Subgroups — C₆₁×#34634 #29538067

Order 15616.

2374 conjugacy classes of subgroups.

The subgroup lattice has 422 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, complemented
2	C₂²×#117×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2629	C₂	1	4	yes	maximal, complemented
4	C₆₁×#2628	C₂	1	4	yes	maximal, complemented
5	C₆₁×#2627	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2626	C₂	1	4	yes	maximal
7	C₆₁×#2396	C₂	1	8	yes	maximal, complemented
8	C₆₁×#2296	C₂	1	2	yes	maximal, complemented
9	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2280	C₂	1	2	yes	maximal
11	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
12	C₆₁×#533	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	complemented
14	C₂×#125×C₆₁	C₂²	1	2	yes	complemented
15	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	complemented
17	C₂×#117×C₆₁	—	2	8	no	—
18	C₂×#117×C₆₁	C₂²	1	2	yes	—
19	C₂×#117×C₆₁	C₂²	1	2	yes	—
20	C₂×#117×C₆₁	C₂²	1	2	yes	—
21	C₂×#117×C₆₁	C₂²	1	2	yes	—
22	C₂×#117×C₆₁	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#400	C₂²	1	8	yes	complemented
28	C₆₁×#399	C₂²	1	8	yes	—
29	C₆₁×#398	C₂²	1	16	yes	complemented
30	C₆₁×#396	C₂²	1	16	yes	—
31	C₆₁×#395	C₂²	1	8	yes	complemented
32	C₆₁×#393	C₂²	1	8	yes	—
33	C₆₁×#389	C₂²	1	8	yes	complemented
34	C₆₁×#385	C₂²	1	8	yes	—
35	C₆₁×#384	C₂²	1	2	yes	complemented
36	C₆₁×#382	C₂²	1	2	yes	complemented
37	C₆₁×#381	C₂²	1	4	yes	—
38	C₆₁×#380	C₂²	1	8	yes	—
39	C₆₁×#380	C₂²	1	4	yes	—
40	C₆₁×#379	C₂²	1	4	yes	—
41	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	complemented
42	C₄×C₄⋊C₄×C₆₁	C₂²	1	8	yes	complemented
43	C₄×C₂²⋊C₄×C₆₁	C₂²	1	8	yes	—
44	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
46	C₂³×C₄×C₆₁	—	2	4	no	—
47	C₂³×C₄×C₆₁	—	2	4	no	—
48	C₂³×C₄×C₆₁	Q₈	1	8	yes	complemented
49	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₆₁	—	2	8	no	—
56	#125×C₆₁	—	2	8	no	—
57	C₂²⋊Q₈×C₆₁	—	2	16	no	—
58	C₄×Q₈×C₆₁	—	2	16	no	—
59	#117×C₆₁	—	2	8	no	—
60	#117×C₆₁	—	2	8	no	—
61	#117×C₆₁	—	2	16	no	—
62	#117×C₆₁	—	2	8	no	—
63	#117×C₆₁	—	2	8	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
79	C₂×C₄²×C₆₁	—	2	4	no	—
80	C₂×C₄²×C₆₁	D₄	1	8	yes	—
81	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
83	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
84	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
88	#95×C₆₁	C₂³	1	16	yes	—
89	#95×C₆₁	C₂³	1	8	yes	—
90	#95×C₆₁	C₂³	1	16	yes	—
91	C₂⁴×C₆₁	—	2	2	no	—
92	C₂⁴×C₆₁	—	2	2	no	—
93	C₂⁴×C₆₁	—	4	4	no	—
94	C₂⁴×C₆₁	C₂×Q₈	1	4	yes	—
95	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
96	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
97	C₂×Q₈×C₆₁	—	2	8	no	—
98	C₂×Q₈×C₆₁	—	4	8	no	—
99	C₂²×C₄×C₆₁	—	2	2	no	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	32	no	—
102	C₂²×C₄×C₆₁	—	2	4	no	—
103	C₂²×C₄×C₆₁	—	2	4	no	—
104	C₂²×C₄×C₆₁	—	2	4	no	—
105	C₂²×C₄×C₆₁	—	2	4	no	—
106	C₂²×C₄×C₆₁	—	2	4	no	—
107	C₂²×C₄×C₆₁	—	4	4	no	—
108	C₂²×C₄×C₆₁	—	4	4	no	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₆₁	C₂×Q₈	1	8	yes	—
113	C₂²×C₄×C₆₁	C₂×Q₈	1	8	yes	—
114	C₂²×C₄×C₆₁	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₆₁	#41	1	4	yes	—
116	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₆₁	—	2	8	no	—
125	C₄⋊C₄×C₆₁	—	2	8	no	—
126	C₄⋊C₄×C₆₁	—	2	8	no	—
127	C₄⋊C₄×C₆₁	—	2	16	no	—
128	C₄⋊C₄×C₆₁	—	2	8	no	—
129	C₄⋊C₄×C₆₁	—	2	8	no	—
130	C₄⋊C₄×C₆₁	—	4	8	no	—
131	C₄⋊C₄×C₆₁	—	4	16	no	—
132	C₂²⋊C₄×C₆₁	—	2	8	no	—
133	C₂²⋊C₄×C₆₁	—	2	8	no	—
134	C₂²⋊C₄×C₆₁	—	2	8	no	—
135	C₂²⋊C₄×C₆₁	—	2	8	no	—
136	C₂²⋊C₄×C₆₁	—	4	16	no	—
137	C₄²×C₆₁	—	2	4	no	—
138	C₄²×C₆₁	—	2	4	no	—
139	C₄²×C₆₁	—	2	8	no	—
140	C₄²×C₆₁	—	2	8	no	—
141	C₄²×C₆₁	C₂×D₄	1	8	yes	—
142	C₄²×C₆₁	C₂×D₄	1	4	yes	—
143	C₄²×C₆₁	C₂×D₄	1	4	yes	—
144	C₂³×C₆₁	—	2	4	no	—
145	C₂³×C₆₁	—	2	8	no	—
146	C₂³×C₆₁	—	2	2	no	—
147	C₂³×C₆₁	—	2	2	no	—
148	C₂³×C₆₁	—	2	8	no	—
149	C₂³×C₆₁	—	4	8	no	—
150	C₂³×C₆₁	—	4	8	no	—
151	C₂³×C₆₁	—	4	8	no	—
152	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
153	C₂³×C₆₁	C₂²×Q₈	1	4	yes	—
154	C₂³×C₆₁	C₂²×Q₈	1	2	yes	—
155	C₂³×C₆₁	C₂×#41	1	2	yes	—
156	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
157	Q₈×C₆₁	—	4	16	no	—
158	C₂×C₄×C₆₁	—	2	8	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	2	no	—
161	C₂×C₄×C₆₁	—	2	4	no	—
162	C₂×C₄×C₆₁	—	2	4	no	—
163	C₂×C₄×C₆₁	—	2	16	no	—
164	C₂×C₄×C₆₁	—	2	16	no	—
165	C₂×C₄×C₆₁	—	2	4	no	—
166	C₂×C₄×C₆₁	—	2	8	no	—
167	C₂×C₄×C₆₁	—	2	8	no	—
168	C₂×C₄×C₆₁	—	2	16	no	—
169	C₂×C₄×C₆₁	—	2	16	no	—
170	C₂×C₄×C₆₁	—	2	8	no	—
171	C₂×C₄×C₆₁	—	4	8	no	—
172	C₂×C₄×C₆₁	—	4	8	no	—
173	C₂×C₄×C₆₁	C₂²⋊Q₈	1	16	yes	—
174	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
176	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
179	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
180	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
181	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
182	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
183	#34634	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₆₁	—	2	4	no	—
185	C₂²×C₆₁	—	2	4	no	—
186	C₂²×C₆₁	—	2	4	no	—
187	C₂²×C₆₁	—	2	4	no	—
188	C₂²×C₆₁	—	2	8	no	—
189	C₂²×C₆₁	—	4	16	no	—
190	C₂²×C₆₁	—	4	4	no	—
191	C₂²×C₆₁	—	4	4	no	—
192	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	4	yes	—
193	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
194	C₂²×C₆₁	C₂³×Q₈	1	1	yes	characteristic
195	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
196	C₂²×C₆₁	#585	1	4	yes	—
197	C₄×C₆₁	—	2	4	no	—
198	C₄×C₆₁	—	2	4	no	—
199	C₄×C₆₁	—	2	4	no	—
200	C₄×C₆₁	—	4	4	no	—
201	C₄×C₆₁	—	4	8	no	—
202	C₄×C₆₁	—	4	8	no	—
203	C₄×C₆₁	C₂×C₂²⋊Q₈	1	4	yes	—
204	C₄×C₆₁	C₂×C₂²⋊Q₈	1	4	yes	—
205	C₂×#533	C₂×C₆₁	1	1	yes	characteristic, complemented
206	C₂²×#117	C₂×C₆₁	1	1	yes	characteristic
207	#2629	C₂×C₆₁	1	4	yes	complemented
208	#2628	C₂×C₆₁	1	4	yes	complemented
209	#2627	C₂×C₆₁	1	4	yes	complemented
210	#2626	C₂×C₆₁	1	4	yes	—
211	#2396	C₂×C₆₁	1	8	yes	complemented
212	#2296	C₂×C₆₁	1	2	yes	complemented
213	#2285	C₂×C₆₁	1	1	yes	characteristic, complemented
214	#2280	C₂×C₆₁	1	2	yes	—
215	C₂×C₆₁	—	2	4	no	—
216	C₂×C₆₁	—	4	4	no	—
217	C₂×C₆₁	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
218	C₂×C₆₁	#3449	1	2	yes	—
219	C₂×C₆₁	#3455	1	2	yes	—
220	C₂×C₆₁	#3458	1	2	yes	—
221	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
222	#533	—	2	8	no	—
223	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	complemented
224	C₂×#125	C₂²×C₆₁	1	2	yes	complemented
225	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
226	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	complemented
227	C₂×#117	—	2	8	no	—
228	C₂×#117	C₂²×C₆₁	1	2	yes	—
229	C₂×#117	C₂²×C₆₁	1	2	yes	—
230	C₂×#117	C₂²×C₆₁	1	4	yes	—
231	C₂×#117	C₂²×C₆₁	1	2	yes	—
232	C₂×#117	C₂²×C₆₁	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
234	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
235	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
236	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
237	#400	C₂²×C₆₁	1	8	yes	complemented
238	#399	C₂²×C₆₁	1	8	yes	—
239	#398	C₂²×C₆₁	1	16	yes	complemented
240	#396	C₂²×C₆₁	1	16	yes	—
241	#395	C₂²×C₆₁	1	8	yes	complemented
242	#393	C₂²×C₆₁	1	8	yes	—
243	#389	C₂²×C₆₁	1	8	yes	complemented
244	#385	C₂²×C₆₁	1	8	yes	—
245	#384	C₂²×C₆₁	1	2	yes	complemented
246	#382	C₂²×C₆₁	1	2	yes	complemented
247	#381	C₂²×C₆₁	1	4	yes	—
248	#380	C₂²×C₆₁	1	4	yes	—
249	#380	C₂²×C₆₁	1	8	yes	—
250	#379	C₂²×C₆₁	1	4	yes	—
251	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	complemented
252	C₄×C₄⋊C₄	C₂²×C₆₁	1	8	yes	complemented
253	C₄×C₂²⋊C₄	C₂²×C₆₁	1	8	yes	—
254	C₆₁	#34634	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
257	C₂³×C₄	—	2	4	no	—
258	C₂³×C₄	—	2	4	no	—
259	C₂³×C₄	Q₈×C₆₁	1	8	yes	complemented
260	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
262	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
263	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
264	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
265	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
266	C₄⋊Q₈	—	2	8	no	—
267	#125	—	2	8	no	—
268	C₂²⋊Q₈	—	2	16	no	—
269	C₄×Q₈	—	2	16	no	—
270	#117	—	2	8	no	—
271	#117	—	2	8	no	—
272	#117	—	2	16	no	—
273	#117	—	2	8	no	—
274	#117	—	2	8	no	—
275	C₂×C₄⋊C₄	—	2	8	no	—
276	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
283	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
290	C₂×C₄²	—	2	4	no	—
291	C₂×C₄²	D₄×C₆₁	1	8	yes	—
292	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
293	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
294	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
295	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
296	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
297	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
299	#95	C₂³×C₆₁	1	16	yes	—
300	#95	C₂³×C₆₁	1	8	yes	—
301	#95	C₂³×C₆₁	1	16	yes	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	4	4	no	—
305	C₂⁴	C₂×Q₈×C₆₁	1	4	yes	—
306	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
307	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
308	C₂×Q₈	—	2	8	no	—
309	C₂×Q₈	—	4	8	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	32	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	C₂×D₄×C₆₁	1	8	yes	—
321	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
322	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
323	C₂²×C₄	C₂×Q₈×C₆₁	1	8	yes	—
324	C₂²×C₄	C₂×Q₈×C₆₁	1	8	yes	—
325	C₂²×C₄	C₂×Q₈×C₆₁	1	4	yes	—
326	C₂²×C₄	#41×C₆₁	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
328	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
330	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	16	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	4	8	no	—
342	C₄⋊C₄	—	4	16	no	—
343	C₂²⋊C₄	—	2	8	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	4	16	no	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	8	no	—
351	C₄²	—	2	8	no	—
352	C₄²	C₂×D₄×C₆₁	1	8	yes	—
353	C₄²	C₂×D₄×C₆₁	1	4	yes	—
354	C₄²	C₂×D₄×C₆₁	1	4	yes	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	4	8	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
364	C₂³	C₂²×Q₈×C₆₁	1	4	yes	—
365	C₂³	C₂²×Q₈×C₆₁	1	2	yes	—
366	C₂³	C₂×#41×C₆₁	1	2	yes	—
367	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
368	Q₈	—	4	16	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	16	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	16	no	—
380	C₂×C₄	—	2	16	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	C₂²⋊Q₈×C₆₁	1	16	yes	—
385	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
386	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
387	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
389	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
390	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
391	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
392	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
393	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	4	16	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	4	yes	—
403	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
404	C₂²	C₂³×Q₈×C₆₁	1	1	yes	characteristic
405	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
406	C₂²	C₆₁×#585	1	4	yes	—
407	C₄	—	2	4	no	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	8	no	—
412	C₄	—	4	8	no	—
413	C₄	C₂×C₂²⋊Q₈×C₆₁	1	4	yes	—
414	C₄	C₂×C₂²⋊Q₈×C₆₁	1	4	yes	—
415	C₂	—	2	4	no	—
416	C₂	—	4	4	no	—
417	C₂	C₂²×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
418	C₂	C₆₁×#3449	1	2	yes	—
419	C₂	C₆₁×#3455	1	2	yes	—
420	C₂	C₆₁×#3458	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂⁵
prime radical	C₂⁵×C₆₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#533	C₂	semidirect
3. C₆₁×#2629	C₂	semidirect
4. C₆₁×#2628	C₂	semidirect
5. C₆₁×#2627	C₂	semidirect
7. C₆₁×#2396	C₂	semidirect
8. C₆₁×#2296	C₂	semidirect
9. C₆₁×#2285	C₂	semidirect
13. C₂×C₄⋊Q₈×C₆₁	C₂²	semidirect
14. C₂×#125×C₆₁	C₂²	semidirect
16. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
27. C₆₁×#400	C₂²	semidirect
29. C₆₁×#398	C₂²	semidirect
31. C₆₁×#395	C₂²	semidirect
33. C₆₁×#389	C₂²	semidirect
35. C₆₁×#384	C₂²	semidirect
36. C₆₁×#382	C₂²	semidirect
41. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
42. C₄×C₄⋊C₄×C₆₁	C₂²	semidirect
48. C₂³×C₄×C₆₁	Q₈	semidirect
183. #34634	C₆₁	direct (N × H)
205. C₂×#533	C₂×C₆₁	semidirect
207. #2629	C₂×C₆₁	semidirect
208. #2628	C₂×C₆₁	semidirect
209. #2627	C₂×C₆₁	semidirect
211. #2396	C₂×C₆₁	semidirect
212. #2296	C₂×C₆₁	semidirect
213. #2285	C₂×C₆₁	semidirect
223. C₂×C₄⋊Q₈	C₂²×C₆₁	semidirect
224. C₂×#125	C₂²×C₆₁	semidirect
226. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
237. #400	C₂²×C₆₁	semidirect
239. #398	C₂²×C₆₁	semidirect
241. #395	C₂²×C₆₁	semidirect
243. #389	C₂²×C₆₁	semidirect
245. #384	C₂²×C₆₁	semidirect
246. #382	C₂²×C₆₁	semidirect
251. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
252. C₄×C₄⋊C₄	C₂²×C₆₁	semidirect
254. C₆₁	#34634	direct (N × H)
259. C₂³×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
C₂²×#117×C₆₁	2
C₆₁×#2629	2
C₆₁×#2628	2
C₆₁×#2627	2
C₆₁×#2626	2
C₆₁×#2396	2
C₆₁×#2296	2
C₆₁×#2285	2
C₆₁×#2280	2
#34634	61

Subgroups — C61×#34634 #29538067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34634 #29538067