Subgroups — C₂×C₃×#64128 #13179516

Order 1728.

1836 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3832	C₂	1	2	yes	maximal, complemented
2	C₂×C₃³×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3755	C₂	1	2	yes	maximal, complemented
4	C₃×#64128	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#3745	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₈×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#64128	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#919	—	3	4	no	maximal
9	C₂×C₃³×Q₈	C₂²	1	2	yes	—
10	C₃×#3832	—	2	4	no	—
11	C₃×#3832	C₂²	1	8	yes	complemented
12	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
14	C₂×C₃×C₄×C₃⋊D₃	—	2	2	no	—
15	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	1	yes	characteristic
16	C₃³×Q₁₆	C₂²	1	4	yes	complemented
17	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
18	C₃×#3755	C₂²	1	8	yes	complemented
19	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₃×#3745	C₂²	1	4	yes	complemented
21	C₃×C₈×C₃⋊D₃	C₂²	1	4	yes	complemented
22	C₂×#3832	C₂×C₃	1	2	yes	complemented
23	C₂×C₃×#239	—	3	8	no	—
24	C₂×C₃²×Q₁₆	—	2	4	no	—
25	C₂×C₃²×Q₁₆	D₃	1	4	yes	complemented
26	C₂×C₃²×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×#3755	C₂×C₃	1	2	yes	complemented
28	#64128	C₂×C₃	1	8	yes	direct product factor
29	C₂×#3745	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₈×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×C₃×#215	—	3	8	no	—
32	C₃×#919	—	3	32	no	—
33	C₂×C₃×D₂₄	—	3	4	no	—
34	C₂×C₃×D₃×C₈	—	3	4	no	—
35	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
36	C₂²×C₃×C₃⋊D₃	D₄	1	1	yes	characteristic
37	C₃³×Q₈	—	2	2	no	—
38	C₃³×Q₈	C₂³	1	4	yes	—
39	C₂×C₃³×C₄	—	2	2	no	—
40	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
41	C₂×C₃×C₃⋊Dic₃	D₄	1	1	yes	characteristic
42	C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
43	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
44	C₃×C₄⋊(C₃⋊D₃)	C₂³	1	4	yes	—
45	C₃×C₄×C₃⋊D₃	—	2	8	no	—
46	C₃×C₄×C₃⋊D₃	D₄	1	2	yes	—
47	C₃×C₄×C₃⋊D₃	C₂³	1	2	yes	—
48	C₃³×C₈	C₂³	1	2	yes	—
49	C₃×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
50	C₂×C₃×#135	—	9	1	no	—
51	C₂×#919	—	3	4	no	—
52	C₂×C₃²×Q₈	—	2	8	no	—
53	C₂×C₃²×Q₈	C₂×D₃	1	8	yes	—
54	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
55	#3832	—	2	4	no	—
56	#3832	C₂²×C₃	1	8	yes	complemented
57	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
58	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
59	C₂×C₄×C₃⋊D₃	—	2	2	no	—
60	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
61	C₃×#239	—	3	32	no	—
62	C₃×#239	—	6	16	no	—
63	C₂×C₃×D₁₂	—	3	8	no	—
64	C₂×C₃×D₁₂	—	6	8	no	—
65	C₂×C₃×C₄×D₃	—	3	4	no	—
66	C₂×C₃×C₄×D₃	—	6	8	no	—
67	C₃²×Q₁₆	—	2	16	no	—
68	C₃²×Q₁₆	C₂×D₃	1	16	yes	complemented
69	C₃²×Q₁₆	C₂²×C₃	1	4	yes	complemented
70	C₂×C₃²×C₈	—	2	4	no	—
71	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
72	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
73	#3755	C₂²×C₃	1	8	yes	complemented
74	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
75	#3745	C₂²×C₃	1	4	yes	complemented
76	C₈×C₃⋊D₃	C₂²×C₃	1	4	yes	complemented
77	C₃×#215	—	3	32	no	—
78	C₂×C₃×C₃⋊C₈	—	3	4	no	—
79	C₃×D₂₄	—	3	16	no	—
80	C₃×D₃×C₈	—	3	16	no	—
81	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×C₃⋊D₃	—	2	2	no	—
83	C₂×C₃×C₃⋊D₃	—	2	4	no	—
84	C₂×C₃×C₃⋊D₃	—	4	4	no	—
85	C₂×C₃×C₃⋊D₃	C₂×D₄	1	2	yes	—
86	C₃³×C₄	—	2	4	no	—
87	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
88	C₃³×C₄	C₂⁴	1	1	yes	characteristic
89	C₃×C₃⋊Dic₃	C₂×D₄	1	2	yes	—
90	C₂×C₃×#41	—	9	2	no	—
91	C₂×#239	—	3	8	no	—
92	C₃×#135	—	9	8	no	—
93	C₂×C₃×Q₁₆	—	2	4	no	—
94	C₂×C₃×Q₁₆	C₃×D₃	1	4	yes	complemented
95	C₂×C₃×Q₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
96	C₂×C₃×SD₁₆	—	9	2	no	—
97	C₂×C₃×D₈	—	9	1	no	—
98	C₂²×C₃×C₈	—	9	1	no	—
99	C₂×#215	—	3	8	no	—
100	#919	—	3	32	no	—
101	C₂×D₂₄	—	3	4	no	—
102	C₂×D₃×C₈	—	3	4	no	—
103	C₂²×C₃⋊D₃	—	2	2	no	—
104	C₂²×C₃⋊D₃	C₃×D₄	1	1	yes	characteristic
105	C₂²×C₃×D₃	—	3	4	no	—
106	C₂²×C₃×D₃	—	6	8	no	—
107	C₃²×Q₈	—	2	2	no	—
108	C₃²×Q₈	—	2	16	no	—
109	C₃²×Q₈	—	2	8	no	—
110	C₃²×Q₈	—	4	8	no	—
111	C₃²×Q₈	C₂²×D₃	1	16	yes	—
112	C₃²×Q₈	C₂³×C₃	1	4	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	—	4	8	no	—
117	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
118	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
119	C₂×C₃⋊Dic₃	C₃×D₄	1	1	yes	characteristic
120	C₄⋊(C₃⋊D₃)	—	2	8	no	—
121	C₄⋊(C₃⋊D₃)	—	2	2	no	—
122	C₄⋊(C₃⋊D₃)	C₂³×C₃	1	4	yes	—
123	C₄×C₃⋊D₃	—	2	8	no	—
124	C₄×C₃⋊D₃	C₃×D₄	1	2	yes	—
125	C₄×C₃⋊D₃	C₂³×C₃	1	2	yes	—
126	C₂×C₃×Dic₃	—	3	4	no	—
127	C₃×D₁₂	—	3	16	no	—
128	C₃×D₁₂	—	6	32	no	—
129	C₃×D₁₂	—	6	8	no	—
130	C₃×C₄×D₃	—	3	8	no	—
131	C₃×C₄×D₃	—	3	8	no	—
132	C₃×C₄×D₃	—	6	32	no	—
133	C₃²×C₈	—	2	8	no	—
134	C₃²×C₈	C₂²×D₃	1	8	yes	—
135	C₃²×C₈	C₂³×C₃	1	2	yes	—
136	C₃⋊(C₃⋊C₈)	C₂³×C₃	1	2	yes	—
137	C₃×C₃⋊C₈	—	3	8	no	—
138	C₂×#135	—	9	1	no	Sylow
139	C₂×C₃³	#135	1	2	yes	complemented
140	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
141	C₃×C₃⋊D₃	—	2	2	no	—
142	C₃×C₃⋊D₃	—	4	4	no	—
143	C₃×#41	—	9	8	no	—
144	C₃×#41	—	18	4	no	—
145	C₂×C₃×Q₈	—	2	8	no	—
146	C₂×C₃×Q₈	C₂×C₃×D₃	1	8	yes	—
147	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	2	yes	—
148	C₂×C₃×D₄	—	9	2	no	—
149	C₂×C₃×D₄	—	18	2	no	—
150	C₂²×C₃×C₄	—	9	1	no	—
151	C₂²×C₃×C₄	—	18	2	no	—
152	#239	—	3	32	no	—
153	#239	—	6	16	no	—
154	C₂×D₁₂	—	3	8	no	—
155	C₂×D₁₂	—	6	8	no	—
156	C₂×C₄×D₃	—	3	4	no	—
157	C₂×C₄×D₃	—	6	8	no	—
158	C₃×Q₁₆	—	2	16	no	—
159	C₃×Q₁₆	C₂×C₃×D₃	1	16	yes	complemented
160	C₃×Q₁₆	C₂×C₃⋊D₃	1	4	yes	complemented
161	C₃×SD₁₆	—	9	8	no	—
162	C₃×D₈	—	9	4	no	—
163	C₂×C₃×C₈	—	2	4	no	—
164	C₂×C₃×C₈	—	9	1	no	—
165	C₂×C₃×C₈	—	9	4	no	—
166	C₂×C₃×C₈	C₂×C₃×D₃	1	4	yes	—
167	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
168	#215	—	3	32	no	—
169	C₂×C₃⋊C₈	—	3	4	no	—
170	D₂₄	—	3	16	no	—
171	D₃×C₈	—	3	16	no	—
172	C₂²×C₃²	—	2	4	no	—
173	C₂²×C₃²	D₃×D₄	1	4	yes	—
174	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
175	C₂×C₃⋊D₃	—	2	2	no	—
176	C₂×C₃⋊D₃	—	2	4	no	—
177	C₂×C₃⋊D₃	—	4	4	no	—
178	C₂×C₃⋊D₃	C₂×C₃×D₄	1	2	yes	—
179	C₂×C₃×D₃	—	3	8	no	—
180	C₂×C₃×D₃	—	6	8	no	—
181	C₂×C₃×D₃	—	6	16	no	—
182	C₂×C₃×D₃	—	12	16	no	—
183	C₃²×C₄	—	2	4	no	—
184	C₃²×C₄	—	2	4	no	—
185	C₃²×C₄	—	2	4	no	—
186	C₃²×C₄	—	2	16	no	—
187	C₃²×C₄	—	4	16	no	—
188	C₃²×C₄	D₃×D₄	1	4	yes	—
189	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
190	C₃²×C₄	C₂³×D₃	1	4	yes	—
191	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
192	C₃⋊Dic₃	C₂×C₃×D₄	1	2	yes	—
193	C₃×Dic₃	—	3	8	no	—
194	C₂×#41	—	9	2	no	—
195	#135	—	9	8	no	—
196	C₂×Q₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
197	C₂×SD₁₆	—	9	2	no	—
198	C₂×D₈	—	9	1	no	—
199	C₂²×C₈	—	9	1	no	—
200	C₃³	C₂×#135	1	1	yes	characteristic, complemented, Sylow
201	C₂³×C₃	—	9	1	no	—
202	C₂³×C₃	—	18	2	no	—
203	C₂²×D₃	—	3	4	no	—
204	C₂²×D₃	—	6	8	no	—
205	C₃×Q₈	—	2	8	no	—
206	C₃×Q₈	—	2	2	no	—
207	C₃×Q₈	—	2	16	no	—
208	C₃×Q₈	—	4	8	no	—
209	C₃×Q₈	C₂²×C₃×D₃	1	16	yes	—
210	C₃×Q₈	C₂²×C₃⋊D₃	1	4	yes	—
211	C₃×D₄	—	9	4	no	—
212	C₃×D₄	—	18	8	no	—
213	C₃×D₄	—	18	2	no	—
214	C₂×C₃×C₄	—	2	8	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	4	8	no	—
218	C₂×C₃×C₄	—	9	1	no	—
219	C₂×C₃×C₄	—	9	2	no	—
220	C₂×C₃×C₄	—	9	2	no	—
221	C₂×C₃×C₄	—	18	8	no	—
222	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
223	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
224	C₂×Dic₃	—	3	4	no	—
225	D₁₂	—	3	16	no	—
226	D₁₂	—	6	32	no	—
227	D₁₂	—	6	8	no	—
228	C₄×D₃	—	3	8	no	—
229	C₄×D₃	—	3	8	no	—
230	C₄×D₃	—	6	32	no	—
231	C₃×C₈	—	2	8	no	—
232	C₃×C₈	—	9	2	no	—
233	C₃×C₈	C₂²×C₃×D₃	1	8	yes	—
234	C₃×C₈	C₂²×C₃⋊D₃	1	2	yes	—
235	C₃⋊C₈	—	3	8	no	—
236	C₂×C₃²	—	2	8	no	—
237	C₂×C₃²	—	2	4	no	—
238	C₂×C₃²	#919	1	8	yes	complemented
239	C₂×C₃²	C₃×#135	1	2	yes	complemented
240	C₂×C₃²	C₂×D₃×D₄	1	4	yes	—
241	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
242	C₃⋊D₃	—	2	2	no	—
243	C₃⋊D₃	—	4	4	no	—
244	C₃×D₃	—	6	8	no	—
245	C₃×D₃	—	12	16	no	—
246	#41	—	9	8	no	—
247	#41	—	18	4	no	—
248	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
249	C₂×D₄	—	9	2	no	—
250	C₂×D₄	—	18	2	no	—
251	C₂²×C₄	—	9	1	no	—
252	C₂²×C₄	—	18	2	no	—
253	Q₁₆	C₂×C₃×C₃⋊D₃	1	4	yes	complemented
254	SD₁₆	—	9	8	no	—
255	D₈	—	9	4	no	—
256	C₂×C₈	—	9	1	no	—
257	C₂×C₈	—	9	4	no	—
258	C₂×C₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
259	C₂²×C₃	—	2	4	no	—
260	C₂²×C₃	—	9	2	no	—
261	C₂²×C₃	—	18	2	no	—
262	C₂²×C₃	—	18	4	no	—
263	C₂²×C₃	—	36	4	no	—
264	C₂²×C₃	C₃×D₃×D₄	1	4	yes	—
265	C₂²×C₃	D₄×C₃⋊D₃	1	1	yes	characteristic
266	C₂×D₃	—	3	8	no	—
267	C₂×D₃	—	6	8	no	—
268	C₂×D₃	—	6	16	no	—
269	C₂×D₃	—	12	16	no	—
270	C₃×C₄	—	2	16	no	—
271	C₃×C₄	—	2	4	no	—
272	C₃×C₄	—	2	4	no	—
273	C₃×C₄	—	2	4	no	—
274	C₃×C₄	—	4	16	no	—
275	C₃×C₄	—	9	2	no	—
276	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
277	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
278	C₃×C₄	C₂³×C₃×D₃	1	4	yes	—
279	C₃×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
280	Dic₃	—	3	8	no	—
281	C₃²	—	2	4	no	—
282	C₃²	C₂×#919	1	4	yes	complemented
283	C₃²	C₂×C₃×#135	1	1	yes	characteristic, complemented
284	C₂³	—	9	1	no	—
285	C₂³	—	18	2	no	—
286	Q₈	—	2	2	no	—
287	Q₈	C₂²×C₃×C₃⋊D₃	1	4	yes	—
288	D₄	—	9	4	no	—
289	D₄	—	18	8	no	—
290	D₄	—	18	2	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	9	1	no	—
293	C₂×C₄	—	9	2	no	—
294	C₂×C₄	—	9	2	no	—
295	C₂×C₄	—	18	8	no	—
296	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
297	C₈	—	9	2	no	—
298	C₈	C₂²×C₃×C₃⋊D₃	1	2	yes	—
299	C₂×C₃	—	2	8	no	—
300	C₂×C₃	—	2	4	no	—
301	C₂×C₃	—	18	2	no	—
302	C₂×C₃	—	36	4	no	—
303	C₂×C₃	C₃×#919	1	8	yes	complemented
304	C₂×C₃	#64128	1	2	yes	direct product factor
305	C₂×C₃	C₂×C₃×D₃×D₄	1	4	yes	—
306	C₂×C₃	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
307	D₃	—	6	8	no	—
308	D₃	—	12	16	no	—
309	C₂²	—	9	2	no	—
310	C₂²	—	18	2	no	—
311	C₂²	—	18	4	no	—
312	C₂²	—	36	4	no	—
313	C₂²	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
314	C₄	—	2	4	no	—
315	C₄	—	9	2	no	—
316	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
317	C₄	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
318	C₃	—	2	4	no	—
319	C₃	C₂×C₃×#919	1	4	yes	complemented
320	C₃	C₂×#64128	1	1	yes	characteristic, direct product factor
321	C₂	—	18	2	no	—
322	C₂	—	36	4	no	—
323	C₂	C₃×#64128	1	2	yes	direct product factor
324	C₂	C₂×C₃×D₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₄×C₃⋊D₃
commutator, cosocle	C₃²×C₄	C₂⁴×C₃
Frattini	C₄	C₂³×C₃×C₃⋊D₃
Fitting	C₂×C₃³×Q₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
hypercenter	C₂×C₃×Q₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×C₃×#135
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#3832	C₂	semidirect
2. C₂×C₃³×Q₁₆	C₂	semidirect
3. C₂×C₃×#3755	C₂	semidirect
4. C₃×#64128	C₂	direct (N × H)
5. C₂×C₃×#3745	C₂	semidirect
6. C₂×C₃×C₈×C₃⋊D₃	C₂	semidirect
7. C₂×#64128	C₃	direct (N × H)
11. C₃×#3832	C₂²	semidirect
16. C₃³×Q₁₆	C₂²	semidirect
18. C₃×#3755	C₂²	semidirect
20. C₃×#3745	C₂²	semidirect
21. C₃×C₈×C₃⋊D₃	C₂²	semidirect
22. C₂×#3832	C₂×C₃	semidirect
25. C₂×C₃²×Q₁₆	D₃	semidirect
26. C₂×C₃²×Q₁₆	C₂×C₃	semidirect
27. C₂×#3755	C₂×C₃	semidirect
28. #64128	C₂×C₃	direct (N × H)
29. C₂×#3745	C₂×C₃	semidirect
30. C₂×C₈×C₃⋊D₃	C₂×C₃	semidirect
56. #3832	C₂²×C₃	semidirect
68. C₃²×Q₁₆	C₂×D₃	semidirect
69. C₃²×Q₁₆	C₂²×C₃	semidirect
73. #3755	C₂²×C₃	semidirect
75. #3745	C₂²×C₃	semidirect
76. C₈×C₃⋊D₃	C₂²×C₃	semidirect
94. C₂×C₃×Q₁₆	C₃×D₃	semidirect
95. C₂×C₃×Q₁₆	C₃⋊D₃	semidirect
139. C₂×C₃³	#135	semidirect
159. C₃×Q₁₆	C₂×C₃×D₃	semidirect
160. C₃×Q₁₆	C₂×C₃⋊D₃	semidirect
196. C₂×Q₁₆	C₃×C₃⋊D₃	semidirect
200. C₃³	C₂×#135	semidirect
238. C₂×C₃²	#919	semidirect
239. C₂×C₃²	C₃×#135	semidirect
253. Q₁₆	C₂×C₃×C₃⋊D₃	semidirect
282. C₃²	C₂×#919	semidirect
283. C₃²	C₂×C₃×#135	semidirect
303. C₂×C₃	C₃×#919	semidirect
304. C₂×C₃	#64128	direct (N × H)
319. C₃	C₂×C₃×#919	semidirect
320. C₃	C₂×#64128	direct (N × H)
323. C₂	C₃×#64128	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×C₃×#3832	2
C₂×C₃³×Q₁₆	2
C₂×C₃×#3755	2
C₃×#64128	2
C₂×C₃×#3745	2
C₂×C₃×C₈×C₃⋊D₃	2
C₂×#64128	3
C₂×C₃×#919	3

Subgroups — C2×C3×#64128 #13179516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#64128 #13179516