Subgroups — C₆₁×#25841 #29529274

Order 15616.

1018 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#500	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#477	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2567	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2057	C₂	1	4	yes	maximal
6	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1984	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1863	C₂	1	4	yes	maximal
9	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₆₁	—	2	4	no	—
11	Q₈²×C₆₁	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₆₁	—	2	2	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×C₄×Q₈×C₆₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#500	—	2	4	no	—
22	C₆₁×#477	—	2	4	no	—
23	C₂×#107×C₆₁	C₂²	1	2	yes	—
24	C₂×#107×C₆₁	C₂²	1	4	yes	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#395	—	2	2	no	—
30	C₆₁×#391	—	2	1	no	—
31	C₆₁×#389	C₂²	1	4	yes	—
32	C₆₁×#384	—	2	1	no	—
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	2	no	—
38	C₂²×Q₈×C₆₁	—	2	1	no	—
39	C₂²×Q₈×C₆₁	—	2	1	no	—
40	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
41	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₆₁	—	2	16	no	—
45	C₄⋊Q₈×C₆₁	—	2	8	no	—
46	C₄⋊Q₈×C₆₁	—	2	4	no	—
47	C₄⋊Q₈×C₆₁	—	2	4	no	—
48	C₄⋊Q₈×C₆₁	—	2	2	no	—
49	C₄⋊Q₈×C₆₁	—	2	2	no	—
50	C₄⋊Q₈×C₆₁	—	2	2	no	—
51	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
52	C₄×Q₈×C₆₁	—	2	8	no	—
53	C₄×Q₈×C₆₁	—	2	4	no	—
54	C₄×Q₈×C₆₁	—	2	4	no	—
55	C₄×Q₈×C₆₁	—	2	2	no	—
56	C₄×Q₈×C₆₁	—	2	2	no	—
57	C₄×Q₈×C₆₁	—	2	2	no	—
58	C₄×Q₈×C₆₁	D₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
65	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₆₁	—	2	2	no	—
72	C₂×C₄²×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	#107×C₆₁	—	2	4	no	—
77	#107×C₆₁	—	2	8	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	#103×C₆₁	—	2	4	no	—
80	#103×C₆₁	Q₈	1	8	yes	complemented
81	C₄×C₈×C₆₁	—	2	2	no	—
82	#95×C₆₁	—	2	1	no	—
83	#95×C₆₁	—	2	4	no	—
84	C₂×Q₈×C₆₁	—	2	8	no	—
85	C₂×Q₈×C₆₁	—	2	2	no	—
86	C₂×Q₈×C₆₁	—	2	4	no	—
87	C₂×Q₈×C₆₁	—	2	2	no	—
88	C₂×Q₈×C₆₁	—	2	1	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	4	2	no	—
91	C₂×Q₈×C₆₁	—	8	2	no	—
92	C₂×Q₈×C₆₁	—	8	2	no	—
93	C₂×Q₈×C₆₁	—	8	4	no	—
94	C₂×Q₈×C₆₁	Q₁₆	1	4	yes	—
95	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
96	C₂×Q₈×C₆₁	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	2	2	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	2	2	no	—
110	C₂×C₈×C₆₁	—	2	4	no	—
111	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
112	C₄⋊C₄×C₆₁	—	2	8	no	—
113	C₄⋊C₄×C₆₁	—	2	8	no	—
114	C₄⋊C₄×C₆₁	—	2	4	no	—
115	C₄⋊C₄×C₆₁	—	2	4	no	—
116	C₄⋊C₄×C₆₁	—	2	4	no	—
117	C₄⋊C₄×C₆₁	—	2	2	no	—
118	C₄⋊C₄×C₆₁	—	2	2	no	—
119	C₄⋊C₄×C₆₁	—	2	1	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	4	2	no	—
124	C₄⋊C₄×C₆₁	—	8	4	no	—
125	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
126	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₄⋊C₄×C₆₁	C₂×Q₈	1	4	yes	—
128	C₄²×C₆₁	—	2	8	no	—
129	C₄²×C₆₁	—	2	4	no	—
130	C₄²×C₆₁	—	2	2	no	—
131	C₄²×C₆₁	—	2	2	no	—
132	C₄²×C₆₁	—	4	2	no	—
133	C₄²×C₆₁	C₂×D₄	1	2	yes	—
134	C₄²×C₆₁	C₂×D₄	1	2	yes	—
135	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₆₁	—	2	2	no	—
137	Q₈×C₆₁	—	2	4	no	—
138	Q₈×C₆₁	—	2	8	no	—
139	Q₈×C₆₁	—	8	4	no	—
140	Q₈×C₆₁	—	8	4	no	—
141	Q₈×C₆₁	—	8	8	no	—
142	Q₈×C₆₁	C₄⋊Q₈	1	4	yes	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	4	no	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	4	no	—
152	C₂×C₄×C₆₁	—	2	4	no	—
153	C₂×C₄×C₆₁	—	4	2	no	—
154	C₂×C₄×C₆₁	—	4	2	no	—
155	C₂×C₄×C₆₁	—	4	4	no	—
156	C₂×C₄×C₆₁	—	4	2	no	—
157	C₂×C₄×C₆₁	—	4	2	no	—
158	C₂×C₄×C₆₁	—	4	4	no	—
159	C₂×C₄×C₆₁	#120	1	2	yes	—
160	C₂×C₄×C₆₁	#120	1	2	yes	—
161	C₂×C₄×C₆₁	C₂×Q₁₆	1	4	yes	—
162	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
163	C₂×C₄×C₆₁	#137	1	2	yes	—
164	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
167	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
168	C₈×C₆₁	—	2	4	no	—
169	C₈×C₆₁	—	4	2	no	—
170	#25841	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
172	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
173	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
174	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
175	C₂²×C₆₁	#576	1	2	yes	—
176	C₄×C₆₁	—	2	4	no	—
177	C₄×C₆₁	—	2	4	no	—
178	C₄×C₆₁	—	2	2	no	—
179	C₄×C₆₁	—	4	4	no	—
180	C₄×C₆₁	—	4	2	no	—
181	C₄×C₆₁	—	4	4	no	—
182	C₄×C₆₁	—	4	2	no	—
183	C₄×C₆₁	—	8	2	no	—
184	C₄×C₆₁	#451	1	4	yes	—
185	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
186	C₄×C₆₁	#536	1	1	yes	characteristic
187	C₄×C₆₁	D₄×Q₈	1	2	yes	—
188	C₂×Q₈²	C₂×C₆₁	1	1	yes	characteristic
189	C₂×#500	C₂×C₆₁	1	1	yes	characteristic
190	C₂×#477	C₂×C₆₁	1	1	yes	characteristic
191	#2567	C₂×C₆₁	1	1	yes	characteristic
192	#2057	C₂×C₆₁	1	4	yes	—
193	#1987	C₂×C₆₁	1	1	yes	characteristic
194	#1984	C₂×C₆₁	1	1	yes	characteristic
195	#1863	C₂×C₆₁	1	4	yes	—
196	C₄×#103	C₂×C₆₁	1	1	yes	characteristic
197	C₂×C₆₁	#2434	1	1	yes	characteristic
198	C₂×C₆₁	C₂×#451	1	1	yes	characteristic
199	C₂×C₆₁	#3008	1	1	yes	characteristic
200	C₂×C₆₁	Q₈×Q₁₆	1	2	yes	—
201	C₂×C₆₁	#3385	1	2	yes	—
202	Q₈²	—	2	4	no	—
203	Q₈²	—	2	4	no	—
204	C₂×C₄⋊Q₈	—	2	1	no	—
205	C₂×C₄⋊Q₈	—	2	2	no	—
206	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
208	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
209	C₂×C₄×Q₈	—	2	1	no	—
210	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
211	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
212	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
213	#500	—	2	4	no	—
214	#477	—	2	4	no	—
215	C₂×#107	C₂²×C₆₁	1	2	yes	—
216	C₂×#107	C₂²×C₆₁	1	4	yes	—
217	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×#103	C₂²×C₆₁	1	2	yes	—
219	C₂×#103	C₂²×C₆₁	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
221	#395	—	2	2	no	—
222	#391	—	2	1	no	—
223	#389	C₂²×C₆₁	1	4	yes	—
224	#384	—	2	1	no	—
225	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
226	#340	C₂²×C₆₁	1	2	yes	—
227	#340	C₂²×C₆₁	1	4	yes	—
228	#336	C₂²×C₆₁	1	4	yes	—
229	C₆₁	#25841	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
234	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
237	C₄⋊Q₈	—	2	16	no	—
238	C₄⋊Q₈	—	2	8	no	—
239	C₄⋊Q₈	—	2	4	no	—
240	C₄⋊Q₈	—	2	4	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	C₄⋊Q₈	—	2	2	no	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
245	C₄×Q₈	—	2	8	no	—
246	C₄×Q₈	—	2	4	no	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	D₄×C₆₁	1	4	yes	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
259	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
269	#107	—	2	4	no	—
270	#107	—	2	8	no	—
271	C₄⋊C₈	—	2	2	no	—
272	#103	—	2	4	no	—
273	#103	Q₈×C₆₁	1	8	yes	complemented
274	C₄×C₈	—	2	2	no	—
275	#95	—	2	1	no	—
276	#95	—	2	4	no	—
277	C₂×Q₈	—	2	8	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	8	2	no	—
285	C₂×Q₈	—	8	2	no	—
286	C₂×Q₈	—	8	4	no	—
287	C₂×Q₈	Q₁₆×C₆₁	1	4	yes	—
288	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
289	C₂×Q₈	C₂×Q₈×C₆₁	1	4	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
298	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
299	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
305	C₄⋊C₄	—	2	8	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	8	4	no	—
318	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
319	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
320	C₄⋊C₄	C₂×Q₈×C₆₁	1	4	yes	—
321	C₄²	—	2	8	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	4	2	no	—
326	C₄²	C₂×D₄×C₆₁	1	2	yes	—
327	C₄²	C₂×D₄×C₆₁	1	2	yes	—
328	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
329	Q₈	—	2	2	no	—
330	Q₈	—	2	4	no	—
331	Q₈	—	2	8	no	—
332	Q₈	—	8	4	no	—
333	Q₈	—	8	4	no	—
334	Q₈	—	8	8	no	—
335	Q₈	C₄⋊Q₈×C₆₁	1	4	yes	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	#120×C₆₁	1	2	yes	—
353	C₂×C₄	#120×C₆₁	1	2	yes	—
354	C₂×C₄	C₂×Q₁₆×C₆₁	1	4	yes	—
355	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
356	C₂×C₄	#137×C₆₁	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
359	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
360	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
364	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
365	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
366	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
367	C₂²	C₆₁×#576	1	2	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	2	4	no	—
370	C₄	—	2	2	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	4	no	—
374	C₄	—	4	2	no	—
375	C₄	—	8	2	no	—
376	C₄	C₆₁×#451	1	4	yes	—
377	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
378	C₄	C₆₁×#536	1	1	yes	characteristic
379	C₄	D₄×Q₈×C₆₁	1	2	yes	—
380	C₂	C₆₁×#2434	1	1	yes	characteristic
381	C₂	C₂×C₆₁×#451	1	1	yes	characteristic
382	C₂	C₆₁×#3008	1	1	yes	characteristic
383	C₂	Q₈×Q₁₆×C₆₁	1	2	yes	—
384	C₂	C₆₁×#3385	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
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
80. #103×C₆₁	Q₈	semidirect
170. #25841	C₆₁	direct (N × H)
229. C₆₁	#25841	direct (N × H)
273. #103	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×Q₈²×C₆₁	2
C₂×C₆₁×#500	2
C₂×C₆₁×#477	2
C₆₁×#2567	2
C₆₁×#2057	2
C₆₁×#1987	2
C₆₁×#1984	2
C₆₁×#1863	2
C₄×#103×C₆₁	2
#25841	61

Subgroups — C61×#25841 #29529274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25841 #29529274