Subgroups — C₂×C₃²×D₃×SD₁₆ #13179135

Order 1728.

2060 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₃×D₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃³×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃²×#215	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃²×#214	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×D₃×SD₁₆	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃²×#204	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₃²×SD₁₆	—	3	1	no	maximal
10	C₂×C₃×D₃×SD₁₆	C₃	1	4	yes	maximal, direct product factor
11	C₂³×C₃²×D₃	—	2	1	no	—
12	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
14	C₂×C₃²×#67	—	2	1	no	—
15	C₃²×D₃×Q₈	—	2	2	no	—
16	C₃²×D₃×Q₈	C₂²	1	4	yes	complemented
17	C₃²×D₃×D₄	—	2	2	no	—
18	C₃²×D₃×D₄	C₂²	1	4	yes	—
19	C₂×C₃²×D₁₂	C₂²	1	1	yes	characteristic
20	C₂×C₃²×C₄×D₃	—	2	1	no	—
21	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃²×Dic₆	—	2	1	no	—
23	C₂×C₃²×Dic₆	C₂²	1	1	yes	characteristic, complemented
24	C₃³×SD₁₆	C₂²	1	4	yes	complemented
25	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
26	C₃²×#215	C₂²	1	4	yes	complemented
27	C₃²×#214	C₂²	1	4	yes	complemented
28	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
29	C₃²×#204	C₂²	1	4	yes	complemented
30	C₃²×D₃×C₈	C₂²	1	4	yes	complemented
31	C₂²×C₃²×Q₈	—	3	1	no	—
32	C₂²×C₃²×D₄	—	3	1	no	—
33	C₂×C₃×D₃×Q₈	C₂×C₃	1	4	yes	complemented
34	C₂×C₃×D₃×D₄	C₂×C₃	1	4	yes	—
35	C₂×C₃²×SD₁₆	—	2	4	no	—
36	C₂×C₃²×SD₁₆	—	3	1	no	—
37	C₂×C₃²×SD₁₆	—	3	1	no	—
38	C₂×C₃²×SD₁₆	—	3	8	no	—
39	C₂×C₃²×SD₁₆	—	3	1	no	—
40	C₂×C₃²×SD₁₆	D₃	1	1	yes	characteristic, direct product factor
41	C₂×C₃²×SD₁₆	C₂×C₃	1	4	yes	complemented
42	C₂²×C₃²×C₈	—	3	1	no	—
43	C₂×C₃×#215	C₂×C₃	1	4	yes	complemented
44	C₂×C₃×#214	C₂×C₃	1	4	yes	complemented
45	C₃×D₃×SD₁₆	C₂×C₃	1	32	yes	direct product factor
46	C₂×C₃×#204	C₂×C₃	1	4	yes	complemented
47	C₂×C₃×D₃×C₈	C₂×C₃	1	4	yes	complemented
48	C₂³×C₃³	—	2	1	no	—
49	C₂²×C₃²×D₃	—	2	1	no	—
50	C₂²×C₃²×D₃	—	2	4	no	—
51	C₂²×C₃²×D₃	—	4	4	no	—
52	C₂²×C₃²×D₃	D₄	1	1	yes	characteristic
53	C₃³×Q₈	—	2	1	no	—
54	C₃³×Q₈	C₂³	1	2	yes	complemented
55	C₃³×D₄	—	2	1	no	—
56	C₃³×D₄	C₂³	1	2	yes	—
57	C₂×C₃³×C₄	—	2	1	no	—
58	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
59	C₃²×#67	—	2	4	no	—
60	C₂×C₃²×Dic₃	—	2	1	no	—
61	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
62	C₃²×D₁₂	—	2	1	no	—
63	C₃²×D₁₂	C₂³	1	2	yes	—
64	C₃²×C₄×D₃	—	2	4	no	—
65	C₃²×C₄×D₃	D₄	1	2	yes	—
66	C₃²×C₄×D₃	C₂³	1	2	yes	—
67	C₃²×Dic₆	—	2	1	no	—
68	C₃²×Dic₆	—	2	4	no	—
69	C₃²×Dic₆	C₂³	1	2	yes	complemented
70	C₃³×C₈	C₂³	1	2	yes	complemented
71	C₃²×C₃⋊C₈	C₂³	1	2	yes	complemented
72	C₂²×C₃×SD₁₆	—	3	4	no	—
73	C₂×D₃×SD₁₆	C₃²	1	1	yes	characteristic, direct product factor
74	C₂⁴×C₃²	—	6	1	no	—
75	C₂³×C₃×D₃	—	2	4	no	—
76	C₂×C₃²×Q₈	—	2	4	no	—
77	C₂×C₃²×Q₈	—	3	4	no	—
78	C₂×C₃²×Q₈	—	3	1	no	—
79	C₂×C₃²×Q₈	—	6	1	no	—
80	C₂×C₃²×Q₈	—	6	2	no	—
81	C₂×C₃²×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
82	C₂×C₃²×Q₈	C₂²×C₃	1	4	yes	complemented
83	C₂×C₃²×D₄	—	2	4	no	—
84	C₂×C₃²×D₄	—	3	4	no	—
85	C₂×C₃²×D₄	—	3	1	no	—
86	C₂×C₃²×D₄	—	6	2	no	—
87	C₂×C₃²×D₄	—	6	1	no	—
88	C₂×C₃²×D₄	C₂×D₃	1	1	yes	characteristic
89	C₂×C₃²×D₄	C₂²×C₃	1	4	yes	—
90	C₂²×C₃²×C₄	—	3	1	no	—
91	C₂²×C₃²×C₄	—	6	1	no	—
92	C₂×C₃×#67	—	2	4	no	—
93	C₃×D₃×Q₈	—	2	8	no	—
94	C₃×D₃×Q₈	C₂²×C₃	1	16	yes	complemented
95	C₃×D₃×D₄	—	2	8	no	—
96	C₃×D₃×D₄	C₂²×C₃	1	16	yes	—
97	C₂×C₃×D₁₂	C₂²×C₃	1	4	yes	—
98	C₂×C₃×C₄×D₃	—	2	4	no	—
99	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
100	C₂×C₃×Dic₆	—	2	4	no	—
101	C₂×C₃×Dic₆	C₂²×C₃	1	4	yes	complemented
102	C₃²×SD₁₆	—	2	16	no	—
103	C₃²×SD₁₆	—	3	4	no	—
104	C₃²×SD₁₆	—	3	4	no	—
105	C₃²×SD₁₆	—	3	4	no	—
106	C₃²×SD₁₆	C₂×D₃	1	4	yes	direct product factor
107	C₃²×SD₁₆	C₂²×C₃	1	16	yes	complemented
108	C₂×C₃²×C₈	—	2	4	no	—
109	C₂×C₃²×C₈	—	3	1	no	—
110	C₂×C₃²×C₈	—	3	4	no	—
111	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic, complemented
112	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	complemented
113	C₃×#215	C₂²×C₃	1	16	yes	complemented
114	C₃×#214	C₂²×C₃	1	16	yes	complemented
115	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	complemented
116	C₃×#204	C₂²×C₃	1	16	yes	complemented
117	C₃×D₃×C₈	C₂²×C₃	1	16	yes	complemented
118	C₂²×C₃³	—	2	2	no	—
119	C₂²×C₃³	—	4	2	no	—
120	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
121	C₂×C₃²×D₃	—	2	2	no	—
122	C₂×C₃²×D₃	—	4	2	no	—
123	C₂×C₃²×D₃	—	4	8	no	—
124	C₂×C₃²×D₃	SD₁₆	1	4	yes	direct product factor
125	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
126	C₃³×C₄	—	2	2	no	—
127	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
128	C₃³×C₄	C₂⁴	1	1	yes	characteristic
129	C₃²×Dic₃	—	2	2	no	—
130	C₃²×Dic₃	C₂×D₄	1	2	yes	—
131	C₂²×C₃×Q₈	—	3	4	no	—
132	C₂²×C₃×D₄	—	3	4	no	—
133	C₂×D₃×Q₈	C₂×C₃²	1	1	yes	characteristic, complemented
134	C₂×D₃×D₄	C₂×C₃²	1	1	yes	characteristic
135	C₂×C₃×SD₁₆	—	2	4	no	—
136	C₂×C₃×SD₁₆	—	3	4	no	—
137	C₂×C₃×SD₁₆	—	3	4	no	—
138	C₂×C₃×SD₁₆	—	3	32	no	—
139	C₂×C₃×SD₁₆	—	3	4	no	—
140	C₂×C₃×SD₁₆	C₃×D₃	1	4	yes	direct product factor
141	C₂×C₃×SD₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
142	C₂²×C₃×C₈	—	3	4	no	—
143	C₂×#215	C₂×C₃²	1	1	yes	characteristic, complemented
144	C₂×#214	C₂×C₃²	1	1	yes	characteristic, complemented
145	D₃×SD₁₆	C₂×C₃²	1	8	yes	direct product factor
146	C₂×#204	C₂×C₃²	1	1	yes	characteristic, complemented
147	C₂×D₃×C₈	C₂×C₃²	1	1	yes	characteristic, complemented
148	C₂³×C₃²	—	2	1	no	—
149	C₂³×C₃²	—	2	4	no	—
150	C₂³×C₃²	—	3	1	no	—
151	C₂³×C₃²	—	4	4	no	—
152	C₂³×C₃²	—	6	4	no	—
153	C₂³×C₃²	—	6	1	no	—
154	C₂³×C₃²	—	12	4	no	—
155	C₂²×C₃×D₃	—	2	4	no	—
156	C₂²×C₃×D₃	—	2	16	no	—
157	C₂²×C₃×D₃	—	4	16	no	—
158	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
159	C₃²×Q₈	—	2	1	no	—
160	C₃²×Q₈	—	2	8	no	—
161	C₃²×Q₈	—	2	4	no	—
162	C₃²×Q₈	—	3	2	no	—
163	C₃²×Q₈	—	4	4	no	—
164	C₃²×Q₈	—	6	4	no	—
165	C₃²×Q₈	—	6	1	no	—
166	C₃²×Q₈	C₂²×D₃	1	2	yes	complemented
167	C₃²×Q₈	C₂³×C₃	1	8	yes	complemented
168	C₃²×D₄	—	2	1	no	—
169	C₃²×D₄	—	2	8	no	—
170	C₃²×D₄	—	2	4	no	—
171	C₃²×D₄	—	3	2	no	—
172	C₃²×D₄	—	4	4	no	—
173	C₃²×D₄	—	6	4	no	—
174	C₃²×D₄	—	6	1	no	—
175	C₃²×D₄	C₂²×D₃	1	2	yes	—
176	C₃²×D₄	C₂³×C₃	1	8	yes	—
177	C₂×C₃²×C₄	—	2	1	no	—
178	C₂×C₃²×C₄	—	2	4	no	—
179	C₂×C₃²×C₄	—	2	4	no	—
180	C₂×C₃²×C₄	—	3	1	no	—
181	C₂×C₃²×C₄	—	3	2	no	—
182	C₂×C₃²×C₄	—	3	2	no	—
183	C₂×C₃²×C₄	—	4	4	no	—
184	C₂×C₃²×C₄	—	6	4	no	—
185	C₂×C₃²×C₄	—	6	1	no	—
186	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
187	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
188	C₃×#67	—	2	16	no	—
189	C₂×C₃×Dic₃	—	2	4	no	—
190	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
191	C₃×D₁₂	—	2	4	no	—
192	C₃×D₁₂	C₂³×C₃	1	8	yes	—
193	C₃×C₄×D₃	—	2	16	no	—
194	C₃×C₄×D₃	C₃×D₄	1	8	yes	—
195	C₃×C₄×D₃	C₂³×C₃	1	8	yes	—
196	C₃×Dic₆	—	2	4	no	—
197	C₃×Dic₆	—	2	16	no	—
198	C₃×Dic₆	C₂³×C₃	1	8	yes	complemented
199	C₃²×C₈	—	2	8	no	—
200	C₃²×C₈	—	3	2	no	—
201	C₃²×C₈	C₂²×D₃	1	2	yes	complemented
202	C₃²×C₈	C₂³×C₃	1	8	yes	complemented
203	C₃×C₃⋊C₈	C₂³×C₃	1	8	yes	complemented
204	C₂²×SD₁₆	—	3	1	no	Sylow
205	C₂×C₃³	—	4	2	no	—
206	C₂×C₃³	C₂×SD₁₆	1	2	yes	complemented
207	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
208	C₃²×D₃	—	4	2	no	—
209	C₃²×D₃	C₂×SD₁₆	1	4	yes	direct product factor
210	C₂⁴×C₃	—	6	4	no	—
211	C₂³×D₃	—	2	1	no	—
212	C₂×C₃×Q₈	—	2	4	no	—
213	C₂×C₃×Q₈	—	3	16	no	—
214	C₂×C₃×Q₈	—	3	4	no	—
215	C₂×C₃×Q₈	—	6	4	no	—
216	C₂×C₃×Q₈	—	6	8	no	—
217	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	complemented
218	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic, complemented
219	C₂×C₃×D₄	—	2	4	no	—
220	C₂×C₃×D₄	—	3	16	no	—
221	C₂×C₃×D₄	—	3	4	no	—
222	C₂×C₃×D₄	—	6	8	no	—
223	C₂×C₃×D₄	—	6	4	no	—
224	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
225	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
226	C₂²×C₃×C₄	—	3	4	no	—
227	C₂²×C₃×C₄	—	6	4	no	—
228	C₂×#67	—	2	1	no	—
229	D₃×Q₈	—	2	2	no	—
230	D₃×Q₈	C₂²×C₃²	1	4	yes	complemented
231	D₃×D₄	—	2	2	no	—
232	D₃×D₄	C₂²×C₃²	1	4	yes	—
233	C₂×D₁₂	C₂²×C₃²	1	1	yes	characteristic
234	C₂×C₄×D₃	—	2	1	no	—
235	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
236	C₂×Dic₆	—	2	1	no	—
237	C₂×Dic₆	C₂²×C₃²	1	1	yes	characteristic, complemented
238	C₃×SD₁₆	—	2	16	no	—
239	C₃×SD₁₆	—	3	16	no	—
240	C₃×SD₁₆	—	3	16	no	—
241	C₃×SD₁₆	—	3	16	no	—
242	C₃×SD₁₆	C₂×C₃×D₃	1	16	yes	direct product factor
243	C₃×SD₁₆	C₂²×C₃²	1	4	yes	complemented
244	C₂×C₃×C₈	—	2	4	no	—
245	C₂×C₃×C₈	—	3	4	no	—
246	C₂×C₃×C₈	—	3	16	no	—
247	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	complemented
248	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
249	#215	C₂²×C₃²	1	4	yes	complemented
250	#214	C₂²×C₃²	1	4	yes	complemented
251	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic, complemented
252	#204	C₂²×C₃²	1	4	yes	complemented
253	D₃×C₈	C₂²×C₃²	1	4	yes	complemented
254	C₂²×C₃²	—	2	2	no	—
255	C₂²×C₃²	—	2	4	no	—
256	C₂²×C₃²	—	2	8	no	—
257	C₂²×C₃²	—	3	4	no	—
258	C₂²×C₃²	—	3	2	no	—
259	C₂²×C₃²	—	4	8	no	—
260	C₂²×C₃²	—	4	2	no	—
261	C₂²×C₃²	—	4	8	no	—
262	C₂²×C₃²	—	6	2	no	—
263	C₂²×C₃²	—	8	8	no	—
264	C₂²×C₃²	—	12	8	no	—
265	C₂²×C₃²	—	12	2	no	—
266	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
267	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
268	C₂×C₃×D₃	—	2	8	no	—
269	C₂×C₃×D₃	—	4	8	no	—
270	C₂×C₃×D₃	—	4	32	no	—
271	C₂×C₃×D₃	C₃×SD₁₆	1	16	yes	direct product factor
272	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
273	C₃²×C₄	—	2	2	no	—
274	C₃²×C₄	—	2	4	no	—
275	C₃²×C₄	—	2	4	no	—
276	C₃²×C₄	—	2	8	no	—
277	C₃²×C₄	—	3	2	no	—
278	C₃²×C₄	—	4	8	no	—
279	C₃²×C₄	—	6	2	no	—
280	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
281	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
282	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
283	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
284	C₃×Dic₃	—	2	8	no	—
285	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
286	C₂²×Q₈	—	3	1	no	—
287	C₂²×D₄	—	3	1	no	—
288	C₂×SD₁₆	—	3	1	no	—
289	C₂×SD₁₆	—	3	1	no	—
290	C₂×SD₁₆	—	3	8	no	—
291	C₂×SD₁₆	—	3	1	no	—
292	C₂×SD₁₆	C₃²×D₃	1	1	yes	characteristic, direct product factor
293	C₂²×C₈	—	3	1	no	—
294	C₃³	C₂²×SD₁₆	1	1	yes	characteristic, complemented, Sylow
295	C₂³×C₃	—	2	4	no	—
296	C₂³×C₃	—	2	1	no	—
297	C₂³×C₃	—	3	4	no	—
298	C₂³×C₃	—	4	4	no	—
299	C₂³×C₃	—	6	16	no	—
300	C₂³×C₃	—	6	4	no	—
301	C₂³×C₃	—	12	16	no	—
302	C₂²×D₃	—	2	1	no	—
303	C₂²×D₃	—	2	4	no	—
304	C₂²×D₃	—	4	4	no	—
305	C₂²×D₃	C₃²×D₄	1	1	yes	characteristic
306	C₃×Q₈	—	2	4	no	—
307	C₃×Q₈	—	2	1	no	—
308	C₃×Q₈	—	2	8	no	—
309	C₃×Q₈	—	3	8	no	—
310	C₃×Q₈	—	4	4	no	—
311	C₃×Q₈	—	6	16	no	—
312	C₃×Q₈	—	6	4	no	—
313	C₃×Q₈	C₂²×C₃×D₃	1	8	yes	complemented
314	C₃×Q₈	C₂³×C₃²	1	2	yes	complemented
315	C₃×D₄	—	2	4	no	—
316	C₃×D₄	—	2	1	no	—
317	C₃×D₄	—	2	8	no	—
318	C₃×D₄	—	3	8	no	—
319	C₃×D₄	—	4	4	no	—
320	C₃×D₄	—	6	16	no	—
321	C₃×D₄	—	6	4	no	—
322	C₃×D₄	C₂²×C₃×D₃	1	8	yes	—
323	C₃×D₄	C₂³×C₃²	1	2	yes	—
324	C₂×C₃×C₄	—	2	4	no	—
325	C₂×C₃×C₄	—	2	1	no	—
326	C₂×C₃×C₄	—	2	4	no	—
327	C₂×C₃×C₄	—	3	4	no	—
328	C₂×C₃×C₄	—	3	8	no	—
329	C₂×C₃×C₄	—	3	8	no	—
330	C₂×C₃×C₄	—	4	4	no	—
331	C₂×C₃×C₄	—	6	16	no	—
332	C₂×C₃×C₄	—	6	4	no	—
333	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
334	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
335	#67	—	2	4	no	—
336	C₂×Dic₃	—	2	1	no	—
337	C₂×Dic₃	C₃²×D₄	1	1	yes	characteristic
338	D₁₂	—	2	1	no	—
339	D₁₂	C₂³×C₃²	1	2	yes	—
340	C₄×D₃	—	2	4	no	—
341	C₄×D₃	C₃²×D₄	1	2	yes	—
342	C₄×D₃	C₂³×C₃²	1	2	yes	—
343	Dic₆	—	2	1	no	—
344	Dic₆	—	2	4	no	—
345	Dic₆	C₂³×C₃²	1	2	yes	complemented
346	C₃×C₈	—	2	8	no	—
347	C₃×C₈	—	3	8	no	—
348	C₃×C₈	C₂²×C₃×D₃	1	8	yes	complemented
349	C₃×C₈	C₂³×C₃²	1	2	yes	complemented
350	C₃⋊C₈	C₂³×C₃²	1	2	yes	complemented
351	C₂×C₃²	—	2	8	no	—
352	C₂×C₃²	—	2	4	no	—
353	C₂×C₃²	—	3	4	no	—
354	C₂×C₃²	—	4	2	no	—
355	C₂×C₃²	—	4	8	no	—
356	C₂×C₃²	—	8	8	no	—
357	C₂×C₃²	—	12	2	no	—
358	C₂×C₃²	D₃×SD₁₆	1	2	yes	direct product factor
359	C₂×C₃²	C₂×C₃×SD₁₆	1	8	yes	complemented
360	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
361	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
362	C₃×D₃	—	4	8	no	—
363	C₃×D₃	C₂×C₃×SD₁₆	1	16	yes	direct product factor
364	C₂⁴	—	6	1	no	—
365	C₂×Q₈	—	3	4	no	—
366	C₂×Q₈	—	3	1	no	—
367	C₂×Q₈	—	6	1	no	—
368	C₂×Q₈	—	6	2	no	—
369	C₂×Q₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
370	C₂×D₄	—	3	4	no	—
371	C₂×D₄	—	3	1	no	—
372	C₂×D₄	—	6	2	no	—
373	C₂×D₄	—	6	1	no	—
374	C₂×D₄	C₂×C₃²×D₃	1	1	yes	characteristic
375	C₂²×C₄	—	3	1	no	—
376	C₂²×C₄	—	6	1	no	—
377	SD₁₆	—	3	4	no	—
378	SD₁₆	—	3	4	no	—
379	SD₁₆	—	3	4	no	—
380	SD₁₆	C₂×C₃²×D₃	1	4	yes	direct product factor
381	C₂×C₈	—	3	1	no	—
382	C₂×C₈	—	3	4	no	—
383	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic, complemented
384	C₂²×C₃	—	2	8	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	2	4	no	—
387	C₂²×C₃	—	3	16	no	—
388	C₂²×C₃	—	3	8	no	—
389	C₂²×C₃	—	4	8	no	—
390	C₂²×C₃	—	4	8	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	6	8	no	—
393	C₂²×C₃	—	8	8	no	—
394	C₂²×C₃	—	12	32	no	—
395	C₂²×C₃	—	12	8	no	—
396	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
397	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
398	C₂×D₃	—	2	2	no	—
399	C₂×D₃	—	4	2	no	—
400	C₂×D₃	—	4	8	no	—
401	C₂×D₃	C₃²×SD₁₆	1	4	yes	direct product factor
402	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
403	C₃×C₄	—	2	8	no	—
404	C₃×C₄	—	2	2	no	—
405	C₃×C₄	—	2	4	no	—
406	C₃×C₄	—	2	4	no	—
407	C₃×C₄	—	3	8	no	—
408	C₃×C₄	—	4	8	no	—
409	C₃×C₄	—	6	8	no	—
410	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
411	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
412	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
413	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
414	Dic₃	—	2	2	no	—
415	Dic₃	C₂×C₃²×D₄	1	2	yes	—
416	C₃²	—	2	4	no	—
417	C₃²	C₂×D₃×SD₁₆	1	1	yes	characteristic, direct product factor
418	C₃²	C₂²×C₃×SD₁₆	1	4	yes	complemented
419	C₂³	—	2	1	no	—
420	C₂³	—	3	1	no	—
421	C₂³	—	6	4	no	—
422	C₂³	—	6	1	no	—
423	C₂³	—	12	4	no	—
424	Q₈	—	2	1	no	—
425	Q₈	—	3	2	no	—
426	Q₈	—	6	4	no	—
427	Q₈	—	6	1	no	—
428	Q₈	C₂²×C₃²×D₃	1	2	yes	complemented
429	D₄	—	2	1	no	—
430	D₄	—	3	2	no	—
431	D₄	—	6	4	no	—
432	D₄	—	6	1	no	—
433	D₄	C₂²×C₃²×D₃	1	2	yes	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	3	1	no	—
436	C₂×C₄	—	3	2	no	—
437	C₂×C₄	—	3	2	no	—
438	C₂×C₄	—	6	4	no	—
439	C₂×C₄	—	6	1	no	—
440	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
441	C₈	—	3	2	no	—
442	C₈	C₂²×C₃²×D₃	1	2	yes	complemented
443	C₂×C₃	—	2	8	no	—
444	C₂×C₃	—	2	4	no	—
445	C₂×C₃	—	3	16	no	—
446	C₂×C₃	—	4	8	no	—
447	C₂×C₃	—	4	2	no	—
448	C₂×C₃	—	8	8	no	—
449	C₂×C₃	—	12	8	no	—
450	C₂×C₃	C₃×D₃×SD₁₆	1	8	yes	direct product factor
451	C₂×C₃	C₂×C₃²×SD₁₆	1	2	yes	complemented
452	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
453	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
454	D₃	—	4	2	no	—
455	D₃	C₂×C₃²×SD₁₆	1	4	yes	direct product factor
456	C₂²	—	2	2	no	—
457	C₂²	—	3	4	no	—
458	C₂²	—	3	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	6	2	no	—
461	C₂²	—	12	8	no	—
462	C₂²	—	12	2	no	—
463	C₂²	C₃²×D₃×D₄	1	1	yes	characteristic
464	C₄	—	2	2	no	—
465	C₄	—	3	2	no	—
466	C₄	—	6	2	no	—
467	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
468	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
469	C₃	—	2	4	no	—
470	C₃	C₂×C₃×D₃×SD₁₆	1	4	yes	direct product factor
471	C₃	C₂²×C₃²×SD₁₆	1	1	yes	characteristic, complemented
472	C₂	—	3	4	no	—
473	C₂	—	4	2	no	—
474	C₂	—	12	2	no	—
475	C₂	C₃²×D₃×SD₁₆	1	2	yes	direct product factor
476	C₂	C₂×C₃²×D₃×D₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃²	D₃×D₄
commutator, cosocle	C₃×C₄	C₂⁴×C₃²
Frattini	C₄	C₂³×C₃²×D₃
Fitting	C₂×C₃³×SD₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃²×D₃×D₄	C₂
hypercenter	C₂×C₃²×SD₁₆	D₃
hypocenter	C₃	C₂²×C₃²×SD₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×D₃×Q₈	C₂	semidirect
3. C₂×C₃³×SD₁₆	C₂	semidirect
4. C₂×C₃²×#215	C₂	semidirect
5. C₂×C₃²×#214	C₂	semidirect
6. C₃²×D₃×SD₁₆	C₂	direct (N × H)
7. C₂×C₃²×#204	C₂	semidirect
8. C₂×C₃²×D₃×C₈	C₂	semidirect
10. C₂×C₃×D₃×SD₁₆	C₃	direct (N × H)
12. C₂×C₃³×Q₈	C₂²	semidirect
16. C₃²×D₃×Q₈	C₂²	semidirect
23. C₂×C₃²×Dic₆	C₂²	semidirect
24. C₃³×SD₁₆	C₂²	semidirect
25. C₂×C₃³×C₈	C₂²	semidirect
26. C₃²×#215	C₂²	semidirect
27. C₃²×#214	C₂²	semidirect
28. C₂×C₃²×C₃⋊C₈	C₂²	semidirect
29. C₃²×#204	C₂²	semidirect
30. C₃²×D₃×C₈	C₂²	semidirect
33. C₂×C₃×D₃×Q₈	C₂×C₃	semidirect
40. C₂×C₃²×SD₁₆	D₃	direct (N × H)
41. C₂×C₃²×SD₁₆	C₂×C₃	semidirect
43. C₂×C₃×#215	C₂×C₃	semidirect
44. C₂×C₃×#214	C₂×C₃	semidirect
45. C₃×D₃×SD₁₆	C₂×C₃	direct (N × H)
46. C₂×C₃×#204	C₂×C₃	semidirect
47. C₂×C₃×D₃×C₈	C₂×C₃	semidirect
54. C₃³×Q₈	C₂³	semidirect
69. C₃²×Dic₆	C₂³	semidirect
70. C₃³×C₈	C₂³	semidirect
71. C₃²×C₃⋊C₈	C₂³	semidirect
73. C₂×D₃×SD₁₆	C₃²	direct (N × H)
81. C₂×C₃²×Q₈	C₂×D₃	semidirect
82. C₂×C₃²×Q₈	C₂²×C₃	semidirect
94. C₃×D₃×Q₈	C₂²×C₃	semidirect
101. C₂×C₃×Dic₆	C₂²×C₃	semidirect
106. C₃²×SD₁₆	C₂×D₃	direct (N × H)
107. C₃²×SD₁₆	C₂²×C₃	semidirect
111. C₂×C₃²×C₈	C₂×D₃	semidirect
112. C₂×C₃²×C₈	C₂²×C₃	semidirect
113. C₃×#215	C₂²×C₃	semidirect
114. C₃×#214	C₂²×C₃	semidirect
115. C₂×C₃×C₃⋊C₈	C₂²×C₃	semidirect
116. C₃×#204	C₂²×C₃	semidirect
117. C₃×D₃×C₈	C₂²×C₃	semidirect
124. C₂×C₃²×D₃	SD₁₆	direct (N × H)
133. C₂×D₃×Q₈	C₂×C₃²	semidirect
140. C₂×C₃×SD₁₆	C₃×D₃	direct (N × H)
141. C₂×C₃×SD₁₆	C₂×C₃²	semidirect
143. C₂×#215	C₂×C₃²	semidirect
144. C₂×#214	C₂×C₃²	semidirect
145. D₃×SD₁₆	C₂×C₃²	direct (N × H)
146. C₂×#204	C₂×C₃²	semidirect
147. C₂×D₃×C₈	C₂×C₃²	semidirect
166. C₃²×Q₈	C₂²×D₃	semidirect
167. C₃²×Q₈	C₂³×C₃	semidirect
198. C₃×Dic₆	C₂³×C₃	semidirect
201. C₃²×C₈	C₂²×D₃	semidirect
202. C₃²×C₈	C₂³×C₃	semidirect
203. C₃×C₃⋊C₈	C₂³×C₃	semidirect
206. C₂×C₃³	C₂×SD₁₆	semidirect
209. C₃²×D₃	C₂×SD₁₆	direct (N × H)
217. C₂×C₃×Q₈	C₂×C₃×D₃	semidirect
218. C₂×C₃×Q₈	C₂²×C₃²	semidirect
230. D₃×Q₈	C₂²×C₃²	semidirect
237. C₂×Dic₆	C₂²×C₃²	semidirect
242. C₃×SD₁₆	C₂×C₃×D₃	direct (N × H)
243. C₃×SD₁₆	C₂²×C₃²	semidirect
247. C₂×C₃×C₈	C₂×C₃×D₃	semidirect
248. C₂×C₃×C₈	C₂²×C₃²	semidirect
249. #215	C₂²×C₃²	semidirect
250. #214	C₂²×C₃²	semidirect
251. C₂×C₃⋊C₈	C₂²×C₃²	semidirect
252. #204	C₂²×C₃²	semidirect
253. D₃×C₈	C₂²×C₃²	semidirect
271. C₂×C₃×D₃	C₃×SD₁₆	direct (N × H)
292. C₂×SD₁₆	C₃²×D₃	direct (N × H)
294. C₃³	C₂²×SD₁₆	semidirect
313. C₃×Q₈	C₂²×C₃×D₃	semidirect
314. C₃×Q₈	C₂³×C₃²	semidirect
345. Dic₆	C₂³×C₃²	semidirect
348. C₃×C₈	C₂²×C₃×D₃	semidirect
349. C₃×C₈	C₂³×C₃²	semidirect
350. C₃⋊C₈	C₂³×C₃²	semidirect
358. C₂×C₃²	D₃×SD₁₆	direct (N × H)
359. C₂×C₃²	C₂×C₃×SD₁₆	semidirect
363. C₃×D₃	C₂×C₃×SD₁₆	direct (N × H)
369. C₂×Q₈	C₂×C₃²×D₃	semidirect
380. SD₁₆	C₂×C₃²×D₃	direct (N × H)
383. C₂×C₈	C₂×C₃²×D₃	semidirect
401. C₂×D₃	C₃²×SD₁₆	direct (N × H)
417. C₃²	C₂×D₃×SD₁₆	direct (N × H)
418. C₃²	C₂²×C₃×SD₁₆	semidirect
428. Q₈	C₂²×C₃²×D₃	semidirect
442. C₈	C₂²×C₃²×D₃	semidirect
450. C₂×C₃	C₃×D₃×SD₁₆	direct (N × H)
451. C₂×C₃	C₂×C₃²×SD₁₆	semidirect
455. D₃	C₂×C₃²×SD₁₆	direct (N × H)
470. C₃	C₂×C₃×D₃×SD₁₆	direct (N × H)
471. C₃	C₂²×C₃²×SD₁₆	semidirect
475. C₂	C₃²×D₃×SD₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₃×Q₈	2
C₂×C₃²×D₃×D₄	2
C₂×C₃³×SD₁₆	2
C₂×C₃²×#215	2
C₂×C₃²×#214	2
C₃²×D₃×SD₁₆	2
C₂×C₃²×#204	2
C₂×C₃²×D₃×C₈	2
C₂²×C₃²×SD₁₆	3
C₂×C₃×D₃×SD₁₆	3

Subgroups — C2×C32×D3×SD16 #13179135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₃×SD₁₆ #13179135