Subgroups — C₆₁×#23806 #29527239

Order 15616.

1174 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#442	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×#440	C₂	1	2	yes	maximal, complemented
3	C₄×#127×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#124×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2093	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2092	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2014	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2012	C₂	1	2	yes	maximal, complemented
10	C₆₁×#2011	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
14	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₆₁	—	2	2	no	—
18	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#442	—	2	8	no	—
21	C₆₁×#440	—	2	8	no	—
22	C₂×#107×C₆₁	C₂²	1	2	yes	—
23	C₂×#106×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	2	yes	—
26	C₂×#102×C₆₁	C₂²	1	2	yes	—
27	C₂×#102×C₆₁	C₂²	1	2	yes	—
28	C₂×#97×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#391	C₂²	1	1	yes	characteristic
30	C₆₁×#390	—	2	2	no	—
31	C₆₁×#390	C₂²	1	1	yes	characteristic
32	C₆₁×#390	C₂²	1	2	yes	—
33	C₆₁×#388	—	2	2	no	—
34	C₆₁×#384	C₂²	1	1	yes	characteristic
35	C₆₁×#382	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₆₁	—	2	2	no	—
37	C₄³×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#336	C₂²	1	1	yes	characteristic
39	C₆₁×#336	C₂²	1	2	yes	—
40	C₆₁×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₆₁	—	2	2	no	—
43	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	1	no	—
46	C₂³×C₄×C₆₁	—	2	2	no	—
47	C₂×SD₁₆×C₆₁	—	2	4	no	—
48	C₂×SD₁₆×C₆₁	—	2	4	no	—
49	C₂×SD₁₆×C₆₁	—	2	4	no	—
50	C₂×D₈×C₆₁	—	2	4	no	—
51	C₂×D₈×C₆₁	—	2	4	no	—
52	C₂×D₈×C₆₁	—	2	4	no	—
53	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
55	#127×C₆₁	—	2	4	no	—
56	#124×C₆₁	—	2	2	no	—
57	#124×C₆₁	—	2	2	no	—
58	C₄×Q₈×C₆₁	—	2	4	no	—
59	C₄×D₄×C₆₁	—	2	4	no	—
60	C₄×D₄×C₆₁	—	2	4	no	—
61	C₄×D₄×C₆₁	—	2	4	no	—
62	C₄×D₄×C₆₁	—	4	8	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
73	C₂×C₄²×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	D₄	1	2	yes	—
75	C₂×C₄²×C₆₁	D₄	1	2	yes	—
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
79	#107×C₆₁	—	2	4	no	—
80	#106×C₆₁	—	2	4	no	—
81	#103×C₆₁	—	2	4	no	—
82	#102×C₆₁	—	2	4	no	—
83	#102×C₆₁	—	2	4	no	—
84	#102×C₆₁	—	2	4	no	—
85	#97×C₆₁	D₄	1	8	yes	complemented
86	#95×C₆₁	—	2	2	no	—
87	#95×C₆₁	—	2	2	no	—
88	C₂⁴×C₆₁	—	2	1	no	—
89	C₂⁴×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	1	no	—
91	C₂×Q₈×C₆₁	—	2	2	no	—
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	#41	1	2	yes	—
94	C₂×D₄×C₆₁	—	2	8	no	—
95	C₂×D₄×C₆₁	—	2	2	no	—
96	C₂×D₄×C₆₁	—	2	2	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	1	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	4	4	no	—
104	C₂×D₄×C₆₁	—	4	4	no	—
105	C₂×D₄×C₆₁	#41	1	2	yes	—
106	C₂×D₄×C₆₁	#41	1	4	yes	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	4	8	no	—
112	C₂²×C₄×C₆₁	—	4	4	no	—
113	C₂²×C₄×C₆₁	—	4	2	no	—
114	C₂²×C₄×C₆₁	—	4	4	no	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
120	SD₁₆×C₆₁	—	2	16	no	—
121	D₈×C₆₁	—	2	16	no	—
122	C₂×C₈×C₆₁	—	2	2	no	—
123	C₂×C₈×C₆₁	—	2	2	no	—
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	4	2	no	—
133	C₄⋊C₄×C₆₁	—	4	4	no	—
134	C₂²⋊C₄×C₆₁	—	2	8	no	—
135	C₂²⋊C₄×C₆₁	—	4	8	no	—
136	C₂²⋊C₄×C₆₁	—	4	4	no	—
137	C₂²⋊C₄×C₆₁	—	4	2	no	—
138	C₂²⋊C₄×C₆₁	—	4	4	no	—
139	C₄²×C₆₁	—	2	4	no	—
140	C₄²×C₆₁	—	2	1	no	—
141	C₄²×C₆₁	—	2	1	no	—
142	C₄²×C₆₁	—	2	2	no	—
143	C₄²×C₆₁	—	4	2	no	—
144	C₄²×C₆₁	—	4	2	no	—
145	C₄²×C₆₁	C₂×D₄	1	4	yes	—
146	C₂³×C₆₁	—	2	2	no	—
147	C₂³×C₆₁	—	2	4	no	—
148	C₂³×C₆₁	—	4	1	no	—
149	C₂³×C₆₁	—	4	2	no	—
150	C₂³×C₆₁	—	4	2	no	—
151	C₂³×C₆₁	—	4	1	no	—
152	C₂³×C₆₁	—	4	4	no	—
153	C₂³×C₆₁	—	4	2	no	—
154	C₂³×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	—	4	4	no	—
156	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₆₁	—	2	4	no	—
158	Q₈×C₆₁	—	4	2	no	—
159	D₄×C₆₁	—	2	4	no	—
160	D₄×C₆₁	—	2	4	no	—
161	D₄×C₆₁	—	2	4	no	—
162	D₄×C₆₁	—	4	16	no	—
163	D₄×C₆₁	—	4	2	no	—
164	D₄×C₆₁	—	4	2	no	—
165	D₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	2	2	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	4	1	no	—
175	C₂×C₄×C₆₁	—	4	1	no	—
176	C₂×C₄×C₆₁	—	4	1	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	4	1	no	—
179	C₂×C₄×C₆₁	—	4	4	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	8	8	no	—
183	C₂×C₄×C₆₁	—	8	4	no	—
184	C₂×C₄×C₆₁	#127	1	2	yes	—
185	C₂×C₄×C₆₁	#127	1	2	yes	—
186	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
187	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
191	C₈×C₆₁	—	2	4	no	—
192	C₈×C₆₁	—	2	4	no	—
193	#23806	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₆₁	—	4	8	no	—
195	C₂²×C₆₁	—	4	4	no	—
196	C₂²×C₆₁	—	4	2	no	—
197	C₂²×C₆₁	—	4	4	no	—
198	C₂²×C₆₁	—	8	2	no	—
199	C₂²×C₆₁	—	8	4	no	—
200	C₂²×C₆₁	—	8	2	no	—
201	C₂²×C₆₁	—	8	1	no	—
202	C₂²×C₆₁	—	8	1	no	—
203	C₂²×C₆₁	—	8	2	no	—
204	C₂²×C₆₁	#525	1	1	yes	characteristic
205	C₂²×C₆₁	#525	1	1	yes	characteristic
206	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
207	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
208	C₂²×C₆₁	#575	1	2	yes	—
209	C₄×C₆₁	—	2	4	no	—
210	C₄×C₆₁	—	2	2	no	—
211	C₄×C₆₁	—	2	2	no	—
212	C₄×C₆₁	—	4	2	no	—
213	C₄×C₆₁	—	4	2	no	—
214	C₄×C₆₁	—	8	1	no	—
215	C₄×C₆₁	—	8	2	no	—
216	C₄×C₆₁	—	8	1	no	—
217	C₄×C₆₁	#525	1	2	yes	—
218	C₄×C₆₁	#525	1	2	yes	—
219	C₂×#442	C₂×C₆₁	1	2	yes	complemented
220	C₂×#440	C₂×C₆₁	1	2	yes	complemented
221	C₄×#127	C₂×C₆₁	1	1	yes	characteristic, complemented
222	C₄×#124	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#2096	C₂×C₆₁	1	1	yes	characteristic, complemented
224	#2093	C₂×C₆₁	1	1	yes	characteristic, complemented
225	#2092	C₂×C₆₁	1	2	yes	complemented
226	#2014	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#2012	C₂×C₆₁	1	2	yes	complemented
228	#2011	C₂×C₆₁	1	1	yes	characteristic
229	#1745	C₂×C₆₁	1	1	yes	characteristic, complemented
230	C₂×C₆₁	—	8	4	no	—
231	C₂×C₆₁	—	8	2	no	—
232	C₂×C₆₁	#2397	1	1	yes	characteristic
233	C₂×C₆₁	#3114	1	2	yes	—
234	C₂×C₆₁	#3115	1	2	yes	—
235	C₂×C₆₁	#3151	1	1	yes	characteristic
236	C₂×C₆₁	#3153	1	1	yes	characteristic
237	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
238	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
239	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
240	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
241	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
242	C₂×C₄×D₄	—	2	2	no	—
243	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
245	#442	—	2	8	no	—
246	#440	—	2	8	no	—
247	C₂×#107	C₂²×C₆₁	1	2	yes	—
248	C₂×#106	C₂²×C₆₁	1	2	yes	—
249	C₂×#103	C₂²×C₆₁	1	2	yes	—
250	C₂×#102	C₂²×C₆₁	1	2	yes	—
251	C₂×#102	C₂²×C₆₁	1	2	yes	—
252	C₂×#102	C₂²×C₆₁	1	2	yes	—
253	C₂×#97	C₂²×C₆₁	1	2	yes	—
254	#391	C₂²×C₆₁	1	1	yes	characteristic
255	#390	—	2	2	no	—
256	#390	C₂²×C₆₁	1	2	yes	—
257	#390	C₂²×C₆₁	1	1	yes	characteristic
258	#388	—	2	2	no	—
259	#384	C₂²×C₆₁	1	1	yes	characteristic
260	#382	C₂²×C₆₁	1	1	yes	characteristic
261	C₄×C₂²⋊C₄	—	2	2	no	—
262	C₄³	C₂²×C₆₁	1	1	yes	characteristic
263	#336	C₂²×C₆₁	1	2	yes	—
264	#336	C₂²×C₆₁	1	1	yes	characteristic
265	#336	C₂²×C₆₁	1	1	yes	characteristic
266	C₆₁	#23806	1	1	yes	characteristic, direct product factor, Sylow
267	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	—	2	1	no	—
273	C₂×SD₁₆	—	2	4	no	—
274	C₂×SD₁₆	—	2	4	no	—
275	C₂×SD₁₆	—	2	4	no	—
276	C₂×D₈	—	2	4	no	—
277	C₂×D₈	—	2	4	no	—
278	C₂×D₈	—	2	4	no	—
279	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
280	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
281	#127	—	2	4	no	—
282	#124	—	2	2	no	—
283	#124	—	2	2	no	—
284	C₄×Q₈	—	2	4	no	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	4	8	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	4	no	—
296	C₂×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	D₄×C₆₁	1	2	yes	—
301	C₂×C₄²	D₄×C₆₁	1	2	yes	—
302	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
303	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
304	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
305	#107	—	2	4	no	—
306	#106	—	2	4	no	—
307	#103	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	#97	D₄×C₆₁	1	8	yes	complemented
312	#95	—	2	2	no	—
313	#95	—	2	2	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	—	2	2	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	#41×C₆₁	1	2	yes	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	#41×C₆₁	1	2	yes	—
332	C₂×D₄	#41×C₆₁	1	4	yes	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	4	8	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
345	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
346	SD₁₆	—	2	16	no	—
347	D₈	—	2	16	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
353	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	4	8	no	—
362	C₂²⋊C₄	—	4	4	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	4	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	—	4	2	no	—
371	C₄²	C₂×D₄×C₆₁	1	4	yes	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	1	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	Q₈	—	4	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	4	16	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	—	8	4	no	—
410	C₂×C₄	#127×C₆₁	1	2	yes	—
411	C₂×C₄	#127×C₆₁	1	2	yes	—
412	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
413	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
414	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
417	C₈	—	2	4	no	—
418	C₈	—	2	4	no	—
419	C₂²	—	4	8	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₆₁×#525	1	1	yes	characteristic
430	C₂²	C₆₁×#525	1	1	yes	characteristic
431	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
432	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
433	C₂²	C₆₁×#575	1	2	yes	—
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	C₆₁×#525	1	2	yes	—
443	C₄	C₆₁×#525	1	2	yes	—
444	C₂	—	8	4	no	—
445	C₂	—	8	2	no	—
446	C₂	C₆₁×#2397	1	1	yes	characteristic
447	C₂	C₆₁×#3114	1	2	yes	—
448	C₂	C₆₁×#3115	1	2	yes	—
449	C₂	C₆₁×#3151	1	1	yes	characteristic
450	C₂	C₆₁×#3153	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2011	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#442	C₂	semidirect
2. C₂×C₆₁×#440	C₂	semidirect
3. C₄×#127×C₆₁	C₂	semidirect
4. C₄×#124×C₆₁	C₂	semidirect
5. C₆₁×#2096	C₂	semidirect
6. C₆₁×#2093	C₂	semidirect
7. C₆₁×#2092	C₂	semidirect
8. C₆₁×#2014	C₂	semidirect
9. C₆₁×#2012	C₂	semidirect
11. C₆₁×#1745	C₂	semidirect
85. #97×C₆₁	D₄	semidirect
193. #23806	C₆₁	direct (N × H)
219. C₂×#442	C₂×C₆₁	semidirect
220. C₂×#440	C₂×C₆₁	semidirect
221. C₄×#127	C₂×C₆₁	semidirect
222. C₄×#124	C₂×C₆₁	semidirect
223. #2096	C₂×C₆₁	semidirect
224. #2093	C₂×C₆₁	semidirect
225. #2092	C₂×C₆₁	semidirect
226. #2014	C₂×C₆₁	semidirect
227. #2012	C₂×C₆₁	semidirect
229. #1745	C₂×C₆₁	semidirect
266. C₆₁	#23806	direct (N × H)
311. #97	D₄×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×#442	2
C₂×C₆₁×#440	2
C₄×#127×C₆₁	2
C₄×#124×C₆₁	2
C₆₁×#2096	2
C₆₁×#2093	2
C₆₁×#2092	2
C₆₁×#2014	2
C₆₁×#2012	2
C₆₁×#2011	2
C₆₁×#1745	2
#23806	61

Subgroups — C61×#23806 #29527239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23806 #29527239