Subgroups — C₆₁×#61888 #29565321

Order 15616.

1970 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3397	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3367	C₂	1	8	yes	maximal, complemented
5	C₆₁×#3213	C₂	1	4	yes	maximal, complemented
6	C₆₁×#3206	C₂	1	2	yes	maximal, complemented
7	C₆₁×#3112	C₂	1	4	yes	maximal, complemented
8	C₆₁×#3100	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₆₁	—	2	1	no	—
11	C₆₁×#556	—	2	4	no	—
12	C₆₁×#556	C₂²	1	8	yes	—
13	C₆₁×#550	C₂²	1	4	yes	complemented
14	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
15	C₆₁×#548	—	2	4	no	—
16	C₆₁×#537	—	2	1	no	—
17	C₆₁×#537	—	2	2	no	—
18	C₆₁×#532	C₂²	1	2	yes	—
19	C₆₁×#532	C₂²	1	4	yes	—
20	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#126×C₆₁	—	2	2	no	—
22	C₂×#124×C₆₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
24	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#117×C₆₁	—	2	1	no	—
28	C₆₁×#496	C₂²	1	8	yes	—
29	C₆₁×#492	C₂²	1	4	yes	complemented
30	C₆₁×#489	C₂²	1	8	yes	—
31	C₆₁×#487	C₂²	1	4	yes	complemented
32	C₆₁×#480	C₂²	1	4	yes	—
33	C₆₁×#477	C₂²	1	8	yes	complemented
34	C₆₁×#474	C₂²	1	4	yes	—
35	C₆₁×#463	C₂²	1	16	yes	—
36	C₆₁×#461	C₂²	1	8	yes	complemented
37	C₆₁×#460	C₂²	1	8	yes	complemented
38	C₆₁×#459	C₂²	1	4	yes	—
39	C₆₁×#448	C₂²	1	8	yes	—
40	C₆₁×#447	C₂²	1	4	yes	—
41	C₆₁×#446	C₂²	1	8	yes	complemented
42	C₆₁×#440	C₂²	1	16	yes	complemented
43	C₄×D₈×C₆₁	C₂²	1	8	yes	—
44	C₆₁×#432	C₂²	1	4	yes	—
45	C₆₁×#431	C₂²	1	2	yes	—
46	2₋¹⁺⁴×C₆₁	—	4	8	no	—
47	C₂×#41×C₆₁	—	2	4	no	—
48	C₂×#41×C₆₁	—	2	4	no	—
49	C₂×#41×C₆₁	—	2	2	no	—
50	C₂²×Q₈×C₆₁	—	2	4	no	—
51	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
52	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
53	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₆₁	—	2	1	no	—
55	C₂×SD₁₆×C₆₁	C₂³	1	16	yes	—
56	C₂×D₈×C₆₁	C₂³	1	8	yes	—
57	C₄⋊Q₈×C₆₁	—	2	2	no	—
58	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
59	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₆₁	C₂³	1	4	yes	—
61	#127×C₆₁	C₂³	1	2	yes	—
62	#127×C₆₁	C₂³	1	4	yes	—
63	#126×C₆₁	—	2	16	no	—
64	#124×C₆₁	—	2	2	no	—
65	#124×C₆₁	—	2	4	no	—
66	#124×C₆₁	—	2	4	no	—
67	#124×C₆₁	C₂³	1	8	yes	—
68	C₂²⋊Q₈×C₆₁	—	2	8	no	—
69	C₂²⋊Q₈×C₆₁	—	2	4	no	—
70	C₂²⋊Q₈×C₆₁	—	2	8	no	—
71	#121×C₆₁	—	2	4	no	—
72	#121×C₆₁	—	2	2	no	—
73	#121×C₆₁	—	2	4	no	—
74	#121×C₆₁	—	2	8	no	—
75	#121×C₆₁	C₂³	1	4	yes	—
76	C₄×Q₈×C₆₁	—	2	4	no	—
77	C₄×Q₈×C₆₁	D₄	1	4	yes	—
78	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
79	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
80	C₄×D₄×C₆₁	—	2	2	no	—
81	C₄×D₄×C₆₁	—	2	4	no	—
82	C₄×D₄×C₆₁	—	2	2	no	—
83	C₄×D₄×C₆₁	C₂³	1	4	yes	—
84	C₄×D₄×C₆₁	C₂³	1	8	yes	—
85	C₄×D₄×C₆₁	C₂³	1	4	yes	—
86	#117×C₆₁	—	2	8	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
90	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
96	C₂×C₄²×C₆₁	—	2	2	no	—
97	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
99	#107×C₆₁	C₂³	1	8	yes	—
100	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
101	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
102	#103×C₆₁	C₂³	1	16	yes	—
103	#102×C₆₁	C₂³	1	8	yes	—
104	#102×C₆₁	C₂³	1	8	yes	—
105	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
106	#97×C₆₁	C₂³	1	8	yes	—
107	C₄×C₈×C₆₁	C₂³	1	4	yes	—
108	C₂⁴×C₆₁	—	2	1	no	—
109	#41×C₆₁	—	4	16	no	—
110	#41×C₆₁	—	4	16	no	—
111	#41×C₆₁	—	4	8	no	—
112	C₂×Q₈×C₆₁	—	2	4	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	4	no	—
115	C₂×Q₈×C₆₁	—	2	2	no	—
116	C₂×Q₈×C₆₁	—	4	4	no	—
117	C₂×Q₈×C₆₁	—	4	16	no	—
118	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
119	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
120	C₂×D₄×C₆₁	—	2	4	no	—
121	C₂×D₄×C₆₁	—	2	1	no	—
122	C₂×D₄×C₆₁	—	2	4	no	—
123	C₂×D₄×C₆₁	—	2	2	no	—
124	C₂×D₄×C₆₁	—	2	4	no	—
125	C₂×D₄×C₆₁	—	2	2	no	—
126	C₂×D₄×C₆₁	—	4	2	no	—
127	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
128	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₆₁	—	2	1	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	4	no	—
132	C₂²×C₄×C₆₁	—	2	8	no	—
133	C₂²×C₄×C₆₁	—	2	4	no	—
134	C₂²×C₄×C₆₁	—	4	4	no	—
135	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
140	SD₁₆×C₆₁	—	4	16	no	—
141	D₈×C₆₁	—	4	8	no	—
142	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
143	C₄⋊C₄×C₆₁	—	2	4	no	—
144	C₄⋊C₄×C₆₁	—	2	8	no	—
145	C₄⋊C₄×C₆₁	—	2	4	no	—
146	C₄⋊C₄×C₆₁	—	2	1	no	—
147	C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₄⋊C₄×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
151	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
153	C₂²⋊C₄×C₆₁	—	2	8	no	—
154	C₂²⋊C₄×C₆₁	—	2	4	no	—
155	C₂²⋊C₄×C₆₁	—	2	8	no	—
156	C₂²⋊C₄×C₆₁	—	2	4	no	—
157	C₂²⋊C₄×C₆₁	—	2	8	no	—
158	C₂²⋊C₄×C₆₁	—	2	4	no	—
159	C₄²×C₆₁	—	2	8	no	—
160	C₄²×C₆₁	C₂×D₄	1	2	yes	—
161	C₄²×C₆₁	C₂×D₄	1	4	yes	—
162	C₄²×C₆₁	C₂⁴	1	2	yes	—
163	C₄²×C₆₁	C₂⁴	1	4	yes	—
164	C₂³×C₆₁	—	2	2	no	—
165	C₂³×C₆₁	—	2	4	no	—
166	C₂³×C₆₁	—	4	2	no	—
167	C₂³×C₆₁	—	4	2	no	—
168	C₂³×C₆₁	—	4	2	no	—
169	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
170	Q₈×C₆₁	—	2	8	no	—
171	Q₈×C₆₁	—	2	8	no	—
172	Q₈×C₆₁	—	4	4	no	—
173	Q₈×C₆₁	—	4	8	no	—
174	Q₈×C₆₁	—	4	4	no	—
175	D₄×C₆₁	—	2	4	no	—
176	D₄×C₆₁	—	2	8	no	—
177	D₄×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	8	no	—
179	D₄×C₆₁	—	4	8	no	—
180	D₄×C₆₁	—	4	4	no	—
181	D₄×C₆₁	—	8	4	no	—
182	D₄×C₆₁	—	8	2	no	—
183	C₂×C₄×C₆₁	—	2	4	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	4	2	no	—
189	C₂×C₄×C₆₁	—	4	1	no	—
190	C₂×C₄×C₆₁	—	4	16	no	—
191	C₂×C₄×C₆₁	—	4	4	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	8	no	—
194	C₂×C₄×C₆₁	—	4	8	no	—
195	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
202	C₈×C₆₁	—	2	8	no	—
203	#61888	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂²×C₆₁	—	2	1	no	—
205	C₂²×C₆₁	—	2	1	no	—
206	C₂²×C₆₁	—	4	4	no	—
207	C₂²×C₆₁	—	4	2	no	—
208	C₂²×C₆₁	—	4	2	no	—
209	C₂²×C₆₁	—	4	4	no	—
210	C₂²×C₆₁	—	4	4	no	—
211	C₂²×C₆₁	—	4	2	no	—
212	C₂²×C₆₁	—	8	4	no	—
213	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
214	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
215	C₄×C₆₁	—	2	4	no	—
216	C₄×C₆₁	—	2	2	no	—
217	C₄×C₆₁	—	2	1	no	—
218	C₄×C₆₁	—	2	4	no	—
219	C₄×C₆₁	—	4	4	no	—
220	C₄×C₆₁	—	4	2	no	—
221	C₄×C₆₁	—	4	4	no	—
222	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
223	C₄×C₆₁	#585	1	2	yes	—
224	#3497	C₂×C₆₁	1	1	yes	characteristic, complemented
225	C₂×#556	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#3397	C₂×C₆₁	1	8	yes	complemented
227	#3367	C₂×C₆₁	1	8	yes	complemented
228	#3213	C₂×C₆₁	1	4	yes	complemented
229	#3206	C₂×C₆₁	1	2	yes	complemented
230	#3112	C₂×C₆₁	1	4	yes	complemented
231	#3100	C₂×C₆₁	1	2	yes	complemented
232	#2983	C₂×C₆₁	1	1	yes	characteristic, complemented
233	C₂×C₆₁	—	2	2	no	—
234	C₂×C₆₁	—	8	4	no	—
235	C₂×C₆₁	—	8	2	no	—
236	C₂×C₆₁	#3487	1	1	yes	characteristic
237	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₂×C₆₁	#3586	1	1	yes	characteristic
239	C₂×2₋¹⁺⁴	—	2	1	no	—
240	#556	—	2	4	no	—
241	#556	C₂²×C₆₁	1	8	yes	—
242	#550	C₂²×C₆₁	1	4	yes	complemented
243	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
244	#548	—	2	4	no	—
245	#537	—	2	1	no	—
246	#537	—	2	2	no	—
247	#532	C₂²×C₆₁	1	2	yes	—
248	#532	C₂²×C₆₁	1	4	yes	—
249	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
250	C₂×#126	—	2	2	no	—
251	C₂×#124	C₂²×C₆₁	1	2	yes	—
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×#117	—	2	1	no	—
257	#496	C₂²×C₆₁	1	8	yes	—
258	#492	C₂²×C₆₁	1	4	yes	complemented
259	#489	C₂²×C₆₁	1	8	yes	—
260	#487	C₂²×C₆₁	1	4	yes	complemented
261	#480	C₂²×C₆₁	1	4	yes	—
262	#477	C₂²×C₆₁	1	8	yes	complemented
263	#474	C₂²×C₆₁	1	4	yes	—
264	#463	C₂²×C₆₁	1	16	yes	—
265	#461	C₂²×C₆₁	1	8	yes	complemented
266	#460	C₂²×C₆₁	1	8	yes	complemented
267	#459	C₂²×C₆₁	1	4	yes	—
268	#448	C₂²×C₆₁	1	8	yes	—
269	#447	C₂²×C₆₁	1	4	yes	—
270	#446	C₂²×C₆₁	1	8	yes	complemented
271	#440	C₂²×C₆₁	1	16	yes	complemented
272	C₄×D₈	C₂²×C₆₁	1	8	yes	—
273	#432	C₂²×C₆₁	1	4	yes	—
274	#431	C₂²×C₆₁	1	2	yes	—
275	C₆₁	#61888	1	1	yes	characteristic, direct product factor, Sylow
276	2₋¹⁺⁴	—	4	8	no	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	2	no	—
280	C₂²×Q₈	—	2	4	no	—
281	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
282	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
283	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
284	C₂³×C₄	—	2	1	no	—
285	C₂×SD₁₆	C₂³×C₆₁	1	16	yes	—
286	C₂×D₈	C₂³×C₆₁	1	8	yes	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
289	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
290	C₄⋊Q₈	C₂³×C₆₁	1	4	yes	—
291	#127	C₂³×C₆₁	1	2	yes	—
292	#127	C₂³×C₆₁	1	4	yes	—
293	#126	—	2	16	no	—
294	#124	—	2	4	no	—
295	#124	—	2	2	no	—
296	#124	—	2	4	no	—
297	#124	C₂³×C₆₁	1	8	yes	—
298	C₂²⋊Q₈	—	2	8	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	2	8	no	—
301	#121	—	2	4	no	—
302	#121	—	2	2	no	—
303	#121	—	2	4	no	—
304	#121	—	2	8	no	—
305	#121	C₂³×C₆₁	1	4	yes	—
306	C₄×Q₈	—	2	4	no	—
307	C₄×Q₈	D₄×C₆₁	1	4	yes	—
308	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
309	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
310	C₄×D₄	—	2	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	C₂³×C₆₁	1	4	yes	—
314	C₄×D₄	C₂³×C₆₁	1	4	yes	—
315	C₄×D₄	C₂³×C₆₁	1	8	yes	—
316	#117	—	2	8	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
321	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
329	#107	C₂³×C₆₁	1	8	yes	—
330	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
331	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
332	#103	C₂³×C₆₁	1	16	yes	—
333	#102	C₂³×C₆₁	1	8	yes	—
334	#102	C₂³×C₆₁	1	8	yes	—
335	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
336	#97	C₂³×C₆₁	1	8	yes	—
337	C₄×C₈	C₂³×C₆₁	1	4	yes	—
338	C₂⁴	—	2	1	no	—
339	#41	—	4	16	no	—
340	#41	—	4	16	no	—
341	#41	—	4	8	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×Q₈	—	4	16	no	—
348	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
349	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
358	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
370	SD₁₆	—	4	16	no	—
371	D₈	—	4	8	no	—
372	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
380	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
381	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
382	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
383	C₂²⋊C₄	—	2	8	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₄²	—	2	8	no	—
390	C₄²	C₂×D₄×C₆₁	1	2	yes	—
391	C₄²	C₂×D₄×C₆₁	1	4	yes	—
392	C₄²	C₂⁴×C₆₁	1	2	yes	—
393	C₄²	C₂⁴×C₆₁	1	4	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	4	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
400	Q₈	—	2	8	no	—
401	Q₈	—	2	8	no	—
402	Q₈	—	4	4	no	—
403	Q₈	—	4	8	no	—
404	Q₈	—	4	4	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	8	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	4	no	—
411	D₄	—	8	4	no	—
412	D₄	—	8	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	16	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	8	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
430	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
431	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
432	C₈	—	2	8	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	4	no	—
442	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
443	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	2	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	4	yes	—
452	C₄	C₆₁×#585	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	8	2	no	—
455	C₂	—	8	4	no	—
456	C₂	C₆₁×#3487	1	1	yes	characteristic
457	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
458	C₂	C₆₁×#3586	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 ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3497	C₂	semidirect
2. C₂×C₆₁×#556	C₂	semidirect
3. C₆₁×#3397	C₂	semidirect
4. C₆₁×#3367	C₂	semidirect
5. C₆₁×#3213	C₂	semidirect
6. C₆₁×#3206	C₂	semidirect
7. C₆₁×#3112	C₂	semidirect
8. C₆₁×#3100	C₂	semidirect
9. C₆₁×#2983	C₂	semidirect
13. C₆₁×#550	C₂²	semidirect
14. D₄×Q₈×C₆₁	C₂²	semidirect
29. C₆₁×#492	C₂²	semidirect
31. C₆₁×#487	C₂²	semidirect
33. C₆₁×#477	C₂²	semidirect
36. C₆₁×#461	C₂²	semidirect
37. C₆₁×#460	C₂²	semidirect
41. C₆₁×#446	C₂²	semidirect
42. C₆₁×#440	C₂²	semidirect
203. #61888	C₆₁	direct (N × H)
224. #3497	C₂×C₆₁	semidirect
225. C₂×#556	C₂×C₆₁	semidirect
226. #3397	C₂×C₆₁	semidirect
227. #3367	C₂×C₆₁	semidirect
228. #3213	C₂×C₆₁	semidirect
229. #3206	C₂×C₆₁	semidirect
230. #3112	C₂×C₆₁	semidirect
231. #3100	C₂×C₆₁	semidirect
232. #2983	C₂×C₆₁	semidirect
242. #550	C₂²×C₆₁	semidirect
243. D₄×Q₈	C₂²×C₆₁	semidirect
258. #492	C₂²×C₆₁	semidirect
260. #487	C₂²×C₆₁	semidirect
262. #477	C₂²×C₆₁	semidirect
265. #461	C₂²×C₆₁	semidirect
266. #460	C₂²×C₆₁	semidirect
270. #446	C₂²×C₆₁	semidirect
271. #440	C₂²×C₆₁	semidirect
275. C₆₁	#61888	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×#3497	2
C₂×C₆₁×#556	2
C₆₁×#3397	2
C₆₁×#3367	2
C₆₁×#3213	2
C₆₁×#3206	2
C₆₁×#3112	2
C₆₁×#3100	2
C₆₁×#2983	2
#61888	61

Subgroups — C61×#61888 #29565321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61888 #29565321