Subgroups — C₈×M₁₆×D₆₁ #29645583

Order 15616.

1046 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	#431×D₆₁	C₂	1	1	yes	maximal, characteristic
2	C₄×M₁₆×D₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	#21444100	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×#11758194	C₂	1	1	yes	maximal, characteristic, complemented
6	#21444098	C₂	1	2	yes	maximal, complemented
7	M₁₆×#92418	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#11758189	C₂	1	2	yes	maximal, complemented
9	#322×D₆₁	C₂	1	2	yes	maximal, complemented
10	C₈²×D₆₁	C₂	1	2	yes	maximal, complemented
11	C₈×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₆₁	C₄	1	2	yes	—
13	C₂²×C₈×D₆₁	C₄	1	2	yes	—
14	C₂×C₄²×D₆₁	C₂²	1	1	yes	characteristic
15	#16839815	C₂²	1	1	yes	characteristic
16	#16839814	C₄	1	2	yes	—
17	#16839813	C₂²	1	2	yes	—
18	#16839812	C₄	1	2	yes	—
19	C₄⋊C₈×D₆₁	C₄	1	2	yes	—
20	C₂²⋊C₈×D₆₁	C₄	1	2	yes	—
21	C₄×#11758194	C₂²	1	1	yes	characteristic
22	#16839714	C₄	1	2	yes	—
23	M₁₆×Dic₆₁	C₄	1	2	yes	—
24	C₄×#11758189	C₂²	1	2	yes	—
25	#97×D₆₁	C₄	1	2	yes	—
26	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₆₁	C₄	1	2	yes	—
28	C₄×C₈×D₆₁	C₄	1	2	yes	—
29	C₄×C₈×D₆₁	C₄	1	2	yes	—
30	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₆₁	C₂²	1	2	yes	—
33	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₆₁	C₂²	1	2	yes	—
36	#16839484	C₂²	1	2	yes	complemented
37	#16839484	C₂²	1	2	yes	complemented
38	#16839483	C₂²	1	2	yes	complemented
39	C₈×#92418	C₂²	1	2	yes	complemented
40	C₈×#92418	C₂²	1	2	yes	complemented
41	C₈×#92418	C₂²	1	2	yes	complemented
42	C₆₁×#431	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#322	C₂²	1	2	yes	complemented
46	C₈²×C₆₁	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂×#11758194	C₂×C₄	1	2	yes	—
51	C₂×#11758189	C₂×C₄	1	4	yes	—
52	M₁₆×D₆₁	C₈	1	16	yes	direct product factor
53	C₂²×#92418	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₆₁	—	2	8	no	—
55	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
58	C₂×C₈×D₆₁	C₂×C₄	1	4	yes	—
59	C₂×C₈×D₆₁	C₂×C₄	1	4	yes	—
60	C₂×C₈×D₆₁	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₆₁	C₂³	1	1	yes	characteristic
71	C₄²×D₆₁	C₂³	1	1	yes	characteristic
72	C₄⋊#92418	C₂×C₄	1	2	yes	—
73	#14519706	C₂×C₄	1	4	yes	—
74	C₂²⋊#92418	C₂×C₄	1	2	yes	—
75	#14519689	C₂×C₄	1	4	yes	—
76	#14519688	C₂×C₄	1	2	yes	—
77	#14519687	C₂×C₄	1	4	yes	—
78	C₄×#92418	C₂×C₄	1	2	yes	—
79	C₄×#92418	C₂³	1	1	yes	characteristic
80	C₄×#92418	C₂³	1	1	yes	characteristic
81	C₄×#92418	C₂³	1	2	yes	—
82	C₄×#92418	C₂³	1	2	yes	—
83	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
84	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
85	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
86	C₈×Dic₆₁	C₂×C₄	1	2	yes	—
87	C₈×Dic₆₁	C₂×C₄	1	4	yes	—
88	C₈×Dic₆₁	C₂×C₄	1	4	yes	—
89	C₂×M₁₆×C₆₁	C₂×C₄	1	2	yes	—
90	C₂²×C₈×C₆₁	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
93	C₂²⋊C₈×C₆₁	C₂×C₄	1	2	yes	—
94	#97×C₆₁	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₆₁	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₆₁	C₂³	1	2	yes	—
98	C₄×C₈×C₆₁	C₂³	1	2	yes	—
99	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₂³×D₆₁	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₆₁	C₄²	1	1	yes	characteristic
105	C₂²×Dic₆₁	C₄²	1	1	yes	characteristic
106	C₂²×Dic₆₁	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₆₁	—	2	4	no	—
108	C₂×C₄×D₆₁	—	2	4	no	—
109	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
113	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
114	C₂×C₄×D₆₁	C₄²	1	1	yes	characteristic
115	C₂×C₄×D₆₁	C₂×C₈	1	8	yes	—
116	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
122	M₁₆×C₆₁	C₂×C₈	1	8	yes	complemented
123	C₂×C₈×C₆₁	—	2	4	no	—
124	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
128	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
132	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
133	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
134	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
135	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
136	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
137	C₄×Dic₆₁	C₄²	1	1	yes	characteristic
138	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
144	#11758194	C₂×C₈	1	8	yes	complemented
145	C₂×#92418	—	2	4	no	—
146	C₂×#92418	C₂²×C₄	1	2	yes	—
147	C₂×#92418	C₂²×C₄	1	4	yes	—
148	C₂×#92418	C₂²×C₄	1	4	yes	—
149	C₂×#92418	C₂²×C₄	1	2	yes	—
150	#11758189	C₂×C₈	1	16	yes	complemented
151	C₈×D₆₁	—	2	4	no	—
152	C₈×D₆₁	—	2	8	no	—
153	C₈×D₆₁	—	2	4	no	—
154	C₈×D₆₁	—	2	4	no	—
155	C₈×D₆₁	C₂×C₈	1	16	yes	complemented
156	C₈×D₆₁	M₁₆	1	8	yes	direct product factor
157	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
158	C₂²×D₆₁	—	2	2	no	—
159	C₂²×D₆₁	—	2	2	no	—
160	C₂²×D₆₁	C₄×C₈	1	4	yes	—
161	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
162	C₂²×D₆₁	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₆₁	C₂²×C₈	1	4	yes	—
169	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
172	C₂×Dic₆₁	—	2	2	no	—
173	C₂×Dic₆₁	—	2	2	no	—
174	C₂×Dic₆₁	C₄×C₈	1	4	yes	—
175	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
176	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
177	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
178	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
179	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
180	C₂×Dic₆₁	C₂×C₄²	1	1	yes	characteristic
181	C₄×D₆₁	—	2	2	no	—
182	C₄×D₆₁	—	2	2	no	—
183	C₄×D₆₁	—	2	2	no	—
184	C₄×D₆₁	—	2	2	no	—
185	C₄×D₆₁	—	2	2	no	—
186	C₄×D₆₁	—	2	2	no	—
187	C₄×D₆₁	C₄×C₈	1	4	yes	—
188	C₄×D₆₁	C₄×C₈	1	4	yes	—
189	C₄×D₆₁	C₂²×C₈	1	4	yes	—
190	C₄×D₆₁	C₂²×C₈	1	4	yes	—
191	C₄×D₆₁	C₂×M₁₆	1	4	yes	—
192	C₄×D₆₁	#131	1	4	yes	—
193	C₈×C₆₁	—	2	2	no	—
194	C₈×C₆₁	—	2	4	no	—
195	C₈×C₆₁	C₂²×C₈	1	8	yes	complemented
196	C₈×C₆₁	C₂×M₁₆	1	4	yes	complemented
197	#92418	—	2	2	no	—
198	#92418	—	2	4	no	—
199	#92418	C₂²×C₈	1	8	yes	complemented
200	#92418	C₂×M₁₆	1	4	yes	complemented
201	C₂×C₈×M₁₆	—	61	1	no	maximal, Sylow
202	C₂²×C₆₁	—	2	1	no	—
203	C₂²×C₆₁	—	2	1	no	—
204	C₂²×C₆₁	C₂×C₄×C₈	1	2	yes	—
205	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
206	C₂×D₆₁	—	2	1	no	—
207	C₂×D₆₁	—	2	1	no	—
208	C₂×D₆₁	—	2	8	no	—
209	C₂×D₆₁	C₂×C₄×C₈	1	2	yes	—
210	C₂×D₆₁	C₂×C₄×C₈	1	2	yes	—
211	C₂×D₆₁	C₄×M₁₆	1	2	yes	—
212	C₂×D₆₁	#405	1	2	yes	—
213	C₄×C₆₁	—	2	1	no	—
214	C₄×C₆₁	—	2	1	no	—
215	C₄×C₆₁	C₂×C₄×C₈	1	2	yes	—
216	C₄×C₆₁	C₂³×C₈	1	2	yes	—
217	C₄×C₆₁	C₂²×M₁₆	1	2	yes	—
218	C₄×C₆₁	C₂×#131	1	2	yes	—
219	Dic₆₁	—	2	1	no	—
220	Dic₆₁	—	2	1	no	—
221	Dic₆₁	C₂×C₄×C₈	1	2	yes	—
222	Dic₆₁	C₂×C₄×C₈	1	2	yes	—
223	Dic₆₁	C₄×M₁₆	1	2	yes	—
224	Dic₆₁	#405	1	2	yes	—
225	C₂×#431	—	61	1	no	—
226	C₂×C₄×M₁₆	—	61	1	no	—
227	C₂²×C₄×C₈	—	61	1	no	—
228	C₈×M₁₆	—	61	1	no	—
229	C₈×M₁₆	—	61	1	no	—
230	C₈×M₁₆	—	61	1	no	—
231	C₈×M₁₆	—	61	2	no	—
232	C₈×M₁₆	—	61	2	no	—
233	C₈×M₁₆	D₆₁	1	1	yes	characteristic, direct product factor
234	C₂×#322	—	61	2	no	—
235	C₂×C₈²	—	61	2	no	—
236	C₂×C₆₁	—	2	2	no	—
237	C₂×C₆₁	C₂²×C₄×C₈	1	1	yes	characteristic
238	C₂×C₆₁	C₂×C₄×M₁₆	1	1	yes	characteristic
239	C₂×C₆₁	C₂×#405	1	1	yes	characteristic
240	D₆₁	—	2	2	no	—
241	D₆₁	C₈×M₁₆	1	4	yes	direct product factor
242	C₂²×M₁₆	—	61	2	no	—
243	C₂³×C₈	—	61	2	no	—
244	C₂²×C₄²	—	61	1	no	—
245	#431	—	61	1	no	—
246	#431	—	61	2	no	—
247	#431	—	61	2	no	—
248	#431	—	61	2	no	—
249	#431	C₂×D₆₁	1	1	yes	characteristic
250	C₂×C₄⋊C₈	—	61	2	no	—
251	C₂×C₂²⋊C₈	—	61	2	no	—
252	C₄×M₁₆	—	61	2	no	—
253	C₄×M₁₆	—	61	1	no	—
254	C₄×M₁₆	—	61	2	no	—
255	C₄×M₁₆	—	61	2	no	—
256	C₄×M₁₆	C₂×D₆₁	1	1	yes	characteristic
257	C₂×#97	—	61	2	no	—
258	C₂×C₄×C₈	—	61	2	no	—
259	C₂×C₄×C₈	—	61	1	no	—
260	C₂×C₄×C₈	—	61	2	no	—
261	C₂×C₄×C₈	—	61	2	no	—
262	C₂×C₄×C₈	—	61	1	no	—
263	C₂×C₄×C₈	—	61	1	no	—
264	C₂×C₄×C₈	—	61	2	no	—
265	C₂×C₄×C₈	—	61	2	no	—
266	C₂×C₄×C₈	—	61	1	no	—
267	C₂×C₄×C₈	—	61	1	no	—
268	C₂×C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
269	#322	—	61	2	no	—
270	#322	—	61	2	no	—
271	#322	—	61	2	no	—
272	#322	C₂×D₆₁	1	2	yes	complemented
273	C₈²	—	61	2	no	—
274	C₈²	—	61	2	no	—
275	C₈²	—	61	2	no	—
276	C₈²	C₂×D₆₁	1	2	yes	complemented
277	C₆₁	C₂×C₈×M₁₆	1	1	yes	characteristic, complemented, Sylow
278	C₂³×C₄	—	61	1	no	—
279	C₂³×C₄	—	61	1	no	—
280	C₂³×C₄	—	61	1	no	—
281	C₂×M₁₆	—	61	2	no	—
282	C₂×M₁₆	—	61	16	no	—
283	C₂×M₁₆	—	61	4	no	—
284	C₂×M₁₆	C₄×D₆₁	1	2	yes	—
285	C₂²×C₈	—	61	2	no	—
286	C₂²×C₈	—	61	4	no	—
287	C₂²×C₈	—	61	2	no	—
288	C₂²×C₈	—	61	2	no	—
289	C₂²×C₈	—	61	2	no	—
290	C₂²×C₈	—	61	2	no	—
291	C₂²×C₈	—	61	4	no	—
292	C₂²×C₈	—	122	8	no	—
293	C₂²×C₈	C₄×D₆₁	1	2	yes	—
294	C₂×C₄²	—	61	1	no	—
295	C₂×C₄²	—	61	1	no	—
296	C₂×C₄²	—	61	1	no	—
297	C₂×C₄²	—	61	1	no	—
298	C₂×C₄²	—	61	1	no	—
299	C₂×C₄²	—	61	1	no	—
300	C₂×C₄²	—	61	1	no	—
301	C₂×C₄²	—	61	1	no	—
302	C₂×C₄²	—	61	1	no	—
303	C₂×C₄²	—	61	1	no	—
304	C₂×C₄²	—	61	1	no	—
305	C₂×C₄²	C₂²×D₆₁	1	1	yes	characteristic
306	C₄⋊C₈	—	61	4	no	—
307	C₄⋊C₈	—	61	2	no	—
308	C₄⋊C₈	C₄×D₆₁	1	2	yes	—
309	C₂²⋊C₈	—	61	2	no	—
310	C₂²⋊C₈	—	61	4	no	—
311	C₂²⋊C₈	C₄×D₆₁	1	2	yes	—
312	#97	—	61	4	no	—
313	#97	—	61	2	no	—
314	#97	C₄×D₆₁	1	2	yes	—
315	C₄×C₈	—	61	2	no	—
316	C₄×C₈	—	61	2	no	—
317	C₄×C₈	—	61	2	no	—
318	C₄×C₈	—	61	2	no	—
319	C₄×C₈	—	61	4	no	—
320	C₄×C₈	—	61	4	no	—
321	C₄×C₈	—	61	2	no	—
322	C₄×C₈	—	61	1	no	—
323	C₄×C₈	—	61	2	no	—
324	C₄×C₈	—	61	2	no	—
325	C₄×C₈	—	61	1	no	—
326	C₄×C₈	C₄×D₆₁	1	2	yes	—
327	C₄×C₈	C₂²×D₆₁	1	2	yes	—
328	C₄×C₈	C₂²×D₆₁	1	2	yes	—
329	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
330	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
331	C₂⁴	—	61	1	no	—
332	C₂²×C₄	—	61	1	no	—
333	C₂²×C₄	—	61	1	no	—
334	C₂²×C₄	—	61	1	no	—
335	C₂²×C₄	—	61	1	no	—
336	C₂²×C₄	—	61	1	no	—
337	C₂²×C₄	—	61	1	no	—
338	C₂²×C₄	—	61	1	no	—
339	C₂²×C₄	—	61	8	no	—
340	C₂²×C₄	—	61	1	no	—
341	C₂²×C₄	—	61	1	no	—
342	C₂²×C₄	—	61	1	no	—
343	C₂²×C₄	—	61	1	no	—
344	C₂²×C₄	—	61	1	no	—
345	C₂²×C₄	—	61	1	no	—
346	C₂²×C₄	—	61	1	no	—
347	C₂²×C₄	—	61	1	no	—
348	C₂²×C₄	—	122	4	no	—
349	C₂²×C₄	—	122	4	no	—
350	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
353	M₁₆	—	61	8	no	—
354	M₁₆	—	61	16	no	—
355	M₁₆	C₈×D₆₁	1	8	yes	direct product factor
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	61	2	no	—
358	C₂×C₈	—	61	4	no	—
359	C₂×C₈	—	61	16	no	—
360	C₂×C₈	—	61	8	no	—
361	C₂×C₈	—	61	2	no	—
362	C₂×C₈	—	61	4	no	—
363	C₂×C₈	—	122	4	no	—
364	C₂×C₈	—	122	8	no	—
365	C₂×C₈	—	122	4	no	—
366	C₂×C₈	—	122	4	no	—
367	C₂×C₈	—	122	4	no	—
368	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
369	C₂×C₈	C₂×C₄×D₆₁	1	4	yes	—
370	C₂×C₈	C₂×C₄×D₆₁	1	4	yes	—
371	C₂×C₈	C₂×C₄×D₆₁	1	2	yes	—
372	C₄²	—	61	1	no	—
373	C₄²	—	61	1	no	—
374	C₄²	—	61	1	no	—
375	C₄²	—	61	1	no	—
376	C₄²	—	61	1	no	—
377	C₄²	—	61	1	no	—
378	C₄²	—	61	1	no	—
379	C₄²	—	61	1	no	—
380	C₄²	—	61	1	no	—
381	C₄²	—	61	1	no	—
382	C₄²	—	61	1	no	—
383	C₄²	—	61	1	no	—
384	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
385	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
386	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
387	C₄²	C₂³×D₆₁	1	1	yes	characteristic
388	C₂³	—	61	1	no	—
389	C₂³	—	61	1	no	—
390	C₂³	—	61	4	no	—
391	C₂³	—	122	2	no	—
392	C₂³	—	122	2	no	—
393	C₂³	C₄²×D₆₁	1	1	yes	characteristic
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	61	1	no	—
397	C₂×C₄	—	61	1	no	—
398	C₂×C₄	—	61	1	no	—
399	C₂×C₄	—	61	1	no	—
400	C₂×C₄	—	61	4	no	—
401	C₂×C₄	—	61	4	no	—
402	C₂×C₄	—	61	4	no	—
403	C₂×C₄	—	61	4	no	—
404	C₂×C₄	—	61	4	no	—
405	C₂×C₄	—	61	4	no	—
406	C₂×C₄	—	61	4	no	—
407	C₂×C₄	—	61	1	no	—
408	C₂×C₄	—	61	1	no	—
409	C₂×C₄	—	122	2	no	—
410	C₂×C₄	—	122	2	no	—
411	C₂×C₄	—	122	2	no	—
412	C₂×C₄	—	122	2	no	—
413	C₂×C₄	—	122	2	no	—
414	C₂×C₄	—	122	2	no	—
415	C₂×C₄	—	122	2	no	—
416	C₂×C₄	—	122	2	no	—
417	C₂×C₄	C₄²×D₆₁	1	1	yes	characteristic
418	C₂×C₄	C₄²×D₆₁	1	1	yes	characteristic
419	C₂×C₄	C₄²×D₆₁	1	1	yes	characteristic
420	C₂×C₄	C₂×C₈×D₆₁	1	4	yes	—
421	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	4	no	—
426	C₈	—	61	8	no	—
427	C₈	—	61	4	no	—
428	C₈	—	122	2	no	—
429	C₈	—	122	4	no	—
430	C₈	C₂×C₈×D₆₁	1	8	yes	complemented
431	C₈	M₁₆×D₆₁	1	4	yes	direct product factor
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	61	2	no	—
435	C₂²	—	61	2	no	—
436	C₂²	—	61	2	no	—
437	C₂²	—	61	2	no	—
438	C₂²	—	122	8	no	—
439	C₂²	—	122	1	no	—
440	C₂²	—	122	1	no	—
441	C₂²	C₄×C₈×D₆₁	1	2	yes	—
442	C₂²	C₂×C₄²×D₆₁	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	61	2	no	—
446	C₄	—	61	2	no	—
447	C₄	—	61	2	no	—
448	C₄	—	61	2	no	—
449	C₄	—	122	1	no	—
450	C₄	—	122	1	no	—
451	C₄	C₄×C₈×D₆₁	1	2	yes	—
452	C₄	C₂²×C₈×D₆₁	1	2	yes	—
453	C₄	C₂×M₁₆×D₆₁	1	2	yes	—
454	C₄	#131×D₆₁	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	61	4	no	—
457	C₂	—	122	2	no	—
458	C₂	C₂×C₄×C₈×D₆₁	1	1	yes	characteristic
459	C₂	C₄×M₁₆×D₆₁	1	1	yes	characteristic
460	C₂	#405×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₆₁
commutator	C₂×C₆₁	C₂²×C₄×C₈
Frattini	C₄²	C₂³×D₆₁
Fitting	C₈×M₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂²×C₄²
prime radical	C₂³×D₆₁	C₄²
cosocle	C₄²×C₆₁	C₂⁴
hypercenter	C₈×M₁₆	D₆₁
hypocenter	C₆₁	C₂×C₈×M₁₆
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #21444100	C₂	semidirect
5. C₈×#11758194	C₂	semidirect
6. #21444098	C₂	semidirect
7. M₁₆×#92418	C₂	semidirect
8. C₈×#11758189	C₂	semidirect
9. #322×D₆₁	C₂	semidirect
10. C₈²×D₆₁	C₂	semidirect
11. C₈×M₁₆×C₆₁	C₂	semidirect
36. #16839484	C₂²	semidirect
37. #16839484	C₂²	semidirect
38. #16839483	C₂²	semidirect
39. C₈×#92418	C₂²	semidirect
40. C₈×#92418	C₂²	semidirect
41. C₈×#92418	C₂²	semidirect
45. C₆₁×#322	C₂²	semidirect
46. C₈²×C₆₁	C₂²	semidirect
52. M₁₆×D₆₁	C₈	direct (N × H)
122. M₁₆×C₆₁	C₂×C₈	semidirect
144. #11758194	C₂×C₈	semidirect
150. #11758189	C₂×C₈	semidirect
155. C₈×D₆₁	C₂×C₈	semidirect
156. C₈×D₆₁	M₁₆	direct (N × H)
195. C₈×C₆₁	C₂²×C₈	semidirect
196. C₈×C₆₁	C₂×M₁₆	semidirect
199. #92418	C₂²×C₈	semidirect
200. #92418	C₂×M₁₆	semidirect
233. C₈×M₁₆	D₆₁	direct (N × H)
241. D₆₁	C₈×M₁₆	direct (N × H)
272. #322	C₂×D₆₁	semidirect
276. C₈²	C₂×D₆₁	semidirect
277. C₆₁	C₂×C₈×M₁₆	semidirect
355. M₁₆	C₈×D₆₁	direct (N × H)
430. C₈	C₂×C₈×D₆₁	semidirect
431. C₈	M₁₆×D₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
#431×D₆₁	2
C₄×M₁₆×D₆₁	2
C₂×C₄×C₈×D₆₁	2
#21444100	2
C₈×#11758194	2
#21444098	2
M₁₆×#92418	2
C₈×#11758189	2
#322×D₆₁	2
C₈²×D₆₁	2
C₈×M₁₆×C₆₁	2
C₂×C₈×M₁₆	61

Subgroups — C8×M16×D61 #29645583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×M₁₆×D₆₁ #29645583