Subgroups — M₁₆×C₃⋊AGL(1,ℤ/9) #72254607

Order 2592.

770 conjugacy classes of subgroups.

The subgroup lattice has 381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₃⋊AGL(1,ℤ/9)	C₂	1	1	yes	maximal, characteristic
2	C₃×M₁₆×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	#13047945	C₂	1	1	yes	maximal, characteristic, complemented
4	#13047907	C₂	1	2	yes	maximal, complemented
5	C₈×C₃⋊AGL(1,ℤ/9)	C₂	1	2	yes	maximal, complemented
6	C₃×M₁₆×C₃⋊D₃	—	3	1	no	maximal
7	M₁₆×C₃⋊D₉	C₃	1	1	yes	maximal, characteristic, complemented
8	M₁₆×AGL(1,ℤ/9)	—	3	3	no	maximal
9	C₂²×C₃⋊AGL(1,ℤ/9)	C₄	1	1	yes	characteristic
10	C₂×C₃×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
11	C₂×C₃⋊(3₋¹⁺²⋊C₄)	C₄	1	1	yes	characteristic
12	C₄×C₃⋊AGL(1,ℤ/9)	C₄	1	1	yes	characteristic
13	C₄×C₃⋊AGL(1,ℤ/9)	C₄	1	1	yes	characteristic
14	C₄×C₃⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
15	C₄×C₃⋊AGL(1,ℤ/9)	C₂²	1	1	yes	characteristic
16	C₃×C₈×3₋¹⁺²	C₂²	1	2	yes	complemented
17	C₃⋊(3₋¹⁺²⋊C₈)	C₂²	1	2	yes	complemented
18	C₂×C₃×C₄×C₃⋊D₃	—	3	1	no	—
19	C₃³×M₁₆	D₃	1	1	yes	characteristic
20	C₃×#3748	—	3	1	no	—
21	C₃×#3743	—	3	2	no	—
22	C₃×C₈×C₃⋊D₃	—	3	2	no	—
23	C₂×C₄×C₃⋊D₉	C₂×C₃	1	1	yes	characteristic
24	C₂×C₄×AGL(1,ℤ/9)	—	3	3	no	—
25	M₁₆×3₋¹⁺²	—	2	3	no	—
26	M₁₆×3₋¹⁺²	D₃	1	3	yes	complemented
27	C₃×C₉×M₁₆	—	2	1	no	—
28	C₃×C₉×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
29	#88532	C₂×C₃	1	1	yes	characteristic, complemented
30	#88523	C₂×C₃	1	2	yes	complemented
31	C₈×C₃⋊D₉	C₂×C₃	1	2	yes	complemented
32	#3667⋊C₃	—	3	3	no	—
33	#3663⋊C₃	—	3	6	no	—
34	C₈×AGL(1,ℤ/9)	—	3	6	no	—
35	C₂²×C₃×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
36	C₂×C₃⋊AGL(1,ℤ/9)	—	2	2	no	—
37	C₂×C₃⋊AGL(1,ℤ/9)	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃⋊AGL(1,ℤ/9)	C₂×C₄	1	1	yes	characteristic
39	C₃×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
40	C₃×C₄×3₋¹⁺²	C₂³	1	1	yes	characteristic
41	C₃⋊(3₋¹⁺²⋊C₄)	C₂×C₄	1	1	yes	characteristic
42	C₃⋊(3₋¹⁺²⋊C₄)	C₂×C₄	1	1	yes	characteristic
43	M₁₆×C₃⋊D₃	—	3	1	no	—
44	C₃×D₃×M₁₆	—	9	3	no	—
45	C₃×D₃×M₁₆	—	9	1	no	—
46	M₁₆×D₉	—	3	3	no	—
47	C₂²×C₃×C₃⋊D₃	—	3	1	no	—
48	C₂×C₃³×C₄	C₂×D₃	1	1	yes	characteristic
49	C₂×C₃×C₃⋊Dic₃	—	3	1	no	—
50	C₃×C₄×C₃⋊D₃	—	3	1	no	—
51	C₃×C₄×C₃⋊D₃	—	3	1	no	—
52	C₃×C₄×C₃⋊D₃	—	3	1	no	—
53	C₃×C₄×C₃⋊D₃	—	3	1	no	—
54	C₂²×C₃⋊D₉	C₃×C₄	1	1	yes	characteristic
55	C₂²×AGL(1,ℤ/9)	—	3	3	no	—
56	C₃³×C₈	C₂×D₃	1	2	yes	—
57	C₃×C₃⋊(C₃⋊C₈)	—	3	2	no	—
58	C₂×C₄×3₋¹⁺²	—	2	3	no	—
59	C₂×C₄×3₋¹⁺²	C₂×D₃	1	3	yes	—
60	C₂×C₃×C₄×C₉	—	2	1	no	—
61	C₂×C₃×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₃⋊Dic₉	C₃×C₄	1	1	yes	characteristic
63	C₄×C₃⋊D₉	C₃×C₄	1	1	yes	characteristic
64	C₄×C₃⋊D₉	C₃×C₄	1	1	yes	characteristic
65	C₄×C₃⋊D₉	C₂²×C₃	1	1	yes	characteristic
66	C₄×C₃⋊D₉	C₂²×C₃	1	1	yes	characteristic
67	C₂×3₋¹⁺²⋊C₄	—	3	3	no	—
68	C₄×AGL(1,ℤ/9)	—	3	3	no	—
69	C₄×AGL(1,ℤ/9)	—	3	3	no	—
70	C₄×AGL(1,ℤ/9)	—	3	3	no	—
71	C₄×AGL(1,ℤ/9)	—	3	3	no	—
72	C₈×3₋¹⁺²	—	2	6	no	—
73	C₈×3₋¹⁺²	C₂×D₃	1	6	yes	complemented
74	C₃×C₈×C₉	—	2	2	no	—
75	C₃×C₈×C₉	C₂²×C₃	1	2	yes	complemented
76	C₃⋊(C₉⋊C₈)	C₂²×C₃	1	2	yes	complemented
77	3₋¹⁺²⋊C₈	—	3	6	no	—
78	C₂×C₃×3₋¹⁺²	—	2	1	no	—
79	C₂×C₃×3₋¹⁺²	C₂²×C₄	1	1	yes	characteristic
80	C₃⋊AGL(1,ℤ/9)	—	2	1	no	—
81	C₃⋊AGL(1,ℤ/9)	M₁₆	1	2	yes	direct product factor
82	C₂×C₄×C₃⋊D₃	—	3	1	no	—
83	C₂×C₃×C₄×D₃	—	9	3	no	—
84	C₂×C₃×C₄×D₃	—	9	1	no	—
85	C₃²×M₁₆	—	2	1	no	—
86	C₃²×M₁₆	—	6	3	no	—
87	C₃²×M₁₆	C₃×D₃	1	1	yes	characteristic
88	C₃²×M₁₆	C₃⋊D₃	1	1	yes	characteristic
89	#3748	—	3	1	no	—
90	#3743	—	3	2	no	—
91	C₈×C₃⋊D₃	—	3	2	no	—
92	C₃×#208	—	9	3	no	—
93	C₃×#208	—	9	1	no	—
94	C₃×ΓL(1,𝔽₂₅)	—	9	6	no	—
95	C₃×ΓL(1,𝔽₂₅)	—	9	2	no	—
96	C₃×D₃×C₈	—	9	6	no	—
97	C₃×D₃×C₈	—	9	2	no	—
98	C₂×C₄×D₉	—	3	3	no	—
99	C₉×M₁₆	—	2	3	no	—
100	C₉×M₁₆	C₃×D₃	1	3	yes	complemented
101	#3667	—	3	3	no	—
102	#3663	—	3	6	no	—
103	C₈×D₉	—	3	6	no	—
104	C₂²×C₃³	C₄×D₃	1	1	yes	characteristic
105	C₂×C₃×C₃⋊D₃	—	3	1	no	—
106	C₂×C₃×C₃⋊D₃	—	3	1	no	—
107	C₂×C₃×C₃⋊D₃	—	6	2	no	—
108	C₃³×C₄	C₄×D₃	1	1	yes	characteristic
109	C₃³×C₄	C₂²×D₃	1	1	yes	characteristic
110	C₃×C₃⋊Dic₃	—	3	1	no	—
111	C₃×C₃⋊Dic₃	—	3	1	no	—
112	C₂²×3₋¹⁺²	—	2	3	no	—
113	C₂²×3₋¹⁺²	C₄×D₃	1	3	yes	—
114	C₂²×C₃×C₉	—	2	1	no	—
115	C₂²×C₃×C₉	C₂×C₃×C₄	1	1	yes	characteristic
116	C₂×C₃⋊D₉	—	2	2	no	—
117	C₂×C₃⋊D₉	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂×C₃⋊D₉	C₂×C₃×C₄	1	1	yes	characteristic
119	C₂×AGL(1,ℤ/9)	—	3	3	no	—
120	C₂×AGL(1,ℤ/9)	—	3	3	no	—
121	C₂×AGL(1,ℤ/9)	—	6	6	no	—
122	C₄×3₋¹⁺²	—	2	3	no	—
123	C₄×3₋¹⁺²	—	2	3	no	—
124	C₄×3₋¹⁺²	C₄×D₃	1	3	yes	—
125	C₄×3₋¹⁺²	C₂²×D₃	1	3	yes	—
126	C₃×C₄×C₉	—	2	1	no	—
127	C₃×C₄×C₉	—	2	1	no	—
128	C₃×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
129	C₃×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
130	C₃⋊Dic₉	C₂×C₃×C₄	1	1	yes	characteristic
131	C₃⋊Dic₉	C₂×C₃×C₄	1	1	yes	characteristic
132	3₋¹⁺²⋊C₄	—	3	3	no	—
133	3₋¹⁺²⋊C₄	—	3	3	no	—
134	C₂×C₃×M₁₆	—	27	1	no	—
135	D₃×M₁₆	—	9	3	no	—
136	D₃×M₁₆	—	9	1	no	—
137	C₃×3₋¹⁺²	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
138	C₂²×C₃⋊D₃	—	3	1	no	—
139	C₂²×C₃×D₃	—	9	3	no	—
140	C₂²×C₃×D₃	—	9	1	no	—
141	C₂×C₃²×C₄	—	2	1	no	—
142	C₂×C₃²×C₄	—	6	3	no	—
143	C₂×C₃²×C₄	C₂×C₃×D₃	1	1	yes	characteristic
144	C₂×C₃²×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
145	C₂×C₃⋊Dic₃	—	3	1	no	—
146	C₄×C₃⋊D₃	—	3	1	no	—
147	C₄×C₃⋊D₃	—	3	1	no	—
148	C₄×C₃⋊D₃	—	3	1	no	—
149	C₄×C₃⋊D₃	—	3	1	no	—
150	C₂×C₃×Dic₃	—	9	3	no	—
151	C₂×C₃×Dic₃	—	9	1	no	—
152	C₃×C₄×D₃	—	9	3	no	—
153	C₃×C₄×D₃	—	9	3	no	—
154	C₃×C₄×D₃	—	9	3	no	—
155	C₃×C₄×D₃	—	9	3	no	—
156	C₃×C₄×D₃	—	9	1	no	—
157	C₃×C₄×D₃	—	9	1	no	—
158	C₃×C₄×D₃	—	9	1	no	—
159	C₃×C₄×D₃	—	9	1	no	—
160	C₂²×D₉	—	3	3	no	—
161	C₃²×C₈	—	2	2	no	—
162	C₃²×C₈	—	6	6	no	—
163	C₃²×C₈	C₂×C₃×D₃	1	2	yes	—
164	C₃²×C₈	C₂×C₃⋊D₃	1	2	yes	—
165	C₃⋊(C₃⋊C₈)	—	3	2	no	—
166	C₃×C₃⋊C₈	—	9	6	no	—
167	C₃×C₃⋊C₈	—	9	2	no	—
168	C₂×C₄×C₉	—	2	3	no	—
169	C₂×C₄×C₉	C₂×C₃×D₃	1	3	yes	—
170	C₂×Dic₉	—	3	3	no	—
171	C₄×D₉	—	3	3	no	—
172	C₄×D₉	—	3	3	no	—
173	C₄×D₉	—	3	3	no	—
174	C₄×D₉	—	3	3	no	—
175	C₈×C₉	—	2	6	no	—
176	C₈×C₉	C₂×C₃×D₃	1	6	yes	complemented
177	C₉⋊C₈	—	3	6	no	—
178	C₂×C₃³	—	2	1	no	—
179	C₂×C₃³	C₂×C₄×D₃	1	1	yes	characteristic
180	C₃×C₃⋊D₃	—	3	2	no	—
181	C₃×C₃⋊D₃	—	6	1	no	—
182	C₂×3₋¹⁺²	—	2	3	no	—
183	C₂×3₋¹⁺²	—	2	3	no	—
184	C₂×3₋¹⁺²	—	4	3	no	—
185	C₂×3₋¹⁺²	C₂×C₄×D₃	1	3	yes	—
186	C₂×C₃×C₉	—	2	1	no	—
187	C₂×C₃×C₉	—	2	1	no	—
188	C₂×C₃×C₉	—	4	1	no	—
189	C₂×C₃×C₉	C₂²×C₃×C₄	1	1	yes	characteristic
190	C₃⋊D₉	—	2	1	no	—
191	C₃⋊D₉	C₃×M₁₆	1	2	yes	complemented
192	AGL(1,ℤ/9)	—	3	6	no	—
193	AGL(1,ℤ/9)	—	6	3	no	—
194	C₂²×C₃×C₄	—	27	1	no	—
195	C₂×C₄×D₃	—	9	3	no	—
196	C₂×C₄×D₃	—	9	1	no	—
197	C₃×M₁₆	—	3	1	no	—
198	C₃×M₁₆	—	6	1	no	—
199	C₃×M₁₆	—	27	2	no	—
200	C₃×M₁₆	—	27	1	no	—
201	C₃×M₁₆	AGL(1,ℤ/9)	1	3	yes	complemented
202	C₃×M₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic
203	C₂×C₃×C₈	—	27	2	no	—
204	#208	—	9	3	no	—
205	#208	—	9	1	no	—
206	ΓL(1,𝔽₂₅)	—	9	6	no	—
207	ΓL(1,𝔽₂₅)	—	9	2	no	—
208	D₃×C₈	—	9	6	no	—
209	D₃×C₈	—	9	2	no	—
210	C₂²×C₃²	—	2	1	no	—
211	C₂²×C₃²	—	6	3	no	—
212	C₂²×C₃²	C₃×C₄×D₃	1	1	yes	characteristic
213	C₂²×C₃²	C₄×C₃⋊D₃	1	1	yes	characteristic
214	C₂×C₃⋊D₃	—	3	1	no	—
215	C₂×C₃⋊D₃	—	3	1	no	—
216	C₂×C₃⋊D₃	—	6	2	no	—
217	C₂×C₃×D₃	—	9	3	no	—
218	C₂×C₃×D₃	—	9	1	no	—
219	C₂×C₃×D₃	—	9	3	no	—
220	C₂×C₃×D₃	—	9	1	no	—
221	C₂×C₃×D₃	—	18	2	no	—
222	C₂×C₃×D₃	—	18	6	no	—
223	C₃²×C₄	—	2	1	no	—
224	C₃²×C₄	—	2	1	no	—
225	C₃²×C₄	—	6	3	no	—
226	C₃²×C₄	—	6	3	no	—
227	C₃²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
228	C₃²×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
229	C₃²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
230	C₃²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
231	C₃⋊Dic₃	—	3	1	no	—
232	C₃⋊Dic₃	—	3	1	no	—
233	C₃×Dic₃	—	9	3	no	—
234	C₃×Dic₃	—	9	3	no	—
235	C₃×Dic₃	—	9	1	no	—
236	C₃×Dic₃	—	9	1	no	—
237	C₂²×C₉	—	2	3	no	—
238	C₂²×C₉	C₃×C₄×D₃	1	3	yes	—
239	C₂×D₉	—	3	3	no	—
240	C₂×D₉	—	3	3	no	—
241	C₂×D₉	—	6	6	no	—
242	C₄×C₉	—	2	3	no	—
243	C₄×C₉	—	2	3	no	—
244	C₄×C₉	C₃×C₄×D₃	1	3	yes	—
245	C₄×C₉	C₂²×C₃×D₃	1	3	yes	—
246	Dic₉	—	3	3	no	—
247	Dic₉	—	3	3	no	—
248	C₂×M₁₆	—	27	1	no	Sylow
249	C₃³	D₃×M₁₆	1	1	yes	characteristic
250	3₋¹⁺²	—	2	3	no	—
251	3₋¹⁺²	D₃×M₁₆	1	3	yes	complemented
252	C₃×C₉	—	2	1	no	—
253	C₃×C₉	C₂×C₃×M₁₆	1	1	yes	characteristic, complemented
254	C₂³×C₃	—	27	1	no	—
255	C₂²×D₃	—	9	3	no	—
256	C₂²×D₃	—	9	1	no	—
257	C₂×C₃×C₄	—	3	1	no	—
258	C₂×C₃×C₄	—	6	1	no	—
259	C₂×C₃×C₄	—	27	1	no	—
260	C₂×C₃×C₄	—	27	1	no	—
261	C₂×C₃×C₄	—	27	1	no	—
262	C₂×C₃×C₄	—	27	1	no	—
263	C₂×C₃×C₄	—	27	1	no	—
264	C₂×C₃×C₄	C₂×AGL(1,ℤ/9)	1	3	yes	—
265	C₂×C₃×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
266	C₂×Dic₃	—	9	3	no	—
267	C₂×Dic₃	—	9	1	no	—
268	C₄×D₃	—	9	3	no	—
269	C₄×D₃	—	9	3	no	—
270	C₄×D₃	—	9	3	no	—
271	C₄×D₃	—	9	3	no	—
272	C₄×D₃	—	9	1	no	—
273	C₄×D₃	—	9	1	no	—
274	C₄×D₃	—	9	1	no	—
275	C₄×D₃	—	9	1	no	—
276	C₃×C₈	—	3	2	no	—
277	C₃×C₈	—	6	2	no	—
278	C₃×C₈	—	27	2	no	—
279	C₃×C₈	C₂×AGL(1,ℤ/9)	1	6	yes	complemented
280	C₃×C₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
281	C₃⋊C₈	—	9	6	no	—
282	C₃⋊C₈	—	9	2	no	—
283	C₂×C₃²	—	2	1	no	—
284	C₂×C₃²	—	2	1	no	—
285	C₂×C₃²	—	2	1	no	—
286	C₂×C₃²	—	4	1	no	—
287	C₂×C₃²	—	6	3	no	—
288	C₂×C₃²	—	12	3	no	—
289	C₂×C₃²	C₂×C₃×C₄×D₃	1	1	yes	characteristic
290	C₂×C₃²	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
291	C₃⋊D₃	—	3	2	no	—
292	C₃⋊D₃	—	6	1	no	—
293	C₃×D₃	—	9	6	no	—
294	C₃×D₃	—	9	2	no	—
295	C₃×D₃	—	18	3	no	—
296	C₃×D₃	—	18	1	no	—
297	C₂×C₉	—	2	3	no	—
298	C₂×C₉	—	2	3	no	—
299	C₂×C₉	—	4	3	no	—
300	C₂×C₉	C₂×C₃×C₄×D₃	1	3	yes	—
301	D₉	—	3	6	no	—
302	D₉	—	6	3	no	—
303	C₂²×C₄	—	27	1	no	—
304	M₁₆	—	27	1	no	—
305	M₁₆	—	27	2	no	—
306	M₁₆	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic, direct product factor
307	C₂×C₈	—	27	2	no	—
308	C₂²×C₃	—	3	1	no	—
309	C₂²×C₃	—	6	1	no	—
310	C₂²×C₃	—	27	1	no	—
311	C₂²×C₃	—	27	1	no	—
312	C₂²×C₃	—	54	2	no	—
313	C₂²×C₃	C₄×AGL(1,ℤ/9)	1	3	yes	—
314	C₂²×C₃	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
315	C₂×D₃	—	9	3	no	—
316	C₂×D₃	—	9	1	no	—
317	C₂×D₃	—	9	3	no	—
318	C₂×D₃	—	9	1	no	—
319	C₂×D₃	—	18	2	no	—
320	C₂×D₃	—	18	6	no	—
321	C₃×C₄	—	3	1	no	—
322	C₃×C₄	—	3	1	no	—
323	C₃×C₄	—	6	1	no	—
324	C₃×C₄	—	6	1	no	—
325	C₃×C₄	—	27	1	no	—
326	C₃×C₄	—	27	1	no	—
327	C₃×C₄	C₄×AGL(1,ℤ/9)	1	3	yes	—
328	C₃×C₄	C₂²×AGL(1,ℤ/9)	1	3	yes	—
329	C₃×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
330	C₃×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
331	Dic₃	—	9	3	no	—
332	Dic₃	—	9	3	no	—
333	Dic₃	—	9	1	no	—
334	Dic₃	—	9	1	no	—
335	C₃²	—	2	1	no	—
336	C₃²	—	6	3	no	—
337	C₃²	C₃×D₃×M₁₆	1	1	yes	characteristic
338	C₃²	M₁₆×C₃⋊D₃	1	1	yes	characteristic
339	C₉	—	2	3	no	—
340	C₉	C₃×D₃×M₁₆	1	3	yes	complemented
341	C₂³	—	27	1	no	—
342	C₂×C₄	—	27	1	no	—
343	C₂×C₄	—	27	1	no	—
344	C₂×C₄	—	27	1	no	—
345	C₂×C₄	—	27	1	no	—
346	C₂×C₄	—	27	1	no	—
347	C₂×C₄	C₂×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
348	C₈	—	27	2	no	—
349	C₈	C₂×C₃⋊AGL(1,ℤ/9)	1	2	yes	complemented
350	C₂×C₃	—	2	3	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	3	1	no	—
353	C₂×C₃	—	6	1	no	—
354	C₂×C₃	—	6	1	no	—
355	C₂×C₃	—	12	1	no	—
356	C₂×C₃	—	27	2	no	—
357	C₂×C₃	—	54	1	no	—
358	C₂×C₃	C₂×C₄×AGL(1,ℤ/9)	1	3	yes	—
359	C₂×C₃	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
360	D₃	—	9	6	no	—
361	D₃	—	9	2	no	—
362	D₃	—	18	3	no	—
363	D₃	—	18	1	no	—
364	C₂²	—	27	1	no	—
365	C₂²	—	27	1	no	—
366	C₂²	—	54	2	no	—
367	C₂²	C₄×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
368	C₄	—	27	1	no	—
369	C₄	—	27	1	no	—
370	C₄	C₄×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
371	C₄	C₂²×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
372	C₃	—	3	1	no	—
373	C₃	—	6	1	no	—
374	C₃	M₁₆×AGL(1,ℤ/9)	1	3	yes	complemented
375	C₃	C₃×M₁₆×C₃⋊D₃	1	1	yes	characteristic
376	C₂	—	2	1	no	—
377	C₂	—	27	2	no	—
378	C₂	—	54	1	no	—
379	C₂	C₂×C₄×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₃⋊AGL(1,ℤ/9)
commutator	C₂×C₃×C₉	C₂²×C₃×C₄
Frattini	C₃×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₃×M₁₆×3₋¹⁺²	C₂
socle	C₂×C₃²	C₂×C₃×C₄×D₃
prime radical	C₂²×C₃⋊AGL(1,ℤ/9)	C₄
cosocle	C₃×C₄×C₉	C₂³×C₃
hypercenter	M₁₆	C₃⋊AGL(1,ℤ/9)
hypocenter	C₃×C₉	C₂×C₃×M₁₆
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×M₁₆×3₋¹⁺²	C₂	semidirect
3. #13047945	C₂	semidirect
4. #13047907	C₂	semidirect
5. C₈×C₃⋊AGL(1,ℤ/9)	C₂	semidirect
7. M₁₆×C₃⋊D₉	C₃	semidirect
16. C₃×C₈×3₋¹⁺²	C₂²	semidirect
17. C₃⋊(3₋¹⁺²⋊C₈)	C₂²	semidirect
26. M₁₆×3₋¹⁺²	D₃	semidirect
28. C₃×C₉×M₁₆	C₂×C₃	semidirect
29. #88532	C₂×C₃	semidirect
30. #88523	C₂×C₃	semidirect
31. C₈×C₃⋊D₉	C₂×C₃	semidirect
73. C₈×3₋¹⁺²	C₂×D₃	semidirect
75. C₃×C₈×C₉	C₂²×C₃	semidirect
76. C₃⋊(C₉⋊C₈)	C₂²×C₃	semidirect
81. C₃⋊AGL(1,ℤ/9)	M₁₆	direct (N × H)
100. C₉×M₁₆	C₃×D₃	semidirect
137. C₃×3₋¹⁺²	C₂×M₁₆	semidirect
176. C₈×C₉	C₂×C₃×D₃	semidirect
191. C₃⋊D₉	C₃×M₁₆	semidirect
201. C₃×M₁₆	AGL(1,ℤ/9)	semidirect
251. 3₋¹⁺²	D₃×M₁₆	semidirect
253. C₃×C₉	C₂×C₃×M₁₆	semidirect
279. C₃×C₈	C₂×AGL(1,ℤ/9)	semidirect
306. M₁₆	C₃⋊AGL(1,ℤ/9)	direct (N × H)
340. C₉	C₃×D₃×M₁₆	semidirect
349. C₈	C₂×C₃⋊AGL(1,ℤ/9)	semidirect
374. C₃	M₁₆×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×C₄×C₃⋊AGL(1,ℤ/9)	2
C₃×M₁₆×3₋¹⁺²	2
#13047945	2
#13047907	2
C₈×C₃⋊AGL(1,ℤ/9)	2
C₃×M₁₆×C₃⋊D₃	3
M₁₆×C₃⋊D₉	3
M₁₆×AGL(1,ℤ/9)	3

Subgroups — M16×C3⋊AGL(1,ℤ/9) #72254607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×C₃⋊AGL(1,ℤ/9) #72254607