Subgroups — C₃×C₄×D₃×M₁₆ #11857135

Order 1152.

1383 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₃×C₄²×D₃	C₂	1	1	yes	maximal, characteristic
3	C₃²×C₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₃×M₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4707	C₂	1	2	yes	maximal, complemented
7	C₃×D₃×#97	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×D₃×C₈	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×C₄×M₁₆	—	3	1	no	maximal
11	C₄×D₃×M₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor
12	C₂²×C₃×C₄×D₃	C₄	1	2	yes	—
13	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
15	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₃	C₄	1	2	yes	—
17	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×#208	C₂²	1	2	yes	—
19	C₃×D₃×M₁₆	C₄	1	16	yes	direct product factor
20	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
21	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
22	C₃×C₄²×D₃	C₄	1	2	yes	—
23	C₃×C₄²×D₃	C₄	1	2	yes	—
24	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
26	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
27	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
28	C₃²×#97	C₂²	1	2	yes	complemented
29	C₃²×C₄×C₈	C₂²	1	2	yes	complemented
30	C₃×#815	C₂²	1	4	yes	complemented
31	C₃×C₈×Dic₃	C₂²	1	4	yes	complemented
32	C₃×#803	C₂²	1	2	yes	complemented
33	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	complemented
34	C₂²×C₃×M₁₆	—	3	2	no	—
35	C₂²×C₃×C₄²	—	3	1	no	—
36	C₂×D₃×M₁₆	C₂×C₃	1	2	yes	—
37	C₂×C₄²×D₃	C₂×C₃	1	1	yes	characteristic
38	C₃×C₄×M₁₆	—	2	1	no	—
39	C₃×C₄×M₁₆	—	3	2	no	—
40	C₃×C₄×M₁₆	—	3	1	no	—
41	C₃×C₄×M₁₆	—	3	2	no	—
42	C₃×C₄×M₁₆	—	3	2	no	—
43	C₃×C₄×M₁₆	D₃	1	1	yes	characteristic, direct product factor
44	C₃×C₄×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×C₃×#97	—	3	2	no	—
46	C₂×C₃×C₄×C₈	—	3	2	no	—
47	Dic₃×M₁₆	C₂×C₃	1	2	yes	complemented
48	C₄×#208	C₂×C₃	1	1	yes	characteristic, complemented
49	#4707	C₂×C₃	1	2	yes	complemented
50	D₃×#97	C₂×C₃	1	2	yes	complemented
51	C₄×ΓL(1,𝔽₂₅)	C₂×C₃	1	2	yes	complemented
52	C₄×D₃×C₈	C₂×C₃	1	2	yes	complemented
53	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
55	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
56	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
57	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₃	—	2	8	no	—
59	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
60	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
61	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
62	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₃	C₂×C₄	1	8	yes	—
65	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
66	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
68	C₃²×M₁₆	C₂×C₄	1	8	yes	complemented
69	C₂×C₃²×C₈	C₂³	1	4	yes	—
70	C₃²×C₄²	C₂×C₄	1	2	yes	—
71	C₃²×C₄²	C₂³	1	1	yes	characteristic
72	C₃²×C₄²	C₂³	1	1	yes	characteristic
73	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
74	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
75	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
76	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
77	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
78	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
79	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
80	C₃×#208	C₂×C₄	1	8	yes	complemented
81	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
82	C₃×ΓL(1,𝔽₂₅)	C₂×C₄	1	16	yes	complemented
83	C₃×D₃×C₈	C₂×C₄	1	16	yes	complemented
84	C₂×C₄×M₁₆	—	3	1	no	Sylow
85	C₂³×C₃×C₄	—	3	1	no	—
86	C₂³×C₃×C₄	—	3	2	no	—
87	C₂²×C₄×D₃	C₃×C₄	1	2	yes	—
88	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₃×M₁₆	—	2	2	no	—
90	C₂×C₃×M₁₆	—	3	2	no	—
91	C₂×C₃×M₁₆	—	3	16	no	—
92	C₂×C₃×M₁₆	—	3	4	no	—
93	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
94	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
95	C₂²×C₃×C₈	—	3	4	no	—
96	C₂×C₃×C₄²	—	2	1	no	—
97	C₂×C₃×C₄²	—	3	2	no	—
98	C₂×C₃×C₄²	—	3	1	no	—
99	C₂×C₃×C₄²	—	3	2	no	—
100	C₂×C₃×C₄²	—	3	2	no	—
101	C₂×C₃×C₄²	—	3	1	no	—
102	C₂×C₃×C₄²	—	3	1	no	—
103	C₂×C₃×C₄²	—	3	1	no	—
104	C₂×C₃×C₄²	—	3	1	no	—
105	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
106	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄×Dic₃	C₃×C₄	1	2	yes	—
108	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
109	C₂×#208	C₂²×C₃	1	2	yes	—
110	D₃×M₁₆	C₃×C₄	1	16	yes	direct product factor
111	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
112	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
113	C₄²×D₃	C₃×C₄	1	2	yes	—
114	C₄²×D₃	C₃×C₄	1	2	yes	—
115	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
116	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
117	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
118	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
119	C₃×#97	—	2	2	no	—
120	C₃×#97	—	3	4	no	—
121	C₃×#97	—	3	2	no	—
122	C₃×#97	C₂×D₃	1	2	yes	complemented
123	C₃×#97	C₂²×C₃	1	2	yes	complemented
124	C₃×C₄×C₈	—	2	2	no	—
125	C₃×C₄×C₈	—	3	4	no	—
126	C₃×C₄×C₈	—	3	2	no	—
127	C₃×C₄×C₈	C₂×D₃	1	2	yes	complemented
128	C₃×C₄×C₈	C₂²×C₃	1	2	yes	complemented
129	#815	C₂²×C₃	1	4	yes	complemented
130	C₈×Dic₃	C₂²×C₃	1	4	yes	complemented
131	#803	C₂²×C₃	1	2	yes	complemented
132	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
133	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₃×D₃	—	2	4	no	—
135	C₂²×C₃×D₃	C₄²	1	4	yes	—
136	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₃×D₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃²×C₄	—	2	4	no	—
139	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
140	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
142	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
143	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
144	C₂×C₃×Dic₃	—	2	4	no	—
145	C₂×C₃×Dic₃	C₄²	1	4	yes	—
146	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
147	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₃×Dic₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
150	C₃×C₄×D₃	—	2	4	no	—
151	C₃×C₄×D₃	—	2	4	no	—
152	C₃×C₄×D₃	—	2	4	no	—
153	C₃×C₄×D₃	C₄²	1	4	yes	—
154	C₃×C₄×D₃	C₄²	1	4	yes	—
155	C₃×C₄×D₃	M₁₆	1	8	yes	direct product factor
156	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
157	C₃×C₄×D₃	C₂²×C₄	1	4	yes	—
158	C₃²×C₈	C₂²×C₄	1	8	yes	complemented
159	C₃×C₃⋊C₈	C₂²×C₄	1	8	yes	complemented
160	C₂²×M₁₆	—	3	2	no	—
161	C₂²×C₄²	—	3	1	no	—
162	C₄×M₁₆	—	3	2	no	—
163	C₄×M₁₆	—	3	1	no	—
164	C₄×M₁₆	—	3	2	no	—
165	C₄×M₁₆	—	3	2	no	—
166	C₄×M₁₆	C₃×D₃	1	1	yes	characteristic, direct product factor
167	C₂×#97	—	3	2	no	—
168	C₂×C₄×C₈	—	3	2	no	—
169	C₂⁴×C₃	—	3	1	no	—
170	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂²×C₃×C₄	—	2	2	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	3	1	no	—
174	C₂²×C₃×C₄	—	3	1	no	—
175	C₂²×C₃×C₄	—	3	1	no	—
176	C₂²×C₃×C₄	—	3	2	no	—
177	C₂²×C₃×C₄	—	3	8	no	—
178	C₂²×C₃×C₄	—	3	1	no	—
179	C₂²×C₃×C₄	—	3	1	no	—
180	C₂²×C₃×C₄	—	3	2	no	—
181	C₂²×C₃×C₄	—	3	2	no	—
182	C₂²×C₃×C₄	—	3	2	no	—
183	C₂²×C₃×C₄	—	3	2	no	—
184	C₂²×C₃×C₄	—	6	8	no	—
185	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
186	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
187	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
188	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
189	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
190	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
191	C₂×C₄×D₃	—	2	8	no	—
192	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
193	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
194	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
195	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
196	C₂×C₄×D₃	C₂×C₃×C₄	1	1	yes	characteristic
197	C₂×C₄×D₃	C₂×C₃×C₄	1	8	yes	—
198	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
199	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
201	C₃×M₁₆	—	2	8	no	—
202	C₃×M₁₆	—	3	8	no	—
203	C₃×M₁₆	—	3	16	no	—
204	C₃×M₁₆	C₄×D₃	1	8	yes	direct product factor
205	C₃×M₁₆	C₂×C₃×C₄	1	8	yes	complemented
206	C₂×C₃×C₈	—	2	4	no	—
207	C₂×C₃×C₈	—	3	4	no	—
208	C₂×C₃×C₈	—	3	16	no	—
209	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
210	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
211	C₃×C₄²	—	2	2	no	—
212	C₃×C₄²	—	2	1	no	—
213	C₃×C₄²	—	2	1	no	—
214	C₃×C₄²	—	3	2	no	—
215	C₃×C₄²	—	3	2	no	—
216	C₃×C₄²	—	3	2	no	—
217	C₃×C₄²	—	3	2	no	—
218	C₃×C₄²	—	3	2	no	—
219	C₃×C₄²	—	3	1	no	—
220	C₃×C₄²	—	3	1	no	—
221	C₃×C₄²	C₄×D₃	1	2	yes	—
222	C₃×C₄²	C₂×C₃×C₄	1	2	yes	—
223	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
224	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
225	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
226	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
227	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
228	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
229	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
230	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
231	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
232	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
233	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
234	#208	C₂×C₃×C₄	1	8	yes	complemented
235	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
236	ΓL(1,𝔽₂₅)	C₂×C₃×C₄	1	16	yes	complemented
237	D₃×C₈	C₂×C₃×C₄	1	16	yes	complemented
238	C₂²×C₃²	—	2	2	no	—
239	C₂²×C₃²	C₂×C₄²	1	2	yes	—
240	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₃×D₃	—	2	2	no	—
242	C₂×C₃×D₃	—	2	8	no	—
243	C₂×C₃×D₃	C₂×C₄²	1	2	yes	—
244	C₂×C₃×D₃	C₂×C₄²	1	2	yes	—
245	C₂×C₃×D₃	C₂×M₁₆	1	4	yes	—
246	C₃²×C₄	—	2	2	no	—
247	C₃²×C₄	C₂×C₄²	1	2	yes	—
248	C₃²×C₄	C₂×M₁₆	1	4	yes	complemented
249	C₃²×C₄	C₂³×C₄	1	2	yes	—
250	C₃×Dic₃	—	2	2	no	—
251	C₃×Dic₃	C₂×C₄²	1	2	yes	—
252	C₃×Dic₃	C₂×C₄²	1	2	yes	—
253	C₃×Dic₃	C₂×M₁₆	1	4	yes	complemented
254	C₂³×C₄	—	3	1	no	—
255	C₂³×C₄	—	3	2	no	—
256	C₂×M₁₆	—	3	2	no	—
257	C₂×M₁₆	—	3	16	no	—
258	C₂×M₁₆	—	3	4	no	—
259	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
260	C₂²×C₈	—	3	4	no	—
261	C₂×C₄²	—	3	2	no	—
262	C₂×C₄²	—	3	1	no	—
263	C₂×C₄²	—	3	2	no	—
264	C₂×C₄²	—	3	2	no	—
265	C₂×C₄²	—	3	1	no	—
266	C₂×C₄²	—	3	1	no	—
267	C₂×C₄²	—	3	1	no	—
268	C₂×C₄²	—	3	1	no	—
269	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
270	#97	—	3	4	no	—
271	#97	—	3	2	no	—
272	#97	C₂×C₃×D₃	1	2	yes	complemented
273	C₄×C₈	—	3	4	no	—
274	C₄×C₈	—	3	2	no	—
275	C₄×C₈	C₂×C₃×D₃	1	2	yes	complemented
276	C₂³×C₃	—	2	1	no	—
277	C₂³×C₃	—	3	1	no	—
278	C₂³×C₃	—	3	4	no	—
279	C₂³×C₃	—	3	1	no	—
280	C₂³×C₃	—	6	4	no	—
281	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
282	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
283	C₂²×D₃	—	2	4	no	—
284	C₂²×D₃	C₃×C₄²	1	4	yes	—
285	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
286	C₂²×D₃	C₂²×C₃×C₄	1	1	yes	characteristic
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	4	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	3	4	no	—
295	C₂×C₃×C₄	—	3	1	no	—
296	C₂×C₃×C₄	—	3	1	no	—
297	C₂×C₃×C₄	—	3	2	no	—
298	C₂×C₃×C₄	—	3	4	no	—
299	C₂×C₃×C₄	—	3	4	no	—
300	C₂×C₃×C₄	—	3	8	no	—
301	C₂×C₃×C₄	—	3	4	no	—
302	C₂×C₃×C₄	—	3	4	no	—
303	C₂×C₃×C₄	—	3	2	no	—
304	C₂×C₃×C₄	—	4	4	no	—
305	C₂×C₃×C₄	—	6	4	no	—
306	C₂×C₃×C₄	—	6	4	no	—
307	C₂×C₃×C₄	—	6	4	no	—
308	C₂×C₃×C₄	—	6	4	no	—
309	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
310	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂×C₄×D₃	1	4	yes	—
312	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
313	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
314	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
316	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
317	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
319	C₂×Dic₃	—	2	4	no	—
320	C₂×Dic₃	C₃×C₄²	1	4	yes	—
321	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
322	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
323	C₂×Dic₃	C₂²×C₃×C₄	1	1	yes	characteristic
324	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
325	C₄×D₃	—	2	4	no	—
326	C₄×D₃	—	2	4	no	—
327	C₄×D₃	—	2	4	no	—
328	C₄×D₃	C₃×C₄²	1	4	yes	—
329	C₄×D₃	C₃×C₄²	1	4	yes	—
330	C₄×D₃	C₃×M₁₆	1	8	yes	direct product factor
331	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
332	C₄×D₃	C₂²×C₃×C₄	1	4	yes	—
333	C₃×C₈	—	2	8	no	—
334	C₃×C₈	—	3	8	no	—
335	C₃×C₈	C₂×C₄×D₃	1	8	yes	complemented
336	C₃×C₈	C₂²×C₃×C₄	1	8	yes	complemented
337	C₃⋊C₈	C₂²×C₃×C₄	1	8	yes	complemented
338	C₂×C₃²	—	2	2	no	—
339	C₂×C₃²	C₂²×C₄²	1	1	yes	characteristic
340	C₂×C₃²	C₂²×M₁₆	1	2	yes	—
341	C₃×D₃	—	2	2	no	—
342	C₃×D₃	C₄×M₁₆	1	4	yes	direct product factor
343	C₂⁴	—	3	1	no	—
344	C₂²×C₄	—	3	1	no	—
345	C₂²×C₄	—	3	1	no	—
346	C₂²×C₄	—	3	1	no	—
347	C₂²×C₄	—	3	2	no	—
348	C₂²×C₄	—	3	1	no	—
349	C₂²×C₄	—	3	1	no	—
350	C₂²×C₄	—	3	8	no	—
351	C₂²×C₄	—	3	2	no	—
352	C₂²×C₄	—	3	2	no	—
353	C₂²×C₄	—	3	2	no	—
354	C₂²×C₄	—	3	2	no	—
355	C₂²×C₄	—	6	8	no	—
356	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
357	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
358	M₁₆	—	3	8	no	—
359	M₁₆	—	3	16	no	—
360	M₁₆	C₃×C₄×D₃	1	8	yes	direct product factor
361	C₂×C₈	—	3	4	no	—
362	C₂×C₈	—	3	16	no	—
363	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
364	C₄²	—	3	1	no	—
365	C₄²	—	3	1	no	—
366	C₄²	—	3	2	no	—
367	C₄²	—	3	2	no	—
368	C₄²	—	3	2	no	—
369	C₄²	—	3	2	no	—
370	C₄²	—	3	2	no	—
371	C₄²	C₃×C₄×D₃	1	2	yes	—
372	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
373	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
374	C₂²×C₃	—	2	2	no	—
375	C₂²×C₃	—	2	2	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	3	2	no	—
379	C₂²×C₃	—	3	4	no	—
380	C₂²×C₃	—	3	2	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	6	8	no	—
383	C₂²×C₃	—	6	2	no	—
384	C₂²×C₃	C₄²×D₃	1	2	yes	—
385	C₂²×C₃	C₂×C₃×C₄²	1	2	yes	—
386	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
387	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
388	C₂×D₃	—	2	2	no	—
389	C₂×D₃	—	2	8	no	—
390	C₂×D₃	C₂×C₃×C₄²	1	2	yes	—
391	C₂×D₃	C₂×C₃×C₄²	1	2	yes	—
392	C₂×D₃	C₂×C₃×M₁₆	1	4	yes	—
393	C₃×C₄	—	2	2	no	—
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	4	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	3	2	no	—
399	C₃×C₄	—	3	2	no	—
400	C₃×C₄	—	3	4	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	6	2	no	—
403	C₃×C₄	C₄²×D₃	1	2	yes	—
404	C₃×C₄	D₃×M₁₆	1	4	yes	direct product factor
405	C₃×C₄	C₂×C₃×C₄²	1	2	yes	—
406	C₃×C₄	C₂×C₃×M₁₆	1	4	yes	complemented
407	C₃×C₄	C₂²×C₄×D₃	1	2	yes	—
408	C₃×C₄	C₂³×C₃×C₄	1	2	yes	—
409	Dic₃	—	2	2	no	—
410	Dic₃	C₂×C₃×C₄²	1	2	yes	—
411	Dic₃	C₂×C₃×C₄²	1	2	yes	—
412	Dic₃	C₂×C₃×M₁₆	1	4	yes	complemented
413	C₃²	C₂×C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
414	C₂³	—	3	1	no	—
415	C₂³	—	3	1	no	—
416	C₂³	—	3	4	no	—
417	C₂³	—	6	4	no	—
418	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	3	2	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	4	no	—
424	C₂×C₄	—	3	8	no	—
425	C₂×C₄	—	3	4	no	—
426	C₂×C₄	—	3	4	no	—
427	C₂×C₄	—	3	4	no	—
428	C₂×C₄	—	3	4	no	—
429	C₂×C₄	—	3	2	no	—
430	C₂×C₄	—	6	4	no	—
431	C₂×C₄	—	6	4	no	—
432	C₂×C₄	—	6	4	no	—
433	C₂×C₄	—	6	4	no	—
434	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
435	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
436	C₂×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
437	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
438	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
439	C₈	—	3	8	no	—
440	C₈	C₂×C₃×C₄×D₃	1	8	yes	complemented
441	C₂×C₃	—	2	2	no	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	—	2	2	no	—
444	C₂×C₃	—	2	1	no	—
445	C₂×C₃	—	3	4	no	—
446	C₂×C₃	—	4	2	no	—
447	C₂×C₃	—	6	2	no	—
448	C₂×C₃	C₂×C₄²×D₃	1	1	yes	characteristic
449	C₂×C₃	C₂×D₃×M₁₆	1	2	yes	—
450	C₂×C₃	C₂²×C₃×C₄²	1	1	yes	characteristic
451	C₂×C₃	C₂²×C₃×M₁₆	1	2	yes	—
452	D₃	—	2	2	no	—
453	D₃	C₃×C₄×M₁₆	1	4	yes	direct product factor
454	C₂²	—	2	2	no	—
455	C₂²	—	3	4	no	—
456	C₂²	—	3	2	no	—
457	C₂²	—	3	2	no	—
458	C₂²	—	6	8	no	—
459	C₂²	—	6	2	no	—
460	C₂²	C₃×C₄²×D₃	1	2	yes	—
461	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	3	4	no	—
464	C₄	—	3	2	no	—
465	C₄	—	3	2	no	—
466	C₄	—	6	2	no	—
467	C₄	C₃×C₄²×D₃	1	2	yes	—
468	C₄	C₃×D₃×M₁₆	1	4	yes	direct product factor
469	C₄	C₂²×C₃×C₄×D₃	1	2	yes	—
470	C₃	—	2	1	no	—
471	C₃	C₄×D₃×M₁₆	1	1	yes	characteristic, direct product factor
472	C₃	C₂×C₃×C₄×M₁₆	1	1	yes	characteristic, complemented
473	C₂	—	2	2	no	—
474	C₂	—	3	4	no	—
475	C₂	—	6	2	no	—
476	C₂	C₂×C₃×C₄²×D₃	1	1	yes	characteristic
477	C₂	C₂×C₃×D₃×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₃×C₄²	C₂²×D₃
commutator	C₂×C₃	C₂²×C₃×C₄²
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×M₁₆	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×M₁₆	D₃
hypocenter	C₃	C₂×C₃×C₄×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₃²×C₄×M₁₆	C₂	semidirect
4. C₃×Dic₃×M₁₆	C₂	semidirect
5. C₃×C₄×#208	C₂	semidirect
6. C₃×#4707	C₂	semidirect
7. C₃×D₃×#97	C₂	semidirect
8. C₃×C₄×ΓL(1,𝔽₂₅)	C₂	semidirect
9. C₃×C₄×D₃×C₈	C₂	semidirect
11. C₄×D₃×M₁₆	C₃	direct (N × H)
19. C₃×D₃×M₁₆	C₄	direct (N × H)
28. C₃²×#97	C₂²	semidirect
29. C₃²×C₄×C₈	C₂²	semidirect
30. C₃×#815	C₂²	semidirect
31. C₃×C₈×Dic₃	C₂²	semidirect
32. C₃×#803	C₂²	semidirect
33. C₃×C₄×C₃⋊C₈	C₂²	semidirect
43. C₃×C₄×M₁₆	D₃	direct (N × H)
44. C₃×C₄×M₁₆	C₂×C₃	semidirect
47. Dic₃×M₁₆	C₂×C₃	semidirect
48. C₄×#208	C₂×C₃	semidirect
49. #4707	C₂×C₃	semidirect
50. D₃×#97	C₂×C₃	semidirect
51. C₄×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
52. C₄×D₃×C₈	C₂×C₃	semidirect
68. C₃²×M₁₆	C₂×C₄	semidirect
80. C₃×#208	C₂×C₄	semidirect
82. C₃×ΓL(1,𝔽₂₅)	C₂×C₄	semidirect
83. C₃×D₃×C₈	C₂×C₄	semidirect
110. D₃×M₁₆	C₃×C₄	direct (N × H)
122. C₃×#97	C₂×D₃	semidirect
123. C₃×#97	C₂²×C₃	semidirect
127. C₃×C₄×C₈	C₂×D₃	semidirect
128. C₃×C₄×C₈	C₂²×C₃	semidirect
129. #815	C₂²×C₃	semidirect
130. C₈×Dic₃	C₂²×C₃	semidirect
131. #803	C₂²×C₃	semidirect
132. C₄×C₃⋊C₈	C₂²×C₃	semidirect
155. C₃×C₄×D₃	M₁₆	direct (N × H)
158. C₃²×C₈	C₂²×C₄	semidirect
159. C₃×C₃⋊C₈	C₂²×C₄	semidirect
166. C₄×M₁₆	C₃×D₃	direct (N × H)
204. C₃×M₁₆	C₄×D₃	direct (N × H)
205. C₃×M₁₆	C₂×C₃×C₄	semidirect
234. #208	C₂×C₃×C₄	semidirect
236. ΓL(1,𝔽₂₅)	C₂×C₃×C₄	semidirect
237. D₃×C₈	C₂×C₃×C₄	semidirect
248. C₃²×C₄	C₂×M₁₆	semidirect
253. C₃×Dic₃	C₂×M₁₆	semidirect
272. #97	C₂×C₃×D₃	semidirect
275. C₄×C₈	C₂×C₃×D₃	semidirect
330. C₄×D₃	C₃×M₁₆	direct (N × H)
335. C₃×C₈	C₂×C₄×D₃	semidirect
336. C₃×C₈	C₂²×C₃×C₄	semidirect
337. C₃⋊C₈	C₂²×C₃×C₄	semidirect
342. C₃×D₃	C₄×M₁₆	direct (N × H)
360. M₁₆	C₃×C₄×D₃	direct (N × H)
404. C₃×C₄	D₃×M₁₆	direct (N × H)
406. C₃×C₄	C₂×C₃×M₁₆	semidirect
412. Dic₃	C₂×C₃×M₁₆	semidirect
413. C₃²	C₂×C₄×M₁₆	semidirect
440. C₈	C₂×C₃×C₄×D₃	semidirect
453. D₃	C₃×C₄×M₁₆	direct (N × H)
468. C₄	C₃×D₃×M₁₆	direct (N × H)
471. C₃	C₄×D₃×M₁₆	direct (N × H)
472. C₃	C₂×C₃×C₄×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×M₁₆	2
C₂×C₃×C₄²×D₃	2
C₃²×C₄×M₁₆	2
C₃×Dic₃×M₁₆	2
C₃×C₄×#208	2
C₃×#4707	2
C₃×D₃×#97	2
C₃×C₄×ΓL(1,𝔽₂₅)	2
C₃×C₄×D₃×C₈	2
C₂×C₃×C₄×M₁₆	3
C₄×D₃×M₁₆	3

Subgroups — C3×C4×D3×M16 #11857135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₃×M₁₆ #11857135