Subgroups — C₆₁×#23800 #29527233

Order 15616.

1050 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₄×#124×C₆₁	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2097	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2092	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2015	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2012	C₂	1	2	yes	maximal
9	C₆₁×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
12	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
16	C₄×Q₁₆×C₆₁	—	2	4	no	—
17	C₄×SD₁₆×C₆₁	—	2	8	no	—
18	C₄×D₈×C₆₁	—	2	4	no	—
19	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#106×C₆₁	C₂²	1	2	yes	—
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	2	yes	—
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#391	C₂²	1	2	yes	—
29	C₆₁×#390	C₂²	1	2	yes	—
30	C₆₁×#388	—	2	4	no	—
31	C₆₁×#382	C₂²	1	2	yes	—
32	C₄×C₂²⋊C₄×C₆₁	—	2	4	no	—
33	C₄³×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#336	C₂²	1	2	yes	—
35	C₆₁×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
37	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
38	C₂³×C₄×C₆₁	—	2	2	no	—
39	C₂×Q₁₆×C₆₁	—	2	4	no	—
40	C₂×Q₁₆×C₆₁	—	2	2	no	—
41	C₂×SD₁₆×C₆₁	—	2	4	no	—
42	C₂×SD₁₆×C₆₁	—	2	4	no	—
43	C₂×SD₁₆×C₆₁	—	2	4	no	—
44	C₂×D₈×C₆₁	—	2	4	no	—
45	C₂×D₈×C₆₁	—	2	2	no	—
46	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
49	#124×C₆₁	—	2	4	no	—
50	#124×C₆₁	—	2	4	no	—
51	C₄×Q₈×C₆₁	—	2	4	no	—
52	C₄×Q₈×C₆₁	—	2	4	no	—
53	C₄×D₄×C₆₁	—	2	4	no	—
54	C₄×D₄×C₆₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄²×C₆₁	—	2	2	no	—
62	C₂×C₄²×C₆₁	D₄	1	2	yes	—
63	C₂×C₄²×C₆₁	D₄	1	2	yes	—
64	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
65	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
66	#107×C₆₁	—	2	2	no	—
67	#107×C₆₁	—	2	2	no	—
68	#106×C₆₁	—	2	4	no	—
69	#103×C₆₁	—	2	4	no	—
70	#103×C₆₁	—	2	4	no	—
71	#102×C₆₁	—	2	4	no	—
72	#102×C₆₁	—	2	4	no	—
73	C₄×C₈×C₆₁	D₄	1	4	yes	—
74	C₄×C₈×C₆₁	D₄	1	4	yes	—
75	#95×C₆₁	—	2	4	no	—
76	#95×C₆₁	—	2	4	no	—
77	C₂⁴×C₆₁	—	2	2	no	—
78	C₂×Q₈×C₆₁	—	2	2	no	—
79	C₂×Q₈×C₆₁	—	2	2	no	—
80	C₂×Q₈×C₆₁	—	2	2	no	—
81	C₂×Q₈×C₆₁	—	2	2	no	—
82	C₂×Q₈×C₆₁	—	2	2	no	—
83	C₂×Q₈×C₆₁	#41	1	4	yes	—
84	C₂×D₄×C₆₁	—	2	2	no	—
85	C₂×D₄×C₆₁	—	2	2	no	—
86	C₂×D₄×C₆₁	—	2	2	no	—
87	C₂×D₄×C₆₁	—	2	2	no	—
88	C₂×D₄×C₆₁	—	2	2	no	—
89	C₂×D₄×C₆₁	#41	1	4	yes	—
90	C₂²×C₄×C₆₁	—	2	2	no	—
91	C₂²×C₄×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	2	2	no	—
93	C₂²×C₄×C₆₁	—	4	4	no	—
94	C₂²×C₄×C₆₁	—	4	8	no	—
95	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
99	Q₁₆×C₆₁	—	2	8	no	—
100	SD₁₆×C₆₁	—	2	16	no	—
101	D₈×C₆₁	—	2	8	no	—
102	C₂×C₈×C₆₁	—	2	2	no	—
103	C₂×C₈×C₆₁	—	2	2	no	—
104	C₂×C₈×C₆₁	—	2	2	no	—
105	C₂×C₈×C₆₁	—	2	2	no	—
106	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
108	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
109	C₄⋊C₄×C₆₁	—	2	2	no	—
110	C₄⋊C₄×C₆₁	—	2	2	no	—
111	C₄⋊C₄×C₆₁	—	2	2	no	—
112	C₄⋊C₄×C₆₁	—	2	2	no	—
113	C₄⋊C₄×C₆₁	—	4	4	no	—
114	C₂²⋊C₄×C₆₁	—	2	16	no	—
115	C₂²⋊C₄×C₆₁	—	4	8	no	—
116	C₂²⋊C₄×C₆₁	—	4	4	no	—
117	C₄²×C₆₁	—	2	4	no	—
118	C₄²×C₆₁	—	2	2	no	—
119	C₄²×C₆₁	—	2	2	no	—
120	C₄²×C₆₁	—	4	2	no	—
121	C₄²×C₆₁	—	4	4	no	—
122	C₄²×C₆₁	C₂×D₄	1	2	yes	—
123	C₄²×C₆₁	C₂×D₄	1	2	yes	—
124	C₂³×C₆₁	—	2	4	no	—
125	C₂³×C₆₁	—	4	2	no	—
126	C₂³×C₆₁	—	4	2	no	—
127	C₂³×C₆₁	—	4	4	no	—
128	C₂³×C₆₁	—	4	4	no	—
129	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₆₁	—	2	4	no	—
131	Q₈×C₆₁	—	2	4	no	—
132	Q₈×C₆₁	—	4	2	no	—
133	Q₈×C₆₁	—	4	2	no	—
134	D₄×C₆₁	—	2	4	no	—
135	D₄×C₆₁	—	2	4	no	—
136	D₄×C₆₁	—	4	2	no	—
137	D₄×C₆₁	—	4	2	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	4	no	—
140	C₂×C₄×C₆₁	—	2	4	no	—
141	C₂×C₄×C₆₁	—	2	4	no	—
142	C₂×C₄×C₆₁	—	2	4	no	—
143	C₂×C₄×C₆₁	—	4	2	no	—
144	C₂×C₄×C₆₁	—	4	2	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	—	8	8	no	—
150	C₂×C₄×C₆₁	#127	1	2	yes	—
151	C₂×C₄×C₆₁	#127	1	2	yes	—
152	C₂×C₄×C₆₁	#135	1	4	yes	—
153	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
157	C₈×C₆₁	—	2	2	no	—
158	C₈×C₆₁	—	2	4	no	—
159	C₈×C₆₁	—	2	2	no	—
160	#23800	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂²×C₆₁	—	4	8	no	—
162	C₂²×C₆₁	—	4	4	no	—
163	C₂²×C₆₁	—	8	4	no	—
164	C₂²×C₆₁	—	8	2	no	—
165	C₂²×C₆₁	—	8	2	no	—
166	C₂²×C₆₁	#525	1	2	yes	—
167	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
168	C₂²×C₆₁	C₂×#135	1	2	yes	—
169	C₂²×C₆₁	#575	1	2	yes	—
170	C₄×C₆₁	—	2	2	no	—
171	C₄×C₆₁	—	4	4	no	—
172	C₄×C₆₁	—	4	4	no	—
173	C₄×C₆₁	—	8	2	no	—
174	C₄×C₆₁	—	8	2	no	—
175	C₄×C₆₁	#495	1	4	yes	—
176	C₄×C₆₁	#525	1	1	yes	characteristic
177	C₄×C₆₁	#525	1	2	yes	—
178	C₄×C₆₁	#525	1	1	yes	characteristic
179	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
180	C₂×C₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
181	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic
182	C₄×#124	C₂×C₆₁	1	2	yes	complemented
183	#2097	C₂×C₆₁	1	2	yes	complemented
184	#2092	C₂×C₆₁	1	2	yes	complemented
185	#2015	C₂×C₆₁	1	2	yes	complemented
186	#2012	C₂×C₆₁	1	2	yes	—
187	#1744	C₂×C₆₁	1	1	yes	characteristic, complemented
188	C₂×C₆₁	—	8	4	no	—
189	C₂×C₆₁	#2397	1	1	yes	characteristic
190	C₂×C₆₁	#3102	1	4	yes	—
191	C₂×C₆₁	C₂×#495	1	1	yes	characteristic
192	C₂×C₆₁	#3150	1	1	yes	characteristic
193	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
194	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
195	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
196	C₂×#124	C₂²×C₆₁	1	2	yes	—
197	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
198	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
199	C₄×Q₁₆	—	2	4	no	—
200	C₄×SD₁₆	—	2	8	no	—
201	C₄×D₈	—	2	4	no	—
202	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
203	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
204	C₂×#106	C₂²×C₆₁	1	2	yes	—
205	C₂×#103	C₂²×C₆₁	1	2	yes	—
206	C₂×#103	C₂²×C₆₁	1	2	yes	—
207	C₂×#102	C₂²×C₆₁	1	2	yes	—
208	C₂×#102	C₂²×C₆₁	1	2	yes	—
209	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
211	#391	C₂²×C₆₁	1	2	yes	—
212	#390	C₂²×C₆₁	1	2	yes	—
213	#388	—	2	4	no	—
214	#382	C₂²×C₆₁	1	2	yes	—
215	C₄×C₂²⋊C₄	—	2	4	no	—
216	C₄³	C₂²×C₆₁	1	1	yes	characteristic
217	#336	C₂²×C₆₁	1	2	yes	—
218	#336	C₂²×C₆₁	1	2	yes	—
219	C₆₁	#23800	1	1	yes	characteristic, direct product factor, Sylow
220	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
221	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
222	C₂³×C₄	—	2	2	no	—
223	C₂×Q₁₆	—	2	4	no	—
224	C₂×Q₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×SD₁₆	—	2	4	no	—
227	C₂×SD₁₆	—	2	4	no	—
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
233	#124	—	2	4	no	—
234	#124	—	2	4	no	—
235	C₄×Q₈	—	2	4	no	—
236	C₄×Q₈	—	2	4	no	—
237	C₄×D₄	—	2	4	no	—
238	C₄×D₄	—	2	4	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
241	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	D₄×C₆₁	1	2	yes	—
247	C₂×C₄²	D₄×C₆₁	1	2	yes	—
248	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
250	#107	—	2	2	no	—
251	#107	—	2	2	no	—
252	#106	—	2	4	no	—
253	#103	—	2	4	no	—
254	#103	—	2	4	no	—
255	#102	—	2	4	no	—
256	#102	—	2	4	no	—
257	C₄×C₈	D₄×C₆₁	1	4	yes	—
258	C₄×C₈	D₄×C₆₁	1	4	yes	—
259	#95	—	2	4	no	—
260	#95	—	2	4	no	—
261	C₂⁴	—	2	2	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	#41×C₆₁	1	4	yes	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	#41×C₆₁	1	4	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
283	Q₁₆	—	2	8	no	—
284	SD₁₆	—	2	16	no	—
285	D₈	—	2	8	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
291	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
292	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	2	16	no	—
299	C₂²⋊C₄	—	4	8	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	4	2	no	—
305	C₄²	—	4	4	no	—
306	C₄²	C₂×D₄×C₆₁	1	2	yes	—
307	C₄²	C₂×D₄×C₆₁	1	2	yes	—
308	C₂³	—	2	4	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	4	no	—
311	C₂³	—	4	4	no	—
312	C₂³	—	4	2	no	—
313	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
314	Q₈	—	2	4	no	—
315	Q₈	—	2	4	no	—
316	Q₈	—	4	2	no	—
317	Q₈	—	4	2	no	—
318	D₄	—	2	4	no	—
319	D₄	—	2	4	no	—
320	D₄	—	4	2	no	—
321	D₄	—	4	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	8	8	no	—
334	C₂×C₄	#127×C₆₁	1	2	yes	—
335	C₂×C₄	#127×C₆₁	1	2	yes	—
336	C₂×C₄	#135×C₆₁	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
340	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
341	C₈	—	2	2	no	—
342	C₈	—	2	4	no	—
343	C₈	—	2	2	no	—
344	C₂²	—	4	8	no	—
345	C₂²	—	4	4	no	—
346	C₂²	—	8	4	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	C₆₁×#525	1	2	yes	—
350	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
351	C₂²	C₂×#135×C₆₁	1	2	yes	—
352	C₂²	C₆₁×#575	1	2	yes	—
353	C₄	—	2	2	no	—
354	C₄	—	4	4	no	—
355	C₄	—	4	4	no	—
356	C₄	—	8	2	no	—
357	C₄	—	8	2	no	—
358	C₄	C₆₁×#495	1	4	yes	—
359	C₄	C₆₁×#525	1	1	yes	characteristic
360	C₄	C₆₁×#525	1	2	yes	—
361	C₄	C₆₁×#525	1	1	yes	characteristic
362	C₂	—	8	4	no	—
363	C₂	C₆₁×#2397	1	1	yes	characteristic
364	C₂	C₆₁×#3102	1	4	yes	—
365	C₂	C₂×C₆₁×#495	1	1	yes	characteristic
366	C₂	C₆₁×#3150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
prime radical	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₄³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
2. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
4. C₄×#124×C₆₁	C₂	semidirect
5. C₆₁×#2097	C₂	semidirect
6. C₆₁×#2092	C₂	semidirect
7. C₆₁×#2015	C₂	semidirect
9. C₆₁×#1744	C₂	semidirect
160. #23800	C₆₁	direct (N × H)
179. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
180. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
182. C₄×#124	C₂×C₆₁	semidirect
183. #2097	C₂×C₆₁	semidirect
184. #2092	C₂×C₆₁	semidirect
185. #2015	C₂×C₆₁	semidirect
187. #1744	C₂×C₆₁	semidirect
219. C₆₁	#23800	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₄×#124×C₆₁	2
C₆₁×#2097	2
C₆₁×#2092	2
C₆₁×#2015	2
C₆₁×#2012	2
C₆₁×#1744	2
#23800	61

Subgroups — C61×#23800 #29527233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23800 #29527233