Subgroups — C₆₁×#19985 #29523418

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3392	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3383	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3287	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1673	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1668	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1666	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1642	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1626	C₂	1	2	yes	maximal, complemented
10	C₈×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	—	2	1	no	—
13	C₆₁×#557	C₂²	1	2	yes	—
14	C₆₁×#550	C₂²	1	2	yes	—
15	C₆₁×#500	C₂²	1	1	yes	characteristic
16	C₆₁×#499	—	2	1	no	—
17	C₆₁×#493	C₂²	1	1	yes	characteristic
18	C₆₁×#492	—	2	2	no	—
19	C₆₁×#492	C₂²	1	2	yes	—
20	C₆₁×#486	C₂²	1	2	yes	—
21	C₆₁×#479	—	2	2	no	—
22	C₆₁×#475	C₂²	1	2	yes	—
23	C₆₁×#466	—	2	1	no	—
24	C₆₁×#461	—	2	2	no	—
25	C₆₁×#461	C₂²	1	2	yes	—
26	C₆₁×#460	—	2	2	no	—
27	C₆₁×#460	C₂²	1	2	yes	—
28	C₆₁×#460	C₂²	1	2	yes	—
29	C₆₁×#449	—	2	2	no	—
30	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
32	C₄×Q₁₆×C₆₁	—	2	1	no	—
33	C₄×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₆₁	—	2	2	no	—
35	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
36	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#334	C₂²	1	1	yes	characteristic
39	C₆₁×#332	C₂²	1	2	yes	—
40	C₆₁×#331	C₂²	1	2	yes	—
41	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₆₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₆₁	—	2	2	no	—
46	#135×C₆₁	—	4	4	no	—
47	C₂×Q₁₆×C₆₁	D₄	1	1	yes	characteristic
48	C₂×SD₁₆×C₆₁	—	2	2	no	—
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×SD₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic
54	C₂×D₈×C₆₁	—	2	1	no	—
55	C₂×D₈×C₆₁	—	2	1	no	—
56	C₂²×C₈×C₆₁	—	2	1	no	—
57	C₄⋊Q₈×C₆₁	—	2	2	no	—
58	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
59	#127×C₆₁	—	2	2	no	—
60	#127×C₆₁	C₂³	1	2	yes	—
61	#125×C₆₁	—	2	2	no	—
62	#125×C₆₁	—	4	2	no	—
63	#121×C₆₁	—	2	2	no	—
64	#121×C₆₁	—	4	2	no	—
65	C₄×Q₈×C₆₁	—	2	2	no	—
66	C₄×Q₈×C₆₁	—	2	2	no	—
67	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
68	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₆₁	—	2	2	no	—
70	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
71	#107×C₆₁	—	2	1	no	—
72	#107×C₆₁	—	2	1	no	—
73	#107×C₆₁	D₄	1	1	yes	characteristic
74	#106×C₆₁	—	2	2	no	—
75	#106×C₆₁	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₆₁	—	2	2	no	—
77	C₄⋊C₈×C₆₁	—	2	1	no	—
78	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
81	#103×C₆₁	—	2	2	no	—
82	#103×C₆₁	—	2	2	no	—
83	#103×C₆₁	D₄	1	1	yes	characteristic
84	#103×C₆₁	D₄	1	2	yes	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	#102×C₆₁	—	4	2	no	—
88	#102×C₆₁	D₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₆₁	—	2	1	no	—
90	C₄×C₈×C₆₁	—	2	2	no	—
91	C₄×C₈×C₆₁	—	2	1	no	—
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
95	#41×C₆₁	—	4	4	no	—
96	#41×C₆₁	—	8	2	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	2	2	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	4	2	no	—
104	C₂×D₄×C₆₁	—	4	2	no	—
105	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	4	2	no	—
108	Q₁₆×C₆₁	SD₁₆	1	4	yes	complemented
109	SD₁₆×C₆₁	—	2	2	no	—
110	SD₁₆×C₆₁	—	4	4	no	—
111	SD₁₆×C₆₁	—	4	4	no	—
112	SD₁₆×C₆₁	—	8	2	no	—
113	SD₁₆×C₆₁	—	8	2	no	—
114	SD₁₆×C₆₁	—	8	2	no	—
115	D₈×C₆₁	—	4	2	no	—
116	D₈×C₆₁	—	8	1	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	2	1	no	—
121	C₂×C₈×C₆₁	—	4	2	no	—
122	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	1	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	4	2	no	—
131	C₄⋊C₄×C₆₁	—	4	2	no	—
132	C₄⋊C₄×C₆₁	—	4	2	no	—
133	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₆₁	—	2	1	no	—
137	C₂²⋊C₄×C₆₁	—	4	2	no	—
138	C₄²×C₆₁	—	2	2	no	—
139	C₄²×C₆₁	—	2	1	no	—
140	C₄²×C₆₁	—	4	2	no	—
141	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
142	C₂³×C₆₁	—	2	1	no	—
143	C₂³×C₆₁	—	4	2	no	—
144	Q₈×C₆₁	—	2	2	no	—
145	Q₈×C₆₁	—	2	1	no	—
146	Q₈×C₆₁	—	2	1	no	—
147	Q₈×C₆₁	—	4	2	no	—
148	Q₈×C₆₁	—	4	2	no	—
149	Q₈×C₆₁	C₂×SD₁₆	1	4	yes	—
150	D₄×C₆₁	—	2	1	no	—
151	D₄×C₆₁	—	2	1	no	—
152	D₄×C₆₁	—	4	2	no	—
153	D₄×C₆₁	—	4	2	no	—
154	D₄×C₆₁	—	4	2	no	—
155	D₄×C₆₁	—	4	2	no	—
156	D₄×C₆₁	—	8	4	no	—
157	D₄×C₆₁	—	8	2	no	—
158	D₄×C₆₁	—	16	2	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	4	1	no	—
165	C₂×C₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	8	4	no	—
168	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
171	C₈×C₆₁	—	2	1	no	—
172	C₈×C₆₁	—	2	1	no	—
173	C₈×C₆₁	—	4	1	no	—
174	C₈×C₆₁	—	4	1	no	—
175	C₈×C₆₁	—	4	2	no	—
176	C₈×C₆₁	—	4	1	no	—
177	C₈×C₆₁	C₂×SD₁₆	1	2	yes	—
178	C₈×C₆₁	#135	1	2	yes	complemented
179	#19985	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₆₁	—	4	1	no	—
181	C₂²×C₆₁	—	4	1	no	—
182	C₂²×C₆₁	—	4	1	no	—
183	C₂²×C₆₁	—	8	2	no	—
184	C₂²×C₆₁	—	8	2	no	—
185	C₂²×C₆₁	—	8	2	no	—
186	C₂²×C₆₁	D₄²	1	1	yes	characteristic
187	C₄×C₆₁	—	2	4	no	—
188	C₄×C₆₁	—	2	1	no	—
189	C₄×C₆₁	—	4	1	no	—
190	C₄×C₆₁	—	4	1	no	—
191	C₄×C₆₁	—	4	1	no	—
192	C₄×C₆₁	—	4	2	no	—
193	C₄×C₆₁	—	8	2	no	—
194	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
195	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
196	C₄×C₆₁	#576	1	1	yes	characteristic
197	C₄×C₆₁	#577	1	1	yes	characteristic
198	#3392	C₂×C₆₁	1	2	yes	complemented
199	#3383	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#3287	C₂×C₆₁	1	1	yes	characteristic
201	#1706	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#1673	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#1668	C₂×C₆₁	1	1	yes	characteristic, complemented
204	#1666	C₂×C₆₁	1	2	yes	complemented
205	#1642	C₂×C₆₁	1	2	yes	complemented
206	#1626	C₂×C₆₁	1	2	yes	complemented
207	C₈×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
208	C₈×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
209	C₂×C₆₁	—	8	1	no	—
210	C₂×C₆₁	—	16	2	no	—
211	C₂×C₆₁	D₄×SD₁₆	1	1	yes	characteristic
212	C₂×C₆₁	#3287	1	1	yes	characteristic
213	C₂×C₆₁	#3290	1	1	yes	characteristic
214	C₂×#135	—	2	1	no	—
215	#557	C₂²×C₆₁	1	2	yes	—
216	#550	C₂²×C₆₁	1	2	yes	—
217	#500	C₂²×C₆₁	1	1	yes	characteristic
218	#499	—	2	1	no	—
219	#493	C₂²×C₆₁	1	1	yes	characteristic
220	#492	—	2	2	no	—
221	#492	C₂²×C₆₁	1	2	yes	—
222	#486	C₂²×C₆₁	1	2	yes	—
223	#479	—	2	2	no	—
224	#475	C₂²×C₆₁	1	2	yes	—
225	#466	—	2	1	no	—
226	#461	—	2	2	no	—
227	#461	C₂²×C₆₁	1	2	yes	—
228	#460	—	2	2	no	—
229	#460	C₂²×C₆₁	1	2	yes	—
230	#460	C₂²×C₆₁	1	2	yes	—
231	#449	—	2	2	no	—
232	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
233	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
234	C₄×Q₁₆	—	2	1	no	—
235	C₄×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
236	C₄×SD₁₆	—	2	2	no	—
237	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
238	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
239	#335	C₂²×C₆₁	1	1	yes	characteristic
240	#334	C₂²×C₆₁	1	1	yes	characteristic
241	#332	C₂²×C₆₁	1	2	yes	—
242	#331	C₂²×C₆₁	1	2	yes	—
243	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
244	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
245	D₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
246	C₈²	C₂²×C₆₁	1	1	yes	characteristic
247	C₆₁	#19985	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×#41	—	2	2	no	—
249	#135	—	4	4	no	—
250	C₂×Q₁₆	D₄×C₆₁	1	1	yes	characteristic
251	C₂×SD₁₆	—	2	2	no	—
252	C₂×SD₁₆	—	2	2	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×SD₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
262	#127	—	2	2	no	—
263	#127	C₂³×C₆₁	1	2	yes	—
264	#125	—	2	2	no	—
265	#125	—	4	2	no	—
266	#121	—	2	2	no	—
267	#121	—	4	2	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
271	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
274	#107	—	2	1	no	—
275	#107	—	2	1	no	—
276	#107	D₄×C₆₁	1	1	yes	characteristic
277	#106	—	2	2	no	—
278	#106	D₄×C₆₁	1	1	yes	characteristic
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
282	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
283	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	D₄×C₆₁	1	1	yes	characteristic
287	#103	D₄×C₆₁	1	2	yes	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	4	2	no	—
291	#102	D₄×C₆₁	1	1	yes	characteristic
292	C₂²⋊C₈	—	2	1	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
298	#41	—	4	4	no	—
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
302	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	2	no	—
311	Q₁₆	SD₁₆×C₆₁	1	4	yes	complemented
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	4	4	no	—
314	SD₁₆	—	4	4	no	—
315	SD₁₆	—	8	2	no	—
316	SD₁₆	—	8	2	no	—
317	SD₁₆	—	8	2	no	—
318	D₈	—	4	2	no	—
319	D₈	—	8	1	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	4	2	no	—
325	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
337	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
338	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	4	2	no	—
344	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
345	C₂³	—	2	1	no	—
346	C₂³	—	4	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	2	1	no	—
349	Q₈	—	2	1	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	C₂×SD₁₆×C₆₁	1	4	yes	—
353	D₄	—	2	1	no	—
354	D₄	—	2	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	4	no	—
360	D₄	—	8	2	no	—
361	D₄	—	16	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	4	no	—
371	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
373	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	4	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	1	no	—
380	C₈	C₂×SD₁₆×C₆₁	1	2	yes	—
381	C₈	#135×C₆₁	1	2	yes	complemented
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	D₄²×C₆₁	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
397	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
398	C₄	C₆₁×#576	1	1	yes	characteristic
399	C₄	C₆₁×#577	1	1	yes	characteristic
400	C₂	—	8	1	no	—
401	C₂	—	16	2	no	—
402	C₂	D₄×SD₁₆×C₆₁	1	1	yes	characteristic
403	C₂	C₆₁×#3287	1	1	yes	characteristic
404	C₂	C₆₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3287	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3392	C₂	semidirect
2. C₆₁×#3383	C₂	semidirect
4. C₆₁×#1706	C₂	semidirect
5. C₆₁×#1673	C₂	semidirect
6. C₆₁×#1668	C₂	semidirect
7. C₆₁×#1666	C₂	semidirect
8. C₆₁×#1642	C₂	semidirect
9. C₆₁×#1626	C₂	semidirect
10. C₈×Q₁₆×C₆₁	C₂	semidirect
11. C₈×SD₁₆×C₆₁	C₂	semidirect
108. Q₁₆×C₆₁	SD₁₆	semidirect
178. C₈×C₆₁	#135	semidirect
179. #19985	C₆₁	direct (N × H)
198. #3392	C₂×C₆₁	semidirect
199. #3383	C₂×C₆₁	semidirect
201. #1706	C₂×C₆₁	semidirect
202. #1673	C₂×C₆₁	semidirect
203. #1668	C₂×C₆₁	semidirect
204. #1666	C₂×C₆₁	semidirect
205. #1642	C₂×C₆₁	semidirect
206. #1626	C₂×C₆₁	semidirect
207. C₈×Q₁₆	C₂×C₆₁	semidirect
208. C₈×SD₁₆	C₂×C₆₁	semidirect
247. C₆₁	#19985	direct (N × H)
311. Q₁₆	SD₁₆×C₆₁	semidirect
381. C₈	#135×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3392	2
C₆₁×#3383	2
C₆₁×#3287	2
C₆₁×#1706	2
C₆₁×#1673	2
C₆₁×#1668	2
C₆₁×#1666	2
C₆₁×#1642	2
C₆₁×#1626	2
C₈×Q₁₆×C₆₁	2
C₈×SD₁₆×C₆₁	2
#19985	61

Subgroups — C61×#19985 #29523418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19985 #29523418