Subgroups — C₂×C₆₁×#3202 #29564179

Order 15616.

2122 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#536	C₂	1	2	yes	maximal
2	C₆₁×#3202	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#485	C₂	1	4	yes	maximal, complemented
4	C₂×C₆₁×#470	C₂	1	2	yes	maximal, complemented
5	C₂×C₆₁×#467	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#451	C₂	1	4	yes	maximal, complemented
7	C₂×C₆₁×#408	C₂	1	1	yes	maximal, characteristic
8	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
10	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#536	—	2	8	no	—
15	C₆₁×#536	C₂²	1	16	yes	—
16	C₂×C₄⋊Q₈×C₆₁	—	2	2	no	—
17	C₂×#124×C₆₁	—	2	2	no	—
18	C₂×#123×C₆₁	—	2	2	no	—
19	C₂×#123×C₆₁	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
22	C₂×#117×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#485	C₂²	1	32	yes	complemented
24	C₆₁×#470	C₂²	1	16	yes	complemented
25	C₆₁×#467	C₂²	1	16	yes	complemented
26	C₆₁×#451	C₂²	1	32	yes	complemented
27	C₂×#107×C₆₁	C₂²	1	2	yes	—
28	C₂×#106×C₆₁	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	C₂²	1	4	yes	—
30	C₂×#103×C₆₁	C₂²	1	4	yes	—
31	C₆₁×#408	C₂²	1	8	yes	—
32	C₂×C₂²⋊C₈×C₆₁	C₂²	1	4	yes	—
33	C₂×#41×C₆₁	—	4	2	no	—
34	C₂×#41×C₆₁	—	4	2	no	—
35	C₂×#41×C₆₁	D₄	1	4	yes	—
36	C₂×#41×C₆₁	C₂³	1	4	yes	—
37	C₂²×Q₈×C₆₁	—	2	2	no	—
38	C₂²×Q₈×C₆₁	—	2	4	no	—
39	C₂²×Q₈×C₆₁	—	4	4	no	—
40	C₂²×Q₈×C₆₁	—	4	4	no	—
41	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
43	C₂²×Q₈×C₆₁	C₂³	1	8	yes	—
44	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₆₁	D₄	1	2	yes	—
46	C₂³×C₄×C₆₁	—	2	2	no	—
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₆₁	—	4	4	no	—
50	C₂×Q₁₆×C₆₁	—	4	4	no	—
51	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
52	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
53	C₂×M₁₆×C₆₁	—	4	2	no	—
54	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
55	C₂²×C₈×C₆₁	—	4	2	no	—
56	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
57	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
59	C₄⋊Q₈×C₆₁	—	2	16	no	—
60	#124×C₆₁	—	2	16	no	—
61	#123×C₆₁	—	2	16	no	—
62	#123×C₆₁	—	2	16	no	—
63	C₂²⋊Q₈×C₆₁	—	2	8	no	—
64	C₂²⋊Q₈×C₆₁	—	2	8	no	—
65	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
66	C₂²⋊Q₈×C₆₁	C₂³	1	16	yes	—
67	#117×C₆₁	—	2	4	no	—
68	#117×C₆₁	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
75	C₂×C₄²×C₆₁	—	2	2	no	—
76	#107×C₆₁	C₂³	1	8	yes	—
77	#106×C₆₁	C₂³	1	8	yes	—
78	#103×C₆₁	C₂³	1	16	yes	—
79	#103×C₆₁	C₂³	1	16	yes	—
80	C₂²⋊C₈×C₆₁	C₂³	1	16	yes	—
81	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
83	#41×C₆₁	—	4	8	no	—
84	#41×C₆₁	—	4	4	no	—
85	#41×C₆₁	—	4	4	no	—
86	C₂×Q₈×C₆₁	—	2	4	no	—
87	C₂×Q₈×C₆₁	—	2	8	no	—
88	C₂×Q₈×C₆₁	—	2	8	no	—
89	C₂×Q₈×C₆₁	—	2	8	no	—
90	C₂×Q₈×C₆₁	—	4	2	no	—
91	C₂×Q₈×C₆₁	—	4	8	no	—
92	C₂×Q₈×C₆₁	—	4	8	no	—
93	C₂×Q₈×C₆₁	—	4	8	no	—
94	C₂×Q₈×C₆₁	—	4	16	no	—
95	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
96	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
97	C₂×D₄×C₆₁	—	4	2	no	—
98	C₂×D₄×C₆₁	—	4	4	no	—
99	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
100	C₂×D₄×C₆₁	C₂×D₄	1	8	yes	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	4	no	—
104	C₂²×C₄×C₆₁	—	2	4	no	—
105	C₂²×C₄×C₆₁	—	2	8	no	—
106	C₂²×C₄×C₆₁	—	2	4	no	—
107	C₂²×C₄×C₆₁	—	2	4	no	—
108	C₂²×C₄×C₆₁	—	4	8	no	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₆₁	—	4	8	no	—
117	Q₁₆×C₆₁	—	4	8	no	—
118	M₁₆×C₆₁	—	4	4	no	—
119	C₂×C₈×C₆₁	—	2	4	no	—
120	C₂×C₈×C₆₁	—	2	4	no	—
121	C₂×C₈×C₆₁	—	4	4	no	—
122	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
123	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
124	C₄⋊C₄×C₆₁	—	2	16	no	—
125	C₄⋊C₄×C₆₁	—	2	16	no	—
126	C₄⋊C₄×C₆₁	—	2	4	no	—
127	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
128	C₂²⋊C₄×C₆₁	—	2	8	no	—
129	C₂²⋊C₄×C₆₁	—	2	16	no	—
130	C₂²⋊C₄×C₆₁	—	2	16	no	—
131	C₄²×C₆₁	—	2	8	no	—
132	C₂³×C₆₁	—	2	4	no	—
133	C₂³×C₆₁	—	2	2	no	—
134	C₂³×C₆₁	—	2	4	no	—
135	C₂³×C₆₁	—	2	8	no	—
136	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
137	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
138	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₆₁	—	2	8	no	—
140	Q₈×C₆₁	—	2	8	no	—
141	Q₈×C₆₁	—	4	4	no	—
142	Q₈×C₆₁	—	4	16	no	—
143	Q₈×C₆₁	—	4	8	no	—
144	D₄×C₆₁	—	4	4	no	—
145	D₄×C₆₁	—	4	8	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	4	no	—
148	C₂×C₄×C₆₁	—	2	8	no	—
149	C₂×C₄×C₆₁	—	2	4	no	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	4	no	—
153	C₂×C₄×C₆₁	—	2	4	no	—
154	C₂×C₄×C₆₁	—	2	8	no	—
155	C₂×C₄×C₆₁	—	2	8	no	—
156	C₂×C₄×C₆₁	—	4	16	no	—
157	C₂×C₄×C₆₁	—	4	8	no	—
158	C₂×C₄×C₆₁	—	4	8	no	—
159	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
160	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
161	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
163	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
164	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
165	C₈×C₆₁	—	2	4	no	—
166	C₈×C₆₁	—	2	4	no	—
167	C₂×#3202	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₆₁	—	2	4	no	—
169	C₂²×C₆₁	—	2	2	no	—
170	C₂²×C₆₁	—	2	4	no	—
171	C₂²×C₆₁	—	2	8	no	—
172	C₂²×C₆₁	—	4	8	no	—
173	C₂²×C₆₁	—	4	4	no	—
174	C₂²×C₆₁	#534	1	2	yes	—
175	C₂²×C₆₁	#578	1	4	yes	—
176	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
177	C₄×C₆₁	—	2	2	no	—
178	C₄×C₆₁	—	2	4	no	—
179	C₄×C₆₁	—	4	8	no	—
180	C₄×C₆₁	—	4	8	no	—
181	C₄×C₆₁	#534	1	2	yes	—
182	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
183	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×#536	C₂×C₆₁	1	2	yes	—
185	#3202	C₂×C₆₁	1	16	yes	direct product factor
186	C₂×#485	C₂×C₆₁	1	4	yes	complemented
187	C₂×#470	C₂×C₆₁	1	2	yes	complemented
188	C₂×#467	C₂×C₆₁	1	2	yes	complemented
189	C₂×#451	C₂×C₆₁	1	4	yes	complemented
190	C₂×#408	C₂×C₆₁	1	1	yes	characteristic
191	C₂×C₆₁	—	4	4	no	—
192	C₂×C₆₁	—	4	2	no	—
193	C₂×C₆₁	#3202	1	4	yes	direct product factor
194	C₂×C₆₁	C₂×#534	1	1	yes	characteristic
195	C₂×C₆₁	C₂×#578	1	2	yes	—
196	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
197	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
198	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
199	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
200	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
201	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
202	#536	—	2	8	no	—
203	#536	C₂²×C₆₁	1	16	yes	—
204	C₂×C₄⋊Q₈	—	2	2	no	—
205	C₂×#124	—	2	2	no	—
206	C₂×#123	—	2	2	no	—
207	C₂×#123	—	2	2	no	—
208	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
209	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
210	C₂×#117	C₂²×C₆₁	1	2	yes	—
211	#485	C₂²×C₆₁	1	32	yes	complemented
212	#470	C₂²×C₆₁	1	16	yes	complemented
213	#467	C₂²×C₆₁	1	16	yes	complemented
214	#451	C₂²×C₆₁	1	32	yes	complemented
215	C₂×#107	C₂²×C₆₁	1	2	yes	—
216	C₂×#106	C₂²×C₆₁	1	2	yes	—
217	C₂×#103	C₂²×C₆₁	1	4	yes	—
218	C₂×#103	C₂²×C₆₁	1	4	yes	—
219	#408	C₂²×C₆₁	1	8	yes	—
220	C₂×C₂²⋊C₈	C₂²×C₆₁	1	4	yes	—
221	C₆₁	C₂×#3202	1	1	yes	characteristic, direct product factor, Sylow
222	C₂×#41	—	4	2	no	—
223	C₂×#41	—	4	2	no	—
224	C₂×#41	D₄×C₆₁	1	4	yes	—
225	C₂×#41	C₂³×C₆₁	1	4	yes	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	4	no	—
228	C₂²×Q₈	—	4	4	no	—
229	C₂²×Q₈	—	4	4	no	—
230	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
231	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
232	C₂²×Q₈	C₂³×C₆₁	1	8	yes	—
233	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
234	C₂²×D₄	D₄×C₆₁	1	2	yes	—
235	C₂³×C₄	—	2	2	no	—
236	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
237	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
238	C₂×Q₁₆	—	4	4	no	—
239	C₂×Q₁₆	—	4	4	no	—
240	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
241	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
242	C₂×M₁₆	—	4	2	no	—
243	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
244	C₂²×C₈	—	4	2	no	—
245	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
246	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
247	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
248	C₄⋊Q₈	—	2	16	no	—
249	#124	—	2	16	no	—
250	#123	—	2	16	no	—
251	#123	—	2	16	no	—
252	C₂²⋊Q₈	—	2	8	no	—
253	C₂²⋊Q₈	—	2	8	no	—
254	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
255	C₂²⋊Q₈	C₂³×C₆₁	1	16	yes	—
256	#117	—	2	4	no	—
257	#117	C₂³×C₆₁	1	8	yes	—
258	C₂×C₄⋊C₄	—	2	4	no	—
259	C₂×C₄⋊C₄	—	2	4	no	—
260	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₄²	—	2	2	no	—
265	#107	C₂³×C₆₁	1	8	yes	—
266	#106	C₂³×C₆₁	1	8	yes	—
267	#103	C₂³×C₆₁	1	16	yes	—
268	#103	C₂³×C₆₁	1	16	yes	—
269	C₂²⋊C₈	C₂³×C₆₁	1	16	yes	—
270	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
271	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
272	#41	—	4	8	no	—
273	#41	—	4	4	no	—
274	#41	—	4	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	2	8	no	—
278	C₂×Q₈	—	2	8	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	4	8	no	—
281	C₂×Q₈	—	4	8	no	—
282	C₂×Q₈	—	4	8	no	—
283	C₂×Q₈	—	4	16	no	—
284	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
285	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
289	C₂×D₄	C₂×D₄×C₆₁	1	8	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	4	8	no	—
298	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
301	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
302	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
303	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
304	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
305	Q₁₆	—	4	8	no	—
306	Q₁₆	—	4	8	no	—
307	M₁₆	—	4	4	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	4	4	no	—
311	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
312	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	16	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
317	C₂²⋊C₄	—	2	8	no	—
318	C₂²⋊C₄	—	2	16	no	—
319	C₂²⋊C₄	—	2	16	no	—
320	C₄²	—	2	8	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	8	no	—
325	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
326	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
327	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
328	Q₈	—	2	8	no	—
329	Q₈	—	2	8	no	—
330	Q₈	—	4	4	no	—
331	Q₈	—	4	16	no	—
332	Q₈	—	4	8	no	—
333	D₄	—	4	4	no	—
334	D₄	—	4	8	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	4	16	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
349	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
350	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
351	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
352	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
353	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
354	C₈	—	2	4	no	—
355	C₈	—	2	4	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	8	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	4	8	no	—
361	C₂²	—	4	4	no	—
362	C₂²	C₆₁×#534	1	2	yes	—
363	C₂²	C₆₁×#578	1	4	yes	—
364	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	2	4	no	—
367	C₄	—	4	8	no	—
368	C₄	—	4	8	no	—
369	C₄	C₆₁×#534	1	2	yes	—
370	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
371	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
372	C₂	—	4	4	no	—
373	C₂	—	4	2	no	—
374	C₂	C₆₁×#3202	1	4	yes	direct product factor
375	C₂	C₂×C₆₁×#534	1	1	yes	characteristic
376	C₂	C₂×C₆₁×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#3202	C₂	direct (N × H)
3. C₂×C₆₁×#485	C₂	semidirect
4. C₂×C₆₁×#470	C₂	semidirect
5. C₂×C₆₁×#467	C₂	semidirect
6. C₂×C₆₁×#451	C₂	semidirect
23. C₆₁×#485	C₂²	semidirect
24. C₆₁×#470	C₂²	semidirect
25. C₆₁×#467	C₂²	semidirect
26. C₆₁×#451	C₂²	semidirect
167. C₂×#3202	C₆₁	direct (N × H)
185. #3202	C₂×C₆₁	direct (N × H)
186. C₂×#485	C₂×C₆₁	semidirect
187. C₂×#470	C₂×C₆₁	semidirect
188. C₂×#467	C₂×C₆₁	semidirect
189. C₂×#451	C₂×C₆₁	semidirect
193. C₂×C₆₁	#3202	direct (N × H)
211. #485	C₂²×C₆₁	semidirect
212. #470	C₂²×C₆₁	semidirect
213. #467	C₂²×C₆₁	semidirect
214. #451	C₂²×C₆₁	semidirect
221. C₆₁	C₂×#3202	direct (N × H)
374. C₂	C₆₁×#3202	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×#536	2
C₆₁×#3202	2
C₂×C₆₁×#485	2
C₂×C₆₁×#470	2
C₂×C₆₁×#467	2
C₂×C₆₁×#451	2
C₂×C₆₁×#408	2
C₂×#3202	61

Subgroups — C2×C61×#3202 #29564179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3202 #29564179