Subgroups — C₆₁×#17925 #29521358

Order 15616.

586 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3104	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2985	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2982	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1587	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1584	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1579	C₂	1	2	yes	maximal, complemented
7	C₈×Q₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1572	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1491	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1485	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1453	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#533	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#484	C₄	1	2	yes	—
15	C₆₁×#477	C₄	1	2	yes	—
16	C₆₁×#462	C₄	1	2	yes	—
17	C₆₁×#451	C₄	1	2	yes	—
18	C₆₁×#446	—	2	2	no	—
19	C₆₁×#446	C₂²	1	2	yes	—
20	C₈×Q₈×C₆₁	—	2	2	no	—
21	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
22	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
23	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
24	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
25	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#433	—	2	2	no	—
27	C₆₁×#432	C₂²	1	1	yes	characteristic
28	C₆₁×#431	—	2	2	no	—
29	C₆₁×#431	C₂²	1	1	yes	characteristic
30	C₆₁×#431	C₂²	1	1	yes	characteristic
31	C₆₁×#431	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#335	C₂²	1	2	yes	—
34	C₆₁×#334	C₂²	1	2	yes	—
35	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₆₁×#322	C₂²	1	1	yes	characteristic
40	C₆₁×#322	C₂²	1	1	yes	characteristic
41	C₆₁×#322	C₂²	1	1	yes	characteristic
42	C₈²×C₆₁	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
45	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
46	C₂×M₁₆×C₆₁	—	2	1	no	—
47	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
49	#125×C₆₁	—	2	1	no	—
50	C₂²⋊Q₈×C₆₁	—	2	1	no	—
51	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
52	C₄×Q₈×C₆₁	—	2	1	no	—
53	C₄×Q₈×C₆₁	—	2	1	no	—
54	C₄×Q₈×C₆₁	—	2	1	no	—
55	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
56	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
57	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
58	#117×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₆₁	—	2	1	no	—
62	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
63	#107×C₆₁	C₂×C₄	1	2	yes	—
64	#107×C₆₁	C₂×C₄	1	2	yes	—
65	C₄⋊C₈×C₆₁	—	2	2	no	—
66	C₄⋊C₈×C₆₁	—	2	2	no	—
67	C₄⋊C₈×C₆₁	—	2	2	no	—
68	C₄⋊C₈×C₆₁	—	2	2	no	—
69	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
70	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
71	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
72	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
73	#103×C₆₁	C₂×C₄	1	2	yes	—
74	#103×C₆₁	C₂×C₄	1	2	yes	—
75	#103×C₆₁	C₂×C₄	1	2	yes	—
76	#103×C₆₁	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₆₁	—	2	1	no	—
78	C₂²⋊C₈×C₆₁	—	2	1	no	—
79	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
80	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
81	#97×C₆₁	—	2	2	no	—
82	#97×C₆₁	—	2	1	no	—
83	#97×C₆₁	—	2	1	no	—
84	C₄×C₈×C₆₁	—	2	2	no	—
85	C₄×C₈×C₆₁	—	2	2	no	—
86	C₄×C₈×C₆₁	—	2	2	no	—
87	C₄×C₈×C₆₁	—	2	1	no	—
88	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₆₁	—	2	4	no	—
95	C₂×Q₈×C₆₁	—	2	1	no	—
96	C₂×Q₈×C₆₁	—	2	1	no	—
97	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
104	Q₁₆×C₆₁	—	2	4	no	—
105	Q₁₆×C₆₁	—	2	4	no	—
106	M₁₆×C₆₁	—	4	2	no	—
107	C₂×C₈×C₆₁	—	2	1	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	2	2	no	—
110	C₂×C₈×C₆₁	—	2	1	no	—
111	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
115	C₄⋊C₄×C₆₁	—	2	2	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	1	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
125	C₂²⋊C₄×C₆₁	—	2	2	no	—
126	C₄²×C₆₁	—	2	2	no	—
127	C₄²×C₆₁	—	2	2	no	—
128	C₄²×C₆₁	—	2	2	no	—
129	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₆₁	#41	1	1	yes	characteristic
132	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
133	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
134	Q₈×C₆₁	—	2	4	no	—
135	Q₈×C₆₁	—	2	2	no	—
136	Q₈×C₆₁	—	2	2	no	—
137	Q₈×C₆₁	—	2	2	no	—
138	Q₈×C₆₁	—	8	1	no	—
139	Q₈×C₆₁	#131	1	4	yes	—
140	C₂×C₄×C₆₁	—	2	4	no	—
141	C₂×C₄×C₆₁	—	2	2	no	—
142	C₂×C₄×C₆₁	—	2	2	no	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	2	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	4	1	no	—
148	C₂×C₄×C₆₁	—	8	1	no	—
149	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
155	C₈×C₆₁	—	2	2	no	—
156	C₈×C₆₁	—	2	2	no	—
157	C₈×C₆₁	—	2	2	no	—
158	C₈×C₆₁	—	2	2	no	—
159	C₈×C₆₁	—	2	2	no	—
160	C₈×C₆₁	—	4	1	no	—
161	C₈×C₆₁	—	4	2	no	—
162	C₈×C₆₁	—	4	2	no	—
163	#17925	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₆₁	—	2	1	no	—
165	C₂²×C₆₁	—	2	1	no	—
166	C₂²×C₆₁	—	2	1	no	—
167	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
168	C₄×C₆₁	—	2	4	no	—
169	C₄×C₆₁	—	2	1	no	—
170	C₄×C₆₁	—	2	1	no	—
171	C₄×C₆₁	—	2	1	no	—
172	C₄×C₆₁	—	2	1	no	—
173	C₄×C₆₁	—	4	2	no	—
174	C₄×C₆₁	—	4	2	no	—
175	C₄×C₆₁	—	4	2	no	—
176	C₄×C₆₁	C₂×#131	1	2	yes	—
177	C₄×C₆₁	#578	1	2	yes	—
178	#3104	C₂×C₆₁	1	1	yes	characteristic
179	#2985	C₂×C₆₁	1	1	yes	characteristic
180	#2982	C₂×C₆₁	1	1	yes	characteristic
181	#1587	C₂×C₆₁	1	2	yes	complemented
182	#1584	C₂×C₆₁	1	2	yes	complemented
183	#1579	C₂×C₆₁	1	2	yes	complemented
184	C₈×Q₁₆	C₂×C₆₁	1	2	yes	complemented
185	#1572	C₂×C₆₁	1	1	yes	characteristic
186	#1491	C₂×C₆₁	1	1	yes	characteristic
187	#1485	C₂×C₆₁	1	1	yes	characteristic
188	#1453	C₂×C₆₁	1	1	yes	characteristic
189	C₂×C₆₁	—	4	1	no	—
190	C₂×C₆₁	#2929	1	1	yes	characteristic
191	C₂×C₆₁	#2950	1	1	yes	characteristic
192	C₂×C₆₁	#2956	1	1	yes	characteristic
193	#533	C₂²×C₆₁	1	1	yes	characteristic
194	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
195	#484	C₄×C₆₁	1	2	yes	—
196	#477	C₄×C₆₁	1	2	yes	—
197	#462	C₄×C₆₁	1	2	yes	—
198	#451	C₄×C₆₁	1	2	yes	—
199	#446	—	2	2	no	—
200	#446	C₂²×C₆₁	1	2	yes	—
201	C₈×Q₈	—	2	2	no	—
202	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
203	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
204	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
205	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
206	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
207	#433	—	2	2	no	—
208	#432	C₂²×C₆₁	1	1	yes	characteristic
209	#431	—	2	2	no	—
210	#431	C₂²×C₆₁	1	1	yes	characteristic
211	#431	C₂²×C₆₁	1	1	yes	characteristic
212	#431	C₂²×C₆₁	1	1	yes	characteristic
213	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
214	#335	C₂²×C₆₁	1	2	yes	—
215	#334	C₂²×C₆₁	1	2	yes	—
216	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
217	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
218	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
219	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
220	#322	C₂²×C₆₁	1	1	yes	characteristic
221	#322	C₂²×C₆₁	1	1	yes	characteristic
222	#322	C₂²×C₆₁	1	1	yes	characteristic
223	C₈²	C₂²×C₆₁	1	1	yes	characteristic
224	C₆₁	#17925	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
226	C₂×Q₁₆	C₂×C₄×C₆₁	1	2	yes	—
227	C₂×Q₁₆	C₂×C₄×C₆₁	1	2	yes	—
228	C₂×M₁₆	—	2	1	no	—
229	C₄⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
230	C₄⋊Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
231	#125	—	2	1	no	—
232	C₂²⋊Q₈	—	2	1	no	—
233	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×Q₈	—	2	1	no	—
236	C₄×Q₈	—	2	1	no	—
237	C₄×Q₈	C₂×C₄×C₆₁	1	2	yes	—
238	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
239	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
240	#117	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
243	C₂×C₄²	—	2	1	no	—
244	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
245	#107	C₂×C₄×C₆₁	1	2	yes	—
246	#107	C₂×C₄×C₆₁	1	2	yes	—
247	C₄⋊C₈	—	2	2	no	—
248	C₄⋊C₈	—	2	2	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
252	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
253	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
254	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
255	#103	C₂×C₄×C₆₁	1	2	yes	—
256	#103	C₂×C₄×C₆₁	1	2	yes	—
257	#103	C₂×C₄×C₆₁	1	2	yes	—
258	#103	C₂×C₄×C₆₁	1	2	yes	—
259	C₂²⋊C₈	—	2	1	no	—
260	C₂²⋊C₈	—	2	1	no	—
261	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
262	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
263	#97	—	2	2	no	—
264	#97	—	2	1	no	—
265	#97	—	2	1	no	—
266	C₄×C₈	—	2	2	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	2	2	no	—
269	C₄×C₈	—	2	1	no	—
270	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
271	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
273	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
274	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
280	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
285	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
286	Q₁₆	—	2	4	no	—
287	Q₁₆	—	2	4	no	—
288	M₁₆	—	4	2	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
294	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
296	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
306	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
313	C₄²	#41×C₆₁	1	1	yes	characteristic
314	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
315	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
316	Q₈	—	2	4	no	—
317	Q₈	—	2	2	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	2	2	no	—
320	Q₈	—	8	1	no	—
321	Q₈	#131×C₆₁	1	4	yes	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	8	1	no	—
331	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
337	C₈	—	2	2	no	—
338	C₈	—	2	2	no	—
339	C₈	—	2	2	no	—
340	C₈	—	2	2	no	—
341	C₈	—	2	2	no	—
342	C₈	—	4	1	no	—
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	2	no	—
357	C₄	C₂×#131×C₆₁	1	2	yes	—
358	C₄	C₆₁×#578	1	2	yes	—
359	C₂	—	4	1	no	—
360	C₂	C₆₁×#2929	1	1	yes	characteristic
361	C₂	C₆₁×#2950	1	1	yes	characteristic
362	C₂	C₆₁×#2956	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₄²	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂³×C₆₁	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₆₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1587	C₂	semidirect
5. C₆₁×#1584	C₂	semidirect
6. C₆₁×#1579	C₂	semidirect
7. C₈×Q₁₆×C₆₁	C₂	semidirect
163. #17925	C₆₁	direct (N × H)
181. #1587	C₂×C₆₁	semidirect
182. #1584	C₂×C₆₁	semidirect
183. #1579	C₂×C₆₁	semidirect
184. C₈×Q₁₆	C₂×C₆₁	semidirect
224. C₆₁	#17925	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×#3104	2
C₆₁×#2985	2
C₆₁×#2982	2
C₆₁×#1587	2
C₆₁×#1584	2
C₆₁×#1579	2
C₈×Q₁₆×C₆₁	2
C₆₁×#1572	2
C₆₁×#1491	2
C₆₁×#1485	2
C₆₁×#1453	2
#17925	61

Subgroups — C61×#17925 #29521358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#17925 #29521358