Subgroups — C₆₁×#34189 #29537622

Order 15616.

2342 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2357	C₂	1	4	yes	maximal, complemented
3	C₆₁×#2356	C₂	1	4	yes	maximal, complemented
4	C₆₁×#2353	C₂	1	8	yes	maximal, complemented
5	C₆₁×#2314	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2311	C₂	1	2	yes	maximal
7	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2283	C₂	1	4	yes	maximal, complemented
9	C₂×C₆₁×#382	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#2274	C₂	1	2	yes	maximal, complemented
11	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
12	C₄×#41×C₆₁	C₄	1	16	yes	complemented
13	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
15	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
16	C₂×#117×C₆₁	C₂²	1	2	yes	—
17	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#117×C₆₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
20	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
22	C₆₁×#391	C₂²	1	4	yes	—
23	C₆₁×#390	C₂²	1	4	yes	—
24	C₆₁×#388	C₂²	1	16	yes	—
25	C₆₁×#387	C₂²	1	16	yes	—
26	C₆₁×#386	C₂²	1	8	yes	—
27	C₆₁×#384	C₂²	1	2	yes	—
28	C₆₁×#383	C₂²	1	8	yes	—
29	C₆₁×#382	C₂²	1	2	yes	—
30	C₆₁×#382	C₂²	1	2	yes	—
31	C₆₁×#382	C₂²	1	4	yes	—
32	C₆₁×#382	C₂²	1	2	yes	—
33	C₆₁×#381	C₂²	1	8	yes	—
34	C₆₁×#380	C₂²	1	8	yes	—
35	C₆₁×#380	C₂²	1	4	yes	—
36	C₄×C₄⋊C₄×C₆₁	C₂²	1	8	yes	—
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	8	yes	—
38	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₆₁	C₂²	1	8	yes	—
40	C₄×C₂²⋊C₄×C₆₁	C₂²	1	8	yes	—
41	C₆₁×#376	C₂²	1	8	yes	—
42	C₂×#95×C₆₁	C₂²	1	4	yes	—
43	C₂×#41×C₆₁	—	2	4	no	—
44	C₂×#41×C₆₁	—	2	4	no	—
45	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
50	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
51	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
52	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
53	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₆₁	C₂×C₄	1	16	yes	complemented
55	C₄×D₄×C₆₁	C₂×C₄	1	32	yes	—
56	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	complemented
57	#117×C₆₁	—	2	8	no	—
58	#117×C₆₁	C₂×C₄	1	8	yes	—
59	#117×C₆₁	C₂×C₄	1	16	yes	complemented
60	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
69	C₂×C₂²⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
71	C₂×C₄²×C₆₁	C₂×C₄	1	8	yes	—
72	C₂×C₄²×C₆₁	C₂×C₄	1	16	yes	complemented
73	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
74	C₂×C₄²×C₆₁	C₂³	1	16	yes	—
75	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
76	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
77	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
78	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	#95×C₆₁	C₂³	1	8	yes	—
81	#95×C₆₁	C₂³	1	8	yes	—
82	#95×C₆₁	C₂³	1	4	yes	—
83	#95×C₆₁	C₂³	1	16	yes	—
84	#95×C₆₁	C₂³	1	4	yes	—
85	#95×C₆₁	C₂³	1	16	yes	—
86	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
87	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
88	#41×C₆₁	—	2	32	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
92	C₂×D₄×C₆₁	—	2	4	no	—
93	C₂×D₄×C₆₁	—	2	4	no	—
94	C₂×D₄×C₆₁	—	2	2	no	—
95	C₂×D₄×C₆₁	—	2	2	no	—
96	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
97	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₆₁	—	2	4	no	—
99	C₂²×C₄×C₆₁	—	2	4	no	—
100	C₂²×C₄×C₆₁	—	2	8	no	—
101	C₂²×C₄×C₆₁	—	4	8	no	—
102	C₂²×C₄×C₆₁	—	4	4	no	—
103	C₂²×C₄×C₆₁	—	4	8	no	—
104	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
105	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₆₁	C₂²×C₄	1	16	yes	—
107	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₆₁	#41	1	4	yes	—
109	C₂²×C₄×C₆₁	#41	1	4	yes	—
110	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
111	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
112	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
113	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₆₁	—	2	8	no	—
119	C₄⋊C₄×C₆₁	—	2	8	no	—
120	C₄⋊C₄×C₆₁	—	2	8	no	—
121	C₄⋊C₄×C₆₁	—	4	8	no	—
122	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
123	C₄⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
124	C₂²⋊C₄×C₆₁	—	2	8	no	—
125	C₂²⋊C₄×C₆₁	—	4	16	no	—
126	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
127	C₂²⋊C₄×C₆₁	C₂²×C₄	1	16	yes	—
128	C₄²×C₆₁	—	2	8	no	—
129	C₄²×C₆₁	—	4	16	no	—
130	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
131	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
132	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
133	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
134	C₄²×C₆₁	C₂²×C₄	1	16	yes	—
135	C₂³×C₆₁	—	2	4	no	—
136	C₂³×C₆₁	—	2	2	no	—
137	C₂³×C₆₁	—	2	2	no	—
138	C₂³×C₆₁	—	2	8	no	—
139	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
140	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
141	C₂³×C₆₁	C₂×#41	1	2	yes	—
142	C₂³×C₆₁	C₂×#41	1	2	yes	—
143	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
144	Q₈×C₆₁	—	2	8	no	—
145	D₄×C₆₁	—	2	16	no	—
146	D₄×C₆₁	—	2	8	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	8	no	—
150	C₂×C₄×C₆₁	—	2	4	no	—
151	C₂×C₄×C₆₁	—	2	4	no	—
152	C₂×C₄×C₆₁	—	2	16	no	—
153	C₂×C₄×C₆₁	—	2	8	no	—
154	C₂×C₄×C₆₁	—	2	8	no	—
155	C₂×C₄×C₆₁	—	2	8	no	—
156	C₂×C₄×C₆₁	—	2	16	no	—
157	C₂×C₄×C₆₁	—	2	8	no	—
158	C₂×C₄×C₆₁	—	4	8	no	—
159	C₂×C₄×C₆₁	—	4	16	no	—
160	C₂×C₄×C₆₁	—	8	8	no	—
161	C₂×C₄×C₆₁	#117	1	16	yes	—
162	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
163	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
164	C₂×C₄×C₆₁	C₂³×C₄	1	8	yes	—
165	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
166	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
167	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
168	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
169	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
170	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
171	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
172	#34189	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₆₁	—	2	4	no	—
174	C₂²×C₆₁	—	2	4	no	—
175	C₂²×C₆₁	—	2	4	no	—
176	C₂²×C₆₁	—	2	4	no	—
177	C₂²×C₆₁	—	2	8	no	—
178	C₂²×C₆₁	—	4	4	no	—
179	C₂²×C₆₁	—	4	4	no	—
180	C₂²×C₆₁	C₂×#117	1	4	yes	—
181	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
182	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
183	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
184	C₂²×C₆₁	#585	1	4	yes	—
185	C₄×C₆₁	—	2	4	no	—
186	C₄×C₆₁	—	2	4	no	—
187	C₄×C₆₁	—	2	8	no	—
188	C₄×C₆₁	—	2	4	no	—
189	C₄×C₆₁	—	4	8	no	—
190	C₄×C₆₁	—	4	8	no	—
191	C₄×C₆₁	C₂×#117	1	4	yes	—
192	C₄×C₆₁	C₂×#117	1	4	yes	—
193	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic
194	#2357	C₂×C₆₁	1	4	yes	complemented
195	#2356	C₂×C₆₁	1	4	yes	complemented
196	#2353	C₂×C₆₁	1	8	yes	complemented
197	#2314	C₂×C₆₁	1	4	yes	complemented
198	#2311	C₂×C₆₁	1	2	yes	—
199	#2285	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#2283	C₂×C₆₁	1	4	yes	complemented
201	C₂×#382	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#2274	C₂×C₆₁	1	2	yes	complemented
203	C₂×C₆₁	—	2	4	no	—
204	C₂×C₆₁	—	4	4	no	—
205	C₂×C₆₁	C₂²×#117	1	1	yes	characteristic
206	C₂×C₆₁	#3428	1	2	yes	—
207	C₂×C₆₁	#3510	1	2	yes	—
208	C₂×C₆₁	#3512	1	2	yes	—
209	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
210	C₄×#41	C₄×C₆₁	1	16	yes	complemented
211	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
212	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
213	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
214	C₂×#117	C₂²×C₆₁	1	2	yes	—
215	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
216	C₂×#117	C₂²×C₆₁	1	2	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
218	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
219	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
220	#391	C₂²×C₆₁	1	4	yes	—
221	#390	C₂²×C₆₁	1	4	yes	—
222	#388	C₂²×C₆₁	1	16	yes	—
223	#387	C₂²×C₆₁	1	16	yes	—
224	#386	C₂²×C₆₁	1	8	yes	—
225	#384	C₂²×C₆₁	1	2	yes	—
226	#383	C₂²×C₆₁	1	8	yes	—
227	#382	C₂²×C₆₁	1	2	yes	—
228	#382	C₂²×C₆₁	1	4	yes	—
229	#382	C₂²×C₆₁	1	2	yes	—
230	#382	C₂²×C₆₁	1	2	yes	—
231	#381	C₂²×C₆₁	1	8	yes	—
232	#380	C₂²×C₆₁	1	8	yes	—
233	#380	C₂²×C₆₁	1	4	yes	—
234	C₄×C₄⋊C₄	C₂²×C₆₁	1	8	yes	—
235	C₄×C₄⋊C₄	C₂²×C₆₁	1	8	yes	—
236	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
237	C₄×C₂²⋊C₄	C₂²×C₆₁	1	8	yes	—
238	C₄×C₂²⋊C₄	C₂²×C₆₁	1	8	yes	—
239	#376	C₂²×C₆₁	1	8	yes	—
240	C₂×#95	C₂²×C₆₁	1	4	yes	—
241	C₆₁	#34189	1	1	yes	characteristic, direct product factor, Sylow
242	C₂×#41	—	2	4	no	—
243	C₂×#41	—	2	4	no	—
244	C₂×#41	C₂×C₄×C₆₁	1	8	yes	—
245	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
246	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
247	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
249	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
250	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
251	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
252	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
253	C₄×Q₈	C₂×C₄×C₆₁	1	16	yes	complemented
254	C₄×D₄	C₂×C₄×C₆₁	1	32	yes	—
255	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	complemented
256	#117	—	2	8	no	—
257	#117	C₂×C₄×C₆₁	1	8	yes	—
258	#117	C₂×C₄×C₆₁	1	16	yes	complemented
259	C₂×C₄⋊C₄	—	2	8	no	—
260	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
263	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
264	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₆₁	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
270	C₂×C₄²	C₂×C₄×C₆₁	1	8	yes	—
271	C₂×C₄²	C₂×C₄×C₆₁	1	16	yes	complemented
272	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
273	C₂×C₄²	C₂³×C₆₁	1	16	yes	—
274	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
275	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
277	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
278	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
279	#95	C₂³×C₆₁	1	8	yes	—
280	#95	C₂³×C₆₁	1	8	yes	—
281	#95	C₂³×C₆₁	1	4	yes	—
282	#95	C₂³×C₆₁	1	16	yes	—
283	#95	C₂³×C₆₁	1	4	yes	—
284	#95	C₂³×C₆₁	1	16	yes	—
285	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
286	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
287	#41	—	2	32	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
296	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	4	8	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	—	4	8	no	—
303	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
304	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
305	C₂²×C₄	C₂²×C₄×C₆₁	1	16	yes	—
306	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
307	C₂²×C₄	#41×C₆₁	1	4	yes	—
308	C₂²×C₄	#41×C₆₁	1	4	yes	—
309	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
310	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
311	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	4	8	no	—
321	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
322	C₄⋊C₄	C₂²×C₄×C₆₁	1	16	yes	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	4	16	no	—
325	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
326	C₂²⋊C₄	C₂²×C₄×C₆₁	1	16	yes	—
327	C₄²	—	2	8	no	—
328	C₄²	—	4	16	no	—
329	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
330	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
331	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
332	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
333	C₄²	C₂²×C₄×C₆₁	1	16	yes	—
334	C₂³	—	2	4	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	8	no	—
338	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
339	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
340	C₂³	C₂×#41×C₆₁	1	2	yes	—
341	C₂³	C₂×#41×C₆₁	1	2	yes	—
342	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
343	Q₈	—	2	8	no	—
344	D₄	—	2	16	no	—
345	D₄	—	2	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	16	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	16	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	16	no	—
359	C₂×C₄	—	8	8	no	—
360	C₂×C₄	#117×C₆₁	1	16	yes	—
361	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
362	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
363	C₂×C₄	C₂³×C₄×C₆₁	1	8	yes	—
364	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
365	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
366	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
367	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
368	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
369	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
370	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
371	C₂²	—	2	4	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₂×#117×C₆₁	1	4	yes	—
379	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
380	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
381	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
382	C₂²	C₆₁×#585	1	4	yes	—
383	C₄	—	2	4	no	—
384	C₄	—	2	4	no	—
385	C₄	—	2	8	no	—
386	C₄	—	2	4	no	—
387	C₄	—	4	8	no	—
388	C₄	—	4	8	no	—
389	C₄	C₂×#117×C₆₁	1	4	yes	—
390	C₄	C₂×#117×C₆₁	1	4	yes	—
391	C₂	—	2	4	no	—
392	C₂	—	4	4	no	—
393	C₂	C₂²×#117×C₆₁	1	1	yes	characteristic
394	C₂	C₆₁×#3428	1	2	yes	—
395	C₂	C₆₁×#3510	1	2	yes	—
396	C₂	C₆₁×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2357	C₂	semidirect
3. C₆₁×#2356	C₂	semidirect
4. C₆₁×#2353	C₂	semidirect
5. C₆₁×#2314	C₂	semidirect
7. C₆₁×#2285	C₂	semidirect
8. C₆₁×#2283	C₂	semidirect
9. C₂×C₆₁×#382	C₂	semidirect
10. C₆₁×#2274	C₂	semidirect
12. C₄×#41×C₆₁	C₄	semidirect
54. C₄×Q₈×C₆₁	C₂×C₄	semidirect
56. C₄×D₄×C₆₁	C₂×C₄	semidirect
59. #117×C₆₁	C₂×C₄	semidirect
72. C₂×C₄²×C₆₁	C₂×C₄	semidirect
172. #34189	C₆₁	direct (N × H)
194. #2357	C₂×C₆₁	semidirect
195. #2356	C₂×C₆₁	semidirect
196. #2353	C₂×C₆₁	semidirect
197. #2314	C₂×C₆₁	semidirect
199. #2285	C₂×C₆₁	semidirect
200. #2283	C₂×C₆₁	semidirect
201. C₂×#382	C₂×C₆₁	semidirect
202. #2274	C₂×C₆₁	semidirect
210. C₄×#41	C₄×C₆₁	semidirect
241. C₆₁	#34189	direct (N × H)
253. C₄×Q₈	C₂×C₄×C₆₁	semidirect
255. C₄×D₄	C₂×C₄×C₆₁	semidirect
258. #117	C₂×C₄×C₆₁	semidirect
271. C₂×C₄²	C₂×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₆₁	2
C₆₁×#2357	2
C₆₁×#2356	2
C₆₁×#2353	2
C₆₁×#2314	2
C₆₁×#2311	2
C₆₁×#2285	2
C₆₁×#2283	2
C₂×C₆₁×#382	2
C₆₁×#2274	2
#34189	61

Subgroups — C61×#34189 #29537622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34189 #29537622