Subgroups — C₆₁×#21394 #29524827

Order 15616.

1238 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1988	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1981	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1872	C₂	1	4	yes	maximal
7	C₆₁×#1763	C₂	1	4	yes	maximal, complemented
8	C₆₁×#533	—	2	4	no	—
9	C₆₁×#533	C₄	1	8	yes	complemented
10	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×#125×C₆₁	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×#117×C₆₁	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₁	—	2	1	no	—
20	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#432	—	2	4	no	—
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	8	yes	—
24	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#97×C₆₁	C₂²	1	2	yes	—
26	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
27	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
28	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
30	C₂×#95×C₆₁	—	2	1	no	—
31	C₆₁×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₆₁	—	2	1	no	—
33	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
34	C₂³×C₄×C₆₁	—	2	2	no	—
35	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
39	C₄⋊Q₈×C₆₁	—	2	2	no	—
40	C₄⋊Q₈×C₆₁	—	2	2	no	—
41	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
42	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
43	#125×C₆₁	—	2	8	no	—
44	C₂²⋊Q₈×C₆₁	—	2	8	no	—
45	C₂²⋊Q₈×C₆₁	—	2	4	no	—
46	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
47	C₄×Q₈×C₆₁	—	2	8	no	—
48	C₄×Q₈×C₆₁	—	2	4	no	—
49	C₄×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
50	#117×C₆₁	—	2	8	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
58	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
60	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄²×C₆₁	—	2	2	no	—
62	C₂×C₄²×C₆₁	—	2	2	no	—
63	C₂×C₄²×C₆₁	—	2	2	no	—
64	C₂×C₄²×C₆₁	—	4	4	no	—
65	C₂×C₄²×C₆₁	C₂×C₄	1	4	yes	—
66	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₆₁	D₄	1	4	yes	—
69	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₆₁	—	2	4	no	—
72	#103×C₆₁	—	2	16	no	—
73	C₂²⋊C₈×C₆₁	—	2	4	no	—
74	#97×C₆₁	—	2	4	no	—
75	#95×C₆₁	—	2	2	no	—
76	#95×C₆₁	—	2	2	no	—
77	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₆₁	—	2	4	no	—
79	C₂×Q₈×C₆₁	—	2	2	no	—
80	C₂×Q₈×C₆₁	—	2	8	no	—
81	C₂×Q₈×C₆₁	—	4	2	no	—
82	C₂×Q₈×C₆₁	—	4	2	no	—
83	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₆₁	—	2	4	no	—
85	C₂²×C₄×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	—	2	2	no	—
87	C₂²×C₄×C₆₁	—	2	4	no	—
88	C₂²×C₄×C₆₁	—	2	8	no	—
89	C₂²×C₄×C₆₁	—	2	4	no	—
90	C₂²×C₄×C₆₁	—	2	2	no	—
91	C₂²×C₄×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	4	4	no	—
93	C₂²×C₄×C₆₁	—	4	4	no	—
94	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₆₁	—	2	4	no	—
105	C₂×C₈×C₆₁	—	2	8	no	—
106	C₄⋊C₄×C₆₁	—	2	8	no	—
107	C₄⋊C₄×C₆₁	—	2	4	no	—
108	C₄⋊C₄×C₆₁	—	2	4	no	—
109	C₄⋊C₄×C₆₁	—	2	4	no	—
110	C₄⋊C₄×C₆₁	—	2	8	no	—
111	C₄⋊C₄×C₆₁	—	2	8	no	—
112	C₄⋊C₄×C₆₁	—	2	2	no	—
113	C₄⋊C₄×C₆₁	—	2	4	no	—
114	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
115	C₄⋊C₄×C₆₁	#41	1	8	yes	—
116	C₂²⋊C₄×C₆₁	—	2	8	no	—
117	C₄²×C₆₁	—	2	8	no	—
118	C₄²×C₆₁	—	4	4	no	—
119	C₄²×C₆₁	—	4	4	no	—
120	C₄²×C₆₁	C₂²⋊C₄	1	4	yes	—
121	C₄²×C₆₁	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
123	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
124	C₄²×C₆₁	C₂×D₄	1	2	yes	—
125	C₄²×C₆₁	C₂×D₄	1	2	yes	—
126	C₂³×C₆₁	—	2	2	no	—
127	C₂³×C₆₁	—	2	1	no	—
128	C₂³×C₆₁	—	2	1	no	—
129	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂³×C₆₁	#137	1	4	yes	—
131	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₆₁	—	2	8	no	—
133	Q₈×C₆₁	—	4	4	no	—
134	Q₈×C₆₁	—	4	8	no	—
135	C₂×C₄×C₆₁	—	2	2	no	—
136	C₂×C₄×C₆₁	—	2	1	no	—
137	C₂×C₄×C₆₁	—	2	2	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	1	no	—
140	C₂×C₄×C₆₁	—	2	8	no	—
141	C₂×C₄×C₆₁	—	2	4	no	—
142	C₂×C₄×C₆₁	—	2	4	no	—
143	C₂×C₄×C₆₁	—	2	8	no	—
144	C₂×C₄×C₆₁	—	2	4	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	—	2	8	no	—
147	C₂×C₄×C₆₁	—	4	16	no	—
148	C₂×C₄×C₆₁	—	4	4	no	—
149	C₂×C₄×C₆₁	—	4	4	no	—
150	C₂×C₄×C₆₁	—	4	2	no	—
151	C₂×C₄×C₆₁	—	4	4	no	—
152	C₂×C₄×C₆₁	—	4	2	no	—
153	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
154	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₆₁	#137	1	2	yes	—
160	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
163	C₈×C₆₁	—	4	4	no	—
164	#21394	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₆₁	—	2	4	no	—
166	C₂²×C₆₁	—	2	4	no	—
167	C₂²×C₆₁	—	2	2	no	—
168	C₂²×C₆₁	—	2	2	no	—
169	C₂²×C₆₁	#419	1	4	yes	—
170	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₂²×C₆₁	#525	1	2	yes	—
172	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂²×C₆₁	C₂×#137	1	2	yes	—
174	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
175	C₄×C₆₁	—	2	2	no	—
176	C₄×C₆₁	—	2	2	no	—
177	C₄×C₆₁	—	2	2	no	—
178	C₄×C₆₁	—	2	2	no	—
179	C₄×C₆₁	—	4	8	no	—
180	C₄×C₆₁	—	4	4	no	—
181	C₄×C₆₁	—	4	4	no	—
182	C₄×C₆₁	#417	1	4	yes	—
183	C₄×C₆₁	C₄×#41	1	2	yes	—
184	C₄×C₆₁	#532	1	2	yes	—
185	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
186	C₂×#432	C₂×C₆₁	1	1	yes	characteristic
187	C₂×C₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
188	#1988	C₂×C₆₁	1	2	yes	complemented
189	#1981	C₂×C₆₁	1	2	yes	complemented
190	#1872	C₂×C₆₁	1	4	yes	—
191	#1763	C₂×C₆₁	1	4	yes	complemented
192	C₂×C₆₁	—	2	4	no	—
193	C₂×C₆₁	#2297	1	1	yes	characteristic
194	C₂×C₆₁	C₂×#419	1	1	yes	characteristic
195	C₂×C₆₁	C₂×#417	1	1	yes	characteristic
196	C₂×C₆₁	#3110	1	2	yes	—
197	C₂×C₆₁	#3113	1	2	yes	—
198	#533	—	2	4	no	—
199	#533	C₄×C₆₁	1	8	yes	complemented
200	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
201	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
202	C₂×#125	—	2	1	no	—
203	C₂×C₂²⋊Q₈	—	2	1	no	—
204	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
205	C₂×C₄×Q₈	—	2	1	no	—
206	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
207	C₂×#117	—	2	1	no	—
208	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
209	C₂²×C₄²	—	2	1	no	—
210	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
211	#432	—	2	4	no	—
212	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
213	C₂×#103	C₂²×C₆₁	1	8	yes	—
214	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
215	C₂×#97	C₂²×C₆₁	1	2	yes	—
216	C₄×C₄⋊C₄	—	2	1	no	—
217	C₄×C₄⋊C₄	—	2	1	no	—
218	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
219	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
220	C₂×#95	—	2	1	no	—
221	#340	C₂²×C₆₁	1	8	yes	—
222	C₆₁	#21394	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
225	C₂³×C₄	—	2	2	no	—
226	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
227	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
228	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	—	2	2	no	—
232	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
233	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
234	#125	—	2	8	no	—
235	C₂²⋊Q₈	—	2	8	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
238	C₄×Q₈	—	2	8	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
241	#117	—	2	8	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	8	no	—
249	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	4	4	no	—
256	C₂×C₄²	C₂×C₄×C₆₁	1	4	yes	—
257	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₆₁	1	4	yes	—
260	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
262	C₄⋊C₈	—	2	4	no	—
263	#103	—	2	16	no	—
264	C₂²⋊C₈	—	2	4	no	—
265	#97	—	2	4	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	8	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	4	no	—
284	C₂²×C₄	—	4	4	no	—
285	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
286	C₂²×C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
293	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
294	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	8	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	2	8	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
306	C₄⋊C₄	#41×C₆₁	1	8	yes	—
307	C₂²⋊C₄	—	2	8	no	—
308	C₄²	—	2	8	no	—
309	C₄²	—	4	4	no	—
310	C₄²	—	4	4	no	—
311	C₄²	C₂²⋊C₄×C₆₁	1	4	yes	—
312	C₄²	C₂²⋊C₄×C₆₁	1	4	yes	—
313	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
314	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
315	C₄²	C₂×D₄×C₆₁	1	2	yes	—
316	C₄²	C₂×D₄×C₆₁	1	2	yes	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	2	no	—
320	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
321	C₂³	#137×C₆₁	1	4	yes	—
322	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
323	Q₈	—	2	8	no	—
324	Q₈	—	4	4	no	—
325	Q₈	—	4	8	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	4	16	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
347	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
348	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
349	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
350	C₂×C₄	#137×C₆₁	1	2	yes	—
351	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
353	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
354	C₈	—	4	4	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	2	no	—
359	C₂²	C₆₁×#419	1	4	yes	—
360	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
361	C₂²	C₆₁×#525	1	2	yes	—
362	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
363	C₂²	C₂×#137×C₆₁	1	2	yes	—
364	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	4	no	—
370	C₄	—	4	8	no	—
371	C₄	—	4	4	no	—
372	C₄	C₆₁×#417	1	4	yes	—
373	C₄	C₄×#41×C₆₁	1	2	yes	—
374	C₄	C₆₁×#532	1	2	yes	—
375	C₂	—	2	4	no	—
376	C₂	C₆₁×#2297	1	1	yes	characteristic
377	C₂	C₂×C₆₁×#419	1	1	yes	characteristic
378	C₂	C₂×C₆₁×#417	1	1	yes	characteristic
379	C₂	C₆₁×#3110	1	2	yes	—
380	C₂	C₆₁×#3113	1	2	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×#1981	C₂	semidirect
7. C₆₁×#1763	C₂	semidirect
9. C₆₁×#533	C₄	semidirect
41. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
42. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
49. C₄×Q₈×C₆₁	C₂×C₄	semidirect
164. #21394	C₆₁	direct (N × H)
188. #1988	C₂×C₆₁	semidirect
189. #1981	C₂×C₆₁	semidirect
191. #1763	C₂×C₆₁	semidirect
199. #533	C₄×C₆₁	semidirect
222. C₆₁	#21394	direct (N × H)
232. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
233. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
240. C₄×Q₈	C₂×C₄×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×#533	2
C₂×C₆₁×#432	2
C₂×C₄×C₄⋊C₄×C₆₁	2
C₆₁×#1988	2
C₆₁×#1981	2
C₆₁×#1872	2
C₆₁×#1763	2
#21394	61

Subgroups — C61×#21394 #29524827

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21394 #29524827