Subgroups — C₂×3₋¹⁺²×(C₃⋊D₃)⋊C₃ #72254053

Order 2916.

1110 conjugacy classes of subgroups.

The subgroup lattice has 930 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×(C₃⋊D₃)⋊C₃	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×C₃⋊D₃×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₃×3₋¹⁺²	—	3	1	no	maximal
5	C₂×C₃²×(C₃⋊D₃)⋊C₃	C₃	1	1	yes	maximal, characteristic
6	C₂×#92262	C₃	1	1	yes	maximal, characteristic, complemented
7	C₂×#92262	C₃	1	1	yes	maximal, characteristic, complemented
8	C₂×#92262	C₃	1	1	yes	maximal, characteristic, complemented
9	C₂×#92262	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂×#92262	C₃	1	1	yes	maximal, characteristic, complemented
11	C₂×#92262	C₃	1	1	yes	maximal, characteristic, complemented
12	C₂×#92259	C₃	1	1	yes	maximal, characteristic, complemented
13	C₂×#92259	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂×C₉×(C₃⋊D₃)⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
15	C₂×C₉×(C₃⋊D₃)⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
16	C₂×C₉×(C₃⋊D₃)⋊C₃	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	—	2	1	no	—
19	C₂×C₃²×3₋¹⁺²	D₃	1	1	yes	characteristic, complemented
20	C₂×C₃²×3₋¹⁺²	C₂×C₃	1	1	yes	characteristic, complemented
21	C₂×C₃²×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic
22	C₃⋊D₃×3₋¹⁺²	C₂×C₃	1	2	yes	complemented
23	C₃×D₃×3₋¹⁺²	—	3	2	no	—
24	C₃²×(C₃⋊D₃)⋊C₃	C₂×C₃	1	2	yes	—
25	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
26	C₂×C₉⋊H(3,𝔽₃)	—	2	1	no	—
27	C₂×C₉⋊H(3,𝔽₃)	—	2	1	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)	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
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×#6891	—	2	1	no	—
41	C₂×#6891	—	2	1	no	—
42	C₂×#6891	—	2	1	no	—
43	C₂×#6891	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂×#6891	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×C₉×H(3,𝔽₃)	C₂×C₃	1	1	yes	characteristic, complemented
48	#92262	C₂×C₃	1	2	yes	complemented
49	#92262	C₂×C₃	1	2	yes	complemented
50	#92262	C₂×C₃	1	2	yes	complemented
51	#92262	C₂×C₃	1	2	yes	complemented
52	#92262	C₂×C₃	1	2	yes	complemented
53	#92262	C₂×C₃	1	2	yes	complemented
54	#92259	C₂×C₃	1	2	yes	complemented
55	#92259	C₂×C₃	1	2	yes	complemented
56	C₉×(C₃⋊D₃)⋊C₃	C₂×C₃	1	2	yes	complemented
57	C₉×(C₃⋊D₃)⋊C₃	C₂×C₃	1	2	yes	complemented
58	C₉×(C₃⋊D₃)⋊C₃	C₂×C₃	1	2	yes	complemented
59	C₂×C₃²×C₃⋊D₃	C₃²	1	1	yes	characteristic
60	C₂×C₃³×D₃	—	3	1	no	—
61	C₂²×C₃×3₋¹⁺²	—	9	1	no	—
62	C₂×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic, complemented
63	C₂×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic, complemented
64	C₂×C₉×C₃⋊D₃	C₃²	1	1	yes	characteristic, complemented
65	C₂×D₃×3₋¹⁺²	—	3	1	no	—
66	C₂×D₃×3₋¹⁺²	—	3	1	no	—
67	C₂×D₃×3₋¹⁺²	—	3	1	no	—
68	C₂×D₃×3₋¹⁺²	—	3	1	no	—
69	C₂×D₃×3₋¹⁺²	—	3	1	no	—
70	C₂×D₃×3₋¹⁺²	—	3	1	no	—
71	C₂×D₃×3₋¹⁺²	—	3	1	no	—
72	C₂×D₃×3₋¹⁺²	—	3	1	no	—
73	C₂×D₃×3₋¹⁺²	—	3	1	no	—
74	C₂×D₃×3₋¹⁺²	—	9	1	no	—
75	C₂×C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
76	C₂×C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
77	C₂×C₃×(C₃⋊D₃)⋊C₃	—	3	1	no	—
78	C₂×C₃×(C₃⋊D₃)⋊C₃	C₃²	1	1	yes	characteristic
79	C₂×C₃×(C₃⋊D₃)⋊C₃	C₃²	1	1	yes	characteristic
80	C₂×C₃×(C₃⋊D₃)⋊C₃	C₃²	1	1	yes	characteristic
81	C₂×C₃×D₃×C₉	—	3	1	no	—
82	C₂×C₃×D₃×C₉	—	3	1	no	—
83	C₂×C₃×D₃×C₉	—	3	1	no	—
84	C₂×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic, complemented
85	C₂×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic, complemented
86	C₂×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic, complemented
87	C₂×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic, complemented
88	C₂×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic, complemented
89	C₂×(C₃⋊D₃)⋊C₉	C₃²	1	1	yes	characteristic, complemented
90	C₃²×3₋¹⁺²	—	2	1	no	—
91	C₃²×3₋¹⁺²	C₂×D₃	1	1	yes	characteristic, complemented
92	C₃²×3₋¹⁺²	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₃²×H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic
94	C₉⋊H(3,𝔽₃)	—	2	1	no	—
95	C₉⋊H(3,𝔽₃)	—	2	1	no	—
96	C₉⋊H(3,𝔽₃)	—	2	1	no	—
97	C₉⋊H(3,𝔽₃)	—	2	1	no	—
98	C₉⋊H(3,𝔽₃)	—	2	1	no	—
99	C₉⋊H(3,𝔽₃)	—	2	1	no	—
100	C₉⋊H(3,𝔽₃)	—	2	1	no	—
101	C₉⋊H(3,𝔽₃)	—	2	1	no	—
102	C₉⋊H(3,𝔽₃)	—	2	1	no	—
103	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
106	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₉⋊H(3,𝔽₃)	C₂²×C₃	1	1	yes	characteristic, complemented
109	#6891	—	2	1	no	—
110	#6891	—	2	1	no	—
111	#6891	—	2	1	no	—
112	#6891	C₂²×C₃	1	1	yes	characteristic, complemented
113	#6891	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	C₂×C₃⁴	—	2	1	no	—
118	C₂×C₃⁴	C₃×D₃	1	1	yes	characteristic
119	C₂×C₃⁴	C₂×C₃²	1	1	yes	characteristic
120	C₃²×C₃⋊D₃	C₂×C₃²	1	2	yes	—
121	C₃³×D₃	—	3	2	no	—
122	C₂×C₃×3₋¹⁺²	—	2	1	no	—
123	C₂×C₃×3₋¹⁺²	—	2	1	no	—
124	C₂×C₃×3₋¹⁺²	—	2	1	no	—
125	C₂×C₃×3₋¹⁺²	—	2	1	no	—
126	C₂×C₃×3₋¹⁺²	—	2	1	no	—
127	C₂×C₃×3₋¹⁺²	—	2	1	no	—
128	C₂×C₃×3₋¹⁺²	—	2	1	no	—
129	C₂×C₃×3₋¹⁺²	—	2	1	no	—
130	C₂×C₃×3₋¹⁺²	—	2	1	no	—
131	C₂×C₃×3₋¹⁺²	—	2	1	no	—
132	C₂×C₃×3₋¹⁺²	—	2	1	no	—
133	C₂×C₃×3₋¹⁺²	—	2	1	no	—
134	C₂×C₃×3₋¹⁺²	—	3	1	no	—
135	C₂×C₃×3₋¹⁺²	—	6	1	no	—
136	C₂×C₃×3₋¹⁺²	—	6	1	no	—
137	C₂×C₃×3₋¹⁺²	—	6	1	no	—
138	C₂×C₃×3₋¹⁺²	—	6	1	no	—
139	C₂×C₃×3₋¹⁺²	—	6	1	no	—
140	C₂×C₃×3₋¹⁺²	—	6	1	no	—
141	C₂×C₃×3₋¹⁺²	—	6	2	no	—
142	C₂×C₃×3₋¹⁺²	—	6	2	no	—
143	C₂×C₃×3₋¹⁺²	—	6	2	no	—
144	C₂×C₃×3₋¹⁺²	—	6	2	no	—
145	C₂×C₃×3₋¹⁺²	—	6	1	no	—
146	C₂×C₃×3₋¹⁺²	—	6	1	no	—
147	C₂×C₃×3₋¹⁺²	—	6	1	no	—
148	C₂×C₃×3₋¹⁺²	—	6	1	no	—
149	C₂×C₃×3₋¹⁺²	—	9	2	no	—
150	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
151	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
152	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic
153	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
154	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
155	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
156	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
157	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
158	C₂×C₃×3₋¹⁺²	C₃×D₃	1	1	yes	characteristic, complemented
159	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
160	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
161	C₂×C₃×H(3,𝔽₃)	—	2	1	no	—
162	C₂×C₃×H(3,𝔽₃)	—	3	1	no	—
163	C₂×C₃×H(3,𝔽₃)	—	3	1	no	—
164	C₂×C₃×H(3,𝔽₃)	—	3	1	no	—
165	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
166	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
167	C₂×C₃×H(3,𝔽₃)	—	6	1	no	—
168	C₂×C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
169	C₂×C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
170	C₂×C₃×H(3,𝔽₃)	C₂×C₃²	1	1	yes	characteristic
171	C₂×C₃²×C₉	—	2	1	no	—
172	C₂×C₃²×C₉	—	2	1	no	—
173	C₂×C₃²×C₉	—	2	1	no	—
174	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic, complemented
175	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic, complemented
176	C₂×C₃²×C₉	C₃×D₃	1	1	yes	characteristic, complemented
177	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
178	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
179	C₂×C₃²×C₉	C₂×C₃²	1	1	yes	characteristic, complemented
180	C₉×C₃⋊D₃	C₂×C₃²	1	2	yes	complemented
181	C₉×C₃⋊D₃	C₂×C₃²	1	2	yes	complemented
182	C₉×C₃⋊D₃	C₂×C₃²	1	2	yes	complemented
183	D₃×3₋¹⁺²	—	3	2	no	—
184	D₃×3₋¹⁺²	—	3	2	no	—
185	D₃×3₋¹⁺²	—	3	2	no	—
186	D₃×3₋¹⁺²	—	3	2	no	—
187	D₃×3₋¹⁺²	—	3	2	no	—
188	D₃×3₋¹⁺²	—	3	2	no	—
189	D₃×3₋¹⁺²	—	3	2	no	—
190	D₃×3₋¹⁺²	—	3	2	no	—
191	D₃×3₋¹⁺²	—	3	2	no	—
192	D₃×3₋¹⁺²	—	9	2	no	—
193	C₃×(C₃⋊D₃)⋊C₃	—	3	2	no	—
194	C₃×(C₃⋊D₃)⋊C₃	—	3	2	no	—
195	C₃×(C₃⋊D₃)⋊C₃	—	3	2	no	—
196	C₃×(C₃⋊D₃)⋊C₃	C₂×C₃²	1	2	yes	—
197	C₃×(C₃⋊D₃)⋊C₃	C₂×C₃²	1	2	yes	—
198	C₃×(C₃⋊D₃)⋊C₃	C₂×C₃²	1	2	yes	—
199	C₃×D₃×C₉	—	3	2	no	—
200	C₃×D₃×C₉	—	3	2	no	—
201	C₃×D₃×C₉	—	3	2	no	—
202	C₂×C₃²⋊C₉	—	2	1	no	—
203	C₂×C₃²⋊C₉	—	2	1	no	—
204	C₂×C₃²⋊C₉	—	2	1	no	—
205	C₂×C₃²⋊C₉	—	2	1	no	—
206	C₂×C₃²⋊C₉	—	2	1	no	—
207	C₂×C₃²⋊C₉	—	2	1	no	—
208	C₂×C₃²⋊C₉	—	2	1	no	—
209	C₂×C₃²⋊C₉	—	2	1	no	—
210	C₂×C₃²⋊C₉	—	2	1	no	—
211	C₂×C₃²⋊C₉	—	2	1	no	—
212	C₂×C₃²⋊C₉	—	2	1	no	—
213	C₂×C₃²⋊C₉	—	2	1	no	—
214	C₂×C₃²⋊C₉	—	2	1	no	—
215	C₂×C₃²⋊C₉	—	2	1	no	—
216	C₂×C₃²⋊C₉	—	2	1	no	—
217	C₂×C₃²⋊C₉	—	2	1	no	—
218	C₂×C₃²⋊C₉	—	2	1	no	—
219	C₂×C₃²⋊C₉	—	2	1	no	—
220	C₂×C₃²⋊C₉	—	2	1	no	—
221	C₂×C₃²⋊C₉	—	2	1	no	—
222	C₂×C₃²⋊C₉	—	2	1	no	—
223	C₂×C₃²⋊C₉	—	2	1	no	—
224	C₂×C₃²⋊C₉	—	2	1	no	—
225	C₂×C₃²⋊C₉	—	2	1	no	—
226	C₂×C₃²⋊C₉	—	2	1	no	—
227	C₂×C₃²⋊C₉	—	2	1	no	—
228	C₂×C₃²⋊C₉	—	2	1	no	—
229	C₂×C₃²⋊C₉	—	2	1	no	—
230	C₂×C₃²⋊C₉	—	2	1	no	—
231	C₂×C₃²⋊C₉	—	2	1	no	—
232	C₂×C₃²⋊C₉	—	2	1	no	—
233	C₂×C₃²⋊C₉	—	2	1	no	—
234	C₂×C₃²⋊C₉	—	2	1	no	—
235	C₂×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic, complemented
236	C₂×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic, complemented
237	C₂×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic, complemented
238	C₂×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic, complemented
239	C₂×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic, complemented
240	C₂×C₃²⋊C₉	C₂×C₃²	1	1	yes	characteristic, complemented
241	(C₃⋊D₃)⋊C₉	C₂×C₃²	1	2	yes	complemented
242	(C₃⋊D₃)⋊C₉	C₂×C₃²	1	2	yes	complemented
243	(C₃⋊D₃)⋊C₉	C₂×C₃²	1	2	yes	complemented
244	(C₃⋊D₃)⋊C₉	C₂×C₃²	1	2	yes	complemented
245	(C₃⋊D₃)⋊C₉	C₂×C₃²	1	2	yes	complemented
246	(C₃⋊D₃)⋊C₉	C₂×C₃²	1	2	yes	complemented
247	C₂²×C₃³	—	9	1	no	—
248	C₂×C₃×C₃⋊D₃	—	3	1	no	—
249	C₂×C₃×C₃⋊D₃	C₃³	1	1	yes	characteristic
250	C₂×C₃²×D₃	—	3	1	no	—
251	C₂×C₃²×D₃	—	3	1	no	—
252	C₂×C₃²×D₃	—	3	1	no	—
253	C₂×C₃²×D₃	—	3	1	no	—
254	C₂×C₃²×D₃	—	9	1	no	—
255	C₂×C₃²×D₃	—	9	1	no	—
256	C₂×C₃²×D₃	—	9	1	no	—
257	C₂×C₃²×D₃	—	9	1	no	—
258	C₂²×3₋¹⁺²	—	9	1	no	—
259	C₂²×3₋¹⁺²	—	9	1	no	—
260	C₂²×3₋¹⁺²	—	9	1	no	—
261	C₂²×3₋¹⁺²	—	9	1	no	—
262	C₂²×3₋¹⁺²	—	9	1	no	—
263	C₂²×3₋¹⁺²	—	9	1	no	—
264	C₂²×3₋¹⁺²	—	9	1	no	—
265	C₂²×3₋¹⁺²	—	9	1	no	—
266	C₂²×3₋¹⁺²	—	9	1	no	—
267	C₂²×C₃×C₉	—	9	1	no	—
268	C₂²×C₃×C₉	—	9	1	no	—
269	C₂²×C₃×C₉	—	9	1	no	—
270	C₂×(C₃⋊D₃)⋊C₃	—	3	1	no	—
271	C₂×(C₃⋊D₃)⋊C₃	—	3	1	no	—
272	C₂×(C₃⋊D₃)⋊C₃	3₋¹⁺²	1	1	yes	characteristic, direct product factor
273	C₂×(C₃⋊D₃)⋊C₃	3₋¹⁺²	1	1	yes	characteristic, direct product factor
274	C₂×(C₃⋊D₃)⋊C₃	3₋¹⁺²	1	1	yes	characteristic, direct product factor
275	C₂×D₃×C₉	—	3	1	no	—
276	C₂×D₃×C₉	—	3	1	no	—
277	C₂×D₃×C₉	—	3	1	no	—
278	C₂×D₃×C₉	—	3	1	no	—
279	C₂×D₃×C₉	—	3	1	no	—
280	C₂×D₃×C₉	—	3	1	no	—
281	C₂×D₃×C₉	—	3	1	no	—
282	C₂×D₃×C₉	—	3	1	no	—
283	C₂×D₃×C₉	—	3	1	no	—
284	C₂×D₃×C₉	—	9	1	no	—
285	C₂×D₃×C₉	—	9	1	no	—
286	C₂×D₃×C₉	—	9	1	no	—
287	C₃⁴	—	2	1	no	—
288	C₃⁴	C₂×C₃×D₃	1	1	yes	characteristic
289	C₃⁴	C₂²×C₃²	1	1	yes	characteristic
290	C₃×3₋¹⁺²	—	2	1	no	—
291	C₃×3₋¹⁺²	—	2	1	no	—
292	C₃×3₋¹⁺²	—	2	1	no	—
293	C₃×3₋¹⁺²	—	2	1	no	—
294	C₃×3₋¹⁺²	—	2	1	no	—
295	C₃×3₋¹⁺²	—	2	1	no	—
296	C₃×3₋¹⁺²	—	2	1	no	—
297	C₃×3₋¹⁺²	—	2	1	no	—
298	C₃×3₋¹⁺²	—	2	1	no	—
299	C₃×3₋¹⁺²	—	2	1	no	—
300	C₃×3₋¹⁺²	—	2	1	no	—
301	C₃×3₋¹⁺²	—	2	1	no	—
302	C₃×3₋¹⁺²	—	3	1	no	—
303	C₃×3₋¹⁺²	—	6	1	no	—
304	C₃×3₋¹⁺²	—	6	1	no	—
305	C₃×3₋¹⁺²	—	6	1	no	—
306	C₃×3₋¹⁺²	—	6	1	no	—
307	C₃×3₋¹⁺²	—	6	1	no	—
308	C₃×3₋¹⁺²	—	6	1	no	—
309	C₃×3₋¹⁺²	—	6	2	no	—
310	C₃×3₋¹⁺²	—	6	2	no	—
311	C₃×3₋¹⁺²	—	6	2	no	—
312	C₃×3₋¹⁺²	—	6	2	no	—
313	C₃×3₋¹⁺²	—	6	1	no	—
314	C₃×3₋¹⁺²	—	6	1	no	—
315	C₃×3₋¹⁺²	—	6	1	no	—
316	C₃×3₋¹⁺²	—	6	1	no	—
317	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
318	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
319	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic
320	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
321	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
322	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
323	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
324	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
325	C₃×3₋¹⁺²	C₂×C₃×D₃	1	1	yes	characteristic, complemented
326	C₃×H(3,𝔽₃)	—	2	1	no	—
327	C₃×H(3,𝔽₃)	—	2	1	no	—
328	C₃×H(3,𝔽₃)	—	2	1	no	—
329	C₃×H(3,𝔽₃)	—	3	1	no	—
330	C₃×H(3,𝔽₃)	—	3	1	no	—
331	C₃×H(3,𝔽₃)	—	3	1	no	—
332	C₃×H(3,𝔽₃)	—	6	1	no	—
333	C₃×H(3,𝔽₃)	—	6	1	no	—
334	C₃×H(3,𝔽₃)	—	6	1	no	—
335	C₃×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
336	C₃×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
337	C₃×H(3,𝔽₃)	C₂²×C₃²	1	1	yes	characteristic
338	C₃²×C₉	—	2	1	no	—
339	C₃²×C₉	—	2	1	no	—
340	C₃²×C₉	—	2	1	no	—
341	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented
342	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented
343	C₃²×C₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented
344	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
345	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
346	C₃²×C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
347	C₃²⋊C₉	—	2	1	no	—
348	C₃²⋊C₉	—	2	1	no	—
349	C₃²⋊C₉	—	2	1	no	—
350	C₃²⋊C₉	—	2	1	no	—
351	C₃²⋊C₉	—	2	1	no	—
352	C₃²⋊C₉	—	2	1	no	—
353	C₃²⋊C₉	—	2	1	no	—
354	C₃²⋊C₉	—	2	1	no	—
355	C₃²⋊C₉	—	2	1	no	—
356	C₃²⋊C₉	—	2	1	no	—
357	C₃²⋊C₉	—	2	1	no	—
358	C₃²⋊C₉	—	2	1	no	—
359	C₃²⋊C₉	—	2	1	no	—
360	C₃²⋊C₉	—	2	1	no	—
361	C₃²⋊C₉	—	2	1	no	—
362	C₃²⋊C₉	—	2	1	no	—
363	C₃²⋊C₉	—	2	1	no	—
364	C₃²⋊C₉	—	2	1	no	—
365	C₃²⋊C₉	—	2	1	no	—
366	C₃²⋊C₉	—	2	1	no	—
367	C₃²⋊C₉	—	2	1	no	—
368	C₃²⋊C₉	—	2	1	no	—
369	C₃²⋊C₉	—	2	1	no	—
370	C₃²⋊C₉	—	2	1	no	—
371	C₃²⋊C₉	—	2	1	no	—
372	C₃²⋊C₉	—	2	1	no	—
373	C₃²⋊C₉	—	2	1	no	—
374	C₃²⋊C₉	—	2	1	no	—
375	C₃²⋊C₉	—	2	1	no	—
376	C₃²⋊C₉	—	2	1	no	—
377	C₃²⋊C₉	—	2	1	no	—
378	C₃²⋊C₉	—	2	1	no	—
379	C₃²⋊C₉	—	2	1	no	—
380	C₃²⋊C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
381	C₃²⋊C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
382	C₃²⋊C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
383	C₃²⋊C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
384	C₃²⋊C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
385	C₃²⋊C₉	C₂²×C₃²	1	1	yes	characteristic, complemented
386	C₂×C₃³	—	2	1	no	—
387	C₂×C₃³	—	2	1	no	—
388	C₂×C₃³	—	2	1	no	—
389	C₂×C₃³	—	2	1	no	—
390	C₂×C₃³	—	3	1	no	—
391	C₂×C₃³	—	3	1	no	—
392	C₂×C₃³	—	3	1	no	—
393	C₂×C₃³	—	3	1	no	—
394	C₂×C₃³	—	3	1	no	—
395	C₂×C₃³	—	6	1	no	—
396	C₂×C₃³	—	6	1	no	—
397	C₂×C₃³	—	6	1	no	—
398	C₂×C₃³	—	6	1	no	—
399	C₂×C₃³	—	6	1	no	—
400	C₂×C₃³	—	6	1	no	—
401	C₂×C₃³	—	6	2	no	—
402	C₂×C₃³	—	6	1	no	—
403	C₂×C₃³	—	6	1	no	—
404	C₂×C₃³	—	9	2	no	—
405	C₂×C₃³	—	18	1	no	—
406	C₂×C₃³	—	18	1	no	—
407	C₂×C₃³	—	18	2	no	—
408	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
409	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
410	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
411	C₂×C₃³	C₃²×D₃	1	1	yes	characteristic
412	C₂×C₃³	C₂×C₃³	1	1	yes	characteristic
413	C₃×C₃⋊D₃	—	3	2	no	—
414	C₃×C₃⋊D₃	C₂×C₃³	1	2	yes	—
415	C₃²×D₃	—	3	2	no	—
416	C₃²×D₃	—	3	2	no	—
417	C₃²×D₃	—	3	2	no	—
418	C₃²×D₃	—	3	2	no	—
419	C₃²×D₃	—	9	2	no	—
420	C₃²×D₃	—	9	2	no	—
421	C₃²×D₃	—	9	2	no	—
422	C₃²×D₃	—	9	2	no	—
423	C₂×3₋¹⁺²	—	2	1	no	—
424	C₂×3₋¹⁺²	—	2	1	no	—
425	C₂×3₋¹⁺²	—	2	1	no	—
426	C₂×3₋¹⁺²	—	2	1	no	—
427	C₂×3₋¹⁺²	—	3	1	no	—
428	C₂×3₋¹⁺²	—	3	1	no	—
429	C₂×3₋¹⁺²	—	6	1	no	—
430	C₂×3₋¹⁺²	—	6	1	no	—
431	C₂×3₋¹⁺²	—	6	1	no	—
432	C₂×3₋¹⁺²	—	6	1	no	—
433	C₂×3₋¹⁺²	—	6	1	no	—
434	C₂×3₋¹⁺²	—	6	2	no	—
435	C₂×3₋¹⁺²	—	6	2	no	—
436	C₂×3₋¹⁺²	—	6	2	no	—
437	C₂×3₋¹⁺²	—	6	2	no	—
438	C₂×3₋¹⁺²	—	6	2	no	—
439	C₂×3₋¹⁺²	—	6	2	no	—
440	C₂×3₋¹⁺²	—	6	2	no	—
441	C₂×3₋¹⁺²	—	6	2	no	—
442	C₂×3₋¹⁺²	—	6	2	no	—
443	C₂×3₋¹⁺²	—	6	1	no	—
444	C₂×3₋¹⁺²	—	6	1	no	—
445	C₂×3₋¹⁺²	—	6	1	no	—
446	C₂×3₋¹⁺²	—	6	1	no	—
447	C₂×3₋¹⁺²	—	6	1	no	—
448	C₂×3₋¹⁺²	—	6	1	no	—
449	C₂×3₋¹⁺²	—	6	1	no	—
450	C₂×3₋¹⁺²	—	6	1	no	—
451	C₂×3₋¹⁺²	—	6	1	no	—
452	C₂×3₋¹⁺²	—	6	2	no	—
453	C₂×3₋¹⁺²	—	6	2	no	—
454	C₂×3₋¹⁺²	—	6	2	no	—
455	C₂×3₋¹⁺²	—	6	1	no	—
456	C₂×3₋¹⁺²	—	6	1	no	—
457	C₂×3₋¹⁺²	—	6	1	no	—
458	C₂×3₋¹⁺²	—	6	1	no	—
459	C₂×3₋¹⁺²	—	6	1	no	—
460	C₂×3₋¹⁺²	—	6	1	no	—
461	C₂×3₋¹⁺²	—	6	1	no	—
462	C₂×3₋¹⁺²	—	6	1	no	—
463	C₂×3₋¹⁺²	—	6	1	no	—
464	C₂×3₋¹⁺²	—	6	1	no	—
465	C₂×3₋¹⁺²	—	6	1	no	—
466	C₂×3₋¹⁺²	—	6	1	no	—
467	C₂×3₋¹⁺²	—	9	2	no	—
468	C₂×3₋¹⁺²	—	9	2	no	—
469	C₂×3₋¹⁺²	—	9	2	no	—
470	C₂×3₋¹⁺²	—	9	2	no	—
471	C₂×3₋¹⁺²	—	9	2	no	—
472	C₂×3₋¹⁺²	—	9	2	no	—
473	C₂×3₋¹⁺²	—	9	2	no	—
474	C₂×3₋¹⁺²	—	9	2	no	—
475	C₂×3₋¹⁺²	—	9	2	no	—
476	C₂×3₋¹⁺²	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, direct product factor
477	C₂×H(3,𝔽₃)	—	2	1	no	—
478	C₂×H(3,𝔽₃)	—	2	1	no	—
479	C₂×H(3,𝔽₃)	—	2	1	no	—
480	C₂×H(3,𝔽₃)	—	3	1	no	—
481	C₂×H(3,𝔽₃)	—	3	1	no	—
482	C₂×H(3,𝔽₃)	—	6	1	no	—
483	C₂×H(3,𝔽₃)	—	6	1	no	—
484	C₂×H(3,𝔽₃)	—	6	1	no	—
485	C₂×H(3,𝔽₃)	—	6	1	no	—
486	C₂×H(3,𝔽₃)	—	6	1	no	—
487	C₂×H(3,𝔽₃)	—	6	1	no	—
488	C₂×H(3,𝔽₃)	—	6	1	no	—
489	C₂×H(3,𝔽₃)	—	6	1	no	—
490	C₂×H(3,𝔽₃)	—	6	1	no	—
491	C₂×H(3,𝔽₃)	—	6	1	no	—
492	C₂×H(3,𝔽₃)	—	6	1	no	—
493	C₂×H(3,𝔽₃)	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
494	C₂×H(3,𝔽₃)	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
495	C₂×H(3,𝔽₃)	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
496	C₂×C₃×C₉	—	2	1	no	—
497	C₂×C₃×C₉	—	2	1	no	—
498	C₂×C₃×C₉	—	2	1	no	—
499	C₂×C₃×C₉	—	2	1	no	—
500	C₂×C₃×C₉	—	2	1	no	—
501	C₂×C₃×C₉	—	2	1	no	—
502	C₂×C₃×C₉	—	2	1	no	—
503	C₂×C₃×C₉	—	2	1	no	—
504	C₂×C₃×C₉	—	2	1	no	—
505	C₂×C₃×C₉	—	3	1	no	—
506	C₂×C₃×C₉	—	3	1	no	—
507	C₂×C₃×C₉	—	3	1	no	—
508	C₂×C₃×C₉	—	3	1	no	—
509	C₂×C₃×C₉	—	6	1	no	—
510	C₂×C₃×C₉	—	6	1	no	—
511	C₂×C₃×C₉	—	6	1	no	—
512	C₂×C₃×C₉	—	6	2	no	—
513	C₂×C₃×C₉	—	6	2	no	—
514	C₂×C₃×C₉	—	6	2	no	—
515	C₂×C₃×C₉	—	6	1	no	—
516	C₂×C₃×C₉	—	6	1	no	—
517	C₂×C₃×C₉	—	6	1	no	—
518	C₂×C₃×C₉	—	6	1	no	—
519	C₂×C₃×C₉	—	6	1	no	—
520	C₂×C₃×C₉	—	6	1	no	—
521	C₂×C₃×C₉	—	6	1	no	—
522	C₂×C₃×C₉	—	6	1	no	—
523	C₂×C₃×C₉	—	9	2	no	—
524	C₂×C₃×C₉	—	9	2	no	—
525	C₂×C₃×C₉	—	9	2	no	—
526	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
527	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
528	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
529	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
530	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
531	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
532	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
533	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
534	C₂×C₃×C₉	C₃²×D₃	1	1	yes	characteristic
535	(C₃⋊D₃)⋊C₃	—	3	2	no	—
536	(C₃⋊D₃)⋊C₃	—	3	2	no	—
537	(C₃⋊D₃)⋊C₃	C₂×3₋¹⁺²	1	2	yes	direct product factor
538	(C₃⋊D₃)⋊C₃	C₂×3₋¹⁺²	1	2	yes	direct product factor
539	(C₃⋊D₃)⋊C₃	C₂×3₋¹⁺²	1	2	yes	direct product factor
540	D₃×C₉	—	3	2	no	—
541	D₃×C₉	—	3	2	no	—
542	D₃×C₉	—	3	2	no	—
543	D₃×C₉	—	3	2	no	—
544	D₃×C₉	—	3	2	no	—
545	D₃×C₉	—	3	2	no	—
546	D₃×C₉	—	3	2	no	—
547	D₃×C₉	—	3	2	no	—
548	D₃×C₉	—	3	2	no	—
549	D₃×C₉	—	9	2	no	—
550	D₃×C₉	—	9	2	no	—
551	D₃×C₉	—	9	2	no	—
552	C₂²×C₃²	—	9	1	no	—
553	C₂²×C₃²	—	9	1	no	—
554	C₂²×C₃²	—	9	1	no	—
555	C₂²×C₃²	—	9	1	no	—
556	C₂²×C₃²	—	27	1	no	—
557	C₂²×C₃²	—	27	1	no	—
558	C₂²×C₃²	—	27	1	no	—
559	C₂×C₃⋊D₃	C₃×3₋¹⁺²	1	1	yes	characteristic, complemented
560	C₂×C₃×D₃	—	3	1	no	—
561	C₂×C₃×D₃	—	3	1	no	—
562	C₂×C₃×D₃	—	3	1	no	—
563	C₂×C₃×D₃	—	3	1	no	—
564	C₂×C₃×D₃	—	9	1	no	—
565	C₂×C₃×D₃	—	9	1	no	—
566	C₂×C₃×D₃	—	9	1	no	—
567	C₂×C₃×D₃	—	9	1	no	—
568	C₂×C₃×D₃	—	27	1	no	—
569	C₂²×C₉	—	9	1	no	—
570	C₂²×C₉	—	9	1	no	—
571	C₂²×C₉	—	9	1	no	—
572	C₂²×C₉	—	9	1	no	—
573	C₂²×C₉	—	9	1	no	—
574	C₂²×C₉	—	9	1	no	—
575	C₂²×C₉	—	9	1	no	—
576	C₂²×C₉	—	9	1	no	—
577	C₂²×C₉	—	9	1	no	—
578	C₃³	—	2	1	no	—
579	C₃³	—	2	1	no	—
580	C₃³	—	2	1	no	—
581	C₃³	—	2	1	no	—
582	C₃³	—	3	1	no	—
583	C₃³	—	3	1	no	—
584	C₃³	—	3	1	no	—
585	C₃³	—	3	1	no	—
586	C₃³	—	3	1	no	—
587	C₃³	—	6	1	no	—
588	C₃³	—	6	1	no	—
589	C₃³	—	6	1	no	—
590	C₃³	—	6	1	no	—
591	C₃³	—	6	1	no	—
592	C₃³	—	6	1	no	—
593	C₃³	—	6	2	no	—
594	C₃³	—	6	1	no	—
595	C₃³	—	6	1	no	—
596	C₃³	—	18	1	no	—
597	C₃³	—	18	1	no	—
598	C₃³	—	18	2	no	—
599	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
600	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
601	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
602	C₃³	C₂×C₃²×D₃	1	1	yes	characteristic
603	C₃³	C₂²×C₃³	1	1	yes	characteristic
604	3₋¹⁺²	—	2	1	no	—
605	3₋¹⁺²	—	2	1	no	—
606	3₋¹⁺²	—	2	1	no	—
607	3₋¹⁺²	—	2	1	no	—
608	3₋¹⁺²	—	3	1	no	—
609	3₋¹⁺²	—	3	1	no	—
610	3₋¹⁺²	—	6	1	no	—
611	3₋¹⁺²	—	6	1	no	—
612	3₋¹⁺²	—	6	1	no	—
613	3₋¹⁺²	—	6	1	no	—
614	3₋¹⁺²	—	6	1	no	—
615	3₋¹⁺²	—	6	2	no	—
616	3₋¹⁺²	—	6	2	no	—
617	3₋¹⁺²	—	6	2	no	—
618	3₋¹⁺²	—	6	2	no	—
619	3₋¹⁺²	—	6	2	no	—
620	3₋¹⁺²	—	6	2	no	—
621	3₋¹⁺²	—	6	2	no	—
622	3₋¹⁺²	—	6	2	no	—
623	3₋¹⁺²	—	6	2	no	—
624	3₋¹⁺²	—	6	1	no	—
625	3₋¹⁺²	—	6	1	no	—
626	3₋¹⁺²	—	6	1	no	—
627	3₋¹⁺²	—	6	1	no	—
628	3₋¹⁺²	—	6	1	no	—
629	3₋¹⁺²	—	6	1	no	—
630	3₋¹⁺²	—	6	1	no	—
631	3₋¹⁺²	—	6	1	no	—
632	3₋¹⁺²	—	6	1	no	—
633	3₋¹⁺²	—	6	2	no	—
634	3₋¹⁺²	—	6	2	no	—
635	3₋¹⁺²	—	6	2	no	—
636	3₋¹⁺²	—	6	1	no	—
637	3₋¹⁺²	—	6	1	no	—
638	3₋¹⁺²	—	6	1	no	—
639	3₋¹⁺²	—	6	1	no	—
640	3₋¹⁺²	—	6	1	no	—
641	3₋¹⁺²	—	6	1	no	—
642	3₋¹⁺²	—	6	1	no	—
643	3₋¹⁺²	—	6	1	no	—
644	3₋¹⁺²	—	6	1	no	—
645	3₋¹⁺²	—	6	1	no	—
646	3₋¹⁺²	—	6	1	no	—
647	3₋¹⁺²	—	6	1	no	—
648	3₋¹⁺²	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, direct product factor
649	H(3,𝔽₃)	—	2	1	no	—
650	H(3,𝔽₃)	—	2	1	no	—
651	H(3,𝔽₃)	—	2	1	no	—
652	H(3,𝔽₃)	—	3	1	no	—
653	H(3,𝔽₃)	—	3	1	no	—
654	H(3,𝔽₃)	—	6	1	no	—
655	H(3,𝔽₃)	—	6	1	no	—
656	H(3,𝔽₃)	—	6	1	no	—
657	H(3,𝔽₃)	—	6	1	no	—
658	H(3,𝔽₃)	—	6	1	no	—
659	H(3,𝔽₃)	—	6	1	no	—
660	H(3,𝔽₃)	—	6	1	no	—
661	H(3,𝔽₃)	—	6	1	no	—
662	H(3,𝔽₃)	—	6	1	no	—
663	H(3,𝔽₃)	—	6	1	no	—
664	H(3,𝔽₃)	—	6	1	no	—
665	H(3,𝔽₃)	C₂²×3₋¹⁺²	1	1	yes	characteristic, complemented
666	H(3,𝔽₃)	C₂²×3₋¹⁺²	1	1	yes	characteristic, complemented
667	H(3,𝔽₃)	C₂²×3₋¹⁺²	1	1	yes	characteristic, complemented
668	C₃×C₉	—	2	1	no	—
669	C₃×C₉	—	2	1	no	—
670	C₃×C₉	—	2	1	no	—
671	C₃×C₉	—	2	1	no	—
672	C₃×C₉	—	2	1	no	—
673	C₃×C₉	—	2	1	no	—
674	C₃×C₉	—	2	1	no	—
675	C₃×C₉	—	2	1	no	—
676	C₃×C₉	—	2	1	no	—
677	C₃×C₉	—	3	1	no	—
678	C₃×C₉	—	3	1	no	—
679	C₃×C₉	—	3	1	no	—
680	C₃×C₉	—	3	1	no	—
681	C₃×C₉	—	6	1	no	—
682	C₃×C₉	—	6	1	no	—
683	C₃×C₉	—	6	1	no	—
684	C₃×C₉	—	6	2	no	—
685	C₃×C₉	—	6	2	no	—
686	C₃×C₉	—	6	2	no	—
687	C₃×C₉	—	6	1	no	—
688	C₃×C₉	—	6	1	no	—
689	C₃×C₉	—	6	1	no	—
690	C₃×C₉	—	6	1	no	—
691	C₃×C₉	—	6	1	no	—
692	C₃×C₉	—	6	1	no	—
693	C₃×C₉	—	6	1	no	—
694	C₃×C₉	—	6	1	no	—
695	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
696	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
697	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
698	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
699	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
700	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
701	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
702	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
703	C₃×C₉	C₂×C₃²×D₃	1	1	yes	characteristic
704	C₂×C₃²	—	2	1	no	—
705	C₂×C₃²	—	2	1	no	—
706	C₂×C₃²	—	2	1	no	—
707	C₂×C₃²	—	2	1	no	—
708	C₂×C₃²	—	2	1	no	—
709	C₂×C₃²	—	3	1	no	—
710	C₂×C₃²	—	3	1	no	—
711	C₂×C₃²	—	3	1	no	—
712	C₂×C₃²	—	3	1	no	—
713	C₂×C₃²	—	3	1	no	—
714	C₂×C₃²	—	6	1	no	—
715	C₂×C₃²	—	6	1	no	—
716	C₂×C₃²	—	6	1	no	—
717	C₂×C₃²	—	6	2	no	—
718	C₂×C₃²	—	6	2	no	—
719	C₂×C₃²	—	6	2	no	—
720	C₂×C₃²	—	6	2	no	—
721	C₂×C₃²	—	6	1	no	—
722	C₂×C₃²	—	6	1	no	—
723	C₂×C₃²	—	6	1	no	—
724	C₂×C₃²	—	6	1	no	—
725	C₂×C₃²	—	6	1	no	—
726	C₂×C₃²	—	6	1	no	—
727	C₂×C₃²	—	6	1	no	—
728	C₂×C₃²	—	6	1	no	—
729	C₂×C₃²	—	6	1	no	—
730	C₂×C₃²	—	6	1	no	—
731	C₂×C₃²	—	6	1	no	—
732	C₂×C₃²	—	9	1	no	—
733	C₂×C₃²	—	9	1	no	—
734	C₂×C₃²	—	9	1	no	—
735	C₂×C₃²	—	9	2	no	—
736	C₂×C₃²	—	9	2	no	—
737	C₂×C₃²	—	9	2	no	—
738	C₂×C₃²	—	9	2	no	—
739	C₂×C₃²	—	18	1	no	—
740	C₂×C₃²	—	18	1	no	—
741	C₂×C₃²	—	18	1	no	—
742	C₂×C₃²	—	18	1	no	—
743	C₂×C₃²	—	18	1	no	—
744	C₂×C₃²	—	18	1	no	—
745	C₂×C₃²	—	18	1	no	—
746	C₂×C₃²	—	18	1	no	—
747	C₂×C₃²	—	18	1	no	—
748	C₂×C₃²	—	18	2	no	—
749	C₂×C₃²	—	18	2	no	—
750	C₂×C₃²	—	18	2	no	—
751	C₂×C₃²	—	18	2	no	—
752	C₂×C₃²	—	27	2	no	—
753	C₂×C₃²	—	27	2	no	—
754	C₂×C₃²	—	27	2	no	—
755	C₂×C₃²	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
756	C₂×C₃²	D₃×3₋¹⁺²	1	1	yes	characteristic, complemented
757	C₂×C₃²	D₃×3₋¹⁺²	1	1	yes	characteristic, complemented
758	C₂×C₃²	D₃×3₋¹⁺²	1	1	yes	characteristic, complemented
759	C₂×C₃²	C₂×C₃×3₋¹⁺²	1	1	yes	characteristic, complemented
760	C₂×C₃²	C₃³×D₃	1	1	yes	characteristic
761	C₃⋊D₃	C₂×C₃×3₋¹⁺²	1	2	yes	complemented
762	C₃×D₃	—	3	2	no	—
763	C₃×D₃	—	3	2	no	—
764	C₃×D₃	—	3	2	no	—
765	C₃×D₃	—	3	2	no	—
766	C₃×D₃	—	9	2	no	—
767	C₃×D₃	—	9	2	no	—
768	C₃×D₃	—	9	2	no	—
769	C₃×D₃	—	9	2	no	—
770	C₃×D₃	—	27	2	no	—
771	C₂×C₉	—	2	1	no	—
772	C₂×C₉	—	2	1	no	—
773	C₂×C₉	—	2	1	no	—
774	C₂×C₉	—	3	1	no	—
775	C₂×C₉	—	3	1	no	—
776	C₂×C₉	—	3	1	no	—
777	C₂×C₉	—	6	1	no	—
778	C₂×C₉	—	6	1	no	—
779	C₂×C₉	—	6	1	no	—
780	C₂×C₉	—	6	1	no	—
781	C₂×C₉	—	6	1	no	—
782	C₂×C₉	—	6	1	no	—
783	C₂×C₉	—	6	1	no	—
784	C₂×C₉	—	6	1	no	—
785	C₂×C₉	—	6	1	no	—
786	C₂×C₉	—	6	1	no	—
787	C₂×C₉	—	6	1	no	—
788	C₂×C₉	—	6	1	no	—
789	C₂×C₉	—	9	2	no	—
790	C₂×C₉	—	9	2	no	—
791	C₂×C₉	—	9	2	no	—
792	C₂×C₉	—	9	2	no	—
793	C₂×C₉	—	9	2	no	—
794	C₂×C₉	—	9	2	no	—
795	C₂×C₉	—	9	2	no	—
796	C₂×C₉	—	9	2	no	—
797	C₂×C₉	—	9	2	no	—
798	C₂×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
799	C₂×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
800	C₂×C₉	C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
801	C₂²×C₃	—	9	1	no	—
802	C₂²×C₃	—	9	1	no	—
803	C₂²×C₃	—	9	1	no	—
804	C₂²×C₃	—	9	1	no	—
805	C₂²×C₃	—	27	1	no	—
806	C₂²×C₃	—	27	1	no	—
807	C₂²×C₃	—	27	1	no	—
808	C₂×D₃	—	3	1	no	—
809	C₂×D₃	—	9	1	no	—
810	C₃²	—	2	1	no	—
811	C₃²	—	2	1	no	—
812	C₃²	—	2	1	no	—
813	C₃²	—	2	1	no	—
814	C₃²	—	2	1	no	—
815	C₃²	—	3	1	no	—
816	C₃²	—	3	1	no	—
817	C₃²	—	3	1	no	—
818	C₃²	—	3	1	no	—
819	C₃²	—	3	1	no	—
820	C₃²	—	6	1	no	—
821	C₃²	—	6	1	no	—
822	C₃²	—	6	1	no	—
823	C₃²	—	6	2	no	—
824	C₃²	—	6	2	no	—
825	C₃²	—	6	2	no	—
826	C₃²	—	6	2	no	—
827	C₃²	—	6	1	no	—
828	C₃²	—	6	1	no	—
829	C₃²	—	6	1	no	—
830	C₃²	—	6	1	no	—
831	C₃²	—	6	1	no	—
832	C₃²	—	6	1	no	—
833	C₃²	—	6	1	no	—
834	C₃²	—	6	1	no	—
835	C₃²	—	6	1	no	—
836	C₃²	—	6	1	no	—
837	C₃²	—	6	1	no	—
838	C₃²	—	9	1	no	—
839	C₃²	—	9	1	no	—
840	C₃²	—	9	1	no	—
841	C₃²	—	18	1	no	—
842	C₃²	—	18	1	no	—
843	C₃²	—	18	1	no	—
844	C₃²	—	18	1	no	—
845	C₃²	—	18	1	no	—
846	C₃²	—	18	1	no	—
847	C₃²	—	18	1	no	—
848	C₃²	—	18	2	no	—
849	C₃²	—	18	1	no	—
850	C₃²	—	18	1	no	—
851	C₃²	—	18	2	no	—
852	C₃²	—	18	2	no	—
853	C₃²	—	18	2	no	—
854	C₃²	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
855	C₃²	C₂×D₃×3₋¹⁺²	1	1	yes	characteristic, complemented
856	C₃²	C₂×D₃×3₋¹⁺²	1	1	yes	characteristic, complemented
857	C₃²	C₂×D₃×3₋¹⁺²	1	1	yes	characteristic, complemented
858	C₃²	C₂²×C₃×3₋¹⁺²	1	1	yes	characteristic, complemented
859	C₃²	C₂×C₃³×D₃	1	1	yes	characteristic
860	C₉	—	2	1	no	—
861	C₉	—	2	1	no	—
862	C₉	—	2	1	no	—
863	C₉	—	3	1	no	—
864	C₉	—	3	1	no	—
865	C₉	—	3	1	no	—
866	C₉	—	6	1	no	—
867	C₉	—	6	1	no	—
868	C₉	—	6	1	no	—
869	C₉	—	6	1	no	—
870	C₉	—	6	1	no	—
871	C₉	—	6	1	no	—
872	C₉	—	6	1	no	—
873	C₉	—	6	1	no	—
874	C₉	—	6	1	no	—
875	C₉	—	6	1	no	—
876	C₉	—	6	1	no	—
877	C₉	—	6	1	no	—
878	C₉	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
879	C₉	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
880	C₉	C₂×C₃×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, complemented
881	C₂×C₃	—	2	1	no	—
882	C₂×C₃	—	3	1	no	—
883	C₂×C₃	—	3	1	no	—
884	C₂×C₃	—	3	1	no	—
885	C₂×C₃	—	6	1	no	—
886	C₂×C₃	—	6	1	no	—
887	C₂×C₃	—	6	1	no	—
888	C₂×C₃	—	6	1	no	—
889	C₂×C₃	—	6	1	no	—
890	C₂×C₃	—	6	1	no	—
891	C₂×C₃	—	6	1	no	—
892	C₂×C₃	—	9	2	no	—
893	C₂×C₃	—	9	2	no	—
894	C₂×C₃	—	9	2	no	—
895	C₂×C₃	—	9	2	no	—
896	C₂×C₃	—	18	1	no	—
897	C₂×C₃	—	18	1	no	—
898	C₂×C₃	—	18	1	no	—
899	C₂×C₃	—	18	1	no	—
900	C₂×C₃	—	18	1	no	—
901	C₂×C₃	—	27	2	no	—
902	C₂×C₃	—	27	2	no	—
903	C₂×C₃	—	27	2	no	—
904	C₂×C₃	C₃²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
905	C₂×C₃	C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
906	D₃	—	3	2	no	—
907	D₃	—	9	2	no	—
908	C₂²	—	9	1	no	Sylow
909	C₃	—	2	1	no	—
910	C₃	—	3	1	no	—
911	C₃	—	3	1	no	—
912	C₃	—	3	1	no	—
913	C₃	—	6	1	no	—
914	C₃	—	6	1	no	—
915	C₃	—	6	1	no	—
916	C₃	—	6	1	no	—
917	C₃	—	6	1	no	—
918	C₃	—	6	1	no	—
919	C₃	—	6	1	no	—
920	C₃	—	18	1	no	—
921	C₃	—	18	1	no	—
922	C₃	—	18	1	no	—
923	C₃	—	18	1	no	—
924	C₃	—	18	1	no	—
925	C₃	C₂×C₃²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
926	C₃	C₂×C₃×D₃×3₋¹⁺²	1	1	yes	characteristic
927	C₂	—	9	2	no	—
928	C₂	3₋¹⁺²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic, direct product factor

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

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×(C₃⋊D₃)⋊C₃	C₂	direct (N × H)
2. C₂×H(3,𝔽₃)×3₋¹⁺²	C₂	semidirect
3. C₂×C₃⋊D₃×3₋¹⁺²	C₃	semidirect
6. C₂×#92262	C₃	semidirect
7. C₂×#92262	C₃	semidirect
8. C₂×#92262	C₃	semidirect
9. C₂×#92262	C₃	semidirect
10. C₂×#92262	C₃	semidirect
11. C₂×#92262	C₃	semidirect
12. C₂×#92259	C₃	semidirect
13. C₂×#92259	C₃	semidirect
14. C₂×C₉×(C₃⋊D₃)⋊C₃	C₃	semidirect
15. C₂×C₉×(C₃⋊D₃)⋊C₃	C₃	semidirect
16. C₂×C₉×(C₃⋊D₃)⋊C₃	C₃	semidirect
17. H(3,𝔽₃)×3₋¹⁺²	C₂²	semidirect
19. C₂×C₃²×3₋¹⁺²	D₃	semidirect
20. C₂×C₃²×3₋¹⁺²	C₂×C₃	semidirect
22. C₃⋊D₃×3₋¹⁺²	C₂×C₃	semidirect
34. C₂×C₉⋊H(3,𝔽₃)	C₂×C₃	semidirect
35. C₂×C₉⋊H(3,𝔽₃)	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
43. C₂×#6891	C₂×C₃	semidirect
44. C₂×#6891	C₂×C₃	semidirect
45. C₂×C₉×H(3,𝔽₃)	C₂×C₃	semidirect
46. C₂×C₉×H(3,𝔽₃)	C₂×C₃	semidirect
47. C₂×C₉×H(3,𝔽₃)	C₂×C₃	semidirect
48. #92262	C₂×C₃	semidirect
49. #92262	C₂×C₃	semidirect
50. #92262	C₂×C₃	semidirect
51. #92262	C₂×C₃	semidirect
52. #92262	C₂×C₃	semidirect
53. #92262	C₂×C₃	semidirect
54. #92259	C₂×C₃	semidirect
55. #92259	C₂×C₃	semidirect
56. C₉×(C₃⋊D₃)⋊C₃	C₂×C₃	semidirect
57. C₉×(C₃⋊D₃)⋊C₃	C₂×C₃	semidirect
58. C₉×(C₃⋊D₃)⋊C₃	C₂×C₃	semidirect
62. C₂×C₉×C₃⋊D₃	C₃²	semidirect
63. C₂×C₉×C₃⋊D₃	C₃²	semidirect
64. C₂×C₉×C₃⋊D₃	C₃²	semidirect
84. C₂×(C₃⋊D₃)⋊C₉	C₃²	semidirect
85. C₂×(C₃⋊D₃)⋊C₉	C₃²	semidirect
86. C₂×(C₃⋊D₃)⋊C₉	C₃²	semidirect
87. C₂×(C₃⋊D₃)⋊C₉	C₃²	semidirect
88. C₂×(C₃⋊D₃)⋊C₉	C₃²	semidirect
89. C₂×(C₃⋊D₃)⋊C₉	C₃²	semidirect
91. C₃²×3₋¹⁺²	C₂×D₃	semidirect
92. C₃²×3₋¹⁺²	C₂²×C₃	semidirect
103. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
104. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
105. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
106. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
107. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
108. C₉⋊H(3,𝔽₃)	C₂²×C₃	semidirect
112. #6891	C₂²×C₃	semidirect
113. #6891	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
153. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
154. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
155. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
156. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
157. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
158. C₂×C₃×3₋¹⁺²	C₃×D₃	semidirect
174. C₂×C₃²×C₉	C₃×D₃	semidirect
175. C₂×C₃²×C₉	C₃×D₃	semidirect
176. C₂×C₃²×C₉	C₃×D₃	semidirect
177. C₂×C₃²×C₉	C₂×C₃²	semidirect
178. C₂×C₃²×C₉	C₂×C₃²	semidirect
179. C₂×C₃²×C₉	C₂×C₃²	semidirect
180. C₉×C₃⋊D₃	C₂×C₃²	semidirect
181. C₉×C₃⋊D₃	C₂×C₃²	semidirect
182. C₉×C₃⋊D₃	C₂×C₃²	semidirect
235. C₂×C₃²⋊C₉	C₂×C₃²	semidirect
236. C₂×C₃²⋊C₉	C₂×C₃²	semidirect
237. C₂×C₃²⋊C₉	C₂×C₃²	semidirect
238. C₂×C₃²⋊C₉	C₂×C₃²	semidirect
239. C₂×C₃²⋊C₉	C₂×C₃²	semidirect
240. C₂×C₃²⋊C₉	C₂×C₃²	semidirect
241. (C₃⋊D₃)⋊C₉	C₂×C₃²	semidirect
242. (C₃⋊D₃)⋊C₉	C₂×C₃²	semidirect
243. (C₃⋊D₃)⋊C₉	C₂×C₃²	semidirect
244. (C₃⋊D₃)⋊C₉	C₂×C₃²	semidirect
245. (C₃⋊D₃)⋊C₉	C₂×C₃²	semidirect
246. (C₃⋊D₃)⋊C₉	C₂×C₃²	semidirect
272. C₂×(C₃⋊D₃)⋊C₃	3₋¹⁺²	direct (N × H)
273. C₂×(C₃⋊D₃)⋊C₃	3₋¹⁺²	direct (N × H)
274. C₂×(C₃⋊D₃)⋊C₃	3₋¹⁺²	direct (N × H)
320. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
321. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
322. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
323. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
324. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
325. C₃×3₋¹⁺²	C₂×C₃×D₃	semidirect
341. C₃²×C₉	C₂×C₃×D₃	semidirect
342. C₃²×C₉	C₂×C₃×D₃	semidirect
343. C₃²×C₉	C₂×C₃×D₃	semidirect
344. C₃²×C₉	C₂²×C₃²	semidirect
345. C₃²×C₉	C₂²×C₃²	semidirect
346. C₃²×C₉	C₂²×C₃²	semidirect
380. C₃²⋊C₉	C₂²×C₃²	semidirect
381. C₃²⋊C₉	C₂²×C₃²	semidirect
382. C₃²⋊C₉	C₂²×C₃²	semidirect
383. C₃²⋊C₉	C₂²×C₃²	semidirect
384. C₃²⋊C₉	C₂²×C₃²	semidirect
385. C₃²⋊C₉	C₂²×C₃²	semidirect
476. C₂×3₋¹⁺²	(C₃⋊D₃)⋊C₃	direct (N × H)
493. C₂×H(3,𝔽₃)	C₂×3₋¹⁺²	semidirect
494. C₂×H(3,𝔽₃)	C₂×3₋¹⁺²	semidirect
495. C₂×H(3,𝔽₃)	C₂×3₋¹⁺²	semidirect
537. (C₃⋊D₃)⋊C₃	C₂×3₋¹⁺²	direct (N × H)
538. (C₃⋊D₃)⋊C₃	C₂×3₋¹⁺²	direct (N × H)
539. (C₃⋊D₃)⋊C₃	C₂×3₋¹⁺²	direct (N × H)
559. C₂×C₃⋊D₃	C₃×3₋¹⁺²	semidirect
648. 3₋¹⁺²	C₂×(C₃⋊D₃)⋊C₃	direct (N × H)
665. H(3,𝔽₃)	C₂²×3₋¹⁺²	semidirect
666. H(3,𝔽₃)	C₂²×3₋¹⁺²	semidirect
667. H(3,𝔽₃)	C₂²×3₋¹⁺²	semidirect
756. C₂×C₃²	D₃×3₋¹⁺²	semidirect
757. C₂×C₃²	D₃×3₋¹⁺²	semidirect
758. C₂×C₃²	D₃×3₋¹⁺²	semidirect
759. C₂×C₃²	C₂×C₃×3₋¹⁺²	semidirect
761. C₃⋊D₃	C₂×C₃×3₋¹⁺²	semidirect
798. C₂×C₉	C₃×(C₃⋊D₃)⋊C₃	semidirect
799. C₂×C₉	C₃×(C₃⋊D₃)⋊C₃	semidirect
800. C₂×C₉	C₃×(C₃⋊D₃)⋊C₃	semidirect
855. C₃²	C₂×D₃×3₋¹⁺²	semidirect
856. C₃²	C₂×D₃×3₋¹⁺²	semidirect
857. C₃²	C₂×D₃×3₋¹⁺²	semidirect
858. C₃²	C₂²×C₃×3₋¹⁺²	semidirect
878. C₉	C₂×C₃×(C₃⋊D₃)⋊C₃	semidirect
879. C₉	C₂×C₃×(C₃⋊D₃)⋊C₃	semidirect
880. C₉	C₂×C₃×(C₃⋊D₃)⋊C₃	semidirect
928. C₂	3₋¹⁺²×(C₃⋊D₃)⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
3₋¹⁺²×(C₃⋊D₃)⋊C₃	2
C₂×H(3,𝔽₃)×3₋¹⁺²	2
C₂×C₃⋊D₃×3₋¹⁺²	3
C₂×C₃×D₃×3₋¹⁺²	3
C₂×C₃²×(C₃⋊D₃)⋊C₃	3
C₂×#92262	3
C₂×#92259	3
C₂×C₉×(C₃⋊D₃)⋊C₃	3

Subgroups — C2×3−1+2×(C3⋊D3)⋊C3 #72254053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×3₋¹⁺²×(C₃⋊D₃)⋊C₃ #72254053