Subgroups — C₂×C₃²×D₃×Q₁₆ #13179140

Order 1728.

1788 conjugacy classes of subgroups.

The subgroup lattice has 314 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	2	yes	maximal
2	C₂×C₃³×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃²×#216	C₂	1	2	yes	maximal, complemented
4	C₃²×D₃×Q₁₆	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃²×Dic₁₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃²×D₃×C₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₃²×Q₁₆	—	3	1	no	maximal
8	C₂×C₃×D₃×Q₁₆	C₃	1	4	yes	maximal, direct product factor
9	C₂×C₃³×Q₈	C₂²	1	2	yes	—
10	C₃²×D₃×Q₈	—	2	4	no	—
11	C₃²×D₃×Q₈	C₂²	1	8	yes	—
12	C₂×C₃²×C₄×D₃	—	2	2	no	—
13	C₂×C₃²×C₄×D₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×Dic₆	—	2	2	no	—
15	C₂×C₃²×Dic₆	C₂²	1	2	yes	—
16	C₃³×Q₁₆	C₂²	1	4	yes	complemented
17	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
18	C₃²×#216	C₂²	1	8	yes	complemented
19	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₃²×Dic₁₂	C₂²	1	4	yes	complemented
21	C₃²×D₃×C₈	C₂²	1	4	yes	—
22	C₂²×C₃²×Q₈	—	3	2	no	—
23	C₂×C₃×D₃×Q₈	C₂×C₃	1	8	yes	—
24	C₂×C₃²×Q₁₆	—	2	4	no	—
25	C₂×C₃²×Q₁₆	—	3	2	no	—
26	C₂×C₃²×Q₁₆	—	3	8	no	—
27	C₂×C₃²×Q₁₆	—	3	1	no	—
28	C₂×C₃²×Q₁₆	D₃	1	1	yes	characteristic, direct product factor
29	C₂×C₃²×Q₁₆	C₂×C₃	1	4	yes	complemented
30	C₂²×C₃²×C₈	—	3	1	no	—
31	C₂×C₃×#216	C₂×C₃	1	8	yes	complemented
32	C₃×D₃×Q₁₆	C₂×C₃	1	32	yes	direct product factor
33	C₂×C₃×Dic₁₂	C₂×C₃	1	4	yes	complemented
34	C₂×C₃×D₃×C₈	C₂×C₃	1	4	yes	—
35	C₂²×C₃²×D₃	D₄	1	1	yes	characteristic
36	C₃³×Q₈	—	2	2	no	—
37	C₃³×Q₈	C₂³	1	4	yes	—
38	C₂×C₃³×C₄	—	2	2	no	—
39	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₃²×Dic₃	—	2	2	no	—
41	C₂×C₃²×Dic₃	D₄	1	1	yes	characteristic
42	C₃²×C₄×D₃	—	2	8	no	—
43	C₃²×C₄×D₃	D₄	1	2	yes	—
44	C₃²×C₄×D₃	C₂³	1	2	yes	—
45	C₃²×Dic₆	—	2	2	no	—
46	C₃²×Dic₆	—	2	8	no	—
47	C₃²×Dic₆	C₂³	1	4	yes	—
48	C₃³×C₈	C₂³	1	2	yes	—
49	C₃²×C₃⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₃×Q₁₆	—	3	4	no	—
51	C₂×D₃×Q₁₆	C₃²	1	1	yes	characteristic, direct product factor
52	C₂×C₃²×Q₈	—	2	8	no	—
53	C₂×C₃²×Q₈	—	3	8	no	—
54	C₂×C₃²×Q₈	—	3	2	no	—
55	C₂×C₃²×Q₈	—	6	2	no	—
56	C₂×C₃²×Q₈	—	6	4	no	—
57	C₂×C₃²×Q₈	C₂×D₃	1	2	yes	—
58	C₂×C₃²×Q₈	C₂²×C₃	1	8	yes	—
59	C₂²×C₃²×C₄	—	3	1	no	—
60	C₂²×C₃²×C₄	—	6	2	no	—
61	C₃×D₃×Q₈	—	2	16	no	—
62	C₃×D₃×Q₈	C₂²×C₃	1	32	yes	—
63	C₂×C₃×C₄×D₃	—	2	8	no	—
64	C₂×C₃×C₄×D₃	C₂²×C₃	1	4	yes	—
65	C₂×C₃×Dic₆	—	2	8	no	—
66	C₂×C₃×Dic₆	C₂²×C₃	1	8	yes	—
67	C₃²×Q₁₆	—	2	16	no	—
68	C₃²×Q₁₆	—	3	8	no	—
69	C₃²×Q₁₆	—	3	4	no	—
70	C₃²×Q₁₆	C₂×D₃	1	4	yes	direct product factor
71	C₃²×Q₁₆	C₂²×C₃	1	16	yes	complemented
72	C₂×C₃²×C₈	—	2	4	no	—
73	C₂×C₃²×C₈	—	3	1	no	—
74	C₂×C₃²×C₈	—	3	4	no	—
75	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
76	C₂×C₃²×C₈	C₂²×C₃	1	4	yes	—
77	C₃×#216	C₂²×C₃	1	32	yes	complemented
78	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	4	yes	—
79	C₃×Dic₁₂	C₂²×C₃	1	16	yes	complemented
80	C₃×D₃×C₈	C₂²×C₃	1	16	yes	—
81	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃²×D₃	Q₁₆	1	4	yes	direct product factor
83	C₂×C₃²×D₃	C₂×D₄	1	2	yes	—
84	C₃³×C₄	—	2	4	no	—
85	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
86	C₃³×C₄	C₂⁴	1	1	yes	characteristic
87	C₃²×Dic₃	—	2	4	no	—
88	C₃²×Dic₃	C₂×D₄	1	2	yes	—
89	C₂²×C₃×Q₈	—	3	8	no	—
90	C₂×D₃×Q₈	C₂×C₃²	1	2	yes	—
91	C₂×C₃×Q₁₆	—	2	4	no	—
92	C₂×C₃×Q₁₆	—	3	8	no	—
93	C₂×C₃×Q₁₆	—	3	32	no	—
94	C₂×C₃×Q₁₆	—	3	4	no	—
95	C₂×C₃×Q₁₆	C₃×D₃	1	4	yes	direct product factor
96	C₂×C₃×Q₁₆	C₂×C₃²	1	1	yes	characteristic, complemented
97	C₂²×C₃×C₈	—	3	4	no	—
98	C₂×#216	C₂×C₃²	1	2	yes	complemented
99	D₃×Q₁₆	C₂×C₃²	1	8	yes	direct product factor
100	C₂×Dic₁₂	C₂×C₃²	1	1	yes	characteristic, complemented
101	C₂×D₃×C₈	C₂×C₃²	1	1	yes	characteristic
102	C₂³×C₃²	—	3	1	no	—
103	C₂²×C₃×D₃	C₃×D₄	1	4	yes	—
104	C₃²×Q₈	—	2	2	no	—
105	C₃²×Q₈	—	2	16	no	—
106	C₃²×Q₈	—	2	8	no	—
107	C₃²×Q₈	—	3	4	no	—
108	C₃²×Q₈	—	4	8	no	—
109	C₃²×Q₈	—	6	8	no	—
110	C₃²×Q₈	—	6	2	no	—
111	C₃²×Q₈	C₂²×D₃	1	4	yes	—
112	C₃²×Q₈	C₂³×C₃	1	16	yes	—
113	C₂×C₃²×C₄	—	2	2	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	—	2	8	no	—
116	C₂×C₃²×C₄	—	3	1	no	—
117	C₂×C₃²×C₄	—	3	2	no	—
118	C₂×C₃²×C₄	—	3	2	no	—
119	C₂×C₃²×C₄	—	4	8	no	—
120	C₂×C₃²×C₄	—	6	8	no	—
121	C₂×C₃²×C₄	—	6	2	no	—
122	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
123	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
124	C₂×C₃×Dic₃	—	2	8	no	—
125	C₂×C₃×Dic₃	C₃×D₄	1	4	yes	—
126	C₃×C₄×D₃	—	2	32	no	—
127	C₃×C₄×D₃	C₃×D₄	1	8	yes	—
128	C₃×C₄×D₃	C₂³×C₃	1	8	yes	—
129	C₃×Dic₆	—	2	8	no	—
130	C₃×Dic₆	—	2	32	no	—
131	C₃×Dic₆	C₂³×C₃	1	16	yes	—
132	C₃²×C₈	—	2	8	no	—
133	C₃²×C₈	—	3	2	no	—
134	C₃²×C₈	C₂²×D₃	1	2	yes	—
135	C₃²×C₈	C₂³×C₃	1	8	yes	—
136	C₃×C₃⋊C₈	C₂³×C₃	1	8	yes	—
137	C₂²×Q₁₆	—	3	1	no	Sylow
138	C₂×C₃³	C₂×Q₁₆	1	2	yes	complemented
139	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
140	C₃²×D₃	C₂×Q₁₆	1	4	yes	direct product factor
141	C₂×C₃×Q₈	—	2	8	no	—
142	C₂×C₃×Q₈	—	3	32	no	—
143	C₂×C₃×Q₈	—	3	8	no	—
144	C₂×C₃×Q₈	—	6	8	no	—
145	C₂×C₃×Q₈	—	6	16	no	—
146	C₂×C₃×Q₈	C₂×C₃×D₃	1	8	yes	—
147	C₂×C₃×Q₈	C₂²×C₃²	1	2	yes	—
148	C₂²×C₃×C₄	—	3	4	no	—
149	C₂²×C₃×C₄	—	6	8	no	—
150	D₃×Q₈	—	2	4	no	—
151	D₃×Q₈	C₂²×C₃²	1	8	yes	—
152	C₂×C₄×D₃	—	2	2	no	—
153	C₂×C₄×D₃	C₂²×C₃²	1	1	yes	characteristic
154	C₂×Dic₆	—	2	2	no	—
155	C₂×Dic₆	C₂²×C₃²	1	2	yes	—
156	C₃×Q₁₆	—	2	16	no	—
157	C₃×Q₁₆	—	3	32	no	—
158	C₃×Q₁₆	—	3	16	no	—
159	C₃×Q₁₆	C₂×C₃×D₃	1	16	yes	direct product factor
160	C₃×Q₁₆	C₂²×C₃²	1	4	yes	complemented
161	C₂×C₃×C₈	—	2	4	no	—
162	C₂×C₃×C₈	—	3	4	no	—
163	C₂×C₃×C₈	—	3	16	no	—
164	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
165	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
166	#216	C₂²×C₃²	1	8	yes	complemented
167	C₂×C₃⋊C₈	C₂²×C₃²	1	1	yes	characteristic
168	Dic₁₂	C₂²×C₃²	1	4	yes	complemented
169	D₃×C₈	C₂²×C₃²	1	4	yes	—
170	C₂²×C₃²	—	2	4	no	—
171	C₂²×C₃²	—	3	4	no	—
172	C₂²×C₃²	—	3	2	no	—
173	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
174	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
175	C₂×C₃×D₃	C₃×Q₁₆	1	16	yes	direct product factor
176	C₂×C₃×D₃	C₂×C₃×D₄	1	8	yes	—
177	C₃²×C₄	—	2	4	no	—
178	C₃²×C₄	—	2	4	no	—
179	C₃²×C₄	—	2	4	no	—
180	C₃²×C₄	—	2	16	no	—
181	C₃²×C₄	—	3	2	no	—
182	C₃²×C₄	—	4	16	no	—
183	C₃²×C₄	—	6	4	no	—
184	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
185	C₃²×C₄	C₂×C₃×D₄	1	4	yes	—
186	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
187	C₃²×C₄	C₂⁴×C₃	1	4	yes	—
188	C₃×Dic₃	—	2	16	no	—
189	C₃×Dic₃	C₂×C₃×D₄	1	8	yes	—
190	C₂²×Q₈	—	3	2	no	—
191	C₂×Q₁₆	—	3	2	no	—
192	C₂×Q₁₆	—	3	8	no	—
193	C₂×Q₁₆	—	3	1	no	—
194	C₂×Q₁₆	C₃²×D₃	1	1	yes	characteristic, direct product factor
195	C₂²×C₈	—	3	1	no	—
196	C₃³	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
197	C₂³×C₃	—	3	4	no	—
198	C₂²×D₃	C₃²×D₄	1	1	yes	characteristic
199	C₃×Q₈	—	2	8	no	—
200	C₃×Q₈	—	2	2	no	—
201	C₃×Q₈	—	2	16	no	—
202	C₃×Q₈	—	3	16	no	—
203	C₃×Q₈	—	4	8	no	—
204	C₃×Q₈	—	6	32	no	—
205	C₃×Q₈	—	6	8	no	—
206	C₃×Q₈	C₂²×C₃×D₃	1	16	yes	—
207	C₃×Q₈	C₂³×C₃²	1	4	yes	—
208	C₂×C₃×C₄	—	2	8	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	3	4	no	—
212	C₂×C₃×C₄	—	3	8	no	—
213	C₂×C₃×C₄	—	3	8	no	—
214	C₂×C₃×C₄	—	4	8	no	—
215	C₂×C₃×C₄	—	6	32	no	—
216	C₂×C₃×C₄	—	6	8	no	—
217	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
218	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
219	C₂×Dic₃	—	2	2	no	—
220	C₂×Dic₃	C₃²×D₄	1	1	yes	characteristic
221	C₄×D₃	—	2	8	no	—
222	C₄×D₃	C₃²×D₄	1	2	yes	—
223	C₄×D₃	C₂³×C₃²	1	2	yes	—
224	Dic₆	—	2	2	no	—
225	Dic₆	—	2	8	no	—
226	Dic₆	C₂³×C₃²	1	4	yes	—
227	C₃×C₈	—	2	8	no	—
228	C₃×C₈	—	3	8	no	—
229	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
230	C₃×C₈	C₂³×C₃²	1	2	yes	—
231	C₃⋊C₈	C₂³×C₃²	1	2	yes	—
232	C₂×C₃²	—	2	8	no	—
233	C₂×C₃²	—	2	4	no	—
234	C₂×C₃²	—	3	4	no	—
235	C₂×C₃²	D₃×Q₁₆	1	2	yes	direct product factor
236	C₂×C₃²	C₂×C₃×Q₁₆	1	8	yes	complemented
237	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
238	C₂×C₃²	C₂²×C₃×D₄	1	4	yes	—
239	C₃×D₃	C₂×C₃×Q₁₆	1	16	yes	direct product factor
240	C₂×Q₈	—	3	8	no	—
241	C₂×Q₈	—	3	2	no	—
242	C₂×Q₈	—	6	2	no	—
243	C₂×Q₈	—	6	4	no	—
244	C₂×Q₈	C₂×C₃²×D₃	1	2	yes	—
245	C₂²×C₄	—	3	1	no	—
246	C₂²×C₄	—	6	2	no	—
247	Q₁₆	—	3	8	no	—
248	Q₁₆	—	3	4	no	—
249	Q₁₆	C₂×C₃²×D₃	1	4	yes	direct product factor
250	C₂×C₈	—	3	1	no	—
251	C₂×C₈	—	3	4	no	—
252	C₂×C₈	C₂×C₃²×D₃	1	1	yes	characteristic
253	C₂²×C₃	—	2	4	no	—
254	C₂²×C₃	—	3	16	no	—
255	C₂²×C₃	—	3	8	no	—
256	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
257	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
258	C₂×D₃	C₃²×Q₁₆	1	4	yes	direct product factor
259	C₂×D₃	C₂×C₃²×D₄	1	2	yes	—
260	C₃×C₄	—	2	16	no	—
261	C₃×C₄	—	2	4	no	—
262	C₃×C₄	—	2	4	no	—
263	C₃×C₄	—	2	4	no	—
264	C₃×C₄	—	3	8	no	—
265	C₃×C₄	—	4	16	no	—
266	C₃×C₄	—	6	16	no	—
267	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
268	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
269	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
270	C₃×C₄	C₂⁴×C₃²	1	1	yes	characteristic
271	Dic₃	—	2	4	no	—
272	Dic₃	C₂×C₃²×D₄	1	2	yes	—
273	C₃²	—	2	4	no	—
274	C₃²	C₂×D₃×Q₁₆	1	1	yes	characteristic, direct product factor
275	C₃²	C₂²×C₃×Q₁₆	1	4	yes	complemented
276	C₂³	—	3	1	no	—
277	Q₈	—	2	2	no	—
278	Q₈	—	3	4	no	—
279	Q₈	—	6	8	no	—
280	Q₈	—	6	2	no	—
281	Q₈	C₂²×C₃²×D₃	1	4	yes	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	3	1	no	—
284	C₂×C₄	—	3	2	no	—
285	C₂×C₄	—	3	2	no	—
286	C₂×C₄	—	6	8	no	—
287	C₂×C₄	—	6	2	no	—
288	C₂×C₄	C₂²×C₃²×D₃	1	1	yes	characteristic
289	C₈	—	3	2	no	—
290	C₈	C₂²×C₃²×D₃	1	2	yes	—
291	C₂×C₃	—	2	8	no	—
292	C₂×C₃	—	2	4	no	—
293	C₂×C₃	—	3	16	no	—
294	C₂×C₃	C₃×D₃×Q₁₆	1	8	yes	direct product factor
295	C₂×C₃	C₂×C₃²×Q₁₆	1	2	yes	complemented
296	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
297	C₂×C₃	C₂²×C₃²×D₄	1	1	yes	characteristic
298	D₃	C₂×C₃²×Q₁₆	1	4	yes	direct product factor
299	C₂²	—	3	4	no	—
300	C₂²	—	3	2	no	—
301	C₂²	C₃²×D₃×D₄	1	1	yes	characteristic
302	C₄	—	2	4	no	—
303	C₄	—	3	2	no	—
304	C₄	—	6	4	no	—
305	C₄	C₃²×D₃×D₄	1	1	yes	characteristic
306	C₄	C₂³×C₃²×D₃	1	1	yes	characteristic
307	C₃	—	2	4	no	—
308	C₃	C₂×C₃×D₃×Q₁₆	1	4	yes	direct product factor
309	C₃	C₂²×C₃²×Q₁₆	1	1	yes	characteristic, complemented
310	C₂	—	3	4	no	—
311	C₂	C₃²×D₃×Q₁₆	1	2	yes	direct product factor
312	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×Q₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂²×C₃²×D₃	D₄
hypercenter	C₂×C₃²×Q₁₆	D₃
hypocenter	C₃	C₂²×C₃²×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃² ◁ C₂×C₃²×C₄ ◁ C₂×C₃²×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×Q₁₆	C₂	semidirect
3. C₂×C₃²×#216	C₂	semidirect
4. C₃²×D₃×Q₁₆	C₂	direct (N × H)
5. C₂×C₃²×Dic₁₂	C₂	semidirect
8. C₂×C₃×D₃×Q₁₆	C₃	direct (N × H)
16. C₃³×Q₁₆	C₂²	semidirect
18. C₃²×#216	C₂²	semidirect
20. C₃²×Dic₁₂	C₂²	semidirect
28. C₂×C₃²×Q₁₆	D₃	direct (N × H)
29. C₂×C₃²×Q₁₆	C₂×C₃	semidirect
31. C₂×C₃×#216	C₂×C₃	semidirect
32. C₃×D₃×Q₁₆	C₂×C₃	direct (N × H)
33. C₂×C₃×Dic₁₂	C₂×C₃	semidirect
51. C₂×D₃×Q₁₆	C₃²	direct (N × H)
70. C₃²×Q₁₆	C₂×D₃	direct (N × H)
71. C₃²×Q₁₆	C₂²×C₃	semidirect
77. C₃×#216	C₂²×C₃	semidirect
79. C₃×Dic₁₂	C₂²×C₃	semidirect
82. C₂×C₃²×D₃	Q₁₆	direct (N × H)
95. C₂×C₃×Q₁₆	C₃×D₃	direct (N × H)
96. C₂×C₃×Q₁₆	C₂×C₃²	semidirect
98. C₂×#216	C₂×C₃²	semidirect
99. D₃×Q₁₆	C₂×C₃²	direct (N × H)
100. C₂×Dic₁₂	C₂×C₃²	semidirect
138. C₂×C₃³	C₂×Q₁₆	semidirect
140. C₃²×D₃	C₂×Q₁₆	direct (N × H)
159. C₃×Q₁₆	C₂×C₃×D₃	direct (N × H)
160. C₃×Q₁₆	C₂²×C₃²	semidirect
166. #216	C₂²×C₃²	semidirect
168. Dic₁₂	C₂²×C₃²	semidirect
175. C₂×C₃×D₃	C₃×Q₁₆	direct (N × H)
194. C₂×Q₁₆	C₃²×D₃	direct (N × H)
196. C₃³	C₂²×Q₁₆	semidirect
235. C₂×C₃²	D₃×Q₁₆	direct (N × H)
236. C₂×C₃²	C₂×C₃×Q₁₆	semidirect
239. C₃×D₃	C₂×C₃×Q₁₆	direct (N × H)
249. Q₁₆	C₂×C₃²×D₃	direct (N × H)
258. C₂×D₃	C₃²×Q₁₆	direct (N × H)
274. C₃²	C₂×D₃×Q₁₆	direct (N × H)
275. C₃²	C₂²×C₃×Q₁₆	semidirect
294. C₂×C₃	C₃×D₃×Q₁₆	direct (N × H)
295. C₂×C₃	C₂×C₃²×Q₁₆	semidirect
298. D₃	C₂×C₃²×Q₁₆	direct (N × H)
308. C₃	C₂×C₃×D₃×Q₁₆	direct (N × H)
309. C₃	C₂²×C₃²×Q₁₆	semidirect
311. C₂	C₃²×D₃×Q₁₆	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×C₃³×Q₁₆	2
C₂×C₃²×#216	2
C₃²×D₃×Q₁₆	2
C₂×C₃²×Dic₁₂	2
C₂×C₃²×D₃×C₈	2
C₂²×C₃²×Q₁₆	3
C₂×C₃×D₃×Q₁₆	3

Subgroups — C2×C32×D3×Q16 #13179140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₃×Q₁₆ #13179140