Subgroups — C₂²×C₃×D₃×M₁₆ #11918432

Order 1152.

3589 conjugacy classes of subgroups.

The subgroup lattice has 407 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃²×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×D₃×M₁₆	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	1	2	yes	maximal, complemented
6	C₂²×C₃×D₃×C₈	C₂	1	2	yes	maximal, complemented
7	C₂³×C₃×M₁₆	—	3	1	no	maximal
8	C₂²×D₃×M₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂⁴×C₃×D₃	C₄	1	1	yes	characteristic
10	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
11	C₂³×C₃×Dic₃	C₄	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₃	C₄	1	12	yes	—
14	C₂²×C₃×C₄×D₃	C₄	1	1	yes	characteristic
15	C₂²×C₃×C₄×D₃	C₂²	1	12	yes	—
16	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃²×M₁₆	C₂²	1	12	yes	complemented
19	C₂²×C₃²×C₈	C₂²	1	2	yes	complemented
20	C₂×C₃×#208	C₂²	1	12	yes	complemented
21	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	complemented
22	C₃×D₃×M₁₆	C₂²	1	64	yes	direct product factor
23	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	24	yes	complemented
24	C₂×C₃×D₃×C₈	C₂²	1	24	yes	complemented
25	C₂⁴×C₃×C₄	—	3	1	no	—
26	C₂³×C₄×D₃	C₂×C₃	1	1	yes	characteristic
27	C₂²×C₃×M₁₆	—	2	1	no	—
28	C₂²×C₃×M₁₆	—	3	1	no	—
29	C₂²×C₃×M₁₆	—	3	24	no	—
30	C₂²×C₃×M₁₆	—	3	2	no	—
31	C₂²×C₃×M₁₆	D₃	1	1	yes	characteristic, direct product factor
32	C₂²×C₃×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂³×C₃×C₈	—	3	2	no	—
34	C₂²×#208	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×D₃×M₁₆	C₂×C₃	1	24	yes	direct product factor
36	C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	1	2	yes	complemented
37	C₂²×D₃×C₈	C₂×C₃	1	2	yes	complemented
38	C₂⁴×C₃²	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₃×D₃	—	2	8	no	—
40	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₃×D₃	C₂×C₄	1	12	yes	—
42	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃²×C₄	C₂×C₄	1	6	yes	—
44	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃²×C₄	C₂³	1	6	yes	—
46	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₃	C₂×C₄	1	12	yes	—
48	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃×C₄×D₃	C₂×C₄	1	48	yes	—
51	C₂×C₃×C₄×D₃	C₂×C₄	1	12	yes	—
52	C₂×C₃×C₄×D₃	C₂×C₄	1	6	yes	—
53	C₂×C₃×C₄×D₃	C₂×C₄	1	12	yes	—
54	C₂×C₃×C₄×D₃	C₂×C₄	1	6	yes	—
55	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
56	C₂×C₃×C₄×D₃	C₂³	1	6	yes	—
57	C₂×C₃×C₄×D₃	C₂³	1	16	yes	—
58	C₃²×M₁₆	C₂³	1	16	yes	complemented
59	C₂×C₃²×C₈	C₂³	1	12	yes	complemented
60	C₃×#208	C₂³	1	16	yes	complemented
61	C₂×C₃×C₃⋊C₈	C₂³	1	12	yes	complemented
62	C₃×ΓL(1,𝔽₂₅)	C₂³	1	32	yes	complemented
63	C₃×D₃×C₈	C₂³	1	32	yes	complemented
64	C₂³×M₁₆	—	3	1	no	Sylow
65	C₂⁵×C₃	—	3	1	no	—
66	C₂⁴×D₃	C₃×C₄	1	1	yes	characteristic
67	C₂³×C₃×C₄	—	2	1	no	—
68	C₂³×C₃×C₄	—	3	1	no	—
69	C₂³×C₃×C₄	—	3	1	no	—
70	C₂³×C₃×C₄	—	3	12	no	—
71	C₂³×C₃×C₄	—	3	1	no	—
72	C₂³×C₃×C₄	—	3	12	no	—
73	C₂³×C₃×C₄	—	3	1	no	—
74	C₂³×C₃×C₄	—	3	1	no	—
75	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
76	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
77	C₂³×Dic₃	C₃×C₄	1	1	yes	characteristic
78	C₂²×C₄×D₃	C₃×C₄	1	12	yes	—
79	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
80	C₂²×C₄×D₃	C₃×C₄	1	1	yes	characteristic
81	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
83	C₂²×C₄×D₃	C₂²×C₃	1	12	yes	—
84	C₂×C₃×M₁₆	—	2	12	no	—
85	C₂×C₃×M₁₆	—	3	12	no	—
86	C₂×C₃×M₁₆	—	3	64	no	—
87	C₂×C₃×M₁₆	—	3	24	no	—
88	C₂×C₃×M₁₆	C₂×D₃	1	12	yes	direct product factor
89	C₂×C₃×M₁₆	C₂²×C₃	1	12	yes	complemented
90	C₂²×C₃×C₈	—	2	2	no	—
91	C₂²×C₃×C₈	—	3	2	no	—
92	C₂²×C₃×C₈	—	3	24	no	—
93	C₂²×C₃×C₈	C₂×D₃	1	2	yes	complemented
94	C₂²×C₃×C₈	C₂²×C₃	1	2	yes	complemented
95	C₂×#208	C₂²×C₃	1	12	yes	complemented
96	C₂²×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
97	D₃×M₁₆	C₂²×C₃	1	64	yes	direct product factor
98	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	24	yes	complemented
99	C₂×D₃×C₈	C₂²×C₃	1	24	yes	complemented
100	C₂³×C₃²	—	2	4	no	—
101	C₂³×C₃²	C₂²×C₄	1	6	yes	—
102	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₃×D₃	—	2	4	no	—
104	C₂²×C₃×D₃	—	2	48	no	—
105	C₂²×C₃×D₃	M₁₆	1	8	yes	direct product factor
106	C₂²×C₃×D₃	C₂²×C₄	1	6	yes	—
107	C₂²×C₃×D₃	C₂²×C₄	1	16	yes	—
108	C₂²×C₃×D₃	C₂²×C₄	1	6	yes	—
109	C₂×C₃²×C₄	C₂²×C₄	1	12	yes	—
110	C₂×C₃²×C₄	C₂²×C₄	1	6	yes	—
111	C₂×C₃²×C₄	C₂²×C₄	1	3	yes	—
112	C₂×C₃²×C₄	C₂⁴	1	3	yes	—
113	C₂×C₃²×C₄	C₂⁴	1	4	yes	—
114	C₂×C₃×Dic₃	C₂²×C₄	1	16	yes	—
115	C₂×C₃×Dic₃	C₂²×C₄	1	6	yes	—
116	C₂×C₃×Dic₃	C₂²×C₄	1	6	yes	—
117	C₃×C₄×D₃	C₂²×C₄	1	12	yes	—
118	C₃×C₄×D₃	C₂²×C₄	1	16	yes	—
119	C₃×C₄×D₃	C₂²×C₄	1	12	yes	—
120	C₃×C₄×D₃	C₂²×C₄	1	16	yes	—
121	C₃×C₄×D₃	C₂⁴	1	4	yes	—
122	C₃×C₄×D₃	C₂⁴	1	4	yes	—
123	C₃²×C₈	C₂⁴	1	8	yes	complemented
124	C₃×C₃⋊C₈	C₂⁴	1	8	yes	complemented
125	C₂⁴×C₄	—	3	1	no	—
126	C₂²×M₁₆	—	3	1	no	—
127	C₂²×M₁₆	—	3	24	no	—
128	C₂²×M₁₆	—	3	2	no	—
129	C₂²×M₁₆	C₃×D₃	1	1	yes	characteristic, direct product factor
130	C₂³×C₈	—	3	2	no	—
131	C₂⁴×C₃	—	2	1	no	—
132	C₂⁴×C₃	—	3	1	no	—
133	C₂⁴×C₃	—	3	12	no	—
134	C₂⁴×C₃	—	3	1	no	—
135	C₂⁴×C₃	—	6	8	no	—
136	C₂⁴×C₃	C₄×D₃	1	1	yes	characteristic
137	C₂⁴×C₃	C₂×C₃×C₄	1	1	yes	characteristic
138	C₂³×D₃	—	2	8	no	—
139	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
140	C₂³×D₃	C₂×C₃×C₄	1	12	yes	—
141	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	6	no	—
144	C₂²×C₃×C₄	—	2	1	no	—
145	C₂²×C₃×C₄	—	2	6	no	—
146	C₂²×C₃×C₄	—	3	12	no	—
147	C₂²×C₃×C₄	—	3	1	no	—
148	C₂²×C₃×C₄	—	3	1	no	—
149	C₂²×C₃×C₄	—	3	12	no	—
150	C₂²×C₃×C₄	—	3	48	no	—
151	C₂²×C₃×C₄	—	3	12	no	—
152	C₂²×C₃×C₄	—	3	6	no	—
153	C₂²×C₃×C₄	—	3	6	no	—
154	C₂²×C₃×C₄	—	3	6	no	—
155	C₂²×C₃×C₄	—	3	16	no	—
156	C₂²×C₃×C₄	—	3	6	no	—
157	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₄×D₃	1	6	yes	—
159	C₂²×C₃×C₄	C₂×C₃×C₄	1	6	yes	—
160	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
161	C₂²×C₃×C₄	C₂²×D₃	1	6	yes	—
162	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
163	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₂³×C₃	1	6	yes	—
165	C₂²×Dic₃	C₂×C₃×C₄	1	12	yes	—
166	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₄×D₃	C₂×C₃×C₄	1	6	yes	—
169	C₂×C₄×D₃	C₂×C₃×C₄	1	48	yes	—
170	C₂×C₄×D₃	C₂×C₃×C₄	1	12	yes	—
171	C₂×C₄×D₃	C₂×C₃×C₄	1	6	yes	—
172	C₂×C₄×D₃	C₂×C₃×C₄	1	12	yes	—
173	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
174	C₂×C₄×D₃	C₂³×C₃	1	6	yes	—
175	C₂×C₄×D₃	C₂³×C₃	1	16	yes	—
176	C₃×M₁₆	—	2	16	no	—
177	C₃×M₁₆	—	3	16	no	—
178	C₃×M₁₆	—	3	32	no	—
179	C₃×M₁₆	C₂²×D₃	1	16	yes	direct product factor
180	C₃×M₁₆	C₂³×C₃	1	16	yes	complemented
181	C₂×C₃×C₈	—	2	12	no	—
182	C₂×C₃×C₈	—	3	12	no	—
183	C₂×C₃×C₈	—	3	32	no	—
184	C₂×C₃×C₈	C₂²×D₃	1	12	yes	complemented
185	C₂×C₃×C₈	C₂³×C₃	1	12	yes	complemented
186	#208	C₂³×C₃	1	16	yes	complemented
187	C₂×C₃⋊C₈	C₂³×C₃	1	12	yes	complemented
188	ΓL(1,𝔽₂₅)	C₂³×C₃	1	32	yes	complemented
189	D₃×C₈	C₂³×C₃	1	32	yes	complemented
190	C₂²×C₃²	—	2	12	no	—
191	C₂²×C₃²	C₂×M₁₆	1	4	yes	complemented
192	C₂²×C₃²	C₂³×C₄	1	4	yes	—
193	C₂²×C₃²	C₂³×C₄	1	3	yes	—
194	C₂×C₃×D₃	—	2	12	no	—
195	C₂×C₃×D₃	—	2	32	no	—
196	C₂×C₃×D₃	C₂×M₁₆	1	24	yes	direct product factor
197	C₂×C₃×D₃	C₂³×C₄	1	4	yes	—
198	C₂×C₃×D₃	C₂³×C₄	1	4	yes	—
199	C₃²×C₄	C₂³×C₄	1	3	yes	—
200	C₃²×C₄	C₂³×C₄	1	4	yes	—
201	C₃²×C₄	C₂⁵	1	1	yes	characteristic
202	C₃×Dic₃	C₂³×C₄	1	4	yes	—
203	C₃×Dic₃	C₂³×C₄	1	4	yes	—
204	C₂⁵	—	3	1	no	—
205	C₂³×C₄	—	3	1	no	—
206	C₂³×C₄	—	3	1	no	—
207	C₂³×C₄	—	3	12	no	—
208	C₂³×C₄	—	3	1	no	—
209	C₂³×C₄	—	3	1	no	—
210	C₂³×C₄	—	3	12	no	—
211	C₂³×C₄	—	3	1	no	—
212	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
213	C₂×M₁₆	—	3	12	no	—
214	C₂×M₁₆	—	3	64	no	—
215	C₂×M₁₆	—	3	24	no	—
216	C₂×M₁₆	C₂×C₃×D₃	1	12	yes	direct product factor
217	C₂²×C₈	—	3	2	no	—
218	C₂²×C₈	—	3	24	no	—
219	C₂²×C₈	C₂×C₃×D₃	1	2	yes	complemented
220	C₂³×C₃	—	2	4	no	—
221	C₂³×C₃	—	2	4	no	—
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	2	6	no	—
224	C₂³×C₃	—	3	8	no	—
225	C₂³×C₃	—	3	6	no	—
226	C₂³×C₃	—	3	16	no	—
227	C₂³×C₃	—	3	6	no	—
228	C₂³×C₃	—	4	4	no	—
229	C₂³×C₃	—	6	48	no	—
230	C₂³×C₃	—	6	4	no	—
231	C₂³×C₃	C₂×C₄×D₃	1	6	yes	—
232	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
233	C₂³×C₃	C₂²×C₃×C₄	1	6	yes	—
234	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
235	C₂²×D₃	—	2	4	no	—
236	C₂²×D₃	—	2	48	no	—
237	C₂²×D₃	C₃×M₁₆	1	8	yes	direct product factor
238	C₂²×D₃	C₂²×C₃×C₄	1	6	yes	—
239	C₂²×D₃	C₂²×C₃×C₄	1	16	yes	—
240	C₂²×D₃	C₂²×C₃×C₄	1	6	yes	—
241	C₂×C₃×C₄	—	2	3	no	—
242	C₂×C₃×C₄	—	2	4	no	—
243	C₂×C₃×C₄	—	2	3	no	—
244	C₂×C₃×C₄	—	2	6	no	—
245	C₂×C₃×C₄	—	2	12	no	—
246	C₂×C₃×C₄	—	3	16	no	—
247	C₂×C₃×C₄	—	3	6	no	—
248	C₂×C₃×C₄	—	3	6	no	—
249	C₂×C₃×C₄	—	3	12	no	—
250	C₂×C₃×C₄	—	3	16	no	—
251	C₂×C₃×C₄	—	3	16	no	—
252	C₂×C₃×C₄	—	3	12	no	—
253	C₂×C₃×C₄	—	3	4	no	—
254	C₂×C₃×C₄	—	3	4	no	—
255	C₂×C₃×C₄	C₂×C₄×D₃	1	12	yes	—
256	C₂×C₃×C₄	C₂×C₄×D₃	1	6	yes	—
257	C₂×C₃×C₄	C₂×C₄×D₃	1	3	yes	—
258	C₂×C₃×C₄	C₂²×C₃×C₄	1	12	yes	—
259	C₂×C₃×C₄	C₂²×C₃×C₄	1	3	yes	—
260	C₂×C₃×C₄	C₂²×C₃×C₄	1	6	yes	—
261	C₂×C₃×C₄	C₂³×D₃	1	3	yes	—
262	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
263	C₂×C₃×C₄	C₂⁴×C₃	1	3	yes	—
264	C₂×C₃×C₄	C₂⁴×C₃	1	4	yes	—
265	C₂×Dic₃	C₂²×C₃×C₄	1	16	yes	—
266	C₂×Dic₃	C₂²×C₃×C₄	1	6	yes	—
267	C₂×Dic₃	C₂²×C₃×C₄	1	6	yes	—
268	C₄×D₃	C₂²×C₃×C₄	1	12	yes	—
269	C₄×D₃	C₂²×C₃×C₄	1	16	yes	—
270	C₄×D₃	C₂²×C₃×C₄	1	12	yes	—
271	C₄×D₃	C₂²×C₃×C₄	1	16	yes	—
272	C₄×D₃	C₂⁴×C₃	1	4	yes	—
273	C₄×D₃	C₂⁴×C₃	1	4	yes	—
274	C₃×C₈	—	2	8	no	—
275	C₃×C₈	—	3	8	no	—
276	C₃×C₈	C₂³×D₃	1	8	yes	complemented
277	C₃×C₈	C₂⁴×C₃	1	8	yes	complemented
278	C₃⋊C₈	C₂⁴×C₃	1	8	yes	complemented
279	C₂×C₃²	—	2	4	no	—
280	C₂×C₃²	C₂²×M₁₆	1	6	yes	complemented
281	C₂×C₃²	C₂⁴×C₄	1	1	yes	characteristic
282	C₃×D₃	—	2	4	no	—
283	C₃×D₃	C₂²×M₁₆	1	8	yes	direct product factor
284	C₂⁴	—	3	1	no	—
285	C₂⁴	—	3	12	no	—
286	C₂⁴	—	3	1	no	—
287	C₂⁴	—	6	8	no	—
288	C₂⁴	C₃×C₄×D₃	1	1	yes	characteristic
289	C₂²×C₄	—	3	12	no	—
290	C₂²×C₄	—	3	1	no	—
291	C₂²×C₄	—	3	1	no	—
292	C₂²×C₄	—	3	6	no	—
293	C₂²×C₄	—	3	16	no	—
294	C₂²×C₄	—	3	6	no	—
295	C₂²×C₄	—	3	6	no	—
296	C₂²×C₄	—	3	12	no	—
297	C₂²×C₄	—	3	48	no	—
298	C₂²×C₄	—	3	12	no	—
299	C₂²×C₄	—	3	6	no	—
300	C₂²×C₄	C₃×C₄×D₃	1	6	yes	—
301	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
302	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₃×D₃	1	6	yes	—
304	M₁₆	—	3	16	no	—
305	M₁₆	—	3	32	no	—
306	M₁₆	C₂²×C₃×D₃	1	16	yes	direct product factor
307	C₂×C₈	—	3	12	no	—
308	C₂×C₈	—	3	32	no	—
309	C₂×C₈	C₂²×C₃×D₃	1	12	yes	complemented
310	C₂²×C₃	—	2	12	no	—
311	C₂²×C₃	—	2	12	no	—
312	C₂²×C₃	—	2	4	no	—
313	C₂²×C₃	—	2	3	no	—
314	C₂²×C₃	—	2	4	no	—
315	C₂²×C₃	—	3	4	no	—
316	C₂²×C₃	—	3	24	no	—
317	C₂²×C₃	—	3	4	no	—
318	C₂²×C₃	—	4	12	no	—
319	C₂²×C₃	—	6	32	no	—
320	C₂²×C₃	—	6	12	no	—
321	C₂²×C₃	D₃×M₁₆	1	4	yes	direct product factor
322	C₂²×C₃	C₂×C₃×M₁₆	1	4	yes	complemented
323	C₂²×C₃	C₂²×C₄×D₃	1	4	yes	—
324	C₂²×C₃	C₂²×C₄×D₃	1	3	yes	—
325	C₂²×C₃	C₂³×C₃×C₄	1	4	yes	—
326	C₂²×C₃	C₂³×C₃×C₄	1	3	yes	—
327	C₂×D₃	—	2	12	no	—
328	C₂×D₃	—	2	32	no	—
329	C₂×D₃	C₂×C₃×M₁₆	1	24	yes	direct product factor
330	C₂×D₃	C₂³×C₃×C₄	1	4	yes	—
331	C₂×D₃	C₂³×C₃×C₄	1	4	yes	—
332	C₃×C₄	—	2	3	no	—
333	C₃×C₄	—	2	4	no	—
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	3	4	no	—
336	C₃×C₄	—	3	4	no	—
337	C₃×C₄	C₂²×C₄×D₃	1	4	yes	—
338	C₃×C₄	C₂²×C₄×D₃	1	3	yes	—
339	C₃×C₄	C₂³×C₃×C₄	1	3	yes	—
340	C₃×C₄	C₂³×C₃×C₄	1	4	yes	—
341	C₃×C₄	C₂⁴×D₃	1	1	yes	characteristic
342	C₃×C₄	C₂⁵×C₃	1	1	yes	characteristic
343	Dic₃	C₂³×C₃×C₄	1	4	yes	—
344	Dic₃	C₂³×C₃×C₄	1	4	yes	—
345	C₃²	C₂³×M₁₆	1	1	yes	characteristic, complemented, Sylow
346	C₂³	—	2	4	no	—
347	C₂³	—	3	8	no	—
348	C₂³	—	3	6	no	—
349	C₂³	—	3	16	no	—
350	C₂³	—	3	6	no	—
351	C₂³	—	6	48	no	—
352	C₂³	—	6	4	no	—
353	C₂³	C₂×C₃×C₄×D₃	1	6	yes	—
354	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
355	C₂×C₄	—	3	16	no	—
356	C₂×C₄	—	3	6	no	—
357	C₂×C₄	—	3	6	no	—
358	C₂×C₄	—	3	12	no	—
359	C₂×C₄	—	3	16	no	—
360	C₂×C₄	—	3	16	no	—
361	C₂×C₄	—	3	12	no	—
362	C₂×C₄	—	3	4	no	—
363	C₂×C₄	—	3	4	no	—
364	C₂×C₄	C₂×C₃×C₄×D₃	1	12	yes	—
365	C₂×C₄	C₂×C₃×C₄×D₃	1	3	yes	—
366	C₂×C₄	C₂×C₃×C₄×D₃	1	6	yes	—
367	C₂×C₄	C₂³×C₃×D₃	1	3	yes	—
368	C₂×C₄	C₂³×C₃×D₃	1	4	yes	—
369	C₈	—	3	8	no	—
370	C₈	C₂³×C₃×D₃	1	8	yes	complemented
371	C₂×C₃	—	2	4	no	—
372	C₂×C₃	—	2	4	no	—
373	C₂×C₃	—	2	6	no	—
374	C₂×C₃	—	2	1	no	—
375	C₂×C₃	—	3	8	no	—
376	C₂×C₃	—	4	4	no	—
377	C₂×C₃	—	6	4	no	—
378	C₂×C₃	C₂×D₃×M₁₆	1	6	yes	direct product factor
379	C₂×C₃	C₂²×C₃×M₁₆	1	6	yes	complemented
380	C₂×C₃	C₂³×C₄×D₃	1	1	yes	characteristic
381	C₂×C₃	C₂⁴×C₃×C₄	1	1	yes	characteristic
382	D₃	—	2	4	no	—
383	D₃	C₂²×C₃×M₁₆	1	8	yes	direct product factor
384	C₂²	—	2	12	no	—
385	C₂²	—	3	24	no	—
386	C₂²	—	3	4	no	—
387	C₂²	—	3	4	no	—
388	C₂²	—	6	32	no	—
389	C₂²	—	6	12	no	—
390	C₂²	C₃×D₃×M₁₆	1	4	yes	direct product factor
391	C₂²	C₂²×C₃×C₄×D₃	1	4	yes	—
392	C₂²	C₂²×C₃×C₄×D₃	1	3	yes	—
393	C₄	—	3	4	no	—
394	C₄	—	3	4	no	—
395	C₄	C₂²×C₃×C₄×D₃	1	3	yes	—
396	C₄	C₂²×C₃×C₄×D₃	1	4	yes	—
397	C₄	C₂⁴×C₃×D₃	1	1	yes	characteristic
398	C₃	—	2	1	no	—
399	C₃	C₂²×D₃×M₁₆	1	1	yes	characteristic, direct product factor
400	C₃	C₂³×C₃×M₁₆	1	1	yes	characteristic, complemented
401	C₂	—	2	4	no	—
402	C₂	—	3	8	no	—
403	C₂	—	6	4	no	—
404	C₂	C₂×C₃×D₃×M₁₆	1	6	yes	direct product factor
405	C₂	C₂³×C₃×C₄×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₃
commutator	C₂×C₃	C₂⁴×C₃×C₄
Frattini	C₄	C₂⁴×C₃×D₃
Fitting	C₂²×C₃²×M₁₆	C₂
socle	C₂³×C₃²	C₂²×C₄
prime radical	C₂⁴×C₃×D₃	C₄
cosocle	C₃×C₄	C₂⁵×C₃
hypercenter	C₂²×C₃×M₁₆	D₃
hypocenter	C₃	C₂³×C₃×M₁₆
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃²×M₁₆	C₂	semidirect
3. C₂²×C₃×#208	C₂	semidirect
4. C₂×C₃×D₃×M₁₆	C₂	direct (N × H)
5. C₂²×C₃×ΓL(1,𝔽₂₅)	C₂	semidirect
6. C₂²×C₃×D₃×C₈	C₂	semidirect
8. C₂²×D₃×M₁₆	C₃	direct (N × H)
18. C₂×C₃²×M₁₆	C₂²	semidirect
19. C₂²×C₃²×C₈	C₂²	semidirect
20. C₂×C₃×#208	C₂²	semidirect
21. C₂²×C₃×C₃⋊C₈	C₂²	semidirect
22. C₃×D₃×M₁₆	C₂²	direct (N × H)
23. C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	semidirect
24. C₂×C₃×D₃×C₈	C₂²	semidirect
31. C₂²×C₃×M₁₆	D₃	direct (N × H)
32. C₂²×C₃×M₁₆	C₂×C₃	semidirect
34. C₂²×#208	C₂×C₃	semidirect
35. C₂×D₃×M₁₆	C₂×C₃	direct (N × H)
36. C₂²×ΓL(1,𝔽₂₅)	C₂×C₃	semidirect
37. C₂²×D₃×C₈	C₂×C₃	semidirect
58. C₃²×M₁₆	C₂³	semidirect
59. C₂×C₃²×C₈	C₂³	semidirect
60. C₃×#208	C₂³	semidirect
61. C₂×C₃×C₃⋊C₈	C₂³	semidirect
62. C₃×ΓL(1,𝔽₂₅)	C₂³	semidirect
63. C₃×D₃×C₈	C₂³	semidirect
88. C₂×C₃×M₁₆	C₂×D₃	direct (N × H)
89. C₂×C₃×M₁₆	C₂²×C₃	semidirect
93. C₂²×C₃×C₈	C₂×D₃	semidirect
94. C₂²×C₃×C₈	C₂²×C₃	semidirect
95. C₂×#208	C₂²×C₃	semidirect
96. C₂²×C₃⋊C₈	C₂²×C₃	semidirect
97. D₃×M₁₆	C₂²×C₃	direct (N × H)
98. C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	semidirect
99. C₂×D₃×C₈	C₂²×C₃	semidirect
105. C₂²×C₃×D₃	M₁₆	direct (N × H)
123. C₃²×C₈	C₂⁴	semidirect
124. C₃×C₃⋊C₈	C₂⁴	semidirect
129. C₂²×M₁₆	C₃×D₃	direct (N × H)
179. C₃×M₁₆	C₂²×D₃	direct (N × H)
180. C₃×M₁₆	C₂³×C₃	semidirect
184. C₂×C₃×C₈	C₂²×D₃	semidirect
185. C₂×C₃×C₈	C₂³×C₃	semidirect
186. #208	C₂³×C₃	semidirect
187. C₂×C₃⋊C₈	C₂³×C₃	semidirect
188. ΓL(1,𝔽₂₅)	C₂³×C₃	semidirect
189. D₃×C₈	C₂³×C₃	semidirect
191. C₂²×C₃²	C₂×M₁₆	semidirect
196. C₂×C₃×D₃	C₂×M₁₆	direct (N × H)
216. C₂×M₁₆	C₂×C₃×D₃	direct (N × H)
219. C₂²×C₈	C₂×C₃×D₃	semidirect
237. C₂²×D₃	C₃×M₁₆	direct (N × H)
276. C₃×C₈	C₂³×D₃	semidirect
277. C₃×C₈	C₂⁴×C₃	semidirect
278. C₃⋊C₈	C₂⁴×C₃	semidirect
280. C₂×C₃²	C₂²×M₁₆	semidirect
283. C₃×D₃	C₂²×M₁₆	direct (N × H)
306. M₁₆	C₂²×C₃×D₃	direct (N × H)
309. C₂×C₈	C₂²×C₃×D₃	semidirect
321. C₂²×C₃	D₃×M₁₆	direct (N × H)
322. C₂²×C₃	C₂×C₃×M₁₆	semidirect
329. C₂×D₃	C₂×C₃×M₁₆	direct (N × H)
345. C₃²	C₂³×M₁₆	semidirect
370. C₈	C₂³×C₃×D₃	semidirect
378. C₂×C₃	C₂×D₃×M₁₆	direct (N × H)
379. C₂×C₃	C₂²×C₃×M₁₆	semidirect
383. D₃	C₂²×C₃×M₁₆	direct (N × H)
390. C₂²	C₃×D₃×M₁₆	direct (N × H)
399. C₃	C₂²×D₃×M₁₆	direct (N × H)
400. C₃	C₂³×C₃×M₁₆	semidirect
404. C₂	C₂×C₃×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
C₂³×C₃×C₄×D₃	2
C₂²×C₃²×M₁₆	2
C₂²×C₃×#208	2
C₂×C₃×D₃×M₁₆	2
C₂²×C₃×ΓL(1,𝔽₂₅)	2
C₂²×C₃×D₃×C₈	2
C₂³×C₃×M₁₆	3
C₂²×D₃×M₁₆	3

Subgroups — C22×C3×D3×M16 #11918432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×D₃×M₁₆ #11918432