Subgroups — C₆₁×#19980 #29523413

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3380	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3335	C₂	1	2	yes	maximal, complemented
3	C₆₁×#3283	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1675	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1671	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1670	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1643	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1635	C₂	1	2	yes	maximal, complemented
10	C₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	—	2	1	no	—
13	C₆₁×#554	C₂²	1	2	yes	—
14	C₆₁×#547	C₂²	1	2	yes	—
15	C₆₁×#500	C₂²	1	1	yes	characteristic
16	C₆₁×#499	—	2	1	no	—
17	C₆₁×#498	C₂²	1	2	yes	—
18	C₆₁×#494	C₂²	1	1	yes	characteristic
19	C₆₁×#487	C₂²	1	2	yes	—
20	C₆₁×#483	—	2	2	no	—
21	C₆₁×#481	—	2	2	no	—
22	C₆₁×#478	—	2	2	no	—
23	C₆₁×#476	C₂²	1	2	yes	—
24	C₆₁×#476	C₂²	1	2	yes	—
25	C₆₁×#475	C₂²	1	2	yes	—
26	C₆₁×#467	—	2	1	no	—
27	C₆₁×#465	—	2	2	no	—
28	C₆₁×#461	C₂²	1	2	yes	—
29	C₆₁×#452	—	2	2	no	—
30	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₆₁	—	2	1	no	—
33	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₆₁	C₂²	1	2	yes	—
35	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#106×C₆₁	—	2	2	no	—
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#334	C₂²	1	1	yes	characteristic
39	C₆₁×#333	C₂²	1	2	yes	—
40	C₆₁×#332	C₂²	1	2	yes	—
41	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
43	C₆₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₆₁	—	2	2	no	—
46	#135×C₆₁	—	4	4	no	—
47	C₂×Q₁₆×C₆₁	—	2	1	no	—
48	C₂×Q₁₆×C₆₁	—	2	1	no	—
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic
51	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	—	2	1	no	—
53	C₂²×C₈×C₆₁	—	2	2	no	—
54	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
56	#125×C₆₁	—	2	2	no	—
57	#123×C₆₁	—	4	2	no	—
58	C₂²⋊Q₈×C₆₁	—	2	2	no	—
59	C₂²⋊Q₈×C₆₁	—	2	2	no	—
60	C₂²⋊Q₈×C₆₁	—	4	2	no	—
61	#121×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₆₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	#107×C₆₁	—	2	1	no	—
69	#107×C₆₁	—	2	1	no	—
70	#107×C₆₁	D₄	1	1	yes	characteristic
71	#106×C₆₁	—	2	2	no	—
72	#106×C₆₁	—	2	2	no	—
73	#106×C₆₁	—	2	2	no	—
74	#106×C₆₁	—	2	2	no	—
75	#106×C₆₁	—	2	2	no	—
76	#106×C₆₁	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₆₁	—	2	1	no	—
78	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
81	#103×C₆₁	—	2	2	no	—
82	#103×C₆₁	—	2	2	no	—
83	#103×C₆₁	—	4	2	no	—
84	#103×C₆₁	D₄	1	1	yes	characteristic
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	D₄	1	2	yes	—
88	#102×C₆₁	D₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₆₁	—	2	1	no	—
90	C₂²⋊C₈×C₆₁	—	2	2	no	—
91	C₄×C₈×C₆₁	—	2	1	no	—
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
95	#41×C₆₁	—	4	4	no	—
96	#41×C₆₁	—	8	2	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₆₁	—	4	2	no	—
101	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	4	2	no	—
106	C₂²×C₄×C₆₁	—	4	2	no	—
107	Q₁₆×C₆₁	—	4	2	no	—
108	Q₁₆×C₆₁	—	8	1	no	—
109	SD₁₆×C₆₁	—	2	2	no	—
110	SD₁₆×C₆₁	—	4	4	no	—
111	D₈×C₆₁	SD₁₆	1	4	yes	complemented
112	C₂×C₈×C₆₁	—	2	1	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	2	1	no	—
116	C₂×C₈×C₆₁	—	4	2	no	—
117	C₂×C₈×C₆₁	—	4	4	no	—
118	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₆₁	—	2	1	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	4	2	no	—
128	C₄⋊C₄×C₆₁	—	4	2	no	—
129	C₄⋊C₄×C₆₁	—	4	2	no	—
130	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₆₁	—	2	2	no	—
134	C₂²⋊C₄×C₆₁	—	2	1	no	—
135	C₂²⋊C₄×C₆₁	—	4	2	no	—
136	C₂²⋊C₄×C₆₁	—	4	2	no	—
137	C₄²×C₆₁	—	2	1	no	—
138	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
139	C₂³×C₆₁	—	2	2	no	—
140	C₂³×C₆₁	—	2	1	no	—
141	Q₈×C₆₁	—	2	1	no	—
142	Q₈×C₆₁	—	2	1	no	—
143	Q₈×C₆₁	—	4	2	no	—
144	Q₈×C₆₁	—	4	2	no	—
145	Q₈×C₆₁	—	8	2	no	—
146	D₄×C₆₁	—	2	1	no	—
147	D₄×C₆₁	—	2	2	no	—
148	D₄×C₆₁	—	2	1	no	—
149	D₄×C₆₁	—	8	4	no	—
150	D₄×C₆₁	C₂×SD₁₆	1	4	yes	—
151	C₂×C₄×C₆₁	—	2	1	no	—
152	C₂×C₄×C₆₁	—	2	1	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	4	2	no	—
157	C₂×C₄×C₆₁	—	4	1	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	8	4	no	—
162	C₂×C₄×C₆₁	—	16	2	no	—
163	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
166	C₈×C₆₁	—	2	1	no	—
167	C₈×C₆₁	—	2	1	no	—
168	C₈×C₆₁	—	4	1	no	—
169	C₈×C₆₁	—	4	1	no	—
170	C₈×C₆₁	—	4	2	no	—
171	C₈×C₆₁	—	4	1	no	—
172	C₈×C₆₁	C₂×SD₁₆	1	2	yes	—
173	C₈×C₆₁	#135	1	2	yes	complemented
174	#19980	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₆₁	—	2	4	no	—
176	C₂²×C₆₁	—	4	2	no	—
177	C₂²×C₆₁	—	4	2	no	—
178	C₂²×C₆₁	—	4	1	no	—
179	C₂²×C₆₁	—	4	1	no	—
180	C₂²×C₆₁	—	4	1	no	—
181	C₂²×C₆₁	D₄²	1	1	yes	characteristic
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	4	1	no	—
184	C₄×C₆₁	—	4	2	no	—
185	C₄×C₆₁	—	4	1	no	—
186	C₄×C₆₁	—	4	1	no	—
187	C₄×C₆₁	—	8	2	no	—
188	C₄×C₆₁	—	8	2	no	—
189	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
190	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
191	C₄×C₆₁	#577	1	1	yes	characteristic
192	C₄×C₆₁	#578	1	1	yes	characteristic
193	#3380	C₂×C₆₁	1	1	yes	characteristic, complemented
194	#3335	C₂×C₆₁	1	2	yes	complemented
195	#3283	C₂×C₆₁	1	1	yes	characteristic
196	#1707	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#1675	C₂×C₆₁	1	1	yes	characteristic, complemented
198	#1671	C₂×C₆₁	1	2	yes	complemented
199	#1670	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#1643	C₂×C₆₁	1	2	yes	complemented
201	#1635	C₂×C₆₁	1	2	yes	complemented
202	C₈×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
203	C₈×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
204	C₂×C₆₁	—	4	4	no	—
205	C₂×C₆₁	—	8	1	no	—
206	C₂×C₆₁	D₄×SD₁₆	1	1	yes	characteristic
207	C₂×C₆₁	#3283	1	1	yes	characteristic
208	C₂×C₆₁	#3290	1	1	yes	characteristic
209	C₂×#135	—	2	1	no	—
210	#554	C₂²×C₆₁	1	2	yes	—
211	#547	C₂²×C₆₁	1	2	yes	—
212	#500	C₂²×C₆₁	1	1	yes	characteristic
213	#499	—	2	1	no	—
214	#498	C₂²×C₆₁	1	2	yes	—
215	#494	C₂²×C₆₁	1	1	yes	characteristic
216	#487	C₂²×C₆₁	1	2	yes	—
217	#483	—	2	2	no	—
218	#481	—	2	2	no	—
219	#478	—	2	2	no	—
220	#476	C₂²×C₆₁	1	2	yes	—
221	#476	C₂²×C₆₁	1	2	yes	—
222	#475	C₂²×C₆₁	1	2	yes	—
223	#467	—	2	1	no	—
224	#465	—	2	2	no	—
225	#461	C₂²×C₆₁	1	2	yes	—
226	#452	—	2	2	no	—
227	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
228	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
229	C₄×D₈	—	2	1	no	—
230	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
231	C₈×D₄	C₂²×C₆₁	1	2	yes	—
232	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×#106	—	2	2	no	—
234	#335	C₂²×C₆₁	1	1	yes	characteristic
235	#334	C₂²×C₆₁	1	1	yes	characteristic
236	#333	C₂²×C₆₁	1	2	yes	—
237	#332	C₂²×C₆₁	1	2	yes	—
238	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
239	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
240	D₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
241	C₈²	C₂²×C₆₁	1	1	yes	characteristic
242	C₆₁	#19980	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×#41	—	2	2	no	—
244	#135	—	4	4	no	—
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	—	2	1	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic
249	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
253	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
254	#125	—	2	2	no	—
255	#123	—	4	2	no	—
256	C₂²⋊Q₈	—	2	2	no	—
257	C₂²⋊Q₈	—	2	2	no	—
258	C₂²⋊Q₈	—	4	2	no	—
259	#121	—	2	2	no	—
260	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
263	C₄×D₄	C₂³×C₆₁	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	#107	—	2	1	no	—
267	#107	—	2	1	no	—
268	#107	D₄×C₆₁	1	1	yes	characteristic
269	#106	—	2	2	no	—
270	#106	—	2	2	no	—
271	#106	—	2	2	no	—
272	#106	—	2	2	no	—
273	#106	—	2	2	no	—
274	#106	D₄×C₆₁	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
277	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
278	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#103	—	4	2	no	—
282	#103	D₄×C₆₁	1	1	yes	characteristic
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	D₄×C₆₁	1	2	yes	—
286	#102	D₄×C₆₁	1	1	yes	characteristic
287	C₂²⋊C₈	—	2	1	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
293	#41	—	4	4	no	—
294	#41	—	8	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
300	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	2	no	—
305	Q₁₆	—	4	2	no	—
306	Q₁₆	—	8	1	no	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	4	4	no	—
309	D₈	SD₁₆×C₆₁	1	4	yes	complemented
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
317	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
318	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
319	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
329	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
330	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
331	C₂²⋊C₄	—	2	2	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₄²	—	2	1	no	—
336	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	1	no	—
339	Q₈	—	2	1	no	—
340	Q₈	—	2	1	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	8	2	no	—
344	D₄	—	2	1	no	—
345	D₄	—	2	2	no	—
346	D₄	—	2	1	no	—
347	D₄	—	8	4	no	—
348	D₄	C₂×SD₁₆×C₆₁	1	4	yes	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	—	16	2	no	—
361	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
363	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	4	1	no	—
367	C₈	—	4	1	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	1	no	—
370	C₈	C₂×SD₁₆×C₆₁	1	2	yes	—
371	C₈	#135×C₆₁	1	2	yes	complemented
372	C₂²	—	2	4	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	D₄²×C₆₁	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
387	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
388	C₄	C₆₁×#577	1	1	yes	characteristic
389	C₄	C₆₁×#578	1	1	yes	characteristic
390	C₂	—	4	4	no	—
391	C₂	—	8	1	no	—
392	C₂	D₄×SD₁₆×C₆₁	1	1	yes	characteristic
393	C₂	C₆₁×#3283	1	1	yes	characteristic
394	C₂	C₆₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3283	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3380	C₂	semidirect
2. C₆₁×#3335	C₂	semidirect
4. C₆₁×#1707	C₂	semidirect
5. C₆₁×#1675	C₂	semidirect
6. C₆₁×#1671	C₂	semidirect
7. C₆₁×#1670	C₂	semidirect
8. C₆₁×#1643	C₂	semidirect
9. C₆₁×#1635	C₂	semidirect
10. C₈×SD₁₆×C₆₁	C₂	semidirect
11. C₈×D₈×C₆₁	C₂	semidirect
111. D₈×C₆₁	SD₁₆	semidirect
173. C₈×C₆₁	#135	semidirect
174. #19980	C₆₁	direct (N × H)
193. #3380	C₂×C₆₁	semidirect
194. #3335	C₂×C₆₁	semidirect
196. #1707	C₂×C₆₁	semidirect
197. #1675	C₂×C₆₁	semidirect
198. #1671	C₂×C₆₁	semidirect
199. #1670	C₂×C₆₁	semidirect
200. #1643	C₂×C₆₁	semidirect
201. #1635	C₂×C₆₁	semidirect
202. C₈×SD₁₆	C₂×C₆₁	semidirect
203. C₈×D₈	C₂×C₆₁	semidirect
242. C₆₁	#19980	direct (N × H)
309. D₈	SD₁₆×C₆₁	semidirect
371. C₈	#135×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3380	2
C₆₁×#3335	2
C₆₁×#3283	2
C₆₁×#1707	2
C₆₁×#1675	2
C₆₁×#1671	2
C₆₁×#1670	2
C₆₁×#1643	2
C₆₁×#1635	2
C₈×SD₁₆×C₆₁	2
C₈×D₈×C₆₁	2
#19980	61

Subgroups — C61×#19980 #29523413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19980 #29523413