Subgroups — #10589581⋊C₃ #13152322

Order 1728.

756 conjugacy classes of subgroups.

The subgroup lattice has 483 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	#63492⋊C₃	C₂	1	1	yes	maximal, characteristic
3	#63491⋊C₃	C₂	1	2	yes	maximal, complemented
4	C₄×#611⋊C₃	C₂	1	2	yes	maximal, complemented
5	#63486⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#11721396	C₂	1	2	yes	maximal, complemented
7	#63437⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₄⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
9	#63434⋊C₃	C₂	1	2	yes	maximal, complemented
10	#63432⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×3₋¹⁺²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#5479	—	3	1	no	maximal
13	#10589581	C₃	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
15	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
16	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
17	C₂×#611⋊C₃	C₂²	1	2	yes	—
18	C₂×C₄⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
19	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	2	yes	—
20	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
22	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
23	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
24	C₄²×3₋¹⁺²	C₂²	1	1	yes	characteristic
25	#3676⋊C₃	C₂²	1	2	yes	—
26	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
27	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
28	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
29	(C₂×AGL(1,ℤ/9))⋊C₄	C₂²	1	2	yes	—
30	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
31	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
32	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
33	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
34	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
35	(3₋¹⁺²⋊C₄)⋊C₄	C₂²	1	2	yes	—
36	C₄×3₋¹⁺²⋊C₄	C₂²	1	2	yes	—
37	C₂×C₃²×C₄²	D₃	1	1	yes	characteristic
38	C₃×#930	—	3	1	no	—
39	C₃×#929	—	3	2	no	—
40	C₃×C₄×#67	—	3	2	no	—
41	C₃×#924	—	3	1	no	—
42	C₃×#876	—	3	2	no	—
43	C₃×#875	—	3	1	no	—
44	C₃×C₄×D₁₂	—	3	1	no	—
45	C₃×#872	—	3	2	no	—
46	C₃×#870	—	3	1	no	—
47	C₃×C₄×Dic₆	—	3	1	no	—
48	C₂×C₄²×C₉	—	2	1	no	—
49	C₂×C₄²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
50	#63492	C₂×C₃	1	1	yes	characteristic
51	#63491	C₂×C₃	1	2	yes	complemented
52	C₄×#611	C₂×C₃	1	2	yes	complemented
53	#63486	C₂×C₃	1	1	yes	characteristic, complemented
54	#63438	C₂×C₃	1	2	yes	complemented
55	#63437	C₂×C₃	1	1	yes	characteristic, complemented
56	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic, complemented
57	#63434	C₂×C₃	1	2	yes	complemented
58	#63432	C₂×C₃	1	1	yes	characteristic, complemented
59	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂³×3₋¹⁺²	C₂³	1	1	yes	characteristic
61	C₂²×AGL(1,ℤ/9)	C₂³	1	2	yes	—
62	C₂×C₄×3₋¹⁺²	—	2	2	no	—
63	C₂×C₄×3₋¹⁺²	—	2	2	no	—
64	C₂×C₄×3₋¹⁺²	—	2	2	no	—
65	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
66	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
67	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
68	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
69	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
70	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
71	#611⋊C₃	—	2	4	no	—
72	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
73	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
74	C₂×3₋¹⁺²⋊C₄	C₂³	1	2	yes	—
75	C₄⋊AGL(1,ℤ/9)	—	2	2	no	—
76	C₄×AGL(1,ℤ/9)	—	2	4	no	—
77	3₋¹⁺²⋊Q₈	—	2	2	no	—
78	C₃×#529	—	9	1	no	—
79	#5479	—	3	1	no	—
80	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
81	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
82	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃×#67	—	3	2	no	—
84	C₂×C₃×D₁₂	—	3	1	no	—
85	C₂×C₃×C₄×D₃	—	3	2	no	—
86	C₂×C₃×Dic₆	—	3	1	no	—
87	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
88	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
89	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
90	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
91	C₃×#217	—	3	2	no	—
92	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
93	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
94	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
95	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
96	C₃×C₄⋊Dic₃	—	3	1	no	—
97	C₃×C₄⋊Dic₃	—	3	1	no	—
98	C₃×Dic₃⋊C₄	—	3	2	no	—
99	C₃×Dic₃⋊C₄	—	3	2	no	—
100	C₃×Dic₃⋊C₄	—	3	2	no	—
101	C₃×Dic₃⋊C₄	—	3	2	no	—
102	C₃×C₄×Dic₃	—	3	2	no	—
103	C₂²×C₄×C₉	—	2	1	no	—
104	C₂²×C₄×C₉	—	2	1	no	—
105	C₂²×C₄×C₉	—	2	1	no	—
106	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
109	C₂×#611	C₂²×C₃	1	2	yes	—
110	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
112	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
113	C₄²×C₉	—	2	1	no	—
114	C₄²×C₉	—	2	1	no	—
115	C₄²×C₉	—	2	1	no	—
116	C₄²×C₉	—	2	1	no	—
117	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
118	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
119	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
120	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
121	#3676	C₂²×C₃	1	2	yes	—
122	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
123	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
124	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
125	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
126	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
127	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
128	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
129	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
130	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
131	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
132	C₄×Dic₉	C₂²×C₃	1	2	yes	—
133	C₂²×3₋¹⁺²	—	2	1	no	—
134	C₂²×3₋¹⁺²	—	2	1	no	—
135	C₂²×3₋¹⁺²	#41	1	2	yes	—
136	C₂²×3₋¹⁺²	C₂⁴	1	1	yes	characteristic
137	C₂×AGL(1,ℤ/9)	—	2	2	no	—
138	C₂×AGL(1,ℤ/9)	—	2	2	no	—
139	C₂×AGL(1,ℤ/9)	—	2	2	no	—
140	C₄×3₋¹⁺²	—	2	1	no	—
141	C₄×3₋¹⁺²	—	2	1	no	—
142	C₄×3₋¹⁺²	—	2	1	no	—
143	C₄×3₋¹⁺²	—	2	1	no	—
144	C₄×3₋¹⁺²	#41	1	2	yes	—
145	C₄×3₋¹⁺²	#41	1	2	yes	—
146	3₋¹⁺²⋊C₄	—	2	2	no	—
147	3₋¹⁺²⋊C₄	—	2	2	no	—
148	3₋¹⁺²⋊C₄	—	2	2	no	—
149	C₃×#126	—	9	2	no	—
150	C₃×#125	—	9	1	no	—
151	C₃×#124	—	9	1	no	—
152	C₃×#123	—	9	2	no	—
153	C₃×C₂²⋊Q₈	—	9	1	no	—
154	C₃×#121	—	9	1	no	—
155	C₃×C₄×Q₈	—	9	1	no	—
156	C₃×C₄×D₄	—	9	1	no	—
157	C₃×C₄×D₄	—	9	2	no	—
158	C₃×#117	—	9	2	no	—
159	C₂×C₃×C₄²	—	3	1	no	—
160	C₂×C₃×C₄²	C₃×D₃	1	1	yes	characteristic
161	#930	—	3	1	no	—
162	#929	—	3	2	no	—
163	C₄×#67	—	3	2	no	—
164	#924	—	3	1	no	—
165	#876	—	3	2	no	—
166	#875	—	3	1	no	—
167	C₄×D₁₂	—	3	1	no	—
168	#872	—	3	2	no	—
169	#870	—	3	1	no	—
170	C₄×Dic₆	—	3	1	no	—
171	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
172	C₂²×C₃×D₃	—	3	2	no	—
173	C₂×C₃²×C₄	—	2	2	no	—
174	C₂×C₃²×C₄	—	2	2	no	—
175	C₂×C₃²×C₄	—	2	2	no	—
176	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
177	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
180	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
181	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
182	C₃×#67	—	6	4	no	—
183	C₂×C₃×Dic₃	—	3	2	no	—
184	C₂×C₃×Dic₃	—	3	2	no	—
185	C₂×C₃×Dic₃	—	3	2	no	—
186	C₃×D₁₂	—	6	2	no	—
187	C₃×C₄×D₃	—	6	4	no	—
188	C₃×Dic₆	—	6	2	no	—
189	C₂³×C₉	—	2	1	no	—
190	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
191	C₂²×D₉	C₂³×C₃	1	2	yes	—
192	C₂×C₄×C₉	—	2	4	no	—
193	C₂×C₄×C₉	—	2	4	no	—
194	C₂×C₄×C₉	—	2	4	no	—
195	C₂×C₄×C₉	—	2	2	no	—
196	C₂×C₄×C₉	—	2	2	no	—
197	C₂×C₄×C₉	—	2	2	no	—
198	C₂×C₄×C₉	—	2	1	no	—
199	C₂×C₄×C₉	—	2	1	no	—
200	C₂×C₄×C₉	—	2	1	no	—
201	C₂×C₄×C₉	—	2	1	no	—
202	C₂×C₄×C₉	—	2	1	no	—
203	C₂×C₄×C₉	—	2	1	no	—
204	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
208	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
210	#611	—	2	4	no	—
211	C₂×Dic₉	C₂³×C₃	1	2	yes	—
212	C₂×Dic₉	C₂³×C₃	1	2	yes	—
213	C₂×Dic₉	C₂³×C₃	1	2	yes	—
214	D₃₆	—	2	2	no	—
215	C₄×D₉	—	2	4	no	—
216	Dic₁₈	—	2	2	no	—
217	#529	—	9	1	no	Sylow
218	C₂×3₋¹⁺²	—	2	2	no	—
219	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
220	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
221	C₂×3₋¹⁺²	C₂×#41	1	1	yes	characteristic
222	AGL(1,ℤ/9)	—	4	2	no	—
223	C₂×C₃×Q₈	—	9	1	no	—
224	C₂×C₃×D₄	—	9	1	no	—
225	C₂×C₃×D₄	—	9	2	no	—
226	C₂²×C₃×C₄	—	3	1	no	—
227	C₂²×C₃×C₄	—	3	1	no	—
228	C₂²×C₃×C₄	—	3	1	no	—
229	C₂²×C₃×C₄	—	9	2	no	—
230	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
231	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
232	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
233	C₂×#67	—	3	2	no	—
234	C₂×D₁₂	—	3	1	no	—
235	C₂×C₄×D₃	—	3	2	no	—
236	C₂×Dic₆	—	3	1	no	—
237	C₃×C₄⋊C₄	—	9	2	no	—
238	C₃×C₄⋊C₄	—	9	2	no	—
239	C₃×C₄⋊C₄	—	9	2	no	—
240	C₃×C₄⋊C₄	—	9	2	no	—
241	C₃×C₄⋊C₄	—	9	1	no	—
242	C₃×C₄⋊C₄	—	9	1	no	—
243	C₃×C₂²⋊C₄	—	9	2	no	—
244	C₃×C₂²⋊C₄	—	9	2	no	—
245	C₃×C₂²⋊C₄	—	9	2	no	—
246	C₃×C₂²⋊C₄	—	9	2	no	—
247	C₃×C₂²⋊C₄	—	9	2	no	—
248	C₃×C₄²	—	3	1	no	—
249	C₃×C₄²	—	3	1	no	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	3	1	no	—
252	C₃×C₄²	—	9	2	no	—
253	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
254	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
255	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
256	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
257	#217	—	3	2	no	—
258	(C₂×D₃)⋊C₄	—	3	2	no	—
259	(C₂×D₃)⋊C₄	—	3	2	no	—
260	(C₂×D₃)⋊C₄	—	3	2	no	—
261	(C₂×D₃)⋊C₄	—	3	2	no	—
262	C₄⋊Dic₃	—	3	1	no	—
263	C₄⋊Dic₃	—	3	1	no	—
264	Dic₃⋊C₄	—	3	2	no	—
265	Dic₃⋊C₄	—	3	2	no	—
266	Dic₃⋊C₄	—	3	2	no	—
267	Dic₃⋊C₄	—	3	2	no	—
268	C₄×Dic₃	—	3	2	no	—
269	C₂²×C₃²	—	2	1	no	—
270	C₂²×C₃²	—	2	1	no	—
271	C₂²×C₃²	#235	1	2	yes	—
272	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
273	C₂×C₃×D₃	—	6	2	no	—
274	C₂×C₃×D₃	—	6	2	no	—
275	C₂×C₃×D₃	—	6	2	no	—
276	C₃²×C₄	—	2	1	no	—
277	C₃²×C₄	—	2	1	no	—
278	C₃²×C₄	—	2	1	no	—
279	C₃²×C₄	—	2	1	no	—
280	C₃²×C₄	#235	1	2	yes	—
281	C₃²×C₄	#235	1	2	yes	—
282	C₃×Dic₃	—	6	2	no	—
283	C₃×Dic₃	—	6	2	no	—
284	C₃×Dic₃	—	6	2	no	—
285	C₂²×C₉	—	2	2	no	—
286	C₂²×C₉	—	2	2	no	—
287	C₂²×C₉	—	2	1	no	—
288	C₂²×C₉	—	2	1	no	—
289	C₂²×C₉	—	2	1	no	—
290	C₂²×C₉	—	2	2	no	—
291	C₂²×C₉	C₃×#41	1	2	yes	—
292	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
293	C₂×D₉	—	2	2	no	—
294	C₂×D₉	—	2	2	no	—
295	C₂×D₉	—	2	2	no	—
296	C₄×C₉	—	2	2	no	—
297	C₄×C₉	—	2	2	no	—
298	C₄×C₉	—	2	2	no	—
299	C₄×C₉	—	2	2	no	—
300	C₄×C₉	—	2	1	no	—
301	C₄×C₉	—	2	1	no	—
302	C₄×C₉	—	2	1	no	—
303	C₄×C₉	—	2	1	no	—
304	C₄×C₉	—	2	2	no	—
305	C₄×C₉	—	2	2	no	—
306	C₄×C₉	C₃×#41	1	2	yes	—
307	C₄×C₉	C₃×#41	1	2	yes	—
308	Dic₉	—	2	2	no	—
309	Dic₉	—	2	2	no	—
310	Dic₉	—	2	2	no	—
311	#126	—	9	2	no	—
312	#125	—	9	1	no	—
313	#124	—	9	1	no	—
314	#123	—	9	2	no	—
315	C₂²⋊Q₈	—	9	1	no	—
316	#121	—	9	1	no	—
317	C₄×Q₈	—	9	1	no	—
318	C₄×D₄	—	9	2	no	—
319	C₄×D₄	—	9	1	no	—
320	#117	—	9	2	no	—
321	C₂×C₄²	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
322	3₋¹⁺²	#529	1	1	yes	characteristic, complemented, Sylow
323	C₂³×C₃	—	3	1	no	—
324	C₂³×C₃	—	9	2	no	—
325	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
326	C₂²×D₃	—	3	2	no	—
327	C₃×Q₈	—	18	2	no	—
328	C₃×D₄	—	18	2	no	—
329	C₃×D₄	—	18	4	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	2	no	—
333	C₂×C₃×C₄	—	3	1	no	—
334	C₂×C₃×C₄	—	3	1	no	—
335	C₂×C₃×C₄	—	3	1	no	—
336	C₂×C₃×C₄	—	3	1	no	—
337	C₂×C₃×C₄	—	3	1	no	—
338	C₂×C₃×C₄	—	3	1	no	—
339	C₂×C₃×C₄	—	6	2	no	—
340	C₂×C₃×C₄	—	6	2	no	—
341	C₂×C₃×C₄	—	6	2	no	—
342	C₂×C₃×C₄	—	9	2	no	—
343	C₂×C₃×C₄	—	9	2	no	—
344	C₂×C₃×C₄	—	9	2	no	—
345	C₂×C₃×C₄	—	18	4	no	—
346	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
349	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
352	#67	—	6	4	no	—
353	C₂×Dic₃	—	3	2	no	—
354	C₂×Dic₃	—	3	2	no	—
355	C₂×Dic₃	—	3	2	no	—
356	D₁₂	—	6	2	no	—
357	C₄×D₃	—	6	4	no	—
358	Dic₆	—	6	2	no	—
359	C₂×C₃²	—	2	2	no	—
360	C₂×C₃²	C₂×#235	1	1	yes	characteristic
361	C₂×C₃²	C₂×#235	1	1	yes	characteristic
362	C₂×C₃²	C₂×#235	1	1	yes	characteristic
363	C₃×D₃	—	12	2	no	—
364	C₂×C₉	—	2	4	no	—
365	C₂×C₉	—	2	2	no	—
366	C₂×C₉	—	2	1	no	—
367	C₂×C₉	—	2	1	no	—
368	C₂×C₉	—	2	1	no	—
369	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
370	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
371	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
372	D₉	—	4	2	no	—
373	C₂×Q₈	—	9	1	no	—
374	C₂×D₄	—	9	2	no	—
375	C₂×D₄	—	9	1	no	—
376	C₂²×C₄	—	9	2	no	—
377	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
378	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
379	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
380	C₄⋊C₄	—	9	2	no	—
381	C₄⋊C₄	—	9	2	no	—
382	C₄⋊C₄	—	9	1	no	—
383	C₄⋊C₄	—	9	2	no	—
384	C₄⋊C₄	—	9	1	no	—
385	C₄⋊C₄	—	9	2	no	—
386	C₂²⋊C₄	—	9	2	no	—
387	C₂²⋊C₄	—	9	2	no	—
388	C₂²⋊C₄	—	9	2	no	—
389	C₂²⋊C₄	—	9	2	no	—
390	C₂²⋊C₄	—	9	2	no	—
391	C₄²	—	9	2	no	—
392	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
393	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
394	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
395	C₄²	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
396	C₂²×C₃	—	2	1	no	—
397	C₂²×C₃	—	2	1	no	—
398	C₂²×C₃	—	3	1	no	—
399	C₂²×C₃	—	3	2	no	—
400	C₂²×C₃	—	6	1	no	—
401	C₂²×C₃	—	6	1	no	—
402	C₂²×C₃	—	18	2	no	—
403	C₂²×C₃	—	18	2	no	—
404	C₂²×C₃	—	18	2	no	—
405	C₂²×C₃	C₃×#235	1	2	yes	—
406	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
407	C₂×D₃	—	6	2	no	—
408	C₂×D₃	—	6	2	no	—
409	C₂×D₃	—	6	2	no	—
410	C₃×C₄	—	2	1	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	3	2	no	—
415	C₃×C₄	—	3	2	no	—
416	C₃×C₄	—	6	1	no	—
417	C₃×C₄	—	6	1	no	—
418	C₃×C₄	—	6	1	no	—
419	C₃×C₄	—	6	1	no	—
420	C₃×C₄	—	18	2	no	—
421	C₃×C₄	—	18	2	no	—
422	C₃×C₄	—	18	2	no	—
423	C₃×C₄	C₃×#235	1	2	yes	—
424	C₃×C₄	C₃×#235	1	2	yes	—
425	Dic₃	—	6	2	no	—
426	Dic₃	—	6	2	no	—
427	Dic₃	—	6	2	no	—
428	C₃²	#5479	1	1	yes	characteristic
429	C₉	—	2	1	no	—
430	C₉	C₃×#529	1	1	yes	characteristic, complemented
431	C₂³	—	9	2	no	—
432	C₂³	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
433	Q₈	—	18	2	no	—
434	D₄	—	18	4	no	—
435	D₄	—	18	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	9	2	no	—
440	C₂×C₄	—	9	2	no	—
441	C₂×C₄	—	9	2	no	—
442	C₂×C₄	—	18	4	no	—
443	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
444	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
445	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
446	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
447	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
448	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
449	C₂×C₃	—	2	2	no	—
450	C₂×C₃	—	3	1	no	—
451	C₂×C₃	—	3	1	no	—
452	C₂×C₃	—	3	1	no	—
453	C₂×C₃	—	6	2	no	—
454	C₂×C₃	—	36	2	no	—
455	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
456	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
457	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
458	D₃	—	12	2	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	18	2	no	—
462	C₂²	—	18	2	no	—
463	C₂²	—	18	2	no	—
464	C₂²	#3697⋊C₃	1	2	yes	—
465	C₂²	C₂³×AGL(1,ℤ/9)	1	1	yes	characteristic
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	18	2	no	—
471	C₄	—	18	2	no	—
472	C₄	—	18	2	no	—
473	C₄	#3697⋊C₃	1	2	yes	—
474	C₄	#3697⋊C₃	1	2	yes	—
475	C₃	—	3	1	no	—
476	C₃	C₃×#5479	1	1	yes	characteristic
477	C₂	—	2	2	no	—
478	C₂	—	36	2	no	—
479	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
480	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic
481	C₂	C₂×#3697⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×AGL(1,ℤ/9)
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini, socle	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₄²×3₋¹⁺²	C₂
prime radical	#63492⋊C₃	C₂
hypercenter	C₂×C₄²	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#529
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₄²×3₋¹⁺²	C₂	semidirect
3. #63491⋊C₃	C₂	semidirect
4. C₄×#611⋊C₃	C₂	semidirect
5. #63486⋊C₃	C₂	semidirect
6. #11721396	C₂	semidirect
7. #63437⋊C₃	C₂	semidirect
8. C₄×C₄⋊AGL(1,ℤ/9)	C₂	semidirect
9. #63434⋊C₃	C₂	semidirect
10. #63432⋊C₃	C₂	semidirect
11. C₄×3₋¹⁺²⋊Q₈	C₂	semidirect
13. #10589581	C₃	semidirect
49. C₂×C₄²×C₉	C₂×C₃	semidirect
51. #63491	C₂×C₃	semidirect
52. C₄×#611	C₂×C₃	semidirect
53. #63486	C₂×C₃	semidirect
54. #63438	C₂×C₃	semidirect
55. #63437	C₂×C₃	semidirect
56. C₄×D₃₆	C₂×C₃	semidirect
57. #63434	C₂×C₃	semidirect
58. #63432	C₂×C₃	semidirect
59. C₄×Dic₁₈	C₂×C₃	semidirect
321. C₂×C₄²	AGL(1,ℤ/9)	semidirect
322. 3₋¹⁺²	#529	semidirect
430. C₉	C₃×#529	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄²×3₋¹⁺²	2
#63492⋊C₃	2
#63491⋊C₃	2
C₄×#611⋊C₃	2
#63486⋊C₃	2
#11721396	2
#63437⋊C₃	2
C₄×C₄⋊AGL(1,ℤ/9)	2
#63434⋊C₃	2
#63432⋊C₃	2
C₄×3₋¹⁺²⋊Q₈	2
C₃×#5479	3
#10589581	3

Subgroups — #10589581⋊C3 #13152322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10589581⋊C₃ #13152322