Subgroups — #10589791⋊C₃ #13153196

Order 1728.

646 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	#63459⋊C₃	C₂	1	2	yes	maximal
3	#63458⋊C₃	C₂	1	2	yes	maximal
4	#63454⋊C₃	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
6	#63452⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63451⋊C₃	C₂	1	2	yes	maximal, complemented
8	#63450⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63450⋊C₃	C₂	1	2	yes	maximal, complemented
10	#63434⋊C₃	C₂	1	1	yes	maximal, characteristic
11	#63431⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5689	—	3	1	no	maximal
13	#10589791	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
15	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
16	C₂×3₋¹⁺²⋊Q₈	C₂²	1	2	yes	—
17	C₂×3₋¹⁺²⋊Q₈	C₂²	1	2	yes	—
18	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
20	C₄⋊C₄×3₋¹⁺²	C₂²	1	2	yes	—
21	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
22	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
23	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
24	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
25	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
26	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
27	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
28	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	2	yes	—
29	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
30	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
31	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
32	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
33	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
34	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
35	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
36	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
37	C₃²×#125	D₃	1	1	yes	characteristic
38	C₃×#897	—	3	2	no	—
39	C₃×#896	—	3	2	no	—
40	C₃×#892	—	3	1	no	—
41	C₃×D₃×C₄⋊C₄	—	3	1	no	—
42	C₃×#890	—	3	1	no	—
43	C₃×#889	—	3	2	no	—
44	C₃×#888	—	3	2	no	—
45	C₃×#888	—	3	1	no	—
46	C₃×#872	—	3	1	no	—
47	C₃×#869	—	3	1	no	—
48	C₉×#125	—	2	1	no	—
49	C₉×#125	C₂×C₃	1	1	yes	characteristic, complemented
50	#63459	C₂×C₃	1	2	yes	—
51	#63458	C₂×C₃	1	2	yes	—
52	#63454	C₂×C₃	1	1	yes	characteristic
53	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic
54	#63452	C₂×C₃	1	1	yes	characteristic, complemented
55	#63451	C₂×C₃	1	2	yes	complemented
56	#63450	C₂×C₃	1	1	yes	characteristic, complemented
57	#63450	C₂×C₃	1	2	yes	complemented
58	#63434	C₂×C₃	1	1	yes	characteristic
59	#63431	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
61	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
62	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
63	C₂×C₄×3₋¹⁺²	C₂³	1	2	yes	—
64	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
65	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
66	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
68	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
69	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
71	C₄×AGL(1,ℤ/9)	—	4	2	no	—
72	C₄×AGL(1,ℤ/9)	Q₈	1	4	yes	complemented
73	3₋¹⁺²⋊Q₈	—	4	2	no	—
74	3₋¹⁺²⋊Q₈	—	4	2	no	—
75	C₃×#544	—	9	1	no	—
76	#5689	—	3	1	no	—
77	C₂×C₃×C₄×D₃	—	3	1	no	—
78	C₂×C₃×C₄×D₃	—	3	2	no	—
79	C₂×C₃×Dic₆	—	3	2	no	—
80	C₂×C₃×Dic₆	—	3	2	no	—
81	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
82	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
83	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
84	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
85	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
86	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
87	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
88	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
89	C₃×C₄⋊Dic₃	—	3	2	no	—
90	C₃×C₄⋊Dic₃	—	3	1	no	—
91	C₃×C₄⋊Dic₃	—	3	2	no	—
92	C₃×C₄⋊Dic₃	—	3	1	no	—
93	C₃×Dic₃⋊C₄	—	3	1	no	—
94	C₃×Dic₃⋊C₄	—	3	2	no	—
95	C₃×Dic₃⋊C₄	—	3	2	no	—
96	C₃×Dic₃⋊C₄	—	3	1	no	—
97	C₃×Dic₃⋊C₄	—	3	2	no	—
98	C₃×C₄×Dic₃	—	3	2	no	—
99	C₃×C₄×Dic₃	—	3	1	no	—
100	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
101	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
102	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
103	C₂×Dic₁₈	C₂²×C₃	1	2	yes	—
104	C₉×C₄⋊C₄	—	2	1	no	—
105	C₉×C₄⋊C₄	—	2	1	no	—
106	C₉×C₄⋊C₄	—	2	2	no	—
107	C₉×C₄⋊C₄	—	2	2	no	—
108	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
111	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₄²×C₉	—	2	1	no	—
113	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
114	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
117	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
118	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
119	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
120	C₄⋊Dic₉	C₂²×C₃	1	2	yes	—
121	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
122	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
124	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
125	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
126	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
127	C₄×Dic₉	C₂²×C₃	1	2	yes	—
128	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
129	C₂×AGL(1,ℤ/9)	—	2	1	no	—
130	C₂×AGL(1,ℤ/9)	—	2	1	no	—
131	C₂×AGL(1,ℤ/9)	C₂×Q₈	1	2	yes	—
132	C₄×3₋¹⁺²	—	2	1	no	—
133	C₄×3₋¹⁺²	—	2	2	no	—
134	C₄×3₋¹⁺²	—	2	2	no	—
135	C₄×3₋¹⁺²	—	2	1	no	—
136	C₄×3₋¹⁺²	C₂×Q₈	1	2	yes	—
137	3₋¹⁺²⋊C₄	—	2	1	no	—
138	3₋¹⁺²⋊C₄	—	2	2	no	—
139	3₋¹⁺²⋊C₄	—	2	2	no	—
140	3₋¹⁺²⋊C₄	—	2	1	no	—
141	3₋¹⁺²⋊C₄	C₂×Q₈	1	2	yes	—
142	C₃×C₄⋊Q₈	—	9	1	no	—
143	C₃×C₄⋊Q₈	—	9	1	no	—
144	C₃×C₄⋊Q₈	—	9	2	no	—
145	C₃×#125	—	3	1	no	—
146	C₃×#125	—	9	2	no	—
147	C₃×#125	—	9	1	no	—
148	C₃×#125	C₃×D₃	1	1	yes	characteristic
149	C₃×C₂²⋊Q₈	—	9	2	no	—
150	C₃×C₂²⋊Q₈	—	9	2	no	—
151	C₃×#117	—	9	1	no	—
152	C₃×#117	—	9	1	no	—
153	C₂×C₃×C₄⋊C₄	—	9	1	no	—
154	#897	—	3	2	no	—
155	#896	—	3	2	no	—
156	#892	—	3	1	no	—
157	D₃×C₄⋊C₄	—	3	1	no	—
158	#890	—	3	1	no	—
159	#889	—	3	2	no	—
160	#888	—	3	1	no	—
161	#888	—	3	2	no	—
162	#872	—	3	1	no	—
163	#869	—	3	1	no	—
164	C₂²×C₃×D₃	—	3	1	no	—
165	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
166	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
167	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
169	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
170	C₂×C₃×Dic₃	—	3	1	no	—
171	C₂×C₃×Dic₃	—	3	1	no	—
172	C₂×C₃×Dic₃	—	3	2	no	—
173	C₂×C₃×Dic₃	—	3	1	no	—
174	C₂×C₃×Dic₃	—	3	2	no	—
175	C₃×C₄×D₃	—	3	4	no	—
176	C₃×C₄×D₃	—	12	2	no	—
177	C₃×Dic₆	—	12	2	no	—
178	C₃×Dic₆	—	12	2	no	—
179	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₄×C₉	—	2	1	no	—
181	C₂×C₄×C₉	—	2	1	no	—
182	C₂×C₄×C₉	—	2	1	no	—
183	C₂×C₄×C₉	—	2	2	no	—
184	C₂×C₄×C₉	—	2	2	no	—
185	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
186	C₂×C₄×C₉	C₂³×C₃	1	2	yes	—
187	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
188	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
190	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
191	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
192	C₂×Dic₉	C₂³×C₃	1	2	yes	—
193	C₂×Dic₉	C₂³×C₃	1	2	yes	—
194	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
195	C₄×D₉	—	4	2	no	—
196	C₄×D₉	C₃×Q₈	1	4	yes	complemented
197	Dic₁₈	—	4	2	no	—
198	Dic₁₈	—	4	2	no	—
199	#544	—	9	1	no	Sylow
200	C₂×3₋¹⁺²	C₂²×Q₈	1	1	yes	characteristic
201	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
203	AGL(1,ℤ/9)	—	2	2	no	—
204	C₂×C₃×Q₈	—	9	2	no	—
205	C₂×C₃×Q₈	—	9	2	no	—
206	C₂²×C₃×C₄	—	9	1	no	—
207	C₂²×C₃×C₄	—	9	2	no	—
208	C₂×C₄×D₃	—	3	1	no	—
209	C₂×C₄×D₃	—	3	2	no	—
210	C₂×Dic₆	—	3	2	no	—
211	C₂×Dic₆	—	3	2	no	—
212	C₃×C₄⋊C₄	—	3	1	no	—
213	C₃×C₄⋊C₄	—	3	1	no	—
214	C₃×C₄⋊C₄	—	3	2	no	—
215	C₃×C₄⋊C₄	—	3	2	no	—
216	C₃×C₄⋊C₄	—	9	2	no	—
217	C₃×C₄⋊C₄	—	9	1	no	—
218	C₃×C₄⋊C₄	—	9	1	no	—
219	C₃×C₄⋊C₄	—	9	2	no	—
220	C₃×C₄⋊C₄	—	9	2	no	—
221	C₃×C₄⋊C₄	—	9	1	no	—
222	C₃×C₄⋊C₄	—	9	1	no	—
223	C₃×C₄⋊C₄	—	9	2	no	—
224	C₃×C₄⋊C₄	—	9	2	no	—
225	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
226	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
227	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
228	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
229	C₃×C₂²⋊C₄	—	9	1	no	—
230	C₃×C₂²⋊C₄	—	9	1	no	—
231	C₃×C₂²⋊C₄	—	9	2	no	—
232	C₃×C₄²	—	3	1	no	—
233	C₃×C₄²	—	9	1	no	—
234	C₃×C₄²	—	9	2	no	—
235	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
236	(C₂×D₃)⋊C₄	—	3	1	no	—
237	(C₂×D₃)⋊C₄	—	3	1	no	—
238	(C₂×D₃)⋊C₄	—	3	2	no	—
239	C₄⋊Dic₃	—	3	1	no	—
240	C₄⋊Dic₃	—	3	2	no	—
241	C₄⋊Dic₃	—	3	1	no	—
242	C₄⋊Dic₃	—	3	2	no	—
243	Dic₃⋊C₄	—	3	1	no	—
244	Dic₃⋊C₄	—	3	1	no	—
245	Dic₃⋊C₄	—	3	2	no	—
246	Dic₃⋊C₄	—	3	2	no	—
247	Dic₃⋊C₄	—	3	2	no	—
248	C₄×Dic₃	—	3	1	no	—
249	C₄×Dic₃	—	3	2	no	—
250	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
251	C₂×C₃×D₃	—	3	2	no	—
252	C₂×C₃×D₃	—	6	1	no	—
253	C₂×C₃×D₃	—	6	1	no	—
254	C₃²×C₄	—	2	1	no	—
255	C₃²×C₄	—	2	2	no	—
256	C₃²×C₄	—	2	2	no	—
257	C₃²×C₄	—	2	1	no	—
258	C₃²×C₄	D₃×Q₈	1	2	yes	—
259	C₃×Dic₃	—	3	2	no	—
260	C₃×Dic₃	—	6	1	no	—
261	C₃×Dic₃	—	6	2	no	—
262	C₃×Dic₃	—	6	2	no	—
263	C₃×Dic₃	—	6	1	no	—
264	C₂²×C₉	—	2	1	no	—
265	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
266	C₂×D₉	—	2	1	no	—
267	C₂×D₉	—	2	1	no	—
268	C₂×D₉	C₂×C₃×Q₈	1	2	yes	—
269	C₄×C₉	—	2	1	no	—
270	C₄×C₉	—	2	2	no	—
271	C₄×C₉	—	2	2	no	—
272	C₄×C₉	—	2	1	no	—
273	C₄×C₉	—	2	2	no	—
274	C₄×C₉	—	4	1	no	—
275	C₄×C₉	—	4	2	no	—
276	C₄×C₉	—	4	1	no	—
277	C₄×C₉	—	4	2	no	—
278	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
279	Dic₉	—	2	1	no	—
280	Dic₉	—	2	2	no	—
281	Dic₉	—	2	2	no	—
282	Dic₉	—	2	1	no	—
283	Dic₉	C₂×C₃×Q₈	1	2	yes	—
284	C₄⋊Q₈	—	9	2	no	—
285	C₄⋊Q₈	—	9	1	no	—
286	C₄⋊Q₈	—	9	1	no	—
287	#125	—	9	2	no	—
288	#125	—	9	1	no	—
289	#125	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
290	C₂²⋊Q₈	—	9	2	no	—
291	C₂²⋊Q₈	—	9	2	no	—
292	#117	—	9	1	no	—
293	#117	—	9	1	no	—
294	C₂×C₄⋊C₄	—	9	1	no	—
295	3₋¹⁺²	#544	1	1	yes	characteristic, complemented, Sylow
296	C₂³×C₃	—	9	1	no	—
297	C₂²×D₃	—	3	1	no	—
298	C₃×Q₈	—	36	2	no	—
299	C₃×Q₈	—	36	2	no	—
300	C₂×C₃×C₄	—	3	1	no	—
301	C₂×C₃×C₄	—	3	1	no	—
302	C₂×C₃×C₄	—	3	1	no	—
303	C₂×C₃×C₄	—	3	2	no	—
304	C₂×C₃×C₄	—	3	2	no	—
305	C₂×C₃×C₄	—	9	4	no	—
306	C₂×C₃×C₄	—	9	1	no	—
307	C₂×C₃×C₄	—	9	1	no	—
308	C₂×C₃×C₄	—	9	1	no	—
309	C₂×C₃×C₄	—	9	2	no	—
310	C₂×C₃×C₄	—	9	2	no	—
311	C₂×C₃×C₄	—	36	2	no	—
312	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
313	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
314	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
317	C₂×Dic₃	—	3	1	no	—
318	C₂×Dic₃	—	3	1	no	—
319	C₂×Dic₃	—	3	1	no	—
320	C₂×Dic₃	—	3	2	no	—
321	C₂×Dic₃	—	3	2	no	—
322	C₄×D₃	—	3	4	no	—
323	C₄×D₃	—	12	2	no	—
324	Dic₆	—	12	2	no	—
325	Dic₆	—	12	2	no	—
326	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
327	C₂×C₃²	#1009	1	1	yes	characteristic
328	C₂×C₃²	#1010	1	1	yes	characteristic
329	C₃×D₃	—	6	2	no	—
330	C₂×C₉	—	2	1	no	—
331	C₂×C₉	—	2	1	no	—
332	C₂×C₉	—	2	1	no	—
333	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
334	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
336	D₉	—	2	2	no	—
337	C₂×Q₈	—	9	2	no	—
338	C₂×Q₈	—	9	2	no	—
339	C₂²×C₄	—	9	1	no	—
340	C₂²×C₄	—	9	2	no	—
341	C₄⋊C₄	—	9	2	no	—
342	C₄⋊C₄	—	9	1	no	—
343	C₄⋊C₄	—	9	1	no	—
344	C₄⋊C₄	—	9	1	no	—
345	C₄⋊C₄	—	9	1	no	—
346	C₄⋊C₄	—	9	2	no	—
347	C₄⋊C₄	—	9	2	no	—
348	C₄⋊C₄	—	9	2	no	—
349	C₄⋊C₄	—	9	2	no	—
350	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
351	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
352	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
353	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
354	C₂²⋊C₄	—	9	1	no	—
355	C₂²⋊C₄	—	9	2	no	—
356	C₂²⋊C₄	—	9	1	no	—
357	C₄²	—	9	2	no	—
358	C₄²	—	9	1	no	—
359	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
360	C₂²×C₃	—	3	1	no	—
361	C₂²×C₃	—	9	2	no	—
362	C₂²×C₃	—	18	1	no	—
363	C₂²×C₃	—	18	1	no	—
364	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
365	C₂×D₃	—	3	2	no	—
366	C₂×D₃	—	6	1	no	—
367	C₂×D₃	—	6	1	no	—
368	C₃×C₄	—	2	1	no	—
369	C₃×C₄	—	2	2	no	—
370	C₃×C₄	—	2	2	no	—
371	C₃×C₄	—	2	1	no	—
372	C₃×C₄	—	3	2	no	—
373	C₃×C₄	—	6	2	no	—
374	C₃×C₄	—	6	1	no	—
375	C₃×C₄	—	6	1	no	—
376	C₃×C₄	—	6	2	no	—
377	C₃×C₄	—	9	2	no	—
378	C₃×C₄	—	18	2	no	—
379	C₃×C₄	—	18	1	no	—
380	C₃×C₄	—	18	2	no	—
381	C₃×C₄	—	18	1	no	—
382	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
383	Dic₃	—	3	2	no	—
384	Dic₃	—	6	1	no	—
385	Dic₃	—	6	2	no	—
386	Dic₃	—	6	2	no	—
387	Dic₃	—	6	1	no	—
388	C₃²	#5689	1	1	yes	characteristic
389	C₉	—	2	1	no	—
390	C₉	C₃×#544	1	1	yes	characteristic, complemented
391	C₂³	—	9	1	no	—
392	Q₈	—	36	2	no	—
393	Q₈	—	36	2	no	—
394	C₂×C₄	—	9	1	no	—
395	C₂×C₄	—	9	4	no	—
396	C₂×C₄	—	9	1	no	—
397	C₂×C₄	—	9	1	no	—
398	C₂×C₄	—	9	2	no	—
399	C₂×C₄	—	9	2	no	—
400	C₂×C₄	—	36	2	no	—
401	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
402	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
403	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
404	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	2	yes	—
405	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
406	C₂×C₃	—	3	1	no	—
407	C₂×C₃	—	3	1	no	—
408	C₂×C₃	—	3	1	no	—
409	C₂×C₃	—	18	2	no	—
410	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
411	C₂×C₃	C₃×#1009	1	1	yes	characteristic
412	C₂×C₃	C₃×#1010	1	1	yes	characteristic
413	D₃	—	6	2	no	—
414	C₂²	—	9	2	no	—
415	C₂²	—	18	1	no	—
416	C₂²	—	18	1	no	—
417	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	1	no	—
422	C₄	—	9	2	no	—
423	C₄	—	18	2	no	—
424	C₄	—	18	1	no	—
425	C₄	—	18	2	no	—
426	C₄	—	18	1	no	—
427	C₄	Q₈×AGL(1,ℤ/9)	1	2	yes	—
428	C₃	—	3	1	no	—
429	C₃	C₃×#5689	1	1	yes	characteristic
430	C₂	—	18	2	no	—
431	C₂	C₂×Q₈×AGL(1,ℤ/9)	1	1	yes	characteristic
432	C₂	#11722641	1	1	yes	characteristic
433	C₂	#11722642	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×#125	C₂
prime radical	C₂²×AGL(1,ℤ/9)	C₂³
hypercenter	#125	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#544
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×#125	C₂	semidirect
6. #63452⋊C₃	C₂	semidirect
7. #63451⋊C₃	C₂	semidirect
8. #63450⋊C₃	C₂	semidirect
9. #63450⋊C₃	C₂	semidirect
11. #63431⋊C₃	C₂	semidirect
13. #10589791	C₃	semidirect
49. C₉×#125	C₂×C₃	semidirect
54. #63452	C₂×C₃	semidirect
55. #63451	C₂×C₃	semidirect
56. #63450	C₂×C₃	semidirect
57. #63450	C₂×C₃	semidirect
59. #63431	C₂×C₃	semidirect
72. C₄×AGL(1,ℤ/9)	Q₈	semidirect
196. C₄×D₉	C₃×Q₈	semidirect
289. #125	AGL(1,ℤ/9)	semidirect
295. 3₋¹⁺²	#544	semidirect
390. C₉	C₃×#544	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×#125	2
#63459⋊C₃	2
#63458⋊C₃	2
#63454⋊C₃	2
C₄⋊C₄×AGL(1,ℤ/9)	2
#63452⋊C₃	2
#63451⋊C₃	2
#63450⋊C₃	2
#63434⋊C₃	2
#63431⋊C₃	2
C₃×#5689	3
#10589791	3

Subgroups — #10589791⋊C3 #13153196

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589791⋊C₃ #13153196