Subgroups — #10589742⋊C₃ #13152974

Order 1728.

685 conjugacy classes of subgroups.

The subgroup lattice has 656 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	#63509⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#63506⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#63491⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63460⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#63458⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#63456⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#63454⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#63449⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#63447⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#63446⋊C₃	C₂	1	1	yes	maximal, characteristic
15	#63441⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃×#5640	—	3	1	no	maximal
17	#10589742	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	C₂×#611⋊C₃	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	C₂×3₋¹⁺²⋊Q₈	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	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
31	C₂²⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
32	#3676⋊C₃	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	(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	C₄⋊(3₋¹⁺²⋊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	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×C₂²⋊Q₈	D₃	1	1	yes	characteristic
54	C₃×#947	—	3	1	no	—
55	C₃×#944	—	3	1	no	—
56	C₃×#929	—	3	1	no	—
57	C₃×C₄×#67	—	3	1	no	—
58	C₃×#898	—	3	1	no	—
59	C₃×#896	—	3	1	no	—
60	C₃×#896	—	3	1	no	—
61	C₃×#894	—	3	1	no	—
62	C₃×#892	—	3	1	no	—
63	C₃×#887	—	3	1	no	—
64	C₃×#885	—	3	1	no	—
65	C₃×#885	—	3	1	no	—
66	C₃×#884	—	3	1	no	—
67	C₃×#879	—	3	1	no	—
68	C₉×C₂²⋊Q₈	—	2	1	no	—
69	C₉×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
70	#63509	C₂×C₃	1	1	yes	characteristic, complemented
71	#63506	C₂×C₃	1	1	yes	characteristic, complemented
72	#63491	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×#611	C₂×C₃	1	1	yes	characteristic, complemented
74	#63460	C₂×C₃	1	1	yes	characteristic, complemented
75	#63458	C₂×C₃	1	1	yes	characteristic, complemented
76	#63458	C₂×C₃	1	1	yes	characteristic, complemented
77	#63456	C₂×C₃	1	1	yes	characteristic, complemented
78	#63454	C₂×C₃	1	1	yes	characteristic, complemented
79	#63449	C₂×C₃	1	1	yes	characteristic, complemented
80	#63447	C₂×C₃	1	1	yes	characteristic, complemented
81	#63447	C₂×C₃	1	1	yes	characteristic, complemented
82	#63446	C₂×C₃	1	1	yes	characteristic
83	#63441	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	C₂²×AGL(1,ℤ/9)	C₂³	1	1	yes	characteristic
87	Q₈×3₋¹⁺²	—	4	1	no	—
88	C₂×C₄×3₋¹⁺²	—	4	1	no	—
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×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
95	#611⋊C₃	—	2	2	no	—
96	#611⋊C₃	—	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	C₄⋊AGL(1,ℤ/9)	—	4	1	no	—
104	C₄×AGL(1,ℤ/9)	—	2	2	no	—
105	C₄×AGL(1,ℤ/9)	—	4	1	no	—
106	3₋¹⁺²⋊Q₈	—	2	2	no	—
107	3₋¹⁺²⋊Q₈	—	4	1	no	—
108	C₃×#542	—	9	1	no	—
109	#5640	—	3	1	no	—
110	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
111	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
112	C₂×C₃×#67	—	3	1	no	—
113	C₂×C₃×#67	—	3	1	no	—
114	C₂×C₃×D₁₂	—	3	1	no	—
115	C₂×C₃×C₄×D₃	—	3	1	no	—
116	C₂×C₃×C₄×D₃	—	3	1	no	—
117	C₂×C₃×Dic₆	—	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×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
123	C₃²×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
124	C₃×#217	—	3	1	no	—
125	C₃×#217	—	3	1	no	—
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×C₄⋊Dic₃	—	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×C₄×Dic₃	—	3	1	no	—
142	C₃×C₄×Dic₃	—	3	1	no	—
143	C₃×C₄×Dic₃	—	3	1	no	—
144	C₃×C₄×Dic₃	—	3	1	no	—
145	C₂×Q₈×C₉	—	2	1	no	—
146	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₄×C₉	—	2	1	no	—
148	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
149	C₂×#611	C₂²×C₃	1	1	yes	characteristic
150	C₂×#611	C₂²×C₃	1	1	yes	characteristic
151	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
154	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
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	C₂²×C₃	1	1	yes	characteristic
160	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
161	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
162	C₉×C₂²⋊C₄	—	2	1	no	—
163	C₉×C₂²⋊C₄	—	2	1	no	—
164	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
165	C₉×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
166	#3676	C₂²×C₃	1	1	yes	characteristic
167	#3676	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	C₄⋊Dic₉	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	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
184	C₄×Dic₉	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	C₂²×3₋¹⁺²	—	2	1	no	—
188	C₂²×3₋¹⁺²	—	2	1	no	—
189	C₂²×3₋¹⁺²	—	2	1	no	—
190	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
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)	—	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	C₄×3₋¹⁺²	—	2	1	no	—
202	C₄×3₋¹⁺²	—	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	—	2	1	no	—
207	3₋¹⁺²⋊C₄	—	2	1	no	—
208	3₋¹⁺²⋊C₄	#41	1	2	yes	—
209	C₃×C₄⋊Q₈	—	9	1	no	—
210	C₃×#126	—	9	1	no	—
211	C₃×#126	—	9	1	no	—
212	C₃×#124	—	9	1	no	—
213	C₃×#124	—	9	1	no	—
214	C₃×#124	—	9	1	no	—
215	C₃×#123	—	9	1	no	—
216	C₃×#123	—	9	1	no	—
217	C₃×C₂²⋊Q₈	—	3	1	no	—
218	C₃×C₂²⋊Q₈	—	9	1	no	—
219	C₃×C₂²⋊Q₈	—	9	1	no	—
220	C₃×C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic
221	C₃×#121	—	9	1	no	—
222	C₃×C₄×Q₈	—	9	1	no	—
223	C₃×C₄×D₄	—	9	1	no	—
224	C₃×#117	—	9	1	no	—
225	#947	—	3	1	no	—
226	#944	—	3	1	no	—
227	#929	—	3	1	no	—
228	C₄×#67	—	3	1	no	—
229	#898	—	3	1	no	—
230	#896	—	3	1	no	—
231	#896	—	3	1	no	—
232	#894	—	3	1	no	—
233	#892	—	3	1	no	—
234	#887	—	3	1	no	—
235	#885	—	3	1	no	—
236	#885	—	3	1	no	—
237	#884	—	3	1	no	—
238	#879	—	3	1	no	—
239	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
240	C₂²×C₃×D₃	—	3	1	no	—
241	C₂²×C₃×D₃	—	3	1	no	—
242	C₃²×Q₈	—	4	1	no	—
243	C₂×C₃²×C₄	—	4	1	no	—
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×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
250	C₃×#67	—	6	2	no	—
251	C₃×#67	—	12	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	—	3	1	no	—
257	C₂×C₃×Dic₃	—	3	1	no	—
258	C₃×D₁₂	—	12	1	no	—
259	C₃×C₄×D₃	—	6	2	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	C₂²×D₉	C₂³×C₃	1	1	yes	characteristic
267	Q₈×C₉	—	4	1	no	—
268	Q₈×C₉	—	4	2	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	—	2	1	no	—
275	C₂×C₄×C₉	—	4	1	no	—
276	C₂×C₄×C₉	—	4	2	no	—
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	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
283	#611	—	2	2	no	—
284	#611	—	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	D₃₆	—	4	1	no	—
292	C₄×D₉	—	2	2	no	—
293	C₄×D₉	—	4	1	no	—
294	Dic₁₈	—	2	2	no	—
295	Dic₁₈	—	4	1	no	—
296	#542	—	9	1	no	Sylow
297	C₂×3₋¹⁺²	—	4	1	no	—
298	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
299	C₂×3₋¹⁺²	H(5,𝔽₂)	1	1	yes	characteristic
300	C₂×3₋¹⁺²	2₋¹⁺⁴	1	1	yes	characteristic
301	AGL(1,ℤ/9)	—	4	1	no	—
302	AGL(1,ℤ/9)	—	4	1	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	C₂×C₃×D₄	—	9	1	no	—
309	C₂×C₃×D₄	—	9	1	no	—
310	C₂²×C₃×C₄	—	3	1	no	—
311	C₂²×C₃×C₄	—	9	1	no	—
312	C₂²×C₃×C₄	—	9	1	no	—
313	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
314	C₂×#67	—	3	1	no	—
315	C₂×#67	—	3	1	no	—
316	C₂×D₁₂	—	3	1	no	—
317	C₂×C₄×D₃	—	3	1	no	—
318	C₂×C₄×D₃	—	3	1	no	—
319	C₂×Dic₆	—	3	1	no	—
320	C₂×Dic₆	—	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	—	9	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	C₂×C₃×D₃	1	1	yes	characteristic
332	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
333	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
334	C₃×C₂²⋊C₄	—	3	1	no	—
335	C₃×C₂²⋊C₄	—	3	1	no	—
336	C₃×C₂²⋊C₄	—	9	1	no	—
337	C₃×C₂²⋊C₄	—	9	1	no	—
338	C₃×C₂²⋊C₄	—	9	1	no	—
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	C₂×C₃×D₃	1	1	yes	characteristic
347	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
348	C₃×C₄²	—	9	1	no	—
349	C₃×C₄²	—	9	1	no	—
350	C₃×C₄²	—	9	1	no	—
351	C₃×C₄²	—	9	1	no	—
352	#217	—	3	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	(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	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	C₄×Dic₃	—	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	—	2	1	no	—
376	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
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	C₂×C₃×D₃	—	6	1	no	—
382	C₂×C₃×D₃	—	6	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	C₃²×C₄	—	2	1	no	—
389	C₃×Dic₃	—	3	2	no	—
390	C₃×Dic₃	—	6	1	no	—
391	C₃×Dic₃	—	6	1	no	—
392	C₃×Dic₃	—	6	1	no	—
393	C₃×Dic₃	—	6	1	no	—
394	C₃×Dic₃	—	6	1	no	—
395	C₂²×C₉	—	2	2	no	—
396	C₂²×C₉	—	2	1	no	—
397	C₂²×C₉	—	2	1	no	—
398	C₂²×C₉	—	2	1	no	—
399	C₂²×C₉	—	2	1	no	—
400	C₂²×C₉	—	4	1	no	—
401	C₂²×C₉	—	4	1	no	—
402	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
403	C₂×D₉	—	2	1	no	—
404	C₂×D₉	—	2	1	no	—
405	C₂×D₉	—	2	1	no	—
406	C₂×D₉	—	2	1	no	—
407	C₂×D₉	—	2	1	no	—
408	C₂×D₉	—	2	1	no	—
409	C₄×C₉	—	2	2	no	—
410	C₄×C₉	—	2	1	no	—
411	C₄×C₉	—	2	1	no	—
412	C₄×C₉	—	2	1	no	—
413	C₄×C₉	—	2	1	no	—
414	C₄×C₉	—	2	1	no	—
415	C₄×C₉	—	2	1	no	—
416	C₄×C₉	—	4	1	no	—
417	C₄×C₉	—	4	1	no	—
418	C₄×C₉	—	4	1	no	—
419	C₄×C₉	—	4	1	no	—
420	C₄×C₉	—	4	1	no	—
421	Dic₉	—	2	1	no	—
422	Dic₉	—	2	1	no	—
423	Dic₉	—	2	1	no	—
424	Dic₉	—	2	1	no	—
425	Dic₉	—	2	1	no	—
426	Dic₉	C₃×#41	1	2	yes	—
427	C₄⋊Q₈	—	9	1	no	—
428	#126	—	9	1	no	—
429	#126	—	9	1	no	—
430	#124	—	9	1	no	—
431	#124	—	9	1	no	—
432	#124	—	9	1	no	—
433	#123	—	9	1	no	—
434	#123	—	9	1	no	—
435	C₂²⋊Q₈	—	9	1	no	—
436	C₂²⋊Q₈	—	9	1	no	—
437	C₂²⋊Q₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
438	#121	—	9	1	no	—
439	C₄×Q₈	—	9	1	no	—
440	C₄×D₄	—	9	1	no	—
441	#117	—	9	1	no	—
442	3₋¹⁺²	#542	1	1	yes	characteristic, complemented, Sylow
443	C₂³×C₃	—	3	1	no	—
444	C₂³×C₃	—	9	1	no	—
445	C₂³×C₃	—	9	1	no	—
446	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
447	C₂²×D₃	—	3	1	no	—
448	C₂²×D₃	—	3	1	no	—
449	C₃×Q₈	—	4	1	no	—
450	C₃×Q₈	—	12	1	no	—
451	C₃×Q₈	—	18	2	no	—
452	C₃×Q₈	—	36	1	no	—
453	C₃×D₄	—	18	2	no	—
454	C₃×D₄	—	36	1	no	—
455	C₃×D₄	—	36	1	no	—
456	C₂×C₃×C₄	—	3	1	no	—
457	C₂×C₃×C₄	—	3	1	no	—
458	C₂×C₃×C₄	—	3	1	no	—
459	C₂×C₃×C₄	—	3	1	no	—
460	C₂×C₃×C₄	—	3	1	no	—
461	C₂×C₃×C₄	—	3	1	no	—
462	C₂×C₃×C₄	—	4	1	no	—
463	C₂×C₃×C₄	—	9	1	no	—
464	C₂×C₃×C₄	—	9	1	no	—
465	C₂×C₃×C₄	—	9	1	no	—
466	C₂×C₃×C₄	—	9	1	no	—
467	C₂×C₃×C₄	—	9	1	no	—
468	C₂×C₃×C₄	—	9	1	no	—
469	C₂×C₃×C₄	—	12	1	no	—
470	C₂×C₃×C₄	—	18	2	no	—
471	C₂×C₃×C₄	—	36	1	no	—
472	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
473	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
474	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
475	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
476	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
477	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
478	#67	—	6	2	no	—
479	#67	—	12	1	no	—
480	C₂×Dic₃	—	3	1	no	—
481	C₂×Dic₃	—	3	1	no	—
482	C₂×Dic₃	—	3	1	no	—
483	C₂×Dic₃	—	3	1	no	—
484	C₂×Dic₃	—	3	1	no	—
485	C₂×Dic₃	—	3	1	no	—
486	D₁₂	—	12	1	no	—
487	C₄×D₃	—	6	2	no	—
488	C₄×D₃	—	12	1	no	—
489	Dic₆	—	6	2	no	—
490	Dic₆	—	12	1	no	—
491	C₂×C₃²	—	4	1	no	—
492	C₂×C₃²	#1004	1	1	yes	characteristic
493	C₂×C₃²	#1007	1	1	yes	characteristic
494	C₂×C₃²	D₃×#41	1	1	yes	characteristic
495	C₃×D₃	—	12	1	no	—
496	C₃×D₃	—	12	1	no	—
497	C₂×C₉	—	2	1	no	—
498	C₂×C₉	—	2	1	no	—
499	C₂×C₉	—	2	1	no	—
500	C₂×C₉	—	4	2	no	—
501	C₂×C₉	—	4	1	no	—
502	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
503	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
504	C₂×C₉	C₃×2₋¹⁺⁴	1	1	yes	characteristic
505	D₉	—	4	1	no	—
506	D₉	—	4	1	no	—
507	C₂×Q₈	—	9	1	no	—
508	C₂×Q₈	—	9	1	no	—
509	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
510	C₂×D₄	—	9	1	no	—
511	C₂×D₄	—	9	1	no	—
512	C₂×D₄	—	9	1	no	—
513	C₂²×C₄	—	9	1	no	—
514	C₂²×C₄	—	9	1	no	—
515	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
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	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
524	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
525	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
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	C₂²⋊C₄	—	9	1	no	—
536	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
537	C₂²⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
538	C₄²	—	9	1	no	—
539	C₄²	—	9	1	no	—
540	C₄²	—	9	1	no	—
541	C₄²	—	9	1	no	—
542	C₂²×C₃	—	2	1	no	—
543	C₂²×C₃	—	2	1	no	—
544	C₂²×C₃	—	2	1	no	—
545	C₂²×C₃	—	3	1	no	—
546	C₂²×C₃	—	6	1	no	—
547	C₂²×C₃	—	6	1	no	—
548	C₂²×C₃	—	6	1	no	—
549	C₂²×C₃	—	18	1	no	—
550	C₂²×C₃	—	18	1	no	—
551	C₂²×C₃	—	18	1	no	—
552	C₂²×C₃	—	18	1	no	—
553	C₂²×C₃	—	18	1	no	—
554	C₂²×C₃	—	18	1	no	—
555	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
556	C₂×D₃	—	6	1	no	—
557	C₂×D₃	—	6	1	no	—
558	C₂×D₃	—	6	1	no	—
559	C₂×D₃	—	6	1	no	—
560	C₂×D₃	—	6	1	no	—
561	C₂×D₃	—	6	1	no	—
562	C₃×C₄	—	2	1	no	—
563	C₃×C₄	—	2	1	no	—
564	C₃×C₄	—	2	1	no	—
565	C₃×C₄	—	2	1	no	—
566	C₃×C₄	—	2	1	no	—
567	C₃×C₄	—	2	1	no	—
568	C₃×C₄	—	6	1	no	—
569	C₃×C₄	—	6	1	no	—
570	C₃×C₄	—	6	1	no	—
571	C₃×C₄	—	6	1	no	—
572	C₃×C₄	—	6	1	no	—
573	C₃×C₄	—	6	1	no	—
574	C₃×C₄	—	9	2	no	—
575	C₃×C₄	—	18	1	no	—
576	C₃×C₄	—	18	1	no	—
577	C₃×C₄	—	18	1	no	—
578	C₃×C₄	—	18	1	no	—
579	C₃×C₄	—	18	1	no	—
580	Dic₃	—	3	2	no	—
581	Dic₃	—	6	1	no	—
582	Dic₃	—	6	1	no	—
583	Dic₃	—	6	1	no	—
584	Dic₃	—	6	1	no	—
585	Dic₃	—	6	1	no	—
586	C₃²	#5640	1	1	yes	characteristic
587	C₉	—	2	1	no	—
588	C₉	C₃×#542	1	1	yes	characteristic, complemented
589	C₂³	—	9	1	no	—
590	C₂³	—	9	1	no	—
591	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
592	Q₈	—	4	1	no	—
593	Q₈	—	18	2	no	—
594	Q₈	—	36	1	no	—
595	D₄	—	18	2	no	—
596	D₄	—	36	1	no	—
597	D₄	—	36	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	9	1	no	—
600	C₂×C₄	—	9	1	no	—
601	C₂×C₄	—	9	1	no	—
602	C₂×C₄	—	9	1	no	—
603	C₂×C₄	—	9	1	no	—
604	C₂×C₄	—	9	1	no	—
605	C₂×C₄	—	18	2	no	—
606	C₂×C₄	—	36	1	no	—
607	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
608	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
609	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
610	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
611	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
612	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
613	C₂×C₃	—	3	1	no	—
614	C₂×C₃	—	3	1	no	—
615	C₂×C₃	—	3	1	no	—
616	C₂×C₃	—	4	1	no	—
617	C₂×C₃	—	12	1	no	—
618	C₂×C₃	—	36	1	no	—
619	C₂×C₃	—	36	1	no	—
620	C₂×C₃	C₃×#1004	1	1	yes	characteristic
621	C₂×C₃	C₃×#1007	1	1	yes	characteristic
622	C₂×C₃	C₃×D₃×#41	1	1	yes	characteristic
623	D₃	—	12	1	no	—
624	D₃	—	12	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	18	1	no	—
629	C₂²	—	18	1	no	—
630	C₂²	—	18	1	no	—
631	C₂²	—	18	1	no	—
632	C₂²	—	18	1	no	—
633	C₂²	—	18	1	no	—
634	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	9	2	no	—
642	C₄	—	18	1	no	—
643	C₄	—	18	1	no	—
644	C₄	—	18	1	no	—
645	C₄	—	18	1	no	—
646	C₄	—	18	1	no	—
647	C₃	—	3	1	no	—
648	C₃	C₃×#5640	1	1	yes	characteristic
649	C₂	—	4	1	no	—
650	C₂	—	36	1	no	—
651	C₂	—	36	1	no	—
652	C₂	#63710⋊C₃	1	1	yes	characteristic
653	C₂	#11722630	1	1	yes	characteristic
654	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	#63446⋊C₃	C₂
hypercenter	C₂²⋊Q₈	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#542
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. #63509⋊C₃	C₂	semidirect
3. #63506⋊C₃	C₂	semidirect
4. #63491⋊C₃	C₂	semidirect
5. C₄×#611⋊C₃	C₂	semidirect
6. #63460⋊C₃	C₂	semidirect
7. #63458⋊C₃	C₂	semidirect
8. #63458⋊C₃	C₂	semidirect
9. #63456⋊C₃	C₂	semidirect
10. #63454⋊C₃	C₂	semidirect
11. #63449⋊C₃	C₂	semidirect
12. #63447⋊C₃	C₂	semidirect
13. #63447⋊C₃	C₂	semidirect
15. #63441⋊C₃	C₂	semidirect
17. #10589742	C₃	semidirect
69. C₉×C₂²⋊Q₈	C₂×C₃	semidirect
70. #63509	C₂×C₃	semidirect
71. #63506	C₂×C₃	semidirect
72. #63491	C₂×C₃	semidirect
73. C₄×#611	C₂×C₃	semidirect
74. #63460	C₂×C₃	semidirect
75. #63458	C₂×C₃	semidirect
76. #63458	C₂×C₃	semidirect
77. #63456	C₂×C₃	semidirect
78. #63454	C₂×C₃	semidirect
79. #63449	C₂×C₃	semidirect
80. #63447	C₂×C₃	semidirect
81. #63447	C₂×C₃	semidirect
83. #63441	C₂×C₃	semidirect
437. C₂²⋊Q₈	AGL(1,ℤ/9)	semidirect
442. 3₋¹⁺²	#542	semidirect
588. C₉	C₃×#542	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
#63509⋊C₃	2
#63506⋊C₃	2
#63491⋊C₃	2
C₄×#611⋊C₃	2
#63460⋊C₃	2
#63458⋊C₃	2
#63456⋊C₃	2
#63454⋊C₃	2
#63449⋊C₃	2
#63447⋊C₃	2
#63446⋊C₃	2
#63441⋊C₃	2
C₃×#5640	3
#10589742	3

Subgroups — #10589742⋊C3 #13152974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589742⋊C₃ #13152974