Subgroups — #1833×D₇₁ #31997621

Order 18176.

786 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₇₁	C₂	1	1	yes	maximal, characteristic
2	#427×D₇₁	C₂	1	1	yes	maximal, characteristic
3	#405×D₇₁	C₂	1	1	yes	maximal, characteristic
4	#22588465	C₂	1	1	yes	maximal, characteristic, complemented
5	#22588464	C₂	1	1	yes	maximal, characteristic, complemented
6	#22588463	C₂	1	1	yes	maximal, characteristic, complemented
7	#22588462	C₂	1	2	yes	maximal, complemented
8	#22588461	C₂	1	2	yes	maximal, complemented
9	#344×D₇₁	C₂	1	2	yes	maximal
10	H(3,ℤ/4)×D₇₁	C₂	1	2	yes	maximal
11	C₇₁×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₇₁	C₂²	1	2	yes	—
13	C₂×M₁₆×D₇₁	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₇₁	C₂²	1	1	yes	characteristic
15	#117×D₇₁	C₂²	1	2	yes	—
16	#117×D₇₁	C₂²	1	1	yes	characteristic
17	C₂×#14556064	C₂²	1	1	yes	characteristic
18	C₂×#14556063	C₂²	1	2	yes	—
19	#108×D₇₁	—	2	1	no	—
20	#108×D₇₁	—	2	1	no	—
21	#108×D₇₁	—	2	1	no	—
22	#108×D₇₁	—	2	1	no	—
23	#17986037	C₂²	1	1	yes	characteristic
24	#17986036	—	2	1	no	—
25	#17986035	C₂²	1	2	yes	—
26	#17986034	—	2	1	no	—
27	#107×D₇₁	—	2	1	no	—
28	#106×D₇₁	—	2	1	no	—
29	#17985957	C₂²	1	1	yes	characteristic
30	#17985956	C₄	1	2	yes	complemented
31	#17985955	C₂²	1	1	yes	characteristic
32	#17985954	C₂²	1	1	yes	characteristic
33	#17985953	C₄	1	2	yes	complemented
34	#97×D₇₁	C₄	1	2	yes	complemented
35	C₄×C₈×D₇₁	C₄	1	2	yes	complemented
36	#17985771	C₂²	1	2	yes	—
37	#17985770	C₂²	1	2	yes	—
38	#17985769	C₂²	1	2	yes	—
39	#17985756	C₂²	1	2	yes	—
40	#17985755	C₂²	1	2	yes	—
41	#17985755	C₂²	1	2	yes	—
42	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
43	#427×C₇₁	C₂²	1	1	yes	characteristic
44	#405×C₇₁	C₂²	1	1	yes	characteristic
45	#344×C₇₁	C₂²	1	2	yes	—
46	H(3,ℤ/4)×C₇₁	C₂²	1	2	yes	—
47	C₂²×C₄×D₇₁	C₂³	1	1	yes	characteristic
48	C₂×#11765849	C₂³	1	2	yes	—
49	C₂×#11765849	C₂³	1	1	yes	characteristic
50	C₂×#11765848	—	2	2	no	—
51	C₂×#11765848	C₂×C₄	1	2	yes	—
52	M₁₆×D₇₁	—	2	1	no	—
53	M₁₆×D₇₁	—	2	1	no	—
54	M₁₆×D₇₁	—	2	1	no	—
55	M₁₆×D₇₁	—	2	1	no	—
56	M₁₆×D₇₁	—	2	2	no	—
57	M₁₆×D₇₁	—	2	2	no	—
58	M₁₆×D₇₁	—	2	2	no	—
59	M₁₆×D₇₁	—	2	2	no	—
60	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₇₁	—	2	2	no	—
62	C₂×C₈×D₇₁	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
68	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
69	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
70	C₂×C₈×D₇₁	D₄	1	1	yes	characteristic
71	C₂×C₈×D₇₁	Q₈	1	1	yes	characteristic
72	C₂×C₈×D₇₁	Q₈	1	1	yes	characteristic
73	C₂×C₈×D₇₁	Q₈	1	1	yes	characteristic
74	C₂×C₈×D₇₁	Q₈	1	1	yes	characteristic
75	#14556087	C₂³	1	2	yes	—
76	#14556087	C₂³	1	1	yes	characteristic
77	#14556086	—	2	1	no	—
78	#14556086	—	2	2	no	—
79	#14556085	—	2	2	no	—
80	#14556085	C₂×C₄	1	2	yes	—
81	#14556084	—	2	1	no	—
82	#14556084	—	2	2	no	—
83	C₄⋊C₄×D₇₁	—	2	1	no	—
84	C₄⋊C₄×D₇₁	—	2	2	no	—
85	C₂²⋊C₄×D₇₁	—	2	1	no	—
86	C₂²⋊C₄×D₇₁	—	2	2	no	—
87	C₄²×D₇₁	—	2	2	no	—
88	C₄²×D₇₁	C₂×C₄	1	2	yes	—
89	#14556064	—	2	1	no	—
90	#14556064	—	2	1	no	—
91	#14556063	—	2	2	no	—
92	#14556063	—	2	2	no	—
93	#14556062	—	2	1	no	—
94	#14556061	—	2	2	no	—
95	#14556060	—	2	1	no	—
96	#14556059	—	2	2	no	—
97	#14556039	C₂×C₄	1	2	yes	complemented
98	#14556038	C₂×C₄	1	2	yes	complemented
99	#14556038	C₂×C₄	1	2	yes	complemented
100	C₄×C₇₁⋊C₈	C₂×C₄	1	2	yes	complemented
101	C₈×Dic₇₁	C₂×C₄	1	2	yes	complemented
102	C₈×Dic₇₁	C₂×C₄	1	2	yes	complemented
103	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
104	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
106	#117×C₇₁	C₂³	1	2	yes	—
107	#117×C₇₁	C₂³	1	1	yes	characteristic
108	#108×C₇₁	—	2	1	no	—
109	#108×C₇₁	—	2	1	no	—
110	#107×C₇₁	—	2	1	no	—
111	#106×C₇₁	—	2	1	no	—
112	#97×C₇₁	C₂×C₄	1	2	yes	complemented
113	C₄×C₈×C₇₁	C₂×C₄	1	2	yes	complemented
114	C₂³×D₇₁	#41	1	1	yes	characteristic
115	C₂²×Dic₇₁	#41	1	1	yes	characteristic
116	C₂×C₄×D₇₁	—	2	2	no	—
117	C₂×C₄×D₇₁	—	4	2	no	—
118	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₇₁	C₂×Q₈	1	1	yes	characteristic
123	C₂×C₄×D₇₁	C₂×Q₈	1	1	yes	characteristic
124	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
125	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
126	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
127	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
128	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
129	C₂×C₄×D₇₁	#41	1	1	yes	characteristic
130	#11765849	—	2	1	no	—
131	#11765849	—	2	1	no	—
132	#11765849	—	2	2	no	—
133	#11765849	—	2	2	no	—
134	#11765848	—	2	2	no	—
135	#11765848	—	2	2	no	—
136	#11765848	—	4	2	no	—
137	#11765848	—	4	2	no	—
138	C₂×C₇₁⋊C₈	—	2	2	no	—
139	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
140	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₇₁⋊C₈	C₂×Q₈	1	1	yes	characteristic
145	C₂×C₇₁⋊C₈	C₂×Q₈	1	1	yes	characteristic
146	C₈×D₇₁	—	2	2	no	—
147	C₈×D₇₁	—	2	2	no	—
148	C₈×D₇₁	—	4	2	no	—
149	C₈×D₇₁	—	4	2	no	—
150	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
151	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
152	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
153	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
154	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
155	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
156	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
157	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
158	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
159	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
160	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
161	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
162	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
163	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
164	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
165	C₈×D₇₁	C₄⋊C₄	1	1	yes	characteristic
166	C₄⋊Dic₇₁	—	2	1	no	—
167	C₄⋊Dic₇₁	—	2	2	no	—
168	Dic₇₁⋊C₄	—	2	2	no	—
169	Dic₇₁⋊C₄	—	4	2	no	—
170	C₂²⋊Dic₇₁	—	2	1	no	—
171	C₂²⋊Dic₇₁	—	2	2	no	—
172	(C₂×D₇₁)⋊C₄	—	2	2	no	—
173	(C₂×D₇₁)⋊C₄	—	4	2	no	—
174	C₄×Dic₇₁	—	2	2	no	—
175	C₄×Dic₇₁	—	2	2	no	—
176	C₄×Dic₇₁	—	4	2	no	—
177	C₄×Dic₇₁	C₂²×C₄	1	2	yes	—
178	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
179	M₁₆×C₇₁	—	2	1	no	—
180	M₁₆×C₇₁	—	2	1	no	—
181	M₁₆×C₇₁	—	2	2	no	—
182	M₁₆×C₇₁	—	2	2	no	—
183	C₂×C₈×C₇₁	—	2	2	no	—
184	C₂×C₈×C₇₁	C₂²×C₄	1	2	yes	—
185	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
188	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
190	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
191	C₄⋊C₄×C₇₁	—	2	1	no	—
192	C₄⋊C₄×C₇₁	—	2	2	no	—
193	C₂²⋊C₄×C₇₁	—	2	1	no	—
194	C₂²⋊C₄×C₇₁	—	2	2	no	—
195	C₄²×C₇₁	—	2	2	no	—
196	C₄²×C₇₁	C₂²×C₄	1	2	yes	—
197	C₂³×C₇₁	C₂×#41	1	1	yes	characteristic
198	C₂²×D₇₁	—	4	2	no	—
199	C₂²×D₇₁	#117	1	1	yes	characteristic
200	C₂²×D₇₁	#117	1	1	yes	characteristic
201	C₂²×D₇₁	#124	1	1	yes	characteristic
202	C₂²×D₇₁	#124	1	1	yes	characteristic
203	C₂²×D₇₁	#125	1	1	yes	characteristic
204	C₂²×D₇₁	#125	1	1	yes	characteristic
205	C₂×C₄×C₇₁	—	2	2	no	—
206	C₂×C₄×C₇₁	—	4	2	no	—
207	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
213	C₂×Dic₇₁	—	2	2	no	—
214	C₂×Dic₇₁	—	4	2	no	—
215	C₂×Dic₇₁	#117	1	1	yes	characteristic
216	C₂×Dic₇₁	#117	1	1	yes	characteristic
217	C₂×Dic₇₁	#124	1	1	yes	characteristic
218	C₂×Dic₇₁	#124	1	1	yes	characteristic
219	C₂×Dic₇₁	#125	1	1	yes	characteristic
220	C₂×Dic₇₁	#125	1	1	yes	characteristic
221	C₄×D₇₁	—	4	4	no	—
222	C₄×D₇₁	—	8	4	no	—
223	C₄×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₄×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₄×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₄×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₄×D₇₁	#117	1	1	yes	characteristic
228	C₄×D₇₁	#117	1	1	yes	characteristic
229	C₄×D₇₁	#117	1	1	yes	characteristic
230	C₄×D₇₁	#117	1	1	yes	characteristic
231	C₄×D₇₁	#124	1	1	yes	characteristic
232	C₄×D₇₁	#124	1	1	yes	characteristic
233	C₄×D₇₁	#124	1	1	yes	characteristic
234	C₄×D₇₁	#124	1	1	yes	characteristic
235	C₄×D₇₁	#125	1	1	yes	characteristic
236	C₄×D₇₁	#125	1	1	yes	characteristic
237	C₄×D₇₁	#125	1	1	yes	characteristic
238	C₄×D₇₁	#125	1	1	yes	characteristic
239	C₈×C₇₁	—	2	2	no	—
240	C₈×C₇₁	—	4	2	no	—
241	C₈×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₈×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₈×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₈×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₇₁⋊C₈	—	2	2	no	—
246	C₇₁⋊C₈	—	4	2	no	—
247	C₇₁⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₇₁⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₇₁⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₇₁⋊C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂²×C₇₁	—	4	1	no	—
252	C₂²×C₇₁	C₂×#117	1	1	yes	characteristic
253	C₂²×C₇₁	C₂×#124	1	1	yes	characteristic
254	C₂²×C₇₁	C₂×#125	1	1	yes	characteristic
255	C₂×D₇₁	—	2	2	no	—
256	C₂×D₇₁	—	2	2	no	—
257	C₂×D₇₁	—	2	2	no	—
258	C₂×D₇₁	—	4	1	no	—
259	C₂×D₇₁	—	4	1	no	—
260	C₂×D₇₁	—	4	1	no	—
261	C₂×D₇₁	#382	1	1	yes	characteristic
262	C₂×D₇₁	#382	1	1	yes	characteristic
263	C₂×D₇₁	#382	1	1	yes	characteristic
264	C₂×D₇₁	#382	1	1	yes	characteristic
265	C₄×C₇₁	—	4	2	no	—
266	C₄×C₇₁	—	8	2	no	—
267	C₄×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
268	C₄×C₇₁	C₂×#117	1	1	yes	characteristic
269	C₄×C₇₁	C₂×#124	1	1	yes	characteristic
270	C₄×C₇₁	C₂×#125	1	1	yes	characteristic
271	Dic₇₁	—	4	2	no	—
272	Dic₇₁	—	8	2	no	—
273	Dic₇₁	#382	1	1	yes	characteristic
274	Dic₇₁	#382	1	1	yes	characteristic
275	Dic₇₁	#382	1	1	yes	characteristic
276	Dic₇₁	#382	1	1	yes	characteristic
277	C₂×#1833	—	71	1	no	maximal, Sylow
278	C₂×C₇₁	—	2	1	no	—
279	C₂×C₇₁	—	2	1	no	—
280	C₂×C₇₁	—	2	1	no	—
281	C₂×C₇₁	C₂×#382	1	1	yes	characteristic
282	D₇₁	—	2	1	no	—
283	D₇₁	—	2	1	no	—
284	D₇₁	—	2	1	no	—
285	D₇₁	#1833	1	2	yes	direct product factor
286	C₂²×#108	—	71	1	no	—
287	C₂×#427	—	71	1	no	—
288	C₂×#405	—	71	1	no	—
289	#1833	—	71	1	no	—
290	#1833	—	71	1	no	—
291	#1833	—	71	1	no	—
292	#1833	—	71	2	no	—
293	#1833	—	71	2	no	—
294	#1833	D₇₁	1	1	yes	characteristic, direct product factor
295	C₂×#344	—	71	2	no	—
296	C₂×H(3,ℤ/4)	—	71	2	no	—
297	C₇₁	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
298	C₂²×M₁₆	—	71	1	no	—
299	C₂²×M₁₆	—	71	2	no	—
300	C₂³×C₈	—	71	1	no	—
301	C₂×#117	—	71	1	no	—
302	C₂×#117	—	71	2	no	—
303	C₂×#108	—	71	2	no	—
304	C₂×#108	—	71	1	no	—
305	C₂×#108	—	142	1	no	—
306	C₂×#108	—	142	1	no	—
307	C₂×#108	—	142	1	no	—
308	C₂×#108	—	142	1	no	—
309	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
310	#427	—	71	1	no	—
311	#427	—	71	2	no	—
312	#427	—	142	1	no	—
313	#427	—	142	1	no	—
314	#427	C₂×D₇₁	1	1	yes	characteristic
315	C₂×#107	—	142	1	no	—
316	C₂×#106	—	142	1	no	—
317	#405	—	71	1	no	—
318	#405	—	71	1	no	—
319	#405	—	71	1	no	—
320	#405	—	71	2	no	—
321	#405	—	71	2	no	—
322	#405	C₂×D₇₁	1	1	yes	characteristic
323	C₂×#97	—	71	2	no	—
324	C₂×C₄×C₈	—	71	2	no	—
325	#344	—	71	2	no	—
326	#344	—	71	2	no	—
327	#344	—	71	2	no	—
328	#344	C₂×D₇₁	1	2	yes	—
329	H(3,ℤ/4)	—	71	2	no	—
330	H(3,ℤ/4)	—	71	2	no	—
331	H(3,ℤ/4)	—	71	2	no	—
332	H(3,ℤ/4)	C₂×D₇₁	1	2	yes	—
333	C₂³×C₄	—	71	1	no	—
334	C₂×M₁₆	—	71	1	no	—
335	C₂×M₁₆	—	71	2	no	—
336	C₂×M₁₆	—	71	2	no	—
337	C₂×M₁₆	—	142	2	no	—
338	C₂×M₁₆	—	142	2	no	—
339	C₂×M₁₆	—	142	2	no	—
340	C₂×M₁₆	—	142	2	no	—
341	C₂×M₁₆	—	142	2	no	—
342	C₂×M₁₆	—	142	1	no	—
343	C₂×M₁₆	—	142	1	no	—
344	C₂×M₁₆	—	142	1	no	—
345	C₂×M₁₆	—	142	1	no	—
346	C₂×M₁₆	C₂²×D₇₁	1	2	yes	—
347	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
348	C₂²×C₈	—	71	1	no	—
349	C₂²×C₈	—	71	1	no	—
350	C₂²×C₈	—	71	1	no	—
351	C₂²×C₈	—	71	1	no	—
352	C₂²×C₈	—	71	1	no	—
353	C₂²×C₈	—	71	1	no	—
354	C₂²×C₈	—	71	1	no	—
355	C₂²×C₈	—	71	1	no	—
356	C₂²×C₈	—	71	1	no	—
357	C₂²×C₈	—	71	1	no	—
358	C₂²×C₈	—	71	1	no	—
359	C₂²×C₈	—	71	1	no	—
360	C₂²×C₈	—	71	1	no	—
361	C₂²×C₈	—	71	2	no	—
362	C₂²×C₈	—	142	2	no	—
363	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
364	#117	—	71	1	no	—
365	#117	—	71	2	no	—
366	#117	—	71	2	no	—
367	#117	—	142	2	no	—
368	#117	—	142	2	no	—
369	#117	—	142	2	no	—
370	#117	—	142	1	no	—
371	#117	—	142	1	no	—
372	#117	C₂²×D₇₁	1	2	yes	—
373	#117	C₂²×D₇₁	1	1	yes	characteristic
374	C₂×C₄⋊C₄	—	142	2	no	—
375	C₂×C₄⋊C₄	—	142	1	no	—
376	C₂×C₂²⋊C₄	—	142	2	no	—
377	C₂×C₂²⋊C₄	—	142	1	no	—
378	C₂×C₄²	—	71	2	no	—
379	C₂×C₄²	—	142	2	no	—
380	#108	—	2	1	no	—
381	#108	—	2	1	no	—
382	#108	—	142	2	no	—
383	#108	—	142	2	no	—
384	#108	—	142	1	no	—
385	#108	—	142	1	no	—
386	#107	—	2	1	no	—
387	#107	—	142	2	no	—
388	#107	—	142	1	no	—
389	#106	—	2	1	no	—
390	#106	—	142	2	no	—
391	#106	—	142	1	no	—
392	#97	—	71	2	no	—
393	#97	—	71	2	no	—
394	#97	—	71	2	no	—
395	#97	C₄×D₇₁	1	2	yes	complemented
396	C₄×C₈	—	71	2	no	—
397	C₄×C₈	—	71	2	no	—
398	C₄×C₈	—	71	2	no	—
399	C₄×C₈	C₄×D₇₁	1	2	yes	complemented
400	C₂⁴	—	71	1	no	—
401	C₂²×C₄	—	284	2	no	—
402	C₂²×C₄	—	71	1	no	—
403	C₂²×C₄	—	71	1	no	—
404	C₂²×C₄	—	71	1	no	—
405	C₂²×C₄	—	71	1	no	—
406	C₂²×C₄	—	71	1	no	—
407	C₂²×C₄	—	71	1	no	—
408	C₂²×C₄	—	71	1	no	—
409	C₂²×C₄	—	71	1	no	—
410	C₂²×C₄	—	71	1	no	—
411	C₂²×C₄	—	71	1	no	—
412	C₂²×C₄	—	71	1	no	—
413	C₂²×C₄	—	71	1	no	—
414	C₂²×C₄	—	71	1	no	—
415	C₂²×C₄	—	142	2	no	—
416	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	284	2	no	—
422	M₁₆	—	284	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	—	142	1	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	284	2	no	—
431	C₂×C₈	—	284	2	no	—
432	C₂×C₈	—	71	1	no	—
433	C₂×C₈	—	71	1	no	—
434	C₂×C₈	—	71	1	no	—
435	C₂×C₈	—	71	1	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	—	71	1	no	—
443	C₂×C₈	—	71	1	no	—
444	C₂×C₈	—	71	1	no	—
445	C₂×C₈	—	71	1	no	—
446	C₂×C₈	—	71	1	no	—
447	C₂×C₈	—	71	1	no	—
448	C₂×C₈	—	71	1	no	—
449	C₂×C₈	—	71	1	no	—
450	C₂×C₈	—	71	1	no	—
451	C₂×C₈	—	71	1	no	—
452	C₂×C₈	—	71	1	no	—
453	C₂×C₈	—	71	1	no	—
454	C₂×C₈	—	71	2	no	—
455	C₂×C₈	—	142	2	no	—
456	C₂×C₈	—	142	2	no	—
457	C₂×C₈	—	142	2	no	—
458	C₂×C₈	C₂×C₄×D₇₁	1	2	yes	—
459	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
461	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
462	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
463	C₂×C₈	Q₈×D₇₁	1	1	yes	characteristic
464	C₂×C₈	Q₈×D₇₁	1	1	yes	characteristic
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	284	2	no	—
468	C₄⋊C₄	—	142	2	no	—
469	C₄⋊C₄	—	142	2	no	—
470	C₄⋊C₄	—	142	1	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	284	2	no	—
474	C₂²⋊C₄	—	142	2	no	—
475	C₂²⋊C₄	—	142	2	no	—
476	C₂²⋊C₄	—	142	1	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	284	2	no	—
479	C₄²	—	71	2	no	—
480	C₄²	—	142	2	no	—
481	C₄²	—	142	2	no	—
482	C₄²	C₂×C₄×D₇₁	1	2	yes	—
483	C₂³	—	284	2	no	—
484	C₂³	—	71	1	no	—
485	C₂³	—	71	1	no	—
486	C₂³	—	71	1	no	—
487	C₂³	—	71	1	no	—
488	C₂³	—	71	1	no	—
489	C₂³	—	71	1	no	—
490	C₂³	#41×D₇₁	1	1	yes	characteristic
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	284	4	no	—
494	C₂×C₄	—	284	2	no	—
495	C₂×C₄	—	568	4	no	—
496	C₂×C₄	—	71	1	no	—
497	C₂×C₄	—	71	1	no	—
498	C₂×C₄	—	71	1	no	—
499	C₂×C₄	—	71	1	no	—
500	C₂×C₄	—	71	1	no	—
501	C₂×C₄	—	71	1	no	—
502	C₂×C₄	—	71	1	no	—
503	C₂×C₄	—	71	1	no	—
504	C₂×C₄	—	71	1	no	—
505	C₂×C₄	—	71	1	no	—
506	C₂×C₄	—	71	1	no	—
507	C₂×C₄	—	71	1	no	—
508	C₂×C₄	—	71	1	no	—
509	C₂×C₄	—	71	1	no	—
510	C₂×C₄	—	71	1	no	—
511	C₂×C₄	—	71	1	no	—
512	C₂×C₄	—	71	1	no	—
513	C₂×C₄	—	71	1	no	—
514	C₂×C₄	—	71	1	no	—
515	C₂×C₄	—	71	1	no	—
516	C₂×C₄	—	71	1	no	—
517	C₂×C₄	—	71	1	no	—
518	C₂×C₄	—	142	2	no	—
519	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
521	C₂×C₄	C₂×Q₈×D₇₁	1	1	yes	characteristic
522	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
523	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
524	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	4	2	no	—
527	C₈	—	284	2	no	—
528	C₈	—	71	1	no	—
529	C₈	—	71	1	no	—
530	C₈	—	71	1	no	—
531	C₈	—	71	1	no	—
532	C₈	—	142	2	no	—
533	C₈	C₄⋊C₄×D₇₁	1	1	yes	characteristic
534	C₈	C₄⋊C₄×D₇₁	1	1	yes	characteristic
535	C₈	C₄⋊C₄×D₇₁	1	1	yes	characteristic
536	C₈	C₄⋊C₄×D₇₁	1	1	yes	characteristic
537	C₂²	—	4	1	no	—
538	C₂²	—	284	1	no	—
539	C₂²	—	284	1	no	—
540	C₂²	—	284	1	no	—
541	C₂²	—	71	1	no	—
542	C₂²	—	71	1	no	—
543	C₂²	—	71	1	no	—
544	C₂²	—	71	1	no	—
545	C₂²	—	142	2	no	—
546	C₂²	—	142	2	no	—
547	C₂²	—	142	2	no	—
548	C₂²	#117×D₇₁	1	1	yes	characteristic
549	C₂²	#124×D₇₁	1	1	yes	characteristic
550	C₂²	#125×D₇₁	1	1	yes	characteristic
551	C₄	—	4	2	no	—
552	C₄	—	8	2	no	—
553	C₄	—	284	2	no	—
554	C₄	—	568	2	no	—
555	C₄	—	71	1	no	—
556	C₄	—	71	1	no	—
557	C₄	—	71	1	no	—
558	C₄	—	71	1	no	—
559	C₄	C₂×C₄⋊C₄×D₇₁	1	1	yes	characteristic
560	C₄	#117×D₇₁	1	1	yes	characteristic
561	C₄	#124×D₇₁	1	1	yes	characteristic
562	C₄	#125×D₇₁	1	1	yes	characteristic
563	C₂	—	2	1	no	—
564	C₂	—	2	1	no	—
565	C₂	—	2	1	no	—
566	C₂	—	71	2	no	—
567	C₂	—	142	1	no	—
568	C₂	—	142	1	no	—
569	C₂	—	142	1	no	—
570	C₂	#382×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₇₁×#1833	C₂
socle	C₂×C₇₁	C₂×#382
prime radical	C₂³×D₇₁	#41
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	#1833	D₇₁
hypocenter	C₇₁	C₂×#1833
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. #22588465	C₂	semidirect
5. #22588464	C₂	semidirect
6. #22588463	C₂	semidirect
7. #22588462	C₂	semidirect
8. #22588461	C₂	semidirect
11. C₇₁×#1833	C₂	semidirect
30. #17985956	C₄	semidirect
33. #17985953	C₄	semidirect
34. #97×D₇₁	C₄	semidirect
35. C₄×C₈×D₇₁	C₄	semidirect
97. #14556039	C₂×C₄	semidirect
98. #14556038	C₂×C₄	semidirect
99. #14556038	C₂×C₄	semidirect
100. C₄×C₇₁⋊C₈	C₂×C₄	semidirect
101. C₈×Dic₇₁	C₂×C₄	semidirect
102. C₈×Dic₇₁	C₂×C₄	semidirect
112. #97×C₇₁	C₂×C₄	semidirect
113. C₄×C₈×C₇₁	C₂×C₄	semidirect
285. D₇₁	#1833	direct (N × H)
294. #1833	D₇₁	direct (N × H)
297. C₇₁	C₂×#1833	semidirect
395. #97	C₄×D₇₁	semidirect
399. C₄×C₈	C₄×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₇₁	2
#427×D₇₁	2
#405×D₇₁	2
#22588465	2
#22588464	2
#22588463	2
#22588462	2
#22588461	2
#344×D₇₁	2
H(3,ℤ/4)×D₇₁	2
C₇₁×#1833	2
C₂×#1833	71

Subgroups — #1833×D71 #31997621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1833×D₇₁ #31997621