Subgroups — #10589803⋊C₃ #13153243

Order 1728.

606 conjugacy classes of subgroups.

The subgroup lattice has 582 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
2	#63452⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63450⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63449⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63441⋊C₃	C₂	1	1	yes	maximal, characteristic
9	#63441⋊C₃	C₂	1	1	yes	maximal, characteristic
10	#63441⋊C₃	C₂	1	1	yes	maximal, characteristic
11	#63440⋊C₃	C₂	1	1	yes	maximal, characteristic
12	#63440⋊C₃	C₂	1	1	yes	maximal, characteristic
13	#63439⋊C₃	C₂	1	1	yes	maximal, characteristic
14	#63432⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5701	—	3	1	no	maximal
17	#10589803	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂²×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
22	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
23	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
24	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
25	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
26	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
27	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
28	#3676⋊C₃	C₂²	1	1	yes	characteristic
29	#3676⋊C₃	C₂²	1	1	yes	characteristic
30	#3676⋊C₃	C₂²	1	1	yes	characteristic
31	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
32	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
33	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
34	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
35	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
36	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
37	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
38	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
39	(3₋¹⁺²⋊C₄)⋊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	(3₋¹⁺²⋊C₄)⋊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×#890	—	3	1	no	—
55	C₃×#889	—	3	1	no	—
56	C₃×#889	—	3	1	no	—
57	C₃×#889	—	3	1	no	—
58	C₃×#888	—	3	1	no	—
59	C₃×#887	—	3	1	no	—
60	C₃×#879	—	3	1	no	—
61	C₃×#879	—	3	1	no	—
62	C₃×#879	—	3	1	no	—
63	C₃×#878	—	3	1	no	—
64	C₃×#878	—	3	1	no	—
65	C₃×#877	—	3	1	no	—
66	C₃×#870	—	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
70	#63452	C₂×C₃	1	1	yes	characteristic, complemented
71	#63451	C₂×C₃	1	1	yes	characteristic, complemented
72	#63451	C₂×C₃	1	1	yes	characteristic, complemented
73	#63451	C₂×C₃	1	1	yes	characteristic, complemented
74	#63450	C₂×C₃	1	1	yes	characteristic, complemented
75	#63449	C₂×C₃	1	1	yes	characteristic, complemented
76	#63441	C₂×C₃	1	1	yes	characteristic
77	#63441	C₂×C₃	1	1	yes	characteristic
78	#63441	C₂×C₃	1	1	yes	characteristic
79	#63440	C₂×C₃	1	1	yes	characteristic
80	#63440	C₂×C₃	1	1	yes	characteristic
81	#63439	C₂×C₃	1	1	yes	characteristic
82	#63432	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	C₂×C₄×3₋¹⁺²	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	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
92	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×3₋¹⁺²⋊C₄	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	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
100	3₋¹⁺²⋊Q₈	—	2	2	no	—
101	3₋¹⁺²⋊Q₈	—	2	2	no	—
102	C₃×#541	—	9	1	no	—
103	#5701	—	3	1	no	—
104	C₂²×C₃×Dic₃	—	3	1	no	—
105	C₂×C₃×Dic₆	—	3	1	no	—
106	C₂×C₃×Dic₆	—	3	1	no	—
107	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
108	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
109	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
110	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
111	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
112	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
113	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
114	C₃×#217	—	3	1	no	—
115	C₃×#217	—	3	1	no	—
116	C₃×#217	—	3	1	no	—
117	C₃×C₄⋊Dic₃	—	3	1	no	—
118	C₃×C₄⋊Dic₃	—	3	1	no	—
119	C₃×C₄⋊Dic₃	—	3	1	no	—
120	C₃×C₄⋊Dic₃	—	3	1	no	—
121	C₃×C₄⋊Dic₃	—	3	1	no	—
122	C₃×Dic₃⋊C₄	—	3	1	no	—
123	C₃×Dic₃⋊C₄	—	3	1	no	—
124	C₃×Dic₃⋊C₄	—	3	1	no	—
125	C₃×Dic₃⋊C₄	—	3	1	no	—
126	C₃×Dic₃⋊C₄	—	3	1	no	—
127	C₃×Dic₃⋊C₄	—	3	1	no	—
128	C₃×Dic₃⋊C₄	—	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×C₄×Dic₃	—	3	1	no	—
135	C₃×C₄×Dic₃	—	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	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
140	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
141	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
142	C₉×C₄⋊C₄	—	2	1	no	—
143	C₉×C₄⋊C₄	—	2	1	no	—
144	C₉×C₄⋊C₄	—	2	1	no	—
145	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₉×C₂²⋊C₄	—	2	1	no	—
149	C₉×C₂²⋊C₄	—	2	1	no	—
150	C₉×C₂²⋊C₄	—	2	1	no	—
151	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₄²×C₉	—	2	1	no	—
155	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
156	#3676	C₂²×C₃	1	1	yes	characteristic
157	#3676	C₂²×C₃	1	1	yes	characteristic
158	#3676	C₂²×C₃	1	1	yes	characteristic
159	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
160	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
161	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
162	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
163	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
164	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
170	Dic₉⋊C₄	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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
177	C₄×Dic₉	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	C₂²×3₋¹⁺²	—	2	1	no	—
182	C₂²×3₋¹⁺²	—	2	1	no	—
183	C₂²×3₋¹⁺²	—	2	1	no	—
184	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
185	C₄×3₋¹⁺²	—	2	1	no	—
186	C₄×3₋¹⁺²	—	2	1	no	—
187	C₄×3₋¹⁺²	—	2	1	no	—
188	C₄×3₋¹⁺²	—	2	1	no	—
189	C₄×3₋¹⁺²	—	2	1	no	—
190	C₄×3₋¹⁺²	—	2	1	no	—
191	3₋¹⁺²⋊C₄	—	2	1	no	—
192	3₋¹⁺²⋊C₄	—	2	1	no	—
193	3₋¹⁺²⋊C₄	—	2	1	no	—
194	3₋¹⁺²⋊C₄	—	2	1	no	—
195	3₋¹⁺²⋊C₄	—	2	1	no	—
196	3₋¹⁺²⋊C₄	—	2	1	no	—
197	3₋¹⁺²⋊C₄	—	2	1	no	—
198	3₋¹⁺²⋊C₄	#41	1	2	yes	—
199	C₃×C₄⋊Q₈	—	9	1	no	—
200	C₃×#126	—	3	1	no	—
201	C₃×#126	—	9	1	no	—
202	C₃×#126	—	9	1	no	—
203	C₃×#126	—	9	1	no	—
204	C₃×#126	C₃×D₃	1	1	yes	characteristic
205	C₃×#125	—	9	1	no	—
206	C₃×#125	—	9	1	no	—
207	C₃×#125	—	9	1	no	—
208	C₃×#125	—	9	1	no	—
209	C₃×#125	—	9	1	no	—
210	C₃×C₂²⋊Q₈	—	9	1	no	—
211	C₃×C₂²⋊Q₈	—	9	1	no	—
212	C₃×C₄×Q₈	—	9	1	no	—
213	C₃×C₄×Q₈	—	9	1	no	—
214	C₃×#117	—	9	1	no	—
215	#890	—	3	1	no	—
216	#889	—	3	1	no	—
217	#889	—	3	1	no	—
218	#889	—	3	1	no	—
219	#888	—	3	1	no	—
220	#887	—	3	1	no	—
221	#879	—	3	1	no	—
222	#879	—	3	1	no	—
223	#879	—	3	1	no	—
224	#878	—	3	1	no	—
225	#878	—	3	1	no	—
226	#877	—	3	1	no	—
227	#870	—	3	1	no	—
228	C₄×Dic₆	—	3	1	no	—
229	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
230	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
233	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
234	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
235	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
236	C₂×C₃×Dic₃	—	3	1	no	—
237	C₂×C₃×Dic₃	—	3	1	no	—
238	C₂×C₃×Dic₃	—	3	1	no	—
239	C₂×C₃×Dic₃	—	3	1	no	—
240	C₂×C₃×Dic₃	—	3	1	no	—
241	C₂×C₃×Dic₃	—	3	1	no	—
242	C₂×C₃×Dic₃	—	3	1	no	—
243	C₂×C₃×Dic₃	—	3	1	no	—
244	C₂×C₃×Dic₃	—	6	2	no	—
245	C₃×Dic₆	—	6	2	no	—
246	C₃×Dic₆	—	6	2	no	—
247	C₂³×C₉	—	2	1	no	—
248	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₄×C₉	—	2	1	no	—
250	C₂×C₄×C₉	—	2	1	no	—
251	C₂×C₄×C₉	—	2	1	no	—
252	C₂×C₄×C₉	—	2	1	no	—
253	C₂×C₄×C₉	—	2	1	no	—
254	C₂×C₄×C₉	—	2	1	no	—
255	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
256	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
258	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
259	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
261	C₂×Dic₉	—	2	2	no	—
262	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
263	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
264	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
265	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
266	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
267	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
268	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
269	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
270	Dic₁₈	—	2	2	no	—
271	Dic₁₈	—	2	2	no	—
272	#541	—	9	1	no	Sylow
273	C₂×3₋¹⁺²	—	4	1	no	—
274	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
275	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
276	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
277	C₂×C₃×Q₈	—	9	1	no	—
278	C₂×C₃×Q₈	—	9	1	no	—
279	C₂²×C₃×C₄	—	9	1	no	—
280	C₂²×Dic₃	—	3	1	no	—
281	C₂×Dic₆	—	3	1	no	—
282	C₂×Dic₆	—	3	1	no	—
283	C₃×C₄⋊C₄	—	3	1	no	—
284	C₃×C₄⋊C₄	—	3	1	no	—
285	C₃×C₄⋊C₄	—	3	1	no	—
286	C₃×C₄⋊C₄	—	9	1	no	—
287	C₃×C₄⋊C₄	—	9	1	no	—
288	C₃×C₄⋊C₄	—	9	1	no	—
289	C₃×C₄⋊C₄	—	9	1	no	—
290	C₃×C₄⋊C₄	—	9	1	no	—
291	C₃×C₄⋊C₄	—	9	1	no	—
292	C₃×C₄⋊C₄	—	9	1	no	—
293	C₃×C₄⋊C₄	—	9	1	no	—
294	C₃×C₄⋊C₄	—	9	1	no	—
295	C₃×C₄⋊C₄	—	9	1	no	—
296	C₃×C₄⋊C₄	—	9	1	no	—
297	C₃×C₄⋊C₄	—	9	1	no	—
298	C₃×C₄⋊C₄	—	9	1	no	—
299	C₃×C₄⋊C₄	—	9	1	no	—
300	C₃×C₄⋊C₄	—	9	1	no	—
301	C₃×C₄⋊C₄	—	9	1	no	—
302	C₃×C₄⋊C₄	—	9	1	no	—
303	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
304	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
305	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
306	C₃×C₂²⋊C₄	—	3	1	no	—
307	C₃×C₂²⋊C₄	—	3	1	no	—
308	C₃×C₂²⋊C₄	—	3	1	no	—
309	C₃×C₂²⋊C₄	—	9	1	no	—
310	C₃×C₂²⋊C₄	—	9	1	no	—
311	C₃×C₂²⋊C₄	—	9	1	no	—
312	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
313	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
314	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
315	C₃×C₄²	—	3	1	no	—
316	C₃×C₄²	—	9	1	no	—
317	C₃×C₄²	—	9	1	no	—
318	C₃×C₄²	—	9	1	no	—
319	C₃×C₄²	—	9	1	no	—
320	C₃×C₄²	—	9	1	no	—
321	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
322	#217	—	3	1	no	—
323	#217	—	3	1	no	—
324	#217	—	3	1	no	—
325	C₄⋊Dic₃	—	3	1	no	—
326	C₄⋊Dic₃	—	3	1	no	—
327	C₄⋊Dic₃	—	3	1	no	—
328	C₄⋊Dic₃	—	3	1	no	—
329	C₄⋊Dic₃	—	3	1	no	—
330	Dic₃⋊C₄	—	3	1	no	—
331	Dic₃⋊C₄	—	3	1	no	—
332	Dic₃⋊C₄	—	3	1	no	—
333	Dic₃⋊C₄	—	3	1	no	—
334	Dic₃⋊C₄	—	3	1	no	—
335	Dic₃⋊C₄	—	3	1	no	—
336	Dic₃⋊C₄	—	3	1	no	—
337	Dic₃⋊C₄	—	3	1	no	—
338	Dic₃⋊C₄	—	3	1	no	—
339	Dic₃⋊C₄	—	3	1	no	—
340	Dic₃⋊C₄	—	3	1	no	—
341	Dic₃⋊C₄	—	3	1	no	—
342	C₄×Dic₃	—	3	1	no	—
343	C₄×Dic₃	—	3	1	no	—
344	C₄×Dic₃	—	3	1	no	—
345	C₄×Dic₃	—	3	1	no	—
346	C₄×Dic₃	—	3	1	no	—
347	C₂²×C₃²	—	2	1	no	—
348	C₂²×C₃²	—	2	1	no	—
349	C₂²×C₃²	—	2	1	no	—
350	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
351	C₃²×C₄	—	2	1	no	—
352	C₃²×C₄	—	2	1	no	—
353	C₃²×C₄	—	2	1	no	—
354	C₃²×C₄	—	2	1	no	—
355	C₃²×C₄	—	2	1	no	—
356	C₃²×C₄	—	2	1	no	—
357	C₃×Dic₃	—	3	2	no	—
358	C₃×Dic₃	—	6	1	no	—
359	C₃×Dic₃	—	6	1	no	—
360	C₃×Dic₃	—	6	1	no	—
361	C₃×Dic₃	—	6	1	no	—
362	C₃×Dic₃	—	6	1	no	—
363	C₃×Dic₃	—	6	1	no	—
364	C₃×Dic₃	—	6	1	no	—
365	C₂²×C₉	—	2	1	no	—
366	C₂²×C₉	—	2	1	no	—
367	C₂²×C₉	—	2	1	no	—
368	C₂²×C₉	—	2	1	no	—
369	C₂²×C₉	—	4	1	no	—
370	C₂²×C₉	—	4	1	no	—
371	C₂²×C₉	—	4	1	no	—
372	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
373	C₄×C₉	—	2	1	no	—
374	C₄×C₉	—	2	1	no	—
375	C₄×C₉	—	2	1	no	—
376	C₄×C₉	—	2	1	no	—
377	C₄×C₉	—	2	1	no	—
378	C₄×C₉	—	2	1	no	—
379	C₄×C₉	—	4	1	no	—
380	C₄×C₉	—	4	1	no	—
381	C₄×C₉	—	4	1	no	—
382	C₄×C₉	—	4	1	no	—
383	C₄×C₉	—	4	1	no	—
384	C₄×C₉	—	4	1	no	—
385	Dic₉	—	2	1	no	—
386	Dic₉	—	2	1	no	—
387	Dic₉	—	2	1	no	—
388	Dic₉	—	2	1	no	—
389	Dic₉	—	2	1	no	—
390	Dic₉	—	2	1	no	—
391	Dic₉	—	2	1	no	—
392	Dic₉	C₃×#41	1	2	yes	—
393	C₄⋊Q₈	—	9	1	no	—
394	#126	—	9	1	no	—
395	#126	—	9	1	no	—
396	#126	—	9	1	no	—
397	#126	AGL(1,ℤ/9)	1	1	yes	characteristic
398	#125	—	9	1	no	—
399	#125	—	9	1	no	—
400	#125	—	9	1	no	—
401	#125	—	9	1	no	—
402	#125	—	9	1	no	—
403	C₂²⋊Q₈	—	9	1	no	—
404	C₂²⋊Q₈	—	9	1	no	—
405	C₄×Q₈	—	9	1	no	—
406	C₄×Q₈	—	9	1	no	—
407	#117	—	9	1	no	—
408	3₋¹⁺²	#541	1	1	yes	characteristic, complemented, Sylow
409	C₂³×C₃	—	3	1	no	—
410	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
411	C₃×Q₈	—	18	2	no	—
412	C₃×Q₈	—	18	2	no	—
413	C₂×C₃×C₄	—	3	1	no	—
414	C₂×C₃×C₄	—	3	1	no	—
415	C₂×C₃×C₄	—	3	1	no	—
416	C₂×C₃×C₄	—	3	1	no	—
417	C₂×C₃×C₄	—	3	1	no	—
418	C₂×C₃×C₄	—	3	1	no	—
419	C₂×C₃×C₄	—	9	1	no	—
420	C₂×C₃×C₄	—	9	1	no	—
421	C₂×C₃×C₄	—	9	1	no	—
422	C₂×C₃×C₄	—	9	1	no	—
423	C₂×C₃×C₄	—	9	1	no	—
424	C₂×C₃×C₄	—	9	1	no	—
425	C₂×C₃×C₄	—	9	1	no	—
426	C₂×C₃×C₄	—	9	1	no	—
427	C₂×C₃×C₄	—	18	2	no	—
428	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
429	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
430	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
434	C₂×Dic₃	—	3	1	no	—
435	C₂×Dic₃	—	3	1	no	—
436	C₂×Dic₃	—	3	1	no	—
437	C₂×Dic₃	—	3	1	no	—
438	C₂×Dic₃	—	3	1	no	—
439	C₂×Dic₃	—	3	1	no	—
440	C₂×Dic₃	—	3	1	no	—
441	C₂×Dic₃	—	3	1	no	—
442	C₂×Dic₃	—	6	2	no	—
443	Dic₆	—	6	2	no	—
444	Dic₆	—	6	2	no	—
445	C₂×C₃²	—	4	1	no	—
446	C₂×C₃²	D₃×#41	1	1	yes	characteristic
447	C₂×C₃²	#1010	1	1	yes	characteristic
448	C₂×C₃²	#1010	1	1	yes	characteristic
449	C₂×C₉	—	2	1	no	—
450	C₂×C₉	—	2	1	no	—
451	C₂×C₉	—	2	1	no	—
452	C₂×C₉	—	4	1	no	—
453	C₂×C₉	—	8	1	no	—
454	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
455	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
457	C₂×Q₈	—	9	1	no	—
458	C₂×Q₈	—	9	1	no	—
459	C₂²×C₄	—	9	1	no	—
460	C₄⋊C₄	—	9	1	no	—
461	C₄⋊C₄	—	9	1	no	—
462	C₄⋊C₄	—	9	1	no	—
463	C₄⋊C₄	—	9	1	no	—
464	C₄⋊C₄	—	9	1	no	—
465	C₄⋊C₄	—	9	1	no	—
466	C₄⋊C₄	—	9	1	no	—
467	C₄⋊C₄	—	9	1	no	—
468	C₄⋊C₄	—	9	1	no	—
469	C₄⋊C₄	—	9	1	no	—
470	C₄⋊C₄	—	9	1	no	—
471	C₄⋊C₄	—	9	1	no	—
472	C₄⋊C₄	—	9	1	no	—
473	C₄⋊C₄	—	9	1	no	—
474	C₄⋊C₄	—	9	1	no	—
475	C₄⋊C₄	—	9	1	no	—
476	C₄⋊C₄	—	9	1	no	—
477	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
478	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
479	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
480	C₂²⋊C₄	—	9	1	no	—
481	C₂²⋊C₄	—	9	1	no	—
482	C₂²⋊C₄	—	9	1	no	—
483	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
484	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
485	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
486	C₄²	—	9	1	no	—
487	C₄²	—	9	1	no	—
488	C₄²	—	9	1	no	—
489	C₄²	—	9	1	no	—
490	C₄²	—	9	1	no	—
491	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
492	C₂²×C₃	—	2	1	no	—
493	C₂²×C₃	—	2	1	no	—
494	C₂²×C₃	—	2	1	no	—
495	C₂²×C₃	—	3	1	no	—
496	C₂²×C₃	—	6	1	no	—
497	C₂²×C₃	—	6	1	no	—
498	C₂²×C₃	—	6	1	no	—
499	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
500	C₃×C₄	—	2	1	no	—
501	C₃×C₄	—	2	1	no	—
502	C₃×C₄	—	2	1	no	—
503	C₃×C₄	—	2	1	no	—
504	C₃×C₄	—	2	1	no	—
505	C₃×C₄	—	2	1	no	—
506	C₃×C₄	—	6	1	no	—
507	C₃×C₄	—	6	1	no	—
508	C₃×C₄	—	6	1	no	—
509	C₃×C₄	—	6	1	no	—
510	C₃×C₄	—	6	1	no	—
511	C₃×C₄	—	6	1	no	—
512	C₃×C₄	—	9	2	no	—
513	C₃×C₄	—	18	1	no	—
514	C₃×C₄	—	18	1	no	—
515	C₃×C₄	—	18	1	no	—
516	C₃×C₄	—	18	1	no	—
517	C₃×C₄	—	18	1	no	—
518	C₃×C₄	—	18	1	no	—
519	C₃×C₄	—	18	1	no	—
520	Dic₃	—	3	2	no	—
521	Dic₃	—	6	1	no	—
522	Dic₃	—	6	1	no	—
523	Dic₃	—	6	1	no	—
524	Dic₃	—	6	1	no	—
525	Dic₃	—	6	1	no	—
526	Dic₃	—	6	1	no	—
527	Dic₃	—	6	1	no	—
528	C₃²	#5701	1	1	yes	characteristic
529	C₉	—	2	1	no	—
530	C₉	C₃×#541	1	1	yes	characteristic, complemented
531	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
532	Q₈	—	18	2	no	—
533	Q₈	—	18	2	no	—
534	C₂×C₄	—	9	1	no	—
535	C₂×C₄	—	9	1	no	—
536	C₂×C₄	—	9	1	no	—
537	C₂×C₄	—	9	1	no	—
538	C₂×C₄	—	9	1	no	—
539	C₂×C₄	—	9	1	no	—
540	C₂×C₄	—	9	1	no	—
541	C₂×C₄	—	9	1	no	—
542	C₂×C₄	—	18	2	no	—
543	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
544	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
545	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
546	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
547	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
548	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
549	C₂×C₃	—	3	1	no	—
550	C₂×C₃	—	3	1	no	—
551	C₂×C₃	—	3	1	no	—
552	C₂×C₃	—	4	1	no	—
553	C₂×C₃	—	12	1	no	—
554	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
555	C₂×C₃	C₃×#1010	1	1	yes	characteristic
556	C₂×C₃	C₃×#1010	1	1	yes	characteristic
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	2	1	no	—
567	C₄	—	9	2	no	—
568	C₄	—	18	1	no	—
569	C₄	—	18	1	no	—
570	C₄	—	18	1	no	—
571	C₄	—	18	1	no	—
572	C₄	—	18	1	no	—
573	C₄	—	18	1	no	—
574	C₄	—	18	1	no	—
575	C₃	—	3	1	no	—
576	C₃	C₃×#5701	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	#41×AGL(1,ℤ/9)	1	1	yes	characteristic
579	C₂	#11722642	1	1	yes	characteristic
580	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	C₂³×C₃²	C₂²×D₃
hypercenter	#126	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#541
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
2. #63452⋊C₃	C₂	semidirect
3. #63451⋊C₃	C₂	semidirect
4. #63451⋊C₃	C₂	semidirect
5. #63451⋊C₃	C₂	semidirect
6. #63450⋊C₃	C₂	semidirect
7. #63449⋊C₃	C₂	semidirect
14. #63432⋊C₃	C₂	semidirect
15. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
17. #10589803	C₃	semidirect
70. #63452	C₂×C₃	semidirect
71. #63451	C₂×C₃	semidirect
72. #63451	C₂×C₃	semidirect
73. #63451	C₂×C₃	semidirect
74. #63450	C₂×C₃	semidirect
75. #63449	C₂×C₃	semidirect
82. #63432	C₂×C₃	semidirect
83. C₄×Dic₁₈	C₂×C₃	semidirect
408. 3₋¹⁺²	#541	semidirect
530. C₉	C₃×#541	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
#63452⋊C₃	2
#63451⋊C₃	2
#63450⋊C₃	2
#63449⋊C₃	2
#63441⋊C₃	2
#63440⋊C₃	2
#63439⋊C₃	2
#63432⋊C₃	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5701	3
#10589803	3

Subgroups — #10589803⋊C3 #13153243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589803⋊C₃ #13153243