Subgroups — C₆₁×#25838 #29529271

Order 15616.

1266 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#474	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2057	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1862	C₂	1	4	yes	maximal
9	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₆₁	—	2	1	no	—
11	D₄×Q₈×C₆₁	—	2	4	no	—
12	D₄×Q₈×C₆₁	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#500	—	2	4	no	—
23	C₆₁×#474	—	2	4	no	—
24	C₂×#107×C₆₁	C₂²	1	2	yes	—
25	C₂×#107×C₆₁	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₆₁	C₂²	1	2	yes	—
28	C₂×#102×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#398	—	2	2	no	—
31	C₆₁×#391	—	2	1	no	—
32	C₆₁×#389	C₂²	1	4	yes	—
33	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#340	C₂²	1	2	yes	—
35	C₆₁×#340	C₂²	1	4	yes	—
36	C₆₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₆₁	—	2	8	no	—
38	C₂²×Q₈×C₆₁	—	2	2	no	—
39	C₂²×Q₈×C₆₁	—	2	1	no	—
40	C₂²×Q₈×C₆₁	—	2	1	no	—
41	C₂²×Q₈×C₆₁	—	4	4	no	—
42	C₂²×Q₈×C₆₁	—	4	4	no	—
43	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	2	no	—
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₆₁	—	2	4	no	—
50	C₄⋊Q₈×C₆₁	—	2	4	no	—
51	C₄⋊Q₈×C₆₁	—	2	2	no	—
52	C₄⋊Q₈×C₆₁	—	2	2	no	—
53	C₄⋊Q₈×C₆₁	—	2	2	no	—
54	C₄⋊Q₈×C₆₁	—	4	4	no	—
55	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
56	C₂²⋊Q₈×C₆₁	—	2	8	no	—
57	C₂²⋊Q₈×C₆₁	—	2	16	no	—
58	C₄×Q₈×C₆₁	—	2	2	no	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×D₄×C₆₁	—	2	4	no	—
61	C₄×D₄×C₆₁	—	2	4	no	—
62	C₄×D₄×C₆₁	—	2	2	no	—
63	C₄×D₄×C₆₁	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄²×C₆₁	—	2	1	no	—
77	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
78	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
79	#107×C₆₁	—	2	4	no	—
80	#107×C₆₁	—	2	8	no	—
81	C₄⋊C₈×C₆₁	—	2	2	no	—
82	#102×C₆₁	—	2	4	no	—
83	#102×C₆₁	Q₈	1	8	yes	complemented
84	C₄×C₈×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	1	no	—
86	#95×C₆₁	—	2	4	no	—
87	C₂⁴×C₆₁	—	2	1	no	—
88	C₂×Q₈×C₆₁	—	2	8	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	4	no	—
91	C₂×Q₈×C₆₁	—	2	2	no	—
92	C₂×Q₈×C₆₁	—	4	4	no	—
93	C₂×Q₈×C₆₁	—	4	32	no	—
94	C₂×Q₈×C₆₁	—	4	2	no	—
95	C₂×Q₈×C₆₁	—	4	4	no	—
96	C₂×Q₈×C₆₁	—	4	2	no	—
97	C₂×Q₈×C₆₁	—	4	2	no	—
98	C₂×Q₈×C₆₁	—	4	2	no	—
99	C₂×Q₈×C₆₁	—	4	2	no	—
100	C₂×Q₈×C₆₁	D₈	1	4	yes	—
101	C₂×D₄×C₆₁	—	2	1	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₆₁	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₆₁	—	2	8	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	4	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	4	4	no	—
112	C₂²×C₄×C₆₁	—	4	4	no	—
113	C₂²×C₄×C₆₁	—	4	2	no	—
114	C₂²×C₄×C₆₁	—	4	2	no	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	—	2	2	no	—
123	C₂×C₈×C₆₁	—	2	4	no	—
124	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	complemented
125	C₄⋊C₄×C₆₁	—	2	8	no	—
126	C₄⋊C₄×C₆₁	—	2	4	no	—
127	C₄⋊C₄×C₆₁	—	2	4	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	4	2	no	—
135	C₄⋊C₄×C₆₁	—	4	8	no	—
136	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₆₁	C₂×Q₈	1	4	yes	complemented
139	C₂²⋊C₄×C₆₁	—	2	8	no	—
140	C₂²⋊C₄×C₆₁	—	2	4	no	—
141	C₄²×C₆₁	—	2	2	no	—
142	C₄²×C₆₁	—	2	2	no	—
143	C₄²×C₆₁	—	4	2	no	—
144	C₄²×C₆₁	C₂×D₄	1	2	yes	—
145	C₄²×C₆₁	C₂×D₄	1	2	yes	—
146	C₂³×C₆₁	—	2	2	no	—
147	C₂³×C₆₁	—	2	4	no	—
148	C₂³×C₆₁	—	4	1	no	—
149	C₂³×C₆₁	—	4	1	no	—
150	C₂³×C₆₁	—	4	2	no	—
151	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₆₁	—	2	8	no	—
153	Q₈×C₆₁	—	4	16	no	—
154	Q₈×C₆₁	—	4	8	no	—
155	Q₈×C₆₁	—	8	4	no	—
156	D₄×C₆₁	—	2	2	no	—
157	D₄×C₆₁	—	2	4	no	—
158	D₄×C₆₁	C₄⋊Q₈	1	4	yes	complemented
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	2	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	2	no	—
163	C₂×C₄×C₆₁	—	2	4	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	4	no	—
166	C₂×C₄×C₆₁	—	2	4	no	—
167	C₂×C₄×C₆₁	—	4	16	no	—
168	C₂×C₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	—	4	2	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	2	no	—
174	C₂×C₄×C₆₁	—	4	8	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	#120	1	2	yes	—
179	C₂×C₄×C₆₁	#120	1	2	yes	—
180	C₂×C₄×C₆₁	C₂×D₈	1	4	yes	—
181	C₂×C₄×C₆₁	C₂×D₈	1	2	yes	—
182	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
186	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
187	C₈×C₆₁	—	2	4	no	—
188	C₈×C₆₁	—	4	2	no	—
189	#25838	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₆₁	—	2	4	no	—
191	C₂²×C₆₁	—	4	4	no	—
192	C₂²×C₆₁	—	4	4	no	—
193	C₂²×C₆₁	—	4	2	no	—
194	C₂²×C₆₁	—	4	2	no	—
195	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
196	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
197	C₂²×C₆₁	C₂²×D₈	1	1	yes	characteristic
198	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₂²×C₆₁	#578	1	2	yes	—
200	C₄×C₆₁	—	2	4	no	—
201	C₄×C₆₁	—	2	2	no	—
202	C₄×C₆₁	—	4	4	no	—
203	C₄×C₆₁	—	4	4	no	—
204	C₄×C₆₁	—	4	2	no	—
205	C₄×C₆₁	—	4	2	no	—
206	C₄×C₆₁	—	8	2	no	—
207	C₄×C₆₁	#447	1	4	yes	—
208	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
209	C₄×C₆₁	#536	1	1	yes	characteristic
210	C₄×C₆₁	D₄×Q₈	1	2	yes	—
211	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic
212	C₂×#500	C₂×C₆₁	1	1	yes	characteristic, complemented
213	C₂×#474	C₂×C₆₁	1	1	yes	characteristic
214	#2546	C₂×C₆₁	1	1	yes	characteristic, complemented
215	#2057	C₂×C₆₁	1	4	yes	complemented
216	#1988	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#1984	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#1862	C₂×C₆₁	1	4	yes	—
219	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
220	C₂×C₆₁	—	4	4	no	—
221	C₂×C₆₁	#2434	1	1	yes	characteristic
222	C₂×C₆₁	C₂×#447	1	1	yes	characteristic
223	C₂×C₆₁	#3011	1	1	yes	characteristic
224	C₂×C₆₁	Q₈×D₈	1	2	yes	—
225	C₂×C₆₁	#3386	1	2	yes	—
226	C₂³×Q₈	—	2	1	no	—
227	D₄×Q₈	—	2	4	no	—
228	D₄×Q₈	—	2	4	no	—
229	C₂×C₄⋊Q₈	—	2	1	no	—
230	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
231	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×C₂²⋊Q₈	—	2	1	no	—
234	C₂×C₂²⋊Q₈	—	2	2	no	—
235	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
236	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
237	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
238	#500	—	2	4	no	—
239	#474	—	2	4	no	—
240	C₂×#107	C₂²×C₆₁	1	2	yes	—
241	C₂×#107	C₂²×C₆₁	1	4	yes	—
242	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
243	C₂×#102	C₂²×C₆₁	1	2	yes	—
244	C₂×#102	C₂²×C₆₁	1	2	yes	—
245	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
246	#398	—	2	2	no	—
247	#391	—	2	1	no	—
248	#389	C₂²×C₆₁	1	4	yes	—
249	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
250	#340	C₂²×C₆₁	1	2	yes	—
251	#340	C₂²×C₆₁	1	4	yes	—
252	#336	C₂²×C₆₁	1	4	yes	—
253	C₆₁	#25838	1	1	yes	characteristic, direct product factor, Sylow
254	C₂²×Q₈	—	2	8	no	—
255	C₂²×Q₈	—	2	2	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×Q₈	—	4	4	no	—
259	C₂²×Q₈	—	4	4	no	—
260	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
261	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	—	2	1	no	—
264	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
265	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
266	C₄⋊Q₈	—	2	4	no	—
267	C₄⋊Q₈	—	2	4	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	4	4	no	—
272	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
273	C₂²⋊Q₈	—	2	8	no	—
274	C₂²⋊Q₈	—	2	16	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	4	no	—
279	C₄×D₄	—	2	2	no	—
280	C₄×D₄	D₄×C₆₁	1	4	yes	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
286	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
295	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
296	#107	—	2	4	no	—
297	#107	—	2	8	no	—
298	C₄⋊C₈	—	2	2	no	—
299	#102	—	2	4	no	—
300	#102	Q₈×C₆₁	1	8	yes	complemented
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	1	no	—
303	#95	—	2	4	no	—
304	C₂⁴	—	2	1	no	—
305	C₂×Q₈	—	2	8	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	—	4	32	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	4	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	4	2	no	—
316	C₂×Q₈	—	4	2	no	—
317	C₂×Q₈	D₈×C₆₁	1	4	yes	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
321	C₂×D₄	C₂×Q₈×C₆₁	1	4	yes	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	4	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	complemented
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	8	no	—
353	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
354	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
355	C₄⋊C₄	C₂×Q₈×C₆₁	1	4	yes	complemented
356	C₂²⋊C₄	—	2	8	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂×D₄×C₆₁	1	2	yes	—
362	C₄²	C₂×D₄×C₆₁	1	2	yes	—
363	C₂³	—	2	4	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
369	Q₈	—	2	8	no	—
370	Q₈	—	4	16	no	—
371	Q₈	—	4	8	no	—
372	Q₈	—	8	4	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	4	no	—
375	D₄	C₄⋊Q₈×C₆₁	1	4	yes	complemented
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	#120×C₆₁	1	2	yes	—
396	C₂×C₄	#120×C₆₁	1	2	yes	—
397	C₂×C₄	C₂×D₈×C₆₁	1	4	yes	—
398	C₂×C₄	C₂×D₈×C₆₁	1	2	yes	—
399	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
403	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
404	C₈	—	2	4	no	—
405	C₈	—	4	2	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	4	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
412	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
413	C₂²	C₂²×D₈×C₆₁	1	1	yes	characteristic
414	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
415	C₂²	C₆₁×#578	1	2	yes	—
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₆₁×#447	1	4	yes	—
424	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
425	C₄	C₆₁×#536	1	1	yes	characteristic
426	C₄	D₄×Q₈×C₆₁	1	2	yes	—
427	C₂	—	4	4	no	—
428	C₂	C₆₁×#2434	1	1	yes	characteristic
429	C₂	C₂×C₆₁×#447	1	1	yes	characteristic
430	C₂	C₆₁×#3011	1	1	yes	characteristic
431	C₂	Q₈×D₈×C₆₁	1	2	yes	—
432	C₂	C₆₁×#3386	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#500	C₂	semidirect
4. C₆₁×#2546	C₂	semidirect
5. C₆₁×#2057	C₂	semidirect
6. C₆₁×#1988	C₂	semidirect
7. C₆₁×#1984	C₂	semidirect
83. #102×C₆₁	Q₈	semidirect
124. C₂×C₈×C₆₁	C₂×Q₈	semidirect
138. C₄⋊C₄×C₆₁	C₂×Q₈	semidirect
158. D₄×C₆₁	C₄⋊Q₈	semidirect
189. #25838	C₆₁	direct (N × H)
212. C₂×#500	C₂×C₆₁	semidirect
214. #2546	C₂×C₆₁	semidirect
215. #2057	C₂×C₆₁	semidirect
216. #1988	C₂×C₆₁	semidirect
217. #1984	C₂×C₆₁	semidirect
253. C₆₁	#25838	direct (N × H)
300. #102	Q₈×C₆₁	semidirect
341. C₂×C₈	C₂×Q₈×C₆₁	semidirect
355. C₄⋊C₄	C₂×Q₈×C₆₁	semidirect
375. D₄	C₄⋊Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₆₁	2
C₂×C₆₁×#500	2
C₂×C₆₁×#474	2
C₆₁×#2546	2
C₆₁×#2057	2
C₆₁×#1988	2
C₆₁×#1984	2
C₆₁×#1862	2
C₄×#102×C₆₁	2
#25838	61

Subgroups — C61×#25838 #29529271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25838 #29529271