Subgroups — C₆₁×#19994 #29523427

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3391	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3305	C₂	1	2	yes	maximal, complemented
4	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1677	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1631	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1624	C₂	1	2	yes	maximal, complemented
10	C₈×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#555	C₂²	1	2	yes	—
13	C₆₁×#550	C₂²	1	2	yes	—
14	C₆₁×#500	C₂²	1	1	yes	characteristic
15	C₆₁×#493	—	2	1	no	—
16	C₆₁×#493	C₂²	1	1	yes	characteristic
17	C₆₁×#492	C₂²	1	2	yes	—
18	C₆₁×#486	C₂²	1	2	yes	—
19	C₆₁×#482	—	2	2	no	—
20	C₆₁×#482	—	2	2	no	—
21	C₆₁×#477	C₂²	1	2	yes	—
22	C₆₁×#476	C₂²	1	2	yes	—
23	C₆₁×#466	—	2	1	no	—
24	C₆₁×#466	—	2	2	no	—
25	C₆₁×#459	—	2	2	no	—
26	C₆₁×#459	C₂²	1	2	yes	—
27	C₆₁×#459	C₂²	1	2	yes	—
28	C₆₁×#449	—	2	2	no	—
29	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₄×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₆₁	—	2	1	no	—
32	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₆₁	C₂²	1	2	yes	—
34	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#427	—	2	1	no	—
36	C₆₁×#416	—	2	2	no	—
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#334	C₂²	1	1	yes	characteristic
39	C₆₁×#333	C₂²	1	2	yes	—
40	C₆₁×#331	C₂²	1	2	yes	—
41	C₆₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×D₄⋊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	C₂×SD₁₆×C₆₁	—	4	2	no	—
47	C₂×SD₁₆×C₆₁	D₄	1	1	yes	characteristic
48	C₂×D₈×C₆₁	—	2	2	no	—
49	C₂×D₈×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	—	2	1	no	—
51	C₂×D₈×C₆₁	—	2	1	no	—
52	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	—	2	1	no	—
54	C₂²×C₈×C₆₁	—	2	2	no	—
55	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
56	#127×C₆₁	—	2	2	no	—
57	#127×C₆₁	C₂³	1	2	yes	—
58	#124×C₆₁	—	4	2	no	—
59	#121×C₆₁	—	2	2	no	—
60	#121×C₆₁	—	2	2	no	—
61	#121×C₆₁	—	2	2	no	—
62	#121×C₆₁	—	4	2	no	—
63	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₆₁	—	2	2	no	—
65	C₄×D₄×C₆₁	C₂³	1	2	yes	—
66	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
67	#117×C₆₁	—	2	2	no	—
68	#117×C₆₁	—	2	2	no	—
69	#107×C₆₁	—	2	1	no	—
70	#107×C₆₁	—	2	1	no	—
71	#107×C₆₁	—	2	2	no	—
72	#107×C₆₁	D₄	1	1	yes	characteristic
73	#106×C₆₁	—	2	2	no	—
74	#106×C₆₁	D₄	1	1	yes	characteristic
75	C₄⋊C₈×C₆₁	—	2	1	no	—
76	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
77	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
79	#103×C₆₁	—	2	2	no	—
80	#103×C₆₁	D₄	1	1	yes	characteristic
81	#102×C₆₁	—	2	2	no	—
82	#102×C₆₁	—	2	2	no	—
83	#102×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	2	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	D₄	1	2	yes	—
87	#102×C₆₁	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₆₁	—	2	2	no	—
89	C₂²⋊C₈×C₆₁	—	2	1	no	—
90	C₄×C₈×C₆₁	—	2	1	no	—
91	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	#41×C₆₁	—	4	4	no	—
95	#41×C₆₁	—	8	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	—	4	2	no	—
102	C₂×D₄×C₆₁	—	4	2	no	—
103	C₂×D₄×C₆₁	—	4	2	no	—
104	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
105	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	4	2	no	—
109	SD₁₆×C₆₁	—	2	2	no	—
110	SD₁₆×C₆₁	—	8	4	no	—
111	D₈×C₆₁	—	2	2	no	—
112	D₈×C₆₁	—	4	2	no	—
113	D₈×C₆₁	—	8	1	no	—
114	D₈×C₆₁	—	8	2	no	—
115	D₈×C₆₁	—	8	2	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	2	no	—
120	C₂×C₈×C₆₁	—	4	2	no	—
121	C₂×C₈×C₆₁	—	8	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	1	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₆₁	—	2	2	no	—
133	C₂²⋊C₄×C₆₁	—	2	1	no	—
134	C₂²⋊C₄×C₆₁	—	4	2	no	—
135	C₂²⋊C₄×C₆₁	—	4	2	no	—
136	C₂²⋊C₄×C₆₁	—	4	2	no	—
137	C₄²×C₆₁	—	2	1	no	—
138	C₄²×C₆₁	—	4	2	no	—
139	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
140	C₂³×C₆₁	—	2	1	no	—
141	C₂³×C₆₁	—	2	2	no	—
142	C₂³×C₆₁	—	4	2	no	—
143	Q₈×C₆₁	—	2	1	no	—
144	Q₈×C₆₁	—	8	2	no	—
145	Q₈×C₆₁	#135	1	2	yes	—
146	D₄×C₆₁	—	2	2	no	—
147	D₄×C₆₁	—	2	1	no	—
148	D₄×C₆₁	—	2	1	no	—
149	D₄×C₆₁	—	2	2	no	—
150	D₄×C₆₁	—	4	2	no	—
151	D₄×C₆₁	—	4	2	no	—
152	D₄×C₆₁	—	4	2	no	—
153	D₄×C₆₁	—	4	2	no	—
154	D₄×C₆₁	—	8	4	no	—
155	D₄×C₆₁	—	8	2	no	—
156	D₄×C₆₁	—	16	2	no	—
157	D₄×C₆₁	—	16	2	no	—
158	C₂×C₄×C₆₁	—	2	1	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	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	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	2	no	—
172	C₈×C₆₁	—	2	1	no	—
173	C₈×C₆₁	—	2	1	no	—
174	C₈×C₆₁	—	2	1	no	—
175	C₈×C₆₁	—	4	1	no	—
176	C₈×C₆₁	—	4	2	no	—
177	C₈×C₆₁	—	4	1	no	—
178	C₈×C₆₁	#135	1	2	yes	—
179	#19994	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₆₁	—	4	2	no	—
181	C₂²×C₆₁	—	4	1	no	—
182	C₂²×C₆₁	—	4	1	no	—
183	C₂²×C₆₁	—	4	2	no	—
184	C₂²×C₆₁	—	4	2	no	—
185	C₂²×C₆₁	—	4	1	no	—
186	C₂²×C₆₁	—	8	2	no	—
187	C₂²×C₆₁	—	8	2	no	—
188	C₂²×C₆₁	—	8	2	no	—
189	C₂²×C₆₁	D₄²	1	1	yes	characteristic
190	C₄×C₆₁	—	2	2	no	—
191	C₄×C₆₁	—	2	1	no	—
192	C₄×C₆₁	—	4	2	no	—
193	C₄×C₆₁	—	4	1	no	—
194	C₄×C₆₁	—	4	1	no	—
195	C₄×C₆₁	—	8	2	no	—
196	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
197	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
198	C₄×C₆₁	#576	1	1	yes	characteristic
199	C₄×C₆₁	#577	1	1	yes	characteristic
200	#3391	C₂×C₆₁	1	1	yes	characteristic, complemented
201	#3341	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#3305	C₂×C₆₁	1	2	yes	complemented
203	#1706	C₂×C₆₁	1	1	yes	characteristic, complemented
204	#1677	C₂×C₆₁	1	2	yes	complemented
205	#1676	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#1667	C₂×C₆₁	1	1	yes	characteristic, complemented
207	#1631	C₂×C₆₁	1	2	yes	complemented
208	#1624	C₂×C₆₁	1	2	yes	complemented
209	C₈×SD₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
210	C₈×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
211	C₂×C₆₁	—	8	2	no	—
212	C₂×C₆₁	—	8	1	no	—
213	C₂×C₆₁	—	16	2	no	—
214	C₂×C₆₁	#3280	1	1	yes	characteristic
215	C₂×C₆₁	#3284	1	1	yes	characteristic
216	C₂×C₆₁	#3292	1	1	yes	characteristic
217	#555	C₂²×C₆₁	1	2	yes	—
218	#550	C₂²×C₆₁	1	2	yes	—
219	#500	C₂²×C₆₁	1	1	yes	characteristic
220	#493	—	2	1	no	—
221	#493	C₂²×C₆₁	1	1	yes	characteristic
222	#492	C₂²×C₆₁	1	2	yes	—
223	#486	C₂²×C₆₁	1	2	yes	—
224	#482	—	2	2	no	—
225	#482	—	2	2	no	—
226	#477	C₂²×C₆₁	1	2	yes	—
227	#476	C₂²×C₆₁	1	2	yes	—
228	#466	—	2	1	no	—
229	#466	—	2	2	no	—
230	#459	—	2	2	no	—
231	#459	C₂²×C₆₁	1	2	yes	—
232	#459	C₂²×C₆₁	1	2	yes	—
233	#449	—	2	2	no	—
234	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
235	C₄×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
236	C₄×D₈	—	2	1	no	—
237	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
238	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
239	C₈×D₄	C₂²×C₆₁	1	2	yes	—
240	#427	—	2	1	no	—
241	#416	—	2	2	no	—
242	#335	C₂²×C₆₁	1	1	yes	characteristic
243	#334	C₂²×C₆₁	1	1	yes	characteristic
244	#333	C₂²×C₆₁	1	2	yes	—
245	#331	C₂²×C₆₁	1	2	yes	—
246	Q₈⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
247	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
248	D₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
249	C₈²	C₂²×C₆₁	1	1	yes	characteristic
250	C₆₁	#19994	1	1	yes	characteristic, direct product factor, Sylow
251	C₂×#41	—	2	2	no	—
252	C₂×SD₁₆	—	4	2	no	—
253	C₂×SD₁₆	D₄×C₆₁	1	1	yes	characteristic
254	C₂×D₈	—	2	2	no	—
255	C₂×D₈	—	2	2	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
262	#127	—	2	2	no	—
263	#127	C₂³×C₆₁	1	2	yes	—
264	#124	—	4	2	no	—
265	#121	—	2	2	no	—
266	#121	—	2	2	no	—
267	#121	—	2	2	no	—
268	#121	—	4	2	no	—
269	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
270	C₄×D₄	—	2	2	no	—
271	C₄×D₄	C₂³×C₆₁	1	2	yes	—
272	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
273	#117	—	2	2	no	—
274	#117	—	2	2	no	—
275	#107	—	2	1	no	—
276	#107	—	2	1	no	—
277	#107	—	2	2	no	—
278	#107	D₄×C₆₁	1	1	yes	characteristic
279	#106	—	2	2	no	—
280	#106	D₄×C₆₁	1	1	yes	characteristic
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
283	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
285	#103	—	2	2	no	—
286	#103	D₄×C₆₁	1	1	yes	characteristic
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	—	2	2	no	—
291	#102	—	2	2	no	—
292	#102	D₄×C₆₁	1	2	yes	—
293	#102	D₄×C₆₁	1	1	yes	characteristic
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
299	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
300	#41	—	4	4	no	—
301	#41	—	8	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
311	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	SD₁₆	—	2	2	no	—
316	SD₁₆	—	8	4	no	—
317	D₈	—	2	2	no	—
318	D₈	—	4	2	no	—
319	D₈	—	8	1	no	—
320	D₈	—	8	2	no	—
321	D₈	—	8	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	8	2	no	—
328	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
329	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
330	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
331	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
336	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
337	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	4	2	no	—
345	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
346	C₂³	—	2	1	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	4	2	no	—
349	Q₈	—	2	1	no	—
350	Q₈	—	8	2	no	—
351	Q₈	#135×C₆₁	1	2	yes	—
352	D₄	—	2	2	no	—
353	D₄	—	2	1	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	4	no	—
361	D₄	—	8	2	no	—
362	D₄	—	16	2	no	—
363	D₄	—	16	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	4	no	—
374	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
376	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₈	—	4	1	no	—
384	C₈	#135×C₆₁	1	2	yes	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	D₄²×C₆₁	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	—	4	1	no	—
400	C₄	—	8	2	no	—
401	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
402	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
403	C₄	C₆₁×#576	1	1	yes	characteristic
404	C₄	C₆₁×#577	1	1	yes	characteristic
405	C₂	—	8	2	no	—
406	C₂	—	8	1	no	—
407	C₂	—	16	2	no	—
408	C₂	C₆₁×#3280	1	1	yes	characteristic
409	C₂	C₆₁×#3284	1	1	yes	characteristic
410	C₂	C₆₁×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
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×#3391	C₂	semidirect
2. C₆₁×#3341	C₂	semidirect
3. C₆₁×#3305	C₂	semidirect
4. C₆₁×#1706	C₂	semidirect
5. C₆₁×#1677	C₂	semidirect
6. C₆₁×#1676	C₂	semidirect
7. C₆₁×#1667	C₂	semidirect
8. C₆₁×#1631	C₂	semidirect
9. C₆₁×#1624	C₂	semidirect
10. C₈×SD₁₆×C₆₁	C₂	semidirect
11. C₈×D₈×C₆₁	C₂	semidirect
179. #19994	C₆₁	direct (N × H)
200. #3391	C₂×C₆₁	semidirect
201. #3341	C₂×C₆₁	semidirect
202. #3305	C₂×C₆₁	semidirect
203. #1706	C₂×C₆₁	semidirect
204. #1677	C₂×C₆₁	semidirect
205. #1676	C₂×C₆₁	semidirect
206. #1667	C₂×C₆₁	semidirect
207. #1631	C₂×C₆₁	semidirect
208. #1624	C₂×C₆₁	semidirect
209. C₈×SD₁₆	C₂×C₆₁	semidirect
210. C₈×D₈	C₂×C₆₁	semidirect
250. C₆₁	#19994	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3391	2
C₆₁×#3341	2
C₆₁×#3305	2
C₆₁×#1706	2
C₆₁×#1677	2
C₆₁×#1676	2
C₆₁×#1667	2
C₆₁×#1631	2
C₆₁×#1624	2
C₈×SD₁₆×C₆₁	2
C₈×D₈×C₆₁	2
#19994	61

Subgroups — C61×#19994 #29523427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19994 #29523427