Subgroups — C₆₁×#24299 #29527732

Order 15616.

1378 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#476	C₂	1	2	yes	maximal, complemented
3	C₄×#121×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2058	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2023	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1987	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1874	C₂	1	2	yes	maximal
8	C₆₁×#1853	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₆₁	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₆₁	—	2	8	no	—
12	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₆₁	—	2	1	no	—
18	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
21	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#476	—	2	8	no	—
23	C₂×#106×C₆₁	C₂²	1	4	yes	—
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
27	C₆₁×#390	C₂²	1	1	yes	characteristic
28	C₆₁×#389	C₂²	1	1	yes	characteristic
29	C₆₁×#388	—	2	1	no	—
30	C₆₁×#386	—	2	1	no	—
31	C₆₁×#380	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
34	C₆₁×#340	C₂²	1	4	yes	—
35	C₆₁×#340	C₂²	1	4	yes	—
36	C₆₁×#336	C₂²	1	2	yes	—
37	C₂²×Q₈×C₆₁	—	2	8	no	—
38	C₂²×Q₈×C₆₁	—	2	2	no	—
39	C₂²×Q₈×C₆₁	—	2	2	no	—
40	C₂²×Q₈×C₆₁	—	4	4	no	—
41	C₂²×Q₈×C₆₁	—	4	4	no	—
42	C₂²×D₄×C₆₁	—	2	1	no	—
43	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	—	2	2	no	—
45	C₂³×C₄×C₆₁	—	2	1	no	—
46	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
50	C₄⋊Q₈×C₆₁	—	2	8	no	—
51	C₄⋊Q₈×C₆₁	—	2	8	no	—
52	C₄⋊Q₈×C₆₁	—	2	8	no	—
53	C₄⋊Q₈×C₆₁	—	2	4	no	—
54	C₄⋊Q₈×C₆₁	D₄	1	8	yes	complemented
55	#121×C₆₁	—	2	2	no	—
56	#121×C₆₁	Q₈	1	4	yes	complemented
57	C₄×D₄×C₆₁	—	2	4	no	—
58	C₄×D₄×C₆₁	—	4	4	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	—	2	4	no	—
75	C₂×C₄²×C₆₁	—	2	1	no	—
76	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	#106×C₆₁	—	2	8	no	—
81	C₄⋊C₈×C₆₁	—	2	4	no	—
82	#102×C₆₁	—	2	8	no	—
83	C₂²⋊C₈×C₆₁	—	2	4	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	1	no	—
86	#95×C₆₁	—	2	1	no	—
87	C₂⁴×C₆₁	—	2	1	no	—
88	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂×Q₈×C₆₁	—	2	8	no	—
90	C₂×Q₈×C₆₁	—	2	8	no	—
91	C₂×Q₈×C₆₁	—	4	32	no	—
92	C₂×Q₈×C₆₁	—	4	4	no	—
93	C₂×Q₈×C₆₁	—	4	4	no	—
94	C₂×Q₈×C₆₁	—	4	4	no	—
95	C₂×Q₈×C₆₁	—	4	4	no	—
96	C₂×D₄×C₆₁	—	2	4	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	2	1	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	4	2	no	—
101	C₂×D₄×C₆₁	—	4	2	no	—
102	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	complemented
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	2	2	no	—
110	C₂²×C₄×C₆₁	—	2	8	no	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	4	no	—
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	1	no	—
115	C₂²×C₄×C₆₁	—	4	4	no	—
116	C₂²×C₄×C₆₁	—	4	4	no	—
117	C₂²×C₄×C₆₁	—	4	2	no	—
118	C₂²×C₄×C₆₁	—	4	2	no	—
119	C₂²×C₄×C₆₁	—	4	2	no	—
120	C₂²×C₄×C₆₁	SD₁₆	1	4	yes	—
121	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₆₁	#41	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₆₁	—	2	4	no	—
130	C₂×C₈×C₆₁	—	2	4	no	—
131	C₂×C₈×C₆₁	—	2	4	no	—
132	C₄⋊C₄×C₆₁	—	2	8	no	—
133	C₄⋊C₄×C₆₁	—	2	8	no	—
134	C₄⋊C₄×C₆₁	—	2	8	no	—
135	C₄⋊C₄×C₆₁	—	2	4	no	—
136	C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	4	2	no	—
140	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
141	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	complemented
142	C₂²⋊C₄×C₆₁	—	2	4	no	—
143	C₂²⋊C₄×C₆₁	—	4	2	no	—
144	C₂²⋊C₄×C₆₁	—	4	2	no	—
145	C₂²⋊C₄×C₆₁	—	4	2	no	—
146	C₂²⋊C₄×C₆₁	—	4	2	no	—
147	C₄²×C₆₁	—	2	2	no	—
148	C₄²×C₆₁	—	2	2	no	—
149	C₄²×C₆₁	—	2	2	no	—
150	C₄²×C₆₁	—	4	2	no	—
151	C₄²×C₆₁	C₂×D₄	1	4	yes	—
152	C₂³×C₆₁	—	2	1	no	—
153	C₂³×C₆₁	—	2	1	no	—
154	C₂³×C₆₁	—	2	1	no	—
155	C₂³×C₆₁	—	2	1	no	—
156	C₂³×C₆₁	—	2	2	no	—
157	C₂³×C₆₁	—	4	1	no	—
158	C₂³×C₆₁	—	4	1	no	—
159	C₂³×C₆₁	—	4	1	no	—
160	C₂³×C₆₁	—	4	1	no	—
161	C₂³×C₆₁	—	4	1	no	—
162	C₂³×C₆₁	—	4	1	no	—
163	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
164	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
165	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
166	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₆₁	—	4	16	no	—
168	Q₈×C₆₁	—	4	16	no	—
169	D₄×C₆₁	—	2	4	no	—
170	D₄×C₆₁	—	4	8	no	—
171	D₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	2	8	no	—
173	C₂×C₄×C₆₁	—	2	1	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	1	no	—
176	C₂×C₄×C₆₁	—	2	1	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	1	no	—
179	C₂×C₄×C₆₁	—	2	1	no	—
180	C₂×C₄×C₆₁	—	2	1	no	—
181	C₂×C₄×C₆₁	—	2	4	no	—
182	C₂×C₄×C₆₁	—	2	4	no	—
183	C₂×C₄×C₆₁	—	2	8	no	—
184	C₂×C₄×C₆₁	—	2	8	no	—
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	4	16	no	—
187	C₂×C₄×C₆₁	—	4	1	no	—
188	C₂×C₄×C₆₁	—	4	4	no	—
189	C₂×C₄×C₆₁	—	4	4	no	—
190	C₂×C₄×C₆₁	—	4	1	no	—
191	C₂×C₄×C₆₁	—	4	1	no	—
192	C₂×C₄×C₆₁	—	4	1	no	—
193	C₂×C₄×C₆₁	—	4	1	no	—
194	C₂×C₄×C₆₁	—	4	1	no	—
195	C₂×C₄×C₆₁	—	4	1	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	8	4	no	—
198	C₂×C₄×C₆₁	#120	1	2	yes	—
199	C₂×C₄×C₆₁	#120	1	2	yes	—
200	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₆₁	#137	1	2	yes	—
205	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
209	C₈×C₆₁	—	4	4	no	—
210	#24299	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₆₁	—	2	2	no	—
212	C₂²×C₆₁	—	2	2	no	—
213	C₂²×C₆₁	—	2	2	no	—
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	2	2	no	—
216	C₂²×C₆₁	—	2	2	no	—
217	C₂²×C₆₁	—	4	2	no	—
218	C₂²×C₆₁	—	4	2	no	—
219	C₂²×C₆₁	—	4	2	no	—
220	C₂²×C₆₁	—	8	1	no	—
221	C₂²×C₆₁	—	8	1	no	—
222	C₂²×C₆₁	—	8	1	no	—
223	C₂²×C₆₁	—	8	1	no	—
224	C₂²×C₆₁	#476	1	4	yes	complemented
225	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
226	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₂²×C₆₁	#536	1	1	yes	characteristic
228	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
229	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
232	C₄×C₆₁	—	2	2	no	—
233	C₄×C₆₁	—	2	2	no	—
234	C₄×C₆₁	—	2	2	no	—
235	C₄×C₆₁	—	2	2	no	—
236	C₄×C₆₁	—	4	8	no	—
237	C₄×C₆₁	—	4	2	no	—
238	C₄×C₆₁	—	8	1	no	—
239	C₄×C₆₁	—	8	1	no	—
240	C₄×C₆₁	#448	1	4	yes	—
241	C₄×C₆₁	#548	1	2	yes	—
242	C₄×C₆₁	D₄×Q₈	1	2	yes	—
243	C₂²×C₄⋊Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
244	C₂×#476	C₂×C₆₁	1	2	yes	complemented
245	C₄×#121	C₂×C₆₁	1	1	yes	characteristic
246	#2058	C₂×C₆₁	1	2	yes	complemented
247	#2023	C₂×C₆₁	1	2	yes	complemented
248	#1987	C₂×C₆₁	1	2	yes	complemented
249	#1874	C₂×C₆₁	1	2	yes	—
250	#1853	C₂×C₆₁	1	2	yes	complemented
251	#1797	C₂×C₆₁	1	1	yes	characteristic, complemented
252	C₂×C₆₁	—	2	4	no	—
253	C₂×C₆₁	—	8	2	no	—
254	C₂×C₆₁	#2409	1	1	yes	characteristic
255	C₂×C₆₁	C₂×#448	1	1	yes	characteristic
256	C₂×C₆₁	#3003	1	1	yes	characteristic
257	C₂×C₆₁	C₂×#476	1	1	yes	characteristic
258	C₂×C₆₁	#3079	1	1	yes	characteristic
259	C₂×C₆₁	#3227	1	1	yes	characteristic
260	C₂×C₆₁	#3238	1	1	yes	characteristic
261	C₂³×Q₈	—	2	1	no	—
262	C₂×C₄⋊Q₈	—	2	8	no	—
263	C₂×C₄⋊Q₈	—	2	1	no	—
264	C₂×C₄⋊Q₈	—	2	1	no	—
265	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
266	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
267	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
268	C₂×C₄×D₄	—	2	1	no	—
269	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	—	2	1	no	—
271	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
272	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
273	#476	—	2	8	no	—
274	C₂×#106	C₂²×C₆₁	1	4	yes	—
275	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
276	C₂×#102	C₂²×C₆₁	1	4	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
278	#390	C₂²×C₆₁	1	1	yes	characteristic
279	#389	C₂²×C₆₁	1	1	yes	characteristic
280	#388	—	2	1	no	—
281	#386	—	2	1	no	—
282	#380	C₂²×C₆₁	1	1	yes	characteristic
283	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
284	C₄×C₂²⋊C₄	—	2	1	no	—
285	#340	C₂²×C₆₁	1	4	yes	—
286	#340	C₂²×C₆₁	1	4	yes	—
287	#336	C₂²×C₆₁	1	2	yes	—
288	C₆₁	#24299	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	—	2	8	no	—
290	C₂²×Q₈	—	2	2	no	—
291	C₂²×Q₈	—	2	2	no	—
292	C₂²×Q₈	—	4	4	no	—
293	C₂²×Q₈	—	4	4	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
296	C₂³×C₄	—	2	2	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
302	C₄⋊Q₈	—	2	8	no	—
303	C₄⋊Q₈	—	2	8	no	—
304	C₄⋊Q₈	—	2	8	no	—
305	C₄⋊Q₈	—	2	4	no	—
306	C₄⋊Q₈	D₄×C₆₁	1	8	yes	complemented
307	#121	—	2	2	no	—
308	#121	Q₈×C₆₁	1	4	yes	complemented
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	4	4	no	—
311	C₂×C₄⋊C₄	—	2	8	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	8	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
320	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	2	4	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
332	#106	—	2	8	no	—
333	C₄⋊C₈	—	2	4	no	—
334	#102	—	2	8	no	—
335	C₂²⋊C₈	—	2	4	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	1	no	—
339	C₂⁴	—	2	1	no	—
340	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	4	32	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×Q₈	—	4	4	no	—
347	C₂×Q₈	—	4	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	complemented
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	SD₁₆×C₆₁	1	4	yes	—
373	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
378	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
379	C₂²×C₄	#41×C₆₁	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	2	4	no	—
383	C₂×C₈	—	2	4	no	—
384	C₄⋊C₄	—	2	8	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
393	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	complemented
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₂²⋊C₄	—	4	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	4	2	no	—
403	C₄²	C₂×D₄×C₆₁	1	4	yes	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	1	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
416	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
417	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
418	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
419	Q₈	—	4	16	no	—
420	Q₈	—	4	16	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	8	no	—
423	D₄	—	4	2	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	16	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	8	4	no	—
450	C₂×C₄	#120×C₆₁	1	2	yes	—
451	C₂×C₄	#120×C₆₁	1	2	yes	—
452	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
453	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
454	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
455	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
456	C₂×C₄	#137×C₆₁	1	2	yes	—
457	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
458	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
460	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
461	C₈	—	4	4	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₆₁×#476	1	4	yes	complemented
476	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
477	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
478	C₂²	C₆₁×#536	1	1	yes	characteristic
479	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
480	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
481	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
482	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
483	C₄	—	2	2	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	2	no	—
486	C₄	—	2	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	8	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	C₆₁×#448	1	4	yes	—
492	C₄	C₆₁×#548	1	2	yes	—
493	C₄	D₄×Q₈×C₆₁	1	2	yes	—
494	C₂	—	2	4	no	—
495	C₂	—	8	2	no	—
496	C₂	C₆₁×#2409	1	1	yes	characteristic
497	C₂	C₂×C₆₁×#448	1	1	yes	characteristic
498	C₂	C₆₁×#3003	1	1	yes	characteristic
499	C₂	C₂×C₆₁×#476	1	1	yes	characteristic
500	C₂	C₆₁×#3079	1	1	yes	characteristic
501	C₂	C₆₁×#3227	1	1	yes	characteristic
502	C₂	C₆₁×#3238	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊Q₈×C₆₁	C₂	semidirect
2. C₂×C₆₁×#476	C₂	semidirect
4. C₆₁×#2058	C₂	semidirect
5. C₆₁×#2023	C₂	semidirect
6. C₆₁×#1987	C₂	semidirect
8. C₆₁×#1853	C₂	semidirect
9. C₆₁×#1797	C₂	semidirect
54. C₄⋊Q₈×C₆₁	D₄	semidirect
56. #121×C₆₁	Q₈	semidirect
102. C₂×D₄×C₆₁	C₂×Q₈	semidirect
141. C₄⋊C₄×C₆₁	C₂×Q₈	semidirect
210. #24299	C₆₁	direct (N × H)
224. C₂²×C₆₁	#476	semidirect
243. C₂²×C₄⋊Q₈	C₂×C₆₁	semidirect
244. C₂×#476	C₂×C₆₁	semidirect
246. #2058	C₂×C₆₁	semidirect
247. #2023	C₂×C₆₁	semidirect
248. #1987	C₂×C₆₁	semidirect
250. #1853	C₂×C₆₁	semidirect
251. #1797	C₂×C₆₁	semidirect
288. C₆₁	#24299	direct (N × H)
306. C₄⋊Q₈	D₄×C₆₁	semidirect
308. #121	Q₈×C₆₁	semidirect
354. C₂×D₄	C₂×Q₈×C₆₁	semidirect
393. C₄⋊C₄	C₂×Q₈×C₆₁	semidirect
475. C₂²	C₆₁×#476	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₆₁	2
C₂×C₆₁×#476	2
C₄×#121×C₆₁	2
C₆₁×#2058	2
C₆₁×#2023	2
C₆₁×#1987	2
C₆₁×#1874	2
C₆₁×#1853	2
C₆₁×#1797	2
#24299	61

Subgroups — C61×#24299 #29527732

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24299 #29527732