Subgroups — #10589794⋊C₃ #13153199

Order 1728.

682 conjugacy classes of subgroups.

The subgroup lattice has 651 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	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63459⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63457⋊C₃	C₂	1	1	yes	maximal, characteristic
7	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63455⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
13	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#11721396	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5692	—	3	1	no	maximal
17	#10589794	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
21	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
22	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
23	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
24	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
25	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
26	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
29	C₄⋊C₄×3₋¹⁺²	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	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
33	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
34	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
35	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
36	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
37	(C₂×AGL(1,ℤ/9))⋊C₄	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	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
43	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	1	yes	characteristic
44	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
45	C₄⋊(3₋¹⁺²⋊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	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
51	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
53	C₃²×#125	D₃	1	1	yes	characteristic
54	C₃×#898	—	3	1	no	—
55	C₃×#897	—	3	1	no	—
56	C₃×#896	—	3	1	no	—
57	C₃×#896	—	3	1	no	—
58	C₃×#895	—	3	1	no	—
59	C₃×#894	—	3	1	no	—
60	C₃×#894	—	3	1	no	—
61	C₃×#894	—	3	1	no	—
62	C₃×#894	—	3	1	no	—
63	C₃×#893	—	3	1	no	—
64	C₃×D₃×C₄⋊C₄	—	3	1	no	—
65	C₃×#889	—	3	1	no	—
66	C₃×#876	—	3	1	no	—
67	C₃×C₄×D₁₂	—	3	1	no	—
68	C₉×#125	—	2	1	no	—
69	C₉×#125	C₂×C₃	1	1	yes	characteristic, complemented
70	#63460	C₂×C₃	1	1	yes	characteristic, complemented
71	#63459	C₂×C₃	1	1	yes	characteristic, complemented
72	#63458	C₂×C₃	1	1	yes	characteristic, complemented
73	#63458	C₂×C₃	1	1	yes	characteristic, complemented
74	#63457	C₂×C₃	1	1	yes	characteristic
75	#63456	C₂×C₃	1	1	yes	characteristic, complemented
76	#63456	C₂×C₃	1	1	yes	characteristic, complemented
77	#63456	C₂×C₃	1	1	yes	characteristic, complemented
78	#63456	C₂×C₃	1	1	yes	characteristic, complemented
79	#63455	C₂×C₃	1	1	yes	characteristic, complemented
80	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
81	#63451	C₂×C₃	1	1	yes	characteristic, complemented
82	#63438	C₂×C₃	1	1	yes	characteristic, complemented
83	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
85	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
86	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
87	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
88	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
89	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
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	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
99	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
100	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
101	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
102	C₄×AGL(1,ℤ/9)	—	2	2	no	—
103	C₄×AGL(1,ℤ/9)	—	4	1	no	—
104	C₄×AGL(1,ℤ/9)	—	4	1	no	—
105	C₄×AGL(1,ℤ/9)	—	4	1	no	—
106	C₄×AGL(1,ℤ/9)	—	4	1	no	—
107	3₋¹⁺²⋊Q₈	—	4	1	no	—
108	C₃×#539	—	9	1	no	—
109	#5692	—	3	1	no	—
110	C₂×C₃×D₁₂	—	3	1	no	—
111	C₂×C₃×D₁₂	—	3	1	no	—
112	C₂×C₃×D₁₂	—	3	1	no	—
113	C₂×C₃×C₄×D₃	—	3	1	no	—
114	C₂×C₃×C₄×D₃	—	3	1	no	—
115	C₂×C₃×C₄×D₃	—	3	1	no	—
116	C₂×C₃×C₄×D₃	—	3	1	no	—
117	C₂×C₃×C₄×D₃	—	3	1	no	—
118	C₂×C₃×Dic₆	—	3	1	no	—
119	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
120	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
121	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
122	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
123	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
125	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
126	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
127	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
128	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
129	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
130	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
131	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
132	C₃×(C₂×D₃)⋊C₄	—	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×C₄⋊Dic₃	—	3	1	no	—
137	C₃×C₄⋊Dic₃	—	3	1	no	—
138	C₃×Dic₃⋊C₄	—	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×C₄×Dic₃	—	3	1	no	—
145	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
146	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
153	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
154	C₉×C₄⋊C₄	—	2	1	no	—
155	C₉×C₄⋊C₄	—	2	1	no	—
156	C₉×C₄⋊C₄	—	2	1	no	—
157	C₉×C₄⋊C₄	—	2	1	no	—
158	C₉×C₄⋊C₄	—	2	1	no	—
159	C₉×C₄⋊C₄	—	2	1	no	—
160	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
163	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
164	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	C₄²×C₉	—	2	1	no	—
167	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
168	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
171	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	(C₂×D₉)⋊C₄	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	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
179	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
180	Dic₉⋊C₄	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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
187	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
188	C₂×AGL(1,ℤ/9)	—	2	1	no	—
189	C₂×AGL(1,ℤ/9)	—	2	1	no	—
190	C₂×AGL(1,ℤ/9)	—	2	1	no	—
191	C₂×AGL(1,ℤ/9)	—	2	1	no	—
192	C₂×AGL(1,ℤ/9)	—	2	1	no	—
193	C₂×AGL(1,ℤ/9)	—	2	1	no	—
194	C₂×AGL(1,ℤ/9)	—	2	1	no	—
195	C₂×AGL(1,ℤ/9)	—	2	1	no	—
196	C₂×AGL(1,ℤ/9)	#41	1	2	yes	—
197	C₄×3₋¹⁺²	—	2	1	no	—
198	C₄×3₋¹⁺²	—	2	1	no	—
199	C₄×3₋¹⁺²	—	2	1	no	—
200	C₄×3₋¹⁺²	—	2	1	no	—
201	C₄×3₋¹⁺²	—	2	1	no	—
202	C₄×3₋¹⁺²	—	2	1	no	—
203	C₄×3₋¹⁺²	—	2	1	no	—
204	3₋¹⁺²⋊C₄	—	2	1	no	—
205	3₋¹⁺²⋊C₄	—	2	1	no	—
206	3₋¹⁺²⋊C₄	—	2	1	no	—
207	3₋¹⁺²⋊C₄	—	2	1	no	—
208	3₋¹⁺²⋊C₄	—	2	1	no	—
209	C₃×#126	—	9	1	no	—
210	C₃×#126	—	9	1	no	—
211	C₃×#125	—	3	1	no	—
212	C₃×#125	—	9	1	no	—
213	C₃×#125	C₃×D₃	1	1	yes	characteristic
214	C₃×#123	—	9	1	no	—
215	C₃×#123	—	9	1	no	—
216	C₃×#123	—	9	1	no	—
217	C₃×#123	—	9	1	no	—
218	C₃×C₂²⋊Q₈	—	9	1	no	—
219	C₃×C₂²⋊Q₈	—	9	1	no	—
220	C₃×C₂²⋊Q₈	—	9	1	no	—
221	C₃×#121	—	9	1	no	—
222	C₃×C₄×D₄	—	9	1	no	—
223	C₃×C₄×D₄	—	9	1	no	—
224	C₂×C₃×C₄⋊C₄	—	9	1	no	—
225	#898	—	3	1	no	—
226	#897	—	3	1	no	—
227	#896	—	3	1	no	—
228	#896	—	3	1	no	—
229	#895	—	3	1	no	—
230	#894	—	3	1	no	—
231	#894	—	3	1	no	—
232	#894	—	3	1	no	—
233	#894	—	3	1	no	—
234	#893	—	3	1	no	—
235	D₃×C₄⋊C₄	—	3	1	no	—
236	#889	—	3	1	no	—
237	#876	—	3	1	no	—
238	C₄×D₁₂	—	3	1	no	—
239	C₂²×C₃×D₃	—	3	1	no	—
240	C₂²×C₃×D₃	—	3	1	no	—
241	C₂²×C₃×D₃	—	3	1	no	—
242	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
243	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
244	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
245	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
246	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
248	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
249	C₂×C₃×Dic₃	—	3	1	no	—
250	C₂×C₃×Dic₃	—	3	1	no	—
251	C₂×C₃×Dic₃	—	3	1	no	—
252	C₂×C₃×Dic₃	—	3	1	no	—
253	C₂×C₃×Dic₃	—	3	1	no	—
254	C₃×D₁₂	—	6	2	no	—
255	C₃×D₁₂	—	6	2	no	—
256	C₃×D₁₂	—	12	1	no	—
257	C₃×C₄×D₃	—	6	2	no	—
258	C₃×C₄×D₃	—	12	1	no	—
259	C₃×C₄×D₃	—	12	1	no	—
260	C₃×C₄×D₃	—	12	1	no	—
261	C₃×C₄×D₃	—	12	1	no	—
262	C₃×Dic₆	—	12	1	no	—
263	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
264	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
265	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₄×C₉	—	2	1	no	—
267	C₂×C₄×C₉	—	2	1	no	—
268	C₂×C₄×C₉	—	2	1	no	—
269	C₂×C₄×C₉	—	2	1	no	—
270	C₂×C₄×C₉	—	2	1	no	—
271	C₂×C₄×C₉	—	2	1	no	—
272	C₂×C₄×C₉	—	2	1	no	—
273	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
277	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
280	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
281	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
282	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
283	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
284	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
285	D₃₆	—	2	2	no	—
286	D₃₆	—	2	2	no	—
287	D₃₆	—	4	1	no	—
288	C₄×D₉	—	2	2	no	—
289	C₄×D₉	—	4	1	no	—
290	C₄×D₉	—	4	1	no	—
291	C₄×D₉	—	4	1	no	—
292	C₄×D₉	—	4	1	no	—
293	Dic₁₈	—	4	1	no	—
294	#539	—	9	1	no	Sylow
295	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
296	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
298	AGL(1,ℤ/9)	—	2	2	no	—
299	AGL(1,ℤ/9)	—	4	1	no	—
300	AGL(1,ℤ/9)	—	4	1	no	—
301	C₂×C₃×Q₈	—	9	1	no	—
302	C₂×C₃×D₄	—	9	1	no	—
303	C₂×C₃×D₄	—	9	1	no	—
304	C₂×C₃×D₄	—	9	1	no	—
305	C₂²×C₃×C₄	—	9	1	no	—
306	C₂²×C₃×C₄	—	9	1	no	—
307	C₂²×C₃×C₄	—	9	1	no	—
308	C₂²×C₃×C₄	—	9	1	no	—
309	C₂²×C₃×C₄	—	9	1	no	—
310	C₂×D₁₂	—	3	1	no	—
311	C₂×D₁₂	—	3	1	no	—
312	C₂×D₁₂	—	3	1	no	—
313	C₂×C₄×D₃	—	3	1	no	—
314	C₂×C₄×D₃	—	3	1	no	—
315	C₂×C₄×D₃	—	3	1	no	—
316	C₂×C₄×D₃	—	3	1	no	—
317	C₂×C₄×D₃	—	3	1	no	—
318	C₂×Dic₆	—	3	1	no	—
319	C₃×C₄⋊C₄	—	3	1	no	—
320	C₃×C₄⋊C₄	—	3	1	no	—
321	C₃×C₄⋊C₄	—	3	1	no	—
322	C₃×C₄⋊C₄	—	3	1	no	—
323	C₃×C₄⋊C₄	—	3	1	no	—
324	C₃×C₄⋊C₄	—	3	1	no	—
325	C₃×C₄⋊C₄	—	9	1	no	—
326	C₃×C₄⋊C₄	—	9	1	no	—
327	C₃×C₄⋊C₄	—	9	1	no	—
328	C₃×C₄⋊C₄	—	9	1	no	—
329	C₃×C₄⋊C₄	—	9	1	no	—
330	C₃×C₄⋊C₄	—	9	1	no	—
331	C₃×C₄⋊C₄	—	9	1	no	—
332	C₃×C₄⋊C₄	—	9	1	no	—
333	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
334	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
335	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
336	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
337	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
338	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
339	C₃×C₂²⋊C₄	—	9	1	no	—
340	C₃×C₂²⋊C₄	—	9	1	no	—
341	C₃×C₂²⋊C₄	—	9	1	no	—
342	C₃×C₂²⋊C₄	—	9	1	no	—
343	C₃×C₂²⋊C₄	—	9	1	no	—
344	C₃×C₂²⋊C₄	—	9	1	no	—
345	C₃×C₂²⋊C₄	—	9	1	no	—
346	C₃×C₂²⋊C₄	—	9	1	no	—
347	C₃×C₂²⋊C₄	—	9	1	no	—
348	C₃×C₂²⋊C₄	—	9	1	no	—
349	C₃×C₄²	—	3	1	no	—
350	C₃×C₄²	—	9	1	no	—
351	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
352	(C₂×D₃)⋊C₄	—	3	1	no	—
353	(C₂×D₃)⋊C₄	—	3	1	no	—
354	(C₂×D₃)⋊C₄	—	3	1	no	—
355	(C₂×D₃)⋊C₄	—	3	1	no	—
356	(C₂×D₃)⋊C₄	—	3	1	no	—
357	(C₂×D₃)⋊C₄	—	3	1	no	—
358	(C₂×D₃)⋊C₄	—	3	1	no	—
359	(C₂×D₃)⋊C₄	—	3	1	no	—
360	(C₂×D₃)⋊C₄	—	3	1	no	—
361	(C₂×D₃)⋊C₄	—	3	1	no	—
362	C₄⋊Dic₃	—	3	1	no	—
363	C₄⋊Dic₃	—	3	1	no	—
364	Dic₃⋊C₄	—	3	1	no	—
365	Dic₃⋊C₄	—	3	1	no	—
366	Dic₃⋊C₄	—	3	1	no	—
367	Dic₃⋊C₄	—	3	1	no	—
368	Dic₃⋊C₄	—	3	1	no	—
369	Dic₃⋊C₄	—	3	1	no	—
370	C₄×Dic₃	—	3	1	no	—
371	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
372	C₂×C₃×D₃	—	3	2	no	—
373	C₂×C₃×D₃	—	6	1	no	—
374	C₂×C₃×D₃	—	6	1	no	—
375	C₂×C₃×D₃	—	6	1	no	—
376	C₂×C₃×D₃	—	6	1	no	—
377	C₂×C₃×D₃	—	6	1	no	—
378	C₂×C₃×D₃	—	6	1	no	—
379	C₂×C₃×D₃	—	6	1	no	—
380	C₂×C₃×D₃	—	6	1	no	—
381	C₃²×C₄	—	2	1	no	—
382	C₃²×C₄	—	2	1	no	—
383	C₃²×C₄	—	2	1	no	—
384	C₃²×C₄	—	2	1	no	—
385	C₃²×C₄	—	2	1	no	—
386	C₃²×C₄	—	2	1	no	—
387	C₃²×C₄	—	2	1	no	—
388	C₃×Dic₃	—	6	1	no	—
389	C₃×Dic₃	—	6	1	no	—
390	C₃×Dic₃	—	6	1	no	—
391	C₃×Dic₃	—	6	1	no	—
392	C₃×Dic₃	—	6	1	no	—
393	C₂²×C₉	—	2	1	no	—
394	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
395	C₂×D₉	—	2	1	no	—
396	C₂×D₉	—	2	1	no	—
397	C₂×D₉	—	2	1	no	—
398	C₂×D₉	—	2	1	no	—
399	C₂×D₉	—	2	1	no	—
400	C₂×D₉	—	2	1	no	—
401	C₂×D₉	—	2	1	no	—
402	C₂×D₉	—	2	1	no	—
403	C₂×D₉	C₃×#41	1	2	yes	—
404	C₄×C₉	—	2	2	no	—
405	C₄×C₉	—	2	1	no	—
406	C₄×C₉	—	2	1	no	—
407	C₄×C₉	—	2	1	no	—
408	C₄×C₉	—	2	1	no	—
409	C₄×C₉	—	2	1	no	—
410	C₄×C₉	—	2	1	no	—
411	C₄×C₉	—	2	1	no	—
412	C₄×C₉	—	4	1	no	—
413	C₄×C₉	—	4	1	no	—
414	C₄×C₉	—	4	1	no	—
415	C₄×C₉	—	4	1	no	—
416	C₄×C₉	—	4	1	no	—
417	C₄×C₉	—	4	1	no	—
418	Dic₉	—	2	1	no	—
419	Dic₉	—	2	1	no	—
420	Dic₉	—	2	1	no	—
421	Dic₉	—	2	1	no	—
422	Dic₉	—	2	1	no	—
423	#126	—	9	1	no	—
424	#126	—	9	1	no	—
425	#125	—	9	1	no	—
426	#125	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
427	#123	—	9	1	no	—
428	#123	—	9	1	no	—
429	#123	—	9	1	no	—
430	#123	—	9	1	no	—
431	C₂²⋊Q₈	—	9	1	no	—
432	C₂²⋊Q₈	—	9	1	no	—
433	C₂²⋊Q₈	—	9	1	no	—
434	#121	—	9	1	no	—
435	C₄×D₄	—	9	1	no	—
436	C₄×D₄	—	9	1	no	—
437	C₂×C₄⋊C₄	—	9	1	no	—
438	3₋¹⁺²	#539	1	1	yes	characteristic, complemented, Sylow
439	C₂³×C₃	—	9	1	no	—
440	C₂³×C₃	—	9	1	no	—
441	C₂³×C₃	—	9	1	no	—
442	C₂²×D₃	—	3	1	no	—
443	C₂²×D₃	—	3	1	no	—
444	C₂²×D₃	—	3	1	no	—
445	C₃×Q₈	—	36	1	no	—
446	C₃×D₄	—	18	2	no	—
447	C₃×D₄	—	18	2	no	—
448	C₃×D₄	—	36	1	no	—
449	C₂×C₃×C₄	—	3	1	no	—
450	C₂×C₃×C₄	—	3	1	no	—
451	C₂×C₃×C₄	—	3	1	no	—
452	C₂×C₃×C₄	—	3	1	no	—
453	C₂×C₃×C₄	—	3	1	no	—
454	C₂×C₃×C₄	—	3	1	no	—
455	C₂×C₃×C₄	—	3	1	no	—
456	C₂×C₃×C₄	—	9	1	no	—
457	C₂×C₃×C₄	—	9	1	no	—
458	C₂×C₃×C₄	—	9	1	no	—
459	C₂×C₃×C₄	—	9	1	no	—
460	C₂×C₃×C₄	—	9	1	no	—
461	C₂×C₃×C₄	—	18	2	no	—
462	C₂×C₃×C₄	—	36	1	no	—
463	C₂×C₃×C₄	—	36	1	no	—
464	C₂×C₃×C₄	—	36	1	no	—
465	C₂×C₃×C₄	—	36	1	no	—
466	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
468	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
469	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
470	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
471	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
472	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
473	C₂×Dic₃	—	3	1	no	—
474	C₂×Dic₃	—	3	1	no	—
475	C₂×Dic₃	—	3	1	no	—
476	C₂×Dic₃	—	3	1	no	—
477	C₂×Dic₃	—	3	1	no	—
478	D₁₂	—	6	2	no	—
479	D₁₂	—	6	2	no	—
480	D₁₂	—	12	1	no	—
481	C₄×D₃	—	6	2	no	—
482	C₄×D₃	—	12	1	no	—
483	C₄×D₃	—	12	1	no	—
484	C₄×D₃	—	12	1	no	—
485	C₄×D₃	—	12	1	no	—
486	Dic₆	—	12	1	no	—
487	C₂×C₃²	#1007	1	1	yes	characteristic
488	C₂×C₃²	D₃×#41	1	1	yes	characteristic
489	C₂×C₃²	#1009	1	1	yes	characteristic
490	C₃×D₃	—	6	2	no	—
491	C₃×D₃	—	12	1	no	—
492	C₃×D₃	—	12	1	no	—
493	C₂×C₉	—	2	1	no	—
494	C₂×C₉	—	2	1	no	—
495	C₂×C₉	—	2	1	no	—
496	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
497	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
498	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
499	D₉	—	2	2	no	—
500	D₉	—	4	1	no	—
501	D₉	—	4	1	no	—
502	C₂×Q₈	—	9	1	no	—
503	C₂×D₄	—	9	1	no	—
504	C₂×D₄	—	9	1	no	—
505	C₂×D₄	—	9	1	no	—
506	C₂²×C₄	—	9	1	no	—
507	C₂²×C₄	—	9	1	no	—
508	C₂²×C₄	—	9	1	no	—
509	C₂²×C₄	—	9	1	no	—
510	C₂²×C₄	—	9	1	no	—
511	C₄⋊C₄	—	9	1	no	—
512	C₄⋊C₄	—	9	1	no	—
513	C₄⋊C₄	—	9	1	no	—
514	C₄⋊C₄	—	9	1	no	—
515	C₄⋊C₄	—	9	1	no	—
516	C₄⋊C₄	—	9	1	no	—
517	C₄⋊C₄	—	9	1	no	—
518	C₄⋊C₄	—	9	1	no	—
519	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
520	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
521	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
522	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
523	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
524	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
525	C₂²⋊C₄	—	9	1	no	—
526	C₂²⋊C₄	—	9	1	no	—
527	C₂²⋊C₄	—	9	1	no	—
528	C₂²⋊C₄	—	9	1	no	—
529	C₂²⋊C₄	—	9	1	no	—
530	C₂²⋊C₄	—	9	1	no	—
531	C₂²⋊C₄	—	9	1	no	—
532	C₂²⋊C₄	—	9	1	no	—
533	C₂²⋊C₄	—	9	1	no	—
534	C₂²⋊C₄	—	9	1	no	—
535	C₄²	—	9	1	no	—
536	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
537	C₂²×C₃	—	3	1	no	—
538	C₂²×C₃	—	9	2	no	—
539	C₂²×C₃	—	18	1	no	—
540	C₂²×C₃	—	18	1	no	—
541	C₂²×C₃	—	18	1	no	—
542	C₂²×C₃	—	18	1	no	—
543	C₂²×C₃	—	18	1	no	—
544	C₂²×C₃	—	18	1	no	—
545	C₂²×C₃	—	18	1	no	—
546	C₂²×C₃	—	18	1	no	—
547	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
548	C₂×D₃	—	3	2	no	—
549	C₂×D₃	—	6	1	no	—
550	C₂×D₃	—	6	1	no	—
551	C₂×D₃	—	6	1	no	—
552	C₂×D₃	—	6	1	no	—
553	C₂×D₃	—	6	1	no	—
554	C₂×D₃	—	6	1	no	—
555	C₂×D₃	—	6	1	no	—
556	C₂×D₃	—	6	1	no	—
557	C₃×C₄	—	2	1	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	2	1	no	—
561	C₃×C₄	—	2	1	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	6	1	no	—
565	C₃×C₄	—	6	1	no	—
566	C₃×C₄	—	6	1	no	—
567	C₃×C₄	—	6	1	no	—
568	C₃×C₄	—	6	1	no	—
569	C₃×C₄	—	6	1	no	—
570	C₃×C₄	—	6	1	no	—
571	C₃×C₄	—	18	1	no	—
572	C₃×C₄	—	18	1	no	—
573	C₃×C₄	—	18	1	no	—
574	C₃×C₄	—	18	1	no	—
575	C₃×C₄	—	18	1	no	—
576	Dic₃	—	6	1	no	—
577	Dic₃	—	6	1	no	—
578	Dic₃	—	6	1	no	—
579	Dic₃	—	6	1	no	—
580	Dic₃	—	6	1	no	—
581	C₃²	#5692	1	1	yes	characteristic
582	C₉	—	2	1	no	—
583	C₉	C₃×#539	1	1	yes	characteristic, complemented
584	C₂³	—	9	1	no	—
585	C₂³	—	9	1	no	—
586	C₂³	—	9	1	no	—
587	Q₈	—	36	1	no	—
588	D₄	—	18	2	no	—
589	D₄	—	18	2	no	—
590	D₄	—	36	1	no	—
591	C₂×C₄	—	9	1	no	—
592	C₂×C₄	—	9	1	no	—
593	C₂×C₄	—	9	1	no	—
594	C₂×C₄	—	9	1	no	—
595	C₂×C₄	—	9	1	no	—
596	C₂×C₄	—	18	2	no	—
597	C₂×C₄	—	36	1	no	—
598	C₂×C₄	—	36	1	no	—
599	C₂×C₄	—	36	1	no	—
600	C₂×C₄	—	36	1	no	—
601	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
602	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
603	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
604	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
605	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
606	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
607	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
608	C₂×C₃	—	3	1	no	—
609	C₂×C₃	—	3	1	no	—
610	C₂×C₃	—	3	1	no	—
611	C₂×C₃	—	18	2	no	—
612	C₂×C₃	—	36	1	no	—
613	C₂×C₃	—	36	1	no	—
614	C₂×C₃	C₃×#1007	1	1	yes	characteristic
615	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
616	C₂×C₃	C₃×#1009	1	1	yes	characteristic
617	D₃	—	6	2	no	—
618	D₃	—	12	1	no	—
619	D₃	—	12	1	no	—
620	C₂²	—	9	2	no	—
621	C₂²	—	18	1	no	—
622	C₂²	—	18	1	no	—
623	C₂²	—	18	1	no	—
624	C₂²	—	18	1	no	—
625	C₂²	—	18	1	no	—
626	C₂²	—	18	1	no	—
627	C₂²	—	18	1	no	—
628	C₂²	—	18	1	no	—
629	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	18	1	no	—
638	C₄	—	18	1	no	—
639	C₄	—	18	1	no	—
640	C₄	—	18	1	no	—
641	C₄	—	18	1	no	—
642	C₃	—	3	1	no	—
643	C₃	C₃×#5692	1	1	yes	characteristic
644	C₂	—	18	2	no	—
645	C₂	—	36	1	no	—
646	C₂	—	36	1	no	—
647	C₂	#11722630	1	1	yes	characteristic
648	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic
649	C₂	#11722641	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	#63457⋊C₃	C₂
hypercenter	#125	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#539
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
2. #63460⋊C₃	C₂	semidirect
3. #63459⋊C₃	C₂	semidirect
4. #63458⋊C₃	C₂	semidirect
5. #63458⋊C₃	C₂	semidirect
7. #63456⋊C₃	C₂	semidirect
8. #63456⋊C₃	C₂	semidirect
9. #63456⋊C₃	C₂	semidirect
10. #63456⋊C₃	C₂	semidirect
11. #63455⋊C₃	C₂	semidirect
12. C₄⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
13. #63451⋊C₃	C₂	semidirect
14. #11721396	C₂	semidirect
15. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
17. #10589794	C₃	semidirect
69. C₉×#125	C₂×C₃	semidirect
70. #63460	C₂×C₃	semidirect
71. #63459	C₂×C₃	semidirect
72. #63458	C₂×C₃	semidirect
73. #63458	C₂×C₃	semidirect
75. #63456	C₂×C₃	semidirect
76. #63456	C₂×C₃	semidirect
77. #63456	C₂×C₃	semidirect
78. #63456	C₂×C₃	semidirect
79. #63455	C₂×C₃	semidirect
80. C₄⋊C₄×D₉	C₂×C₃	semidirect
81. #63451	C₂×C₃	semidirect
82. #63438	C₂×C₃	semidirect
83. C₄×D₃₆	C₂×C₃	semidirect
426. #125	AGL(1,ℤ/9)	semidirect
438. 3₋¹⁺²	#539	semidirect
583. C₉	C₃×#539	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
#63460⋊C₃	2
#63459⋊C₃	2
#63458⋊C₃	2
#63457⋊C₃	2
#63456⋊C₃	2
#63455⋊C₃	2
C₄⋊C₄×AGL(1,ℤ/9)	2
#63451⋊C₃	2
#11721396	2
C₄×C₄⋊AGL(1,ℤ/9)	2
C₃×#5692	3
#10589794	3

Subgroups — #10589794⋊C3 #13153199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589794⋊C₃ #13153199