Subgroups — #31966697

Order 18176.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11765865	C₂	1	1	yes	maximal, characteristic
2	#22597007	C₂	1	2	yes	maximal
3	#22587121	C₂	1	2	yes	maximal, complemented
4	#22587117	C₂	1	2	yes	maximal, complemented
5	#22587109	C₂	1	2	yes	maximal, complemented
6	#22587102	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587097	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587088	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587087	C₂	1	1	yes	maximal, characteristic, complemented
10	#335×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11765865	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₄₂	C₄	1	1	yes	characteristic
14	C₈×Dic₁₄₂	C₄	1	1	yes	characteristic
15	C₈×D₂₈₄	C₄	1	1	yes	characteristic
16	C₈×D₂₈₄	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₇₁	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₇₁	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₇₁	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₇₁	C₄	1	1	yes	characteristic
21	#17986061	—	2	2	no	—
22	#17986057	—	2	2	no	—
23	#17986055	C₂²	1	2	yes	—
24	#17986052	C₂²	1	2	yes	—
25	#17986052	C₂²	1	1	yes	characteristic
26	#17986051	C₂²	1	2	yes	—
27	#17986050	C₂²	1	1	yes	characteristic
28	#17986050	C₂²	1	1	yes	characteristic
29	#17986021	C₂²	1	2	yes	—
30	C₄⋊C₈×D₇₁	C₂²	1	2	yes	—
31	#17985964	—	2	2	no	—
32	#17985956	—	2	2	no	—
33	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₇₁	C₂²	1	1	yes	characteristic
35	#17985752	C₂²	1	1	yes	characteristic
36	#17985752	C₂²	1	1	yes	characteristic
37	#17985751	C₂²	1	2	yes	—
38	#17985751	C₂²	1	2	yes	—
39	#17985750	C₂²	1	2	yes	—
40	#17985749	C₂²	1	2	yes	—
41	#17985749	C₂²	1	2	yes	—
42	#432×C₇₁	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
44	#335×C₇₁	C₂²	1	1	yes	characteristic
45	#335×C₇₁	C₂²	1	1	yes	characteristic
46	#334×C₇₁	C₂²	1	2	yes	—
47	C₂×#11765865	D₄	1	1	yes	characteristic
48	C₂×#11765848	—	2	2	no	—
49	C₂×C₈×D₇₁	—	2	2	no	—
50	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₇₁	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₁₄₂	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₄₂	Q₈	1	1	yes	characteristic
56	C₄×D₂₈₄	C₂×C₄	1	1	yes	characteristic
57	C₄×D₂₈₄	Q₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₇₁	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₇₁	Q₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₇₁	Q₈	1	1	yes	characteristic
62	#14556087	D₄	1	1	yes	characteristic
63	#14556085	D₄	1	1	yes	characteristic
64	#14556085	D₄	1	1	yes	characteristic
65	C₄²×D₇₁	C₂³	1	1	yes	characteristic
66	C₄²×D₇₁	C₂³	1	1	yes	characteristic
67	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
69	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
70	C₄⋊(C₇₁⋊C₈)	C₂³	1	2	yes	—
71	Dic₇₁⋊C₈	—	2	2	no	—
72	Dic₇₁⋊C₈	—	2	2	no	—
73	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
74	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
75	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
76	Dic₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊(C₇₁⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	(C₂×D₇₁)⋊C₈	—	2	2	no	—
81	(C₂×D₇₁)⋊C₈	—	2	2	no	—
82	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
83	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
84	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
85	(C₂×D₇₁)⋊C₈	C₂×C₄	1	1	yes	characteristic
86	#14556038	—	2	2	no	—
87	C₄×C₇₁⋊C₈	—	2	2	no	—
88	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
89	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×Dic₇₁	—	2	2	no	—
91	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₇₁	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
99	C₄⋊C₈×C₇₁	C₂³	1	2	yes	—
100	C₂²⋊C₈×C₇₁	—	2	2	no	—
101	#97×C₇₁	—	2	2	no	—
102	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₇₁	C₂×C₄	1	1	yes	characteristic
104	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₇₁	C₂³	1	1	yes	characteristic
106	#11765865	—	2	2	no	—
107	#11765865	—	2	2	no	—
108	C₂×Dic₁₄₂	C₄⋊C₄	1	1	yes	characteristic
109	C₂×D₂₈₄	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₇₁	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₇₁	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₇₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₇₁	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₇₁	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₇₁	C₂×Q₈	1	1	yes	characteristic
118	#11765848	—	4	4	no	—
119	C₂×C₇₁⋊C₈	—	2	2	no	—
120	C₂×C₇₁⋊C₈	—	2	2	no	—
121	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
125	C₈×D₇₁	—	2	2	no	—
126	C₈×D₇₁	—	2	2	no	—
127	C₈×D₇₁	—	4	1	no	—
128	C₈×D₇₁	—	4	1	no	—
129	C₈×D₇₁	—	4	4	no	—
130	C₄⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
131	C₄⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
132	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
133	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
134	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
135	Dic₇₁⋊C₄	C₄⋊C₄	1	1	yes	characteristic
136	C₂²⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
137	C₂²⋊Dic₇₁	C₄⋊C₄	1	1	yes	characteristic
138	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
139	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
140	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
141	(C₂×D₇₁)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
142	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₇₁	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
145	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₇₁	C₂×Q₈	1	1	yes	characteristic
147	C₄×Dic₇₁	C₂×Q₈	1	1	yes	characteristic
148	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
151	C₂×C₈×C₇₁	—	2	2	no	—
152	C₂×C₈×C₇₁	—	2	2	no	—
153	C₂×C₈×C₇₁	—	2	2	no	—
154	C₂×C₈×C₇₁	—	4	1	no	—
155	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₇₁	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
162	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
163	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₇₁	—	2	1	no	—
167	C₂×C₄×C₇₁	—	2	1	no	—
168	C₂×C₄×C₇₁	—	2	1	no	—
169	C₂×C₄×C₇₁	—	2	1	no	—
170	C₂×C₄×C₇₁	—	4	1	no	—
171	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
177	C₂²⋊D₇₁	—	2	2	no	—
178	C₂²⋊D₇₁	—	2	2	no	—
179	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
185	D₂₈₄	—	2	2	no	—
186	C₄×D₇₁	—	2	1	no	—
187	C₄×D₇₁	—	2	1	no	—
188	C₄×D₇₁	—	2	1	no	—
189	C₄×D₇₁	—	2	1	no	—
190	C₄×D₇₁	—	2	1	no	—
191	C₄×D₇₁	—	2	1	no	—
192	C₄×D₇₁	—	4	1	no	—
193	C₄×D₇₁	—	4	1	no	—
194	C₄×D₇₁	#135	1	2	yes	—
195	C₄×D₇₁	#135	1	2	yes	—
196	Dic₁₄₂	—	2	2	no	—
197	C₈×C₇₁	—	2	1	no	—
198	C₈×C₇₁	—	2	1	no	—
199	C₈×C₇₁	—	2	1	no	—
200	C₈×C₇₁	—	4	2	no	—
201	C₈×C₇₁	—	4	2	no	—
202	C₈×C₇₁	#131	1	2	yes	—
203	C₇₁⋊C₈	—	2	1	no	—
204	C₇₁⋊C₈	—	2	1	no	—
205	C₇₁⋊C₈	—	2	1	no	—
206	C₇₁⋊C₈	—	2	1	no	—
207	C₇₁⋊C₈	—	4	2	no	—
208	C₇₁⋊C₈	—	4	2	no	—
209	C₂²×C₇₁	—	2	1	no	—
210	C₂²×C₇₁	—	2	1	no	—
211	C₂²×C₇₁	—	2	1	no	—
212	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
213	C₂×D₇₁	—	2	1	no	—
214	C₂×D₇₁	—	2	1	no	—
215	C₂×D₇₁	—	2	1	no	—
216	C₂×D₇₁	—	2	1	no	—
217	C₂×D₇₁	—	2	1	no	—
218	C₂×D₇₁	#427	1	2	yes	—
219	C₄×C₇₁	—	2	1	no	—
220	C₄×C₇₁	—	2	1	no	—
221	C₄×C₇₁	—	2	1	no	—
222	C₄×C₇₁	—	2	1	no	—
223	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
224	C₄×C₇₁	#568	1	1	yes	characteristic
225	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
226	C₄×C₇₁	C₂×#135	1	1	yes	characteristic
227	Dic₇₁	—	2	1	no	—
228	Dic₇₁	—	2	1	no	—
229	Dic₇₁	—	2	1	no	—
230	Dic₇₁	—	2	1	no	—
231	Dic₇₁	—	2	1	no	—
232	Dic₇₁	#427	1	2	yes	—
233	#17829	—	71	1	no	maximal, Sylow
234	C₂×C₇₁	—	4	1	no	—
235	C₂×C₇₁	#2906	1	1	yes	characteristic
236	C₂×C₇₁	C₂×#427	1	1	yes	characteristic
237	C₂×C₇₁	#2916	1	1	yes	characteristic
238	D₇₁	—	2	2	no	—
239	D₇₁	—	4	1	no	—
240	C₈×#41	—	71	1	no	—
241	#2925	—	71	2	no	—
242	#1572	—	71	2	no	—
243	#1572	—	71	2	no	—
244	#1570	—	71	2	no	—
245	#1568	—	71	1	no	—
246	#1568	D₇₁	1	1	yes	characteristic, complemented
247	#1567	—	71	1	no	—
248	#1564	—	71	1	no	—
249	#1564	—	71	1	no	—
250	C₂×#335	—	71	1	no	—
251	C₇₁	#17829	1	1	yes	characteristic, complemented, Sylow
252	C₄×#41	—	71	1	no	—
253	C₈×Q₈	—	71	1	no	—
254	C₈×Q₈	—	71	1	no	—
255	C₈×D₄	—	71	1	no	—
256	C₈×D₄	—	71	1	no	—
257	C₈×D₄	—	71	1	no	—
258	C₈×D₄	—	71	1	no	—
259	C₈×D₄	—	71	1	no	—
260	C₈×D₄	—	71	1	no	—
261	#433	—	142	2	no	—
262	#433	—	142	2	no	—
263	#432	—	71	2	no	—
264	#432	C₂×D₇₁	1	2	yes	—
265	#431	—	71	1	no	—
266	#431	—	71	1	no	—
267	#431	—	71	1	no	—
268	#431	—	71	2	no	—
269	#431	—	71	2	no	—
270	#423	—	71	2	no	—
271	C₂×C₄⋊C₈	—	71	2	no	—
272	#408	—	142	2	no	—
273	#405	—	142	2	no	—
274	C₂×C₄×C₈	—	71	1	no	—
275	C₂×C₄×C₈	—	71	1	no	—
276	C₂×C₄×C₈	C₂×D₇₁	1	1	yes	characteristic
277	#335	—	71	2	no	—
278	#335	—	71	2	no	—
279	#335	—	71	1	no	—
280	#335	—	71	1	no	—
281	#335	C₂×D₇₁	1	1	yes	characteristic
282	#335	C₂×D₇₁	1	1	yes	characteristic
283	#334	—	71	2	no	—
284	#334	—	71	2	no	—
285	#334	—	71	2	no	—
286	#334	C₂×D₇₁	1	2	yes	—
287	C₂×#41	—	71	1	no	—
288	C₂×M₁₆	—	142	2	no	—
289	C₂²×C₈	—	71	1	no	—
290	C₂²×C₈	—	71	1	no	—
291	C₂²×C₈	—	71	1	no	—
292	C₂²×C₈	—	71	1	no	—
293	C₂²×C₈	—	142	2	no	—
294	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
295	C₂²×C₈	C₄×D₇₁	1	1	yes	characteristic
296	C₄×Q₈	—	71	1	no	—
297	C₄×Q₈	—	71	1	no	—
298	C₄×D₄	—	71	1	no	—
299	C₄×D₄	—	71	1	no	—
300	C₄×D₄	—	71	1	no	—
301	C₄×D₄	—	71	1	no	—
302	C₄×D₄	—	71	1	no	—
303	C₄×D₄	—	71	1	no	—
304	#117	—	71	1	no	—
305	#117	—	71	1	no	—
306	#117	—	71	1	no	—
307	C₂×C₄²	—	71	1	no	—
308	C₂×C₄²	—	71	1	no	—
309	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
310	C₄⋊C₈	—	71	1	no	—
311	C₄⋊C₈	—	71	1	no	—
312	C₄⋊C₈	—	71	1	no	—
313	C₄⋊C₈	—	71	1	no	—
314	C₄⋊C₈	—	71	1	no	—
315	C₄⋊C₈	—	71	1	no	—
316	C₄⋊C₈	—	71	2	no	—
317	C₄⋊C₈	—	71	2	no	—
318	C₄⋊C₈	—	142	2	no	—
319	C₄⋊C₈	—	142	2	no	—
320	C₄⋊C₈	C₂²×D₇₁	1	2	yes	—
321	C₄⋊C₈	C₂²×D₇₁	1	2	yes	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	71	1	no	—
324	C₂²⋊C₈	—	71	1	no	—
325	C₂²⋊C₈	—	71	1	no	—
326	C₂²⋊C₈	—	71	1	no	—
327	C₂²⋊C₈	—	71	1	no	—
328	C₂²⋊C₈	—	71	1	no	—
329	C₂²⋊C₈	—	142	2	no	—
330	C₂²⋊C₈	—	142	2	no	—
331	C₂²⋊C₈	—	142	2	no	—
332	#97	—	2	2	no	—
333	#97	—	142	2	no	—
334	C₄×C₈	—	71	1	no	—
335	C₄×C₈	—	71	1	no	—
336	C₄×C₈	—	71	1	no	—
337	C₄×C₈	—	71	1	no	—
338	C₄×C₈	—	71	1	no	—
339	C₄×C₈	—	71	1	no	—
340	C₄×C₈	—	142	2	no	—
341	C₄×C₈	—	142	2	no	—
342	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
343	C₄×C₈	C₄×D₇₁	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
345	C₄×C₈	C₂²×D₇₁	1	1	yes	characteristic
346	#41	—	142	2	no	—
347	#41	—	142	2	no	—
348	C₂×Q₈	—	71	1	no	—
349	C₂×D₄	—	71	1	no	—
350	C₂×D₄	—	71	1	no	—
351	C₂×D₄	—	71	1	no	—
352	C₂²×C₄	—	71	1	no	—
353	C₂²×C₄	—	71	1	no	—
354	C₂²×C₄	—	71	1	no	—
355	C₂²×C₄	—	71	1	no	—
356	C₂²×C₄	—	71	1	no	—
357	C₂²×C₄	—	71	1	no	—
358	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
359	C₂²×C₄	D₄×D₇₁	1	1	yes	characteristic
360	C₂²×C₄	Q₈×D₇₁	1	1	yes	characteristic
361	M₁₆	—	284	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	284	1	no	—
367	C₂×C₈	—	284	1	no	—
368	C₂×C₈	—	284	4	no	—
369	C₂×C₈	—	71	1	no	—
370	C₂×C₈	—	71	1	no	—
371	C₂×C₈	—	71	1	no	—
372	C₂×C₈	—	71	1	no	—
373	C₂×C₈	—	142	2	no	—
374	C₂×C₈	—	142	2	no	—
375	C₂×C₈	—	142	2	no	—
376	C₂×C₈	—	142	2	no	—
377	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
378	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
380	C₂×C₈	C₂×C₄×D₇₁	1	1	yes	characteristic
381	C₄⋊C₄	—	71	1	no	—
382	C₄⋊C₄	—	71	1	no	—
383	C₄⋊C₄	—	71	1	no	—
384	C₄⋊C₄	—	71	1	no	—
385	C₄⋊C₄	—	71	1	no	—
386	C₄⋊C₄	—	71	1	no	—
387	C₂²⋊C₄	—	71	1	no	—
388	C₂²⋊C₄	—	71	1	no	—
389	C₂²⋊C₄	—	71	1	no	—
390	C₂²⋊C₄	—	71	1	no	—
391	C₂²⋊C₄	—	71	1	no	—
392	C₂²⋊C₄	—	71	1	no	—
393	C₄²	—	71	1	no	—
394	C₄²	—	71	1	no	—
395	C₄²	—	71	1	no	—
396	C₄²	—	71	1	no	—
397	C₄²	—	71	1	no	—
398	C₄²	—	71	1	no	—
399	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
400	C₄²	D₄×D₇₁	1	1	yes	characteristic
401	C₄²	Q₈×D₇₁	1	1	yes	characteristic
402	C₄²	C₂³×D₇₁	1	1	yes	characteristic
403	C₂³	—	71	1	no	—
404	C₂³	—	71	1	no	—
405	C₂³	C₄⋊C₄×D₇₁	1	1	yes	characteristic
406	Q₈	—	142	2	no	—
407	D₄	—	142	2	no	—
408	D₄	—	142	2	no	—
409	D₄	—	142	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	284	1	no	—
416	C₂×C₄	—	284	1	no	—
417	C₂×C₄	—	71	1	no	—
418	C₂×C₄	—	71	2	no	—
419	C₂×C₄	—	71	2	no	—
420	C₂×C₄	—	71	1	no	—
421	C₂×C₄	—	71	1	no	—
422	C₂×C₄	—	71	1	no	—
423	C₂×C₄	—	71	1	no	—
424	C₂×C₄	—	71	1	no	—
425	C₂×C₄	—	142	1	no	—
426	C₂×C₄	—	142	1	no	—
427	C₂×C₄	—	142	1	no	—
428	C₂×C₄	—	142	1	no	—
429	C₂×C₄	—	142	1	no	—
430	C₂×C₄	—	142	1	no	—
431	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
432	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
433	C₂×C₄	C₄⋊C₄×D₇₁	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
436	C₂×C₄	C₂×Q₈×D₇₁	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	284	2	no	—
443	C₈	—	284	2	no	—
444	C₈	—	142	1	no	—
445	C₈	—	142	1	no	—
446	C₈	—	142	1	no	—
447	C₈	—	142	1	no	—
448	C₈	#14556136	1	2	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	71	2	no	—
453	C₂²	—	142	1	no	—
454	C₂²	—	142	1	no	—
455	C₂²	—	142	1	no	—
456	C₂²	—	142	1	no	—
457	C₂²	—	142	1	no	—
458	C₂²	C₂×C₄⋊C₄×D₇₁	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	71	2	no	—
464	C₄	—	142	1	no	—
465	C₄	—	142	1	no	—
466	C₄	—	142	1	no	—
467	C₄	—	142	1	no	—
468	C₄	—	142	1	no	—
469	C₄	C₂×#14556136	1	1	yes	characteristic
470	C₄	#17986765	1	1	yes	characteristic
471	C₄	#135×D₇₁	1	1	yes	characteristic
472	C₄	#135×D₇₁	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	284	1	no	—
475	C₂	—	142	2	no	—
476	C₂	#22596909	1	1	yes	characteristic
477	C₂	#427×D₇₁	1	1	yes	characteristic
478	C₂	#22596948	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×#1568	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂×#11765865	D₄
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#1568	D₇₁
hypocenter	C₇₁	#17829
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #22587121	C₂	semidirect
4. #22587117	C₂	semidirect
5. #22587109	C₂	semidirect
6. #22587102	C₂	semidirect
7. #22587097	C₂	semidirect
8. #22587088	C₂	semidirect
9. #22587087	C₂	semidirect
10. #335×D₇₁	C₂	semidirect
11. C₇₁×#1568	C₂	semidirect
246. #1568	D₇₁	semidirect
251. C₇₁	#17829	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11765865	2
#22597007	2
#22587121	2
#22587117	2
#22587109	2
#22587102	2
#22587097	2
#22587088	2
#22587087	2
#335×D₇₁	2
C₇₁×#1568	2
#17829	71