Subgroups — C₆₁×#34953 #29538386

Order 15616.

2402 conjugacy classes of subgroups.

The subgroup lattice has 462 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	C₂²×C₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2584	C₂	1	4	yes	maximal, complemented
4	C₆₁×#2583	C₂	1	4	yes	maximal
5	C₆₁×#2567	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2546	C₂	1	2	yes	maximal, complemented
7	C₆₁×#2502	C₂	1	2	yes	maximal
8	C₆₁×#2434	C₂	1	2	yes	maximal
9	C₆₁×#2399	C₂	1	4	yes	maximal, complemented
10	C₄×C₄⋊Q₈×C₆₁	C₂	1	4	yes	maximal, complemented
11	C₆₁×#2296	C₂	1	4	yes	maximal
12	C₄×#117×C₆₁	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#533	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	4	yes	—
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#125×C₆₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₆₁	—	2	8	no	—
22	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
28	C₂×#117×C₆₁	C₂²	1	2	yes	—
29	C₂×#117×C₆₁	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
33	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#398	C₂²	1	8	yes	—
35	C₆₁×#398	C₂²	1	8	yes	—
36	C₆₁×#395	C₂²	1	8	yes	—
37	C₆₁×#395	C₂²	1	8	yes	—
38	C₆₁×#391	C₂²	1	4	yes	—
39	C₆₁×#391	C₂²	1	4	yes	—
40	C₆₁×#389	C₂²	1	8	yes	—
41	C₆₁×#389	C₂²	1	8	yes	—
42	C₆₁×#389	C₂²	1	16	yes	—
43	C₆₁×#385	C₂²	1	8	yes	—
44	C₆₁×#385	C₂²	1	8	yes	—
45	C₆₁×#384	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
48	C₄×C₄⋊C₄×C₆₁	C₂²	1	16	yes	—
49	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
50	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
51	C₆₁×#376	C₂²	1	2	yes	—
52	C₄³×C₆₁	C₂²	1	2	yes	—
53	C₂²×Q₈×C₆₁	—	2	8	no	—
54	C₂²×Q₈×C₆₁	—	2	4	no	—
55	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
56	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
59	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
60	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	—	2	16	no	—
65	C₄⋊Q₈×C₆₁	—	2	4	no	—
66	C₄⋊Q₈×C₆₁	—	2	4	no	—
67	#125×C₆₁	—	2	8	no	—
68	C₂²⋊Q₈×C₆₁	—	2	8	no	—
69	C₂²⋊Q₈×C₆₁	—	2	8	no	—
70	C₄×Q₈×C₆₁	—	2	8	no	—
71	C₄×Q₈×C₆₁	—	2	8	no	—
72	C₄×Q₈×C₆₁	—	2	8	no	—
73	C₄×Q₈×C₆₁	—	2	8	no	—
74	C₄×Q₈×C₆₁	—	2	8	no	—
75	C₄×Q₈×C₆₁	—	2	8	no	—
76	#117×C₆₁	—	2	8	no	—
77	#117×C₆₁	Q₈	1	16	yes	complemented
78	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
95	C₂×C₄²×C₆₁	—	2	8	no	—
96	C₂×C₄²×C₆₁	D₄	1	8	yes	—
97	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
98	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
99	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
100	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
101	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
107	#95×C₆₁	C₂³	1	4	yes	—
108	#95×C₆₁	C₂³	1	4	yes	—
109	#95×C₆₁	C₂³	1	16	yes	—
110	#95×C₆₁	C₂³	1	16	yes	—
111	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
112	C₂×Q₈×C₆₁	—	2	32	no	—
113	C₂×Q₈×C₆₁	—	2	4	no	—
114	C₂×Q₈×C₆₁	—	2	4	no	—
115	C₂×Q₈×C₆₁	—	2	4	no	—
116	C₂×Q₈×C₆₁	—	2	4	no	—
117	C₂×Q₈×C₆₁	—	2	8	no	—
118	C₂×Q₈×C₆₁	—	2	4	no	—
119	C₂×Q₈×C₆₁	—	2	8	no	—
120	C₂×Q₈×C₆₁	—	4	4	no	—
121	C₂×Q₈×C₆₁	#41	1	8	yes	—
122	C₂²×C₄×C₆₁	—	2	4	no	—
123	C₂²×C₄×C₆₁	—	2	8	no	—
124	C₂²×C₄×C₆₁	—	2	4	no	—
125	C₂²×C₄×C₆₁	—	2	4	no	—
126	C₂²×C₄×C₆₁	—	4	2	no	—
127	C₂²×C₄×C₆₁	—	4	4	no	—
128	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₆₁	C₂×Q₈	1	8	yes	—
132	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
139	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
143	C₄⋊C₄×C₆₁	—	2	8	no	—
144	C₄⋊C₄×C₆₁	—	2	8	no	—
145	C₄⋊C₄×C₆₁	—	2	4	no	—
146	C₄⋊C₄×C₆₁	—	2	4	no	—
147	C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₄⋊C₄×C₆₁	—	2	4	no	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	—	2	8	no	—
151	C₄⋊C₄×C₆₁	—	2	4	no	—
152	C₄⋊C₄×C₆₁	—	2	4	no	—
153	C₄⋊C₄×C₆₁	—	2	32	no	—
154	C₄⋊C₄×C₆₁	—	4	16	no	—
155	C₄⋊C₄×C₆₁	C₂×Q₈	1	16	yes	complemented
156	C₂²⋊C₄×C₆₁	—	2	8	no	—
157	C₂²⋊C₄×C₆₁	C₂×Q₈	1	16	yes	—
158	C₄²×C₆₁	—	2	8	no	—
159	C₄²×C₆₁	—	2	8	no	—
160	C₄²×C₆₁	—	2	8	no	—
161	C₄²×C₆₁	—	2	8	no	—
162	C₄²×C₆₁	—	4	4	no	—
163	C₄²×C₆₁	C₂×D₄	1	4	yes	—
164	C₄²×C₆₁	C₂×D₄	1	4	yes	—
165	C₄²×C₆₁	C₂×D₄	1	4	yes	—
166	C₄²×C₆₁	C₂×D₄	1	4	yes	—
167	C₄²×C₆₁	C₂×Q₈	1	16	yes	complemented
168	C₂³×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	2	no	—
170	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
171	C₂³×C₆₁	C₂²×Q₈	1	4	yes	—
172	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
173	Q₈×C₆₁	—	2	16	no	—
174	Q₈×C₆₁	—	2	16	no	—
175	Q₈×C₆₁	—	4	8	no	—
176	Q₈×C₆₁	—	4	8	no	—
177	C₂×C₄×C₆₁	—	2	16	no	—
178	C₂×C₄×C₆₁	—	2	4	no	—
179	C₂×C₄×C₆₁	—	2	8	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	4	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	8	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	8	no	—
186	C₂×C₄×C₆₁	—	2	4	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	2	4	no	—
189	C₂×C₄×C₆₁	—	2	8	no	—
190	C₂×C₄×C₆₁	—	2	8	no	—
191	C₂×C₄×C₆₁	—	2	8	no	—
192	C₂×C₄×C₆₁	—	4	4	no	—
193	C₂×C₄×C₆₁	—	4	8	no	—
194	C₂×C₄×C₆₁	C₄⋊Q₈	1	16	yes	complemented
195	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₆₁	C₂²×Q₈	1	16	yes	—
202	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
203	C₂×C₄×C₆₁	C₂²×Q₈	1	4	yes	—
204	C₂×C₄×C₆₁	C₂×#41	1	8	yes	—
205	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
206	#34953	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₆₁	—	2	2	no	—
208	C₂²×C₆₁	—	2	2	no	—
209	C₂²×C₆₁	—	2	8	no	—
210	C₂²×C₆₁	C₂×C₄⋊Q₈	1	4	yes	—
211	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
212	C₂²×C₆₁	C₂³×Q₈	1	2	yes	—
213	C₂²×C₆₁	C₂²×#41	1	2	yes	—
214	C₂²×C₆₁	#585	1	2	yes	—
215	C₄×C₆₁	—	2	2	no	—
216	C₄×C₆₁	—	2	8	no	—
217	C₄×C₆₁	—	2	2	no	—
218	C₄×C₆₁	—	2	2	no	—
219	C₄×C₆₁	—	2	16	no	—
220	C₄×C₆₁	—	4	4	no	—
221	C₄×C₆₁	—	4	4	no	—
222	C₄×C₆₁	—	4	4	no	—
223	C₄×C₆₁	#525	1	4	yes	—
224	C₄×C₆₁	C₂×C₄⋊Q₈	1	4	yes	—
225	C₄×C₆₁	C₂×C₄⋊Q₈	1	4	yes	—
226	C₂×#533	C₂×C₆₁	1	1	yes	characteristic
227	C₂²×C₄×Q₈	C₂×C₆₁	1	1	yes	characteristic
228	#2584	C₂×C₆₁	1	4	yes	complemented
229	#2583	C₂×C₆₁	1	4	yes	—
230	#2567	C₂×C₆₁	1	2	yes	complemented
231	#2546	C₂×C₆₁	1	2	yes	complemented
232	#2502	C₂×C₆₁	1	2	yes	—
233	#2434	C₂×C₆₁	1	2	yes	—
234	#2399	C₂×C₆₁	1	4	yes	complemented
235	C₄×C₄⋊Q₈	C₂×C₆₁	1	4	yes	complemented
236	#2296	C₂×C₆₁	1	4	yes	—
237	C₄×#117	C₂×C₆₁	1	1	yes	characteristic
238	C₂×C₆₁	—	2	4	no	—
239	C₂×C₆₁	C₂×#525	1	1	yes	characteristic
240	C₂×C₆₁	C₂²×C₄⋊Q₈	1	1	yes	characteristic
241	C₂×C₆₁	#3449	1	1	yes	characteristic
242	C₂×C₆₁	Q₈×#41	1	4	yes	—
243	C₂³×Q₈	C₂²×C₆₁	1	1	yes	characteristic
244	#533	—	2	8	no	—
245	C₂×C₄⋊Q₈	C₂²×C₆₁	1	4	yes	—
246	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
247	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
248	C₂×#125	C₂²×C₆₁	1	2	yes	—
249	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
250	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
251	C₂×C₄×Q₈	—	2	8	no	—
252	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
253	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
255	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
256	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
257	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
258	C₂×#117	C₂²×C₆₁	1	2	yes	—
259	C₂×#117	C₂²×C₆₁	1	2	yes	—
260	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
261	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
262	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
263	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
264	#398	C₂²×C₆₁	1	8	yes	—
265	#398	C₂²×C₆₁	1	8	yes	—
266	#395	C₂²×C₆₁	1	8	yes	—
267	#395	C₂²×C₆₁	1	8	yes	—
268	#391	C₂²×C₆₁	1	4	yes	—
269	#391	C₂²×C₆₁	1	4	yes	—
270	#389	C₂²×C₆₁	1	16	yes	—
271	#389	C₂²×C₆₁	1	8	yes	—
272	#389	C₂²×C₆₁	1	8	yes	—
273	#385	C₂²×C₆₁	1	8	yes	—
274	#385	C₂²×C₆₁	1	8	yes	—
275	#384	C₂²×C₆₁	1	4	yes	—
276	C₄×C₄⋊C₄	C₂²×C₆₁	1	16	yes	—
277	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
278	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
279	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
280	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
281	#376	C₂²×C₆₁	1	2	yes	—
282	C₄³	C₂²×C₆₁	1	2	yes	—
283	C₆₁	#34953	1	1	yes	characteristic, direct product factor, Sylow
284	C₂²×Q₈	—	2	8	no	—
285	C₂²×Q₈	—	2	4	no	—
286	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
287	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
288	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
289	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
290	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
291	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
293	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
295	C₄⋊Q₈	—	2	16	no	—
296	C₄⋊Q₈	—	2	4	no	—
297	C₄⋊Q₈	—	2	4	no	—
298	#125	—	2	8	no	—
299	C₂²⋊Q₈	—	2	8	no	—
300	C₂²⋊Q₈	—	2	8	no	—
301	C₄×Q₈	—	2	8	no	—
302	C₄×Q₈	—	2	8	no	—
303	C₄×Q₈	—	2	8	no	—
304	C₄×Q₈	—	2	8	no	—
305	C₄×Q₈	—	2	8	no	—
306	C₄×Q₈	—	2	8	no	—
307	#117	—	2	8	no	—
308	#117	Q₈×C₆₁	1	16	yes	complemented
309	C₂×C₄⋊C₄	—	2	8	no	—
310	C₂×C₄⋊C₄	—	2	4	no	—
311	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
322	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
323	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
324	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
325	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
326	C₂×C₄²	—	2	8	no	—
327	C₂×C₄²	D₄×C₆₁	1	8	yes	—
328	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
329	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
330	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
331	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
332	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
333	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
338	#95	C₂³×C₆₁	1	4	yes	—
339	#95	C₂³×C₆₁	1	4	yes	—
340	#95	C₂³×C₆₁	1	16	yes	—
341	#95	C₂³×C₆₁	1	16	yes	—
342	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
343	C₂×Q₈	—	2	32	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	4	no	—
346	C₂×Q₈	—	2	4	no	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	2	8	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	8	no	—
351	C₂×Q₈	—	4	4	no	—
352	C₂×Q₈	#41×C₆₁	1	8	yes	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
360	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
361	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
362	C₂²×C₄	C₂×Q₈×C₆₁	1	8	yes	—
363	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
370	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
371	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
372	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
373	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	32	no	—
385	C₄⋊C₄	—	4	16	no	—
386	C₄⋊C₄	C₂×Q₈×C₆₁	1	16	yes	complemented
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	C₂×Q₈×C₆₁	1	16	yes	—
389	C₄²	—	2	8	no	—
390	C₄²	—	2	8	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	2	8	no	—
393	C₄²	—	4	4	no	—
394	C₄²	C₂×D₄×C₆₁	1	4	yes	—
395	C₄²	C₂×D₄×C₆₁	1	4	yes	—
396	C₄²	C₂×D₄×C₆₁	1	4	yes	—
397	C₄²	C₂×D₄×C₆₁	1	4	yes	—
398	C₄²	C₂×Q₈×C₆₁	1	16	yes	complemented
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
402	C₂³	C₂²×Q₈×C₆₁	1	4	yes	—
403	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
404	Q₈	—	2	16	no	—
405	Q₈	—	2	16	no	—
406	Q₈	—	4	8	no	—
407	Q₈	—	4	8	no	—
408	C₂×C₄	—	2	16	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	8	no	—
425	C₂×C₄	C₄⋊Q₈×C₆₁	1	16	yes	complemented
426	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
431	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
432	C₂×C₄	C₂²×Q₈×C₆₁	1	16	yes	—
433	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
434	C₂×C₄	C₂²×Q₈×C₆₁	1	4	yes	—
435	C₂×C₄	C₂×#41×C₆₁	1	8	yes	—
436	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	8	no	—
440	C₂²	C₂×C₄⋊Q₈×C₆₁	1	4	yes	—
441	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
442	C₂²	C₂³×Q₈×C₆₁	1	2	yes	—
443	C₂²	C₂²×#41×C₆₁	1	2	yes	—
444	C₂²	C₆₁×#585	1	2	yes	—
445	C₄	—	2	2	no	—
446	C₄	—	2	8	no	—
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	16	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	4	no	—
453	C₄	C₆₁×#525	1	4	yes	—
454	C₄	C₂×C₄⋊Q₈×C₆₁	1	4	yes	—
455	C₄	C₂×C₄⋊Q₈×C₆₁	1	4	yes	—
456	C₂	—	2	4	no	—
457	C₂	C₂×C₆₁×#525	1	1	yes	characteristic
458	C₂	C₂²×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
459	C₂	C₆₁×#3449	1	1	yes	characteristic
460	C₂	Q₈×#41×C₆₁	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂⁵
prime radical	C₂⁴×C₆₁	C₂⁴
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
3. C₆₁×#2584	C₂	semidirect
5. C₆₁×#2567	C₂	semidirect
6. C₆₁×#2546	C₂	semidirect
9. C₆₁×#2399	C₂	semidirect
10. C₄×C₄⋊Q₈×C₆₁	C₂	semidirect
77. #117×C₆₁	Q₈	semidirect
155. C₄⋊C₄×C₆₁	C₂×Q₈	semidirect
167. C₄²×C₆₁	C₂×Q₈	semidirect
194. C₂×C₄×C₆₁	C₄⋊Q₈	semidirect
206. #34953	C₆₁	direct (N × H)
228. #2584	C₂×C₆₁	semidirect
230. #2567	C₂×C₆₁	semidirect
231. #2546	C₂×C₆₁	semidirect
234. #2399	C₂×C₆₁	semidirect
235. C₄×C₄⋊Q₈	C₂×C₆₁	semidirect
283. C₆₁	#34953	direct (N × H)
308. #117	Q₈×C₆₁	semidirect
386. C₄⋊C₄	C₂×Q₈×C₆₁	semidirect
398. C₄²	C₂×Q₈×C₆₁	semidirect
425. 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
C₂²×C₄×Q₈×C₆₁	2
C₆₁×#2584	2
C₆₁×#2583	2
C₆₁×#2567	2
C₆₁×#2546	2
C₆₁×#2502	2
C₆₁×#2434	2
C₆₁×#2399	2
C₄×C₄⋊Q₈×C₆₁	2
C₆₁×#2296	2
C₄×#117×C₆₁	2
#34953	61

Subgroups — C61×#34953 #29538386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34953 #29538386