Subgroups — #32004392

Order 18176.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597243	C₂	1	2	yes	maximal, complemented
2	C₂×#17986116	C₂	1	1	yes	maximal, characteristic, complemented
3	#131×Dic₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#22589239	C₂	1	1	yes	maximal, characteristic, complemented
5	#22589131	C₂	1	1	yes	maximal, characteristic, complemented
6	#22589011	C₂	1	2	yes	maximal, complemented
7	#22588843	C₂	1	2	yes	maximal, complemented
8	#22588394	C₂	1	1	yes	maximal, characteristic, complemented
9	#22588222	C₂	1	1	yes	maximal, characteristic, complemented
10	#22588143	C₂	1	2	yes	maximal, complemented
11	C₇₁×#3067	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556135	C₂²	1	2	yes	—
13	C₂×#14556135	C₂²	1	1	yes	characteristic
14	#41×Dic₇₁	C₂²	1	1	yes	characteristic
15	#17986121	—	2	4	no	—
16	#17986116	—	2	4	no	—
17	#17986116	—	2	1	no	—
18	#17986116	—	2	1	no	—
19	#17986116	—	2	1	no	—
20	#17986116	—	2	1	no	—
21	#17986048	C₂²	1	2	yes	—
22	C₂×#14556064	C₂²	1	1	yes	characteristic
23	#17986037	C₂²	1	1	yes	characteristic
24	#17986016	C₂²	1	2	yes	—
25	#17986016	C₂²	1	2	yes	—
26	C₂×#14556055	C₂²	1	2	yes	—
27	#17985973	C₂²	1	2	yes	—
28	#17985957	—	2	1	no	—
29	#17985957	C₂²	1	2	yes	—
30	#17985957	C₂²	1	1	yes	characteristic
31	#17985954	—	2	1	no	—
32	#17985954	C₂²	1	1	yes	characteristic
33	M₁₆×Dic₇₁	—	2	1	no	—
34	M₁₆×Dic₇₁	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₇₁	—	2	1	no	—
36	C₂×C₈×Dic₇₁	C₂²	1	1	yes	characteristic
37	#17985771	C₂²	1	2	yes	—
38	#17985771	C₂²	1	2	yes	—
39	#17985760	C₂²	1	2	yes	—
40	#575×C₇₁	C₂²	1	2	yes	—
41	C₂×#135×C₇₁	C₂²	1	1	yes	characteristic
42	C₂×#131×C₇₁	C₂²	1	1	yes	characteristic
43	#473×C₇₁	C₄	1	2	yes	complemented
44	#472×C₇₁	C₄	1	2	yes	complemented
45	#471×C₇₁	C₄	1	4	yes	complemented
46	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
47	#413×C₇₁	C₂²	1	2	yes	—
48	#14556135	—	2	1	no	—
49	#14556135	—	2	1	no	—
50	#14556135	—	2	2	no	—
51	#14556135	—	2	2	no	—
52	#14556135	—	2	2	no	—
53	#14556135	—	2	2	no	—
54	#14556135	D₄	1	2	yes	—
55	#14556135	D₄	1	2	yes	—
56	C₂×#11765849	—	2	1	no	—
57	C₂×#11765849	—	2	2	no	—
58	C₂×#11765849	C₂³	1	2	yes	—
59	C₂×#11765849	C₂³	1	1	yes	characteristic
60	C₂²×C₇₁⋊C₈	—	2	1	no	—
61	C₂²×C₇₁⋊C₈	—	2	2	no	—
62	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
63	Q₈×Dic₇₁	—	2	1	no	—
64	D₄×Dic₇₁	—	2	2	no	—
65	D₄×Dic₇₁	—	2	1	no	—
66	#14556087	—	2	1	no	—
67	#14556087	C₂³	1	2	yes	—
68	#14556087	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₇₁	—	2	1	no	—
70	C₂×C₄×Dic₇₁	C₂³	1	1	yes	characteristic
71	#14556064	—	2	4	no	—
72	#14556064	—	2	1	no	—
73	#14556064	—	2	1	no	—
74	#14556062	—	2	1	no	—
75	#14556060	—	2	1	no	—
76	#14556055	—	2	4	no	—
77	#14556055	—	2	2	no	—
78	#14556055	—	2	2	no	—
79	#14556055	—	2	4	no	—
80	#14556043	—	2	4	no	—
81	#14556038	—	2	2	no	—
82	#14556038	—	2	1	no	—
83	#14556038	—	2	1	no	—
84	#14556038	—	2	1	no	—
85	C₈×Dic₇₁	—	2	2	no	—
86	C₈×Dic₇₁	—	2	1	no	—
87	C₈×Dic₇₁	—	2	1	no	—
88	C₈×Dic₇₁	—	2	1	no	—
89	C₈×Dic₇₁	D₄	1	1	yes	characteristic
90	C₈×Dic₇₁	D₄	1	1	yes	characteristic
91	C₈×Dic₇₁	D₄	1	1	yes	characteristic
92	C₈×Dic₇₁	D₄	1	1	yes	characteristic
93	C₂×#41×C₇₁	C₂³	1	2	yes	—
94	C₂×#41×C₇₁	C₂³	1	1	yes	characteristic
95	#137×C₇₁	—	2	2	no	—
96	#137×C₇₁	C₂×C₄	1	4	yes	—
97	AGL(1,ℤ/8)×C₇₁	—	2	2	no	—
98	AGL(1,ℤ/8)×C₇₁	C₂×C₄	1	4	yes	—
99	#135×C₇₁	—	2	4	no	—
100	#135×C₇₁	—	2	1	no	—
101	#135×C₇₁	—	2	1	no	—
102	#135×C₇₁	—	2	1	no	—
103	#135×C₇₁	—	2	1	no	—
104	C₂×Q₁₆×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×SD₁₆×C₇₁	C₂×C₄	1	2	yes	complemented
106	C₂×D₈×C₇₁	C₂×C₄	1	1	yes	characteristic, complemented
107	#131×C₇₁	—	2	1	no	—
108	#131×C₇₁	—	2	1	no	—
109	#131×C₇₁	C₂×C₄	1	2	yes	—
110	#131×C₇₁	C₂×C₄	1	2	yes	—
111	C₂×M₁₆×C₇₁	—	2	1	no	—
112	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
113	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₁	—	2	1	no	—
115	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
116	#108×C₇₁	C₂×C₄	1	2	yes	complemented
117	#108×C₇₁	C₂×C₄	1	2	yes	complemented
118	#101×C₇₁	C₂×C₄	1	4	yes	complemented
119	#100×C₇₁	C₂×C₄	1	4	yes	complemented
120	C₂²×Dic₇₁	—	2	2	no	—
121	C₂²×Dic₇₁	—	2	1	no	—
122	#11765849	—	2	1	no	—
123	#11765849	—	2	2	no	—
124	#11765849	—	2	2	no	—
125	#11765849	—	2	2	no	—
126	#11765849	—	2	2	no	—
127	#11765849	—	4	2	no	—
128	#11765849	—	4	2	no	—
129	#11765849	C₂×D₄	1	2	yes	—
130	C₂×C₇₁⋊C₈	—	2	1	no	—
131	C₂×C₇₁⋊C₈	—	2	2	no	—
132	C₂×C₇₁⋊C₈	—	2	2	no	—
133	C₂×C₇₁⋊C₈	—	2	2	no	—
134	C₂×C₇₁⋊C₈	—	4	2	no	—
135	C₂×C₇₁⋊C₈	—	4	2	no	—
136	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
141	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
142	C₄⋊Dic₇₁	—	2	2	no	—
143	C₄⋊Dic₇₁	—	2	1	no	—
144	C₄⋊Dic₇₁	—	2	2	no	—
145	C₂²⋊Dic₇₁	—	2	2	no	—
146	C₂²⋊Dic₇₁	—	2	2	no	—
147	C₂²⋊Dic₇₁	#41	1	2	yes	—
148	C₄×Dic₇₁	—	2	2	no	—
149	C₄×Dic₇₁	—	2	1	no	—
150	C₄×Dic₇₁	—	2	1	no	—
151	C₄×Dic₇₁	—	2	2	no	—
152	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
154	#41×C₇₁	—	2	1	no	—
155	#41×C₇₁	—	2	1	no	—
156	#41×C₇₁	—	2	2	no	—
157	#41×C₇₁	—	2	2	no	—
158	#41×C₇₁	—	2	2	no	—
159	#41×C₇₁	—	2	2	no	—
160	#41×C₇₁	C₂²×C₄	1	2	yes	—
161	#41×C₇₁	C₂×D₄	1	2	yes	—
162	C₂×Q₈×C₇₁	C₂²×C₄	1	2	yes	—
163	C₂×Q₈×C₇₁	#41	1	1	yes	characteristic
164	C₂×D₄×C₇₁	—	2	1	no	—
165	C₂×D₄×C₇₁	—	2	2	no	—
166	C₂×D₄×C₇₁	C₂²×C₄	1	2	yes	—
167	C₂×D₄×C₇₁	#41	1	1	yes	characteristic
168	C₂²×C₄×C₇₁	—	2	1	no	—
169	C₂²×C₄×C₇₁	—	2	2	no	—
170	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
171	Q₁₆×C₇₁	—	2	4	no	—
172	Q₁₆×C₇₁	—	2	1	no	—
173	Q₁₆×C₇₁	—	2	1	no	—
174	SD₁₆×C₇₁	—	2	4	no	—
175	SD₁₆×C₇₁	—	2	4	no	—
176	SD₁₆×C₇₁	—	2	2	no	—
177	SD₁₆×C₇₁	—	2	2	no	—
178	D₈×C₇₁	—	2	4	no	—
179	D₈×C₇₁	—	2	1	no	—
180	D₈×C₇₁	—	2	1	no	—
181	M₁₆×C₇₁	—	2	1	no	—
182	M₁₆×C₇₁	—	2	2	no	—
183	M₁₆×C₇₁	—	2	2	no	—
184	M₁₆×C₇₁	—	2	2	no	—
185	M₁₆×C₇₁	C₂²×C₄	1	2	yes	—
186	M₁₆×C₇₁	C₂²×C₄	1	4	yes	—
187	C₂×C₈×C₇₁	—	2	1	no	—
188	C₂×C₈×C₇₁	—	2	2	no	—
189	C₂×C₈×C₇₁	—	2	2	no	—
190	C₂×C₈×C₇₁	—	2	2	no	—
191	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
196	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
197	C₂³×C₇₁	—	2	1	no	—
198	C₂³×C₇₁	—	2	2	no	—
199	C₂³×C₇₁	C₂×#41	1	1	yes	characteristic
200	Q₈×C₇₁	—	2	1	no	—
201	Q₈×C₇₁	—	2	2	no	—
202	Q₈×C₇₁	—	2	2	no	—
203	Q₈×C₇₁	C₄×D₄	1	2	yes	—
204	D₄×C₇₁	—	2	2	no	—
205	D₄×C₇₁	—	2	2	no	—
206	D₄×C₇₁	—	2	2	no	—
207	D₄×C₇₁	—	2	2	no	—
208	D₄×C₇₁	—	2	1	no	—
209	D₄×C₇₁	—	4	2	no	—
210	D₄×C₇₁	—	4	2	no	—
211	D₄×C₇₁	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₇₁	—	2	1	no	—
213	C₂×C₄×C₇₁	—	2	2	no	—
214	C₂×C₄×C₇₁	—	2	2	no	—
215	C₂×C₄×C₇₁	—	2	2	no	—
216	C₂×C₄×C₇₁	—	4	2	no	—
217	C₂×C₄×C₇₁	—	4	2	no	—
218	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₇₁	—	2	1	no	—
225	C₂×Dic₇₁	—	2	2	no	—
226	C₂×Dic₇₁	—	2	1	no	—
227	C₂×Dic₇₁	—	4	2	no	—
228	C₂×Dic₇₁	—	4	4	no	—
229	C₂×Dic₇₁	—	4	2	no	—
230	C₈×C₇₁	—	2	2	no	—
231	C₈×C₇₁	—	2	4	no	—
232	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
233	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
234	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
235	C₈×C₇₁	C₄×D₄	1	1	yes	characteristic
236	C₇₁⋊C₈	—	2	2	no	—
237	C₇₁⋊C₈	—	4	2	no	—
238	C₇₁⋊C₈	#121	1	1	yes	characteristic
239	C₇₁⋊C₈	#121	1	1	yes	characteristic
240	C₇₁⋊C₈	#121	1	1	yes	characteristic
241	C₇₁⋊C₈	#121	1	1	yes	characteristic
242	C₂²×C₇₁	—	2	2	no	—
243	C₂²×C₇₁	—	4	1	no	—
244	C₂²×C₇₁	—	4	2	no	—
245	C₂²×C₇₁	—	4	2	no	—
246	C₂²×C₇₁	—	8	2	no	—
247	C₂²×C₇₁	C₄×#41	1	1	yes	characteristic
248	C₂²×C₇₁	#525	1	1	yes	characteristic
249	C₂²×C₇₁	#532	1	1	yes	characteristic
250	C₄×C₇₁	—	2	2	no	—
251	C₄×C₇₁	—	4	2	no	—
252	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₇₁	C₂×#121	1	1	yes	characteristic
255	C₄×C₇₁	#529	1	1	yes	characteristic
256	Dic₇₁	—	2	2	no	—
257	Dic₇₁	—	4	2	no	—
258	Dic₇₁	—	4	1	no	—
259	Dic₇₁	—	8	2	no	—
260	#21558	—	71	1	no	maximal, Sylow
261	C₂×C₇₁	—	2	1	no	—
262	C₂×C₇₁	—	2	1	no	—
263	C₂×C₇₁	—	2	1	no	—
264	C₂×C₇₁	—	4	2	no	—
265	C₂×C₇₁	—	8	2	no	—
266	C₂×C₇₁	C₄×#121	1	1	yes	characteristic
267	#3067	D₇₁	1	1	yes	characteristic
268	#2955	—	71	2	no	—
269	C₂×#443	—	71	1	no	—
270	C₄×#131	—	71	1	no	—
271	#1976	—	71	1	no	—
272	#1953	—	71	1	no	—
273	#1932	—	71	2	no	—
274	#1906	—	71	2	no	—
275	#1814	—	71	1	no	—
276	#1772	—	71	1	no	—
277	#1757	—	71	2	no	—
278	C₇₁	#21558	1	1	yes	characteristic, complemented, Sylow
279	#575	C₂×D₇₁	1	2	yes	—
280	C₂×#135	C₂×D₇₁	1	1	yes	characteristic
281	C₂×#131	—	71	1	no	—
282	C₂×#131	—	71	2	no	—
283	C₂×#131	C₂×D₇₁	1	1	yes	characteristic
284	C₄×#41	—	71	1	no	—
285	#473	Dic₇₁	1	2	yes	complemented
286	#472	Dic₇₁	1	2	yes	complemented
287	#471	Dic₇₁	1	4	yes	complemented
288	#444	—	142	4	no	—
289	#443	—	142	1	no	—
290	#443	—	142	1	no	—
291	#443	—	142	1	no	—
292	#443	—	142	1	no	—
293	#443	—	142	4	no	—
294	#430	—	71	2	no	—
295	C₂×#108	—	71	1	no	—
296	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
297	#427	—	71	1	no	—
298	#421	—	71	2	no	—
299	#421	—	71	2	no	—
300	C₂×#104	—	71	2	no	—
301	#413	C₂×D₇₁	1	2	yes	—
302	#410	—	71	2	no	—
303	#405	—	71	1	no	—
304	#405	—	71	2	no	—
305	#405	—	71	1	no	—
306	#405	—	142	1	no	—
307	#405	—	142	1	no	—
308	C₄×M₁₆	—	71	1	no	—
309	C₄×M₁₆	—	142	1	no	—
310	C₂×C₄×C₈	—	71	1	no	—
311	C₂×C₄×C₈	—	142	1	no	—
312	#344	—	71	2	no	—
313	#344	—	71	2	no	—
314	#339	—	71	2	no	—
315	C₂×#41	C₂²×D₇₁	1	2	yes	—
316	C₂×#41	C₂²×D₇₁	1	1	yes	characteristic
317	#137	—	2	2	no	—
318	#137	C₂×Dic₇₁	1	4	yes	—
319	AGL(1,ℤ/8)	—	2	2	no	—
320	AGL(1,ℤ/8)	C₂×Dic₇₁	1	4	yes	—
321	#135	—	2	4	no	—
322	#135	—	2	1	no	—
323	#135	—	2	1	no	—
324	#135	—	2	1	no	—
325	#135	—	2	1	no	—
326	C₂×Q₁₆	C₂×Dic₇₁	1	1	yes	characteristic, complemented
327	C₂×SD₁₆	C₂×Dic₇₁	1	2	yes	complemented
328	C₂×D₈	C₂×Dic₇₁	1	1	yes	characteristic, complemented
329	#131	—	2	1	no	—
330	#131	—	2	1	no	—
331	#131	—	71	2	no	—
332	#131	—	71	2	no	—
333	#131	—	142	2	no	—
334	#131	—	142	2	no	—
335	#131	—	142	2	no	—
336	#131	—	142	2	no	—
337	#131	—	142	1	no	—
338	#131	—	142	1	no	—
339	#131	C₂×Dic₇₁	1	2	yes	—
340	#131	C₂×Dic₇₁	1	2	yes	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	71	1	no	—
343	C₂×M₁₆	—	71	2	no	—
344	C₂×M₁₆	—	142	2	no	—
345	C₂×M₁₆	—	142	1	no	—
346	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
347	C₂×M₁₆	C₂²×D₇₁	1	2	yes	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	71	1	no	—
350	C₂²×C₈	—	142	2	no	—
351	C₂²×C₈	—	142	1	no	—
352	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
353	C₄×Q₈	—	142	1	no	—
354	C₄×D₄	—	142	2	no	—
355	C₄×D₄	—	142	1	no	—
356	#117	—	71	1	no	—
357	#117	—	71	2	no	—
358	#117	—	142	1	no	—
359	C₂×C₄²	—	71	1	no	—
360	C₂×C₄²	—	142	1	no	—
361	#108	—	142	4	no	—
362	#108	—	142	1	no	—
363	#108	—	142	1	no	—
364	#108	C₂×Dic₇₁	1	2	yes	complemented
365	#108	C₂×Dic₇₁	1	2	yes	complemented
366	#107	—	142	1	no	—
367	#106	—	142	1	no	—
368	#104	—	142	2	no	—
369	#104	—	142	2	no	—
370	#104	—	142	4	no	—
371	#104	—	142	4	no	—
372	#101	C₂×Dic₇₁	1	4	yes	complemented
373	#100	C₂×Dic₇₁	1	4	yes	complemented
374	#99	—	142	4	no	—
375	#97	—	142	1	no	—
376	#97	—	142	1	no	—
377	#97	—	142	2	no	—
378	#97	—	142	1	no	—
379	C₄×C₈	—	71	1	no	—
380	C₄×C₈	—	71	1	no	—
381	C₄×C₈	—	71	1	no	—
382	C₄×C₈	—	71	1	no	—
383	C₄×C₈	—	142	1	no	—
384	C₄×C₈	—	142	1	no	—
385	C₄×C₈	—	142	2	no	—
386	C₄×C₈	—	142	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	C₂²×Dic₇₁	1	2	yes	—
394	#41	D₄×D₇₁	1	2	yes	—
395	C₂×Q₈	C₂²×Dic₇₁	1	2	yes	—
396	C₂×Q₈	#11765864	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	C₂²×Dic₇₁	1	2	yes	—
400	C₂×D₄	#11765864	1	1	yes	characteristic
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	142	2	no	—
404	C₂²×C₄	—	142	1	no	—
405	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
406	Q₁₆	—	2	4	no	—
407	Q₁₆	—	2	1	no	—
408	Q₁₆	—	2	1	no	—
409	SD₁₆	—	2	4	no	—
410	SD₁₆	—	2	4	no	—
411	SD₁₆	—	2	2	no	—
412	SD₁₆	—	2	2	no	—
413	D₈	—	2	4	no	—
414	D₈	—	2	1	no	—
415	D₈	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	284	2	no	—
421	M₁₆	—	284	2	no	—
422	M₁₆	—	71	2	no	—
423	M₁₆	—	142	2	no	—
424	M₁₆	—	142	2	no	—
425	M₁₆	—	142	2	no	—
426	M₁₆	—	142	2	no	—
427	M₁₆	—	142	1	no	—
428	M₁₆	C₂²×Dic₇₁	1	2	yes	—
429	M₁₆	C₂²×Dic₇₁	1	4	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	284	2	no	—
435	C₂×C₈	—	284	2	no	—
436	C₂×C₈	—	71	1	no	—
437	C₂×C₈	—	71	1	no	—
438	C₂×C₈	—	71	1	no	—
439	C₂×C₈	—	71	1	no	—
440	C₂×C₈	—	71	1	no	—
441	C₂×C₈	—	71	1	no	—
442	C₂×C₈	—	142	2	no	—
443	C₂×C₈	—	142	2	no	—
444	C₂×C₈	—	142	2	no	—
445	C₂×C₈	—	142	1	no	—
446	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
447	C₂×C₈	C₂²×Dic₇₁	1	1	yes	characteristic
448	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
449	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
450	C₂×C₈	#11765864	1	1	yes	characteristic
451	C₂×C₈	#11765864	1	1	yes	characteristic
452	C₄⋊C₄	—	142	2	no	—
453	C₄⋊C₄	—	142	2	no	—
454	C₄⋊C₄	—	142	1	no	—
455	C₂²⋊C₄	—	71	2	no	—
456	C₂²⋊C₄	—	142	2	no	—
457	C₂²⋊C₄	—	142	2	no	—
458	C₄²	—	71	1	no	—
459	C₄²	—	71	1	no	—
460	C₄²	—	142	2	no	—
461	C₄²	—	142	2	no	—
462	C₄²	—	142	1	no	—
463	C₄²	—	142	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	#41×D₇₁	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	D₄×Dic₇₁	1	2	yes	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	1	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	D₄×Dic₇₁	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	284	2	no	—
486	C₂×C₄	—	284	4	no	—
487	C₂×C₄	—	284	2	no	—
488	C₂×C₄	—	142	1	no	—
489	C₂×C₄	—	142	2	no	—
490	C₂×C₄	—	142	1	no	—
491	C₂×C₄	C₂³×Dic₇₁	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
494	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
495	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
496	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	4	no	—
499	C₈	—	284	2	no	—
500	C₈	—	71	1	no	—
501	C₈	—	71	1	no	—
502	C₈	—	71	1	no	—
503	C₈	—	71	1	no	—
504	C₈	—	142	2	no	—
505	C₈	D₄×Dic₇₁	1	1	yes	characteristic
506	C₈	D₄×Dic₇₁	1	1	yes	characteristic
507	C₈	D₄×Dic₇₁	1	1	yes	characteristic
508	C₈	D₄×Dic₇₁	1	1	yes	characteristic
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	8	2	no	—
514	C₂²	#41×Dic₇₁	1	1	yes	characteristic
515	C₂²	#17986509	1	1	yes	characteristic
516	C₂²	#17986544	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	2	no	—
519	C₄	—	284	1	no	—
520	C₄	—	284	2	no	—
521	C₄	—	568	2	no	—
522	C₄	—	142	2	no	—
523	C₄	C₂×D₄×Dic₇₁	1	1	yes	characteristic
524	C₄	C₂×D₄×Dic₇₁	1	1	yes	characteristic
525	C₄	#121×D₇₁	1	1	yes	characteristic
526	C₄	#17986530	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	2	no	—
532	C₂	#121×Dic₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting, prime radical	C₇₁×#3067	C₂
socle	C₂×C₇₁	C₄×#121
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	#3067	D₇₁
hypocenter	C₇₁	#21558
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3067

Complements

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

N	H ≅ G/N	type
1. #22597243	C₂	semidirect
2. C₂×#17986116	C₂	semidirect
3. #131×Dic₇₁	C₂	semidirect
4. #22589239	C₂	semidirect
5. #22589131	C₂	semidirect
6. #22589011	C₂	semidirect
7. #22588843	C₂	semidirect
8. #22588394	C₂	semidirect
9. #22588222	C₂	semidirect
10. #22588143	C₂	semidirect
43. #473×C₇₁	C₄	semidirect
44. #472×C₇₁	C₄	semidirect
45. #471×C₇₁	C₄	semidirect
104. C₂×Q₁₆×C₇₁	C₂×C₄	semidirect
105. C₂×SD₁₆×C₇₁	C₂×C₄	semidirect
106. C₂×D₈×C₇₁	C₂×C₄	semidirect
116. #108×C₇₁	C₂×C₄	semidirect
117. #108×C₇₁	C₂×C₄	semidirect
118. #101×C₇₁	C₂×C₄	semidirect
119. #100×C₇₁	C₂×C₄	semidirect
278. C₇₁	#21558	semidirect
285. #473	Dic₇₁	semidirect
286. #472	Dic₇₁	semidirect
287. #471	Dic₇₁	semidirect
326. C₂×Q₁₆	C₂×Dic₇₁	semidirect
327. C₂×SD₁₆	C₂×Dic₇₁	semidirect
328. C₂×D₈	C₂×Dic₇₁	semidirect
364. #108	C₂×Dic₇₁	semidirect
365. #108	C₂×Dic₇₁	semidirect
372. #101	C₂×Dic₇₁	semidirect
373. #100	C₂×Dic₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22597243	2
C₂×#17986116	2
#131×Dic₇₁	2
#22589239	2
#22589131	2
#22589011	2
#22588843	2
#22588394	2
#22588222	2
#22588143	2
C₇₁×#3067	2
#21558	71