Subgroups — C₆₁×#61847 #29565280

Order 15616.

1772 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3389	C₂	1	4	yes	maximal, complemented
4	C₆₁×#3384	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3380	C₂	1	2	yes	maximal, complemented
6	C₆₁×#3366	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3366	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3358	C₂	1	2	yes	maximal, complemented
9	C₆₁×#3241	C₂	1	4	yes	maximal, complemented
10	C₆₁×#3235	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#3122	C₂	1	4	yes	maximal, complemented
13	C₆₁×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#3100	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₁×#562	—	2	2	no	—
17	C₆₁×#554	—	2	1	no	—
18	C₆₁×#554	—	2	2	no	—
19	C₆₁×#554	C₂²	1	2	yes	—
20	C₆₁×#554	C₂²	1	4	yes	—
21	C₆₁×#554	C₂²	1	2	yes	complemented
22	C₆₁×#554	C₂²	1	2	yes	complemented
23	C₆₁×#550	C₂²	1	2	yes	complemented
24	C₆₁×#550	C₂²	1	2	yes	complemented
25	D₄×Q₈×C₆₁	—	2	1	no	—
26	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#547	—	2	1	no	—
28	C₆₁×#547	—	2	1	no	—
29	C₆₁×#544	C₂²	1	2	yes	—
30	C₆₁×#543	—	2	2	no	—
31	C₆₁×#540	C₂²	1	4	yes	—
32	C₆₁×#537	—	2	2	no	—
33	C₆₁×#537	—	2	2	no	—
34	C₆₁×#533	C₂²	1	1	yes	characteristic
35	C₆₁×#533	C₂²	1	1	yes	characteristic
36	C₆₁×#532	C₂²	1	1	yes	characteristic
37	C₆₁×#532	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
39	C₆₁×#518	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#501	C₂²	1	4	yes	complemented
42	C₆₁×#501	C₂²	1	2	yes	complemented
43	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#499	C₂²	1	4	yes	complemented
45	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#490	C₂²	1	2	yes	complemented
47	C₆₁×#490	C₂²	1	4	yes	complemented
48	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
49	C₆₁×#486	C₂²	1	4	yes	complemented
50	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
51	C₆₁×#482	C₂²	1	4	yes	—
52	C₆₁×#482	C₂²	1	4	yes	—
53	C₆₁×#481	C₂²	1	2	yes	—
54	C₆₁×#480	C₂²	1	2	yes	—
55	C₆₁×#478	C₂²	1	4	yes	—
56	C₆₁×#478	C₂²	1	4	yes	—
57	C₆₁×#478	C₂²	1	4	yes	complemented
58	C₆₁×#478	C₂²	1	4	yes	complemented
59	C₆₁×#478	C₂²	1	4	yes	complemented
60	C₆₁×#476	C₂²	1	2	yes	—
61	C₆₁×#476	C₂²	1	2	yes	complemented
62	C₆₁×#476	C₂²	1	4	yes	complemented
63	C₆₁×#474	C₂²	1	2	yes	—
64	C₆₁×#474	C₂²	1	2	yes	complemented
65	C₆₁×#474	C₂²	1	4	yes	complemented
66	C₆₁×#459	C₂²	1	2	yes	—
67	C₆₁×#459	C₂²	1	2	yes	—
68	C₆₁×#459	C₂²	1	4	yes	—
69	C₆₁×#459	C₂²	1	4	yes	—
70	C₆₁×#447	C₂²	1	2	yes	—
71	C₆₁×#447	C₂²	1	2	yes	—
72	C₆₁×#446	C₂²	1	2	yes	complemented
73	C₆₁×#446	C₂²	1	4	yes	complemented
74	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
75	C₆₁×#442	C₂²	1	4	yes	—
76	C₆₁×#442	C₂²	1	4	yes	—
77	C₆₁×#442	C₂²	1	4	yes	—
78	C₄×D₈×C₆₁	C₂²	1	2	yes	—
79	C₄×D₈×C₆₁	C₂²	1	2	yes	—
80	C₄×D₈×C₆₁	C₂²	1	4	yes	—
81	C₄×D₈×C₆₁	C₂²	1	4	yes	—
82	C₆₁×#433	C₂²	1	4	yes	—
83	C₆₁×#432	C₂²	1	1	yes	characteristic
84	C₆₁×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₆₁	—	2	2	no	—
86	C₂×#41×C₆₁	—	2	2	no	—
87	C₂×#41×C₆₁	—	2	1	no	—
88	C₂×#41×C₆₁	—	2	1	no	—
89	C₂²×Q₈×C₆₁	—	2	2	no	—
90	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₁	—	2	1	no	—
92	C₂×D₈×C₆₁	C₂³	1	2	yes	—
93	C₂×D₈×C₆₁	C₂³	1	2	yes	—
94	C₂×D₈×C₆₁	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₆₁	—	2	2	no	—
96	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
97	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
103	#127×C₆₁	C₂³	1	1	yes	characteristic
104	#127×C₆₁	C₂³	1	1	yes	characteristic
105	#127×C₆₁	C₂³	1	4	yes	—
106	#125×C₆₁	—	2	2	no	—
107	#125×C₆₁	D₄	1	2	yes	—
108	#125×C₆₁	C₂³	1	2	yes	—
109	#125×C₆₁	C₂³	1	4	yes	—
110	#125×C₆₁	C₂³	1	4	yes	—
111	#124×C₆₁	—	2	1	no	—
112	#124×C₆₁	—	2	1	no	—
113	#123×C₆₁	—	2	4	no	—
114	#123×C₆₁	—	2	4	no	—
115	C₂²⋊Q₈×C₆₁	—	2	2	no	—
116	C₂²⋊Q₈×C₆₁	—	2	2	no	—
117	C₂²⋊Q₈×C₆₁	—	2	4	no	—
118	C₂²⋊Q₈×C₆₁	—	2	2	no	—
119	C₂²⋊Q₈×C₆₁	—	2	1	no	—
120	C₂²⋊Q₈×C₆₁	—	2	1	no	—
121	C₂²⋊Q₈×C₆₁	—	2	4	no	—
122	C₂²⋊Q₈×C₆₁	—	2	4	no	—
123	C₂²⋊Q₈×C₆₁	—	2	4	no	—
124	C₂²⋊Q₈×C₆₁	—	2	4	no	—
125	C₂²⋊Q₈×C₆₁	—	2	4	no	—
126	C₂²⋊Q₈×C₆₁	—	2	2	no	—
127	C₂²⋊Q₈×C₆₁	—	2	4	no	—
128	C₂²⋊Q₈×C₆₁	—	2	4	no	—
129	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
130	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
131	#121×C₆₁	—	2	1	no	—
132	#121×C₆₁	—	2	1	no	—
133	#121×C₆₁	—	2	2	no	—
134	#121×C₆₁	—	2	2	no	—
135	#121×C₆₁	—	2	4	no	—
136	#121×C₆₁	—	2	4	no	—
137	#121×C₆₁	—	2	4	no	—
138	#121×C₆₁	—	2	4	no	—
139	#121×C₆₁	C₂³	1	2	yes	—
140	#121×C₆₁	C₂³	1	2	yes	—
141	C₄×Q₈×C₆₁	—	2	1	no	—
142	C₄×Q₈×C₆₁	—	2	1	no	—
143	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
144	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
145	C₄×D₄×C₆₁	—	2	2	no	—
146	C₄×D₄×C₆₁	—	2	2	no	—
147	C₄×D₄×C₆₁	—	2	1	no	—
148	C₄×D₄×C₆₁	—	2	1	no	—
149	C₄×D₄×C₆₁	—	2	1	no	—
150	C₄×D₄×C₆₁	—	2	1	no	—
151	C₄×D₄×C₆₁	C₂³	1	2	yes	—
152	C₄×D₄×C₆₁	C₂³	1	2	yes	—
153	C₄×D₄×C₆₁	C₂³	1	4	yes	—
154	C₄×D₄×C₆₁	C₂³	1	4	yes	—
155	C₄×D₄×C₆₁	C₂³	1	2	yes	—
156	C₄×D₄×C₆₁	C₂³	1	4	yes	—
157	C₄×D₄×C₆₁	C₂³	1	4	yes	—
158	C₄×D₄×C₆₁	C₂³	1	2	yes	—
159	#117×C₆₁	C₂³	1	2	yes	—
160	#117×C₆₁	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
162	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
164	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
165	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
166	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
167	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
168	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
169	#107×C₆₁	C₂³	1	2	yes	—
170	#107×C₆₁	C₂³	1	2	yes	—
171	#107×C₆₁	C₂³	1	4	yes	—
172	#107×C₆₁	C₂³	1	4	yes	—
173	#106×C₆₁	C₂³	1	4	yes	—
174	#106×C₆₁	C₂³	1	4	yes	—
175	#106×C₆₁	C₂³	1	4	yes	—
176	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
177	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
178	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
179	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
180	#102×C₆₁	C₂³	1	2	yes	—
181	#102×C₆₁	C₂³	1	2	yes	—
182	#102×C₆₁	C₂³	1	4	yes	—
183	#102×C₆₁	C₂³	1	4	yes	—
184	#102×C₆₁	C₂³	1	2	yes	—
185	#102×C₆₁	C₂³	1	4	yes	—
186	#102×C₆₁	C₂³	1	2	yes	—
187	#102×C₆₁	C₂³	1	4	yes	—
188	#102×C₆₁	C₂³	1	4	yes	—
189	#102×C₆₁	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₆₁	C₂³	1	2	yes	—
192	#97×C₆₁	C₂³	1	2	yes	—
193	#97×C₆₁	C₂³	1	4	yes	—
194	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₆₁	C₂³	1	4	yes	—
197	C₂⁴×C₆₁	—	2	1	no	—
198	#41×C₆₁	—	8	2	no	—
199	#41×C₆₁	—	8	2	no	—
200	#41×C₆₁	—	8	4	no	—
201	#41×C₆₁	—	8	4	no	—
202	C₂×Q₈×C₆₁	—	2	1	no	—
203	C₂×Q₈×C₆₁	—	2	1	no	—
204	C₂×Q₈×C₆₁	—	2	1	no	—
205	C₂×Q₈×C₆₁	—	2	1	no	—
206	C₂×Q₈×C₆₁	—	2	4	no	—
207	C₂×Q₈×C₆₁	—	8	4	no	—
208	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
210	C₂×D₄×C₆₁	—	2	4	no	—
211	C₂×D₄×C₆₁	—	2	2	no	—
212	C₂×D₄×C₆₁	—	2	2	no	—
213	C₂×D₄×C₆₁	—	2	1	no	—
214	C₂×D₄×C₆₁	—	2	1	no	—
215	C₂×D₄×C₆₁	—	2	1	no	—
216	C₂×D₄×C₆₁	—	2	4	no	—
217	C₂×D₄×C₆₁	—	2	4	no	—
218	C₂×D₄×C₆₁	—	2	1	no	—
219	C₂×D₄×C₆₁	—	2	1	no	—
220	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
221	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
222	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₆₁	—	2	1	no	—
224	C₂²×C₄×C₆₁	—	2	2	no	—
225	C₂²×C₄×C₆₁	—	2	2	no	—
226	C₂²×C₄×C₆₁	—	2	2	no	—
227	C₂²×C₄×C₆₁	—	2	4	no	—
228	C₂²×C₄×C₆₁	—	2	4	no	—
229	C₂²×C₄×C₆₁	—	2	2	no	—
230	C₂²×C₄×C₆₁	—	2	4	no	—
231	C₂²×C₄×C₆₁	—	2	4	no	—
232	C₂²×C₄×C₆₁	—	8	2	no	—
233	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
236	D₈×C₆₁	—	2	4	no	—
237	D₈×C₆₁	—	2	4	no	—
238	D₈×C₆₁	—	2	8	no	—
239	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
240	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
241	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
242	C₄⋊C₄×C₆₁	—	2	1	no	—
243	C₄⋊C₄×C₆₁	—	2	1	no	—
244	C₄⋊C₄×C₆₁	—	2	2	no	—
245	C₄⋊C₄×C₆₁	—	2	1	no	—
246	C₄⋊C₄×C₆₁	—	2	4	no	—
247	C₄⋊C₄×C₆₁	—	2	4	no	—
248	C₄⋊C₄×C₆₁	—	2	4	no	—
249	C₄⋊C₄×C₆₁	—	2	4	no	—
250	C₄⋊C₄×C₆₁	—	2	4	no	—
251	C₄⋊C₄×C₆₁	—	2	1	no	—
252	C₄⋊C₄×C₆₁	—	2	2	no	—
253	C₄⋊C₄×C₆₁	—	2	1	no	—
254	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
255	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
256	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
257	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
265	C₂²⋊C₄×C₆₁	—	2	2	no	—
266	C₂²⋊C₄×C₆₁	—	2	4	no	—
267	C₂²⋊C₄×C₆₁	—	2	4	no	—
268	C₂²⋊C₄×C₆₁	—	2	2	no	—
269	C₂²⋊C₄×C₆₁	—	2	2	no	—
270	C₂²⋊C₄×C₆₁	—	2	2	no	—
271	C₂²⋊C₄×C₆₁	—	2	2	no	—
272	C₂²⋊C₄×C₆₁	—	2	4	no	—
273	C₂²⋊C₄×C₆₁	—	2	4	no	—
274	C₂²⋊C₄×C₆₁	—	2	2	no	—
275	C₂²⋊C₄×C₆₁	—	2	2	no	—
276	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
277	C₄²×C₆₁	—	2	2	no	—
278	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
281	C₄²×C₆₁	C₂⁴	1	4	yes	—
282	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
283	C₂³×C₆₁	—	2	4	no	—
284	C₂³×C₆₁	—	2	2	no	—
285	C₂³×C₆₁	—	2	2	no	—
286	C₂³×C₆₁	—	2	2	no	—
287	C₂³×C₆₁	—	8	1	no	—
288	C₂³×C₆₁	—	8	1	no	—
289	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₆₁	—	2	4	no	—
291	Q₈×C₆₁	—	4	2	no	—
292	Q₈×C₆₁	—	4	2	no	—
293	Q₈×C₆₁	—	8	1	no	—
294	Q₈×C₆₁	—	8	4	no	—
295	Q₈×C₆₁	—	8	1	no	—
296	Q₈×C₆₁	—	8	1	no	—
297	D₄×C₆₁	—	2	4	no	—
298	D₄×C₆₁	—	2	2	no	—
299	D₄×C₆₁	—	2	2	no	—
300	D₄×C₆₁	—	2	4	no	—
301	D₄×C₆₁	—	2	2	no	—
302	D₄×C₆₁	—	4	2	no	—
303	D₄×C₆₁	—	4	2	no	—
304	D₄×C₆₁	—	8	1	no	—
305	D₄×C₆₁	—	8	4	no	—
306	D₄×C₆₁	—	8	1	no	—
307	D₄×C₆₁	—	8	4	no	—
308	D₄×C₆₁	—	8	2	no	—
309	D₄×C₆₁	—	8	2	no	—
310	D₄×C₆₁	2₋¹⁺⁴	1	4	yes	—
311	C₂×C₄×C₆₁	—	2	2	no	—
312	C₂×C₄×C₆₁	—	2	2	no	—
313	C₂×C₄×C₆₁	—	2	2	no	—
314	C₂×C₄×C₆₁	—	2	2	no	—
315	C₂×C₄×C₆₁	—	2	2	no	—
316	C₂×C₄×C₆₁	—	2	2	no	—
317	C₂×C₄×C₆₁	—	2	2	no	—
318	C₂×C₄×C₆₁	—	4	1	no	—
319	C₂×C₄×C₆₁	—	4	4	no	—
320	C₂×C₄×C₆₁	—	4	4	no	—
321	C₂×C₄×C₆₁	—	4	4	no	—
322	C₂×C₄×C₆₁	—	8	4	no	—
323	C₂×C₄×C₆₁	—	8	2	no	—
324	C₂×C₄×C₆₁	—	8	4	no	—
325	C₂×C₄×C₆₁	—	8	4	no	—
326	C₂×C₄×C₆₁	—	8	4	no	—
327	C₂×C₄×C₆₁	—	8	1	no	—
328	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
334	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
336	C₈×C₆₁	—	2	2	no	—
337	C₈×C₆₁	—	2	2	no	—
338	C₈×C₆₁	—	2	4	no	—
339	#61847	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
340	C₂²×C₆₁	—	2	1	no	—
341	C₂²×C₆₁	—	2	1	no	—
342	C₂²×C₆₁	—	2	4	no	—
343	C₂²×C₆₁	—	2	1	no	—
344	C₂²×C₆₁	—	4	2	no	—
345	C₂²×C₆₁	—	4	2	no	—
346	C₂²×C₆₁	—	4	2	no	—
347	C₂²×C₆₁	—	4	2	no	—
348	C₂²×C₆₁	—	4	2	no	—
349	C₂²×C₆₁	—	4	2	no	—
350	C₂²×C₆₁	—	4	2	no	—
351	C₂²×C₆₁	—	4	2	no	—
352	C₂²×C₆₁	—	8	4	no	—
353	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
354	C₄×C₆₁	—	2	1	no	—
355	C₄×C₆₁	—	2	1	no	—
356	C₄×C₆₁	—	2	4	no	—
357	C₄×C₆₁	—	2	1	no	—
358	C₄×C₆₁	—	2	1	no	—
359	C₄×C₆₁	—	2	4	no	—
360	C₄×C₆₁	—	4	2	no	—
361	C₄×C₆₁	—	4	2	no	—
362	C₄×C₆₁	—	4	2	no	—
363	C₄×C₆₁	—	4	2	no	—
364	C₄×C₆₁	—	4	2	no	—
365	C₄×C₆₁	#576	1	2	yes	—
366	C₄×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
367	#3548	C₂×C₆₁	1	1	yes	characteristic, complemented
368	#3501	C₂×C₆₁	1	1	yes	characteristic, complemented
369	#3389	C₂×C₆₁	1	4	yes	complemented
370	#3384	C₂×C₆₁	1	2	yes	complemented
371	#3380	C₂×C₆₁	1	2	yes	complemented
372	#3366	C₂×C₆₁	1	2	yes	complemented
373	#3366	C₂×C₆₁	1	4	yes	complemented
374	#3358	C₂×C₆₁	1	2	yes	complemented
375	#3241	C₂×C₆₁	1	4	yes	complemented
376	#3235	C₂×C₆₁	1	1	yes	characteristic, complemented
377	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
378	#3122	C₂×C₆₁	1	4	yes	complemented
379	#3109	C₂×C₆₁	1	1	yes	characteristic, complemented
380	#3100	C₂×C₆₁	1	1	yes	characteristic, complemented
381	#2985	C₂×C₆₁	1	1	yes	characteristic, complemented
382	C₂×C₆₁	—	4	1	no	—
383	C₂×C₆₁	—	4	4	no	—
384	C₂×C₆₁	—	8	2	no	—
385	C₂×C₆₁	—	8	2	no	—
386	C₂×C₆₁	#3486	1	1	yes	characteristic
387	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
388	C₂×C₆₁	#3585	1	1	yes	characteristic
389	#562	—	2	2	no	—
390	#554	—	2	1	no	—
391	#554	—	2	2	no	—
392	#554	C₂²×C₆₁	1	2	yes	—
393	#554	C₂²×C₆₁	1	4	yes	—
394	#554	C₂²×C₆₁	1	2	yes	complemented
395	#554	C₂²×C₆₁	1	2	yes	complemented
396	#550	C₂²×C₆₁	1	2	yes	complemented
397	#550	C₂²×C₆₁	1	2	yes	complemented
398	D₄×Q₈	—	2	1	no	—
399	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
400	#547	—	2	1	no	—
401	#547	—	2	1	no	—
402	#544	C₂²×C₆₁	1	2	yes	—
403	#543	—	2	2	no	—
404	#540	C₂²×C₆₁	1	4	yes	—
405	#537	—	2	2	no	—
406	#537	—	2	2	no	—
407	#533	C₂²×C₆₁	1	1	yes	characteristic
408	#533	C₂²×C₆₁	1	1	yes	characteristic
409	#532	C₂²×C₆₁	1	1	yes	characteristic
410	#532	C₂²×C₆₁	1	1	yes	characteristic
411	C₂×C₂²⋊Q₈	—	2	2	no	—
412	#518	C₂²×C₆₁	1	2	yes	—
413	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
414	#501	C₂²×C₆₁	1	4	yes	complemented
415	#501	C₂²×C₆₁	1	2	yes	complemented
416	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
417	#499	C₂²×C₆₁	1	4	yes	complemented
418	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
419	#490	C₂²×C₆₁	1	2	yes	complemented
420	#490	C₂²×C₆₁	1	4	yes	complemented
421	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
422	#486	C₂²×C₆₁	1	4	yes	complemented
423	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
424	#482	C₂²×C₆₁	1	4	yes	—
425	#482	C₂²×C₆₁	1	4	yes	—
426	#481	C₂²×C₆₁	1	2	yes	—
427	#480	C₂²×C₆₁	1	2	yes	—
428	#478	C₂²×C₆₁	1	4	yes	—
429	#478	C₂²×C₆₁	1	4	yes	—
430	#478	C₂²×C₆₁	1	4	yes	complemented
431	#478	C₂²×C₆₁	1	4	yes	complemented
432	#478	C₂²×C₆₁	1	4	yes	complemented
433	#476	C₂²×C₆₁	1	2	yes	—
434	#476	C₂²×C₆₁	1	2	yes	complemented
435	#476	C₂²×C₆₁	1	4	yes	complemented
436	#474	C₂²×C₆₁	1	2	yes	—
437	#474	C₂²×C₆₁	1	2	yes	complemented
438	#474	C₂²×C₆₁	1	4	yes	complemented
439	#459	C₂²×C₆₁	1	2	yes	—
440	#459	C₂²×C₆₁	1	2	yes	—
441	#459	C₂²×C₆₁	1	4	yes	—
442	#459	C₂²×C₆₁	1	4	yes	—
443	#447	C₂²×C₆₁	1	2	yes	—
444	#447	C₂²×C₆₁	1	2	yes	—
445	#446	C₂²×C₆₁	1	2	yes	complemented
446	#446	C₂²×C₆₁	1	4	yes	complemented
447	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
448	#442	C₂²×C₆₁	1	4	yes	—
449	#442	C₂²×C₆₁	1	4	yes	—
450	#442	C₂²×C₆₁	1	4	yes	—
451	C₄×D₈	C₂²×C₆₁	1	2	yes	—
452	C₄×D₈	C₂²×C₆₁	1	2	yes	—
453	C₄×D₈	C₂²×C₆₁	1	4	yes	—
454	C₄×D₈	C₂²×C₆₁	1	4	yes	—
455	#433	C₂²×C₆₁	1	4	yes	—
456	#432	C₂²×C₆₁	1	1	yes	characteristic
457	#431	C₂²×C₆₁	1	1	yes	characteristic
458	C₆₁	#61847	1	1	yes	characteristic, direct product factor, Sylow
459	C₂×#41	—	2	2	no	—
460	C₂×#41	—	2	2	no	—
461	C₂×#41	—	2	1	no	—
462	C₂×#41	—	2	1	no	—
463	C₂²×Q₈	—	2	2	no	—
464	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
465	C₂³×C₄	—	2	1	no	—
466	C₂×D₈	C₂³×C₆₁	1	2	yes	—
467	C₂×D₈	C₂³×C₆₁	1	2	yes	—
468	C₂×D₈	C₂³×C₆₁	1	4	yes	—
469	C₄⋊Q₈	—	2	2	no	—
470	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
471	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
472	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
473	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
474	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
475	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
477	#127	C₂³×C₆₁	1	1	yes	characteristic
478	#127	C₂³×C₆₁	1	1	yes	characteristic
479	#127	C₂³×C₆₁	1	4	yes	—
480	#125	—	2	2	no	—
481	#125	D₄×C₆₁	1	2	yes	—
482	#125	C₂³×C₆₁	1	2	yes	—
483	#125	C₂³×C₆₁	1	4	yes	—
484	#125	C₂³×C₆₁	1	4	yes	—
485	#124	—	2	1	no	—
486	#124	—	2	1	no	—
487	#123	—	2	4	no	—
488	#123	—	2	4	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	—	2	1	no	—
494	C₂²⋊Q₈	—	2	1	no	—
495	C₂²⋊Q₈	—	2	2	no	—
496	C₂²⋊Q₈	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	4	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	—	2	4	no	—
501	C₂²⋊Q₈	—	2	4	no	—
502	C₂²⋊Q₈	—	2	4	no	—
503	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
504	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
505	#121	—	2	1	no	—
506	#121	—	2	1	no	—
507	#121	—	2	2	no	—
508	#121	—	2	2	no	—
509	#121	—	2	4	no	—
510	#121	—	2	4	no	—
511	#121	—	2	4	no	—
512	#121	—	2	4	no	—
513	#121	C₂³×C₆₁	1	2	yes	—
514	#121	C₂³×C₆₁	1	2	yes	—
515	C₄×Q₈	—	2	1	no	—
516	C₄×Q₈	—	2	1	no	—
517	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
518	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	C₄×D₄	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	2	1	no	—
525	C₄×D₄	C₂³×C₆₁	1	2	yes	—
526	C₄×D₄	C₂³×C₆₁	1	2	yes	—
527	C₄×D₄	C₂³×C₆₁	1	4	yes	—
528	C₄×D₄	C₂³×C₆₁	1	4	yes	—
529	C₄×D₄	C₂³×C₆₁	1	2	yes	—
530	C₄×D₄	C₂³×C₆₁	1	2	yes	—
531	C₄×D₄	C₂³×C₆₁	1	4	yes	—
532	C₄×D₄	C₂³×C₆₁	1	4	yes	—
533	#117	C₂³×C₆₁	1	2	yes	—
534	#117	C₂³×C₆₁	1	2	yes	—
535	C₂×C₄⋊C₄	—	2	4	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	—	2	2	no	—
539	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
540	C₂×C₂²⋊C₄	—	2	1	no	—
541	C₂×C₂²⋊C₄	—	2	4	no	—
542	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
543	#107	C₂³×C₆₁	1	2	yes	—
544	#107	C₂³×C₆₁	1	2	yes	—
545	#107	C₂³×C₆₁	1	4	yes	—
546	#107	C₂³×C₆₁	1	4	yes	—
547	#106	C₂³×C₆₁	1	4	yes	—
548	#106	C₂³×C₆₁	1	4	yes	—
549	#106	C₂³×C₆₁	1	4	yes	—
550	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
551	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
552	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
553	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
554	#102	C₂³×C₆₁	1	2	yes	—
555	#102	C₂³×C₆₁	1	2	yes	—
556	#102	C₂³×C₆₁	1	4	yes	—
557	#102	C₂³×C₆₁	1	4	yes	—
558	#102	C₂³×C₆₁	1	2	yes	—
559	#102	C₂³×C₆₁	1	4	yes	—
560	#102	C₂³×C₆₁	1	2	yes	—
561	#102	C₂³×C₆₁	1	4	yes	—
562	#102	C₂³×C₆₁	1	4	yes	—
563	#102	C₂³×C₆₁	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₆₁	1	2	yes	—
566	#97	C₂³×C₆₁	1	2	yes	—
567	#97	C₂³×C₆₁	1	4	yes	—
568	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₆₁	1	4	yes	—
571	C₂⁴	—	2	1	no	—
572	#41	—	8	2	no	—
573	#41	—	8	2	no	—
574	#41	—	8	4	no	—
575	#41	—	8	4	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	1	no	—
579	C₂×Q₈	—	2	1	no	—
580	C₂×Q₈	—	2	4	no	—
581	C₂×Q₈	—	8	4	no	—
582	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
583	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	2	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	1	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	1	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
595	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
596	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
597	C₂²×C₄	—	2	1	no	—
598	C₂²×C₄	—	2	2	no	—
599	C₂²×C₄	—	2	2	no	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	4	no	—
602	C₂²×C₄	—	2	4	no	—
603	C₂²×C₄	—	2	2	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	8	2	no	—
607	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
610	D₈	—	2	4	no	—
611	D₈	—	2	4	no	—
612	D₈	—	2	8	no	—
613	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
614	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
615	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	4	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	2	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
629	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
630	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
631	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
632	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
633	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
634	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
638	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
651	C₄²	—	2	2	no	—
652	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
653	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
654	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
655	C₄²	C₂⁴×C₆₁	1	4	yes	—
656	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
657	C₂³	—	2	4	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	8	1	no	—
662	C₂³	—	8	1	no	—
663	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
664	Q₈	—	2	4	no	—
665	Q₈	—	4	2	no	—
666	Q₈	—	4	2	no	—
667	Q₈	—	8	1	no	—
668	Q₈	—	8	4	no	—
669	Q₈	—	8	1	no	—
670	Q₈	—	8	1	no	—
671	D₄	—	2	4	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	2	4	no	—
675	D₄	—	2	2	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	2	no	—
678	D₄	—	8	1	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	1	no	—
681	D₄	—	8	4	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	D₄	2₋¹⁺⁴×C₆₁	1	4	yes	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	4	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	8	4	no	—
697	C₂×C₄	—	8	2	no	—
698	C₂×C₄	—	8	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	—	8	4	no	—
701	C₂×C₄	—	8	1	no	—
702	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
707	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
708	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
709	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
710	C₈	—	2	2	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	4	no	—
713	C₂²	—	2	1	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	4	no	—
717	C₂²	—	4	2	no	—
718	C₂²	—	4	2	no	—
719	C₂²	—	4	2	no	—
720	C₂²	—	4	2	no	—
721	C₂²	—	4	2	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	8	4	no	—
726	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
727	C₄	—	2	1	no	—
728	C₄	—	2	4	no	—
729	C₄	—	2	1	no	—
730	C₄	—	2	1	no	—
731	C₄	—	2	4	no	—
732	C₄	—	2	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	2	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	C₆₁×#576	1	2	yes	—
739	C₄	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
740	C₂	—	4	1	no	—
741	C₂	—	4	4	no	—
742	C₂	—	8	2	no	—
743	C₂	—	8	2	no	—
744	C₂	C₆₁×#3486	1	1	yes	characteristic
745	C₂	C₂×C₆₁×#576	1	1	yes	characteristic
746	C₂	C₆₁×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3548	C₂	semidirect
2. C₆₁×#3501	C₂	semidirect
3. C₆₁×#3389	C₂	semidirect
4. C₆₁×#3384	C₂	semidirect
5. C₆₁×#3380	C₂	semidirect
6. C₆₁×#3366	C₂	semidirect
7. C₆₁×#3366	C₂	semidirect
8. C₆₁×#3358	C₂	semidirect
9. C₆₁×#3241	C₂	semidirect
10. C₆₁×#3235	C₂	semidirect
11. C₆₁×#3228	C₂	semidirect
12. C₆₁×#3122	C₂	semidirect
13. C₆₁×#3109	C₂	semidirect
14. C₆₁×#3100	C₂	semidirect
15. C₆₁×#2985	C₂	semidirect
21. C₆₁×#554	C₂²	semidirect
22. C₆₁×#554	C₂²	semidirect
23. C₆₁×#550	C₂²	semidirect
24. C₆₁×#550	C₂²	semidirect
41. C₆₁×#501	C₂²	semidirect
42. C₆₁×#501	C₂²	semidirect
43. C₆₁×#500	C₂²	semidirect
44. C₆₁×#499	C₂²	semidirect
45. C₆₁×#498	C₂²	semidirect
46. C₆₁×#490	C₂²	semidirect
47. C₆₁×#490	C₂²	semidirect
48. C₆₁×#486	C₂²	semidirect
49. C₆₁×#486	C₂²	semidirect
50. C₆₁×#486	C₂²	semidirect
57. C₆₁×#478	C₂²	semidirect
58. C₆₁×#478	C₂²	semidirect
59. C₆₁×#478	C₂²	semidirect
61. C₆₁×#476	C₂²	semidirect
62. C₆₁×#476	C₂²	semidirect
64. C₆₁×#474	C₂²	semidirect
65. C₆₁×#474	C₂²	semidirect
72. C₆₁×#446	C₂²	semidirect
73. C₆₁×#446	C₂²	semidirect
74. C₈×Q₈×C₆₁	C₂²	semidirect
339. #61847	C₆₁	direct (N × H)
367. #3548	C₂×C₆₁	semidirect
368. #3501	C₂×C₆₁	semidirect
369. #3389	C₂×C₆₁	semidirect
370. #3384	C₂×C₆₁	semidirect
371. #3380	C₂×C₆₁	semidirect
372. #3366	C₂×C₆₁	semidirect
373. #3366	C₂×C₆₁	semidirect
374. #3358	C₂×C₆₁	semidirect
375. #3241	C₂×C₆₁	semidirect
376. #3235	C₂×C₆₁	semidirect
377. #3228	C₂×C₆₁	semidirect
378. #3122	C₂×C₆₁	semidirect
379. #3109	C₂×C₆₁	semidirect
380. #3100	C₂×C₆₁	semidirect
381. #2985	C₂×C₆₁	semidirect
394. #554	C₂²×C₆₁	semidirect
395. #554	C₂²×C₆₁	semidirect
396. #550	C₂²×C₆₁	semidirect
397. #550	C₂²×C₆₁	semidirect
414. #501	C₂²×C₆₁	semidirect
415. #501	C₂²×C₆₁	semidirect
416. #500	C₂²×C₆₁	semidirect
417. #499	C₂²×C₆₁	semidirect
418. #498	C₂²×C₆₁	semidirect
419. #490	C₂²×C₆₁	semidirect
420. #490	C₂²×C₆₁	semidirect
421. #486	C₂²×C₆₁	semidirect
422. #486	C₂²×C₆₁	semidirect
423. #486	C₂²×C₆₁	semidirect
430. #478	C₂²×C₆₁	semidirect
431. #478	C₂²×C₆₁	semidirect
432. #478	C₂²×C₆₁	semidirect
434. #476	C₂²×C₆₁	semidirect
435. #476	C₂²×C₆₁	semidirect
437. #474	C₂²×C₆₁	semidirect
438. #474	C₂²×C₆₁	semidirect
445. #446	C₂²×C₆₁	semidirect
446. #446	C₂²×C₆₁	semidirect
447. C₈×Q₈	C₂²×C₆₁	semidirect
458. C₆₁	#61847	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×#3548	2
C₆₁×#3501	2
C₆₁×#3389	2
C₆₁×#3384	2
C₆₁×#3380	2
C₆₁×#3366	2
C₆₁×#3358	2
C₆₁×#3241	2
C₆₁×#3235	2
C₆₁×#3228	2
C₆₁×#3122	2
C₆₁×#3109	2
C₆₁×#3100	2
C₆₁×#2985	2
#61847	61

Subgroups — C61×#61847 #29565280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61847 #29565280