Subgroups — C₂³×D₃×D₁₂ #11919167

Order 1152.

21785 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃²	C₂	1	2	yes	maximal, complemented
2	C₂³×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×#626	C₂	1	2	yes	maximal, complemented
6	C₂²×D₃×D₁₂	C₂	1	56	yes	maximal, direct product factor
7	C₂³×D₃×D₄	—	3	1	no	maximal
8	C₂⁴×D₁₂	—	3	1	no	maximal
9	C₂⁴×C₃⋊D₃	C₂²	1	2	yes	complemented
10	C₂⁴×C₃×D₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₃×D₃	C₂²	1	2	yes	complemented
12	C₂³×D₃²	—	2	32	no	—
13	C₂³×D₃²	C₂²	1	56	yes	complemented
14	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic, complemented
15	C₂²×C₄⋊(C₃⋊D₃)	C₂²	1	28	yes	complemented
16	C₂³×C₃×Dic₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₃×D₁₂	C₂²	1	28	yes	complemented
18	C₂²×C₃×C₄×D₃	C₂²	1	28	yes	complemented
19	C₂²×#626	C₂²	1	56	yes	complemented
20	C₂×D₃×D₁₂	C₂²	1	448	yes	direct product factor
21	C₂⁵×D₃	—	3	2	no	—
22	C₂⁵×D₃	—	3	2	no	—
23	C₂³×C₃×D₄	—	3	1	no	—
24	C₂⁴×C₃×C₄	—	3	1	no	—
25	C₂³×#67	—	3	2	no	—
26	C₂²×D₃×D₄	—	3	56	no	—
27	C₂³×D₁₂	—	3	2	no	—
28	C₂³×D₁₂	—	3	1	no	—
29	C₂³×D₁₂	—	3	1	no	—
30	C₂³×D₁₂	—	3	56	no	—
31	C₂³×D₁₂	—	6	1	no	—
32	C₂³×D₁₂	D₃	1	1	yes	characteristic, direct product factor
33	C₂³×C₄×D₃	D₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
35	C₂³×C₃⋊D₃	—	2	16	no	—
36	C₂³×C₃⋊D₃	C₂³	1	28	yes	complemented
37	C₂³×C₃×D₃	—	2	16	no	—
38	C₂³×C₃×D₃	D₄	1	16	yes	complemented
39	C₂³×C₃×D₃	C₂³	1	14	yes	—
40	C₂³×C₃×D₃	C₂³	1	28	yes	complemented
41	C₂²×D₃²	—	2	448	no	—
42	C₂²×D₃²	C₂³	1	224	yes	complemented
43	C₂²×C₃²×C₄	C₂³	1	14	yes	complemented
44	C₂×C₄⋊(C₃⋊D₃)	C₂³	1	112	yes	complemented
45	C₂²×C₃×Dic₃	C₂³	1	14	yes	complemented
46	C₂×C₃×D₁₂	C₂³	1	112	yes	complemented
47	C₂×C₃×C₄×D₃	C₂³	1	112	yes	complemented
48	C₂×#626	C₂³	1	224	yes	complemented
49	D₃×D₁₂	C₂³	1	512	yes	direct product factor
50	C₂⁴×D₄	—	9	1	no	Sylow
51	C₂⁵×C₃	—	3	1	no	—
52	C₂⁵×C₃	—	3	2	no	—
53	C₂⁴×D₃	—	3	2	no	—
54	C₂⁴×D₃	—	3	2	no	—
55	C₂⁴×D₃	—	3	56	no	—
56	C₂⁴×D₃	—	3	56	no	—
57	C₂⁴×D₃	—	6	2	no	—
58	C₂⁴×D₃	—	6	32	no	—
59	C₂⁴×D₃	—	6	32	no	—
60	C₂⁴×D₃	C₂×D₃	1	1	yes	characteristic
61	C₂⁴×D₃	C₂×D₃	1	2	yes	complemented
62	C₂²×C₃×D₄	—	3	28	no	—
63	C₂³×C₃×C₄	—	2	1	no	—
64	C₂³×C₃×C₄	—	3	1	no	—
65	C₂³×C₃×C₄	—	3	28	no	—
66	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
67	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic, complemented
68	C₂²×#67	—	3	56	no	—
69	C₂³×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
70	C₂×D₃×D₄	—	3	448	no	—
71	C₂²×D₁₂	—	3	56	no	—
72	C₂²×D₁₂	—	3	28	no	—
73	C₂²×D₁₂	—	3	28	no	—
74	C₂²×D₁₂	—	3	448	no	—
75	C₂²×D₁₂	—	6	28	no	—
76	C₂²×D₁₂	C₂×D₃	1	28	yes	direct product factor
77	C₂²×C₄×D₃	C₂×D₃	1	28	yes	complemented
78	C₂³×C₃²	C₂×D₄	1	8	yes	complemented
79	C₂³×C₃²	C₂⁴	1	7	yes	—
80	C₂²×C₃⋊D₃	—	2	112	no	—
81	C₂²×C₃⋊D₃	C₂⁴	1	56	yes	complemented
82	C₂²×C₃×D₃	—	2	112	no	—
83	C₂²×C₃×D₃	C₂×D₄	1	112	yes	complemented
84	C₂²×C₃×D₃	C₂⁴	1	28	yes	—
85	C₂²×C₃×D₃	C₂⁴	1	56	yes	complemented
86	C₂×D₃²	—	2	896	no	—
87	C₂×D₃²	C₂⁴	1	128	yes	complemented
88	C₂×C₃²×C₄	C₂⁴	1	28	yes	complemented
89	C₄⋊(C₃⋊D₃)	C₂⁴	1	64	yes	complemented
90	C₂×C₃×Dic₃	C₂⁴	1	28	yes	complemented
91	C₃×D₁₂	C₂⁴	1	64	yes	complemented
92	C₃×C₄×D₃	C₂⁴	1	64	yes	complemented
93	#626	C₂⁴	1	128	yes	complemented
94	C₂⁶	—	9	2	no	—
95	C₂³×D₄	—	3	1	no	—
96	C₂³×D₄	—	9	56	no	—
97	C₂³×D₄	—	9	2	no	—
98	C₂³×D₄	—	9	1	no	—
99	C₂⁴×C₄	—	3	1	no	—
100	C₂⁴×C₃	—	2	1	no	—
101	C₂⁴×C₃	—	3	16	no	—
102	C₂⁴×C₃	—	3	14	no	—
103	C₂⁴×C₃	—	3	28	no	—
104	C₂⁴×C₃	—	6	16	no	—
105	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
106	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
107	C₂³×D₃	—	2	16	no	—
108	C₂³×D₃	—	3	28	no	—
109	C₂³×D₃	—	3	28	no	—
110	C₂³×D₃	—	3	224	no	—
111	C₂³×D₃	—	3	224	no	—
112	C₂³×D₃	—	6	28	no	—
113	C₂³×D₃	—	6	448	no	—
114	C₂³×D₃	—	6	16	no	—
115	C₂³×D₃	—	6	16	no	—
116	C₂³×D₃	—	6	448	no	—
117	C₂³×D₃	—	12	16	no	—
118	C₂³×D₃	D₁₂	1	16	yes	direct product factor
119	C₂³×D₃	C₂²×D₃	1	14	yes	—
120	C₂³×D₃	C₂²×D₃	1	28	yes	complemented
121	C₂×C₃×D₄	—	3	112	no	—
122	C₂²×C₃×C₄	—	2	14	no	—
123	C₂²×C₃×C₄	—	3	14	no	—
124	C₂²×C₃×C₄	—	3	112	no	—
125	C₂²×C₃×C₄	C₂²×D₃	1	14	yes	complemented
126	C₂²×C₃×C₄	C₂²×D₃	1	14	yes	complemented
127	C₂×#67	—	3	224	no	—
128	C₂²×Dic₃	C₂²×D₃	1	14	yes	complemented
129	D₃×D₄	—	3	512	no	—
130	C₂×D₁₂	—	3	224	no	—
131	C₂×D₁₂	—	3	112	no	—
132	C₂×D₁₂	—	3	112	no	—
133	C₂×D₁₂	—	3	512	no	—
134	C₂×D₁₂	—	6	112	no	—
135	C₂×D₁₂	C₂²×D₃	1	112	yes	direct product factor
136	C₂×C₄×D₃	C₂²×D₃	1	112	yes	complemented
137	C₂²×C₃²	C₂²×D₄	1	28	yes	complemented
138	C₂²×C₃²	C₂⁵	1	7	yes	—
139	C₂×C₃⋊D₃	—	2	112	no	—
140	C₂×C₃⋊D₃	C₂⁵	1	16	yes	complemented
141	C₂×C₃×D₃	—	2	112	no	—
142	C₂×C₃×D₃	C₂²×D₄	1	112	yes	complemented
143	C₂×C₃×D₃	C₂⁵	1	8	yes	—
144	C₂×C₃×D₃	C₂⁵	1	16	yes	complemented
145	D₃²	—	2	256	no	—
146	C₃²×C₄	C₂⁵	1	8	yes	complemented
147	C₃×Dic₃	C₂⁵	1	8	yes	complemented
148	C₂⁵	—	3	1	no	—
149	C₂⁵	—	3	2	no	—
150	C₂⁵	—	9	56	no	—
151	C₂⁵	—	9	2	no	—
152	C₂⁵	—	18	32	no	—
153	C₂²×D₄	—	3	28	no	—
154	C₂²×D₄	—	9	448	no	—
155	C₂²×D₄	—	9	56	no	—
156	C₂²×D₄	—	9	28	no	—
157	C₂³×C₄	—	3	1	no	—
158	C₂³×C₄	—	3	28	no	—
159	C₂³×C₄	D₃²	1	1	yes	characteristic, complemented
160	C₂³×C₃	—	2	7	no	—
161	C₂³×C₃	—	2	8	no	—
162	C₂³×C₃	—	3	112	no	—
163	C₂³×C₃	—	3	28	no	—
164	C₂³×C₃	—	3	56	no	—
165	C₂³×C₃	—	6	112	no	—
166	C₂³×C₃	C₂×D₁₂	1	8	yes	complemented
167	C₂³×C₃	D₃×D₄	1	8	yes	complemented
168	C₂³×C₃	C₂³×D₃	1	7	yes	—
169	C₂³×C₃	C₂³×D₃	1	7	yes	—
170	C₂²×D₃	—	2	112	no	—
171	C₂²×D₃	—	3	56	no	—
172	C₂²×D₃	—	3	56	no	—
173	C₂²×D₃	—	3	128	no	—
174	C₂²×D₃	—	3	128	no	—
175	C₂²×D₃	—	6	56	no	—
176	C₂²×D₃	—	6	896	no	—
177	C₂²×D₃	—	6	112	no	—
178	C₂²×D₃	—	6	112	no	—
179	C₂²×D₃	—	6	896	no	—
180	C₂²×D₃	—	12	112	no	—
181	C₂²×D₃	C₂×D₁₂	1	112	yes	direct product factor
182	C₂²×D₃	C₂³×D₃	1	28	yes	—
183	C₂²×D₃	C₂³×D₃	1	56	yes	complemented
184	C₃×D₄	—	3	64	no	—
185	C₂×C₃×C₄	—	2	28	no	—
186	C₂×C₃×C₄	—	3	28	no	—
187	C₂×C₃×C₄	—	3	64	no	—
188	C₂×C₃×C₄	C₂³×D₃	1	28	yes	complemented
189	C₂×C₃×C₄	C₂³×D₃	1	28	yes	complemented
190	#67	—	3	128	no	—
191	C₂×Dic₃	C₂³×D₃	1	28	yes	complemented
192	D₁₂	—	3	128	no	—
193	D₁₂	—	3	64	no	—
194	D₁₂	—	3	64	no	—
195	D₁₂	—	6	64	no	—
196	D₁₂	C₂³×D₃	1	64	yes	direct product factor
197	C₄×D₃	C₂³×D₃	1	64	yes	complemented
198	C₂×C₃²	C₂³×D₄	1	14	yes	complemented
199	C₂×C₃²	C₂⁶	1	1	yes	characteristic
200	C₃⋊D₃	—	2	16	no	—
201	C₃×D₃	—	2	16	no	—
202	C₃×D₃	C₂³×D₄	1	16	yes	complemented
203	C₂⁴	—	3	14	no	—
204	C₂⁴	—	3	16	no	—
205	C₂⁴	—	3	28	no	—
206	C₂⁴	—	6	16	no	—
207	C₂⁴	—	9	224	no	—
208	C₂⁴	—	9	28	no	—
209	C₂⁴	—	18	448	no	—
210	C₂⁴	—	18	16	no	—
211	C₂⁴	C₂×D₃²	1	1	yes	characteristic
212	C₂×D₄	—	3	112	no	—
213	C₂×D₄	—	9	512	no	—
214	C₂×D₄	—	9	224	no	—
215	C₂×D₄	—	9	112	no	—
216	C₂²×C₄	—	3	14	no	—
217	C₂²×C₄	—	3	112	no	—
218	C₂²×C₄	C₂×D₃²	1	14	yes	complemented
219	C₂²×C₃	—	2	28	no	—
220	C₂²×C₃	—	2	7	no	—
221	C₂²×C₃	—	3	112	no	—
222	C₂²×C₃	—	3	8	no	—
223	C₂²×C₃	—	3	16	no	—
224	C₂²×C₃	—	6	112	no	—
225	C₂²×C₃	C₂²×D₁₂	1	28	yes	complemented
226	C₂²×C₃	C₂×D₃×D₄	1	28	yes	complemented
227	C₂²×C₃	C₂⁴×D₃	1	7	yes	—
228	C₂²×C₃	C₂⁴×D₃	1	7	yes	—
229	C₂×D₃	—	2	112	no	—
230	C₂×D₃	—	3	16	no	—
231	C₂×D₃	—	3	16	no	—
232	C₂×D₃	—	6	16	no	—
233	C₂×D₃	—	6	256	no	—
234	C₂×D₃	—	6	112	no	—
235	C₂×D₃	—	6	112	no	—
236	C₂×D₃	—	6	256	no	—
237	C₂×D₃	—	12	112	no	—
238	C₂×D₃	C₂²×D₁₂	1	112	yes	direct product factor
239	C₂×D₃	C₂⁴×D₃	1	8	yes	—
240	C₂×D₃	C₂⁴×D₃	1	16	yes	complemented
241	C₃×C₄	—	2	8	no	—
242	C₃×C₄	—	3	8	no	—
243	C₃×C₄	C₂⁴×D₃	1	8	yes	complemented
244	C₃×C₄	C₂⁴×D₃	1	8	yes	complemented
245	Dic₃	C₂⁴×D₃	1	8	yes	complemented
246	C₃²	C₂⁴×D₄	1	1	yes	characteristic, complemented, Sylow
247	C₂³	—	3	112	no	—
248	C₂³	—	3	28	no	—
249	C₂³	—	3	56	no	—
250	C₂³	—	6	112	no	—
251	C₂³	—	9	128	no	—
252	C₂³	—	9	56	no	—
253	C₂³	—	18	896	no	—
254	C₂³	—	18	112	no	—
255	C₂³	D₃×D₁₂	1	8	yes	direct product factor
256	C₂³	C₂²×D₃²	1	7	yes	—
257	D₄	—	3	64	no	—
258	D₄	—	9	128	no	—
259	D₄	—	9	64	no	—
260	C₂×C₄	—	3	28	no	—
261	C₂×C₄	—	3	64	no	—
262	C₂×C₄	C₂²×D₃²	1	28	yes	complemented
263	C₂×C₃	—	2	14	no	—
264	C₂×C₃	—	2	1	no	—
265	C₂×C₃	—	3	16	no	—
266	C₂×C₃	—	6	16	no	—
267	C₂×C₃	C₂³×D₁₂	1	14	yes	complemented
268	C₂×C₃	C₂²×D₃×D₄	1	14	yes	complemented
269	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
270	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
271	D₃	—	2	16	no	—
272	D₃	—	6	16	no	—
273	D₃	—	6	16	no	—
274	D₃	—	12	16	no	—
275	D₃	C₂³×D₁₂	1	16	yes	direct product factor
276	C₂²	—	3	112	no	—
277	C₂²	—	3	8	no	—
278	C₂²	—	3	16	no	—
279	C₂²	—	6	112	no	—
280	C₂²	—	9	16	no	—
281	C₂²	—	18	256	no	—
282	C₂²	—	18	112	no	—
283	C₂²	C₂×D₃×D₁₂	1	28	yes	direct product factor
284	C₂²	C₂³×D₃²	1	7	yes	—
285	C₄	—	3	8	no	—
286	C₄	C₂³×D₃²	1	8	yes	complemented
287	C₃	—	2	1	no	—
288	C₃	C₂⁴×D₁₂	1	1	yes	characteristic, complemented
289	C₃	C₂³×D₃×D₄	1	1	yes	characteristic, complemented
290	C₂	—	3	16	no	—
291	C₂	—	6	16	no	—
292	C₂	—	18	16	no	—
293	C₂	C₂²×D₃×D₁₂	1	14	yes	direct product factor
294	C₂	C₂⁴×D₃²	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃²
commutator, cosocle	C₂×C₃²	C₂⁶
Frattini	C₂	C₂⁴×D₃²
Fitting	C₂³×C₃²×C₄	C₂²
socle	C₂⁴×C₃²	C₂³
hypercenter	C₂³×C₄	D₃²
hypocenter	C₃²	C₂⁴×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₃²	C₂	semidirect
2. C₂³×C₄⋊(C₃⋊D₃)	C₂	semidirect
3. C₂³×C₃×D₁₂	C₂	semidirect
4. C₂³×C₃×C₄×D₃	C₂	semidirect
5. C₂³×#626	C₂	semidirect
6. C₂²×D₃×D₁₂	C₂	direct (N × H)
9. C₂⁴×C₃⋊D₃	C₂²	semidirect
11. C₂⁴×C₃×D₃	C₂²	semidirect
13. C₂³×D₃²	C₂²	semidirect
14. C₂³×C₃²×C₄	C₂²	semidirect
15. C₂²×C₄⋊(C₃⋊D₃)	C₂²	semidirect
16. C₂³×C₃×Dic₃	C₂²	semidirect
17. C₂²×C₃×D₁₂	C₂²	semidirect
18. C₂²×C₃×C₄×D₃	C₂²	semidirect
19. C₂²×#626	C₂²	semidirect
20. C₂×D₃×D₁₂	C₂²	direct (N × H)
32. C₂³×D₁₂	D₃	direct (N × H)
33. C₂³×C₄×D₃	D₃	semidirect
36. C₂³×C₃⋊D₃	C₂³	semidirect
38. C₂³×C₃×D₃	D₄	semidirect
40. C₂³×C₃×D₃	C₂³	semidirect
42. C₂²×D₃²	C₂³	semidirect
43. C₂²×C₃²×C₄	C₂³	semidirect
44. C₂×C₄⋊(C₃⋊D₃)	C₂³	semidirect
45. C₂²×C₃×Dic₃	C₂³	semidirect
46. C₂×C₃×D₁₂	C₂³	semidirect
47. C₂×C₃×C₄×D₃	C₂³	semidirect
48. C₂×#626	C₂³	semidirect
49. D₃×D₁₂	C₂³	direct (N × H)
61. C₂⁴×D₃	C₂×D₃	semidirect
66. C₂³×C₃×C₄	C₂×D₃	semidirect
67. C₂³×C₃×C₄	C₂×D₃	semidirect
69. C₂³×Dic₃	C₂×D₃	semidirect
76. C₂²×D₁₂	C₂×D₃	direct (N × H)
77. C₂²×C₄×D₃	C₂×D₃	semidirect
78. C₂³×C₃²	C₂×D₄	semidirect
81. C₂²×C₃⋊D₃	C₂⁴	semidirect
83. C₂²×C₃×D₃	C₂×D₄	semidirect
85. C₂²×C₃×D₃	C₂⁴	semidirect
87. C₂×D₃²	C₂⁴	semidirect
88. C₂×C₃²×C₄	C₂⁴	semidirect
89. C₄⋊(C₃⋊D₃)	C₂⁴	semidirect
90. C₂×C₃×Dic₃	C₂⁴	semidirect
91. C₃×D₁₂	C₂⁴	semidirect
92. C₃×C₄×D₃	C₂⁴	semidirect
93. #626	C₂⁴	semidirect
118. C₂³×D₃	D₁₂	direct (N × H)
120. C₂³×D₃	C₂²×D₃	semidirect
125. C₂²×C₃×C₄	C₂²×D₃	semidirect
126. C₂²×C₃×C₄	C₂²×D₃	semidirect
128. C₂²×Dic₃	C₂²×D₃	semidirect
135. C₂×D₁₂	C₂²×D₃	direct (N × H)
136. C₂×C₄×D₃	C₂²×D₃	semidirect
137. C₂²×C₃²	C₂²×D₄	semidirect
140. C₂×C₃⋊D₃	C₂⁵	semidirect
142. C₂×C₃×D₃	C₂²×D₄	semidirect
144. C₂×C₃×D₃	C₂⁵	semidirect
146. C₃²×C₄	C₂⁵	semidirect
147. C₃×Dic₃	C₂⁵	semidirect
159. C₂³×C₄	D₃²	semidirect
166. C₂³×C₃	C₂×D₁₂	semidirect
167. C₂³×C₃	D₃×D₄	semidirect
181. C₂²×D₃	C₂×D₁₂	direct (N × H)
183. C₂²×D₃	C₂³×D₃	semidirect
188. C₂×C₃×C₄	C₂³×D₃	semidirect
189. C₂×C₃×C₄	C₂³×D₃	semidirect
191. C₂×Dic₃	C₂³×D₃	semidirect
196. D₁₂	C₂³×D₃	direct (N × H)
197. C₄×D₃	C₂³×D₃	semidirect
198. C₂×C₃²	C₂³×D₄	semidirect
202. C₃×D₃	C₂³×D₄	semidirect
218. C₂²×C₄	C₂×D₃²	semidirect
225. C₂²×C₃	C₂²×D₁₂	semidirect
226. C₂²×C₃	C₂×D₃×D₄	semidirect
238. C₂×D₃	C₂²×D₁₂	direct (N × H)
240. C₂×D₃	C₂⁴×D₃	semidirect
243. C₃×C₄	C₂⁴×D₃	semidirect
244. C₃×C₄	C₂⁴×D₃	semidirect
245. Dic₃	C₂⁴×D₃	semidirect
246. C₃²	C₂⁴×D₄	semidirect
255. C₂³	D₃×D₁₂	direct (N × H)
262. C₂×C₄	C₂²×D₃²	semidirect
267. C₂×C₃	C₂³×D₁₂	semidirect
268. C₂×C₃	C₂²×D₃×D₄	semidirect
275. D₃	C₂³×D₁₂	direct (N × H)
283. C₂²	C₂×D₃×D₁₂	direct (N × H)
286. C₄	C₂³×D₃²	semidirect
288. C₃	C₂⁴×D₁₂	semidirect
289. C₃	C₂³×D₃×D₄	semidirect
293. C₂	C₂²×D₃×D₁₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃²	2
C₂³×C₄⋊(C₃⋊D₃)	2
C₂³×C₃×D₁₂	2
C₂³×C₃×C₄×D₃	2
C₂³×#626	2
C₂²×D₃×D₁₂	2
C₂³×D₃×D₄	3
C₂⁴×D₁₂	3

Subgroups — C23×D3×D12 #11919167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₃×D₁₂ #11919167