Subgroups — C₆₁×#33482 #29536915

Order 15616.

518 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2966	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2183	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2168	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2168	C₂	1	2	yes	maximal, complemented
5	D₄×C₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2164	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2108	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#529	C₄	1	1	yes	characteristic
11	C₂×M₃₂×C₆₁	C₂²	1	2	yes	—
12	C₂²×C₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×C₁₆×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#446	C₄	1	1	yes	characteristic
15	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#436	C₄	1	1	yes	characteristic
17	C₆₁×#435	C₄	1	2	yes	—
18	C₈×D₄×C₆₁	C₂²	1	2	yes	—
19	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#433	C₄	1	2	yes	—
21	C₆₁×#432	C₄	1	1	yes	characteristic
22	C₆₁×#405	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	—
25	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	—
26	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	—
27	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
30	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
31	C₆₁×#346	C₂²	1	1	yes	characteristic
32	C₆₁×#346	C₂²	1	1	yes	characteristic
33	C₆₁×#346	C₂²	1	2	yes	—
34	C₆₁×#346	C₂²	1	2	yes	—
35	C₄×C₁₆×C₆₁	C₂²	1	2	yes	—
36	C₄×C₁₆×C₆₁	C₂²	1	2	yes	—
37	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
38	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
40	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
41	#126×C₆₁	C₈	1	2	yes	—
42	#125×C₆₁	C₈	1	1	yes	characteristic
43	#124×C₆₁	C₈	1	1	yes	characteristic
44	#123×C₆₁	C₈	1	2	yes	—
45	C₂²⋊Q₈×C₆₁	C₈	1	1	yes	characteristic
46	#121×C₆₁	C₈	1	1	yes	characteristic
47	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
49	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
50	#117×C₆₁	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
52	M₃₂×C₆₁	—	2	4	no	—
53	C₂×C₁₆×C₆₁	—	2	4	no	—
54	C₂×C₁₆×C₆₁	—	2	4	no	—
55	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
56	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
57	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
58	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
59	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
60	C₄⋊C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
62	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
63	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
64	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
65	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
66	#97×C₆₁	C₂×C₄	1	2	yes	—
67	#97×C₆₁	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
69	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₄×C₈×C₆₁	C₂³	1	2	yes	—
72	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
74	C₂×D₄×C₆₁	C₂×C₈	1	2	yes	—
75	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
80	M₁₆×C₆₁	—	2	4	no	—
81	C₂×C₈×C₆₁	—	2	2	no	—
82	C₂×C₈×C₆₁	—	2	2	no	—
83	C₂×C₈×C₆₁	—	2	2	no	—
84	C₂×C₈×C₆₁	—	2	2	no	—
85	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
87	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
88	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
91	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
92	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
93	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
94	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
95	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
96	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
97	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
98	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
99	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
100	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
101	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
102	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
103	C₄²×C₆₁	C₂×C₈	1	1	yes	characteristic
104	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
107	C₁₆×C₆₁	—	2	2	no	—
108	C₁₆×C₆₁	—	2	2	no	—
109	C₁₆×C₆₁	—	2	2	no	—
110	C₁₆×C₆₁	#41	1	4	yes	—
111	C₂³×C₆₁	C₂²×C₈	1	2	yes	—
112	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
113	Q₈×C₆₁	—	4	1	no	—
114	D₄×C₆₁	—	2	4	no	—
115	D₄×C₆₁	—	4	1	no	—
116	C₂×C₄×C₆₁	—	2	2	no	—
117	C₂×C₄×C₆₁	—	2	1	no	—
118	C₂×C₄×C₆₁	—	2	2	no	—
119	C₂×C₄×C₆₁	—	2	1	no	—
120	C₂×C₄×C₆₁	—	2	2	no	—
121	C₂×C₄×C₆₁	—	4	1	no	—
122	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
123	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
124	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
125	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
126	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
127	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
128	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
129	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
130	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
131	C₈×C₆₁	—	2	1	no	—
132	C₈×C₆₁	—	2	2	no	—
133	C₈×C₆₁	—	2	1	no	—
134	C₈×C₆₁	—	2	2	no	—
135	C₈×C₆₁	#131	1	2	yes	—
136	C₈×C₆₁	C₂×#41	1	2	yes	—
137	#33482	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂²×C₆₁	—	2	1	no	—
139	C₂²×C₆₁	—	2	1	no	—
140	C₂²×C₆₁	—	2	2	no	—
141	C₂²×C₆₁	—	2	2	no	—
142	C₂²×C₆₁	—	2	2	no	—
143	C₂²×C₆₁	#504	1	2	yes	—
144	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
145	C₄×C₆₁	—	2	1	no	—
146	C₄×C₆₁	—	2	1	no	—
147	C₄×C₆₁	—	2	2	no	—
148	C₄×C₆₁	—	2	1	no	—
149	C₄×C₆₁	—	2	1	no	—
150	C₄×C₆₁	—	2	2	no	—
151	C₄×C₆₁	—	2	1	no	—
152	C₄×C₆₁	—	2	2	no	—
153	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
154	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
155	#2966	C₂×C₆₁	1	1	yes	characteristic
156	#2183	C₂×C₆₁	1	2	yes	complemented
157	#2168	C₂×C₆₁	1	2	yes	complemented
158	#2168	C₂×C₆₁	1	2	yes	complemented
159	D₄×C₁₆	C₂×C₆₁	1	2	yes	complemented
160	#2164	C₂×C₆₁	1	2	yes	complemented
161	#2162	C₂×C₆₁	1	1	yes	characteristic, complemented
162	#2108	C₂×C₆₁	1	2	yes	complemented
163	C₂×#346	C₂×C₆₁	1	1	yes	characteristic, complemented
164	C₂×C₆₁	—	2	2	no	—
165	C₂×C₆₁	—	4	2	no	—
166	C₂×C₆₁	C₈×#41	1	1	yes	characteristic
167	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
168	C₂×C₆₁	#3407	1	1	yes	characteristic
169	#529	C₄×C₆₁	1	1	yes	characteristic
170	C₂×M₃₂	C₂²×C₆₁	1	2	yes	—
171	C₂²×C₁₆	C₂²×C₆₁	1	2	yes	—
172	C₂²×C₁₆	C₂²×C₆₁	1	2	yes	—
173	#446	C₄×C₆₁	1	1	yes	characteristic
174	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
175	#436	C₄×C₆₁	1	1	yes	characteristic
176	#435	C₄×C₆₁	1	2	yes	—
177	C₈×D₄	C₂²×C₆₁	1	2	yes	—
178	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
179	#433	C₄×C₆₁	1	2	yes	—
180	#432	C₄×C₆₁	1	1	yes	characteristic
181	#405	C₂²×C₆₁	1	2	yes	—
182	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
183	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	—
184	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	—
185	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	—
186	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
187	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
188	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	—
189	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	—
190	#346	C₂²×C₆₁	1	1	yes	characteristic
191	#346	C₂²×C₆₁	1	1	yes	characteristic
192	#346	C₂²×C₆₁	1	2	yes	—
193	#346	C₂²×C₆₁	1	2	yes	—
194	C₄×C₁₆	C₂²×C₆₁	1	2	yes	—
195	C₄×C₁₆	C₂²×C₆₁	1	2	yes	—
196	C₆₁	#33482	1	1	yes	characteristic, direct product factor, Sylow
197	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
198	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
199	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
200	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
201	#126	C₈×C₆₁	1	2	yes	—
202	#125	C₈×C₆₁	1	1	yes	characteristic
203	#124	C₈×C₆₁	1	1	yes	characteristic
204	#123	C₈×C₆₁	1	2	yes	—
205	C₂²⋊Q₈	C₈×C₆₁	1	1	yes	characteristic
206	#121	C₈×C₆₁	1	1	yes	characteristic
207	C₄×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
208	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
209	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
210	#117	C₂×C₄×C₆₁	1	2	yes	—
211	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
212	M₃₂	—	2	4	no	—
213	C₂×C₁₆	—	2	4	no	—
214	C₂×C₁₆	—	2	4	no	—
215	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
216	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
217	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
218	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
219	C₄⋊C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
220	C₄⋊C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
221	C₄⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
222	C₄⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
223	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
224	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
225	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
226	#97	C₂×C₄×C₆₁	1	2	yes	—
227	#97	C₂×C₄×C₆₁	1	2	yes	—
228	C₄×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
229	C₄×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
230	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
231	C₄×C₈	C₂³×C₆₁	1	2	yes	—
232	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
233	C₂×Q₈	C₂×C₈×C₆₁	1	1	yes	characteristic
234	C₂×D₄	C₂×C₈×C₆₁	1	2	yes	—
235	C₂×D₄	C₂×C₈×C₆₁	1	1	yes	characteristic
236	C₂²×C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
237	C₂²×C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
240	M₁₆	—	2	4	no	—
241	C₂×C₈	—	2	2	no	—
242	C₂×C₈	—	2	2	no	—
243	C₂×C₈	—	2	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
246	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
247	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
248	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
249	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
250	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
251	C₄⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
252	C₄⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
253	C₄⋊C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
254	C₄⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
255	C₄⋊C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
256	C₄⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
257	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
258	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
259	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
260	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
261	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
262	C₄²	C₂×C₈×C₆₁	1	1	yes	characteristic
263	C₄²	C₂×C₈×C₆₁	1	1	yes	characteristic
264	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
265	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
266	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
267	C₁₆	—	2	2	no	—
268	C₁₆	—	2	2	no	—
269	C₁₆	—	2	2	no	—
270	C₁₆	#41×C₆₁	1	4	yes	—
271	C₂³	C₂²×C₈×C₆₁	1	2	yes	—
272	C₂³	C₂²×C₈×C₆₁	1	1	yes	characteristic
273	Q₈	—	4	1	no	—
274	D₄	—	2	4	no	—
275	D₄	—	4	1	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	4	1	no	—
282	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
283	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
284	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
285	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
286	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
287	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
288	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
289	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
290	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
291	C₈	—	2	1	no	—
292	C₈	—	2	2	no	—
293	C₈	—	2	1	no	—
294	C₈	—	2	2	no	—
295	C₈	#131×C₆₁	1	2	yes	—
296	C₈	C₂×#41×C₆₁	1	2	yes	—
297	C₂²	—	2	1	no	—
298	C₂²	—	2	1	no	—
299	C₂²	—	2	2	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	C₆₁×#504	1	2	yes	—
303	C₂²	C₂³×C₈×C₆₁	1	1	yes	characteristic
304	C₄	—	2	1	no	—
305	C₄	—	2	1	no	—
306	C₄	—	2	2	no	—
307	C₄	—	2	1	no	—
308	C₄	—	2	1	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	1	no	—
311	C₄	—	2	2	no	—
312	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
313	C₄	C₂×#131×C₆₁	1	1	yes	characteristic
314	C₂	—	2	2	no	—
315	C₂	—	4	2	no	—
316	C₂	C₈×#41×C₆₁	1	1	yes	characteristic
317	C₂	C₂×C₆₁×#504	1	1	yes	characteristic
318	C₂	C₆₁×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₆₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₆₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂³×C₈
prime radical	#121×C₆₁	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2183	C₂	semidirect
3. C₆₁×#2168	C₂	semidirect
4. C₆₁×#2168	C₂	semidirect
5. D₄×C₁₆×C₆₁	C₂	semidirect
6. C₆₁×#2164	C₂	semidirect
7. C₆₁×#2162	C₂	semidirect
8. C₆₁×#2108	C₂	semidirect
9. C₂×C₆₁×#346	C₂	semidirect
137. #33482	C₆₁	direct (N × H)
156. #2183	C₂×C₆₁	semidirect
157. #2168	C₂×C₆₁	semidirect
158. #2168	C₂×C₆₁	semidirect
159. D₄×C₁₆	C₂×C₆₁	semidirect
160. #2164	C₂×C₆₁	semidirect
161. #2162	C₂×C₆₁	semidirect
162. #2108	C₂×C₆₁	semidirect
163. C₂×#346	C₂×C₆₁	semidirect
196. C₆₁	#33482	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#2966	2
C₆₁×#2183	2
C₆₁×#2168	2
D₄×C₁₆×C₆₁	2
C₆₁×#2164	2
C₆₁×#2162	2
C₆₁×#2108	2
C₂×C₆₁×#346	2
#33482	61

Subgroups — C61×#33482 #29536915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33482 #29536915