Subgroups — C₆₁×#33433 #29536866

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 324 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	4	yes	maximal, complemented
5	C₆₁×#2168	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₆₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₆₁×#525	C₄	1	1	yes	characteristic
13	C₆₁×#504	—	2	4	no	—
14	C₂×M₃₂×C₆₁	—	2	4	no	—
15	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×M₃₂×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×M₃₂×C₆₁	C₂²	1	2	yes	—
18	C₂×M₃₂×C₆₁	C₂²	1	2	yes	—
19	C₂×M₃₂×C₆₁	C₂²	1	2	yes	complemented
20	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₁₆×C₆₁	C₂²	1	2	yes	complemented
23	C₆₁×#435	C₄	1	4	yes	—
24	C₈×D₄×C₆₁	C₂²	1	4	yes	—
25	C₆₁×#424	C₄	1	1	yes	characteristic
26	C₆₁×#408	C₄	1	1	yes	characteristic
27	C₆₁×#407	C₄	1	1	yes	characteristic
28	C₆₁×#405	C₂²	1	1	yes	characteristic
29	C₆₁×C₄⋊C₁₆	C₂²	1	4	yes	complemented
30	C₆₁×C₂²⋊C₁₆	C₂²	1	4	yes	—
31	C₆₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
32	C₆₁×#346	C₂²	1	2	yes	complemented
33	C₄×C₁₆×C₆₁	C₂²	1	2	yes	complemented
34	C₂×#41×C₆₁	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
36	#131×C₆₁	—	2	2	no	—
37	#131×C₆₁	—	2	2	no	—
38	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
40	C₂×M₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₆₁	—	2	2	no	—
42	C₂²×C₈×C₆₁	—	2	2	no	—
43	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
48	#123×C₆₁	C₈	1	2	yes	—
49	C₂²⋊Q₈×C₆₁	C₈	1	2	yes	—
50	#121×C₆₁	C₈	1	2	yes	—
51	#120×C₆₁	C₈	1	2	yes	—
52	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
53	#117×C₆₁	C₂×C₄	1	1	yes	characteristic
54	M₃₂×C₆₁	—	2	2	no	—
55	M₃₂×C₆₁	—	2	2	no	—
56	M₃₂×C₆₁	—	2	4	no	—
57	M₃₂×C₆₁	—	2	4	no	—
58	M₃₂×C₆₁	—	2	4	no	—
59	C₂×C₁₆×C₆₁	—	2	2	no	—
60	C₂×C₁₆×C₆₁	—	2	4	no	—
61	C₂×C₁₆×C₆₁	D₄	1	4	yes	complemented
62	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
63	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
64	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
65	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
68	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
69	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
70	#97×C₆₁	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₆₁	C₂³	1	2	yes	—
72	C₂⁴×C₆₁	C₂×C₈	1	1	yes	characteristic
73	#41×C₆₁	—	2	2	no	—
74	#41×C₆₁	—	2	2	no	—
75	C₂×Q₈×C₆₁	C₂×C₈	1	1	yes	characteristic
76	C₂×D₄×C₆₁	C₂×C₈	1	2	yes	—
77	C₂×D₄×C₆₁	C₂×C₈	1	1	yes	characteristic
78	C₂×D₄×C₆₁	C₂×C₈	1	4	yes	—
79	C₂²×C₄×C₆₁	—	2	2	no	—
80	C₂²×C₄×C₆₁	—	2	2	no	—
81	C₂²×C₄×C₆₁	C₂×C₈	1	2	yes	—
82	C₂²×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
83	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
86	M₁₆×C₆₁	—	2	2	no	—
87	M₁₆×C₆₁	—	2	2	no	—
88	M₁₆×C₆₁	—	2	4	no	—
89	C₂×C₈×C₆₁	—	2	2	no	—
90	C₂×C₈×C₆₁	—	2	4	no	—
91	C₂×C₈×C₆₁	—	2	2	no	—
92	C₂×C₈×C₆₁	—	2	2	no	—
93	C₂×C₈×C₆₁	—	2	2	no	—
94	C₂×C₈×C₆₁	—	2	2	no	—
95	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
100	C₂×C₈×C₆₁	#41	1	2	yes	—
101	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
103	C₄⋊C₄×C₆₁	C₂×C₈	1	4	yes	—
104	C₂²⋊C₄×C₆₁	C₂×C₈	1	2	yes	—
105	C₂²⋊C₄×C₆₁	C₂×C₈	1	4	yes	—
106	C₂²⋊C₄×C₆₁	C₂×C₈	1	4	yes	—
107	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
108	C₁₆×C₆₁	—	2	2	no	—
109	C₁₆×C₆₁	—	2	2	no	—
110	C₁₆×C₆₁	—	2	2	no	—
111	C₁₆×C₆₁	C₂×D₄	1	2	yes	—
112	C₁₆×C₆₁	C₂×D₄	1	2	yes	—
113	C₂³×C₆₁	—	2	2	no	—
114	C₂³×C₆₁	—	4	2	no	—
115	C₂³×C₆₁	C₂²×C₈	1	2	yes	—
116	C₂³×C₆₁	C₂²×C₈	1	2	yes	—
117	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
118	Q₈×C₆₁	—	2	2	no	—
119	D₄×C₆₁	—	2	4	no	—
120	D₄×C₆₁	—	2	2	no	—
121	D₄×C₆₁	—	4	4	no	—
122	C₂×C₄×C₆₁	—	2	2	no	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	2	no	—
126	C₂×C₄×C₆₁	—	2	2	no	—
127	C₂×C₄×C₆₁	—	2	4	no	—
128	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
129	C₂×C₄×C₆₁	C₂²×C₈	1	4	yes	—
130	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
133	C₂×C₄×C₆₁	#131	1	2	yes	—
134	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
135	C₈×C₆₁	—	2	2	no	—
136	C₈×C₆₁	—	2	2	no	—
137	C₈×C₆₁	—	2	2	no	—
138	C₈×C₆₁	C₄×D₄	1	2	yes	—
139	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
140	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
141	#33433	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
142	C₂²×C₆₁	—	2	2	no	—
143	C₂²×C₆₁	—	2	2	no	—
144	C₂²×C₆₁	—	2	4	no	—
145	C₂²×C₆₁	—	2	2	no	—
146	C₂²×C₆₁	—	2	2	no	—
147	C₂²×C₆₁	—	2	2	no	—
148	C₂²×C₆₁	—	4	4	no	—
149	C₂²×C₆₁	C₈×D₄	1	2	yes	—
150	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
151	C₄×C₆₁	—	2	4	no	—
152	C₄×C₆₁	—	2	2	no	—
153	C₄×C₆₁	—	2	2	no	—
154	C₄×C₆₁	C₈×D₄	1	2	yes	—
155	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
156	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
157	C₂×#504	C₂×C₆₁	1	1	yes	characteristic, complemented
158	C₂²×M₃₂	C₂×C₆₁	1	1	yes	characteristic, complemented
159	#2929	C₂×C₆₁	1	1	yes	characteristic
160	#2169	C₂×C₆₁	1	4	yes	complemented
161	#2168	C₂×C₆₁	1	4	yes	complemented
162	#2151	C₂×C₆₁	1	1	yes	characteristic, complemented
163	#2113	C₂×C₆₁	1	1	yes	characteristic, complemented
164	#2112	C₂×C₆₁	1	1	yes	characteristic, complemented
165	#2108	C₂×C₆₁	1	1	yes	characteristic, complemented
166	C₂×C₆₁	—	2	2	no	—
167	C₂×C₆₁	—	4	2	no	—
168	C₂×C₆₁	—	4	2	no	—
169	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
170	C₂×C₆₁	#3407	1	2	yes	—
171	C₂×#131	C₂²×C₆₁	1	1	yes	characteristic
172	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
173	#525	C₄×C₆₁	1	1	yes	characteristic
174	#504	—	2	4	no	—
175	C₂×M₃₂	—	2	4	no	—
176	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
177	C₂×M₃₂	C₂²×C₆₁	1	1	yes	characteristic
178	C₂×M₃₂	C₂²×C₆₁	1	2	yes	—
179	C₂×M₃₂	C₂²×C₆₁	1	2	yes	—
180	C₂×M₃₂	C₂²×C₆₁	1	2	yes	complemented
181	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
182	C₂²×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
183	C₂²×C₁₆	C₂²×C₆₁	1	2	yes	complemented
184	#435	C₄×C₆₁	1	4	yes	—
185	C₈×D₄	C₂²×C₆₁	1	4	yes	—
186	#424	C₄×C₆₁	1	1	yes	characteristic
187	#408	C₄×C₆₁	1	1	yes	characteristic
188	#407	C₄×C₆₁	1	1	yes	characteristic
189	#405	C₂²×C₆₁	1	1	yes	characteristic
190	C₄⋊C₁₆	C₂²×C₆₁	1	4	yes	complemented
191	C₂²⋊C₁₆	C₂²×C₆₁	1	4	yes	—
192	C₂²⋊C₁₆	C₂²×C₆₁	1	4	yes	complemented
193	#346	C₂²×C₆₁	1	2	yes	complemented
194	C₄×C₁₆	C₂²×C₆₁	1	2	yes	complemented
195	C₆₁	#33433	1	1	yes	characteristic, direct product factor, Sylow
196	C₂×#41	C₂×C₄×C₆₁	1	1	yes	characteristic
197	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
198	#131	—	2	2	no	—
199	#131	—	2	2	no	—
200	C₂×M₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic
201	C₂×M₁₆	C₂×C₄×C₆₁	1	2	yes	—
202	C₂×M₁₆	C₂×C₄×C₆₁	1	1	yes	characteristic
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	—	2	2	no	—
205	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
206	C₂²×C₈	C₂×C₄×C₆₁	1	2	yes	—
207	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
208	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
209	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
210	#123	C₈×C₆₁	1	2	yes	—
211	C₂²⋊Q₈	C₈×C₆₁	1	2	yes	—
212	#121	C₈×C₆₁	1	2	yes	—
213	#120	C₈×C₆₁	1	2	yes	—
214	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
215	#117	C₂×C₄×C₆₁	1	1	yes	characteristic
216	M₃₂	—	2	2	no	—
217	M₃₂	—	2	2	no	—
218	M₃₂	—	2	4	no	—
219	M₃₂	—	2	4	no	—
220	M₃₂	—	2	4	no	—
221	C₂×C₁₆	—	2	2	no	—
222	C₂×C₁₆	—	2	4	no	—
223	C₂×C₁₆	D₄×C₆₁	1	4	yes	complemented
224	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
225	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
226	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
227	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
228	C₂×C₁₆	C₂³×C₆₁	1	1	yes	characteristic
229	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
230	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
231	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
232	#97	C₂×C₄×C₆₁	1	2	yes	—
233	C₄×C₈	C₂³×C₆₁	1	2	yes	—
234	C₂⁴	C₂×C₈×C₆₁	1	1	yes	characteristic
235	#41	—	2	2	no	—
236	#41	—	2	2	no	—
237	C₂×Q₈	C₂×C₈×C₆₁	1	1	yes	characteristic
238	C₂×D₄	C₂×C₈×C₆₁	1	2	yes	—
239	C₂×D₄	C₂×C₈×C₆₁	1	1	yes	characteristic
240	C₂×D₄	C₂×C₈×C₆₁	1	4	yes	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	C₂×C₈×C₆₁	1	2	yes	—
244	C₂²×C₄	C₂×C₈×C₆₁	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
248	M₁₆	—	2	2	no	—
249	M₁₆	—	2	2	no	—
250	M₁₆	—	2	4	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	4	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
259	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
260	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
261	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
262	C₂×C₈	#41×C₆₁	1	2	yes	—
263	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
264	C₄⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
265	C₄⋊C₄	C₂×C₈×C₆₁	1	4	yes	—
266	C₂²⋊C₄	C₂×C₈×C₆₁	1	2	yes	—
267	C₂²⋊C₄	C₂×C₈×C₆₁	1	4	yes	—
268	C₂²⋊C₄	C₂×C₈×C₆₁	1	4	yes	—
269	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
270	C₁₆	—	2	2	no	—
271	C₁₆	—	2	2	no	—
272	C₁₆	—	2	2	no	—
273	C₁₆	C₂×D₄×C₆₁	1	2	yes	—
274	C₁₆	C₂×D₄×C₆₁	1	2	yes	—
275	C₂³	—	2	2	no	—
276	C₂³	—	4	2	no	—
277	C₂³	C₂²×C₈×C₆₁	1	2	yes	—
278	C₂³	C₂²×C₈×C₆₁	1	2	yes	—
279	C₂³	C₂²×C₈×C₆₁	1	1	yes	characteristic
280	Q₈	—	2	2	no	—
281	D₄	—	2	4	no	—
282	D₄	—	2	2	no	—
283	D₄	—	4	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
291	C₂×C₄	C₂²×C₈×C₆₁	1	4	yes	—
292	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₆₁	1	2	yes	—
294	C₂×C₄	C₂²×C₈×C₆₁	1	1	yes	characteristic
295	C₂×C₄	#131×C₆₁	1	2	yes	—
296	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
297	C₈	—	2	2	no	—
298	C₈	—	2	2	no	—
299	C₈	—	2	2	no	—
300	C₈	C₄×D₄×C₆₁	1	2	yes	—
301	C₈	C₂²×D₄×C₆₁	1	1	yes	characteristic
302	C₈	C₂×#41×C₆₁	1	1	yes	characteristic
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	2	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	4	4	no	—
310	C₂²	C₈×D₄×C₆₁	1	2	yes	—
311	C₂²	C₂³×C₈×C₆₁	1	1	yes	characteristic
312	C₄	—	2	4	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	C₈×D₄×C₆₁	1	2	yes	—
316	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
317	C₄	C₂×#131×C₆₁	1	1	yes	characteristic
318	C₂	—	2	2	no	—
319	C₂	—	4	2	no	—
320	C₂	—	4	2	no	—
321	C₂	C₂×C₈×D₄×C₆₁	1	1	yes	characteristic
322	C₂	C₆₁×#3407	1	2	yes	—

	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×#2151	C₂	semidirect
7. C₆₁×#2113	C₂	semidirect
8. C₆₁×#2112	C₂	semidirect
9. C₆₁×#2108	C₂	semidirect
19. C₂×M₃₂×C₆₁	C₂²	semidirect
22. C₂²×C₁₆×C₆₁	C₂²	semidirect
29. C₆₁×C₄⋊C₁₆	C₂²	semidirect
31. C₆₁×C₂²⋊C₁₆	C₂²	semidirect
32. C₆₁×#346	C₂²	semidirect
33. C₄×C₁₆×C₆₁	C₂²	semidirect
61. C₂×C₁₆×C₆₁	D₄	semidirect
141. #33433	C₆₁	direct (N × H)
157. C₂×#504	C₂×C₆₁	semidirect
158. C₂²×M₃₂	C₂×C₆₁	semidirect
160. #2169	C₂×C₆₁	semidirect
161. #2168	C₂×C₆₁	semidirect
162. #2151	C₂×C₆₁	semidirect
163. #2113	C₂×C₆₁	semidirect
164. #2112	C₂×C₆₁	semidirect
165. #2108	C₂×C₆₁	semidirect
180. C₂×M₃₂	C₂²×C₆₁	semidirect
183. C₂²×C₁₆	C₂²×C₆₁	semidirect
190. C₄⋊C₁₆	C₂²×C₆₁	semidirect
192. C₂²⋊C₁₆	C₂²×C₆₁	semidirect
193. #346	C₂²×C₆₁	semidirect
194. C₄×C₁₆	C₂²×C₆₁	semidirect
195. C₆₁	#33433	direct (N × H)
223. C₂×C₁₆	D₄×C₆₁	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
C₆₁×#2151	2
C₆₁×#2113	2
C₆₁×#2112	2
C₆₁×#2108	2
#33433	61

Subgroups — C61×#33433 #29536866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33433 #29536866