Subgroups — C₆₁×#21304 #29524737

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 390 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×#424	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1985	C₂	1	4	yes	maximal, complemented
5	C₆₁×#1984	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1729	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1729	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1728	C₂	1	1	yes	maximal, characteristic
9	C₂×C₆₁×#336	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#533	—	2	4	no	—
15	C₆₁×#533	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₆₁	C₄	1	2	yes	—
17	C₂×#125×C₆₁	C₄	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₆₁	C₄	1	4	yes	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	—
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#424	—	2	4	no	—
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	4	yes	—
25	C₆₁×#405	—	2	4	no	—
26	C₂×#97×C₆₁	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
28	C₆₁×#336	C₂²	1	2	yes	—
29	C₆₁×#336	C₂²	1	2	yes	—
30	C₆₁×#336	C₂²	1	4	yes	—
31	C₆₁×#336	C₂²	1	2	yes	—
32	C₆₁×#336	C₂²	1	4	yes	—
33	C₆₁×#336	C₂²	1	2	yes	—
34	C₂²×Q₈×C₆₁	C₂×C₄	1	4	yes	—
35	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₆₁	—	2	2	no	—
38	C₂×M₁₆×C₆₁	—	2	2	no	—
39	C₂×M₁₆×C₆₁	—	2	2	no	—
40	C₂×M₁₆×C₆₁	—	2	2	no	—
41	C₂×M₁₆×C₆₁	—	2	2	no	—
42	C₂×M₁₆×C₆₁	Q₈	1	4	yes	complemented
43	C₂²×C₈×C₆₁	—	2	2	no	—
44	C₂²×C₈×C₆₁	—	2	2	no	—
45	C₂²×C₈×C₆₁	—	2	2	no	—
46	C₂²×C₈×C₆₁	—	2	2	no	—
47	C₂²×C₈×C₆₁	—	2	2	no	—
48	C₂²×C₈×C₆₁	Q₈	1	4	yes	complemented
49	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₆₁	—	2	8	no	—
55	#125×C₆₁	—	2	8	no	—
56	C₂²⋊Q₈×C₆₁	—	2	16	no	—
57	C₄×Q₈×C₆₁	—	2	8	no	—
58	C₄×Q₈×C₆₁	—	2	8	no	—
59	#117×C₆₁	—	2	2	no	—
60	#117×C₆₁	—	2	2	no	—
61	#117×C₆₁	D₄	1	4	yes	—
62	#117×C₆₁	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	8	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₆₁	—	2	2	no	—
70	C₂×C₄²×C₆₁	—	2	2	no	—
71	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
76	C₄⋊C₈×C₆₁	—	2	8	no	—
77	#97×C₆₁	—	2	4	no	—
78	C₄×C₈×C₆₁	—	2	4	no	—
79	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
80	C₂×Q₈×C₆₁	—	2	8	no	—
81	C₂×Q₈×C₆₁	—	2	8	no	—
82	C₂×Q₈×C₆₁	—	4	4	no	—
83	C₂²×C₄×C₆₁	—	2	4	no	—
84	C₂²×C₄×C₆₁	—	2	4	no	—
85	C₂²×C₄×C₆₁	—	4	2	no	—
86	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
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×Q₈	1	2	yes	—
94	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₆₁	#41	1	2	yes	—
96	C₂²×C₄×C₆₁	#41	1	2	yes	—
97	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
98	M₁₆×C₆₁	—	2	8	no	—
99	M₁₆×C₆₁	—	4	4	no	—
100	C₂×C₈×C₆₁	—	2	8	no	—
101	C₂×C₈×C₆₁	—	2	1	no	—
102	C₂×C₈×C₆₁	—	2	2	no	—
103	C₂×C₈×C₆₁	—	2	1	no	—
104	C₂×C₈×C₆₁	—	2	1	no	—
105	C₂×C₈×C₆₁	—	2	1	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
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	2	no	—
111	C₂×C₈×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	—	4	4	no	—
114	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
116	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
117	C₄⋊C₄×C₆₁	—	2	4	no	—
118	C₄⋊C₄×C₆₁	—	2	16	no	—
119	C₄⋊C₄×C₆₁	—	2	8	no	—
120	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	8	yes	—
121	C₂²⋊C₄×C₆₁	—	2	4	no	—
122	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	8	yes	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	—	2	2	no	—
125	C₄²×C₆₁	—	2	2	no	—
126	C₄²×C₆₁	—	2	2	no	—
127	C₄²×C₆₁	—	2	2	no	—
128	C₄²×C₆₁	—	2	2	no	—
129	C₄²×C₆₁	C₂×D₄	1	4	yes	—
130	C₄²×C₆₁	C₂×D₄	1	4	yes	—
131	C₂³×C₆₁	—	2	2	no	—
132	C₂³×C₆₁	—	2	2	no	—
133	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₆₁	C₄×Q₈	1	2	yes	—
135	C₂³×C₆₁	C₄×Q₈	1	2	yes	—
136	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
137	Q₈×C₆₁	—	4	16	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	4	no	—
140	C₂×C₄×C₆₁	—	2	2	no	—
141	C₂×C₄×C₆₁	—	2	4	no	—
142	C₂×C₄×C₆₁	—	2	2	no	—
143	C₂×C₄×C₆₁	—	2	4	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	4	no	—
148	C₂×C₄×C₆₁	—	4	8	no	—
149	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	8	yes	—
150	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
153	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
154	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₆₁	#124	1	4	yes	—
156	C₂×C₄×C₆₁	C₄⋊Q₈	1	4	yes	—
157	C₂×C₄×C₆₁	#131	1	4	yes	—
158	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
164	C₈×C₆₁	—	2	2	no	—
165	C₈×C₆₁	—	2	2	no	—
166	C₈×C₆₁	—	2	4	no	—
167	C₈×C₆₁	—	4	2	no	—
168	C₈×C₆₁	—	4	2	no	—
169	#21304	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₆₁	—	2	4	no	—
171	C₂²×C₆₁	—	2	2	no	—
172	C₂²×C₆₁	—	2	2	no	—
173	C₂²×C₆₁	—	2	4	no	—
174	C₂²×C₆₁	#391	1	4	yes	—
175	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
177	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
178	C₂²×C₆₁	C₂×#131	1	2	yes	—
179	C₂²×C₆₁	#568	1	2	yes	—
180	C₄×C₆₁	—	2	4	no	—
181	C₄×C₆₁	—	2	8	no	—
182	C₄×C₆₁	—	4	2	no	—
183	C₄×C₆₁	—	4	4	no	—
184	C₄×C₆₁	#391	1	4	yes	—
185	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
186	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₄×C₆₁	C₂×#124	1	1	yes	characteristic
188	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
189	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
190	C₂×#424	C₂×C₆₁	1	1	yes	characteristic
191	C₂×#405	C₂×C₆₁	1	1	yes	characteristic
192	#1985	C₂×C₆₁	1	4	yes	complemented
193	#1984	C₂×C₆₁	1	4	yes	complemented
194	#1729	C₂×C₆₁	1	1	yes	characteristic
195	#1729	C₂×C₆₁	1	1	yes	characteristic
196	#1728	C₂×C₆₁	1	1	yes	characteristic
197	C₂×#336	C₂×C₆₁	1	1	yes	characteristic
198	C₂×C₆₁	—	2	4	no	—
199	C₂×C₆₁	C₂×#391	1	1	yes	characteristic
200	C₂×C₆₁	#2880	1	2	yes	—
201	C₂×C₆₁	#2960	1	1	yes	characteristic
202	C₂×C₆₁	#2961	1	1	yes	characteristic
203	C₂×C₆₁	#2962	1	2	yes	—
204	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
205	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
206	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
208	#533	—	2	4	no	—
209	#533	—	2	4	no	—
210	C₂×C₄⋊Q₈	C₄×C₆₁	1	2	yes	—
211	C₂×#125	C₄×C₆₁	1	2	yes	—
212	C₂×C₂²⋊Q₈	C₄×C₆₁	1	4	yes	—
213	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	—
214	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
215	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
216	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
217	#424	—	2	4	no	—
218	C₂×C₄⋊C₈	C₂²×C₆₁	1	4	yes	—
219	#405	—	2	4	no	—
220	C₂×#97	C₂²×C₆₁	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
222	#336	C₂²×C₆₁	1	2	yes	—
223	#336	C₂²×C₆₁	1	2	yes	—
224	#336	C₂²×C₆₁	1	4	yes	—
225	#336	C₂²×C₆₁	1	2	yes	—
226	#336	C₂²×C₆₁	1	4	yes	—
227	#336	C₂²×C₆₁	1	2	yes	—
228	C₆₁	#21304	1	1	yes	characteristic, direct product factor, Sylow
229	C₂²×Q₈	C₂×C₄×C₆₁	1	4	yes	—
230	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
231	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	Q₈×C₆₁	1	4	yes	complemented
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	Q₈×C₆₁	1	4	yes	complemented
244	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
245	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
246	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
249	C₄⋊Q₈	—	2	8	no	—
250	#125	—	2	8	no	—
251	C₂²⋊Q₈	—	2	16	no	—
252	C₄×Q₈	—	2	8	no	—
253	C₄×Q₈	—	2	8	no	—
254	#117	—	2	2	no	—
255	#117	—	2	2	no	—
256	#117	D₄×C₆₁	1	4	yes	—
257	#117	D₄×C₆₁	1	4	yes	—
258	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	8	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
261	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
269	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
270	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
271	C₄⋊C₈	—	2	8	no	—
272	#97	—	2	4	no	—
273	C₄×C₈	—	2	4	no	—
274	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
275	C₂×Q₈	—	2	8	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	2	4	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
283	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
284	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
288	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
289	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
290	C₂²×C₄	#41×C₆₁	1	2	yes	—
291	C₂²×C₄	#41×C₆₁	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
293	M₁₆	—	2	8	no	—
294	M₁₆	—	4	4	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	4	4	no	—
309	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
310	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
311	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	8	yes	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	C₂²⋊C₄×C₆₁	1	8	yes	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	C₂×D₄×C₆₁	1	4	yes	—
325	C₄²	C₂×D₄×C₆₁	1	4	yes	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
329	C₂³	C₄×Q₈×C₆₁	1	2	yes	—
330	C₂³	C₄×Q₈×C₆₁	1	2	yes	—
331	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
332	Q₈	—	4	16	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	8	yes	—
345	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
346	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
347	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
348	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
349	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
350	C₂×C₄	#124×C₆₁	1	4	yes	—
351	C₂×C₄	C₄⋊Q₈×C₆₁	1	4	yes	—
352	C₂×C₄	#131×C₆₁	1	4	yes	—
353	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
355	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
356	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	4	no	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	4	no	—
368	C₂²	C₆₁×#391	1	4	yes	—
369	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
370	C₂²	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
371	C₂²	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
372	C₂²	C₂×#131×C₆₁	1	2	yes	—
373	C₂²	C₆₁×#568	1	2	yes	—
374	C₄	—	2	4	no	—
375	C₄	—	2	8	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	4	no	—
378	C₄	C₆₁×#391	1	4	yes	—
379	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
380	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
381	C₄	C₂×#124×C₆₁	1	1	yes	characteristic
382	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
383	C₂	—	2	4	no	—
384	C₂	C₂×C₆₁×#391	1	1	yes	characteristic
385	C₂	C₆₁×#2880	1	2	yes	—
386	C₂	C₆₁×#2960	1	1	yes	characteristic
387	C₂	C₆₁×#2961	1	1	yes	characteristic
388	C₂	C₆₁×#2962	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1985	C₂	semidirect
5. C₆₁×#1984	C₂	semidirect
42. C₂×M₁₆×C₆₁	Q₈	semidirect
48. C₂²×C₈×C₆₁	Q₈	semidirect
169. #21304	C₆₁	direct (N × H)
192. #1985	C₂×C₆₁	semidirect
193. #1984	C₂×C₆₁	semidirect
228. C₆₁	#21304	direct (N × H)
237. C₂×M₁₆	Q₈×C₆₁	semidirect
243. C₂²×C₈	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×C₆₁×#424	2
C₂×C₆₁×#405	2
C₆₁×#1985	2
C₆₁×#1984	2
C₆₁×#1729	2
C₆₁×#1728	2
C₂×C₆₁×#336	2
#21304	61

Subgroups — C61×#21304 #29524737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21304 #29524737