Subgroups — #10588809⋊C₃ #13143234

Order 1728.

406 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#611⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic, complemented
4	#63389⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
5	(C₂×AGL(1,ℤ/9))⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#63375⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	(3₋¹⁺²⋊C₄)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5127	—	3	1	no	maximal
9	#10588809	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
11	C₂×#611⋊C₃	C₄	1	1	yes	characteristic
12	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
13	M₁₆×3₋¹⁺²	—	2	2	no	—
14	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
15	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
16	#3676⋊C₃	C₄	1	1	yes	characteristic
17	(C₂×AGL(1,ℤ/9))⋊C₄	C₄	1	1	yes	characteristic
18	(3₋¹⁺²⋊C₄)⋊C₄	C₄	1	1	yes	characteristic
19	C₄×3₋¹⁺²⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
22	C₈×AGL(1,ℤ/9)	—	2	2	no	—
23	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic
24	C₃×C₄×#67	—	3	1	no	—
25	C₂×C₃×D₃×C₈	—	3	1	no	—
26	C₃×#830	—	3	1	no	—
27	C₃×(C₂×D₃)⋊C₈	—	3	1	no	—
28	C₃×#815	—	3	1	no	—
29	C₃×Dic₃⋊C₈	—	3	1	no	—
30	C₂×C₉×M₁₆	—	2	1	no	—
31	C₂×C₉×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
32	C₄×#611	C₂×C₃	1	1	yes	characteristic
33	C₂×C₈×D₉	C₂×C₃	1	1	yes	characteristic, complemented
34	#63389	C₂×C₃	1	1	yes	characteristic, complemented
35	(C₂×D₉)⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
36	#63375	C₂×C₃	1	1	yes	characteristic, complemented
37	Dic₉⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂³×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
39	C₂²×AGL(1,ℤ/9)	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×3₋¹⁺²	—	2	1	no	—
41	C₂×C₄×3₋¹⁺²	—	2	1	no	—
42	C₂×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
44	#611⋊C₃	—	2	2	no	—
45	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	1	yes	characteristic
47	C₂×3₋¹⁺²⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₄×AGL(1,ℤ/9)	—	2	1	no	—
49	C₄×AGL(1,ℤ/9)	—	2	1	no	—
50	C₈×3₋¹⁺²	—	2	1	no	—
51	C₈×3₋¹⁺²	D₄	1	2	yes	complemented
52	3₋¹⁺²⋊C₈	—	2	1	no	—
53	3₋¹⁺²⋊C₈	—	2	1	no	—
54	C₃×#435	—	9	1	no	—
55	#5127	—	3	1	no	—
56	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
57	C₂×C₃×#67	—	3	1	no	—
58	C₂×C₃×C₄×D₃	—	3	1	no	—
59	C₃²×M₁₆	—	2	2	no	—
60	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
62	C₃×#217	—	3	1	no	—
63	C₃×(C₂×D₃)⋊C₄	—	3	1	no	—
64	C₃×Dic₃⋊C₄	—	3	1	no	—
65	C₃×C₄×Dic₃	—	3	1	no	—
66	C₂×C₃×C₃⋊C₈	—	3	1	no	—
67	C₂×C₃×C₃⋊C₈	—	3	1	no	—
68	C₃×D₃×C₈	—	6	2	no	—
69	C₂²×C₄×C₉	—	2	1	no	—
70	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
71	C₂×#611	C₃×C₄	1	1	yes	characteristic
72	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
73	C₉×M₁₆	—	2	4	no	—
74	C₉×M₁₆	—	2	2	no	—
75	C₂×C₈×C₉	—	2	1	no	—
76	C₂×C₈×C₉	—	2	1	no	—
77	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
79	#3676	C₃×C₄	1	1	yes	characteristic
80	(C₂×D₉)⋊C₄	C₃×C₄	1	1	yes	characteristic
81	Dic₉⋊C₄	C₃×C₄	1	1	yes	characteristic
82	C₄×Dic₉	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
85	C₈×D₉	—	2	2	no	—
86	C₂²×3₋¹⁺²	—	2	1	no	—
87	C₂²×3₋¹⁺²	—	2	1	no	—
88	C₂²×3₋¹⁺²	—	2	1	no	—
89	C₂²×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
90	C₂×AGL(1,ℤ/9)	—	2	1	no	—
91	C₂×AGL(1,ℤ/9)	—	2	1	no	—
92	C₂×AGL(1,ℤ/9)	M₁₆	1	2	yes	complemented
93	C₄×3₋¹⁺²	—	2	1	no	—
94	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
95	C₄×3₋¹⁺²	#41	1	1	yes	characteristic
96	3₋¹⁺²⋊C₄	—	2	1	no	—
97	3₋¹⁺²⋊C₄	—	2	1	no	—
98	3₋¹⁺²⋊C₄	—	2	1	no	—
99	C₂×C₃×M₁₆	—	3	1	no	—
100	C₂×C₃×M₁₆	C₃×D₃	1	1	yes	characteristic
101	C₂²×C₃×C₈	—	9	1	no	—
102	C₃×C₄×D₄	—	9	1	no	—
103	C₄×#67	—	3	1	no	—
104	C₂×D₃×C₈	—	3	1	no	—
105	C₃×C₄⋊C₈	—	9	1	no	—
106	C₃×C₂²⋊C₈	—	9	1	no	—
107	C₃×C₂²⋊C₈	—	9	1	no	—
108	C₃×#97	—	9	1	no	—
109	#830	—	3	1	no	—
110	(C₂×D₃)⋊C₈	—	3	1	no	—
111	#815	—	3	1	no	—
112	Dic₃⋊C₈	—	3	1	no	—
113	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
114	C₂²×C₃×D₃	—	3	1	no	—
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
119	C₃×#67	—	6	2	no	—
120	C₂×C₃×Dic₃	—	3	1	no	—
121	C₂×C₃×Dic₃	—	3	1	no	—
122	C₂×C₃×Dic₃	—	3	1	no	—
123	C₃×C₄×D₃	—	6	1	no	—
124	C₃×C₄×D₃	—	6	1	no	—
125	C₂³×C₉	—	2	1	no	—
126	C₂³×C₉	C₂×C₃×C₄	1	1	yes	characteristic
127	C₂²×D₉	C₂×C₃×C₄	1	1	yes	characteristic
128	C₃²×C₈	—	2	1	no	—
129	C₃²×C₈	#67	1	2	yes	—
130	C₃×C₃⋊C₈	—	6	1	no	—
131	C₃×C₃⋊C₈	—	6	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	1	no	—
137	C₂×C₄×C₉	—	2	1	no	—
138	C₂×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
139	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
140	#611	—	2	2	no	—
141	C₂×Dic₉	C₂×C₃×C₄	1	1	yes	characteristic
142	C₂×Dic₉	C₂×C₃×C₄	1	1	yes	characteristic
143	C₂×Dic₉	C₂×C₃×C₄	1	1	yes	characteristic
144	C₄×D₉	—	2	1	no	—
145	C₄×D₉	—	2	1	no	—
146	C₈×C₉	—	2	2	no	—
147	C₈×C₉	—	2	1	no	—
148	C₈×C₉	—	2	2	no	—
149	C₈×C₉	C₃×D₄	1	2	yes	complemented
150	C₉⋊C₈	—	2	1	no	—
151	C₉⋊C₈	—	2	1	no	—
152	#435	—	9	1	no	Sylow
153	C₂×3₋¹⁺²	—	4	1	no	—
154	C₂×3₋¹⁺²	C₄×D₄	1	1	yes	characteristic
155	C₂×3₋¹⁺²	C₂×M₁₆	1	1	yes	characteristic
156	C₂×3₋¹⁺²	#131	1	1	yes	characteristic
157	AGL(1,ℤ/9)	—	2	2	no	—
158	C₂×C₃×D₄	—	9	1	no	—
159	C₂²×C₃×C₄	—	3	1	no	—
160	C₂²×C₃×C₄	—	9	1	no	—
161	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
162	C₂×#67	—	3	1	no	—
163	C₂×C₄×D₃	—	3	1	no	—
164	C₃×M₁₆	—	2	2	no	—
165	C₃×M₁₆	—	6	2	no	—
166	C₂×C₃×C₈	—	3	1	no	—
167	C₂×C₃×C₈	—	3	1	no	—
168	C₂×C₃×C₈	—	9	1	no	—
169	C₂×C₃×C₈	—	9	1	no	—
170	C₂×C₃×C₈	—	18	2	no	—
171	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
172	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
173	C₃×C₄⋊C₄	—	9	1	no	—
174	C₃×C₂²⋊C₄	—	9	1	no	—
175	C₃×C₂²⋊C₄	—	9	1	no	—
176	C₃×C₄²	—	9	1	no	—
177	#217	—	3	1	no	—
178	(C₂×D₃)⋊C₄	—	3	1	no	—
179	Dic₃⋊C₄	—	3	1	no	—
180	C₄×Dic₃	—	3	1	no	—
181	C₂×C₃⋊C₈	—	3	1	no	—
182	C₂×C₃⋊C₈	—	3	1	no	—
183	D₃×C₈	—	6	2	no	—
184	C₂²×C₃²	—	2	1	no	—
185	C₂²×C₃²	—	2	1	no	—
186	C₂²×C₃²	—	2	1	no	—
187	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
188	C₂×C₃×D₃	—	3	2	no	—
189	C₂×C₃×D₃	—	6	1	no	—
190	C₂×C₃×D₃	—	6	1	no	—
191	C₃²×C₄	—	2	1	no	—
192	C₃²×C₄	#235	1	1	yes	characteristic
193	C₃²×C₄	C₂×#67	1	1	yes	characteristic
194	C₃×Dic₃	—	6	1	no	—
195	C₃×Dic₃	—	6	1	no	—
196	C₃×Dic₃	—	6	1	no	—
197	C₂²×C₉	—	2	2	no	—
198	C₂²×C₉	—	2	1	no	—
199	C₂²×C₉	—	2	1	no	—
200	C₂²×C₉	—	2	1	no	—
201	C₂²×C₉	—	2	1	no	—
202	C₂²×C₉	—	4	1	no	—
203	C₂²×C₉	—	4	1	no	—
204	C₂²×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
205	C₂×D₉	—	2	1	no	—
206	C₂×D₉	—	2	1	no	—
207	C₂×D₉	C₃×M₁₆	1	2	yes	complemented
208	C₄×C₉	—	2	2	no	—
209	C₄×C₉	—	2	1	no	—
210	C₄×C₉	—	2	1	no	—
211	C₄×C₉	—	2	1	no	—
212	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
213	C₄×C₉	C₃×#41	1	1	yes	characteristic
214	Dic₉	—	2	1	no	—
215	Dic₉	—	2	1	no	—
216	Dic₉	—	2	1	no	—
217	C₂×M₁₆	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
218	C₂²×C₈	—	9	1	no	—
219	C₄×D₄	—	9	1	no	—
220	C₄⋊C₈	—	9	1	no	—
221	C₂²⋊C₈	—	9	1	no	—
222	C₂²⋊C₈	—	9	1	no	—
223	#97	—	9	1	no	—
224	3₋¹⁺²	#435	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₃	—	3	1	no	—
226	C₂³×C₃	—	9	1	no	—
227	C₂³×C₃	C₃×C₄×D₃	1	1	yes	characteristic
228	C₂²×D₃	—	3	1	no	—
229	C₃×D₄	—	18	2	no	—
230	C₂×C₃×C₄	—	2	1	no	—
231	C₂×C₃×C₄	—	2	1	no	—
232	C₂×C₃×C₄	—	3	1	no	—
233	C₂×C₃×C₄	—	3	1	no	—
234	C₂×C₃×C₄	—	6	1	no	—
235	C₂×C₃×C₄	—	6	1	no	—
236	C₂×C₃×C₄	—	9	1	no	—
237	C₂×C₃×C₄	—	9	1	no	—
238	C₂×C₃×C₄	—	9	1	no	—
239	C₂×C₃×C₄	—	18	1	no	—
240	C₂×C₃×C₄	—	18	1	no	—
241	C₂×C₃×C₄	C₃×C₄×D₃	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
243	#67	—	6	2	no	—
244	C₂×Dic₃	—	3	1	no	—
245	C₂×Dic₃	—	3	1	no	—
246	C₂×Dic₃	—	3	1	no	—
247	C₄×D₃	—	6	1	no	—
248	C₄×D₃	—	6	1	no	—
249	C₃×C₈	—	2	1	no	—
250	C₃×C₈	—	3	2	no	—
251	C₃×C₈	—	6	1	no	—
252	C₃×C₈	—	18	1	no	—
253	C₃×C₈	—	18	1	no	—
254	C₃×C₈	C₃×#67	1	2	yes	—
255	C₃⋊C₈	—	6	1	no	—
256	C₃⋊C₈	—	6	1	no	—
257	C₂×C₃²	—	4	1	no	—
258	C₂×C₃²	D₃×M₁₆	1	1	yes	characteristic
259	C₂×C₃²	#907	1	1	yes	characteristic
260	C₂×C₃²	C₄×#67	1	1	yes	characteristic
261	C₃×D₃	—	6	2	no	—
262	C₂×C₉	—	2	1	no	—
263	C₂×C₉	—	2	1	no	—
264	C₂×C₉	—	2	1	no	—
265	C₂×C₉	—	4	2	no	—
266	C₂×C₉	—	4	1	no	—
267	C₂×C₉	C₃×C₄×D₄	1	1	yes	characteristic
268	C₂×C₉	C₂×C₃×M₁₆	1	1	yes	characteristic
269	C₂×C₉	C₃×#131	1	1	yes	characteristic
270	D₉	—	2	2	no	—
271	C₂×D₄	—	9	1	no	—
272	C₂²×C₄	—	9	1	no	—
273	C₂²×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
274	M₁₆	—	2	2	no	—
275	C₂×C₈	—	9	1	no	—
276	C₂×C₈	—	9	1	no	—
277	C₂×C₈	—	18	2	no	—
278	C₂×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
279	C₂×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
280	C₄⋊C₄	—	9	1	no	—
281	C₂²⋊C₄	—	9	1	no	—
282	C₂²⋊C₄	—	9	1	no	—
283	C₄²	—	9	1	no	—
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	2	1	no	—
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	3	1	no	—
288	C₂²×C₃	—	6	1	no	—
289	C₂²×C₃	—	6	1	no	—
290	C₂²×C₃	—	6	1	no	—
291	C₂²×C₃	—	9	2	no	—
292	C₂²×C₃	—	18	1	no	—
293	C₂²×C₃	—	18	1	no	—
294	C₂²×C₃	C₂×C₃×C₄×D₃	1	1	yes	characteristic
295	C₂×D₃	—	3	2	no	—
296	C₂×D₃	—	6	1	no	—
297	C₂×D₃	—	6	1	no	—
298	C₃×C₄	—	2	1	no	—
299	C₃×C₄	—	3	1	no	—
300	C₃×C₄	—	3	1	no	—
301	C₃×C₄	—	6	1	no	—
302	C₃×C₄	—	18	1	no	—
303	C₃×C₄	—	18	1	no	—
304	C₃×C₄	—	18	1	no	—
305	C₃×C₄	C₃×#235	1	1	yes	characteristic
306	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
307	Dic₃	—	6	1	no	—
308	Dic₃	—	6	1	no	—
309	Dic₃	—	6	1	no	—
310	C₃²	#5127	1	1	yes	characteristic
311	C₉	—	2	1	no	—
312	C₉	C₃×#435	1	1	yes	characteristic, complemented
313	C₂³	—	9	1	no	—
314	C₂³	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
315	D₄	—	18	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	9	1	no	—
319	C₂×C₄	—	9	1	no	—
320	C₂×C₄	—	9	1	no	—
321	C₂×C₄	—	18	1	no	—
322	C₂×C₄	—	18	1	no	—
323	C₂×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
324	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
325	C₈	—	2	1	no	—
326	C₈	—	18	1	no	—
327	C₈	—	18	1	no	—
328	C₈	#611⋊C₃	1	2	yes	complemented
329	C₂×C₃	—	3	1	no	—
330	C₂×C₃	—	3	1	no	—
331	C₂×C₃	—	3	1	no	—
332	C₂×C₃	—	4	1	no	—
333	C₂×C₃	—	12	1	no	—
334	C₂×C₃	—	18	2	no	—
335	C₂×C₃	C₃×D₃×M₁₆	1	1	yes	characteristic
336	C₂×C₃	C₃×#907	1	1	yes	characteristic
337	C₂×C₃	C₃×C₄×#67	1	1	yes	characteristic
338	D₃	—	6	2	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	9	2	no	—
343	C₂²	—	18	1	no	—
344	C₂²	—	18	1	no	—
345	C₂²	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
346	C₄	—	2	1	no	—
347	C₄	—	18	1	no	—
348	C₄	—	18	1	no	—
349	C₄	—	18	1	no	—
350	C₄	#3697⋊C₃	1	1	yes	characteristic
351	C₄	C₂×#611⋊C₃	1	1	yes	characteristic
352	C₃	—	3	1	no	—
353	C₃	C₃×#5127	1	1	yes	characteristic
354	C₂	—	4	1	no	—
355	C₂	—	18	2	no	—
356	C₂	M₁₆×AGL(1,ℤ/9)	1	1	yes	characteristic
357	C₂	#63469⋊C₃	1	1	yes	characteristic
358	C₂	C₄×#611⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×AGL(1,ℤ/9)
commutator	C₂²×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×M₁₆×3₋¹⁺²	C₂
socle	C₂²×C₃	C₂×C₃×C₄×D₃
prime radical	C₂×#611⋊C₃	C₄
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	C₂×M₁₆	AGL(1,ℤ/9)
hypocenter	C₉	C₃×#435
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×M₁₆×3₋¹⁺²	C₂	semidirect
3. C₂×C₈×AGL(1,ℤ/9)	C₂	semidirect
4. #63389⋊C₃	C₂	semidirect
5. (C₂×AGL(1,ℤ/9))⋊C₈	C₂	semidirect
6. #63375⋊C₃	C₂	semidirect
7. (3₋¹⁺²⋊C₄)⋊C₈	C₂	semidirect
9. #10588809	C₃	semidirect
31. C₂×C₉×M₁₆	C₂×C₃	semidirect
33. C₂×C₈×D₉	C₂×C₃	semidirect
34. #63389	C₂×C₃	semidirect
35. (C₂×D₉)⋊C₈	C₂×C₃	semidirect
36. #63375	C₂×C₃	semidirect
37. Dic₉⋊C₈	C₂×C₃	semidirect
51. C₈×3₋¹⁺²	D₄	semidirect
92. C₂×AGL(1,ℤ/9)	M₁₆	semidirect
149. C₈×C₉	C₃×D₄	semidirect
207. C₂×D₉	C₃×M₁₆	semidirect
217. C₂×M₁₆	AGL(1,ℤ/9)	semidirect
224. 3₋¹⁺²	#435	semidirect
312. C₉	C₃×#435	semidirect
328. C₈	#611⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×3₋¹⁺²	2
C₄×#611⋊C₃	2
C₂×C₈×AGL(1,ℤ/9)	2
#63389⋊C₃	2
(C₂×AGL(1,ℤ/9))⋊C₈	2
#63375⋊C₃	2
(3₋¹⁺²⋊C₄)⋊C₈	2
C₃×#5127	3
#10588809	3

Subgroups — #10588809⋊C3 #13143234

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10588809⋊C₃ #13143234