Subgroups — C₆₁×#21512 #29524945

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2326	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2276	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1983	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1928	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1925	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1880	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1763	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#464	C₄	1	8	yes	complemented
25	C₆₁×#440	—	2	4	no	—
26	C₄×Q₁₆×C₆₁	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#391	C₂²	1	1	yes	characteristic
42	C₆₁×#390	C₂²	1	1	yes	characteristic
43	C₆₁×#388	—	2	1	no	—
44	C₆₁×#388	—	2	1	no	—
45	C₆₁×#385	—	2	1	no	—
46	C₆₁×#385	—	2	1	no	—
47	C₆₁×#384	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
49	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
50	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
51	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
54	C₆₁×#376	—	2	1	no	—
55	C₆₁×#376	C₂²	1	1	yes	characteristic
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#340	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₆₁×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂×Q₁₆×C₆₁	—	2	2	no	—
67	C₂×Q₁₆×C₆₁	—	2	2	no	—
68	C₂×Q₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
76	#124×C₆₁	—	2	2	no	—
77	#124×C₆₁	C₂×C₄	1	4	yes	—
78	C₄×Q₈×C₆₁	—	2	2	no	—
79	C₄×Q₈×C₆₁	—	2	2	no	—
80	C₄×Q₈×C₆₁	—	2	2	no	—
81	C₄×Q₈×C₆₁	—	2	2	no	—
82	C₄×Q₈×C₆₁	—	2	2	no	—
83	C₄×Q₈×C₆₁	—	2	2	no	—
84	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
85	C₄×Q₈×C₆₁	D₄	1	4	yes	—
86	C₄×D₄×C₆₁	—	2	2	no	—
87	C₄×D₄×C₆₁	—	2	2	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
104	C₂×C₄²×C₆₁	—	2	1	no	—
105	C₂×C₄²×C₆₁	—	2	1	no	—
106	C₂×C₄²×C₆₁	—	2	1	no	—
107	C₂×C₄²×C₆₁	—	2	1	no	—
108	C₂×C₄²×C₆₁	—	2	1	no	—
109	C₂×C₄²×C₆₁	—	2	1	no	—
110	C₂×C₄²×C₆₁	—	2	1	no	—
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
114	#107×C₆₁	—	2	2	no	—
115	#107×C₆₁	—	2	2	no	—
116	C₄⋊C₈×C₆₁	—	2	2	no	—
117	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
118	#103×C₆₁	—	2	2	no	—
119	#103×C₆₁	—	2	2	no	—
120	#103×C₆₁	—	2	2	no	—
121	#103×C₆₁	—	2	2	no	—
122	#103×C₆₁	C₂×C₄	1	4	yes	complemented
123	#102×C₆₁	—	2	2	no	—
124	#102×C₆₁	—	2	2	no	—
125	#102×C₆₁	C₂×C₄	1	4	yes	—
126	#97×C₆₁	—	2	2	no	—
127	C₄×C₈×C₆₁	—	2	2	no	—
128	#95×C₆₁	—	2	1	no	—
129	#95×C₆₁	—	2	1	no	—
130	#95×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	D₄	1	1	yes	characteristic
134	#95×C₆₁	D₄	1	1	yes	characteristic
135	#95×C₆₁	D₄	1	1	yes	characteristic
136	#95×C₆₁	D₄	1	1	yes	characteristic
137	C₂⁴×C₆₁	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	1	no	—
139	C₂×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×Q₈×C₆₁	—	2	1	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	—	2	1	no	—
145	C₂×Q₈×C₆₁	—	2	1	no	—
146	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
147	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
148	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₆₁	#41	1	2	yes	—
150	C₂×D₄×C₆₁	—	2	1	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	—	2	1	no	—
154	C₂×D₄×C₆₁	—	2	1	no	—
155	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₆₁	—	2	1	no	—
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	1	no	—
160	C₂²×C₄×C₆₁	—	2	1	no	—
161	C₂²×C₄×C₆₁	—	2	1	no	—
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	4	2	no	—
164	C₂²×C₄×C₆₁	—	8	1	no	—
165	C₂²×C₄×C₆₁	—	8	1	no	—
166	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
173	Q₁₆×C₆₁	—	2	8	no	—
174	SD₁₆×C₆₁	—	2	8	no	—
175	C₂×C₈×C₆₁	—	2	1	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	1	no	—
178	C₂×C₈×C₆₁	—	2	1	no	—
179	C₂×C₈×C₆₁	—	2	1	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	—	2	1	no	—
182	C₂×C₈×C₆₁	—	2	1	no	—
183	C₂×C₈×C₆₁	—	2	1	no	—
184	C₂×C₈×C₆₁	—	2	1	no	—
185	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
186	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₆₁	—	2	4	no	—
188	C₄⋊C₄×C₆₁	—	2	4	no	—
189	C₄⋊C₄×C₆₁	—	2	4	no	—
190	C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₄⋊C₄×C₆₁	—	2	1	no	—
192	C₄⋊C₄×C₆₁	—	2	1	no	—
193	C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₄⋊C₄×C₆₁	—	2	1	no	—
196	C₄⋊C₄×C₆₁	—	2	1	no	—
197	C₄⋊C₄×C₆₁	—	4	2	no	—
198	C₄⋊C₄×C₆₁	—	8	1	no	—
199	C₄⋊C₄×C₆₁	—	8	1	no	—
200	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
201	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
202	C₄⋊C₄×C₆₁	#41	1	2	yes	—
203	C₂²⋊C₄×C₆₁	—	2	4	no	—
204	C₂²⋊C₄×C₆₁	—	2	4	no	—
205	C₂²⋊C₄×C₆₁	—	4	2	no	—
206	C₂²⋊C₄×C₆₁	—	8	1	no	—
207	C₂²⋊C₄×C₆₁	—	8	1	no	—
208	C₄²×C₆₁	—	2	4	no	—
209	C₄²×C₆₁	—	2	4	no	—
210	C₄²×C₆₁	—	2	4	no	—
211	C₄²×C₆₁	—	2	1	no	—
212	C₄²×C₆₁	—	2	1	no	—
213	C₄²×C₆₁	—	4	2	no	—
214	C₄²×C₆₁	—	8	1	no	—
215	C₄²×C₆₁	—	8	1	no	—
216	C₄²×C₆₁	—	8	1	no	—
217	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
218	C₄²×C₆₁	C₂×D₄	1	2	yes	—
219	C₄²×C₆₁	#41	1	2	yes	—
220	C₄²×C₆₁	#41	1	2	yes	—
221	C₂³×C₆₁	—	2	2	no	—
222	C₂³×C₆₁	—	4	1	no	—
223	C₂³×C₆₁	—	4	1	no	—
224	C₂³×C₆₁	—	4	1	no	—
225	C₂³×C₆₁	—	4	1	no	—
226	C₂³×C₆₁	—	4	1	no	—
227	C₂³×C₆₁	—	4	1	no	—
228	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
229	Q₈×C₆₁	—	2	2	no	—
230	Q₈×C₆₁	—	2	2	no	—
231	Q₈×C₆₁	—	2	2	no	—
232	Q₈×C₆₁	—	2	2	no	—
233	Q₈×C₆₁	—	2	2	no	—
234	Q₈×C₆₁	—	4	1	no	—
235	Q₈×C₆₁	—	4	1	no	—
236	Q₈×C₆₁	C₄×D₄	1	4	yes	—
237	D₄×C₆₁	—	2	2	no	—
238	D₄×C₆₁	—	2	2	no	—
239	D₄×C₆₁	—	4	1	no	—
240	D₄×C₆₁	—	4	1	no	—
241	C₂×C₄×C₆₁	—	2	2	no	—
242	C₂×C₄×C₆₁	—	2	2	no	—
243	C₂×C₄×C₆₁	—	2	2	no	—
244	C₂×C₄×C₆₁	—	2	1	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	2	1	no	—
247	C₂×C₄×C₆₁	—	2	1	no	—
248	C₂×C₄×C₆₁	—	2	1	no	—
249	C₂×C₄×C₆₁	—	2	1	no	—
250	C₂×C₄×C₆₁	—	2	1	no	—
251	C₂×C₄×C₆₁	—	2	1	no	—
252	C₂×C₄×C₆₁	—	2	2	no	—
253	C₂×C₄×C₆₁	—	2	2	no	—
254	C₂×C₄×C₆₁	—	2	2	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	2	no	—
258	C₂×C₄×C₆₁	—	2	1	no	—
259	C₂×C₄×C₆₁	—	2	1	no	—
260	C₂×C₄×C₆₁	—	2	1	no	—
261	C₂×C₄×C₆₁	—	2	1	no	—
262	C₂×C₄×C₆₁	—	4	1	no	—
263	C₂×C₄×C₆₁	—	4	1	no	—
264	C₂×C₄×C₆₁	—	4	1	no	—
265	C₂×C₄×C₆₁	—	4	1	no	—
266	C₂×C₄×C₆₁	—	4	1	no	—
267	C₂×C₄×C₆₁	—	4	1	no	—
268	C₂×C₄×C₆₁	—	4	1	no	—
269	C₂×C₄×C₆₁	—	4	1	no	—
270	C₂×C₄×C₆₁	—	4	1	no	—
271	C₂×C₄×C₆₁	—	4	1	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	8	4	no	—
277	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
278	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
279	C₂×C₄×C₆₁	#121	1	2	yes	—
280	C₂×C₄×C₆₁	#121	1	2	yes	—
281	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
282	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
287	C₈×C₆₁	—	2	2	no	—
288	C₈×C₆₁	—	2	2	no	—
289	C₈×C₆₁	—	4	1	no	—
290	C₈×C₆₁	—	4	1	no	—
291	#21512	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂²×C₆₁	—	4	2	no	—
293	C₂²×C₆₁	—	4	2	no	—
294	C₂²×C₆₁	—	4	2	no	—
295	C₂²×C₆₁	—	8	1	no	—
296	C₂²×C₆₁	—	8	1	no	—
297	C₂²×C₆₁	—	8	1	no	—
298	C₂²×C₆₁	—	8	1	no	—
299	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
301	C₂²×C₆₁	#525	1	1	yes	characteristic
302	C₂²×C₆₁	#576	1	1	yes	characteristic
303	C₂²×C₆₁	#577	1	1	yes	characteristic
304	C₂²×C₆₁	#578	1	1	yes	characteristic
305	C₂²×C₆₁	#578	1	1	yes	characteristic
306	C₄×C₆₁	—	2	2	no	—
307	C₄×C₆₁	—	2	2	no	—
308	C₄×C₆₁	—	2	2	no	—
309	C₄×C₆₁	—	2	2	no	—
310	C₄×C₆₁	—	2	4	no	—
311	C₄×C₆₁	—	4	1	no	—
312	C₄×C₆₁	—	4	1	no	—
313	C₄×C₆₁	—	4	2	no	—
314	C₄×C₆₁	—	4	2	no	—
315	C₄×C₆₁	—	4	2	no	—
316	C₄×C₆₁	—	4	2	no	—
317	C₄×C₆₁	—	8	1	no	—
318	C₄×C₆₁	—	8	1	no	—
319	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
320	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
321	C₄×C₆₁	#529	1	1	yes	characteristic
322	C₄×C₆₁	#532	1	1	yes	characteristic
323	C₂×#464	C₂×C₆₁	1	1	yes	characteristic
324	C₂×#440	C₂×C₆₁	1	1	yes	characteristic
325	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
326	#2326	C₂×C₆₁	1	1	yes	characteristic
327	#2276	C₂×C₆₁	1	1	yes	characteristic, complemented
328	#1983	C₂×C₆₁	1	1	yes	characteristic
329	#1947	C₂×C₆₁	1	1	yes	characteristic, complemented
330	#1928	C₂×C₆₁	1	1	yes	characteristic, complemented
331	#1925	C₂×C₆₁	1	1	yes	characteristic
332	#1880	C₂×C₆₁	1	1	yes	characteristic
333	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
334	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
335	#1768	C₂×C₆₁	1	1	yes	characteristic, complemented
336	#1763	C₂×C₆₁	1	1	yes	characteristic, complemented
337	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
338	C₂×C₆₁	—	8	2	no	—
339	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
340	C₂×C₆₁	#2947	1	1	yes	characteristic
341	C₂×C₆₁	#2951	1	1	yes	characteristic
342	C₂×C₆₁	#3044	1	1	yes	characteristic
343	C₂×C₆₁	#3045	1	1	yes	characteristic
344	C₂×C₆₁	#3121	1	1	yes	characteristic
345	C₂×C₆₁	#3124	1	1	yes	characteristic
346	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
347	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
349	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
350	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
352	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
353	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
354	#464	C₄×C₆₁	1	8	yes	complemented
355	#440	—	2	4	no	—
356	C₄×Q₁₆	—	2	4	no	—
357	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
360	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
362	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
366	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
367	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
368	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
369	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
371	#391	C₂²×C₆₁	1	1	yes	characteristic
372	#390	C₂²×C₆₁	1	1	yes	characteristic
373	#388	—	2	1	no	—
374	#388	—	2	1	no	—
375	#385	—	2	1	no	—
376	#385	—	2	1	no	—
377	#384	C₂²×C₆₁	1	1	yes	characteristic
378	C₄×C₄⋊C₄	—	2	1	no	—
379	C₄×C₄⋊C₄	—	2	1	no	—
380	C₄×C₄⋊C₄	—	2	1	no	—
381	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
382	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
383	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
384	#376	—	2	1	no	—
385	#376	C₂²×C₆₁	1	1	yes	characteristic
386	#340	C₂²×C₆₁	1	1	yes	characteristic
387	#340	C₂²×C₆₁	1	1	yes	characteristic
388	#340	C₂²×C₆₁	1	1	yes	characteristic
389	#340	C₂²×C₆₁	1	1	yes	characteristic
390	#336	C₂²×C₆₁	1	1	yes	characteristic
391	#336	C₂²×C₆₁	1	1	yes	characteristic
392	C₆₁	#21512	1	1	yes	characteristic, direct product factor, Sylow
393	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
394	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂×Q₁₆	—	2	2	no	—
398	C₂×Q₁₆	—	2	2	no	—
399	C₂×Q₁₆	C₂×C₄×C₆₁	1	4	yes	complemented
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	2	2	no	—
402	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	—
403	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
407	#124	—	2	2	no	—
408	#124	C₂×C₄×C₆₁	1	4	yes	—
409	C₄×Q₈	—	2	2	no	—
410	C₄×Q₈	—	2	2	no	—
411	C₄×Q₈	—	2	2	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×Q₈	—	2	2	no	—
414	C₄×Q₈	—	2	2	no	—
415	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
416	C₄×Q₈	D₄×C₆₁	1	4	yes	—
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	—	2	1	no	—
439	C₂×C₄²	—	2	1	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
445	#107	—	2	2	no	—
446	#107	—	2	2	no	—
447	C₄⋊C₈	—	2	2	no	—
448	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#103	—	2	2	no	—
452	#103	—	2	2	no	—
453	#103	C₂×C₄×C₆₁	1	4	yes	complemented
454	#102	—	2	2	no	—
455	#102	—	2	2	no	—
456	#102	C₂×C₄×C₆₁	1	4	yes	—
457	#97	—	2	2	no	—
458	C₄×C₈	—	2	2	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	D₄×C₆₁	1	1	yes	characteristic
465	#95	D₄×C₆₁	1	1	yes	characteristic
466	#95	D₄×C₆₁	1	1	yes	characteristic
467	#95	D₄×C₆₁	1	1	yes	characteristic
468	C₂⁴	—	2	1	no	—
469	C₂×Q₈	—	2	1	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
478	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
479	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
480	C₂×Q₈	#41×C₆₁	1	2	yes	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	8	1	no	—
496	C₂²×C₄	—	8	1	no	—
497	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
503	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
504	Q₁₆	—	2	8	no	—
505	SD₁₆	—	2	8	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
517	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
518	C₄⋊C₄	—	2	4	no	—
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	4	2	no	—
529	C₄⋊C₄	—	8	1	no	—
530	C₄⋊C₄	—	8	1	no	—
531	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
532	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
533	C₄⋊C₄	#41×C₆₁	1	2	yes	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	4	2	no	—
537	C₂²⋊C₄	—	8	1	no	—
538	C₂²⋊C₄	—	8	1	no	—
539	C₄²	—	2	4	no	—
540	C₄²	—	2	4	no	—
541	C₄²	—	2	4	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	4	2	no	—
545	C₄²	—	8	1	no	—
546	C₄²	—	8	1	no	—
547	C₄²	—	8	1	no	—
548	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
549	C₄²	C₂×D₄×C₆₁	1	2	yes	—
550	C₄²	#41×C₆₁	1	2	yes	—
551	C₄²	#41×C₆₁	1	2	yes	—
552	C₂³	—	2	2	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
560	Q₈	—	2	2	no	—
561	Q₈	—	2	2	no	—
562	Q₈	—	2	2	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	4	1	no	—
566	Q₈	—	4	1	no	—
567	Q₈	C₄×D₄×C₆₁	1	4	yes	—
568	D₄	—	2	2	no	—
569	D₄	—	2	2	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	8	4	no	—
608	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
609	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
610	C₂×C₄	#121×C₆₁	1	2	yes	—
611	C₂×C₄	#121×C₆₁	1	2	yes	—
612	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
613	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
614	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
615	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
616	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
617	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
618	C₈	—	2	2	no	—
619	C₈	—	2	2	no	—
620	C₈	—	4	1	no	—
621	C₈	—	4	1	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
630	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
631	C₂²	C₆₁×#525	1	1	yes	characteristic
632	C₂²	C₆₁×#576	1	1	yes	characteristic
633	C₂²	C₆₁×#577	1	1	yes	characteristic
634	C₂²	C₆₁×#578	1	1	yes	characteristic
635	C₂²	C₆₁×#578	1	1	yes	characteristic
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	4	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	1	no	—
644	C₄	—	4	1	no	—
645	C₄	—	4	2	no	—
646	C₄	—	4	2	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
650	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
651	C₄	C₆₁×#529	1	1	yes	characteristic
652	C₄	C₆₁×#532	1	1	yes	characteristic
653	C₂	—	8	2	no	—
654	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
655	C₂	C₆₁×#2947	1	1	yes	characteristic
656	C₂	C₆₁×#2951	1	1	yes	characteristic
657	C₂	C₆₁×#3044	1	1	yes	characteristic
658	C₂	C₆₁×#3045	1	1	yes	characteristic
659	C₂	C₆₁×#3121	1	1	yes	characteristic
660	C₂	C₆₁×#3124	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₆₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
5. C₆₁×#2276	C₂	semidirect
7. C₆₁×#1947	C₂	semidirect
8. C₆₁×#1928	C₂	semidirect
11. C₆₁×#1878	C₂	semidirect
12. C₆₁×#1803	C₂	semidirect
13. C₆₁×#1768	C₂	semidirect
14. C₆₁×#1763	C₂	semidirect
24. C₆₁×#464	C₄	semidirect
68. C₂×Q₁₆×C₆₁	C₂×C₄	semidirect
84. C₄×Q₈×C₆₁	C₂×C₄	semidirect
117. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
122. #103×C₆₁	C₂×C₄	semidirect
291. #21512	C₆₁	direct (N × H)
325. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
327. #2276	C₂×C₆₁	semidirect
329. #1947	C₂×C₆₁	semidirect
330. #1928	C₂×C₆₁	semidirect
333. #1878	C₂×C₆₁	semidirect
334. #1803	C₂×C₆₁	semidirect
335. #1768	C₂×C₆₁	semidirect
336. #1763	C₂×C₆₁	semidirect
354. #464	C₄×C₆₁	semidirect
392. C₆₁	#21512	direct (N × H)
399. C₂×Q₁₆	C₂×C₄×C₆₁	semidirect
415. C₄×Q₈	C₂×C₄×C₆₁	semidirect
448. C₄⋊C₈	C₂×C₄×C₆₁	semidirect
453. #103	C₂×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#464	2
C₂×C₆₁×#440	2
C₂×C₄×Q₁₆×C₆₁	2
C₆₁×#2326	2
C₆₁×#2276	2
C₆₁×#1983	2
C₆₁×#1947	2
C₆₁×#1928	2
C₆₁×#1925	2
C₆₁×#1880	2
C₆₁×#1878	2
C₆₁×#1803	2
C₆₁×#1768	2
C₆₁×#1763	2
C₄×#102×C₆₁	2
#21512	61

Subgroups — C61×#21512 #29524945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21512 #29524945