Subgroups — C₆₁×#7984 #29511417

Order 15616.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#432	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2283	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1289	C₂	1	4	yes	maximal
5	C₂×#117×C₆₁	—	2	1	no	—
6	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
7	C₆₁×#432	—	2	1	no	—
8	C₆₁×#432	—	2	1	no	—
9	C₆₁×#432	—	2	1	no	—
10	C₆₁×#432	—	2	1	no	—
11	C₂×C₄⋊C₈×C₆₁	C₄	1	2	yes	complemented
12	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
13	C₂×#97×C₆₁	C₄	1	2	yes	complemented
14	C₆₁×#384	—	2	1	no	—
15	C₆₁×#383	C₄	1	2	yes	complemented
16	C₆₁×#382	—	2	1	no	—
17	C₆₁×#382	C₄	1	2	yes	complemented
18	C₆₁×#381	—	2	1	no	—
19	C₆₁×#380	—	2	1	no	—
20	C₆₁×#380	C₂²	1	2	yes	—
21	C₆₁×#380	C₂²	1	2	yes	—
22	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
24	C₄×C₄⋊C₄×C₆₁	C₄	1	2	yes	complemented
25	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
26	C₆₁×#376	C₄	1	2	yes	complemented
27	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
31	#117×C₆₁	—	4	4	no	—
32	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
33	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
38	C₂×C₄²×C₆₁	—	2	2	no	—
39	C₂×C₄²×C₆₁	—	2	2	no	—
40	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
50	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
51	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
52	C₄⋊C₈×C₆₁	—	2	2	no	—
53	C₄⋊C₈×C₆₁	—	2	2	no	—
54	C₂²⋊C₈×C₆₁	—	2	2	no	—
55	C₂²⋊C₈×C₆₁	—	2	2	no	—
56	#97×C₆₁	—	2	2	no	—
57	#97×C₆₁	—	2	2	no	—
58	#95×C₆₁	—	2	2	no	—
59	#95×C₆₁	—	2	2	no	—
60	#95×C₆₁	—	2	2	no	—
61	#95×C₆₁	—	2	2	no	—
62	#95×C₆₁	C₂×C₄	1	4	yes	—
63	#95×C₆₁	C₂×C₄	1	4	yes	—
64	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₆₁	—	2	2	no	—
66	C₂²×C₄×C₆₁	—	2	2	no	—
67	C₂²×C₄×C₆₁	—	2	4	no	—
68	C₂²×C₄×C₆₁	—	2	4	no	—
69	C₂²×C₄×C₆₁	—	4	2	no	—
70	C₂²×C₄×C₆₁	—	4	2	no	—
71	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₈×C₆₁	—	2	4	no	—
90	C₂×C₈×C₆₁	—	4	4	no	—
91	C₄⋊C₄×C₆₁	—	4	4	no	—
92	C₄⋊C₄×C₆₁	—	4	4	no	—
93	C₄⋊C₄×C₆₁	—	4	4	no	—
94	C₄⋊C₄×C₆₁	—	4	4	no	—
95	C₂²⋊C₄×C₆₁	—	4	2	no	—
96	C₂²⋊C₄×C₆₁	—	4	4	no	—
97	C₂²⋊C₄×C₆₁	—	4	2	no	—
98	C₄²×C₆₁	—	4	4	no	—
99	C₄²×C₆₁	—	4	4	no	—
100	C₄²×C₆₁	C₄²	1	1	yes	characteristic
101	C₄²×C₆₁	C₄²	1	1	yes	characteristic
102	C₄²×C₆₁	C₄²	1	1	yes	characteristic
103	C₄²×C₆₁	C₄²	1	1	yes	characteristic
104	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
113	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
114	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
115	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
116	C₂³×C₆₁	—	4	1	no	—
117	C₂³×C₆₁	—	4	1	no	—
118	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
122	C₂³×C₆₁	#137	1	2	yes	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	1	no	—
126	C₂×C₄×C₆₁	—	2	1	no	—
127	C₂×C₄×C₆₁	—	2	1	no	—
128	C₂×C₄×C₆₁	—	2	1	no	—
129	C₂×C₄×C₆₁	—	2	2	no	—
130	C₂×C₄×C₆₁	—	2	2	no	—
131	C₂×C₄×C₆₁	—	2	2	no	—
132	C₂×C₄×C₆₁	—	2	2	no	—
133	C₂×C₄×C₆₁	—	2	2	no	—
134	C₂×C₄×C₆₁	—	2	2	no	—
135	C₂×C₄×C₆₁	—	2	2	no	—
136	C₂×C₄×C₆₁	—	2	2	no	—
137	C₂×C₄×C₆₁	—	4	1	no	—
138	C₂×C₄×C₆₁	—	4	1	no	—
139	C₂×C₄×C₆₁	—	4	1	no	—
140	C₂×C₄×C₆₁	—	4	1	no	—
141	C₂×C₄×C₆₁	—	4	1	no	—
142	C₂×C₄×C₆₁	—	4	1	no	—
143	C₂×C₄×C₆₁	—	4	4	no	—
144	C₂×C₄×C₆₁	—	4	4	no	—
145	C₂×C₄×C₆₁	—	4	4	no	—
146	C₂×C₄×C₆₁	—	4	4	no	—
147	C₂×C₄×C₆₁	—	4	4	no	—
148	C₂×C₄×C₆₁	—	4	4	no	—
149	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
150	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
151	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
152	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
153	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
154	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
155	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
156	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
157	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₈×C₆₁	—	4	4	no	—
162	#7984	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₆₁	—	2	1	no	—
164	C₂²×C₆₁	—	2	1	no	—
165	C₂²×C₆₁	—	2	1	no	—
166	C₂²×C₆₁	—	2	1	no	—
167	C₂²×C₆₁	—	2	1	no	—
168	C₂²×C₆₁	—	2	1	no	—
169	C₂²×C₆₁	—	4	2	no	—
170	C₂²×C₆₁	—	4	2	no	—
171	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
172	C₂²×C₆₁	#417	1	2	yes	—
173	C₂²×C₆₁	#418	1	1	yes	characteristic
174	C₂²×C₆₁	#419	1	1	yes	characteristic
175	C₂²×C₆₁	#428	1	2	yes	—
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	2	1	no	—
179	C₄×C₆₁	—	2	1	no	—
180	C₄×C₆₁	—	2	1	no	—
181	C₄×C₆₁	—	2	1	no	—
182	C₄×C₆₁	—	2	1	no	—
183	C₄×C₆₁	—	2	1	no	—
184	C₄×C₆₁	—	2	1	no	—
185	C₄×C₆₁	—	2	1	no	—
186	C₄×C₆₁	—	8	4	no	—
187	C₄×C₆₁	—	8	4	no	—
188	C₄×C₆₁	H(3,ℤ/4)	1	2	yes	—
189	C₄×C₆₁	#410	1	2	yes	—
190	C₂×#432	C₂×C₆₁	1	1	yes	characteristic
191	#2285	C₂×C₆₁	1	1	yes	characteristic
192	#2283	C₂×C₆₁	1	1	yes	characteristic
193	#1289	C₂×C₆₁	1	4	yes	—
194	C₂×C₆₁	—	2	1	no	—
195	C₂×C₆₁	—	2	2	no	—
196	C₂×C₆₁	—	2	1	no	—
197	C₂×C₆₁	—	2	2	no	—
198	C₂×C₆₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
199	C₂×C₆₁	#1736	1	1	yes	characteristic
200	C₂×C₆₁	#1740	1	1	yes	characteristic
201	C₂×#117	—	2	1	no	—
202	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
203	#432	—	2	1	no	—
204	#432	—	2	1	no	—
205	#432	—	2	1	no	—
206	#432	—	2	1	no	—
207	C₂×C₄⋊C₈	C₄×C₆₁	1	2	yes	complemented
208	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
209	C₂×#97	C₄×C₆₁	1	2	yes	complemented
210	#384	—	2	1	no	—
211	#383	C₄×C₆₁	1	2	yes	complemented
212	#382	—	2	1	no	—
213	#382	C₄×C₆₁	1	2	yes	complemented
214	#381	—	2	1	no	—
215	#380	—	2	1	no	—
216	#380	C₂²×C₆₁	1	2	yes	—
217	#380	C₂²×C₆₁	1	2	yes	—
218	C₄×C₄⋊C₄	—	2	1	no	—
219	C₄×C₄⋊C₄	—	2	1	no	—
220	C₄×C₄⋊C₄	C₄×C₆₁	1	2	yes	complemented
221	C₄×C₂²⋊C₄	—	2	1	no	—
222	#376	C₄×C₆₁	1	2	yes	complemented
223	C₆₁	#7984	1	1	yes	characteristic, direct product factor, Sylow
224	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
225	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
227	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
228	#117	—	4	4	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊C₄	—	2	2	no	—
234	C₂×C₂²⋊C₄	—	2	2	no	—
235	C₂×C₄²	—	2	2	no	—
236	C₂×C₄²	—	2	2	no	—
237	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
238	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
239	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
240	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
241	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
242	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
243	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
244	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
245	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
246	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
247	C₂×C₄²	Q₈×C₆₁	1	1	yes	characteristic
248	C₂×C₄²	Q₈×C₆₁	1	1	yes	characteristic
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	2	2	no	—
253	#97	—	2	2	no	—
254	#97	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	C₂×C₄×C₆₁	1	4	yes	—
260	#95	C₂×C₄×C₆₁	1	4	yes	—
261	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
275	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
276	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
280	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
282	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×Q₈×C₆₁	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	4	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	4	2	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	4	4	no	—
297	C₄²	C₄²×C₆₁	1	1	yes	characteristic
298	C₄²	C₄²×C₆₁	1	1	yes	characteristic
299	C₄²	C₄²×C₆₁	1	1	yes	characteristic
300	C₄²	C₄²×C₆₁	1	1	yes	characteristic
301	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
302	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
303	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
304	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
305	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
306	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
307	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
308	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
309	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
310	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
311	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
312	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
313	C₂³	—	4	1	no	—
314	C₂³	—	4	1	no	—
315	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
316	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
317	C₂³	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
318	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
319	C₂³	#137×C₆₁	1	2	yes	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
347	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
348	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
349	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
350	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
351	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
352	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
353	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄²×C₆₁	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
358	C₈	—	4	4	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×#95×C₆₁	1	1	yes	characteristic
368	C₂²	C₆₁×#417	1	2	yes	—
369	C₂²	C₆₁×#418	1	1	yes	characteristic
370	C₂²	C₆₁×#419	1	1	yes	characteristic
371	C₂²	C₆₁×#428	1	2	yes	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	8	4	no	—
383	C₄	—	8	4	no	—
384	C₄	C₆₁×H(3,ℤ/4)	1	2	yes	—
385	C₄	C₆₁×#410	1	2	yes	—
386	C₂	—	2	1	no	—
387	C₂	—	2	2	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	2	no	—
390	C₂	C₂×C₆₁×H(3,ℤ/4)	1	1	yes	characteristic
391	C₂	C₆₁×#1736	1	1	yes	characteristic
392	C₂	C₆₁×#1740	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#95
commutator	C₂×C₄	C₂×C₄²×C₆₁
Frattini, cosocle	C₂³×C₄	C₂³×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
11. C₂×C₄⋊C₈×C₆₁	C₄	semidirect
13. C₂×#97×C₆₁	C₄	semidirect
15. C₆₁×#383	C₄	semidirect
17. C₆₁×#382	C₄	semidirect
24. C₄×C₄⋊C₄×C₆₁	C₄	semidirect
26. C₆₁×#376	C₄	semidirect
162. #7984	C₆₁	direct (N × H)
207. C₂×C₄⋊C₈	C₄×C₆₁	semidirect
209. C₂×#97	C₄×C₆₁	semidirect
211. #383	C₄×C₆₁	semidirect
213. #382	C₄×C₆₁	semidirect
220. C₄×C₄⋊C₄	C₄×C₆₁	semidirect
222. #376	C₄×C₆₁	semidirect
223. C₆₁	#7984	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#432	2
C₆₁×#2285	2
C₆₁×#2283	2
C₆₁×#1289	2
#7984	61

Subgroups — C61×#7984 #29511417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#7984 #29511417