no	—
755	C₄	—	2	1	no	—
756	C₄	—	2	1	no	—
757	C₄	—	9	2	no	—
758	C₄	—	18	1	no	—
759	C₄	—	18	1	no	—
760	C₄	—	18	1	no	—
761	C₄	—	18	1	no	—
762	C₄	D₄×AGL(1,ℤ/9)	1	2	yes	—
763	C₃	—	3	1	no	—
764	C₃	C₃×#5547	1	1	yes	characteristic
765	C₂	—	2	2	no	—
766	C₂	—	4	1	no	—
767	C₂	—	18	2	no	—
768	C₂	—	18	2	no	—
769	C₂	—	36	1	no	—
770	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
771	C₂	C₂×D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
772	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×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×#525
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#3697⋊C₃	C₂	semidirect
2. C₂²×C₄×AGL(1,ℤ/9)	C₂	semidirect
3. C₄×D₄×3₋¹⁺²	C₂	semidirect
4. #63501⋊C₃	C₂	semidirect
5. #63499⋊C₃	C₂	semidirect
6. C₄×#611⋊C₃	C₂	semidirect
7. C₄×#611⋊C₃	C₂	semidirect
8. #63458⋊C₃	C₂	semidirect
9. #63456⋊C₃	C₂	semidirect
10. #63446⋊C₃	C₂	semidirect
11. #63445⋊C₃	C₂	semidirect
12. #63444⋊C₃	C₂	semidirect
13. #63440⋊C₃	C₂	semidirect
14. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
15. #63434⋊C₃	C₂	semidirect
17. #10589649	C₃	semidirect
21. C₂²×C₄×3₋¹⁺²	C₂²	semidirect
25. C₂×#611⋊C₃	C₂²	semidirect
35. C₂×C₄×AGL(1,ℤ/9)	C₂²	semidirect
36. C₂×3₋¹⁺²⋊Q₈	C₂²	semidirect
37. C₄⋊C₄×3₋¹⁺²	C₂²	semidirect
39. C₂²⋊C₄×3₋¹⁺²	C₂²	semidirect
40. C₄²×3₋¹⁺²	C₂²	semidirect
42. #3676⋊C₃	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. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
53. (3₋¹⁺²⋊C₄)⋊C₄	C₂²	semidirect
54. C₄×3₋¹⁺²⋊C₄	C₂²	semidirect
70. C₂×#3697	C₂×C₃	semidirect
71. C₂²×C₄×D₉	C₂×C₃	semidirect
73. C₄×D₄×C₉	C₂×C₃	semidirect
74. #63501	C₂×C₃	semidirect
75. #63499	C₂×C₃	semidirect
76. C₄×#611	C₂×C₃	semidirect
77. C₄×#611	C₂×C₃	semidirect
78. #63458	C₂×C₃	semidirect
79. #63456	C₂×C₃	semidirect
80. #63446	C₂×C₃	semidirect
81. #63445	C₂×C₃	semidirect
82. #63444	C₂×C₃	semidirect
83. #63440	C₂×C₃	semidirect
84. C₄×D₃₆	C₂×C₃	semidirect
85. #63434	C₂×C₃	semidirect
118. C₄×AGL(1,ℤ/9)	D₄	semidirect
165. C₂²×C₄×C₉	C₂²×C₃	semidirect
169. C₂×#611	C₂²×C₃	semidirect
179. C₂×C₄×D₉	C₂²×C₃	semidirect
180. C₂×Dic₁₈	C₂²×C₃	semidirect
182. C₉×C₄⋊C₄	C₂²×C₃	semidirect
186. C₉×C₂²⋊C₄	C₂²×C₃	semidirect
188. C₄²×C₉	C₂²×C₃	semidirect
190. #3676	C₂²×C₃	semidirect
195. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
196. (C₂×D₉)⋊C₄	C₂²×C₃	semidirect
197. C₄⋊Dic₉	C₂²×C₃	semidirect
198. Dic₉⋊C₄	C₂²×C₃	semidirect
199. Dic₉⋊C₄	C₂²×C₃	semidirect
200. Dic₉⋊C₄	C₂²×C₃	semidirect
201. Dic₉⋊C₄	C₂²×C₃	semidirect
202. C₄×Dic₉	C₂²×C₃	semidirect
208. C₂²×3₋¹⁺²	#41	semidirect
219. C₂×AGL(1,ℤ/9)	#41	semidirect
336. C₄×D₉	C₃×D₄	semidirect
460. C₂²×C₉	C₃×#41	semidirect
471. C₂×D₉	C₃×#41	semidirect
500. C₄×D₄	AGL(1,ℤ/9)	semidirect
502. 3₋¹⁺²	#525	semidirect
610. C₂²×C₄	C₂×AGL(1,ℤ/9)	semidirect
616. C₄⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
626. C₂²⋊C₄	C₂×AGL(1,ℤ/9)	semidirect
628. C₄²	C₂×AGL(1,ℤ/9)	semidirect
685. C₉	C₃×#525	semidirect
751. C₂²	#3697⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#3697⋊C₃	2
C₂²×C₄×AGL(1,ℤ/9)	2
C₄×D₄×3₋¹⁺²	2
#63501⋊C₃	2
#63499⋊C₃	2
C₄×#611⋊C₃	2
#63458⋊C₃	2
#63456⋊C₃	2
#63446⋊C₃	2
#63445⋊C₃	2
#63444⋊C₃	2
#63440⋊C₃	2
C₄×C₄⋊AGL(1,ℤ/9)	2
#63434⋊C₃	2
C₃×#5547	3
#10589649	3

Subgroups — #10589649⋊C3 #13152651

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589649⋊C₃ #13152651