Subgroups — C₆₁×#19354 #29522787

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3239	C₂	1	2	yes	maximal
2	C₂×C₆₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2966	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1690	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1689	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1670	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1669	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1556	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₆₁	—	2	1	no	—
11	C₂²×Q₁₆×C₆₁	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
13	C₆₁×#529	C₂²	1	1	yes	characteristic
14	C₆₁×#501	—	2	2	no	—
15	C₆₁×#494	—	2	1	no	—
16	C₆₁×#494	—	2	1	no	—
17	C₆₁×#494	C₂²	1	2	yes	—
18	C₆₁×#494	C₂²	1	2	yes	—
19	C₆₁×#489	—	2	2	no	—
20	C₆₁×#484	—	2	2	no	—
21	C₆₁×#481	—	2	2	no	—
22	C₆₁×#475	C₂²	1	4	yes	—
23	C₆₁×#474	C₂²	1	4	yes	—
24	C₆₁×#446	C₂²	1	1	yes	characteristic
25	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#436	C₂²	1	1	yes	characteristic
27	C₆₁×#435	—	2	1	no	—
28	C₈×D₄×C₆₁	—	2	1	no	—
29	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#433	—	2	1	no	—
31	C₆₁×#432	C₂²	1	1	yes	characteristic
32	C₆₁×#432	C₂²	1	2	yes	—
33	C₆₁×#405	—	2	1	no	—
34	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#335	C₂²	1	2	yes	—
36	C₆₁×#334	C₂²	1	2	yes	—
37	C₆₁×#332	C₂²	1	4	yes	—
38	C₆₁×#332	C₂²	1	4	yes	—
39	C₂²×Q₈×C₆₁	—	2	2	no	—
40	C₂×Q₁₆×C₆₁	—	2	2	no	—
41	C₂×Q₁₆×C₆₁	—	2	2	no	—
42	C₂×Q₁₆×C₆₁	—	2	2	no	—
43	C₂×Q₁₆×C₆₁	—	2	2	no	—
44	C₂×Q₁₆×C₆₁	—	4	4	no	—
45	C₂×Q₁₆×C₆₁	—	4	4	no	—
46	C₂×M₁₆×C₆₁	—	2	1	no	—
47	C₂²×C₈×C₆₁	—	2	1	no	—
48	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₆₁	—	2	2	no	—
51	C₄⋊Q₈×C₆₁	—	2	2	no	—
52	C₄⋊Q₈×C₆₁	—	2	2	no	—
53	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
54	#126×C₆₁	—	2	1	no	—
55	#125×C₆₁	D₄	1	1	yes	characteristic
56	#124×C₆₁	D₄	1	1	yes	characteristic
57	#123×C₆₁	—	2	1	no	—
58	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
59	#121×C₆₁	D₄	1	1	yes	characteristic
60	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₆₁	—	2	1	no	—
62	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
63	#117×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
67	#107×C₆₁	—	2	4	no	—
68	#106×C₆₁	—	2	4	no	—
69	C₄⋊C₈×C₆₁	—	2	1	no	—
70	C₄⋊C₈×C₆₁	—	2	1	no	—
71	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
74	#103×C₆₁	—	2	4	no	—
75	#102×C₆₁	—	2	4	no	—
76	C₂²⋊C₈×C₆₁	—	2	1	no	—
77	C₂²⋊C₈×C₆₁	—	2	2	no	—
78	C₂²⋊C₈×C₆₁	—	2	1	no	—
79	C₂²⋊C₈×C₆₁	—	2	1	no	—
80	#97×C₆₁	—	2	1	no	—
81	#97×C₆₁	—	2	1	no	—
82	#97×C₆₁	—	2	2	no	—
83	C₄×C₈×C₆₁	—	2	1	no	—
84	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
85	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×Q₈×C₆₁	—	2	4	no	—
89	C₂×Q₈×C₆₁	—	4	4	no	—
90	C₂×Q₈×C₆₁	—	4	4	no	—
91	C₂×Q₈×C₆₁	—	4	2	no	—
92	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂×D₄×C₆₁	—	2	1	no	—
94	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	—	2	1	no	—
96	C₂²×C₄×C₆₁	—	4	2	no	—
97	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
100	Q₁₆×C₆₁	—	4	4	no	—
101	Q₁₆×C₆₁	—	4	4	no	—
102	Q₁₆×C₆₁	—	4	4	no	—
103	Q₁₆×C₆₁	—	4	4	no	—
104	M₁₆×C₆₁	—	4	2	no	—
105	C₂×C₈×C₆₁	—	2	2	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
107	C₂×C₈×C₆₁	—	2	1	no	—
108	C₂×C₈×C₆₁	—	2	1	no	—
109	C₂×C₈×C₆₁	—	2	4	no	—
110	C₂×C₈×C₆₁	—	4	2	no	—
111	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₄⋊C₄×C₆₁	—	2	1	no	—
116	C₄⋊C₄×C₆₁	—	2	1	no	—
117	C₄⋊C₄×C₆₁	—	2	1	no	—
118	C₄⋊C₄×C₆₁	—	2	1	no	—
119	C₄⋊C₄×C₆₁	—	2	4	no	—
120	C₄⋊C₄×C₆₁	—	2	4	no	—
121	C₄⋊C₄×C₆₁	—	4	2	no	—
122	C₄⋊C₄×C₆₁	—	4	2	no	—
123	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²⋊C₄×C₆₁	—	2	1	no	—
126	C₂²⋊C₄×C₆₁	—	2	1	no	—
127	C₂²⋊C₄×C₆₁	—	2	1	no	—
128	C₂²⋊C₄×C₆₁	—	2	1	no	—
129	C₂²⋊C₄×C₆₁	—	2	1	no	—
130	C₄²×C₆₁	—	2	1	no	—
131	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₆₁	#41	1	1	yes	characteristic
134	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
135	C₂³×C₆₁	—	2	1	no	—
136	C₂³×C₆₁	#121	1	1	yes	characteristic
137	Q₈×C₆₁	—	2	2	no	—
138	Q₈×C₆₁	—	4	4	no	—
139	Q₈×C₆₁	—	4	4	no	—
140	Q₈×C₆₁	—	8	4	no	—
141	D₄×C₆₁	—	2	2	no	—
142	D₄×C₆₁	—	4	2	no	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	1	no	—
145	C₂×C₄×C₆₁	—	2	1	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	1	no	—
148	C₂×C₄×C₆₁	—	2	1	no	—
149	C₂×C₄×C₆₁	—	2	1	no	—
150	C₂×C₄×C₆₁	—	4	1	no	—
151	C₂×C₄×C₆₁	—	4	1	no	—
152	C₂×C₄×C₆₁	—	4	4	no	—
153	C₂×C₄×C₆₁	—	8	4	no	—
154	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
155	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
156	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
160	C₈×C₆₁	—	2	1	no	—
161	C₈×C₆₁	—	2	1	no	—
162	C₈×C₆₁	—	4	1	no	—
163	C₈×C₆₁	—	4	1	no	—
164	C₈×C₆₁	—	4	4	no	—
165	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
166	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
167	#19354	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₆₁	—	2	1	no	—
169	C₂²×C₆₁	—	2	1	no	—
170	C₂²×C₆₁	—	4	1	no	—
171	C₂²×C₆₁	—	4	1	no	—
172	C₂²×C₆₁	—	4	1	no	—
173	C₂²×C₆₁	#473	1	2	yes	—
174	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
175	C₄×C₆₁	—	2	1	no	—
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	2	1	no	—
179	C₄×C₆₁	—	4	1	no	—
180	C₄×C₆₁	—	4	1	no	—
181	C₄×C₆₁	—	4	1	no	—
182	C₄×C₆₁	—	8	4	no	—
183	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₄×C₆₁	#578	1	2	yes	—
186	#3239	C₂×C₆₁	1	2	yes	—
187	C₂×#494	C₂×C₆₁	1	1	yes	characteristic, complemented
188	#2966	C₂×C₆₁	1	1	yes	characteristic
189	#1690	C₂×C₆₁	1	2	yes	complemented
190	#1689	C₂×C₆₁	1	2	yes	complemented
191	#1670	C₂×C₆₁	1	2	yes	complemented
192	#1669	C₂×C₆₁	1	2	yes	complemented
193	#1568	C₂×C₆₁	1	1	yes	characteristic, complemented
194	#1556	C₂×C₆₁	1	2	yes	complemented
195	C₂×C₆₁	—	2	2	no	—
196	C₂×C₆₁	—	8	1	no	—
197	C₂×C₆₁	#3038	1	1	yes	characteristic
198	C₂×C₆₁	#3059	1	1	yes	characteristic
199	C₂×C₆₁	C₂×#473	1	1	yes	characteristic
200	C₂²×Q₁₆	—	2	1	no	—
201	C₂²×Q₁₆	—	2	1	no	—
202	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
203	#529	C₂²×C₆₁	1	1	yes	characteristic
204	#501	—	2	2	no	—
205	#494	—	2	1	no	—
206	#494	—	2	1	no	—
207	#494	C₂²×C₆₁	1	2	yes	—
208	#494	C₂²×C₆₁	1	2	yes	—
209	#489	—	2	2	no	—
210	#484	—	2	2	no	—
211	#481	—	2	2	no	—
212	#475	C₂²×C₆₁	1	4	yes	—
213	#474	C₂²×C₆₁	1	4	yes	—
214	#446	C₂²×C₆₁	1	1	yes	characteristic
215	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
216	#436	C₂²×C₆₁	1	1	yes	characteristic
217	#435	—	2	1	no	—
218	C₈×D₄	—	2	1	no	—
219	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
220	#433	—	2	1	no	—
221	#432	C₂²×C₆₁	1	1	yes	characteristic
222	#432	C₂²×C₆₁	1	2	yes	—
223	#405	—	2	1	no	—
224	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
225	#335	C₂²×C₆₁	1	2	yes	—
226	#334	C₂²×C₆₁	1	2	yes	—
227	#332	C₂²×C₆₁	1	4	yes	—
228	#332	C₂²×C₆₁	1	4	yes	—
229	C₆₁	#19354	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×Q₈	—	2	2	no	—
231	C₂×Q₁₆	—	2	2	no	—
232	C₂×Q₁₆	—	2	2	no	—
233	C₂×Q₁₆	—	2	2	no	—
234	C₂×Q₁₆	—	2	2	no	—
235	C₂×Q₁₆	—	4	4	no	—
236	C₂×Q₁₆	—	4	4	no	—
237	C₂×M₁₆	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
245	#126	—	2	1	no	—
246	#125	D₄×C₆₁	1	1	yes	characteristic
247	#124	D₄×C₆₁	1	1	yes	characteristic
248	#123	—	2	1	no	—
249	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
250	#121	D₄×C₆₁	1	1	yes	characteristic
251	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
254	#117	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
258	#107	—	2	4	no	—
259	#106	—	2	4	no	—
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
263	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
264	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
265	#103	—	2	4	no	—
266	#102	—	2	4	no	—
267	C₂²⋊C₈	—	2	1	no	—
268	C₂²⋊C₈	—	2	2	no	—
269	C₂²⋊C₈	—	2	1	no	—
270	C₂²⋊C₈	—	2	1	no	—
271	#97	—	2	1	no	—
272	#97	—	2	1	no	—
273	#97	—	2	2	no	—
274	C₄×C₈	—	2	1	no	—
275	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
276	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	—	4	4	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
290	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
291	Q₁₆	—	4	4	no	—
292	Q₁₆	—	4	4	no	—
293	Q₁₆	—	4	4	no	—
294	Q₁₆	—	4	4	no	—
295	M₁₆	—	4	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	4	2	no	—
302	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
306	C₄⋊C₄	—	2	1	no	—
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
315	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
316	C₂²⋊C₄	—	2	1	no	—
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	1	no	—
321	C₄²	—	2	1	no	—
322	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
323	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
324	C₄²	#41×C₆₁	1	1	yes	characteristic
325	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
326	C₂³	—	2	1	no	—
327	C₂³	#121×C₆₁	1	1	yes	characteristic
328	Q₈	—	2	2	no	—
329	Q₈	—	4	4	no	—
330	Q₈	—	4	4	no	—
331	Q₈	—	8	4	no	—
332	D₄	—	2	2	no	—
333	D₄	—	4	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	8	4	no	—
345	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
346	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
347	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
350	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
351	C₈	—	2	1	no	—
352	C₈	—	2	1	no	—
353	C₈	—	4	1	no	—
354	C₈	—	4	1	no	—
355	C₈	—	4	4	no	—
356	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
357	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₆₁×#473	1	2	yes	—
364	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	8	4	no	—
373	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
374	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
375	C₄	C₆₁×#578	1	2	yes	—
376	C₂	—	2	2	no	—
377	C₂	—	8	1	no	—
378	C₂	C₆₁×#3038	1	1	yes	characteristic
379	C₂	C₆₁×#3059	1	1	yes	characteristic
380	C₂	C₂×C₆₁×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	#121×C₆₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#494	C₂	semidirect
4. C₆₁×#1690	C₂	semidirect
5. C₆₁×#1689	C₂	semidirect
6. C₆₁×#1670	C₂	semidirect
7. C₆₁×#1669	C₂	semidirect
8. C₆₁×#1568	C₂	semidirect
9. C₆₁×#1556	C₂	semidirect
167. #19354	C₆₁	direct (N × H)
187. C₂×#494	C₂×C₆₁	semidirect
189. #1690	C₂×C₆₁	semidirect
190. #1689	C₂×C₆₁	semidirect
191. #1670	C₂×C₆₁	semidirect
192. #1669	C₂×C₆₁	semidirect
193. #1568	C₂×C₆₁	semidirect
194. #1556	C₂×C₆₁	semidirect
229. C₆₁	#19354	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×#3239	2
C₂×C₆₁×#494	2
C₆₁×#2966	2
C₆₁×#1690	2
C₆₁×#1689	2
C₆₁×#1670	2
C₆₁×#1669	2
C₆₁×#1568	2
C₆₁×#1556	2
#19354	61

Subgroups — C61×#19354 #29522787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19354 #29522787