Subgroups — #32016224

Order 18176.

796 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#11765849	C₂	1	1	yes	maximal, characteristic
2	C₂×#17986071	C₂	1	1	yes	maximal, characteristic
3	#22589115	C₂	1	1	yes	maximal, characteristic, complemented
4	#22589113	C₂	1	1	yes	maximal, characteristic, complemented
5	#22588545	C₂	1	1	yes	maximal, characteristic, complemented
6	#22588545	C₂	1	1	yes	maximal, characteristic, complemented
7	#22588544	C₂	1	1	yes	maximal, characteristic, complemented
8	#22588544	C₂	1	1	yes	maximal, characteristic, complemented
9	#22588480	C₂	1	1	yes	maximal, characteristic, complemented
10	#22588380	C₂	1	1	yes	maximal, characteristic, complemented
11	#22588376	C₂	1	1	yes	maximal, characteristic, complemented
12	#22588247	C₂	1	1	yes	maximal, characteristic, complemented
13	#22588066	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#17985763	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×M₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11765849	C₂²	1	1	yes	characteristic
17	C₂²×#11765849	C₂²	1	1	yes	characteristic
18	C₂²×#11765849	C₂²	1	1	yes	characteristic
19	C₂³×C₇₁⋊C₈	C₂²	1	1	yes	characteristic
20	#17986077	—	2	1	no	—
21	#17986071	—	2	1	no	—
22	#17986071	—	2	1	no	—
23	#17986071	C₄	1	2	yes	—
24	#17986071	C₄	1	2	yes	—
25	#17986071	C₄	1	2	yes	—
26	#17986071	C₄	1	2	yes	—
27	D₄×C₇₁⋊C₈	—	2	1	no	—
28	C₂×#14556063	C₂²	1	1	yes	characteristic
29	C₂×#14556063	C₂²	1	1	yes	characteristic
30	C₂×#14556063	C₂²	1	1	yes	characteristic
31	C₂×#14556063	C₂²	1	1	yes	characteristic
32	C₂×#14556063	C₂²	1	1	yes	characteristic
33	C₂×#14556063	C₂²	1	1	yes	characteristic
34	#17986023	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
36	#17985963	C₂²	1	1	yes	characteristic
37	#17985963	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊(C₇₁⋊C₈)	C₂²	1	1	yes	characteristic
40	C₄×#11765849	C₂²	1	1	yes	characteristic
41	C₂×#14556039	C₂²	1	1	yes	characteristic
42	#17985763	C₂²	1	1	yes	characteristic
43	#17985763	C₂²	1	1	yes	characteristic
44	#17985763	C₂²	1	1	yes	characteristic
45	#17985763	C₂²	1	1	yes	characteristic
46	#17985763	C₂²	1	1	yes	characteristic
47	#17985763	C₂²	1	1	yes	characteristic
48	#17985763	C₂²	1	1	yes	characteristic
49	#17985763	C₂²	1	1	yes	characteristic
50	#17985763	C₂²	1	1	yes	characteristic
51	#17985763	C₂²	1	1	yes	characteristic
52	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
53	C₂²×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₇₁	C₂²	1	1	yes	characteristic
55	#436×C₇₁	—	2	1	no	—
56	#435×C₇₁	—	2	1	no	—
57	#435×C₇₁	—	2	1	no	—
58	C₈×D₄×C₇₁	—	2	1	no	—
59	#423×C₇₁	C₂²	1	1	yes	characteristic
60	#407×C₇₁	C₂²	1	1	yes	characteristic
61	#407×C₇₁	C₂²	1	1	yes	characteristic
62	C₄×M₁₆×C₇₁	C₂²	1	1	yes	characteristic
63	C₂×#11765849	—	2	2	no	—
64	C₂×#11765849	—	2	2	no	—
65	C₂×#11765849	—	2	1	no	—
66	C₂×#11765849	—	2	1	no	—
67	C₂×#11765849	—	4	1	no	—
68	C₂×#11765849	—	4	1	no	—
69	C₂×#11765849	—	4	1	no	—
70	C₂×#11765849	—	4	1	no	—
71	C₂×#11765849	C₂×C₄	1	2	yes	—
72	C₂×#11765849	C₂×C₄	1	2	yes	—
73	C₂×#11765849	C₂³	1	1	yes	characteristic
74	C₂×#11765849	C₂³	1	1	yes	characteristic
75	C₂×#11765849	C₂³	1	1	yes	characteristic
76	C₂×#11765849	C₂³	1	1	yes	characteristic
77	C₂²×C₇₁⋊C₈	—	2	1	no	—
78	C₂²×C₇₁⋊C₈	—	2	1	no	—
79	C₂²×C₇₁⋊C₈	—	4	1	no	—
80	C₂²×C₇₁⋊C₈	—	4	1	no	—
81	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
82	C₂²×C₇₁⋊C₈	C₂×C₄	1	2	yes	—
83	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
84	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
87	#14556063	—	2	2	no	—
88	#14556063	—	2	2	no	—
89	#14556063	—	4	1	no	—
90	#14556063	—	4	1	no	—
91	#14556063	—	4	1	no	—
92	#14556063	—	4	1	no	—
93	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
94	C₄⋊(C₇₁⋊C₈)	—	2	1	no	—
95	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
96	C₄⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
97	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
98	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
99	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
100	C₂²⋊(C₇₁⋊C₈)	—	2	1	no	—
101	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
102	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
103	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
104	C₂²⋊(C₇₁⋊C₈)	C₂×C₄	1	2	yes	—
105	#14556039	—	2	1	no	—
106	#14556039	C₂×C₄	1	2	yes	—
107	#14556039	C₂×C₄	1	2	yes	—
108	C₄×C₇₁⋊C₈	—	2	1	no	—
109	C₂²×D₄×C₇₁	Q₈	1	1	yes	characteristic
110	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₇₁	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₇₁	—	2	1	no	—
113	C₂×M₁₆×C₇₁	—	2	1	no	—
114	C₂×M₁₆×C₇₁	—	2	2	no	—
115	C₂×M₁₆×C₇₁	—	2	2	no	—
116	C₂×M₁₆×C₇₁	—	4	1	no	—
117	C₂×M₁₆×C₇₁	—	4	1	no	—
118	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
120	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
121	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₇₁	—	2	1	no	—
123	C₂²×C₈×C₇₁	—	2	1	no	—
124	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
125	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
126	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
127	C₄×D₄×C₇₁	C₂×C₄	1	1	yes	characteristic
128	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
129	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
130	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
131	C₄×D₄×C₇₁	D₄	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₇₁	Q₈	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₇₁	Q₈	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₇₁	Q₈	1	1	yes	characteristic
135	C₂×C₄²×C₇₁	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₇₁	—	2	1	no	—
137	C₄⋊C₈×C₇₁	—	2	1	no	—
138	C₂²⋊C₈×C₇₁	—	2	1	no	—
139	C₂²⋊C₈×C₇₁	—	2	1	no	—
140	C₂²⋊C₈×C₇₁	—	2	1	no	—
141	C₂²⋊C₈×C₇₁	—	2	1	no	—
142	#97×C₇₁	—	2	1	no	—
143	C₄×C₈×C₇₁	—	2	1	no	—
144	#11765849	—	2	1	no	—
145	#11765849	—	2	1	no	—
146	#11765849	—	2	1	no	—
147	#11765849	—	2	1	no	—
148	#11765849	—	2	1	no	—
149	#11765849	—	2	1	no	—
150	#11765849	—	2	1	no	—
151	#11765849	—	4	2	no	—
152	#11765849	—	4	2	no	—
153	#11765849	—	4	2	no	—
154	#11765849	—	4	2	no	—
155	#11765849	#41	1	2	yes	—
156	C₂×C₇₁⋊C₈	—	2	1	no	—
157	C₂×C₇₁⋊C₈	—	2	1	no	—
158	C₂×C₇₁⋊C₈	—	2	1	no	—
159	C₂×C₇₁⋊C₈	—	2	1	no	—
160	C₂×C₇₁⋊C₈	—	2	1	no	—
161	C₂×C₇₁⋊C₈	—	2	1	no	—
162	C₂×C₇₁⋊C₈	—	2	1	no	—
163	C₂×C₇₁⋊C₈	—	2	1	no	—
164	C₂×C₇₁⋊C₈	—	2	1	no	—
165	C₂×C₇₁⋊C₈	—	2	1	no	—
166	C₂×C₇₁⋊C₈	—	2	1	no	—
167	C₂×C₇₁⋊C₈	—	2	1	no	—
168	C₂×C₇₁⋊C₈	—	4	2	no	—
169	C₂×C₇₁⋊C₈	—	4	2	no	—
170	C₂×C₇₁⋊C₈	—	4	2	no	—
171	C₂×C₇₁⋊C₈	—	4	2	no	—
172	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
173	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₇₁⋊C₈	C₂²×C₄	1	2	yes	—
176	C₂⁴×C₇₁	C₂×Q₈	1	1	yes	characteristic
177	C₂⁴×C₇₁	C₂×Q₈	1	1	yes	characteristic
178	C₂×D₄×C₇₁	—	4	2	no	—
179	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
180	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
181	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
182	C₂×D₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
183	C₂²×C₄×C₇₁	—	2	1	no	—
184	C₂²×C₄×C₇₁	—	2	1	no	—
185	C₂²×C₄×C₇₁	—	2	1	no	—
186	C₂²×C₄×C₇₁	—	2	1	no	—
187	C₂²×C₄×C₇₁	—	2	1	no	—
188	C₂²×C₄×C₇₁	—	2	1	no	—
189	C₂²×C₄×C₇₁	—	2	1	no	—
190	C₂²×C₄×C₇₁	—	2	1	no	—
191	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₁	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
200	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
201	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
202	C₂²×C₄×C₇₁	C₂×Q₈	1	1	yes	characteristic
203	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
204	M₁₆×C₇₁	—	2	1	no	—
205	M₁₆×C₇₁	—	2	1	no	—
206	M₁₆×C₇₁	—	2	1	no	—
207	M₁₆×C₇₁	—	2	1	no	—
208	M₁₆×C₇₁	—	2	1	no	—
209	M₁₆×C₇₁	—	2	1	no	—
210	M₁₆×C₇₁	—	2	1	no	—
211	M₁₆×C₇₁	—	4	2	no	—
212	M₁₆×C₇₁	—	4	2	no	—
213	M₁₆×C₇₁	#41	1	2	yes	—
214	C₂×C₈×C₇₁	—	2	1	no	—
215	C₂×C₈×C₇₁	—	2	1	no	—
216	C₂×C₈×C₇₁	—	2	1	no	—
217	C₂×C₈×C₇₁	—	2	1	no	—
218	C₂×C₈×C₇₁	—	4	2	no	—
219	C₂×C₈×C₇₁	—	4	2	no	—
220	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
221	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
222	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
223	C₄⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
224	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
225	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
226	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
227	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
228	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
229	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
230	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
231	C₂²⋊C₄×C₇₁	C₄⋊C₄	1	1	yes	characteristic
232	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
233	C₄²×C₇₁	C₂²×C₄	1	1	yes	characteristic
234	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₇₁	C₂×D₄	1	1	yes	characteristic
236	C₂³×C₇₁	—	2	1	no	—
237	C₂³×C₇₁	—	2	1	no	—
238	C₂³×C₇₁	—	2	2	no	—
239	C₂³×C₇₁	—	2	1	no	—
240	C₂³×C₇₁	—	2	1	no	—
241	C₂³×C₇₁	—	4	1	no	—
242	C₂³×C₇₁	—	4	1	no	—
243	C₂³×C₇₁	—	4	1	no	—
244	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂³×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂³×C₇₁	C₂²×Q₈	1	1	yes	characteristic
249	D₄×C₇₁	—	2	2	no	—
250	D₄×C₇₁	—	2	2	no	—
251	D₄×C₇₁	—	4	1	no	—
252	D₄×C₇₁	—	4	1	no	—
253	C₂×C₄×C₇₁	—	2	1	no	—
254	C₂×C₄×C₇₁	—	2	1	no	—
255	C₂×C₄×C₇₁	—	2	1	no	—
256	C₂×C₄×C₇₁	—	2	1	no	—
257	C₂×C₄×C₇₁	—	2	1	no	—
258	C₂×C₄×C₇₁	—	2	1	no	—
259	C₂×C₄×C₇₁	—	2	1	no	—
260	C₂×C₄×C₇₁	—	2	1	no	—
261	C₂×C₄×C₇₁	—	2	1	no	—
262	C₂×C₄×C₇₁	—	2	1	no	—
263	C₂×C₄×C₇₁	—	2	1	no	—
264	C₂×C₄×C₇₁	—	2	1	no	—
265	C₂×C₄×C₇₁	—	2	1	no	—
266	C₂×C₄×C₇₁	—	2	1	no	—
267	C₂×C₄×C₇₁	—	2	1	no	—
268	C₂×C₄×C₇₁	—	2	1	no	—
269	C₂×C₄×C₇₁	—	2	1	no	—
270	C₂×C₄×C₇₁	—	2	1	no	—
271	C₂×C₄×C₇₁	—	2	1	no	—
272	C₂×C₄×C₇₁	—	2	1	no	—
273	C₂×C₄×C₇₁	—	4	1	no	—
274	C₂×C₄×C₇₁	—	4	1	no	—
275	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
281	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₇₁	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
288	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
289	C₈×C₇₁	—	2	2	no	—
290	C₈×C₇₁	—	4	1	no	—
291	C₈×C₇₁	—	4	1	no	—
292	C₈×C₇₁	—	4	1	no	—
293	C₇₁⋊C₈	—	2	2	no	—
294	C₇₁⋊C₈	—	2	2	no	—
295	C₇₁⋊C₈	—	2	2	no	—
296	C₇₁⋊C₈	—	2	2	no	—
297	C₇₁⋊C₈	—	2	2	no	—
298	C₇₁⋊C₈	—	4	1	no	—
299	C₇₁⋊C₈	—	4	1	no	—
300	C₇₁⋊C₈	—	4	1	no	—
301	C₂²×C₇₁	—	2	1	no	—
302	C₂²×C₇₁	—	2	1	no	—
303	C₂²×C₇₁	—	2	1	no	—
304	C₂²×C₇₁	—	2	1	no	—
305	C₂²×C₇₁	—	2	1	no	—
306	C₂²×C₇₁	—	2	1	no	—
307	C₂²×C₇₁	—	2	1	no	—
308	C₂²×C₇₁	—	2	1	no	—
309	C₂²×C₇₁	—	2	1	no	—
310	C₂²×C₇₁	—	2	1	no	—
311	C₂²×C₇₁	—	2	1	no	—
312	C₂²×C₇₁	—	2	1	no	—
313	C₂²×C₇₁	—	2	1	no	—
314	C₂²×C₇₁	—	4	2	no	—
315	C₂²×C₇₁	—	4	2	no	—
316	C₂²×C₇₁	—	8	1	no	—
317	C₂²×C₇₁	—	8	1	no	—
318	C₂²×C₇₁	#430	1	2	yes	—
319	C₂²×C₇₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
320	C₂²×C₇₁	#554	1	1	yes	characteristic
321	C₂²×C₇₁	#554	1	1	yes	characteristic
322	C₄×C₇₁	—	2	1	no	—
323	C₄×C₇₁	—	2	1	no	—
324	C₄×C₇₁	—	2	1	no	—
325	C₄×C₇₁	—	2	1	no	—
326	C₄×C₇₁	—	2	1	no	—
327	C₄×C₇₁	—	2	1	no	—
328	C₄×C₇₁	—	2	1	no	—
329	C₄×C₇₁	—	2	1	no	—
330	C₄×C₇₁	C₄×#41	1	1	yes	characteristic
331	C₄×C₇₁	#518	1	1	yes	characteristic
332	C₄×C₇₁	#546	1	1	yes	characteristic
333	C₄×C₇₁	#546	1	1	yes	characteristic
334	#22718	—	71	1	no	maximal, Sylow
335	C₂×C₇₁	—	2	1	no	—
336	C₂×C₇₁	—	2	1	no	—
337	C₂×C₇₁	—	2	2	no	—
338	C₂×C₇₁	—	4	1	no	—
339	C₂×C₇₁	—	4	1	no	—
340	C₂×C₇₁	—	4	1	no	—
341	C₂×C₇₁	#2349	1	1	yes	characteristic
342	C₂×C₇₁	C₂×#430	1	1	yes	characteristic
343	C₂×C₇₁	#2916	1	1	yes	characteristic
344	D₄×M₁₆	—	71	1	no	—
345	D₄×M₁₆	D₇₁	1	1	yes	characteristic
346	C₂×#435	—	71	1	no	—
347	#1950	—	71	1	no	—
348	#1950	—	71	1	no	—
349	#1855	—	71	1	no	—
350	#1855	—	71	1	no	—
351	#1855	—	71	1	no	—
352	#1855	—	71	1	no	—
353	#1838	—	71	1	no	—
354	#1811	—	71	1	no	—
355	#1810	—	71	1	no	—
356	#1778	—	71	1	no	—
357	#1738	—	71	1	no	—
358	C₂×#341	—	71	1	no	—
359	C₇₁	#22718	1	1	yes	characteristic, complemented, Sylow
360	C₂²×M₁₆	—	71	1	no	—
361	C₂²×M₁₆	—	71	1	no	—
362	C₂²×M₁₆	—	71	1	no	—
363	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
364	C₂²×M₁₆	C₂×D₇₁	1	1	yes	characteristic
365	C₂³×C₈	—	71	1	no	—
366	C₂×C₄×D₄	C₂×D₇₁	1	1	yes	characteristic
367	#436	—	2	1	no	—
368	#436	—	142	1	no	—
369	#435	—	2	1	no	—
370	#435	—	2	1	no	—
371	#435	—	71	2	no	—
372	#435	—	71	2	no	—
373	#435	—	71	2	no	—
374	#435	—	71	2	no	—
375	#435	—	142	1	no	—
376	#435	—	142	1	no	—
377	C₈×D₄	—	2	1	no	—
378	C₈×D₄	—	142	1	no	—
379	C₂×#108	—	71	1	no	—
380	C₂×#108	—	71	1	no	—
381	C₂×#108	—	71	1	no	—
382	C₂×#108	—	71	1	no	—
383	C₂×#108	—	71	1	no	—
384	C₂×#108	—	71	1	no	—
385	#423	—	71	1	no	—
386	#423	C₂×D₇₁	1	1	yes	characteristic
387	C₂×C₄⋊C₈	—	71	1	no	—
388	#407	—	71	1	no	—
389	#407	—	71	1	no	—
390	#407	C₂×D₇₁	1	1	yes	characteristic
391	#407	C₂×D₇₁	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	—	71	1	no	—
393	C₂×C₂²⋊C₈	—	71	1	no	—
394	C₄×M₁₆	—	71	1	no	—
395	C₄×M₁₆	C₂×D₇₁	1	1	yes	characteristic
396	C₂×#97	—	71	1	no	—
397	#341	—	71	1	no	—
398	#341	—	71	1	no	—
399	#341	—	71	1	no	—
400	#341	—	71	1	no	—
401	#341	—	71	1	no	—
402	#341	—	71	1	no	—
403	#341	—	71	1	no	—
404	#341	—	71	1	no	—
405	#341	—	71	1	no	—
406	#341	—	71	1	no	—
407	C₂²×D₄	Dic₁₄₂	1	1	yes	characteristic
408	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
409	C₂³×C₄	C₂²×D₇₁	1	1	yes	characteristic
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	2	no	—
413	C₂×M₁₆	—	2	2	no	—
414	C₂×M₁₆	—	4	1	no	—
415	C₂×M₁₆	—	4	1	no	—
416	C₂×M₁₆	—	284	1	no	—
417	C₂×M₁₆	—	284	1	no	—
418	C₂×M₁₆	—	284	1	no	—
419	C₂×M₁₆	—	284	1	no	—
420	C₂×M₁₆	—	71	2	no	—
421	C₂×M₁₆	—	71	2	no	—
422	C₂×M₁₆	—	71	1	no	—
423	C₂×M₁₆	—	71	1	no	—
424	C₂×M₁₆	—	71	1	no	—
425	C₂×M₁₆	—	71	1	no	—
426	C₂×M₁₆	—	142	2	no	—
427	C₂×M₁₆	—	142	2	no	—
428	C₂×M₁₆	—	142	1	no	—
429	C₂×M₁₆	—	142	1	no	—
430	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
431	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
432	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
433	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
434	C₂²×C₈	—	2	1	no	—
435	C₂²×C₈	—	2	1	no	—
436	C₂²×C₈	—	284	1	no	—
437	C₂²×C₈	—	284	1	no	—
438	C₂²×C₈	—	71	2	no	—
439	C₂²×C₈	—	71	2	no	—
440	C₂²×C₈	—	71	1	no	—
441	C₂²×C₈	—	71	1	no	—
442	C₂²×C₈	—	71	1	no	—
443	C₂²×C₈	—	71	1	no	—
444	C₂²×C₈	—	142	1	no	—
445	C₂²×C₈	—	142	1	no	—
446	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
447	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
448	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
449	C₄×D₄	C₄×D₇₁	1	1	yes	characteristic
450	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
451	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
452	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
453	C₄×D₄	C₂²⋊D₇₁	1	1	yes	characteristic
454	C₂×C₄⋊C₄	Dic₁₄₂	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	Dic₁₄₂	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	Dic₁₄₂	1	1	yes	characteristic
457	C₂×C₄²	C₂²×D₇₁	1	1	yes	characteristic
458	#108	—	284	1	no	—
459	#108	—	284	1	no	—
460	#108	—	284	1	no	—
461	#108	—	284	1	no	—
462	#108	—	142	2	no	—
463	#108	—	142	2	no	—
464	C₄⋊C₈	—	2	1	no	—
465	C₄⋊C₈	—	2	1	no	—
466	C₄⋊C₈	—	71	2	no	—
467	C₄⋊C₈	—	71	2	no	—
468	C₄⋊C₈	—	142	1	no	—
469	C₄⋊C₈	—	142	1	no	—
470	C₂²⋊C₈	—	2	1	no	—
471	C₂²⋊C₈	—	2	1	no	—
472	C₂²⋊C₈	—	2	1	no	—
473	C₂²⋊C₈	—	2	1	no	—
474	C₂²⋊C₈	—	71	2	no	—
475	C₂²⋊C₈	—	71	2	no	—
476	C₂²⋊C₈	—	71	2	no	—
477	C₂²⋊C₈	—	71	2	no	—
478	C₂²⋊C₈	—	142	1	no	—
479	C₂²⋊C₈	—	142	1	no	—
480	C₂²⋊C₈	—	142	1	no	—
481	C₂²⋊C₈	—	142	1	no	—
482	#97	—	2	1	no	—
483	#97	—	71	2	no	—
484	#97	—	71	2	no	—
485	#97	—	142	1	no	—
486	C₄×C₈	—	2	1	no	—
487	C₄×C₈	—	142	1	no	—
488	C₂⁴	C₂×Dic₁₄₂	1	1	yes	characteristic
489	C₂⁴	C₂×Dic₁₄₂	1	1	yes	characteristic
490	C₂×D₄	—	4	2	no	—
491	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
492	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
493	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
494	C₂×D₄	Dic₇₁⋊C₄	1	1	yes	characteristic
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₄×D₇₁	1	1	yes	characteristic
507	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
509	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
511	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
512	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
513	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
514	C₂²×C₄	C₂×Dic₁₄₂	1	1	yes	characteristic
515	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	4	2	no	—
524	M₁₆	—	4	2	no	—
525	M₁₆	—	284	2	no	—
526	M₁₆	—	284	2	no	—
527	M₁₆	—	284	2	no	—
528	M₁₆	—	284	2	no	—
529	M₁₆	—	71	2	no	—
530	M₁₆	—	142	1	no	—
531	M₁₆	—	142	1	no	—
532	M₁₆	—	142	1	no	—
533	M₁₆	—	142	1	no	—
534	M₁₆	—	142	1	no	—
535	M₁₆	—	142	1	no	—
536	M₁₆	—	142	1	no	—
537	M₁₆	#11765864	1	2	yes	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	4	2	no	—
543	C₂×C₈	—	4	2	no	—
544	C₂×C₈	—	284	2	no	—
545	C₂×C₈	—	284	2	no	—
546	C₂×C₈	—	284	2	no	—
547	C₂×C₈	—	284	2	no	—
548	C₂×C₈	—	71	2	no	—
549	C₂×C₈	—	71	2	no	—
550	C₂×C₈	—	71	2	no	—
551	C₂×C₈	—	71	2	no	—
552	C₂×C₈	—	142	1	no	—
553	C₂×C₈	—	142	1	no	—
554	C₂×C₈	—	142	1	no	—
555	C₂×C₈	—	142	1	no	—
556	C₂×C₈	—	142	1	no	—
557	C₂×C₈	—	142	1	no	—
558	C₂×C₈	—	142	1	no	—
559	C₂×C₈	—	142	1	no	—
560	C₂×C₈	—	142	1	no	—
561	C₂×C₈	—	142	1	no	—
562	C₂×C₈	—	142	1	no	—
563	C₂×C₈	—	142	1	no	—
564	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
565	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
566	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
567	C₄⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
568	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
569	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
570	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
571	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
572	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
573	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
574	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
575	C₂²⋊C₄	Dic₇₁⋊C₄	1	1	yes	characteristic
576	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
577	C₄²	C₂×C₄×D₇₁	1	1	yes	characteristic
578	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
579	C₄²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
589	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
590	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
591	C₂³	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
592	C₂³	C₂²×Dic₁₄₂	1	1	yes	characteristic
593	D₄	—	2	2	no	—
594	D₄	—	2	2	no	—
595	D₄	—	4	1	no	—
596	D₄	—	4	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
620	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
621	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
622	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
623	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
624	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
625	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
626	C₂×C₄	C₂×Dic₇₁⋊C₄	1	1	yes	characteristic
627	C₂×C₄	C₂²×C₄×D₇₁	1	1	yes	characteristic
628	C₂×C₄	C₂²×C₂²⋊D₇₁	1	1	yes	characteristic
629	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
630	C₂×C₄	C₂×#11765864	1	1	yes	characteristic
631	C₂×C₄	#14556173	1	1	yes	characteristic
632	C₂×C₄	#14556174	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	4	1	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	284	1	no	—
638	C₈	—	284	1	no	—
639	C₈	—	284	1	no	—
640	C₈	—	142	2	no	—
641	C₈	—	142	2	no	—
642	C₈	—	142	2	no	—
643	C₈	—	142	2	no	—
644	C₈	—	142	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	1	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	4	2	no	—
659	C₂²	—	4	2	no	—
660	C₂²	—	8	1	no	—
661	C₂²	—	8	1	no	—
662	C₂²	#17986047	1	2	yes	—
663	C₂²	C₂²×Dic₇₁⋊C₄	1	1	yes	characteristic
664	C₂²	#17986706	1	1	yes	characteristic
665	C₂²	#17986708	1	1	yes	characteristic
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	1	no	—
670	C₄	—	2	1	no	—
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	2	1	no	—
674	C₄	C₄×#11765864	1	1	yes	characteristic
675	C₄	#17986471	1	1	yes	characteristic
676	C₄	#17986637	1	1	yes	characteristic
677	C₄	#17986643	1	1	yes	characteristic
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	2	2	no	—
681	C₂	—	4	1	no	—
682	C₂	—	4	1	no	—
683	C₂	—	4	1	no	—
684	C₂	#22591245	1	1	yes	characteristic
685	C₂	C₂×#17986047	1	1	yes	characteristic
686	C₂	#22596949	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₁
commutator	C₂×C₄×C₇₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	D₄×M₁₆×C₇₁	C₂
socle	C₂²×C₇₁	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₇₁	Q₈
cosocle	C₂²×C₄×C₇₁	C₂⁴
hypercenter	D₄×M₁₆	D₇₁
hypocenter	C₇₁	#22718
LCS	G ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #22589115	C₂	semidirect
4. #22589113	C₂	semidirect
5. #22588545	C₂	semidirect
6. #22588545	C₂	semidirect
7. #22588544	C₂	semidirect
8. #22588544	C₂	semidirect
9. #22588480	C₂	semidirect
10. #22588380	C₂	semidirect
11. #22588376	C₂	semidirect
12. #22588247	C₂	semidirect
13. #22588066	C₂	semidirect
14. C₂×#17985763	C₂	semidirect
359. C₇₁	#22718	semidirect

Maximal subgroups

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

subgroup	index
D₄×#11765849	2
C₂×#17986071	2
#22589115	2
#22589113	2
#22588545	2
#22588544	2
#22588480	2
#22588380	2
#22588376	2
#22588247	2
#22588066	2
C₂×#17985763	2
D₄×M₁₆×C₇₁	2
#22718	71