Subgroups — #10589738⋊C₃ #13152984

Order 1728.

721 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	#63508⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63506⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic
5	C₂×(3₋¹⁺²⋊C₄)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
9	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63451⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63449⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	(#611⋊C₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
13	(#611⋊C₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
14	#63440⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#63440⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5636	—	3	1	no	maximal
17	#10589738	C₃	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₂×#611⋊C₃	C₂²	1	1	yes	characteristic
21	C₂²×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂²×3₋¹⁺²⋊C₄	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	C₂×3₋¹⁺²⋊Q₈	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	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
32	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
33	#3676⋊C₃	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	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
38	C₄⋊(3₋¹⁺²⋊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	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	1	yes	characteristic
49	(3₋¹⁺²⋊C₄)⋊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×C₂²⋊Q₈	D₃	1	1	yes	characteristic
54	C₃×#946	—	3	1	no	—
55	C₃×#944	—	3	1	no	—
56	C₃×C₄×#67	—	3	1	no	—
57	C₂×C₃×Dic₃⋊C₄	—	3	1	no	—
58	C₃×#896	—	3	1	no	—
59	C₃×#896	—	3	1	no	—
60	C₃×D₃×C₄⋊C₄	—	3	1	no	—
61	C₃×#889	—	3	1	no	—
62	C₃×#889	—	3	1	no	—
63	C₃×#887	—	3	1	no	—
64	C₃×#67⋊C₄	—	3	1	no	—
65	C₃×#67⋊C₄	—	3	1	no	—
66	C₃×#878	—	3	1	no	—
67	C₃×#878	—	3	1	no	—
68	C₉×C₂²⋊Q₈	—	2	1	no	—
69	C₉×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
70	#63508	C₂×C₃	1	1	yes	characteristic, complemented
71	#63506	C₂×C₃	1	1	yes	characteristic, complemented
72	C₄×#611	C₂×C₃	1	1	yes	characteristic
73	C₂×Dic₉⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
74	#63458	C₂×C₃	1	1	yes	characteristic, complemented
75	#63458	C₂×C₃	1	1	yes	characteristic, complemented
76	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic, complemented
77	#63451	C₂×C₃	1	1	yes	characteristic, complemented
78	#63451	C₂×C₃	1	1	yes	characteristic, complemented
79	#63449	C₂×C₃	1	1	yes	characteristic, complemented
80	#611⋊C₄	C₂×C₃	1	1	yes	characteristic
81	#611⋊C₄	C₂×C₃	1	1	yes	characteristic
82	#63440	C₂×C₃	1	1	yes	characteristic, complemented
83	#63440	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	Q₈×3₋¹⁺²	—	4	1	no	—
87	C₂×C₄×3₋¹⁺²	—	4	1	no	—
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	#611⋊C₃	Q₈	1	4	yes	complemented
95	C₂×3₋¹⁺²⋊C₄	—	2	2	no	—
96	C₂×3₋¹⁺²⋊C₄	—	4	1	no	—
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	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×3₋¹⁺²⋊C₄	C₂³	1	1	yes	characteristic
104	C₄×AGL(1,ℤ/9)	—	2	2	no	—
105	C₄×AGL(1,ℤ/9)	—	4	1	no	—
106	C₄×AGL(1,ℤ/9)	—	4	1	no	—
107	3₋¹⁺²⋊Q₈	—	2	2	no	—
108	3₋¹⁺²⋊Q₈	—	4	1	no	—
109	C₃×#554	—	9	1	no	—
110	#5636	—	3	1	no	—
111	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
112	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
113	C₂×C₃×#67	—	3	1	no	—
114	C₂²×C₃×Dic₃	—	3	1	no	—
115	C₂²×C₃×Dic₃	—	3	1	no	—
116	C₂×C₃×C₄×D₃	—	3	1	no	—
117	C₂×C₃×C₄×D₃	—	3	1	no	—
118	C₂×C₃×C₄×D₃	—	3	1	no	—
119	C₂×C₃×Dic₆	—	3	1	no	—
120	C₂×C₃×Dic₆	—	3	1	no	—
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×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
125	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
126	C₃×#217	—	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×C₄⋊Dic₃	—	3	1	no	—
131	C₃×C₄⋊Dic₃	—	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×Dic₃⋊C₄	—	3	1	no	—
137	C₃×Dic₃⋊C₄	—	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×C₄×Dic₃	—	3	1	no	—
144	C₃×C₄×Dic₃	—	3	1	no	—
145	C₃×C₄×Dic₃	—	3	1	no	—
146	C₂×Q₈×C₉	—	2	1	no	—
147	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
148	C₂²×C₄×C₉	—	2	1	no	—
149	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
150	C₂×#611	C₂²×C₃	1	1	yes	characteristic
151	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
152	C₂²×Dic₉	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
156	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
157	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
158	C₉×C₄⋊C₄	—	2	1	no	—
159	C₉×C₄⋊C₄	—	2	1	no	—
160	C₉×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
165	C₉×C₂²⋊C₄	—	2	1	no	—
166	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
167	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
168	#3676	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	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
173	C₄⋊Dic₉	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	Dic₉⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	Dic₉⋊C₄	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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
186	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
187	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
188	C₂²×3₋¹⁺²	—	2	1	no	—
189	C₂²×3₋¹⁺²	—	2	1	no	—
190	C₂²×3₋¹⁺²	C₂×Q₈	1	2	yes	—
191	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
192	C₂×AGL(1,ℤ/9)	—	2	1	no	—
193	C₂×AGL(1,ℤ/9)	—	2	1	no	—
194	C₂×AGL(1,ℤ/9)	C₂×Q₈	1	2	yes	—
195	C₄×3₋¹⁺²	—	2	1	no	—
196	C₄×3₋¹⁺²	—	2	1	no	—
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	3₋¹⁺²⋊C₄	—	2	1	no	—
202	3₋¹⁺²⋊C₄	—	2	1	no	—
203	3₋¹⁺²⋊C₄	—	2	1	no	—
204	3₋¹⁺²⋊C₄	—	2	1	no	—
205	3₋¹⁺²⋊C₄	—	2	1	no	—
206	3₋¹⁺²⋊C₄	C₂×Q₈	1	2	yes	—
207	3₋¹⁺²⋊C₄	#41	1	2	yes	—
208	C₃×C₄⋊Q₈	—	9	1	no	—
209	C₃×#125	—	9	1	no	—
210	C₃×#125	—	9	1	no	—
211	C₃×C₂²⋊Q₈	—	3	1	no	—
212	C₃×C₂²⋊Q₈	—	9	1	no	—
213	C₃×C₂²⋊Q₈	—	9	1	no	—
214	C₃×C₂²⋊Q₈	—	9	1	no	—
215	C₃×C₂²⋊Q₈	—	9	1	no	—
216	C₃×C₂²⋊Q₈	—	9	1	no	—
217	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
218	C₃×C₄×Q₈	—	9	1	no	—
219	C₃×C₄×D₄	—	9	1	no	—
220	C₃×C₄×D₄	—	9	1	no	—
221	C₃×C₄×D₄	—	9	1	no	—
222	C₂×C₃×C₄⋊C₄	—	9	1	no	—
223	C₂×C₃×C₄⋊C₄	—	9	1	no	—
224	#946	—	3	1	no	—
225	#944	—	3	1	no	—
226	C₄×#67	—	3	1	no	—
227	C₂×Dic₃⋊C₄	—	3	1	no	—
228	#896	—	3	1	no	—
229	#896	—	3	1	no	—
230	D₃×C₄⋊C₄	—	3	1	no	—
231	#889	—	3	1	no	—
232	#889	—	3	1	no	—
233	#887	—	3	1	no	—
234	#67⋊C₄	—	3	1	no	—
235	#67⋊C₄	—	3	1	no	—
236	#878	—	3	1	no	—
237	#878	—	3	1	no	—
238	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
239	C₂²×C₃×D₃	—	3	1	no	—
240	C₃²×Q₈	—	4	1	no	—
241	C₂×C₃²×C₄	—	4	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	C₃×#67	—	3	4	no	—
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	C₂×C₃×Dic₃	—	3	1	no	—
255	C₂×C₃×Dic₃	—	3	1	no	—
256	C₂×C₃×Dic₃	—	6	2	no	—
257	C₂×C₃×Dic₃	—	12	1	no	—
258	C₃×C₄×D₃	—	6	2	no	—
259	C₃×C₄×D₃	—	12	1	no	—
260	C₃×C₄×D₃	—	12	1	no	—
261	C₃×Dic₆	—	6	2	no	—
262	C₃×Dic₆	—	12	1	no	—
263	C₂³×C₉	—	2	1	no	—
264	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
265	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
266	Q₈×C₉	—	4	1	no	—
267	Q₈×C₉	—	4	2	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	—	2	1	no	—
274	C₂×C₄×C₉	—	4	1	no	—
275	C₂×C₄×C₉	—	4	2	no	—
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×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
281	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
282	#611	C₃×Q₈	1	4	yes	complemented
283	C₂×Dic₉	—	2	2	no	—
284	C₂×Dic₉	—	4	1	no	—
285	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
286	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
287	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
288	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
289	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
290	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
291	C₂×Dic₉	C₂³×C₃	1	1	yes	characteristic
292	C₄×D₉	—	2	2	no	—
293	C₄×D₉	—	4	1	no	—
294	C₄×D₉	—	4	1	no	—
295	Dic₁₈	—	2	2	no	—
296	Dic₁₈	—	4	1	no	—
297	#554	—	9	1	no	Sylow
298	C₂×3₋¹⁺²	—	2	2	no	—
299	C₂×3₋¹⁺²	C₂²×Q₈	1	1	yes	characteristic
300	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
301	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
302	AGL(1,ℤ/9)	—	2	2	no	—
303	C₂×C₃×Q₈	—	3	1	no	—
304	C₂×C₃×Q₈	—	9	1	no	—
305	C₂×C₃×Q₈	—	9	1	no	—
306	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
307	C₂×C₃×D₄	—	9	1	no	—
308	C₂²×C₃×C₄	—	3	1	no	—
309	C₂²×C₃×C₄	—	9	1	no	—
310	C₂²×C₃×C₄	—	9	1	no	—
311	C₂²×C₃×C₄	—	9	1	no	—
312	C₂²×C₃×C₄	—	9	1	no	—
313	C₂²×C₃×C₄	—	9	1	no	—
314	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
315	C₂×#67	—	3	1	no	—
316	C₂²×Dic₃	—	3	1	no	—
317	C₂²×Dic₃	—	3	1	no	—
318	C₂×C₄×D₃	—	3	1	no	—
319	C₂×C₄×D₃	—	3	1	no	—
320	C₂×C₄×D₃	—	3	1	no	—
321	C₂×Dic₆	—	3	1	no	—
322	C₂×Dic₆	—	3	1	no	—
323	C₃×C₄⋊C₄	—	3	1	no	—
324	C₃×C₄⋊C₄	—	3	1	no	—
325	C₃×C₄⋊C₄	—	3	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	—	9	1	no	—
334	C₃×C₄⋊C₄	—	9	1	no	—
335	C₃×C₄⋊C₄	—	9	1	no	—
336	C₃×C₄⋊C₄	—	9	1	no	—
337	C₃×C₄⋊C₄	—	9	1	no	—
338	C₃×C₄⋊C₄	—	9	1	no	—
339	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
340	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
341	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
342	C₃×C₂²⋊C₄	—	3	1	no	—
343	C₃×C₂²⋊C₄	—	3	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	C₂×C₃×D₃	1	1	yes	characteristic
349	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
350	C₃×C₄²	—	9	1	no	—
351	C₃×C₄²	—	9	1	no	—
352	C₃×C₄²	—	9	1	no	—
353	#217	—	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	C₄⋊Dic₃	—	3	1	no	—
358	C₄⋊Dic₃	—	3	1	no	—
359	Dic₃⋊C₄	—	3	1	no	—
360	Dic₃⋊C₄	—	3	1	no	—
361	Dic₃⋊C₄	—	3	1	no	—
362	Dic₃⋊C₄	—	3	1	no	—
363	Dic₃⋊C₄	—	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	C₄×Dic₃	—	3	1	no	—
372	C₄×Dic₃	—	3	1	no	—
373	C₂²×C₃²	—	2	1	no	—
374	C₂²×C₃²	—	2	1	no	—
375	C₂²×C₃²	D₃×Q₈	1	2	yes	—
376	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
377	C₂×C₃×D₃	—	3	2	no	—
378	C₂×C₃×D₃	—	6	1	no	—
379	C₂×C₃×D₃	—	6	1	no	—
380	C₃²×C₄	—	2	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	C₃×Dic₃	—	3	2	no	—
387	C₃×Dic₃	—	3	2	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	—	2	1	no	—
395	C₂²×C₉	—	2	1	no	—
396	C₂²×C₉	—	2	2	no	—
397	C₂²×C₉	—	4	1	no	—
398	C₂²×C₉	—	4	1	no	—
399	C₂²×C₉	C₂×C₃×Q₈	1	2	yes	—
400	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
401	C₂×D₉	—	2	1	no	—
402	C₂×D₉	—	2	1	no	—
403	C₂×D₉	C₂×C₃×Q₈	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	—	4	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	Dic₉	—	2	1	no	—
417	Dic₉	—	2	1	no	—
418	Dic₉	—	2	1	no	—
419	Dic₉	—	2	1	no	—
420	Dic₉	—	2	1	no	—
421	Dic₉	C₂×C₃×Q₈	1	2	yes	—
422	Dic₉	C₃×#41	1	2	yes	—
423	C₄⋊Q₈	—	9	1	no	—
424	#125	—	9	1	no	—
425	#125	—	9	1	no	—
426	C₂²⋊Q₈	—	9	1	no	—
427	C₂²⋊Q₈	—	9	1	no	—
428	C₂²⋊Q₈	—	9	1	no	—
429	C₂²⋊Q₈	—	9	1	no	—
430	C₂²⋊Q₈	—	9	1	no	—
431	C₂²⋊Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
432	C₄×Q₈	—	9	1	no	—
433	C₄×D₄	—	9	1	no	—
434	C₄×D₄	—	9	1	no	—
435	C₄×D₄	—	9	1	no	—
436	C₂×C₄⋊C₄	—	9	1	no	—
437	C₂×C₄⋊C₄	—	9	1	no	—
438	3₋¹⁺²	#554	1	1	yes	characteristic, complemented, Sylow
439	C₂³×C₃	—	3	1	no	—
440	C₂³×C₃	—	9	1	no	—
441	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
442	C₂²×D₃	—	3	1	no	—
443	C₃×Q₈	—	4	1	no	—
444	C₃×Q₈	—	12	1	no	—
445	C₃×Q₈	—	18	2	no	—
446	C₃×Q₈	—	36	1	no	—
447	C₃×D₄	—	9	4	no	—
448	C₂×C₃×C₄	—	3	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	—	4	1	no	—
455	C₂×C₃×C₄	—	9	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	—	9	1	no	—
462	C₂×C₃×C₄	—	12	1	no	—
463	C₂×C₃×C₄	—	18	2	no	—
464	C₂×C₃×C₄	—	18	2	no	—
465	C₂×C₃×C₄	—	36	1	no	—
466	C₂×C₃×C₄	—	36	1	no	—
467	C₂×C₃×C₄	—	36	1	no	—
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×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
474	#67	—	3	4	no	—
475	C₂×Dic₃	—	3	1	no	—
476	C₂×Dic₃	—	3	1	no	—
477	C₂×Dic₃	—	3	1	no	—
478	C₂×Dic₃	—	3	1	no	—
479	C₂×Dic₃	—	3	1	no	—
480	C₂×Dic₃	—	3	1	no	—
481	C₂×Dic₃	—	3	1	no	—
482	C₂×Dic₃	—	6	2	no	—
483	C₂×Dic₃	—	12	1	no	—
484	C₄×D₃	—	6	2	no	—
485	C₄×D₃	—	12	1	no	—
486	C₄×D₃	—	12	1	no	—
487	Dic₆	—	6	2	no	—
488	Dic₆	—	12	1	no	—
489	C₂×C₃²	—	2	2	no	—
490	C₂×C₃²	#1004	1	1	yes	characteristic
491	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
492	C₂×C₃²	D₃×#41	1	1	yes	characteristic
493	C₃×D₃	—	6	2	no	—
494	C₂×C₉	—	2	2	no	—
495	C₂×C₉	—	2	1	no	—
496	C₂×C₉	—	2	1	no	—
497	C₂×C₉	—	2	1	no	—
498	C₂×C₉	—	4	2	no	—
499	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
500	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
501	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
502	D₉	—	2	2	no	—
503	C₂×Q₈	—	9	1	no	—
504	C₂×Q₈	—	9	1	no	—
505	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
506	C₂×D₄	—	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	C₂²×C₄	—	9	1	no	—
512	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
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	—	9	1	no	—
520	C₄⋊C₄	—	9	1	no	—
521	C₄⋊C₄	—	9	1	no	—
522	C₄⋊C₄	—	9	1	no	—
523	C₄⋊C₄	—	9	1	no	—
524	C₄⋊C₄	—	9	1	no	—
525	C₄⋊C₄	—	9	1	no	—
526	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
527	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
528	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
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	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
534	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
535	C₄²	—	9	1	no	—
536	C₄²	—	9	1	no	—
537	C₄²	—	9	1	no	—
538	C₂²×C₃	—	2	1	no	—
539	C₂²×C₃	—	2	1	no	—
540	C₂²×C₃	—	3	1	no	—
541	C₂²×C₃	—	3	2	no	—
542	C₂²×C₃	—	6	1	no	—
543	C₂²×C₃	—	6	1	no	—
544	C₂²×C₃	—	9	2	no	—
545	C₂²×C₃	—	18	1	no	—
546	C₂²×C₃	—	18	1	no	—
547	C₂²×C₃	C₃×D₃×Q₈	1	2	yes	—
548	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
549	C₂×D₃	—	3	2	no	—
550	C₂×D₃	—	6	1	no	—
551	C₂×D₃	—	6	1	no	—
552	C₃×C₄	—	2	1	no	—
553	C₃×C₄	—	2	1	no	—
554	C₃×C₄	—	2	1	no	—
555	C₃×C₄	—	2	1	no	—
556	C₃×C₄	—	2	1	no	—
557	C₃×C₄	—	2	1	no	—
558	C₃×C₄	—	6	1	no	—
559	C₃×C₄	—	6	1	no	—
560	C₃×C₄	—	6	1	no	—
561	C₃×C₄	—	6	1	no	—
562	C₃×C₄	—	6	1	no	—
563	C₃×C₄	—	6	1	no	—
564	C₃×C₄	—	9	2	no	—
565	C₃×C₄	—	9	2	no	—
566	C₃×C₄	—	18	1	no	—
567	C₃×C₄	—	18	1	no	—
568	C₃×C₄	—	18	1	no	—
569	C₃×C₄	—	18	1	no	—
570	C₃×C₄	—	18	1	no	—
571	Dic₃	—	3	2	no	—
572	Dic₃	—	3	2	no	—
573	Dic₃	—	6	1	no	—
574	Dic₃	—	6	1	no	—
575	Dic₃	—	6	1	no	—
576	Dic₃	—	6	1	no	—
577	Dic₃	—	6	1	no	—
578	C₃²	#5636	1	1	yes	characteristic
579	C₉	—	2	1	no	—
580	C₉	C₃×#554	1	1	yes	characteristic, complemented
581	C₂³	—	9	1	no	—
582	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
583	Q₈	—	4	1	no	—
584	Q₈	—	18	2	no	—
585	Q₈	—	36	1	no	—
586	D₄	—	9	4	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	9	1	no	—
589	C₂×C₄	—	9	1	no	—
590	C₂×C₄	—	9	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	—	18	2	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	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
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×C₃	—	2	2	no	—
607	C₂×C₃	—	3	1	no	—
608	C₂×C₃	—	3	1	no	—
609	C₂×C₃	—	3	1	no	—
610	C₂×C₃	—	6	2	no	—
611	C₂×C₃	—	18	2	no	—
612	C₂×C₃	C₃×#1004	1	1	yes	characteristic
613	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
614	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
615	D₃	—	6	2	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	9	2	no	—
619	C₂²	—	18	1	no	—
620	C₂²	—	18	1	no	—
621	C₂²	Q₈×AGL(1,ℤ/9)	1	2	yes	—
622	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	2	1	no	—
629	C₄	—	9	2	no	—
630	C₄	—	9	2	no	—
631	C₄	—	18	1	no	—
632	C₄	—	18	1	no	—
633	C₄	—	18	1	no	—
634	C₄	—	18	1	no	—
635	C₄	—	18	1	no	—
636	C₃	—	3	1	no	—
637	C₃	C₃×#5636	1	1	yes	characteristic
638	C₂	—	2	2	no	—
639	C₂	—	18	2	no	—
640	C₂	#63710⋊C₃	1	1	yes	characteristic
641	C₂	C₂×Q₈×AGL(1,ℤ/9)	1	1	yes	characteristic
642	C₂	#41×AGL(1,ℤ/9)	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×C₂²⋊Q₈	C₂
prime radical	C₂×#611⋊C₃	C₂²
hypercenter	C₂²⋊Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#554
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. 3₋¹⁺²×C₂²⋊Q₈	C₂	semidirect
2. #63508⋊C₃	C₂	semidirect
3. #63506⋊C₃	C₂	semidirect
5. C₂×(3₋¹⁺²⋊C₄)⋊C₄	C₂	semidirect
6. #63458⋊C₃	C₂	semidirect
7. #63458⋊C₃	C₂	semidirect
8. C₄⋊C₄×AGL(1,ℤ/9)	C₂	semidirect
9. #63451⋊C₃	C₂	semidirect
10. #63451⋊C₃	C₂	semidirect
11. #63449⋊C₃	C₂	semidirect
14. #63440⋊C₃	C₂	semidirect
15. #63440⋊C₃	C₂	semidirect
17. #10589738	C₃	semidirect
69. C₉×C₂²⋊Q₈	C₂×C₃	semidirect
70. #63508	C₂×C₃	semidirect
71. #63506	C₂×C₃	semidirect
73. C₂×Dic₉⋊C₄	C₂×C₃	semidirect
74. #63458	C₂×C₃	semidirect
75. #63458	C₂×C₃	semidirect
76. C₄⋊C₄×D₉	C₂×C₃	semidirect
77. #63451	C₂×C₃	semidirect
78. #63451	C₂×C₃	semidirect
79. #63449	C₂×C₃	semidirect
82. #63440	C₂×C₃	semidirect
83. #63440	C₂×C₃	semidirect
94. #611⋊C₃	Q₈	semidirect
282. #611	C₃×Q₈	semidirect
431. C₂²⋊Q₈	AGL(1,ℤ/9)	semidirect
438. 3₋¹⁺²	#554	semidirect
580. C₉	C₃×#554	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×C₂²⋊Q₈	2
#63508⋊C₃	2
#63506⋊C₃	2
C₄×#611⋊C₃	2
C₂×(3₋¹⁺²⋊C₄)⋊C₄	2
#63458⋊C₃	2
C₄⋊C₄×AGL(1,ℤ/9)	2
#63451⋊C₃	2
#63449⋊C₃	2
(#611⋊C₃)⋊C₄	2
#63440⋊C₃	2
C₃×#5636	3
#10589738	3

Subgroups — #10589738⋊C3 #13152984

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589738⋊C₃ #13152984