Subgroups — C₆₁×#61378 #29564811

Order 15616.

1810 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3501	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3389	C₂	1	8	yes	maximal, complemented
3	C₆₁×#3384	C₂	1	8	yes	maximal, complemented
4	C₆₁×#3163	C₂	1	2	yes	maximal, complemented
5	C₆₁×#3162	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3081	C₂	1	4	yes	maximal, complemented
7	C₆₁×#3077	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#2948	C₂	1	2	yes	maximal
10	C₂×C₆₁×#442	C₂	1	1	yes	maximal, characteristic
11	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₆₁×#554	—	2	2	no	—
13	C₆₁×#554	—	2	4	no	—
14	C₆₁×#554	C₂²	1	8	yes	complemented
15	C₆₁×#554	C₂²	1	4	yes	complemented
16	D₄×Q₈×C₆₁	—	2	2	no	—
17	D₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
18	C₆₁×#544	C₂²	1	4	yes	—
19	C₆₁×#543	—	2	4	no	—
20	C₆₁×#533	C₂²	1	2	yes	—
21	C₆₁×#533	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₆₁	—	2	4	no	—
23	C₆₁×#518	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#501	C₂²	1	4	yes	complemented
26	C₆₁×#501	C₂²	1	8	yes	complemented
27	C₆₁×#501	C₂²	1	4	yes	complemented
28	C₆₁×#499	C₂²	1	4	yes	complemented
29	C₆₁×#498	C₂²	1	4	yes	complemented
30	C₆₁×#478	C₂²	1	8	yes	complemented
31	C₆₁×#478	C₂²	1	8	yes	complemented
32	C₆₁×#478	C₂²	1	8	yes	complemented
33	C₆₁×#476	C₂²	1	4	yes	complemented
34	C₆₁×#476	C₂²	1	8	yes	complemented
35	C₆₁×#474	C₂²	1	4	yes	complemented
36	C₆₁×#474	C₂²	1	8	yes	complemented
37	C₆₁×#446	C₂²	1	8	yes	complemented
38	C₆₁×#442	C₂²	1	4	yes	—
39	C₆₁×#442	C₂²	1	8	yes	—
40	C₆₁×#442	C₂²	1	4	yes	—
41	C₄×D₈×C₆₁	C₂²	1	8	yes	—
42	C₆₁×#428	C₂²	1	4	yes	—
43	C₆₁×#427	C₂²	1	2	yes	—
44	C₆₁×#427	C₂²	1	2	yes	—
45	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
46	C₆₁×#424	C₂²	1	2	yes	—
47	C₆₁×#423	C₂²	1	1	yes	characteristic
48	C₆₁×#418	C₂²	1	4	yes	—
49	C₂×#102×C₆₁	C₂²	1	2	yes	—
50	C₆₁×#405	C₂²	1	2	yes	—
51	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₆₁	—	2	4	no	—
53	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₆₁	—	2	2	no	—
55	C₂×D₈×C₆₁	Q₈	1	8	yes	complemented
56	C₂×D₈×C₆₁	C₂³	1	4	yes	—
57	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
60	C₄⋊Q₈×C₆₁	—	2	4	no	—
61	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
62	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
65	#125×C₆₁	—	2	4	no	—
66	#125×C₆₁	D₄	1	2	yes	—
67	#125×C₆₁	C₂³	1	4	yes	—
68	#125×C₆₁	C₂³	1	8	yes	—
69	C₂²⋊Q₈×C₆₁	—	2	8	no	—
70	C₂²⋊Q₈×C₆₁	—	2	4	no	—
71	C₂²⋊Q₈×C₆₁	—	2	2	no	—
72	C₂²⋊Q₈×C₆₁	—	2	2	no	—
73	C₂²⋊Q₈×C₆₁	—	2	8	no	—
74	C₂²⋊Q₈×C₆₁	—	2	8	no	—
75	C₂²⋊Q₈×C₆₁	—	2	8	no	—
76	C₂²⋊Q₈×C₆₁	—	2	4	no	—
77	C₂²⋊Q₈×C₆₁	—	2	8	no	—
78	C₂²⋊Q₈×C₆₁	—	2	8	no	—
79	C₂²⋊Q₈×C₆₁	D₄	1	4	yes	—
80	C₄×Q₈×C₆₁	—	2	2	no	—
81	C₄×Q₈×C₆₁	—	2	2	no	—
82	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
83	C₄×D₄×C₆₁	—	2	4	no	—
84	C₄×D₄×C₆₁	—	2	4	no	—
85	C₄×D₄×C₆₁	—	2	2	no	—
86	C₄×D₄×C₆₁	—	2	2	no	—
87	C₄×D₄×C₆₁	C₂³	1	8	yes	—
88	C₄×D₄×C₆₁	C₂³	1	4	yes	—
89	C₄×D₄×C₆₁	C₂³	1	8	yes	—
90	C₄×D₄×C₆₁	C₂³	1	4	yes	—
91	#117×C₆₁	C₂³	1	4	yes	—
92	#117×C₆₁	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
94	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
96	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
98	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
99	#107×C₆₁	C₂³	1	4	yes	—
100	#107×C₆₁	C₂³	1	4	yes	—
101	#107×C₆₁	C₂³	1	8	yes	—
102	#106×C₆₁	C₂³	1	4	yes	—
103	#106×C₆₁	C₂³	1	2	yes	—
104	#106×C₆₁	C₂³	1	2	yes	—
105	#106×C₆₁	C₂³	1	2	yes	—
106	#106×C₆₁	C₂³	1	2	yes	—
107	#106×C₆₁	C₂³	1	8	yes	—
108	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
109	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
110	#102×C₆₁	C₂³	1	8	yes	—
111	#102×C₆₁	C₂³	1	8	yes	—
112	#102×C₆₁	C₂³	1	8	yes	—
113	#97×C₆₁	C₂³	1	4	yes	—
114	#97×C₆₁	C₂³	1	4	yes	—
115	C₄×C₈×C₆₁	C₂³	1	4	yes	—
116	C₂⁴×C₆₁	—	2	2	no	—
117	C₂×Q₈×C₆₁	—	2	2	no	—
118	C₂×Q₈×C₆₁	—	2	2	no	—
119	C₂×Q₈×C₆₁	—	2	8	no	—
120	C₂×Q₈×C₆₁	—	8	8	no	—
121	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
122	C₂×D₄×C₆₁	—	2	2	no	—
123	C₂×D₄×C₆₁	—	2	4	no	—
124	C₂×D₄×C₆₁	C₂×Q₈	1	8	yes	complemented
125	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₆₁	—	2	2	no	—
127	C₂²×C₄×C₆₁	—	2	4	no	—
128	C₂²×C₄×C₆₁	—	2	8	no	—
129	C₂²×C₄×C₆₁	—	2	8	no	—
130	C₂²×C₄×C₆₁	—	2	4	no	—
131	C₂²×C₄×C₆₁	—	8	4	no	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
134	D₈×C₆₁	C₂×Q₈	1	16	yes	complemented
135	M₁₆×C₆₁	—	2	4	no	—
136	C₂×C₈×C₆₁	—	2	2	no	—
137	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	complemented
138	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
139	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
140	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
141	C₄⋊C₄×C₆₁	—	2	4	no	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	8	no	—
144	C₄⋊C₄×C₆₁	—	2	8	no	—
145	C₄⋊C₄×C₆₁	—	2	8	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₄⋊C₄×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
150	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
153	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
154	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
155	C₂²⋊C₄×C₆₁	—	2	4	no	—
156	C₂²⋊C₄×C₆₁	—	2	8	no	—
157	C₂²⋊C₄×C₆₁	—	2	8	no	—
158	C₂²⋊C₄×C₆₁	—	2	4	no	—
159	C₂²⋊C₄×C₆₁	—	2	4	no	—
160	C₂²⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
161	C₄²×C₆₁	—	2	4	no	—
162	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₆₁	C₂⁴	1	4	yes	—
165	C₄²×C₆₁	C₂⁴	1	2	yes	—
166	C₂³×C₆₁	—	2	4	no	—
167	C₂³×C₆₁	—	2	8	no	—
168	C₂³×C₆₁	—	8	2	no	—
169	C₂³×C₆₁	—	8	2	no	—
170	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₆₁	—	4	4	no	—
172	Q₈×C₆₁	—	4	4	no	—
173	Q₈×C₆₁	—	8	2	no	—
174	Q₈×C₆₁	—	8	8	no	—
175	D₄×C₆₁	—	2	8	no	—
176	D₄×C₆₁	—	2	4	no	—
177	D₄×C₆₁	C₂²×Q₈	1	8	yes	—
178	C₂×C₄×C₆₁	—	2	4	no	—
179	C₂×C₄×C₆₁	—	2	4	no	—
180	C₂×C₄×C₆₁	—	2	4	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	8	no	—
183	C₂×C₄×C₆₁	—	8	8	no	—
184	C₂×C₄×C₆₁	—	8	4	no	—
185	C₂×C₄×C₆₁	—	8	8	no	—
186	C₂×C₄×C₆₁	—	8	2	no	—
187	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₆₁	C₂²×D₄	1	8	yes	—
190	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
192	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
193	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
194	C₈×C₆₁	—	2	2	no	—
195	C₈×C₆₁	—	2	4	no	—
196	C₈×C₆₁	C₂²×Q₈	1	4	yes	—
197	#61378	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₆₁	—	2	2	no	—
199	C₂²×C₆₁	—	2	8	no	—
200	C₂²×C₆₁	—	4	4	no	—
201	C₂²×C₆₁	—	4	4	no	—
202	C₂²×C₆₁	—	8	8	no	—
203	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
204	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
205	C₄×C₆₁	—	2	2	no	—
206	C₄×C₆₁	—	2	2	no	—
207	C₄×C₆₁	—	2	8	no	—
208	C₄×C₆₁	—	4	4	no	—
209	C₄×C₆₁	—	4	4	no	—
210	C₄×C₆₁	—	4	4	no	—
211	C₄×C₆₁	D₄×Q₈	1	2	yes	—
212	C₄×C₆₁	C₂³×Q₈	1	1	yes	characteristic
213	C₄×C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
214	#3501	C₂×C₆₁	1	2	yes	complemented
215	#3389	C₂×C₆₁	1	8	yes	complemented
216	#3384	C₂×C₆₁	1	8	yes	complemented
217	#3163	C₂×C₆₁	1	2	yes	complemented
218	#3162	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#3081	C₂×C₆₁	1	4	yes	complemented
220	#3077	C₂×C₆₁	1	2	yes	complemented
221	#2961	C₂×C₆₁	1	1	yes	characteristic, complemented
222	#2948	C₂×C₆₁	1	2	yes	—
223	C₂×#442	C₂×C₆₁	1	1	yes	characteristic
224	C₂×C₆₁	—	2	2	no	—
225	C₂×C₆₁	—	4	8	no	—
226	C₂×C₆₁	C₂×D₄×Q₈	1	1	yes	characteristic
227	C₂×C₆₁	#3585	1	2	yes	—
228	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
229	#554	—	2	2	no	—
230	#554	—	2	4	no	—
231	#554	C₂²×C₆₁	1	8	yes	complemented
232	#554	C₂²×C₆₁	1	4	yes	complemented
233	D₄×Q₈	—	2	2	no	—
234	D₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
235	#544	C₂²×C₆₁	1	4	yes	—
236	#543	—	2	4	no	—
237	#533	C₂²×C₆₁	1	2	yes	—
238	#533	C₂²×C₆₁	1	1	yes	characteristic
239	C₂×C₂²⋊Q₈	—	2	4	no	—
240	#518	C₂²×C₆₁	1	4	yes	—
241	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
242	#501	C₂²×C₆₁	1	4	yes	complemented
243	#501	C₂²×C₆₁	1	8	yes	complemented
244	#501	C₂²×C₆₁	1	4	yes	complemented
245	#499	C₂²×C₆₁	1	4	yes	complemented
246	#498	C₂²×C₆₁	1	4	yes	complemented
247	#478	C₂²×C₆₁	1	8	yes	complemented
248	#478	C₂²×C₆₁	1	8	yes	complemented
249	#478	C₂²×C₆₁	1	8	yes	complemented
250	#476	C₂²×C₆₁	1	4	yes	complemented
251	#476	C₂²×C₆₁	1	8	yes	complemented
252	#474	C₂²×C₆₁	1	4	yes	complemented
253	#474	C₂²×C₆₁	1	8	yes	complemented
254	#446	C₂²×C₆₁	1	8	yes	complemented
255	#442	C₂²×C₆₁	1	4	yes	—
256	#442	C₂²×C₆₁	1	8	yes	—
257	#442	C₂²×C₆₁	1	4	yes	—
258	C₄×D₈	C₂²×C₆₁	1	8	yes	—
259	#428	C₂²×C₆₁	1	4	yes	—
260	#427	C₂²×C₆₁	1	2	yes	—
261	#427	C₂²×C₆₁	1	2	yes	—
262	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
263	#424	C₂²×C₆₁	1	2	yes	—
264	#423	C₂²×C₆₁	1	1	yes	characteristic
265	#418	C₂²×C₆₁	1	4	yes	—
266	C₂×#102	C₂²×C₆₁	1	2	yes	—
267	#405	C₂²×C₆₁	1	2	yes	—
268	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
269	C₆₁	#61378	1	1	yes	characteristic, direct product factor, Sylow
270	C₂²×Q₈	—	2	4	no	—
271	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
272	C₂³×C₄	—	2	2	no	—
273	C₂×D₈	Q₈×C₆₁	1	8	yes	complemented
274	C₂×D₈	C₂³×C₆₁	1	4	yes	—
275	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
276	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
278	C₄⋊Q₈	—	2	4	no	—
279	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
280	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
281	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
282	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
283	#125	—	2	4	no	—
284	#125	D₄×C₆₁	1	2	yes	—
285	#125	C₂³×C₆₁	1	4	yes	—
286	#125	C₂³×C₆₁	1	8	yes	—
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	—	2	8	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	2	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₂²⋊Q₈	—	2	8	no	—
295	C₂²⋊Q₈	—	2	8	no	—
296	C₂²⋊Q₈	—	2	8	no	—
297	C₂²⋊Q₈	D₄×C₆₁	1	4	yes	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
301	C₄×D₄	—	2	4	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	C₂³×C₆₁	1	4	yes	—
306	C₄×D₄	C₂³×C₆₁	1	4	yes	—
307	C₄×D₄	C₂³×C₆₁	1	8	yes	—
308	C₄×D₄	C₂³×C₆₁	1	8	yes	—
309	#117	C₂³×C₆₁	1	4	yes	—
310	#117	C₂³×C₆₁	1	2	yes	—
311	C₂×C₄⋊C₄	—	2	8	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	8	no	—
316	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
317	#107	C₂³×C₆₁	1	4	yes	—
318	#107	C₂³×C₆₁	1	4	yes	—
319	#107	C₂³×C₆₁	1	8	yes	—
320	#106	C₂³×C₆₁	1	4	yes	—
321	#106	C₂³×C₆₁	1	2	yes	—
322	#106	C₂³×C₆₁	1	2	yes	—
323	#106	C₂³×C₆₁	1	2	yes	—
324	#106	C₂³×C₆₁	1	2	yes	—
325	#106	C₂³×C₆₁	1	8	yes	—
326	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
327	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
328	#102	C₂³×C₆₁	1	8	yes	—
329	#102	C₂³×C₆₁	1	8	yes	—
330	#102	C₂³×C₆₁	1	8	yes	—
331	#97	C₂³×C₆₁	1	4	yes	—
332	#97	C₂³×C₆₁	1	4	yes	—
333	C₄×C₈	C₂³×C₆₁	1	4	yes	—
334	C₂⁴	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	8	8	no	—
339	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	C₂×Q₈×C₆₁	1	8	yes	complemented
343	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	8	4	no	—
350	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
352	D₈	C₂×Q₈×C₆₁	1	16	yes	complemented
353	M₁₆	—	2	4	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	complemented
356	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
357	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
358	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
368	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
369	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
370	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
371	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
372	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	8	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
379	C₄²	—	2	4	no	—
380	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
381	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
382	C₄²	C₂⁴×C₆₁	1	4	yes	—
383	C₄²	C₂⁴×C₆₁	1	2	yes	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	8	no	—
386	C₂³	—	8	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
389	Q₈	—	4	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	—	8	2	no	—
392	Q₈	—	8	8	no	—
393	D₄	—	2	8	no	—
394	D₄	—	2	4	no	—
395	D₄	C₂²×Q₈×C₆₁	1	8	yes	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	8	no	—
401	C₂×C₄	—	8	8	no	—
402	C₂×C₄	—	8	4	no	—
403	C₂×C₄	—	8	8	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
406	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₆₁	1	8	yes	—
408	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
410	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
411	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	4	no	—
414	C₈	C₂²×Q₈×C₆₁	1	4	yes	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	8	no	—
420	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
421	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	2	8	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	D₄×Q₈×C₆₁	1	2	yes	—
429	C₄	C₂³×Q₈×C₆₁	1	1	yes	characteristic
430	C₄	C₂×2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
431	C₂	—	2	2	no	—
432	C₂	—	4	8	no	—
433	C₂	C₂×D₄×Q₈×C₆₁	1	1	yes	characteristic
434	C₂	C₆₁×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₆₁×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3501	C₂	semidirect
2. C₆₁×#3389	C₂	semidirect
3. C₆₁×#3384	C₂	semidirect
4. C₆₁×#3163	C₂	semidirect
5. C₆₁×#3162	C₂	semidirect
6. C₆₁×#3081	C₂	semidirect
7. C₆₁×#3077	C₂	semidirect
8. C₆₁×#2961	C₂	semidirect
14. C₆₁×#554	C₂²	semidirect
15. C₆₁×#554	C₂²	semidirect
17. D₄×Q₈×C₆₁	C₂²	semidirect
25. C₆₁×#501	C₂²	semidirect
26. C₆₁×#501	C₂²	semidirect
27. C₆₁×#501	C₂²	semidirect
28. C₆₁×#499	C₂²	semidirect
29. C₆₁×#498	C₂²	semidirect
30. C₆₁×#478	C₂²	semidirect
31. C₆₁×#478	C₂²	semidirect
32. C₆₁×#478	C₂²	semidirect
33. C₆₁×#476	C₂²	semidirect
34. C₆₁×#476	C₂²	semidirect
35. C₆₁×#474	C₂²	semidirect
36. C₆₁×#474	C₂²	semidirect
37. C₆₁×#446	C₂²	semidirect
55. C₂×D₈×C₆₁	Q₈	semidirect
124. C₂×D₄×C₆₁	C₂×Q₈	semidirect
134. D₈×C₆₁	C₂×Q₈	semidirect
137. C₂×C₈×C₆₁	C₂×Q₈	semidirect
197. #61378	C₆₁	direct (N × H)
214. #3501	C₂×C₆₁	semidirect
215. #3389	C₂×C₆₁	semidirect
216. #3384	C₂×C₆₁	semidirect
217. #3163	C₂×C₆₁	semidirect
218. #3162	C₂×C₆₁	semidirect
219. #3081	C₂×C₆₁	semidirect
220. #3077	C₂×C₆₁	semidirect
221. #2961	C₂×C₆₁	semidirect
231. #554	C₂²×C₆₁	semidirect
232. #554	C₂²×C₆₁	semidirect
234. D₄×Q₈	C₂²×C₆₁	semidirect
242. #501	C₂²×C₆₁	semidirect
243. #501	C₂²×C₆₁	semidirect
244. #501	C₂²×C₆₁	semidirect
245. #499	C₂²×C₆₁	semidirect
246. #498	C₂²×C₆₁	semidirect
247. #478	C₂²×C₆₁	semidirect
248. #478	C₂²×C₆₁	semidirect
249. #478	C₂²×C₆₁	semidirect
250. #476	C₂²×C₆₁	semidirect
251. #476	C₂²×C₆₁	semidirect
252. #474	C₂²×C₆₁	semidirect
253. #474	C₂²×C₆₁	semidirect
254. #446	C₂²×C₆₁	semidirect
269. C₆₁	#61378	direct (N × H)
273. C₂×D₈	Q₈×C₆₁	semidirect
342. C₂×D₄	C₂×Q₈×C₆₁	semidirect
352. D₈	C₂×Q₈×C₆₁	semidirect
355. C₂×C₈	C₂×Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3501	2
C₆₁×#3389	2
C₆₁×#3384	2
C₆₁×#3163	2
C₆₁×#3162	2
C₆₁×#3081	2
C₆₁×#3077	2
C₆₁×#2961	2
C₆₁×#2948	2
C₂×C₆₁×#442	2
#61378	61

Subgroups — C61×#61378 #29564811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#61378 #29564811