Subgroups — C₆₁×#22526 #29525959

Order 15616.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2355	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1991	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1762	C₂	1	1	yes	maximal, characteristic
14	C₆₁×#1762	C₂	1	1	yes	maximal, characteristic
15	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
16	C₆₁×#554	—	2	4	no	—
17	C₆₁×#554	C₄	1	8	yes	complemented
18	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
24	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
29	C₆₁×#446	—	2	4	no	—
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#391	—	2	1	no	—
41	C₆₁×#387	—	2	1	no	—
42	C₆₁×#387	—	2	1	no	—
43	C₆₁×#384	C₂²	1	1	yes	characteristic
44	C₆₁×#382	C₂²	1	1	yes	characteristic
45	C₆₁×#382	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
47	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
49	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
50	C₆₁×#340	C₂²	1	1	yes	characteristic
51	C₆₁×#340	C₂²	1	1	yes	characteristic
52	C₆₁×#340	C₂²	1	1	yes	characteristic
53	C₆₁×#340	C₂²	1	1	yes	characteristic
54	C₆₁×#340	C₂²	1	1	yes	characteristic
55	C₆₁×#340	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×#340	C₂²	1	1	yes	characteristic
61	C₆₁×#340	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₆₁	—	2	1	no	—
63	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂³×C₄×C₆₁	—	2	1	no	—
67	C₂³×C₄×C₆₁	—	2	1	no	—
68	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₆₁	—	2	2	no	—
73	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
74	#125×C₆₁	—	2	2	no	—
75	#125×C₆₁	—	2	2	no	—
76	#125×C₆₁	C₂×C₄	1	4	yes	—
77	#125×C₆₁	C₂×C₄	1	4	yes	—
78	C₂²⋊Q₈×C₆₁	—	2	8	no	—
79	C₂²⋊Q₈×C₆₁	—	2	8	no	—
80	C₂²⋊Q₈×C₆₁	—	2	8	no	—
81	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
82	C₄×Q₈×C₆₁	D₄	1	4	yes	—
83	C₄×D₄×C₆₁	—	2	2	no	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	C₄×D₄×C₆₁	—	2	2	no	—
86	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
87	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
88	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
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	—	2	8	no	—
95	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
96	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
110	C₂×C₄²×C₆₁	—	2	1	no	—
111	C₂×C₄²×C₆₁	—	2	1	no	—
112	C₂×C₄²×C₆₁	—	2	1	no	—
113	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₆₁	—	2	2	no	—
117	C₄⋊C₈×C₆₁	—	2	2	no	—
118	C₄⋊C₈×C₆₁	—	2	2	no	—
119	#102×C₆₁	—	2	2	no	—
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	Q₈	1	4	yes	complemented
123	#97×C₆₁	—	2	2	no	—
124	#97×C₆₁	—	2	2	no	—
125	C₄×C₈×C₆₁	—	2	2	no	—
126	#95×C₆₁	—	2	1	no	—
127	#95×C₆₁	—	2	1	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	C₂⁴×C₆₁	—	2	1	no	—
134	C₂×Q₈×C₆₁	—	2	4	no	—
135	C₂×Q₈×C₆₁	—	4	1	no	—
136	C₂×Q₈×C₆₁	—	4	1	no	—
137	C₂×Q₈×C₆₁	—	8	1	no	—
138	C₂×Q₈×C₆₁	—	8	1	no	—
139	C₂×Q₈×C₆₁	C₂²⋊C₄	1	4	yes	—
140	C₂×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	—	2	1	no	—
142	C₂×D₄×C₆₁	—	2	1	no	—
143	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
144	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
145	C₂×D₄×C₆₁	#41	1	2	yes	—
146	C₂²×C₄×C₆₁	—	2	1	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	1	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	4	no	—
151	C₂²×C₄×C₆₁	—	2	4	no	—
152	C₂²×C₄×C₆₁	—	2	4	no	—
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	1	no	—
155	C₂²×C₄×C₆₁	—	2	1	no	—
156	C₂²×C₄×C₆₁	—	4	2	no	—
157	C₂²×C₄×C₆₁	—	4	2	no	—
158	C₂²×C₄×C₆₁	—	8	1	no	—
159	C₂²×C₄×C₆₁	—	8	1	no	—
160	C₂²×C₄×C₆₁	—	8	1	no	—
161	C₂²×C₄×C₆₁	—	8	1	no	—
162	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
169	C₂×C₈×C₆₁	—	2	1	no	—
170	C₂×C₈×C₆₁	—	2	1	no	—
171	C₂×C₈×C₆₁	—	2	1	no	—
172	C₂×C₈×C₆₁	—	2	1	no	—
173	C₂×C₈×C₆₁	—	2	1	no	—
174	C₂×C₈×C₆₁	—	2	1	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	C₂×Q₈	1	2	yes	—
181	C₄⋊C₄×C₆₁	—	2	4	no	—
182	C₄⋊C₄×C₆₁	—	2	4	no	—
183	C₄⋊C₄×C₆₁	—	2	4	no	—
184	C₄⋊C₄×C₆₁	—	2	4	no	—
185	C₄⋊C₄×C₆₁	—	2	4	no	—
186	C₄⋊C₄×C₆₁	—	2	1	no	—
187	C₄⋊C₄×C₆₁	—	2	1	no	—
188	C₄⋊C₄×C₆₁	—	2	1	no	—
189	C₄⋊C₄×C₆₁	—	2	1	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	—	4	2	no	—
197	C₄⋊C₄×C₆₁	—	8	1	no	—
198	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
199	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
200	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
201	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
202	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
203	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
204	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
205	C₂²⋊C₄×C₆₁	—	2	4	no	—
206	C₂²⋊C₄×C₆₁	—	2	4	no	—
207	C₂²⋊C₄×C₆₁	—	2	4	no	—
208	C₄²×C₆₁	—	4	2	no	—
209	C₄²×C₆₁	—	8	1	no	—
210	C₄²×C₆₁	—	8	1	no	—
211	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
212	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
213	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
214	C₄²×C₆₁	C₂×D₄	1	2	yes	—
215	C₄²×C₆₁	C₂×D₄	1	2	yes	—
216	C₄²×C₆₁	C₂×D₄	1	2	yes	—
217	C₂³×C₆₁	—	2	2	no	—
218	C₂³×C₆₁	—	2	2	no	—
219	C₂³×C₆₁	—	2	2	no	—
220	C₂³×C₆₁	—	4	1	no	—
221	C₂³×C₆₁	—	4	1	no	—
222	C₂³×C₆₁	—	4	1	no	—
223	C₂³×C₆₁	—	4	1	no	—
224	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
225	Q₈×C₆₁	—	4	4	no	—
226	Q₈×C₆₁	—	8	4	no	—
227	D₄×C₆₁	—	2	2	no	—
228	D₄×C₆₁	—	2	2	no	—
229	D₄×C₆₁	—	2	2	no	—
230	D₄×C₆₁	C₄×Q₈	1	4	yes	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	2	1	no	—
234	C₂×C₄×C₆₁	—	2	1	no	—
235	C₂×C₄×C₆₁	—	2	1	no	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	2	1	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	1	no	—
243	C₂×C₄×C₆₁	—	2	2	no	—
244	C₂×C₄×C₆₁	—	2	2	no	—
245	C₂×C₄×C₆₁	—	2	2	no	—
246	C₂×C₄×C₆₁	—	2	2	no	—
247	C₂×C₄×C₆₁	—	4	8	no	—
248	C₂×C₄×C₆₁	—	4	1	no	—
249	C₂×C₄×C₆₁	—	4	1	no	—
250	C₂×C₄×C₆₁	—	4	1	no	—
251	C₂×C₄×C₆₁	—	4	1	no	—
252	C₂×C₄×C₆₁	—	4	1	no	—
253	C₂×C₄×C₆₁	—	4	1	no	—
254	C₂×C₄×C₆₁	—	4	1	no	—
255	C₂×C₄×C₆₁	—	4	1	no	—
256	C₂×C₄×C₆₁	—	4	1	no	—
257	C₂×C₄×C₆₁	—	4	1	no	—
258	C₂×C₄×C₆₁	—	4	1	no	—
259	C₂×C₄×C₆₁	—	4	1	no	—
260	C₂×C₄×C₆₁	—	4	1	no	—
261	C₂×C₄×C₆₁	—	4	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	—	8	4	no	—
266	C₂×C₄×C₆₁	—	8	4	no	—
267	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
269	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
272	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
273	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
276	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
278	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
279	C₈×C₆₁	—	2	2	no	—
280	C₈×C₆₁	—	4	1	no	—
281	C₈×C₆₁	—	4	1	no	—
282	C₈×C₆₁	—	4	1	no	—
283	#22526	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂²×C₆₁	—	2	4	no	—
285	C₂²×C₆₁	—	4	2	no	—
286	C₂²×C₆₁	—	4	2	no	—
287	C₂²×C₆₁	—	4	2	no	—
288	C₂²×C₆₁	—	4	2	no	—
289	C₂²×C₆₁	—	4	2	no	—
290	C₂²×C₆₁	—	4	2	no	—
291	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₆₁	#548	1	1	yes	characteristic
293	C₂²×C₆₁	D₄×Q₈	1	1	yes	characteristic
294	C₂²×C₆₁	#575	1	1	yes	characteristic
295	C₂²×C₆₁	#575	1	1	yes	characteristic
296	C₂²×C₆₁	#576	1	1	yes	characteristic
297	C₂²×C₆₁	#577	1	1	yes	characteristic
298	C₄×C₆₁	—	2	2	no	—
299	C₄×C₆₁	—	2	2	no	—
300	C₄×C₆₁	—	2	2	no	—
301	C₄×C₆₁	—	2	2	no	—
302	C₄×C₆₁	—	2	2	no	—
303	C₄×C₆₁	—	2	2	no	—
304	C₄×C₆₁	—	4	2	no	—
305	C₄×C₆₁	—	4	2	no	—
306	C₄×C₆₁	—	4	2	no	—
307	C₄×C₆₁	—	4	2	no	—
308	C₄×C₆₁	—	8	1	no	—
309	C₄×C₆₁	—	8	1	no	—
310	C₄×C₆₁	—	8	1	no	—
311	C₄×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
312	C₄×C₆₁	#519	1	1	yes	characteristic
313	C₄×C₆₁	#548	1	1	yes	characteristic
314	C₄×C₆₁	D₄×Q₈	1	1	yes	characteristic
315	C₂×#554	C₂×C₆₁	1	1	yes	characteristic
316	C₂×#446	C₂×C₆₁	1	1	yes	characteristic, complemented
317	#2355	C₂×C₆₁	1	1	yes	characteristic, complemented
318	#1993	C₂×C₆₁	1	1	yes	characteristic, complemented
319	#1992	C₂×C₆₁	1	1	yes	characteristic, complemented
320	#1991	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#1989	C₂×C₆₁	1	1	yes	characteristic, complemented
322	#1989	C₂×C₆₁	1	1	yes	characteristic, complemented
323	#1988	C₂×C₆₁	1	1	yes	characteristic, complemented
324	#1804	C₂×C₆₁	1	1	yes	characteristic
325	#1804	C₂×C₆₁	1	1	yes	characteristic
326	#1802	C₂×C₆₁	1	1	yes	characteristic
327	#1762	C₂×C₆₁	1	1	yes	characteristic
328	#1762	C₂×C₆₁	1	1	yes	characteristic
329	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
330	C₂×C₆₁	—	4	4	no	—
331	C₂×C₆₁	Q₈×C₂²⋊C₄	1	1	yes	characteristic
332	C₂×C₆₁	#2896	1	1	yes	characteristic
333	C₂×C₆₁	#2897	1	1	yes	characteristic
334	C₂×C₆₁	#3370	1	1	yes	characteristic
335	C₂×C₆₁	#3376	1	1	yes	characteristic
336	C₂×C₆₁	#3388	1	1	yes	characteristic
337	C₂×C₆₁	#3389	1	1	yes	characteristic
338	#554	—	2	4	no	—
339	#554	C₄×C₆₁	1	8	yes	complemented
340	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
341	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
342	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
343	C₂×C₂²⋊Q₈	—	2	1	no	—
344	C₂×C₂²⋊Q₈	—	2	1	no	—
345	C₂×C₂²⋊Q₈	—	2	1	no	—
346	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
347	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
349	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
350	C₂²×C₄⋊C₄	—	2	1	no	—
351	#446	—	2	4	no	—
352	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
353	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
354	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
360	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
362	#391	—	2	1	no	—
363	#387	—	2	1	no	—
364	#387	—	2	1	no	—
365	#384	C₂²×C₆₁	1	1	yes	characteristic
366	#382	C₂²×C₆₁	1	1	yes	characteristic
367	#382	C₂²×C₆₁	1	1	yes	characteristic
368	C₄×C₄⋊C₄	—	2	1	no	—
369	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
370	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
371	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
372	#340	C₂²×C₆₁	1	1	yes	characteristic
373	#340	C₂²×C₆₁	1	1	yes	characteristic
374	#340	C₂²×C₆₁	1	1	yes	characteristic
375	#340	C₂²×C₆₁	1	1	yes	characteristic
376	#340	C₂²×C₆₁	1	1	yes	characteristic
377	#340	C₂²×C₆₁	1	1	yes	characteristic
378	#340	C₂²×C₆₁	1	1	yes	characteristic
379	#340	C₂²×C₆₁	1	1	yes	characteristic
380	#340	C₂²×C₆₁	1	1	yes	characteristic
381	#340	C₂²×C₆₁	1	1	yes	characteristic
382	#340	C₂²×C₆₁	1	1	yes	characteristic
383	#340	C₂²×C₆₁	1	1	yes	characteristic
384	C₆₁	#22526	1	1	yes	characteristic, direct product factor, Sylow
385	C₂²×Q₈	—	2	1	no	—
386	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	—	2	1	no	—
390	C₂³×C₄	—	2	1	no	—
391	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
392	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
393	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
395	C₄⋊Q₈	—	2	2	no	—
396	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
397	#125	—	2	2	no	—
398	#125	—	2	2	no	—
399	#125	C₂×C₄×C₆₁	1	4	yes	—
400	#125	C₂×C₄×C₆₁	1	4	yes	—
401	C₂²⋊Q₈	—	2	8	no	—
402	C₂²⋊Q₈	—	2	8	no	—
403	C₂²⋊Q₈	—	2	8	no	—
404	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
405	C₄×Q₈	D₄×C₆₁	1	4	yes	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
410	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
411	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₄⋊C₄	—	2	8	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
421	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
422	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
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×C₄²	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
439	C₄⋊C₈	—	2	2	no	—
440	C₄⋊C₈	—	2	2	no	—
441	C₄⋊C₈	—	2	2	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	2	no	—
445	#102	Q₈×C₆₁	1	4	yes	complemented
446	#97	—	2	2	no	—
447	#97	—	2	2	no	—
448	C₄×C₈	—	2	2	no	—
449	#95	—	2	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	C₂⁴	—	2	1	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	4	1	no	—
459	C₂×Q₈	—	4	1	no	—
460	C₂×Q₈	—	8	1	no	—
461	C₂×Q₈	—	8	1	no	—
462	C₂×Q₈	C₂²⋊C₄×C₆₁	1	4	yes	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
467	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
468	C₂×D₄	#41×C₆₁	1	2	yes	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	8	1	no	—
482	C₂²×C₄	—	8	1	no	—
483	C₂²×C₄	—	8	1	no	—
484	C₂²×C₄	—	8	1	no	—
485	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	4	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	8	1	no	—
521	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
522	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
523	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
524	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
525	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
526	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
527	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	2	4	no	—
531	C₄²	—	4	2	no	—
532	C₄²	—	8	1	no	—
533	C₄²	—	8	1	no	—
534	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
535	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
536	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
537	C₄²	C₂×D₄×C₆₁	1	2	yes	—
538	C₄²	C₂×D₄×C₆₁	1	2	yes	—
539	C₄²	C₂×D₄×C₆₁	1	2	yes	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
548	Q₈	—	4	4	no	—
549	Q₈	—	8	4	no	—
550	D₄	—	2	2	no	—
551	D₄	—	2	2	no	—
552	D₄	—	2	2	no	—
553	D₄	C₄×Q₈×C₆₁	1	4	yes	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	8	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	8	4	no	—
589	C₂×C₄	—	8	4	no	—
590	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
591	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
592	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
593	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
594	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
595	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
596	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
597	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
598	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
599	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
600	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
601	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
602	C₈	—	2	2	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₂²	—	2	4	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	2	no	—
613	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
614	C₂²	C₆₁×#548	1	1	yes	characteristic
615	C₂²	D₄×Q₈×C₆₁	1	1	yes	characteristic
616	C₂²	C₆₁×#575	1	1	yes	characteristic
617	C₂²	C₆₁×#575	1	1	yes	characteristic
618	C₂²	C₆₁×#576	1	1	yes	characteristic
619	C₂²	C₆₁×#577	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	—	4	2	no	—
630	C₄	—	8	1	no	—
631	C₄	—	8	1	no	—
632	C₄	—	8	1	no	—
633	C₄	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
634	C₄	C₆₁×#519	1	1	yes	characteristic
635	C₄	C₆₁×#548	1	1	yes	characteristic
636	C₄	D₄×Q₈×C₆₁	1	1	yes	characteristic
637	C₂	—	4	4	no	—
638	C₂	Q₈×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
639	C₂	C₆₁×#2896	1	1	yes	characteristic
640	C₂	C₆₁×#2897	1	1	yes	characteristic
641	C₂	C₆₁×#3370	1	1	yes	characteristic
642	C₂	C₆₁×#3376	1	1	yes	characteristic
643	C₂	C₆₁×#3388	1	1	yes	characteristic
644	C₂	C₆₁×#3389	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 ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#446	C₂	semidirect
3. C₆₁×#2355	C₂	semidirect
4. C₆₁×#1993	C₂	semidirect
5. C₆₁×#1992	C₂	semidirect
6. C₆₁×#1991	C₂	semidirect
7. C₆₁×#1989	C₂	semidirect
8. C₆₁×#1989	C₂	semidirect
9. C₆₁×#1988	C₂	semidirect
17. C₆₁×#554	C₄	semidirect
122. #102×C₆₁	Q₈	semidirect
283. #22526	C₆₁	direct (N × H)
316. C₂×#446	C₂×C₆₁	semidirect
317. #2355	C₂×C₆₁	semidirect
318. #1993	C₂×C₆₁	semidirect
319. #1992	C₂×C₆₁	semidirect
320. #1991	C₂×C₆₁	semidirect
321. #1989	C₂×C₆₁	semidirect
322. #1989	C₂×C₆₁	semidirect
323. #1988	C₂×C₆₁	semidirect
339. #554	C₄×C₆₁	semidirect
384. C₆₁	#22526	direct (N × H)
445. #102	Q₈×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×#554	2
C₂×C₆₁×#446	2
C₆₁×#2355	2
C₆₁×#1993	2
C₆₁×#1992	2
C₆₁×#1991	2
C₆₁×#1989	2
C₆₁×#1988	2
C₆₁×#1804	2
C₆₁×#1802	2
C₆₁×#1762	2
C₄×#102×C₆₁	2
#22526	61

Subgroups — C61×#22526 #29525959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22526 #29525959