Subgroups — #31966767

Order 18176.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22597465	C₂	1	1	yes	maximal, characteristic
2	#22597307	C₂	1	1	yes	maximal, characteristic
3	#22587126	C₂	1	1	yes	maximal, characteristic, complemented
4	#22587123	C₂	1	1	yes	maximal, characteristic, complemented
5	#22587121	C₂	1	1	yes	maximal, characteristic, complemented
6	#22587118	C₂	1	1	yes	maximal, characteristic, complemented
7	#22587112	C₂	1	1	yes	maximal, characteristic, complemented
8	#22587110	C₂	1	1	yes	maximal, characteristic, complemented
9	#22587108	C₂	1	1	yes	maximal, characteristic, complemented
10	#22587105	C₂	1	1	yes	maximal, characteristic, complemented
11	#22587101	C₂	1	1	yes	maximal, characteristic, complemented
12	#22587093	C₂	1	1	yes	maximal, characteristic, complemented
13	#22587090	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17985749	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₁×#2990	C₂	1	1	yes	maximal, characteristic
16	#17986130	—	2	1	no	—
17	#17986130	C₄	1	1	yes	characteristic
18	#17986130	C₄	1	1	yes	characteristic
19	#17986077	C₄	1	1	yes	characteristic
20	#17986077	C₄	1	1	yes	characteristic
21	#17986071	—	2	1	no	—
22	#17986071	—	2	1	no	—
23	#17986071	C₄	1	1	yes	characteristic
24	#17986071	C₄	1	1	yes	characteristic
25	#17986071	C₄	1	1	yes	characteristic
26	#17986071	C₄	1	1	yes	characteristic
27	D₄×C₇₁⋊C₈	—	2	1	no	—
28	#17986056	C₂²	1	1	yes	characteristic
29	#17986056	C₂²	1	1	yes	characteristic
30	#17986052	C₂²	1	1	yes	characteristic
31	#17986052	C₂²	1	1	yes	characteristic
32	#17986052	C₂²	1	1	yes	characteristic
33	#17986052	C₂²	1	1	yes	characteristic
34	#17986023	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
37	C₄×#11765849	C₂²	1	1	yes	characteristic
38	C₄×#11765849	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
40	#17985751	C₂²	1	1	yes	characteristic
41	#17985751	C₂²	1	1	yes	characteristic
42	#17985751	C₂²	1	1	yes	characteristic
43	#17985751	C₂²	1	1	yes	characteristic
44	#17985751	C₂²	1	1	yes	characteristic
45	#17985751	C₂²	1	1	yes	characteristic
46	#17985749	C₂²	1	1	yes	characteristic
47	#17985749	C₂²	1	1	yes	characteristic
48	#17985749	C₂²	1	1	yes	characteristic
49	#17985749	C₂²	1	1	yes	characteristic
50	#17985749	C₂²	1	1	yes	characteristic
51	#17985749	C₂²	1	1	yes	characteristic
52	#17985749	C₂²	1	1	yes	characteristic
53	#17985749	C₂²	1	1	yes	characteristic
54	#17985749	C₂²	1	1	yes	characteristic
55	#17985749	C₂²	1	1	yes	characteristic
56	C₄×#41×C₇₁	C₂²	1	1	yes	characteristic
57	#446×C₇₁	—	2	1	no	—
58	#435×C₇₁	—	2	1	no	—
59	#435×C₇₁	—	2	1	no	—
60	C₈×D₄×C₇₁	—	2	1	no	—
61	#432×C₇₁	C₂²	1	1	yes	characteristic
62	#432×C₇₁	C₂²	1	1	yes	characteristic
63	#431×C₇₁	C₂²	1	1	yes	characteristic
64	#423×C₇₁	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊C₈×C₇₁	C₂²	1	1	yes	characteristic
67	C₂×#11765849	—	2	1	no	—
68	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
69	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
70	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
71	C₂×#11765849	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₇₁⋊C₈	—	2	1	no	—
73	C₂²×C₇₁⋊C₈	—	2	1	no	—
74	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
77	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
78	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
79	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
83	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
84	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
85	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
86	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
87	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
88	C₄⋊(C₇₁⋊C₈)	C₂³	1	1	yes	characteristic
89	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
98	#14556039	—	2	1	no	—
99	#14556039	—	2	1	no	—
100	#14556039	C₂×C₄	1	1	yes	characteristic
101	#14556039	C₂×C₄	1	1	yes	characteristic
102	#14556039	C₂×C₄	1	1	yes	characteristic
103	#14556039	C₂×C₄	1	1	yes	characteristic
104	C₄×C₇₁⋊C₈	—	2	1	no	—
105	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₄×C₇₁⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
109	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
110	C₄×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×#41×C₇₁	Q₈	1	1	yes	characteristic
112	C₂×M₁₆×C₇₁	—	2	1	no	—
113	C₂²×C₈×C₇₁	—	2	1	no	—
114	C₂²×C₈×C₇₁	—	2	1	no	—
115	C₄×Q₈×C₇₁	C₂×C₄	1	1	yes	characteristic
116	C₄×Q₈×C₇₁	D₄	1	1	yes	characteristic
117	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
118	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
121	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
122	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
123	#117×C₇₁	Q₈	1	1	yes	characteristic
124	#117×C₇₁	Q₈	1	1	yes	characteristic
125	#117×C₇₁	Q₈	1	1	yes	characteristic
126	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₇₁	—	2	1	no	—
130	C₄⋊C₈×C₇₁	—	2	1	no	—
131	C₄⋊C₈×C₇₁	—	2	1	no	—
132	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₇₁	C₂³	1	1	yes	characteristic
136	C₂²⋊C₈×C₇₁	—	2	1	no	—
137	C₂²⋊C₈×C₇₁	—	2	1	no	—
138	C₂²⋊C₈×C₇₁	—	2	1	no	—
139	#97×C₇₁	—	2	1	no	—
140	#97×C₇₁	—	2	1	no	—
141	C₄×C₈×C₇₁	—	2	1	no	—
142	#11765849	—	2	2	no	—
143	#11765849	—	2	2	no	—
144	#11765849	—	4	1	no	—
145	#11765849	—	4	1	no	—
146	#11765849	—	8	1	no	—
147	C₂×C₇₁⋊C₈	—	2	2	no	—
148	C₂×C₇₁⋊C₈	—	2	1	no	—
149	C₂×C₇₁⋊C₈	—	2	1	no	—
150	C₂×C₇₁⋊C₈	—	2	1	no	—
151	C₂×C₇₁⋊C₈	—	2	1	no	—
152	C₂×C₇₁⋊C₈	—	4	1	no	—
153	C₂×C₇₁⋊C₈	—	8	1	no	—
154	C₂×C₇₁⋊C₈	—	8	1	no	—
155	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₇₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	#41×C₇₁	—	4	2	no	—
164	C₂×Q₈×C₇₁	C₄⋊C₄	1	1	yes	characteristic
165	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
166	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
167	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
175	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
176	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
177	M₁₆×C₇₁	—	8	1	no	—
178	C₂×C₈×C₇₁	—	2	1	no	—
179	C₂×C₈×C₇₁	—	2	1	no	—
180	C₂×C₈×C₇₁	—	2	1	no	—
181	C₂×C₈×C₇₁	—	2	1	no	—
182	C₂×C₈×C₇₁	—	8	1	no	—
183	C₂×C₈×C₇₁	—	8	1	no	—
184	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
185	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
187	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
188	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
190	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
191	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
194	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
196	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
197	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
199	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
203	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
204	C₄²×C₇₁	C₂×Q₈	1	1	yes	characteristic
205	C₄²×C₇₁	C₂⁴	1	1	yes	characteristic
206	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
209	Q₈×C₇₁	—	4	1	no	—
210	D₄×C₇₁	—	2	2	no	—
211	D₄×C₇₁	—	2	2	no	—
212	D₄×C₇₁	—	4	1	no	—
213	C₂×C₄×C₇₁	—	2	2	no	—
214	C₂×C₄×C₇₁	—	2	1	no	—
215	C₂×C₄×C₇₁	—	2	1	no	—
216	C₂×C₄×C₇₁	—	2	1	no	—
217	C₂×C₄×C₇₁	—	2	1	no	—
218	C₂×C₄×C₇₁	—	2	1	no	—
219	C₂×C₄×C₇₁	—	2	1	no	—
220	C₂×C₄×C₇₁	—	2	1	no	—
221	C₂×C₄×C₇₁	—	2	1	no	—
222	C₂×C₄×C₇₁	—	2	1	no	—
223	C₂×C₄×C₇₁	—	2	1	no	—
224	C₂×C₄×C₇₁	—	2	1	no	—
225	C₂×C₄×C₇₁	—	2	1	no	—
226	C₂×C₄×C₇₁	—	4	1	no	—
227	C₂×C₄×C₇₁	—	4	1	no	—
228	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
240	C₈×C₇₁	—	4	1	no	—
241	C₈×C₇₁	—	4	1	no	—
242	C₈×C₇₁	—	4	1	no	—
243	C₈×C₇₁	—	4	1	no	—
244	C₇₁⋊C₈	—	2	1	no	—
245	C₇₁⋊C₈	—	2	1	no	—
246	C₇₁⋊C₈	—	2	1	no	—
247	C₇₁⋊C₈	—	2	1	no	—
248	C₇₁⋊C₈	—	2	1	no	—
249	C₇₁⋊C₈	—	2	1	no	—
250	C₇₁⋊C₈	—	2	1	no	—
251	C₇₁⋊C₈	—	4	1	no	—
252	C₇₁⋊C₈	—	4	1	no	—
253	C₇₁⋊C₈	—	4	1	no	—
254	C₇₁⋊C₈	—	4	1	no	—
255	C₇₁⋊C₈	#131	1	2	yes	—
256	C₂²×C₇₁	—	2	1	no	—
257	C₂²×C₇₁	—	2	1	no	—
258	C₂²×C₇₁	—	2	1	no	—
259	C₂²×C₇₁	—	2	1	no	—
260	C₂²×C₇₁	—	2	1	no	—
261	C₂²×C₇₁	—	2	1	no	—
262	C₂²×C₇₁	—	2	1	no	—
263	C₂²×C₇₁	—	2	1	no	—
264	C₂²×C₇₁	#430	1	2	yes	—
265	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
266	C₄×C₇₁	—	2	1	no	—
267	C₄×C₇₁	—	2	1	no	—
268	C₄×C₇₁	—	2	1	no	—
269	C₄×C₇₁	—	2	1	no	—
270	C₄×C₇₁	—	2	1	no	—
271	C₄×C₇₁	—	2	1	no	—
272	C₄×C₇₁	—	2	1	no	—
273	C₄×C₇₁	—	2	1	no	—
274	C₄×C₇₁	—	2	1	no	—
275	C₄×C₇₁	—	2	1	no	—
276	C₄×C₇₁	C₂×#131	1	1	yes	characteristic
277	C₄×C₇₁	#568	1	1	yes	characteristic
278	C₄×C₇₁	#577	1	1	yes	characteristic
279	C₄×C₇₁	#577	1	1	yes	characteristic
280	#17838	—	71	1	no	maximal, Sylow
281	C₂×C₇₁	—	2	2	no	—
282	C₂×C₇₁	—	4	1	no	—
283	C₂×C₇₁	—	4	1	no	—
284	C₂×C₇₁	#2906	1	1	yes	characteristic
285	C₂×C₇₁	#2912	1	1	yes	characteristic
286	C₂×C₇₁	C₂×#430	1	1	yes	characteristic
287	#2990	—	71	1	no	—
288	#2990	D₇₁	1	1	yes	characteristic
289	#2965	—	71	1	no	—
290	#1573	—	71	1	no	—
291	#1573	—	71	1	no	—
292	#1572	—	71	1	no	—
293	#1572	—	71	1	no	—
294	#1570	—	71	1	no	—
295	#1570	—	71	1	no	—
296	#1569	—	71	1	no	—
297	#1569	—	71	1	no	—
298	#1568	—	71	1	no	—
299	#1565	—	71	1	no	—
300	#1565	—	71	1	no	—
301	C₂×#334	—	71	1	no	—
302	C₇₁	#17838	1	1	yes	characteristic, complemented, Sylow
303	C₄×#41	C₂×D₇₁	1	1	yes	characteristic
304	#446	—	2	1	no	—
305	#446	—	71	1	no	—
306	#446	—	71	1	no	—
307	#446	—	142	1	no	—
308	#436	—	71	1	no	—
309	#436	—	71	1	no	—
310	#435	—	2	1	no	—
311	#435	—	2	1	no	—
312	#435	—	71	1	no	—
313	#435	—	71	1	no	—
314	#435	—	71	1	no	—
315	#435	—	71	1	no	—
316	#435	—	142	1	no	—
317	#435	—	142	1	no	—
318	C₈×D₄	—	2	1	no	—
319	C₈×D₄	—	142	1	no	—
320	#432	—	71	1	no	—
321	#432	—	71	1	no	—
322	#432	C₂×D₇₁	1	1	yes	characteristic
323	#432	C₂×D₇₁	1	1	yes	characteristic
324	#431	—	71	1	no	—
325	#431	—	71	1	no	—
326	#431	—	71	1	no	—
327	#431	—	71	1	no	—
328	#431	C₂×D₇₁	1	1	yes	characteristic
329	#423	—	71	1	no	—
330	#423	C₂×D₇₁	1	1	yes	characteristic
331	C₂×C₄⋊C₈	—	71	1	no	—
332	C₂×C₄⋊C₈	—	71	1	no	—
333	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
334	C₂×C₄⋊C₈	C₂×D₇₁	1	1	yes	characteristic
335	C₄×M₁₆	—	71	1	no	—
336	C₄×M₁₆	—	71	1	no	—
337	C₂×C₄×C₈	—	71	1	no	—
338	#335	—	71	1	no	—
339	#335	—	71	1	no	—
340	#335	—	71	1	no	—
341	#335	—	71	1	no	—
342	#335	—	71	1	no	—
343	#335	—	71	1	no	—
344	#334	—	71	1	no	—
345	#334	—	71	1	no	—
346	#334	—	71	1	no	—
347	#334	—	71	1	no	—
348	#334	—	71	1	no	—
349	#334	—	71	1	no	—
350	#334	—	71	1	no	—
351	#334	—	71	1	no	—
352	#334	—	71	1	no	—
353	#334	—	71	1	no	—
354	C₂×#41	Dic₁₄₂	1	1	yes	characteristic
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	71	1	no	—
357	C₂×M₁₆	—	71	1	no	—
358	C₂×M₁₆	—	71	1	no	—
359	C₂×M₁₆	—	71	1	no	—
360	C₂×M₁₆	—	142	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	71	1	no	—
364	C₂²×C₈	—	71	1	no	—
365	C₂²×C₈	—	142	1	no	—
366	C₂²×C₈	—	142	1	no	—
367	C₄×Q₈	C₄×D₇₁	1	1	yes	characteristic
368	C₄×Q₈	C₂²⋊D₇₁	1	1	yes	characteristic
369	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
370	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
371	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
372	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
373	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
374	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
375	#117	Dic₁₄₂	1	1	yes	characteristic
376	#117	Dic₁₄₂	1	1	yes	characteristic
377	#117	Dic₁₄₂	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	71	1	no	—
385	C₄⋊C₈	—	71	1	no	—
386	C₄⋊C₈	—	71	1	no	—
387	C₄⋊C₈	—	71	1	no	—
388	C₄⋊C₈	—	71	1	no	—
389	C₄⋊C₈	—	71	1	no	—
390	C₄⋊C₈	—	71	1	no	—
391	C₄⋊C₈	—	71	1	no	—
392	C₄⋊C₈	—	71	1	no	—
393	C₄⋊C₈	—	71	1	no	—
394	C₄⋊C₈	—	142	1	no	—
395	C₄⋊C₈	—	142	1	no	—
396	C₄⋊C₈	—	142	1	no	—
397	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
398	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
399	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
400	C₄⋊C₈	C₂²×D₇₁	1	1	yes	characteristic
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	71	1	no	—
405	C₂²⋊C₈	—	71	1	no	—
406	C₂²⋊C₈	—	71	1	no	—
407	C₂²⋊C₈	—	71	1	no	—
408	C₂²⋊C₈	—	71	1	no	—
409	C₂²⋊C₈	—	71	1	no	—
410	C₂²⋊C₈	—	142	1	no	—
411	C₂²⋊C₈	—	142	1	no	—
412	C₂²⋊C₈	—	142	1	no	—
413	#97	—	2	1	no	—
414	#97	—	2	1	no	—
415	#97	—	71	1	no	—
416	#97	—	71	1	no	—
417	#97	—	71	1	no	—
418	#97	—	71	1	no	—
419	#97	—	142	1	no	—
420	#97	—	142	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	71	1	no	—
423	C₄×C₈	—	71	1	no	—
424	C₄×C₈	—	71	1	no	—
425	C₄×C₈	—	71	1	no	—
426	C₄×C₈	—	71	1	no	—
427	C₄×C₈	—	71	1	no	—
428	C₄×C₈	—	142	1	no	—
429	#41	—	4	2	no	—
430	C₂×Q₈	Dic₇₁⋊C₄	1	1	yes	characteristic
431	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
432	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
433	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
440	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
441	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
442	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
443	M₁₆	—	8	1	no	—
444	M₁₆	—	284	1	no	—
445	M₁₆	—	284	1	no	—
446	M₁₆	—	568	1	no	—
447	M₁₆	—	142	2	no	—
448	M₁₆	—	142	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	8	1	no	—
454	C₂×C₈	—	8	1	no	—
455	C₂×C₈	—	284	1	no	—
456	C₂×C₈	—	568	1	no	—
457	C₂×C₈	—	568	1	no	—
458	C₂×C₈	—	71	1	no	—
459	C₂×C₈	—	71	1	no	—
460	C₂×C₈	—	71	1	no	—
461	C₂×C₈	—	71	1	no	—
462	C₂×C₈	—	71	1	no	—
463	C₂×C₈	—	71	1	no	—
464	C₂×C₈	—	71	1	no	—
465	C₂×C₈	—	71	1	no	—
466	C₂×C₈	—	142	1	no	—
467	C₂×C₈	—	142	1	no	—
468	C₂×C₈	—	142	1	no	—
469	C₂×C₈	—	142	1	no	—
470	C₂×C₈	—	142	2	no	—
471	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
472	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
473	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
474	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
475	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
476	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
477	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
478	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
479	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
480	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
481	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
482	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
483	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
484	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
485	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
486	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
487	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
488	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
489	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
490	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
491	C₄²	C₂×Dic₁₄₂	1	1	yes	characteristic
492	C₄²	C₂³×D₇₁	1	1	yes	characteristic
493	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
494	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
495	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
496	Q₈	—	4	1	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	4	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
516	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
517	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
518	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
519	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
520	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
521	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
522	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
525	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
526	C₂×C₄	C₂²×Dic₁₄₂	1	1	yes	characteristic
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	284	1	no	—
532	C₈	—	284	1	no	—
533	C₈	—	284	1	no	—
534	C₈	—	284	1	no	—
535	C₈	—	71	2	no	—
536	C₈	—	142	1	no	—
537	C₈	—	142	1	no	—
538	C₈	—	142	1	no	—
539	C₈	—	142	1	no	—
540	C₈	—	142	1	no	—
541	C₈	—	142	1	no	—
542	C₈	—	142	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	#17986047	1	2	yes	—
552	C₂²	C₂²×Dic₇₁⋊C₄	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	#131×D₇₁	1	1	yes	characteristic
564	C₄	#17986764	1	1	yes	characteristic
565	C₄	#17986807	1	1	yes	characteristic
566	C₄	#17986810	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	4	1	no	—
570	C₂	#22596906	1	1	yes	characteristic
571	C₂	#22596933	1	1	yes	characteristic
572	C₂	C₂×#17986047	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₄²	C₂³×D₇₁
Fitting	C₇₁×#2990	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₇₁	Q₈
cosocle	C₄²×C₇₁	C₂⁴
hypercenter	#2990	D₇₁
hypocenter	C₇₁	#17838
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
3. #22587126	C₂	semidirect
4. #22587123	C₂	semidirect
5. #22587121	C₂	semidirect
6. #22587118	C₂	semidirect
7. #22587112	C₂	semidirect
8. #22587110	C₂	semidirect
9. #22587108	C₂	semidirect
10. #22587105	C₂	semidirect
11. #22587101	C₂	semidirect
12. #22587093	C₂	semidirect
13. #22587090	C₂	semidirect
14. C₂×#17985749	C₂	semidirect
302. C₇₁	#17838	semidirect

Maximal subgroups

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

subgroup	index
#22597465	2
#22597307	2
#22587126	2
#22587123	2
#22587121	2
#22587118	2
#22587112	2
#22587110	2
#22587108	2
#22587105	2
#22587101	2
#22587093	2
#22587090	2
C₂×#17985749	2
C₇₁×#2990	2
#17838	71