Subgroups — C₂×C₆₁×#3393 #29564822

Order 15616.

1958 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×#556	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3393	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#495	C₂	1	2	yes	maximal
4	C₂×C₆₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#464	C₂	1	4	yes	maximal, complemented
6	C₂×C₆₁×#461	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×Q₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₆₁	C₂²	1	4	yes	—
13	C₂²×D₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#556	—	2	8	no	—
15	C₆₁×#556	C₂²	1	16	yes	complemented
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×#126×C₆₁	—	2	4	no	—
18	C₂×#124×C₆₁	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
20	C₂×C₄×Q₈×C₆₁	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
23	C₂×#117×C₆₁	—	2	2	no	—
24	C₆₁×#495	C₂²	1	16	yes	—
25	C₆₁×#494	C₂²	1	8	yes	complemented
26	C₆₁×#464	C₂²	1	32	yes	complemented
27	C₆₁×#461	C₂²	1	16	yes	complemented
28	C₈×Q₈×C₆₁	C₂²	1	8	yes	complemented
29	C₄×Q₁₆×C₆₁	C₂²	1	16	yes	complemented
30	C₄×D₈×C₆₁	C₂²	1	8	yes	—
31	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₆₁	C₂²	1	4	yes	—
35	C₂×#102×C₆₁	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
38	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
40	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₆₁	—	2	2	no	—
42	C₂×Q₁₆×C₆₁	—	2	8	no	—
43	C₂×Q₁₆×C₆₁	—	4	4	no	—
44	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
45	C₂×Q₁₆×C₆₁	C₂³	1	8	yes	—
46	C₂×SD₁₆×C₆₁	—	4	8	no	—
47	C₂×SD₁₆×C₆₁	C₂³	1	16	yes	—
48	C₂×D₈×C₆₁	—	2	4	no	—
49	C₂×D₈×C₆₁	C₂³	1	4	yes	—
50	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₄⋊Q₈×C₆₁	—	2	4	no	—
54	C₄⋊Q₈×C₆₁	C₂³	1	8	yes	—
55	#126×C₆₁	—	2	32	no	—
56	#124×C₆₁	—	2	8	no	—
57	#124×C₆₁	C₂³	1	16	yes	—
58	C₂²⋊Q₈×C₆₁	—	2	16	no	—
59	C₄×Q₈×C₆₁	—	2	8	no	—
60	C₄×Q₈×C₆₁	D₄	1	4	yes	—
61	C₄×Q₈×C₆₁	C₂³	1	16	yes	—
62	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
63	C₄×D₄×C₆₁	—	2	4	no	—
64	C₄×D₄×C₆₁	C₂³	1	8	yes	—
65	#117×C₆₁	—	2	16	no	—
66	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
69	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
75	C₂×C₄²×C₆₁	—	2	4	no	—
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
78	#107×C₆₁	C₂³	1	4	yes	—
79	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
80	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
81	#103×C₆₁	C₂³	1	16	yes	—
82	#102×C₆₁	C₂³	1	8	yes	—
83	C₄×C₈×C₆₁	C₂³	1	4	yes	—
84	C₄×C₈×C₆₁	C₂³	1	8	yes	—
85	C₂⁴×C₆₁	—	2	2	no	—
86	C₂×Q₈×C₆₁	—	2	4	no	—
87	C₂×Q₈×C₆₁	—	2	4	no	—
88	C₂×Q₈×C₆₁	—	2	8	no	—
89	C₂×Q₈×C₆₁	—	2	8	no	—
90	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
91	C₂×Q₈×C₆₁	C₂⁴	1	8	yes	—
92	C₂×D₄×C₆₁	—	2	2	no	—
93	C₂×D₄×C₆₁	—	2	4	no	—
94	C₂×D₄×C₆₁	—	2	4	no	—
95	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	4	no	—
98	C₂²×C₄×C₆₁	—	2	8	no	—
99	C₂²×C₄×C₆₁	—	4	8	no	—
100	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
105	Q₁₆×C₆₁	—	2	16	no	—
106	Q₁₆×C₆₁	—	4	8	no	—
107	SD₁₆×C₆₁	—	4	16	no	—
108	D₈×C₆₁	—	2	8	no	—
109	C₂×C₈×C₆₁	—	2	4	no	—
110	C₂×C₈×C₆₁	—	2	2	no	—
111	C₂×C₈×C₆₁	#41	1	4	yes	—
112	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
113	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
114	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
115	C₄⋊C₄×C₆₁	—	2	8	no	—
116	C₄⋊C₄×C₆₁	—	2	16	no	—
117	C₄⋊C₄×C₆₁	—	2	8	no	—
118	C₄⋊C₄×C₆₁	—	2	2	no	—
119	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
120	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
121	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
122	C₂²⋊C₄×C₆₁	—	2	16	no	—
123	C₂²⋊C₄×C₆₁	—	2	8	no	—
124	C₂²⋊C₄×C₆₁	—	2	16	no	—
125	C₄²×C₆₁	—	2	16	no	—
126	C₄²×C₆₁	C₂×D₄	1	2	yes	—
127	C₄²×C₆₁	C₂×D₄	1	4	yes	—
128	C₄²×C₆₁	C₂⁴	1	2	yes	—
129	C₄²×C₆₁	C₂⁴	1	4	yes	—
130	C₂³×C₆₁	—	2	4	no	—
131	C₂³×C₆₁	—	4	4	no	—
132	C₂³×C₆₁	—	4	4	no	—
133	C₂³×C₆₁	—	4	4	no	—
134	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₆₁	—	2	8	no	—
136	Q₈×C₆₁	—	2	8	no	—
137	Q₈×C₆₁	—	2	8	no	—
138	Q₈×C₆₁	—	4	8	no	—
139	D₄×C₆₁	—	2	4	no	—
140	D₄×C₆₁	—	2	4	no	—
141	D₄×C₆₁	—	4	4	no	—
142	C₂×C₄×C₆₁	—	2	4	no	—
143	C₂×C₄×C₆₁	—	2	4	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	—	2	8	no	—
147	C₂×C₄×C₆₁	—	4	8	no	—
148	C₂×C₄×C₆₁	—	4	4	no	—
149	C₂×C₄×C₆₁	—	4	16	no	—
150	C₂×C₄×C₆₁	#135	1	4	yes	—
151	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
156	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
157	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
158	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
159	C₈×C₆₁	—	2	4	no	—
160	C₈×C₆₁	—	2	2	no	—
161	C₈×C₆₁	C₂×#41	1	4	yes	—
162	C₂×#3393	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂²×C₆₁	—	4	4	no	—
164	C₂²×C₆₁	—	4	4	no	—
165	C₂²×C₆₁	—	4	4	no	—
166	C₂²×C₆₁	—	8	8	no	—
167	C₂²×C₆₁	#550	1	2	yes	—
168	C₂²×C₆₁	C₂×#135	1	2	yes	—
169	C₂²×C₆₁	#578	1	2	yes	—
170	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
171	C₄×C₆₁	—	2	4	no	—
172	C₄×C₆₁	—	2	4	no	—
173	C₄×C₆₁	—	2	2	no	—
174	C₄×C₆₁	—	4	8	no	—
175	C₄×C₆₁	—	4	4	no	—
176	C₄×C₆₁	#550	1	2	yes	—
177	C₄×C₆₁	C₂×#135	1	4	yes	—
178	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
179	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
180	C₂×#556	C₂×C₆₁	1	2	yes	complemented
181	#3393	C₂×C₆₁	1	16	yes	direct product factor
182	C₂×#495	C₂×C₆₁	1	2	yes	—
183	C₂×#494	C₂×C₆₁	1	1	yes	characteristic, complemented
184	C₂×#464	C₂×C₆₁	1	4	yes	complemented
185	C₂×#461	C₂×C₆₁	1	2	yes	complemented
186	C₂×C₈×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
187	C₂×C₄×Q₁₆	C₂×C₆₁	1	2	yes	complemented
188	C₂×C₄×D₈	C₂×C₆₁	1	1	yes	characteristic
189	C₂×C₆₁	—	8	4	no	—
190	C₂×C₆₁	#3393	1	4	yes	direct product factor
191	C₂×C₆₁	C₂×#550	1	1	yes	characteristic
192	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
193	C₂×C₆₁	C₂×#578	1	1	yes	characteristic
194	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
195	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
196	C₂²×SD₁₆	C₂²×C₆₁	1	4	yes	—
197	C₂²×D₈	C₂²×C₆₁	1	1	yes	characteristic
198	#556	—	2	8	no	—
199	#556	C₂²×C₆₁	1	16	yes	complemented
200	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
201	C₂×#126	—	2	4	no	—
202	C₂×#124	C₂²×C₆₁	1	4	yes	—
203	C₂×C₂²⋊Q₈	—	2	2	no	—
204	C₂×C₄×Q₈	C₂²×C₆₁	1	4	yes	—
205	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
207	C₂×#117	—	2	2	no	—
208	#495	C₂²×C₆₁	1	16	yes	—
209	#494	C₂²×C₆₁	1	8	yes	complemented
210	#464	C₂²×C₆₁	1	32	yes	complemented
211	#461	C₂²×C₆₁	1	16	yes	complemented
212	C₈×Q₈	C₂²×C₆₁	1	8	yes	complemented
213	C₄×Q₁₆	C₂²×C₆₁	1	16	yes	complemented
214	C₄×D₈	C₂²×C₆₁	1	8	yes	—
215	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
216	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
218	C₂×#103	C₂²×C₆₁	1	4	yes	—
219	C₂×#102	C₂²×C₆₁	1	2	yes	—
220	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
222	C₆₁	C₂×#3393	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
224	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
225	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
226	C₂³×C₄	—	2	2	no	—
227	C₂×Q₁₆	—	2	8	no	—
228	C₂×Q₁₆	—	4	4	no	—
229	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
230	C₂×Q₁₆	C₂³×C₆₁	1	8	yes	—
231	C₂×SD₁₆	—	4	8	no	—
232	C₂×SD₁₆	C₂³×C₆₁	1	16	yes	—
233	C₂×D₈	—	2	4	no	—
234	C₂×D₈	C₂³×C₆₁	1	4	yes	—
235	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
236	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
238	C₄⋊Q₈	—	2	4	no	—
239	C₄⋊Q₈	C₂³×C₆₁	1	8	yes	—
240	#126	—	2	32	no	—
241	#124	—	2	8	no	—
242	#124	C₂³×C₆₁	1	16	yes	—
243	C₂²⋊Q₈	—	2	16	no	—
244	C₄×Q₈	—	2	8	no	—
245	C₄×Q₈	D₄×C₆₁	1	4	yes	—
246	C₄×Q₈	C₂³×C₆₁	1	16	yes	—
247	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
248	C₄×D₄	—	2	4	no	—
249	C₄×D₄	C₂³×C₆₁	1	8	yes	—
250	#117	—	2	16	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
255	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₄²	—	2	4	no	—
261	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
262	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
263	#107	C₂³×C₆₁	1	4	yes	—
264	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
265	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
266	#103	C₂³×C₆₁	1	16	yes	—
267	#102	C₂³×C₆₁	1	8	yes	—
268	C₄×C₈	C₂³×C₆₁	1	4	yes	—
269	C₄×C₈	C₂³×C₆₁	1	8	yes	—
270	C₂⁴	—	2	2	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	8	no	—
274	C₂×Q₈	—	2	8	no	—
275	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
276	C₂×Q₈	C₂⁴×C₆₁	1	8	yes	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	2	8	no	—
284	C₂²×C₄	—	4	8	no	—
285	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
288	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
290	Q₁₆	—	2	16	no	—
291	Q₁₆	—	4	8	no	—
292	SD₁₆	—	4	16	no	—
293	D₈	—	2	8	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	#41×C₆₁	1	4	yes	—
297	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
298	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
299	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
300	C₄⋊C₄	—	2	8	no	—
301	C₄⋊C₄	—	2	16	no	—
302	C₄⋊C₄	—	2	8	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
305	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
306	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	—	2	8	no	—
309	C₂²⋊C₄	—	2	16	no	—
310	C₄²	—	2	16	no	—
311	C₄²	C₂×D₄×C₆₁	1	2	yes	—
312	C₄²	C₂×D₄×C₆₁	1	4	yes	—
313	C₄²	C₂⁴×C₆₁	1	2	yes	—
314	C₄²	C₂⁴×C₆₁	1	4	yes	—
315	C₂³	—	2	4	no	—
316	C₂³	—	4	4	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
320	Q₈	—	2	8	no	—
321	Q₈	—	2	8	no	—
322	Q₈	—	2	8	no	—
323	Q₈	—	4	8	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	4	no	—
326	D₄	—	4	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	#135×C₆₁	1	4	yes	—
336	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
338	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
339	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
340	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
341	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
342	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
343	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
344	C₈	—	2	4	no	—
345	C₈	—	2	2	no	—
346	C₈	C₂×#41×C₆₁	1	4	yes	—
347	C₂²	—	4	4	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	8	8	no	—
351	C₂²	C₆₁×#550	1	2	yes	—
352	C₂²	C₂×#135×C₆₁	1	2	yes	—
353	C₂²	C₆₁×#578	1	2	yes	—
354	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
355	C₄	—	2	4	no	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	8	no	—
360	C₄	C₆₁×#550	1	2	yes	—
361	C₄	C₂×#135×C₆₁	1	4	yes	—
362	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
363	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
364	C₂	—	8	4	no	—
365	C₂	C₆₁×#3393	1	4	yes	direct product factor
366	C₂	C₂×C₆₁×#550	1	1	yes	characteristic
367	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
368	C₂	C₂×C₆₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂²×D₈×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#556	C₂	semidirect
2. C₆₁×#3393	C₂	direct (N × H)
4. C₂×C₆₁×#494	C₂	semidirect
5. C₂×C₆₁×#464	C₂	semidirect
6. C₂×C₆₁×#461	C₂	semidirect
7. C₂×C₈×Q₈×C₆₁	C₂	semidirect
8. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
15. C₆₁×#556	C₂²	semidirect
25. C₆₁×#494	C₂²	semidirect
26. C₆₁×#464	C₂²	semidirect
27. C₆₁×#461	C₂²	semidirect
28. C₈×Q₈×C₆₁	C₂²	semidirect
29. C₄×Q₁₆×C₆₁	C₂²	semidirect
162. C₂×#3393	C₆₁	direct (N × H)
180. C₂×#556	C₂×C₆₁	semidirect
181. #3393	C₂×C₆₁	direct (N × H)
183. C₂×#494	C₂×C₆₁	semidirect
184. C₂×#464	C₂×C₆₁	semidirect
185. C₂×#461	C₂×C₆₁	semidirect
186. C₂×C₈×Q₈	C₂×C₆₁	semidirect
187. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
190. C₂×C₆₁	#3393	direct (N × H)
199. #556	C₂²×C₆₁	semidirect
209. #494	C₂²×C₆₁	semidirect
210. #464	C₂²×C₆₁	semidirect
211. #461	C₂²×C₆₁	semidirect
212. C₈×Q₈	C₂²×C₆₁	semidirect
213. C₄×Q₁₆	C₂²×C₆₁	semidirect
222. C₆₁	C₂×#3393	direct (N × H)
365. C₂	C₆₁×#3393	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×#556	2
C₆₁×#3393	2
C₂×C₆₁×#495	2
C₂×C₆₁×#494	2
C₂×C₆₁×#464	2
C₂×C₆₁×#461	2
C₂×C₈×Q₈×C₆₁	2
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₂×#3393	61

Subgroups — C2×C61×#3393 #29564822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3393 #29564822