Subgroups — C₂×C₆₁×#3176 #29564113

Order 15616.

2098 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#540	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3176	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₆₁×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₆₁	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
12	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#540	—	2	8	no	—
16	C₆₁×#540	C₂²	1	16	yes	complemented
17	C₂×#127×C₆₁	C₂²	1	2	yes	—
18	C₂×#125×C₆₁	C₂²	1	2	yes	—
19	C₂×#123×C₆₁	—	2	4	no	—
20	C₂×#121×C₆₁	—	2	4	no	—
21	C₂×#121×C₆₁	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
23	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#499	C₂²	1	8	yes	complemented
25	C₆₁×#493	C₂²	1	8	yes	complemented
26	C₆₁×#490	C₂²	1	16	yes	complemented
27	C₆₁×#469	C₂²	1	16	yes	complemented
28	C₆₁×#466	C₂²	1	16	yes	complemented
29	C₆₁×#442	C₂²	1	16	yes	complemented
30	C₄×D₈×C₆₁	C₂²	1	16	yes	complemented
31	C₂×#107×C₆₁	C₂²	1	2	yes	—
32	C₂×#106×C₆₁	C₂²	1	2	yes	—
33	C₂×#102×C₆₁	C₂²	1	4	yes	—
34	C₂×#102×C₆₁	C₂²	1	4	yes	—
35	C₆₁×#405	C₂²	1	8	yes	complemented
36	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₂²×D₄×C₆₁	—	2	4	no	—
41	C₂²×D₄×C₆₁	—	2	4	no	—
42	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
43	C₂³×C₄×C₆₁	—	2	4	no	—
44	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₆₁	—	2	8	no	—
46	C₂×D₈×C₆₁	—	2	8	no	—
47	C₂×D₈×C₆₁	C₂³	1	8	yes	—
48	C₂×D₈×C₆₁	C₂³	1	8	yes	—
49	C₂×M₁₆×C₆₁	—	2	4	no	—
50	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
51	C₂²×C₈×C₆₁	—	2	4	no	—
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
54	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	#127×C₆₁	—	2	4	no	—
58	#127×C₆₁	C₂³	1	8	yes	—
59	#125×C₆₁	—	2	4	no	—
60	#125×C₆₁	C₂³	1	8	yes	—
61	#123×C₆₁	—	2	32	no	—
62	#121×C₆₁	—	2	8	no	—
63	#121×C₆₁	—	2	32	no	—
64	#121×C₆₁	C₂³	1	16	yes	—
65	C₄×D₄×C₆₁	—	2	8	no	—
66	C₄×D₄×C₆₁	C₂³	1	16	yes	—
67	#117×C₆₁	D₄	1	4	yes	—
68	#117×C₆₁	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
70	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	#107×C₆₁	C₂³	1	8	yes	—
78	#106×C₆₁	C₂³	1	8	yes	—
79	#102×C₆₁	C₂³	1	16	yes	—
80	#102×C₆₁	C₂³	1	16	yes	—
81	#97×C₆₁	C₂³	1	4	yes	—
82	#97×C₆₁	C₂³	1	4	yes	—
83	C₄×C₈×C₆₁	C₂³	1	4	yes	—
84	C₄×C₈×C₆₁	C₂³	1	4	yes	—
85	C₂⁴×C₆₁	—	2	4	no	—
86	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
87	C₂×D₄×C₆₁	—	2	16	no	—
88	C₂×D₄×C₆₁	—	2	4	no	—
89	C₂×D₄×C₆₁	—	2	16	no	—
90	C₂×D₄×C₆₁	—	2	8	no	—
91	C₂×D₄×C₆₁	—	2	8	no	—
92	C₂×D₄×C₆₁	—	8	8	no	—
93	C₂×D₄×C₆₁	—	8	8	no	—
94	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
95	C₂²×C₄×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	4	no	—
98	C₂²×C₄×C₆₁	—	2	16	no	—
99	C₂²×C₄×C₆₁	—	8	8	no	—
100	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
106	D₈×C₆₁	—	2	16	no	—
107	D₈×C₆₁	—	2	16	no	—
108	M₁₆×C₆₁	—	2	8	no	—
109	C₂×C₈×C₆₁	—	2	2	no	—
110	C₂×C₈×C₆₁	—	2	2	no	—
111	C₂×C₈×C₆₁	—	2	8	no	—
112	C₂×C₈×C₆₁	#41	1	4	yes	—
113	C₂×C₈×C₆₁	#41	1	4	yes	—
114	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
115	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
116	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
117	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
118	C₄⋊C₄×C₆₁	—	2	16	no	—
119	C₄⋊C₄×C₆₁	—	2	4	no	—
120	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
121	C₄⋊C₄×C₆₁	C₂⁴	1	8	yes	—
122	C₂²⋊C₄×C₆₁	—	2	16	no	—
123	C₂²⋊C₄×C₆₁	—	2	16	no	—
124	C₂²⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
125	C₄²×C₆₁	C₂×D₄	1	2	yes	—
126	C₄²×C₆₁	C₂×D₄	1	2	yes	—
127	C₄²×C₆₁	C₂⁴	1	2	yes	—
128	C₄²×C₆₁	C₂⁴	1	2	yes	—
129	C₂³×C₆₁	—	2	2	no	—
130	C₂³×C₆₁	—	2	4	no	—
131	C₂³×C₆₁	—	2	8	no	—
132	C₂³×C₆₁	—	4	8	no	—
133	C₂³×C₆₁	—	4	8	no	—
134	C₂³×C₆₁	—	4	8	no	—
135	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
136	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
137	D₄×C₆₁	—	2	8	no	—
138	D₄×C₆₁	—	2	8	no	—
139	D₄×C₆₁	—	4	8	no	—
140	D₄×C₆₁	—	8	16	no	—
141	D₄×C₆₁	—	8	16	no	—
142	C₂×C₄×C₆₁	—	2	2	no	—
143	C₂×C₄×C₆₁	—	2	4	no	—
144	C₂×C₄×C₆₁	—	2	4	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	2	no	—
148	C₂×C₄×C₆₁	—	2	8	no	—
149	C₂×C₄×C₆₁	—	4	8	no	—
150	C₂×C₄×C₆₁	—	8	16	no	—
151	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
154	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
157	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
158	C₈×C₆₁	—	2	2	no	—
159	C₈×C₆₁	—	2	2	no	—
160	C₈×C₆₁	C₂×#41	1	4	yes	—
161	C₈×C₆₁	C₂×#41	1	4	yes	—
162	C₂×#3176	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₆₁	—	2	2	no	—
164	C₂²×C₆₁	—	2	4	no	—
165	C₂²×C₆₁	—	4	4	no	—
166	C₂²×C₆₁	—	4	8	no	—
167	C₂²×C₆₁	—	4	8	no	—
168	C₂²×C₆₁	—	4	8	no	—
169	C₂²×C₆₁	—	8	16	no	—
170	C₂²×C₆₁	#532	1	2	yes	—
171	C₂²×C₆₁	#576	1	4	yes	—
172	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
173	C₄×C₆₁	—	2	2	no	—
174	C₄×C₆₁	—	2	4	no	—
175	C₄×C₆₁	—	2	4	no	—
176	C₄×C₆₁	—	4	8	no	—
177	C₄×C₆₁	#532	1	2	yes	—
178	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
179	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
180	C₂×#540	C₂×C₆₁	1	2	yes	complemented
181	#3176	C₂×C₆₁	1	16	yes	direct product factor
182	C₂×#499	C₂×C₆₁	1	1	yes	characteristic, complemented
183	C₂×#493	C₂×C₆₁	1	1	yes	characteristic, complemented
184	C₂×#490	C₂×C₆₁	1	2	yes	complemented
185	C₂×#469	C₂×C₆₁	1	2	yes	complemented
186	C₂×#466	C₂×C₆₁	1	2	yes	complemented
187	C₂×#442	C₂×C₆₁	1	2	yes	complemented
188	C₂×C₄×D₈	C₂×C₆₁	1	2	yes	complemented
189	C₂×#405	C₂×C₆₁	1	1	yes	characteristic, complemented
190	C₂×C₆₁	—	4	2	no	—
191	C₂×C₆₁	—	8	8	no	—
192	C₂×C₆₁	#3176	1	4	yes	direct product factor
193	C₂×C₆₁	C₂×#532	1	1	yes	characteristic
194	C₂×C₆₁	C₂×#576	1	2	yes	—
195	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
196	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
197	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
198	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
199	#540	—	2	8	no	—
200	#540	C₂²×C₆₁	1	16	yes	complemented
201	C₂×#127	C₂²×C₆₁	1	2	yes	—
202	C₂×#125	C₂²×C₆₁	1	2	yes	—
203	C₂×#123	—	2	4	no	—
204	C₂×#121	—	2	4	no	—
205	C₂×#121	C₂²×C₆₁	1	4	yes	—
206	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
207	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
208	#499	C₂²×C₆₁	1	8	yes	complemented
209	#493	C₂²×C₆₁	1	8	yes	complemented
210	#490	C₂²×C₆₁	1	16	yes	complemented
211	#469	C₂²×C₆₁	1	16	yes	complemented
212	#466	C₂²×C₆₁	1	16	yes	complemented
213	#442	C₂²×C₆₁	1	16	yes	complemented
214	C₄×D₈	C₂²×C₆₁	1	16	yes	complemented
215	C₂×#107	C₂²×C₆₁	1	2	yes	—
216	C₂×#106	C₂²×C₆₁	1	2	yes	—
217	C₂×#102	C₂²×C₆₁	1	4	yes	—
218	C₂×#102	C₂²×C₆₁	1	4	yes	—
219	#405	C₂²×C₆₁	1	8	yes	complemented
220	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
221	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
224	C₆₁	C₂×#3176	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
228	C₂³×C₄	—	2	4	no	—
229	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
230	C₂×D₈	—	2	8	no	—
231	C₂×D₈	—	2	8	no	—
232	C₂×D₈	C₂³×C₆₁	1	8	yes	—
233	C₂×D₈	C₂³×C₆₁	1	8	yes	—
234	C₂×M₁₆	—	2	4	no	—
235	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
239	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
242	#127	—	2	4	no	—
243	#127	C₂³×C₆₁	1	8	yes	—
244	#125	—	2	4	no	—
245	#125	C₂³×C₆₁	1	8	yes	—
246	#123	—	2	32	no	—
247	#121	—	2	8	no	—
248	#121	—	2	32	no	—
249	#121	C₂³×C₆₁	1	16	yes	—
250	C₄×D₄	—	2	8	no	—
251	C₄×D₄	C₂³×C₆₁	1	16	yes	—
252	#117	D₄×C₆₁	1	4	yes	—
253	#117	C₂³×C₆₁	1	4	yes	—
254	C₂×C₄⋊C₄	—	2	4	no	—
255	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
260	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
262	#107	C₂³×C₆₁	1	8	yes	—
263	#106	C₂³×C₆₁	1	8	yes	—
264	#102	C₂³×C₆₁	1	16	yes	—
265	#102	C₂³×C₆₁	1	16	yes	—
266	#97	C₂³×C₆₁	1	4	yes	—
267	#97	C₂³×C₆₁	1	4	yes	—
268	C₄×C₈	C₂³×C₆₁	1	4	yes	—
269	C₄×C₈	C₂³×C₆₁	1	4	yes	—
270	C₂⁴	—	2	4	no	—
271	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
272	C₂×D₄	—	2	16	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	2	16	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	2	8	no	—
277	C₂×D₄	—	8	8	no	—
278	C₂×D₄	—	8	8	no	—
279	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	16	no	—
284	C₂²×C₄	—	8	8	no	—
285	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
290	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
291	D₈	—	2	16	no	—
292	D₈	—	2	16	no	—
293	M₁₆	—	2	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	#41×C₆₁	1	4	yes	—
298	C₂×C₈	#41×C₆₁	1	4	yes	—
299	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
300	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
301	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
302	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
303	C₄⋊C₄	—	2	16	no	—
304	C₄⋊C₄	—	2	4	no	—
305	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
306	C₄⋊C₄	C₂⁴×C₆₁	1	8	yes	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	16	no	—
309	C₂²⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
310	C₄²	C₂×D₄×C₆₁	1	2	yes	—
311	C₄²	C₂×D₄×C₆₁	1	2	yes	—
312	C₄²	C₂⁴×C₆₁	1	2	yes	—
313	C₄²	C₂⁴×C₆₁	1	2	yes	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	8	no	—
320	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
321	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
322	D₄	—	2	8	no	—
323	D₄	—	2	8	no	—
324	D₄	—	4	8	no	—
325	D₄	—	8	16	no	—
326	D₄	—	8	16	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	8	16	no	—
336	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
340	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
341	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
342	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	2	2	no	—
345	C₈	C₂×#41×C₆₁	1	4	yes	—
346	C₈	C₂×#41×C₆₁	1	4	yes	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₆₁×#532	1	2	yes	—
355	C₂²	C₆₁×#576	1	4	yes	—
356	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	8	no	—
361	C₄	C₆₁×#532	1	2	yes	—
362	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
363	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₆₁×#3176	1	4	yes	direct product factor
367	C₂	C₂×C₆₁×#532	1	1	yes	characteristic
368	C₂	C₂×C₆₁×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#540	C₂	semidirect
2. C₆₁×#3176	C₂	direct (N × H)
3. C₂×C₆₁×#499	C₂	semidirect
4. C₂×C₆₁×#493	C₂	semidirect
5. C₂×C₆₁×#490	C₂	semidirect
6. C₂×C₆₁×#469	C₂	semidirect
7. C₂×C₆₁×#466	C₂	semidirect
8. C₂×C₆₁×#442	C₂	semidirect
9. C₂×C₄×D₈×C₆₁	C₂	semidirect
10. C₂×C₆₁×#405	C₂	semidirect
16. C₆₁×#540	C₂²	semidirect
24. C₆₁×#499	C₂²	semidirect
25. C₆₁×#493	C₂²	semidirect
26. C₆₁×#490	C₂²	semidirect
27. C₆₁×#469	C₂²	semidirect
28. C₆₁×#466	C₂²	semidirect
29. C₆₁×#442	C₂²	semidirect
30. C₄×D₈×C₆₁	C₂²	semidirect
35. C₆₁×#405	C₂²	semidirect
162. C₂×#3176	C₆₁	direct (N × H)
180. C₂×#540	C₂×C₆₁	semidirect
181. #3176	C₂×C₆₁	direct (N × H)
182. C₂×#499	C₂×C₆₁	semidirect
183. C₂×#493	C₂×C₆₁	semidirect
184. C₂×#490	C₂×C₆₁	semidirect
185. C₂×#469	C₂×C₆₁	semidirect
186. C₂×#466	C₂×C₆₁	semidirect
187. C₂×#442	C₂×C₆₁	semidirect
188. C₂×C₄×D₈	C₂×C₆₁	semidirect
189. C₂×#405	C₂×C₆₁	semidirect
192. C₂×C₆₁	#3176	direct (N × H)
200. #540	C₂²×C₆₁	semidirect
208. #499	C₂²×C₆₁	semidirect
209. #493	C₂²×C₆₁	semidirect
210. #490	C₂²×C₆₁	semidirect
211. #469	C₂²×C₆₁	semidirect
212. #466	C₂²×C₆₁	semidirect
213. #442	C₂²×C₆₁	semidirect
214. C₄×D₈	C₂²×C₆₁	semidirect
219. #405	C₂²×C₆₁	semidirect
224. C₆₁	C₂×#3176	direct (N × H)
366. C₂	C₆₁×#3176	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×#540	2
C₆₁×#3176	2
C₂×C₆₁×#499	2
C₂×C₆₁×#493	2
C₂×C₆₁×#490	2
C₂×C₆₁×#469	2
C₂×C₆₁×#466	2
C₂×C₆₁×#442	2
C₂×C₄×D₈×C₆₁	2
C₂×C₆₁×#405	2
C₂×#3176	61

Subgroups — C2×C61×#3176 #29564113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3176 #29564113