Subgroups — C₂×C₃²×D₃×M₁₆ #13179120

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×D₃×M₁₆	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
6	C₂×C₃²×D₃×C₈	C₂	1	2	yes	maximal, complemented
7	C₂²×C₃²×M₁₆	—	3	1	no	maximal
8	C₂×C₃×D₃×M₁₆	C₃	1	4	yes	maximal, direct product factor
9	C₂³×C₃²×D₃	C₄	1	1	yes	characteristic
10	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×Dic₃	C₄	1	1	yes	characteristic
12	C₂×C₃²×C₄×D₃	C₄	1	4	yes	—
13	C₂×C₃²×C₄×D₃	C₄	1	1	yes	characteristic
14	C₂×C₃²×C₄×D₃	C₄	1	1	yes	characteristic
15	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
16	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃²×C₄×D₃	C₂²	1	4	yes	—
18	C₃³×M₁₆	C₂²	1	4	yes	complemented
19	C₂×C₃³×C₈	C₂²	1	2	yes	complemented
20	C₃²×#208	C₂²	1	4	yes	complemented
21	C₂×C₃²×C₃⋊C₈	C₂²	1	2	yes	complemented
22	C₃²×ΓL(1,𝔽₂₅)	C₂²	1	8	yes	complemented
23	C₃²×D₃×C₈	C₂²	1	8	yes	complemented
24	C₂³×C₃²×C₄	—	3	1	no	—
25	C₂²×C₃×C₄×D₃	C₂×C₃	1	4	yes	—
26	C₂×C₃²×M₁₆	—	2	4	no	—
27	C₂×C₃²×M₁₆	—	3	1	no	—
28	C₂×C₃²×M₁₆	—	3	8	no	—
29	C₂×C₃²×M₁₆	—	3	2	no	—
30	C₂×C₃²×M₁₆	D₃	1	1	yes	characteristic, direct product factor
31	C₂×C₃²×M₁₆	C₂×C₃	1	4	yes	complemented
32	C₂²×C₃²×C₈	—	3	2	no	—
33	C₂×C₃×#208	C₂×C₃	1	4	yes	complemented
34	C₃×D₃×M₁₆	C₂×C₃	1	32	yes	direct product factor
35	C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	1	8	yes	complemented
36	C₂×C₃×D₃×C₈	C₂×C₃	1	8	yes	complemented
37	C₂³×C₃³	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃²×D₃	—	2	4	no	—
39	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₃²×D₃	C₂×C₄	1	4	yes	—
41	C₂²×C₃²×D₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
43	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃³×C₄	C₂³	1	2	yes	—
45	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
46	C₂×C₃²×Dic₃	C₂×C₄	1	4	yes	—
47	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₃²×C₄×D₃	C₂×C₄	1	2	yes	—
50	C₃²×C₄×D₃	C₂×C₄	1	4	yes	—
51	C₃²×C₄×D₃	C₂×C₄	1	2	yes	—
52	C₃²×C₄×D₃	C₂×C₄	1	4	yes	—
53	C₃²×C₄×D₃	C₂³	1	2	yes	—
54	C₃²×C₄×D₃	C₂³	1	2	yes	—
55	C₃³×C₈	C₂³	1	4	yes	complemented
56	C₃²×C₃⋊C₈	C₂³	1	4	yes	complemented
57	C₂²×C₃×M₁₆	—	3	4	no	—
58	C₂×D₃×M₁₆	C₃²	1	1	yes	characteristic, direct product factor
59	C₂⁴×C₃²	—	3	1	no	—
60	C₂³×C₃×D₃	C₃×C₄	1	4	yes	—
61	C₂²×C₃²×C₄	—	2	4	no	—
62	C₂²×C₃²×C₄	—	3	1	no	—
63	C₂²×C₃²×C₄	—	3	1	no	—
64	C₂²×C₃²×C₄	—	3	4	no	—
65	C₂²×C₃²×C₄	—	3	1	no	—
66	C₂²×C₃²×C₄	—	3	4	no	—
67	C₂²×C₃²×C₄	—	3	1	no	—
68	C₂²×C₃²×C₄	—	3	1	no	—
69	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
70	C₂²×C₃²×C₄	C₂²×C₃	1	4	yes	—
71	C₂²×C₃×Dic₃	C₃×C₄	1	4	yes	—
72	C₂×C₃×C₄×D₃	C₃×C₄	1	16	yes	—
73	C₂×C₃×C₄×D₃	C₃×C₄	1	4	yes	—
74	C₂×C₃×C₄×D₃	C₃×C₄	1	4	yes	—
75	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
76	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
77	C₂×C₃×C₄×D₃	C₂²×C₃	1	16	yes	—
78	C₃²×M₁₆	—	2	16	no	—
79	C₃²×M₁₆	—	3	4	no	—
80	C₃²×M₁₆	—	3	8	no	—
81	C₃²×M₁₆	C₂×D₃	1	4	yes	direct product factor
82	C₃²×M₁₆	C₂²×C₃	1	16	yes	complemented
83	C₂×C₃²×C₈	—	2	8	no	—
84	C₂×C₃²×C₈	—	3	2	no	—
85	C₂×C₃²×C₈	—	3	8	no	—
86	C₂×C₃²×C₈	C₂×D₃	1	2	yes	complemented
87	C₂×C₃²×C₈	C₂²×C₃	1	8	yes	complemented
88	C₃×#208	C₂²×C₃	1	16	yes	complemented
89	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	8	yes	complemented
90	C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	1	32	yes	complemented
91	C₃×D₃×C₈	C₂²×C₃	1	32	yes	complemented
92	C₂²×C₃³	—	2	2	no	—
93	C₂²×C₃³	C₂²×C₄	1	2	yes	—
94	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃²×D₃	—	2	2	no	—
96	C₂×C₃²×D₃	—	2	8	no	—
97	C₂×C₃²×D₃	M₁₆	1	4	yes	direct product factor
98	C₂×C₃²×D₃	C₂²×C₄	1	2	yes	—
99	C₂×C₃²×D₃	C₂²×C₄	1	2	yes	—
100	C₃³×C₄	C₂²×C₄	1	2	yes	—
101	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
102	C₃³×C₄	C₂⁴	1	1	yes	characteristic
103	C₃²×Dic₃	C₂²×C₄	1	2	yes	—
104	C₃²×Dic₃	C₂²×C₄	1	2	yes	—
105	C₂³×C₃×C₄	—	3	4	no	—
106	C₂²×C₄×D₃	C₂×C₃²	1	1	yes	characteristic
107	C₂×C₃×M₁₆	—	2	4	no	—
108	C₂×C₃×M₁₆	—	3	4	no	—
109	C₂×C₃×M₁₆	—	3	32	no	—
110	C₂×C₃×M₁₆	—	3	8	no	—
111	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	direct product factor
112	C₂×C₃×M₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
113	C₂²×C₃×C₈	—	3	8	no	—
114	C₂×#208	C₂×C₃²	1	1	yes	characteristic, complemented
115	D₃×M₁₆	C₂×C₃²	1	8	yes	direct product factor
116	C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	1	2	yes	complemented
117	C₂×D₃×C₈	C₂×C₃²	1	2	yes	complemented
118	C₂³×C₃²	—	2	4	no	—
119	C₂³×C₃²	—	3	1	no	—
120	C₂³×C₃²	—	3	4	no	—
121	C₂³×C₃²	—	3	1	no	—
122	C₂³×C₃²	—	6	4	no	—
123	C₂³×C₃²	C₄×D₃	1	1	yes	characteristic
124	C₂³×C₃²	C₂×C₃×C₄	1	4	yes	—
125	C₂²×C₃×D₃	—	2	16	no	—
126	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
127	C₂²×C₃×D₃	C₂×C₃×C₄	1	16	yes	—
128	C₂²×C₃×D₃	C₂×C₃×C₄	1	4	yes	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	8	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	8	no	—
133	C₂×C₃²×C₄	—	3	4	no	—
134	C₂×C₃²×C₄	—	3	1	no	—
135	C₂×C₃²×C₄	—	3	1	no	—
136	C₂×C₃²×C₄	—	3	4	no	—
137	C₂×C₃²×C₄	—	3	4	no	—
138	C₂×C₃²×C₄	—	3	2	no	—
139	C₂×C₃²×C₄	—	3	2	no	—
140	C₂×C₃²×C₄	—	3	2	no	—
141	C₂×C₃²×C₄	—	3	2	no	—
142	C₂×C₃²×C₄	C₄×D₃	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₄×D₃	1	2	yes	—
144	C₂×C₃²×C₄	C₂×C₃×C₄	1	8	yes	—
145	C₂×C₃²×C₄	C₂×C₃×C₄	1	4	yes	—
146	C₂×C₃²×C₄	C₂²×D₃	1	2	yes	—
147	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
148	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
149	C₂×C₃²×C₄	C₂³×C₃	1	8	yes	—
150	C₂×C₃×Dic₃	C₂×C₃×C₄	1	16	yes	—
151	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
152	C₂×C₃×Dic₃	C₂×C₃×C₄	1	4	yes	—
153	C₃×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
154	C₃×C₄×D₃	C₂×C₃×C₄	1	16	yes	—
155	C₃×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
156	C₃×C₄×D₃	C₂×C₃×C₄	1	16	yes	—
157	C₃×C₄×D₃	C₂³×C₃	1	8	yes	—
158	C₃×C₄×D₃	C₂³×C₃	1	8	yes	—
159	C₃²×C₈	—	2	16	no	—
160	C₃²×C₈	—	3	4	no	—
161	C₃²×C₈	C₂²×D₃	1	4	yes	complemented
162	C₃²×C₈	C₂³×C₃	1	16	yes	complemented
163	C₃×C₃⋊C₈	C₂³×C₃	1	16	yes	complemented
164	C₂²×M₁₆	—	3	1	no	Sylow
165	C₂×C₃³	—	2	2	no	—
166	C₂×C₃³	C₂×M₁₆	1	2	yes	complemented
167	C₂×C₃³	C₂³×C₄	1	1	yes	characteristic
168	C₃²×D₃	—	2	2	no	—
169	C₃²×D₃	C₂×M₁₆	1	4	yes	direct product factor
170	C₂⁴×C₃	—	3	4	no	—
171	C₂³×D₃	C₃²×C₄	1	1	yes	characteristic
172	C₂²×C₃×C₄	—	2	4	no	—
173	C₂²×C₃×C₄	—	3	4	no	—
174	C₂²×C₃×C₄	—	3	4	no	—
175	C₂²×C₃×C₄	—	3	16	no	—
176	C₂²×C₃×C₄	—	3	4	no	—
177	C₂²×C₃×C₄	—	3	4	no	—
178	C₂²×C₃×C₄	—	3	16	no	—
179	C₂²×C₃×C₄	—	3	4	no	—
180	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
181	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
182	C₂²×Dic₃	C₃²×C₄	1	1	yes	characteristic
183	C₂×C₄×D₃	C₃²×C₄	1	4	yes	—
184	C₂×C₄×D₃	C₃²×C₄	1	1	yes	characteristic
185	C₂×C₄×D₃	C₃²×C₄	1	1	yes	characteristic
186	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
187	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
188	C₂×C₄×D₃	C₂²×C₃²	1	4	yes	—
189	C₃×M₁₆	—	2	16	no	—
190	C₃×M₁₆	—	3	16	no	—
191	C₃×M₁₆	—	3	32	no	—
192	C₃×M₁₆	C₂×C₃×D₃	1	16	yes	direct product factor
193	C₃×M₁₆	C₂²×C₃²	1	4	yes	complemented
194	C₂×C₃×C₈	—	2	8	no	—
195	C₂×C₃×C₈	—	3	8	no	—
196	C₂×C₃×C₈	—	3	32	no	—
197	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	complemented
198	C₂×C₃×C₈	C₂²×C₃²	1	2	yes	complemented
199	#208	C₂²×C₃²	1	4	yes	complemented
200	C₂×C₃⋊C₈	C₂²×C₃²	1	2	yes	complemented
201	ΓL(1,𝔽₂₅)	C₂²×C₃²	1	8	yes	complemented
202	D₃×C₈	C₂²×C₃²	1	8	yes	complemented
203	C₂²×C₃²	—	2	2	no	—
204	C₂²×C₃²	—	2	4	no	—
205	C₂²×C₃²	—	2	8	no	—
206	C₂²×C₃²	—	2	8	no	—
207	C₂²×C₃²	—	3	4	no	—
208	C₂²×C₃²	—	3	2	no	—
209	C₂²×C₃²	—	3	2	no	—
210	C₂²×C₃²	—	4	8	no	—
211	C₂²×C₃²	—	6	8	no	—
212	C₂²×C₃²	—	6	2	no	—
213	C₂²×C₃²	C₂×C₄×D₃	1	2	yes	—
214	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
215	C₂²×C₃²	C₂²×C₃×C₄	1	8	yes	—
216	C₂²×C₃²	C₂²×C₃×C₄	1	4	yes	—
217	C₂×C₃×D₃	—	2	8	no	—
218	C₂×C₃×D₃	—	2	32	no	—
219	C₂×C₃×D₃	C₃×M₁₆	1	16	yes	direct product factor
220	C₂×C₃×D₃	C₂²×C₃×C₄	1	8	yes	—
221	C₂×C₃×D₃	C₂²×C₃×C₄	1	8	yes	—
222	C₃²×C₄	—	2	4	no	—
223	C₃²×C₄	—	2	4	no	—
224	C₃²×C₄	—	2	8	no	—
225	C₃²×C₄	—	3	2	no	—
226	C₃²×C₄	—	3	2	no	—
227	C₃²×C₄	C₂×C₄×D₃	1	2	yes	—
228	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
229	C₃²×C₄	C₂²×C₃×C₄	1	4	yes	—
230	C₃²×C₄	C₂²×C₃×C₄	1	8	yes	—
231	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
232	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
233	C₃×Dic₃	C₂²×C₃×C₄	1	8	yes	—
234	C₃×Dic₃	C₂²×C₃×C₄	1	8	yes	—
235	C₂³×C₄	—	3	1	no	—
236	C₂×M₁₆	—	3	1	no	—
237	C₂×M₁₆	—	3	8	no	—
238	C₂×M₁₆	—	3	2	no	—
239	C₂×M₁₆	C₃²×D₃	1	1	yes	characteristic, direct product factor
240	C₂²×C₈	—	3	2	no	—
241	C₃³	C₂²×M₁₆	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₃	—	2	4	no	—
243	C₂³×C₃	—	3	4	no	—
244	C₂³×C₃	—	3	16	no	—
245	C₂³×C₃	—	3	4	no	—
246	C₂³×C₃	—	6	16	no	—
247	C₂³×C₃	C₃×C₄×D₃	1	4	yes	—
248	C₂³×C₃	C₂×C₃²×C₄	1	1	yes	characteristic
249	C₂²×D₃	—	2	4	no	—
250	C₂²×D₃	C₂×C₃²×C₄	1	1	yes	characteristic
251	C₂²×D₃	C₂×C₃²×C₄	1	4	yes	—
252	C₂²×D₃	C₂×C₃²×C₄	1	1	yes	characteristic
253	C₂×C₃×C₄	—	2	4	no	—
254	C₂×C₃×C₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	2	8	no	—
257	C₂×C₃×C₄	—	3	16	no	—
258	C₂×C₃×C₄	—	3	4	no	—
259	C₂×C₃×C₄	—	3	4	no	—
260	C₂×C₃×C₄	—	3	8	no	—
261	C₂×C₃×C₄	—	3	8	no	—
262	C₂×C₃×C₄	—	3	8	no	—
263	C₂×C₃×C₄	—	3	16	no	—
264	C₂×C₃×C₄	—	3	16	no	—
265	C₂×C₃×C₄	—	3	8	no	—
266	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
267	C₂×C₃×C₄	C₃×C₄×D₃	1	4	yes	—
268	C₂×C₃×C₄	C₂×C₃²×C₄	1	2	yes	—
269	C₂×C₃×C₄	C₂×C₃²×C₄	1	1	yes	characteristic
270	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
271	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
272	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
273	C₂×C₃×C₄	C₂³×C₃²	1	2	yes	—
274	C₂×Dic₃	C₂×C₃²×C₄	1	4	yes	—
275	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
276	C₂×Dic₃	C₂×C₃²×C₄	1	1	yes	characteristic
277	C₄×D₃	C₂×C₃²×C₄	1	2	yes	—
278	C₄×D₃	C₂×C₃²×C₄	1	4	yes	—
279	C₄×D₃	C₂×C₃²×C₄	1	2	yes	—
280	C₄×D₃	C₂×C₃²×C₄	1	4	yes	—
281	C₄×D₃	C₂³×C₃²	1	2	yes	—
282	C₄×D₃	C₂³×C₃²	1	2	yes	—
283	C₃×C₈	—	2	16	no	—
284	C₃×C₈	—	3	16	no	—
285	C₃×C₈	C₂²×C₃×D₃	1	16	yes	complemented
286	C₃×C₈	C₂³×C₃²	1	4	yes	complemented
287	C₃⋊C₈	C₂³×C₃²	1	4	yes	complemented
288	C₂×C₃²	—	2	2	no	—
289	C₂×C₃²	—	2	8	no	—
290	C₂×C₃²	—	2	4	no	—
291	C₂×C₃²	—	2	8	no	—
292	C₂×C₃²	—	3	4	no	—
293	C₂×C₃²	—	4	8	no	—
294	C₂×C₃²	—	6	2	no	—
295	C₂×C₃²	D₃×M₁₆	1	2	yes	direct product factor
296	C₂×C₃²	C₂×C₃×M₁₆	1	8	yes	complemented
297	C₂×C₃²	C₂²×C₄×D₃	1	1	yes	characteristic
298	C₂×C₃²	C₂³×C₃×C₄	1	4	yes	—
299	C₃×D₃	—	2	8	no	—
300	C₃×D₃	C₂×C₃×M₁₆	1	16	yes	direct product factor
301	C₂⁴	—	3	1	no	—
302	C₂²×C₄	—	3	1	no	—
303	C₂²×C₄	—	3	1	no	—
304	C₂²×C₄	—	3	4	no	—
305	C₂²×C₄	—	3	1	no	—
306	C₂²×C₄	—	3	1	no	—
307	C₂²×C₄	—	3	4	no	—
308	C₂²×C₄	—	3	1	no	—
309	C₂²×C₄	C₂×C₃²×D₃	1	1	yes	characteristic
310	M₁₆	—	3	4	no	—
311	M₁₆	—	3	8	no	—
312	M₁₆	C₂×C₃²×D₃	1	4	yes	direct product factor
313	C₂×C₈	—	3	2	no	—
314	C₂×C₈	—	3	8	no	—
315	C₂×C₈	C₂×C₃²×D₃	1	2	yes	complemented
316	C₂²×C₃	—	2	8	no	—
317	C₂²×C₃	—	2	2	no	—
318	C₂²×C₃	—	2	4	no	—
319	C₂²×C₃	—	2	8	no	—
320	C₂²×C₃	—	3	16	no	—
321	C₂²×C₃	—	3	8	no	—
322	C₂²×C₃	—	3	8	no	—
323	C₂²×C₃	—	4	8	no	—
324	C₂²×C₃	—	6	32	no	—
325	C₂²×C₃	—	6	8	no	—
326	C₂²×C₃	C₂×C₃×C₄×D₃	1	8	yes	—
327	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
328	C₂²×C₃	C₂²×C₃²×C₄	1	2	yes	—
329	C₂²×C₃	C₂²×C₃²×C₄	1	1	yes	characteristic
330	C₂×D₃	—	2	2	no	—
331	C₂×D₃	—	2	8	no	—
332	C₂×D₃	C₃²×M₁₆	1	4	yes	direct product factor
333	C₂×D₃	C₂²×C₃²×C₄	1	2	yes	—
334	C₂×D₃	C₂²×C₃²×C₄	1	2	yes	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	4	no	—
337	C₃×C₄	—	2	8	no	—
338	C₃×C₄	—	3	8	no	—
339	C₃×C₄	—	3	8	no	—
340	C₃×C₄	C₂×C₃×C₄×D₃	1	8	yes	—
341	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
342	C₃×C₄	C₂²×C₃²×C₄	1	1	yes	characteristic
343	C₃×C₄	C₂²×C₃²×C₄	1	2	yes	—
344	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
345	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
346	Dic₃	C₂²×C₃²×C₄	1	2	yes	—
347	Dic₃	C₂²×C₃²×C₄	1	2	yes	—
348	C₃²	—	2	4	no	—
349	C₃²	C₂×D₃×M₁₆	1	1	yes	characteristic, direct product factor
350	C₃²	C₂²×C₃×M₁₆	1	4	yes	complemented
351	C₂³	—	3	1	no	—
352	C₂³	—	3	4	no	—
353	C₂³	—	3	1	no	—
354	C₂³	—	6	4	no	—
355	C₂³	C₃²×C₄×D₃	1	1	yes	characteristic
356	C₂×C₄	—	3	4	no	—
357	C₂×C₄	—	3	1	no	—
358	C₂×C₄	—	3	1	no	—
359	C₂×C₄	—	3	2	no	—
360	C₂×C₄	—	3	2	no	—
361	C₂×C₄	—	3	2	no	—
362	C₂×C₄	—	3	4	no	—
363	C₂×C₄	—	3	4	no	—
364	C₂×C₄	—	3	2	no	—
365	C₂×C₄	C₃²×C₄×D₃	1	2	yes	—
366	C₂×C₄	C₃²×C₄×D₃	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₃²×D₃	1	2	yes	—
369	C₈	—	3	4	no	—
370	C₈	C₂²×C₃²×D₃	1	4	yes	complemented
371	C₂×C₃	—	2	8	no	—
372	C₂×C₃	—	2	2	no	—
373	C₂×C₃	—	2	4	no	—
374	C₂×C₃	—	2	8	no	—
375	C₂×C₃	—	3	16	no	—
376	C₂×C₃	—	4	8	no	—
377	C₂×C₃	—	6	8	no	—
378	C₂×C₃	C₃×D₃×M₁₆	1	8	yes	direct product factor
379	C₂×C₃	C₂×C₃²×M₁₆	1	2	yes	complemented
380	C₂×C₃	C₂²×C₃×C₄×D₃	1	4	yes	—
381	C₂×C₃	C₂³×C₃²×C₄	1	1	yes	characteristic
382	D₃	—	2	2	no	—
383	D₃	C₂×C₃²×M₁₆	1	4	yes	direct product factor
384	C₂²	—	2	2	no	—
385	C₂²	—	3	2	no	—
386	C₂²	—	3	4	no	—
387	C₂²	—	3	2	no	—
388	C₂²	—	6	8	no	—
389	C₂²	—	6	2	no	—
390	C₂²	C₂×C₃²×C₄×D₃	1	2	yes	—
391	C₂²	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
392	C₄	—	3	2	no	—
393	C₄	—	3	2	no	—
394	C₄	C₂×C₃²×C₄×D₃	1	1	yes	characteristic
395	C₄	C₂×C₃²×C₄×D₃	1	2	yes	—
396	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
397	C₃	—	2	4	no	—
398	C₃	C₂×C₃×D₃×M₁₆	1	4	yes	direct product factor
399	C₃	C₂²×C₃²×M₁₆	1	1	yes	characteristic, complemented
400	C₂	—	2	2	no	—
401	C₂	—	3	4	no	—
402	C₂	—	6	2	no	—
403	C₂	C₃²×D₃×M₁₆	1	2	yes	direct product factor
404	C₂	C₂²×C₃²×C₄×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃²×C₄	C₂²×D₃
commutator	C₂×C₃	C₂³×C₃²×C₄
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂³×C₃²×D₃	C₄
cosocle	C₃×C₄	C₂⁴×C₃²
hypercenter	C₂×C₃²×M₁₆	D₃
hypocenter	C₃	C₂²×C₃²×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×M₁₆	C₂	semidirect
3. C₂×C₃²×#208	C₂	semidirect
4. C₃²×D₃×M₁₆	C₂	direct (N × H)
5. C₂×C₃²×ΓL(1,𝔽₂₅)	C₂	semidirect
6. C₂×C₃²×D₃×C₈	C₂	semidirect
8. C₂×C₃×D₃×M₁₆	C₃	direct (N × H)
18. C₃³×M₁₆	C₂²	semidirect
19. C₂×C₃³×C₈	C₂²	semidirect
20. C₃²×#208	C₂²	semidirect
21. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
22. C₃²×ΓL(1,𝔽₂₅)	C₂²	semidirect
23. C₃²×D₃×C₈	C₂²	semidirect
30. C₂×C₃²×M₁₆	D₃	direct (N × H)
31. C₂×C₃²×M₁₆	C₂×C₃	semidirect
33. C₂×C₃×#208	C₂×C₃	semidirect
34. C₃×D₃×M₁₆	C₂×C₃	direct (N × H)
35. C₂×C₃×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
36. C₂×C₃×D₃×C₈	C₂×C₃	semidirect
55. C₃³×C₈	C₂³	semidirect
56. C₃²×C₃⋊C₈	C₂³	semidirect
58. C₂×D₃×M₁₆	C₃²	direct (N × H)
81. C₃²×M₁₆	C₂×D₃	direct (N × H)
82. C₃²×M₁₆	C₂²×C₃	semidirect
86. C₂×C₃²×C₈	C₂×D₃	semidirect
87. C₂×C₃²×C₈	C₂²×C₃	semidirect
88. C₃×#208	C₂²×C₃	semidirect
89. C₂×C₃×C₃⋊C₈	C₂²×C₃	semidirect
90. C₃×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
91. C₃×D₃×C₈	C₂²×C₃	semidirect
97. C₂×C₃²×D₃	M₁₆	direct (N × H)
111. C₂×C₃×M₁₆	C₃×D₃	direct (N × H)
112. C₂×C₃×M₁₆	C₂×C₃²	semidirect
114. C₂×#208	C₂×C₃²	semidirect
115. D₃×M₁₆	C₂×C₃²	direct (N × H)
116. C₂×ΓL(1,𝔽₂₅)	C₂×C₃²	semidirect
117. C₂×D₃×C₈	C₂×C₃²	semidirect
161. C₃²×C₈	C₂²×D₃	semidirect
162. C₃²×C₈	C₂³×C₃	semidirect
163. C₃×C₃⋊C₈	C₂³×C₃	semidirect
166. C₂×C₃³	C₂×M₁₆	semidirect
169. C₃²×D₃	C₂×M₁₆	direct (N × H)
192. C₃×M₁₆	C₂×C₃×D₃	direct (N × H)
193. C₃×M₁₆	C₂²×C₃²	semidirect
197. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
198. C₂×C₃×C₈	C₂²×C₃²	semidirect
199. #208	C₂²×C₃²	semidirect
200. C₂×C₃⋊C₈	C₂²×C₃²	semidirect
201. ΓL(1,𝔽₂₅)	C₂²×C₃²	semidirect
202. D₃×C₈	C₂²×C₃²	semidirect
219. C₂×C₃×D₃	C₃×M₁₆	direct (N × H)
239. C₂×M₁₆	C₃²×D₃	direct (N × H)
241. C₃³	C₂²×M₁₆	semidirect
285. C₃×C₈	C₂²×C₃×D₃	semidirect
286. C₃×C₈	C₂³×C₃²	semidirect
287. C₃⋊C₈	C₂³×C₃²	semidirect
295. C₂×C₃²	D₃×M₁₆	direct (N × H)
296. C₂×C₃²	C₂×C₃×M₁₆	semidirect
300. C₃×D₃	C₂×C₃×M₁₆	direct (N × H)
312. M₁₆	C₂×C₃²×D₃	direct (N × H)
315. C₂×C₈	C₂×C₃²×D₃	semidirect
332. C₂×D₃	C₃²×M₁₆	direct (N × H)
349. C₃²	C₂×D₃×M₁₆	direct (N × H)
350. C₃²	C₂²×C₃×M₁₆	semidirect
370. C₈	C₂²×C₃²×D₃	semidirect
378. C₂×C₃	C₃×D₃×M₁₆	direct (N × H)
379. C₂×C₃	C₂×C₃²×M₁₆	semidirect
383. D₃	C₂×C₃²×M₁₆	direct (N × H)
398. C₃	C₂×C₃×D₃×M₁₆	direct (N × H)
399. C₃	C₂²×C₃²×M₁₆	semidirect
403. C₂	C₃²×D₃×M₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₄×D₃	2
C₂×C₃³×M₁₆	2
C₂×C₃²×#208	2
C₃²×D₃×M₁₆	2
C₂×C₃²×ΓL(1,𝔽₂₅)	2
C₂×C₃²×D₃×C₈	2
C₂²×C₃²×M₁₆	3
C₂×C₃×D₃×M₁₆	3

Subgroups — C2×C32×D3×M16 #13179120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₃×M₁₆ #13179120