Subgroups — C₂×C₆₁×#3396 #29564825

Order 15616.

2086 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×#559	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3396	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#495	C₂	1	2	yes	maximal, complemented
4	C₂×C₆₁×#493	C₂	1	1	yes	maximal, characteristic
5	C₂×C₆₁×#460	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#463	C₂	1	4	yes	maximal, complemented
7	C₂×C₈×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄×D₈×C₆₁	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₆₁	C₂²	1	4	yes	—
12	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
13	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#559	—	2	8	no	—
15	C₆₁×#559	C₂²	1	16	yes	complemented
16	C₂×#127×C₆₁	C₂²	1	2	yes	—
17	C₂×#124×C₆₁	—	2	2	no	—
18	C₂×#124×C₆₁	C₂²	1	4	yes	—
19	C₂×#123×C₆₁	—	2	4	no	—
20	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	—	2	2	no	—
23	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
24	C₆₁×#495	C₂²	1	16	yes	complemented
25	C₆₁×#493	C₂²	1	8	yes	—
26	C₆₁×#463	C₂²	1	32	yes	complemented
27	C₆₁×#460	C₂²	1	16	yes	complemented
28	C₈×Q₈×C₆₁	C₂²	1	8	yes	complemented
29	C₄×Q₁₆×C₆₁	C₂²	1	8	yes	complemented
30	C₄×D₈×C₆₁	C₂²	1	16	yes	complemented
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	2	yes	—
35	C₂×#102×C₆₁	C₂²	1	4	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	2	yes	—
40	C₂²×D₄×C₆₁	—	2	2	no	—
41	C₂²×D₄×C₆₁	—	2	2	no	—
42	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
43	C₂³×C₄×C₆₁	—	2	4	no	—
44	C₂×Q₁₆×C₆₁	—	2	4	no	—
45	C₂×Q₁₆×C₆₁	C₂³	1	4	yes	—
46	C₂×SD₁₆×C₆₁	—	4	8	no	—
47	C₂×SD₁₆×C₆₁	C₂³	1	16	yes	—
48	C₂×D₈×C₆₁	—	2	8	no	—
49	C₂×D₈×C₆₁	—	4	4	no	—
50	C₂×D₈×C₆₁	C₂³	1	8	yes	—
51	C₂×D₈×C₆₁	C₂³	1	8	yes	—
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
55	#127×C₆₁	—	2	4	no	—
56	#127×C₆₁	C₂³	1	8	yes	—
57	#124×C₆₁	—	2	16	no	—
58	#124×C₆₁	—	2	8	no	—
59	#124×C₆₁	C₂³	1	16	yes	—
60	#123×C₆₁	—	2	32	no	—
61	C₄×Q₈×C₆₁	—	2	4	no	—
62	C₄×Q₈×C₆₁	D₄	1	4	yes	—
63	C₄×Q₈×C₆₁	C₂³	1	8	yes	—
64	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
65	C₄×D₄×C₆₁	—	2	16	no	—
66	C₄×D₄×C₆₁	—	2	8	no	—
67	C₄×D₄×C₆₁	C₂³	1	16	yes	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	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	4	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
75	C₂×C₄²×C₆₁	—	2	2	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	8	yes	—
82	#102×C₆₁	C₂³	1	16	yes	—
83	C₄×C₈×C₆₁	C₂³	1	8	yes	—
84	C₄×C₈×C₆₁	C₂³	1	4	yes	—
85	C₂⁴×C₆₁	—	2	4	no	—
86	C₂×Q₈×C₆₁	—	2	4	no	—
87	C₂×Q₈×C₆₁	—	2	2	no	—
88	C₂×Q₈×C₆₁	—	2	4	no	—
89	C₂×Q₈×C₆₁	—	2	4	no	—
90	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
91	C₂×Q₈×C₆₁	C₂⁴	1	4	yes	—
92	C₂×D₄×C₆₁	—	2	4	no	—
93	C₂×D₄×C₆₁	—	2	8	no	—
94	C₂×D₄×C₆₁	—	2	8	no	—
95	C₂×D₄×C₆₁	—	2	8	no	—
96	C₂×D₄×C₆₁	—	2	8	no	—
97	C₂×D₄×C₆₁	—	4	8	no	—
98	C₂×D₄×C₆₁	—	8	4	no	—
99	C₂×D₄×C₆₁	C₂⁴	1	8	yes	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	16	no	—
103	C₂²×C₄×C₆₁	—	8	8	no	—
104	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
109	Q₁₆×C₆₁	—	2	8	no	—
110	SD₁₆×C₆₁	—	4	16	no	—
111	D₈×C₆₁	—	2	16	no	—
112	D₈×C₆₁	—	4	8	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	4	no	—
115	C₂×C₈×C₆₁	#41	1	4	yes	—
116	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
117	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
118	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
119	C₄⋊C₄×C₆₁	—	2	8	no	—
120	C₄⋊C₄×C₆₁	—	2	2	no	—
121	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
122	C₄⋊C₄×C₆₁	C₂×D₄	1	8	yes	—
123	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
124	C₂²⋊C₄×C₆₁	—	2	16	no	—
125	C₂²⋊C₄×C₆₁	—	2	16	no	—
126	C₂²⋊C₄×C₆₁	—	2	16	no	—
127	C₄²×C₆₁	—	2	8	no	—
128	C₄²×C₆₁	C₂×D₄	1	4	yes	—
129	C₄²×C₆₁	C₂×D₄	1	2	yes	—
130	C₄²×C₆₁	C₂⁴	1	4	yes	—
131	C₄²×C₆₁	C₂⁴	1	2	yes	—
132	C₂³×C₆₁	—	2	8	no	—
133	C₂³×C₆₁	—	4	8	no	—
134	C₂³×C₆₁	—	4	8	no	—
135	C₂³×C₆₁	—	4	8	no	—
136	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₆₁	—	2	8	no	—
138	Q₈×C₆₁	—	2	4	no	—
139	Q₈×C₆₁	—	2	4	no	—
140	Q₈×C₆₁	—	4	4	no	—
141	D₄×C₆₁	—	2	8	no	—
142	D₄×C₆₁	—	2	8	no	—
143	D₄×C₆₁	—	4	8	no	—
144	D₄×C₆₁	—	4	16	no	—
145	D₄×C₆₁	—	8	8	no	—
146	C₂×C₄×C₆₁	—	2	4	no	—
147	C₂×C₄×C₆₁	—	2	4	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	4	no	—
150	C₂×C₄×C₆₁	—	2	4	no	—
151	C₂×C₄×C₆₁	—	4	4	no	—
152	C₂×C₄×C₆₁	—	4	4	no	—
153	C₂×C₄×C₆₁	—	8	16	no	—
154	C₂×C₄×C₆₁	#135	1	4	yes	—
155	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
156	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
157	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
158	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
161	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
162	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
163	C₈×C₆₁	—	2	2	no	—
164	C₈×C₆₁	—	2	4	no	—
165	C₈×C₆₁	C₂×#41	1	4	yes	—
166	C₂×#3396	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂²×C₆₁	—	4	8	no	—
168	C₂²×C₆₁	—	4	8	no	—
169	C₂²×C₆₁	—	4	8	no	—
170	C₂²×C₆₁	—	8	16	no	—
171	C₂²×C₆₁	#550	1	2	yes	—
172	C₂²×C₆₁	C₂×#135	1	2	yes	—
173	C₂²×C₆₁	#576	1	2	yes	—
174	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
175	C₄×C₆₁	—	2	4	no	—
176	C₄×C₆₁	—	2	4	no	—
177	C₄×C₆₁	—	2	2	no	—
178	C₄×C₆₁	—	4	4	no	—
179	C₄×C₆₁	—	4	4	no	—
180	C₄×C₆₁	#550	1	2	yes	—
181	C₄×C₆₁	C₂×#135	1	4	yes	—
182	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
183	C₄×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×#559	C₂×C₆₁	1	2	yes	complemented
185	#3396	C₂×C₆₁	1	16	yes	direct product factor
186	C₂×#495	C₂×C₆₁	1	2	yes	complemented
187	C₂×#493	C₂×C₆₁	1	1	yes	characteristic
188	C₂×#460	C₂×C₆₁	1	2	yes	complemented
189	C₂×#463	C₂×C₆₁	1	4	yes	complemented
190	C₂×C₈×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
191	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
192	C₂×C₄×D₈	C₂×C₆₁	1	2	yes	complemented
193	C₂×C₆₁	—	8	8	no	—
194	C₂×C₆₁	#3396	1	4	yes	direct product factor
195	C₂×C₆₁	C₂×#550	1	1	yes	characteristic
196	C₂×C₆₁	C₂²×#135	1	1	yes	characteristic
197	C₂×C₆₁	C₂×#576	1	1	yes	characteristic
198	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
199	C₂²×SD₁₆	C₂²×C₆₁	1	4	yes	—
200	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
201	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
202	#559	—	2	8	no	—
203	#559	C₂²×C₆₁	1	16	yes	complemented
204	C₂×#127	C₂²×C₆₁	1	2	yes	—
205	C₂×#124	—	2	2	no	—
206	C₂×#124	C₂²×C₆₁	1	4	yes	—
207	C₂×#123	—	2	4	no	—
208	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
209	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
210	C₂×C₄×D₄	—	2	2	no	—
211	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
212	#495	C₂²×C₆₁	1	16	yes	complemented
213	#493	C₂²×C₆₁	1	8	yes	—
214	#463	C₂²×C₆₁	1	32	yes	complemented
215	#460	C₂²×C₆₁	1	16	yes	complemented
216	C₈×Q₈	C₂²×C₆₁	1	8	yes	complemented
217	C₄×Q₁₆	C₂²×C₆₁	1	8	yes	complemented
218	C₄×D₈	C₂²×C₆₁	1	16	yes	complemented
219	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×#103	C₂²×C₆₁	1	2	yes	—
223	C₂×#102	C₂²×C₆₁	1	4	yes	—
224	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
225	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
226	C₆₁	C₂×#3396	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
228	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	—	2	2	no	—
231	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
232	C₂³×C₄	—	2	4	no	—
233	C₂×Q₁₆	—	2	4	no	—
234	C₂×Q₁₆	C₂³×C₆₁	1	4	yes	—
235	C₂×SD₁₆	—	4	8	no	—
236	C₂×SD₁₆	C₂³×C₆₁	1	16	yes	—
237	C₂×D₈	—	2	8	no	—
238	C₂×D₈	—	4	4	no	—
239	C₂×D₈	C₂³×C₆₁	1	8	yes	—
240	C₂×D₈	C₂³×C₆₁	1	8	yes	—
241	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
243	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
244	#127	—	2	4	no	—
245	#127	C₂³×C₆₁	1	8	yes	—
246	#124	—	2	16	no	—
247	#124	—	2	8	no	—
248	#124	C₂³×C₆₁	1	16	yes	—
249	#123	—	2	32	no	—
250	C₄×Q₈	—	2	4	no	—
251	C₄×Q₈	D₄×C₆₁	1	4	yes	—
252	C₄×Q₈	C₂³×C₆₁	1	8	yes	—
253	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
254	C₄×D₄	—	2	16	no	—
255	C₄×D₄	—	2	8	no	—
256	C₄×D₄	C₂³×C₆₁	1	16	yes	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
259	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
266	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
267	#107	C₂³×C₆₁	1	4	yes	—
268	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
269	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
270	#103	C₂³×C₆₁	1	8	yes	—
271	#102	C₂³×C₆₁	1	16	yes	—
272	C₄×C₈	C₂³×C₆₁	1	8	yes	—
273	C₄×C₈	C₂³×C₆₁	1	4	yes	—
274	C₂⁴	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
280	C₂×Q₈	C₂⁴×C₆₁	1	4	yes	—
281	C₂×D₄	—	2	4	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂×D₄	—	8	4	no	—
288	C₂×D₄	C₂⁴×C₆₁	1	8	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	16	no	—
292	C₂²×C₄	—	8	8	no	—
293	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
295	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
298	Q₁₆	—	2	8	no	—
299	SD₁₆	—	4	16	no	—
300	D₈	—	2	16	no	—
301	D₈	—	4	8	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	#41×C₆₁	1	4	yes	—
305	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
306	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
307	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
308	C₄⋊C₄	—	2	8	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
311	C₄⋊C₄	C₂×D₄×C₆₁	1	8	yes	—
312	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
313	C₂²⋊C₄	—	2	16	no	—
314	C₂²⋊C₄	—	2	16	no	—
315	C₂²⋊C₄	—	2	16	no	—
316	C₄²	—	2	8	no	—
317	C₄²	C₂×D₄×C₆₁	1	4	yes	—
318	C₄²	C₂×D₄×C₆₁	1	2	yes	—
319	C₄²	C₂⁴×C₆₁	1	4	yes	—
320	C₄²	C₂⁴×C₆₁	1	2	yes	—
321	C₂³	—	2	8	no	—
322	C₂³	—	4	8	no	—
323	C₂³	—	4	8	no	—
324	C₂³	—	4	8	no	—
325	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
326	Q₈	—	2	8	no	—
327	Q₈	—	2	4	no	—
328	Q₈	—	2	4	no	—
329	Q₈	—	4	4	no	—
330	D₄	—	2	8	no	—
331	D₄	—	2	8	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	16	no	—
334	D₄	—	8	8	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	8	16	no	—
343	C₂×C₄	#135×C₆₁	1	4	yes	—
344	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
345	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
346	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
349	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
350	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
351	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
352	C₈	—	2	2	no	—
353	C₈	—	2	4	no	—
354	C₈	C₂×#41×C₆₁	1	4	yes	—
355	C₂²	—	4	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	4	8	no	—
358	C₂²	—	8	16	no	—
359	C₂²	C₆₁×#550	1	2	yes	—
360	C₂²	C₂×#135×C₆₁	1	2	yes	—
361	C₂²	C₆₁×#576	1	2	yes	—
362	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	2	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	C₆₁×#550	1	2	yes	—
369	C₄	C₂×#135×C₆₁	1	4	yes	—
370	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
371	C₄	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
372	C₂	—	8	8	no	—
373	C₂	C₆₁×#3396	1	4	yes	direct product factor
374	C₂	C₂×C₆₁×#550	1	1	yes	characteristic
375	C₂	C₂²×#135×C₆₁	1	1	yes	characteristic
376	C₂	C₂×C₆₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
prime radical	C₂×C₆₁×#493	C₂
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×#559	C₂	semidirect
2. C₆₁×#3396	C₂	direct (N × H)
3. C₂×C₆₁×#495	C₂	semidirect
5. C₂×C₆₁×#460	C₂	semidirect
6. C₂×C₆₁×#463	C₂	semidirect
7. C₂×C₈×Q₈×C₆₁	C₂	semidirect
8. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
9. C₂×C₄×D₈×C₆₁	C₂	semidirect
15. C₆₁×#559	C₂²	semidirect
24. C₆₁×#495	C₂²	semidirect
26. C₆₁×#463	C₂²	semidirect
27. C₆₁×#460	C₂²	semidirect
28. C₈×Q₈×C₆₁	C₂²	semidirect
29. C₄×Q₁₆×C₆₁	C₂²	semidirect
30. C₄×D₈×C₆₁	C₂²	semidirect
166. C₂×#3396	C₆₁	direct (N × H)
184. C₂×#559	C₂×C₆₁	semidirect
185. #3396	C₂×C₆₁	direct (N × H)
186. C₂×#495	C₂×C₆₁	semidirect
188. C₂×#460	C₂×C₆₁	semidirect
189. C₂×#463	C₂×C₆₁	semidirect
190. C₂×C₈×Q₈	C₂×C₆₁	semidirect
191. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
192. C₂×C₄×D₈	C₂×C₆₁	semidirect
194. C₂×C₆₁	#3396	direct (N × H)
203. #559	C₂²×C₆₁	semidirect
212. #495	C₂²×C₆₁	semidirect
214. #463	C₂²×C₆₁	semidirect
215. #460	C₂²×C₆₁	semidirect
216. C₈×Q₈	C₂²×C₆₁	semidirect
217. C₄×Q₁₆	C₂²×C₆₁	semidirect
218. C₄×D₈	C₂²×C₆₁	semidirect
226. C₆₁	C₂×#3396	direct (N × H)
373. C₂	C₆₁×#3396	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×#559	2
C₆₁×#3396	2
C₂×C₆₁×#495	2
C₂×C₆₁×#493	2
C₂×C₆₁×#460	2
C₂×C₆₁×#463	2
C₂×C₈×Q₈×C₆₁	2
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₂×#3396	61

Subgroups — C2×C61×#3396 #29564825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#3396 #29564825