Subgroups — #72254723

Order 5184.

1500 conjugacy classes of subgroups.

The subgroup lattice has 565 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72254713	C₂	1	2	yes	maximal, complemented
2	C₄×C₄⋊(C₃⋊AGL(1,ℤ/9))	C₂	1	2	yes	maximal, complemented
3	C₂×#13047909	C₂	1	1	yes	maximal, characteristic
4	#72254651	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×3₋¹⁺²×#97	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#10592410	—	3	1	no	maximal
7	#13143798	C₃	1	1	yes	maximal, characteristic, complemented
8	#10588392⋊C₃	—	3	3	no	maximal
9	C₂×C₄⋊(C₃⋊AGL(1,ℤ/9))	C₂²	1	2	yes	—
10	C₂×C₄×C₃⋊AGL(1,ℤ/9)	—	2	2	no	—
11	C₂×C₃×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
13	C₃×C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
14	#13047949	—	2	2	no	—
15	C₄⋊(C₃⋊(3₋¹⁺²⋊C₄))	C₂²	1	2	yes	—
16	#13047909	C₄	1	4	yes	complemented
17	C₂×C₃×#3745	—	3	1	no	—
18	C₃×C₄×C₄⋊(C₃⋊D₃)	—	3	2	no	—
19	C₃³×#97	D₃	1	1	yes	characteristic
20	C₃×#63648	—	3	2	no	—
21	C₃×#63644	—	3	1	no	—
22	C₂×#88525	C₂×C₃	1	1	yes	characteristic
23	C₄×C₄⋊(C₃⋊D₉)	C₂×C₃	1	2	yes	complemented
24	C₂×D₇₂⋊C₃	—	3	3	no	—
25	C₄×C₄⋊AGL(1,ℤ/9)	—	3	6	no	—
26	3₋¹⁺²×#97	—	2	3	no	—
27	3₋¹⁺²×#97	D₃	1	3	yes	complemented
28	C₃×C₉×#97	—	2	1	no	—
29	C₃×C₉×#97	C₂×C₃	1	1	yes	characteristic, complemented
30	#11720543	C₂×C₃	1	2	yes	complemented
31	#11720540	C₂×C₃	1	1	yes	characteristic, complemented
32	#63380⋊C₃	—	3	6	no	—
33	#63377⋊C₃	—	3	3	no	—
34	C₂²×C₃⋊AGL(1,ℤ/9)	—	2	2	no	—
35	C₂×C₃×C₄×3₋¹⁺²	D₄	1	2	yes	—
36	C₂×C₃×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
37	C₂×C₃⋊(3₋¹⁺²⋊C₄)	—	2	2	no	—
38	C₄⋊(C₃⋊AGL(1,ℤ/9))	—	2	2	no	—
39	C₄⋊(C₃⋊AGL(1,ℤ/9))	C₂×C₄	1	4	yes	complemented
40	C₄×C₃⋊AGL(1,ℤ/9)	—	4	4	no	—
41	C₃×C₈×3₋¹⁺²	—	2	1	no	—
42	C₃×C₈×3₋¹⁺²	C₂×C₄	1	2	yes	complemented
43	#10592410	—	3	1	no	—
44	C₃×#4711	—	9	1	no	—
45	C₃×#4711	—	9	2	no	—
46	C₃×#4711	—	9	1	no	—
47	#10588392	—	3	3	no	—
48	C₂×C₃×C₄⋊(C₃⋊D₃)	—	3	2	no	—
49	C₂×C₃×C₄×C₃⋊D₃	—	6	2	no	—
50	C₂×C₃³×C₈	C₂×D₃	1	1	yes	characteristic
51	C₂×C₃³×C₈	C₂×D₃	1	1	yes	characteristic
52	C₃³×C₄²	C₂×D₃	1	1	yes	characteristic
53	C₃×#3752	—	6	2	no	—
54	C₃×C₄⋊(C₃⋊Dic₃)	—	3	2	no	—
55	C₃×#3745	—	3	4	no	—
56	C₂×C₄⋊(C₃⋊D₉)	C₂²×C₃	1	2	yes	—
57	C₂×C₄×C₃⋊D₉	—	2	2	no	—
58	C₂×C₄⋊AGL(1,ℤ/9)	—	3	6	no	—
59	C₂×C₄×AGL(1,ℤ/9)	—	6	6	no	—
60	C₂×C₈×3₋¹⁺²	—	2	3	no	—
61	C₂×C₈×3₋¹⁺²	—	2	3	no	—
62	C₂×C₈×3₋¹⁺²	C₂×D₃	1	3	yes	—
63	C₂×C₈×3₋¹⁺²	C₂×D₃	1	3	yes	—
64	C₂×C₃×C₈×C₉	—	2	1	no	—
65	C₂×C₃×C₈×C₉	—	2	1	no	—
66	C₂×C₃×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
67	C₂×C₃×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
68	C₄²×3₋¹⁺²	—	2	3	no	—
69	C₄²×3₋¹⁺²	C₂×D₃	1	3	yes	—
70	C₃×C₄²×C₉	—	2	1	no	—
71	C₃×C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
72	#88536	—	2	2	no	—
73	C₄⋊(C₃⋊Dic₉)	C₂²×C₃	1	2	yes	—
74	#88525	C₃×C₄	1	4	yes	complemented
75	(C₂×AGL(1,ℤ/9))⋊C₄	—	6	6	no	—
76	C₄⋊(3₋¹⁺²⋊C₄)	—	3	6	no	—
77	D₇₂⋊C₃	—	3	12	no	—
78	C₂²×C₃×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
79	C₂×C₃⋊AGL(1,ℤ/9)	—	2	4	no	—
80	C₂×C₃⋊AGL(1,ℤ/9)	—	4	2	no	—
81	C₂×C₃⋊AGL(1,ℤ/9)	—	4	2	no	—
82	C₃×C₄×3₋¹⁺²	—	2	2	no	—
83	C₃×C₄×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
84	C₃×C₄×3₋¹⁺²	#41	1	1	yes	characteristic
85	C₃⋊(3₋¹⁺²⋊C₄)	—	4	2	no	—
86	C₂×#3745	—	3	1	no	—
87	C₄×C₄⋊(C₃⋊D₃)	—	3	2	no	—
88	C₂×C₃×D₂₄	—	9	1	no	—
89	C₂×C₃×D₂₄	—	9	2	no	—
90	C₂×C₃×D₂₄	—	9	1	no	—
91	C₃×C₄×D₁₂	—	9	2	no	—
92	C₃×C₄×D₁₂	—	9	4	no	—
93	C₃×C₄×D₁₂	—	9	2	no	—
94	C₃²×#97	—	2	1	no	—
95	C₃²×#97	—	3	1	no	—
96	C₃²×#97	—	6	2	no	—
97	C₃²×#97	C₃×D₃	1	1	yes	characteristic
98	C₃²×#97	C₃⋊D₃	1	1	yes	characteristic
99	#63648	—	3	2	no	—
100	#63644	—	3	1	no	—
101	C₃×#821	—	9	2	no	—
102	C₃×#821	—	9	4	no	—
103	C₃×#821	—	9	2	no	—
104	C₃×#817	—	9	1	no	—
105	C₃×#817	—	9	2	no	—
106	C₃×#817	—	9	1	no	—
107	C₂×D₇₂	—	3	3	no	—
108	C₄×D₃₆	—	3	6	no	—
109	C₉×#97	—	2	3	no	—
110	C₉×#97	C₃×D₃	1	3	yes	complemented
111	#63380	—	3	6	no	—
112	#63377	—	3	3	no	—
113	C₂²×C₃×C₃⋊D₃	—	6	2	no	—
114	C₂×C₃³×C₄	D₁₂	1	2	yes	—
115	C₂×C₃³×C₄	C₂²×D₃	1	1	yes	characteristic
116	C₂×C₃×C₃⋊Dic₃	—	6	2	no	—
117	C₃×C₄⋊(C₃⋊D₃)	—	3	4	no	—
118	C₃×C₄⋊(C₃⋊D₃)	—	6	2	no	—
119	C₃×C₄×C₃⋊D₃	—	12	4	no	—
120	C₂²×C₃⋊D₉	—	2	2	no	—
121	C₂²×AGL(1,ℤ/9)	—	6	6	no	—
122	C₃³×C₈	—	2	1	no	—
123	C₃³×C₈	C₄×D₃	1	2	yes	—
124	C₂×C₄×3₋¹⁺²	—	2	3	no	—
125	C₂×C₄×3₋¹⁺²	—	2	6	no	—
126	C₂×C₄×3₋¹⁺²	D₁₂	1	6	yes	—
127	C₂×C₄×3₋¹⁺²	C₂²×D₃	1	3	yes	—
128	C₂×C₃×C₄×C₉	—	2	1	no	—
129	C₂×C₃×C₄×C₉	—	2	2	no	—
130	C₂×C₃×C₄×C₉	C₃×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
132	C₂×C₃⋊Dic₉	—	2	2	no	—
133	C₄⋊(C₃⋊D₉)	—	2	2	no	—
134	C₄⋊(C₃⋊D₉)	C₂×C₃×C₄	1	4	yes	complemented
135	C₄×C₃⋊D₉	—	4	4	no	—
136	C₂×3₋¹⁺²⋊C₄	—	6	6	no	—
137	C₄⋊AGL(1,ℤ/9)	—	3	12	no	—
138	C₄⋊AGL(1,ℤ/9)	—	6	6	no	—
139	C₄×AGL(1,ℤ/9)	—	12	12	no	—
140	C₈×3₋¹⁺²	—	2	6	no	—
141	C₈×3₋¹⁺²	—	2	6	no	—
142	C₈×3₋¹⁺²	—	2	3	no	—
143	C₈×3₋¹⁺²	C₄×D₃	1	6	yes	complemented
144	C₃×C₈×C₉	—	2	2	no	—
145	C₃×C₈×C₉	—	2	2	no	—
146	C₃×C₈×C₉	—	2	1	no	—
147	C₃×C₈×C₉	C₂×C₃×C₄	1	2	yes	complemented
148	C₃×#442	—	27	1	no	—
149	#4711	—	9	1	no	—
150	#4711	—	9	2	no	—
151	#4711	—	9	1	no	—
152	C₂×C₃×3₋¹⁺²	C₄×D₄	1	1	yes	characteristic
153	C₂×C₃×3₋¹⁺²	AGL(1,ℤ/8)	1	2	yes	—
154	C₃⋊AGL(1,ℤ/9)	—	4	4	no	—
155	C₂×C₄⋊(C₃⋊D₃)	—	3	2	no	—
156	C₂×C₄×C₃⋊D₃	—	6	2	no	—
157	C₂×C₃×D₁₂	—	9	2	no	—
158	C₂×C₃×D₁₂	—	9	4	no	—
159	C₂×C₃×D₁₂	—	9	2	no	—
160	C₂×C₃×C₄×D₃	—	18	2	no	—
161	C₂×C₃×C₄×D₃	—	18	4	no	—
162	C₂×C₃×C₄×D₃	—	18	2	no	—
163	C₂×C₃²×C₈	—	2	1	no	—
164	C₂×C₃²×C₈	—	2	1	no	—
165	C₂×C₃²×C₈	—	3	1	no	—
166	C₂×C₃²×C₈	—	3	1	no	—
167	C₂×C₃²×C₈	—	6	2	no	—
168	C₂×C₃²×C₈	—	6	2	no	—
169	C₂×C₃²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
170	C₂×C₃²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
171	C₂×C₃²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
172	C₂×C₃²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
173	C₃²×C₄²	—	2	1	no	—
174	C₃²×C₄²	—	3	1	no	—
175	C₃²×C₄²	—	6	2	no	—
176	C₃²×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
177	C₃²×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
178	#3752	—	6	2	no	—
179	C₄⋊(C₃⋊Dic₃)	—	3	2	no	—
180	#3745	—	3	4	no	—
181	C₃×(C₂×D₃)⋊C₄	—	18	2	no	—
182	C₃×(C₂×D₃)⋊C₄	—	18	4	no	—
183	C₃×(C₂×D₃)⋊C₄	—	18	2	no	—
184	C₃×C₄⋊Dic₃	—	9	2	no	—
185	C₃×C₄⋊Dic₃	—	9	4	no	—
186	C₃×C₄⋊Dic₃	—	9	2	no	—
187	C₃×D₂₄	—	9	4	no	—
188	C₃×D₂₄	—	9	8	no	—
189	C₃×D₂₄	—	9	4	no	—
190	C₂×D₃₆	—	3	6	no	—
191	C₂×C₄×D₉	—	6	6	no	—
192	C₂×C₈×C₉	—	2	3	no	—
193	C₂×C₈×C₉	—	2	3	no	—
194	C₂×C₈×C₉	C₂×C₃×D₃	1	3	yes	—
195	C₂×C₈×C₉	C₂×C₃×D₃	1	3	yes	—
196	C₄²×C₉	—	2	3	no	—
197	C₄²×C₉	C₂×C₃×D₃	1	3	yes	—
198	(C₂×D₉)⋊C₄	—	6	6	no	—
199	C₄⋊Dic₉	—	3	6	no	—
200	D₇₂	—	3	12	no	—
201	C₂²×C₃³	C₂×D₁₂	1	1	yes	characteristic
202	C₂×C₃×C₃⋊D₃	—	6	4	no	—
203	C₂×C₃×C₃⋊D₃	—	12	2	no	—
204	C₂×C₃×C₃⋊D₃	—	12	2	no	—
205	C₃³×C₄	—	2	2	no	—
206	C₃³×C₄	C₂×C₄×D₃	1	1	yes	characteristic
207	C₃³×C₄	#235	1	1	yes	characteristic
208	C₃×C₃⋊Dic₃	—	12	2	no	—
209	C₂²×3₋¹⁺²	—	2	3	no	—
210	C₂²×3₋¹⁺²	C₂×D₁₂	1	3	yes	—
211	C₂²×C₃×C₉	—	2	1	no	—
212	C₂²×C₃×C₉	C₂×C₃×D₄	1	1	yes	characteristic
213	C₂×C₃⋊D₉	—	2	4	no	—
214	C₂×C₃⋊D₉	—	4	2	no	—
215	C₂×C₃⋊D₉	—	4	2	no	—
216	C₂×AGL(1,ℤ/9)	—	6	12	no	—
217	C₂×AGL(1,ℤ/9)	—	12	6	no	—
218	C₂×AGL(1,ℤ/9)	—	12	6	no	—
219	C₄×3₋¹⁺²	—	2	3	no	—
220	C₄×3₋¹⁺²	—	2	3	no	—
221	C₄×3₋¹⁺²	—	2	6	no	—
222	C₄×3₋¹⁺²	—	4	6	no	—
223	C₄×3₋¹⁺²	C₂×C₄×D₃	1	3	yes	—
224	C₄×3₋¹⁺²	#235	1	3	yes	—
225	C₃×C₄×C₉	—	2	1	no	—
226	C₃×C₄×C₉	—	2	1	no	—
227	C₃×C₄×C₉	—	2	2	no	—
228	C₃×C₄×C₉	—	4	2	no	—
229	C₃×C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₃×C₄×C₉	C₃×#41	1	1	yes	characteristic
231	C₃⋊Dic₉	—	4	2	no	—
232	3₋¹⁺²⋊C₄	—	12	6	no	—
233	C₂×C₃×D₈	—	27	1	no	—
234	C₃×C₄×D₄	—	27	2	no	—
235	C₂×D₂₄	—	9	1	no	—
236	C₂×D₂₄	—	9	2	no	—
237	C₂×D₂₄	—	9	1	no	—
238	C₄×D₁₂	—	9	2	no	—
239	C₄×D₁₂	—	9	4	no	—
240	C₄×D₁₂	—	9	2	no	—
241	C₃×#106	—	27	1	no	—
242	C₃×#102	—	27	2	no	—
243	C₃×#97	—	3	1	no	—
244	C₃×#97	—	6	1	no	—
245	C₃×#97	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
246	C₃×#97	AGL(1,ℤ/9)	1	2	yes	complemented
247	C₃×#97	C₃×C₃⋊D₃	1	1	yes	characteristic
248	#821	—	9	2	no	—
249	#821	—	9	4	no	—
250	#821	—	9	2	no	—
251	#817	—	9	1	no	—
252	#817	—	9	2	no	—
253	#817	—	9	1	no	—
254	C₃×3₋¹⁺²	#442	1	1	yes	characteristic, complemented, Sylow
255	C₂²×C₃⋊D₃	—	6	2	no	—
256	C₂²×C₃×D₃	—	18	2	no	—
257	C₂²×C₃×D₃	—	18	4	no	—
258	C₂²×C₃×D₃	—	18	2	no	—
259	C₂×C₃²×C₄	—	2	2	no	—
260	C₂×C₃²×C₄	—	2	1	no	—
261	C₂×C₃²×C₄	—	3	2	no	—
262	C₂×C₃²×C₄	—	3	1	no	—
263	C₂×C₃²×C₄	—	6	4	no	—
264	C₂×C₃²×C₄	—	6	2	no	—
265	C₂×C₃²×C₄	C₃×D₁₂	1	2	yes	—
266	C₂×C₃²×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
267	C₂×C₃²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
268	C₂×C₃²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
269	C₂×C₃⋊Dic₃	—	6	2	no	—
270	C₄⋊(C₃⋊D₃)	—	3	4	no	—
271	C₄⋊(C₃⋊D₃)	—	6	2	no	—
272	C₄×C₃⋊D₃	—	12	4	no	—
273	C₂×C₃×Dic₃	—	18	2	no	—
274	C₂×C₃×Dic₃	—	18	4	no	—
275	C₂×C₃×Dic₃	—	18	2	no	—
276	C₃×D₁₂	—	9	4	no	—
277	C₃×D₁₂	—	9	8	no	—
278	C₃×D₁₂	—	9	4	no	—
279	C₃×D₁₂	—	18	2	no	—
280	C₃×D₁₂	—	18	4	no	—
281	C₃×D₁₂	—	18	2	no	—
282	C₃×C₄×D₃	—	36	4	no	—
283	C₃×C₄×D₃	—	36	4	no	—
284	C₃×C₄×D₃	—	36	8	no	—
285	C₂²×D₉	—	6	6	no	—
286	C₃²×C₈	—	2	1	no	—
287	C₃²×C₈	—	2	2	no	—
288	C₃²×C₈	—	2	1	no	—
289	C₃²×C₈	—	2	2	no	—
290	C₃²×C₈	—	3	2	no	—
291	C₃²×C₈	—	6	1	no	—
292	C₃²×C₈	—	6	2	no	—
293	C₃²×C₈	—	6	4	no	—
294	C₃²×C₈	C₃×C₄×D₃	1	2	yes	—
295	C₃²×C₈	C₄×C₃⋊D₃	1	2	yes	—
296	C₂×C₄×C₉	—	2	6	no	—
297	C₂×C₄×C₉	—	2	3	no	—
298	C₂×C₄×C₉	C₃×D₁₂	1	6	yes	—
299	C₂×C₄×C₉	C₂²×C₃×D₃	1	3	yes	—
300	C₂×Dic₉	—	6	6	no	—
301	D₃₆	—	3	12	no	—
302	D₃₆	—	6	6	no	—
303	C₄×D₉	—	12	12	no	—
304	C₈×C₉	—	2	6	no	—
305	C₈×C₉	—	2	3	no	—
306	C₈×C₉	—	2	6	no	—
307	C₈×C₉	C₃×C₄×D₃	1	6	yes	complemented
308	#442	—	27	1	no	Sylow
309	C₂×C₃³	C₄×D₁₂	1	1	yes	characteristic
310	C₂×C₃³	#908	1	2	yes	—
311	C₃×C₃⋊D₃	—	12	4	no	—
312	C₂×3₋¹⁺²	—	2	6	no	—
313	C₂×3₋¹⁺²	—	2	3	no	—
314	C₂×3₋¹⁺²	C₄×D₁₂	1	3	yes	—
315	C₂×3₋¹⁺²	#908	1	6	yes	—
316	C₂×C₃×C₉	—	2	2	no	—
317	C₂×C₃×C₉	—	2	1	no	—
318	C₂×C₃×C₉	C₃×C₄×D₄	1	1	yes	characteristic
319	C₂×C₃×C₉	C₃×AGL(1,ℤ/8)	1	2	yes	—
320	C₃⋊D₉	—	4	4	no	—
321	AGL(1,ℤ/9)	—	12	12	no	—
322	C₂×C₃×D₄	—	27	2	no	—
323	C₂²×C₃×C₄	—	54	2	no	—
324	C₂×D₁₂	—	9	2	no	—
325	C₂×D₁₂	—	9	4	no	—
326	C₂×D₁₂	—	9	2	no	—
327	C₂×C₄×D₃	—	18	2	no	—
328	C₂×C₄×D₃	—	18	4	no	—
329	C₂×C₄×D₃	—	18	2	no	—
330	C₃×D₈	—	27	4	no	—
331	C₂×C₃×C₈	—	3	1	no	—
332	C₂×C₃×C₈	—	3	1	no	—
333	C₂×C₃×C₈	—	6	1	no	—
334	C₂×C₃×C₈	—	6	1	no	—
335	C₂×C₃×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
336	C₂×C₃×C₈	C₂×AGL(1,ℤ/9)	1	2	yes	—
337	C₂×C₃×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
338	C₂×C₃×C₈	C₂×AGL(1,ℤ/9)	1	2	yes	—
339	C₂×C₃×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
340	C₂×C₃×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
341	C₃×C₄⋊C₄	—	27	2	no	—
342	C₃×C₂²⋊C₄	—	54	2	no	—
343	C₃×C₄²	—	3	1	no	—
344	C₃×C₄²	—	6	1	no	—
345	C₃×C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
346	C₃×C₄²	C₂×AGL(1,ℤ/9)	1	2	yes	—
347	C₃×C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
348	(C₂×D₃)⋊C₄	—	18	2	no	—
349	(C₂×D₃)⋊C₄	—	18	4	no	—
350	(C₂×D₃)⋊C₄	—	18	2	no	—
351	C₄⋊Dic₃	—	9	2	no	—
352	C₄⋊Dic₃	—	9	4	no	—
353	C₄⋊Dic₃	—	9	2	no	—
354	D₂₄	—	9	4	no	—
355	D₂₄	—	9	8	no	—
356	D₂₄	—	9	4	no	—
357	C₂²×C₃²	—	2	1	no	—
358	C₂²×C₃²	—	3	1	no	—
359	C₂²×C₃²	—	6	2	no	—
360	C₂²×C₃²	C₂×C₃×D₁₂	1	1	yes	characteristic
361	C₂²×C₃²	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
362	C₂×C₃⋊D₃	—	6	4	no	—
363	C₂×C₃⋊D₃	—	12	2	no	—
364	C₂×C₃⋊D₃	—	12	2	no	—
365	C₂×C₃×D₃	—	18	4	no	—
366	C₂×C₃×D₃	—	18	8	no	—
367	C₂×C₃×D₃	—	18	4	no	—
368	C₂×C₃×D₃	—	36	2	no	—
369	C₂×C₃×D₃	—	36	2	no	—
370	C₂×C₃×D₃	—	36	4	no	—
371	C₂×C₃×D₃	—	36	4	no	—
372	C₂×C₃×D₃	—	36	2	no	—
373	C₂×C₃×D₃	—	36	2	no	—
374	C₃²×C₄	—	2	2	no	—
375	C₃²×C₄	—	2	2	no	—
376	C₃²×C₄	—	2	1	no	—
377	C₃²×C₄	—	2	1	no	—
378	C₃²×C₄	—	3	1	no	—
379	C₃²×C₄	—	3	1	no	—
380	C₃²×C₄	—	4	2	no	—
381	C₃²×C₄	—	6	2	no	—
382	C₃²×C₄	—	6	2	no	—
383	C₃²×C₄	—	6	2	no	—
384	C₃²×C₄	—	12	4	no	—
385	C₃²×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
386	C₃²×C₄	C₃×#235	1	1	yes	characteristic
387	C₃²×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
388	C₃²×C₄	#3828	1	1	yes	characteristic
389	C₃⋊Dic₃	—	12	2	no	—
390	C₃×Dic₃	—	36	2	no	—
391	C₃×Dic₃	—	36	4	no	—
392	C₃×Dic₃	—	36	2	no	—
393	C₂²×C₉	—	2	3	no	—
394	C₂²×C₉	C₂×C₃×D₁₂	1	3	yes	—
395	C₂×D₉	—	6	12	no	—
396	C₂×D₉	—	12	6	no	—
397	C₂×D₉	—	12	6	no	—
398	C₄×C₉	—	2	6	no	—
399	C₄×C₉	—	2	3	no	—
400	C₄×C₉	—	2	3	no	—
401	C₄×C₉	—	4	6	no	—
402	C₄×C₉	C₂×C₃×C₄×D₃	1	3	yes	—
403	C₄×C₉	C₃×#235	1	3	yes	—
404	Dic₉	—	12	6	no	—
405	C₂×D₈	—	27	1	no	—
406	C₄×D₄	—	27	2	no	—
407	#106	—	27	1	no	—
408	#102	—	27	2	no	—
409	#97	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
410	C₃³	#4711	1	1	yes	characteristic
411	3₋¹⁺²	—	2	3	no	—
412	3₋¹⁺²	#4711	1	3	yes	complemented
413	C₃×C₉	—	2	1	no	—
414	C₃×C₉	C₃×#442	1	1	yes	characteristic, complemented
415	C₂³×C₃	—	54	2	no	—
416	C₂²×D₃	—	18	2	no	—
417	C₂²×D₃	—	18	4	no	—
418	C₂²×D₃	—	18	2	no	—
419	C₃×D₄	—	27	4	no	—
420	C₃×D₄	—	54	2	no	—
421	C₂×C₃×C₄	—	3	2	no	—
422	C₂×C₃×C₄	—	3	1	no	—
423	C₂×C₃×C₄	—	6	2	no	—
424	C₂×C₃×C₄	—	6	1	no	—
425	C₂×C₃×C₄	—	54	2	no	—
426	C₂×C₃×C₄	—	108	4	no	—
427	C₂×C₃×C₄	C₄⋊AGL(1,ℤ/9)	1	2	yes	—
428	C₂×C₃×C₄	C₄⋊AGL(1,ℤ/9)	1	4	yes	—
429	C₂×C₃×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
430	C₂×C₃×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
431	C₂×C₃×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
432	C₂×C₃×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
433	C₂×Dic₃	—	18	2	no	—
434	C₂×Dic₃	—	18	4	no	—
435	C₂×Dic₃	—	18	2	no	—
436	D₁₂	—	9	4	no	—
437	D₁₂	—	9	8	no	—
438	D₁₂	—	9	4	no	—
439	D₁₂	—	18	2	no	—
440	D₁₂	—	18	4	no	—
441	D₁₂	—	18	2	no	—
442	C₄×D₃	—	36	4	no	—
443	C₄×D₃	—	36	4	no	—
444	C₄×D₃	—	36	8	no	—
445	C₃×C₈	—	2	1	no	—
446	C₃×C₈	—	2	2	no	—
447	C₃×C₈	—	2	1	no	—
448	C₃×C₈	—	3	2	no	—
449	C₃×C₈	—	6	1	no	—
450	C₃×C₈	—	6	2	no	—
451	C₃×C₈	—	6	2	no	—
452	C₃×C₈	C₄×AGL(1,ℤ/9)	1	2	yes	complemented
453	C₃×C₈	C₄×AGL(1,ℤ/9)	1	4	yes	complemented
454	C₃×C₈	C₃×C₄×C₃⋊D₃	1	2	yes	—
455	C₂×C₃²	—	2	1	no	—
456	C₂×C₃²	—	2	2	no	—
457	C₂×C₃²	—	3	2	no	—
458	C₂×C₃²	—	3	1	no	—
459	C₂×C₃²	—	6	4	no	—
460	C₂×C₃²	—	6	2	no	—
461	C₂×C₃²	C₃×C₄×D₁₂	1	1	yes	characteristic
462	C₂×C₃²	C₃×#908	1	2	yes	—
463	C₂×C₃²	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
464	C₂×C₃²	#64117	1	2	yes	—
465	C₃⋊D₃	—	12	4	no	—
466	C₃×D₃	—	36	4	no	—
467	C₃×D₃	—	36	8	no	—
468	C₃×D₃	—	36	4	no	—
469	C₂×C₉	—	2	3	no	—
470	C₂×C₉	—	2	6	no	—
471	C₂×C₉	C₃×C₄×D₁₂	1	3	yes	—
472	C₂×C₉	C₃×#908	1	6	yes	—
473	D₉	—	12	12	no	—
474	C₂×D₄	—	27	2	no	—
475	C₂²×C₄	—	54	2	no	—
476	D₈	—	27	4	no	—
477	C₂×C₈	C₂×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
478	C₂×C₈	C₂×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
479	C₄⋊C₄	—	27	2	no	—
480	C₂²⋊C₄	—	54	2	no	—
481	C₄²	C₂×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
482	C₂²×C₃	—	3	1	no	—
483	C₂²×C₃	—	6	1	no	—
484	C₂²×C₃	—	54	4	no	—
485	C₂²×C₃	—	108	2	no	—
486	C₂²×C₃	—	108	2	no	—
487	C₂²×C₃	C₂×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
488	C₂²×C₃	C₂×C₄⋊AGL(1,ℤ/9)	1	2	yes	—
489	C₂²×C₃	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
490	C₂×D₃	—	18	4	no	—
491	C₂×D₃	—	18	4	no	—
492	C₂×D₃	—	18	8	no	—
493	C₂×D₃	—	36	2	no	—
494	C₂×D₃	—	36	4	no	—
495	C₂×D₃	—	36	2	no	—
496	C₂×D₃	—	36	4	no	—
497	C₂×D₃	—	36	2	no	—
498	C₂×D₃	—	36	2	no	—
499	C₃×C₄	—	2	2	no	—
500	C₃×C₄	—	2	4	no	—
501	C₃×C₄	—	2	2	no	—
502	C₃×C₄	—	3	1	no	—
503	C₃×C₄	—	3	1	no	—
504	C₃×C₄	—	6	2	no	—
505	C₃×C₄	—	6	1	no	—
506	C₃×C₄	—	6	1	no	—
507	C₃×C₄	—	12	2	no	—
508	C₃×C₄	—	108	2	no	—
509	C₃×C₄	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
510	C₃×C₄	C₂×C₄×AGL(1,ℤ/9)	1	2	yes	—
511	C₃×C₄	#3697⋊C₃	1	1	yes	characteristic
512	C₃×C₄	#3697⋊C₃	1	2	yes	—
513	C₃×C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
514	C₃×C₄	C₃×#3828	1	1	yes	characteristic
515	Dic₃	—	36	2	no	—
516	Dic₃	—	36	4	no	—
517	Dic₃	—	36	2	no	—
518	C₃²	—	2	1	no	—
519	C₃²	—	3	1	no	—
520	C₃²	—	6	2	no	—
521	C₃²	C₃×#4711	1	1	yes	characteristic
522	C₃²	#10592410	1	1	yes	characteristic
523	C₉	—	2	3	no	—
524	C₉	C₃×#4711	1	3	yes	complemented
525	C₂³	—	54	2	no	—
526	D₄	—	27	4	no	—
527	D₄	—	54	2	no	—
528	C₂×C₄	—	54	2	no	—
529	C₂×C₄	—	108	4	no	—
530	C₂×C₄	C₄⋊(C₃⋊AGL(1,ℤ/9))	1	2	yes	—
531	C₂×C₄	C₂²×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
532	C₈	—	2	1	no	—
533	C₈	C₄×C₃⋊AGL(1,ℤ/9)	1	2	yes	complemented
534	C₂×C₃	—	3	1	no	—
535	C₂×C₃	—	3	2	no	—
536	C₂×C₃	—	6	1	no	—
537	C₂×C₃	—	6	2	no	—
538	C₂×C₃	—	108	4	no	—
539	C₂×C₃	C₄×C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
540	C₂×C₃	C₄×C₄⋊AGL(1,ℤ/9)	1	2	yes	—
541	C₂×C₃	#63470⋊C₃	1	2	yes	—
542	C₂×C₃	#63470⋊C₃	1	4	yes	—
543	C₂×C₃	C₃×C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
544	C₂×C₃	C₃×#64117	1	2	yes	—
545	D₃	—	36	4	no	—
546	D₃	—	36	8	no	—
547	D₃	—	36	4	no	—
548	C₂²	—	54	4	no	—
549	C₂²	—	108	2	no	—
550	C₂²	—	108	2	no	—
551	C₂²	C₂×C₄⋊(C₃⋊AGL(1,ℤ/9))	1	1	yes	characteristic
552	C₄	—	2	2	no	—
553	C₄	—	108	2	no	—
554	C₄	C₂×C₄×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
555	C₄	#13048900	1	1	yes	characteristic
556	C₃	—	3	1	no	—
557	C₃	—	6	1	no	—
558	C₃	#10588392⋊C₃	1	1	yes	characteristic, complemented
559	C₃	#10588392⋊C₃	1	2	yes	complemented
560	C₃	C₃×#10592410	1	1	yes	characteristic
561	C₂	—	108	4	no	—
562	C₂	C₄×C₄⋊(C₃⋊AGL(1,ℤ/9))	1	1	yes	characteristic
563	C₂	#72254718	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊(C₃⋊AGL(1,ℤ/9))
commutator	C₃×C₄×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₃×3₋¹⁺²×#97	C₂
socle	C₂²×C₃²	C₂×C₃×D₁₂
prime radical	C₂×#13047909	C₂
cosocle	C₂×C₃×C₄×C₉	C₂³×C₃
hypercenter	#97	C₃⋊AGL(1,ℤ/9)
hypocenter	C₃×C₉	C₃×#442
LCS	G ▷ C₃×C₄×C₉ ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. #72254713	C₂	semidirect
2. C₄×C₄⋊(C₃⋊AGL(1,ℤ/9))	C₂	semidirect
4. #72254651	C₂	semidirect
5. C₃×3₋¹⁺²×#97	C₂	semidirect
7. #13143798	C₃	semidirect
16. #13047909	C₄	semidirect
23. C₄×C₄⋊(C₃⋊D₉)	C₂×C₃	semidirect
27. 3₋¹⁺²×#97	D₃	semidirect
29. C₃×C₉×#97	C₂×C₃	semidirect
30. #11720543	C₂×C₃	semidirect
31. #11720540	C₂×C₃	semidirect
39. C₄⋊(C₃⋊AGL(1,ℤ/9))	C₂×C₄	semidirect
42. C₃×C₈×3₋¹⁺²	C₂×C₄	semidirect
74. #88525	C₃×C₄	semidirect
110. C₉×#97	C₃×D₃	semidirect
134. C₄⋊(C₃⋊D₉)	C₂×C₃×C₄	semidirect
143. C₈×3₋¹⁺²	C₄×D₃	semidirect
147. C₃×C₈×C₉	C₂×C₃×C₄	semidirect
245. C₃×#97	AGL(1,ℤ/9)	semidirect
246. C₃×#97	AGL(1,ℤ/9)	semidirect
254. C₃×3₋¹⁺²	#442	semidirect
307. C₈×C₉	C₃×C₄×D₃	semidirect
409. #97	C₃⋊AGL(1,ℤ/9)	semidirect
412. 3₋¹⁺²	#4711	semidirect
414. C₃×C₉	C₃×#442	semidirect
452. C₃×C₈	C₄×AGL(1,ℤ/9)	semidirect
453. C₃×C₈	C₄×AGL(1,ℤ/9)	semidirect
524. C₉	C₃×#4711	semidirect
533. C₈	C₄×C₃⋊AGL(1,ℤ/9)	semidirect
558. C₃	#10588392⋊C₃	semidirect
559. C₃	#10588392⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#72254713	2
C₄×C₄⋊(C₃⋊AGL(1,ℤ/9))	2
C₂×#13047909	2
#72254651	2
C₃×3₋¹⁺²×#97	2
C₃×#10592410	3
#13143798	3
#10588392⋊C₃	3