Subgroups — C₂³×SD₁₆×D₇₁ #32911228

Order 18176.

13310 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₇₁	C₂	1	1	yes	maximal, characteristic
3	C₂³×#11765854	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×#11765853	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×#11765852	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×SD₁₆×D₇₁	C₂	1	56	yes	maximal, direct product factor
7	C₂³×C₈×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×SD₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁵×D₇₁	—	2	1	no	—
10	C₂³×Dic₁₄₂	—	2	1	no	—
11	C₂³×Dic₁₄₂	C₂²	1	1	yes	characteristic, complemented
12	C₂²×Q₈×D₇₁	—	2	14	no	—
13	C₂²×Q₈×D₇₁	C₂²	1	28	yes	complemented
14	C₂³×D₂₈₄	C₂²	1	1	yes	characteristic
15	C₂³×C₂²⋊D₇₁	—	2	1	no	—
16	C₂²×D₄×D₇₁	—	2	14	no	—
17	C₂²×D₄×D₇₁	C₂²	1	28	yes	—
18	C₂³×C₄×D₇₁	—	2	1	no	—
19	C₂³×C₄×D₇₁	C₂²	1	1	yes	characteristic
20	C₂²×#11765854	C₂²	1	28	yes	complemented
21	C₂²×#11765853	C₂²	1	28	yes	complemented
22	C₂²×#11765852	C₂²	1	28	yes	complemented
23	C₂×SD₁₆×D₇₁	C₂²	1	448	yes	direct product factor
24	C₂³×C₇₁⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₈×D₇₁	C₂²	1	28	yes	complemented
26	C₂³×Q₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
27	C₂³×D₄×C₇₁	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₇₁	C₂²	1	28	yes	complemented
29	C₂³×C₈×C₇₁	C₂²	1	1	yes	characteristic, complemented
30	C₂⁴×D₇₁	—	2	28	no	—
31	C₂⁴×D₇₁	—	2	1	no	—
32	C₂⁴×D₇₁	—	4	16	no	—
33	C₂⁴×D₇₁	D₄	1	1	yes	characteristic
34	C₂²×Dic₁₄₂	—	2	28	no	—
35	C₂²×Dic₁₄₂	—	2	7	no	—
36	C₂²×Dic₁₄₂	C₂³	1	14	yes	complemented
37	C₂×Q₈×D₇₁	—	2	168	no	—
38	C₂×Q₈×D₇₁	C₂³	1	112	yes	complemented
39	C₂²×D₂₈₄	—	2	7	no	—
40	C₂²×D₂₈₄	C₂³	1	14	yes	—
41	C₂²×C₂²⋊D₇₁	—	2	28	no	—
42	C₂×D₄×D₇₁	—	2	168	no	—
43	C₂×D₄×D₇₁	C₂³	1	112	yes	—
44	C₂³×Dic₇₁	—	2	1	no	—
45	C₂³×Dic₇₁	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₇₁	—	2	28	no	—
47	C₂²×C₄×D₇₁	D₄	1	14	yes	—
48	C₂²×C₄×D₇₁	C₂³	1	14	yes	—
49	C₂×#11765854	C₂³	1	112	yes	complemented
50	C₂×#11765853	C₂³	1	112	yes	complemented
51	C₂×#11765852	C₂³	1	112	yes	complemented
52	SD₁₆×D₇₁	C₂³	1	512	yes	direct product factor
53	C₂²×C₇₁⋊C₈	C₂³	1	14	yes	complemented
54	C₂×C₈×D₇₁	C₂³	1	112	yes	complemented
55	C₂⁵×C₇₁	—	2	1	no	—
56	C₂²×Q₈×C₇₁	—	2	7	no	—
57	C₂²×Q₈×C₇₁	C₂³	1	14	yes	complemented
58	C₂²×D₄×C₇₁	—	2	7	no	—
59	C₂²×D₄×C₇₁	C₂³	1	14	yes	—
60	C₂³×C₄×C₇₁	—	2	1	no	—
61	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
62	C₂×SD₁₆×C₇₁	C₂³	1	112	yes	complemented
63	C₂²×C₈×C₇₁	C₂³	1	14	yes	complemented
64	C₂³×D₇₁	—	2	14	no	—
65	C₂³×D₇₁	—	2	112	no	—
66	C₂³×D₇₁	—	4	8	no	—
67	C₂³×D₇₁	—	4	224	no	—
68	C₂³×D₇₁	SD₁₆	1	16	yes	direct product factor
69	C₂³×D₇₁	C₂×D₄	1	14	yes	—
70	C₂×Dic₁₄₂	—	2	42	no	—
71	C₂×Dic₁₄₂	—	2	112	no	—
72	C₂×Dic₁₄₂	C₂⁴	1	28	yes	complemented
73	Q₈×D₇₁	—	2	224	no	—
74	Q₈×D₇₁	C₂⁴	1	64	yes	complemented
75	C₂×D₂₈₄	—	2	42	no	—
76	C₂×D₂₈₄	C₂⁴	1	28	yes	—
77	C₂×C₂²⋊D₇₁	—	2	112	no	—
78	D₄×D₇₁	—	2	224	no	—
79	D₄×D₇₁	C₂⁴	1	64	yes	—
80	C₂²×Dic₇₁	—	2	14	no	—
81	C₂²×Dic₇₁	C₂×D₄	1	14	yes	—
82	C₂×C₄×D₇₁	—	2	112	no	—
83	C₂×C₄×D₇₁	C₂×D₄	1	84	yes	—
84	C₂×C₄×D₇₁	C₂⁴	1	28	yes	—
85	#11765854	C₂⁴	1	64	yes	complemented
86	#11765853	C₂⁴	1	64	yes	complemented
87	#11765852	C₂⁴	1	64	yes	complemented
88	C₂×C₇₁⋊C₈	C₂⁴	1	28	yes	complemented
89	C₈×D₇₁	C₂⁴	1	64	yes	complemented
90	C₂⁴×C₇₁	—	2	14	no	—
91	C₂⁴×C₇₁	—	4	8	no	—
92	C₂⁴×C₇₁	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₇₁	—	2	42	no	—
94	C₂×Q₈×C₇₁	C₂⁴	1	28	yes	complemented
95	C₂×D₄×C₇₁	—	2	42	no	—
96	C₂×D₄×C₇₁	C₂⁴	1	28	yes	—
97	C₂²×C₄×C₇₁	—	2	14	no	—
98	C₂²×C₄×C₇₁	C₂×D₄	1	7	yes	—
99	C₂²×C₄×C₇₁	C₂⁴	1	7	yes	—
100	SD₁₆×C₇₁	C₂⁴	1	64	yes	complemented
101	C₂×C₈×C₇₁	C₂⁴	1	28	yes	complemented
102	C₂³×C₇₁	—	2	28	no	—
103	C₂³×C₇₁	—	4	56	no	—
104	C₂³×C₇₁	C₂×SD₁₆	1	8	yes	complemented
105	C₂³×C₇₁	C₂²×D₄	1	7	yes	—
106	C₂²×D₇₁	—	2	28	no	—
107	C₂²×D₇₁	—	2	64	no	—
108	C₂²×D₇₁	—	4	56	no	—
109	C₂²×D₇₁	—	4	448	no	—
110	C₂²×D₇₁	C₂×SD₁₆	1	112	yes	direct product factor
111	C₂²×D₇₁	C₂²×D₄	1	28	yes	—
112	Q₈×C₇₁	—	2	28	no	—
113	Q₈×C₇₁	C₂⁵	1	8	yes	complemented
114	D₄×C₇₁	—	2	28	no	—
115	D₄×C₇₁	C₂⁵	1	8	yes	—
116	C₂×C₄×C₇₁	—	2	28	no	—
117	C₂×C₄×C₇₁	C₂²×D₄	1	21	yes	—
118	C₂×C₄×C₇₁	C₂⁵	1	7	yes	—
119	C₂²⋊D₇₁	—	2	64	no	—
120	C₂×Dic₇₁	—	2	28	no	—
121	C₂×Dic₇₁	C₂²×D₄	1	28	yes	—
122	D₂₈₄	—	2	28	no	—
123	D₂₈₄	C₂⁵	1	8	yes	—
124	C₄×D₇₁	—	2	64	no	—
125	C₄×D₇₁	C₂²×D₄	1	56	yes	—
126	C₄×D₇₁	C₂⁵	1	8	yes	—
127	Dic₁₄₂	—	2	28	no	—
128	Dic₁₄₂	—	2	64	no	—
129	Dic₁₄₂	C₂⁵	1	8	yes	complemented
130	C₈×C₇₁	C₂⁵	1	8	yes	complemented
131	C₇₁⋊C₈	C₂⁵	1	8	yes	complemented
132	C₂²×C₇₁	—	2	8	no	—
133	C₂²×C₇₁	—	4	56	no	—
134	C₂²×C₇₁	C₂²×SD₁₆	1	28	yes	complemented
135	C₂²×C₇₁	C₂³×D₄	1	7	yes	—
136	C₂×D₇₁	—	2	8	no	—
137	C₂×D₇₁	—	4	56	no	—
138	C₂×D₇₁	—	4	128	no	—
139	C₂×D₇₁	C₂²×SD₁₆	1	112	yes	direct product factor
140	C₂×D₇₁	C₂³×D₄	1	8	yes	—
141	C₄×C₇₁	—	2	8	no	—
142	C₄×C₇₁	C₂³×D₄	1	7	yes	—
143	C₄×C₇₁	C₂⁶	1	1	yes	characteristic
144	Dic₇₁	—	2	8	no	—
145	Dic₇₁	C₂³×D₄	1	8	yes	—
146	C₂⁴×SD₁₆	—	71	1	no	maximal, Sylow
147	C₂×C₇₁	—	4	8	no	—
148	C₂×C₇₁	C₂³×SD₁₆	1	14	yes	complemented
149	C₂×C₇₁	C₂⁴×D₄	1	1	yes	characteristic
150	D₇₁	—	4	8	no	—
151	D₇₁	C₂³×SD₁₆	1	16	yes	direct product factor
152	C₂⁴×Q₈	—	71	1	no	—
153	C₂⁴×D₄	—	71	1	no	—
154	C₂³×SD₁₆	—	71	1	no	—
155	C₂³×SD₁₆	—	71	1	no	—
156	C₂³×SD₁₆	—	71	56	no	—
157	C₂³×SD₁₆	—	71	1	no	—
158	C₂³×SD₁₆	D₇₁	1	1	yes	characteristic, direct product factor
159	C₂⁴×C₈	—	71	1	no	—
160	C₇₁	C₂⁴×SD₁₆	1	1	yes	characteristic, complemented, Sylow
161	C₂⁶	—	142	1	no	—
162	C₂³×Q₈	—	71	28	no	—
163	C₂³×Q₈	—	71	1	no	—
164	C₂³×Q₈	—	142	1	no	—
165	C₂³×Q₈	—	142	14	no	—
166	C₂³×Q₈	C₂×D₇₁	1	1	yes	characteristic, complemented
167	C₂³×D₄	—	71	28	no	—
168	C₂³×D₄	—	71	1	no	—
169	C₂³×D₄	—	142	14	no	—
170	C₂³×D₄	—	142	1	no	—
171	C₂³×D₄	C₂×D₇₁	1	1	yes	characteristic
172	C₂⁴×C₄	—	71	1	no	—
173	C₂⁴×C₄	—	142	1	no	—
174	C₂²×SD₁₆	—	71	28	no	—
175	C₂²×SD₁₆	—	71	28	no	—
176	C₂²×SD₁₆	—	71	448	no	—
177	C₂²×SD₁₆	—	71	28	no	—
178	C₂²×SD₁₆	C₂×D₇₁	1	28	yes	direct product factor
179	C₂³×C₈	—	71	1	no	—
180	C₂³×C₈	—	71	28	no	—
181	C₂³×C₈	C₂×D₇₁	1	1	yes	characteristic, complemented
182	C₂⁵	—	2	1	no	—
183	C₂⁵	—	284	16	no	—
184	C₂⁵	—	71	1	no	—
185	C₂⁵	—	142	28	no	—
186	C₂⁵	—	142	1	no	—
187	C₂²×Q₈	—	2	7	no	—
188	C₂²×Q₈	—	71	112	no	—
189	C₂²×Q₈	—	71	14	no	—
190	C₂²×Q₈	—	142	28	no	—
191	C₂²×Q₈	—	142	168	no	—
192	C₂²×Q₈	—	142	7	no	—
193	C₂²×Q₈	C₂²×D₇₁	1	14	yes	complemented
194	C₂²×D₄	—	2	7	no	—
195	C₂²×D₄	—	71	112	no	—
196	C₂²×D₄	—	71	14	no	—
197	C₂²×D₄	—	142	168	no	—
198	C₂²×D₄	—	142	28	no	—
199	C₂²×D₄	—	142	7	no	—
200	C₂²×D₄	C₂²×D₇₁	1	14	yes	—
201	C₂³×C₄	—	2	1	no	—
202	C₂³×C₄	—	71	1	no	—
203	C₂³×C₄	—	71	14	no	—
204	C₂³×C₄	—	71	14	no	—
205	C₂³×C₄	—	142	28	no	—
206	C₂³×C₄	—	142	1	no	—
207	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
208	C₂×SD₁₆	—	71	112	no	—
209	C₂×SD₁₆	—	71	112	no	—
210	C₂×SD₁₆	—	71	512	no	—
211	C₂×SD₁₆	—	71	112	no	—
212	C₂×SD₁₆	C₂²×D₇₁	1	112	yes	direct product factor
213	C₂²×C₈	—	71	14	no	—
214	C₂²×C₈	—	71	112	no	—
215	C₂²×C₈	C₂²×D₇₁	1	14	yes	complemented
216	C₂⁴	—	2	14	no	—
217	C₂⁴	—	4	8	no	—
218	C₂⁴	—	284	224	no	—
219	C₂⁴	—	284	8	no	—
220	C₂⁴	—	71	14	no	—
221	C₂⁴	—	71	16	no	—
222	C₂⁴	—	142	112	no	—
223	C₂⁴	—	142	14	no	—
224	C₂⁴	D₄×D₇₁	1	1	yes	characteristic
225	C₂×Q₈	—	2	42	no	—
226	C₂×Q₈	—	71	64	no	—
227	C₂×Q₈	—	71	28	no	—
228	C₂×Q₈	—	142	112	no	—
229	C₂×Q₈	—	142	224	no	—
230	C₂×Q₈	—	142	42	no	—
231	C₂×Q₈	C₂³×D₇₁	1	28	yes	complemented
232	C₂×D₄	—	2	42	no	—
233	C₂×D₄	—	71	64	no	—
234	C₂×D₄	—	71	28	no	—
235	C₂×D₄	—	142	224	no	—
236	C₂×D₄	—	142	112	no	—
237	C₂×D₄	—	142	42	no	—
238	C₂×D₄	C₂³×D₇₁	1	28	yes	—
239	C₂²×C₄	—	2	14	no	—
240	C₂²×C₄	—	71	14	no	—
241	C₂²×C₄	—	71	84	no	—
242	C₂²×C₄	—	71	28	no	—
243	C₂²×C₄	—	142	112	no	—
244	C₂²×C₄	—	142	14	no	—
245	C₂²×C₄	D₄×D₇₁	1	7	yes	—
246	C₂²×C₄	C₂³×D₇₁	1	7	yes	—
247	SD₁₆	—	71	64	no	—
248	SD₁₆	—	71	64	no	—
249	SD₁₆	—	71	64	no	—
250	SD₁₆	C₂³×D₇₁	1	64	yes	direct product factor
251	C₂×C₈	—	71	28	no	—
252	C₂×C₈	—	71	64	no	—
253	C₂×C₈	C₂³×D₇₁	1	28	yes	complemented
254	C₂³	—	2	28	no	—
255	C₂³	—	4	56	no	—
256	C₂³	—	284	448	no	—
257	C₂³	—	284	56	no	—
258	C₂³	—	71	28	no	—
259	C₂³	—	71	112	no	—
260	C₂³	—	142	64	no	—
261	C₂³	—	142	28	no	—
262	C₂³	SD₁₆×D₇₁	1	8	yes	direct product factor
263	C₂³	C₂×D₄×D₇₁	1	7	yes	—
264	Q₈	—	2	28	no	—
265	Q₈	—	71	8	no	—
266	Q₈	—	142	64	no	—
267	Q₈	—	142	28	no	—
268	Q₈	C₂⁴×D₇₁	1	8	yes	complemented
269	D₄	—	2	28	no	—
270	D₄	—	71	8	no	—
271	D₄	—	142	64	no	—
272	D₄	—	142	28	no	—
273	D₄	C₂⁴×D₇₁	1	8	yes	—
274	C₂×C₄	—	2	28	no	—
275	C₂×C₄	—	71	28	no	—
276	C₂×C₄	—	71	56	no	—
277	C₂×C₄	—	71	8	no	—
278	C₂×C₄	—	142	64	no	—
279	C₂×C₄	—	142	28	no	—
280	C₂×C₄	C₂×D₄×D₇₁	1	21	yes	—
281	C₂×C₄	C₂⁴×D₇₁	1	7	yes	—
282	C₈	—	71	8	no	—
283	C₈	C₂⁴×D₇₁	1	8	yes	complemented
284	C₂²	—	2	8	no	—
285	C₂²	—	4	56	no	—
286	C₂²	—	284	128	no	—
287	C₂²	—	284	56	no	—
288	C₂²	—	71	112	no	—
289	C₂²	—	71	8	no	—
290	C₂²	—	142	8	no	—
291	C₂²	C₂×SD₁₆×D₇₁	1	28	yes	direct product factor
292	C₂²	C₂²×D₄×D₇₁	1	7	yes	—
293	C₄	—	2	8	no	—
294	C₄	—	71	8	no	—
295	C₄	—	142	8	no	—
296	C₄	C₂²×D₄×D₇₁	1	7	yes	—
297	C₄	C₂⁵×D₇₁	1	1	yes	characteristic
298	C₂	—	4	8	no	—
299	C₂	—	284	8	no	—
300	C₂	—	71	16	no	—
301	C₂	C₂²×SD₁₆×D₇₁	1	14	yes	direct product factor
302	C₂	C₂³×D₄×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄×D₇₁
commutator, cosocle	C₄×C₇₁	C₂⁶
Frattini	C₄	C₂⁵×D₇₁
Fitting	C₂³×SD₁₆×C₇₁	C₂
socle	C₂⁴×C₇₁	C₂×D₄
prime radical	C₂³×D₄×D₇₁	C₂
hypercenter	C₂³×SD₁₆	D₇₁
hypocenter	C₇₁	C₂⁴×SD₁₆
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×D₇₁	C₂	semidirect
3. C₂³×#11765854	C₂	semidirect
4. C₂³×#11765853	C₂	semidirect
5. C₂³×#11765852	C₂	semidirect
6. C₂²×SD₁₆×D₇₁	C₂	direct (N × H)
7. C₂³×C₈×D₇₁	C₂	semidirect
8. C₂³×SD₁₆×C₇₁	C₂	semidirect
11. C₂³×Dic₁₄₂	C₂²	semidirect
13. C₂²×Q₈×D₇₁	C₂²	semidirect
20. C₂²×#11765854	C₂²	semidirect
21. C₂²×#11765853	C₂²	semidirect
22. C₂²×#11765852	C₂²	semidirect
23. C₂×SD₁₆×D₇₁	C₂²	direct (N × H)
24. C₂³×C₇₁⋊C₈	C₂²	semidirect
25. C₂²×C₈×D₇₁	C₂²	semidirect
26. C₂³×Q₈×C₇₁	C₂²	semidirect
28. C₂²×SD₁₆×C₇₁	C₂²	semidirect
29. C₂³×C₈×C₇₁	C₂²	semidirect
36. C₂²×Dic₁₄₂	C₂³	semidirect
38. C₂×Q₈×D₇₁	C₂³	semidirect
49. C₂×#11765854	C₂³	semidirect
50. C₂×#11765853	C₂³	semidirect
51. C₂×#11765852	C₂³	semidirect
52. SD₁₆×D₇₁	C₂³	direct (N × H)
53. C₂²×C₇₁⋊C₈	C₂³	semidirect
54. C₂×C₈×D₇₁	C₂³	semidirect
57. C₂²×Q₈×C₇₁	C₂³	semidirect
62. C₂×SD₁₆×C₇₁	C₂³	semidirect
63. C₂²×C₈×C₇₁	C₂³	semidirect
68. C₂³×D₇₁	SD₁₆	direct (N × H)
72. C₂×Dic₁₄₂	C₂⁴	semidirect
74. Q₈×D₇₁	C₂⁴	semidirect
85. #11765854	C₂⁴	semidirect
86. #11765853	C₂⁴	semidirect
87. #11765852	C₂⁴	semidirect
88. C₂×C₇₁⋊C₈	C₂⁴	semidirect
89. C₈×D₇₁	C₂⁴	semidirect
94. C₂×Q₈×C₇₁	C₂⁴	semidirect
100. SD₁₆×C₇₁	C₂⁴	semidirect
101. C₂×C₈×C₇₁	C₂⁴	semidirect
104. C₂³×C₇₁	C₂×SD₁₆	semidirect
110. C₂²×D₇₁	C₂×SD₁₆	direct (N × H)
113. Q₈×C₇₁	C₂⁵	semidirect
129. Dic₁₄₂	C₂⁵	semidirect
130. C₈×C₇₁	C₂⁵	semidirect
131. C₇₁⋊C₈	C₂⁵	semidirect
134. C₂²×C₇₁	C₂²×SD₁₆	semidirect
139. C₂×D₇₁	C₂²×SD₁₆	direct (N × H)
148. C₂×C₇₁	C₂³×SD₁₆	semidirect
151. D₇₁	C₂³×SD₁₆	direct (N × H)
158. C₂³×SD₁₆	D₇₁	direct (N × H)
160. C₇₁	C₂⁴×SD₁₆	semidirect
166. C₂³×Q₈	C₂×D₇₁	semidirect
178. C₂²×SD₁₆	C₂×D₇₁	direct (N × H)
181. C₂³×C₈	C₂×D₇₁	semidirect
193. C₂²×Q₈	C₂²×D₇₁	semidirect
212. C₂×SD₁₆	C₂²×D₇₁	direct (N × H)
215. C₂²×C₈	C₂²×D₇₁	semidirect
231. C₂×Q₈	C₂³×D₇₁	semidirect
250. SD₁₆	C₂³×D₇₁	direct (N × H)
253. C₂×C₈	C₂³×D₇₁	semidirect
262. C₂³	SD₁₆×D₇₁	direct (N × H)
268. Q₈	C₂⁴×D₇₁	semidirect
283. C₈	C₂⁴×D₇₁	semidirect
291. C₂²	C₂×SD₁₆×D₇₁	direct (N × H)
301. C₂	C₂²×SD₁₆×D₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×D₇₁	2
C₂³×D₄×D₇₁	2
C₂³×#11765854	2
C₂³×#11765853	2
C₂³×#11765852	2
C₂²×SD₁₆×D₇₁	2
C₂³×C₈×D₇₁	2
C₂³×SD₁₆×C₇₁	2
C₂⁴×SD₁₆	71

Subgroups — C23×SD16×D71 #32911228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×SD₁₆×D₇₁ #32911228