Subgroups — C₆₁×#8988 #29512421

Order 15616.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×SD₁₆×C₆₁	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×#117×C₆₁	—	2	1	no	—
12	C₆₁×#461	—	2	2	no	—
13	C₆₁×#461	C₄	1	4	yes	complemented
14	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#103×C₆₁	—	2	1	no	—
17	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#390	—	2	1	no	—
19	C₆₁×#388	—	2	2	no	—
20	C₆₁×#384	C₂²	1	1	yes	characteristic
21	C₆₁×#380	—	2	1	no	—
22	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
23	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#340	—	2	1	no	—
25	C₆₁×#340	—	2	1	no	—
26	C₆₁×#340	—	2	2	no	—
27	C₆₁×D₄⋊C₈	—	2	2	no	—
28	C₂²×Q₈×C₆₁	—	2	1	no	—
29	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₆₁	—	2	1	no	—
31	C₂×SD₁₆×C₆₁	—	2	4	no	—
32	C₂×SD₁₆×C₆₁	—	4	2	no	—
33	C₂×SD₁₆×C₆₁	—	4	2	no	—
34	C₂²×C₈×C₆₁	—	2	1	no	—
35	C₂²×C₈×C₆₁	—	2	1	no	—
36	C₂²×C₈×C₆₁	—	2	1	no	—
37	C₄⋊Q₈×C₆₁	—	2	1	no	—
38	C₄⋊Q₈×C₆₁	—	2	1	no	—
39	C₄⋊Q₈×C₆₁	—	2	1	no	—
40	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
41	C₄×D₄×C₆₁	—	2	1	no	—
42	C₄×D₄×C₆₁	—	2	1	no	—
43	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
44	C₄×D₄×C₆₁	D₄	1	2	yes	—
45	#117×C₆₁	—	4	2	no	—
46	#117×C₆₁	—	4	2	no	—
47	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
48	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
49	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
51	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
58	C₂×C₄²×C₆₁	—	2	2	no	—
59	C₂×C₄²×C₆₁	—	2	1	no	—
60	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₆₁	—	2	1	no	—
62	C₄⋊C₈×C₆₁	—	2	1	no	—
63	C₄⋊C₈×C₆₁	—	2	1	no	—
64	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
65	#103×C₆₁	—	2	4	no	—
66	C₄×C₈×C₆₁	—	2	1	no	—
67	C₄×C₈×C₆₁	—	2	1	no	—
68	#95×C₆₁	—	2	2	no	—
69	#95×C₆₁	—	2	1	no	—
70	C₂⁴×C₆₁	—	2	1	no	—
71	C₂×Q₈×C₆₁	—	2	2	no	—
72	C₂×Q₈×C₆₁	—	4	1	no	—
73	C₂×Q₈×C₆₁	—	4	1	no	—
74	C₂×Q₈×C₆₁	—	4	1	no	—
75	C₂×Q₈×C₆₁	—	4	1	no	—
76	C₂×Q₈×C₆₁	—	4	1	no	—
77	C₂×D₄×C₆₁	—	2	1	no	—
78	C₂×D₄×C₆₁	—	2	1	no	—
79	C₂×D₄×C₆₁	—	2	1	no	—
80	C₂×D₄×C₆₁	—	2	1	no	—
81	C₂×D₄×C₆₁	—	2	1	no	—
82	C₂×D₄×C₆₁	C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄×C₆₁	—	2	1	no	—
84	C₂²×C₄×C₆₁	—	2	1	no	—
85	C₂²×C₄×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	—	2	2	no	—
87	C₂²×C₄×C₆₁	—	2	1	no	—
88	C₂²×C₄×C₆₁	—	2	2	no	—
89	C₂²×C₄×C₆₁	—	4	1	no	—
90	C₂²×C₄×C₆₁	—	4	1	no	—
91	C₂²×C₄×C₆₁	—	4	1	no	—
92	C₂²×C₄×C₆₁	—	4	1	no	—
93	C₂²×C₄×C₆₁	—	4	1	no	—
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×D₄	1	1	yes	characteristic
97	SD₁₆×C₆₁	—	4	8	no	—
98	C₂×C₈×C₆₁	—	2	2	no	—
99	C₂×C₈×C₆₁	—	2	2	no	—
100	C₂×C₈×C₆₁	—	4	1	no	—
101	C₂×C₈×C₆₁	—	4	1	no	—
102	C₂×C₈×C₆₁	—	4	1	no	—
103	C₂×C₈×C₆₁	—	4	1	no	—
104	C₂×C₈×C₆₁	—	4	1	no	—
105	C₂×C₈×C₆₁	—	4	1	no	—
106	C₂×C₈×C₆₁	—	4	1	no	—
107	C₄⋊C₄×C₆₁	—	2	1	no	—
108	C₄⋊C₄×C₆₁	—	2	1	no	—
109	C₄⋊C₄×C₆₁	—	2	2	no	—
110	C₄⋊C₄×C₆₁	—	2	2	no	—
111	C₄⋊C₄×C₆₁	—	2	1	no	—
112	C₄⋊C₄×C₆₁	—	2	1	no	—
113	C₄⋊C₄×C₆₁	—	4	2	no	—
114	C₄⋊C₄×C₆₁	—	4	1	no	—
115	C₄⋊C₄×C₆₁	—	4	1	no	—
116	C₄⋊C₄×C₆₁	—	4	1	no	—
117	C₄⋊C₄×C₆₁	—	4	1	no	—
118	C₄⋊C₄×C₆₁	—	4	1	no	—
119	C₄⋊C₄×C₆₁	—	4	1	no	—
120	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
121	C₄⋊C₄×C₆₁	SD₁₆	1	2	yes	complemented
122	C₂²⋊C₄×C₆₁	—	2	2	no	—
123	C₂²⋊C₄×C₆₁	—	2	2	no	—
124	C₂²⋊C₄×C₆₁	—	4	4	no	—
125	C₂²⋊C₄×C₆₁	—	8	2	no	—
126	C₄²×C₆₁	—	4	4	no	—
127	C₄²×C₆₁	—	4	1	no	—
128	C₄²×C₆₁	—	4	1	no	—
129	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₆₁	#41	1	1	yes	characteristic
132	C₄²×C₆₁	#41	1	1	yes	characteristic
133	C₂³×C₆₁	—	2	2	no	—
134	C₂³×C₆₁	—	4	1	no	—
135	C₂³×C₆₁	—	4	1	no	—
136	C₂³×C₆₁	—	4	1	no	—
137	C₂³×C₆₁	—	4	1	no	—
138	C₂³×C₆₁	—	4	1	no	—
139	C₂³×C₆₁	—	4	1	no	—
140	C₂³×C₆₁	#120	1	1	yes	characteristic
141	Q₈×C₆₁	—	4	2	no	—
142	Q₈×C₆₁	—	4	2	no	—
143	Q₈×C₆₁	—	8	1	no	—
144	Q₈×C₆₁	—	8	1	no	—
145	D₄×C₆₁	—	2	2	no	—
146	D₄×C₆₁	—	2	2	no	—
147	D₄×C₆₁	—	4	1	no	—
148	D₄×C₆₁	—	4	1	no	—
149	C₂×C₄×C₆₁	—	2	1	no	—
150	C₂×C₄×C₆₁	—	2	1	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	4	1	no	—
154	C₂×C₄×C₆₁	—	4	1	no	—
155	C₂×C₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	4	1	no	—
157	C₂×C₄×C₆₁	—	4	2	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	4	1	no	—
163	C₂×C₄×C₆₁	—	4	2	no	—
164	C₂×C₄×C₆₁	—	4	2	no	—
165	C₂×C₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	—	4	1	no	—
167	C₂×C₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	—	8	1	no	—
169	C₂×C₄×C₆₁	—	8	1	no	—
170	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
174	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
175	C₂×C₄×C₆₁	#123	1	1	yes	characteristic
176	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
177	C₂×C₄×C₆₁	#135	1	1	yes	characteristic
178	C₂×C₄×C₆₁	#135	1	1	yes	characteristic
179	C₂×C₄×C₆₁	#135	1	1	yes	characteristic
180	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
184	C₈×C₆₁	—	4	2	no	—
185	C₈×C₆₁	—	4	2	no	—
186	C₈×C₆₁	—	8	1	no	—
187	#8988	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₆₁	—	4	2	no	—
189	C₂²×C₆₁	—	4	2	no	—
190	C₂²×C₆₁	—	4	2	no	—
191	C₂²×C₆₁	—	8	1	no	—
192	C₂²×C₆₁	—	8	1	no	—
193	C₂²×C₆₁	—	8	1	no	—
194	C₂²×C₆₁	—	8	1	no	—
195	C₂²×C₆₁	#386	1	1	yes	characteristic
196	C₂²×C₆₁	#449	1	1	yes	characteristic
197	C₂²×C₆₁	#449	1	1	yes	characteristic
198	C₂²×C₆₁	#450	1	1	yes	characteristic
199	C₂²×C₆₁	#452	1	1	yes	characteristic
200	C₂²×C₆₁	#455	1	1	yes	characteristic
201	C₂²×C₆₁	#456	1	1	yes	characteristic
202	C₄×C₆₁	—	2	1	no	—
203	C₄×C₆₁	—	2	1	no	—
204	C₄×C₆₁	—	4	2	no	—
205	C₄×C₆₁	—	4	2	no	—
206	C₄×C₆₁	—	8	2	no	—
207	C₄×C₆₁	—	8	2	no	—
208	C₄×C₆₁	—	8	1	no	—
209	C₄×C₆₁	#416	1	1	yes	characteristic
210	C₄×C₆₁	#418	1	1	yes	characteristic
211	C₄×C₆₁	C₄×SD₁₆	1	1	yes	characteristic
212	C₄×C₆₁	#440	1	1	yes	characteristic
213	C₄×C₆₁	#461	1	1	yes	characteristic
214	C₄×C₆₁	#463	1	1	yes	characteristic
215	C₄×C₆₁	#482	1	1	yes	characteristic
216	C₄×C₆₁	#482	1	1	yes	characteristic
217	C₂×#461	C₂×C₆₁	1	1	yes	characteristic
218	#2354	C₂×C₆₁	1	1	yes	characteristic
219	#1990	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#1988	C₂×C₆₁	1	1	yes	characteristic, complemented
221	C₂×D₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic
222	#1296	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#1279	C₂×C₆₁	1	1	yes	characteristic, complemented
224	C₂×C₆₁	—	8	2	no	—
225	C₂×C₆₁	#1642	1	1	yes	characteristic
226	C₂×C₆₁	#1646	1	1	yes	characteristic
227	C₂×C₆₁	#1650	1	1	yes	characteristic
228	C₂×C₆₁	#1654	1	1	yes	characteristic
229	C₂×C₆₁	#1875	1	1	yes	characteristic
230	C₂×C₆₁	#1877	1	1	yes	characteristic
231	C₂×C₆₁	#1882	1	1	yes	characteristic
232	C₂²×SD₁₆	—	2	1	no	—
233	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
234	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
235	C₂×#117	—	2	1	no	—
236	#461	—	2	2	no	—
237	#461	C₄×C₆₁	1	4	yes	complemented
238	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
240	C₂×#103	—	2	1	no	—
241	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
242	#390	—	2	1	no	—
243	#388	—	2	2	no	—
244	#384	C₂²×C₆₁	1	1	yes	characteristic
245	#380	—	2	1	no	—
246	C₄×C₄⋊C₄	—	2	1	no	—
247	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
248	#340	—	2	1	no	—
249	#340	—	2	1	no	—
250	#340	—	2	2	no	—
251	D₄⋊C₈	—	2	2	no	—
252	C₆₁	#8988	1	1	yes	characteristic, direct product factor, Sylow
253	C₂²×Q₈	—	2	1	no	—
254	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂×SD₁₆	—	2	4	no	—
257	C₂×SD₁₆	—	4	2	no	—
258	C₂×SD₁₆	—	4	2	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
269	C₄×D₄	D₄×C₆₁	1	2	yes	—
270	#117	—	4	2	no	—
271	#117	—	4	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
277	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
278	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
279	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	C₂×C₄×C₆₁	1	2	yes	—
290	#103	—	2	4	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	#95	—	2	2	no	—
294	#95	—	2	1	no	—
295	C₂⁴	—	2	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	C₂²⋊C₄×C₆₁	1	2	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	—	4	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
322	SD₁₆	—	4	8	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
346	C₄⋊C₄	SD₁₆×C₆₁	1	2	yes	complemented
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	8	2	no	—
351	C₄²	—	4	4	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
356	C₄²	#41×C₆₁	1	1	yes	characteristic
357	C₄²	#41×C₆₁	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	1	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	#120×C₆₁	1	1	yes	characteristic
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	8	1	no	—
369	Q₈	—	8	1	no	—
370	D₄	—	2	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	1	no	—
373	D₄	—	4	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
396	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
397	C₂×C₄	C₄×D₄×C₆₁	1	1	yes	characteristic
398	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
399	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
400	C₂×C₄	#123×C₆₁	1	1	yes	characteristic
401	C₂×C₄	C₂×SD₁₆×C₆₁	1	1	yes	characteristic
402	C₂×C₄	#135×C₆₁	1	1	yes	characteristic
403	C₂×C₄	#135×C₆₁	1	1	yes	characteristic
404	C₂×C₄	#135×C₆₁	1	1	yes	characteristic
405	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
406	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
407	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
408	C₂×C₄	#137×C₆₁	1	1	yes	characteristic
409	C₈	—	4	2	no	—
410	C₈	—	4	2	no	—
411	C₈	—	8	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	C₆₁×#386	1	1	yes	characteristic
420	C₂²	C₆₁×#449	1	1	yes	characteristic
421	C₂²	C₆₁×#449	1	1	yes	characteristic
422	C₂²	C₆₁×#450	1	1	yes	characteristic
423	C₂²	C₆₁×#452	1	1	yes	characteristic
424	C₂²	C₆₁×#455	1	1	yes	characteristic
425	C₂²	C₆₁×#456	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	1	no	—
433	C₄	C₆₁×#416	1	1	yes	characteristic
434	C₄	C₆₁×#418	1	1	yes	characteristic
435	C₄	C₄×SD₁₆×C₆₁	1	1	yes	characteristic
436	C₄	C₆₁×#440	1	1	yes	characteristic
437	C₄	C₆₁×#461	1	1	yes	characteristic
438	C₄	C₆₁×#463	1	1	yes	characteristic
439	C₄	C₆₁×#482	1	1	yes	characteristic
440	C₄	C₆₁×#482	1	1	yes	characteristic
441	C₂	—	8	2	no	—
442	C₂	C₆₁×#1642	1	1	yes	characteristic
443	C₂	C₆₁×#1646	1	1	yes	characteristic
444	C₂	C₆₁×#1650	1	1	yes	characteristic
445	C₂	C₆₁×#1654	1	1	yes	characteristic
446	C₂	C₆₁×#1875	1	1	yes	characteristic
447	C₂	C₆₁×#1877	1	1	yes	characteristic
448	C₂	C₆₁×#1882	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	#120
commutator	C₄²	C₂²×C₄×C₆₁
Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₂²×D₄×C₆₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#1990	C₂	semidirect
4. C₆₁×#1988	C₂	semidirect
6. C₆₁×#1296	C₂	semidirect
7. C₆₁×#1279	C₂	semidirect
13. C₆₁×#461	C₄	semidirect
121. C₄⋊C₄×C₆₁	SD₁₆	semidirect
187. #8988	C₆₁	direct (N × H)
219. #1990	C₂×C₆₁	semidirect
220. #1988	C₂×C₆₁	semidirect
222. #1296	C₂×C₆₁	semidirect
223. #1279	C₂×C₆₁	semidirect
237. #461	C₄×C₆₁	semidirect
252. C₆₁	#8988	direct (N × H)
346. C₄⋊C₄	SD₁₆×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×#461	2
C₆₁×#2354	2
C₆₁×#1990	2
C₆₁×#1988	2
C₂×C₆₁×D₄⋊C₈	2
C₆₁×#1296	2
C₆₁×#1279	2
#8988	61

Subgroups — C61×#8988 #29512421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#8988 #29512421