Subgroups — C₆₁×#33436 #29536869

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2929	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2169	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2168	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2168	C₂	1	2	yes	maximal, complemented
7	D₄×C₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2151	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#525	C₄	1	1	yes	characteristic
15	C₆₁×#504	—	2	4	no	—
16	C₂×M₃₂×C₆₁	—	2	4	no	—
17	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×M₃₂×C₆₁	C₂²	1	2	yes	—
19	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×M₃₂×C₆₁	C₂²	1	2	yes	complemented
21	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₁₆×C₆₁	C₂²	1	2	yes	—
24	C₂²×C₁₆×C₆₁	C₂²	1	2	yes	complemented
25	C₆₁×#435	C₄	1	2	yes	—
26	C₆₁×#435	C₄	1	2	yes	—
27	C₈×D₄×C₆₁	C₂²	1	2	yes	—
28	C₈×D₄×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#424	C₄	1	1	yes	characteristic
30	C₆₁×#408	C₄	1	1	yes	characteristic
31	C₆₁×#407	C₄	1	1	yes	characteristic
32	C₆₁×#405	C₂²	1	1	yes	characteristic
33	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	complemented
34	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	complemented
35	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₆₁×#346	C₂²	1	2	yes	complemented
42	C₄×C₁₆×C₆₁	C₂²	1	2	yes	complemented
43	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
45	#131×C₆₁	—	2	2	no	—
46	#131×C₆₁	—	2	2	no	—
47	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
49	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	—	2	2	no	—
51	C₂²×C₈×C₆₁	—	2	2	no	—
52	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	#123×C₆₁	C₈	1	2	yes	—
60	C₂²⋊Q₈×C₆₁	C₈	1	1	yes	characteristic
61	C₂²⋊Q₈×C₆₁	C₈	1	1	yes	characteristic
62	#121×C₆₁	C₈	1	1	yes	characteristic
63	#121×C₆₁	C₈	1	1	yes	characteristic
64	#120×C₆₁	C₈	1	2	yes	—
65	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
67	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
68	M₃₂×C₆₁	—	2	2	no	—
69	M₃₂×C₆₁	—	2	4	no	—
70	M₃₂×C₆₁	—	2	4	no	—
71	M₃₂×C₆₁	D₄	1	4	yes	complemented
72	C₂×C₁₆×C₆₁	—	2	2	no	—
73	C₂×C₁₆×C₆₁	—	2	2	no	—
74	C₂×C₁₆×C₆₁	—	2	4	no	—
75	C₂×C₁₆×C₆₁	—	2	4	no	—
76	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
81	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
82	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
83	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
84	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
85	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
86	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
87	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
88	#97×C₆₁	C₂×C₄	1	2	yes	—
89	C₄×C₈×C₆₁	C₂³	1	2	yes	—
90	C₂⁴×C₆₁	C₂×C₈	1	1	yes	characteristic
91	#41×C₆₁	—	2	2	no	—
92	#41×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
94	C₂×D₄×C₆₁	C₂×C₈	1	2	yes	—
95	C₂×D₄×C₆₁	C₂×C₈	1	2	yes	—
96	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
97	C₂×D₄×C₆₁	C₂×C₈	1	2	yes	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	2	2	no	—
100	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
107	M₁₆×C₆₁	—	2	2	no	—
108	M₁₆×C₆₁	—	2	2	no	—
109	M₁₆×C₆₁	—	2	4	no	—
110	C₂×C₈×C₆₁	—	2	2	no	—
111	C₂×C₈×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	—	2	1	no	—
114	C₂×C₈×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	—	2	1	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	2	no	—
119	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₆₁	#41	1	2	yes	—
126	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
128	C₄⋊C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
129	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
130	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
131	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
132	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
133	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
134	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
135	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
136	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
137	C₁₆×C₆₁	—	2	1	no	—
138	C₁₆×C₆₁	—	2	1	no	—
139	C₁₆×C₆₁	—	2	2	no	—
140	C₁₆×C₆₁	—	2	1	no	—
141	C₁₆×C₆₁	—	2	1	no	—
142	C₁₆×C₆₁	C₂×D₄	1	4	yes	—
143	C₂³×C₆₁	—	2	2	no	—
144	C₂³×C₆₁	—	2	2	no	—
145	C₂³×C₆₁	—	4	1	no	—
146	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₆₁	C₂²×C₈	1	2	yes	—
148	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
149	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
150	Q₈×C₆₁	—	2	2	no	—
151	D₄×C₆₁	—	2	4	no	—
152	D₄×C₆₁	—	2	4	no	—
153	D₄×C₆₁	—	2	2	no	—
154	D₄×C₆₁	—	4	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	2	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
166	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
167	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₆₁	#131	1	2	yes	—
172	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
173	C₈×C₆₁	—	2	1	no	—
174	C₈×C₆₁	—	2	1	no	—
175	C₈×C₆₁	—	2	2	no	—
176	C₈×C₆₁	—	2	2	no	—
177	C₈×C₆₁	C₄×D₄	1	2	yes	—
178	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
180	#33436	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₆₁	—	2	1	no	—
182	C₂²×C₆₁	—	2	1	no	—
183	C₂²×C₆₁	—	2	1	no	—
184	C₂²×C₆₁	—	2	1	no	—
185	C₂²×C₆₁	—	2	2	no	—
186	C₂²×C₆₁	—	2	1	no	—
187	C₂²×C₆₁	—	2	1	no	—
188	C₂²×C₆₁	—	2	2	no	—
189	C₂²×C₆₁	—	2	1	no	—
190	C₂²×C₆₁	—	2	2	no	—
191	C₂²×C₆₁	—	4	4	no	—
192	C₂²×C₆₁	C₈×D₄	1	2	yes	—
193	C₂²×C₆₁	#504	1	2	yes	complemented
194	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
195	C₄×C₆₁	—	2	2	no	—
196	C₄×C₆₁	—	2	2	no	—
197	C₄×C₆₁	—	2	1	no	—
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	—	2	2	no	—
200	C₄×C₆₁	C₈×D₄	1	2	yes	—
201	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
202	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
203	C₂×#504	C₂×C₆₁	1	1	yes	characteristic, complemented
204	C₂²×M₃₂	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#2929	C₂×C₆₁	1	1	yes	characteristic
206	#2169	C₂×C₆₁	1	2	yes	complemented
207	#2168	C₂×C₆₁	1	2	yes	complemented
208	#2168	C₂×C₆₁	1	2	yes	complemented
209	D₄×C₁₆	C₂×C₆₁	1	2	yes	complemented
210	#2151	C₂×C₆₁	1	1	yes	characteristic, complemented
211	#2113	C₂×C₆₁	1	1	yes	characteristic, complemented
212	C₂×C₂²⋊C₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
213	#2108	C₂×C₆₁	1	1	yes	characteristic, complemented
214	C₂×C₆₁	—	2	2	no	—
215	C₂×C₆₁	—	2	2	no	—
216	C₂×C₆₁	—	4	2	no	—
217	C₂×C₆₁	—	4	1	no	—
218	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
219	C₂×C₆₁	C₂×#504	1	1	yes	characteristic
220	C₂×C₆₁	#3407	1	1	yes	characteristic
221	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
223	#525	C₄×C₆₁	1	1	yes	characteristic
224	#504	—	2	4	no	—
225	C₂×M₃₂	—	2	4	no	—
226	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
227	C₂×M₃₂	C₂²×C₆₁	1	2	yes	—
228	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
229	C₂×M₃₂	C₂²×C₆₁	1	2	yes	complemented
230	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
231	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
232	C₂²×C₁₆	C₂²×C₆₁	1	2	yes	—
233	C₂²×C₁₆	C₂²×C₆₁	1	2	yes	complemented
234	#435	C₄×C₆₁	1	2	yes	—
235	#435	C₄×C₆₁	1	2	yes	—
236	C₈×D₄	C₂²×C₆₁	1	2	yes	—
237	C₈×D₄	C₂²×C₆₁	1	2	yes	—
238	#424	C₄×C₆₁	1	1	yes	characteristic
239	#408	C₄×C₆₁	1	1	yes	characteristic
240	#407	C₄×C₆₁	1	1	yes	characteristic
241	#405	C₂²×C₆₁	1	1	yes	characteristic
242	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	complemented
243	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	complemented
244	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
245	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
246	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
247	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
248	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	complemented
249	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	complemented
250	#346	C₂²×C₆₁	1	2	yes	complemented
251	C₄×C₁₆	C₂²×C₆₁	1	2	yes	complemented
252	C₆₁	#33436	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×#41	C₂×C₄×C₆₁	1	1	yes	characteristic
254	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
255	#131	—	2	2	no	—
256	#131	—	2	2	no	—
257	C₂×M₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic
258	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
259	C₂×M₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
263	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
264	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
268	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
269	#123	C₈×C₆₁	1	2	yes	—
270	C₂²⋊Q₈	C₈×C₆₁	1	1	yes	characteristic
271	C₂²⋊Q₈	C₈×C₆₁	1	1	yes	characteristic
272	#121	C₈×C₆₁	1	1	yes	characteristic
273	#121	C₈×C₆₁	1	1	yes	characteristic
274	#120	C₈×C₆₁	1	2	yes	—
275	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
276	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
277	#117	C₂×C₄×C₆₁	1	1	yes	characteristic
278	M₃₂	—	2	2	no	—
279	M₃₂	—	2	4	no	—
280	M₃₂	—	2	4	no	—
281	M₃₂	D₄×C₆₁	1	4	yes	complemented
282	C₂×C₁₆	—	2	2	no	—
283	C₂×C₁₆	—	2	2	no	—
284	C₂×C₁₆	—	2	4	no	—
285	C₂×C₁₆	—	2	4	no	—
286	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
287	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
288	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
289	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
290	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
291	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
292	C₄⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
293	C₄⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
294	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
295	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
296	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
297	C₂²⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
298	#97	C₂×C₄×C₆₁	1	2	yes	—
299	C₄×C₈	C₂³×C₆₁	1	2	yes	—
300	C₂⁴	C₂×C₈×C₆₁	1	1	yes	characteristic
301	#41	—	2	2	no	—
302	#41	—	2	2	no	—
303	C₂×Q₈	C₂×C₈×C₆₁	1	1	yes	characteristic
304	C₂×D₄	C₂×C₈×C₆₁	1	2	yes	—
305	C₂×D₄	C₂×C₈×C₆₁	1	2	yes	—
306	C₂×D₄	C₂×C₈×C₆₁	1	1	yes	characteristic
307	C₂×D₄	C₂×C₈×C₆₁	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
316	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
330	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
331	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
332	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
335	C₂×C₈	#41×C₆₁	1	2	yes	—
336	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
337	C₄⋊C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
338	C₄⋊C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
339	C₄⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
340	C₄⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
341	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
342	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
343	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
344	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
345	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
346	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
347	C₁₆	—	2	1	no	—
348	C₁₆	—	2	1	no	—
349	C₁₆	—	2	2	no	—
350	C₁₆	—	2	1	no	—
351	C₁₆	—	2	1	no	—
352	C₁₆	C₂×D₄×C₆₁	1	4	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	C₂²×C₈×C₆₁	1	1	yes	characteristic
357	C₂³	C₂²×C₈×C₆₁	1	2	yes	—
358	C₂³	C₂²×C₈×C₆₁	1	1	yes	characteristic
359	C₂³	C₂²×C₈×C₆₁	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	D₄	—	2	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	2	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
375	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
376	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
377	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
378	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
380	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
381	C₂×C₄	#131×C₆₁	1	2	yes	—
382	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	2	1	no	—
385	C₈	—	2	1	no	—
386	C₈	—	2	2	no	—
387	C₈	C₄×D₄×C₆₁	1	2	yes	—
388	C₈	C₂²×D₄×C₆₁	1	1	yes	characteristic
389	C₈	C₂×#41×C₆₁	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	4	no	—
401	C₂²	C₈×D₄×C₆₁	1	2	yes	—
402	C₂²	C₆₁×#504	1	2	yes	complemented
403	C₂²	C₂³×C₈×C₆₁	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	C₈×D₄×C₆₁	1	2	yes	—
410	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
411	C₄	C₂×#131×C₆₁	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂×C₈×D₄×C₆₁	1	1	yes	characteristic
417	C₂	C₂×C₆₁×#504	1	1	yes	characteristic
418	C₂	C₆₁×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₆₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₆₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂³×C₈
prime radical	C₆₁×#525	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#504	C₂	semidirect
2. C₂²×M₃₂×C₆₁	C₂	semidirect
4. C₆₁×#2169	C₂	semidirect
5. C₆₁×#2168	C₂	semidirect
6. C₆₁×#2168	C₂	semidirect
7. D₄×C₁₆×C₆₁	C₂	semidirect
8. C₆₁×#2151	C₂	semidirect
9. C₆₁×#2113	C₂	semidirect
10. C₂×C₆₁×C₂²⋊C₁₆	C₂	semidirect
11. C₆₁×#2108	C₂	semidirect
20. C₂×M₃₂×C₆₁	C₂²	semidirect
24. C₂²×C₁₆×C₆₁	C₂²	semidirect
33. C₆₁×C₄⋊C₁₆	C₂²	semidirect
34. C₆₁×C₄⋊C₁₆	C₂²	semidirect
39. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
40. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
41. C₆₁×#346	C₂²	semidirect
42. C₄×C₁₆×C₆₁	C₂²	semidirect
71. M₃₂×C₆₁	D₄	semidirect
180. #33436	C₆₁	direct (N × H)
193. C₂²×C₆₁	#504	semidirect
203. C₂×#504	C₂×C₆₁	semidirect
204. C₂²×M₃₂	C₂×C₆₁	semidirect
206. #2169	C₂×C₆₁	semidirect
207. #2168	C₂×C₆₁	semidirect
208. #2168	C₂×C₆₁	semidirect
209. D₄×C₁₆	C₂×C₆₁	semidirect
210. #2151	C₂×C₆₁	semidirect
211. #2113	C₂×C₆₁	semidirect
212. C₂×C₂²⋊C₁₆	C₂×C₆₁	semidirect
213. #2108	C₂×C₆₁	semidirect
229. C₂×M₃₂	C₂²×C₆₁	semidirect
233. C₂²×C₁₆	C₂²×C₆₁	semidirect
242. C₄⋊C₁₆	C₂²×C₆₁	semidirect
243. C₄⋊C₁₆	C₂²×C₆₁	semidirect
248. C₂²⋊C₁₆	C₂²×C₆₁	semidirect
249. C₂²⋊C₁₆	C₂²×C₆₁	semidirect
250. #346	C₂²×C₆₁	semidirect
251. C₄×C₁₆	C₂²×C₆₁	semidirect
252. C₆₁	#33436	direct (N × H)
281. M₃₂	D₄×C₆₁	semidirect
402. C₂²	C₆₁×#504	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#504	2
C₂²×M₃₂×C₆₁	2
C₆₁×#2929	2
C₆₁×#2169	2
C₆₁×#2168	2
D₄×C₁₆×C₆₁	2
C₆₁×#2151	2
C₆₁×#2113	2
C₂×C₆₁×C₂²⋊C₁₆	2
C₆₁×#2108	2
#33436	61

Subgroups — C61×#33436 #29536869

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33436 #29536869