Subgroups — #10589763⋊C₃ #13153071

Order 1728.

753 conjugacy classes of subgroups.

The subgroup lattice has 695 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	#63501⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63500⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63455⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
9	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#63445⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	(#611⋊C₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	#63441⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#63439⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5661	—	3	1	no	maximal
17	#10589763	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂×D₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
21	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
22	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
23	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
24	C₂²×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
26	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
27	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
28	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
29	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
30	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
31	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
32	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
33	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
34	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
35	#3676⋊C₃	C₂²	1	1	yes	characteristic
36	#3676⋊C₃	C₂²	1	1	yes	characteristic
37	#3676⋊C₃	C₂²	1	1	yes	characteristic
38	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
39	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
40	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
41	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
42	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
43	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
44	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
45	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
46	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
47	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
48	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
49	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
53	C₃²×#123	D₃	1	1	yes	characteristic
54	C₃×#939	—	3	1	no	—
55	C₃×#938	—	3	1	no	—
56	C₃×C₄×#67	—	3	1	no	—
57	C₃×C₄×#67	—	3	1	no	—
58	C₃×#898	—	3	1	no	—
59	C₃×#893	—	3	1	no	—
60	C₃×D₃×C₄⋊C₄	—	3	1	no	—
61	C₃×#889	—	3	1	no	—
62	C₃×#884	—	3	1	no	—
63	C₃×#884	—	3	1	no	—
64	C₃×#883	—	3	1	no	—
65	C₃×#67⋊C₄	—	3	1	no	—
66	C₃×#879	—	3	1	no	—
67	C₃×#877	—	3	1	no	—
68	C₉×#123	—	2	1	no	—
69	C₉×#123	C₂×C₃	1	1	yes	characteristic, complemented
70	#63501	C₂×C₃	1	1	yes	characteristic, complemented
71	#63500	C₂×C₃	1	1	yes	characteristic, complemented
72	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
74	#63460	C₂×C₃	1	1	yes	characteristic, complemented
75	#63455	C₂×C₃	1	1	yes	characteristic, complemented
76	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
77	#63451	C₂×C₃	1	1	yes	characteristic, complemented
78	#63446	C₂×C₃	1	1	yes	characteristic, complemented
79	#63446	C₂×C₃	1	1	yes	characteristic, complemented
80	#63445	C₂×C₃	1	1	yes	characteristic, complemented
81	#611⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
82	#63441	C₂×C₃	1	1	yes	characteristic, complemented
83	#63439	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
85	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
86	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
87	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
88	D₄×3₋¹⁺²	—	4	1	no	—
89	C₂×C₄×3₋¹⁺²	—	4	1	no	—
90	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
91	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
92	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
93	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
94	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
95	#611⋊C₃	—	2	2	no	—
96	#611⋊C₃	—	2	2	no	—
97	#611⋊C₃	—	2	2	no	—
98	#611⋊C₃	—	4	1	no	—
99	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
100	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
105	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
106	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
107	C₄×AGL(1,ℤ/9)	—	2	2	no	—
108	C₄×AGL(1,ℤ/9)	—	4	1	no	—
109	C₄×AGL(1,ℤ/9)	—	4	1	no	—
110	C₄×AGL(1,ℤ/9)	—	4	1	no	—
111	C₃×#553	—	9	1	no	—
112	#5661	—	3	1	no	—
113	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
115	C₂×C₃×#67	—	3	1	no	—
116	C₂×C₃×#67	—	3	1	no	—
117	C₂×C₃×#67	—	3	1	no	—
118	C₂×C₃×#67	—	3	1	no	—
119	C₂²×C₃×Dic₃	—	3	1	no	—
120	C₂×C₃×D₁₂	—	3	1	no	—
121	C₂×C₃×C₄×D₃	—	3	1	no	—
122	C₂×C₃×C₄×D₃	—	3	1	no	—
123	C₂×C₃×C₄×D₃	—	3	1	no	—
124	C₂×C₃×C₄×D₃	—	3	1	no	—
125	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
127	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
128	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
129	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
130	C₃×#217	—	3	1	no	—
131	C₃×#217	—	3	1	no	—
132	C₃×#217	—	3	1	no	—
133	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
134	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
135	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
136	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
137	C₃×C₄⋊Dic₃	—	3	1	no	—
138	C₃×C₄⋊Dic₃	—	3	1	no	—
139	C₃×Dic₃⋊C₄	—	3	1	no	—
140	C₃×Dic₃⋊C₄	—	3	1	no	—
141	C₃×Dic₃⋊C₄	—	3	1	no	—
142	C₃×Dic₃⋊C₄	—	3	1	no	—
143	C₃×Dic₃⋊C₄	—	3	1	no	—
144	C₃×Dic₃⋊C₄	—	3	1	no	—
145	C₃×C₄×Dic₃	—	3	1	no	—
146	C₃×C₄×Dic₃	—	3	1	no	—
147	C₃×C₄×Dic₃	—	3	1	no	—
148	C₂×D₄×C₉	—	2	1	no	—
149	C₂×D₄×C₉	C₂²×C₃	1	1	yes	characteristic
150	C₂²×C₄×C₉	—	2	1	no	—
151	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
152	C₂×#611	C₂²×C₃	1	1	yes	characteristic
153	C₂×#611	C₂²×C₃	1	1	yes	characteristic
154	C₂×#611	C₂²×C₃	1	1	yes	characteristic
155	C₂×#611	C₂²×C₃	1	1	yes	characteristic
156	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
157	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
158	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
159	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
160	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
161	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
162	C₉×C₄⋊C₄	—	2	1	no	—
163	C₉×C₄⋊C₄	—	2	1	no	—
164	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₉×C₂²⋊C₄	—	2	1	no	—
167	C₉×C₂²⋊C₄	—	2	1	no	—
168	C₉×C₂²⋊C₄	—	2	1	no	—
169	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	#3676	C₂²×C₃	1	1	yes	characteristic
173	#3676	C₂²×C₃	1	1	yes	characteristic
174	#3676	C₂²×C₃	1	1	yes	characteristic
175	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
180	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
181	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
185	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
186	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
187	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
188	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
189	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
190	C₂²×3₋¹⁺²	—	2	1	no	—
191	C₂²×3₋¹⁺²	—	2	1	no	—
192	C₂²×3₋¹⁺²	—	2	1	no	—
193	C₂²×3₋¹⁺²	—	2	1	no	—
194	C₂²×3₋¹⁺²	—	2	1	no	—
195	C₂²×3₋¹⁺²	—	2	1	no	—
196	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
197	C₂×AGL(1,ℤ/9)	—	2	1	no	—
198	C₂×AGL(1,ℤ/9)	—	2	1	no	—
199	C₂×AGL(1,ℤ/9)	—	2	1	no	—
200	C₂×AGL(1,ℤ/9)	—	2	1	no	—
201	C₂×AGL(1,ℤ/9)	—	2	1	no	—
202	C₂×AGL(1,ℤ/9)	#41	1	2	yes	—
203	C₄×3₋¹⁺²	—	2	1	no	—
204	C₄×3₋¹⁺²	—	2	1	no	—
205	C₄×3₋¹⁺²	—	2	1	no	—
206	C₄×3₋¹⁺²	—	2	1	no	—
207	C₄×3₋¹⁺²	—	2	1	no	—
208	3₋¹⁺²⋊C₄	—	2	1	no	—
209	3₋¹⁺²⋊C₄	—	2	1	no	—
210	3₋¹⁺²⋊C₄	—	2	1	no	—
211	3₋¹⁺²⋊C₄	—	2	1	no	—
212	3₋¹⁺²⋊C₄	—	2	1	no	—
213	3₋¹⁺²⋊C₄	#41	1	2	yes	—
214	C₃×#126	—	9	1	no	—
215	C₃×#126	—	9	1	no	—
216	C₃×#125	—	9	1	no	—
217	C₃×#123	—	3	1	no	—
218	C₃×#123	—	9	1	no	—
219	C₃×#123	C₃×D₃	1	1	yes	characteristic
220	C₃×#121	—	9	1	no	—
221	C₃×#121	—	9	1	no	—
222	C₃×#121	—	9	1	no	—
223	C₃×#121	—	9	1	no	—
224	C₃×C₄×D₄	—	9	1	no	—
225	C₃×C₄×D₄	—	9	1	no	—
226	C₃×C₄×D₄	—	9	1	no	—
227	C₃×C₄×D₄	—	9	1	no	—
228	C₃×#117	—	9	1	no	—
229	C₂×C₃×C₄⋊C₄	—	9	1	no	—
230	#939	—	3	1	no	—
231	#938	—	3	1	no	—
232	C₄×#67	—	3	1	no	—
233	C₄×#67	—	3	1	no	—
234	#898	—	3	1	no	—
235	#893	—	3	1	no	—
236	D₃×C₄⋊C₄	—	3	1	no	—
237	#889	—	3	1	no	—
238	#884	—	3	1	no	—
239	#884	—	3	1	no	—
240	#883	—	3	1	no	—
241	#67⋊C₄	—	3	1	no	—
242	#879	—	3	1	no	—
243	#877	—	3	1	no	—
244	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
245	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
246	C₂²×C₃×D₃	—	3	1	no	—
247	C₂²×C₃×D₃	—	3	1	no	—
248	C₃²×D₄	—	4	1	no	—
249	C₂×C₃²×C₄	—	4	1	no	—
250	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
251	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
252	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
253	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
254	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
255	C₃×#67	—	6	2	no	—
256	C₃×#67	—	6	2	no	—
257	C₃×#67	—	6	2	no	—
258	C₃×#67	—	12	1	no	—
259	C₂×C₃×Dic₃	—	3	1	no	—
260	C₂×C₃×Dic₃	—	3	1	no	—
261	C₂×C₃×Dic₃	—	3	1	no	—
262	C₂×C₃×Dic₃	—	3	1	no	—
263	C₂×C₃×Dic₃	—	3	1	no	—
264	C₂×C₃×Dic₃	—	3	1	no	—
265	C₂×C₃×Dic₃	—	6	2	no	—
266	C₃×D₁₂	—	6	2	no	—
267	C₃×C₄×D₃	—	6	2	no	—
268	C₃×C₄×D₃	—	12	1	no	—
269	C₃×C₄×D₃	—	12	1	no	—
270	C₃×C₄×D₃	—	12	1	no	—
271	C₂³×C₉	—	2	1	no	—
272	C₂³×C₉	—	2	1	no	—
273	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
274	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
275	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
276	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
277	D₄×C₉	—	4	1	no	—
278	D₄×C₉	—	4	2	no	—
279	C₂×C₄×C₉	—	2	1	no	—
280	C₂×C₄×C₉	—	2	1	no	—
281	C₂×C₄×C₉	—	2	1	no	—
282	C₂×C₄×C₉	—	2	1	no	—
283	C₂×C₄×C₉	—	2	1	no	—
284	C₂×C₄×C₉	—	4	1	no	—
285	C₂×C₄×C₉	—	4	2	no	—
286	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
287	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
291	#611	—	2	2	no	—
292	#611	—	2	2	no	—
293	#611	—	2	2	no	—
294	#611	—	4	1	no	—
295	C₂×Dic₉	—	2	2	no	—
296	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
297	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
298	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
299	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
300	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
301	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
302	D₃₆	—	2	2	no	—
303	C₄×D₉	—	2	2	no	—
304	C₄×D₉	—	4	1	no	—
305	C₄×D₉	—	4	1	no	—
306	C₄×D₉	—	4	1	no	—
307	#553	—	9	1	no	Sylow
308	C₂×3₋¹⁺²	—	4	1	no	—
309	C₂×3₋¹⁺²	—	4	1	no	—
310	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
311	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
312	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
313	AGL(1,ℤ/9)	—	2	2	no	—
314	AGL(1,ℤ/9)	—	4	1	no	—
315	C₂×C₃×D₄	—	3	1	no	—
316	C₂×C₃×D₄	—	9	1	no	—
317	C₂×C₃×D₄	—	9	1	no	—
318	C₂×C₃×D₄	—	9	1	no	—
319	C₂×C₃×D₄	—	9	1	no	—
320	C₂×C₃×D₄	—	9	1	no	—
321	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
322	C₂²×C₃×C₄	—	3	1	no	—
323	C₂²×C₃×C₄	—	9	1	no	—
324	C₂²×C₃×C₄	—	9	1	no	—
325	C₂²×C₃×C₄	—	9	1	no	—
326	C₂²×C₃×C₄	—	9	1	no	—
327	C₂²×C₃×C₄	—	9	1	no	—
328	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
329	C₂×#67	—	3	1	no	—
330	C₂×#67	—	3	1	no	—
331	C₂×#67	—	3	1	no	—
332	C₂×#67	—	3	1	no	—
333	C₂²×Dic₃	—	3	1	no	—
334	C₂×D₁₂	—	3	1	no	—
335	C₂×C₄×D₃	—	3	1	no	—
336	C₂×C₄×D₃	—	3	1	no	—
337	C₂×C₄×D₃	—	3	1	no	—
338	C₂×C₄×D₃	—	3	1	no	—
339	C₃×C₄⋊C₄	—	3	1	no	—
340	C₃×C₄⋊C₄	—	3	1	no	—
341	C₃×C₄⋊C₄	—	9	1	no	—
342	C₃×C₄⋊C₄	—	9	1	no	—
343	C₃×C₄⋊C₄	—	9	1	no	—
344	C₃×C₄⋊C₄	—	9	1	no	—
345	C₃×C₄⋊C₄	—	9	1	no	—
346	C₃×C₄⋊C₄	—	9	1	no	—
347	C₃×C₄⋊C₄	—	9	1	no	—
348	C₃×C₄⋊C₄	—	9	1	no	—
349	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
350	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
351	C₃×C₂²⋊C₄	—	3	1	no	—
352	C₃×C₂²⋊C₄	—	3	1	no	—
353	C₃×C₂²⋊C₄	—	3	1	no	—
354	C₃×C₂²⋊C₄	—	9	1	no	—
355	C₃×C₂²⋊C₄	—	9	1	no	—
356	C₃×C₂²⋊C₄	—	9	1	no	—
357	C₃×C₂²⋊C₄	—	9	1	no	—
358	C₃×C₂²⋊C₄	—	9	1	no	—
359	C₃×C₂²⋊C₄	—	9	1	no	—
360	C₃×C₂²⋊C₄	—	9	1	no	—
361	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
362	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
363	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
364	C₃×C₄²	—	9	1	no	—
365	C₃×C₄²	—	9	1	no	—
366	C₃×C₄²	—	9	1	no	—
367	#217	—	3	1	no	—
368	#217	—	3	1	no	—
369	#217	—	3	1	no	—
370	(C₂×D₃)⋊C₄	—	3	1	no	—
371	(C₂×D₃)⋊C₄	—	3	1	no	—
372	(C₂×D₃)⋊C₄	—	3	1	no	—
373	(C₂×D₃)⋊C₄	—	3	1	no	—
374	C₄⋊Dic₃	—	3	1	no	—
375	C₄⋊Dic₃	—	3	1	no	—
376	Dic₃⋊C₄	—	3	1	no	—
377	Dic₃⋊C₄	—	3	1	no	—
378	Dic₃⋊C₄	—	3	1	no	—
379	Dic₃⋊C₄	—	3	1	no	—
380	Dic₃⋊C₄	—	3	1	no	—
381	Dic₃⋊C₄	—	3	1	no	—
382	C₄×Dic₃	—	3	1	no	—
383	C₄×Dic₃	—	3	1	no	—
384	C₄×Dic₃	—	3	1	no	—
385	C₂²×C₃²	—	2	1	no	—
386	C₂²×C₃²	—	2	1	no	—
387	C₂²×C₃²	—	2	1	no	—
388	C₂²×C₃²	—	2	1	no	—
389	C₂²×C₃²	—	2	1	no	—
390	C₂²×C₃²	—	2	1	no	—
391	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
392	C₂×C₃×D₃	—	3	2	no	—
393	C₂×C₃×D₃	—	6	1	no	—
394	C₂×C₃×D₃	—	6	1	no	—
395	C₂×C₃×D₃	—	6	1	no	—
396	C₂×C₃×D₃	—	6	1	no	—
397	C₂×C₃×D₃	—	6	1	no	—
398	C₃²×C₄	—	2	1	no	—
399	C₃²×C₄	—	2	1	no	—
400	C₃²×C₄	—	2	1	no	—
401	C₃²×C₄	—	2	1	no	—
402	C₃²×C₄	—	2	1	no	—
403	C₃×Dic₃	—	3	2	no	—
404	C₃×Dic₃	—	6	1	no	—
405	C₃×Dic₃	—	6	1	no	—
406	C₃×Dic₃	—	6	1	no	—
407	C₃×Dic₃	—	6	1	no	—
408	C₃×Dic₃	—	6	1	no	—
409	C₂²×C₉	—	2	2	no	—
410	C₂²×C₉	—	2	1	no	—
411	C₂²×C₉	—	2	1	no	—
412	C₂²×C₉	—	2	1	no	—
413	C₂²×C₉	—	2	1	no	—
414	C₂²×C₉	—	2	1	no	—
415	C₂²×C₉	—	2	1	no	—
416	C₂²×C₉	—	2	1	no	—
417	C₂²×C₉	—	4	1	no	—
418	C₂²×C₉	—	4	1	no	—
419	C₂²×C₉	—	4	1	no	—
420	C₂²×C₉	—	4	1	no	—
421	C₂²×C₉	—	4	1	no	—
422	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
423	C₂×D₉	—	2	1	no	—
424	C₂×D₉	—	2	1	no	—
425	C₂×D₉	—	2	1	no	—
426	C₂×D₉	—	2	1	no	—
427	C₂×D₉	—	2	1	no	—
428	C₂×D₉	C₃×#41	1	2	yes	—
429	C₄×C₉	—	2	1	no	—
430	C₄×C₉	—	2	1	no	—
431	C₄×C₉	—	2	1	no	—
432	C₄×C₉	—	2	1	no	—
433	C₄×C₉	—	2	1	no	—
434	C₄×C₉	—	4	1	no	—
435	C₄×C₉	—	4	1	no	—
436	C₄×C₉	—	4	1	no	—
437	C₄×C₉	—	4	1	no	—
438	C₄×C₉	—	4	1	no	—
439	Dic₉	—	2	1	no	—
440	Dic₉	—	2	1	no	—
441	Dic₉	—	2	1	no	—
442	Dic₉	—	2	1	no	—
443	Dic₉	—	2	1	no	—
444	Dic₉	C₃×#41	1	2	yes	—
445	#126	—	9	1	no	—
446	#126	—	9	1	no	—
447	#125	—	9	1	no	—
448	#123	—	9	1	no	—
449	#123	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
450	#121	—	9	1	no	—
451	#121	—	9	1	no	—
452	#121	—	9	1	no	—
453	#121	—	9	1	no	—
454	C₄×D₄	—	9	1	no	—
455	C₄×D₄	—	9	1	no	—
456	C₄×D₄	—	9	1	no	—
457	C₄×D₄	—	9	1	no	—
458	#117	—	9	1	no	—
459	C₂×C₄⋊C₄	—	9	1	no	—
460	3₋¹⁺²	#553	1	1	yes	characteristic, complemented, Sylow
461	C₂³×C₃	—	3	1	no	—
462	C₂³×C₃	—	3	1	no	—
463	C₂³×C₃	—	9	1	no	—
464	C₂³×C₃	—	9	1	no	—
465	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
466	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
467	C₂²×D₃	—	3	1	no	—
468	C₂²×D₃	—	3	1	no	—
469	C₃×D₄	—	4	1	no	—
470	C₃×D₄	—	12	1	no	—
471	C₃×D₄	—	18	2	no	—
472	C₃×D₄	—	18	2	no	—
473	C₃×D₄	—	18	2	no	—
474	C₃×D₄	—	18	2	no	—
475	C₃×D₄	—	36	1	no	—
476	C₂×C₃×C₄	—	3	1	no	—
477	C₂×C₃×C₄	—	3	1	no	—
478	C₂×C₃×C₄	—	3	1	no	—
479	C₂×C₃×C₄	—	3	1	no	—
480	C₂×C₃×C₄	—	3	1	no	—
481	C₂×C₃×C₄	—	4	1	no	—
482	C₂×C₃×C₄	—	9	1	no	—
483	C₂×C₃×C₄	—	9	1	no	—
484	C₂×C₃×C₄	—	9	1	no	—
485	C₂×C₃×C₄	—	9	1	no	—
486	C₂×C₃×C₄	—	9	1	no	—
487	C₂×C₃×C₄	—	9	1	no	—
488	C₂×C₃×C₄	—	12	1	no	—
489	C₂×C₃×C₄	—	18	2	no	—
490	C₂×C₃×C₄	—	18	2	no	—
491	C₂×C₃×C₄	—	36	1	no	—
492	C₂×C₃×C₄	—	36	1	no	—
493	C₂×C₃×C₄	—	36	1	no	—
494	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
495	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
496	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
497	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
498	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
499	#67	—	6	2	no	—
500	#67	—	6	2	no	—
501	#67	—	6	2	no	—
502	#67	—	12	1	no	—
503	C₂×Dic₃	—	3	1	no	—
504	C₂×Dic₃	—	3	1	no	—
505	C₂×Dic₃	—	3	1	no	—
506	C₂×Dic₃	—	3	1	no	—
507	C₂×Dic₃	—	3	1	no	—
508	C₂×Dic₃	—	3	1	no	—
509	C₂×Dic₃	—	6	2	no	—
510	D₁₂	—	6	2	no	—
511	C₄×D₃	—	6	2	no	—
512	C₄×D₃	—	12	1	no	—
513	C₄×D₃	—	12	1	no	—
514	C₄×D₃	—	12	1	no	—
515	C₂×C₃²	—	4	1	no	—
516	C₂×C₃²	—	4	1	no	—
517	C₂×C₃²	#1004	1	1	yes	characteristic
518	C₂×C₃²	D₃×#41	1	1	yes	characteristic
519	C₂×C₃²	D₃×#41	1	1	yes	characteristic
520	C₃×D₃	—	6	2	no	—
521	C₃×D₃	—	12	1	no	—
522	C₂×C₉	—	2	1	no	—
523	C₂×C₉	—	2	1	no	—
524	C₂×C₉	—	2	1	no	—
525	C₂×C₉	—	4	2	no	—
526	C₂×C₉	—	4	1	no	—
527	C₂×C₉	—	4	1	no	—
528	C₂×C₉	—	8	1	no	—
529	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
530	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
531	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
532	D₉	—	2	2	no	—
533	D₉	—	4	1	no	—
534	C₂×D₄	—	9	1	no	—
535	C₂×D₄	—	9	1	no	—
536	C₂×D₄	—	9	1	no	—
537	C₂×D₄	—	9	1	no	—
538	C₂×D₄	—	9	1	no	—
539	C₂×D₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
540	C₂²×C₄	—	9	1	no	—
541	C₂²×C₄	—	9	1	no	—
542	C₂²×C₄	—	9	1	no	—
543	C₂²×C₄	—	9	1	no	—
544	C₂²×C₄	—	9	1	no	—
545	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
546	C₄⋊C₄	—	9	1	no	—
547	C₄⋊C₄	—	9	1	no	—
548	C₄⋊C₄	—	9	1	no	—
549	C₄⋊C₄	—	9	1	no	—
550	C₄⋊C₄	—	9	1	no	—
551	C₄⋊C₄	—	9	1	no	—
552	C₄⋊C₄	—	9	1	no	—
553	C₄⋊C₄	—	9	1	no	—
554	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
555	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
556	C₂²⋊C₄	—	9	1	no	—
557	C₂²⋊C₄	—	9	1	no	—
558	C₂²⋊C₄	—	9	1	no	—
559	C₂²⋊C₄	—	9	1	no	—
560	C₂²⋊C₄	—	9	1	no	—
561	C₂²⋊C₄	—	9	1	no	—
562	C₂²⋊C₄	—	9	1	no	—
563	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
564	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
565	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
566	C₄²	—	9	1	no	—
567	C₄²	—	9	1	no	—
568	C₄²	—	9	1	no	—
569	C₂²×C₃	—	2	1	no	—
570	C₂²×C₃	—	2	1	no	—
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	2	1	no	—
573	C₂²×C₃	—	2	1	no	—
574	C₂²×C₃	—	2	1	no	—
575	C₂²×C₃	—	3	1	no	—
576	C₂²×C₃	—	6	1	no	—
577	C₂²×C₃	—	6	1	no	—
578	C₂²×C₃	—	6	1	no	—
579	C₂²×C₃	—	6	1	no	—
580	C₂²×C₃	—	6	1	no	—
581	C₂²×C₃	—	6	1	no	—
582	C₂²×C₃	—	9	2	no	—
583	C₂²×C₃	—	18	1	no	—
584	C₂²×C₃	—	18	1	no	—
585	C₂²×C₃	—	18	1	no	—
586	C₂²×C₃	—	18	1	no	—
587	C₂²×C₃	—	18	1	no	—
588	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
589	C₂×D₃	—	3	2	no	—
590	C₂×D₃	—	6	1	no	—
591	C₂×D₃	—	6	1	no	—
592	C₂×D₃	—	6	1	no	—
593	C₂×D₃	—	6	1	no	—
594	C₂×D₃	—	6	1	no	—
595	C₃×C₄	—	2	1	no	—
596	C₃×C₄	—	2	1	no	—
597	C₃×C₄	—	2	1	no	—
598	C₃×C₄	—	2	1	no	—
599	C₃×C₄	—	2	1	no	—
600	C₃×C₄	—	6	1	no	—
601	C₃×C₄	—	6	1	no	—
602	C₃×C₄	—	6	1	no	—
603	C₃×C₄	—	6	1	no	—
604	C₃×C₄	—	6	1	no	—
605	C₃×C₄	—	9	2	no	—
606	C₃×C₄	—	18	1	no	—
607	C₃×C₄	—	18	1	no	—
608	C₃×C₄	—	18	1	no	—
609	C₃×C₄	—	18	1	no	—
610	C₃×C₄	—	18	1	no	—
611	Dic₃	—	3	2	no	—
612	Dic₃	—	6	1	no	—
613	Dic₃	—	6	1	no	—
614	Dic₃	—	6	1	no	—
615	Dic₃	—	6	1	no	—
616	Dic₃	—	6	1	no	—
617	C₃²	#5661	1	1	yes	characteristic
618	C₉	—	2	1	no	—
619	C₉	C₃×#553	1	1	yes	characteristic, complemented
620	C₂³	—	9	1	no	—
621	C₂³	—	9	1	no	—
622	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
623	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
624	D₄	—	4	1	no	—
625	D₄	—	18	2	no	—
626	D₄	—	18	2	no	—
627	D₄	—	18	2	no	—
628	D₄	—	18	2	no	—
629	D₄	—	36	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	9	1	no	—
632	C₂×C₄	—	9	1	no	—
633	C₂×C₄	—	9	1	no	—
634	C₂×C₄	—	9	1	no	—
635	C₂×C₄	—	9	1	no	—
636	C₂×C₄	—	9	1	no	—
637	C₂×C₄	—	18	2	no	—
638	C₂×C₄	—	18	2	no	—
639	C₂×C₄	—	36	1	no	—
640	C₂×C₄	—	36	1	no	—
641	C₂×C₄	—	36	1	no	—
642	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
643	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
644	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
645	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
646	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
647	C₂×C₃	—	3	1	no	—
648	C₂×C₃	—	3	1	no	—
649	C₂×C₃	—	3	1	no	—
650	C₂×C₃	—	4	1	no	—
651	C₂×C₃	—	4	1	no	—
652	C₂×C₃	—	12	1	no	—
653	C₂×C₃	—	12	1	no	—
654	C₂×C₃	—	18	2	no	—
655	C₂×C₃	—	36	1	no	—
656	C₂×C₃	C₃×#1004	1	1	yes	characteristic
657	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
658	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
659	D₃	—	6	2	no	—
660	D₃	—	12	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	2	1	no	—
667	C₂²	—	9	2	no	—
668	C₂²	—	18	1	no	—
669	C₂²	—	18	1	no	—
670	C₂²	—	18	1	no	—
671	C₂²	—	18	1	no	—
672	C₂²	—	18	1	no	—
673	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	2	1	no	—
677	C₄	—	2	1	no	—
678	C₄	—	2	1	no	—
679	C₄	—	9	2	no	—
680	C₄	—	18	1	no	—
681	C₄	—	18	1	no	—
682	C₄	—	18	1	no	—
683	C₄	—	18	1	no	—
684	C₄	—	18	1	no	—
685	C₃	—	3	1	no	—
686	C₃	C₃×#5661	1	1	yes	characteristic
687	C₂	—	4	1	no	—
688	C₂	—	4	1	no	—
689	C₂	—	18	2	no	—
690	C₂	—	36	1	no	—
691	C₂	#63710⋊C₃	1	1	yes	characteristic
692	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic
693	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×AGL(1,ℤ/9)
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini, socle	C₂²×C₃	C₂³×C₃×D₃
Fitting	3₋¹⁺²×#123	C₂
hypercenter	#123	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#553
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ #123

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×#123	C₂	semidirect
2. #63501⋊C₃	C₂	semidirect
3. #63500⋊C₃	C₂	semidirect
4. C₄×#611⋊C₃	C₂	semidirect
5. C₄×#611⋊C₃	C₂	semidirect
6. #63460⋊C₃	C₂	semidirect
7. #63455⋊C₃	C₂	semidirect
8. C₄⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
9. #63451⋊C₃	C₂	semidirect
10. #63446⋊C₃	C₂	semidirect
11. #63446⋊C₃	C₂	semidirect
12. #63445⋊C₃	C₂	semidirect
13. (#611⋊C₃)⋊C₄	C₂	semidirect
14. #63441⋊C₃	C₂	semidirect
15. #63439⋊C₃	C₂	semidirect
17. #10589763	C₃	semidirect
69. C₉×#123	C₂×C₃	semidirect
70. #63501	C₂×C₃	semidirect
71. #63500	C₂×C₃	semidirect
72. C₄×#611	C₂×C₃	semidirect
73. C₄×#611	C₂×C₃	semidirect
74. #63460	C₂×C₃	semidirect
75. #63455	C₂×C₃	semidirect
76. C₄⋊C₄×D₉	C₂×C₃	semidirect
77. #63451	C₂×C₃	semidirect
78. #63446	C₂×C₃	semidirect
79. #63446	C₂×C₃	semidirect
80. #63445	C₂×C₃	semidirect
81. #611⋊C₄	C₂×C₃	semidirect
82. #63441	C₂×C₃	semidirect
83. #63439	C₂×C₃	semidirect
449. #123	AGL(1,ℤ/9)	semidirect
460. 3₋¹⁺²	#553	semidirect
619. C₉	C₃×#553	semidirect

Maximal subgroups

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

subgroup	index
3₋¹⁺²×#123	2
#63501⋊C₃	2
#63500⋊C₃	2
C₄×#611⋊C₃	2
#63460⋊C₃	2
#63455⋊C₃	2
C₄⋊C₄×AGL(1,ℤ/9)	2
#63451⋊C₃	2
#63446⋊C₃	2
#63445⋊C₃	2
(#611⋊C₃)⋊C₄	2
#63441⋊C₃	2
#63439⋊C₃	2
C₃×#5661	3
#10589763	3

Subgroups — #10589763⋊C3 #13153071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589763⋊C₃ #13153071