Subgroups — C₆₁×#19995 #29523428

Order 15616.

638 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	C₆₁×#3393	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3391	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3304	C₂	1	2	yes	maximal, complemented
4	C₆₁×#1709	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1681	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1670	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1642	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1628	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#556	C₂²	1	2	yes	—
13	C₆₁×#550	C₂²	1	2	yes	—
14	C₆₁×#495	—	2	1	no	—
15	C₆₁×#494	C₂²	1	1	yes	characteristic
16	C₆₁×#493	—	2	1	no	—
17	C₆₁×#493	C₂²	1	1	yes	characteristic
18	C₆₁×#486	C₂²	1	2	yes	—
19	C₆₁×#486	C₂²	1	2	yes	—
20	C₆₁×#482	—	2	2	no	—
21	C₆₁×#475	C₂²	1	2	yes	—
22	C₆₁×#465	—	2	2	no	—
23	C₆₁×#464	—	2	2	no	—
24	C₆₁×#461	C₂²	1	2	yes	—
25	C₆₁×#460	C₂²	1	2	yes	—
26	C₆₁×#459	—	2	2	no	—
27	C₆₁×#459	C₂²	1	2	yes	—
28	C₆₁×#452	—	2	2	no	—
29	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₆₁	—	2	1	no	—
32	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₆₁	—	2	1	no	—
34	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₈×D₄×C₆₁	C₂²	1	2	yes	—
36	C₆₁×#416	—	2	2	no	—
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#335	C₂²	1	1	yes	characteristic
39	C₆₁×#332	C₂²	1	2	yes	—
40	C₆₁×#331	C₂²	1	2	yes	—
41	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
43	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₆₁	—	2	2	no	—
46	C₂×Q₁₆×C₆₁	—	2	1	no	—
47	C₂×Q₁₆×C₆₁	—	2	1	no	—
48	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	C₂×D₈×C₆₁	—	2	2	no	—
52	C₂×D₈×C₆₁	—	2	1	no	—
53	C₂×D₈×C₆₁	—	2	1	no	—
54	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₆₁	—	2	2	no	—
56	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
57	#127×C₆₁	—	2	2	no	—
58	#127×C₆₁	C₂³	1	2	yes	—
59	#126×C₆₁	—	4	2	no	—
60	#124×C₆₁	—	2	2	no	—
61	C₂²⋊Q₈×C₆₁	—	2	2	no	—
62	#121×C₆₁	—	2	2	no	—
63	#121×C₆₁	—	4	2	no	—
64	C₄×Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₄×D₄×C₆₁	—	2	2	no	—
68	C₄×D₄×C₆₁	C₂³	1	2	yes	—
69	#117×C₆₁	—	2	2	no	—
70	#107×C₆₁	D₄	1	1	yes	characteristic
71	#107×C₆₁	D₄	1	1	yes	characteristic
72	#106×C₆₁	—	2	2	no	—
73	C₄⋊C₈×C₆₁	—	2	1	no	—
74	C₄⋊C₈×C₆₁	—	2	1	no	—
75	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
76	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
78	#103×C₆₁	—	2	2	no	—
79	#103×C₆₁	—	2	2	no	—
80	#103×C₆₁	D₄	1	1	yes	characteristic
81	#103×C₆₁	D₄	1	1	yes	characteristic
82	#102×C₆₁	—	2	2	no	—
83	#102×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	2	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	4	2	no	—
87	#102×C₆₁	D₄	1	2	yes	—
88	C₂²⋊C₈×C₆₁	—	2	2	no	—
89	C₄×C₈×C₆₁	—	2	1	no	—
90	C₄×C₈×C₆₁	—	2	1	no	—
91	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	#41×C₆₁	—	4	4	no	—
95	#41×C₆₁	—	8	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
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	—	4	2	no	—
103	C₂×D₄×C₆₁	—	4	2	no	—
104	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	4	2	no	—
107	Q₁₆×C₆₁	—	2	2	no	—
108	Q₁₆×C₆₁	—	4	2	no	—
109	Q₁₆×C₆₁	—	8	1	no	—
110	SD₁₆×C₆₁	—	8	2	no	—
111	SD₁₆×C₆₁	—	8	2	no	—
112	D₈×C₆₁	—	2	2	no	—
113	D₈×C₆₁	—	4	2	no	—
114	D₈×C₆₁	—	8	1	no	—
115	D₈×C₆₁	—	8	2	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	2	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	8	2	no	—
121	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₄⋊C₄×C₆₁	—	2	1	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	4	2	no	—
130	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₆₁	—	2	2	no	—
134	C₂²⋊C₄×C₆₁	—	4	2	no	—
135	C₂²⋊C₄×C₆₁	—	4	2	no	—
136	C₂²⋊C₄×C₆₁	—	4	2	no	—
137	C₄²×C₆₁	—	2	1	no	—
138	C₄²×C₆₁	—	2	1	no	—
139	C₄²×C₆₁	—	4	2	no	—
140	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
141	C₂³×C₆₁	—	2	2	no	—
142	C₂³×C₆₁	—	4	2	no	—
143	Q₈×C₆₁	—	2	1	no	—
144	Q₈×C₆₁	—	2	1	no	—
145	Q₈×C₆₁	—	2	1	no	—
146	Q₈×C₆₁	—	4	2	no	—
147	Q₈×C₆₁	—	4	2	no	—
148	Q₈×C₆₁	#135	1	2	yes	—
149	D₄×C₆₁	—	2	2	no	—
150	D₄×C₆₁	—	2	2	no	—
151	D₄×C₆₁	—	4	2	no	—
152	D₄×C₆₁	—	4	2	no	—
153	D₄×C₆₁	—	4	2	no	—
154	D₄×C₆₁	—	4	2	no	—
155	D₄×C₆₁	—	8	4	no	—
156	D₄×C₆₁	—	8	2	no	—
157	D₄×C₆₁	—	16	2	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	2	no	—
163	C₂×C₄×C₆₁	—	4	2	no	—
164	C₂×C₄×C₆₁	—	4	2	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	8	4	no	—
167	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
170	C₈×C₆₁	—	2	1	no	—
171	C₈×C₆₁	—	2	1	no	—
172	C₈×C₆₁	—	2	1	no	—
173	C₈×C₆₁	—	4	1	no	—
174	C₈×C₆₁	—	4	2	no	—
175	C₈×C₆₁	—	4	1	no	—
176	C₈×C₆₁	—	4	1	no	—
177	C₈×C₆₁	#135	1	2	yes	—
178	#19995	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₆₁	—	4	2	no	—
180	C₂²×C₆₁	—	4	2	no	—
181	C₂²×C₆₁	—	4	2	no	—
182	C₂²×C₆₁	—	8	2	no	—
183	C₂²×C₆₁	—	8	2	no	—
184	C₂²×C₆₁	—	8	2	no	—
185	C₂²×C₆₁	D₄²	1	1	yes	characteristic
186	C₄×C₆₁	—	2	2	no	—
187	C₄×C₆₁	—	2	1	no	—
188	C₄×C₆₁	—	4	2	no	—
189	C₄×C₆₁	—	4	1	no	—
190	C₄×C₆₁	—	4	1	no	—
191	C₄×C₆₁	—	4	1	no	—
192	C₄×C₆₁	—	8	2	no	—
193	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
194	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
195	C₄×C₆₁	#576	1	1	yes	characteristic
196	C₄×C₆₁	#576	1	1	yes	characteristic
197	#3393	C₂×C₆₁	1	1	yes	characteristic, complemented
198	#3391	C₂×C₆₁	1	1	yes	characteristic
199	#3304	C₂×C₆₁	1	2	yes	complemented
200	#1709	C₂×C₆₁	1	1	yes	characteristic, complemented
201	#1681	C₂×C₆₁	1	2	yes	complemented
202	#1670	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#1668	C₂×C₆₁	1	1	yes	characteristic, complemented
204	#1642	C₂×C₆₁	1	2	yes	complemented
205	#1628	C₂×C₆₁	1	2	yes	complemented
206	C₈×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
207	C₈×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
208	C₂×C₆₁	—	8	2	no	—
209	C₂×C₆₁	—	16	2	no	—
210	C₂×C₆₁	#3280	1	1	yes	characteristic
211	C₂×C₆₁	#3287	1	1	yes	characteristic
212	C₂×C₆₁	#3290	1	1	yes	characteristic
213	#556	C₂²×C₆₁	1	2	yes	—
214	#550	C₂²×C₆₁	1	2	yes	—
215	#495	—	2	1	no	—
216	#494	C₂²×C₆₁	1	1	yes	characteristic
217	#493	—	2	1	no	—
218	#493	C₂²×C₆₁	1	1	yes	characteristic
219	#486	C₂²×C₆₁	1	2	yes	—
220	#486	C₂²×C₆₁	1	2	yes	—
221	#482	—	2	2	no	—
222	#475	C₂²×C₆₁	1	2	yes	—
223	#465	—	2	2	no	—
224	#464	—	2	2	no	—
225	#461	C₂²×C₆₁	1	2	yes	—
226	#460	C₂²×C₆₁	1	2	yes	—
227	#459	—	2	2	no	—
228	#459	C₂²×C₆₁	1	2	yes	—
229	#452	—	2	2	no	—
230	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
231	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
232	C₄×Q₁₆	—	2	1	no	—
233	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
234	C₄×D₈	—	2	1	no	—
235	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
236	C₈×D₄	C₂²×C₆₁	1	2	yes	—
237	#416	—	2	2	no	—
238	#335	C₂²×C₆₁	1	1	yes	characteristic
239	#335	C₂²×C₆₁	1	1	yes	characteristic
240	#332	C₂²×C₆₁	1	2	yes	—
241	#331	C₂²×C₆₁	1	2	yes	—
242	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
243	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
244	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
245	C₈²	C₂²×C₆₁	1	1	yes	characteristic
246	C₆₁	#19995	1	1	yes	characteristic, direct product factor, Sylow
247	C₂×#41	—	2	2	no	—
248	C₂×Q₁₆	—	2	1	no	—
249	C₂×Q₁₆	—	2	1	no	—
250	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×SD₁₆	—	2	2	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×D₈	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
257	C₂²×C₈	—	2	2	no	—
258	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
259	#127	—	2	2	no	—
260	#127	C₂³×C₆₁	1	2	yes	—
261	#126	—	4	2	no	—
262	#124	—	2	2	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	#121	—	2	2	no	—
265	#121	—	4	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
268	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	C₂³×C₆₁	1	2	yes	—
271	#117	—	2	2	no	—
272	#107	D₄×C₆₁	1	1	yes	characteristic
273	#107	D₄×C₆₁	1	1	yes	characteristic
274	#106	—	2	2	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
278	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
279	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#103	D₄×C₆₁	1	1	yes	characteristic
283	#103	D₄×C₆₁	1	1	yes	characteristic
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	4	2	no	—
289	#102	D₄×C₆₁	1	2	yes	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
296	#41	—	4	4	no	—
297	#41	—	8	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
300	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	4	2	no	—
311	Q₁₆	—	8	1	no	—
312	SD₁₆	—	8	2	no	—
313	SD₁₆	—	8	2	no	—
314	D₈	—	2	2	no	—
315	D₈	—	4	2	no	—
316	D₈	—	8	1	no	—
317	D₈	—	8	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	8	2	no	—
323	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
324	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
334	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₂²⋊C₄	—	4	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	4	2	no	—
342	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	—	4	2	no	—
345	Q₈	—	2	1	no	—
346	Q₈	—	2	1	no	—
347	Q₈	—	2	1	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	4	2	no	—
350	Q₈	#135×C₆₁	1	2	yes	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	4	no	—
358	D₄	—	8	2	no	—
359	D₄	—	16	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	4	no	—
369	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
371	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	#135×C₆₁	1	2	yes	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	D₄²×C₆₁	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	2	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	1	no	—
393	C₄	—	8	2	no	—
394	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
395	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
396	C₄	C₆₁×#576	1	1	yes	characteristic
397	C₄	C₆₁×#576	1	1	yes	characteristic
398	C₂	—	8	2	no	—
399	C₂	—	16	2	no	—
400	C₂	C₆₁×#3280	1	1	yes	characteristic
401	C₂	C₆₁×#3287	1	1	yes	characteristic
402	C₂	C₆₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3391	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×#3393	C₂	semidirect
3. C₆₁×#3304	C₂	semidirect
4. C₆₁×#1709	C₂	semidirect
5. C₆₁×#1681	C₂	semidirect
6. C₆₁×#1670	C₂	semidirect
7. C₆₁×#1668	C₂	semidirect
8. C₆₁×#1642	C₂	semidirect
9. C₆₁×#1628	C₂	semidirect
10. C₈×Q₁₆×C₆₁	C₂	semidirect
11. C₈×D₈×C₆₁	C₂	semidirect
178. #19995	C₆₁	direct (N × H)
197. #3393	C₂×C₆₁	semidirect
199. #3304	C₂×C₆₁	semidirect
200. #1709	C₂×C₆₁	semidirect
201. #1681	C₂×C₆₁	semidirect
202. #1670	C₂×C₆₁	semidirect
203. #1668	C₂×C₆₁	semidirect
204. #1642	C₂×C₆₁	semidirect
205. #1628	C₂×C₆₁	semidirect
206. C₈×Q₁₆	C₂×C₆₁	semidirect
207. C₈×D₈	C₂×C₆₁	semidirect
246. C₆₁	#19995	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×#3393	2
C₆₁×#3391	2
C₆₁×#3304	2
C₆₁×#1709	2
C₆₁×#1681	2
C₆₁×#1670	2
C₆₁×#1668	2
C₆₁×#1642	2
C₆₁×#1628	2
C₈×Q₁₆×C₆₁	2
C₈×D₈×C₆₁	2
#19995	61

Subgroups — C61×#19995 #29523428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19995 #29523428