Subgroups — C₆₁×#23716 #29527149

Order 15616.

816 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2089	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2078	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2063	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2051	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2018	C₂	1	1	yes	maximal, characteristic
10	C₄×#108×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#100×C₆₁	C₂	1	2	yes	maximal, complemented
12	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
16	C₆₁×#442	—	2	2	no	—
17	C₆₁×#440	—	2	2	no	—
18	C₄×SD₁₆×C₆₁	—	2	2	no	—
19	C₄×D₈×C₆₁	—	2	2	no	—
20	C₄×D₈×C₆₁	—	2	2	no	—
21	C₄×D₈×C₆₁	—	2	2	no	—
22	C₆₁×#433	—	2	2	no	—
23	C₆₁×#431	—	2	2	no	—
24	C₂×#108×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#428	C₂²	1	2	yes	—
26	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#424	C₂²	1	1	yes	characteristic
28	C₆₁×#424	C₂²	1	1	yes	characteristic
29	C₆₁×#418	C₂²	1	2	yes	—
30	C₆₁×#417	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	2	yes	—
32	C₂×#100×C₆₁	C₂²	1	2	yes	—
33	C₂×#100×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#408	C₂²	1	1	yes	characteristic
35	C₆₁×#408	C₂²	1	1	yes	characteristic
36	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
37	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#343	C₂²	1	2	yes	—
40	C₆₁×#343	C₂²	1	2	yes	—
41	C₆₁×#341	C₂²	1	1	yes	characteristic
42	C₆₁×#341	C₂²	1	1	yes	characteristic
43	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
45	C₂³×C₄×C₆₁	—	2	2	no	—
46	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
47	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
48	C₂×SD₁₆×C₆₁	—	2	2	no	—
49	C₂×D₈×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	—	2	4	no	—
51	C₂×D₈×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
53	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
59	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
60	C₄×D₄×C₆₁	—	2	1	no	—
61	C₄×D₄×C₆₁	—	2	1	no	—
62	C₄×D₄×C₆₁	—	2	2	no	—
63	C₄×D₄×C₆₁	—	2	2	no	—
64	C₄×D₄×C₆₁	—	2	2	no	—
65	C₄×D₄×C₆₁	—	2	2	no	—
66	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
67	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
68	#117×C₆₁	—	2	1	no	—
69	#117×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄²×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
74	#108×C₆₁	—	2	4	no	—
75	#107×C₆₁	—	2	2	no	—
76	#107×C₆₁	—	2	2	no	—
77	#106×C₆₁	—	2	2	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	C₄⋊C₈×C₆₁	—	2	2	no	—
80	#103×C₆₁	—	2	2	no	—
81	#102×C₆₁	—	2	2	no	—
82	#102×C₆₁	—	2	4	no	—
83	#102×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	2	no	—
85	#100×C₆₁	—	2	4	no	—
86	#100×C₆₁	—	2	4	no	—
87	C₂²⋊C₈×C₆₁	—	2	2	no	—
88	C₂²⋊C₈×C₆₁	—	2	2	no	—
89	#97×C₆₁	—	2	1	no	—
90	#97×C₆₁	—	2	2	no	—
91	C₄×C₈×C₆₁	—	2	1	no	—
92	C₄×C₈×C₆₁	—	2	2	no	—
93	C₄×C₈×C₆₁	D₄	1	2	yes	—
94	C₄×C₈×C₆₁	D₄	1	2	yes	—
95	C₂⁴×C₆₁	—	2	2	no	—
96	#41×C₆₁	—	2	2	no	—
97	#41×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₆₁	—	2	1	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	2	no	—
104	C₂×D₄×C₆₁	—	2	2	no	—
105	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₆₁	#41	1	4	yes	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	4	2	no	—
112	C₂²×C₄×C₆₁	—	4	2	no	—
113	C₂²×C₄×C₆₁	—	8	4	no	—
114	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
116	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
117	SD₁₆×C₆₁	—	2	8	no	—
118	D₈×C₆₁	—	2	8	no	—
119	D₈×C₆₁	—	2	8	no	—
120	M₁₆×C₆₁	—	2	2	no	—
121	M₁₆×C₆₁	—	2	2	no	—
122	M₁₆×C₆₁	—	2	2	no	—
123	M₁₆×C₆₁	—	2	2	no	—
124	M₁₆×C₆₁	—	2	2	no	—
125	M₁₆×C₆₁	#41	1	4	yes	—
126	C₂×C₈×C₆₁	—	2	2	no	—
127	C₂×C₈×C₆₁	—	2	2	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	1	no	—
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	—	2	2	no	—
132	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	1	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₆₁	—	2	1	no	—
141	C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂²⋊C₄×C₆₁	—	2	1	no	—
143	C₂²⋊C₄×C₆₁	—	4	2	no	—
144	C₂²⋊C₄×C₆₁	—	4	2	no	—
145	C₄²×C₆₁	—	2	1	no	—
146	C₄²×C₆₁	—	2	1	no	—
147	C₄²×C₆₁	—	2	1	no	—
148	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₂³×C₆₁	—	2	1	no	—
153	C₂³×C₆₁	—	2	4	no	—
154	C₂³×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	—	4	2	no	—
156	C₂³×C₆₁	—	8	2	no	—
157	C₂³×C₆₁	—	8	2	no	—
158	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
159	Q₈×C₆₁	—	2	2	no	—
160	D₄×C₆₁	—	2	4	no	—
161	D₄×C₆₁	—	2	2	no	—
162	D₄×C₆₁	—	2	4	no	—
163	D₄×C₆₁	—	4	2	no	—
164	D₄×C₆₁	—	4	2	no	—
165	D₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	8	4	no	—
177	C₂×C₄×C₆₁	—	8	4	no	—
178	C₂×C₄×C₆₁	—	8	2	no	—
179	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
183	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
186	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
187	C₈×C₆₁	—	2	2	no	—
188	C₈×C₆₁	—	2	4	no	—
189	C₈×C₆₁	—	2	2	no	—
190	C₈×C₆₁	—	4	1	no	—
191	C₈×C₆₁	—	4	2	no	—
192	C₈×C₆₁	—	4	1	no	—
193	#23716	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₆₁	—	2	1	no	—
195	C₂²×C₆₁	—	2	1	no	—
196	C₂²×C₆₁	—	4	1	no	—
197	C₂²×C₆₁	—	4	4	no	—
198	C₂²×C₆₁	—	4	1	no	—
199	C₂²×C₆₁	—	4	1	no	—
200	C₂²×C₆₁	—	8	4	no	—
201	C₂²×C₆₁	—	8	4	no	—
202	C₂²×C₆₁	—	8	2	no	—
203	C₂²×C₆₁	—	8	2	no	—
204	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
205	C₂²×C₆₁	#529	1	2	yes	—
206	C₄×C₆₁	—	2	1	no	—
207	C₄×C₆₁	—	2	1	no	—
208	C₄×C₆₁	—	2	1	no	—
209	C₄×C₆₁	—	4	1	no	—
210	C₄×C₆₁	—	4	1	no	—
211	C₄×C₆₁	—	4	1	no	—
212	C₄×C₆₁	—	8	2	no	—
213	C₄×C₆₁	#472	1	2	yes	—
214	C₄×C₆₁	#525	1	1	yes	characteristic
215	C₄×C₆₁	#525	1	2	yes	—
216	C₄×C₆₁	#532	1	1	yes	characteristic
217	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	2	yes	complemented
218	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#2922	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#2089	C₂×C₆₁	1	1	yes	characteristic, complemented
221	#2078	C₂×C₆₁	1	1	yes	characteristic, complemented
222	#2063	C₂×C₆₁	1	2	yes	complemented
223	#2051	C₂×C₆₁	1	2	yes	complemented
224	#2045	C₂×C₆₁	1	1	yes	characteristic, complemented
225	#2018	C₂×C₆₁	1	1	yes	characteristic
226	C₄×#108	C₂×C₆₁	1	1	yes	characteristic, complemented
227	C₄×#100	C₂×C₆₁	1	2	yes	complemented
228	C₂×C₆₁	—	2	2	no	—
229	C₂×C₆₁	—	8	1	no	—
230	C₂×C₆₁	—	8	4	no	—
231	C₂×C₆₁	#2392	1	1	yes	characteristic
232	C₂×C₆₁	C₂×#472	1	1	yes	characteristic
233	C₂×C₆₁	#3067	1	1	yes	characteristic
234	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
235	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
236	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
237	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
238	#442	—	2	2	no	—
239	#440	—	2	2	no	—
240	C₄×SD₁₆	—	2	2	no	—
241	C₄×D₈	—	2	2	no	—
242	C₄×D₈	—	2	2	no	—
243	C₄×D₈	—	2	2	no	—
244	#433	—	2	2	no	—
245	#431	—	2	2	no	—
246	C₂×#108	C₂²×C₆₁	1	2	yes	—
247	#428	C₂²×C₆₁	1	2	yes	—
248	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
249	#424	C₂²×C₆₁	1	1	yes	characteristic
250	#424	C₂²×C₆₁	1	1	yes	characteristic
251	#418	C₂²×C₆₁	1	2	yes	—
252	#417	C₂²×C₆₁	1	2	yes	—
253	C₂×#102	C₂²×C₆₁	1	2	yes	—
254	C₂×#100	C₂²×C₆₁	1	2	yes	—
255	C₂×#100	C₂²×C₆₁	1	2	yes	—
256	#408	C₂²×C₆₁	1	1	yes	characteristic
257	#408	C₂²×C₆₁	1	1	yes	characteristic
258	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
259	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
261	#343	C₂²×C₆₁	1	2	yes	—
262	#343	C₂²×C₆₁	1	2	yes	—
263	#341	C₂²×C₆₁	1	1	yes	characteristic
264	#341	C₂²×C₆₁	1	1	yes	characteristic
265	C₆₁	#23716	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
267	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
268	C₂³×C₄	—	2	2	no	—
269	AGL(1,ℤ/8)	—	2	4	no	—
270	AGL(1,ℤ/8)	—	2	4	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×D₈	—	2	2	no	—
273	C₂×D₈	—	2	4	no	—
274	C₂×D₈	—	2	2	no	—
275	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
276	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
277	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
278	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
279	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
280	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
281	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
282	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
290	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
291	#117	—	2	1	no	—
292	#117	C₂³×C₆₁	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
297	#108	—	2	4	no	—
298	#107	—	2	2	no	—
299	#107	—	2	2	no	—
300	#106	—	2	2	no	—
301	C₄⋊C₈	—	2	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	#103	—	2	2	no	—
304	#102	—	2	2	no	—
305	#102	—	2	4	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#100	—	2	4	no	—
309	#100	—	2	4	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	#97	—	2	1	no	—
313	#97	—	2	2	no	—
314	C₄×C₈	—	2	1	no	—
315	C₄×C₈	—	2	2	no	—
316	C₄×C₈	D₄×C₆₁	1	2	yes	—
317	C₄×C₈	D₄×C₆₁	1	2	yes	—
318	C₂⁴	—	2	2	no	—
319	#41	—	2	2	no	—
320	#41	—	2	2	no	—
321	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
329	C₂×D₄	#41×C₆₁	1	4	yes	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	8	4	no	—
337	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
338	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
339	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
340	SD₁₆	—	2	8	no	—
341	D₈	—	2	8	no	—
342	D₈	—	2	8	no	—
343	M₁₆	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	#41×C₆₁	1	4	yes	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
356	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
362	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
374	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
375	C₂³	—	2	1	no	—
376	C₂³	—	2	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	D₄	—	2	4	no	—
384	D₄	—	2	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
403	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
404	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
405	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
409	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	4	no	—
413	C₈	—	4	1	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	2	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	8	4	no	—
423	C₂²	—	8	4	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
427	C₂²	C₆₁×#529	1	2	yes	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₆₁×#472	1	2	yes	—
436	C₄	C₆₁×#525	1	1	yes	characteristic
437	C₄	C₆₁×#525	1	2	yes	—
438	C₄	C₆₁×#532	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	8	1	no	—
441	C₂	—	8	4	no	—
442	C₂	C₆₁×#2392	1	1	yes	characteristic
443	C₂	C₂×C₆₁×#472	1	1	yes	characteristic
444	C₂	C₆₁×#3067	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂×#121
prime radical	C₆₁×#2018	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
2. C₂×C₄×D₈×C₆₁	C₂	semidirect
3. C₆₁×#2922	C₂	semidirect
4. C₆₁×#2089	C₂	semidirect
5. C₆₁×#2078	C₂	semidirect
6. C₆₁×#2063	C₂	semidirect
7. C₆₁×#2051	C₂	semidirect
8. C₆₁×#2045	C₂	semidirect
10. C₄×#108×C₆₁	C₂	semidirect
11. C₄×#100×C₆₁	C₂	semidirect
193. #23716	C₆₁	direct (N × H)
217. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
218. C₂×C₄×D₈	C₂×C₆₁	semidirect
219. #2922	C₂×C₆₁	semidirect
220. #2089	C₂×C₆₁	semidirect
221. #2078	C₂×C₆₁	semidirect
222. #2063	C₂×C₆₁	semidirect
223. #2051	C₂×C₆₁	semidirect
224. #2045	C₂×C₆₁	semidirect
226. C₄×#108	C₂×C₆₁	semidirect
227. C₄×#100	C₂×C₆₁	semidirect
265. C₆₁	#23716	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×AGL(1,ℤ/8)×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₆₁×#2922	2
C₆₁×#2089	2
C₆₁×#2078	2
C₆₁×#2063	2
C₆₁×#2051	2
C₆₁×#2045	2
C₆₁×#2018	2
C₄×#108×C₆₁	2
C₄×#100×C₆₁	2
#23716	61

Subgroups — C61×#23716 #29527149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23716 #29527149