Subgroups — C₆₁×#3308 #21443349

Order 7808.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#489	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#468	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#463	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#435	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₆₁	—	2	1	no	—
17	C₂×#41×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×D₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	#124×C₆₁	—	2	1	no	—
26	#124×C₆₁	C₂²	1	1	yes	characteristic
27	#123×C₆₁	—	2	1	no	—
28	#123×C₆₁	—	2	1	no	—
29	C₂²⋊Q₈×C₆₁	—	2	1	no	—
30	C₂²⋊Q₈×C₆₁	—	2	1	no	—
31	C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
32	#121×C₆₁	—	2	1	no	—
33	#121×C₆₁	C₂²	1	1	yes	characteristic
34	#121×C₆₁	C₂²	1	1	yes	characteristic
35	#121×C₆₁	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₆₁	—	2	1	no	—
38	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
42	#107×C₆₁	C₂²	1	1	yes	characteristic
43	#107×C₆₁	C₂²	1	1	yes	characteristic
44	#107×C₆₁	C₂²	1	1	yes	characteristic
45	C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
46	#103×C₆₁	C₂²	1	1	yes	characteristic
47	#103×C₆₁	C₂²	1	1	yes	characteristic
48	#103×C₆₁	C₂²	1	1	yes	characteristic
49	#103×C₆₁	C₂²	1	1	yes	characteristic
50	#103×C₆₁	C₂²	1	1	yes	characteristic
51	#103×C₆₁	C₂²	1	1	yes	characteristic
52	#102×C₆₁	C₂²	1	1	yes	characteristic
53	#102×C₆₁	C₂²	1	1	yes	characteristic
54	#102×C₆₁	C₂²	1	1	yes	characteristic
55	#102×C₆₁	C₂²	1	1	yes	characteristic
56	C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
57	C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
58	#97×C₆₁	C₂²	1	1	yes	characteristic
59	#41×C₆₁	—	2	2	no	—
60	#41×C₆₁	—	4	1	no	—
61	#41×C₆₁	—	4	4	no	—
62	C₂×Q₈×C₆₁	—	2	1	no	—
63	C₂×Q₈×C₆₁	—	2	1	no	—
64	C₂×Q₈×C₆₁	—	2	2	no	—
65	C₂×Q₈×C₆₁	—	4	1	no	—
66	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×Q₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₆₁	—	2	1	no	—
69	C₂×D₄×C₆₁	—	2	1	no	—
70	C₂×D₄×C₆₁	—	2	1	no	—
71	C₂×D₄×C₆₁	—	2	1	no	—
72	C₂×D₄×C₆₁	D₄	1	1	yes	characteristic
73	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₆₁	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	—	2	1	no	—
76	C₂²×C₄×C₆₁	—	2	1	no	—
77	C₂²×C₄×C₆₁	—	2	1	no	—
78	C₂²×C₄×C₆₁	—	2	1	no	—
79	C₂²×C₄×C₆₁	—	2	1	no	—
80	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
82	SD₁₆×C₆₁	—	2	2	no	—
83	SD₁₆×C₆₁	—	4	1	no	—
84	D₈×C₆₁	—	4	1	no	—
85	M₁₆×C₆₁	—	4	1	no	—
86	C₂×C₈×C₆₁	—	4	1	no	—
87	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₄⋊C₄×C₆₁	—	2	1	no	—
94	C₄⋊C₄×C₆₁	—	2	1	no	—
95	C₄⋊C₄×C₆₁	—	2	1	no	—
96	C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
97	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂²⋊C₄×C₆₁	—	2	1	no	—
103	C₂²⋊C₄×C₆₁	—	2	1	no	—
104	C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂²⋊C₄×C₆₁	—	2	1	no	—
106	C₂²⋊C₄×C₆₁	—	2	1	no	—
107	C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
109	C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
110	C₄²×C₆₁	—	2	1	no	—
111	C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	C₂³×C₆₁	—	2	1	no	—
113	C₂³×C₆₁	—	2	1	no	—
114	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂³×C₆₁	C₂×D₄	1	1	yes	characteristic
116	Q₈×C₆₁	—	2	1	no	—
117	Q₈×C₆₁	—	2	1	no	—
118	Q₈×C₆₁	—	2	1	no	—
119	Q₈×C₆₁	—	4	2	no	—
120	Q₈×C₆₁	—	4	2	no	—
121	Q₈×C₆₁	#41	1	2	yes	complemented
122	D₄×C₆₁	—	2	2	no	—
123	D₄×C₆₁	—	2	1	no	—
124	D₄×C₆₁	—	2	1	no	—
125	D₄×C₆₁	—	2	1	no	—
126	D₄×C₆₁	—	2	1	no	—
127	D₄×C₆₁	—	4	2	no	—
128	D₄×C₆₁	—	4	2	no	—
129	D₄×C₆₁	—	4	2	no	—
130	D₄×C₆₁	—	4	2	no	—
131	C₂×C₄×C₆₁	—	2	1	no	—
132	C₂×C₄×C₆₁	—	2	1	no	—
133	C₂×C₄×C₆₁	—	2	1	no	—
134	C₂×C₄×C₆₁	—	2	1	no	—
135	C₂×C₄×C₆₁	—	2	1	no	—
136	C₂×C₄×C₆₁	—	2	1	no	—
137	C₂×C₄×C₆₁	—	2	1	no	—
138	C₂×C₄×C₆₁	—	2	1	no	—
139	C₂×C₄×C₆₁	—	2	1	no	—
140	C₂×C₄×C₆₁	—	2	1	no	—
141	C₂×C₄×C₆₁	—	4	2	no	—
142	C₂×C₄×C₆₁	—	4	2	no	—
143	C₂×C₄×C₆₁	—	4	2	no	—
144	C₂×C₄×C₆₁	—	4	2	no	—
145	C₂×C₄×C₆₁	—	4	2	no	—
146	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
151	C₈×C₆₁	—	2	1	no	—
152	C₈×C₆₁	—	2	1	no	—
153	C₈×C₆₁	—	2	1	no	—
154	C₈×C₆₁	—	2	1	no	—
155	C₂²×C₆₁	—	2	1	no	—
156	C₂²×C₆₁	—	2	1	no	—
157	C₂²×C₆₁	—	2	1	no	—
158	C₂²×C₆₁	—	2	1	no	—
159	C₂²×C₆₁	—	2	1	no	—
160	C₂²×C₆₁	—	4	1	no	—
161	C₂²×C₆₁	—	4	1	no	—
162	C₂²×C₆₁	—	4	1	no	—
163	C₂²×C₆₁	—	4	1	no	—
164	C₂²×C₆₁	—	4	1	no	—
165	C₂²×C₆₁	—	4	1	no	—
166	C₂²×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
167	C₂²×C₆₁	C₂²×D₄	1	1	yes	characteristic
168	C₄×C₆₁	—	2	1	no	—
169	C₄×C₆₁	—	2	1	no	—
170	C₄×C₆₁	—	2	2	no	—
171	C₄×C₆₁	—	2	1	no	—
172	C₄×C₆₁	—	2	1	no	—
173	C₄×C₆₁	—	4	1	no	—
174	C₄×C₆₁	—	4	1	no	—
175	C₄×C₆₁	—	4	1	no	—
176	C₄×C₆₁	—	4	1	no	—
177	C₄×C₆₁	—	4	1	no	—
178	C₄×C₆₁	C₂×#41	1	1	yes	characteristic
179	C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
180	#3308	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂×C₆₁	—	2	2	no	—
182	C₂×C₆₁	—	4	1	no	—
183	C₂×C₆₁	—	8	1	no	—
184	C₂×C₆₁	—	8	1	no	—
185	C₂×C₆₁	#546	1	1	yes	characteristic
186	C₂×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₆₁	#578	1	1	yes	characteristic
188	#548	C₂×C₆₁	1	1	yes	characteristic, complemented
189	#547	C₂×C₆₁	1	1	yes	characteristic, complemented
190	#489	C₂×C₆₁	1	1	yes	characteristic, complemented
191	#484	C₂×C₆₁	1	1	yes	characteristic, complemented
192	#480	C₂×C₆₁	1	1	yes	characteristic, complemented
193	#477	C₂×C₆₁	1	1	yes	characteristic, complemented
194	#468	C₂×C₆₁	1	1	yes	characteristic, complemented
195	#466	C₂×C₆₁	1	1	yes	characteristic, complemented
196	#463	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#449	C₂×C₆₁	1	1	yes	characteristic, complemented
198	#448	C₂×C₆₁	1	1	yes	characteristic, complemented
199	#440	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#435	C₂×C₆₁	1	1	yes	characteristic, complemented
201	#417	C₂×C₆₁	1	1	yes	characteristic, complemented
202	C₂×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
203	C₆₁	#3308	1	1	yes	characteristic, direct product factor, Sylow
204	C₂×#41	—	2	1	no	—
205	C₂×#41	C₂²×C₆₁	1	1	yes	characteristic
206	C₂²×Q₈	C₂²×C₆₁	1	1	yes	characteristic
207	C₂×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
208	C₂×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
209	C₂×D₈	C₂²×C₆₁	1	1	yes	characteristic
210	C₂×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
211	C₂²×C₈	C₂²×C₆₁	1	1	yes	characteristic
212	C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
213	#124	—	2	1	no	—
214	#124	C₂²×C₆₁	1	1	yes	characteristic
215	#123	—	2	1	no	—
216	#123	—	2	1	no	—
217	C₂²⋊Q₈	—	2	1	no	—
218	C₂²⋊Q₈	—	2	1	no	—
219	C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
220	#121	—	2	1	no	—
221	#121	C₂²×C₆₁	1	1	yes	characteristic
222	#121	C₂²×C₆₁	1	1	yes	characteristic
223	#121	C₂²×C₆₁	1	1	yes	characteristic
224	C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
225	C₄×D₄	—	2	1	no	—
226	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
227	C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
228	C₂×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
229	C₂×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
230	#107	C₂²×C₆₁	1	1	yes	characteristic
231	#107	C₂²×C₆₁	1	1	yes	characteristic
232	#107	C₂²×C₆₁	1	1	yes	characteristic
233	C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
234	#103	C₂²×C₆₁	1	1	yes	characteristic
235	#103	C₂²×C₆₁	1	1	yes	characteristic
236	#103	C₂²×C₆₁	1	1	yes	characteristic
237	#103	C₂²×C₆₁	1	1	yes	characteristic
238	#103	C₂²×C₆₁	1	1	yes	characteristic
239	#103	C₂²×C₆₁	1	1	yes	characteristic
240	#102	C₂²×C₆₁	1	1	yes	characteristic
241	#102	C₂²×C₆₁	1	1	yes	characteristic
242	#102	C₂²×C₆₁	1	1	yes	characteristic
243	#102	C₂²×C₆₁	1	1	yes	characteristic
244	C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
245	C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
246	#97	C₂²×C₆₁	1	1	yes	characteristic
247	#41	—	2	2	no	—
248	#41	—	4	1	no	—
249	#41	—	4	4	no	—
250	C₂×Q₈	—	2	1	no	—
251	C₂×Q₈	—	2	1	no	—
252	C₂×Q₈	—	2	2	no	—
253	C₂×Q₈	—	4	1	no	—
254	C₂×Q₈	C₂³×C₆₁	1	1	yes	characteristic
255	C₂×Q₈	C₂³×C₆₁	1	1	yes	characteristic
256	C₂×D₄	—	2	1	no	—
257	C₂×D₄	—	2	1	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	—	2	1	no	—
260	C₂×D₄	D₄×C₆₁	1	1	yes	characteristic
261	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
262	C₂×D₄	C₂³×C₆₁	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	C₂³×C₆₁	1	1	yes	characteristic
269	C₂²×C₄	C₂³×C₆₁	1	1	yes	characteristic
270	SD₁₆	—	2	2	no	—
271	SD₁₆	—	4	1	no	—
272	D₈	—	4	1	no	—
273	M₁₆	—	4	1	no	—
274	C₂×C₈	—	4	1	no	—
275	C₂×C₈	C₂³×C₆₁	1	1	yes	characteristic
276	C₂×C₈	C₂³×C₆₁	1	1	yes	characteristic
277	C₂×C₈	C₂³×C₆₁	1	1	yes	characteristic
278	C₂×C₈	C₂³×C₆₁	1	1	yes	characteristic
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	1	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	—	2	1	no	—
284	C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
285	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
286	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
287	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
288	C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	2	1	no	—
292	C₂²⋊C₄	—	2	1	no	—
293	C₂²⋊C₄	—	2	1	no	—
294	C₂²⋊C₄	—	2	1	no	—
295	C₂²⋊C₄	—	2	1	no	—
296	C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
297	C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
298	C₄²	—	2	1	no	—
299	C₄²	C₂³×C₆₁	1	1	yes	characteristic
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	C₂×D₄×C₆₁	1	1	yes	characteristic
303	C₂³	C₂×D₄×C₆₁	1	1	yes	characteristic
304	Q₈	—	2	1	no	—
305	Q₈	—	2	1	no	—
306	Q₈	—	2	1	no	—
307	Q₈	—	4	2	no	—
308	Q₈	—	4	2	no	—
309	Q₈	#41×C₆₁	1	2	yes	complemented
310	D₄	—	2	2	no	—
311	D₄	—	2	1	no	—
312	D₄	—	2	1	no	—
313	D₄	—	2	1	no	—
314	D₄	—	2	1	no	—
315	D₄	—	4	2	no	—
316	D₄	—	4	2	no	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
335	C₂×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
336	C₂×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
337	C₂×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
338	C₂×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	1	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	4	1	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	4	1	no	—
354	C₂²	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
355	C₂²	C₂²×D₄×C₆₁	1	1	yes	characteristic
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	4	1	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	C₂×#41×C₆₁	1	1	yes	characteristic
367	C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
368	C₂	—	2	2	no	—
369	C₂	—	4	1	no	—
370	C₂	—	8	1	no	—
371	C₂	—	8	1	no	—
372	C₂	C₆₁×#546	1	1	yes	characteristic
373	C₂	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
374	C₂	C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×D₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#548	C₂	semidirect
2. C₆₁×#547	C₂	semidirect
3. C₆₁×#489	C₂	semidirect
4. C₆₁×#484	C₂	semidirect
5. C₆₁×#480	C₂	semidirect
6. C₆₁×#477	C₂	semidirect
7. C₆₁×#468	C₂	semidirect
8. C₆₁×#466	C₂	semidirect
9. C₆₁×#463	C₂	semidirect
10. C₆₁×#449	C₂	semidirect
11. C₆₁×#448	C₂	semidirect
12. C₆₁×#440	C₂	semidirect
13. C₆₁×#435	C₂	semidirect
14. C₆₁×#417	C₂	semidirect
15. C₂×#103×C₆₁	C₂	semidirect
121. Q₈×C₆₁	#41	semidirect
180. #3308	C₆₁	direct (N × H)
188. #548	C₂×C₆₁	semidirect
189. #547	C₂×C₆₁	semidirect
190. #489	C₂×C₆₁	semidirect
191. #484	C₂×C₆₁	semidirect
192. #480	C₂×C₆₁	semidirect
193. #477	C₂×C₆₁	semidirect
194. #468	C₂×C₆₁	semidirect
195. #466	C₂×C₆₁	semidirect
196. #463	C₂×C₆₁	semidirect
197. #449	C₂×C₆₁	semidirect
198. #448	C₂×C₆₁	semidirect
199. #440	C₂×C₆₁	semidirect
200. #435	C₂×C₆₁	semidirect
201. #417	C₂×C₆₁	semidirect
202. C₂×#103	C₂×C₆₁	semidirect
203. C₆₁	#3308	direct (N × H)
309. Q₈	#41×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#548	2
C₆₁×#547	2
C₆₁×#489	2
C₆₁×#484	2
C₆₁×#480	2
C₆₁×#477	2
C₆₁×#468	2
C₆₁×#466	2
C₆₁×#463	2
C₆₁×#449	2
C₆₁×#448	2
C₆₁×#440	2
C₆₁×#435	2
C₆₁×#417	2
C₂×#103×C₆₁	2
#3308	61

Subgroups — C61×#3308 #21443349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#3308 #21443349