Subgroups — C₆₁×#21313 #29524746

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#423	C₂	1	1	yes	maximal, characteristic
3	C₄×#117×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1988	C₂	1	4	yes	maximal, complemented
5	C₆₁×#1987	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1736	C₂	1	4	yes	maximal
7	C₂³×Q₈×C₆₁	—	2	1	no	—
8	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
10	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₆₁	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₆₁	C₄	1	8	yes	complemented
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×#117×C₆₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#423	—	2	4	no	—
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
22	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
23	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
24	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
25	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
26	C₆₁×#376	—	2	1	no	—
27	C₄³×C₆₁	—	2	1	no	—
28	C₆₁×#340	C₂²	1	16	yes	—
29	C₂²×Q₈×C₆₁	—	2	8	no	—
30	C₂²×Q₈×C₆₁	—	2	2	no	—
31	C₂²×Q₈×C₆₁	—	2	2	no	—
32	C₂²×Q₈×C₆₁	—	4	8	no	—
33	C₂³×C₄×C₆₁	—	2	2	no	—
34	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₆₁	—	2	4	no	—
38	C₂×M₁₆×C₆₁	—	2	8	no	—
39	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₆₁	—	2	8	no	—
41	C₄⋊Q₈×C₆₁	—	2	8	no	—
42	C₄⋊Q₈×C₆₁	—	2	4	no	—
43	C₄⋊Q₈×C₆₁	—	2	4	no	—
44	C₄⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
45	C₄⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
46	#117×C₆₁	—	2	4	no	—
47	#117×C₆₁	Q₈	1	8	yes	complemented
48	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
49	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
55	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
57	C₂×C₄²×C₆₁	—	2	2	no	—
58	C₂×C₄²×C₆₁	—	2	2	no	—
59	C₂×C₄²×C₆₁	—	2	2	no	—
60	C₂×C₄²×C₆₁	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₁	D₄	1	4	yes	—
64	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₆₁	—	2	4	no	—
67	C₄⋊C₈×C₆₁	—	2	4	no	—
68	#95×C₆₁	—	2	2	no	—
69	#95×C₆₁	—	2	2	no	—
70	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
71	C₂×Q₈×C₆₁	—	2	8	no	—
72	C₂×Q₈×C₆₁	—	2	8	no	—
73	C₂×Q₈×C₆₁	—	4	8	no	—
74	C₂×Q₈×C₆₁	—	4	32	no	—
75	C₂×Q₈×C₆₁	—	4	8	no	—
76	C₂²×C₄×C₆₁	—	2	4	no	—
77	C₂²×C₄×C₆₁	—	2	4	no	—
78	C₂²×C₄×C₆₁	—	2	8	no	—
79	C₂²×C₄×C₆₁	—	2	4	no	—
80	C₂²×C₄×C₆₁	—	2	4	no	—
81	C₂²×C₄×C₆₁	—	4	8	no	—
82	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
83	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
84	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
92	C₂²×C₄×C₆₁	#41	1	4	yes	—
93	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
94	M₁₆×C₆₁	—	4	8	no	—
95	C₂×C₈×C₆₁	—	2	4	no	—
96	C₂×C₈×C₆₁	—	2	8	no	—
97	C₄⋊C₄×C₆₁	—	2	8	no	—
98	C₄⋊C₄×C₆₁	—	2	8	no	—
99	C₄⋊C₄×C₆₁	—	2	8	no	—
100	C₄⋊C₄×C₆₁	—	2	4	no	—
101	C₄⋊C₄×C₆₁	—	2	4	no	—
102	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
103	C₄⋊C₄×C₆₁	C₂×Q₈	1	8	yes	complemented
104	C₂²⋊C₄×C₆₁	—	2	8	no	—
105	C₄²×C₆₁	—	2	8	no	—
106	C₄²×C₆₁	—	4	4	no	—
107	C₄²×C₆₁	—	4	4	no	—
108	C₄²×C₆₁	C₂²⋊C₄	1	4	yes	—
109	C₄²×C₆₁	C₂²⋊C₄	1	4	yes	—
110	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
111	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
112	C₄²×C₆₁	C₂×D₄	1	2	yes	—
113	C₄²×C₆₁	C₂×D₄	1	2	yes	—
114	C₂³×C₆₁	—	2	2	no	—
115	C₂³×C₆₁	—	2	2	no	—
116	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
117	C₂³×C₆₁	C₂²⋊Q₈	1	4	yes	—
118	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
119	Q₈×C₆₁	—	4	16	no	—
120	Q₈×C₆₁	—	4	16	no	—
121	C₂×C₄×C₆₁	—	2	2	no	—
122	C₂×C₄×C₆₁	—	2	2	no	—
123	C₂×C₄×C₆₁	—	2	8	no	—
124	C₂×C₄×C₆₁	—	2	8	no	—
125	C₂×C₄×C₆₁	—	2	8	no	—
126	C₂×C₄×C₆₁	—	2	8	no	—
127	C₂×C₄×C₆₁	—	4	16	no	—
128	C₂×C₄×C₆₁	—	4	4	no	—
129	C₂×C₄×C₆₁	—	4	8	no	—
130	C₂×C₄×C₆₁	—	4	4	no	—
131	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
132	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
133	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
135	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
136	C₂×C₄×C₆₁	C₄×Q₈	1	8	yes	—
137	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
138	C₂×C₄×C₆₁	#124	1	4	yes	—
139	C₂×C₄×C₆₁	C₄⋊Q₈	1	4	yes	—
140	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
141	C₂×C₄×C₆₁	#137	1	4	yes	—
142	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
143	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
144	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
145	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
146	C₈×C₆₁	—	4	4	no	—
147	#21313	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂²×C₆₁	—	2	8	no	—
149	C₂²×C₆₁	—	2	2	no	—
150	C₂²×C₆₁	—	2	2	no	—
151	C₂²×C₆₁	#391	1	4	yes	—
152	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	2	yes	—
154	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
155	C₂²×C₆₁	C₂×#137	1	2	yes	—
156	C₄×C₆₁	—	2	2	no	—
157	C₄×C₆₁	—	2	2	no	—
158	C₄×C₆₁	—	4	8	no	—
159	C₄×C₆₁	—	4	8	no	—
160	C₄×C₆₁	#391	1	4	yes	—
161	C₄×C₆₁	#418	1	4	yes	—
162	C₄×C₆₁	#419	1	4	yes	—
163	C₄×C₆₁	C₂×C₄×Q₈	1	2	yes	—
164	C₄×C₆₁	C₂×#124	1	1	yes	characteristic
165	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
166	C₂²×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic
167	C₂×#423	C₂×C₆₁	1	1	yes	characteristic
168	C₄×#117	C₂×C₆₁	1	1	yes	characteristic
169	#1988	C₂×C₆₁	1	4	yes	complemented
170	#1987	C₂×C₆₁	1	4	yes	complemented
171	#1736	C₂×C₆₁	1	4	yes	—
172	C₂×C₆₁	—	2	4	no	—
173	C₂×C₆₁	C₂×#391	1	1	yes	characteristic
174	C₂×C₆₁	C₂×#418	1	1	yes	characteristic
175	C₂×C₆₁	C₂×#419	1	1	yes	characteristic
176	C₂×C₆₁	#3079	1	4	yes	—
177	C₂³×Q₈	—	2	1	no	—
178	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
179	C₂×C₄⋊Q₈	—	2	1	no	—
180	C₂×C₄⋊Q₈	—	2	1	no	—
181	C₂×C₄⋊Q₈	—	2	4	no	—
182	C₂×C₄⋊Q₈	C₄×C₆₁	1	8	yes	complemented
183	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
184	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
185	C₂×#117	C₂²×C₆₁	1	2	yes	—
186	C₂²×C₄⋊C₄	—	2	1	no	—
187	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
188	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
189	#423	—	2	4	no	—
190	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
191	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
192	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
193	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
194	C₄×C₂²⋊C₄	—	2	1	no	—
195	C₄×C₂²⋊C₄	—	2	1	no	—
196	#376	—	2	1	no	—
197	C₄³	—	2	1	no	—
198	#340	C₂²×C₆₁	1	16	yes	—
199	C₆₁	#21313	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²×Q₈	—	2	8	no	—
201	C₂²×Q₈	—	2	2	no	—
202	C₂²×Q₈	—	2	2	no	—
203	C₂²×Q₈	—	4	8	no	—
204	C₂³×C₄	—	2	2	no	—
205	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
206	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
207	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
208	C₂×M₁₆	—	2	4	no	—
209	C₂×M₁₆	—	2	8	no	—
210	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
211	C₄⋊Q₈	—	2	8	no	—
212	C₄⋊Q₈	—	2	8	no	—
213	C₄⋊Q₈	—	2	4	no	—
214	C₄⋊Q₈	—	2	4	no	—
215	C₄⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
216	C₄⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
217	#117	—	2	4	no	—
218	#117	Q₈×C₆₁	1	8	yes	complemented
219	C₂×C₄⋊C₄	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	4	no	—
224	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
226	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	—	2	2	no	—
230	C₂×C₄²	—	2	2	no	—
231	C₂×C₄²	C₂×C₄×C₆₁	1	4	yes	—
232	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₆₁	1	4	yes	—
235	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
236	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
237	C₄⋊C₈	—	2	4	no	—
238	C₄⋊C₈	—	2	4	no	—
239	#95	—	2	2	no	—
240	#95	—	2	2	no	—
241	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
242	C₂×Q₈	—	2	8	no	—
243	C₂×Q₈	—	2	8	no	—
244	C₂×Q₈	—	4	8	no	—
245	C₂×Q₈	—	4	32	no	—
246	C₂×Q₈	—	4	8	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	8	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	8	no	—
253	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
254	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
255	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
256	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
259	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
260	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
261	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
262	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
263	C₂²×C₄	#41×C₆₁	1	4	yes	—
264	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
265	M₁₆	—	4	8	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	2	8	no	—
268	C₄⋊C₄	—	2	8	no	—
269	C₄⋊C₄	—	2	8	no	—
270	C₄⋊C₄	—	2	8	no	—
271	C₄⋊C₄	—	2	4	no	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
274	C₄⋊C₄	C₂×Q₈×C₆₁	1	8	yes	complemented
275	C₂²⋊C₄	—	2	8	no	—
276	C₄²	—	2	8	no	—
277	C₄²	—	4	4	no	—
278	C₄²	—	4	4	no	—
279	C₄²	C₂²⋊C₄×C₆₁	1	4	yes	—
280	C₄²	C₂²⋊C₄×C₆₁	1	4	yes	—
281	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
282	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
283	C₄²	C₂×D₄×C₆₁	1	2	yes	—
284	C₄²	C₂×D₄×C₆₁	1	2	yes	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	2	no	—
287	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
288	C₂³	C₂²⋊Q₈×C₆₁	1	4	yes	—
289	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
290	Q₈	—	4	16	no	—
291	Q₈	—	4	16	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	4	16	no	—
299	C₂×C₄	—	4	4	no	—
300	C₂×C₄	—	4	8	no	—
301	C₂×C₄	—	4	4	no	—
302	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
304	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
305	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
306	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
307	C₂×C₄	C₄×Q₈×C₆₁	1	8	yes	—
308	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
309	C₂×C₄	#124×C₆₁	1	4	yes	—
310	C₂×C₄	C₄⋊Q₈×C₆₁	1	4	yes	—
311	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
312	C₂×C₄	#137×C₆₁	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
315	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
316	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
317	C₈	—	4	4	no	—
318	C₂²	—	2	8	no	—
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	C₆₁×#391	1	4	yes	—
322	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
323	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	2	yes	—
324	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
325	C₂²	C₂×#137×C₆₁	1	2	yes	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	4	8	no	—
329	C₄	—	4	8	no	—
330	C₄	C₆₁×#391	1	4	yes	—
331	C₄	C₆₁×#418	1	4	yes	—
332	C₄	C₆₁×#419	1	4	yes	—
333	C₄	C₂×C₄×Q₈×C₆₁	1	2	yes	—
334	C₄	C₂×#124×C₆₁	1	1	yes	characteristic
335	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
336	C₂	—	2	4	no	—
337	C₂	C₂×C₆₁×#391	1	1	yes	characteristic
338	C₂	C₂×C₆₁×#418	1	1	yes	characteristic
339	C₂	C₂×C₆₁×#419	1	1	yes	characteristic
340	C₂	C₆₁×#3079	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1988	C₂	semidirect
5. C₆₁×#1987	C₂	semidirect
12. C₂×C₄⋊Q₈×C₆₁	C₄	semidirect
47. #117×C₆₁	Q₈	semidirect
103. C₄⋊C₄×C₆₁	C₂×Q₈	semidirect
147. #21313	C₆₁	direct (N × H)
169. #1988	C₂×C₆₁	semidirect
170. #1987	C₂×C₆₁	semidirect
182. C₂×C₄⋊Q₈	C₄×C₆₁	semidirect
199. C₆₁	#21313	direct (N × H)
218. #117	Q₈×C₆₁	semidirect
274. C₄⋊C₄	C₂×Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₆₁	2
C₂×C₆₁×#423	2
C₄×#117×C₆₁	2
C₆₁×#1988	2
C₆₁×#1987	2
C₆₁×#1736	2
#21313	61

Subgroups — C61×#21313 #29524746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21313 #29524746