Subgroups — #31966791

Order 18176.

594 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597465	C₂	1	2	yes	maximal
2	#22587125	C₂	1	2	yes	maximal, complemented
3	#22587120	C₂	1	2	yes	maximal, complemented
4	#22587115	C₂	1	2	yes	maximal, complemented
5	#22587107	C₂	1	2	yes	maximal, complemented
6	#22587103	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587092	C₂	1	2	yes	maximal, complemented
8	C₂×#17985752	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₁×#2965	C₂	1	1	yes	maximal, characteristic
10	#17986130	—	2	2	no	—
11	#17986071	—	2	2	no	—
12	#17986071	—	2	2	no	—
13	D₄×C₇₁⋊C₈	—	2	2	no	—
14	#17986056	C₂²	1	2	yes	—
15	#17986056	C₂²	1	2	yes	—
16	#17986052	C₂²	1	2	yes	—
17	#17986023	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
20	#17985752	C₂²	1	1	yes	characteristic
21	#17985752	C₂²	1	1	yes	characteristic
22	#17985752	C₂²	1	2	yes	—
23	#17985752	C₂²	1	2	yes	—
24	#17985752	C₂²	1	1	yes	characteristic
25	#17985752	C₂²	1	1	yes	characteristic
26	#17985752	C₂²	1	2	yes	—
27	#17985750	C₂²	1	2	yes	—
28	#17985750	C₂²	1	2	yes	—
29	#17985750	C₂²	1	2	yes	—
30	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
31	#446×C₇₁	C₄	1	1	yes	characteristic
32	#446×C₇₁	C₄	1	1	yes	characteristic
33	#436×C₇₁	C₄	1	1	yes	characteristic
34	#436×C₇₁	C₄	1	1	yes	characteristic
35	#435×C₇₁	C₄	1	2	yes	—
36	#435×C₇₁	C₄	1	2	yes	—
37	#431×C₇₁	C₂²	1	2	yes	—
38	#431×C₇₁	C₂²	1	1	yes	characteristic
39	C₄×M₁₆×C₇₁	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
41	C₂×#11765849	—	2	2	no	—
42	C₂²×C₇₁⋊C₈	—	2	2	no	—
43	C₂²×C₇₁⋊C₈	—	2	2	no	—
44	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
45	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
46	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
47	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
48	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
49	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
50	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
51	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
52	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
54	#14556039	—	2	2	no	—
55	#14556039	—	2	2	no	—
56	C₄×C₇₁⋊C₈	—	2	2	no	—
57	C₂×#41×C₇₁	Q₈	1	1	yes	characteristic
58	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₇₁	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
63	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
64	C₄×D₄×C₇₁	C₂×C₄	1	2	yes	—
65	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄×C₇₁	D₄	1	2	yes	—
67	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
68	#117×C₇₁	Q₈	1	1	yes	characteristic
69	#117×C₇₁	Q₈	1	2	yes	—
70	C₂×C₄²×C₇₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
73	C₄⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
74	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
75	C₄⋊C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
76	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
78	C₂²⋊C₈×C₇₁	C₂×C₄	1	2	yes	—
79	#97×C₇₁	C₂×C₄	1	2	yes	—
80	#97×C₇₁	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₇₁	C₂³	1	2	yes	—
84	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
86	#11765849	—	8	2	no	—
87	C₂×C₇₁⋊C₈	—	2	2	no	—
88	C₂×C₇₁⋊C₈	—	2	2	no	—
89	C₂×C₇₁⋊C₈	—	2	2	no	—
90	C₂×C₇₁⋊C₈	—	2	2	no	—
91	C₂×C₇₁⋊C₈	—	8	2	no	—
92	C₂×C₇₁⋊C₈	—	8	2	no	—
93	#41×C₇₁	—	4	2	no	—
94	C₂×Q₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
95	C₂×D₄×C₇₁	C₄⋊C₄	1	2	yes	—
96	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₇₁	C₂×Q₈	1	2	yes	—
103	M₁₆×C₇₁	—	2	4	no	—
104	M₁₆×C₇₁	—	4	2	no	—
105	C₂×C₈×C₇₁	—	2	2	no	—
106	C₂×C₈×C₇₁	—	4	1	no	—
107	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
111	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
114	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
116	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
118	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
119	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	2	yes	—
120	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
122	C₄²×C₇₁	C₂×D₄	1	2	yes	—
123	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₇₁	C₂×Q₈	1	2	yes	—
125	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
126	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
127	C₂³×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
129	Q₈×C₇₁	—	4	1	no	—
130	D₄×C₇₁	—	2	4	no	—
131	D₄×C₇₁	—	4	1	no	—
132	C₂×C₄×C₇₁	—	2	2	no	—
133	C₂×C₄×C₇₁	—	2	1	no	—
134	C₂×C₄×C₇₁	—	2	2	no	—
135	C₂×C₄×C₇₁	—	2	1	no	—
136	C₂×C₄×C₇₁	—	2	2	no	—
137	C₂×C₄×C₇₁	—	2	1	no	—
138	C₂×C₄×C₇₁	—	2	2	no	—
139	C₂×C₄×C₇₁	—	2	1	no	—
140	C₂×C₄×C₇₁	—	2	2	no	—
141	C₂×C₄×C₇₁	—	4	2	no	—
142	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
151	C₈×C₇₁	—	2	1	no	—
152	C₈×C₇₁	—	2	2	no	—
153	C₈×C₇₁	—	2	1	no	—
154	C₈×C₇₁	—	2	1	no	—
155	C₈×C₇₁	—	2	2	no	—
156	C₈×C₇₁	#131	1	2	yes	—
157	C₇₁⋊C₈	—	4	2	no	—
158	C₇₁⋊C₈	—	4	2	no	—
159	C₇₁⋊C₈	—	4	2	no	—
160	C₇₁⋊C₈	—	4	2	no	—
161	C₂²×C₇₁	—	2	1	no	—
162	C₂²×C₇₁	—	2	1	no	—
163	C₂²×C₇₁	—	2	2	no	—
164	C₂²×C₇₁	—	2	2	no	—
165	C₂²×C₇₁	—	2	2	no	—
166	C₂²×C₇₁	#430	1	2	yes	—
167	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₇₁	—	2	1	no	—
169	C₄×C₇₁	—	2	2	no	—
170	C₄×C₇₁	—	2	1	no	—
171	C₄×C₇₁	—	2	2	no	—
172	C₄×C₇₁	—	2	1	no	—
173	C₄×C₇₁	—	2	1	no	—
174	C₄×C₇₁	—	2	2	no	—
175	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
176	C₄×C₇₁	#568	1	1	yes	characteristic
177	C₄×C₇₁	#576	1	1	yes	characteristic
178	C₄×C₇₁	#578	1	1	yes	characteristic
179	#17840	—	71	1	no	maximal, Sylow
180	C₂×C₇₁	—	2	2	no	—
181	C₂×C₇₁	—	4	2	no	—
182	C₂×C₇₁	#2906	1	1	yes	characteristic
183	C₂×C₇₁	#2913	1	1	yes	characteristic
184	C₂×C₇₁	C₂×#430	1	1	yes	characteristic
185	#2990	—	71	2	no	—
186	#2965	D₇₁	1	1	yes	characteristic
187	#1573	—	71	2	no	—
188	#1572	—	71	2	no	—
189	#1571	—	71	2	no	—
190	#1569	—	71	2	no	—
191	#1568	—	71	1	no	—
192	#1565	—	71	2	no	—
193	C₂×#335	—	71	1	no	—
194	C₇₁	#17840	1	1	yes	characteristic, complemented, Sylow
195	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
196	#446	—	142	2	no	—
197	#446	Dic₇₁	1	1	yes	characteristic
198	#446	Dic₇₁	1	1	yes	characteristic
199	#436	Dic₇₁	1	1	yes	characteristic
200	#436	Dic₇₁	1	1	yes	characteristic
201	#435	—	142	2	no	—
202	#435	—	142	2	no	—
203	#435	Dic₇₁	1	2	yes	—
204	#435	Dic₇₁	1	2	yes	—
205	C₈×D₄	—	142	2	no	—
206	#432	—	71	2	no	—
207	#432	—	71	2	no	—
208	#431	—	71	2	no	—
209	#431	C₂×D₇₁	1	2	yes	—
210	#431	C₂×D₇₁	1	1	yes	characteristic
211	#423	—	71	2	no	—
212	C₂×C₄⋊C₈	—	71	2	no	—
213	C₂×C₄⋊C₈	—	71	2	no	—
214	C₄×M₁₆	C₂×D₇₁	1	2	yes	—
215	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
216	#335	—	71	1	no	—
217	#335	—	71	1	no	—
218	#335	—	71	2	no	—
219	#335	—	71	2	no	—
220	#335	—	71	1	no	—
221	#335	—	71	1	no	—
222	#335	—	71	2	no	—
223	#334	—	71	2	no	—
224	#334	—	71	2	no	—
225	#334	—	71	2	no	—
226	C₂×#41	Dic₁₄₂	1	1	yes	characteristic
227	C₂×M₁₆	—	142	2	no	—
228	C₂×M₁₆	C₂×Dic₇₁	1	2	yes	—
229	C₂×M₁₆	C₂×Dic₇₁	1	2	yes	—
230	C₂²×C₈	—	142	2	no	—
231	C₂²×C₈	—	142	2	no	—
232	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
233	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
234	C₄×Q₈	D₂₈₄	1	1	yes	characteristic
235	C₄×Q₈	C₂×Dic₇₁	1	1	yes	characteristic
236	C₄×D₄	D₂₈₄	1	2	yes	—
237	C₄×D₄	D₂₈₄	1	1	yes	characteristic
238	C₄×D₄	C₂×Dic₇₁	1	2	yes	—
239	C₄×D₄	C₂×Dic₇₁	1	1	yes	characteristic
240	#117	Dic₁₄₂	1	1	yes	characteristic
241	#117	Dic₁₄₂	1	2	yes	—
242	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₇₁	1	2	yes	—
244	C₄⋊C₈	—	71	2	no	—
245	C₄⋊C₈	—	71	2	no	—
246	C₄⋊C₈	—	71	2	no	—
247	C₄⋊C₈	—	71	2	no	—
248	C₄⋊C₈	—	142	2	no	—
249	C₄⋊C₈	—	142	2	no	—
250	C₄⋊C₈	—	142	2	no	—
251	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
252	C₄⋊C₈	C₂×Dic₇₁	1	2	yes	—
253	C₄⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
254	C₄⋊C₈	C₂×Dic₇₁	1	1	yes	characteristic
255	C₂²⋊C₈	—	142	2	no	—
256	C₂²⋊C₈	—	142	2	no	—
257	C₂²⋊C₈	—	142	2	no	—
258	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
259	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
260	C₂²⋊C₈	C₂×Dic₇₁	1	2	yes	—
261	#97	—	142	2	no	—
262	#97	—	142	2	no	—
263	#97	C₂×Dic₇₁	1	2	yes	—
264	#97	C₂×Dic₇₁	1	2	yes	—
265	C₄×C₈	—	142	2	no	—
266	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
267	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
268	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
269	C₄×C₈	C₂²×D₇₁	1	2	yes	—
270	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
271	#41	—	4	2	no	—
272	C₂×Q₈	C₄⋊Dic₇₁	1	1	yes	characteristic
273	C₂×D₄	C₄⋊Dic₇₁	1	2	yes	—
274	C₂×D₄	C₄⋊Dic₇₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₇₁	1	2	yes	—
277	C₂²×C₄	C₂×D₂₈₄	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₂₈₄	1	2	yes	—
279	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
280	C₂²×C₄	C₂×Dic₁₄₂	1	2	yes	—
281	M₁₆	—	2	4	no	—
282	M₁₆	—	4	2	no	—
283	M₁₆	—	568	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	568	2	no	—
287	C₂×C₈	—	568	2	no	—
288	C₂×C₈	—	142	2	no	—
289	C₂×C₈	—	142	2	no	—
290	C₂×C₈	—	142	2	no	—
291	C₂×C₈	—	142	2	no	—
292	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
293	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
294	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
295	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
296	C₂×C₈	C₂²×Dic₇₁	1	2	yes	—
297	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
298	C₄⋊C₄	C₄⋊Dic₇₁	1	2	yes	—
299	C₄⋊C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
300	C₄⋊C₄	C₄⋊Dic₇₁	1	2	yes	—
301	C₄⋊C₄	C₄⋊Dic₇₁	1	1	yes	characteristic
302	C₂²⋊C₄	C₄⋊Dic₇₁	1	2	yes	—
303	C₂²⋊C₄	C₄⋊Dic₇₁	1	2	yes	—
304	C₂²⋊C₄	C₄⋊Dic₇₁	1	2	yes	—
305	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
306	C₄²	C₂²×Dic₇₁	1	2	yes	—
307	C₄²	C₂×D₂₈₄	1	2	yes	—
308	C₄²	C₂×D₂₈₄	1	1	yes	characteristic
309	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
310	C₄²	C₂×Dic₁₄₂	1	2	yes	—
311	C₄²	C₂³×D₇₁	1	1	yes	characteristic
312	C₂³	C₂×C₄⋊Dic₇₁	1	2	yes	—
313	C₂³	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
314	Q₈	—	4	1	no	—
315	D₄	—	2	4	no	—
316	D₄	—	4	1	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
328	C₂×C₄	C₂×C₄⋊Dic₇₁	1	2	yes	—
329	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
330	C₂×C₄	C₂×C₄⋊Dic₇₁	1	2	yes	—
331	C₂×C₄	C₂×C₄⋊Dic₇₁	1	2	yes	—
332	C₂×C₄	C₂×C₄⋊Dic₇₁	1	1	yes	characteristic
333	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
334	C₂×C₄	C₂²×D₂₈₄	1	1	yes	characteristic
335	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
336	C₈	—	2	1	no	—
337	C₈	—	2	2	no	—
338	C₈	—	2	1	no	—
339	C₈	—	2	1	no	—
340	C₈	—	2	2	no	—
341	C₈	—	284	2	no	—
342	C₈	—	284	2	no	—
343	C₈	—	284	2	no	—
344	C₈	—	284	2	no	—
345	C₈	#14556135	1	2	yes	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	#17986048	1	2	yes	—
352	C₂²	C₂²×C₄⋊Dic₇₁	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	2	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	2	no	—
360	C₄	C₂×#14556135	1	1	yes	characteristic
361	C₄	#17986766	1	1	yes	characteristic
362	C₄	#17986804	1	1	yes	characteristic
363	C₄	#17986816	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	4	2	no	—
366	C₂	#22596908	1	1	yes	characteristic
367	C₂	#22596940	1	1	yes	characteristic
368	C₂	C₂×#17986048	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₈₄
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#2965	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₇₁	Q₈
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#2965	D₇₁
hypocenter	C₇₁	#17840
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2965

Complements

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

N	H ≅ G/N	type
2. #22587125	C₂	semidirect
3. #22587120	C₂	semidirect
4. #22587115	C₂	semidirect
5. #22587107	C₂	semidirect
6. #22587103	C₂	semidirect
7. #22587092	C₂	semidirect
8. C₂×#17985752	C₂	semidirect
194. C₇₁	#17840	semidirect

Maximal subgroups

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

subgroup	index
#22597465	2
#22587125	2
#22587120	2
#22587115	2
#22587107	2
#22587103	2
#22587092	2
C₂×#17985752	2
C₇₁×#2965	2
#17840	71