Subgroups — #32150899

Order 18176.

652 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22601472	C₂	1	1	yes	maximal, characteristic
2	#444×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#22597137	C₂	1	1	yes	maximal, characteristic, complemented
4	#22590241	C₂	1	1	yes	maximal, characteristic, complemented
5	#22590239	C₂	1	1	yes	maximal, characteristic, complemented
6	#22590236	C₂	1	1	yes	maximal, characteristic, complemented
7	#22590233	C₂	1	1	yes	maximal, characteristic, complemented
8	#22590231	C₂	1	1	yes	maximal, characteristic, complemented
9	#22590230	C₂	1	1	yes	maximal, characteristic, complemented
10	#22590228	C₂	1	1	yes	maximal, characteristic, complemented
11	#22590111	C₂	1	1	yes	maximal, characteristic, complemented
12	#22590086	C₂	1	1	yes	maximal, characteristic, complemented
13	#22590074	C₂	1	1	yes	maximal, characteristic, complemented
14	#347×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×AGL(1,ℤ/16)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14556147	C₂²	1	1	yes	characteristic
17	#135×D₇₁	C₂²	1	1	yes	characteristic
18	#131×D₇₁	—	2	1	no	—
19	C₄×#11765864	—	2	1	no	—
20	#17986442	C₂²	1	1	yes	characteristic
21	#17986439	C₂²	1	1	yes	characteristic
22	#17986438	C₄	1	2	yes	complemented
23	#17986435	C₂²	1	1	yes	characteristic
24	#17986433	C₄	1	2	yes	complemented
25	#17986430	C₄	1	2	yes	complemented
26	#17986428	C₄	1	2	yes	complemented
27	M₃₂×D₇₁	C₂²	1	1	yes	characteristic
28	M₃₂×D₇₁	C₂²	1	1	yes	characteristic
29	#17986122	C₂²	1	1	yes	characteristic
30	#17986121	C₂²	1	1	yes	characteristic
31	#17986120	C₂²	1	1	yes	characteristic
32	#17986119	—	2	1	no	—
33	#17986118	—	2	1	no	—
34	#17986111	C₂²	1	1	yes	characteristic, complemented
35	#17986107	C₂²	1	1	yes	characteristic, complemented
36	#17986105	C₂²	1	1	yes	characteristic, complemented
37	#17986099	—	2	1	no	—
38	#17986096	—	2	1	no	—
39	#108×D₇₁	C₂²	1	1	yes	characteristic
40	#17986034	C₂²	1	1	yes	characteristic
41	#104×D₇₁	—	2	1	no	—
42	#17985992	—	2	1	no	—
43	#97×D₇₁	C₂²	1	1	yes	characteristic
44	#17985823	C₂²	1	1	yes	characteristic, complemented
45	#17985822	C₂²	1	1	yes	characteristic, complemented
46	#17985821	C₂²	1	1	yes	characteristic, complemented
47	#17985816	C₂²	1	1	yes	characteristic, complemented
48	#17985814	C₂²	1	1	yes	characteristic, complemented
49	#17985812	C₂²	1	1	yes	characteristic, complemented
50	#17985810	C₂²	1	1	yes	characteristic
51	#17985809	C₂²	1	1	yes	characteristic
52	#17985808	C₂²	1	1	yes	characteristic
53	#17985777	C₂²	1	1	yes	characteristic, complemented
54	#17985776	C₂²	1	1	yes	characteristic, complemented
55	#17985776	C₂²	1	1	yes	characteristic, complemented
56	#509×C₇₁	C₂²	1	1	yes	characteristic
57	#444×C₇₁	C₂²	1	1	yes	characteristic
58	#442×C₇₁	C₂²	1	1	yes	characteristic, complemented
59	#365×C₇₁	C₂²	1	1	yes	characteristic, complemented
60	#361×C₇₁	C₂²	1	1	yes	characteristic, complemented
61	#360×C₇₁	C₂²	1	1	yes	characteristic
62	#347×C₇₁	C₂²	1	1	yes	characteristic, complemented
63	C₂×#11765864	—	2	1	no	—
64	#41×D₇₁	—	2	1	no	—
65	#14556151	C₂×C₄	1	1	yes	characteristic, complemented
66	#14556150	C₂³	1	1	yes	characteristic
67	#14556149	—	2	1	no	—
68	#14556148	—	2	1	no	—
69	#14556147	—	2	1	no	—
70	#14556147	—	2	1	no	—
71	#14556147	C₂×C₄	1	2	yes	—
72	#14556147	C₂×C₄	1	2	yes	—
73	#14556147	C₂×C₄	1	1	yes	characteristic, complemented
74	C₂×Dic₂₈₄	C₂³	1	1	yes	characteristic
75	Q₁₆×D₇₁	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂×#11765853	—	2	1	no	—
77	SD₁₆×D₇₁	—	2	1	no	—
78	D₈×D₇₁	C₂×C₄	1	1	yes	characteristic, complemented
79	#14556136	—	2	1	no	—
80	#14556136	—	4	1	no	—
81	#14556135	—	2	1	no	—
82	#14556134	—	2	1	no	—
83	#14556134	—	4	1	no	—
84	M₁₆×D₇₁	—	2	1	no	—
85	M₁₆×D₇₁	—	4	1	no	—
86	C₂×C₈×D₇₁	—	4	1	no	—
87	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
88	C₂×C₈×D₇₁	C₂³	1	1	yes	characteristic
89	C₄×Dic₁₄₂	—	2	1	no	—
90	#14556093	—	2	1	no	—
91	D₄×Dic₇₁	—	2	1	no	—
92	C₄×C₂²⋊D₇₁	—	4	1	no	—
93	(C₂²⋊D₇₁)⋊C₄	—	4	1	no	—
94	#14556086	—	2	1	no	—
95	#14556084	—	4	1	no	—
96	C₂×C₄×Dic₇₁	—	4	1	no	—
97	C₄²×D₇₁	D₄	1	1	yes	characteristic
98	Dic₅₆₈	C₂×C₄	1	2	yes	complemented
99	#14556074	C₂×C₄	1	2	yes	complemented
100	#14556073	C₂×C₄	1	2	yes	complemented
101	#14556072	C₂×C₄	1	2	yes	complemented
102	#14556072	C₂×C₄	1	2	yes	complemented
103	#14556069	C₂×C₄	1	2	yes	complemented
104	#14556068	C₂³	1	1	yes	characteristic
105	#14556068	C₂³	1	1	yes	characteristic
106	#14556067	—	2	1	no	—
107	#14556067	C₂×C₄	1	2	yes	complemented
108	C₁₆×D₇₁	—	2	1	no	—
109	C₁₆×D₇₁	C₂×C₄	1	2	yes	complemented
110	#14556064	C₂³	1	1	yes	characteristic
111	#14556063	—	2	1	no	—
112	#14556061	—	2	1	no	—
113	#14556060	C₂³	1	1	yes	characteristic
114	#14556056	—	2	1	no	—
115	#14556055	—	2	1	no	—
116	#14556054	—	2	1	no	—
117	#14556053	—	2	1	no	—
118	#14556051	—	2	1	no	—
119	#14556049	—	2	1	no	—
120	#14556039	D₄	1	1	yes	characteristic
121	#14556038	D₄	1	1	yes	characteristic
122	#14556038	C₂³	1	1	yes	characteristic
123	#135×C₇₁	C₂³	1	1	yes	characteristic
124	C₂×D₈×C₇₁	C₂³	1	1	yes	characteristic
125	#131×C₇₁	—	2	1	no	—
126	C₄×D₄×C₇₁	—	2	1	no	—
127	SD₃₂×C₇₁	C₂×C₄	1	2	yes	complemented
128	D₁₆×C₇₁	C₂×C₄	1	2	yes	complemented
129	M₃₂×C₇₁	C₂³	1	1	yes	characteristic
130	M₃₂×C₇₁	C₂³	1	1	yes	characteristic
131	#108×C₇₁	C₂³	1	1	yes	characteristic
132	#106×C₇₁	C₂³	1	1	yes	characteristic
133	#104×C₇₁	—	2	1	no	—
134	#102×C₇₁	—	2	1	no	—
135	#97×C₇₁	C₂³	1	1	yes	characteristic
136	#11765866	—	2	1	no	—
137	#11765865	—	2	1	no	—
138	#11765865	—	4	1	no	—
139	#11765864	—	2	1	no	—
140	#11765864	—	2	2	no	—
141	#11765864	—	2	2	no	—
142	#11765864	—	4	1	no	—
143	#11765864	—	4	1	no	—
144	#11765864	—	4	1	no	—
145	C₂×Dic₁₄₂	—	2	1	no	—
146	Q₈×D₇₁	—	2	1	no	—
147	C₂×C₂²⋊D₇₁	—	4	1	no	—
148	D₄×D₇₁	—	2	1	no	—
149	D₄×D₇₁	—	4	1	no	—
150	C₂²×Dic₇₁	—	4	1	no	—
151	C₂²×Dic₇₁	—	4	1	no	—
152	C₂×C₄×D₇₁	—	2	1	no	—
153	C₂×C₄×D₇₁	—	4	1	no	—
154	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
155	Dic₂₈₄	—	2	1	no	—
156	Dic₂₈₄	C₂²×C₄	1	1	yes	characteristic
157	Dic₂₈₄	C₂²×C₄	1	2	yes	—
158	#11765855	—	2	1	no	—
159	#11765854	—	2	1	no	—
160	#11765853	—	2	1	no	—
161	#11765853	—	2	2	no	—
162	#11765853	—	2	2	no	—
163	#11765852	—	2	1	no	—
164	D₅₆₈	C₂²×C₄	1	1	yes	characteristic
165	#11765850	—	2	1	no	—
166	#11765849	—	2	1	no	—
167	#11765849	—	4	1	no	—
168	#11765848	—	4	1	no	—
169	#11765848	—	4	1	no	—
170	#11765848	—	4	1	no	—
171	C₂×C₇₁⋊C₈	—	4	1	no	—
172	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
173	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₈×D₇₁	—	2	1	no	—
175	C₈×D₇₁	—	2	1	no	—
176	C₈×D₇₁	—	4	1	no	—
177	C₈×D₇₁	—	4	1	no	—
178	C₈×D₇₁	—	4	1	no	—
179	C₈×D₇₁	C₂²×C₄	1	1	yes	characteristic
180	C₈×D₇₁	C₂²×C₄	1	1	yes	characteristic
181	C₈×D₇₁	#41	1	1	yes	characteristic
182	C₈×D₇₁	#41	1	1	yes	characteristic
183	C₄⋊Dic₇₁	—	2	1	no	—
184	Dic₇₁⋊C₄	—	4	1	no	—
185	Dic₇₁⋊C₄	—	4	1	no	—
186	C₂²⋊Dic₇₁	—	4	1	no	—
187	(C₂×D₇₁)⋊C₄	—	4	1	no	—
188	C₄×Dic₇₁	—	2	1	no	—
189	C₄×Dic₇₁	—	4	1	no	—
190	C₄×Dic₇₁	—	4	1	no	—
191	C₄×Dic₇₁	—	4	1	no	—
192	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
193	C₇₁⋊C₁₆	—	2	1	no	—
194	C₇₁⋊C₁₆	C₂²×C₄	1	2	yes	—
195	#41×C₇₁	—	2	1	no	—
196	C₂×D₄×C₇₁	—	2	1	no	—
197	C₂²×C₄×C₇₁	—	4	1	no	—
198	Q₁₆×C₇₁	C₂²×C₄	1	1	yes	characteristic
199	SD₁₆×C₇₁	—	2	1	no	—
200	D₈×C₇₁	—	2	1	no	—
201	D₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
202	D₈×C₇₁	C₂²×C₄	1	2	yes	—
203	M₁₆×C₇₁	—	2	1	no	—
204	M₁₆×C₇₁	—	4	1	no	—
205	C₂×C₈×C₇₁	—	4	1	no	—
206	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₇₁	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₇₁	—	2	1	no	—
209	C₂²⋊C₄×C₇₁	—	4	1	no	—
210	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
211	C₁₆×C₇₁	—	2	1	no	—
212	C₁₆×C₇₁	C₂²×C₄	1	2	yes	—
213	C₂³×C₇₁	—	4	1	no	—
214	C₂²×D₇₁	—	4	1	no	—
215	C₂²×D₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
216	Q₈×C₇₁	—	2	1	no	—
217	D₄×C₇₁	—	2	2	no	—
218	D₄×C₇₁	—	2	1	no	—
219	D₄×C₇₁	—	4	1	no	—
220	D₄×C₇₁	—	4	1	no	—
221	C₂×C₄×C₇₁	—	2	1	no	—
222	C₂×C₄×C₇₁	—	4	1	no	—
223	C₂×C₄×C₇₁	—	4	1	no	—
224	C₂×C₄×C₇₁	—	8	2	no	—
225	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
226	C₂²⋊D₇₁	—	4	1	no	—
227	C₂²⋊D₇₁	—	4	1	no	—
228	C₂²⋊D₇₁	—	4	2	no	—
229	C₂²⋊D₇₁	—	4	2	no	—
230	C₂²⋊D₇₁	—	4	1	no	—
231	C₂×Dic₇₁	—	2	1	no	—
232	C₂×Dic₇₁	—	4	1	no	—
233	C₂×Dic₇₁	—	4	1	no	—
234	C₂×Dic₇₁	—	4	2	no	—
235	C₂×Dic₇₁	—	4	2	no	—
236	C₂×Dic₇₁	—	4	1	no	—
237	C₂×Dic₇₁	—	8	2	no	—
238	C₂×Dic₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
239	D₂₈₄	—	2	1	no	—
240	D₂₈₄	—	4	1	no	—
241	C₄×D₇₁	—	4	1	no	—
242	C₄×D₇₁	—	4	1	no	—
243	C₄×D₇₁	—	4	1	no	—
244	C₄×D₇₁	—	8	1	no	—
245	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
246	C₄×D₇₁	C₄×D₄	1	1	yes	characteristic
247	C₄×D₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₄×D₇₁	AGL(1,ℤ/8)	1	1	yes	characteristic
249	Dic₁₄₂	—	2	2	no	—
250	Dic₁₄₂	—	2	1	no	—
251	Dic₁₄₂	—	4	1	no	—
252	Dic₁₄₂	—	4	1	no	—
253	C₈×C₇₁	—	2	1	no	—
254	C₈×C₇₁	—	4	1	no	—
255	C₈×C₇₁	C₂³×C₄	1	1	yes	characteristic
256	C₈×C₇₁	C₂×#41	1	1	yes	characteristic
257	C₇₁⋊C₈	—	2	1	no	—
258	C₇₁⋊C₈	—	4	1	no	—
259	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
260	C₇₁⋊C₈	C₄×D₄	1	1	yes	characteristic
261	C₂²×C₇₁	—	4	2	no	—
262	C₂²×C₇₁	—	4	1	no	—
263	C₂²×C₇₁	—	8	1	no	—
264	C₂²×C₇₁	—	8	1	no	—
265	C₂²×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂×D₇₁	—	4	1	no	—
267	C₂×D₇₁	—	4	1	no	—
268	C₂×D₇₁	—	8	2	no	—
269	C₂×D₇₁	#442	1	1	yes	characteristic
270	C₂×D₇₁	#442	1	1	yes	characteristic
271	C₄×C₇₁	—	4	1	no	—
272	C₄×C₇₁	—	4	1	no	—
273	C₄×C₇₁	—	8	1	no	—
274	C₄×C₇₁	C₂×C₄×D₄	1	1	yes	characteristic
275	C₄×C₇₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	Dic₇₁	—	4	1	no	—
277	Dic₇₁	—	4	1	no	—
278	Dic₇₁	—	4	2	no	—
279	Dic₇₁	—	8	1	no	—
280	Dic₇₁	#442	1	1	yes	characteristic
281	Dic₇₁	#442	1	1	yes	characteristic
282	#33468	—	71	1	no	maximal, Sylow
283	C₂×C₇₁	—	2	1	no	—
284	C₂×C₇₁	—	8	1	no	—
285	C₂×C₇₁	—	8	2	no	—
286	C₂×C₇₁	C₂×#442	1	1	yes	characteristic
287	D₇₁	—	2	1	no	—
288	D₇₁	—	2	1	no	—
289	D₇₁	—	8	1	no	—
290	#3414	—	71	1	no	—
291	C₂×#444	—	71	1	no	—
292	#2943	—	71	1	no	—
293	AGL(1,ℤ/16)	—	71	1	no	—
294	AGL(1,ℤ/16)	—	71	1	no	—
295	AGL(1,ℤ/16)	—	71	1	no	—
296	AGL(1,ℤ/16)	D₇₁	1	1	yes	characteristic, complemented
297	#2180	—	71	1	no	—
298	#2180	—	71	1	no	—
299	#2180	—	71	1	no	—
300	#2180	—	71	1	no	—
301	#2155	—	71	1	no	—
302	#2148	—	71	1	no	—
303	#2145	—	71	1	no	—
304	C₂×#347	—	71	1	no	—
305	C₇₁	#33468	1	1	yes	characteristic, complemented, Sylow
306	C₂×#135	—	71	1	no	—
307	C₂×#135	—	71	1	no	—
308	C₂×#131	—	142	1	no	—
309	C₄×#41	—	142	1	no	—
310	#510	—	71	1	no	—
311	#510	—	71	2	no	—
312	#510	—	71	1	no	—
313	#509	—	71	1	no	—
314	#509	—	71	2	no	—
315	#509	C₂×D₇₁	1	1	yes	characteristic
316	#508	—	71	2	no	—
317	#508	—	71	2	no	—
318	C₂×M₃₂	—	71	1	no	—
319	C₂×M₃₂	—	71	1	no	—
320	#444	—	71	1	no	—
321	#444	—	71	1	no	—
322	#444	—	71	1	no	—
323	#444	—	142	1	no	—
324	#444	—	142	1	no	—
325	#444	C₂×D₇₁	1	1	yes	characteristic
326	#442	—	71	1	no	—
327	#442	C₂×D₇₁	1	1	yes	characteristic, complemented
328	#441	—	71	1	no	—
329	#441	—	71	1	no	—
330	#440	—	142	1	no	—
331	#440	—	142	1	no	—
332	C₂×#108	—	71	1	no	—
333	#427	—	71	1	no	—
334	C₂×#104	—	142	1	no	—
335	#416	—	142	1	no	—
336	C₂×#97	—	71	1	no	—
337	#365	—	71	1	no	—
338	#365	—	71	1	no	—
339	#365	—	71	1	no	—
340	#365	C₂×D₇₁	1	1	yes	characteristic, complemented
341	#362	—	71	1	no	—
342	#362	—	71	1	no	—
343	#361	—	71	1	no	—
344	#361	C₂×D₇₁	1	1	yes	characteristic, complemented
345	#360	—	71	1	no	—
346	#360	—	71	1	no	—
347	#360	—	71	1	no	—
348	#360	C₂×D₇₁	1	1	yes	characteristic
349	#347	—	71	1	no	—
350	#347	—	71	1	no	—
351	#347	—	71	1	no	—
352	#347	C₂×D₇₁	1	1	yes	characteristic, complemented
353	C₂×#41	—	142	1	no	—
354	C₂×#41	—	142	1	no	—
355	#135	—	71	1	no	—
356	#135	—	71	2	no	—
357	#135	—	71	2	no	—
358	#135	—	71	1	no	—
359	#135	—	71	1	no	—
360	#135	—	142	1	no	—
361	#135	—	142	1	no	—
362	#135	—	142	1	no	—
363	#135	—	142	1	no	—
364	#135	C₂²×D₇₁	1	1	yes	characteristic
365	C₂×Q₁₆	—	71	1	no	—
366	C₂×Q₁₆	—	71	1	no	—
367	C₂×SD₁₆	—	142	1	no	—
368	C₂×SD₁₆	—	142	1	no	—
369	C₂×D₈	—	71	1	no	—
370	C₂×D₈	C₂²×D₇₁	1	1	yes	characteristic
371	#131	—	2	1	no	—
372	#131	—	284	1	no	—
373	#131	—	284	1	no	—
374	#131	—	142	1	no	—
375	#131	—	142	1	no	—
376	#131	—	142	1	no	—
377	C₂×M₁₆	—	284	1	no	—
378	C₂×M₁₆	—	142	1	no	—
379	C₂²×C₈	—	284	1	no	—
380	C₂²×C₈	—	71	1	no	—
381	C₂²×C₈	—	71	1	no	—
382	C₄×Q₈	—	142	1	no	—
383	C₄×Q₈	—	142	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	284	1	no	—
386	C₄×D₄	—	284	1	no	—
387	C₄×D₄	—	142	1	no	—
388	#117	—	284	1	no	—
389	#117	—	142	1	no	—
390	C₂×C₄²	—	284	1	no	—
391	C₂×C₄²	—	71	1	no	—
392	Q₃₂	—	71	2	no	—
393	Q₃₂	—	71	2	no	—
394	SD₃₂	—	71	2	no	—
395	SD₃₂	—	71	2	no	—
396	SD₃₂	—	71	2	no	—
397	SD₃₂	C₄×D₇₁	1	2	yes	complemented
398	D₁₆	—	71	2	no	—
399	D₁₆	C₄×D₇₁	1	2	yes	complemented
400	M₃₂	—	71	1	no	—
401	M₃₂	—	71	2	no	—
402	M₃₂	—	71	1	no	—
403	M₃₂	—	142	1	no	—
404	M₃₂	C₂²×D₇₁	1	1	yes	characteristic
405	M₃₂	C₂²×D₇₁	1	1	yes	characteristic
406	C₂×C₁₆	—	71	2	no	—
407	C₂×C₁₆	—	142	1	no	—
408	#108	—	71	1	no	—
409	#108	—	142	1	no	—
410	#108	C₂²×D₇₁	1	1	yes	characteristic
411	#107	—	142	1	no	—
412	#106	—	71	1	no	—
413	#106	C₂²×D₇₁	1	1	yes	characteristic
414	#104	—	2	1	no	—
415	#104	—	142	1	no	—
416	#104	—	142	1	no	—
417	#104	—	142	1	no	—
418	#103	—	142	1	no	—
419	#103	—	142	1	no	—
420	#102	—	2	1	no	—
421	#102	—	142	1	no	—
422	#97	—	71	1	no	—
423	#97	—	71	1	no	—
424	#97	—	71	1	no	—
425	#97	C₂²×D₇₁	1	1	yes	characteristic
426	#41	—	2	1	no	—
427	#41	—	284	1	no	—
428	#41	—	284	1	no	—
429	#41	—	284	1	no	—
430	#41	—	284	1	no	—
431	#41	—	142	2	no	—
432	#41	—	142	2	no	—
433	#41	—	142	1	no	—
434	#41	—	142	1	no	—
435	#41	—	142	1	no	—
436	C₂×Q₈	—	142	1	no	—
437	C₂×Q₈	—	142	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	284	1	no	—
440	C₂×D₄	—	284	1	no	—
441	C₂×D₄	—	142	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	284	1	no	—
444	C₂²×C₄	—	284	1	no	—
445	C₂²×C₄	—	284	1	no	—
446	C₂²×C₄	—	71	1	no	—
447	C₂²×C₄	—	142	1	no	—
448	Q₁₆	—	71	1	no	—
449	Q₁₆	—	71	2	no	—
450	Q₁₆	—	142	1	no	—
451	Q₁₆	—	142	1	no	—
452	Q₁₆	C₂×C₄×D₇₁	1	1	yes	characteristic
453	SD₁₆	—	2	1	no	—
454	SD₁₆	—	142	2	no	—
455	SD₁₆	—	142	2	no	—
456	SD₁₆	—	142	1	no	—
457	SD₁₆	—	142	1	no	—
458	SD₁₆	—	142	1	no	—
459	D₈	—	2	1	no	—
460	D₈	—	71	1	no	—
461	D₈	—	142	1	no	—
462	D₈	C₂×C₄×D₇₁	1	2	yes	—
463	D₈	C₂×C₄×D₇₁	1	1	yes	characteristic
464	M₁₆	—	2	1	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	284	1	no	—
467	M₁₆	—	284	1	no	—
468	M₁₆	—	284	1	no	—
469	M₁₆	—	284	1	no	—
470	M₁₆	—	142	1	no	—
471	C₂×C₈	—	4	1	no	—
472	C₂×C₈	—	284	1	no	—
473	C₂×C₈	—	284	1	no	—
474	C₂×C₈	—	284	1	no	—
475	C₂×C₈	—	284	1	no	—
476	C₂×C₈	—	71	1	no	—
477	C₂×C₈	—	71	1	no	—
478	C₂×C₈	—	71	1	no	—
479	C₂×C₈	—	71	1	no	—
480	C₂×C₈	—	71	1	no	—
481	C₂×C₈	—	71	1	no	—
482	C₂×C₈	—	142	1	no	—
483	C₂×C₈	—	142	1	no	—
484	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
485	C₂×C₈	C₂³×D₇₁	1	1	yes	characteristic
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	284	1	no	—
488	C₄⋊C₄	—	284	1	no	—
489	C₄⋊C₄	—	142	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	284	1	no	—
492	C₂²⋊C₄	—	284	1	no	—
493	C₄²	—	284	1	no	—
494	C₄²	—	284	1	no	—
495	C₄²	—	284	1	no	—
496	C₄²	—	71	1	no	—
497	C₄²	—	142	1	no	—
498	C₄²	D₄×D₇₁	1	1	yes	characteristic
499	C₁₆	—	2	1	no	—
500	C₁₆	—	71	2	no	—
501	C₁₆	—	142	1	no	—
502	C₁₆	C₂×C₄×D₇₁	1	2	yes	—
503	C₂³	—	4	1	no	—
504	C₂³	—	284	1	no	—
505	C₂³	—	71	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	284	1	no	—
508	Q₈	—	284	1	no	—
509	Q₈	—	142	2	no	—
510	Q₈	—	142	1	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	284	1	no	—
516	D₄	—	284	1	no	—
517	D₄	—	284	2	no	—
518	D₄	—	284	2	no	—
519	D₄	—	284	1	no	—
520	D₄	—	284	1	no	—
521	D₄	—	142	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	284	1	no	—
527	C₂×C₄	—	284	1	no	—
528	C₂×C₄	—	284	1	no	—
529	C₂×C₄	—	284	1	no	—
530	C₂×C₄	—	284	2	no	—
531	C₂×C₄	—	284	2	no	—
532	C₂×C₄	—	284	1	no	—
533	C₂×C₄	—	284	1	no	—
534	C₂×C₄	—	568	1	no	—
535	C₂×C₄	—	568	2	no	—
536	C₂×C₄	—	71	1	no	—
537	C₂×C₄	—	71	1	no	—
538	C₂×C₄	—	71	1	no	—
539	C₂×C₄	—	71	1	no	—
540	C₂×C₄	—	71	1	no	—
541	C₂×C₄	—	142	1	no	—
542	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
543	C₈	—	2	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	284	1	no	—
546	C₈	—	71	1	no	—
547	C₈	—	71	1	no	—
548	C₈	—	142	1	no	—
549	C₈	C₂²×C₄×D₇₁	1	1	yes	characteristic
550	C₈	#41×D₇₁	1	1	yes	characteristic
551	C₂²	—	4	1	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	284	1	no	—
556	C₂²	—	284	1	no	—
557	C₂²	—	568	2	no	—
558	C₂²	—	71	1	no	—
559	C₂²	—	71	1	no	—
560	C₂²	AGL(1,ℤ/8)×D₇₁	1	1	yes	characteristic
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	284	1	no	—
565	C₄	—	284	1	no	—
566	C₄	—	284	2	no	—
567	C₄	—	568	1	no	—
568	C₄	—	71	1	no	—
569	C₄	—	71	1	no	—
570	C₄	C₄×D₄×D₇₁	1	1	yes	characteristic
571	C₄	AGL(1,ℤ/8)×D₇₁	1	1	yes	characteristic
572	C₂	—	2	1	no	—
573	C₂	—	8	2	no	—
574	C₂	—	8	1	no	—
575	C₂	—	568	1	no	—
576	C₂	—	142	1	no	—
577	C₂	—	142	1	no	—
578	C₂	#442×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#442×D₇₁
commutator	C₈×C₇₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₁
Fitting	C₇₁×AGL(1,ℤ/16)	C₂
socle	C₂×C₇₁	C₂×#442
prime radical	#22601472	C₂
cosocle	C₂×C₈×C₇₁	C₂⁴
hypercenter	AGL(1,ℤ/16)	D₇₁
hypocenter	C₇₁	#33468
LCS	G ▷ C₈×C₇₁ ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ AGL(1,ℤ/16)

Complements

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

N	H ≅ G/N	type
2. #444×D₇₁	C₂	semidirect
3. #22597137	C₂	semidirect
4. #22590241	C₂	semidirect
5. #22590239	C₂	semidirect
6. #22590236	C₂	semidirect
7. #22590233	C₂	semidirect
8. #22590231	C₂	semidirect
9. #22590230	C₂	semidirect
10. #22590228	C₂	semidirect
11. #22590111	C₂	semidirect
12. #22590086	C₂	semidirect
13. #22590074	C₂	semidirect
14. #347×D₇₁	C₂	semidirect
15. C₇₁×AGL(1,ℤ/16)	C₂	semidirect
22. #17986438	C₄	semidirect
24. #17986433	C₄	semidirect
25. #17986430	C₄	semidirect
26. #17986428	C₄	semidirect
34. #17986111	C₂²	semidirect
35. #17986107	C₂²	semidirect
36. #17986105	C₂²	semidirect
44. #17985823	C₂²	semidirect
45. #17985822	C₂²	semidirect
46. #17985821	C₂²	semidirect
47. #17985816	C₂²	semidirect
48. #17985814	C₂²	semidirect
49. #17985812	C₂²	semidirect
53. #17985777	C₂²	semidirect
54. #17985776	C₂²	semidirect
55. #17985776	C₂²	semidirect
58. #442×C₇₁	C₂²	semidirect
59. #365×C₇₁	C₂²	semidirect
60. #361×C₇₁	C₂²	semidirect
62. #347×C₇₁	C₂²	semidirect
65. #14556151	C₂×C₄	semidirect
73. #14556147	C₂×C₄	semidirect
75. Q₁₆×D₇₁	C₂×C₄	semidirect
78. D₈×D₇₁	C₂×C₄	semidirect
98. Dic₅₆₈	C₂×C₄	semidirect
99. #14556074	C₂×C₄	semidirect
100. #14556073	C₂×C₄	semidirect
101. #14556072	C₂×C₄	semidirect
102. #14556072	C₂×C₄	semidirect
103. #14556069	C₂×C₄	semidirect
107. #14556067	C₂×C₄	semidirect
109. C₁₆×D₇₁	C₂×C₄	semidirect
127. SD₃₂×C₇₁	C₂×C₄	semidirect
128. D₁₆×C₇₁	C₂×C₄	semidirect
296. AGL(1,ℤ/16)	D₇₁	semidirect
305. C₇₁	#33468	semidirect
327. #442	C₂×D₇₁	semidirect
340. #365	C₂×D₇₁	semidirect
344. #361	C₂×D₇₁	semidirect
352. #347	C₂×D₇₁	semidirect
397. SD₃₂	C₄×D₇₁	semidirect
399. D₁₆	C₄×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
#22601472	2
#444×D₇₁	2
#22597137	2
#22590241	2
#22590239	2
#22590236	2
#22590233	2
#22590231	2
#22590230	2
#22590228	2
#22590111	2
#22590086	2
#22590074	2
#347×D₇₁	2
C₇₁×AGL(1,ℤ/16)	2
#33468	71