Subgroups — D₃×M₁₆×C₃⋊D₃ #13176679

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	M₁₆×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×M₁₆×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#11723358	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃⋊D₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
7	D₃×#3748	C₂	1	1	yes	maximal, characteristic, complemented
8	#11723312	C₂	1	2	yes	maximal, complemented
9	C₃⋊D₃×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
10	D₃×#3743	C₂	1	2	yes	maximal, complemented
11	D₃×C₈×C₃⋊D₃	C₂	1	2	yes	maximal, complemented
12	C₂×M₁₆×C₃⋊D₃	—	3	1	no	maximal
13	D₃²×M₁₆	—	3	4	no	maximal
14	C₂²×D₃×C₃⋊D₃	C₄	1	1	yes	characteristic
15	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
18	C₂×#6289	C₄	1	1	yes	characteristic
19	C₂×Dic₃×C₃⋊D₃	C₄	1	1	yes	characteristic
20	C₂×D₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic
21	C₄×D₃×C₃⋊D₃	C₄	1	1	yes	characteristic
22	C₄×D₃×C₃⋊D₃	C₄	1	1	yes	characteristic
23	C₄×D₃×C₃⋊D₃	C₄	1	1	yes	characteristic
24	C₄×D₃×C₃⋊D₃	C₄	1	1	yes	characteristic
25	C₄×D₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
26	C₄×D₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
27	C₄×D₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
28	C₄×D₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
29	C₃³×M₁₆	C₂²	1	1	yes	characteristic, complemented
30	#88855	C₂²	1	1	yes	characteristic, complemented
31	#88850	C₂²	1	2	yes	complemented
32	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	complemented
33	C₃×#3748	C₂²	1	1	yes	characteristic, complemented
34	C₃×#3743	C₂²	1	2	yes	complemented
35	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	complemented
36	C₃²×#208	C₂²	1	1	yes	characteristic, complemented
37	C₃²×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	complemented
38	C₃²×D₃×C₈	C₂²	1	2	yes	complemented
39	#88788	C₂²	1	2	yes	complemented
40	#88787	C₂²	1	2	yes	complemented
41	#88786	C₂²	1	2	yes	complemented
42	#88785	C₂²	1	2	yes	complemented
43	C₃⋊D₃×C₃⋊C₈	C₂²	1	2	yes	complemented
44	D₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	complemented
45	C₂²×C₄×C₃⋊D₃	—	3	1	no	—
46	C₂×C₄×D₃²	—	3	4	no	—
47	C₂×C₃²×M₁₆	—	3	1	no	—
48	C₂×#3748	—	3	1	no	—
49	M₁₆×C₃⋊D₃	—	3	1	no	—
50	M₁₆×C₃⋊D₃	—	3	1	no	—
51	M₁₆×C₃⋊D₃	—	3	1	no	—
52	M₁₆×C₃⋊D₃	—	3	2	no	—
53	M₁₆×C₃⋊D₃	—	3	2	no	—
54	M₁₆×C₃⋊D₃	—	3	4	no	—
55	M₁₆×C₃⋊D₃	—	6	4	no	—
56	M₁₆×C₃⋊D₃	D₃	1	1	yes	characteristic, direct product factor
57	C₂×#3743	—	3	2	no	—
58	C₂×C₈×C₃⋊D₃	—	3	2	no	—
59	C₃×D₃×M₁₆	—	3	4	no	—
60	C₃×D₃×M₁₆	D₃	1	4	yes	complemented
61	#63818	—	3	4	no	—
62	D₃×#208	—	3	4	no	—
63	D₃×#208	—	3	4	no	—
64	#63791	—	3	8	no	—
65	D₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
66	D₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
67	D₃²×C₈	—	3	8	no	—
68	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
71	C₂×D₃×C₃⋊D₃	—	2	4	no	—
72	C₂×D₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
73	C₂×D₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
74	C₂×D₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
75	C₂×D₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
77	C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
78	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
79	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
80	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
81	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
85	C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
86	C₃×C₄×C₃⋊D₃	C₂³	1	1	yes	characteristic
87	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
88	C₃²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
89	C₃²×C₄×D₃	C₂×C₄	1	1	yes	characteristic
90	C₃²×C₄×D₃	C₂³	1	1	yes	characteristic
91	C₃²×C₄×D₃	C₂³	1	1	yes	characteristic
92	#6289	C₂×C₄	1	1	yes	characteristic
93	#6289	C₂×C₄	1	1	yes	characteristic
94	#6289	C₂×C₄	1	1	yes	characteristic
95	#6289	C₂×C₄	1	1	yes	characteristic
96	Dic₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
97	Dic₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
98	Dic₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
99	Dic₃×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
100	D₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
101	D₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
102	D₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
103	D₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
104	C₃³×C₈	C₂³	1	2	yes	complemented
105	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	2	yes	complemented
106	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	complemented
107	C₃²×C₃⋊C₈	C₂³	1	2	yes	complemented
108	C₂×D₃×M₁₆	—	9	4	no	—
109	C₂×D₃×M₁₆	—	9	1	no	—
110	C₂³×C₃⋊D₃	—	3	1	no	—
111	C₂²×D₃²	—	3	4	no	—
112	C₂²×C₃²×C₄	—	3	1	no	—
113	C₂²×C₃⋊Dic₃	—	3	1	no	—
114	C₂×C₄×C₃⋊D₃	—	3	1	no	—
115	C₂×C₄×C₃⋊D₃	—	3	1	no	—
116	C₂×C₄×C₃⋊D₃	—	3	4	no	—
117	C₂×C₄×C₃⋊D₃	—	3	1	no	—
118	C₂×C₄×C₃⋊D₃	—	3	1	no	—
119	C₂×C₄×C₃⋊D₃	—	3	1	no	—
120	C₂×C₄×C₃⋊D₃	—	3	1	no	—
121	C₂×C₄×C₃⋊D₃	—	3	1	no	—
122	C₂×C₄×C₃⋊D₃	—	3	1	no	—
123	C₂×C₄×C₃⋊D₃	—	3	1	no	—
124	C₂×C₄×C₃⋊D₃	—	3	1	no	—
125	C₂×C₄×C₃⋊D₃	—	3	1	no	—
126	C₂×C₄×C₃⋊D₃	—	6	4	no	—
127	C₂×C₄×C₃⋊D₃	C₂×D₃	1	1	yes	characteristic
128	C₂×C₃×C₄×D₃	—	3	4	no	—
129	C₂×C₃×C₄×D₃	C₂×D₃	1	4	yes	—
130	C₂×#624	—	3	4	no	—
131	C₂×D₃×Dic₃	—	3	4	no	—
132	C₂×D₃×Dic₃	—	3	4	no	—
133	C₄×D₃²	—	3	4	no	—
134	C₄×D₃²	—	3	4	no	—
135	C₄×D₃²	—	3	4	no	—
136	C₄×D₃²	—	3	4	no	—
137	C₄×D₃²	—	3	4	no	—
138	C₄×D₃²	—	3	4	no	—
139	C₄×D₃²	—	3	4	no	—
140	C₄×D₃²	—	3	4	no	—
141	C₃²×M₁₆	—	2	4	no	—
142	C₃²×M₁₆	—	3	1	no	—
143	C₃²×M₁₆	—	3	2	no	—
144	C₃²×M₁₆	C₂×D₃	1	4	yes	complemented
145	C₃²×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
146	C₂×C₃²×C₈	—	3	2	no	—
147	#3748	—	3	1	no	—
148	#3748	—	3	4	no	—
149	#3748	—	3	2	no	—
150	#3748	—	6	4	no	—
151	#3748	C₂×D₃	1	1	yes	characteristic, complemented
152	C₂×C₃⋊(C₃⋊C₈)	—	3	2	no	—
153	#3743	—	3	2	no	—
154	#3743	—	3	2	no	—
155	#3743	—	3	8	no	—
156	#3743	—	3	2	no	—
157	#3743	—	6	8	no	—
158	#3743	C₂×D₃	1	2	yes	complemented
159	C₈×C₃⋊D₃	—	3	2	no	—
160	C₈×C₃⋊D₃	—	3	2	no	—
161	C₈×C₃⋊D₃	—	3	8	no	—
162	C₈×C₃⋊D₃	—	3	2	no	—
163	C₈×C₃⋊D₃	—	6	8	no	—
164	C₈×C₃⋊D₃	C₂×D₃	1	2	yes	complemented
165	C₃×#208	—	3	4	no	—
166	C₃×#208	C₂×D₃	1	4	yes	complemented
167	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
168	C₃×ΓL(1,𝔽₂₅)	C₂×D₃	1	8	yes	complemented
169	C₃×D₃×C₈	—	3	8	no	—
170	C₃×D₃×C₈	C₂×D₃	1	8	yes	complemented
171	#3712	—	3	8	no	—
172	#3711	—	3	8	no	—
173	#3711	—	3	8	no	—
174	#3710	—	3	8	no	—
175	D₃×C₃⋊C₈	—	3	8	no	—
176	D₃×C₃⋊C₈	—	3	8	no	—
177	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
179	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₃×C₃⋊D₃	—	2	2	no	—
182	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₃²×D₃	—	2	2	no	—
185	C₂×C₃²×D₃	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₃²×D₃	C₂²×C₄	1	1	yes	characteristic
187	D₃×C₃⋊D₃	—	2	2	no	—
188	D₃×C₃⋊D₃	—	2	2	no	—
189	D₃×C₃⋊D₃	—	2	2	no	—
190	D₃×C₃⋊D₃	M₁₆	1	4	yes	direct product factor
191	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
192	C₃³×C₄	C₂⁴	1	1	yes	characteristic
193	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	1	yes	characteristic
194	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	1	yes	characteristic
195	C₃×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
196	C₃×C₃⋊Dic₃	C₂²×C₄	1	1	yes	characteristic
197	C₃²×Dic₃	C₂²×C₄	1	1	yes	characteristic
198	C₃²×Dic₃	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×D₃	—	9	4	no	—
200	C₂²×C₄×D₃	—	9	1	no	—
201	C₂×C₃×M₁₆	—	3	4	no	—
202	C₂×C₃×M₁₆	—	9	1	no	—
203	C₂×#208	—	9	4	no	—
204	C₂×#208	—	9	1	no	—
205	D₃×M₁₆	—	3	4	no	—
206	D₃×M₁₆	—	9	8	no	—
207	D₃×M₁₆	—	9	8	no	—
208	D₃×M₁₆	—	9	4	no	—
209	D₃×M₁₆	—	9	4	no	—
210	D₃×M₁₆	—	9	1	no	—
211	D₃×M₁₆	—	9	4	no	—
212	D₃×M₁₆	—	9	1	no	—
213	D₃×M₁₆	—	9	1	no	—
214	D₃×M₁₆	—	9	2	no	—
215	D₃×M₁₆	—	9	2	no	—
216	D₃×M₁₆	—	18	4	no	—
217	D₃×M₁₆	C₃⋊D₃	1	1	yes	characteristic, direct product factor
218	C₂×ΓL(1,𝔽₂₅)	—	9	8	no	—
219	C₂×ΓL(1,𝔽₂₅)	—	9	2	no	—
220	C₂×D₃×C₈	—	9	8	no	—
221	C₂×D₃×C₈	—	9	2	no	—
222	C₂³×C₃²	—	3	1	no	—
223	C₂²×C₃⋊D₃	—	3	1	no	—
224	C₂²×C₃⋊D₃	—	3	1	no	—
225	C₂²×C₃⋊D₃	—	3	1	no	—
226	C₂²×C₃⋊D₃	—	3	1	no	—
227	C₂²×C₃⋊D₃	—	3	1	no	—
228	C₂²×C₃⋊D₃	—	3	4	no	—
229	C₂²×C₃⋊D₃	—	6	4	no	—
230	C₂²×C₃⋊D₃	—	6	4	no	—
231	C₂²×C₃⋊D₃	C₄×D₃	1	1	yes	characteristic
232	C₂²×C₃×D₃	—	3	4	no	—
233	C₂²×C₃×D₃	C₄×D₃	1	4	yes	—
234	C₂×D₃²	—	3	4	no	—
235	C₂×D₃²	—	3	4	no	—
236	C₂×D₃²	—	3	4	no	—
237	C₂×D₃²	—	3	4	no	—
238	C₂×D₃²	—	6	16	no	—
239	C₂×C₃²×C₄	—	2	4	no	—
240	C₂×C₃²×C₄	—	3	1	no	—
241	C₂×C₃²×C₄	—	3	1	no	—
242	C₂×C₃²×C₄	—	3	1	no	—
243	C₂×C₃²×C₄	—	3	1	no	—
244	C₂×C₃²×C₄	—	3	1	no	—
245	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
246	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
247	C₂×C₃⋊Dic₃	—	3	1	no	—
248	C₂×C₃⋊Dic₃	—	3	1	no	—
249	C₂×C₃⋊Dic₃	—	3	1	no	—
250	C₂×C₃⋊Dic₃	—	3	1	no	—
251	C₂×C₃⋊Dic₃	—	3	1	no	—
252	C₂×C₃⋊Dic₃	—	3	4	no	—
253	C₂×C₃⋊Dic₃	—	6	4	no	—
254	C₂×C₃⋊Dic₃	C₄×D₃	1	1	yes	characteristic
255	C₄×C₃⋊D₃	—	3	1	no	—
256	C₄×C₃⋊D₃	—	3	1	no	—
257	C₄×C₃⋊D₃	—	3	1	no	—
258	C₄×C₃⋊D₃	—	3	1	no	—
259	C₄×C₃⋊D₃	—	3	1	no	—
260	C₄×C₃⋊D₃	—	3	1	no	—
261	C₄×C₃⋊D₃	—	3	1	no	—
262	C₄×C₃⋊D₃	—	3	1	no	—
263	C₄×C₃⋊D₃	—	3	1	no	—
264	C₄×C₃⋊D₃	—	3	1	no	—
265	C₄×C₃⋊D₃	—	3	1	no	—
266	C₄×C₃⋊D₃	—	3	1	no	—
267	C₄×C₃⋊D₃	—	3	4	no	—
268	C₄×C₃⋊D₃	—	3	4	no	—
269	C₄×C₃⋊D₃	—	3	4	no	—
270	C₄×C₃⋊D₃	—	3	4	no	—
271	C₄×C₃⋊D₃	—	6	4	no	—
272	C₄×C₃⋊D₃	—	6	4	no	—
273	C₄×C₃⋊D₃	—	6	4	no	—
274	C₄×C₃⋊D₃	—	6	4	no	—
275	C₄×C₃⋊D₃	C₄×D₃	1	1	yes	characteristic
276	C₄×C₃⋊D₃	C₄×D₃	1	1	yes	characteristic
277	C₄×C₃⋊D₃	C₂²×D₃	1	1	yes	characteristic
278	C₄×C₃⋊D₃	C₂²×D₃	1	1	yes	characteristic
279	C₂×C₃×Dic₃	—	3	4	no	—
280	C₂×C₃×Dic₃	C₄×D₃	1	4	yes	—
281	C₃×C₄×D₃	—	3	4	no	—
282	C₃×C₄×D₃	—	3	4	no	—
283	C₃×C₄×D₃	—	3	4	no	—
284	C₃×C₄×D₃	—	3	4	no	—
285	C₃×C₄×D₃	C₄×D₃	1	4	yes	—
286	C₃×C₄×D₃	C₄×D₃	1	4	yes	—
287	C₃×C₄×D₃	C₂²×D₃	1	4	yes	—
288	C₃×C₄×D₃	C₂²×D₃	1	4	yes	—
289	#624	—	3	4	no	—
290	#624	—	3	4	no	—
291	#624	—	3	4	no	—
292	#624	—	3	4	no	—
293	D₃×Dic₃	—	3	4	no	—
294	D₃×Dic₃	—	3	4	no	—
295	D₃×Dic₃	—	3	4	no	—
296	D₃×Dic₃	—	3	4	no	—
297	D₃×Dic₃	—	3	4	no	—
298	D₃×Dic₃	—	3	4	no	—
299	D₃×Dic₃	—	3	4	no	—
300	D₃×Dic₃	—	3	4	no	—
301	C₃²×C₈	—	2	8	no	—
302	C₃²×C₈	—	3	2	no	—
303	C₃²×C₈	C₂²×D₃	1	8	yes	complemented
304	C₃²×C₈	C₂²×D₃	1	2	yes	complemented
305	C₃⋊(C₃⋊C₈)	—	3	2	no	—
306	C₃⋊(C₃⋊C₈)	—	3	8	no	—
307	C₃⋊(C₃⋊C₈)	—	6	8	no	—
308	C₃⋊(C₃⋊C₈)	C₂²×D₃	1	2	yes	complemented
309	C₃×C₃⋊C₈	—	3	8	no	—
310	C₃×C₃⋊C₈	C₂²×D₃	1	8	yes	complemented
311	C₂²×M₁₆	—	27	1	no	Sylow
312	C₂×C₃³	—	2	1	no	—
313	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
314	C₃⋊(C₃⋊D₃)	—	2	1	no	—
315	C₃⋊(C₃⋊D₃)	C₂×M₁₆	1	2	yes	complemented
316	C₃×C₃⋊D₃	—	2	1	no	—
317	C₃×C₃⋊D₃	C₂×M₁₆	1	2	yes	complemented
318	C₃²×D₃	—	2	1	no	—
319	C₃²×D₃	C₂×M₁₆	1	2	yes	complemented
320	C₂³×D₃	—	9	4	no	—
321	C₂³×D₃	—	9	1	no	—
322	C₂²×C₃×C₄	—	3	4	no	—
323	C₂²×C₃×C₄	—	9	1	no	—
324	C₂²×Dic₃	—	9	4	no	—
325	C₂²×Dic₃	—	9	1	no	—
326	C₂×C₄×D₃	—	3	4	no	—
327	C₂×C₄×D₃	—	9	4	no	—
328	C₂×C₄×D₃	—	9	4	no	—
329	C₂×C₄×D₃	—	9	4	no	—
330	C₂×C₄×D₃	—	9	4	no	—
331	C₂×C₄×D₃	—	9	4	no	—
332	C₂×C₄×D₃	—	9	4	no	—
333	C₂×C₄×D₃	—	9	4	no	—
334	C₂×C₄×D₃	—	9	4	no	—
335	C₂×C₄×D₃	—	9	4	no	—
336	C₂×C₄×D₃	—	9	4	no	—
337	C₂×C₄×D₃	—	9	1	no	—
338	C₂×C₄×D₃	—	9	4	no	—
339	C₂×C₄×D₃	—	9	1	no	—
340	C₂×C₄×D₃	—	9	1	no	—
341	C₂×C₄×D₃	—	9	1	no	—
342	C₂×C₄×D₃	—	9	1	no	—
343	C₂×C₄×D₃	—	9	1	no	—
344	C₂×C₄×D₃	—	9	1	no	—
345	C₂×C₄×D₃	—	9	1	no	—
346	C₂×C₄×D₃	—	9	1	no	—
347	C₂×C₄×D₃	—	9	1	no	—
348	C₂×C₄×D₃	—	9	1	no	—
349	C₂×C₄×D₃	—	18	4	no	—
350	C₂×C₄×D₃	C₂×C₃⋊D₃	1	1	yes	characteristic
351	C₃×M₁₆	—	2	4	no	—
352	C₃×M₁₆	—	3	4	no	—
353	C₃×M₁₆	—	3	8	no	—
354	C₃×M₁₆	—	9	1	no	—
355	C₃×M₁₆	—	9	2	no	—
356	C₃×M₁₆	D₃²	1	4	yes	complemented
357	C₃×M₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
358	C₂×C₃×C₈	—	3	8	no	—
359	C₂×C₃×C₈	—	9	2	no	—
360	#208	—	3	4	no	—
361	#208	—	9	8	no	—
362	#208	—	9	4	no	—
363	#208	—	9	1	no	—
364	#208	—	9	2	no	—
365	#208	—	18	4	no	—
366	#208	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
367	C₂×C₃⋊C₈	—	9	8	no	—
368	C₂×C₃⋊C₈	—	9	2	no	—
369	ΓL(1,𝔽₂₅)	—	3	8	no	—
370	ΓL(1,𝔽₂₅)	—	9	8	no	—
371	ΓL(1,𝔽₂₅)	—	9	8	no	—
372	ΓL(1,𝔽₂₅)	—	9	2	no	—
373	ΓL(1,𝔽₂₅)	—	9	8	no	—
374	ΓL(1,𝔽₂₅)	—	9	2	no	—
375	ΓL(1,𝔽₂₅)	—	9	2	no	—
376	ΓL(1,𝔽₂₅)	—	18	8	no	—
377	ΓL(1,𝔽₂₅)	C₂×C₃⋊D₃	1	2	yes	complemented
378	D₃×C₈	—	3	8	no	—
379	D₃×C₈	—	9	8	no	—
380	D₃×C₈	—	9	8	no	—
381	D₃×C₈	—	9	2	no	—
382	D₃×C₈	—	9	8	no	—
383	D₃×C₈	—	9	2	no	—
384	D₃×C₈	—	9	2	no	—
385	D₃×C₈	—	18	8	no	—
386	D₃×C₈	C₂×C₃⋊D₃	1	2	yes	complemented
387	C₂²×C₃²	—	2	4	no	—
388	C₂²×C₃²	—	3	1	no	—
389	C₂²×C₃²	—	3	1	no	—
390	C₂²×C₃²	—	6	2	no	—
391	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
392	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
393	C₂×C₃⋊D₃	—	2	2	no	—
394	C₂×C₃⋊D₃	—	3	1	no	—
395	C₂×C₃⋊D₃	—	3	4	no	—
396	C₂×C₃⋊D₃	—	3	1	no	—
397	C₂×C₃⋊D₃	—	3	4	no	—
398	C₂×C₃⋊D₃	—	3	4	no	—
399	C₂×C₃⋊D₃	—	6	4	no	—
400	C₂×C₃⋊D₃	—	6	4	no	—
401	C₂×C₃⋊D₃	—	6	2	no	—
402	C₂×C₃⋊D₃	—	6	2	no	—
403	C₂×C₃⋊D₃	—	6	2	no	—
404	C₂×C₃⋊D₃	—	6	2	no	—
405	C₂×C₃⋊D₃	—	6	8	no	—
406	C₂×C₃⋊D₃	—	12	8	no	—
407	C₂×C₃⋊D₃	C₂×C₄×D₃	1	1	yes	characteristic
408	C₂×C₃⋊D₃	C₂×C₄×D₃	1	1	yes	characteristic
409	C₂×C₃×D₃	—	2	8	no	—
410	C₂×C₃×D₃	—	3	4	no	—
411	C₂×C₃×D₃	—	3	4	no	—
412	C₂×C₃×D₃	—	6	8	no	—
413	C₂×C₃×D₃	C₂×C₄×D₃	1	4	yes	—
414	C₂×C₃×D₃	C₂×C₄×D₃	1	4	yes	—
415	D₃²	—	3	16	no	—
416	D₃²	—	6	8	no	—
417	D₃²	—	6	8	no	—
418	D₃²	—	6	8	no	—
419	C₃²×C₄	—	2	4	no	—
420	C₃²×C₄	—	2	4	no	—
421	C₃²×C₄	—	3	1	no	—
422	C₃²×C₄	—	3	1	no	—
423	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
424	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
425	C₃²×C₄	C₂³×D₃	1	4	yes	—
426	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
427	C₃⋊Dic₃	—	3	1	no	—
428	C₃⋊Dic₃	—	3	1	no	—
429	C₃⋊Dic₃	—	3	4	no	—
430	C₃⋊Dic₃	—	3	4	no	—
431	C₃⋊Dic₃	—	6	4	no	—
432	C₃⋊Dic₃	—	6	4	no	—
433	C₃⋊Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
434	C₃⋊Dic₃	C₂×C₄×D₃	1	1	yes	characteristic
435	C₃×Dic₃	—	3	4	no	—
436	C₃×Dic₃	—	3	4	no	—
437	C₃×Dic₃	C₂×C₄×D₃	1	4	yes	—
438	C₃×Dic₃	C₂×C₄×D₃	1	4	yes	—
439	C₂³×C₄	—	27	1	no	—
440	C₂×M₁₆	—	3	1	no	—
441	C₂×M₁₆	—	9	1	no	—
442	C₂×M₁₆	—	27	2	no	—
443	C₂×M₁₆	—	27	2	no	—
444	C₂×M₁₆	—	27	1	no	—
445	C₂×M₁₆	—	27	2	no	—
446	C₂×M₁₆	—	27	1	no	—
447	C₂×M₁₆	—	27	1	no	—
448	C₂×M₁₆	—	27	1	no	—
449	C₂²×C₈	—	27	2	no	—
450	C₃³	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
451	C₂³×C₃	—	3	4	no	—
452	C₂³×C₃	—	9	1	no	—
453	C₂²×D₃	—	3	4	no	—
454	C₂²×D₃	—	9	4	no	—
455	C₂²×D₃	—	9	4	no	—
456	C₂²×D₃	—	9	4	no	—
457	C₂²×D₃	—	9	4	no	—
458	C₂²×D₃	—	9	1	no	—
459	C₂²×D₃	—	9	4	no	—
460	C₂²×D₃	—	9	1	no	—
461	C₂²×D₃	—	9	1	no	—
462	C₂²×D₃	—	9	1	no	—
463	C₂²×D₃	—	9	1	no	—
464	C₂²×D₃	—	18	4	no	—
465	C₂²×D₃	—	18	4	no	—
466	C₂²×D₃	—	18	16	no	—
467	C₂²×D₃	C₄×C₃⋊D₃	1	1	yes	characteristic
468	C₂×C₃×C₄	—	2	4	no	—
469	C₂×C₃×C₄	—	3	4	no	—
470	C₂×C₃×C₄	—	3	4	no	—
471	C₂×C₃×C₄	—	3	4	no	—
472	C₂×C₃×C₄	—	3	4	no	—
473	C₂×C₃×C₄	—	3	4	no	—
474	C₂×C₃×C₄	—	9	1	no	—
475	C₂×C₃×C₄	—	9	1	no	—
476	C₂×C₃×C₄	—	9	1	no	—
477	C₂×C₃×C₄	—	9	1	no	—
478	C₂×C₃×C₄	—	9	1	no	—
479	C₂×C₃×C₄	C₂×D₃²	1	4	yes	—
480	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
481	C₂×Dic₃	—	3	4	no	—
482	C₂×Dic₃	—	9	4	no	—
483	C₂×Dic₃	—	9	4	no	—
484	C₂×Dic₃	—	9	4	no	—
485	C₂×Dic₃	—	9	4	no	—
486	C₂×Dic₃	—	9	4	no	—
487	C₂×Dic₃	—	9	1	no	—
488	C₂×Dic₃	—	9	1	no	—
489	C₂×Dic₃	—	9	1	no	—
490	C₂×Dic₃	—	9	1	no	—
491	C₂×Dic₃	—	9	1	no	—
492	C₂×Dic₃	—	18	4	no	—
493	C₂×Dic₃	C₄×C₃⋊D₃	1	1	yes	characteristic
494	C₄×D₃	—	3	4	no	—
495	C₄×D₃	—	3	4	no	—
496	C₄×D₃	—	3	4	no	—
497	C₄×D₃	—	3	4	no	—
498	C₄×D₃	—	9	4	no	—
499	C₄×D₃	—	9	4	no	—
500	C₄×D₃	—	9	4	no	—
501	C₄×D₃	—	9	4	no	—
502	C₄×D₃	—	9	4	no	—
503	C₄×D₃	—	9	4	no	—
504	C₄×D₃	—	9	4	no	—
505	C₄×D₃	—	9	4	no	—
506	C₄×D₃	—	9	1	no	—
507	C₄×D₃	—	9	1	no	—
508	C₄×D₃	—	9	1	no	—
509	C₄×D₃	—	9	1	no	—
510	C₄×D₃	—	9	4	no	—
511	C₄×D₃	—	9	4	no	—
512	C₄×D₃	—	9	1	no	—
513	C₄×D₃	—	9	1	no	—
514	C₄×D₃	—	9	4	no	—
515	C₄×D₃	—	9	4	no	—
516	C₄×D₃	—	9	1	no	—
517	C₄×D₃	—	9	1	no	—
518	C₄×D₃	—	9	1	no	—
519	C₄×D₃	—	9	1	no	—
520	C₄×D₃	—	9	1	no	—
521	C₄×D₃	—	9	1	no	—
522	C₄×D₃	—	18	4	no	—
523	C₄×D₃	—	18	4	no	—
524	C₄×D₃	—	18	4	no	—
525	C₄×D₃	—	18	4	no	—
526	C₄×D₃	C₄×C₃⋊D₃	1	1	yes	characteristic
527	C₄×D₃	C₄×C₃⋊D₃	1	1	yes	characteristic
528	C₄×D₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
529	C₄×D₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
530	C₃×C₈	—	2	8	no	—
531	C₃×C₈	—	3	8	no	—
532	C₃×C₈	—	9	2	no	—
533	C₃×C₈	C₂×D₃²	1	8	yes	complemented
534	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	complemented
535	C₃⋊C₈	—	3	8	no	—
536	C₃⋊C₈	—	9	8	no	—
537	C₃⋊C₈	—	9	2	no	—
538	C₃⋊C₈	—	18	8	no	—
539	C₃⋊C₈	C₂²×C₃⋊D₃	1	2	yes	complemented
540	C₂×C₃²	—	2	1	no	—
541	C₂×C₃²	—	2	4	no	—
542	C₂×C₃²	—	2	4	no	—
543	C₂×C₃²	—	3	2	no	—
544	C₂×C₃²	—	4	4	no	—
545	C₂×C₃²	—	6	1	no	—
546	C₂×C₃²	C₂²×C₄×D₃	1	4	yes	—
547	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
548	C₃⋊D₃	—	2	1	no	—
549	C₃⋊D₃	—	3	2	no	—
550	C₃⋊D₃	—	3	8	no	—
551	C₃⋊D₃	—	6	8	no	—
552	C₃⋊D₃	—	6	1	no	—
553	C₃⋊D₃	—	6	4	no	—
554	C₃⋊D₃	—	12	4	no	—
555	C₃⋊D₃	D₃×M₁₆	1	2	yes	direct product factor
556	C₃×D₃	—	2	4	no	—
557	C₃×D₃	—	3	8	no	—
558	C₃×D₃	—	6	4	no	—
559	C₃×D₃	D₃×M₁₆	1	8	yes	complemented
560	C₂⁴	—	27	1	no	—
561	C₂²×C₄	—	3	1	no	—
562	C₂²×C₄	—	9	1	no	—
563	C₂²×C₄	—	27	1	no	—
564	C₂²×C₄	—	27	1	no	—
565	C₂²×C₄	—	27	1	no	—
566	C₂²×C₄	—	27	1	no	—
567	C₂²×C₄	—	27	1	no	—
568	C₂²×C₄	—	27	1	no	—
569	C₂²×C₄	—	27	1	no	—
570	C₂²×C₄	—	27	1	no	—
571	C₂²×C₄	—	27	1	no	—
572	C₂²×C₄	—	27	1	no	—
573	C₂²×C₄	—	27	1	no	—
574	C₂²×C₄	—	27	1	no	—
575	M₁₆	—	3	1	no	—
576	M₁₆	—	3	2	no	—
577	M₁₆	—	9	1	no	—
578	M₁₆	—	9	2	no	—
579	M₁₆	—	27	2	no	—
580	M₁₆	—	27	2	no	—
581	M₁₆	—	27	2	no	—
582	M₁₆	—	27	1	no	—
583	M₁₆	—	27	2	no	—
584	M₁₆	D₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
585	C₂×C₈	—	3	2	no	—
586	C₂×C₈	—	9	2	no	—
587	C₂×C₈	—	27	2	no	—
588	C₂×C₈	—	27	2	no	—
589	C₂×C₈	—	27	2	no	—
590	C₂×C₈	—	27	2	no	—
591	C₂²×C₃	—	2	4	no	—
592	C₂²×C₃	—	3	4	no	—
593	C₂²×C₃	—	3	4	no	—
594	C₂²×C₃	—	6	8	no	—
595	C₂²×C₃	—	9	1	no	—
596	C₂²×C₃	—	9	1	no	—
597	C₂²×C₃	—	18	2	no	—
598	C₂²×C₃	C₄×D₃²	1	4	yes	—
599	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
600	C₂×D₃	—	2	2	no	—
601	C₂×D₃	—	3	4	no	—
602	C₂×D₃	—	3	4	no	—
603	C₂×D₃	—	6	8	no	—
604	C₂×D₃	—	9	16	no	—
605	C₂×D₃	—	9	4	no	—
606	C₂×D₃	—	9	1	no	—
607	C₂×D₃	—	9	4	no	—
608	C₂×D₃	—	9	4	no	—
609	C₂×D₃	—	9	1	no	—
610	C₂×D₃	—	18	4	no	—
611	C₂×D₃	—	18	4	no	—
612	C₂×D₃	—	18	2	no	—
613	C₂×D₃	—	18	2	no	—
614	C₂×D₃	—	18	8	no	—
615	C₂×D₃	—	18	8	no	—
616	C₂×D₃	—	18	8	no	—
617	C₂×D₃	—	18	2	no	—
618	C₂×D₃	—	18	8	no	—
619	C₂×D₃	—	18	2	no	—
620	C₂×D₃	—	36	8	no	—
621	C₂×D₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
622	C₂×D₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
623	C₃×C₄	—	2	4	no	—
624	C₃×C₄	—	2	4	no	—
625	C₃×C₄	—	3	4	no	—
626	C₃×C₄	—	3	4	no	—
627	C₃×C₄	—	9	1	no	—
628	C₃×C₄	—	9	1	no	—
629	C₃×C₄	C₄×D₃²	1	4	yes	—
630	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
631	C₃×C₄	C₂²×D₃²	1	4	yes	—
632	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
633	Dic₃	—	3	4	no	—
634	Dic₃	—	3	4	no	—
635	Dic₃	—	9	4	no	—
636	Dic₃	—	9	4	no	—
637	Dic₃	—	9	1	no	—
638	Dic₃	—	9	1	no	—
639	Dic₃	—	18	4	no	—
640	Dic₃	—	18	4	no	—
641	Dic₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
642	Dic₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
643	C₃²	—	2	4	no	—
644	C₃²	C₂×D₃×M₁₆	1	4	yes	complemented
645	C₃²	C₂×D₃×M₁₆	1	1	yes	characteristic, complemented
646	C₂³	—	3	1	no	—
647	C₂³	—	9	1	no	—
648	C₂³	—	27	1	no	—
649	C₂³	—	27	1	no	—
650	C₂³	—	27	1	no	—
651	C₂³	—	27	1	no	—
652	C₂³	—	27	1	no	—
653	C₂³	—	54	4	no	—
654	C₂×C₄	—	3	1	no	—
655	C₂×C₄	—	3	1	no	—
656	C₂×C₄	—	3	1	no	—
657	C₂×C₄	—	3	1	no	—
658	C₂×C₄	—	3	1	no	—
659	C₂×C₄	—	9	1	no	—
660	C₂×C₄	—	9	1	no	—
661	C₂×C₄	—	9	1	no	—
662	C₂×C₄	—	9	1	no	—
663	C₂×C₄	—	9	1	no	—
664	C₂×C₄	—	27	1	no	—
665	C₂×C₄	—	27	1	no	—
666	C₂×C₄	—	27	1	no	—
667	C₂×C₄	—	27	1	no	—
668	C₂×C₄	—	27	1	no	—
669	C₂×C₄	—	27	1	no	—
670	C₂×C₄	—	27	1	no	—
671	C₂×C₄	—	27	1	no	—
672	C₂×C₄	—	27	1	no	—
673	C₂×C₄	—	27	1	no	—
674	C₂×C₄	—	27	1	no	—
675	C₂×C₄	—	27	1	no	—
676	C₂×C₄	—	27	1	no	—
677	C₂×C₄	—	27	1	no	—
678	C₂×C₄	—	27	1	no	—
679	C₂×C₄	—	27	1	no	—
680	C₂×C₄	—	27	1	no	—
681	C₂×C₄	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
682	C₈	—	3	2	no	—
683	C₈	—	9	2	no	—
684	C₈	—	27	2	no	—
685	C₈	C₂×D₃×C₃⋊D₃	1	2	yes	complemented
686	C₂×C₃	—	2	1	no	—
687	C₂×C₃	—	2	4	no	—
688	C₂×C₃	—	2	4	no	—
689	C₂×C₃	—	3	8	no	—
690	C₂×C₃	—	4	4	no	—
691	C₂×C₃	—	6	4	no	—
692	C₂×C₃	—	9	2	no	—
693	C₂×C₃	—	18	1	no	—
694	C₂×C₃	C₂×C₄×D₃²	1	4	yes	—
695	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
696	D₃	—	2	1	no	—
697	D₃	—	3	8	no	—
698	D₃	—	6	4	no	—
699	D₃	—	9	2	no	—
700	D₃	—	9	8	no	—
701	D₃	—	18	8	no	—
702	D₃	—	18	1	no	—
703	D₃	—	18	4	no	—
704	D₃	—	36	4	no	—
705	D₃	M₁₆×C₃⋊D₃	1	2	yes	direct product factor
706	C₂²	—	3	1	no	—
707	C₂²	—	3	1	no	—
708	C₂²	—	6	2	no	—
709	C₂²	—	9	1	no	—
710	C₂²	—	9	1	no	—
711	C₂²	—	18	2	no	—
712	C₂²	—	27	4	no	—
713	C₂²	—	27	1	no	—
714	C₂²	—	27	1	no	—
715	C₂²	—	54	2	no	—
716	C₂²	—	54	2	no	—
717	C₂²	—	54	2	no	—
718	C₂²	—	54	2	no	—
719	C₂²	C₄×D₃×C₃⋊D₃	1	1	yes	characteristic
720	C₄	—	3	1	no	—
721	C₄	—	3	1	no	—
722	C₄	—	9	1	no	—
723	C₄	—	9	1	no	—
724	C₄	—	27	1	no	—
725	C₄	—	27	1	no	—
726	C₄	C₄×D₃×C₃⋊D₃	1	1	yes	characteristic
727	C₄	C₂²×D₃×C₃⋊D₃	1	1	yes	characteristic
728	C₃	—	2	4	no	—
729	C₃	D₃²×M₁₆	1	4	yes	complemented
730	C₃	C₂×M₁₆×C₃⋊D₃	1	1	yes	characteristic, complemented
731	C₂	—	2	1	no	—
732	C₂	—	3	2	no	—
733	C₂	—	6	1	no	—
734	C₂	—	9	2	no	—
735	C₂	—	18	1	no	—
736	C₂	—	27	2	no	—
737	C₂	—	54	1	no	—
738	C₂	C₂×C₄×D₃×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂²×D₃×C₃⋊D₃
commutator, socle	C₂×C₃³	C₂³×C₄
Fitting	C₃³×M₁₆	C₂²
prime radical	C₂²×D₃×C₃⋊D₃	C₄
cosocle	C₃³×C₄	C₂⁴
hypercenter	M₁₆	D₃×C₃⋊D₃
hypocenter	C₃³	C₂²×M₁₆
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. M₁₆×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₃×M₁₆×C₃⋊D₃	C₂	semidirect
4. C₃²×D₃×M₁₆	C₂	semidirect
5. #11723358	C₂	semidirect
6. C₃⋊D₃×#208	C₂	semidirect
7. D₃×#3748	C₂	semidirect
8. #11723312	C₂	semidirect
9. C₃⋊D₃×ΓL(1,𝔽₂₅)	C₂	semidirect
10. D₃×#3743	C₂	semidirect
11. D₃×C₈×C₃⋊D₃	C₂	semidirect
29. C₃³×M₁₆	C₂²	semidirect
30. #88855	C₂²	semidirect
31. #88850	C₂²	semidirect
32. C₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
33. C₃×#3748	C₂²	semidirect
34. C₃×#3743	C₂²	semidirect
35. C₃×C₈×C₃⋊D₃	C₂²	semidirect
36. C₃²×#208	C₂²	semidirect
37. C₃²×ΓL(1,𝔽₂₅)	C₂²	semidirect
38. C₃²×D₃×C₈	C₂²	semidirect
39. #88788	C₂²	semidirect
40. #88787	C₂²	semidirect
41. #88786	C₂²	semidirect
42. #88785	C₂²	semidirect
43. C₃⋊D₃×C₃⋊C₈	C₂²	semidirect
44. D₃×C₃⋊(C₃⋊C₈)	C₂²	semidirect
56. M₁₆×C₃⋊D₃	D₃	direct (N × H)
60. C₃×D₃×M₁₆	D₃	semidirect
104. C₃³×C₈	C₂³	semidirect
105. C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	semidirect
106. C₃×C₃⋊(C₃⋊C₈)	C₂³	semidirect
107. C₃²×C₃⋊C₈	C₂³	semidirect
144. C₃²×M₁₆	C₂×D₃	semidirect
145. C₃²×M₁₆	C₂×D₃	semidirect
151. #3748	C₂×D₃	semidirect
158. #3743	C₂×D₃	semidirect
164. C₈×C₃⋊D₃	C₂×D₃	semidirect
166. C₃×#208	C₂×D₃	semidirect
168. C₃×ΓL(1,𝔽₂₅)	C₂×D₃	semidirect
170. C₃×D₃×C₈	C₂×D₃	semidirect
190. D₃×C₃⋊D₃	M₁₆	direct (N × H)
217. D₃×M₁₆	C₃⋊D₃	direct (N × H)
303. C₃²×C₈	C₂²×D₃	semidirect
304. C₃²×C₈	C₂²×D₃	semidirect
308. C₃⋊(C₃⋊C₈)	C₂²×D₃	semidirect
310. C₃×C₃⋊C₈	C₂²×D₃	semidirect
315. C₃⋊(C₃⋊D₃)	C₂×M₁₆	semidirect
317. C₃×C₃⋊D₃	C₂×M₁₆	semidirect
319. C₃²×D₃	C₂×M₁₆	semidirect
356. C₃×M₁₆	D₃²	semidirect
357. C₃×M₁₆	C₂×C₃⋊D₃	semidirect
366. #208	C₂×C₃⋊D₃	semidirect
377. ΓL(1,𝔽₂₅)	C₂×C₃⋊D₃	semidirect
386. D₃×C₈	C₂×C₃⋊D₃	semidirect
450. C₃³	C₂²×M₁₆	semidirect
533. C₃×C₈	C₂×D₃²	semidirect
534. C₃×C₈	C₂²×C₃⋊D₃	semidirect
539. C₃⋊C₈	C₂²×C₃⋊D₃	semidirect
555. C₃⋊D₃	D₃×M₁₆	direct (N × H)
559. C₃×D₃	D₃×M₁₆	semidirect
584. M₁₆	D₃×C₃⋊D₃	direct (N × H)
644. C₃²	C₂×D₃×M₁₆	semidirect
645. C₃²	C₂×D₃×M₁₆	semidirect
685. C₈	C₂×D₃×C₃⋊D₃	semidirect
705. D₃	M₁₆×C₃⋊D₃	direct (N × H)
729. C₃	D₃²×M₁₆	semidirect
730. C₃	C₂×M₁₆×C₃⋊D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃×C₃⋊D₃	2
M₁₆×C₃⋊(C₃⋊D₃)	2
C₃×M₁₆×C₃⋊D₃	2
C₃²×D₃×M₁₆	2
#11723358	2
C₃⋊D₃×#208	2
D₃×#3748	2
#11723312	2
C₃⋊D₃×ΓL(1,𝔽₂₅)	2
D₃×#3743	2
D₃×C₈×C₃⋊D₃	2
C₂×M₁₆×C₃⋊D₃	3
D₃²×M₁₆	3

Subgroups — D3×M16×C3⋊D3 #13176679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×M₁₆×C₃⋊D₃ #13176679