Subgroups — C₆₁×#23554 #29526987

Order 15616.

1202 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#428	C₂	1	2	yes	maximal
3	C₂×C₆₁×#389	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2059	C₂	1	4	yes	maximal, complemented
5	C₆₁×#2058	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2057	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1736	C₂	1	2	yes	maximal
8	C₆₁×#1728	C₂	1	1	yes	maximal, characteristic
9	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
10	C₆₁×#533	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#125×C₆₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
16	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
17	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
18	C₂×#117×C₆₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
20	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#428	—	2	8	no	—
24	C₂×#107×C₆₁	C₂²	1	4	yes	—
25	C₂×#106×C₆₁	C₂²	1	4	yes	—
26	C₆₁×#389	—	2	1	no	—
27	C₆₁×#389	—	2	1	no	—
28	C₆₁×#389	C₂²	1	2	yes	—
29	C₆₁×#389	C₂²	1	2	yes	—
30	C₂×#95×C₆₁	—	2	1	no	—
31	C₆₁×#340	C₂²	1	4	yes	—
32	C₆₁×#340	C₂²	1	4	yes	—
33	C₆₁×#336	C₂²	1	2	yes	—
34	C₆₁×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₆₁	—	2	1	no	—
36	C₂²×Q₈×C₆₁	—	2	1	no	—
37	C₂³×C₄×C₆₁	—	2	1	no	—
38	C₂³×C₄×C₆₁	—	2	1	no	—
39	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₆₁	—	2	4	no	—
43	C₂×M₁₆×C₆₁	—	2	4	no	—
44	C₂×M₁₆×C₆₁	Q₈	1	8	yes	complemented
45	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
46	C₄⋊Q₈×C₆₁	—	2	4	no	—
47	C₄⋊Q₈×C₆₁	—	2	4	no	—
48	#125×C₆₁	—	2	4	no	—
49	#125×C₆₁	—	2	4	no	—
50	C₂²⋊Q₈×C₆₁	—	2	8	no	—
51	C₂²⋊Q₈×C₆₁	—	2	8	no	—
52	C₄×Q₈×C₆₁	—	2	8	no	—
53	C₄×Q₈×C₆₁	—	2	8	no	—
54	#117×C₆₁	—	2	4	no	—
55	#117×C₆₁	D₄	1	8	yes	—
56	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
66	C₂×C₄⋊C₄×C₆₁	—	4	4	no	—
67	C₂×C₄⋊C₄×C₆₁	Q₈	1	4	yes	complemented
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄²×C₆₁	—	2	4	no	—
74	C₂×C₄²×C₆₁	—	2	2	no	—
75	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
79	#107×C₆₁	—	2	8	no	—
80	#106×C₆₁	—	2	8	no	—
81	#95×C₆₁	—	2	2	no	—
82	#95×C₆₁	—	2	2	no	—
83	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₆₁	—	2	4	no	—
85	C₂×Q₈×C₆₁	—	2	4	no	—
86	C₂×Q₈×C₆₁	—	4	2	no	—
87	C₂×Q₈×C₆₁	—	4	2	no	—
88	C₂×Q₈×C₆₁	—	4	2	no	—
89	C₂×Q₈×C₆₁	—	4	2	no	—
90	C₂²×C₄×C₆₁	—	2	2	no	—
91	C₂²×C₄×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	2	4	no	—
93	C₂²×C₄×C₆₁	—	2	2	no	—
94	C₂²×C₄×C₆₁	—	2	2	no	—
95	C₂²×C₄×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	4	1	no	—
100	C₂²×C₄×C₆₁	—	4	1	no	—
101	C₂²×C₄×C₆₁	—	4	2	no	—
102	C₂²×C₄×C₆₁	—	4	2	no	—
103	C₂²×C₄×C₆₁	—	4	2	no	—
104	C₂²×C₄×C₆₁	—	4	2	no	—
105	C₂²×C₄×C₆₁	—	4	2	no	—
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
113	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₆₁	#41	1	2	yes	—
115	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₆₁	—	2	16	no	—
117	C₂×C₈×C₆₁	—	2	4	no	—
118	C₂×C₈×C₆₁	—	2	4	no	—
119	C₂×C₈×C₆₁	C₂×Q₈	1	8	yes	—
120	C₄⋊C₄×C₆₁	—	2	8	no	—
121	C₄⋊C₄×C₆₁	—	2	8	no	—
122	C₄⋊C₄×C₆₁	—	2	4	no	—
123	C₄⋊C₄×C₆₁	—	2	4	no	—
124	C₄⋊C₄×C₆₁	—	2	4	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	4	no	—
129	C₄⋊C₄×C₆₁	—	4	4	no	—
130	C₄⋊C₄×C₆₁	—	4	2	no	—
131	C₄⋊C₄×C₆₁	—	4	4	no	—
132	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
133	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
134	C₄⋊C₄×C₆₁	C₂×Q₈	1	4	yes	—
135	C₂²⋊C₄×C₆₁	—	2	8	no	—
136	C₄²×C₆₁	—	2	2	no	—
137	C₄²×C₆₁	—	2	2	no	—
138	C₄²×C₆₁	—	2	8	no	—
139	C₄²×C₆₁	—	2	2	no	—
140	C₄²×C₆₁	—	2	2	no	—
141	C₂³×C₆₁	—	2	1	no	—
142	C₂³×C₆₁	—	2	1	no	—
143	C₂³×C₆₁	—	2	1	no	—
144	C₂³×C₆₁	—	2	1	no	—
145	C₂³×C₆₁	#120	1	2	yes	—
146	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
147	C₂³×C₆₁	C₄⋊Q₈	1	2	yes	—
148	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₆₁	—	4	8	no	—
150	Q₈×C₆₁	—	4	8	no	—
151	C₂×C₄×C₆₁	—	2	1	no	—
152	C₂×C₄×C₆₁	—	2	1	no	—
153	C₂×C₄×C₆₁	—	2	1	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	2	4	no	—
158	C₂×C₄×C₆₁	—	2	4	no	—
159	C₂×C₄×C₆₁	—	2	4	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	4	4	no	—
165	C₂×C₄×C₆₁	—	4	4	no	—
166	C₂×C₄×C₆₁	—	4	8	no	—
167	C₂×C₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	—	4	2	no	—
170	C₂×C₄×C₆₁	—	4	2	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	8	4	no	—
177	C₂×C₄×C₆₁	#120	1	2	yes	—
178	C₂×C₄×C₆₁	C₂²⋊Q₈	1	8	yes	—
179	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
180	C₂×C₄×C₆₁	C₄⋊Q₈	1	8	yes	—
181	C₂×C₄×C₆₁	C₄⋊Q₈	1	2	yes	—
182	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₆₁	#137	1	2	yes	—
184	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
186	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
187	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
188	C₈×C₆₁	—	2	8	no	—
189	#23554	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₆₁	—	2	2	no	—
191	C₂²×C₆₁	—	2	2	no	—
192	C₂²×C₆₁	—	2	2	no	—
193	C₂²×C₆₁	—	2	2	no	—
194	C₂²×C₆₁	—	2	2	no	—
195	C₂²×C₆₁	—	2	2	no	—
196	C₂²×C₆₁	#395	1	4	yes	—
197	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
198	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
199	C₂²×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
200	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
201	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
202	C₂²×C₆₁	#575	1	1	yes	characteristic
203	C₂²×C₆₁	#575	1	1	yes	characteristic
204	C₄×C₆₁	—	2	2	no	—
205	C₄×C₆₁	—	2	2	no	—
206	C₄×C₆₁	—	4	4	no	—
207	C₄×C₆₁	—	4	1	no	—
208	C₄×C₆₁	—	4	4	no	—
209	C₄×C₆₁	—	4	1	no	—
210	C₄×C₆₁	—	4	4	no	—
211	C₄×C₆₁	—	8	2	no	—
212	C₄×C₆₁	#395	1	4	yes	—
213	C₄×C₆₁	C₂×C₂²⋊Q₈	1	2	yes	—
214	C₄×C₆₁	C₂×C₄⋊Q₈	1	2	yes	—
215	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
216	C₂×#428	C₂×C₆₁	1	2	yes	—
217	C₂×#389	C₂×C₆₁	1	1	yes	characteristic
218	#2059	C₂×C₆₁	1	4	yes	complemented
219	#2058	C₂×C₆₁	1	2	yes	complemented
220	#2057	C₂×C₆₁	1	2	yes	complemented
221	#1736	C₂×C₆₁	1	2	yes	—
222	#1728	C₂×C₆₁	1	1	yes	characteristic
223	C₂×C₆₁	—	2	4	no	—
224	C₂×C₆₁	C₂×#395	1	1	yes	characteristic
225	C₂×C₆₁	#3006	1	1	yes	characteristic
226	C₂×C₆₁	#3007	1	1	yes	characteristic
227	C₂×C₆₁	#3077	1	1	yes	characteristic
228	C₂×C₆₁	#3078	1	1	yes	characteristic
229	C₂×C₆₁	#3165	1	1	yes	characteristic
230	C₂×C₆₁	#3166	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
232	#533	—	2	8	no	—
233	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
235	C₂×#125	C₂²×C₆₁	1	2	yes	—
236	C₂×C₂²⋊Q₈	—	2	1	no	—
237	C₂×C₂²⋊Q₈	—	2	1	no	—
238	C₂×C₄×Q₈	—	2	1	no	—
239	C₂×C₄×Q₈	—	2	1	no	—
240	C₂×#117	C₂²×C₆₁	1	2	yes	—
241	C₂²×C₄⋊C₄	—	2	1	no	—
242	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
243	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
245	#428	—	2	8	no	—
246	C₂×#107	C₂²×C₆₁	1	4	yes	—
247	C₂×#106	C₂²×C₆₁	1	4	yes	—
248	#389	—	2	1	no	—
249	#389	—	2	1	no	—
250	#389	C₂²×C₆₁	1	2	yes	—
251	#389	C₂²×C₆₁	1	2	yes	—
252	C₂×#95	—	2	1	no	—
253	#340	C₂²×C₆₁	1	4	yes	—
254	#340	C₂²×C₆₁	1	4	yes	—
255	#336	C₂²×C₆₁	1	2	yes	—
256	#336	C₂²×C₆₁	1	2	yes	—
257	C₆₁	#23554	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	Q₈×C₆₁	1	8	yes	complemented
268	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
269	C₄⋊Q₈	—	2	4	no	—
270	C₄⋊Q₈	—	2	4	no	—
271	#125	—	2	4	no	—
272	#125	—	2	4	no	—
273	C₂²⋊Q₈	—	2	8	no	—
274	C₂²⋊Q₈	—	2	8	no	—
275	C₄×Q₈	—	2	8	no	—
276	C₄×Q₈	—	2	8	no	—
277	#117	—	2	4	no	—
278	#117	D₄×C₆₁	1	8	yes	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	4	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	4	4	no	—
290	C₂×C₄⋊C₄	Q₈×C₆₁	1	4	yes	complemented
291	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	4	no	—
298	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
299	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
300	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
302	#107	—	2	8	no	—
303	#106	—	2	8	no	—
304	#95	—	2	2	no	—
305	#95	—	2	2	no	—
306	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	—	4	2	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
335	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
336	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
337	C₂²×C₄	#41×C₆₁	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
339	M₁₆	—	2	16	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	C₂×Q₈×C₆₁	1	8	yes	—
343	C₄⋊C₄	—	2	8	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
356	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
357	C₄⋊C₄	C₂×Q₈×C₆₁	1	4	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	8	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	#120×C₆₁	1	2	yes	—
369	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
370	C₂³	C₄⋊Q₈×C₆₁	1	2	yes	—
371	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
372	Q₈	—	4	8	no	—
373	Q₈	—	4	8	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	#120×C₆₁	1	2	yes	—
401	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
402	C₂×C₄	C₂²⋊Q₈×C₆₁	1	8	yes	—
403	C₂×C₄	C₄⋊Q₈×C₆₁	1	8	yes	—
404	C₂×C₄	C₄⋊Q₈×C₆₁	1	2	yes	—
405	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
406	C₂×C₄	#137×C₆₁	1	2	yes	—
407	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
408	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
409	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
410	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
411	C₈	—	2	8	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	C₆₁×#395	1	4	yes	—
419	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
420	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
421	C₂²	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
422	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
423	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
424	C₂²	C₆₁×#575	1	1	yes	characteristic
425	C₂²	C₆₁×#575	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	4	4	no	—
429	C₄	—	4	1	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	2	no	—
434	C₄	C₆₁×#395	1	4	yes	—
435	C₄	C₂×C₂²⋊Q₈×C₆₁	1	2	yes	—
436	C₄	C₂×C₄⋊Q₈×C₆₁	1	2	yes	—
437	C₂	—	2	4	no	—
438	C₂	C₂×C₆₁×#395	1	1	yes	characteristic
439	C₂	C₆₁×#3006	1	1	yes	characteristic
440	C₂	C₆₁×#3007	1	1	yes	characteristic
441	C₂	C₆₁×#3077	1	1	yes	characteristic
442	C₂	C₆₁×#3078	1	1	yes	characteristic
443	C₂	C₆₁×#3165	1	1	yes	characteristic
444	C₂	C₆₁×#3166	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
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
4. C₆₁×#2059	C₂	semidirect
5. C₆₁×#2058	C₂	semidirect
6. C₆₁×#2057	C₂	semidirect
44. C₂×M₁₆×C₆₁	Q₈	semidirect
67. C₂×C₄⋊C₄×C₆₁	Q₈	semidirect
189. #23554	C₆₁	direct (N × H)
218. #2059	C₂×C₆₁	semidirect
219. #2058	C₂×C₆₁	semidirect
220. #2057	C₂×C₆₁	semidirect
257. C₆₁	#23554	direct (N × H)
267. C₂×M₁₆	Q₈×C₆₁	semidirect
290. C₂×C₄⋊C₄	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#533	2
C₂×C₆₁×#428	2
C₂×C₆₁×#389	2
C₆₁×#2059	2
C₆₁×#2058	2
C₆₁×#2057	2
C₆₁×#1736	2
C₆₁×#1728	2
#23554	61

Subgroups — C61×#23554 #29526987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23554 #29526987