Subgroups — C₆₁×#33668 #29537101

Order 15616.

552 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3168	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2235	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2232	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2229	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2211	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2185	C₂	1	1	yes	maximal, characteristic
9	C₄×Q₃₂×C₆₁	C₂	1	2	yes	maximal, complemented
10	C₄×SD₃₂×C₆₁	C₂	1	2	yes	maximal, complemented
11	C₆₁×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#529	—	2	1	no	—
14	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
15	C₂×Q₃₂×C₆₁	C₂²	1	2	yes	—
16	C₂×SD₃₂×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#499	C₂²	1	1	yes	characteristic
18	C₆₁×#495	C₂²	1	1	yes	characteristic
19	C₆₁×#488	—	2	1	no	—
20	C₆₁×#467	C₂²	1	1	yes	characteristic
21	C₆₁×#466	C₂²	1	1	yes	characteristic
22	C₆₁×#465	—	2	1	no	—
23	C₄×Q₁₆×C₆₁	—	2	1	no	—
24	C₄×Q₁₆×C₆₁	—	2	1	no	—
25	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
26	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
27	C₄×Q₁₆×C₆₁	C₂²	1	2	yes	—
28	C₄×SD₁₆×C₆₁	—	2	1	no	—
29	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	—	2	1	no	—
32	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#367	C₂²	1	2	yes	—
34	C₆₁×#366	C₂²	1	2	yes	—
35	C₆₁×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₆₁×#358	C₂²	1	2	yes	—
37	C₆₁×#358	C₂²	1	2	yes	—
38	C₆₁×#358	C₂²	1	2	yes	—
39	C₆₁×#357	C₂²	1	2	yes	—
40	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₆₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₆₁	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	—	2	1	no	—
44	C₂×Q₁₆×C₆₁	—	2	4	no	—
45	C₂×Q₁₆×C₆₁	—	2	1	no	—
46	C₂×Q₁₆×C₆₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₆₁	C₂³	1	2	yes	—
48	C₂×SD₁₆×C₆₁	—	2	1	no	—
49	C₂×D₈×C₆₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	#126×C₆₁	—	4	1	no	—
53	#125×C₆₁	—	2	1	no	—
54	#124×C₆₁	—	2	1	no	—
55	#123×C₆₁	—	4	1	no	—
56	C₂²⋊Q₈×C₆₁	—	2	1	no	—
57	#121×C₆₁	—	2	1	no	—
58	C₄×Q₈×C₆₁	—	2	1	no	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	—	4	1	no	—
62	C₄×Q₈×C₆₁	—	4	1	no	—
63	C₄×D₄×C₆₁	—	2	1	no	—
64	C₄×D₄×C₆₁	—	4	1	no	—
65	#117×C₆₁	—	4	1	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	4	1	no	—
68	C₂×C₄²×C₆₁	—	4	1	no	—
69	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
70	Q₃₂×C₆₁	—	2	4	no	—
71	SD₃₂×C₆₁	—	2	4	no	—
72	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
73	C₂×C₁₆×C₆₁	C₂³	1	2	yes	—
74	#107×C₆₁	—	2	1	no	—
75	#107×C₆₁	C₂³	1	2	yes	—
76	#107×C₆₁	C₂³	1	1	yes	characteristic
77	#107×C₆₁	C₂³	1	1	yes	characteristic
78	#106×C₆₁	—	2	1	no	—
79	#103×C₆₁	—	2	2	no	—
80	#103×C₆₁	—	2	2	no	—
81	#103×C₆₁	—	2	1	no	—
82	#103×C₆₁	—	2	1	no	—
83	#102×C₆₁	—	2	1	no	—
84	#102×C₆₁	—	2	1	no	—
85	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
86	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
87	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×Q₈×C₆₁	—	2	4	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	—	2	1	no	—
92	C₂×Q₈×C₆₁	—	4	2	no	—
93	C₂×Q₈×C₆₁	—	4	1	no	—
94	C₂×D₄×C₆₁	—	2	1	no	—
95	C₂×D₄×C₆₁	—	4	1	no	—
96	C₂²×C₄×C₆₁	—	4	1	no	—
97	C₂²×C₄×C₆₁	—	4	1	no	—
98	C₂²×C₄×C₆₁	—	4	1	no	—
99	C₂²×C₄×C₆₁	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	D₈	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
102	Q₁₆×C₆₁	—	2	4	no	—
103	Q₁₆×C₆₁	—	2	2	no	—
104	Q₁₆×C₆₁	—	2	2	no	—
105	Q₁₆×C₆₁	#41	1	4	yes	—
106	SD₁₆×C₆₁	—	4	2	no	—
107	D₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	4	1	no	—
110	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
118	C₄⋊C₄×C₆₁	—	4	2	no	—
119	C₄⋊C₄×C₆₁	—	4	2	no	—
120	C₄⋊C₄×C₆₁	—	4	1	no	—
121	C₄⋊C₄×C₆₁	—	4	1	no	—
122	C₄⋊C₄×C₆₁	—	4	1	no	—
123	C₄⋊C₄×C₆₁	—	4	1	no	—
124	C₂²⋊C₄×C₆₁	—	4	1	no	—
125	C₂²⋊C₄×C₆₁	—	4	1	no	—
126	C₂²⋊C₄×C₆₁	—	4	1	no	—
127	C₂²⋊C₄×C₆₁	—	4	1	no	—
128	C₂²⋊C₄×C₆₁	—	4	1	no	—
129	C₄²×C₆₁	—	4	2	no	—
130	C₄²×C₆₁	—	4	2	no	—
131	C₄²×C₆₁	—	4	1	no	—
132	C₄²×C₆₁	D₈	1	1	yes	characteristic
133	C₄²×C₆₁	D₈	1	1	yes	characteristic
134	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₆₁	—	2	2	no	—
137	C₁₆×C₆₁	—	2	2	no	—
138	C₂³×C₆₁	—	4	1	no	—
139	C₂³×C₆₁	C₂×D₈	1	1	yes	characteristic
140	Q₈×C₆₁	—	2	4	no	—
141	Q₈×C₆₁	—	4	4	no	—
142	Q₈×C₆₁	—	4	2	no	—
143	Q₈×C₆₁	—	4	1	no	—
144	Q₈×C₆₁	—	4	1	no	—
145	D₄×C₆₁	—	4	1	no	—
146	D₄×C₆₁	—	4	1	no	—
147	D₄×C₆₁	—	8	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	1	no	—
150	C₂×C₄×C₆₁	—	2	1	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	4	4	no	—
153	C₂×C₄×C₆₁	—	4	2	no	—
154	C₂×C₄×C₆₁	—	4	2	no	—
155	C₂×C₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	4	1	no	—
157	C₂×C₄×C₆₁	—	4	1	no	—
158	C₂×C₄×C₆₁	—	8	2	no	—
159	C₂×C₄×C₆₁	—	8	2	no	—
160	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
163	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
166	C₈×C₆₁	—	2	1	no	—
167	C₈×C₆₁	—	2	1	no	—
168	C₈×C₆₁	—	2	1	no	—
169	C₈×C₆₁	C₂×#41	1	2	yes	—
170	#33668	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₆₁	—	2	1	no	—
172	C₂²×C₆₁	—	2	1	no	—
173	C₂²×C₆₁	—	8	1	no	—
174	C₂²×C₆₁	—	8	1	no	—
175	C₂²×C₆₁	—	8	1	no	—
176	C₂²×C₆₁	#508	1	2	yes	—
177	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
178	C₄×C₆₁	—	2	1	no	—
179	C₄×C₆₁	—	2	1	no	—
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	2	1	no	—
182	C₄×C₆₁	—	4	4	no	—
183	C₄×C₆₁	—	8	1	no	—
184	C₄×C₆₁	—	8	2	no	—
185	C₄×C₆₁	—	8	1	no	—
186	C₄×C₆₁	—	8	1	no	—
187	C₄×C₆₁	#510	1	2	yes	—
188	C₄×C₆₁	#525	1	1	yes	characteristic
189	C₄×C₆₁	#575	1	1	yes	characteristic
190	#3168	C₂×C₆₁	1	1	yes	characteristic
191	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
192	#2235	C₂×C₆₁	1	1	yes	characteristic, complemented
193	#2232	C₂×C₆₁	1	1	yes	characteristic
194	#2229	C₂×C₆₁	1	2	yes	complemented
195	#2211	C₂×C₆₁	1	2	yes	complemented
196	#2188	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#2185	C₂×C₆₁	1	1	yes	characteristic
198	C₄×Q₃₂	C₂×C₆₁	1	2	yes	complemented
199	C₄×SD₃₂	C₂×C₆₁	1	2	yes	complemented
200	#2162	C₂×C₆₁	1	1	yes	characteristic, complemented
201	C₂×C₆₁	—	2	2	no	—
202	C₂×C₆₁	—	16	1	no	—
203	C₂×C₆₁	#3100	1	1	yes	characteristic
204	C₂×C₆₁	C₂×#508	1	1	yes	characteristic
205	C₂×C₆₁	C₂×#510	1	1	yes	characteristic
206	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
207	#529	—	2	1	no	—
208	C₂×C₄×Q₈	—	2	1	no	—
209	C₂×Q₃₂	C₂²×C₆₁	1	2	yes	—
210	C₂×SD₃₂	C₂²×C₆₁	1	2	yes	—
211	#499	C₂²×C₆₁	1	1	yes	characteristic
212	#495	C₂²×C₆₁	1	1	yes	characteristic
213	#488	—	2	1	no	—
214	#467	C₂²×C₆₁	1	1	yes	characteristic
215	#466	C₂²×C₆₁	1	1	yes	characteristic
216	#465	—	2	1	no	—
217	C₄×Q₁₆	—	2	1	no	—
218	C₄×Q₁₆	—	2	1	no	—
219	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
220	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
221	C₄×Q₁₆	C₂²×C₆₁	1	2	yes	—
222	C₄×SD₁₆	—	2	1	no	—
223	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
224	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
225	C₂×#103	—	2	1	no	—
226	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
227	#367	C₂²×C₆₁	1	2	yes	—
228	#366	C₂²×C₆₁	1	2	yes	—
229	C₄⋊C₁₆	C₂²×C₆₁	1	2	yes	—
230	#358	C₂²×C₆₁	1	2	yes	—
231	#358	C₂²×C₆₁	1	2	yes	—
232	#358	C₂²×C₆₁	1	2	yes	—
233	#357	C₂²×C₆₁	1	2	yes	—
234	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
235	C₂²⋊C₁₆	C₂²×C₆₁	1	1	yes	characteristic
236	C₄×C₁₆	C₂²×C₆₁	1	2	yes	—
237	C₆₁	#33668	1	1	yes	characteristic, direct product factor, Sylow
238	C₂²×Q₈	—	2	1	no	—
239	C₂×Q₁₆	—	2	4	no	—
240	C₂×Q₁₆	—	2	1	no	—
241	C₂×Q₁₆	C₂³×C₆₁	1	1	yes	characteristic
242	C₂×Q₁₆	C₂³×C₆₁	1	2	yes	—
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×D₈	C₂³×C₆₁	1	1	yes	characteristic
245	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
247	#126	—	4	1	no	—
248	#125	—	2	1	no	—
249	#124	—	2	1	no	—
250	#123	—	4	1	no	—
251	C₂²⋊Q₈	—	2	1	no	—
252	#121	—	2	1	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×Q₈	—	4	1	no	—
257	C₄×Q₈	—	4	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	4	1	no	—
260	#117	—	4	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	4	1	no	—
263	C₂×C₄²	—	4	1	no	—
264	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
265	Q₃₂	—	2	4	no	—
266	SD₃₂	—	2	4	no	—
267	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
268	C₂×C₁₆	C₂³×C₆₁	1	2	yes	—
269	#107	—	2	1	no	—
270	#107	C₂³×C₆₁	1	2	yes	—
271	#107	C₂³×C₆₁	1	1	yes	characteristic
272	#107	C₂³×C₆₁	1	1	yes	characteristic
273	#106	—	2	1	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	2	1	no	—
277	#103	—	2	1	no	—
278	#102	—	2	1	no	—
279	#102	—	2	1	no	—
280	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
281	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
282	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	D₈×C₆₁	1	1	yes	characteristic
295	C₂²×C₄	D₈×C₆₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
297	Q₁₆	—	2	4	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	2	2	no	—
300	Q₁₆	#41×C₆₁	1	4	yes	—
301	SD₁₆	—	4	2	no	—
302	D₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
308	C₂×C₈	C₂⁴×C₆₁	1	1	yes	characteristic
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	—	4	1	no	—
327	C₄²	D₈×C₆₁	1	1	yes	characteristic
328	C₄²	D₈×C₆₁	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
330	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
331	C₁₆	—	2	2	no	—
332	C₁₆	—	2	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	C₂×D₈×C₆₁	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	4	4	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	1	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
356	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
357	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
358	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
359	C₂×C₄	C₂×D₈×C₆₁	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	C₂×#41×C₆₁	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	C₆₁×#508	1	2	yes	—
371	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	4	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	C₆₁×#510	1	2	yes	—
382	C₄	C₆₁×#525	1	1	yes	characteristic
383	C₄	C₆₁×#575	1	1	yes	characteristic
384	C₂	—	2	2	no	—
385	C₂	—	16	1	no	—
386	C₂	C₆₁×#3100	1	1	yes	characteristic
387	C₂	C₂×C₆₁×#508	1	1	yes	characteristic
388	C₂	C₂×C₆₁×#510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂²×D₈
prime radical	C₆₁×#466	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ C₂×C₄×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
3. C₆₁×#2235	C₂	semidirect
5. C₆₁×#2229	C₂	semidirect
6. C₆₁×#2211	C₂	semidirect
7. C₆₁×#2188	C₂	semidirect
9. C₄×Q₃₂×C₆₁	C₂	semidirect
10. C₄×SD₃₂×C₆₁	C₂	semidirect
11. C₆₁×#2162	C₂	semidirect
170. #33668	C₆₁	direct (N × H)
191. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
192. #2235	C₂×C₆₁	semidirect
194. #2229	C₂×C₆₁	semidirect
195. #2211	C₂×C₆₁	semidirect
196. #2188	C₂×C₆₁	semidirect
198. C₄×Q₃₂	C₂×C₆₁	semidirect
199. C₄×SD₃₂	C₂×C₆₁	semidirect
200. #2162	C₂×C₆₁	semidirect
237. C₆₁	#33668	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×#3168	2
C₂×C₄×Q₁₆×C₆₁	2
C₆₁×#2235	2
C₆₁×#2232	2
C₆₁×#2229	2
C₆₁×#2211	2
C₆₁×#2188	2
C₆₁×#2185	2
C₄×Q₃₂×C₆₁	2
C₄×SD₃₂×C₆₁	2
C₆₁×#2162	2
#33668	61

Subgroups — C61×#33668 #29537101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#33668 #29537101