Subgroups — C₆₁×#18668 #29522101

Order 15616.

936 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3245	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1652	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1644	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1628	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1622	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1550	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₆₁	—	2	1	no	—
13	C₆₁×#559	—	2	1	no	—
14	C₆₁×#557	—	2	1	no	—
15	C₆₁×#556	—	2	2	no	—
16	C₆₁×#556	C₂²	1	2	yes	—
17	C₆₁×#554	C₂²	1	2	yes	—
18	C₆₁×#552	—	2	2	no	—
19	C₆₁×#539	—	2	2	no	—
20	C₆₁×#536	—	2	1	no	—
21	C₆₁×#533	C₂²	1	1	yes	characteristic
22	C₆₁×#532	C₂²	1	1	yes	characteristic
23	C₆₁×#532	C₂²	1	1	yes	characteristic
24	C₆₁×#529	—	2	2	no	—
25	C₆₁×#520	—	2	1	no	—
26	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#498	C₂²	1	1	yes	characteristic
28	C₆₁×#492	C₂²	1	1	yes	characteristic
29	C₆₁×#487	C₂²	1	1	yes	characteristic
30	C₆₁×#486	C₂²	1	1	yes	characteristic
31	C₆₁×#474	—	2	1	no	—
32	C₆₁×#474	C₂²	1	2	yes	—
33	C₆₁×#466	—	2	2	no	—
34	C₆₁×#465	—	2	2	no	—
35	C₆₁×#464	—	2	2	no	—
36	C₆₁×#462	C₂²	1	2	yes	—
37	C₆₁×#460	C₂²	1	2	yes	—
38	C₆₁×#459	—	2	1	no	—
39	C₆₁×#459	C₂²	1	2	yes	—
40	C₄×SD₁₆×C₆₁	—	2	2	no	—
41	C₆₁×#423	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#417	—	2	1	no	—
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#333	C₂²	1	2	yes	—
46	C₆₁×#332	C₂²	1	2	yes	—
47	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
50	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×#41×C₆₁	—	2	1	no	—
52	C₂×#41×C₆₁	—	2	1	no	—
53	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
54	#137×C₆₁	—	4	4	no	—
55	C₂×Q₁₆×C₆₁	—	2	2	no	—
56	C₂×SD₁₆×C₆₁	—	2	2	no	—
57	C₂×SD₁₆×C₆₁	—	2	2	no	—
58	C₂×D₈×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	—	2	1	no	—
60	C₂²×C₈×C₆₁	—	2	1	no	—
61	C₂²×C₈×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	—	2	2	no	—
63	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	#127×C₆₁	D₄	1	1	yes	characteristic
68	#127×C₆₁	C₂³	1	1	yes	characteristic
69	#126×C₆₁	—	2	4	no	—
70	#126×C₆₁	—	2	4	no	—
71	#125×C₆₁	—	2	4	no	—
72	#125×C₆₁	—	2	2	no	—
73	#125×C₆₁	—	2	1	no	—
74	#124×C₆₁	—	2	2	no	—
75	#124×C₆₁	—	2	2	no	—
76	#124×C₆₁	—	2	1	no	—
77	#124×C₆₁	—	2	1	no	—
78	#123×C₆₁	—	2	4	no	—
79	#123×C₆₁	—	2	4	no	—
80	C₂²⋊Q₈×C₆₁	—	2	2	no	—
81	C₂²⋊Q₈×C₆₁	—	2	2	no	—
82	C₂²⋊Q₈×C₆₁	—	2	4	no	—
83	C₂²⋊Q₈×C₆₁	—	2	1	no	—
84	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
85	#121×C₆₁	—	2	1	no	—
86	#121×C₆₁	—	2	1	no	—
87	#121×C₆₁	—	2	1	no	—
88	#121×C₆₁	D₄	1	2	yes	—
89	C₄×Q₈×C₆₁	—	2	2	no	—
90	C₄×Q₈×C₆₁	—	2	2	no	—
91	C₄×Q₈×C₆₁	—	2	1	no	—
92	C₄×Q₈×C₆₁	—	2	1	no	—
93	C₄×Q₈×C₆₁	—	2	1	no	—
94	C₄×Q₈×C₆₁	D₄	1	2	yes	—
95	C₄×Q₈×C₆₁	D₄	1	2	yes	—
96	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
97	C₄×D₄×C₆₁	—	2	4	no	—
98	C₄×D₄×C₆₁	—	2	2	no	—
99	C₄×D₄×C₆₁	—	2	2	no	—
100	C₄×D₄×C₆₁	—	2	1	no	—
101	C₄×D₄×C₆₁	—	2	1	no	—
102	C₄×D₄×C₆₁	—	2	1	no	—
103	C₄×D₄×C₆₁	C₂³	1	2	yes	—
104	#117×C₆₁	—	2	4	no	—
105	#117×C₆₁	—	2	1	no	—
106	#117×C₆₁	—	2	2	no	—
107	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
109	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₆₁	—	2	1	no	—
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	#107×C₆₁	—	2	2	no	—
113	#106×C₆₁	—	2	2	no	—
114	C₄⋊C₈×C₆₁	—	2	1	no	—
115	C₄⋊C₈×C₆₁	—	2	1	no	—
116	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
117	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
118	#103×C₆₁	—	2	2	no	—
119	#103×C₆₁	—	2	2	no	—
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	—	2	2	no	—
123	#102×C₆₁	—	2	2	no	—
124	C₄×C₈×C₆₁	—	2	1	no	—
125	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
126	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
127	#41×C₆₁	—	4	2	no	—
128	#41×C₆₁	—	4	2	no	—
129	#41×C₆₁	—	4	2	no	—
130	#41×C₆₁	—	4	2	no	—
131	C₂×Q₈×C₆₁	—	2	1	no	—
132	C₂×Q₈×C₆₁	—	2	1	no	—
133	C₂×Q₈×C₆₁	—	2	1	no	—
134	C₂×Q₈×C₆₁	—	2	2	no	—
135	C₂×Q₈×C₆₁	—	2	2	no	—
136	C₂×Q₈×C₆₁	—	2	1	no	—
137	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₆₁	—	2	2	no	—
140	C₂×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	—	2	1	no	—
142	C₂×D₄×C₆₁	—	2	1	no	—
143	C₂×D₄×C₆₁	—	2	1	no	—
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	—	4	1	no	—
146	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	4	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	2	no	—
151	C₂²×C₄×C₆₁	—	4	1	no	—
152	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
155	Q₁₆×C₆₁	—	4	4	no	—
156	SD₁₆×C₆₁	—	4	4	no	—
157	SD₁₆×C₆₁	—	4	4	no	—
158	D₈×C₆₁	—	8	2	no	—
159	M₁₆×C₆₁	—	4	2	no	—
160	C₂×C₈×C₆₁	—	2	1	no	—
161	C₂×C₈×C₆₁	—	2	1	no	—
162	C₂×C₈×C₆₁	—	2	2	no	—
163	C₂×C₈×C₆₁	—	2	2	no	—
164	C₂×C₈×C₆₁	—	4	2	no	—
165	C₂×C₈×C₆₁	—	8	1	no	—
166	C₄⋊C₄×C₆₁	—	2	4	no	—
167	C₄⋊C₄×C₆₁	—	2	4	no	—
168	C₄⋊C₄×C₆₁	—	2	4	no	—
169	C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₄⋊C₄×C₆₁	—	2	1	no	—
171	C₄⋊C₄×C₆₁	—	2	2	no	—
172	C₄⋊C₄×C₆₁	—	2	1	no	—
173	C₄⋊C₄×C₆₁	—	2	2	no	—
174	C₄⋊C₄×C₆₁	—	2	1	no	—
175	C₄⋊C₄×C₆₁	—	2	2	no	—
176	C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₄⋊C₄×C₆₁	—	2	1	no	—
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
182	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
183	C₂²⋊C₄×C₆₁	—	2	4	no	—
184	C₂²⋊C₄×C₆₁	—	2	4	no	—
185	C₂²⋊C₄×C₆₁	—	2	4	no	—
186	C₂²⋊C₄×C₆₁	—	2	2	no	—
187	C₂²⋊C₄×C₆₁	—	2	2	no	—
188	C₂²⋊C₄×C₆₁	—	2	2	no	—
189	C₂²⋊C₄×C₆₁	—	4	1	no	—
190	C₂²⋊C₄×C₆₁	—	4	1	no	—
191	C₄²×C₆₁	—	2	4	no	—
192	C₄²×C₆₁	—	2	2	no	—
193	C₄²×C₆₁	—	2	2	no	—
194	C₄²×C₆₁	—	2	2	no	—
195	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
199	C₂³×C₆₁	—	2	2	no	—
200	C₂³×C₆₁	—	4	1	no	—
201	C₂³×C₆₁	#120	1	1	yes	characteristic
202	Q₈×C₆₁	—	2	2	no	—
203	Q₈×C₆₁	—	2	2	no	—
204	Q₈×C₆₁	—	4	2	no	—
205	Q₈×C₆₁	—	4	1	no	—
206	Q₈×C₆₁	—	4	1	no	—
207	Q₈×C₆₁	—	4	2	no	—
208	Q₈×C₆₁	—	4	2	no	—
209	Q₈×C₆₁	—	4	1	no	—
210	Q₈×C₆₁	—	4	1	no	—
211	D₄×C₆₁	—	2	2	no	—
212	D₄×C₆₁	—	2	2	no	—
213	D₄×C₆₁	—	4	2	no	—
214	D₄×C₆₁	—	4	4	no	—
215	D₄×C₆₁	—	4	1	no	—
216	D₄×C₆₁	—	4	1	no	—
217	D₄×C₆₁	—	4	1	no	—
218	D₄×C₆₁	—	4	1	no	—
219	D₄×C₆₁	—	4	2	no	—
220	D₄×C₆₁	—	8	1	no	—
221	D₄×C₆₁	—	8	2	no	—
222	C₂×C₄×C₆₁	—	2	1	no	—
223	C₂×C₄×C₆₁	—	2	1	no	—
224	C₂×C₄×C₆₁	—	2	2	no	—
225	C₂×C₄×C₆₁	—	2	2	no	—
226	C₂×C₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	4	1	no	—
230	C₂×C₄×C₆₁	—	4	2	no	—
231	C₂×C₄×C₆₁	—	4	2	no	—
232	C₂×C₄×C₆₁	—	4	2	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	8	1	no	—
235	C₂×C₄×C₆₁	—	8	4	no	—
236	C₂×C₄×C₆₁	—	8	2	no	—
237	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
238	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
239	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
240	C₂×C₄×C₆₁	#135	1	2	yes	—
241	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
242	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
245	C₈×C₆₁	—	2	2	no	—
246	C₈×C₆₁	—	4	1	no	—
247	C₈×C₆₁	—	4	2	no	—
248	C₈×C₆₁	—	4	2	no	—
249	#18668	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂²×C₆₁	—	2	1	no	—
251	C₂²×C₆₁	—	2	1	no	—
252	C₂²×C₆₁	—	4	2	no	—
253	C₂²×C₆₁	—	4	2	no	—
254	C₂²×C₆₁	—	4	2	no	—
255	C₂²×C₆₁	—	8	1	no	—
256	C₂²×C₆₁	—	8	1	no	—
257	C₂²×C₆₁	—	8	1	no	—
258	C₂²×C₆₁	#449	1	2	yes	—
259	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
260	C₄×C₆₁	—	2	1	no	—
261	C₄×C₆₁	—	2	1	no	—
262	C₄×C₆₁	—	2	1	no	—
263	C₄×C₆₁	—	4	2	no	—
264	C₄×C₆₁	—	4	2	no	—
265	C₄×C₆₁	—	4	2	no	—
266	C₄×C₆₁	—	4	2	no	—
267	C₄×C₆₁	—	4	2	no	—
268	C₄×C₆₁	—	8	1	no	—
269	C₄×C₆₁	#449	1	2	yes	—
270	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
271	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₄×C₆₁	#577	1	1	yes	characteristic
273	C₄×C₆₁	#578	1	1	yes	characteristic
274	#3507	C₂×C₆₁	1	1	yes	characteristic, complemented
275	#3245	C₂×C₆₁	1	1	yes	characteristic
276	#3167	C₂×C₆₁	1	1	yes	characteristic, complemented
277	#3037	C₂×C₆₁	1	1	yes	characteristic, complemented
278	#1652	C₂×C₆₁	1	2	yes	complemented
279	#1644	C₂×C₆₁	1	2	yes	complemented
280	#1628	C₂×C₆₁	1	2	yes	complemented
281	#1622	C₂×C₆₁	1	2	yes	complemented
282	#1550	C₂×C₆₁	1	1	yes	characteristic, complemented
283	#1492	C₂×C₆₁	1	1	yes	characteristic, complemented
284	C₂×Q₈⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
285	C₂×C₆₁	—	2	2	no	—
286	C₂×C₆₁	—	8	2	no	—
287	C₂×C₆₁	—	16	1	no	—
288	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
289	C₂×C₆₁	#3013	1	1	yes	characteristic
290	C₂×C₆₁	#3018	1	1	yes	characteristic
291	C₂×#137	—	2	1	no	—
292	#559	—	2	1	no	—
293	#557	—	2	1	no	—
294	#556	—	2	2	no	—
295	#556	C₂²×C₆₁	1	2	yes	—
296	#554	C₂²×C₆₁	1	2	yes	—
297	#552	—	2	2	no	—
298	#539	—	2	2	no	—
299	#536	—	2	1	no	—
300	#533	C₂²×C₆₁	1	1	yes	characteristic
301	#532	C₂²×C₆₁	1	1	yes	characteristic
302	#532	C₂²×C₆₁	1	1	yes	characteristic
303	#529	—	2	2	no	—
304	#520	—	2	1	no	—
305	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
306	#498	C₂²×C₆₁	1	1	yes	characteristic
307	#492	C₂²×C₆₁	1	1	yes	characteristic
308	#487	C₂²×C₆₁	1	1	yes	characteristic
309	#486	C₂²×C₆₁	1	1	yes	characteristic
310	#474	—	2	1	no	—
311	#474	C₂²×C₆₁	1	2	yes	—
312	#466	—	2	2	no	—
313	#465	—	2	2	no	—
314	#464	—	2	2	no	—
315	#462	C₂²×C₆₁	1	2	yes	—
316	#460	C₂²×C₆₁	1	2	yes	—
317	#459	—	2	1	no	—
318	#459	C₂²×C₆₁	1	2	yes	—
319	C₄×SD₁₆	—	2	2	no	—
320	#423	C₂²×C₆₁	1	1	yes	characteristic
321	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
322	#417	—	2	1	no	—
323	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
324	#333	C₂²×C₆₁	1	2	yes	—
325	#332	C₂²×C₆₁	1	2	yes	—
326	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
327	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
328	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
329	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
330	C₆₁	#18668	1	1	yes	characteristic, direct product factor, Sylow
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
334	#137	—	4	4	no	—
335	C₂×Q₁₆	—	2	2	no	—
336	C₂×SD₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×D₈	—	2	2	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
344	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
346	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
347	#127	D₄×C₆₁	1	1	yes	characteristic
348	#127	C₂³×C₆₁	1	1	yes	characteristic
349	#126	—	2	4	no	—
350	#126	—	2	4	no	—
351	#125	—	2	4	no	—
352	#125	—	2	2	no	—
353	#125	—	2	1	no	—
354	#124	—	2	2	no	—
355	#124	—	2	2	no	—
356	#124	—	2	1	no	—
357	#124	—	2	1	no	—
358	#123	—	2	4	no	—
359	#123	—	2	4	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	—	2	1	no	—
364	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
365	#121	—	2	1	no	—
366	#121	—	2	1	no	—
367	#121	—	2	1	no	—
368	#121	D₄×C₆₁	1	2	yes	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	D₄×C₆₁	1	2	yes	—
375	C₄×Q₈	D₄×C₆₁	1	2	yes	—
376	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂³×C₆₁	1	2	yes	—
384	#117	—	2	4	no	—
385	#117	—	2	1	no	—
386	#117	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
392	#107	—	2	2	no	—
393	#106	—	2	2	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
397	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
398	#103	—	2	2	no	—
399	#103	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	C₄×C₈	—	2	1	no	—
405	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
406	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
407	#41	—	4	2	no	—
408	#41	—	4	2	no	—
409	#41	—	4	2	no	—
410	#41	—	4	2	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
418	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
435	Q₁₆	—	4	4	no	—
436	SD₁₆	—	4	4	no	—
437	SD₁₆	—	4	4	no	—
438	D₈	—	8	2	no	—
439	M₁₆	—	4	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	4	2	no	—
445	C₂×C₈	—	8	1	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
461	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
462	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	4	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	2	no	—
474	C₄²	—	2	2	no	—
475	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
476	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
478	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
479	C₂³	—	2	2	no	—
480	C₂³	—	4	1	no	—
481	C₂³	#120×C₆₁	1	1	yes	characteristic
482	Q₈	—	2	2	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	4	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	1	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	2	no	—
500	D₄	—	8	1	no	—
501	D₄	—	8	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	8	1	no	—
515	C₂×C₄	—	8	4	no	—
516	C₂×C₄	—	8	2	no	—
517	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
518	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
519	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
520	C₂×C₄	#135×C₆₁	1	2	yes	—
521	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	2	no	—
528	C₈	—	4	2	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	C₆₁×#449	1	2	yes	—
538	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	4	2	no	—
547	C₄	—	8	1	no	—
548	C₄	C₆₁×#449	1	2	yes	—
549	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
550	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
551	C₄	C₆₁×#577	1	1	yes	characteristic
552	C₄	C₆₁×#578	1	1	yes	characteristic
553	C₂	—	2	2	no	—
554	C₂	—	8	2	no	—
555	C₂	—	16	1	no	—
556	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
557	C₂	C₆₁×#3013	1	1	yes	characteristic
558	C₂	C₆₁×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3245	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ 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. C₆₁×#3507	C₂	semidirect
3. C₆₁×#3167	C₂	semidirect
4. C₆₁×#3037	C₂	semidirect
5. C₆₁×#1652	C₂	semidirect
6. C₆₁×#1644	C₂	semidirect
7. C₆₁×#1628	C₂	semidirect
8. C₆₁×#1622	C₂	semidirect
9. C₆₁×#1550	C₂	semidirect
10. C₆₁×#1492	C₂	semidirect
11. C₂×C₆₁×Q₈⋊C₈	C₂	semidirect
249. #18668	C₆₁	direct (N × H)
274. #3507	C₂×C₆₁	semidirect
276. #3167	C₂×C₆₁	semidirect
277. #3037	C₂×C₆₁	semidirect
278. #1652	C₂×C₆₁	semidirect
279. #1644	C₂×C₆₁	semidirect
280. #1628	C₂×C₆₁	semidirect
281. #1622	C₂×C₆₁	semidirect
282. #1550	C₂×C₆₁	semidirect
283. #1492	C₂×C₆₁	semidirect
284. C₂×Q₈⋊C₈	C₂×C₆₁	semidirect
330. C₆₁	#18668	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×#3507	2
C₆₁×#3245	2
C₆₁×#3167	2
C₆₁×#3037	2
C₆₁×#1652	2
C₆₁×#1644	2
C₆₁×#1628	2
C₆₁×#1622	2
C₆₁×#1550	2
C₆₁×#1492	2
C₂×C₆₁×Q₈⋊C₈	2
#18668	61

Subgroups — C61×#18668 #29522101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18668 #29522101