Subgroups — C₃×C₄×D₃×Q₁₆ #11859917

Order 1152.

1031 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×D₃×Q₈	C₂	1	2	yes	maximal
3	C₃²×C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#216	C₂	1	2	yes	maximal, complemented
6	C₃×D₃×#107	C₂	1	1	yes	maximal, characteristic
7	C₃×#4873	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₃×#103	C₂	1	2	yes	maximal
9	C₃×#4790	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₃×C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₃×C₄×Q₁₆	—	3	1	no	maximal
13	C₄×D₃×Q₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃×D₃×Q₈	C₂²	1	2	yes	—
15	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
16	C₃²×C₄×Q₈	C₂²	1	2	yes	—
17	C₃×Q₈×Dic₃	C₂²	1	2	yes	—
18	C₂×C₃×#216	C₂²	1	2	yes	—
19	C₃×D₃×Q₁₆	C₄	1	8	yes	direct product factor
20	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
21	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
23	C₃×D₃×C₄⋊C₄	—	2	2	no	—
24	C₃×D₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₃×#887	—	2	2	no	—
26	C₃×#887	C₂²	1	2	yes	—
27	C₃×C₄²×D₃	—	2	2	no	—
28	C₃×C₄²×D₃	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₆	—	2	2	no	—
30	C₃×C₄×Dic₆	C₂²	1	2	yes	—
31	C₃²×#107	C₂²	1	1	yes	characteristic
32	C₃²×#103	C₂²	1	2	yes	—
33	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₃×#835	C₂²	1	2	yes	—
35	C₃×#818	C₂²	1	1	yes	characteristic
36	C₃×#816	C₂²	1	2	yes	—
37	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
38	C₃×C₈×Dic₃	C₂²	1	1	yes	characteristic
39	C₃×#810	C₂²	1	2	yes	—
40	C₃×#807	C₂²	1	2	yes	—
41	C₃×C₄×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	C₂²×C₃×Q₁₆	—	3	1	no	—
43	C₂×C₃×C₄×Q₈	—	3	2	no	—
44	C₂×D₃×Q₁₆	C₂×C₃	1	1	yes	characteristic
45	C₄×D₃×Q₈	C₂×C₃	1	2	yes	—
46	C₃×C₄×Q₁₆	—	2	1	no	—
47	C₃×C₄×Q₁₆	—	3	1	no	—
48	C₃×C₄×Q₁₆	—	3	2	no	—
49	C₃×C₄×Q₁₆	—	3	1	no	—
50	C₃×C₄×Q₁₆	—	3	2	no	—
51	C₃×C₄×Q₁₆	—	3	1	no	—
52	C₃×C₄×Q₁₆	D₃	1	1	yes	characteristic, direct product factor
53	C₃×C₄×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×#107	—	3	1	no	—
55	C₂×C₃×#103	—	3	2	no	—
56	C₂×C₃×C₄×C₈	—	3	1	no	—
57	Dic₃×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
58	C₄×#216	C₂×C₃	1	2	yes	complemented
59	D₃×#107	C₂×C₃	1	1	yes	characteristic
60	#4873	C₂×C₃	1	1	yes	characteristic, complemented
61	D₃×#103	C₂×C₃	1	2	yes	—
62	#4790	C₂×C₃	1	2	yes	complemented
63	C₄×Dic₁₂	C₂×C₃	1	1	yes	characteristic, complemented
64	C₄×D₃×C₈	C₂×C₃	1	1	yes	characteristic
65	C₂×C₃²×Q₈	C₂³	1	2	yes	—
66	C₃×D₃×Q₈	—	2	4	no	—
67	C₃×D₃×Q₈	C₂×C₄	1	8	yes	—
68	C₂×C₃×C₄×D₃	—	2	2	no	—
69	C₂×C₃×C₄×D₃	—	2	2	no	—
70	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
71	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
72	C₂×C₃×C₄×D₃	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₆	—	2	2	no	—
74	C₂×C₃×Dic₆	C₂³	1	2	yes	—
75	C₃²×Q₁₆	C₂×C₄	1	4	yes	complemented
76	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
77	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
78	C₃²×C₄⋊C₄	—	2	2	no	—
79	C₃²×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃²×C₄²	—	2	2	no	—
81	C₃²×C₄²	C₂³	1	1	yes	characteristic
82	C₃×#216	C₂×C₄	1	8	yes	complemented
83	C₃×C₄⋊Dic₃	—	2	2	no	—
84	C₃×C₄⋊Dic₃	C₂³	1	2	yes	—
85	C₃×Dic₃⋊C₄	—	2	2	no	—
86	C₃×Dic₃⋊C₄	—	2	2	no	—
87	C₃×Dic₃⋊C₄	—	2	2	no	—
88	C₃×C₄×Dic₃	—	2	2	no	—
89	C₃×C₄×Dic₃	—	2	2	no	—
90	C₃×C₄×Dic₃	—	2	2	no	—
91	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
92	C₃×C₄×Dic₃	D₄	1	1	yes	characteristic
93	C₃×C₄×Dic₃	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
96	C₃×Dic₁₂	C₂×C₄	1	4	yes	complemented
97	C₃×D₃×C₈	—	2	2	no	—
98	C₃×D₃×C₈	C₂×C₄	1	4	yes	—
99	C₂×C₄×Q₁₆	—	3	1	no	Sylow
100	C₂²×C₃×Q₈	—	3	2	no	—
101	C₂×D₃×Q₈	C₂²×C₃	1	2	yes	—
102	C₂×C₃×Q₁₆	—	2	1	no	—
103	C₂×C₃×Q₁₆	—	3	2	no	—
104	C₂×C₃×Q₁₆	—	3	8	no	—
105	C₂×C₃×Q₁₆	—	3	1	no	—
106	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
107	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₃×C₈	—	3	1	no	—
109	C₂²×C₃×C₈	—	3	1	no	—
110	C₃×C₄×Q₈	—	2	2	no	—
111	C₃×C₄×Q₈	—	3	2	no	—
112	C₃×C₄×Q₈	—	3	2	no	—
113	C₃×C₄×Q₈	—	3	2	no	—
114	C₃×C₄×Q₈	—	6	2	no	—
115	C₃×C₄×Q₈	—	6	2	no	—
116	C₃×C₄×Q₈	C₂×D₃	1	2	yes	—
117	C₃×C₄×Q₈	C₂²×C₃	1	2	yes	—
118	C₂×C₃×C₄⋊C₄	—	3	2	no	—
119	C₂×C₃×C₄⋊C₄	—	6	2	no	—
120	C₂×C₃×C₄²	—	3	1	no	—
121	C₂×C₃×C₄²	—	6	2	no	—
122	Q₈×Dic₃	C₂²×C₃	1	2	yes	—
123	C₂×#216	C₂²×C₃	1	2	yes	—
124	D₃×Q₁₆	C₃×C₄	1	8	yes	direct product factor
125	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
126	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
127	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
128	D₃×C₄⋊C₄	—	2	2	no	—
129	D₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
130	#887	—	2	2	no	—
131	#887	C₂²×C₃	1	2	yes	—
132	C₄²×D₃	—	2	2	no	—
133	C₄²×D₃	C₂²×C₃	1	1	yes	characteristic
134	C₄×Dic₆	—	2	2	no	—
135	C₄×Dic₆	C₂²×C₃	1	2	yes	—
136	C₃×#107	—	2	1	no	—
137	C₃×#107	—	3	1	no	—
138	C₃×#107	—	3	2	no	—
139	C₃×#107	C₂×D₃	1	1	yes	characteristic
140	C₃×#107	C₂²×C₃	1	1	yes	characteristic
141	C₃×#103	—	2	2	no	—
142	C₃×#103	—	3	2	no	—
143	C₃×#103	—	3	2	no	—
144	C₃×#103	—	3	2	no	—
145	C₃×#103	C₂×D₃	1	2	yes	—
146	C₃×#103	C₂²×C₃	1	2	yes	—
147	C₃×C₄×C₈	—	2	1	no	—
148	C₃×C₄×C₈	—	3	1	no	—
149	C₃×C₄×C₈	—	3	1	no	—
150	C₃×C₄×C₈	—	3	1	no	—
151	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
152	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
153	#835	C₂²×C₃	1	2	yes	—
154	#818	C₂²×C₃	1	1	yes	characteristic
155	#816	C₂²×C₃	1	2	yes	—
156	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
157	C₈×Dic₃	C₂²×C₃	1	1	yes	characteristic
158	#810	C₂²×C₃	1	2	yes	—
159	#807	C₂²×C₃	1	2	yes	—
160	C₄×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
161	C₂²×C₃×D₃	C₂×D₄	1	1	yes	characteristic
162	C₃²×Q₈	—	2	2	no	—
163	C₃²×Q₈	C₂²×C₄	1	4	yes	—
164	C₂×C₃²×C₄	—	2	2	no	—
165	C₂×C₃²×C₄	—	2	2	no	—
166	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
167	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
168	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
169	C₂×C₃×Dic₃	—	2	2	no	—
170	C₂×C₃×Dic₃	—	2	2	no	—
171	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
173	C₂×C₃×Dic₃	C₂×D₄	1	1	yes	characteristic
174	C₃×C₄×D₃	—	2	8	no	—
175	C₃×C₄×D₃	—	2	2	no	—
176	C₃×C₄×D₃	—	4	4	no	—
177	C₃×C₄×D₃	Q₁₆	1	4	yes	direct product factor
178	C₃×C₄×D₃	C₂²×C₄	1	2	yes	—
179	C₃×C₄×D₃	#41	1	2	yes	—
180	C₃×Dic₆	—	2	2	no	—
181	C₃×Dic₆	—	2	8	no	—
182	C₃×Dic₆	C₂²×C₄	1	4	yes	—
183	C₃²×C₈	—	2	1	no	—
184	C₃²×C₈	C₂²×C₄	1	2	yes	—
185	C₃×C₃⋊C₈	—	2	1	no	—
186	C₃×C₃⋊C₈	C₂²×C₄	1	2	yes	—
187	C₂²×Q₁₆	—	3	1	no	—
188	C₂×C₄×Q₈	—	3	2	no	—
189	C₄×Q₁₆	—	3	1	no	—
190	C₄×Q₁₆	—	3	2	no	—
191	C₄×Q₁₆	—	3	1	no	—
192	C₄×Q₁₆	—	3	2	no	—
193	C₄×Q₁₆	—	3	1	no	—
194	C₄×Q₁₆	C₃×D₃	1	1	yes	characteristic, direct product factor
195	C₂×#107	—	3	1	no	—
196	C₂×#103	—	3	2	no	—
197	C₂×C₄×C₈	—	3	1	no	—
198	C₂×C₃×Q₈	—	2	2	no	—
199	C₂×C₃×Q₈	—	3	8	no	—
200	C₂×C₃×Q₈	—	3	2	no	—
201	C₂×C₃×Q₈	—	6	2	no	—
202	C₂×C₃×Q₈	—	6	4	no	—
203	C₂×C₃×Q₈	C₂²×D₃	1	2	yes	—
204	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
205	C₂²×C₃×C₄	—	3	1	no	—
206	C₂²×C₃×C₄	—	3	1	no	—
207	C₂²×C₃×C₄	—	3	1	no	—
208	C₂²×C₃×C₄	—	6	2	no	—
209	C₂²×C₃×C₄	—	6	2	no	—
210	D₃×Q₈	—	2	4	no	—
211	D₃×Q₈	C₂×C₃×C₄	1	8	yes	—
212	C₂×C₄×D₃	—	2	2	no	—
213	C₂×C₄×D₃	—	2	2	no	—
214	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
215	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
216	C₂×C₄×D₃	C₂³×C₃	1	1	yes	characteristic
217	C₂×Dic₆	—	2	2	no	—
218	C₂×Dic₆	C₂³×C₃	1	2	yes	—
219	C₃×Q₁₆	—	2	4	no	—
220	C₃×Q₁₆	—	3	8	no	—
221	C₃×Q₁₆	—	3	4	no	—
222	C₃×Q₁₆	C₄×D₃	1	4	yes	direct product factor
223	C₃×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
224	C₂×C₃×C₈	—	2	1	no	—
225	C₂×C₃×C₈	—	2	1	no	—
226	C₂×C₃×C₈	—	3	1	no	—
227	C₂×C₃×C₈	—	3	4	no	—
228	C₂×C₃×C₈	—	3	1	no	—
229	C₂×C₃×C₈	—	6	2	no	—
230	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
231	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
232	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
233	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
234	C₃×C₄⋊C₄	—	2	2	no	—
235	C₃×C₄⋊C₄	—	2	2	no	—
236	C₃×C₄⋊C₄	—	2	2	no	—
237	C₃×C₄⋊C₄	—	3	2	no	—
238	C₃×C₄⋊C₄	—	4	2	no	—
239	C₃×C₄⋊C₄	—	6	2	no	—
240	C₃×C₄⋊C₄	—	6	2	no	—
241	C₃×C₄⋊C₄	—	6	2	no	—
242	C₃×C₄⋊C₄	—	6	2	no	—
243	C₃×C₄⋊C₄	C₂²×D₃	1	2	yes	—
244	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
245	C₃×C₄²	—	2	2	no	—
246	C₃×C₄²	—	2	2	no	—
247	C₃×C₄²	—	2	1	no	—
248	C₃×C₄²	—	3	1	no	—
249	C₃×C₄²	—	3	1	no	—
250	C₃×C₄²	—	3	1	no	—
251	C₃×C₄²	—	4	2	no	—
252	C₃×C₄²	—	6	2	no	—
253	C₃×C₄²	—	6	2	no	—
254	C₃×C₄²	—	6	2	no	—
255	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
256	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
257	#216	C₂×C₃×C₄	1	8	yes	complemented
258	C₄⋊Dic₃	—	2	2	no	—
259	C₄⋊Dic₃	C₂³×C₃	1	2	yes	—
260	Dic₃⋊C₄	—	2	2	no	—
261	Dic₃⋊C₄	—	2	2	no	—
262	Dic₃⋊C₄	—	2	2	no	—
263	C₄×Dic₃	—	2	2	no	—
264	C₄×Dic₃	—	2	2	no	—
265	C₄×Dic₃	—	2	2	no	—
266	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
267	C₄×Dic₃	C₃×D₄	1	1	yes	characteristic
268	C₄×Dic₃	C₂³×C₃	1	1	yes	characteristic
269	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
271	Dic₁₂	C₂×C₃×C₄	1	4	yes	complemented
272	D₃×C₈	—	2	2	no	—
273	D₃×C₈	C₂×C₃×C₄	1	4	yes	—
274	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₃×D₃	C₄×D₄	1	2	yes	—
276	C₂×C₃×D₃	C₂×Q₁₆	1	2	yes	—
277	C₂×C₃×D₃	#135	1	2	yes	—
278	C₃²×C₄	—	2	4	no	—
279	C₃²×C₄	—	2	1	no	—
280	C₃²×C₄	—	4	2	no	—
281	C₃²×C₄	C₂×Q₁₆	1	2	yes	complemented
282	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
283	C₃²×C₄	C₂×#41	1	1	yes	characteristic
284	C₃×Dic₃	—	2	4	no	—
285	C₃×Dic₃	—	2	1	no	—
286	C₃×Dic₃	—	4	2	no	—
287	C₃×Dic₃	C₄×D₄	1	2	yes	—
288	C₃×Dic₃	C₂×Q₁₆	1	2	yes	complemented
289	C₂²×Q₈	—	3	2	no	—
290	C₂×Q₁₆	—	3	2	no	—
291	C₂×Q₁₆	—	3	8	no	—
292	C₂×Q₁₆	—	3	1	no	—
293	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
294	C₂²×C₈	—	3	1	no	—
295	C₂²×C₈	—	3	1	no	—
296	C₄×Q₈	—	3	2	no	—
297	C₄×Q₈	—	3	2	no	—
298	C₄×Q₈	—	3	2	no	—
299	C₄×Q₈	—	6	2	no	—
300	C₄×Q₈	—	6	2	no	—
301	C₄×Q₈	C₂×C₃×D₃	1	2	yes	—
302	C₂×C₄⋊C₄	—	3	2	no	—
303	C₂×C₄⋊C₄	—	6	2	no	—
304	C₂×C₄²	—	3	1	no	—
305	C₂×C₄²	—	6	2	no	—
306	#107	—	3	1	no	—
307	#107	—	3	2	no	—
308	#107	C₂×C₃×D₃	1	1	yes	characteristic
309	#103	—	3	2	no	—
310	#103	—	3	2	no	—
311	#103	—	3	2	no	—
312	#103	C₂×C₃×D₃	1	2	yes	—
313	C₄×C₈	—	3	1	no	—
314	C₄×C₈	—	3	1	no	—
315	C₄×C₈	—	3	1	no	—
316	C₄×C₈	C₂×C₃×D₃	1	1	yes	characteristic
317	C₂³×C₃	—	3	1	no	—
318	C₂²×D₃	C₂×C₃×D₄	1	1	yes	characteristic
319	C₃×Q₈	—	2	2	no	—
320	C₃×Q₈	—	2	2	no	—
321	C₃×Q₈	—	2	4	no	—
322	C₃×Q₈	—	3	4	no	—
323	C₃×Q₈	—	4	2	no	—
324	C₃×Q₈	—	6	8	no	—
325	C₃×Q₈	—	6	2	no	—
326	C₃×Q₈	C₂×C₄×D₃	1	4	yes	—
327	C₃×Q₈	C₂²×C₃×C₄	1	4	yes	—
328	C₂×C₃×C₄	—	2	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	2	2	no	—
332	C₂×C₃×C₄	—	2	1	no	—
333	C₂×C₃×C₄	—	2	1	no	—
334	C₂×C₃×C₄	—	2	1	no	—
335	C₂×C₃×C₄	—	3	1	no	—
336	C₂×C₃×C₄	—	3	1	no	—
337	C₂×C₃×C₄	—	3	4	no	—
338	C₂×C₃×C₄	—	3	2	no	—
339	C₂×C₃×C₄	—	3	2	no	—
340	C₂×C₃×C₄	—	3	1	no	—
341	C₂×C₃×C₄	—	4	2	no	—
342	C₂×C₃×C₄	—	4	2	no	—
343	C₂×C₃×C₄	—	6	2	no	—
344	C₂×C₃×C₄	—	6	8	no	—
345	C₂×C₃×C₄	—	6	2	no	—
346	C₂×C₃×C₄	—	6	2	no	—
347	C₂×C₃×C₄	—	12	4	no	—
348	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
349	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
350	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
351	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
352	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
353	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
354	C₂×Dic₃	—	2	2	no	—
355	C₂×Dic₃	—	2	2	no	—
356	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
357	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
358	C₂×Dic₃	C₂×C₃×D₄	1	1	yes	characteristic
359	C₄×D₃	—	2	8	no	—
360	C₄×D₃	—	2	2	no	—
361	C₄×D₃	—	4	4	no	—
362	C₄×D₃	C₃×Q₁₆	1	4	yes	direct product factor
363	C₄×D₃	C₂²×C₃×C₄	1	2	yes	—
364	C₄×D₃	C₃×#41	1	2	yes	—
365	Dic₆	—	2	2	no	—
366	Dic₆	—	2	8	no	—
367	Dic₆	C₂²×C₃×C₄	1	4	yes	—
368	C₃×C₈	—	2	1	no	—
369	C₃×C₈	—	2	1	no	—
370	C₃×C₈	—	2	2	no	—
371	C₃×C₈	—	3	2	no	—
372	C₃×C₈	—	4	1	no	—
373	C₃×C₈	—	6	1	no	—
374	C₃×C₈	C₂×C₄×D₃	1	2	yes	—
375	C₃×C₈	C₂²×C₃×C₄	1	2	yes	—
376	C₃⋊C₈	—	2	1	no	—
377	C₃⋊C₈	C₂²×C₃×C₄	1	2	yes	—
378	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
379	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
380	C₂×C₃²	C₂×#135	1	1	yes	characteristic
381	C₃×D₃	C₄×Q₁₆	1	4	yes	direct product factor
382	C₂×Q₈	—	3	8	no	—
383	C₂×Q₈	—	3	2	no	—
384	C₂×Q₈	—	6	2	no	—
385	C₂×Q₈	—	6	4	no	—
386	C₂×Q₈	C₂²×C₃×D₃	1	2	yes	—
387	C₂²×C₄	—	3	1	no	—
388	C₂²×C₄	—	3	1	no	—
389	C₂²×C₄	—	3	1	no	—
390	C₂²×C₄	—	6	2	no	—
391	C₂²×C₄	—	6	2	no	—
392	Q₁₆	—	3	8	no	—
393	Q₁₆	—	3	4	no	—
394	Q₁₆	C₃×C₄×D₃	1	4	yes	direct product factor
395	C₂×C₈	—	3	1	no	—
396	C₂×C₈	—	3	4	no	—
397	C₂×C₈	—	3	1	no	—
398	C₂×C₈	—	6	2	no	—
399	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
400	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	3	2	no	—
403	C₄⋊C₄	—	6	2	no	—
404	C₄⋊C₄	—	6	2	no	—
405	C₄⋊C₄	—	6	2	no	—
406	C₄⋊C₄	—	6	2	no	—
407	C₄⋊C₄	C₂²×C₃×D₃	1	2	yes	—
408	C₄²	—	2	2	no	—
409	C₄²	—	3	1	no	—
410	C₄²	—	3	1	no	—
411	C₄²	—	3	1	no	—
412	C₄²	—	6	2	no	—
413	C₄²	—	6	2	no	—
414	C₄²	—	6	2	no	—
415	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
416	C₂²×C₃	—	2	1	no	—
417	C₂²×C₃	—	3	2	no	—
418	C₂²×C₃	—	3	2	no	—
419	C₂²×C₃	—	3	2	no	—
420	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
421	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
422	C₂×D₃	C₃×C₄×D₄	1	2	yes	—
423	C₂×D₃	C₂×C₃×Q₁₆	1	2	yes	—
424	C₂×D₃	C₃×#135	1	2	yes	—
425	C₃×C₄	—	2	1	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	2	4	no	—
428	C₃×C₄	—	2	4	no	—
429	C₃×C₄	—	2	2	no	—
430	C₃×C₄	—	2	1	no	—
431	C₃×C₄	—	2	1	no	—
432	C₃×C₄	—	3	2	no	—
433	C₃×C₄	—	3	2	no	—
434	C₃×C₄	—	4	1	no	—
435	C₃×C₄	—	4	4	no	—
436	C₃×C₄	—	4	2	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	—	6	1	no	—
439	C₃×C₄	—	6	4	no	—
440	C₃×C₄	—	8	2	no	—
441	C₃×C₄	—	12	2	no	—
442	C₃×C₄	D₃×Q₁₆	1	2	yes	direct product factor
443	C₃×C₄	C₂×C₃×Q₁₆	1	2	yes	complemented
444	C₃×C₄	C₂²×C₄×D₃	1	1	yes	characteristic
445	C₃×C₄	D₃×#41	1	1	yes	characteristic
446	C₃×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
447	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
448	Dic₃	—	2	1	no	—
449	Dic₃	—	2	4	no	—
450	Dic₃	—	4	2	no	—
451	Dic₃	C₃×C₄×D₄	1	2	yes	—
452	Dic₃	C₂×C₃×Q₁₆	1	2	yes	complemented
453	C₃²	C₂×C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
454	C₂³	—	3	1	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	3	4	no	—
457	Q₈	—	6	8	no	—
458	Q₈	—	6	2	no	—
459	Q₈	C₂×C₃×C₄×D₃	1	4	yes	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	3	1	no	—
463	C₂×C₄	—	3	1	no	—
464	C₂×C₄	—	3	4	no	—
465	C₂×C₄	—	3	2	no	—
466	C₂×C₄	—	3	2	no	—
467	C₂×C₄	—	3	1	no	—
468	C₂×C₄	—	6	2	no	—
469	C₂×C₄	—	6	8	no	—
470	C₂×C₄	—	6	2	no	—
471	C₂×C₄	—	6	2	no	—
472	C₂×C₄	—	12	4	no	—
473	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
474	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
475	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
476	C₈	—	2	1	no	—
477	C₈	—	3	2	no	—
478	C₈	—	6	1	no	—
479	C₈	C₂×C₃×C₄×D₃	1	2	yes	—
480	C₂×C₃	—	2	1	no	—
481	C₂×C₃	—	2	1	no	—
482	C₂×C₃	—	2	1	no	—
483	C₂×C₃	—	3	4	no	—
484	C₂×C₃	C₄×D₃×D₄	1	1	yes	characteristic
485	C₂×C₃	C₂×D₃×Q₁₆	1	1	yes	characteristic
486	C₂×C₃	D₃×#135	1	1	yes	characteristic
487	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
488	C₂×C₃	C₂²×C₃×Q₁₆	1	1	yes	characteristic
489	C₂×C₃	C₂×C₃×#135	1	1	yes	characteristic
490	D₃	C₃×C₄×Q₁₆	1	4	yes	direct product factor
491	C₂²	—	3	2	no	—
492	C₂²	—	3	2	no	—
493	C₂²	—	3	2	no	—
494	C₂²	C₂×C₃×D₃×D₄	1	1	yes	characteristic
495	C₄	—	2	1	no	—
496	C₄	—	2	4	no	—
497	C₄	—	3	2	no	—
498	C₄	—	3	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	6	1	no	—
501	C₄	—	6	4	no	—
502	C₄	—	12	2	no	—
503	C₄	C₃×D₃×Q₁₆	1	2	yes	direct product factor
504	C₄	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
505	C₄	C₃×D₃×#41	1	1	yes	characteristic
506	C₃	—	2	1	no	—
507	C₃	C₄×D₃×Q₁₆	1	1	yes	characteristic, direct product factor
508	C₃	C₂×C₃×C₄×Q₁₆	1	1	yes	characteristic, complemented
509	C₂	—	3	4	no	—
510	C₂	C₃×C₄×D₃×D₄	1	1	yes	characteristic
511	C₂	C₂×C₃×D₃×Q₁₆	1	1	yes	characteristic
512	C₂	C₃×D₃×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₃×C₄	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×C₄×Q₁₆	C₂
socle	C₂²×C₃²	C₂²×D₄
prime radical	C₂²×C₃×D₃	C₂×D₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×C₄×Q₁₆	D₃
hypocenter	C₃	C₂×C₃×C₄×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄² ◁ C₃×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
3. C₃²×C₄×Q₁₆	C₂	semidirect
4. C₃×Dic₃×Q₁₆	C₂	semidirect
5. C₃×C₄×#216	C₂	semidirect
7. C₃×#4873	C₂	semidirect
9. C₃×#4790	C₂	semidirect
10. C₃×C₄×Dic₁₂	C₂	semidirect
13. C₄×D₃×Q₁₆	C₃	direct (N × H)
19. C₃×D₃×Q₁₆	C₄	direct (N × H)
52. C₃×C₄×Q₁₆	D₃	direct (N × H)
53. C₃×C₄×Q₁₆	C₂×C₃	semidirect
57. Dic₃×Q₁₆	C₂×C₃	semidirect
58. C₄×#216	C₂×C₃	semidirect
60. #4873	C₂×C₃	semidirect
62. #4790	C₂×C₃	semidirect
63. C₄×Dic₁₂	C₂×C₃	semidirect
75. C₃²×Q₁₆	C₂×C₄	semidirect
82. C₃×#216	C₂×C₄	semidirect
96. C₃×Dic₁₂	C₂×C₄	semidirect
124. D₃×Q₁₆	C₃×C₄	direct (N × H)
177. C₃×C₄×D₃	Q₁₆	direct (N × H)
194. C₄×Q₁₆	C₃×D₃	direct (N × H)
222. C₃×Q₁₆	C₄×D₃	direct (N × H)
223. C₃×Q₁₆	C₂×C₃×C₄	semidirect
257. #216	C₂×C₃×C₄	semidirect
271. Dic₁₂	C₂×C₃×C₄	semidirect
281. C₃²×C₄	C₂×Q₁₆	semidirect
288. C₃×Dic₃	C₂×Q₁₆	semidirect
362. C₄×D₃	C₃×Q₁₆	direct (N × H)
381. C₃×D₃	C₄×Q₁₆	direct (N × H)
394. Q₁₆	C₃×C₄×D₃	direct (N × H)
442. C₃×C₄	D₃×Q₁₆	direct (N × H)
443. C₃×C₄	C₂×C₃×Q₁₆	semidirect
452. Dic₃	C₂×C₃×Q₁₆	semidirect
453. C₃²	C₂×C₄×Q₁₆	semidirect
490. D₃	C₃×C₄×Q₁₆	direct (N × H)
503. C₄	C₃×D₃×Q₁₆	direct (N × H)
507. C₃	C₄×D₃×Q₁₆	direct (N × H)
508. C₃	C₂×C₃×C₄×Q₁₆	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×Q₁₆	2
C₃×C₄×D₃×Q₈	2
C₃²×C₄×Q₁₆	2
C₃×Dic₃×Q₁₆	2
C₃×C₄×#216	2
C₃×D₃×#107	2
C₃×#4873	2
C₃×D₃×#103	2
C₃×#4790	2
C₃×C₄×Dic₁₂	2
C₃×C₄×D₃×C₈	2
C₂×C₃×C₄×Q₁₆	3
C₄×D₃×Q₁₆	3

Subgroups — C3×C4×D3×Q16 #11859917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×D₃×Q₁₆ #11859917