Subgroups — #103×AGL(1,ℤ/9) #13141946

Order 1728.

507 conjugacy classes of subgroups.

The subgroup lattice has 355 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
4	3₋¹⁺²×#103	C₂	1	1	yes	maximal, characteristic, complemented
5	#63395⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#63376⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
7	#63368⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#103	—	3	1	no	maximal
9	D₉×#103	C₃	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
11	Q₈×AGL(1,ℤ/9)	—	2	2	no	—
12	Q₈×AGL(1,ℤ/9)	C₄	1	4	yes	complemented
13	C₂×C₄×AGL(1,ℤ/9)	—	2	1	no	—
14	C₂×C₄×AGL(1,ℤ/9)	—	2	1	no	—
15	C₂×C₄×AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
16	C₂×3₋¹⁺²⋊Q₈	—	2	1	no	—
17	C₂×3₋¹⁺²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₈×3₋¹⁺²	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
20	C₄⋊(3₋¹⁺²⋊C₄)	C₂²	1	1	yes	characteristic
21	(3₋¹⁺²⋊C₄)⋊C₄	—	2	1	no	—
22	C₂×3₋¹⁺²⋊C₈	C₂²	1	1	yes	characteristic
23	C₈×AGL(1,ℤ/9)	—	2	2	no	—
24	C₂×C₃×D₃×Q₈	—	3	1	no	—
25	C₂×C₃×D₃×C₈	—	3	1	no	—
26	C₃×D₃×C₄⋊C₄	—	3	1	no	—
27	C₂×Q₈×D₉	C₂×C₃	1	1	yes	characteristic
28	C₃²×#103	D₃	1	1	yes	characteristic
29	C₃×#835	—	3	1	no	—
30	C₃×#816	—	3	1	no	—
31	C₃×#810	—	3	1	no	—
32	C₂×C₈×D₉	C₂×C₃	1	1	yes	characteristic
33	C₄⋊C₄×D₉	C₂×C₃	1	1	yes	characteristic
34	C₉×#103	—	2	1	no	—
35	C₉×#103	C₂×C₃	1	1	yes	characteristic, complemented
36	#63395	C₂×C₃	1	1	yes	characteristic, complemented
37	#63376	C₂×C₃	1	1	yes	characteristic, complemented
38	#63368	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂²×AGL(1,ℤ/9)	D₄	1	1	yes	characteristic
40	Q₈×3₋¹⁺²	—	2	1	no	—
41	Q₈×3₋¹⁺²	C₂×C₄	1	2	yes	complemented
42	C₂×C₄×3₋¹⁺²	—	2	1	no	—
43	C₂×C₄×3₋¹⁺²	—	2	1	no	—
44	C₂×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
45	C₂×3₋¹⁺²⋊C₄	—	2	1	no	—
46	C₂×3₋¹⁺²⋊C₄	—	2	1	no	—
47	C₂×3₋¹⁺²⋊C₄	D₄	1	1	yes	characteristic
48	C₄×AGL(1,ℤ/9)	—	2	4	no	—
49	C₄×AGL(1,ℤ/9)	—	4	2	no	—
50	C₄×AGL(1,ℤ/9)	C₂×C₄	1	2	yes	—
51	C₄×AGL(1,ℤ/9)	D₄	1	2	yes	—
52	3₋¹⁺²⋊Q₈	—	2	1	no	—
53	3₋¹⁺²⋊Q₈	—	2	4	no	—
54	3₋¹⁺²⋊Q₈	C₂×C₄	1	2	yes	complemented
55	C₈×3₋¹⁺²	—	2	1	no	—
56	3₋¹⁺²⋊C₈	—	2	1	no	—
57	C₂×C₃×#103	—	9	1	no	—
58	D₃×#103	—	3	1	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic
60	C₃×D₃×Q₈	—	3	4	no	—
61	C₃×D₃×Q₈	—	6	2	no	—
62	C₂×C₃×C₄×D₃	—	3	1	no	—
63	C₂×C₃×C₄×D₃	—	6	1	no	—
64	C₂×C₃×C₄×D₃	—	6	1	no	—
65	C₂×C₃×Dic₆	—	3	1	no	—
66	C₂×C₃×Dic₆	—	6	1	no	—
67	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
68	C₃²×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
69	C₃×C₄⋊Dic₃	—	3	1	no	—
70	C₃×Dic₃⋊C₄	—	6	1	no	—
71	C₂×C₃×C₃⋊C₈	—	3	1	no	—
72	C₃×D₃×C₈	—	6	2	no	—
73	C₂×Q₈×C₉	—	2	1	no	—
74	C₂×Q₈×C₉	C₂²×C₃	1	1	yes	characteristic
75	Q₈×D₉	—	2	2	no	—
76	Q₈×D₉	C₃×C₄	1	4	yes	complemented
77	C₂×C₄×D₉	—	2	1	no	—
78	C₂×C₄×D₉	—	2	1	no	—
79	C₂×C₄×D₉	C₂²×C₃	1	1	yes	characteristic
80	C₂×Dic₁₈	—	2	1	no	—
81	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₈×C₉	—	2	1	no	—
83	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
84	C₉×C₄⋊C₄	—	2	1	no	—
85	C₉×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
87	Dic₉⋊C₄	—	2	1	no	—
88	C₂×C₉⋊C₈	C₂²×C₃	1	1	yes	characteristic
89	C₈×D₉	—	2	2	no	—
90	C₂²×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
91	C₂×AGL(1,ℤ/9)	C₂²⋊C₄	1	2	yes	—
92	C₂×AGL(1,ℤ/9)	SD₁₆	1	2	yes	—
93	C₂×AGL(1,ℤ/9)	Q₁₆	1	2	yes	—
94	C₄×3₋¹⁺²	—	2	2	no	—
95	C₄×3₋¹⁺²	—	4	1	no	—
96	C₄×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
97	C₄×3₋¹⁺²	C₂×D₄	1	1	yes	characteristic
98	3₋¹⁺²⋊C₄	—	2	2	no	—
99	3₋¹⁺²⋊C₄	—	4	1	no	—
100	3₋¹⁺²⋊C₄	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₃×Q₈	—	9	1	no	—
102	C₂×D₃×Q₈	—	3	1	no	—
103	C₂²×C₃×C₈	—	9	1	no	—
104	C₂×C₃×C₄⋊C₄	—	9	1	no	—
105	C₂×D₃×C₈	—	3	1	no	—
106	D₃×C₄⋊C₄	—	3	1	no	—
107	C₃×#103	—	3	1	no	—
108	C₃×#103	—	9	1	no	—
109	C₃×#103	—	9	1	no	—
110	C₃×#103	—	9	1	no	—
111	C₃×#103	C₃×D₃	1	1	yes	characteristic
112	#835	—	3	1	no	—
113	#816	—	3	1	no	—
114	#810	—	3	1	no	—
115	C₂²×C₃×D₃	—	3	1	no	—
116	C₃²×Q₈	—	2	1	no	—
117	C₃²×Q₈	C₄×D₃	1	2	yes	—
118	C₂×C₃²×C₄	—	2	1	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
121	C₂×C₃×Dic₃	—	3	1	no	—
122	C₂×C₃×Dic₃	—	6	1	no	—
123	C₂×C₃×Dic₃	—	6	1	no	—
124	C₃×C₄×D₃	—	3	2	no	—
125	C₃×C₄×D₃	—	3	2	no	—
126	C₃×C₄×D₃	—	6	4	no	—
127	C₃×C₄×D₃	—	12	2	no	—
128	C₃×Dic₆	—	3	2	no	—
129	C₃×Dic₆	—	6	4	no	—
130	C₃×Dic₆	—	6	1	no	—
131	C₂²×D₉	C₃×D₄	1	1	yes	characteristic
132	C₃²×C₈	—	2	1	no	—
133	C₃×C₃⋊C₈	—	6	1	no	—
134	Q₈×C₉	—	2	1	no	—
135	Q₈×C₉	—	2	2	no	—
136	Q₈×C₉	—	4	1	no	—
137	Q₈×C₉	C₂×C₃×C₄	1	2	yes	complemented
138	C₂×C₄×C₉	—	2	1	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	4	1	no	—
142	C₂×C₄×C₉	—	4	1	no	—
143	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
144	C₂×Dic₉	—	2	1	no	—
145	C₂×Dic₉	—	2	1	no	—
146	C₂×Dic₉	C₃×D₄	1	1	yes	characteristic
147	C₄×D₉	—	2	4	no	—
148	C₄×D₉	—	4	2	no	—
149	C₄×D₉	C₂×C₃×C₄	1	2	yes	—
150	C₄×D₉	C₃×D₄	1	2	yes	—
151	Dic₁₈	—	2	1	no	—
152	Dic₁₈	—	2	4	no	—
153	Dic₁₈	C₂×C₃×C₄	1	2	yes	complemented
154	C₈×C₉	—	2	1	no	—
155	C₈×C₉	—	4	1	no	—
156	C₉⋊C₈	—	2	1	no	—
157	C₂×#103	—	9	1	no	Sylow
158	C₂×3₋¹⁺²	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×3₋¹⁺²	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×3₋¹⁺²	C₂×Q₁₆	1	1	yes	characteristic
161	AGL(1,ℤ/9)	#103	1	4	yes	direct product factor
162	C₂×C₃×Q₈	—	3	1	no	—
163	C₂×C₃×Q₈	—	9	1	no	—
164	C₂×C₃×Q₈	—	9	4	no	—
165	C₂×C₃×Q₈	—	18	1	no	—
166	C₂×C₃×Q₈	—	18	2	no	—
167	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	—	9	1	no	—
169	C₂²×C₃×C₄	—	18	1	no	—
170	C₂²×C₃×C₄	—	18	1	no	—
171	D₃×Q₈	—	3	4	no	—
172	D₃×Q₈	—	6	2	no	—
173	C₂×C₄×D₃	—	3	1	no	—
174	C₂×C₄×D₃	—	6	1	no	—
175	C₂×C₄×D₃	—	6	1	no	—
176	C₂×Dic₆	—	3	1	no	—
177	C₂×Dic₆	—	6	1	no	—
178	C₂×C₃×C₈	—	3	1	no	—
179	C₂×C₃×C₈	—	9	1	no	—
180	C₂×C₃×C₈	—	18	2	no	—
181	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
182	C₃×C₄⋊C₄	—	3	1	no	—
183	C₃×C₄⋊C₄	—	9	1	no	—
184	C₃×C₄⋊C₄	—	18	1	no	—
185	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
186	C₄⋊Dic₃	—	3	1	no	—
187	Dic₃⋊C₄	—	6	1	no	—
188	C₂×C₃⋊C₈	—	3	1	no	—
189	D₃×C₈	—	6	2	no	—
190	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
191	C₂×C₃×D₃	—	3	2	no	—
192	C₂×C₃×D₃	—	3	2	no	—
193	C₂×C₃×D₃	—	3	2	no	—
194	C₃²×C₄	—	2	2	no	—
195	C₃²×C₄	—	4	1	no	—
196	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
197	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
198	C₃×Dic₃	—	3	2	no	—
199	C₃×Dic₃	—	6	2	no	—
200	C₃×Dic₃	—	12	1	no	—
201	C₂²×C₉	—	2	1	no	—
202	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
203	C₂×D₉	C₃×C₂²⋊C₄	1	2	yes	—
204	C₂×D₉	C₃×SD₁₆	1	2	yes	—
205	C₂×D₉	C₃×Q₁₆	1	2	yes	—
206	C₄×C₉	—	2	2	no	—
207	C₄×C₉	—	2	1	no	—
208	C₄×C₉	—	2	1	no	—
209	C₄×C₉	—	4	2	no	—
210	C₄×C₉	—	4	1	no	—
211	C₄×C₉	—	8	1	no	—
212	C₄×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
213	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
214	Dic₉	—	2	2	no	—
215	Dic₉	—	4	1	no	—
216	Dic₉	C₃×C₂²⋊C₄	1	2	yes	—
217	C₂²×Q₈	—	9	1	no	—
218	C₂²×C₈	—	9	1	no	—
219	C₂×C₄⋊C₄	—	9	1	no	—
220	#103	—	9	1	no	—
221	#103	—	9	1	no	—
222	#103	—	9	1	no	—
223	#103	AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
224	3₋¹⁺²	C₂×#103	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₃	—	9	1	no	—
226	C₂²×D₃	—	3	1	no	—
227	C₃×Q₈	—	2	1	no	—
228	C₃×Q₈	—	3	2	no	—
229	C₃×Q₈	—	6	1	no	—
230	C₃×Q₈	—	9	2	no	—
231	C₃×Q₈	—	18	1	no	—
232	C₃×Q₈	—	18	4	no	—
233	C₃×Q₈	C₃×C₄×D₃	1	2	yes	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	3	1	no	—
237	C₂×C₃×C₄	—	6	1	no	—
238	C₂×C₃×C₄	—	6	1	no	—
239	C₂×C₃×C₄	—	9	2	no	—
240	C₂×C₃×C₄	—	9	2	no	—
241	C₂×C₃×C₄	—	9	1	no	—
242	C₂×C₃×C₄	—	18	4	no	—
243	C₂×C₃×C₄	—	18	1	no	—
244	C₂×C₃×C₄	—	18	1	no	—
245	C₂×C₃×C₄	—	36	2	no	—
246	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
247	C₂×Dic₃	—	3	1	no	—
248	C₂×Dic₃	—	6	1	no	—
249	C₂×Dic₃	—	6	1	no	—
250	C₄×D₃	—	3	2	no	—
251	C₄×D₃	—	3	2	no	—
252	C₄×D₃	—	6	4	no	—
253	C₄×D₃	—	12	2	no	—
254	Dic₆	—	3	2	no	—
255	Dic₆	—	6	4	no	—
256	Dic₆	—	6	1	no	—
257	C₃×C₈	—	2	1	no	—
258	C₃×C₈	—	6	1	no	—
259	C₃×C₈	—	18	1	no	—
260	C₃⋊C₈	—	6	1	no	—
261	C₂×C₃²	D₃×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₃²	D₃×SD₁₆	1	1	yes	characteristic
263	C₂×C₃²	D₃×Q₁₆	1	1	yes	characteristic
264	C₃×D₃	—	3	4	no	—
265	C₂×C₉	—	2	1	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₉	C₂×C₃×SD₁₆	1	1	yes	characteristic
270	C₂×C₉	C₂×C₃×Q₁₆	1	1	yes	characteristic
271	D₉	C₃×#103	1	4	yes	complemented
272	C₂×Q₈	—	9	4	no	—
273	C₂×Q₈	—	9	1	no	—
274	C₂×Q₈	—	18	1	no	—
275	C₂×Q₈	—	18	2	no	—
276	C₂×Q₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
277	C₂²×C₄	—	9	1	no	—
278	C₂²×C₄	—	18	1	no	—
279	C₂²×C₄	—	18	1	no	—
280	C₂×C₈	—	9	1	no	—
281	C₂×C₈	—	18	2	no	—
282	C₂×C₈	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
283	C₄⋊C₄	—	9	1	no	—
284	C₄⋊C₄	—	18	1	no	—
285	C₄⋊C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
286	C₂²×C₃	—	3	1	no	—
287	C₂²×C₃	—	9	2	no	—
288	C₂²×C₃	—	9	2	no	—
289	C₂²×C₃	—	9	2	no	—
290	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
291	C₂×D₃	—	3	2	no	—
292	C₂×D₃	—	3	2	no	—
293	C₂×D₃	—	3	2	no	—
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	3	1	no	—
296	C₃×C₄	—	3	1	no	—
297	C₃×C₄	—	4	1	no	—
298	C₃×C₄	—	6	2	no	—
299	C₃×C₄	—	9	2	no	—
300	C₃×C₄	—	12	1	no	—
301	C₃×C₄	—	18	2	no	—
302	C₃×C₄	—	36	1	no	—
303	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
304	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
305	Dic₃	—	3	2	no	—
306	Dic₃	—	6	2	no	—
307	Dic₃	—	12	1	no	—
308	C₃²	D₃×#103	1	1	yes	characteristic
309	C₉	—	2	1	no	—
310	C₉	C₂×C₃×#103	1	1	yes	characteristic, complemented
311	C₂³	—	9	1	no	—
312	Q₈	—	2	1	no	—
313	Q₈	—	9	2	no	—
314	Q₈	—	18	4	no	—
315	Q₈	—	18	1	no	—
316	Q₈	C₄×AGL(1,ℤ/9)	1	2	yes	complemented
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	9	1	no	—
320	C₂×C₄	—	9	2	no	—
321	C₂×C₄	—	9	2	no	—
322	C₂×C₄	—	18	4	no	—
323	C₂×C₄	—	18	1	no	—
324	C₂×C₄	—	18	1	no	—
325	C₂×C₄	—	36	2	no	—
326	C₂×C₄	C₂²×AGL(1,ℤ/9)	1	1	yes	characteristic
327	C₈	—	2	1	no	—
328	C₈	—	18	1	no	—
329	C₂×C₃	—	3	1	no	—
330	C₂×C₃	—	3	1	no	—
331	C₂×C₃	—	3	1	no	—
332	C₂×C₃	—	9	4	no	—
333	C₂×C₃	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
334	C₂×C₃	C₃×D₃×SD₁₆	1	1	yes	characteristic
335	C₂×C₃	C₃×D₃×Q₁₆	1	1	yes	characteristic
336	D₃	—	3	4	no	—
337	C₂²	—	9	2	no	—
338	C₂²	—	9	2	no	—
339	C₂²	—	9	2	no	—
340	C₂²	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	4	1	no	—
343	C₄	—	9	2	no	—
344	C₄	—	18	2	no	—
345	C₄	—	36	1	no	—
346	C₄	C₂×C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
347	C₄	D₄×AGL(1,ℤ/9)	1	1	yes	characteristic
348	C₃	—	3	1	no	—
349	C₃	C₃×D₃×#103	1	1	yes	characteristic
350	C₂	—	9	4	no	—
351	C₂	C₂²⋊C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
352	C₂	SD₁₆×AGL(1,ℤ/9)	1	1	yes	characteristic
353	C₂	Q₁₆×AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×AGL(1,ℤ/9)
commutator	C₄×C₉	C₂²×C₃×C₄
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	3₋¹⁺²×#103	C₂
socle	C₂²×C₃	C₃×D₃×D₄
prime radical	C₂²×AGL(1,ℤ/9)	D₄
cosocle	C₂×C₄×C₉	C₂³×C₃
hypercenter	#103	AGL(1,ℤ/9)
hypocenter	C₉	C₂×C₃×#103
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
4. 3₋¹⁺²×#103	C₂	semidirect
5. #63395⋊C₃	C₂	semidirect
6. #63376⋊C₃	C₂	semidirect
7. #63368⋊C₃	C₂	semidirect
9. D₉×#103	C₃	semidirect
12. Q₈×AGL(1,ℤ/9)	C₄	semidirect
35. C₉×#103	C₂×C₃	semidirect
36. #63395	C₂×C₃	semidirect
37. #63376	C₂×C₃	semidirect
38. #63368	C₂×C₃	semidirect
41. Q₈×3₋¹⁺²	C₂×C₄	semidirect
54. 3₋¹⁺²⋊Q₈	C₂×C₄	semidirect
76. Q₈×D₉	C₃×C₄	semidirect
137. Q₈×C₉	C₂×C₃×C₄	semidirect
153. Dic₁₈	C₂×C₃×C₄	semidirect
161. AGL(1,ℤ/9)	#103	direct (N × H)
223. #103	AGL(1,ℤ/9)	direct (N × H)
224. 3₋¹⁺²	C₂×#103	semidirect
271. D₉	C₃×#103	semidirect
310. C₉	C₂×C₃×#103	semidirect
316. Q₈	C₄×AGL(1,ℤ/9)	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×AGL(1,ℤ/9)	2
C₂×C₈×AGL(1,ℤ/9)	2
C₄⋊C₄×AGL(1,ℤ/9)	2
3₋¹⁺²×#103	2
#63395⋊C₃	2
#63376⋊C₃	2
#63368⋊C₃	2
C₃×D₃×#103	3
D₉×#103	3