Subgroups — C₆₁×#33787 #29537220

Order 15616.

586 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×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3156	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2245	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2210	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2208	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2186	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2185	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₆₁	—	2	1	no	—
13	C₂×#135×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#540	—	2	1	no	—
16	C₆₁×#536	—	2	1	no	—
17	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
18	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
19	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
20	C₂×D₁₆×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#499	C₂²	1	1	yes	characteristic
22	C₆₁×#497	—	2	1	no	—
23	C₆₁×#497	—	2	1	no	—
24	C₆₁×#495	C₂²	1	1	yes	characteristic
25	C₆₁×#495	C₂²	1	1	yes	characteristic
26	C₆₁×#494	C₂²	1	1	yes	characteristic
27	C₆₁×#494	C₂²	1	1	yes	characteristic
28	C₆₁×#493	C₂²	1	1	yes	characteristic
29	C₆₁×#490	—	2	1	no	—
30	C₆₁×#469	—	2	1	no	—
31	C₆₁×#466	C₂²	1	2	yes	—
32	C₆₁×#442	—	2	1	no	—
33	C₄×D₈×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#405	C₂²	1	1	yes	characteristic
35	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₆₁×#358	C₂²	1	2	yes	—
37	C₆₁×#358	C₂²	1	2	yes	—
38	C₆₁×#358	C₂²	1	2	yes	—
39	C₆₁×#357	C₂²	1	2	yes	—
40	C₆₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₆₁×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
43	C₂×#41×C₆₁	—	2	1	no	—
44	C₂²×Q₈×C₆₁	—	2	1	no	—
45	#137×C₆₁	—	4	4	no	—
46	#135×C₆₁	—	4	2	no	—
47	C₂×Q₁₆×C₆₁	—	2	1	no	—
48	C₂×Q₁₆×C₆₁	—	2	1	no	—
49	C₂×Q₁₆×C₆₁	—	2	1	no	—
50	C₂×Q₁₆×C₆₁	—	4	2	no	—
51	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
53	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×SD₁₆×C₆₁	—	2	1	no	—
55	C₂×SD₁₆×C₆₁	—	2	1	no	—
56	C₂×SD₁₆×C₆₁	—	2	1	no	—
57	C₂×D₈×C₆₁	—	2	1	no	—
58	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂×D₈×C₆₁	C₂³	1	2	yes	—
60	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₆₁	—	2	1	no	—
63	C₄⋊Q₈×C₆₁	—	2	1	no	—
64	#127×C₆₁	—	2	1	no	—
65	#125×C₆₁	—	2	1	no	—
66	#124×C₆₁	—	2	1	no	—
67	#124×C₆₁	—	2	1	no	—
68	#123×C₆₁	—	4	2	no	—
69	#123×C₆₁	—	4	2	no	—
70	C₂²⋊Q₈×C₆₁	—	4	2	no	—
71	#121×C₆₁	—	2	2	no	—
72	#121×C₆₁	—	4	2	no	—
73	C₄×D₄×C₆₁	—	2	2	no	—
74	#117×C₆₁	D₄	1	1	yes	characteristic
75	SD₃₂×C₆₁	—	4	2	no	—
76	SD₃₂×C₆₁	—	4	2	no	—
77	SD₃₂×C₆₁	—	4	2	no	—
78	D₁₆×C₆₁	—	4	2	no	—
79	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
80	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
81	#107×C₆₁	C₂³	1	2	yes	—
82	#106×C₆₁	—	2	1	no	—
83	#102×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	2	no	—
85	#97×C₆₁	D₄	1	1	yes	characteristic
86	#97×C₆₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	#41×C₆₁	—	4	2	no	—
90	#41×C₆₁	—	4	2	no	—
91	C₂×Q₈×C₆₁	—	2	1	no	—
92	C₂×Q₈×C₆₁	—	2	1	no	—
93	C₂×Q₈×C₆₁	—	2	1	no	—
94	C₂×Q₈×C₆₁	—	4	2	no	—
95	C₂×Q₈×C₆₁	—	4	2	no	—
96	C₂×Q₈×C₆₁	—	4	1	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	2	1	no	—
99	C₂×D₄×C₆₁	—	4	1	no	—
100	C₂×D₄×C₆₁	—	4	2	no	—
101	C₂×D₄×C₆₁	—	4	2	no	—
102	C₂²×C₄×C₆₁	—	4	1	no	—
103	C₂²×C₄×C₆₁	—	4	1	no	—
104	C₂²×C₄×C₆₁	—	4	2	no	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	Q₁₆×C₆₁	—	2	2	no	—
107	Q₁₆×C₆₁	—	2	2	no	—
108	Q₁₆×C₆₁	—	2	2	no	—
109	Q₁₆×C₆₁	—	4	2	no	—
110	Q₁₆×C₆₁	—	4	2	no	—
111	Q₁₆×C₆₁	—	4	2	no	—
112	SD₁₆×C₆₁	—	4	2	no	—
113	SD₁₆×C₆₁	—	4	2	no	—
114	SD₁₆×C₆₁	—	4	2	no	—
115	D₈×C₆₁	—	2	2	no	—
116	D₈×C₆₁	—	2	2	no	—
117	D₈×C₆₁	—	2	2	no	—
118	D₈×C₆₁	—	4	2	no	—
119	M₁₆×C₆₁	—	2	2	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	4	2	no	—
127	C₄⋊C₄×C₆₁	—	4	2	no	—
128	C₄⋊C₄×C₆₁	—	4	2	no	—
129	C₄⋊C₄×C₆₁	D₈	1	2	yes	—
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	C₂²⋊C₄×C₆₁	D₈	1	2	yes	—
135	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₆₁	—	2	2	no	—
138	C₁₆×C₆₁	—	2	2	no	—
139	C₂³×C₆₁	—	4	1	no	—
140	C₂³×C₆₁	—	4	2	no	—
141	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
142	Q₈×C₆₁	—	4	1	no	—
143	Q₈×C₆₁	—	4	1	no	—
144	Q₈×C₆₁	—	4	1	no	—
145	Q₈×C₆₁	—	4	1	no	—
146	Q₈×C₆₁	—	4	1	no	—
147	Q₈×C₆₁	—	4	1	no	—
148	Q₈×C₆₁	—	8	2	no	—
149	D₄×C₆₁	—	4	1	no	—
150	D₄×C₆₁	—	4	2	no	—
151	D₄×C₆₁	—	4	2	no	—
152	D₄×C₆₁	—	4	1	no	—
153	D₄×C₆₁	—	8	2	no	—
154	D₄×C₆₁	—	16	2	no	—
155	D₄×C₆₁	—	16	2	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	1	no	—
160	C₂×C₄×C₆₁	—	4	1	no	—
161	C₂×C₄×C₆₁	—	4	1	no	—
162	C₂×C₄×C₆₁	—	8	2	no	—
163	C₂×C₄×C₆₁	—	8	2	no	—
164	C₂×C₄×C₆₁	—	16	2	no	—
165	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
166	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₆₁	—	2	1	no	—
170	C₈×C₆₁	—	2	1	no	—
171	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
172	C₈×C₆₁	H(5,𝔽₂)	1	2	yes	—
173	#33787	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₆₁	—	2	2	no	—
175	C₂²×C₆₁	—	2	1	no	—
176	C₂²×C₆₁	—	8	2	no	—
177	C₂²×C₆₁	—	8	2	no	—
178	C₂²×C₆₁	—	8	2	no	—
179	C₂²×C₆₁	—	8	1	no	—
180	C₂²×C₆₁	—	8	2	no	—
181	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
182	C₄×C₆₁	—	2	2	no	—
183	C₄×C₆₁	—	2	2	no	—
184	C₄×C₆₁	—	2	1	no	—
185	C₄×C₆₁	—	8	2	no	—
186	C₄×C₆₁	—	8	1	no	—
187	C₄×C₆₁	—	8	1	no	—
188	C₄×C₆₁	—	8	1	no	—
189	C₄×C₆₁	#535	1	1	yes	characteristic
190	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	#3176	C₂×C₆₁	1	1	yes	characteristic, complemented
192	#3156	C₂×C₆₁	1	1	yes	characteristic, complemented
193	#2250	C₂×C₆₁	1	1	yes	characteristic, complemented
194	#2248	C₂×C₆₁	1	1	yes	characteristic, complemented
195	#2245	C₂×C₆₁	1	1	yes	characteristic, complemented
196	#2242	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#2210	C₂×C₆₁	1	2	yes	complemented
198	#2208	C₂×C₆₁	1	2	yes	complemented
199	#2186	C₂×C₆₁	1	2	yes	complemented
200	#2185	C₂×C₆₁	1	2	yes	complemented
201	#2164	C₂×C₆₁	1	1	yes	characteristic, complemented
202	C₂×C₆₁	—	4	1	no	—
203	C₂×C₆₁	—	16	2	no	—
204	C₂×C₆₁	—	16	1	no	—
205	C₂×C₆₁	#3205	1	1	yes	characteristic
206	C₂×C₆₁	#3416	1	2	yes	—
207	C₂×#137	—	2	1	no	—
208	C₂×#135	C₂²×C₆₁	1	1	yes	characteristic
209	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
210	#540	—	2	1	no	—
211	#536	—	2	1	no	—
212	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
213	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
214	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
215	C₂×D₁₆	C₂²×C₆₁	1	2	yes	—
216	#499	C₂²×C₆₁	1	1	yes	characteristic
217	#497	—	2	1	no	—
218	#497	—	2	1	no	—
219	#495	C₂²×C₆₁	1	1	yes	characteristic
220	#495	C₂²×C₆₁	1	1	yes	characteristic
221	#494	C₂²×C₆₁	1	1	yes	characteristic
222	#494	C₂²×C₆₁	1	1	yes	characteristic
223	#493	C₂²×C₆₁	1	1	yes	characteristic
224	#490	—	2	1	no	—
225	#469	—	2	1	no	—
226	#466	C₂²×C₆₁	1	2	yes	—
227	#442	—	2	1	no	—
228	C₄×D₈	C₂²×C₆₁	1	2	yes	—
229	#405	C₂²×C₆₁	1	1	yes	characteristic
230	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	—
231	#358	C₂²×C₆₁	1	2	yes	—
232	#358	C₂²×C₆₁	1	2	yes	—
233	#358	C₂²×C₆₁	1	2	yes	—
234	#357	C₂²×C₆₁	1	2	yes	—
235	C₂²⋊C₁₆	C₂²×C₆₁	1	2	yes	—
236	#346	C₂²×C₆₁	1	1	yes	characteristic
237	C₄×C₁₆	C₂²×C₆₁	1	1	yes	characteristic
238	C₆₁	#33787	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#41	—	2	1	no	—
240	C₂²×Q₈	—	2	1	no	—
241	#137	—	4	4	no	—
242	#135	—	4	2	no	—
243	C₂×Q₁₆	—	2	1	no	—
244	C₂×Q₁₆	—	2	1	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	—	4	2	no	—
247	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
248	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
249	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
250	C₂×SD₁₆	—	2	1	no	—
251	C₂×SD₁₆	—	2	1	no	—
252	C₂×SD₁₆	—	2	1	no	—
253	C₂×D₈	—	2	1	no	—
254	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
255	C₂×D₈	C₂³×C₆₁	1	2	yes	—
256	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	#127	—	2	1	no	—
261	#125	—	2	1	no	—
262	#124	—	2	1	no	—
263	#124	—	2	1	no	—
264	#123	—	4	2	no	—
265	#123	—	4	2	no	—
266	C₂²⋊Q₈	—	4	2	no	—
267	#121	—	2	2	no	—
268	#121	—	4	2	no	—
269	C₄×D₄	—	2	2	no	—
270	#117	D₄×C₆₁	1	1	yes	characteristic
271	SD₃₂	—	4	2	no	—
272	SD₃₂	—	4	2	no	—
273	SD₃₂	—	4	2	no	—
274	D₁₆	—	4	2	no	—
275	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
276	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
277	#107	C₂³×C₆₁	1	2	yes	—
278	#106	—	2	1	no	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#97	D₄×C₆₁	1	1	yes	characteristic
282	#97	D₄×C₆₁	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
285	#41	—	4	2	no	—
286	#41	—	4	2	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
302	Q₁₆	—	2	2	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	2	2	no	—
305	Q₁₆	—	4	2	no	—
306	Q₁₆	—	4	2	no	—
307	Q₁₆	—	4	2	no	—
308	SD₁₆	—	4	2	no	—
309	SD₁₆	—	4	2	no	—
310	SD₁₆	—	4	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	4	2	no	—
315	M₁₆	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
320	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	D₈×C₆₁	1	2	yes	—
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	C₂²⋊C₄	D₈×C₆₁	1	2	yes	—
331	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₁₆	—	2	2	no	—
334	C₁₆	—	2	2	no	—
335	C₂³	—	4	1	no	—
336	C₂³	—	4	2	no	—
337	C₂³	C₂×D₈×C₆₁	1	1	yes	characteristic
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	Q₈	—	4	1	no	—
341	Q₈	—	4	1	no	—
342	Q₈	—	4	1	no	—
343	Q₈	—	4	1	no	—
344	Q₈	—	8	2	no	—
345	D₄	—	4	1	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	2	no	—
348	D₄	—	4	1	no	—
349	D₄	—	8	2	no	—
350	D₄	—	16	2	no	—
351	D₄	—	16	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
362	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
363	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
364	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
368	C₈	H(5,𝔽₂)×C₆₁	1	2	yes	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	1	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	1	no	—
382	C₄	—	8	1	no	—
383	C₄	—	8	1	no	—
384	C₄	C₆₁×#535	1	1	yes	characteristic
385	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
386	C₂	—	4	1	no	—
387	C₂	—	16	2	no	—
388	C₂	—	16	1	no	—
389	C₂	C₆₁×#3205	1	1	yes	characteristic
390	C₂	C₆₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ #117×C₆₁ ◁ C₆₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3176	C₂	semidirect
2. C₆₁×#3156	C₂	semidirect
3. C₆₁×#2250	C₂	semidirect
4. C₆₁×#2248	C₂	semidirect
5. C₆₁×#2245	C₂	semidirect
6. C₆₁×#2242	C₂	semidirect
7. C₆₁×#2210	C₂	semidirect
8. C₆₁×#2208	C₂	semidirect
9. C₆₁×#2186	C₂	semidirect
10. C₆₁×#2185	C₂	semidirect
11. C₆₁×#2164	C₂	semidirect
173. #33787	C₆₁	direct (N × H)
191. #3176	C₂×C₆₁	semidirect
192. #3156	C₂×C₆₁	semidirect
193. #2250	C₂×C₆₁	semidirect
194. #2248	C₂×C₆₁	semidirect
195. #2245	C₂×C₆₁	semidirect
196. #2242	C₂×C₆₁	semidirect
197. #2210	C₂×C₆₁	semidirect
198. #2208	C₂×C₆₁	semidirect
199. #2186	C₂×C₆₁	semidirect
200. #2185	C₂×C₆₁	semidirect
201. #2164	C₂×C₆₁	semidirect
238. C₆₁	#33787	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×#3176	2
C₆₁×#3156	2
C₆₁×#2250	2
C₆₁×#2248	2
C₆₁×#2245	2
C₆₁×#2242	2
C₆₁×#2210	2
C₆₁×#2208	2
C₆₁×#2186	2
C₆₁×#2185	2
C₆₁×#2164	2
#33787	61

Subgroups — C61×#33787 #29537220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33787 #29537220