Subgroups — C₂×H(3,𝔽₃)×AGL(1,ℤ/9) #72244057

Order 2916.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(3,𝔽₃)×AGL(1,ℤ/9)	C₂	1	2	yes	maximal, direct product factor
2	C₂×H(3,𝔽₃)×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃²×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃²×AGL(1,ℤ/9)	C₃	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×D₃×H(3,𝔽₃)	—	3	1	no	maximal
8	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
9	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
11	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
12	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
13	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
15	C₂×D₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
16	C₂×D₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
17	H(3,𝔽₃)×3₋¹⁺²	C₂²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂×C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
20	C₂×C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂×C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₃²×H(3,𝔽₃)	D₃	1	1	yes	characteristic
23	C₃²×AGL(1,ℤ/9)	C₂×C₃	1	2	yes	complemented
24	C₃²×AGL(1,ℤ/9)	C₂×C₃	1	2	yes	complemented
25	C₃²×AGL(1,ℤ/9)	C₂×C₃	1	2	yes	complemented
26	C₃²×AGL(1,ℤ/9)	C₂×C₃	1	2	yes	complemented
27	C₃×D₃×H(3,𝔽₃)	—	3	2	no	—
28	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
29	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
30	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
31	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
32	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
33	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
34	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
35	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
36	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#6891	—	2	1	no	—
45	C₂×#6891	—	2	1	no	—
46	C₂×#6891	—	2	1	no	—
47	C₂×#6891	—	2	1	no	—
48	C₂×C₉×H(3,𝔽₃)	—	2	1	no	—
49	C₂×C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
50	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
51	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
52	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
53	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
54	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
55	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
56	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
57	D₉⋊H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
58	D₉×H(3,𝔽₃)	C₂×C₃	1	2	yes	complemented
59	C₂×C₃³×D₃	—	3	1	no	—
60	C₂×C₃³×D₃	—	3	1	no	—
61	C₂×C₃³×D₃	—	3	1	no	—
62	C₂×C₃³×D₃	—	3	1	no	—
63	C₂²×C₃×H(3,𝔽₃)	—	9	1	no	—
64	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
65	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
66	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
67	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
68	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
69	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
70	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
71	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
72	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
73	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
74	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
75	C₂×C₃×AGL(1,ℤ/9)	—	3	1	no	—
76	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic
77	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
78	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
79	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
80	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
81	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
82	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
83	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
84	C₂×C₃×AGL(1,ℤ/9)	C₃²	1	1	yes	characteristic, complemented
85	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
86	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
87	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
88	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
89	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
90	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
91	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
92	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
93	C₂×D₃×H(3,𝔽₃)	—	3	1	no	—
94	C₂×C₃²×D₉	C₃²	1	1	yes	characteristic, complemented
95	C₂×C₃²×D₉	C₃²	1	1	yes	characteristic, complemented
96	C₂×C₃²×D₉	C₃²	1	1	yes	characteristic, complemented
97	C₂×C₃²×D₉	C₃²	1	1	yes	characteristic, complemented
98	C₃²×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₃²×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
100	C₃²×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
101	C₃²×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
102	C₃²×H(3,𝔽₃)	C₂×D₃	1	1	yes	characteristic
103	C₉⋊H(3,𝔽₃)	—	2	1	no	—
104	C₉⋊H(3,𝔽₃)	—	2	1	no	—
105	C₉⋊H(3,𝔽₃)	—	2	1	no	—
106	C₉⋊H(3,𝔽₃)	—	2	1	no	—
107	C₉⋊H(3,𝔽₃)	—	2	1	no	—
108	C₉⋊H(3,𝔽₃)	—	2	1	no	—
109	C₉⋊H(3,𝔽₃)	—	2	1	no	—
110	C₉⋊H(3,𝔽₃)	—	2	1	no	—
111	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
112	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
113	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
114	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
117	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
118	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
119	#6891	—	2	1	no	—
120	#6891	—	2	1	no	—
121	#6891	—	2	1	no	—
122	#6891	—	2	1	no	—
123	C₉×H(3,𝔽₃)	—	2	1	no	—
124	C₉×H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₂×C₃⁴	C₃×D₃	1	1	yes	characteristic
126	C₂×C₃⁴	C₃×D₃	1	1	yes	characteristic
127	C₂×C₃⁴	C₃×D₃	1	1	yes	characteristic
128	C₂×C₃⁴	C₃×D₃	1	1	yes	characteristic
129	C₃³×D₃	—	3	2	no	—
130	C₃³×D₃	—	3	2	no	—
131	C₃³×D₃	—	3	2	no	—
132	C₃³×D₃	—	3	2	no	—
133	C₂×C₃×3₋¹⁺²	—	2	1	no	—
134	C₂×C₃×3₋¹⁺²	—	2	1	no	—
135	C₂×C₃×3₋¹⁺²	—	2	1	no	—
136	C₂×C₃×3₋¹⁺²	—	2	1	no	—
137	C₂×C₃×3₋¹⁺²	—	2	1	no	—
138	C₂×C₃×3₋¹⁺²	—	2	1	no	—
139	C₂×C₃×3₋¹⁺²	—	2	1	no	—
140	C₂×C₃×3₋¹⁺²	—	2	1	no	—
141	C₂×C₃×3₋¹⁺²	—	2	1	no	—
142	C₂×C₃×3₋¹⁺²	—	2	1	no	—
143	C₂×C₃×3₋¹⁺²	—	2	1	no	—
144	C₂×C₃×3₋¹⁺²	—	2	1	no	—
145	C₂×C₃×3₋¹⁺²	—	3	1	no	—
146	C₂×C₃×3₋¹⁺²	—	3	1	no	—
147	C₂×C₃×3₋¹⁺²	—	3	1	no	—
148	C₂×C₃×3₋¹⁺²	—	3	1	no	—
149	C₂×C₃×3₋¹⁺²	—	3	1	no	—
150	C₂×C₃×3₋¹⁺²	—	3	1	no	—
151	C₂×C₃×3₋¹⁺²	—	3	1	no	—
152	C₂×C₃×3₋¹⁺²	—	3	1	no	—
153	C₂×C₃×3₋¹⁺²	—	3	1	no	—
154	C₂×C₃×3₋¹⁺²	—	3	1	no	—
155	C₂×C₃×3₋¹⁺²	—	3	1	no	—
156	C₂×C₃×3₋¹⁺²	—	3	1	no	—
157	C₂×C₃×3₋¹⁺²	—	6	1	no	—
158	C₂×C₃×3₋¹⁺²	—	6	1	no	—
159	C₂×C₃×3₋¹⁺²	—	6	1	no	—
160	C₂×C₃×3₋¹⁺²	—	6	1	no	—
161	C₂×C₃×3₋¹⁺²	—	6	1	no	—
162	C₂×C₃×3₋¹⁺²	—	6	1	no	—
163	C₂×C₃×3₋¹⁺²	—	6	1	no	—
164	C₂×C₃×3₋¹⁺²	—	6	1	no	—
165	C₂×C₃×3₋¹⁺²	—	6	1	no	—
166	C₂×C₃×3₋¹⁺²	—	6	1	no	—
167	C₂×C₃×3₋¹⁺²	—	6	1	no	—
168	C₂×C₃×3₋¹⁺²	—	6	1	no	—
169	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic
170	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
171	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
172	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
173	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
174	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
175	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
176	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
177	C₂×C₃×3₋¹⁺²	C₂×C₃²	1	1	yes	characteristic, complemented
178	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
179	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
180	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
181	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
182	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
183	C₂×C₃×H(3,𝔽₃)	—	9	2	no	—
184	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
185	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
186	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
187	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
188	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
189	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
190	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
191	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
192	C₂×C₃×H(3,𝔽₃)	C₃×D₃	1	1	yes	characteristic
193	C₂×C₃²×C₉	—	2	1	no	—
194	C₂×C₃²×C₉	—	2	1	no	—
195	C₂×C₃²×C₉	—	2	1	no	—
196	C₂×C₃²×C₉	—	2	1	no	—
197	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
198	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
199	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
200	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
201	C₃×AGL(1,ℤ/9)	—	3	2	no	—
202	C₃×AGL(1,ℤ/9)	—	3	2	no	—
203	C₃×AGL(1,ℤ/9)	—	3	2	no	—
204	C₃×AGL(1,ℤ/9)	—	3	2	no	—
205	C₃×AGL(1,ℤ/9)	—	3	2	no	—
206	C₃×AGL(1,ℤ/9)	—	3	2	no	—
207	C₃×AGL(1,ℤ/9)	—	3	2	no	—
208	C₃×AGL(1,ℤ/9)	—	3	2	no	—
209	C₃×AGL(1,ℤ/9)	—	3	2	no	—
210	C₃×AGL(1,ℤ/9)	—	3	2	no	—
211	C₃×AGL(1,ℤ/9)	—	3	2	no	—
212	C₃×AGL(1,ℤ/9)	—	3	2	no	—
213	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	—
214	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
215	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
216	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
217	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
218	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
219	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
220	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
221	C₃×AGL(1,ℤ/9)	C₂×C₃²	1	2	yes	complemented
222	D₃×H(3,𝔽₃)	—	3	2	no	—
223	D₃×H(3,𝔽₃)	—	3	2	no	—
224	D₃×H(3,𝔽₃)	—	3	2	no	—
225	D₃×H(3,𝔽₃)	—	3	2	no	—
226	D₃×H(3,𝔽₃)	—	3	2	no	—
227	D₃×H(3,𝔽₃)	—	3	2	no	—
228	D₃×H(3,𝔽₃)	—	3	2	no	—
229	D₃×H(3,𝔽₃)	—	3	2	no	—
230	D₃×H(3,𝔽₃)	—	3	2	no	—
231	C₃²×D₉	C₂×C₃²	1	2	yes	complemented
232	C₃²×D₉	C₂×C₃²	1	2	yes	complemented
233	C₃²×D₉	C₂×C₃²	1	2	yes	complemented
234	C₃²×D₉	C₂×C₃²	1	2	yes	complemented
235	C₂×C₃²⋊C₉	—	2	1	no	—
236	C₂×C₃²⋊C₉	—	2	1	no	—
237	C₂×C₃²⋊C₉	—	2	1	no	—
238	C₂×C₃²⋊C₉	—	2	1	no	—
239	C₂×C₃²⋊C₉	—	2	1	no	—
240	C₂×C₃²⋊C₉	—	2	1	no	—
241	C₂×C₃²⋊C₉	—	2	1	no	—
242	C₂×C₃²⋊C₉	—	2	1	no	—
243	C₂×C₃²⋊C₉	—	2	1	no	—
244	C₂×C₃²⋊C₉	—	2	1	no	—
245	C₂×C₃²⋊C₉	—	2	1	no	—
246	C₂×C₃²⋊C₉	—	2	1	no	—
247	C₂×C₃²⋊C₉	—	2	1	no	—
248	C₂×C₃²⋊C₉	—	2	1	no	—
249	C₂×C₃²⋊C₉	—	2	1	no	—
250	C₂×C₃²⋊C₉	—	2	1	no	—
251	C₂×C₃²⋊C₉	—	2	1	no	—
252	C₂×C₃²⋊C₉	—	2	1	no	—
253	C₂×C₃²⋊C₉	—	2	1	no	—
254	C₂×C₃²⋊C₉	—	2	1	no	—
255	C₂×C₃²⋊C₉	—	2	1	no	—
256	C₂×C₃²⋊C₉	—	2	1	no	—
257	C₂×C₃²⋊C₉	—	2	1	no	—
258	C₂×C₃²⋊C₉	—	2	1	no	—
259	C₂×C₃²⋊C₉	—	2	1	no	—
260	C₂×C₃²⋊C₉	—	2	1	no	—
261	C₂×C₃²⋊C₉	—	2	1	no	—
262	C₂×C₃²⋊C₉	—	2	1	no	—
263	C₂×C₃²⋊C₉	—	2	1	no	—
264	C₂×C₃²⋊C₉	—	2	1	no	—
265	C₂×C₃²⋊C₉	—	2	1	no	—
266	C₂×C₃²⋊C₉	—	2	1	no	—
267	C₂×C₃²⋊C₉	—	2	1	no	—
268	C₂×C₃²⋊C₉	—	2	1	no	—
269	C₂×C₃²⋊C₉	—	2	1	no	—
270	C₂×C₃²⋊C₉	—	2	1	no	—
271	C₂²×C₃³	—	9	1	no	—
272	C₂²×C₃³	—	9	1	no	—
273	C₂²×C₃³	—	9	1	no	—
274	C₂²×C₃³	—	9	1	no	—
275	C₂×C₃²×D₃	—	3	1	no	—
276	C₂×C₃²×D₃	—	3	1	no	—
277	C₂×C₃²×D₃	—	3	1	no	—
278	C₂×C₃²×D₃	—	3	1	no	—
279	C₂×C₃²×D₃	—	3	1	no	—
280	C₂×C₃²×D₃	—	3	1	no	—
281	C₂×C₃²×D₃	—	3	1	no	—
282	C₂×C₃²×D₃	—	3	1	no	—
283	C₂×C₃²×D₃	—	3	1	no	—
284	C₂×C₃²×D₃	—	3	1	no	—
285	C₂×C₃²×D₃	—	3	1	no	—
286	C₂×C₃²×D₃	—	3	1	no	—
287	C₂×C₃²×D₃	—	3	1	no	—
288	C₂×C₃²×D₃	—	9	1	no	—
289	C₂×C₃²×D₃	—	9	1	no	—
290	C₂×C₃²×D₃	—	9	1	no	—
291	C₂×C₃²×D₃	—	9	1	no	—
292	C₂×C₃²×D₃	—	9	1	no	—
293	C₂×C₃²×D₃	—	9	1	no	—
294	C₂×C₃²×D₃	—	9	1	no	—
295	C₂×C₃²×D₃	—	9	1	no	—
296	C₂×C₃²×D₃	—	9	1	no	—
297	C₂×C₃²×D₃	—	9	1	no	—
298	C₂×C₃²×D₃	—	9	1	no	—
299	C₂×C₃²×D₃	—	9	1	no	—
300	C₂²×H(3,𝔽₃)	—	9	1	no	—
301	C₂²×H(3,𝔽₃)	—	9	1	no	—
302	C₂²×H(3,𝔽₃)	—	9	1	no	—
303	C₂²×H(3,𝔽₃)	—	9	1	no	—
304	C₂²×H(3,𝔽₃)	—	9	1	no	—
305	C₂²×H(3,𝔽₃)	—	9	1	no	—
306	C₂²×H(3,𝔽₃)	—	9	1	no	—
307	C₂²×H(3,𝔽₃)	—	9	1	no	—
308	C₂²×H(3,𝔽₃)	—	9	1	no	—
309	C₂×AGL(1,ℤ/9)	—	3	1	no	—
310	C₂×AGL(1,ℤ/9)	—	3	1	no	—
311	C₂×AGL(1,ℤ/9)	—	3	1	no	—
312	C₂×AGL(1,ℤ/9)	—	3	1	no	—
313	C₂×AGL(1,ℤ/9)	—	3	1	no	—
314	C₂×AGL(1,ℤ/9)	—	3	1	no	—
315	C₂×AGL(1,ℤ/9)	—	3	1	no	—
316	C₂×AGL(1,ℤ/9)	—	3	1	no	—
317	C₂×AGL(1,ℤ/9)	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
318	C₂×AGL(1,ℤ/9)	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
319	C₂×AGL(1,ℤ/9)	H(3,𝔽₃)	1	1	yes	characteristic, direct product factor
320	C₂×C₃×D₉	—	3	1	no	—
321	C₂×C₃×D₉	—	3	1	no	—
322	C₂×C₃×D₉	—	3	1	no	—
323	C₂×C₃×D₉	—	3	1	no	—
324	C₂×C₃×D₉	C₃³	1	1	yes	characteristic
325	C₃⁴	C₂×C₃×D₃	1	1	yes	characteristic
326	C₃⁴	C₂×C₃×D₃	1	1	yes	characteristic
327	C₃⁴	C₂×C₃×D₃	1	1	yes	characteristic
328	C₃⁴	C₂×C₃×D₃	1	1	yes	characteristic
329	C₃×3₋¹⁺²	—	2	1	no	—
330	C₃×3₋¹⁺²	—	2	1	no	—
331	C₃×3₋¹⁺²	—	2	1	no	—
332	C₃×3₋¹⁺²	—	2	1	no	—
333	C₃×3₋¹⁺²	—	2	1	no	—
334	C₃×3₋¹⁺²	—	2	1	no	—
335	C₃×3₋¹⁺²	—	2	1	no	—
336	C₃×3₋¹⁺²	—	2	1	no	—
337	C₃×3₋¹⁺²	—	2	1	no	—
338	C₃×3₋¹⁺²	—	2	1	no	—
339	C₃×3₋¹⁺²	—	2	1	no	—
340	C₃×3₋¹⁺²	—	2	1	no	—
341	C₃×3₋¹⁺²	—	3	1	no	—
342	C₃×3₋¹⁺²	—	3	1	no	—
343	C₃×3₋¹⁺²	—	3	1	no	—
344	C₃×3₋¹⁺²	—	3	1	no	—
345	C₃×3₋¹⁺²	—	3	1	no	—
346	C₃×3₋¹⁺²	—	3	1	no	—
347	C₃×3₋¹⁺²	—	3	1	no	—
348	C₃×3₋¹⁺²	—	3	1	no	—
349	C₃×3₋¹⁺²	—	3	1	no	—
350	C₃×3₋¹⁺²	—	3	1	no	—
351	C₃×3₋¹⁺²	—	3	1	no	—
352	C₃×3₋¹⁺²	—	3	1	no	—
353	C₃×3₋¹⁺²	—	6	1	no	—
354	C₃×3₋¹⁺²	—	6	1	no	—
355	C₃×3₋¹⁺²	—	6	1	no	—
356	C₃×3₋¹⁺²	—	6	1	no	—
357	C₃×3₋¹⁺²	—	6	1	no	—
358	C₃×3₋¹⁺²	—	6	1	no	—
359	C₃×3₋¹⁺²	—	6	1	no	—
360	C₃×3₋¹⁺²	—	6	1	no	—
361	C₃×3₋¹⁺²	—	6	1	no	—
362	C₃×3₋¹⁺²	—	6	1	no	—
363	C₃×3₋¹⁺²	—	6	1	no	—
364	C₃×3₋¹⁺²	—	6	1	no	—
365	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic
366	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
367	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
368	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
369	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
370	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
371	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
372	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
373	C₃×3₋¹⁺²	C₂²×C₃²	1	1	yes	characteristic, complemented
374	C₃×H(3,𝔽₃)	—	6	1	no	—
375	C₃×H(3,𝔽₃)	—	6	1	no	—
376	C₃×H(3,𝔽₃)	—	6	1	no	—
377	C₃×H(3,𝔽₃)	—	6	1	no	—
378	C₃×H(3,𝔽₃)	—	6	1	no	—
379	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
380	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
381	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
382	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
383	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
384	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
385	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
386	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
387	C₃×H(3,𝔽₃)	C₂×C₃×D₃	1	1	yes	characteristic
388	C₃²×C₉	—	2	1	no	—
389	C₃²×C₉	—	2	1	no	—
390	C₃²×C₉	—	2	1	no	—
391	C₃²×C₉	—	2	1	no	—
392	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
393	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
394	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
395	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
396	C₃²⋊C₉	—	2	1	no	—
397	C₃²⋊C₉	—	2	1	no	—
398	C₃²⋊C₉	—	2	1	no	—
399	C₃²⋊C₉	—	2	1	no	—
400	C₃²⋊C₉	—	2	1	no	—
401	C₃²⋊C₉	—	2	1	no	—
402	C₃²⋊C₉	—	2	1	no	—
403	C₃²⋊C₉	—	2	1	no	—
404	C₃²⋊C₉	—	2	1	no	—
405	C₃²⋊C₉	—	2	1	no	—
406	C₃²⋊C₉	—	2	1	no	—
407	C₃²⋊C₉	—	2	1	no	—
408	C₃²⋊C₉	—	2	1	no	—
409	C₃²⋊C₉	—	2	1	no	—
410	C₃²⋊C₉	—	2	1	no	—
411	C₃²⋊C₉	—	2	1	no	—
412	C₃²⋊C₉	—	2	1	no	—
413	C₃²⋊C₉	—	2	1	no	—
414	C₃²⋊C₉	—	2	1	no	—
415	C₃²⋊C₉	—	2	1	no	—
416	C₃²⋊C₉	—	2	1	no	—
417	C₃²⋊C₉	—	2	1	no	—
418	C₃²⋊C₉	—	2	1	no	—
419	C₃²⋊C₉	—	2	1	no	—
420	C₃²⋊C₉	—	2	1	no	—
421	C₃²⋊C₉	—	2	1	no	—
422	C₃²⋊C₉	—	2	1	no	—
423	C₃²⋊C₉	—	2	1	no	—
424	C₃²⋊C₉	—	2	1	no	—
425	C₃²⋊C₉	—	2	1	no	—
426	C₃²⋊C₉	—	2	1	no	—
427	C₃²⋊C₉	—	2	1	no	—
428	C₃²⋊C₉	—	2	1	no	—
429	C₃²⋊C₉	—	2	1	no	—
430	C₃²⋊C₉	—	2	1	no	—
431	C₃²⋊C₉	—	2	1	no	—
432	C₂×C₃³	—	3	1	no	—
433	C₂×C₃³	—	3	1	no	—
434	C₂×C₃³	—	3	1	no	—
435	C₂×C₃³	—	3	1	no	—
436	C₂×C₃³	—	3	1	no	—
437	C₂×C₃³	—	3	1	no	—
438	C₂×C₃³	—	3	1	no	—
439	C₂×C₃³	—	3	1	no	—
440	C₂×C₃³	—	3	1	no	—
441	C₂×C₃³	—	3	1	no	—
442	C₂×C₃³	—	3	1	no	—
443	C₂×C₃³	—	3	1	no	—
444	C₂×C₃³	—	3	1	no	—
445	C₂×C₃³	—	3	1	no	—
446	C₂×C₃³	—	6	1	no	—
447	C₂×C₃³	—	6	1	no	—
448	C₂×C₃³	—	6	1	no	—
449	C₂×C₃³	—	6	1	no	—
450	C₂×C₃³	—	6	1	no	—
451	C₂×C₃³	—	6	1	no	—
452	C₂×C₃³	—	9	2	no	—
453	C₂×C₃³	—	9	2	no	—
454	C₂×C₃³	—	9	2	no	—
455	C₂×C₃³	—	9	2	no	—
456	C₂×C₃³	—	18	1	no	—
457	C₂×C₃³	—	18	1	no	—
458	C₂×C₃³	—	18	1	no	—
459	C₂×C₃³	—	18	1	no	—
460	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
461	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
462	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
463	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
464	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
465	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
466	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
467	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
468	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
469	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
470	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
471	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
472	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
473	C₃²×D₃	—	3	2	no	—
474	C₃²×D₃	—	3	2	no	—
475	C₃²×D₃	—	3	2	no	—
476	C₃²×D₃	—	3	2	no	—
477	C₃²×D₃	—	3	2	no	—
478	C₃²×D₃	—	3	2	no	—
479	C₃²×D₃	—	3	2	no	—
480	C₃²×D₃	—	3	2	no	—
481	C₃²×D₃	—	3	2	no	—
482	C₃²×D₃	—	3	2	no	—
483	C₃²×D₃	—	3	2	no	—
484	C₃²×D₃	—	3	2	no	—
485	C₃²×D₃	—	3	2	no	—
486	C₃²×D₃	—	9	2	no	—
487	C₃²×D₃	—	9	2	no	—
488	C₃²×D₃	—	9	2	no	—
489	C₃²×D₃	—	9	2	no	—
490	C₃²×D₃	—	9	2	no	—
491	C₃²×D₃	—	9	2	no	—
492	C₃²×D₃	—	9	2	no	—
493	C₃²×D₃	—	9	2	no	—
494	C₃²×D₃	—	9	2	no	—
495	C₃²×D₃	—	9	2	no	—
496	C₃²×D₃	—	9	2	no	—
497	C₃²×D₃	—	9	2	no	—
498	C₂×3₋¹⁺²	—	2	1	no	—
499	C₂×3₋¹⁺²	—	2	1	no	—
500	C₂×3₋¹⁺²	—	2	1	no	—
501	C₂×3₋¹⁺²	—	3	1	no	—
502	C₂×3₋¹⁺²	—	3	1	no	—
503	C₂×3₋¹⁺²	—	3	1	no	—
504	C₂×3₋¹⁺²	—	3	1	no	—
505	C₂×3₋¹⁺²	—	3	1	no	—
506	C₂×3₋¹⁺²	—	3	1	no	—
507	C₂×3₋¹⁺²	—	3	1	no	—
508	C₂×3₋¹⁺²	—	3	1	no	—
509	C₂×3₋¹⁺²	—	6	1	no	—
510	C₂×3₋¹⁺²	—	6	1	no	—
511	C₂×3₋¹⁺²	—	6	1	no	—
512	C₂×3₋¹⁺²	—	6	1	no	—
513	C₂×3₋¹⁺²	—	6	1	no	—
514	C₂×3₋¹⁺²	—	6	1	no	—
515	C₂×3₋¹⁺²	—	6	1	no	—
516	C₂×3₋¹⁺²	—	6	1	no	—
517	C₂×3₋¹⁺²	—	6	1	no	—
518	C₂×3₋¹⁺²	—	6	1	no	—
519	C₂×3₋¹⁺²	—	6	1	no	—
520	C₂×3₋¹⁺²	—	6	1	no	—
521	C₂×3₋¹⁺²	—	6	1	no	—
522	C₂×3₋¹⁺²	—	6	1	no	—
523	C₂×3₋¹⁺²	—	6	1	no	—
524	C₂×3₋¹⁺²	—	6	1	no	—
525	C₂×3₋¹⁺²	—	6	1	no	—
526	C₂×3₋¹⁺²	—	6	1	no	—
527	C₂×3₋¹⁺²	—	6	1	no	—
528	C₂×3₋¹⁺²	—	6	1	no	—
529	C₂×3₋¹⁺²	—	6	1	no	—
530	C₂×3₋¹⁺²	—	6	1	no	—
531	C₂×3₋¹⁺²	—	6	1	no	—
532	C₂×3₋¹⁺²	—	6	1	no	—
533	C₂×3₋¹⁺²	—	6	1	no	—
534	C₂×3₋¹⁺²	—	6	1	no	—
535	C₂×3₋¹⁺²	—	6	1	no	—
536	C₂×3₋¹⁺²	—	6	1	no	—
537	C₂×3₋¹⁺²	—	6	1	no	—
538	C₂×3₋¹⁺²	—	6	1	no	—
539	C₂×3₋¹⁺²	—	6	1	no	—
540	C₂×3₋¹⁺²	—	6	1	no	—
541	C₂×3₋¹⁺²	—	6	1	no	—
542	C₂×3₋¹⁺²	—	6	1	no	—
543	C₂×3₋¹⁺²	—	6	1	no	—
544	C₂×3₋¹⁺²	—	6	1	no	—
545	C₂×3₋¹⁺²	—	6	1	no	—
546	C₂×3₋¹⁺²	—	6	1	no	—
547	C₂×3₋¹⁺²	—	6	1	no	—
548	C₂×3₋¹⁺²	—	6	1	no	—
549	C₂×3₋¹⁺²	—	6	1	no	—
550	C₂×3₋¹⁺²	—	6	1	no	—
551	C₂×3₋¹⁺²	—	6	1	no	—
552	C₂×3₋¹⁺²	—	6	1	no	—
553	C₂×3₋¹⁺²	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
554	C₂×3₋¹⁺²	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
555	C₂×3₋¹⁺²	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
556	C₂×H(3,𝔽₃)	—	2	1	no	—
557	C₂×H(3,𝔽₃)	—	2	1	no	—
558	C₂×H(3,𝔽₃)	—	2	1	no	—
559	C₂×H(3,𝔽₃)	—	2	1	no	—
560	C₂×H(3,𝔽₃)	—	3	1	no	—
561	C₂×H(3,𝔽₃)	—	3	1	no	—
562	C₂×H(3,𝔽₃)	—	3	1	no	—
563	C₂×H(3,𝔽₃)	—	6	1	no	—
564	C₂×H(3,𝔽₃)	—	6	1	no	—
565	C₂×H(3,𝔽₃)	—	6	1	no	—
566	C₂×H(3,𝔽₃)	—	6	1	no	—
567	C₂×H(3,𝔽₃)	—	6	1	no	—
568	C₂×H(3,𝔽₃)	—	6	1	no	—
569	C₂×H(3,𝔽₃)	—	6	1	no	—
570	C₂×H(3,𝔽₃)	—	6	1	no	—
571	C₂×H(3,𝔽₃)	—	6	1	no	—
572	C₂×H(3,𝔽₃)	—	6	1	no	—
573	C₂×H(3,𝔽₃)	—	6	1	no	—
574	C₂×H(3,𝔽₃)	—	6	1	no	—
575	C₂×H(3,𝔽₃)	—	6	1	no	—
576	C₂×H(3,𝔽₃)	—	9	2	no	—
577	C₂×H(3,𝔽₃)	—	9	2	no	—
578	C₂×H(3,𝔽₃)	—	9	2	no	—
579	C₂×H(3,𝔽₃)	—	9	2	no	—
580	C₂×H(3,𝔽₃)	—	9	2	no	—
581	C₂×H(3,𝔽₃)	—	9	2	no	—
582	C₂×H(3,𝔽₃)	—	9	2	no	—
583	C₂×H(3,𝔽₃)	—	9	2	no	—
584	C₂×H(3,𝔽₃)	—	9	2	no	—
585	C₂×H(3,𝔽₃)	AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
586	C₂×C₃×C₉	—	2	1	no	—
587	C₂×C₃×C₉	—	2	1	no	—
588	C₂×C₃×C₉	—	2	1	no	—
589	C₂×C₃×C₉	—	2	1	no	—
590	C₂×C₃×C₉	—	2	1	no	—
591	C₂×C₃×C₉	—	2	1	no	—
592	C₂×C₃×C₉	—	2	1	no	—
593	C₂×C₃×C₉	—	2	1	no	—
594	C₂×C₃×C₉	—	2	1	no	—
595	C₂×C₃×C₉	—	2	1	no	—
596	C₂×C₃×C₉	—	2	1	no	—
597	C₂×C₃×C₉	—	2	1	no	—
598	C₂×C₃×C₉	—	2	1	no	—
599	C₂×C₃×C₉	—	3	1	no	—
600	C₂×C₃×C₉	—	3	1	no	—
601	C₂×C₃×C₉	—	3	1	no	—
602	C₂×C₃×C₉	—	3	1	no	—
603	C₂×C₃×C₉	—	6	1	no	—
604	C₂×C₃×C₉	—	6	1	no	—
605	C₂×C₃×C₉	—	6	1	no	—
606	C₂×C₃×C₉	—	6	1	no	—
607	C₂×C₃×C₉	—	6	1	no	—
608	C₂×C₃×C₉	—	6	1	no	—
609	C₂×C₃×C₉	—	6	1	no	—
610	C₂×C₃×C₉	—	6	1	no	—
611	C₂×C₃×C₉	—	6	1	no	—
612	C₂×C₃×C₉	—	6	1	no	—
613	C₂×C₃×C₉	—	6	1	no	—
614	C₂×C₃×C₉	—	6	1	no	—
615	C₂×C₃×C₉	—	6	1	no	—
616	C₂×C₃×C₉	—	6	1	no	—
617	C₂×C₃×C₉	—	6	1	no	—
618	C₂×C₃×C₉	—	6	1	no	—
619	C₂×C₃×C₉	C₂×C₃³	1	1	yes	characteristic
620	AGL(1,ℤ/9)	—	3	2	no	—
621	AGL(1,ℤ/9)	—	3	2	no	—
622	AGL(1,ℤ/9)	—	3	2	no	—
623	AGL(1,ℤ/9)	—	3	2	no	—
624	AGL(1,ℤ/9)	—	3	2	no	—
625	AGL(1,ℤ/9)	—	3	2	no	—
626	AGL(1,ℤ/9)	—	3	2	no	—
627	AGL(1,ℤ/9)	—	3	2	no	—
628	AGL(1,ℤ/9)	C₂×H(3,𝔽₃)	1	2	yes	direct product factor
629	AGL(1,ℤ/9)	C₂×H(3,𝔽₃)	1	2	yes	direct product factor
630	AGL(1,ℤ/9)	C₂×H(3,𝔽₃)	1	2	yes	direct product factor
631	C₃×D₉	—	3	2	no	—
632	C₃×D₉	—	3	2	no	—
633	C₃×D₉	—	3	2	no	—
634	C₃×D₉	—	3	2	no	—
635	C₃×D₉	C₂×C₃³	1	2	yes	—
636	C₂²×C₃²	—	9	1	no	—
637	C₂²×C₃²	—	9	1	no	—
638	C₂²×C₃²	—	9	1	no	—
639	C₂²×C₃²	—	9	1	no	—
640	C₂²×C₃²	—	9	1	no	—
641	C₂²×C₃²	—	9	1	no	—
642	C₂²×C₃²	—	9	1	no	—
643	C₂²×C₃²	—	9	1	no	—
644	C₂²×C₃²	—	9	1	no	—
645	C₂²×C₃²	—	9	1	no	—
646	C₂²×C₃²	—	9	1	no	—
647	C₂²×C₃²	—	9	1	no	—
648	C₂²×C₃²	—	9	1	no	—
649	C₂²×C₃²	—	27	1	no	—
650	C₂²×C₃²	—	27	1	no	—
651	C₂²×C₃²	—	27	1	no	—
652	C₂²×C₃²	—	27	1	no	—
653	C₂²×C₃²	—	27	1	no	—
654	C₂²×C₃²	—	27	1	no	—
655	C₂²×C₃²	—	27	1	no	—
656	C₂²×C₃²	—	27	1	no	—
657	C₂²×C₃²	—	27	1	no	—
658	C₂²×C₃²	—	27	1	no	—
659	C₂²×C₃²	—	27	1	no	—
660	C₂²×C₃²	—	27	1	no	—
661	C₂×C₃×D₃	—	3	1	no	—
662	C₂×C₃×D₃	—	3	1	no	—
663	C₂×C₃×D₃	—	3	1	no	—
664	C₂×C₃×D₃	—	3	1	no	—
665	C₂×C₃×D₃	—	9	1	no	—
666	C₂×C₃×D₃	—	9	1	no	—
667	C₂×C₃×D₃	—	9	1	no	—
668	C₂×C₃×D₃	—	9	1	no	—
669	C₂×C₃×D₃	—	9	1	no	—
670	C₂×C₃×D₃	—	9	1	no	—
671	C₂×C₃×D₃	—	9	1	no	—
672	C₂×C₃×D₃	—	9	1	no	—
673	C₂×C₃×D₃	—	9	1	no	—
674	C₂×C₃×D₃	—	9	1	no	—
675	C₂×C₃×D₃	—	9	1	no	—
676	C₂×C₃×D₃	—	9	1	no	—
677	C₂×D₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic, complemented
678	C₃³	—	3	1	no	—
679	C₃³	—	3	1	no	—
680	C₃³	—	3	1	no	—
681	C₃³	—	3	1	no	—
682	C₃³	—	3	1	no	—
683	C₃³	—	3	1	no	—
684	C₃³	—	3	1	no	—
685	C₃³	—	3	1	no	—
686	C₃³	—	3	1	no	—
687	C₃³	—	3	1	no	—
688	C₃³	—	3	1	no	—
689	C₃³	—	3	1	no	—
690	C₃³	—	3	1	no	—
691	C₃³	—	3	1	no	—
692	C₃³	—	6	1	no	—
693	C₃³	—	6	1	no	—
694	C₃³	—	6	1	no	—
695	C₃³	—	6	1	no	—
696	C₃³	—	6	1	no	—
697	C₃³	—	6	1	no	—
698	C₃³	—	18	1	no	—
699	C₃³	—	18	1	no	—
700	C₃³	—	18	1	no	—
701	C₃³	—	18	1	no	—
702	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
703	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
704	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
705	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
706	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
707	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
708	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
709	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
710	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
711	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
712	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
713	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
714	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
715	3₋¹⁺²	—	2	1	no	—
716	3₋¹⁺²	—	2	1	no	—
717	3₋¹⁺²	—	2	1	no	—
718	3₋¹⁺²	—	3	1	no	—
719	3₋¹⁺²	—	3	1	no	—
720	3₋¹⁺²	—	3	1	no	—
721	3₋¹⁺²	—	3	1	no	—
722	3₋¹⁺²	—	3	1	no	—
723	3₋¹⁺²	—	3	1	no	—
724	3₋¹⁺²	—	3	1	no	—
725	3₋¹⁺²	—	3	1	no	—
726	3₋¹⁺²	—	6	1	no	—
727	3₋¹⁺²	—	6	1	no	—
728	3₋¹⁺²	—	6	1	no	—
729	3₋¹⁺²	—	6	1	no	—
730	3₋¹⁺²	—	6	1	no	—
731	3₋¹⁺²	—	6	1	no	—
732	3₋¹⁺²	—	6	1	no	—
733	3₋¹⁺²	—	6	1	no	—
734	3₋¹⁺²	—	6	1	no	—
735	3₋¹⁺²	—	6	1	no	—
736	3₋¹⁺²	—	6	1	no	—
737	3₋¹⁺²	—	6	1	no	—
738	3₋¹⁺²	—	6	1	no	—
739	3₋¹⁺²	—	6	1	no	—
740	3₋¹⁺²	—	6	1	no	—
741	3₋¹⁺²	—	6	1	no	—
742	3₋¹⁺²	—	6	1	no	—
743	3₋¹⁺²	—	6	1	no	—
744	3₋¹⁺²	—	6	1	no	—
745	3₋¹⁺²	—	6	1	no	—
746	3₋¹⁺²	—	6	1	no	—
747	3₋¹⁺²	—	6	1	no	—
748	3₋¹⁺²	—	6	1	no	—
749	3₋¹⁺²	—	6	1	no	—
750	3₋¹⁺²	—	6	1	no	—
751	3₋¹⁺²	—	6	1	no	—
752	3₋¹⁺²	—	6	1	no	—
753	3₋¹⁺²	—	6	1	no	—
754	3₋¹⁺²	—	6	1	no	—
755	3₋¹⁺²	—	6	1	no	—
756	3₋¹⁺²	—	6	1	no	—
757	3₋¹⁺²	—	6	1	no	—
758	3₋¹⁺²	—	6	1	no	—
759	3₋¹⁺²	—	6	1	no	—
760	3₋¹⁺²	—	6	1	no	—
761	3₋¹⁺²	—	6	1	no	—
762	3₋¹⁺²	—	6	1	no	—
763	3₋¹⁺²	—	6	1	no	—
764	3₋¹⁺²	—	6	1	no	—
765	3₋¹⁺²	—	6	1	no	—
766	3₋¹⁺²	—	6	1	no	—
767	3₋¹⁺²	—	6	1	no	—
768	3₋¹⁺²	—	6	1	no	—
769	3₋¹⁺²	—	6	1	no	—
770	3₋¹⁺²	C₂²×H(3,𝔽₃)	1	1	yes	characteristic, complemented
771	3₋¹⁺²	C₂²×H(3,𝔽₃)	1	1	yes	characteristic, complemented
772	3₋¹⁺²	C₂²×H(3,𝔽₃)	1	1	yes	characteristic, complemented
773	H(3,𝔽₃)	—	2	1	no	—
774	H(3,𝔽₃)	—	2	1	no	—
775	H(3,𝔽₃)	—	2	1	no	—
776	H(3,𝔽₃)	—	2	1	no	—
777	H(3,𝔽₃)	—	3	1	no	—
778	H(3,𝔽₃)	—	3	1	no	—
779	H(3,𝔽₃)	—	3	1	no	—
780	H(3,𝔽₃)	—	6	1	no	—
781	H(3,𝔽₃)	—	6	1	no	—
782	H(3,𝔽₃)	—	6	1	no	—
783	H(3,𝔽₃)	—	6	1	no	—
784	H(3,𝔽₃)	—	6	1	no	—
785	H(3,𝔽₃)	—	6	1	no	—
786	H(3,𝔽₃)	—	6	1	no	—
787	H(3,𝔽₃)	—	6	1	no	—
788	H(3,𝔽₃)	—	6	1	no	—
789	H(3,𝔽₃)	—	6	1	no	—
790	H(3,𝔽₃)	—	6	1	no	—
791	H(3,𝔽₃)	—	6	1	no	—
792	H(3,𝔽₃)	—	6	1	no	—
793	H(3,𝔽₃)	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
794	C₃×C₉	—	2	1	no	—
795	C₃×C₉	—	2	1	no	—
796	C₃×C₉	—	2	1	no	—
797	C₃×C₉	—	2	1	no	—
798	C₃×C₉	—	2	1	no	—
799	C₃×C₉	—	2	1	no	—
800	C₃×C₉	—	2	1	no	—
801	C₃×C₉	—	2	1	no	—
802	C₃×C₉	—	2	1	no	—
803	C₃×C₉	—	2	1	no	—
804	C₃×C₉	—	2	1	no	—
805	C₃×C₉	—	2	1	no	—
806	C₃×C₉	—	2	1	no	—
807	C₃×C₉	—	3	1	no	—
808	C₃×C₉	—	3	1	no	—
809	C₃×C₉	—	3	1	no	—
810	C₃×C₉	—	3	1	no	—
811	C₃×C₉	—	6	1	no	—
812	C₃×C₉	—	6	1	no	—
813	C₃×C₉	—	6	1	no	—
814	C₃×C₉	—	6	1	no	—
815	C₃×C₉	—	6	1	no	—
816	C₃×C₉	—	6	1	no	—
817	C₃×C₉	—	6	1	no	—
818	C₃×C₉	—	6	1	no	—
819	C₃×C₉	—	6	1	no	—
820	C₃×C₉	—	6	1	no	—
821	C₃×C₉	—	6	1	no	—
822	C₃×C₉	—	6	1	no	—
823	C₃×C₉	—	6	1	no	—
824	C₃×C₉	—	6	1	no	—
825	C₃×C₉	—	6	1	no	—
826	C₃×C₉	—	6	1	no	—
827	C₃×C₉	C₂²×C₃³	1	1	yes	characteristic
828	C₂×C₃²	—	2	1	no	—
829	C₂×C₃²	—	2	1	no	—
830	C₂×C₃²	—	2	1	no	—
831	C₂×C₃²	—	2	1	no	—
832	C₂×C₃²	—	3	1	no	—
833	C₂×C₃²	—	3	1	no	—
834	C₂×C₃²	—	3	1	no	—
835	C₂×C₃²	—	3	1	no	—
836	C₂×C₃²	—	3	1	no	—
837	C₂×C₃²	—	3	1	no	—
838	C₂×C₃²	—	3	1	no	—
839	C₂×C₃²	—	3	1	no	—
840	C₂×C₃²	—	3	1	no	—
841	C₂×C₃²	—	3	1	no	—
842	C₂×C₃²	—	3	1	no	—
843	C₂×C₃²	—	3	1	no	—
844	C₂×C₃²	—	3	1	no	—
845	C₂×C₃²	—	3	1	no	—
846	C₂×C₃²	—	3	1	no	—
847	C₂×C₃²	—	6	1	no	—
848	C₂×C₃²	—	6	1	no	—
849	C₂×C₃²	—	6	1	no	—
850	C₂×C₃²	—	6	1	no	—
851	C₂×C₃²	—	6	1	no	—
852	C₂×C₃²	—	6	1	no	—
853	C₂×C₃²	—	6	1	no	—
854	C₂×C₃²	—	6	1	no	—
855	C₂×C₃²	—	6	1	no	—
856	C₂×C₃²	—	6	1	no	—
857	C₂×C₃²	—	6	1	no	—
858	C₂×C₃²	—	6	1	no	—
859	C₂×C₃²	—	6	1	no	—
860	C₂×C₃²	—	6	1	no	—
861	C₂×C₃²	—	6	1	no	—
862	C₂×C₃²	—	6	1	no	—
863	C₂×C₃²	—	6	1	no	—
864	C₂×C₃²	—	6	1	no	—
865	C₂×C₃²	—	6	1	no	—
866	C₂×C₃²	—	9	1	no	—
867	C₂×C₃²	—	9	1	no	—
868	C₂×C₃²	—	9	1	no	—
869	C₂×C₃²	—	9	1	no	—
870	C₂×C₃²	—	9	1	no	—
871	C₂×C₃²	—	9	1	no	—
872	C₂×C₃²	—	9	2	no	—
873	C₂×C₃²	—	9	2	no	—
874	C₂×C₃²	—	9	2	no	—
875	C₂×C₃²	—	9	2	no	—
876	C₂×C₃²	—	9	2	no	—
877	C₂×C₃²	—	9	2	no	—
878	C₂×C₃²	—	9	2	no	—
879	C₂×C₃²	—	9	2	no	—
880	C₂×C₃²	—	9	2	no	—
881	C₂×C₃²	—	9	2	no	—
882	C₂×C₃²	—	9	2	no	—
883	C₂×C₃²	—	9	2	no	—
884	C₂×C₃²	—	9	2	no	—
885	C₂×C₃²	—	18	1	no	—
886	C₂×C₃²	—	18	1	no	—
887	C₂×C₃²	—	18	1	no	—
888	C₂×C₃²	—	18	1	no	—
889	C₂×C₃²	—	18	1	no	—
890	C₂×C₃²	—	18	1	no	—
891	C₂×C₃²	—	18	1	no	—
892	C₂×C₃²	—	18	1	no	—
893	C₂×C₃²	—	18	1	no	—
894	C₂×C₃²	—	18	1	no	—
895	C₂×C₃²	—	18	1	no	—
896	C₂×C₃²	—	18	1	no	—
897	C₂×C₃²	—	18	1	no	—
898	C₂×C₃²	—	18	1	no	—
899	C₂×C₃²	—	18	1	no	—
900	C₂×C₃²	—	18	1	no	—
901	C₂×C₃²	—	18	1	no	—
902	C₂×C₃²	—	18	1	no	—
903	C₂×C₃²	—	27	2	no	—
904	C₂×C₃²	—	27	2	no	—
905	C₂×C₃²	—	27	2	no	—
906	C₂×C₃²	—	27	2	no	—
907	C₂×C₃²	—	27	2	no	—
908	C₂×C₃²	—	27	2	no	—
909	C₂×C₃²	—	27	2	no	—
910	C₂×C₃²	—	27	2	no	—
911	C₂×C₃²	—	27	2	no	—
912	C₂×C₃²	—	27	2	no	—
913	C₂×C₃²	—	27	2	no	—
914	C₂×C₃²	—	27	2	no	—
915	C₂×C₃²	D₃×H(3,𝔽₃)	1	1	yes	characteristic
916	C₂×C₃²	D₃×H(3,𝔽₃)	1	1	yes	characteristic
917	C₂×C₃²	D₃×H(3,𝔽₃)	1	1	yes	characteristic
918	C₂×C₃²	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
919	C₂×C₃²	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
920	C₂×C₃²	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
921	C₂×C₃²	C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
922	C₂×C₃²	C₃³×D₃	1	1	yes	characteristic
923	C₃×D₃	—	3	2	no	—
924	C₃×D₃	—	3	2	no	—
925	C₃×D₃	—	3	2	no	—
926	C₃×D₃	—	3	2	no	—
927	C₃×D₃	—	9	2	no	—
928	C₃×D₃	—	9	2	no	—
929	C₃×D₃	—	9	2	no	—
930	C₃×D₃	—	9	2	no	—
931	C₃×D₃	—	9	2	no	—
932	C₃×D₃	—	9	2	no	—
933	C₃×D₃	—	9	2	no	—
934	C₃×D₃	—	9	2	no	—
935	C₃×D₃	—	9	2	no	—
936	C₃×D₃	—	9	2	no	—
937	C₃×D₃	—	9	2	no	—
938	C₃×D₃	—	9	2	no	—
939	C₂×C₉	—	2	1	no	—
940	C₂×C₉	—	2	1	no	—
941	C₂×C₉	—	2	1	no	—
942	C₂×C₉	—	2	1	no	—
943	C₂×C₉	—	6	1	no	—
944	C₂×C₉	—	6	1	no	—
945	C₂×C₉	—	6	1	no	—
946	C₂×C₉	—	6	1	no	—
947	C₂×C₉	—	6	1	no	—
948	C₂×C₉	—	6	1	no	—
949	C₂×C₉	—	6	1	no	—
950	C₂×C₉	—	6	1	no	—
951	C₂×C₉	—	6	1	no	—
952	C₂×C₉	—	6	1	no	—
953	C₂×C₉	—	6	1	no	—
954	C₂×C₉	—	6	1	no	—
955	C₂×C₉	C₂×C₃×H(3,𝔽₃)	1	1	yes	characteristic, complemented
956	D₉	C₂×C₃×H(3,𝔽₃)	1	2	yes	complemented
957	C₂²×C₃	—	9	1	no	—
958	C₂²×C₃	—	9	1	no	—
959	C₂²×C₃	—	9	1	no	—
960	C₂²×C₃	—	9	1	no	—
961	C₂²×C₃	—	27	1	no	—
962	C₂²×C₃	—	27	1	no	—
963	C₂²×C₃	—	27	1	no	—
964	C₂²×C₃	—	27	1	no	—
965	C₂²×C₃	—	27	1	no	—
966	C₂²×C₃	—	27	1	no	—
967	C₂²×C₃	—	27	1	no	—
968	C₂²×C₃	—	27	1	no	—
969	C₂²×C₃	—	27	1	no	—
970	C₂²×C₃	—	27	1	no	—
971	C₂²×C₃	—	27	1	no	—
972	C₂²×C₃	—	27	1	no	—
973	C₂×D₃	—	3	1	no	—
974	C₃²	—	2	1	no	—
975	C₃²	—	2	1	no	—
976	C₃²	—	2	1	no	—
977	C₃²	—	2	1	no	—
978	C₃²	—	3	1	no	—
979	C₃²	—	3	1	no	—
980	C₃²	—	3	1	no	—
981	C₃²	—	3	1	no	—
982	C₃²	—	3	1	no	—
983	C₃²	—	3	1	no	—
984	C₃²	—	3	1	no	—
985	C₃²	—	3	1	no	—
986	C₃²	—	3	1	no	—
987	C₃²	—	3	1	no	—
988	C₃²	—	3	1	no	—
989	C₃²	—	3	1	no	—
990	C₃²	—	3	1	no	—
991	C₃²	—	3	1	no	—
992	C₃²	—	3	1	no	—
993	C₃²	—	6	1	no	—
994	C₃²	—	6	1	no	—
995	C₃²	—	6	1	no	—
996	C₃²	—	6	1	no	—
997	C₃²	—	6	1	no	—
998	C₃²	—	6	1	no	—
999	C₃²	—	6	1	no	—
1000	C₃²	—	6	1	no	—
1001	C₃²	—	6	1	no	—
1002	C₃²	—	6	1	no	—
1003	C₃²	—	6	1	no	—
1004	C₃²	—	6	1	no	—
1005	C₃²	—	6	1	no	—
1006	C₃²	—	6	1	no	—
1007	C₃²	—	6	1	no	—
1008	C₃²	—	6	1	no	—
1009	C₃²	—	6	1	no	—
1010	C₃²	—	6	1	no	—
1011	C₃²	—	6	1	no	—
1012	C₃²	—	9	1	no	—
1013	C₃²	—	9	1	no	—
1014	C₃²	—	9	1	no	—
1015	C₃²	—	9	1	no	—
1016	C₃²	—	9	1	no	—
1017	C₃²	—	9	1	no	—
1018	C₃²	—	18	1	no	—
1019	C₃²	—	18	1	no	—
1020	C₃²	—	18	1	no	—
1021	C₃²	—	18	1	no	—
1022	C₃²	—	18	1	no	—
1023	C₃²	—	18	1	no	—
1024	C₃²	—	18	1	no	—
1025	C₃²	—	18	1	no	—
1026	C₃²	—	18	1	no	—
1027	C₃²	—	18	1	no	—
1028	C₃²	—	18	1	no	—
1029	C₃²	—	18	1	no	—
1030	C₃²	—	18	1	no	—
1031	C₃²	—	18	1	no	—
1032	C₃²	—	18	1	no	—
1033	C₃²	—	18	1	no	—
1034	C₃²	—	18	1	no	—
1035	C₃²	—	18	1	no	—
1036	C₃²	C₂×D₃×H(3,𝔽₃)	1	1	yes	characteristic
1037	C₃²	C₂×D₃×H(3,𝔽₃)	1	1	yes	characteristic
1038	C₃²	C₂×D₃×H(3,𝔽₃)	1	1	yes	characteristic
1039	C₃²	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
1040	C₃²	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
1041	C₃²	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
1042	C₃²	C₂×C₃×AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
1043	C₃²	C₂×C₃³×D₃	1	1	yes	characteristic
1044	C₉	—	2	1	no	—
1045	C₉	—	2	1	no	—
1046	C₉	—	2	1	no	—
1047	C₉	—	2	1	no	—
1048	C₉	—	6	1	no	—
1049	C₉	—	6	1	no	—
1050	C₉	—	6	1	no	—
1051	C₉	—	6	1	no	—
1052	C₉	—	6	1	no	—
1053	C₉	—	6	1	no	—
1054	C₉	—	6	1	no	—
1055	C₉	—	6	1	no	—
1056	C₉	—	6	1	no	—
1057	C₉	—	6	1	no	—
1058	C₉	—	6	1	no	—
1059	C₉	—	6	1	no	—
1060	C₉	C₂²×C₃×H(3,𝔽₃)	1	1	yes	characteristic, complemented
1061	C₂×C₃	—	2	1	no	—
1062	C₂×C₃	—	3	1	no	—
1063	C₂×C₃	—	3	1	no	—
1064	C₂×C₃	—	3	1	no	—
1065	C₂×C₃	—	3	1	no	—
1066	C₂×C₃	—	6	1	no	—
1067	C₂×C₃	—	6	1	no	—
1068	C₂×C₃	—	6	1	no	—
1069	C₂×C₃	—	6	1	no	—
1070	C₂×C₃	—	6	1	no	—
1071	C₂×C₃	—	6	1	no	—
1072	C₂×C₃	—	6	1	no	—
1073	C₂×C₃	—	9	2	no	—
1074	C₂×C₃	—	9	2	no	—
1075	C₂×C₃	—	9	2	no	—
1076	C₂×C₃	—	9	2	no	—
1077	C₂×C₃	—	9	1	no	—
1078	C₂×C₃	—	9	1	no	—
1079	C₂×C₃	—	9	1	no	—
1080	C₂×C₃	—	18	1	no	—
1081	C₂×C₃	—	18	1	no	—
1082	C₂×C₃	—	18	1	no	—
1083	C₂×C₃	—	18	1	no	—
1084	C₂×C₃	—	18	1	no	—
1085	C₂×C₃	—	27	2	no	—
1086	C₂×C₃	—	27	2	no	—
1087	C₂×C₃	—	27	2	no	—
1088	C₂×C₃	—	27	2	no	—
1089	C₂×C₃	—	27	2	no	—
1090	C₂×C₃	—	27	2	no	—
1091	C₂×C₃	—	27	2	no	—
1092	C₂×C₃	—	27	2	no	—
1093	C₂×C₃	—	27	2	no	—
1094	C₂×C₃	—	27	2	no	—
1095	C₂×C₃	—	27	2	no	—
1096	C₂×C₃	—	27	2	no	—
1097	C₂×C₃	C₃×D₃×H(3,𝔽₃)	1	1	yes	characteristic
1098	C₂×C₃	C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
1099	D₃	—	3	2	no	—
1100	C₂²	—	9	1	no	Sylow
1101	C₃	—	2	1	no	—
1102	C₃	—	3	1	no	—
1103	C₃	—	3	1	no	—
1104	C₃	—	3	1	no	—
1105	C₃	—	3	1	no	—
1106	C₃	—	6	1	no	—
1107	C₃	—	6	1	no	—
1108	C₃	—	6	1	no	—
1109	C₃	—	6	1	no	—
1110	C₃	—	6	1	no	—
1111	C₃	—	6	1	no	—
1112	C₃	—	6	1	no	—
1113	C₃	—	9	1	no	—
1114	C₃	—	9	1	no	—
1115	C₃	—	9	1	no	—
1116	C₃	—	18	1	no	—
1117	C₃	—	18	1	no	—
1118	C₃	—	18	1	no	—
1119	C₃	—	18	1	no	—
1120	C₃	—	18	1	no	—
1121	C₃	C₂×C₃×D₃×H(3,𝔽₃)	1	1	yes	characteristic
1122	C₃	C₂×C₃²×AGL(1,ℤ/9)	1	1	yes	characteristic
1123	C₂	—	9	2	no	—
1124	C₂	H(3,𝔽₃)×AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center	C₂×C₃	C₃²×AGL(1,ℤ/9)
commutator, cosocle	C₃×C₉	C₂²×C₃³
Frattini	C₃²	C₂×C₃³×D₃
Fitting	C₂×H(3,𝔽₃)×3₋¹⁺²	C₂
socle	C₂×C₃²	C₃³×D₃
hypercenter	C₂×H(3,𝔽₃)	AGL(1,ℤ/9)
hypocenter	C₉	C₂²×C₃×H(3,𝔽₃)
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. H(3,𝔽₃)×AGL(1,ℤ/9)	C₂	direct (N × H)
2. C₂×H(3,𝔽₃)×3₋¹⁺²	C₂	semidirect
3. C₂×C₃²×AGL(1,ℤ/9)	C₃	semidirect
4. C₂×C₃²×AGL(1,ℤ/9)	C₃	semidirect
5. C₂×C₃²×AGL(1,ℤ/9)	C₃	semidirect
6. C₂×C₃²×AGL(1,ℤ/9)	C₃	semidirect
8. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
9. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
10. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
11. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
12. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
13. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
14. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
15. C₂×D₉⋊H(3,𝔽₃)	C₃	semidirect
16. C₂×D₉×H(3,𝔽₃)	C₃	semidirect
17. H(3,𝔽₃)×3₋¹⁺²	C₂²	semidirect
18. C₂×C₃²×3₋¹⁺²	C₂×C₃	semidirect
19. C₂×C₃²×3₋¹⁺²	C₂×C₃	semidirect
20. C₂×C₃²×3₋¹⁺²	C₂×C₃	semidirect
21. C₂×C₃²×3₋¹⁺²	C₂×C₃	semidirect
23. C₃²×AGL(1,ℤ/9)	C₂×C₃	semidirect
24. C₃²×AGL(1,ℤ/9)	C₂×C₃	semidirect
25. C₃²×AGL(1,ℤ/9)	C₂×C₃	semidirect
26. C₃²×AGL(1,ℤ/9)	C₂×C₃	semidirect
36. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
37. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
38. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
39. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
40. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
41. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
42. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
43. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
49. C₂×C₉×H(3,𝔽₃)	C₂×C₃	semidirect
50. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
51. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
52. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
53. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
54. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
55. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
56. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
57. D₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
58. D₉×H(3,𝔽₃)	C₂×C₃	semidirect
77. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
78. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
79. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
80. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
81. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
82. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
83. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
84. C₂×C₃×AGL(1,ℤ/9)	C₃²	semidirect
94. C₂×C₃²×D₉	C₃²	semidirect
95. C₂×C₃²×D₉	C₃²	semidirect
96. C₂×C₃²×D₉	C₃²	semidirect
97. C₂×C₃²×D₉	C₃²	semidirect
98. C₃²×3₋¹⁺²	C₂²×C₃	semidirect
99. C₃²×3₋¹⁺²	C₂²×C₃	semidirect
100. C₃²×3₋¹⁺²	C₂²×C₃	semidirect
101. C₃²×3₋¹⁺²	C₂²×C₃	semidirect
111. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
112. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
113. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
114. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
115. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
116. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
117. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
118. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
124. C₉×H(3,𝔽₃)	C₂²×C₃	semidirect
170. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
171. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
172. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
173. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
174. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
175. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
176. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
177. C₂×C₃×3₋¹⁺²	C₂×C₃²	semidirect
197. C₂×C₃²×C₉	C₂×C₃²	semidirect
198. C₂×C₃²×C₉	C₂×C₃²	semidirect
199. C₂×C₃²×C₉	C₂×C₃²	semidirect
200. C₂×C₃²×C₉	C₂×C₃²	semidirect
214. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
215. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
216. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
217. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
218. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
219. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
220. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
221. C₃×AGL(1,ℤ/9)	C₂×C₃²	semidirect
231. C₃²×D₉	C₂×C₃²	semidirect
232. C₃²×D₉	C₂×C₃²	semidirect
233. C₃²×D₉	C₂×C₃²	semidirect
234. C₃²×D₉	C₂×C₃²	semidirect
317. C₂×AGL(1,ℤ/9)	H(3,𝔽₃)	direct (N × H)
318. C₂×AGL(1,ℤ/9)	H(3,𝔽₃)	direct (N × H)
319. C₂×AGL(1,ℤ/9)	H(3,𝔽₃)	direct (N × H)
366. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
367. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
368. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
369. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
370. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
371. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
372. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
373. C₃×3₋¹⁺²	C₂²×C₃²	semidirect
392. C₃²×C₉	C₂²×C₃²	semidirect
393. C₃²×C₉	C₂²×C₃²	semidirect
394. C₃²×C₉	C₂²×C₃²	semidirect
395. C₃²×C₉	C₂²×C₃²	semidirect
553. C₂×3₋¹⁺²	C₂×H(3,𝔽₃)	semidirect
554. C₂×3₋¹⁺²	C₂×H(3,𝔽₃)	semidirect
555. C₂×3₋¹⁺²	C₂×H(3,𝔽₃)	semidirect
585. C₂×H(3,𝔽₃)	AGL(1,ℤ/9)	direct (N × H)
628. AGL(1,ℤ/9)	C₂×H(3,𝔽₃)	direct (N × H)
629. AGL(1,ℤ/9)	C₂×H(3,𝔽₃)	direct (N × H)
630. AGL(1,ℤ/9)	C₂×H(3,𝔽₃)	direct (N × H)
677. C₂×D₉	C₃×H(3,𝔽₃)	semidirect
770. 3₋¹⁺²	C₂²×H(3,𝔽₃)	semidirect
771. 3₋¹⁺²	C₂²×H(3,𝔽₃)	semidirect
772. 3₋¹⁺²	C₂²×H(3,𝔽₃)	semidirect
793. H(3,𝔽₃)	C₂×AGL(1,ℤ/9)	direct (N × H)
918. C₂×C₃²	C₃×AGL(1,ℤ/9)	semidirect
919. C₂×C₃²	C₃×AGL(1,ℤ/9)	semidirect
920. C₂×C₃²	C₃×AGL(1,ℤ/9)	semidirect
921. C₂×C₃²	C₃×AGL(1,ℤ/9)	semidirect
955. C₂×C₉	C₂×C₃×H(3,𝔽₃)	semidirect
956. D₉	C₂×C₃×H(3,𝔽₃)	semidirect
1039. C₃²	C₂×C₃×AGL(1,ℤ/9)	semidirect
1040. C₃²	C₂×C₃×AGL(1,ℤ/9)	semidirect
1041. C₃²	C₂×C₃×AGL(1,ℤ/9)	semidirect
1042. C₃²	C₂×C₃×AGL(1,ℤ/9)	semidirect
1060. C₉	C₂²×C₃×H(3,𝔽₃)	semidirect
1124. C₂	H(3,𝔽₃)×AGL(1,ℤ/9)	direct (N × H)

Maximal subgroups

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

subgroup	index
H(3,𝔽₃)×AGL(1,ℤ/9)	2
C₂×H(3,𝔽₃)×3₋¹⁺²	2
C₂×C₃²×AGL(1,ℤ/9)	3
C₂×C₃×D₃×H(3,𝔽₃)	3
C₂×D₉⋊H(3,𝔽₃)	3
C₂×D₉×H(3,𝔽₃)	3

Subgroups — C2×H(3,𝔽3)×AGL(1,ℤ/9) #72244057

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×H(3,𝔽₃)×AGL(1,ℤ/9) #72244057