Subgroups — #10589804⋊C₃ #13153244

Order 1728.

666 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63450⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63449⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63449⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic
9	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic
10	(#611⋊C₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
11	#63441⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#63440⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#63439⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#63434⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5702	—	3	1	no	maximal
17	#10589804	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
19	C₂²×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
21	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
25	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
26	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
27	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
28	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
29	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
30	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
31	#3676⋊C₃	C₂²	1	1	yes	characteristic
32	#3676⋊C₃	C₂²	1	1	yes	characteristic
33	(C₂×AGL(1,ℤ/9))⋊C₄	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	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
39	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
40	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
41	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
42	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
43	(3₋¹⁺²⋊C₄)⋊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	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×3₋¹⁺²⋊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×#126	D₃	1	1	yes	characteristic
54	C₃×#898	—	3	1	no	—
55	C₃×#898	—	3	1	no	—
56	C₃×#896	—	3	1	no	—
57	C₃×#888	—	3	1	no	—
58	C₃×#887	—	3	1	no	—
59	C₃×#887	—	3	1	no	—
60	C₃×#885	—	3	1	no	—
61	C₃×#885	—	3	1	no	—
62	C₃×#67⋊C₄	—	3	1	no	—
63	C₃×#879	—	3	1	no	—
64	C₃×#878	—	3	1	no	—
65	C₃×#877	—	3	1	no	—
66	C₃×#872	—	3	1	no	—
67	C₃×C₄×Dic₆	—	3	1	no	—
68	C₉×#126	—	2	1	no	—
69	C₉×#126	C₂×C₃	1	1	yes	characteristic, complemented
70	#63460	C₂×C₃	1	1	yes	characteristic, complemented
71	#63460	C₂×C₃	1	1	yes	characteristic, complemented
72	#63458	C₂×C₃	1	1	yes	characteristic, complemented
73	#63450	C₂×C₃	1	1	yes	characteristic, complemented
74	#63449	C₂×C₃	1	1	yes	characteristic, complemented
75	#63449	C₂×C₃	1	1	yes	characteristic, complemented
76	#63447	C₂×C₃	1	1	yes	characteristic
77	#63447	C₂×C₃	1	1	yes	characteristic
78	#611⋊C₄	C₂×C₃	1	1	yes	characteristic
79	#63441	C₂×C₃	1	1	yes	characteristic, complemented
80	#63440	C₂×C₃	1	1	yes	characteristic, complemented
81	#63439	C₂×C₃	1	1	yes	characteristic, complemented
82	#63434	C₂×C₃	1	1	yes	characteristic, complemented
83	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
85	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
86	C₂×C₄×3₋¹⁺²	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	#611⋊C₃	—	2	2	no	—
93	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
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	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
101	C₄×AGL(1,ℤ/9)	—	2	2	no	—
102	3₋¹⁺²⋊Q₈	—	2	2	no	—
103	3₋¹⁺²⋊Q₈	—	2	2	no	—
104	3₋¹⁺²⋊Q₈	—	2	2	no	—
105	C₃×#556	—	9	1	no	—
106	#5702	—	3	1	no	—
107	C₂×C₃×#67	—	3	1	no	—
108	C₂²×C₃×Dic₃	—	3	1	no	—
109	C₂×C₃×C₄×D₃	—	3	1	no	—
110	C₂×C₃×Dic₆	—	3	1	no	—
111	C₂×C₃×Dic₆	—	3	1	no	—
112	C₂×C₃×Dic₆	—	3	1	no	—
113	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
114	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
115	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
116	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
117	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
119	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
120	C₃×#217	—	3	1	no	—
121	C₃×#217	—	3	1	no	—
122	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
123	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
124	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
125	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
126	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
127	C₃×C₄⋊Dic₃	—	3	1	no	—
128	C₃×C₄⋊Dic₃	—	3	1	no	—
129	C₃×Dic₃⋊C₄	—	3	1	no	—
130	C₃×Dic₃⋊C₄	—	3	1	no	—
131	C₃×Dic₃⋊C₄	—	3	1	no	—
132	C₃×Dic₃⋊C₄	—	3	1	no	—
133	C₃×Dic₃⋊C₄	—	3	1	no	—
134	C₃×Dic₃⋊C₄	—	3	1	no	—
135	C₃×Dic₃⋊C₄	—	3	1	no	—
136	C₃×C₄×Dic₃	—	3	1	no	—
137	C₃×C₄×Dic₃	—	3	1	no	—
138	C₃×C₄×Dic₃	—	3	1	no	—
139	C₃×C₄×Dic₃	—	3	1	no	—
140	C₃×C₄×Dic₃	—	3	1	no	—
141	C₃×C₄×Dic₃	—	3	1	no	—
142	C₂×#611	C₂²×C₃	1	1	yes	characteristic
143	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
145	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
146	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
147	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
148	C₉×C₄⋊C₄	—	2	1	no	—
149	C₉×C₄⋊C₄	—	2	1	no	—
150	C₉×C₄⋊C₄	—	2	1	no	—
151	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₉×C₂²⋊C₄	—	2	1	no	—
155	C₉×C₂²⋊C₄	—	2	1	no	—
156	C₉×C₂²⋊C₄	—	2	1	no	—
157	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
158	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
159	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
160	C₄²×C₉	—	2	1	no	—
161	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
162	#3676	C₂²×C₃	1	1	yes	characteristic
163	#3676	C₂²×C₃	1	1	yes	characteristic
164	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	(C₂×D₉)⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
170	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
171	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
172	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	Dic₉⋊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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
181	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
182	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
183	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
184	C₂²×3₋¹⁺²	—	2	1	no	—
185	C₂²×3₋¹⁺²	—	2	1	no	—
186	C₂²×3₋¹⁺²	—	2	1	no	—
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	C₄×3₋¹⁺²	—	2	1	no	—
192	C₄×3₋¹⁺²	—	2	1	no	—
193	C₄×3₋¹⁺²	—	2	1	no	—
194	C₄×3₋¹⁺²	—	2	1	no	—
195	C₄×3₋¹⁺²	—	2	1	no	—
196	C₄×3₋¹⁺²	—	2	1	no	—
197	3₋¹⁺²⋊C₄	—	2	1	no	—
198	3₋¹⁺²⋊C₄	—	2	1	no	—
199	3₋¹⁺²⋊C₄	—	2	1	no	—
200	3₋¹⁺²⋊C₄	—	2	1	no	—
201	3₋¹⁺²⋊C₄	—	2	1	no	—
202	3₋¹⁺²⋊C₄	#41	1	2	yes	—
203	3₋¹⁺²⋊C₄	#41	1	2	yes	—
204	C₃×C₄⋊Q₈	—	9	1	no	—
205	C₃×#126	—	3	1	no	—
206	C₃×#126	—	9	1	no	—
207	C₃×#126	—	9	1	no	—
208	C₃×#126	—	9	1	no	—
209	C₃×#126	C₃×D₃	1	1	yes	characteristic
210	C₃×#124	—	9	1	no	—
211	C₃×#124	—	9	1	no	—
212	C₃×C₂²⋊Q₈	—	9	1	no	—
213	C₃×C₂²⋊Q₈	—	9	1	no	—
214	C₃×C₄×Q₈	—	9	1	no	—
215	C₃×C₄×Q₈	—	9	1	no	—
216	C₃×C₄×Q₈	—	9	1	no	—
217	C₃×C₄×D₄	—	9	1	no	—
218	C₃×#117	—	9	1	no	—
219	C₃×#117	—	9	1	no	—
220	#898	—	3	1	no	—
221	#898	—	3	1	no	—
222	#896	—	3	1	no	—
223	#888	—	3	1	no	—
224	#887	—	3	1	no	—
225	#887	—	3	1	no	—
226	#885	—	3	1	no	—
227	#885	—	3	1	no	—
228	#67⋊C₄	—	3	1	no	—
229	#879	—	3	1	no	—
230	#878	—	3	1	no	—
231	#877	—	3	1	no	—
232	#872	—	3	1	no	—
233	C₄×Dic₆	—	3	1	no	—
234	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
235	C₂²×C₃×D₃	—	3	1	no	—
236	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
237	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
238	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
239	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
240	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
241	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
242	C₃×#67	—	6	2	no	—
243	C₂×C₃×Dic₃	—	3	1	no	—
244	C₂×C₃×Dic₃	—	3	1	no	—
245	C₂×C₃×Dic₃	—	3	1	no	—
246	C₂×C₃×Dic₃	—	3	1	no	—
247	C₂×C₃×Dic₃	—	3	1	no	—
248	C₂×C₃×Dic₃	—	3	1	no	—
249	C₂×C₃×Dic₃	—	3	1	no	—
250	C₂×C₃×Dic₃	—	6	2	no	—
251	C₃×C₄×D₃	—	6	2	no	—
252	C₃×Dic₆	—	6	2	no	—
253	C₃×Dic₆	—	6	2	no	—
254	C₃×Dic₆	—	6	2	no	—
255	C₂³×C₉	—	2	1	no	—
256	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
257	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₄×C₉	—	2	1	no	—
259	C₂×C₄×C₉	—	2	1	no	—
260	C₂×C₄×C₉	—	2	1	no	—
261	C₂×C₄×C₉	—	2	1	no	—
262	C₂×C₄×C₉	—	2	1	no	—
263	C₂×C₄×C₉	—	2	1	no	—
264	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
267	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
268	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
270	#611	—	2	2	no	—
271	C₂×Dic₉	—	2	2	no	—
272	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
273	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
274	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
275	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
276	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
277	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
278	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
279	C₄×D₉	—	2	2	no	—
280	Dic₁₈	—	2	2	no	—
281	Dic₁₈	—	2	2	no	—
282	Dic₁₈	—	2	2	no	—
283	#556	—	9	1	no	Sylow
284	C₂×3₋¹⁺²	—	4	1	no	—
285	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
286	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
287	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
288	AGL(1,ℤ/9)	—	4	1	no	—
289	C₂×C₃×Q₈	—	9	1	no	—
290	C₂×C₃×Q₈	—	9	1	no	—
291	C₂×C₃×Q₈	—	9	1	no	—
292	C₂×C₃×D₄	—	9	1	no	—
293	C₂²×C₃×C₄	—	9	1	no	—
294	C₂²×C₃×C₄	—	9	1	no	—
295	C₂×#67	—	3	1	no	—
296	C₂²×Dic₃	—	3	1	no	—
297	C₂×C₄×D₃	—	3	1	no	—
298	C₂×Dic₆	—	3	1	no	—
299	C₂×Dic₆	—	3	1	no	—
300	C₂×Dic₆	—	3	1	no	—
301	C₃×C₄⋊C₄	—	3	1	no	—
302	C₃×C₄⋊C₄	—	3	1	no	—
303	C₃×C₄⋊C₄	—	3	1	no	—
304	C₃×C₄⋊C₄	—	9	1	no	—
305	C₃×C₄⋊C₄	—	9	1	no	—
306	C₃×C₄⋊C₄	—	9	1	no	—
307	C₃×C₄⋊C₄	—	9	1	no	—
308	C₃×C₄⋊C₄	—	9	1	no	—
309	C₃×C₄⋊C₄	—	9	1	no	—
310	C₃×C₄⋊C₄	—	9	1	no	—
311	C₃×C₄⋊C₄	—	9	1	no	—
312	C₃×C₄⋊C₄	—	9	1	no	—
313	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
314	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
315	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
316	C₃×C₂²⋊C₄	—	3	1	no	—
317	C₃×C₂²⋊C₄	—	3	1	no	—
318	C₃×C₂²⋊C₄	—	3	1	no	—
319	C₃×C₂²⋊C₄	—	9	1	no	—
320	C₃×C₂²⋊C₄	—	9	1	no	—
321	C₃×C₂²⋊C₄	—	9	1	no	—
322	C₃×C₂²⋊C₄	—	9	1	no	—
323	C₃×C₂²⋊C₄	—	9	1	no	—
324	C₃×C₂²⋊C₄	—	9	1	no	—
325	C₃×C₂²⋊C₄	—	9	1	no	—
326	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
327	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
328	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
329	C₃×C₄²	—	3	1	no	—
330	C₃×C₄²	—	9	1	no	—
331	C₃×C₄²	—	9	1	no	—
332	C₃×C₄²	—	9	1	no	—
333	C₃×C₄²	—	9	1	no	—
334	C₃×C₄²	—	9	1	no	—
335	C₃×C₄²	—	9	1	no	—
336	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
337	#217	—	3	1	no	—
338	#217	—	3	1	no	—
339	(C₂×D₃)⋊C₄	—	3	1	no	—
340	(C₂×D₃)⋊C₄	—	3	1	no	—
341	(C₂×D₃)⋊C₄	—	3	1	no	—
342	(C₂×D₃)⋊C₄	—	3	1	no	—
343	(C₂×D₃)⋊C₄	—	3	1	no	—
344	C₄⋊Dic₃	—	3	1	no	—
345	C₄⋊Dic₃	—	3	1	no	—
346	Dic₃⋊C₄	—	3	1	no	—
347	Dic₃⋊C₄	—	3	1	no	—
348	Dic₃⋊C₄	—	3	1	no	—
349	Dic₃⋊C₄	—	3	1	no	—
350	Dic₃⋊C₄	—	3	1	no	—
351	Dic₃⋊C₄	—	3	1	no	—
352	Dic₃⋊C₄	—	3	1	no	—
353	C₄×Dic₃	—	3	1	no	—
354	C₄×Dic₃	—	3	1	no	—
355	C₄×Dic₃	—	3	1	no	—
356	C₄×Dic₃	—	3	1	no	—
357	C₄×Dic₃	—	3	1	no	—
358	C₄×Dic₃	—	3	1	no	—
359	C₂²×C₃²	—	2	1	no	—
360	C₂²×C₃²	—	2	1	no	—
361	C₂²×C₃²	—	2	1	no	—
362	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
363	C₂×C₃×D₃	—	6	1	no	—
364	C₂×C₃×D₃	—	6	1	no	—
365	C₂×C₃×D₃	—	6	1	no	—
366	C₃²×C₄	—	2	1	no	—
367	C₃²×C₄	—	2	1	no	—
368	C₃²×C₄	—	2	1	no	—
369	C₃²×C₄	—	2	1	no	—
370	C₃²×C₄	—	2	1	no	—
371	C₃²×C₄	—	2	1	no	—
372	C₃×Dic₃	—	3	2	no	—
373	C₃×Dic₃	—	3	2	no	—
374	C₃×Dic₃	—	6	1	no	—
375	C₃×Dic₃	—	6	1	no	—
376	C₃×Dic₃	—	6	1	no	—
377	C₃×Dic₃	—	6	1	no	—
378	C₃×Dic₃	—	6	1	no	—
379	C₂²×C₉	—	2	1	no	—
380	C₂²×C₉	—	2	1	no	—
381	C₂²×C₉	—	2	1	no	—
382	C₂²×C₉	—	2	1	no	—
383	C₂²×C₉	—	4	1	no	—
384	C₂²×C₉	—	4	1	no	—
385	C₂²×C₉	—	4	1	no	—
386	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
387	C₂×D₉	—	2	1	no	—
388	C₂×D₉	—	2	1	no	—
389	C₂×D₉	—	2	1	no	—
390	C₄×C₉	—	2	1	no	—
391	C₄×C₉	—	2	1	no	—
392	C₄×C₉	—	2	1	no	—
393	C₄×C₉	—	2	1	no	—
394	C₄×C₉	—	2	1	no	—
395	C₄×C₉	—	2	1	no	—
396	C₄×C₉	—	4	1	no	—
397	C₄×C₉	—	4	1	no	—
398	C₄×C₉	—	4	1	no	—
399	C₄×C₉	—	4	1	no	—
400	C₄×C₉	—	4	1	no	—
401	C₄×C₉	—	4	1	no	—
402	Dic₉	—	2	1	no	—
403	Dic₉	—	2	1	no	—
404	Dic₉	—	2	1	no	—
405	Dic₉	—	2	1	no	—
406	Dic₉	—	2	1	no	—
407	Dic₉	C₃×#41	1	2	yes	—
408	Dic₉	C₃×#41	1	2	yes	—
409	C₄⋊Q₈	—	9	1	no	—
410	#126	—	9	1	no	—
411	#126	—	9	1	no	—
412	#126	—	9	1	no	—
413	#126	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
414	#124	—	9	1	no	—
415	#124	—	9	1	no	—
416	C₂²⋊Q₈	—	9	1	no	—
417	C₂²⋊Q₈	—	9	1	no	—
418	C₄×Q₈	—	9	1	no	—
419	C₄×Q₈	—	9	1	no	—
420	C₄×Q₈	—	9	1	no	—
421	C₄×D₄	—	9	1	no	—
422	#117	—	9	1	no	—
423	#117	—	9	1	no	—
424	3₋¹⁺²	#556	1	1	yes	characteristic, complemented, Sylow
425	C₂³×C₃	—	3	1	no	—
426	C₂³×C₃	—	9	1	no	—
427	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
428	C₂²×D₃	—	3	1	no	—
429	C₃×Q₈	—	18	2	no	—
430	C₃×Q₈	—	18	2	no	—
431	C₃×Q₈	—	18	2	no	—
432	C₃×D₄	—	18	2	no	—
433	C₂×C₃×C₄	—	3	1	no	—
434	C₂×C₃×C₄	—	3	1	no	—
435	C₂×C₃×C₄	—	3	1	no	—
436	C₂×C₃×C₄	—	3	1	no	—
437	C₂×C₃×C₄	—	3	1	no	—
438	C₂×C₃×C₄	—	3	1	no	—
439	C₂×C₃×C₄	—	9	1	no	—
440	C₂×C₃×C₄	—	9	1	no	—
441	C₂×C₃×C₄	—	9	1	no	—
442	C₂×C₃×C₄	—	9	1	no	—
443	C₂×C₃×C₄	—	9	1	no	—
444	C₂×C₃×C₄	—	9	1	no	—
445	C₂×C₃×C₄	—	9	1	no	—
446	C₂×C₃×C₄	—	18	2	no	—
447	C₂×C₃×C₄	—	18	2	no	—
448	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
449	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
450	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
451	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
452	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
453	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
454	#67	—	6	2	no	—
455	C₂×Dic₃	—	3	1	no	—
456	C₂×Dic₃	—	3	1	no	—
457	C₂×Dic₃	—	3	1	no	—
458	C₂×Dic₃	—	3	1	no	—
459	C₂×Dic₃	—	3	1	no	—
460	C₂×Dic₃	—	3	1	no	—
461	C₂×Dic₃	—	3	1	no	—
462	C₂×Dic₃	—	6	2	no	—
463	C₄×D₃	—	6	2	no	—
464	Dic₆	—	6	2	no	—
465	Dic₆	—	6	2	no	—
466	Dic₆	—	6	2	no	—
467	C₂×C₃²	—	4	1	no	—
468	C₂×C₃²	D₃×#41	1	1	yes	characteristic
469	C₂×C₃²	D₃×#41	1	1	yes	characteristic
470	C₂×C₃²	#1010	1	1	yes	characteristic
471	C₃×D₃	—	12	1	no	—
472	C₂×C₉	—	2	1	no	—
473	C₂×C₉	—	2	1	no	—
474	C₂×C₉	—	2	1	no	—
475	C₂×C₉	—	4	1	no	—
476	C₂×C₉	—	8	1	no	—
477	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
478	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
479	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
480	D₉	—	4	1	no	—
481	C₂×Q₈	—	9	1	no	—
482	C₂×Q₈	—	9	1	no	—
483	C₂×Q₈	—	9	1	no	—
484	C₂×D₄	—	9	1	no	—
485	C₂²×C₄	—	9	1	no	—
486	C₂²×C₄	—	9	1	no	—
487	C₄⋊C₄	—	9	1	no	—
488	C₄⋊C₄	—	9	1	no	—
489	C₄⋊C₄	—	9	1	no	—
490	C₄⋊C₄	—	9	1	no	—
491	C₄⋊C₄	—	9	1	no	—
492	C₄⋊C₄	—	9	1	no	—
493	C₄⋊C₄	—	9	1	no	—
494	C₄⋊C₄	—	9	1	no	—
495	C₄⋊C₄	—	9	1	no	—
496	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
497	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
498	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
499	C₂²⋊C₄	—	9	1	no	—
500	C₂²⋊C₄	—	9	1	no	—
501	C₂²⋊C₄	—	9	1	no	—
502	C₂²⋊C₄	—	9	1	no	—
503	C₂²⋊C₄	—	9	1	no	—
504	C₂²⋊C₄	—	9	1	no	—
505	C₂²⋊C₄	—	9	1	no	—
506	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
507	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
508	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
509	C₄²	—	9	1	no	—
510	C₄²	—	9	1	no	—
511	C₄²	—	9	1	no	—
512	C₄²	—	9	1	no	—
513	C₄²	—	9	1	no	—
514	C₄²	—	9	1	no	—
515	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
516	C₂²×C₃	—	2	1	no	—
517	C₂²×C₃	—	2	1	no	—
518	C₂²×C₃	—	2	1	no	—
519	C₂²×C₃	—	3	1	no	—
520	C₂²×C₃	—	6	1	no	—
521	C₂²×C₃	—	6	1	no	—
522	C₂²×C₃	—	6	1	no	—
523	C₂²×C₃	—	18	1	no	—
524	C₂²×C₃	—	18	1	no	—
525	C₂²×C₃	—	18	1	no	—
526	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
527	C₂×D₃	—	6	1	no	—
528	C₂×D₃	—	6	1	no	—
529	C₂×D₃	—	6	1	no	—
530	C₃×C₄	—	2	1	no	—
531	C₃×C₄	—	2	1	no	—
532	C₃×C₄	—	2	1	no	—
533	C₃×C₄	—	2	1	no	—
534	C₃×C₄	—	2	1	no	—
535	C₃×C₄	—	2	1	no	—
536	C₃×C₄	—	6	1	no	—
537	C₃×C₄	—	6	1	no	—
538	C₃×C₄	—	6	1	no	—
539	C₃×C₄	—	6	1	no	—
540	C₃×C₄	—	6	1	no	—
541	C₃×C₄	—	6	1	no	—
542	C₃×C₄	—	9	2	no	—
543	C₃×C₄	—	9	2	no	—
544	C₃×C₄	—	18	1	no	—
545	C₃×C₄	—	18	1	no	—
546	C₃×C₄	—	18	1	no	—
547	C₃×C₄	—	18	1	no	—
548	C₃×C₄	—	18	1	no	—
549	Dic₃	—	3	2	no	—
550	Dic₃	—	3	2	no	—
551	Dic₃	—	6	1	no	—
552	Dic₃	—	6	1	no	—
553	Dic₃	—	6	1	no	—
554	Dic₃	—	6	1	no	—
555	Dic₃	—	6	1	no	—
556	C₃²	#5702	1	1	yes	characteristic
557	C₉	—	2	1	no	—
558	C₉	C₃×#556	1	1	yes	characteristic, complemented
559	C₂³	—	9	1	no	—
560	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
561	Q₈	—	18	2	no	—
562	Q₈	—	18	2	no	—
563	Q₈	—	18	2	no	—
564	D₄	—	18	2	no	—
565	C₂×C₄	—	9	1	no	—
566	C₂×C₄	—	9	1	no	—
567	C₂×C₄	—	9	1	no	—
568	C₂×C₄	—	9	1	no	—
569	C₂×C₄	—	9	1	no	—
570	C₂×C₄	—	9	1	no	—
571	C₂×C₄	—	9	1	no	—
572	C₂×C₄	—	18	2	no	—
573	C₂×C₄	—	18	2	no	—
574	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
575	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
576	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
577	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
578	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
579	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
580	C₂×C₃	—	3	1	no	—
581	C₂×C₃	—	3	1	no	—
582	C₂×C₃	—	3	1	no	—
583	C₂×C₃	—	4	1	no	—
584	C₂×C₃	—	12	1	no	—
585	C₂×C₃	—	36	1	no	—
586	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
587	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
588	C₂×C₃	C₃×#1010	1	1	yes	characteristic
589	D₃	—	12	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	18	1	no	—
594	C₂²	—	18	1	no	—
595	C₂²	—	18	1	no	—
596	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	9	2	no	—
604	C₄	—	9	2	no	—
605	C₄	—	18	1	no	—
606	C₄	—	18	1	no	—
607	C₄	—	18	1	no	—
608	C₄	—	18	1	no	—
609	C₄	—	18	1	no	—
610	C₃	—	3	1	no	—
611	C₃	C₃×#5702	1	1	yes	characteristic
612	C₂	—	4	1	no	—
613	C₂	—	36	1	no	—
614	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic
615	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic
616	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×#126	C₂
prime radical	C₂×#611⋊C₃	C₂²
hypercenter	#126	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#556
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ #126

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×#126	C₂	semidirect
2. #63460⋊C₃	C₂	semidirect
3. #63460⋊C₃	C₂	semidirect
4. #63458⋊C₃	C₂	semidirect
5. #63450⋊C₃	C₂	semidirect
6. #63449⋊C₃	C₂	semidirect
7. #63449⋊C₃	C₂	semidirect
11. #63441⋊C₃	C₂	semidirect
12. #63440⋊C₃	C₂	semidirect
13. #63439⋊C₃	C₂	semidirect
14. #63434⋊C₃	C₂	semidirect
15. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
17. #10589804	C₃	semidirect
69. C₉×#126	C₂×C₃	semidirect
70. #63460	C₂×C₃	semidirect
71. #63460	C₂×C₃	semidirect
72. #63458	C₂×C₃	semidirect
73. #63450	C₂×C₃	semidirect
74. #63449	C₂×C₃	semidirect
75. #63449	C₂×C₃	semidirect
79. #63441	C₂×C₃	semidirect
80. #63440	C₂×C₃	semidirect
81. #63439	C₂×C₃	semidirect
82. #63434	C₂×C₃	semidirect
83. C₄×Dic₁₈	C₂×C₃	semidirect
413. #126	AGL(1,ℤ/9)	semidirect
424. 3₋¹⁺²	#556	semidirect
558. C₉	C₃×#556	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×#126	2
#63460⋊C₃	2
#63458⋊C₃	2
#63450⋊C₃	2
#63449⋊C₃	2
#63447⋊C₃	2
(#611⋊C₃)⋊C₄	2
#63441⋊C₃	2
#63440⋊C₃	2
#63439⋊C₃	2
#63434⋊C₃	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5702	3
#10589804	3

Subgroups — #10589804⋊C3 #13153244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589804⋊C₃ #13153244