Subgroups — C₂×C₆₁×#1497 #29520908

Order 15616.

990 conjugacy classes of subgroups.

The subgroup lattice has 374 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×C₆₁×#432	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1497	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₆₁×Q₈⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₆₁×#533	—	2	2	no	—
7	C₆₁×#533	—	2	2	no	—
8	C₆₁×#533	C₄	1	4	yes	—
9	C₆₁×#533	C₂²	1	4	yes	—
10	C₂×C₄⋊Q₈×C₆₁	C₄	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₆₁	C₄	1	1	yes	characteristic
12	C₂×#125×C₆₁	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₆₁	C₄	1	2	yes	—
15	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×#117×C₆₁	—	2	1	no	—
18	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#432	—	2	2	no	—
20	C₆₁×#432	C₂²	1	4	yes	—
21	C₆₁×#431	—	2	2	no	—
22	C₆₁×#431	C₂²	1	4	yes	—
23	C₂×C₄⋊C₈×C₆₁	—	2	1	no	—
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
26	C₂×C₂²⋊C₈×C₆₁	—	2	1	no	—
27	C₂×#97×C₆₁	—	2	1	no	—
28	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
29	C₆₁×Q₈⋊C₈	C₂²	1	16	yes	complemented
30	C₂²×Q₈×C₆₁	—	2	1	no	—
31	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₆₁	—	2	2	no	—
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	4	no	—
42	#125×C₆₁	—	2	4	no	—
43	C₂²⋊Q₈×C₆₁	—	2	4	no	—
44	C₂²⋊Q₈×C₆₁	—	2	4	no	—
45	C₂²⋊Q₈×C₆₁	—	2	4	no	—
46	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
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	4	no	—
51	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
52	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
53	#117×C₆₁	—	2	4	no	—
54	#117×C₆₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄²×C₆₁	—	2	2	no	—
63	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₆₁	D₄	1	2	yes	—
66	C₂×C₄²×C₆₁	D₄	1	2	yes	—
67	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₆₁	—	2	4	no	—
72	C₄⋊C₈×C₆₁	—	2	2	no	—
73	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
74	C₂²⋊C₈×C₆₁	—	2	4	no	—
75	C₂²⋊C₈×C₆₁	—	2	4	no	—
76	#97×C₆₁	—	2	4	no	—
77	C₄×C₈×C₆₁	—	2	2	no	—
78	C₄×C₈×C₆₁	C₂³	1	4	yes	—
79	C₂⁴×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×Q₈×C₆₁	—	2	2	no	—
81	C₂×Q₈×C₆₁	—	2	4	no	—
82	C₂×Q₈×C₆₁	—	2	8	no	—
83	C₂×Q₈×C₆₁	—	4	4	no	—
84	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₆₁	—	2	4	no	—
86	C₂²×C₄×C₆₁	—	2	4	no	—
87	C₂²×C₄×C₆₁	—	2	2	no	—
88	C₂²×C₄×C₆₁	—	2	2	no	—
89	C₂²×C₄×C₆₁	—	4	2	no	—
90	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
96	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₆₁	—	2	4	no	—
103	C₂×C₈×C₆₁	—	2	4	no	—
104	C₂×C₈×C₆₁	—	4	4	no	—
105	C₂×C₈×C₆₁	—	4	4	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	—	2	8	no	—
110	C₄⋊C₄×C₆₁	—	2	4	no	—
111	C₄⋊C₄×C₆₁	—	2	2	no	—
112	C₄⋊C₄×C₆₁	—	2	4	no	—
113	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
114	C₂²⋊C₄×C₆₁	—	2	8	no	—
115	C₄²×C₆₁	—	2	4	no	—
116	C₄²×C₆₁	—	2	4	no	—
117	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
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	2	yes	—
122	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₆₁	C₂×D₄	1	2	yes	—
124	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₆₁	C₂×D₄	1	2	yes	—
126	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
127	C₂³×C₆₁	—	2	2	no	—
128	C₂³×C₆₁	—	2	2	no	—
129	C₂³×C₆₁	—	2	2	no	—
130	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
131	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	Q₈×C₆₁	—	2	8	no	—
133	Q₈×C₆₁	—	4	8	no	—
134	Q₈×C₆₁	—	4	4	no	—
135	C₂×C₄×C₆₁	—	2	2	no	—
136	C₂×C₄×C₆₁	—	2	2	no	—
137	C₂×C₄×C₆₁	—	2	2	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	4	no	—
140	C₂×C₄×C₆₁	—	2	4	no	—
141	C₂×C₄×C₆₁	—	2	4	no	—
142	C₂×C₄×C₆₁	—	2	4	no	—
143	C₂×C₄×C₆₁	—	2	4	no	—
144	C₂×C₄×C₆₁	—	2	4	no	—
145	C₂×C₄×C₆₁	—	4	2	no	—
146	C₂×C₄×C₆₁	—	4	2	no	—
147	C₂×C₄×C₆₁	—	4	4	no	—
148	C₂×C₄×C₆₁	—	4	4	no	—
149	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
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	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₆₁	#131	1	4	yes	—
156	C₂×C₄×C₆₁	#137	1	4	yes	—
157	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₆₁	—	4	4	no	—
161	C₈×C₆₁	—	4	4	no	—
162	C₂×#1497	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₆₁	—	2	2	no	—
164	C₂²×C₆₁	—	2	2	no	—
165	C₂²×C₆₁	—	2	2	no	—
166	C₂²×C₆₁	—	4	4	no	—
167	C₂²×C₆₁	#408	1	2	yes	—
168	C₂²×C₆₁	#419	1	2	yes	—
169	C₂²×C₆₁	#421	1	2	yes	—
170	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
171	C₄×C₆₁	—	2	2	no	—
172	C₄×C₆₁	—	2	2	no	—
173	C₄×C₆₁	—	2	1	no	—
174	C₄×C₆₁	—	2	1	no	—
175	C₄×C₆₁	—	2	2	no	—
176	C₄×C₆₁	—	4	4	no	—
177	C₄×C₆₁	—	4	4	no	—
178	C₄×C₆₁	#408	1	2	yes	—
179	C₄×C₆₁	#419	1	2	yes	—
180	C₄×C₆₁	C₂×#131	1	2	yes	—
181	C₄×C₆₁	C₂×#137	1	2	yes	—
182	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
183	C₂×#432	C₂×C₆₁	1	1	yes	characteristic
184	C₂×#431	C₂×C₆₁	1	1	yes	characteristic
185	#1497	C₂×C₆₁	1	8	yes	direct product factor
186	C₂×Q₈⋊C₈	C₂×C₆₁	1	4	yes	complemented
187	C₂×C₆₁	—	4	2	no	—
188	C₂×C₆₁	#1497	1	4	yes	direct product factor
189	C₂×C₆₁	C₂×#408	1	1	yes	characteristic
190	C₂×C₆₁	C₂×#419	1	1	yes	characteristic
191	C₂×C₆₁	C₂×#421	1	1	yes	characteristic
192	#533	—	2	2	no	—
193	#533	—	2	2	no	—
194	#533	C₄×C₆₁	1	4	yes	—
195	#533	C₂²×C₆₁	1	4	yes	—
196	C₂×C₄⋊Q₈	C₄×C₆₁	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₄×C₆₁	1	1	yes	characteristic
198	C₂×#125	—	2	1	no	—
199	C₂×C₂²⋊Q₈	—	2	1	no	—
200	C₂×C₂²⋊Q₈	C₄×C₆₁	1	2	yes	—
201	C₂×C₄×Q₈	—	2	1	no	—
202	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
203	C₂×#117	—	2	1	no	—
204	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
205	#432	—	2	2	no	—
206	#432	C₂²×C₆₁	1	4	yes	—
207	#431	—	2	2	no	—
208	#431	C₂²×C₆₁	1	4	yes	—
209	C₂×C₄⋊C₈	—	2	1	no	—
210	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
211	C₂×C₂²⋊C₈	—	2	1	no	—
212	C₂×C₂²⋊C₈	—	2	1	no	—
213	C₂×#97	—	2	1	no	—
214	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
215	Q₈⋊C₈	C₂²×C₆₁	1	16	yes	complemented
216	C₆₁	C₂×#1497	1	1	yes	characteristic, direct product factor, Sylow
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
219	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
220	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
221	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	—	2	2	no	—
226	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
227	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
228	#125	—	2	4	no	—
229	#125	—	2	4	no	—
230	C₂²⋊Q₈	—	2	4	no	—
231	C₂²⋊Q₈	—	2	4	no	—
232	C₂²⋊Q₈	—	2	4	no	—
233	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
234	C₄×Q₈	—	2	4	no	—
235	C₄×Q₈	—	2	4	no	—
236	C₄×Q₈	—	2	2	no	—
237	C₄×Q₈	—	2	2	no	—
238	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
239	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
240	#117	—	2	4	no	—
241	#117	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
252	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
253	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
254	C₂×C₄²	D₄×C₆₁	1	2	yes	—
255	C₂×C₄²	D₄×C₆₁	1	2	yes	—
256	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
258	C₄⋊C₈	—	2	4	no	—
259	C₄⋊C₈	—	2	2	no	—
260	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
261	C₂²⋊C₈	—	2	4	no	—
262	C₂²⋊C₈	—	2	4	no	—
263	#97	—	2	4	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	C₂³×C₆₁	1	4	yes	—
266	C₂⁴	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	8	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
280	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
281	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
282	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	4	4	no	—
292	C₂×C₈	—	4	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	2	8	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	4	no	—
304	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
305	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
306	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
307	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
308	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
309	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₆₁	1	2	yes	—
311	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₆₁	1	2	yes	—
313	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
318	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
319	Q₈	—	2	8	no	—
320	Q₈	—	4	8	no	—
321	Q₈	—	4	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	4	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	1	yes	characteristic
338	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
339	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
340	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
342	C₂×C₄	#131×C₆₁	1	4	yes	—
343	C₂×C₄	#137×C₆₁	1	4	yes	—
344	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
347	C₈	—	4	4	no	—
348	C₈	—	4	4	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	2	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	4	4	no	—
353	C₂²	C₆₁×#408	1	2	yes	—
354	C₂²	C₆₁×#419	1	2	yes	—
355	C₂²	C₆₁×#421	1	2	yes	—
356	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	2	no	—
362	C₄	—	4	4	no	—
363	C₄	—	4	4	no	—
364	C₄	C₆₁×#408	1	2	yes	—
365	C₄	C₆₁×#419	1	2	yes	—
366	C₄	C₂×#131×C₆₁	1	2	yes	—
367	C₄	C₂×#137×C₆₁	1	2	yes	—
368	C₂	—	4	2	no	—
369	C₂	C₆₁×#1497	1	4	yes	direct product factor
370	C₂	C₂×C₆₁×#408	1	1	yes	characteristic
371	C₂	C₂×C₆₁×#419	1	1	yes	characteristic
372	C₂	C₂×C₆₁×#421	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1497	C₂	direct (N × H)
5. C₂×C₆₁×Q₈⋊C₈	C₂	semidirect
29. C₆₁×Q₈⋊C₈	C₂²	semidirect
162. C₂×#1497	C₆₁	direct (N × H)
185. #1497	C₂×C₆₁	direct (N × H)
186. C₂×Q₈⋊C₈	C₂×C₆₁	semidirect
188. C₂×C₆₁	#1497	direct (N × H)
215. Q₈⋊C₈	C₂²×C₆₁	semidirect
216. C₆₁	C₂×#1497	direct (N × H)
369. C₂	C₆₁×#1497	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×#533	2
C₂×C₆₁×#432	2
C₂×C₆₁×#431	2
C₆₁×#1497	2
C₂×C₆₁×Q₈⋊C₈	2
C₂×#1497	61

Subgroups — C2×C61×#1497 #29520908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1497 #29520908