Subgroups — #31968122

Order 18176.

600 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597435	C₂	1	1	yes	maximal, characteristic, complemented
2	#22597416	C₂	1	1	yes	maximal, characteristic
3	#22587243	C₂	1	2	yes	maximal, complemented
4	#22587231	C₂	1	2	yes	maximal, complemented
5	SD₁₆⋊(C₇₁⋊C₈)	C₂	1	2	yes	maximal, complemented
6	SD₁₆×C₇₁⋊C₈	C₂	1	2	yes	maximal, complemented
7	#22587103	C₂	1	1	yes	maximal, characteristic, complemented
8	#22586813	C₂	1	1	yes	maximal, characteristic, complemented
9	#22586809	C₂	1	1	yes	maximal, characteristic
10	#22586623	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#3167	C₂	1	1	yes	maximal, characteristic
12	#17986130	—	2	2	no	—
13	#17986130	C₂²	1	2	yes	—
14	Q₈×C₇₁⋊C₈	C₂²	1	2	yes	—
15	#17986077	C₂²	1	2	yes	—
16	#17986071	—	2	2	no	—
17	D₄×C₇₁⋊C₈	C₂²	1	2	yes	—
18	#17986060	—	2	2	no	—
19	#17986056	C₂²	1	1	yes	characteristic
20	#17986056	C₂²	1	1	yes	characteristic
21	#17986052	C₂²	1	1	yes	characteristic
22	#17986052	C₂²	1	1	yes	characteristic
23	#17985966	—	2	2	no	—
24	#17985752	C₂²	1	2	yes	—
25	#17985750	C₂²	1	2	yes	—
26	Q₈⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
27	Q₈⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
28	D₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
29	D₄⋊(C₇₁⋊C₈)	C₂²	1	2	yes	—
30	#17985720	C₂²	1	1	yes	characteristic
31	#17985720	C₂²	1	1	yes	characteristic
32	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
33	C₈×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
34	#533×C₇₁	C₂²	1	1	yes	characteristic
35	#532×C₇₁	C₂²	1	1	yes	characteristic
36	#498×C₇₁	C₄	1	1	yes	characteristic
37	#492×C₇₁	C₄	1	1	yes	characteristic
38	#487×C₇₁	C₄	1	1	yes	characteristic
39	#486×C₇₁	C₄	1	1	yes	characteristic
40	#465×C₇₁	C₄	1	2	yes	—
41	#465×C₇₁	C₄	1	2	yes	—
42	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
43	C₄×SD₁₆×C₇₁	C₂²	1	2	yes	—
44	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
45	C₂×#11765849	—	2	2	no	—
46	C₂²×C₇₁⋊C₈	—	2	2	no	—
47	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
48	C₄⋊(C₇₁⋊C₈)	—	2	2	no	—
49	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
50	C₄⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
51	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
52	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
53	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
54	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
56	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
57	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
58	C₂²⋊(C₇₁⋊C₈)	D₄	1	2	yes	—
59	#14556039	—	2	2	no	—
60	#14556039	—	2	1	no	—
61	#14556039	—	2	1	no	—
62	C₄×C₇₁⋊C₈	—	2	2	no	—
63	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
65	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
66	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×#41×C₇₁	—	2	1	no	—
68	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	—
69	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
72	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
73	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
75	#127×C₇₁	C₂×C₄	1	1	yes	characteristic
76	#125×C₇₁	—	2	1	no	—
77	#124×C₇₁	—	2	1	no	—
78	C₂²⋊Q₈×C₇₁	—	2	1	no	—
79	C₂²⋊Q₈×C₇₁	C₂×C₄	1	2	yes	—
80	#121×C₇₁	—	2	1	no	—
81	#121×C₇₁	C₂×C₄	1	2	yes	—
82	C₄×Q₈×C₇₁	—	2	1	no	—
83	C₄×Q₈×C₇₁	C₂³	1	2	yes	—
84	C₄×D₄×C₇₁	—	2	1	no	—
85	C₄×D₄×C₇₁	C₂³	1	2	yes	—
86	#117×C₇₁	—	2	1	no	—
87	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
88	#106×C₇₁	C₂×C₄	1	2	yes	—
89	#106×C₇₁	C₂×C₄	1	2	yes	—
90	#103×C₇₁	C₂×C₄	1	2	yes	—
91	#103×C₇₁	C₂×C₄	1	2	yes	—
92	#102×C₇₁	C₂×C₄	1	2	yes	—
93	#102×C₇₁	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
98	#11765849	—	8	2	no	—
99	C₂×C₇₁⋊C₈	—	2	2	no	—
100	C₂×C₇₁⋊C₈	—	2	2	no	—
101	C₂×C₇₁⋊C₈	—	2	1	no	—
102	C₂×C₇₁⋊C₈	—	2	1	no	—
103	C₂×C₇₁⋊C₈	—	8	2	no	—
104	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
105	C₂×C₇₁⋊C₈	C₂×D₄	1	2	yes	—
106	#41×C₇₁	—	8	2	no	—
107	C₂×Q₈×C₇₁	—	2	1	no	—
108	C₂×Q₈×C₇₁	—	2	1	no	—
109	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
110	C₂×D₄×C₇₁	—	2	2	no	—
111	C₂×D₄×C₇₁	—	2	1	no	—
112	C₂×D₄×C₇₁	—	2	1	no	—
113	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₇₁	—	2	2	no	—
115	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₁	#41	1	1	yes	characteristic
118	SD₁₆×C₇₁	—	2	4	no	—
119	SD₁₆×C₇₁	—	2	4	no	—
120	C₂×C₈×C₇₁	—	2	2	no	—
121	C₂×C₈×C₇₁	—	2	2	no	—
122	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
126	C₄⋊C₄×C₇₁	—	2	1	no	—
127	C₄⋊C₄×C₇₁	—	2	1	no	—
128	C₄⋊C₄×C₇₁	—	2	1	no	—
129	C₄⋊C₄×C₇₁	—	2	1	no	—
130	C₄⋊C₄×C₇₁	—	2	2	no	—
131	C₄⋊C₄×C₇₁	—	2	2	no	—
132	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₇₁	C₂²×C₄	1	2	yes	—
134	C₂²⋊C₄×C₇₁	—	2	2	no	—
135	C₂²⋊C₄×C₇₁	—	2	2	no	—
136	C₂²⋊C₄×C₇₁	—	2	2	no	—
137	C₄²×C₇₁	—	2	2	no	—
138	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₇₁	#41	1	1	yes	characteristic
141	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
142	C₂³×C₇₁	—	2	2	no	—
143	C₂³×C₇₁	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₇₁	—	2	2	no	—
145	Q₈×C₇₁	—	2	2	no	—
146	Q₈×C₇₁	—	8	1	no	—
147	Q₈×C₇₁	—	8	1	no	—
148	D₄×C₇₁	—	2	2	no	—
149	D₄×C₇₁	—	2	2	no	—
150	D₄×C₇₁	—	8	1	no	—
151	D₄×C₇₁	—	8	1	no	—
152	D₄×C₇₁	—	8	2	no	—
153	C₂×C₄×C₇₁	—	2	1	no	—
154	C₂×C₄×C₇₁	—	2	1	no	—
155	C₂×C₄×C₇₁	—	2	2	no	—
156	C₂×C₄×C₇₁	—	2	2	no	—
157	C₂×C₄×C₇₁	—	2	2	no	—
158	C₂×C₄×C₇₁	—	2	2	no	—
159	C₂×C₄×C₇₁	—	4	1	no	—
160	C₂×C₄×C₇₁	—	4	2	no	—
161	C₂×C₄×C₇₁	—	4	2	no	—
162	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
168	C₈×C₇₁	—	2	1	no	—
169	C₈×C₇₁	—	2	1	no	—
170	C₈×C₇₁	#131	1	2	yes	—
171	C₈×C₇₁	#131	1	2	yes	—
172	C₇₁⋊C₈	—	2	2	no	—
173	C₇₁⋊C₈	—	2	2	no	—
174	C₇₁⋊C₈	—	4	1	no	—
175	C₇₁⋊C₈	—	4	1	no	—
176	C₇₁⋊C₈	—	4	2	no	—
177	C₇₁⋊C₈	—	4	2	no	—
178	C₂²×C₇₁	—	2	1	no	—
179	C₂²×C₇₁	—	2	1	no	—
180	C₂²×C₇₁	—	2	1	no	—
181	C₂²×C₇₁	—	4	2	no	—
182	C₂²×C₇₁	—	4	2	no	—
183	C₂²×C₇₁	—	4	2	no	—
184	C₂²×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
185	C₄×C₇₁	—	2	1	no	—
186	C₄×C₇₁	—	2	1	no	—
187	C₄×C₇₁	—	2	1	no	—
188	C₄×C₇₁	—	2	1	no	—
189	C₄×C₇₁	—	4	2	no	—
190	C₄×C₇₁	—	4	2	no	—
191	C₄×C₇₁	—	4	2	no	—
192	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
193	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
194	C₄×C₇₁	#577	1	2	yes	—
195	#17971	—	71	1	no	maximal, Sylow
196	C₂×C₇₁	—	4	1	no	—
197	C₂×C₇₁	—	8	2	no	—
198	C₂×C₇₁	#2931	1	1	yes	characteristic
199	C₂×C₇₁	#2949	1	1	yes	characteristic
200	C₂×C₇₁	#2957	1	1	yes	characteristic
201	#3167	D₇₁	1	1	yes	characteristic
202	#2985	—	71	1	no	—
203	#2981	—	71	1	no	—
204	#1592	—	71	2	no	—
205	#1590	—	71	2	no	—
206	SD₁₆⋊C₈	—	71	2	no	—
207	C₈×SD₁₆	—	71	2	no	—
208	#1568	—	71	1	no	—
209	#1497	—	71	1	no	—
210	#1496	—	71	1	no	—
211	#1450	—	71	1	no	—
212	C₇₁	#17971	1	1	yes	characteristic, complemented, Sylow
213	#533	C₂×D₇₁	1	1	yes	characteristic
214	#532	C₂×D₇₁	1	1	yes	characteristic
215	#498	Dic₇₁	1	1	yes	characteristic
216	#492	Dic₇₁	1	1	yes	characteristic
217	#487	Dic₇₁	1	1	yes	characteristic
218	#486	Dic₇₁	1	1	yes	characteristic
219	#465	Dic₇₁	1	2	yes	—
220	#465	Dic₇₁	1	2	yes	—
221	#446	—	71	2	no	—
222	#446	—	142	2	no	—
223	C₈×Q₈	—	71	2	no	—
224	C₄×SD₁₆	C₂×D₇₁	1	2	yes	—
225	C₄×SD₁₆	C₂×D₇₁	1	2	yes	—
226	#436	—	71	2	no	—
227	#435	—	142	2	no	—
228	C₈×D₄	—	71	2	no	—
229	#433	—	142	2	no	—
230	#432	—	71	1	no	—
231	#432	—	71	1	no	—
232	#431	—	71	1	no	—
233	#431	—	71	1	no	—
234	#408	—	142	2	no	—
235	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
236	#335	—	71	2	no	—
237	#334	—	71	2	no	—
238	Q₈⋊C₈	—	71	2	no	—
239	Q₈⋊C₈	—	71	2	no	—
240	D₄⋊C₈	—	71	2	no	—
241	D₄⋊C₈	—	71	2	no	—
242	#322	—	71	1	no	—
243	#322	—	71	1	no	—
244	C₈²	—	71	1	no	—
245	C₈²	—	71	1	no	—
246	C₂×#41	—	2	1	no	—
247	C₂×SD₁₆	C₂×Dic₇₁	1	2	yes	—
248	C₂×SD₁₆	C₂×Dic₇₁	1	2	yes	—
249	C₂×M₁₆	—	142	2	no	—
250	C₂²×C₈	—	142	2	no	—
251	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
252	C₂²×C₈	C₂×Dic₇₁	1	1	yes	characteristic
253	C₄⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
254	C₄⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
255	C₄⋊Q₈	C₂×Dic₇₁	1	1	yes	characteristic
256	#127	C₂×Dic₇₁	1	1	yes	characteristic
257	#125	—	2	1	no	—
258	#124	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	C₂×Dic₇₁	1	2	yes	—
261	#121	—	2	1	no	—
262	#121	C₂×Dic₇₁	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	C₂²×D₇₁	1	2	yes	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂²×D₇₁	1	2	yes	—
267	#117	—	2	1	no	—
268	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
269	#106	C₂×Dic₇₁	1	2	yes	—
270	#106	C₂×Dic₇₁	1	2	yes	—
271	C₄⋊C₈	—	71	2	no	—
272	C₄⋊C₈	—	71	2	no	—
273	C₄⋊C₈	—	71	2	no	—
274	C₄⋊C₈	—	142	2	no	—
275	C₄⋊C₈	—	142	2	no	—
276	C₄⋊C₈	—	142	1	no	—
277	#103	C₂×Dic₇₁	1	2	yes	—
278	#103	C₂×Dic₇₁	1	2	yes	—
279	#102	C₂×Dic₇₁	1	2	yes	—
280	#102	C₂×Dic₇₁	1	2	yes	—
281	C₂²⋊C₈	—	71	2	no	—
282	C₂²⋊C₈	—	142	2	no	—
283	C₂²⋊C₈	—	142	2	no	—
284	C₂²⋊C₈	—	142	1	no	—
285	C₂²⋊C₈	—	142	1	no	—
286	C₂²⋊C₈	—	142	1	no	—
287	#97	—	142	2	no	—
288	#97	—	142	1	no	—
289	#97	—	142	1	no	—
290	C₄×C₈	—	71	1	no	—
291	C₄×C₈	—	71	1	no	—
292	C₄×C₈	—	71	1	no	—
293	C₄×C₈	—	71	1	no	—
294	C₄×C₈	—	142	2	no	—
295	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
296	C₄×C₈	C₂×Dic₇₁	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	C₂²×Dic₇₁	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²×Dic₇₁	1	1	yes	characteristic
309	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
310	C₂²×C₄	#11765864	1	1	yes	characteristic
311	SD₁₆	—	2	4	no	—
312	SD₁₆	—	2	4	no	—
313	M₁₆	—	568	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	568	2	no	—
317	C₂×C₈	—	71	2	no	—
318	C₂×C₈	—	71	2	no	—
319	C₂×C₈	—	142	2	no	—
320	C₂×C₈	—	142	2	no	—
321	C₂×C₈	—	142	1	no	—
322	C₂×C₈	—	142	1	no	—
323	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
324	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
325	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
334	C₄⋊C₄	C₂²×Dic₇₁	1	2	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	C₂²×Dic₇₁	1	1	yes	characteristic
340	C₄²	D₄×D₇₁	1	1	yes	characteristic
341	C₄²	#11765864	1	1	yes	characteristic
342	C₄²	C₂³×D₇₁	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	D₄×Dic₇₁	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	8	1	no	—
348	Q₈	—	8	1	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
364	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
365	C₂×C₄	D₄×Dic₇₁	1	1	yes	characteristic
366	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
367	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
368	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	284	1	no	—
372	C₈	—	284	1	no	—
373	C₈	—	284	2	no	—
374	C₈	—	284	2	no	—
375	C₈	—	142	2	no	—
376	C₈	—	142	2	no	—
377	C₈	#14556135	1	2	yes	—
378	C₈	#14556135	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	C₂×D₄×Dic₇₁	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₂×#14556135	1	1	yes	characteristic
394	C₄	C₂×#14556135	1	1	yes	characteristic
395	C₄	#17986805	1	2	yes	—
396	C₂	—	4	1	no	—
397	C₂	—	8	2	no	—
398	C₂	#22597052	1	1	yes	characteristic
399	C₂	#22597200	1	1	yes	characteristic
400	C₂	#22597257	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#3167	C₂
socle	C₂²×C₇₁	C₂×C₄×D₄
prime radical	#532×C₇₁	C₂²
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#3167	D₇₁
hypocenter	C₇₁	#17971
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #22597435	C₂	semidirect
3. #22587243	C₂	semidirect
4. #22587231	C₂	semidirect
5. SD₁₆⋊(C₇₁⋊C₈)	C₂	semidirect
6. SD₁₆×C₇₁⋊C₈	C₂	semidirect
7. #22587103	C₂	semidirect
8. #22586813	C₂	semidirect
10. #22586623	C₂	semidirect
212. C₇₁	#17971	semidirect

Maximal subgroups

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

subgroup	index
#22597435	2
#22597416	2
#22587243	2
#22587231	2
SD₁₆⋊(C₇₁⋊C₈)	2
SD₁₆×C₇₁⋊C₈	2
#22587103	2
#22586813	2
#22586809	2
#22586623	2
C₇₁×#3167	2
#17971	71