Subgroups — C₆₁×#21306 #29524739

Order 15616.

1154 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1986	C₂	1	8	yes	maximal, complemented
5	C₆₁×#1733	C₂	1	4	yes	maximal
6	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
7	C₆₁×#533	—	2	1	no	—
8	C₆₁×#533	—	2	1	no	—
9	C₆₁×#533	—	2	1	no	—
10	C₆₁×#533	—	2	1	no	—
11	C₆₁×#533	C₄	1	4	yes	complemented
12	C₆₁×#533	C₂²	1	4	yes	—
13	C₂×C₄⋊Q₈×C₆₁	C₄	1	2	yes	complemented
14	C₂×#125×C₆₁	C₄	1	2	yes	complemented
15	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
16	C₂×C₄×Q₈×C₆₁	—	2	2	no	—
17	C₂×#117×C₆₁	C₂²	1	2	yes	—
18	C₂×#117×C₆₁	C₂²	1	2	yes	—
19	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
20	C₄×M₁₆×C₆₁	—	2	2	no	—
21	C₄×M₁₆×C₆₁	C₂²	1	4	yes	—
22	C₂×#97×C₆₁	—	2	1	no	—
23	C₂×C₄×C₈×C₆₁	—	2	1	no	—
24	C₆₁×#384	—	2	1	no	—
25	C₆₁×#382	—	2	1	no	—
26	C₆₁×#380	—	2	2	no	—
27	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
28	C₆₁×#339	C₂²	1	16	yes	—
29	C₂²×Q₈×C₆₁	—	2	2	no	—
30	C₂³×C₄×C₆₁	D₄	1	2	yes	—
31	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
32	C₂×M₁₆×C₆₁	—	2	2	no	—
33	C₂×M₁₆×C₆₁	—	2	4	no	—
34	C₂×M₁₆×C₆₁	Q₈	1	8	yes	complemented
35	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
36	C₂²×C₈×C₆₁	—	2	2	no	—
37	C₄⋊Q₈×C₆₁	—	2	2	no	—
38	C₄⋊Q₈×C₆₁	—	2	2	no	—
39	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
40	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
41	#125×C₆₁	—	2	2	no	—
42	#125×C₆₁	—	2	2	no	—
43	#125×C₆₁	C₂×C₄	1	8	yes	—
44	C₂²⋊Q₈×C₆₁	—	2	4	no	—
45	C₂²⋊Q₈×C₆₁	—	2	4	no	—
46	C₂²⋊Q₈×C₆₁	—	2	4	no	—
47	C₂²⋊Q₈×C₆₁	—	2	4	no	—
48	C₄×Q₈×C₆₁	—	2	4	no	—
49	C₄×Q₈×C₆₁	—	2	4	no	—
50	C₄×Q₈×C₆₁	—	2	4	no	—
51	C₄×Q₈×C₆₁	—	2	4	no	—
52	#117×C₆₁	—	2	2	no	—
53	#117×C₆₁	—	2	2	no	—
54	#117×C₆₁	—	2	8	no	—
55	#117×C₆₁	C₂×C₄	1	4	yes	—
56	#117×C₆₁	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
62	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄²×C₆₁	—	2	2	no	—
65	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	D₄	1	2	yes	—
73	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
75	#97×C₆₁	—	2	4	no	—
76	C₄×C₈×C₆₁	—	2	4	no	—
77	#95×C₆₁	—	2	4	no	—
78	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₆₁	—	2	4	no	—
80	C₂×Q₈×C₆₁	—	2	4	no	—
81	C₂×Q₈×C₆₁	—	4	8	no	—
82	C₂²×C₄×C₆₁	—	2	4	no	—
83	C₂²×C₄×C₆₁	—	2	4	no	—
84	C₂²×C₄×C₆₁	—	4	4	no	—
85	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
86	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
89	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
97	C₂²×C₄×C₆₁	#41	1	4	yes	—
98	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
99	M₁₆×C₆₁	—	2	8	no	—
100	M₁₆×C₆₁	—	2	4	no	—
101	M₁₆×C₆₁	C₂×Q₈	1	8	yes	complemented
102	C₂×C₈×C₆₁	—	2	8	no	—
103	C₂×C₈×C₆₁	—	2	4	no	—
104	C₄⋊C₄×C₆₁	—	2	8	no	—
105	C₄⋊C₄×C₆₁	—	2	8	no	—
106	C₄⋊C₄×C₆₁	—	2	4	no	—
107	C₄⋊C₄×C₆₁	—	2	4	no	—
108	C₄⋊C₄×C₆₁	—	2	4	no	—
109	C₄⋊C₄×C₆₁	—	4	8	no	—
110	C₄⋊C₄×C₆₁	—	4	4	no	—
111	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
112	C₂²⋊C₄×C₆₁	—	2	4	no	—
113	C₂²⋊C₄×C₆₁	—	2	4	no	—
114	C₂²⋊C₄×C₆₁	—	4	4	no	—
115	C₄²×C₆₁	—	2	4	no	—
116	C₄²×C₆₁	—	2	4	no	—
117	C₄²×C₆₁	—	2	8	no	—
118	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
119	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
120	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
121	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
122	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
123	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
124	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
125	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
126	C₄²×C₆₁	C₂×D₄	1	2	yes	—
127	C₄²×C₆₁	C₂×D₄	1	2	yes	—
128	C₂³×C₆₁	—	4	2	no	—
129	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₆₁	#124	1	2	yes	—
132	C₂³×C₆₁	C₄⋊Q₈	1	2	yes	—
133	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₆₁	—	4	8	no	—
135	Q₈×C₆₁	—	4	8	no	—
136	C₂×C₄×C₆₁	—	2	4	no	—
137	C₂×C₄×C₆₁	—	2	4	no	—
138	C₂×C₄×C₆₁	—	2	4	no	—
139	C₂×C₄×C₆₁	—	2	8	no	—
140	C₂×C₄×C₆₁	—	4	2	no	—
141	C₂×C₄×C₆₁	—	4	2	no	—
142	C₂×C₄×C₆₁	—	4	2	no	—
143	C₂×C₄×C₆₁	—	4	8	no	—
144	C₂×C₄×C₆₁	—	4	8	no	—
145	C₂×C₄×C₆₁	—	4	4	no	—
146	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₆₁	C₄×Q₈	1	4	yes	—
153	C₂×C₄×C₆₁	C₄×Q₈	1	4	yes	—
154	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
156	C₂×C₄×C₆₁	#124	1	2	yes	—
157	C₂×C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
158	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
161	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
162	C₈×C₆₁	—	2	8	no	—
163	#21306	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₆₁	—	2	2	no	—
165	C₂²×C₆₁	—	2	2	no	—
166	C₂²×C₆₁	—	2	2	no	—
167	C₂²×C₆₁	—	4	2	no	—
168	C₂²×C₆₁	—	4	2	no	—
169	C₂²×C₆₁	#391	1	2	yes	—
170	C₂²×C₆₁	#391	1	2	yes	—
171	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₆₁	C₂×#124	1	1	yes	characteristic
173	C₂²×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
174	C₄×C₆₁	—	2	2	no	—
175	C₄×C₆₁	—	2	2	no	—
176	C₄×C₆₁	—	2	2	no	—
177	C₄×C₆₁	—	4	8	no	—
178	C₄×C₆₁	—	8	4	no	—
179	C₄×C₆₁	#391	1	2	yes	—
180	C₄×C₆₁	#391	1	2	yes	—
181	C₄×C₆₁	#421	1	4	yes	—
182	C₄×C₆₁	C₂×C₄×Q₈	1	2	yes	—
183	C₄×C₆₁	C₂×C₂²⋊Q₈	1	2	yes	—
184	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
185	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic
186	#2285	C₂×C₆₁	1	1	yes	characteristic
187	#1986	C₂×C₆₁	1	8	yes	complemented
188	#1733	C₂×C₆₁	1	4	yes	—
189	C₂×C₆₁	—	2	1	no	—
190	C₂×C₆₁	—	2	1	no	—
191	C₂×C₆₁	—	2	2	no	—
192	C₂×C₆₁	—	2	2	no	—
193	C₂×C₆₁	C₂×#391	1	1	yes	characteristic
194	C₂×C₆₁	C₂×#421	1	2	yes	—
195	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
196	#533	—	2	1	no	—
197	#533	—	2	1	no	—
198	#533	—	2	1	no	—
199	#533	—	2	1	no	—
200	#533	C₄×C₆₁	1	4	yes	complemented
201	#533	C₂²×C₆₁	1	4	yes	—
202	C₂×C₄⋊Q₈	C₄×C₆₁	1	2	yes	complemented
203	C₂×#125	C₄×C₆₁	1	2	yes	complemented
204	C₂×C₂²⋊Q₈	—	2	2	no	—
205	C₂×C₄×Q₈	—	2	2	no	—
206	C₂×#117	C₂²×C₆₁	1	2	yes	—
207	C₂×#117	C₂²×C₆₁	1	2	yes	—
208	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
209	C₄×M₁₆	—	2	2	no	—
210	C₄×M₁₆	C₂²×C₆₁	1	4	yes	—
211	C₂×#97	—	2	1	no	—
212	C₂×C₄×C₈	—	2	1	no	—
213	#384	—	2	1	no	—
214	#382	—	2	1	no	—
215	#380	—	2	2	no	—
216	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
217	#339	C₂²×C₆₁	1	16	yes	—
218	C₆₁	#21306	1	1	yes	characteristic, direct product factor, Sylow
219	C₂²×Q₈	—	2	2	no	—
220	C₂³×C₄	D₄×C₆₁	1	2	yes	—
221	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	4	no	—
224	C₂×M₁₆	Q₈×C₆₁	1	8	yes	complemented
225	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
226	C₂²×C₈	—	2	2	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
230	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
231	#125	—	2	2	no	—
232	#125	—	2	2	no	—
233	#125	C₂×C₄×C₆₁	1	8	yes	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	—	2	4	no	—
236	C₂²⋊Q₈	—	2	4	no	—
237	C₂²⋊Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₄×Q₈	—	2	4	no	—
240	C₄×Q₈	—	2	4	no	—
241	C₄×Q₈	—	2	4	no	—
242	#117	—	2	2	no	—
243	#117	—	2	2	no	—
244	#117	—	2	8	no	—
245	#117	C₂×C₄×C₆₁	1	4	yes	—
246	#117	C₂³×C₆₁	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
258	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
260	C₂×C₄²	D₄×C₆₁	1	2	yes	—
261	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
263	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
264	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
265	#97	—	2	4	no	—
266	C₄×C₈	—	2	4	no	—
267	#95	—	2	4	no	—
268	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
269	C₂×Q₈	—	2	4	no	—
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	4	8	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	4	4	no	—
275	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
276	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
277	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
278	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
287	C₂²×C₄	#41×C₆₁	1	4	yes	—
288	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
289	M₁₆	—	2	8	no	—
290	M₁₆	—	2	4	no	—
291	M₁₆	C₂×Q₈×C₆₁	1	8	yes	complemented
292	C₂×C₈	—	2	8	no	—
293	C₂×C₈	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	4	8	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
302	C₂²⋊C₄	—	2	4	no	—
303	C₂²⋊C₄	—	2	4	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₄²	—	2	4	no	—
306	C₄²	—	2	4	no	—
307	C₄²	—	2	8	no	—
308	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
309	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
310	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
311	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
312	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
313	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
314	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
315	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
316	C₄²	C₂×D₄×C₆₁	1	2	yes	—
317	C₄²	C₂×D₄×C₆₁	1	2	yes	—
318	C₂³	—	4	2	no	—
319	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
320	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
321	C₂³	#124×C₆₁	1	2	yes	—
322	C₂³	C₄⋊Q₈×C₆₁	1	2	yes	—
323	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
324	Q₈	—	4	8	no	—
325	Q₈	—	4	8	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	8	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
338	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
340	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
342	C₂×C₄	C₄×Q₈×C₆₁	1	4	yes	—
343	C₂×C₄	C₄×Q₈×C₆₁	1	4	yes	—
344	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
345	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
346	C₂×C₄	#124×C₆₁	1	2	yes	—
347	C₂×C₄	C₄⋊Q₈×C₆₁	1	2	yes	—
348	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
349	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
350	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
351	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
352	C₈	—	2	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	C₆₁×#391	1	2	yes	—
359	C₂²	C₆₁×#391	1	2	yes	—
360	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
361	C₂²	C₂×#124×C₆₁	1	1	yes	characteristic
362	C₂²	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
363	C₄	—	2	2	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	8	no	—
367	C₄	—	8	4	no	—
368	C₄	C₆₁×#391	1	2	yes	—
369	C₄	C₆₁×#391	1	2	yes	—
370	C₄	C₆₁×#421	1	4	yes	—
371	C₄	C₂×C₄×Q₈×C₆₁	1	2	yes	—
372	C₄	C₂×C₂²⋊Q₈×C₆₁	1	2	yes	—
373	C₂	—	2	1	no	—
374	C₂	—	2	1	no	—
375	C₂	—	2	2	no	—
376	C₂	—	2	2	no	—
377	C₂	C₂×C₆₁×#391	1	1	yes	characteristic
378	C₂	C₂×C₆₁×#421	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1986	C₂	semidirect
11. C₆₁×#533	C₄	semidirect
13. C₂×C₄⋊Q₈×C₆₁	C₄	semidirect
14. C₂×#125×C₆₁	C₄	semidirect
34. C₂×M₁₆×C₆₁	Q₈	semidirect
101. M₁₆×C₆₁	C₂×Q₈	semidirect
163. #21306	C₆₁	direct (N × H)
187. #1986	C₂×C₆₁	semidirect
200. #533	C₄×C₆₁	semidirect
202. C₂×C₄⋊Q₈	C₄×C₆₁	semidirect
203. C₂×#125	C₄×C₆₁	semidirect
218. C₆₁	#21306	direct (N × H)
224. C₂×M₁₆	Q₈×C₆₁	semidirect
291. M₁₆	C₂×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×C₆₁×#533	2
C₂×C₄×M₁₆×C₆₁	2
C₆₁×#2285	2
C₆₁×#1986	2
C₆₁×#1733	2
#21306	61

Subgroups — C61×#21306 #29524739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21306 #29524739