Subgroups — C₆₁×#17880 #29521313

Order 15616.

626 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2983	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2982	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1587	C₂	1	4	yes	maximal, complemented
5	C₆₁×#1584	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1564	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1479	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1479	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1452	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₆₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#446	—	2	2	no	—
14	C₆₁×#446	C₂²	1	4	yes	—
15	C₈×Q₈×C₆₁	—	2	2	no	—
16	C₈×Q₈×C₆₁	C₂²	1	4	yes	—
17	C₄×Q₁₆×C₆₁	C₄	1	2	yes	—
18	C₄×Q₁₆×C₆₁	C₄	1	2	yes	—
19	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
20	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#432	—	2	2	no	—
22	C₆₁×#431	—	2	2	no	—
23	C₆₁×#431	C₂²	1	1	yes	characteristic
24	C₆₁×#431	C₂²	1	1	yes	characteristic
25	C₆₁×#431	C₂²	1	1	yes	characteristic
26	C₆₁×#431	C₂²	1	1	yes	characteristic
27	C₂×#107×C₆₁	C₄	1	1	yes	characteristic
28	C₂×#103×C₆₁	C₄	1	1	yes	characteristic
29	C₂×#103×C₆₁	C₄	1	1	yes	characteristic
30	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#335	C₂²	1	2	yes	—
32	C₆₁×#334	C₂²	1	2	yes	—
33	C₆₁×Q₈⋊C₈	C₂²	1	4	yes	—
34	C₆₁×Q₈⋊C₈	C₂²	1	4	yes	—
35	C₆₁×#322	C₂²	1	2	yes	—
36	C₆₁×#322	C₂²	1	2	yes	—
37	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂×Q₁₆×C₆₁	—	2	4	no	—
40	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
41	C₂×Q₁₆×C₆₁	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₄×Q₈×C₆₁	—	2	1	no	—
45	C₄×Q₈×C₆₁	—	2	1	no	—
46	C₄×Q₈×C₆₁	—	2	1	no	—
47	C₄×Q₈×C₆₁	—	2	1	no	—
48	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
49	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
50	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
51	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₁	—	2	1	no	—
57	C₂×C₄²×C₆₁	—	2	1	no	—
58	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
59	#107×C₆₁	C₂×C₄	1	2	yes	—
60	#107×C₆₁	C₂×C₄	1	2	yes	—
61	C₄⋊C₈×C₆₁	—	2	4	no	—
62	C₄⋊C₈×C₆₁	—	2	4	no	—
63	C₄⋊C₈×C₆₁	—	2	1	no	—
64	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
65	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
66	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
67	#103×C₆₁	C₂×C₄	1	2	yes	—
68	#103×C₆₁	C₂×C₄	1	2	yes	—
69	#103×C₆₁	C₂×C₄	1	2	yes	—
70	#103×C₆₁	C₂×C₄	1	2	yes	—
71	C₂²⋊C₈×C₆₁	—	2	1	no	—
72	C₂²⋊C₈×C₆₁	—	2	1	no	—
73	C₂²⋊C₈×C₆₁	—	2	1	no	—
74	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
75	#97×C₆₁	—	2	4	no	—
76	C₄×C₈×C₆₁	—	2	4	no	—
77	C₄×C₈×C₆₁	—	2	1	no	—
78	C₄×C₈×C₆₁	—	2	1	no	—
79	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₆₁	C₂³	1	2	yes	—
82	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₆₁	C₂³	1	2	yes	—
85	C₂×Q₈×C₆₁	—	2	1	no	—
86	C₂×Q₈×C₆₁	—	2	1	no	—
87	C₂×Q₈×C₆₁	—	2	2	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	M₁₆	1	4	yes	—
91	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
92	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₆₁	—	2	1	no	—
94	C₂²×C₄×C₆₁	—	2	1	no	—
95	C₂²×C₄×C₆₁	—	2	1	no	—
96	C₂²×C₄×C₆₁	—	2	1	no	—
97	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
100	Q₁₆×C₆₁	—	2	4	no	—
101	Q₁₆×C₆₁	—	2	4	no	—
102	C₂×C₈×C₆₁	—	2	2	no	—
103	C₂×C₈×C₆₁	—	2	2	no	—
104	C₂×C₈×C₆₁	—	2	2	no	—
105	C₂×C₈×C₆₁	—	2	2	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
107	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
112	C₄⋊C₄×C₆₁	—	2	2	no	—
113	C₄⋊C₄×C₆₁	—	2	2	no	—
114	C₄⋊C₄×C₆₁	—	2	1	no	—
115	C₄⋊C₄×C₆₁	—	2	1	no	—
116	C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	2	2	no	—
118	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
120	C₄²×C₆₁	—	2	2	no	—
121	C₄²×C₆₁	—	2	2	no	—
122	C₄²×C₆₁	—	2	2	no	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₆₁	#41	1	1	yes	characteristic
127	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
128	C₂³×C₆₁	C₄×D₄	1	1	yes	characteristic
129	Q₈×C₆₁	—	2	2	no	—
130	Q₈×C₆₁	—	2	4	no	—
131	Q₈×C₆₁	—	2	2	no	—
132	Q₈×C₆₁	—	2	2	no	—
133	Q₈×C₆₁	—	4	2	no	—
134	Q₈×C₆₁	C₂×M₁₆	1	4	yes	—
135	C₂×C₄×C₆₁	—	2	2	no	—
136	C₂×C₄×C₆₁	—	2	4	no	—
137	C₂×C₄×C₆₁	—	2	2	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	2	no	—
140	C₂×C₄×C₆₁	—	2	2	no	—
141	C₂×C₄×C₆₁	—	4	1	no	—
142	C₂×C₄×C₆₁	—	4	2	no	—
143	C₂×C₄×C₆₁	—	8	1	no	—
144	C₂×C₄×C₆₁	—	8	1	no	—
145	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
149	C₂×C₄×C₆₁	#131	1	2	yes	—
150	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
153	C₈×C₆₁	—	2	1	no	—
154	C₈×C₆₁	—	2	1	no	—
155	C₈×C₆₁	—	2	1	no	—
156	C₈×C₆₁	—	2	1	no	—
157	C₈×C₆₁	—	2	4	no	—
158	C₈×C₆₁	—	4	2	no	—
159	C₈×C₆₁	—	4	2	no	—
160	C₈×C₆₁	—	4	2	no	—
161	#17880	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂²×C₆₁	—	2	1	no	—
163	C₂²×C₆₁	—	2	1	no	—
164	C₂²×C₆₁	#435	1	2	yes	—
165	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
166	C₄×C₆₁	—	2	4	no	—
167	C₄×C₆₁	—	2	1	no	—
168	C₄×C₆₁	—	2	1	no	—
169	C₄×C₆₁	—	2	1	no	—
170	C₄×C₆₁	—	4	2	no	—
171	C₄×C₆₁	—	4	2	no	—
172	C₄×C₆₁	—	4	2	no	—
173	C₄×C₆₁	#435	1	2	yes	—
174	C₄×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
175	C₄×C₆₁	C₂×#131	1	1	yes	characteristic
176	C₄×C₆₁	#578	1	2	yes	—
177	#2983	C₂×C₆₁	1	1	yes	characteristic
178	#2982	C₂×C₆₁	1	1	yes	characteristic
179	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic
180	#1587	C₂×C₆₁	1	4	yes	complemented
181	#1584	C₂×C₆₁	1	4	yes	complemented
182	#1564	C₂×C₆₁	1	1	yes	characteristic
183	#1479	C₂×C₆₁	1	1	yes	characteristic
184	#1479	C₂×C₆₁	1	1	yes	characteristic
185	#1452	C₂×C₆₁	1	1	yes	characteristic
186	C₂×C₆₁	—	2	2	no	—
187	C₂×C₆₁	C₂×#435	1	1	yes	characteristic
188	C₂×C₆₁	#2950	1	1	yes	characteristic
189	C₂×C₆₁	#2957	1	1	yes	characteristic
190	C₂²×Q₁₆	C₄×C₆₁	1	1	yes	characteristic
191	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
192	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
193	#446	—	2	2	no	—
194	#446	C₂²×C₆₁	1	4	yes	—
195	C₈×Q₈	—	2	2	no	—
196	C₈×Q₈	C₂²×C₆₁	1	4	yes	—
197	C₄×Q₁₆	C₄×C₆₁	1	2	yes	—
198	C₄×Q₁₆	C₄×C₆₁	1	2	yes	—
199	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
200	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
201	#432	—	2	2	no	—
202	#431	—	2	2	no	—
203	#431	C₂²×C₆₁	1	1	yes	characteristic
204	#431	C₂²×C₆₁	1	1	yes	characteristic
205	#431	C₂²×C₆₁	1	1	yes	characteristic
206	#431	C₂²×C₆₁	1	1	yes	characteristic
207	C₂×#107	C₄×C₆₁	1	1	yes	characteristic
208	C₂×#103	C₄×C₆₁	1	1	yes	characteristic
209	C₂×#103	C₄×C₆₁	1	1	yes	characteristic
210	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
211	#335	C₂²×C₆₁	1	2	yes	—
212	#334	C₂²×C₆₁	1	2	yes	—
213	Q₈⋊C₈	C₂²×C₆₁	1	4	yes	—
214	Q₈⋊C₈	C₂²×C₆₁	1	4	yes	—
215	#322	C₂²×C₆₁	1	2	yes	—
216	#322	C₂²×C₆₁	1	2	yes	—
217	C₆₁	#17880	1	1	yes	characteristic, direct product factor, Sylow
218	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
219	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
220	C₂×Q₁₆	—	2	4	no	—
221	C₂×Q₁₆	C₂×C₄×C₆₁	1	2	yes	—
222	C₂×Q₁₆	C₂×C₄×C₆₁	1	2	yes	—
223	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
224	C₂²×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
225	C₄×Q₈	—	2	1	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	2	1	no	—
229	C₄×Q₈	C₂×C₄×C₆₁	1	2	yes	—
230	C₄×Q₈	C₂×C₄×C₆₁	1	2	yes	—
231	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
232	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
236	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	—	2	1	no	—
239	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
240	#107	C₂×C₄×C₆₁	1	2	yes	—
241	#107	C₂×C₄×C₆₁	1	2	yes	—
242	C₄⋊C₈	—	2	4	no	—
243	C₄⋊C₈	—	2	4	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
246	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
247	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
248	#103	C₂×C₄×C₆₁	1	2	yes	—
249	#103	C₂×C₄×C₆₁	1	2	yes	—
250	#103	C₂×C₄×C₆₁	1	2	yes	—
251	#103	C₂×C₄×C₆₁	1	2	yes	—
252	C₂²⋊C₈	—	2	1	no	—
253	C₂²⋊C₈	—	2	1	no	—
254	C₂²⋊C₈	—	2	1	no	—
255	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
256	#97	—	2	4	no	—
257	C₄×C₈	—	2	4	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	—	2	1	no	—
260	C₄×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
261	C₄×C₈	C₂×C₄×C₆₁	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₆₁	1	2	yes	—
263	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₆₁	1	2	yes	—
266	C₂×Q₈	—	2	1	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	M₁₆×C₆₁	1	4	yes	—
272	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
273	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
280	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
281	Q₁₆	—	2	4	no	—
282	Q₁₆	—	2	4	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	C₂²×C₄×C₆₁	1	1	yes	characteristic
289	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
290	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
291	C₂×C₈	C₂²×C₄×C₆₁	1	1	yes	characteristic
292	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	1	no	—
296	C₄⋊C₄	—	2	1	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
300	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
306	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
307	C₄²	#41×C₆₁	1	1	yes	characteristic
308	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
309	C₂³	C₄×D₄×C₆₁	1	1	yes	characteristic
310	Q₈	—	2	2	no	—
311	Q₈	—	2	4	no	—
312	Q₈	—	2	2	no	—
313	Q₈	—	2	2	no	—
314	Q₈	—	4	2	no	—
315	Q₈	C₂×M₁₆×C₆₁	1	4	yes	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	8	1	no	—
325	C₂×C₄	—	8	1	no	—
326	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
327	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
328	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
329	C₂×C₄	C₂×M₁₆×C₆₁	1	2	yes	—
330	C₂×C₄	#131×C₆₁	1	2	yes	—
331	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
334	C₈	—	2	1	no	—
335	C₈	—	2	1	no	—
336	C₈	—	2	1	no	—
337	C₈	—	2	1	no	—
338	C₈	—	2	4	no	—
339	C₈	—	4	2	no	—
340	C₈	—	4	2	no	—
341	C₈	—	4	2	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	C₆₁×#435	1	2	yes	—
345	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
346	C₄	—	2	4	no	—
347	C₄	—	2	1	no	—
348	C₄	—	2	1	no	—
349	C₄	—	2	1	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	2	no	—
353	C₄	C₆₁×#435	1	2	yes	—
354	C₄	C₂²×M₁₆×C₆₁	1	1	yes	characteristic
355	C₄	C₂×#131×C₆₁	1	1	yes	characteristic
356	C₄	C₆₁×#578	1	2	yes	—
357	C₂	—	2	2	no	—
358	C₂	C₂×C₆₁×#435	1	1	yes	characteristic
359	C₂	C₆₁×#2950	1	1	yes	characteristic
360	C₂	C₆₁×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₄²	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂×C₄×D₄
prime radical	C₂³×C₆₁	C₄×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₆₁×#431 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1587	C₂	semidirect
5. C₆₁×#1584	C₂	semidirect
161. #17880	C₆₁	direct (N × H)
180. #1587	C₂×C₆₁	semidirect
181. #1584	C₂×C₆₁	semidirect
217. C₆₁	#17880	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#2983	2
C₆₁×#2982	2
C₂×C₄×Q₁₆×C₆₁	2
C₆₁×#1587	2
C₆₁×#1584	2
C₆₁×#1564	2
C₆₁×#1479	2
C₆₁×#1452	2
#17880	61

Subgroups — C61×#17880 #29521313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#17880 #29521313