Subgroups — C₆₁×#11226 #29514659

Order 15616.

882 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2296	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#339	C₂	1	2	yes	maximal
4	C₂×C₆₁×#339	C₂	1	2	yes	maximal
5	C₆₁×#1728	C₂	1	1	yes	maximal, characteristic
6	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
7	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
8	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
10	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
11	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₆₁×#389	C₄	1	2	yes	complemented
13	C₆₁×#389	C₄	1	2	yes	complemented
14	C₆₁×#385	—	2	1	no	—
15	C₆₁×#385	—	2	1	no	—
16	C₄×C₄⋊C₄×C₆₁	—	2	4	no	—
17	C₄×C₄⋊C₄×C₆₁	—	2	2	no	—
18	C₂×#95×C₆₁	—	2	1	no	—
19	C₆₁×#339	—	2	4	no	—
20	C₆₁×#339	—	2	4	no	—
21	C₆₁×#336	—	2	2	no	—
22	C₂³×C₄×C₆₁	—	2	2	no	—
23	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₆₁	—	2	2	no	—
27	C₂×M₁₆×C₆₁	—	2	2	no	—
28	C₂×M₁₆×C₆₁	—	2	2	no	—
29	C₂×M₁₆×C₆₁	—	2	2	no	—
30	C₂×M₁₆×C₆₁	—	2	2	no	—
31	C₂×M₁₆×C₆₁	Q₈	1	4	yes	—
32	C₂²×C₈×C₆₁	—	2	2	no	—
33	#117×C₆₁	—	2	1	no	—
34	#117×C₆₁	—	2	1	no	—
35	#117×C₆₁	—	2	2	no	—
36	#117×C₆₁	—	2	2	no	—
37	#117×C₆₁	D₄	1	2	yes	—
38	#117×C₆₁	Q₈	1	2	yes	—
39	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
40	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
41	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
43	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
48	C₂×C₄²×C₆₁	—	2	2	no	—
49	C₂×C₄²×C₆₁	—	2	1	no	—
50	C₂×C₄²×C₆₁	—	2	2	no	—
51	C₂×C₄²×C₆₁	—	2	2	no	—
52	C₂×C₄²×C₆₁	—	2	2	no	—
53	C₂×C₄²×C₆₁	—	2	2	no	—
54	C₂×C₄²×C₆₁	—	2	2	no	—
55	C₂×C₄²×C₆₁	—	2	2	no	—
56	C₂×C₄²×C₆₁	—	2	1	no	—
57	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₆₁	D₄	1	4	yes	—
59	C₂×C₄²×C₆₁	D₄	1	2	yes	—
60	#95×C₆₁	—	2	4	no	—
61	#95×C₆₁	—	2	2	no	—
62	#95×C₆₁	—	2	2	no	—
63	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₆₁	—	2	1	no	—
65	C₂²×C₄×C₆₁	—	2	1	no	—
66	C₂²×C₄×C₆₁	—	2	4	no	—
67	C₂²×C₄×C₆₁	—	2	8	no	—
68	C₂²×C₄×C₆₁	—	2	2	no	—
69	C₂²×C₄×C₆₁	—	2	1	no	—
70	C₂²×C₄×C₆₁	—	2	4	no	—
71	C₂²×C₄×C₆₁	—	2	1	no	—
72	C₂²×C₄×C₆₁	—	2	1	no	—
73	C₂²×C₄×C₆₁	—	2	1	no	—
74	C₂²×C₄×C₆₁	—	4	2	no	—
75	C₂²×C₄×C₆₁	—	4	4	no	—
76	C₂²×C₄×C₆₁	—	4	2	no	—
77	C₂²×C₄×C₆₁	—	4	2	no	—
78	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
80	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
88	C₂²×C₄×C₆₁	#41	1	2	yes	—
89	C₂²×C₄×C₆₁	#41	1	2	yes	—
90	M₁₆×C₆₁	—	2	4	no	—
91	M₁₆×C₆₁	—	2	4	no	—
92	M₁₆×C₆₁	—	4	2	no	—
93	M₁₆×C₆₁	—	4	2	no	—
94	C₂×C₈×C₆₁	—	2	4	no	—
95	C₂×C₈×C₆₁	—	4	2	no	—
96	C₂×C₈×C₆₁	—	4	2	no	—
97	C₄⋊C₄×C₆₁	—	2	16	no	—
98	C₄⋊C₄×C₆₁	—	2	2	no	—
99	C₄⋊C₄×C₆₁	—	2	2	no	—
100	C₄⋊C₄×C₆₁	—	2	2	no	—
101	C₄⋊C₄×C₆₁	—	4	4	no	—
102	C₄⋊C₄×C₆₁	—	4	4	no	—
103	C₄⋊C₄×C₆₁	C₄⋊C₄	1	4	yes	complemented
104	C₂²⋊C₄×C₆₁	—	2	2	no	—
105	C₂²⋊C₄×C₆₁	—	2	2	no	—
106	C₂²⋊C₄×C₆₁	—	4	1	no	—
107	C₂²⋊C₄×C₆₁	—	4	1	no	—
108	C₄²×C₆₁	—	2	4	no	—
109	C₄²×C₆₁	—	2	4	no	—
110	C₄²×C₆₁	—	2	2	no	—
111	C₄²×C₆₁	—	2	2	no	—
112	C₄²×C₆₁	—	2	4	no	—
113	C₄²×C₆₁	—	2	4	no	—
114	C₄²×C₆₁	—	4	2	no	—
115	C₄²×C₆₁	—	4	2	no	—
116	C₄²×C₆₁	—	4	2	no	—
117	C₂³×C₆₁	—	2	2	no	—
118	C₂³×C₆₁	—	2	2	no	—
119	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₆₁	#120	1	1	yes	characteristic
121	C₂³×C₆₁	#121	1	1	yes	characteristic
122	C₂³×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
123	C₂³×C₆₁	#123	1	1	yes	characteristic
124	C₂³×C₆₁	#124	1	1	yes	characteristic
125	C₂³×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
126	C₂×C₄×C₆₁	—	2	4	no	—
127	C₂×C₄×C₆₁	—	2	4	no	—
128	C₂×C₄×C₆₁	—	2	2	no	—
129	C₂×C₄×C₆₁	—	2	2	no	—
130	C₂×C₄×C₆₁	—	2	8	no	—
131	C₂×C₄×C₆₁	—	2	4	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	—	4	8	no	—
136	C₂×C₄×C₆₁	—	4	4	no	—
137	C₂×C₄×C₆₁	—	4	8	no	—
138	C₂×C₄×C₆₁	—	4	2	no	—
139	C₂×C₄×C₆₁	—	4	2	no	—
140	C₂×C₄×C₆₁	—	4	4	no	—
141	C₂×C₄×C₆₁	—	4	2	no	—
142	C₂×C₄×C₆₁	—	4	2	no	—
143	C₂×C₄×C₆₁	—	4	1	no	—
144	C₂×C₄×C₆₁	—	4	1	no	—
145	C₂×C₄×C₆₁	—	4	2	no	—
146	C₂×C₄×C₆₁	—	4	2	no	—
147	C₂×C₄×C₆₁	#104	1	4	yes	—
148	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₁	#117	1	1	yes	characteristic
150	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
152	C₂×C₄×C₆₁	#121	1	2	yes	—
153	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
154	C₂×C₄×C₆₁	#121	1	2	yes	—
155	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₆₁	#123	1	2	yes	—
160	C₂×C₄×C₆₁	#125	1	2	yes	—
161	C₂×C₄×C₆₁	#125	1	2	yes	—
162	C₂×C₄×C₆₁	#126	1	2	yes	—
163	C₂×C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
164	C₈×C₆₁	—	4	4	no	—
165	#11226	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
166	C₂²×C₆₁	—	2	2	no	—
167	C₂²×C₆₁	—	2	2	no	—
168	C₂²×C₆₁	—	2	1	no	—
169	C₂²×C₆₁	—	2	1	no	—
170	C₂²×C₆₁	—	2	1	no	—
171	C₂²×C₆₁	—	2	1	no	—
172	C₂²×C₆₁	—	2	2	no	—
173	C₂²×C₆₁	—	2	2	no	—
174	C₂²×C₆₁	#380	1	1	yes	characteristic
175	C₂²×C₆₁	#386	1	1	yes	characteristic
176	C₂²×C₆₁	#391	1	1	yes	characteristic
177	C₂²×C₆₁	#394	1	1	yes	characteristic
178	C₂²×C₆₁	#395	1	1	yes	characteristic
179	C₂²×C₆₁	#398	1	1	yes	characteristic
180	C₂²×C₆₁	#400	1	1	yes	characteristic
181	C₂²×C₆₁	C₂×#104	1	2	yes	—
182	C₂²×C₆₁	#421	1	2	yes	—
183	C₄×C₆₁	—	2	4	no	—
184	C₄×C₆₁	—	4	8	no	—
185	C₄×C₆₁	—	4	4	no	—
186	C₄×C₆₁	—	4	2	no	—
187	C₄×C₆₁	—	8	1	no	—
188	C₄×C₆₁	—	8	1	no	—
189	C₄×C₆₁	#387	1	2	yes	—
190	C₄×C₆₁	#389	1	2	yes	—
191	C₄×C₆₁	#396	1	2	yes	—
192	C₄×C₆₁	#398	1	2	yes	—
193	#2296	C₂×C₆₁	1	1	yes	characteristic
194	C₂×C₄×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic
195	C₂×#339	C₂×C₆₁	1	2	yes	—
196	C₂×#339	C₂×C₆₁	1	2	yes	—
197	#1728	C₂×C₆₁	1	1	yes	characteristic
198	C₂×C₆₁	—	2	1	no	—
199	C₂×C₆₁	—	2	1	no	—
200	C₂×C₆₁	—	2	1	no	—
201	C₂×C₆₁	—	2	1	no	—
202	C₂×C₆₁	#1441	1	1	yes	characteristic
203	C₂×C₆₁	#1806	1	2	yes	—
204	C₂×C₆₁	#1896	1	1	yes	characteristic
205	C₂×C₆₁	#1897	1	1	yes	characteristic
206	C₂×C₆₁	#1986	1	2	yes	—
207	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
208	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
209	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
210	C₂²×C₄⋊C₄	—	2	1	no	—
211	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
212	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
213	#389	C₄×C₆₁	1	2	yes	complemented
214	#389	C₄×C₆₁	1	2	yes	complemented
215	#385	—	2	1	no	—
216	#385	—	2	1	no	—
217	C₄×C₄⋊C₄	—	2	4	no	—
218	C₄×C₄⋊C₄	—	2	2	no	—
219	C₂×#95	—	2	1	no	—
220	#339	—	2	4	no	—
221	#339	—	2	4	no	—
222	#336	—	2	2	no	—
223	C₆₁	#11226	1	1	yes	characteristic, direct product factor, Sylow
224	C₂³×C₄	—	2	2	no	—
225	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
226	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	Q₈×C₆₁	1	4	yes	—
234	C₂²×C₈	—	2	2	no	—
235	#117	—	2	1	no	—
236	#117	—	2	1	no	—
237	#117	—	2	2	no	—
238	#117	—	2	2	no	—
239	#117	D₄×C₆₁	1	2	yes	—
240	#117	Q₈×C₆₁	1	2	yes	—
241	C₂×C₄⋊C₄	—	2	8	no	—
242	C₂×C₄⋊C₄	—	2	4	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
247	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
260	C₂×C₄²	D₄×C₆₁	1	4	yes	—
261	C₂×C₄²	D₄×C₆₁	1	2	yes	—
262	#95	—	2	4	no	—
263	#95	—	2	2	no	—
264	#95	—	2	2	no	—
265	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
281	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
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	2	yes	—
285	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
286	C₂²×C₄	C₂×Q₈×C₆₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
288	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
289	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
290	C₂²×C₄	#41×C₆₁	1	2	yes	—
291	C₂²×C₄	#41×C₆₁	1	2	yes	—
292	M₁₆	—	2	4	no	—
293	M₁₆	—	2	4	no	—
294	M₁₆	—	4	2	no	—
295	M₁₆	—	4	2	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₄⋊C₄	—	2	16	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	4	no	—
304	C₄⋊C₄	—	4	4	no	—
305	C₄⋊C₄	C₄⋊C₄×C₆₁	1	4	yes	complemented
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₄²	—	2	4	no	—
311	C₄²	—	2	4	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	4	no	—
315	C₄²	—	2	4	no	—
316	C₄²	—	4	2	no	—
317	C₄²	—	4	2	no	—
318	C₄²	—	4	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
322	C₂³	#120×C₆₁	1	1	yes	characteristic
323	C₂³	#121×C₆₁	1	1	yes	characteristic
324	C₂³	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
325	C₂³	#123×C₆₁	1	1	yes	characteristic
326	C₂³	#124×C₆₁	1	1	yes	characteristic
327	C₂³	C₄⋊Q₈×C₆₁	1	1	yes	characteristic
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	8	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	8	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	#104×C₆₁	1	4	yes	—
350	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
351	C₂×C₄	#117×C₆₁	1	1	yes	characteristic
352	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
353	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
354	C₂×C₄	#121×C₆₁	1	2	yes	—
355	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
356	C₂×C₄	#121×C₆₁	1	2	yes	—
357	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
358	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
359	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
360	C₂×C₄	C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
361	C₂×C₄	#123×C₆₁	1	2	yes	—
362	C₂×C₄	#125×C₆₁	1	2	yes	—
363	C₂×C₄	#125×C₆₁	1	2	yes	—
364	C₂×C₄	#126×C₆₁	1	2	yes	—
365	C₂×C₄	C₄⋊Q₈×C₆₁	1	2	yes	—
366	C₈	—	4	4	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	C₆₁×#380	1	1	yes	characteristic
376	C₂²	C₆₁×#386	1	1	yes	characteristic
377	C₂²	C₆₁×#391	1	1	yes	characteristic
378	C₂²	C₆₁×#394	1	1	yes	characteristic
379	C₂²	C₆₁×#395	1	1	yes	characteristic
380	C₂²	C₆₁×#398	1	1	yes	characteristic
381	C₂²	C₆₁×#400	1	1	yes	characteristic
382	C₂²	C₂×#104×C₆₁	1	2	yes	—
383	C₂²	C₆₁×#421	1	2	yes	—
384	C₄	—	2	4	no	—
385	C₄	—	4	8	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	1	no	—
389	C₄	—	8	1	no	—
390	C₄	C₆₁×#387	1	2	yes	—
391	C₄	C₆₁×#389	1	2	yes	—
392	C₄	C₆₁×#396	1	2	yes	—
393	C₄	C₆₁×#398	1	2	yes	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	2	1	no	—
397	C₂	—	2	1	no	—
398	C₂	C₆₁×#1441	1	1	yes	characteristic
399	C₂	C₆₁×#1806	1	2	yes	—
400	C₂	C₆₁×#1896	1	1	yes	characteristic
401	C₂	C₆₁×#1897	1	1	yes	characteristic
402	C₂	C₆₁×#1986	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₆₁
Frattini, cosocle	C₂³×C₄	C₂³×C₆₁
socle	C₂³×C₆₁	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×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
12. C₆₁×#389	C₄	semidirect
13. C₆₁×#389	C₄	semidirect
103. C₄⋊C₄×C₆₁	C₄⋊C₄	semidirect
165. #11226	C₆₁	direct (N × H)
213. #389	C₄×C₆₁	semidirect
214. #389	C₄×C₆₁	semidirect
223. C₆₁	#11226	direct (N × H)
305. C₄⋊C₄	C₄⋊C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2296	2
C₂×C₄×C₄⋊C₄×C₆₁	2
C₂×C₆₁×#339	2
C₆₁×#1728	2
#11226	61

Subgroups — C61×#11226 #29514659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#11226 #29514659