Subgroups — C₆₁×#20012 #29523445

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3396	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3361	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1678	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1667	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1630	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1622	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#559	C₂²	1	2	yes	—
13	C₆₁×#554	C₂²	1	2	yes	—
14	C₆₁×#500	C₂²	1	1	yes	characteristic
15	C₆₁×#495	—	2	1	no	—
16	C₆₁×#493	C₂²	1	1	yes	characteristic
17	C₆₁×#492	C₂²	1	2	yes	—
18	C₆₁×#488	—	2	2	no	—
19	C₆₁×#486	C₂²	1	2	yes	—
20	C₆₁×#484	—	2	2	no	—
21	C₆₁×#478	—	2	2	no	—
22	C₆₁×#477	C₂²	1	2	yes	—
23	C₆₁×#477	C₂²	1	2	yes	—
24	C₆₁×#467	—	2	1	no	—
25	C₆₁×#463	—	2	2	no	—
26	C₆₁×#463	—	2	2	no	—
27	C₆₁×#460	C₂²	1	2	yes	—
28	C₆₁×#459	C₂²	1	2	yes	—
29	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
30	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₆₁	—	2	1	no	—
34	C₄×D₈×C₆₁	—	2	2	no	—
35	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#107×C₆₁	—	2	1	no	—
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#334	C₂²	1	1	yes	characteristic
39	C₆₁×#333	C₂²	1	2	yes	—
40	C₆₁×#331	C₂²	1	2	yes	—
41	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₆₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
46	C₂×SD₁₆×C₆₁	—	2	2	no	—
47	C₂×SD₁₆×C₆₁	—	4	2	no	—
48	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic
49	C₂×D₈×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	—	2	1	no	—
51	C₂×D₈×C₆₁	—	2	1	no	—
52	C₂²×C₈×C₆₁	—	2	1	no	—
53	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
54	#127×C₆₁	C₂³	1	2	yes	—
55	#125×C₆₁	—	2	2	no	—
56	#124×C₆₁	—	2	2	no	—
57	#124×C₆₁	—	2	2	no	—
58	#123×C₆₁	—	4	2	no	—
59	C₂²⋊Q₈×C₆₁	—	2	2	no	—
60	C₂²⋊Q₈×C₆₁	—	4	2	no	—
61	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
62	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	—	2	2	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	#107×C₆₁	—	2	1	no	—
69	#107×C₆₁	—	2	1	no	—
70	#107×C₆₁	—	2	2	no	—
71	#107×C₆₁	—	2	2	no	—
72	#107×C₆₁	D₄	1	1	yes	characteristic
73	#106×C₆₁	D₄	1	1	yes	characteristic
74	C₄⋊C₈×C₆₁	—	2	1	no	—
75	C₄⋊C₈×C₆₁	—	2	2	no	—
76	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
79	#103×C₆₁	—	2	2	no	—
80	#103×C₆₁	—	2	2	no	—
81	#103×C₆₁	D₄	1	1	yes	characteristic
82	#103×C₆₁	D₄	1	2	yes	—
83	#102×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	2	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₆₁	—	2	1	no	—
89	C₄×C₈×C₆₁	—	2	2	no	—
90	C₄×C₈×C₆₁	—	2	1	no	—
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	2	no	—
95	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	4	2	no	—
103	C₂²×C₄×C₆₁	—	4	2	no	—
104	Q₁₆×C₆₁	—	2	2	no	—
105	SD₁₆×C₆₁	—	2	2	no	—
106	SD₁₆×C₆₁	—	8	4	no	—
107	SD₁₆×C₆₁	—	8	2	no	—
108	D₈×C₆₁	—	4	4	no	—
109	D₈×C₆₁	—	4	2	no	—
110	D₈×C₆₁	—	8	1	no	—
111	C₂×C₈×C₆₁	—	2	1	no	—
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	4	2	no	—
116	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	1	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	4	2	no	—
125	C₄⋊C₄×C₆₁	—	4	2	no	—
126	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₆₁	—	2	1	no	—
130	C₂²⋊C₄×C₆₁	—	4	2	no	—
131	C₂²⋊C₄×C₆₁	—	4	2	no	—
132	C₂²⋊C₄×C₆₁	—	4	2	no	—
133	C₂²⋊C₄×C₆₁	—	4	2	no	—
134	C₄²×C₆₁	—	2	1	no	—
135	C₄²×C₆₁	—	2	2	no	—
136	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
137	C₂³×C₆₁	—	2	1	no	—
138	C₂³×C₆₁	—	4	2	no	—
139	Q₈×C₆₁	—	2	1	no	—
140	Q₈×C₆₁	—	2	2	no	—
141	Q₈×C₆₁	—	2	2	no	—
142	Q₈×C₆₁	—	2	1	no	—
143	Q₈×C₆₁	—	8	2	no	—
144	D₄×C₆₁	—	2	1	no	—
145	D₄×C₆₁	—	4	2	no	—
146	D₄×C₆₁	—	4	2	no	—
147	D₄×C₆₁	—	4	2	no	—
148	D₄×C₆₁	—	4	2	no	—
149	D₄×C₆₁	—	8	2	no	—
150	D₄×C₆₁	#135	1	2	yes	—
151	C₂×C₄×C₆₁	—	2	1	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	1	no	—
154	C₂×C₄×C₆₁	—	2	2	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	4	1	no	—
157	C₂×C₄×C₆₁	—	4	1	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	16	2	no	—
160	C₂×C₄×C₆₁	—	16	2	no	—
161	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₆₁	—	2	2	no	—
165	C₈×C₆₁	—	2	1	no	—
166	C₈×C₆₁	—	2	1	no	—
167	C₈×C₆₁	—	2	1	no	—
168	C₈×C₆₁	—	4	1	no	—
169	C₈×C₆₁	—	4	2	no	—
170	C₈×C₆₁	—	4	1	no	—
171	C₈×C₆₁	#135	1	2	yes	—
172	#20012	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₆₁	—	2	2	no	—
174	C₂²×C₆₁	—	4	1	no	—
175	C₂²×C₆₁	—	4	1	no	—
176	C₂²×C₆₁	—	8	2	no	—
177	C₂²×C₆₁	—	8	2	no	—
178	C₂²×C₆₁	—	8	2	no	—
179	C₂²×C₆₁	D₄²	1	1	yes	characteristic
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	4	1	no	—
182	C₄×C₆₁	—	4	2	no	—
183	C₄×C₆₁	—	4	1	no	—
184	C₄×C₆₁	—	4	1	no	—
185	C₄×C₆₁	—	4	2	no	—
186	C₄×C₆₁	—	8	2	no	—
187	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
188	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
189	C₄×C₆₁	#577	1	1	yes	characteristic
190	C₄×C₆₁	#578	1	1	yes	characteristic
191	#3396	C₂×C₆₁	1	1	yes	characteristic, complemented
192	#3361	C₂×C₆₁	1	2	yes	complemented
193	#3338	C₂×C₆₁	1	1	yes	characteristic, complemented
194	#1706	C₂×C₆₁	1	1	yes	characteristic, complemented
195	#1678	C₂×C₆₁	1	2	yes	complemented
196	#1676	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#1667	C₂×C₆₁	1	1	yes	characteristic
198	#1630	C₂×C₆₁	1	2	yes	complemented
199	#1622	C₂×C₆₁	1	2	yes	complemented
200	C₈×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
201	C₈×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
202	C₂×C₆₁	—	4	2	no	—
203	C₂×C₆₁	—	16	2	no	—
204	C₂×C₆₁	#3284	1	1	yes	characteristic
205	C₂×C₆₁	#3285	1	1	yes	characteristic
206	C₂×C₆₁	#3292	1	1	yes	characteristic
207	#559	C₂²×C₆₁	1	2	yes	—
208	#554	C₂²×C₆₁	1	2	yes	—
209	#500	C₂²×C₆₁	1	1	yes	characteristic
210	#495	—	2	1	no	—
211	#493	C₂²×C₆₁	1	1	yes	characteristic
212	#492	C₂²×C₆₁	1	2	yes	—
213	#488	—	2	2	no	—
214	#486	C₂²×C₆₁	1	2	yes	—
215	#484	—	2	2	no	—
216	#478	—	2	2	no	—
217	#477	C₂²×C₆₁	1	2	yes	—
218	#477	C₂²×C₆₁	1	2	yes	—
219	#467	—	2	1	no	—
220	#463	—	2	2	no	—
221	#463	—	2	2	no	—
222	#460	C₂²×C₆₁	1	2	yes	—
223	#459	C₂²×C₆₁	1	2	yes	—
224	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
225	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
226	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
227	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
228	C₄×D₈	—	2	1	no	—
229	C₄×D₈	—	2	2	no	—
230	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
231	C₂×#107	—	2	1	no	—
232	#335	C₂²×C₆₁	1	1	yes	characteristic
233	#334	C₂²×C₆₁	1	1	yes	characteristic
234	#333	C₂²×C₆₁	1	2	yes	—
235	#331	C₂²×C₆₁	1	2	yes	—
236	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
237	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
238	D₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
239	C₈²	C₂²×C₆₁	1	1	yes	characteristic
240	C₆₁	#20012	1	1	yes	characteristic, direct product factor, Sylow
241	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	2	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic
245	C₂×D₈	—	2	2	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
250	#127	C₂³×C₆₁	1	2	yes	—
251	#125	—	2	2	no	—
252	#124	—	2	2	no	—
253	#124	—	2	2	no	—
254	#123	—	4	2	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	4	2	no	—
257	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
258	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
259	C₄×D₄	—	2	2	no	—
260	C₄×D₄	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	2	2	no	—
264	#107	—	2	1	no	—
265	#107	—	2	1	no	—
266	#107	—	2	2	no	—
267	#107	—	2	2	no	—
268	#107	D₄×C₆₁	1	1	yes	characteristic
269	#106	D₄×C₆₁	1	1	yes	characteristic
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
274	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#103	D₄×C₆₁	1	1	yes	characteristic
278	#103	D₄×C₆₁	1	2	yes	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	#102	—	2	2	no	—
283	#102	D₄×C₆₁	1	1	yes	characteristic
284	C₂²⋊C₈	—	2	1	no	—
285	C₄×C₈	—	2	2	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
292	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	4	2	no	—
300	Q₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	8	4	no	—
303	SD₁₆	—	8	2	no	—
304	D₈	—	4	4	no	—
305	D₈	—	4	2	no	—
306	D₈	—	8	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
313	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
314	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
323	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
324	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
325	C₂²⋊C₄	—	2	1	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	2	no	—
332	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
333	C₂³	—	2	1	no	—
334	C₂³	—	4	2	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	2	1	no	—
339	Q₈	—	8	2	no	—
340	D₄	—	2	1	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	8	2	no	—
346	D₄	#135×C₆₁	1	2	yes	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	16	2	no	—
356	C₂×C₄	—	16	2	no	—
357	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
359	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	1	no	—
367	C₈	#135×C₆₁	1	2	yes	—
368	C₂²	—	2	2	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	D₄²×C₆₁	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	1	no	—
381	C₄	—	8	2	no	—
382	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
383	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
384	C₄	C₆₁×#577	1	1	yes	characteristic
385	C₄	C₆₁×#578	1	1	yes	characteristic
386	C₂	—	4	2	no	—
387	C₂	—	16	2	no	—
388	C₂	C₆₁×#3284	1	1	yes	characteristic
389	C₂	C₆₁×#3285	1	1	yes	characteristic
390	C₂	C₆₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#1667	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3396	C₂	semidirect
2. C₆₁×#3361	C₂	semidirect
3. C₆₁×#3338	C₂	semidirect
4. C₆₁×#1706	C₂	semidirect
5. C₆₁×#1678	C₂	semidirect
6. C₆₁×#1676	C₂	semidirect
8. C₆₁×#1630	C₂	semidirect
9. C₆₁×#1622	C₂	semidirect
10. C₈×Q₁₆×C₆₁	C₂	semidirect
11. C₈×SD₁₆×C₆₁	C₂	semidirect
172. #20012	C₆₁	direct (N × H)
191. #3396	C₂×C₆₁	semidirect
192. #3361	C₂×C₆₁	semidirect
193. #3338	C₂×C₆₁	semidirect
194. #1706	C₂×C₆₁	semidirect
195. #1678	C₂×C₆₁	semidirect
196. #1676	C₂×C₆₁	semidirect
198. #1630	C₂×C₆₁	semidirect
199. #1622	C₂×C₆₁	semidirect
200. C₈×Q₁₆	C₂×C₆₁	semidirect
201. C₈×SD₁₆	C₂×C₆₁	semidirect
240. C₆₁	#20012	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×#3396	2
C₆₁×#3361	2
C₆₁×#3338	2
C₆₁×#1706	2
C₆₁×#1678	2
C₆₁×#1676	2
C₆₁×#1667	2
C₆₁×#1630	2
C₆₁×#1622	2
C₈×Q₁₆×C₆₁	2
C₈×SD₁₆×C₆₁	2
#20012	61

Subgroups — C61×#20012 #29523445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20012 #29523445