Subgroups — C₆₁×#22824 #29526257

Order 15616.

636 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2295	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#1985	C₂	1	2	yes	maximal
3	C₆₁×#1917	C₂	1	2	yes	maximal
4	C₆₁×#1916	C₂	1	2	yes	maximal
5	C₆₁×#1842	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1832	C₂	1	2	yes	maximal
7	C₆₁×#1771	C₂	1	2	yes	maximal
8	C₆₁×#1768	C₂	1	2	yes	maximal
9	C₆₁×#1767	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
13	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#97×C₆₁	C₂²	1	2	yes	—
18	C₂×#97×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#391	C₄	1	1	yes	characteristic
21	C₆₁×#391	C₄	1	1	yes	characteristic
22	C₆₁×#389	C₄	1	1	yes	characteristic
23	C₆₁×#389	C₄	1	1	yes	characteristic
24	C₆₁×#387	C₄	1	2	yes	—
25	C₆₁×#387	C₄	1	2	yes	—
26	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
28	C₆₁×#376	C₂²	1	2	yes	—
29	C₄³×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#336	C₂²	1	2	yes	—
31	C₆₁×#336	C₂²	1	2	yes	—
32	C₆₁×#336	C₂²	1	2	yes	—
33	C₆₁×#336	C₂²	1	2	yes	—
34	C₆₁×#336	C₂²	1	2	yes	—
35	C₆₁×#336	C₂²	1	2	yes	—
36	C₆₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
40	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
41	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
42	C₄×Q₈×C₆₁	—	2	2	no	—
43	C₄×Q₈×C₆₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
45	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
46	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
55	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
57	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₆₁	—	2	4	no	—
60	C₄⋊C₈×C₆₁	—	2	2	no	—
61	C₄⋊C₈×C₆₁	—	2	4	no	—
62	C₄⋊C₈×C₆₁	—	4	1	no	—
63	C₄⋊C₈×C₆₁	—	4	1	no	—
64	C₄⋊C₈×C₆₁	Q₈	1	4	yes	complemented
65	#97×C₆₁	—	2	4	no	—
66	#97×C₆₁	—	4	2	no	—
67	C₄×C₈×C₆₁	—	4	2	no	—
68	#95×C₆₁	C₂×C₄	1	2	yes	—
69	#95×C₆₁	C₂×C₄	1	2	yes	—
70	#95×C₆₁	C₂×C₄	1	2	yes	—
71	#95×C₆₁	C₂×C₄	1	2	yes	—
72	#95×C₆₁	C₂×C₄	1	2	yes	—
73	#95×C₆₁	C₂×C₄	1	2	yes	—
74	#95×C₆₁	C₂×C₄	1	2	yes	—
75	C₂×Q₈×C₆₁	—	2	2	no	—
76	C₂×Q₈×C₆₁	—	4	1	no	—
77	C₂×Q₈×C₆₁	—	4	1	no	—
78	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
89	C₂×C₈×C₆₁	—	2	2	no	—
90	C₂×C₈×C₆₁	—	2	2	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	—	2	2	no	—
96	C₂×C₈×C₆₁	—	2	2	no	—
97	C₂×C₈×C₆₁	—	2	2	no	—
98	C₂×C₈×C₆₁	—	2	2	no	—
99	C₂×C₈×C₆₁	—	2	2	no	—
100	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
101	C₄⋊C₄×C₆₁	—	2	2	no	—
102	C₄⋊C₄×C₆₁	—	2	4	no	—
103	C₄⋊C₄×C₆₁	—	2	4	no	—
104	C₄⋊C₄×C₆₁	—	4	1	no	—
105	C₄⋊C₄×C₆₁	—	4	1	no	—
106	C₄⋊C₄×C₆₁	—	4	2	no	—
107	C₄²×C₆₁	—	2	2	no	—
108	C₄²×C₆₁	—	2	2	no	—
109	C₄²×C₆₁	—	2	2	no	—
110	C₄²×C₆₁	—	2	2	no	—
111	C₄²×C₆₁	—	2	1	no	—
112	C₄²×C₆₁	—	2	1	no	—
113	C₄²×C₆₁	—	2	2	no	—
114	C₄²×C₆₁	—	4	1	no	—
115	C₄²×C₆₁	—	4	1	no	—
116	C₄²×C₆₁	—	4	1	no	—
117	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
118	C₄²×C₆₁	#41	1	2	yes	—
119	C₄²×C₆₁	#41	1	2	yes	—
120	C₄²×C₆₁	#41	1	2	yes	—
121	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
122	Q₈×C₆₁	—	4	4	no	—
123	C₂×C₄×C₆₁	—	2	1	no	—
124	C₂×C₄×C₆₁	—	2	1	no	—
125	C₂×C₄×C₆₁	—	2	1	no	—
126	C₂×C₄×C₆₁	—	2	1	no	—
127	C₂×C₄×C₆₁	—	2	1	no	—
128	C₂×C₄×C₆₁	—	2	1	no	—
129	C₂×C₄×C₆₁	—	2	1	no	—
130	C₂×C₄×C₆₁	—	2	1	no	—
131	C₂×C₄×C₆₁	—	2	1	no	—
132	C₂×C₄×C₆₁	—	2	1	no	—
133	C₂×C₄×C₆₁	—	2	2	no	—
134	C₂×C₄×C₆₁	—	2	2	no	—
135	C₂×C₄×C₆₁	—	2	2	no	—
136	C₂×C₄×C₆₁	—	2	2	no	—
137	C₂×C₄×C₆₁	—	2	1	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	2	no	—
140	C₂×C₄×C₆₁	—	2	1	no	—
141	C₂×C₄×C₆₁	—	2	1	no	—
142	C₂×C₄×C₆₁	—	2	2	no	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	2	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	#117	1	2	yes	—
149	C₂×C₄×C₆₁	#117	1	2	yes	—
150	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₆₁	#131	1	2	yes	—
153	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
159	C₈×C₆₁	—	2	4	no	—
160	C₈×C₆₁	—	4	2	no	—
161	C₈×C₆₁	—	4	2	no	—
162	C₈×C₆₁	—	4	2	no	—
163	#22824	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
165	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
166	C₂²×C₆₁	#520	1	1	yes	characteristic
167	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
168	C₂²×C₆₁	#568	1	1	yes	characteristic
169	C₂²×C₆₁	#568	1	1	yes	characteristic
170	C₂²×C₆₁	#568	1	1	yes	characteristic
171	C₄×C₆₁	—	2	2	no	—
172	C₄×C₆₁	—	2	2	no	—
173	C₄×C₆₁	—	2	2	no	—
174	C₄×C₆₁	—	2	2	no	—
175	C₄×C₆₁	—	2	2	no	—
176	C₄×C₆₁	—	4	2	no	—
177	C₄×C₆₁	—	4	2	no	—
178	C₄×C₆₁	—	4	2	no	—
179	C₄×C₆₁	—	4	1	no	—
180	C₄×C₆₁	—	4	2	no	—
181	C₄×C₆₁	#554	1	1	yes	characteristic
182	C₄×C₆₁	#556	1	1	yes	characteristic
183	C₄×C₆₁	#557	1	1	yes	characteristic
184	C₄×C₆₁	#559	1	1	yes	characteristic
185	#2295	C₂×C₆₁	1	1	yes	characteristic
186	#1985	C₂×C₆₁	1	2	yes	—
187	#1917	C₂×C₆₁	1	2	yes	—
188	#1916	C₂×C₆₁	1	2	yes	—
189	#1842	C₂×C₆₁	1	1	yes	characteristic
190	#1832	C₂×C₆₁	1	2	yes	—
191	#1771	C₂×C₆₁	1	2	yes	—
192	#1768	C₂×C₆₁	1	2	yes	—
193	#1767	C₂×C₆₁	1	1	yes	characteristic
194	C₂×C₆₁	#2355	1	1	yes	characteristic
195	C₂×C₆₁	#2921	1	1	yes	characteristic
196	C₂×C₆₁	#2925	1	1	yes	characteristic
197	C₂×C₆₁	#2961	1	1	yes	characteristic
198	C₂×C₆₁	#2962	1	1	yes	characteristic
199	C₂×C₆₁	#2992	1	1	yes	characteristic
200	C₂×C₆₁	#2995	1	1	yes	characteristic
201	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
203	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
205	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
206	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
207	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
208	C₂×#97	C₂²×C₆₁	1	2	yes	—
209	C₂×#97	C₂²×C₆₁	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
211	#391	C₄×C₆₁	1	1	yes	characteristic
212	#391	C₄×C₆₁	1	1	yes	characteristic
213	#389	C₄×C₆₁	1	1	yes	characteristic
214	#389	C₄×C₆₁	1	1	yes	characteristic
215	#387	C₄×C₆₁	1	2	yes	—
216	#387	C₄×C₆₁	1	2	yes	—
217	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
218	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
219	#376	C₂²×C₆₁	1	2	yes	—
220	C₄³	C₂²×C₆₁	1	1	yes	characteristic
221	#336	C₂²×C₆₁	1	2	yes	—
222	#336	C₂²×C₆₁	1	2	yes	—
223	#336	C₂²×C₆₁	1	2	yes	—
224	#336	C₂²×C₆₁	1	2	yes	—
225	#336	C₂²×C₆₁	1	2	yes	—
226	#336	C₂²×C₆₁	1	2	yes	—
227	#336	C₂²×C₆₁	1	2	yes	—
228	C₆₁	#22824	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
230	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
232	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
233	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
234	C₄×Q₈	—	2	2	no	—
235	C₄×Q₈	—	2	2	no	—
236	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
238	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
239	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
243	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
244	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
245	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
247	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
249	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	4	1	no	—
255	C₄⋊C₈	—	4	1	no	—
256	C₄⋊C₈	Q₈×C₆₁	1	4	yes	complemented
257	#97	—	2	4	no	—
258	#97	—	4	2	no	—
259	C₄×C₈	—	4	2	no	—
260	#95	C₂×C₄×C₆₁	1	2	yes	—
261	#95	C₂×C₄×C₆₁	1	2	yes	—
262	#95	C₂×C₄×C₆₁	1	2	yes	—
263	#95	C₂×C₄×C₆₁	1	2	yes	—
264	#95	C₂×C₄×C₆₁	1	2	yes	—
265	#95	C₂×C₄×C₆₁	1	2	yes	—
266	#95	C₂×C₄×C₆₁	1	2	yes	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	4	1	no	—
269	C₂×Q₈	—	4	1	no	—
270	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
273	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
280	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	4	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	4	1	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	4	1	no	—
309	C₄²	C₂×Q₈×C₆₁	1	2	yes	—
310	C₄²	#41×C₆₁	1	2	yes	—
311	C₄²	#41×C₆₁	1	2	yes	—
312	C₄²	#41×C₆₁	1	2	yes	—
313	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
314	Q₈	—	4	4	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	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	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	#117×C₆₁	1	2	yes	—
341	C₂×C₄	#117×C₆₁	1	2	yes	—
342	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
343	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
344	C₂×C₄	#131×C₆₁	1	2	yes	—
345	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
346	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
348	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
349	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
350	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
351	C₈	—	2	4	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	—	4	2	no	—
355	C₂²	C₂×#117×C₆₁	1	1	yes	characteristic
356	C₂²	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
357	C₂²	C₆₁×#520	1	1	yes	characteristic
358	C₂²	C₂×#131×C₆₁	1	1	yes	characteristic
359	C₂²	C₆₁×#568	1	1	yes	characteristic
360	C₂²	C₆₁×#568	1	1	yes	characteristic
361	C₂²	C₆₁×#568	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	4	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	C₆₁×#554	1	1	yes	characteristic
373	C₄	C₆₁×#556	1	1	yes	characteristic
374	C₄	C₆₁×#557	1	1	yes	characteristic
375	C₄	C₆₁×#559	1	1	yes	characteristic
376	C₂	C₆₁×#2355	1	1	yes	characteristic
377	C₂	C₆₁×#2921	1	1	yes	characteristic
378	C₂	C₆₁×#2925	1	1	yes	characteristic
379	C₂	C₆₁×#2961	1	1	yes	characteristic
380	C₂	C₆₁×#2962	1	1	yes	characteristic
381	C₂	C₆₁×#2992	1	1	yes	characteristic
382	C₂	C₆₁×#2995	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
64. C₄⋊C₈×C₆₁	Q₈	semidirect
163. #22824	C₆₁	direct (N × H)
228. C₆₁	#22824	direct (N × H)
256. C₄⋊C₈	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2295	2
C₆₁×#1985	2
C₆₁×#1917	2
C₆₁×#1916	2
C₆₁×#1842	2
C₆₁×#1832	2
C₆₁×#1771	2
C₆₁×#1768	2
C₆₁×#1767	2
#22824	61

Subgroups — C61×#22824 #29526257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22824 #29526257