Subgroups — C₆₁×#25780 #29529213

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#494	C₂	1	2	yes	maximal, complemented
3	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#451	C₂	1	2	yes	maximal
5	C₆₁×#2434	C₂	1	2	yes	maximal
6	C₆₁×#2016	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1969	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
10	C₂²×Q₁₆×C₆₁	—	2	8	no	—
11	C₂²×Q₁₆×C₆₁	—	2	4	no	—
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₆₁	C₂²	1	4	yes	—
15	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
16	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
19	C₆₁×#494	—	2	8	no	—
20	C₆₁×#467	—	2	4	no	—
21	C₆₁×#451	—	2	8	no	—
22	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#395	—	2	4	no	—
28	C₆₁×#391	C₂²	1	4	yes	—
29	C₆₁×#385	—	2	4	no	—
30	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#336	C₂²	1	2	yes	—
32	C₂²×Q₈×C₆₁	—	2	2	no	—
33	C₂²×Q₈×C₆₁	—	2	8	no	—
34	C₂²×Q₈×C₆₁	—	2	4	no	—
35	C₂²×Q₈×C₆₁	—	2	4	no	—
36	C₂²×Q₈×C₆₁	—	4	4	no	—
37	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
38	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
39	C₂³×C₄×C₆₁	—	2	2	no	—
40	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
41	C₂×Q₁₆×C₆₁	—	2	32	no	—
42	C₂×Q₁₆×C₆₁	—	2	8	no	—
43	C₂×Q₁₆×C₆₁	—	2	8	no	—
44	C₂×Q₁₆×C₆₁	—	2	4	no	—
45	C₂×Q₁₆×C₆₁	—	2	4	no	—
46	C₂×Q₁₆×C₆₁	—	2	4	no	—
47	C₂×Q₁₆×C₆₁	—	2	8	no	—
48	C₂×Q₁₆×C₆₁	—	2	2	no	—
49	C₂×Q₁₆×C₆₁	—	2	4	no	—
50	C₂×Q₁₆×C₆₁	—	4	4	no	—
51	C₂×Q₁₆×C₆₁	D₄	1	8	yes	—
52	C₂²×C₈×C₆₁	—	2	4	no	—
53	C₂²×C₈×C₆₁	D₄	1	4	yes	—
54	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₆₁	—	2	8	no	—
58	C₄⋊Q₈×C₆₁	—	4	4	no	—
59	C₂²⋊Q₈×C₆₁	—	2	4	no	—
60	C₂²⋊Q₈×C₆₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
66	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
67	#107×C₆₁	—	2	2	no	—
68	#103×C₆₁	—	2	8	no	—
69	#103×C₆₁	—	2	4	no	—
70	C₂²⋊C₈×C₆₁	D₄	1	4	yes	—
71	C₄×C₈×C₆₁	—	2	4	no	—
72	#95×C₆₁	—	2	8	no	—
73	#95×C₆₁	D₄	1	2	yes	—
74	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
75	C₂×Q₈×C₆₁	—	2	4	no	—
76	C₂×Q₈×C₆₁	—	2	16	no	—
77	C₂×Q₈×C₆₁	—	2	4	no	—
78	C₂×Q₈×C₆₁	—	2	4	no	—
79	C₂×Q₈×C₆₁	—	2	4	no	—
80	C₂×Q₈×C₆₁	—	2	2	no	—
81	C₂×Q₈×C₆₁	—	2	2	no	—
82	C₂×Q₈×C₆₁	—	2	4	no	—
83	C₂×Q₈×C₆₁	—	2	4	no	—
84	C₂×Q₈×C₆₁	—	2	4	no	—
85	C₂×Q₈×C₆₁	—	4	8	no	—
86	C₂×Q₈×C₆₁	—	4	16	no	—
87	C₂×Q₈×C₆₁	—	4	8	no	—
88	C₂×Q₈×C₆₁	—	4	4	no	—
89	C₂×Q₈×C₆₁	C₂×D₄	1	8	yes	—
90	C₂²×C₄×C₆₁	—	2	2	no	—
91	C₂²×C₄×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	2	4	no	—
93	C₂²×C₄×C₆₁	—	2	2	no	—
94	C₂²×C₄×C₆₁	—	2	2	no	—
95	C₂²×C₄×C₆₁	—	4	8	no	—
96	C₂²×C₄×C₆₁	—	4	4	no	—
97	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
102	Q₁₆×C₆₁	—	2	16	no	—
103	Q₁₆×C₆₁	—	2	16	no	—
104	Q₁₆×C₆₁	—	4	16	no	—
105	Q₁₆×C₆₁	—	4	4	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	2	8	no	—
110	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
113	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
114	C₄⋊C₄×C₆₁	—	2	2	no	—
115	C₄⋊C₄×C₆₁	—	2	2	no	—
116	C₄⋊C₄×C₆₁	—	4	16	no	—
117	C₄⋊C₄×C₆₁	—	4	4	no	—
118	C₂²⋊C₄×C₆₁	—	4	4	no	—
119	C₂²⋊C₄×C₆₁	Q₁₆	1	8	yes	complemented
120	C₄²×C₆₁	—	2	2	no	—
121	C₄²×C₆₁	—	2	2	no	—
122	C₂³×C₆₁	—	2	2	no	—
123	C₂³×C₆₁	—	2	2	no	—
124	C₂³×C₆₁	#127	1	2	yes	—
125	C₂³×C₆₁	C₂×Q₁₆	1	4	yes	—
126	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₆₁	—	2	8	no	—
128	Q₈×C₆₁	—	2	8	no	—
129	Q₈×C₆₁	—	4	16	no	—
130	Q₈×C₆₁	—	4	4	no	—
131	Q₈×C₆₁	—	4	4	no	—
132	Q₈×C₆₁	—	4	2	no	—
133	Q₈×C₆₁	—	4	2	no	—
134	Q₈×C₆₁	—	4	4	no	—
135	C₂×C₄×C₆₁	—	2	4	no	—
136	C₂×C₄×C₆₁	—	2	2	no	—
137	C₂×C₄×C₆₁	—	2	4	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	2	no	—
140	C₂×C₄×C₆₁	—	2	4	no	—
141	C₂×C₄×C₆₁	—	2	8	no	—
142	C₂×C₄×C₆₁	—	4	16	no	—
143	C₂×C₄×C₆₁	—	4	4	no	—
144	C₂×C₄×C₆₁	—	4	4	no	—
145	C₂×C₄×C₆₁	—	4	2	no	—
146	C₂×C₄×C₆₁	—	4	2	no	—
147	C₂×C₄×C₆₁	—	4	4	no	—
148	C₂×C₄×C₆₁	—	4	4	no	—
149	C₂×C₄×C₆₁	#127	1	2	yes	—
150	C₂×C₄×C₆₁	C₂×Q₁₆	1	8	yes	complemented
151	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
155	C₈×C₆₁	—	2	2	no	—
156	C₈×C₆₁	—	2	4	no	—
157	C₈×C₆₁	#120	1	4	yes	—
158	#25780	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₆₁	—	2	2	no	—
160	C₂²×C₆₁	—	2	2	no	—
161	C₂²×C₆₁	—	2	8	no	—
162	C₂²×C₆₁	#494	1	4	yes	complemented
163	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
164	C₂²×C₆₁	D₄²	1	2	yes	—
165	C₂²×C₆₁	C₂²×Q₁₆	1	2	yes	—
166	C₂²×C₆₁	#578	1	2	yes	—
167	C₄×C₆₁	—	2	2	no	—
168	C₄×C₆₁	—	2	8	no	—
169	C₄×C₆₁	—	4	8	no	—
170	C₄×C₆₁	—	8	2	no	—
171	C₄×C₆₁	—	8	2	no	—
172	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
173	C₄×C₆₁	#535	1	1	yes	characteristic
174	C₄×C₆₁	D₄²	1	2	yes	—
175	C₂³×Q₁₆	C₂×C₆₁	1	1	yes	characteristic
176	C₂×#494	C₂×C₆₁	1	2	yes	complemented
177	C₂×#467	C₂×C₆₁	1	1	yes	characteristic
178	C₂×#451	C₂×C₆₁	1	2	yes	—
179	#2434	C₂×C₆₁	1	2	yes	—
180	#2016	C₂×C₆₁	1	4	yes	complemented
181	#1969	C₂×C₆₁	1	2	yes	complemented
182	C₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
183	C₂×C₆₁	—	2	4	no	—
184	C₂×C₆₁	#2433	1	1	yes	characteristic
185	C₂×C₆₁	C₂×#494	1	1	yes	characteristic
186	C₂×C₆₁	#3156	1	1	yes	characteristic
187	C₂×C₆₁	D₄×Q₁₆	1	4	yes	—
188	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
189	C₂²×Q₁₆	—	2	8	no	—
190	C₂²×Q₁₆	—	2	4	no	—
191	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
192	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
193	C₂²×Q₁₆	C₂²×C₆₁	1	4	yes	—
194	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
195	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
196	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	—
197	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
198	#494	—	2	8	no	—
199	#467	—	2	4	no	—
200	#451	—	2	8	no	—
201	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
202	C₂×#103	C₂²×C₆₁	1	4	yes	—
203	C₂×#103	C₂²×C₆₁	1	2	yes	—
204	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
205	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
206	#395	—	2	4	no	—
207	#391	C₂²×C₆₁	1	4	yes	—
208	#385	—	2	4	no	—
209	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
210	#336	C₂²×C₆₁	1	2	yes	—
211	C₆₁	#25780	1	1	yes	characteristic, direct product factor, Sylow
212	C₂²×Q₈	—	2	2	no	—
213	C₂²×Q₈	—	2	8	no	—
214	C₂²×Q₈	—	2	4	no	—
215	C₂²×Q₈	—	2	4	no	—
216	C₂²×Q₈	—	4	4	no	—
217	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
218	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
221	C₂×Q₁₆	—	2	32	no	—
222	C₂×Q₁₆	—	2	8	no	—
223	C₂×Q₁₆	—	2	8	no	—
224	C₂×Q₁₆	—	2	4	no	—
225	C₂×Q₁₆	—	2	4	no	—
226	C₂×Q₁₆	—	2	4	no	—
227	C₂×Q₁₆	—	2	8	no	—
228	C₂×Q₁₆	—	2	2	no	—
229	C₂×Q₁₆	—	2	4	no	—
230	C₂×Q₁₆	—	4	4	no	—
231	C₂×Q₁₆	D₄×C₆₁	1	8	yes	—
232	C₂²×C₈	—	2	4	no	—
233	C₂²×C₈	D₄×C₆₁	1	4	yes	—
234	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
237	C₄⋊Q₈	—	2	8	no	—
238	C₄⋊Q₈	—	4	4	no	—
239	C₂²⋊Q₈	—	2	4	no	—
240	C₂²⋊Q₈	—	2	4	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	8	no	—
243	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
246	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
247	#107	—	2	2	no	—
248	#103	—	2	8	no	—
249	#103	—	2	4	no	—
250	C₂²⋊C₈	D₄×C₆₁	1	4	yes	—
251	C₄×C₈	—	2	4	no	—
252	#95	—	2	8	no	—
253	#95	D₄×C₆₁	1	2	yes	—
254	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	16	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	2	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	4	8	no	—
266	C₂×Q₈	—	4	16	no	—
267	C₂×Q₈	—	4	8	no	—
268	C₂×Q₈	—	4	4	no	—
269	C₂×Q₈	C₂×D₄×C₆₁	1	8	yes	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	8	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
281	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
282	Q₁₆	—	2	16	no	—
283	Q₁₆	—	2	16	no	—
284	Q₁₆	—	4	16	no	—
285	Q₁₆	—	4	4	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	8	no	—
290	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
291	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
292	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
293	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	4	16	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	4	no	—
299	C₂²⋊C₄	Q₁₆×C₆₁	1	8	yes	complemented
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	#127×C₆₁	1	2	yes	—
305	C₂³	C₂×Q₁₆×C₆₁	1	4	yes	—
306	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
307	Q₈	—	2	8	no	—
308	Q₈	—	2	8	no	—
309	Q₈	—	4	16	no	—
310	Q₈	—	4	4	no	—
311	Q₈	—	4	4	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	4	no	—
314	Q₈	—	4	2	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	#127×C₆₁	1	2	yes	—
330	C₂×C₄	C₂×Q₁₆×C₆₁	1	8	yes	complemented
331	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
334	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
335	C₈	—	2	4	no	—
336	C₈	—	2	2	no	—
337	C₈	#120×C₆₁	1	4	yes	—
338	C₂²	—	2	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	2	8	no	—
341	C₂²	C₆₁×#494	1	4	yes	complemented
342	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
343	C₂²	D₄²×C₆₁	1	2	yes	—
344	C₂²	C₂²×Q₁₆×C₆₁	1	2	yes	—
345	C₂²	C₆₁×#578	1	2	yes	—
346	C₄	—	2	2	no	—
347	C₄	—	2	8	no	—
348	C₄	—	4	8	no	—
349	C₄	—	8	2	no	—
350	C₄	—	8	2	no	—
351	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
352	C₄	C₆₁×#535	1	1	yes	characteristic
353	C₄	D₄²×C₆₁	1	2	yes	—
354	C₂	—	2	4	no	—
355	C₂	C₆₁×#2433	1	1	yes	characteristic
356	C₂	C₂×C₆₁×#494	1	1	yes	characteristic
357	C₂	C₆₁×#3156	1	1	yes	characteristic
358	C₂	D₄×Q₁₆×C₆₁	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#494	C₂	semidirect
6. C₆₁×#2016	C₂	semidirect
7. C₆₁×#1969	C₂	semidirect
119. C₂²⋊C₄×C₆₁	Q₁₆	semidirect
150. C₂×C₄×C₆₁	C₂×Q₁₆	semidirect
158. #25780	C₆₁	direct (N × H)
162. C₂²×C₆₁	#494	semidirect
176. C₂×#494	C₂×C₆₁	semidirect
180. #2016	C₂×C₆₁	semidirect
181. #1969	C₂×C₆₁	semidirect
211. C₆₁	#25780	direct (N × H)
299. C₂²⋊C₄	Q₁₆×C₆₁	semidirect
330. C₂×C₄	C₂×Q₁₆×C₆₁	semidirect
341. C₂²	C₆₁×#494	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₆₁	2
C₂×C₆₁×#494	2
C₂×C₆₁×#467	2
C₂×C₆₁×#451	2
C₆₁×#2434	2
C₆₁×#2016	2
C₆₁×#1969	2
C₈×C₂²⋊C₄×C₆₁	2
#25780	61

Subgroups — C61×#25780 #29529213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25780 #29529213