Subgroups — C₆₁×#62148 #29565581

Order 15616.

1942 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₈×C₆₁	C₂	1	2	yes	maximal, complemented
4	C₆₁×#3359	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3353	C₂	1	6	yes	maximal, complemented
6	C₆₁×#3330	C₂	1	6	yes	maximal, complemented
7	C₆₁×#3254	C₂	1	3	yes	maximal, complemented
8	C₆₁×#3230	C₂	1	3	yes	maximal, complemented
9	C₆₁×#3106	C₂	1	3	yes	maximal, complemented
10	C₆₁×#3079	C₂	1	3	yes	maximal, complemented
11	C₆₁×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₆₁	—	2	1	no	—
13	C₆₁×#557	C₂²	1	1	yes	characteristic
14	C₆₁×#556	C₂²	1	3	yes	—
15	C₆₁×#552	—	2	3	no	—
16	D₄×Q₈×C₆₁	—	2	1	no	—
17	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
18	D₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#548	—	2	1	no	—
20	C₆₁×#547	—	2	3	no	—
21	C₆₁×#547	C₂²	1	3	yes	—
22	C₆₁×#547	C₂²	1	6	yes	—
23	C₆₁×#536	—	2	3	no	—
24	C₆₁×#533	C₂²	1	3	yes	—
25	C₆₁×#532	C₂²	1	3	yes	—
26	C₂×C₄⋊Q₈×C₆₁	C₂²	1	3	yes	—
27	C₆₁×#529	—	2	3	no	—
28	C₄×#41×C₆₁	C₂²	1	3	yes	—
29	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
31	C₆₁×#500	C₂²	1	6	yes	—
32	C₆₁×#487	C₂²	1	6	yes	—
33	C₆₁×#484	C₂²	1	12	yes	—
34	C₆₁×#482	C₂²	1	6	yes	—
35	C₆₁×#477	C₂²	1	6	yes	—
36	C₆₁×#477	C₂²	1	3	yes	—
37	C₆₁×#476	C₂²	1	3	yes	—
38	C₆₁×#475	C₂²	1	6	yes	—
39	C₆₁×#474	C₂²	1	6	yes	—
40	C₆₁×#474	C₂²	1	6	yes	—
41	C₆₁×#468	C₂²	1	12	yes	—
42	C₆₁×#461	C₂²	1	6	yes	—
43	C₆₁×#460	C₂²	1	3	yes	—
44	C₆₁×#459	C₂²	1	1	yes	characteristic
45	C₆₁×#449	C₂²	1	6	yes	—
46	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
47	C₄×SD₁₆×C₆₁	C₂²	1	6	yes	—
48	C₄×D₈×C₆₁	C₂²	1	6	yes	—
49	C₆₁×#436	C₂²	1	6	yes	—
50	C₆₁×#431	C₂²	1	3	yes	—
51	C₆₁×#428	C₂²	1	6	yes	—
52	C₆₁×#423	C₂²	1	3	yes	—
53	C₆₁×#417	C₂²	1	6	yes	—
54	2₋¹⁺⁴×C₆₁	—	4	8	no	—
55	C₂×#41×C₆₁	—	2	6	no	—
56	C₂×#41×C₆₁	—	2	3	no	—
57	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
58	C₂×#41×C₆₁	C₂³	1	3	yes	—
59	C₂²×Q₈×C₆₁	—	2	1	no	—
60	C₂²×Q₈×C₆₁	—	2	2	no	—
61	C₂²×Q₈×C₆₁	—	2	3	no	—
62	C₂×SD₁₆×C₆₁	C₂³	1	6	yes	—
63	C₂×D₈×C₆₁	C₂³	1	2	yes	—
64	C₂×M₁₆×C₆₁	C₂³	1	6	yes	—
65	C₄⋊Q₈×C₆₁	—	2	3	no	—
66	C₄⋊Q₈×C₆₁	—	2	3	no	—
67	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
68	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
69	C₄⋊Q₈×C₆₁	C₂³	1	6	yes	—
70	C₄⋊Q₈×C₆₁	C₂³	1	3	yes	—
71	#127×C₆₁	C₂³	1	1	yes	characteristic
72	#126×C₆₁	—	2	6	no	—
73	#125×C₆₁	—	2	3	no	—
74	#125×C₆₁	—	2	3	no	—
75	#124×C₆₁	—	2	3	no	—
76	#124×C₆₁	—	2	3	no	—
77	#123×C₆₁	—	2	12	no	—
78	#123×C₆₁	—	2	6	no	—
79	C₂²⋊Q₈×C₆₁	—	2	3	no	—
80	C₂²⋊Q₈×C₆₁	—	2	6	no	—
81	C₂²⋊Q₈×C₆₁	—	2	6	no	—
82	C₂²⋊Q₈×C₆₁	—	2	3	no	—
83	C₂²⋊Q₈×C₆₁	C₂³	1	6	yes	—
84	#121×C₆₁	—	2	3	no	—
85	#121×C₆₁	—	2	3	no	—
86	#121×C₆₁	C₂³	1	6	yes	—
87	C₄×Q₈×C₆₁	—	2	1	no	—
88	C₄×Q₈×C₆₁	—	2	3	no	—
89	C₄×Q₈×C₆₁	—	2	3	no	—
90	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
92	C₄×Q₈×C₆₁	C₂³	1	3	yes	—
93	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₆₁	—	2	3	no	—
95	C₄×D₄×C₆₁	—	2	3	no	—
96	C₄×D₄×C₆₁	—	2	3	no	—
97	C₄×D₄×C₆₁	D₄	1	3	yes	—
98	C₄×D₄×C₆₁	C₂³	1	6	yes	—
99	C₄×D₄×C₆₁	C₂³	1	3	yes	—
100	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₆₁	C₂³	1	3	yes	—
102	#117×C₆₁	—	2	3	no	—
103	#117×C₆₁	—	2	3	no	—
104	#117×C₆₁	D₄	1	3	yes	—
105	#117×C₆₁	C₂³	1	3	yes	—
106	C₂×C₄⋊C₄×C₆₁	—	2	3	no	—
107	C₂×C₄⋊C₄×C₆₁	—	2	3	no	—
108	C₂×C₄⋊C₄×C₆₁	C₂³	1	6	yes	—
109	C₂×C₄²×C₆₁	—	2	3	no	—
110	C₂×C₄²×C₆₁	C₂³	1	3	yes	—
111	#107×C₆₁	C₂³	1	12	yes	—
112	#107×C₆₁	C₂³	1	6	yes	—
113	#106×C₆₁	C₂³	1	6	yes	—
114	C₄⋊C₈×C₆₁	C₂³	1	3	yes	—
115	C₄⋊C₈×C₆₁	C₂³	1	6	yes	—
116	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
117	#103×C₆₁	C₂³	1	12	yes	—
118	#103×C₆₁	C₂³	1	6	yes	—
119	#102×C₆₁	C₂³	1	6	yes	—
120	#102×C₆₁	C₂³	1	6	yes	—
121	#102×C₆₁	C₂³	1	2	yes	—
122	C₂²⋊C₈×C₆₁	C₂³	1	6	yes	—
123	C₄×C₈×C₆₁	C₂³	1	6	yes	—
124	#41×C₆₁	—	2	4	no	—
125	#41×C₆₁	—	2	6	no	—
126	#41×C₆₁	—	4	3	no	—
127	#41×C₆₁	—	4	12	no	—
128	#41×C₆₁	—	4	24	no	—
129	C₂×Q₈×C₆₁	—	2	3	no	—
130	C₂×Q₈×C₆₁	—	2	6	no	—
131	C₂×Q₈×C₆₁	—	2	3	no	—
132	C₂×Q₈×C₆₁	—	4	12	no	—
133	C₂×Q₈×C₆₁	—	4	4	no	—
134	C₂×Q₈×C₆₁	—	4	8	no	—
135	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂×Q₈×C₆₁	C₂⁴	1	3	yes	—
137	C₂×D₄×C₆₁	—	2	3	no	—
138	C₂×D₄×C₆₁	—	2	6	no	—
139	C₂×D₄×C₆₁	—	2	1	no	—
140	C₂×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	C₂×D₄	1	3	yes	—
142	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
143	C₂×D₄×C₆₁	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	—	2	6	no	—
145	C₂²×C₄×C₆₁	—	2	1	no	—
146	C₂²×C₄×C₆₁	—	2	3	no	—
147	C₂²×C₄×C₆₁	—	2	3	no	—
148	C₂²×C₄×C₆₁	—	2	6	no	—
149	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
150	C₂²×C₄×C₆₁	C₂×D₄	1	3	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	3	yes	—
152	SD₁₆×C₆₁	—	4	6	no	—
153	D₈×C₆₁	—	2	4	no	—
154	M₁₆×C₆₁	—	4	6	no	—
155	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
156	C₂×C₈×C₆₁	C₂⁴	1	6	yes	—
157	C₄⋊C₄×C₆₁	—	2	3	no	—
158	C₄⋊C₄×C₆₁	—	2	3	no	—
159	C₄⋊C₄×C₆₁	—	2	6	no	—
160	C₄⋊C₄×C₆₁	—	2	6	no	—
161	C₄⋊C₄×C₆₁	—	2	6	no	—
162	C₄⋊C₄×C₆₁	—	2	3	no	—
163	C₄⋊C₄×C₆₁	—	2	3	no	—
164	C₄⋊C₄×C₆₁	—	2	3	no	—
165	C₄⋊C₄×C₆₁	—	2	3	no	—
166	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
167	C₄⋊C₄×C₆₁	C₂×D₄	1	3	yes	—
168	C₄⋊C₄×C₆₁	C₂⁴	1	1	yes	characteristic
169	C₄⋊C₄×C₆₁	C₂⁴	1	3	yes	—
170	C₄⋊C₄×C₆₁	C₂⁴	1	6	yes	—
171	C₂²⋊C₄×C₆₁	—	2	6	no	—
172	C₂²⋊C₄×C₆₁	—	2	3	no	—
173	C₂²⋊C₄×C₆₁	—	2	1	no	—
174	C₂²⋊C₄×C₆₁	—	2	3	no	—
175	C₂²⋊C₄×C₆₁	—	2	6	no	—
176	C₂²⋊C₄×C₆₁	—	2	6	no	—
177	C₂²⋊C₄×C₆₁	C₂×D₄	1	6	yes	—
178	C₄²×C₆₁	—	2	3	no	—
179	C₄²×C₆₁	—	2	3	no	—
180	C₄²×C₆₁	—	2	3	no	—
181	C₄²×C₆₁	C₂×D₄	1	3	yes	—
182	C₄²×C₆₁	C₂×D₄	1	3	yes	—
183	C₄²×C₆₁	C₂⁴	1	3	yes	—
184	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
185	C₂³×C₆₁	—	2	1	no	—
186	C₂³×C₆₁	—	2	2	no	—
187	C₂³×C₆₁	C₂²×D₄	1	3	yes	—
188	Q₈×C₆₁	—	2	3	no	—
189	Q₈×C₆₁	—	2	3	no	—
190	Q₈×C₆₁	—	4	6	no	—
191	Q₈×C₆₁	—	4	6	no	—
192	Q₈×C₆₁	—	4	12	no	—
193	Q₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
194	D₄×C₆₁	—	2	6	no	—
195	D₄×C₆₁	—	2	2	no	—
196	D₄×C₆₁	—	2	1	no	—
197	D₄×C₆₁	—	2	2	no	—
198	D₄×C₆₁	—	4	2	no	—
199	D₄×C₆₁	—	4	6	no	—
200	D₄×C₆₁	—	4	12	no	—
201	D₄×C₆₁	—	4	2	no	—
202	D₄×C₆₁	2₋¹⁺⁴	1	2	yes	complemented
203	C₂×C₄×C₆₁	—	2	6	no	—
204	C₂×C₄×C₆₁	—	2	6	no	—
205	C₂×C₄×C₆₁	—	2	3	no	—
206	C₂×C₄×C₆₁	—	2	3	no	—
207	C₂×C₄×C₆₁	—	2	1	no	—
208	C₂×C₄×C₆₁	—	2	3	no	—
209	C₂×C₄×C₆₁	—	2	3	no	—
210	C₂×C₄×C₆₁	—	2	6	no	—
211	C₂×C₄×C₆₁	—	4	6	no	—
212	C₂×C₄×C₆₁	—	4	12	no	—
213	C₂×C₄×C₆₁	—	4	6	no	—
214	C₂×C₄×C₆₁	—	4	12	no	—
215	C₂×C₄×C₆₁	—	4	2	no	—
216	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
219	C₂×C₄×C₆₁	C₂²×D₄	1	3	yes	—
220	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
222	C₈×C₆₁	—	2	2	no	—
223	C₈×C₆₁	—	2	6	no	—
224	#62148	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₆₁	—	2	3	no	—
226	C₂²×C₆₁	—	2	2	no	—
227	C₂²×C₆₁	—	2	3	no	—
228	C₂²×C₆₁	—	2	3	no	—
229	C₂²×C₆₁	—	4	1	no	—
230	C₂²×C₆₁	—	4	1	no	—
231	C₂²×C₆₁	—	4	2	no	—
232	C₂²×C₆₁	—	4	2	no	—
233	C₂²×C₆₁	—	4	2	no	—
234	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
235	C₄×C₆₁	—	2	3	no	—
236	C₄×C₆₁	—	2	1	no	—
237	C₄×C₆₁	—	2	3	no	—
238	C₄×C₆₁	—	4	3	no	—
239	C₄×C₆₁	—	4	6	no	—
240	C₄×C₆₁	—	4	3	no	—
241	C₄×C₆₁	—	4	1	no	—
242	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	6	yes	—
243	C₄×C₆₁	#578	1	2	yes	—
244	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
245	C₄×C₆₁	#585	1	1	yes	characteristic
246	#3499	C₂×C₆₁	1	1	yes	characteristic, complemented
247	#3482	C₂×C₆₁	1	1	yes	characteristic, complemented
248	Q₈×D₈	C₂×C₆₁	1	2	yes	complemented
249	#3359	C₂×C₆₁	1	2	yes	complemented
250	#3353	C₂×C₆₁	1	6	yes	complemented
251	#3330	C₂×C₆₁	1	6	yes	complemented
252	#3254	C₂×C₆₁	1	3	yes	complemented
253	#3230	C₂×C₆₁	1	3	yes	complemented
254	#3106	C₂×C₆₁	1	3	yes	complemented
255	#3079	C₂×C₆₁	1	3	yes	complemented
256	#2991	C₂×C₆₁	1	1	yes	characteristic, complemented
257	C₂×C₆₁	—	4	3	no	—
258	C₂×C₆₁	—	4	2	no	—
259	C₂×C₆₁	—	8	2	no	—
260	C₂×C₆₁	#3489	1	1	yes	characteristic
261	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
263	C₂×2₋¹⁺⁴	—	2	1	no	—
264	#557	C₂²×C₆₁	1	1	yes	characteristic
265	#556	C₂²×C₆₁	1	3	yes	—
266	#552	—	2	3	no	—
267	D₄×Q₈	—	2	1	no	—
268	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
269	D₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
270	#548	—	2	1	no	—
271	#547	—	2	3	no	—
272	#547	C₂²×C₆₁	1	3	yes	—
273	#547	C₂²×C₆₁	1	6	yes	—
274	#536	—	2	3	no	—
275	#533	C₂²×C₆₁	1	3	yes	—
276	#532	C₂²×C₆₁	1	3	yes	—
277	C₂×C₄⋊Q₈	C₂²×C₆₁	1	3	yes	—
278	#529	—	2	3	no	—
279	C₄×#41	C₂²×C₆₁	1	3	yes	—
280	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
281	C₂×C₄×Q₈	—	2	1	no	—
282	#500	C₂²×C₆₁	1	6	yes	—
283	#487	C₂²×C₆₁	1	6	yes	—
284	#484	C₂²×C₆₁	1	12	yes	—
285	#482	C₂²×C₆₁	1	6	yes	—
286	#477	C₂²×C₆₁	1	6	yes	—
287	#477	C₂²×C₆₁	1	3	yes	—
288	#476	C₂²×C₆₁	1	3	yes	—
289	#475	C₂²×C₆₁	1	6	yes	—
290	#474	C₂²×C₆₁	1	6	yes	—
291	#474	C₂²×C₆₁	1	6	yes	—
292	#468	C₂²×C₆₁	1	12	yes	—
293	#461	C₂²×C₆₁	1	6	yes	—
294	#460	C₂²×C₆₁	1	3	yes	—
295	#459	C₂²×C₆₁	1	1	yes	characteristic
296	#449	C₂²×C₆₁	1	6	yes	—
297	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
298	C₄×SD₁₆	C₂²×C₆₁	1	6	yes	—
299	C₄×D₈	C₂²×C₆₁	1	6	yes	—
300	#436	C₂²×C₆₁	1	6	yes	—
301	#431	C₂²×C₆₁	1	3	yes	—
302	#428	C₂²×C₆₁	1	6	yes	—
303	#423	C₂²×C₆₁	1	3	yes	—
304	#417	C₂²×C₆₁	1	6	yes	—
305	C₆₁	#62148	1	1	yes	characteristic, direct product factor, Sylow
306	2₋¹⁺⁴	—	4	8	no	—
307	C₂×#41	—	2	6	no	—
308	C₂×#41	—	2	3	no	—
309	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
310	C₂×#41	C₂³×C₆₁	1	3	yes	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	2	no	—
313	C₂²×Q₈	—	2	3	no	—
314	C₂×SD₁₆	C₂³×C₆₁	1	6	yes	—
315	C₂×D₈	C₂³×C₆₁	1	2	yes	—
316	C₂×M₁₆	C₂³×C₆₁	1	6	yes	—
317	C₄⋊Q₈	—	2	3	no	—
318	C₄⋊Q₈	—	2	3	no	—
319	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
320	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
321	C₄⋊Q₈	C₂³×C₆₁	1	6	yes	—
322	C₄⋊Q₈	C₂³×C₆₁	1	3	yes	—
323	#127	C₂³×C₆₁	1	1	yes	characteristic
324	#126	—	2	6	no	—
325	#125	—	2	3	no	—
326	#125	—	2	3	no	—
327	#124	—	2	3	no	—
328	#124	—	2	3	no	—
329	#123	—	2	6	no	—
330	#123	—	2	12	no	—
331	C₂²⋊Q₈	—	2	3	no	—
332	C₂²⋊Q₈	—	2	3	no	—
333	C₂²⋊Q₈	—	2	6	no	—
334	C₂²⋊Q₈	—	2	6	no	—
335	C₂²⋊Q₈	C₂³×C₆₁	1	6	yes	—
336	#121	—	2	3	no	—
337	#121	—	2	3	no	—
338	#121	C₂³×C₆₁	1	6	yes	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	3	no	—
341	C₄×Q₈	—	2	3	no	—
342	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
343	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
344	C₄×Q₈	C₂³×C₆₁	1	3	yes	—
345	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	—	2	3	no	—
348	C₄×D₄	—	2	3	no	—
349	C₄×D₄	D₄×C₆₁	1	3	yes	—
350	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
351	C₄×D₄	C₂³×C₆₁	1	3	yes	—
352	C₄×D₄	C₂³×C₆₁	1	6	yes	—
353	C₄×D₄	C₂³×C₆₁	1	3	yes	—
354	#117	—	2	3	no	—
355	#117	—	2	3	no	—
356	#117	D₄×C₆₁	1	3	yes	—
357	#117	C₂³×C₆₁	1	3	yes	—
358	C₂×C₄⋊C₄	—	2	3	no	—
359	C₂×C₄⋊C₄	—	2	3	no	—
360	C₂×C₄⋊C₄	C₂³×C₆₁	1	6	yes	—
361	C₂×C₄²	—	2	3	no	—
362	C₂×C₄²	C₂³×C₆₁	1	3	yes	—
363	#107	C₂³×C₆₁	1	12	yes	—
364	#107	C₂³×C₆₁	1	6	yes	—
365	#106	C₂³×C₆₁	1	6	yes	—
366	C₄⋊C₈	C₂³×C₆₁	1	3	yes	—
367	C₄⋊C₈	C₂³×C₆₁	1	6	yes	—
368	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
369	#103	C₂³×C₆₁	1	12	yes	—
370	#103	C₂³×C₆₁	1	6	yes	—
371	#102	C₂³×C₆₁	1	6	yes	—
372	#102	C₂³×C₆₁	1	6	yes	—
373	#102	C₂³×C₆₁	1	2	yes	—
374	C₂²⋊C₈	C₂³×C₆₁	1	6	yes	—
375	C₄×C₈	C₂³×C₆₁	1	6	yes	—
376	#41	—	2	4	no	—
377	#41	—	2	6	no	—
378	#41	—	4	3	no	—
379	#41	—	4	12	no	—
380	#41	—	4	24	no	—
381	C₂×Q₈	—	2	3	no	—
382	C₂×Q₈	—	2	6	no	—
383	C₂×Q₈	—	2	3	no	—
384	C₂×Q₈	—	4	12	no	—
385	C₂×Q₈	—	4	8	no	—
386	C₂×Q₈	—	4	4	no	—
387	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
388	C₂×Q₈	C₂⁴×C₆₁	1	3	yes	—
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	—	2	6	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	C₂×D₄×C₆₁	1	3	yes	—
394	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
395	C₂×D₄	C₂⁴×C₆₁	1	1	yes	characteristic
396	C₂²×C₄	—	2	6	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	3	no	—
399	C₂²×C₄	—	2	3	no	—
400	C₂²×C₄	—	2	6	no	—
401	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
402	C₂²×C₄	C₂×D₄×C₆₁	1	3	yes	—
403	C₂²×C₄	C₂⁴×C₆₁	1	3	yes	—
404	SD₁₆	—	4	6	no	—
405	D₈	—	2	4	no	—
406	M₁₆	—	4	6	no	—
407	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
408	C₂×C₈	C₂⁴×C₆₁	1	6	yes	—
409	C₄⋊C₄	—	2	3	no	—
410	C₄⋊C₄	—	2	3	no	—
411	C₄⋊C₄	—	2	6	no	—
412	C₄⋊C₄	—	2	6	no	—
413	C₄⋊C₄	—	2	6	no	—
414	C₄⋊C₄	—	2	3	no	—
415	C₄⋊C₄	—	2	3	no	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	—	2	3	no	—
418	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
419	C₄⋊C₄	C₂×D₄×C₆₁	1	3	yes	—
420	C₄⋊C₄	C₂⁴×C₆₁	1	1	yes	characteristic
421	C₄⋊C₄	C₂⁴×C₆₁	1	3	yes	—
422	C₄⋊C₄	C₂⁴×C₆₁	1	6	yes	—
423	C₂²⋊C₄	—	2	6	no	—
424	C₂²⋊C₄	—	2	3	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	3	no	—
427	C₂²⋊C₄	—	2	6	no	—
428	C₂²⋊C₄	—	2	6	no	—
429	C₂²⋊C₄	C₂×D₄×C₆₁	1	6	yes	—
430	C₄²	—	2	3	no	—
431	C₄²	—	2	3	no	—
432	C₄²	—	2	3	no	—
433	C₄²	C₂×D₄×C₆₁	1	3	yes	—
434	C₄²	C₂×D₄×C₆₁	1	3	yes	—
435	C₄²	C₂⁴×C₆₁	1	3	yes	—
436	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
437	C₂³	—	2	1	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₂²×D₄×C₆₁	1	3	yes	—
440	Q₈	—	2	3	no	—
441	Q₈	—	2	3	no	—
442	Q₈	—	4	6	no	—
443	Q₈	—	4	6	no	—
444	Q₈	—	4	12	no	—
445	Q₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
446	D₄	—	2	6	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	1	no	—
449	D₄	—	2	2	no	—
450	D₄	—	4	2	no	—
451	D₄	—	4	6	no	—
452	D₄	—	4	12	no	—
453	D₄	—	4	2	no	—
454	D₄	2₋¹⁺⁴×C₆₁	1	2	yes	complemented
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	2	6	no	—
457	C₂×C₄	—	2	3	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	2	3	no	—
462	C₂×C₄	—	2	6	no	—
463	C₂×C₄	—	4	6	no	—
464	C₂×C₄	—	4	12	no	—
465	C₂×C₄	—	4	6	no	—
466	C₂×C₄	—	4	12	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
469	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
471	C₂×C₄	C₂²×D₄×C₆₁	1	3	yes	—
472	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
473	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	6	no	—
476	C₂²	—	2	3	no	—
477	C₂²	—	2	3	no	—
478	C₂²	—	2	3	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	3	no	—
488	C₄	—	2	3	no	—
489	C₄	—	4	6	no	—
490	C₄	—	4	3	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	3	no	—
493	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	6	yes	—
494	C₄	C₆₁×#578	1	2	yes	—
495	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
496	C₄	C₆₁×#585	1	1	yes	characteristic
497	C₂	—	4	3	no	—
498	C₂	—	4	2	no	—
499	C₂	—	8	2	no	—
500	C₂	C₆₁×#3489	1	1	yes	characteristic
501	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
502	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3499	C₂	semidirect
2. C₆₁×#3482	C₂	semidirect
3. Q₈×D₈×C₆₁	C₂	semidirect
4. C₆₁×#3359	C₂	semidirect
5. C₆₁×#3353	C₂	semidirect
6. C₆₁×#3330	C₂	semidirect
7. C₆₁×#3254	C₂	semidirect
8. C₆₁×#3230	C₂	semidirect
9. C₆₁×#3106	C₂	semidirect
10. C₆₁×#3079	C₂	semidirect
11. C₆₁×#2991	C₂	semidirect
202. D₄×C₆₁	2₋¹⁺⁴	semidirect
224. #62148	C₆₁	direct (N × H)
246. #3499	C₂×C₆₁	semidirect
247. #3482	C₂×C₆₁	semidirect
248. Q₈×D₈	C₂×C₆₁	semidirect
249. #3359	C₂×C₆₁	semidirect
250. #3353	C₂×C₆₁	semidirect
251. #3330	C₂×C₆₁	semidirect
252. #3254	C₂×C₆₁	semidirect
253. #3230	C₂×C₆₁	semidirect
254. #3106	C₂×C₆₁	semidirect
255. #3079	C₂×C₆₁	semidirect
256. #2991	C₂×C₆₁	semidirect
305. C₆₁	#62148	direct (N × H)
454. D₄	2₋¹⁺⁴×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3499	2
C₆₁×#3482	2
Q₈×D₈×C₆₁	2
C₆₁×#3359	2
C₆₁×#3353	2
C₆₁×#3330	2
C₆₁×#3254	2
C₆₁×#3230	2
C₆₁×#3106	2
C₆₁×#3079	2
C₆₁×#2991	2
#62148	61

Subgroups — C61×#62148 #29565581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#62148 #29565581