Subgroups — C₆₁×#23719 #29527152

Order 15616.

808 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2923	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2090	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2079	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2063	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2051	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2018	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#100×C₆₁	C₂	1	2	yes	maximal, complemented
12	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
16	C₆₁×#442	—	2	2	no	—
17	C₆₁×#442	—	2	2	no	—
18	C₆₁×#442	—	2	2	no	—
19	C₆₁×#440	—	2	2	no	—
20	C₄×SD₁₆×C₆₁	—	2	2	no	—
21	C₄×D₈×C₆₁	—	2	2	no	—
22	C₆₁×#433	—	2	2	no	—
23	C₆₁×#432	—	2	2	no	—
24	C₂×#108×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#428	C₂²	1	2	yes	—
26	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#424	C₂²	1	1	yes	characteristic
28	C₆₁×#424	C₂²	1	1	yes	characteristic
29	C₆₁×#418	C₂²	1	2	yes	—
30	C₆₁×#417	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	2	yes	—
32	C₂×#100×C₆₁	C₂²	1	2	yes	—
33	C₂×#100×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#408	C₂²	1	1	yes	characteristic
35	C₆₁×#408	C₂²	1	1	yes	characteristic
36	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
38	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#343	C₂²	1	2	yes	—
40	C₆₁×#343	C₂²	1	2	yes	—
41	C₆₁×#341	C₂²	1	1	yes	characteristic
42	C₆₁×#341	C₂²	1	1	yes	characteristic
43	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₆₁	—	2	2	no	—
46	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
47	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
48	C₂×SD₁₆×C₆₁	—	2	2	no	—
49	C₂×D₈×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	—	2	4	no	—
51	C₂×D₈×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
53	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₆₁	D₄	1	2	yes	—
59	C₄×D₄×C₆₁	—	2	2	no	—
60	C₄×D₄×C₆₁	—	2	2	no	—
61	C₄×D₄×C₆₁	—	2	2	no	—
62	C₄×D₄×C₆₁	—	2	2	no	—
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	D₄	1	2	yes	—
65	#117×C₆₁	—	2	1	no	—
66	#117×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×C₄²×C₆₁	—	2	1	no	—
70	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
71	#108×C₆₁	—	2	4	no	—
72	#107×C₆₁	—	2	2	no	—
73	#106×C₆₁	—	2	2	no	—
74	#106×C₆₁	—	2	2	no	—
75	C₄⋊C₈×C₆₁	—	2	2	no	—
76	C₄⋊C₈×C₆₁	—	2	2	no	—
77	#103×C₆₁	—	2	2	no	—
78	#102×C₆₁	—	2	2	no	—
79	#102×C₆₁	—	2	4	no	—
80	#102×C₆₁	—	2	2	no	—
81	#102×C₆₁	—	2	2	no	—
82	#100×C₆₁	—	2	4	no	—
83	#100×C₆₁	—	2	4	no	—
84	C₂²⋊C₈×C₆₁	—	2	2	no	—
85	C₂²⋊C₈×C₆₁	—	2	2	no	—
86	#97×C₆₁	—	2	1	no	—
87	#97×C₆₁	—	2	2	no	—
88	#97×C₆₁	D₄	1	2	yes	—
89	#97×C₆₁	D₄	1	2	yes	—
90	C₄×C₈×C₆₁	—	2	1	no	—
91	C₄×C₈×C₆₁	—	2	2	no	—
92	C₂⁴×C₆₁	—	2	2	no	—
93	#41×C₆₁	—	2	2	no	—
94	#41×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂×D₄×C₆₁	—	2	1	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	2	no	—
102	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₆₁	#41	1	4	yes	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	4	2	no	—
108	C₂²×C₄×C₆₁	—	4	2	no	—
109	C₂²×C₄×C₆₁	—	8	4	no	—
110	C₂²×C₄×C₆₁	#41	1	2	yes	—
111	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
112	SD₁₆×C₆₁	—	2	8	no	—
113	D₈×C₆₁	—	2	8	no	—
114	D₈×C₆₁	—	2	8	no	—
115	M₁₆×C₆₁	—	2	2	no	—
116	M₁₆×C₆₁	—	2	2	no	—
117	M₁₆×C₆₁	—	2	2	no	—
118	M₁₆×C₆₁	—	2	2	no	—
119	M₁₆×C₆₁	—	2	2	no	—
120	M₁₆×C₆₁	#41	1	4	yes	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	—	2	2	no	—
123	C₂×C₈×C₆₁	—	2	2	no	—
124	C₂×C₈×C₆₁	—	2	1	no	—
125	C₂×C₈×C₆₁	—	2	1	no	—
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₆₁	—	2	1	no	—
134	C₂²⋊C₄×C₆₁	—	2	2	no	—
135	C₂²⋊C₄×C₆₁	—	4	2	no	—
136	C₂²⋊C₄×C₆₁	—	4	2	no	—
137	C₄²×C₆₁	—	2	2	no	—
138	C₄²×C₆₁	—	2	1	no	—
139	C₄²×C₆₁	C₂×D₄	1	2	yes	—
140	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₂³×C₆₁	—	2	1	no	—
143	C₂³×C₆₁	—	2	4	no	—
144	C₂³×C₆₁	—	4	2	no	—
145	C₂³×C₆₁	—	4	2	no	—
146	C₂³×C₆₁	—	8	2	no	—
147	C₂³×C₆₁	—	8	2	no	—
148	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
149	Q₈×C₆₁	—	2	2	no	—
150	D₄×C₆₁	—	2	4	no	—
151	D₄×C₆₁	—	2	2	no	—
152	D₄×C₆₁	—	2	4	no	—
153	D₄×C₆₁	—	4	2	no	—
154	D₄×C₆₁	—	4	2	no	—
155	D₄×C₆₁	—	4	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	1	no	—
160	C₂×C₄×C₆₁	—	4	1	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	8	2	no	—
163	C₂×C₄×C₆₁	—	8	4	no	—
164	C₂×C₄×C₆₁	—	8	4	no	—
165	C₂×C₄×C₆₁	—	8	2	no	—
166	C₂×C₄×C₆₁	#121	1	2	yes	—
167	C₂×C₄×C₆₁	#121	1	2	yes	—
168	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
171	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
172	C₈×C₆₁	—	2	2	no	—
173	C₈×C₆₁	—	2	4	no	—
174	C₈×C₆₁	—	2	2	no	—
175	C₈×C₆₁	—	4	1	no	—
176	C₈×C₆₁	—	4	2	no	—
177	C₈×C₆₁	—	4	1	no	—
178	#23719	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₆₁	—	2	2	no	—
180	C₂²×C₆₁	—	4	1	no	—
181	C₂²×C₆₁	—	4	4	no	—
182	C₂²×C₆₁	—	4	2	no	—
183	C₂²×C₆₁	—	8	4	no	—
184	C₂²×C₆₁	—	8	4	no	—
185	C₂²×C₆₁	—	8	2	no	—
186	C₂²×C₆₁	—	8	2	no	—
187	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
188	C₂²×C₆₁	#529	1	2	yes	—
189	C₄×C₆₁	—	2	2	no	—
190	C₄×C₆₁	—	2	2	no	—
191	C₄×C₆₁	—	4	1	no	—
192	C₄×C₆₁	—	4	2	no	—
193	C₄×C₆₁	—	8	2	no	—
194	C₄×C₆₁	#525	1	1	yes	characteristic
195	C₄×C₆₁	#525	1	2	yes	—
196	C₄×C₆₁	#532	1	1	yes	characteristic
197	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	2	yes	complemented
198	C₂×#442	C₂×C₆₁	1	1	yes	characteristic, complemented
199	#2923	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#2090	C₂×C₆₁	1	1	yes	characteristic, complemented
201	#2079	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#2063	C₂×C₆₁	1	2	yes	complemented
203	#2051	C₂×C₆₁	1	2	yes	complemented
204	#2045	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#2018	C₂×C₆₁	1	1	yes	characteristic
206	#1778	C₂×C₆₁	1	1	yes	characteristic, complemented
207	C₄×#100	C₂×C₆₁	1	2	yes	complemented
208	C₂×C₆₁	—	2	2	no	—
209	C₂×C₆₁	—	8	1	no	—
210	C₂×C₆₁	—	8	4	no	—
211	C₂×C₆₁	#2392	1	1	yes	characteristic
212	C₂×C₆₁	#3068	1	2	yes	—
213	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
214	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
215	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
217	#442	—	2	2	no	—
218	#442	—	2	2	no	—
219	#442	—	2	2	no	—
220	#440	—	2	2	no	—
221	C₄×SD₁₆	—	2	2	no	—
222	C₄×D₈	—	2	2	no	—
223	#433	—	2	2	no	—
224	#432	—	2	2	no	—
225	C₂×#108	C₂²×C₆₁	1	2	yes	—
226	#428	C₂²×C₆₁	1	2	yes	—
227	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
228	#424	C₂²×C₆₁	1	1	yes	characteristic
229	#424	C₂²×C₆₁	1	1	yes	characteristic
230	#418	C₂²×C₆₁	1	2	yes	—
231	#417	C₂²×C₆₁	1	2	yes	—
232	C₂×#102	C₂²×C₆₁	1	2	yes	—
233	C₂×#100	C₂²×C₆₁	1	2	yes	—
234	C₂×#100	C₂²×C₆₁	1	2	yes	—
235	#408	C₂²×C₆₁	1	1	yes	characteristic
236	#408	C₂²×C₆₁	1	1	yes	characteristic
237	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
238	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
239	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
240	#343	C₂²×C₆₁	1	2	yes	—
241	#343	C₂²×C₆₁	1	2	yes	—
242	#341	C₂²×C₆₁	1	1	yes	characteristic
243	#341	C₂²×C₆₁	1	1	yes	characteristic
244	C₆₁	#23719	1	1	yes	characteristic, direct product factor, Sylow
245	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
246	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
247	C₂³×C₄	—	2	2	no	—
248	AGL(1,ℤ/8)	—	2	4	no	—
249	AGL(1,ℤ/8)	—	2	4	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
255	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
256	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
257	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
260	C₄×Q₈	D₄×C₆₁	1	2	yes	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	C₄×D₄	—	2	2	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	D₄×C₆₁	1	2	yes	—
267	#117	—	2	1	no	—
268	#117	C₂³×C₆₁	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
273	#108	—	2	4	no	—
274	#107	—	2	2	no	—
275	#106	—	2	2	no	—
276	#106	—	2	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	#103	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	4	no	—
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#100	—	2	4	no	—
285	#100	—	2	4	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	#97	—	2	1	no	—
289	#97	—	2	2	no	—
290	#97	D₄×C₆₁	1	2	yes	—
291	#97	D₄×C₆₁	1	2	yes	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	2	no	—
294	C₂⁴	—	2	2	no	—
295	#41	—	2	2	no	—
296	#41	—	2	2	no	—
297	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
305	C₂×D₄	#41×C₆₁	1	4	yes	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	8	4	no	—
312	C₂²×C₄	#41×C₆₁	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
314	SD₁₆	—	2	8	no	—
315	D₈	—	2	8	no	—
316	D₈	—	2	8	no	—
317	M₁₆	—	2	2	no	—
318	M₁₆	—	2	2	no	—
319	M₁₆	—	2	2	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	#41×C₆₁	1	4	yes	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
335	C₂²⋊C₄	—	2	1	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	C₂×D₄×C₆₁	1	2	yes	—
342	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	2	4	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	2	no	—
350	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	D₄	—	2	4	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	4	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	8	4	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	#121×C₆₁	1	2	yes	—
369	C₂×C₄	#121×C₆₁	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
373	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₈	—	2	4	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	—	4	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	8	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
389	C₂²	C₆₁×#529	1	2	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	8	2	no	—
395	C₄	C₆₁×#525	1	1	yes	characteristic
396	C₄	C₆₁×#525	1	2	yes	—
397	C₄	C₆₁×#532	1	1	yes	characteristic
398	C₂	—	2	2	no	—
399	C₂	—	8	1	no	—
400	C₂	—	8	4	no	—
401	C₂	C₆₁×#2392	1	1	yes	characteristic
402	C₂	C₆₁×#3068	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₆₁×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
2. C₂×C₆₁×#442	C₂	semidirect
3. C₆₁×#2923	C₂	semidirect
4. C₆₁×#2090	C₂	semidirect
5. C₆₁×#2079	C₂	semidirect
6. C₆₁×#2063	C₂	semidirect
7. C₆₁×#2051	C₂	semidirect
8. C₆₁×#2045	C₂	semidirect
10. C₆₁×#1778	C₂	semidirect
11. C₄×#100×C₆₁	C₂	semidirect
178. #23719	C₆₁	direct (N × H)
197. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
198. C₂×#442	C₂×C₆₁	semidirect
199. #2923	C₂×C₆₁	semidirect
200. #2090	C₂×C₆₁	semidirect
201. #2079	C₂×C₆₁	semidirect
202. #2063	C₂×C₆₁	semidirect
203. #2051	C₂×C₆₁	semidirect
204. #2045	C₂×C₆₁	semidirect
206. #1778	C₂×C₆₁	semidirect
207. C₄×#100	C₂×C₆₁	semidirect
244. C₆₁	#23719	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×AGL(1,ℤ/8)×C₆₁	2
C₂×C₆₁×#442	2
C₆₁×#2923	2
C₆₁×#2090	2
C₆₁×#2079	2
C₆₁×#2063	2
C₆₁×#2051	2
C₆₁×#2045	2
C₆₁×#2018	2
C₆₁×#1778	2
C₄×#100×C₆₁	2
#23719	61

Subgroups — C61×#23719 #29527152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23719 #29527152