Subgroups — C₂×C₆₁×#3168 #29564103

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#529	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3168	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₆₁×#466	C₂	1	1	yes	maximal, characteristic
8	C₂×C₆₁×#465	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
15	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#529	—	2	8	no	—
19	C₆₁×#529	C₂²	1	16	yes	complemented
20	C₂×#126×C₆₁	—	2	2	no	—
21	C₂×#125×C₆₁	C₂²	1	2	yes	—
22	C₂×#124×C₆₁	C₂²	1	2	yes	—
23	C₂×#123×C₆₁	—	2	2	no	—
24	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#121×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₁	—	2	2	no	—
28	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
29	C₂×#117×C₆₁	—	2	2	no	—
30	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#499	C₂²	1	8	yes	complemented
32	C₆₁×#495	C₂²	1	8	yes	complemented
33	C₆₁×#488	C₂²	1	16	yes	complemented
34	C₆₁×#467	C₂²	1	8	yes	complemented
35	C₆₁×#466	C₂²	1	8	yes	—
36	C₆₁×#465	C₂²	1	16	yes	complemented
37	C₄×Q₁₆×C₆₁	C₂²	1	8	yes	complemented
38	C₄×SD₁₆×C₆₁	C₂²	1	16	yes	complemented
39	C₄×D₈×C₆₁	C₂²	1	8	yes	complemented
40	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
41	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
42	C₂×#106×C₆₁	C₂²	1	2	yes	—
43	C₂×#103×C₆₁	C₂²	1	2	yes	—
44	C₂×#103×C₆₁	C₂²	1	2	yes	—
45	C₂×#102×C₆₁	C₂²	1	2	yes	—
46	C₂×#102×C₆₁	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₆₁	C₂²	1	8	yes	complemented
52	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
53	C₂²×D₄×C₆₁	—	2	2	no	—
54	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
55	C₂³×C₄×C₆₁	—	2	2	no	—
56	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
59	C₂×Q₁₆×C₆₁	—	2	4	no	—
60	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
61	C₂×SD₁₆×C₆₁	—	2	8	no	—
62	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
63	C₂×D₈×C₆₁	—	2	4	no	—
64	C₂×D₈×C₆₁	C₂³	1	4	yes	—
65	C₂²×C₈×C₆₁	—	2	4	no	—
66	C₂²×C₈×C₆₁	—	2	4	no	—
67	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
70	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	#126×C₆₁	—	2	16	no	—
74	#125×C₆₁	—	2	4	no	—
75	#125×C₆₁	C₂³	1	8	yes	—
76	#124×C₆₁	—	2	4	no	—
77	#124×C₆₁	C₂³	1	8	yes	—
78	#123×C₆₁	—	2	16	no	—
79	C₂²⋊Q₈×C₆₁	—	2	4	no	—
80	C₂²⋊Q₈×C₆₁	C₂³	1	8	yes	—
81	#121×C₆₁	—	2	4	no	—
82	#121×C₆₁	C₂³	1	8	yes	—
83	C₄×Q₈×C₆₁	—	2	4	no	—
84	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
85	C₄×D₄×C₆₁	—	2	16	no	—
86	C₄×D₄×C₆₁	—	2	4	no	—
87	C₄×D₄×C₆₁	C₂³	1	8	yes	—
88	#117×C₆₁	—	2	16	no	—
89	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
90	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
100	C₂×C₄²×C₆₁	—	2	2	no	—
101	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₆₁	D₄	1	4	yes	—
103	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
106	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
107	#107×C₆₁	C₂³	1	4	yes	—
108	#107×C₆₁	C₂³	1	4	yes	—
109	#106×C₆₁	C₂³	1	8	yes	—
110	#103×C₆₁	C₂³	1	8	yes	—
111	#103×C₆₁	C₂³	1	8	yes	—
112	#102×C₆₁	C₂³	1	8	yes	—
113	#102×C₆₁	C₂³	1	8	yes	—
114	C₄×C₈×C₆₁	C₂³	1	4	yes	—
115	C₄×C₈×C₆₁	C₂³	1	4	yes	—
116	C₄×C₈×C₆₁	C₂³	1	4	yes	—
117	C₄×C₈×C₆₁	C₂³	1	4	yes	—
118	C₂⁴×C₆₁	—	2	2	no	—
119	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₆₁	—	2	2	no	—
121	C₂×Q₈×C₆₁	—	2	4	no	—
122	C₂×Q₈×C₆₁	—	2	4	no	—
123	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
124	C₂×D₄×C₆₁	—	2	8	no	—
125	C₂×D₄×C₆₁	—	2	2	no	—
126	C₂×D₄×C₆₁	—	2	4	no	—
127	C₂×D₄×C₆₁	—	2	4	no	—
128	C₂×D₄×C₆₁	—	4	8	no	—
129	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₆₁	—	2	4	no	—
131	C₂²×C₄×C₆₁	—	2	4	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	2	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	2	no	—
137	C₂²×C₄×C₆₁	—	2	8	no	—
138	C₂²×C₄×C₆₁	—	4	8	no	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
146	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
149	Q₁₆×C₆₁	—	2	8	no	—
150	SD₁₆×C₆₁	—	2	16	no	—
151	D₈×C₆₁	—	2	8	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	2	2	no	—
154	C₂×C₈×C₆₁	—	2	8	no	—
155	C₂×C₈×C₆₁	—	2	8	no	—
156	C₂×C₈×C₆₁	#41	1	4	yes	—
157	C₂×C₈×C₆₁	#41	1	4	yes	—
158	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
159	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
160	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
161	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
162	C₄⋊C₄×C₆₁	—	2	8	no	—
163	C₄⋊C₄×C₆₁	—	2	8	no	—
164	C₄⋊C₄×C₆₁	—	2	8	no	—
165	C₄⋊C₄×C₆₁	—	2	8	no	—
166	C₄⋊C₄×C₆₁	—	2	2	no	—
167	C₄⋊C₄×C₆₁	—	2	2	no	—
168	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
169	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
170	C₂²⋊C₄×C₆₁	—	2	8	no	—
171	C₂²⋊C₄×C₆₁	—	2	8	no	—
172	C₂²⋊C₄×C₆₁	—	2	8	no	—
173	C₂²⋊C₄×C₆₁	—	2	8	no	—
174	C₂²⋊C₄×C₆₁	—	2	8	no	—
175	C₄²×C₆₁	—	2	8	no	—
176	C₄²×C₆₁	C₂×D₄	1	4	yes	—
177	C₄²×C₆₁	C₂×D₄	1	2	yes	—
178	C₄²×C₆₁	C₂×D₄	1	2	yes	—
179	C₄²×C₆₁	C₂×D₄	1	4	yes	—
180	C₄²×C₆₁	C₂⁴	1	2	yes	—
181	C₄²×C₆₁	C₂⁴	1	2	yes	—
182	C₂³×C₆₁	—	2	2	no	—
183	C₂³×C₆₁	—	2	2	no	—
184	C₂³×C₆₁	—	2	4	no	—
185	C₂³×C₆₁	—	4	4	no	—
186	C₂³×C₆₁	—	4	4	no	—
187	C₂³×C₆₁	—	4	4	no	—
188	C₂³×C₆₁	#135	1	4	yes	—
189	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
190	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₆₁	—	2	4	no	—
192	Q₈×C₆₁	—	2	4	no	—
193	Q₈×C₆₁	—	4	4	no	—
194	D₄×C₆₁	—	2	4	no	—
195	D₄×C₆₁	—	2	4	no	—
196	D₄×C₆₁	—	4	16	no	—
197	D₄×C₆₁	—	4	4	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	8	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	8	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	2	no	—
207	C₂×C₄×C₆₁	—	2	4	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	2	4	no	—
210	C₂×C₄×C₆₁	—	4	4	no	—
211	C₂×C₄×C₆₁	—	4	4	no	—
212	C₂×C₄×C₆₁	—	4	4	no	—
213	C₂×C₄×C₆₁	—	4	16	no	—
214	C₂×C₄×C₆₁	#135	1	4	yes	—
215	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
222	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
223	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
224	C₈×C₆₁	—	2	2	no	—
225	C₈×C₆₁	—	2	2	no	—
226	C₈×C₆₁	C₂×#41	1	4	yes	—
227	C₈×C₆₁	C₂×#41	1	4	yes	—
228	C₂×#3168	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₆₁	—	2	8	no	—
230	C₂²×C₆₁	—	2	2	no	—
231	C₂²×C₆₁	—	2	2	no	—
232	C₂²×C₆₁	—	4	4	no	—
233	C₂²×C₆₁	—	4	4	no	—
234	C₂²×C₆₁	—	4	4	no	—
235	C₂²×C₆₁	—	8	8	no	—
236	C₂²×C₆₁	#532	1	2	yes	—
237	C₂²×C₆₁	C₂×#135	1	4	yes	—
238	C₂²×C₆₁	C₂×#135	1	2	yes	—
239	C₂²×C₆₁	C₂×#135	1	2	yes	—
240	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
241	C₄×C₆₁	—	2	2	no	—
242	C₄×C₆₁	—	2	2	no	—
243	C₄×C₆₁	—	2	2	no	—
244	C₄×C₆₁	—	2	2	no	—
245	C₄×C₆₁	—	4	4	no	—
246	C₄×C₆₁	—	4	4	no	—
247	C₄×C₆₁	—	4	4	no	—
248	C₄×C₆₁	#532	1	2	yes	—
249	C₄×C₆₁	C₂×#135	1	4	yes	—
250	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
251	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
252	C₂×#529	C₂×C₆₁	1	2	yes	complemented
253	#3168	C₂×C₆₁	1	16	yes	direct product factor
254	C₂×#499	C₂×C₆₁	1	1	yes	characteristic, complemented
255	C₂×#495	C₂×C₆₁	1	1	yes	characteristic, complemented
256	C₂×#488	C₂×C₆₁	1	2	yes	complemented
257	C₂×#467	C₂×C₆₁	1	1	yes	characteristic, complemented
258	C₂×#466	C₂×C₆₁	1	1	yes	characteristic
259	C₂×#465	C₂×C₆₁	1	2	yes	complemented
260	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
261	C₂×C₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
262	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
263	C₂²×C₄×C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
264	C₂×C₆₁	—	2	4	no	—
265	C₂×C₆₁	—	8	4	no	—
266	C₂×C₆₁	#3168	1	4	yes	direct product factor
267	C₂×C₆₁	C₂×#532	1	1	yes	characteristic
268	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
269	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
270	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
271	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
272	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
273	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
274	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
275	#529	—	2	8	no	—
276	#529	C₂²×C₆₁	1	16	yes	complemented
277	C₂×#126	—	2	2	no	—
278	C₂×#125	C₂²×C₆₁	1	2	yes	—
279	C₂×#124	C₂²×C₆₁	1	2	yes	—
280	C₂×#123	—	2	2	no	—
281	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
282	C₂×#121	C₂²×C₆₁	1	2	yes	—
283	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
284	C₂×C₄×D₄	—	2	2	no	—
285	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
286	C₂×#117	—	2	2	no	—
287	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
288	#499	C₂²×C₆₁	1	8	yes	complemented
289	#495	C₂²×C₆₁	1	8	yes	complemented
290	#488	C₂²×C₆₁	1	16	yes	complemented
291	#467	C₂²×C₆₁	1	8	yes	complemented
292	#466	C₂²×C₆₁	1	8	yes	—
293	#465	C₂²×C₆₁	1	16	yes	complemented
294	C₄×Q₁₆	C₂²×C₆₁	1	8	yes	complemented
295	C₄×SD₁₆	C₂²×C₆₁	1	16	yes	complemented
296	C₄×D₈	C₂²×C₆₁	1	8	yes	complemented
297	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
298	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
299	C₂×#106	C₂²×C₆₁	1	2	yes	—
300	C₂×#103	C₂²×C₆₁	1	2	yes	—
301	C₂×#103	C₂²×C₆₁	1	2	yes	—
302	C₂×#102	C₂²×C₆₁	1	2	yes	—
303	C₂×#102	C₂²×C₆₁	1	2	yes	—
304	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
305	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
306	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
307	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
308	C₂×C₄×C₈	C₂²×C₆₁	1	8	yes	complemented
309	C₆₁	C₂×#3168	1	1	yes	characteristic, direct product factor, Sylow
310	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
313	C₂³×C₄	—	2	2	no	—
314	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
315	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
316	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
317	C₂×Q₁₆	—	2	4	no	—
318	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
319	C₂×SD₁₆	—	2	8	no	—
320	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
321	C₂×D₈	—	2	4	no	—
322	C₂×D₈	C₂³×C₆₁	1	4	yes	—
323	C₂²×C₈	—	2	4	no	—
324	C₂²×C₈	—	2	4	no	—
325	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
328	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
329	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
331	#126	—	2	16	no	—
332	#125	—	2	4	no	—
333	#125	C₂³×C₆₁	1	8	yes	—
334	#124	—	2	4	no	—
335	#124	C₂³×C₆₁	1	8	yes	—
336	#123	—	2	16	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	C₂³×C₆₁	1	8	yes	—
339	#121	—	2	4	no	—
340	#121	C₂³×C₆₁	1	8	yes	—
341	C₄×Q₈	—	2	4	no	—
342	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
343	C₄×D₄	—	2	16	no	—
344	C₄×D₄	—	2	4	no	—
345	C₄×D₄	C₂³×C₆₁	1	8	yes	—
346	#117	—	2	16	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₄²	—	2	2	no	—
359	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
360	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
361	C₂×C₄²	D₄×C₆₁	1	4	yes	—
362	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
364	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
365	#107	C₂³×C₆₁	1	4	yes	—
366	#107	C₂³×C₆₁	1	4	yes	—
367	#106	C₂³×C₆₁	1	8	yes	—
368	#103	C₂³×C₆₁	1	8	yes	—
369	#103	C₂³×C₆₁	1	8	yes	—
370	#102	C₂³×C₆₁	1	8	yes	—
371	#102	C₂³×C₆₁	1	8	yes	—
372	C₄×C₈	C₂³×C₆₁	1	4	yes	—
373	C₄×C₈	C₂³×C₆₁	1	4	yes	—
374	C₄×C₈	C₂³×C₆₁	1	4	yes	—
375	C₄×C₈	C₂³×C₆₁	1	4	yes	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	4	8	no	—
397	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
403	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
404	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
407	Q₁₆	—	2	8	no	—
408	SD₁₆	—	2	16	no	—
409	D₈	—	2	8	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	8	no	—
413	C₂×C₈	—	2	8	no	—
414	C₂×C₈	#41×C₆₁	1	4	yes	—
415	C₂×C₈	#41×C₆₁	1	4	yes	—
416	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
417	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
418	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
419	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
427	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₄²	—	2	8	no	—
434	C₄²	C₂×D₄×C₆₁	1	4	yes	—
435	C₄²	C₂×D₄×C₆₁	1	2	yes	—
436	C₄²	C₂×D₄×C₆₁	1	2	yes	—
437	C₄²	C₂×D₄×C₆₁	1	4	yes	—
438	C₄²	C₂⁴×C₆₁	1	2	yes	—
439	C₄²	C₂⁴×C₆₁	1	2	yes	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	4	no	—
445	C₂³	—	4	4	no	—
446	C₂³	#135×C₆₁	1	4	yes	—
447	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
448	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
449	Q₈	—	2	4	no	—
450	Q₈	—	2	4	no	—
451	Q₈	—	4	4	no	—
452	D₄	—	2	4	no	—
453	D₄	—	2	4	no	—
454	D₄	—	4	16	no	—
455	D₄	—	4	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	16	no	—
472	C₂×C₄	#135×C₆₁	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
478	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
479	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
480	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
481	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	C₂×#41×C₆₁	1	4	yes	—
485	C₈	C₂×#41×C₆₁	1	4	yes	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	8	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	8	8	no	—
493	C₂²	C₆₁×#532	1	2	yes	—
494	C₂²	C₂×#135×C₆₁	1	4	yes	—
495	C₂²	C₂×#135×C₆₁	1	2	yes	—
496	C₂²	C₂×#135×C₆₁	1	2	yes	—
497	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	4	no	—
504	C₄	—	4	4	no	—
505	C₄	C₆₁×#532	1	2	yes	—
506	C₄	C₂×#135×C₆₁	1	4	yes	—
507	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
508	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
509	C₂	—	2	4	no	—
510	C₂	—	8	4	no	—
511	C₂	C₆₁×#3168	1	4	yes	direct product factor
512	C₂	C₂×C₆₁×#532	1	1	yes	characteristic
513	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
514	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
prime radical	C₂×C₆₁×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#529	C₂	semidirect
2. C₆₁×#3168	C₂	direct (N × H)
3. C₂×C₆₁×#499	C₂	semidirect
4. C₂×C₆₁×#495	C₂	semidirect
5. C₂×C₆₁×#488	C₂	semidirect
6. C₂×C₆₁×#467	C₂	semidirect
8. C₂×C₆₁×#465	C₂	semidirect
9. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
10. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
11. C₂×C₄×D₈×C₆₁	C₂	semidirect
12. C₂²×C₄×C₈×C₆₁	C₂	semidirect
19. C₆₁×#529	C₂²	semidirect
31. C₆₁×#499	C₂²	semidirect
32. C₆₁×#495	C₂²	semidirect
33. C₆₁×#488	C₂²	semidirect
34. C₆₁×#467	C₂²	semidirect
36. C₆₁×#465	C₂²	semidirect
37. C₄×Q₁₆×C₆₁	C₂²	semidirect
38. C₄×SD₁₆×C₆₁	C₂²	semidirect
39. C₄×D₈×C₆₁	C₂²	semidirect
51. C₂×C₄×C₈×C₆₁	C₂²	semidirect
228. C₂×#3168	C₆₁	direct (N × H)
252. C₂×#529	C₂×C₆₁	semidirect
253. #3168	C₂×C₆₁	direct (N × H)
254. C₂×#499	C₂×C₆₁	semidirect
255. C₂×#495	C₂×C₆₁	semidirect
256. C₂×#488	C₂×C₆₁	semidirect
257. C₂×#467	C₂×C₆₁	semidirect
259. C₂×#465	C₂×C₆₁	semidirect
260. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
261. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
262. C₂×C₄×D₈	C₂×C₆₁	semidirect
263. C₂²×C₄×C₈	C₂×C₆₁	semidirect
266. C₂×C₆₁	#3168	direct (N × H)
276. #529	C₂²×C₆₁	semidirect
288. #499	C₂²×C₆₁	semidirect
289. #495	C₂²×C₆₁	semidirect
290. #488	C₂²×C₆₁	semidirect
291. #467	C₂²×C₆₁	semidirect
293. #465	C₂²×C₆₁	semidirect
294. C₄×Q₁₆	C₂²×C₆₁	semidirect
295. C₄×SD₁₆	C₂²×C₆₁	semidirect
296. C₄×D₈	C₂²×C₆₁	semidirect
308. C₂×C₄×C₈	C₂²×C₆₁	semidirect
309. C₆₁	C₂×#3168	direct (N × H)
511. C₂	C₆₁×#3168	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#529	2
C₆₁×#3168	2
C₂×C₆₁×#499	2
C₂×C₆₁×#495	2
C₂×C₆₁×#488	2
C₂×C₆₁×#467	2
C₂×C₆₁×#466	2
C₂×C₆₁×#465	2
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₂²×C₄×C₈×C₆₁	2
C₂×#3168	61

Subgroups — C2×C61×#3168 #29564103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3168 #29564103