Subgroups — C₂×C₆₁×#1816 #29524110

Order 15616.

1374 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×#108×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#417	C₂	1	2	yes	maximal
5	C₆₁×#1816	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₆₁×#343	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
8	C₂×#131×C₆₁	—	2	4	no	—
9	C₂×#131×C₆₁	—	2	2	no	—
10	C₂×#131×C₆₁	C₄	1	8	yes	complemented
11	C₂×#131×C₆₁	C₂²	1	4	yes	—
12	C₂²×M₁₆×C₆₁	—	2	1	no	—
13	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₁	—	2	1	no	—
16	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
18	C₂×#108×C₆₁	—	2	4	no	—
19	C₂×#108×C₆₁	C₂²	1	4	yes	complemented
20	C₂×#107×C₆₁	—	2	1	no	—
21	C₂×#107×C₆₁	—	2	1	no	—
22	C₂×#107×C₆₁	—	2	2	no	—
23	C₂×#107×C₆₁	C₂²	1	4	yes	complemented
24	C₆₁×#417	—	2	4	no	—
25	C₆₁×#417	C₂²	1	8	yes	—
26	C₂×#103×C₆₁	—	2	2	no	—
27	C₂×#102×C₆₁	—	2	2	no	—
28	C₆₁×#343	C₂²	1	8	yes	complemented
29	C₂×#41×C₆₁	—	2	2	no	—
30	C₂×#41×C₆₁	—	2	1	no	—
31	C₂×#41×C₆₁	—	2	1	no	—
32	C₂×#41×C₆₁	—	2	2	no	—
33	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
34	C₂×#41×C₆₁	D₄	1	2	yes	—
35	C₂×#41×C₆₁	Q₈	1	4	yes	—
36	C₂×#41×C₆₁	C₂³	1	2	yes	—
37	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
38	C₂²×D₄×C₆₁	—	2	1	no	—
39	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₆₁	—	2	1	no	—
41	C₂³×C₄×C₆₁	—	2	2	no	—
42	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
43	#131×C₆₁	—	2	16	no	—
44	#131×C₆₁	—	2	8	no	—
45	#131×C₆₁	C₂×C₄	1	16	yes	complemented
46	C₂×M₁₆×C₆₁	—	2	2	no	—
47	C₂×M₁₆×C₆₁	—	2	1	no	—
48	C₂×M₁₆×C₆₁	—	2	2	no	—
49	C₂×M₁₆×C₆₁	—	2	8	no	—
50	C₂×M₁₆×C₆₁	—	2	4	no	—
51	C₂×M₁₆×C₆₁	—	2	4	no	—
52	C₂×M₁₆×C₆₁	—	2	4	no	—
53	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	—
54	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
55	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₆₁	—	2	1	no	—
57	C₂²×C₈×C₆₁	—	2	8	no	—
58	C₂²×C₈×C₆₁	—	2	4	no	—
59	C₂²×C₈×C₆₁	—	2	2	no	—
60	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
61	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₆₁	D₄	1	2	yes	—
64	C₂²×C₈×C₆₁	D₄	1	4	yes	—
65	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
72	#108×C₆₁	—	2	8	no	—
73	#107×C₆₁	—	2	4	no	—
74	#107×C₆₁	—	2	4	no	—
75	#103×C₆₁	—	2	8	no	—
76	#102×C₆₁	—	2	8	no	—
77	C₂⁴×C₆₁	—	2	1	no	—
78	C₂⁴×C₆₁	#41	1	1	yes	characteristic
79	#41×C₆₁	—	2	4	no	—
80	#41×C₆₁	—	2	4	no	—
81	#41×C₆₁	—	2	4	no	—
82	#41×C₆₁	—	2	4	no	—
83	#41×C₆₁	—	2	4	no	—
84	#41×C₆₁	—	2	2	no	—
85	#41×C₆₁	—	2	2	no	—
86	#41×C₆₁	C₄⋊C₄	1	8	yes	—
87	#41×C₆₁	C₂²×C₄	1	4	yes	—
88	#41×C₆₁	C₂×Q₈	1	4	yes	—
89	C₂×Q₈×C₆₁	—	2	1	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	C₄⋊C₄	1	4	yes	—
92	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
93	C₂×D₄×C₆₁	—	2	4	no	—
94	C₂×D₄×C₆₁	—	2	2	no	—
95	C₂×D₄×C₆₁	—	2	4	no	—
96	C₂×D₄×C₆₁	—	2	2	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	2	1	no	—
99	C₂×D₄×C₆₁	C₄⋊C₄	1	4	yes	—
100	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	4	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	4	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	2	4	no	—
107	C₂²×C₄×C₆₁	—	4	2	no	—
108	C₂²×C₄×C₆₁	—	4	2	no	—
109	C₂²×C₄×C₆₁	—	8	4	no	—
110	C₂²×C₄×C₆₁	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	#41	1	2	yes	—
119	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₆₁	—	2	4	no	—
121	M₁₆×C₆₁	—	2	2	no	—
122	M₁₆×C₆₁	—	2	16	no	—
123	M₁₆×C₆₁	—	2	4	no	—
124	M₁₆×C₆₁	—	2	4	no	—
125	M₁₆×C₆₁	—	4	4	no	—
126	M₁₆×C₆₁	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₆₁	—	2	4	no	—
128	C₂×C₈×C₆₁	—	2	2	no	—
129	C₂×C₈×C₆₁	—	2	16	no	—
130	C₂×C₈×C₆₁	—	2	4	no	—
131	C₂×C₈×C₆₁	—	4	4	no	—
132	C₂×C₈×C₆₁	C₂²⋊C₄	1	4	yes	—
133	C₂×C₈×C₆₁	C₂²⋊C₄	1	4	yes	—
134	C₂×C₈×C₆₁	C₂²⋊C₄	1	8	yes	—
135	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
139	C₄⋊C₄×C₆₁	—	2	4	no	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	4	2	no	—
142	C₄⋊C₄×C₆₁	—	4	2	no	—
143	C₂³×C₆₁	—	2	2	no	—
144	C₂³×C₆₁	—	2	2	no	—
145	C₂³×C₆₁	—	2	2	no	—
146	C₂³×C₆₁	—	2	4	no	—
147	C₂³×C₆₁	—	4	2	no	—
148	C₂³×C₆₁	—	4	2	no	—
149	C₂³×C₆₁	#117	1	2	yes	—
150	C₂³×C₆₁	#121	1	1	yes	characteristic
151	C₂³×C₆₁	#121	1	1	yes	characteristic
152	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
153	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
154	Q₈×C₆₁	—	2	2	no	—
155	Q₈×C₆₁	—	2	4	no	—
156	Q₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
157	D₄×C₆₁	—	2	4	no	—
158	D₄×C₆₁	—	2	4	no	—
159	D₄×C₆₁	—	2	8	no	—
160	D₄×C₆₁	—	2	2	no	—
161	D₄×C₆₁	—	2	4	no	—
162	D₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	4	no	—
165	C₂×C₄×C₆₁	—	2	4	no	—
166	C₂×C₄×C₆₁	—	2	4	no	—
167	C₂×C₄×C₆₁	—	2	8	no	—
168	C₂×C₄×C₆₁	—	4	4	no	—
169	C₂×C₄×C₆₁	—	8	4	no	—
170	C₂×C₄×C₆₁	—	8	4	no	—
171	C₂×C₄×C₆₁	—	8	4	no	—
172	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₆₁	#117	1	2	yes	—
177	C₂×C₄×C₆₁	#121	1	2	yes	—
178	C₂×C₄×C₆₁	#121	1	2	yes	—
179	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
182	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
183	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
184	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
190	C₈×C₆₁	—	2	4	no	—
191	C₈×C₆₁	—	4	4	no	—
192	C₈×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
193	C₈×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
194	C₂×#1816	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₆₁	—	2	4	no	—
196	C₂²×C₆₁	—	2	4	no	—
197	C₂²×C₆₁	—	2	1	no	—
198	C₂²×C₆₁	—	2	1	no	—
199	C₂²×C₆₁	—	2	1	no	—
200	C₂²×C₆₁	—	2	1	no	—
201	C₂²×C₆₁	—	2	4	no	—
202	C₂²×C₆₁	—	4	8	no	—
203	C₂²×C₆₁	—	4	2	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	#380	1	2	yes	—
206	C₂²×C₆₁	#380	1	2	yes	—
207	C₂²×C₆₁	#472	1	2	yes	—
208	C₂²×C₆₁	#473	1	2	yes	—
209	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
210	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
211	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
212	C₄×C₆₁	—	2	4	no	—
213	C₄×C₆₁	—	8	4	no	—
214	C₄×C₆₁	#380	1	2	yes	—
215	C₄×C₆₁	#380	1	2	yes	—
216	C₄×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
217	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
218	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
219	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
220	C₂²×#131	C₂×C₆₁	1	1	yes	characteristic
221	C₂²×#108	C₂×C₆₁	1	1	yes	characteristic, complemented
222	C₂²×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
223	C₂×#417	C₂×C₆₁	1	2	yes	—
224	#1816	C₂×C₆₁	1	8	yes	direct product factor
225	C₂×#343	C₂×C₆₁	1	2	yes	complemented
226	C₂×C₆₁	—	2	1	no	—
227	C₂×C₆₁	—	2	1	no	—
228	C₂×C₆₁	—	2	2	no	—
229	C₂×C₆₁	—	4	4	no	—
230	C₂×C₆₁	#1816	1	4	yes	direct product factor
231	C₂×C₆₁	C₂×#380	1	1	yes	characteristic
232	C₂×C₆₁	C₂×#472	1	1	yes	characteristic
233	C₂×C₆₁	C₂×#473	1	1	yes	characteristic
234	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
235	C₂×#131	—	2	4	no	—
236	C₂×#131	—	2	2	no	—
237	C₂×#131	C₄×C₆₁	1	8	yes	complemented
238	C₂×#131	C₂²×C₆₁	1	4	yes	—
239	C₂²×M₁₆	—	2	1	no	—
240	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
241	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
242	C₂³×C₈	—	2	1	no	—
243	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
244	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
245	C₂×#108	—	2	4	no	—
246	C₂×#108	C₂²×C₆₁	1	4	yes	complemented
247	C₂×#107	—	2	1	no	—
248	C₂×#107	—	2	1	no	—
249	C₂×#107	—	2	2	no	—
250	C₂×#107	C₂²×C₆₁	1	4	yes	complemented
251	#417	—	2	4	no	—
252	#417	C₂²×C₆₁	1	8	yes	—
253	C₂×#103	—	2	2	no	—
254	C₂×#102	—	2	2	no	—
255	#343	C₂²×C₆₁	1	8	yes	complemented
256	C₆₁	C₂×#1816	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#41	—	2	2	no	—
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	2	1	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	C₂×C₄×C₆₁	1	4	yes	—
262	C₂×#41	D₄×C₆₁	1	2	yes	—
263	C₂×#41	Q₈×C₆₁	1	4	yes	—
264	C₂×#41	C₂³×C₆₁	1	2	yes	—
265	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
271	#131	—	2	16	no	—
272	#131	—	2	8	no	—
273	#131	C₂×C₄×C₆₁	1	16	yes	complemented
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	—	2	8	no	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	—	2	4	no	—
281	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	—
282	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
283	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	8	no	—
286	C₂²×C₈	—	2	4	no	—
287	C₂²×C₈	—	2	2	no	—
288	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
289	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
290	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
291	C₂²×C₈	D₄×C₆₁	1	2	yes	—
292	C₂²×C₈	D₄×C₆₁	1	4	yes	—
293	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
300	#108	—	2	8	no	—
301	#107	—	2	4	no	—
302	#107	—	2	4	no	—
303	#103	—	2	8	no	—
304	#102	—	2	8	no	—
305	C₂⁴	—	2	1	no	—
306	C₂⁴	#41×C₆₁	1	1	yes	characteristic
307	#41	—	2	4	no	—
308	#41	—	2	4	no	—
309	#41	—	2	4	no	—
310	#41	—	2	4	no	—
311	#41	—	2	4	no	—
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	C₄⋊C₄×C₆₁	1	8	yes	—
315	#41	C₂²×C₄×C₆₁	1	4	yes	—
316	#41	C₂×Q₈×C₆₁	1	4	yes	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	C₄⋊C₄×C₆₁	1	4	yes	—
320	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₄⋊C₄×C₆₁	1	4	yes	—
328	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	8	4	no	—
338	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
345	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
346	C₂²×C₄	#41×C₆₁	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
348	M₁₆	—	2	4	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	2	16	no	—
351	M₁₆	—	2	4	no	—
352	M₁₆	—	2	4	no	—
353	M₁₆	—	4	4	no	—
354	M₁₆	C₂²×C₄×C₆₁	1	4	yes	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	16	no	—
358	C₂×C₈	—	2	4	no	—
359	C₂×C₈	—	4	4	no	—
360	C₂×C₈	C₂²⋊C₄×C₆₁	1	4	yes	—
361	C₂×C₈	C₂²⋊C₄×C₆₁	1	4	yes	—
362	C₂×C₈	C₂²⋊C₄×C₆₁	1	8	yes	—
363	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
364	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
366	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	2	4	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	#117×C₆₁	1	2	yes	—
378	C₂³	#121×C₆₁	1	1	yes	characteristic
379	C₂³	#121×C₆₁	1	1	yes	characteristic
380	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
381	C₂³	C₂×#41×C₆₁	1	1	yes	characteristic
382	Q₈	—	2	4	no	—
383	Q₈	—	2	2	no	—
384	Q₈	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
385	D₄	—	2	8	no	—
386	D₄	—	2	4	no	—
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	2	no	—
390	D₄	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	8	4	no	—
398	C₂×C₄	—	8	4	no	—
399	C₂×C₄	—	8	4	no	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
402	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
403	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
404	C₂×C₄	#117×C₆₁	1	2	yes	—
405	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
406	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
407	C₂×C₄	#121×C₆₁	1	2	yes	—
408	C₂×C₄	#121×C₆₁	1	2	yes	—
409	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
410	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
411	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
412	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
415	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	4	4	no	—
420	C₈	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
421	C₈	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	8	no	—
432	C₂²	C₆₁×#380	1	2	yes	—
433	C₂²	C₆₁×#380	1	2	yes	—
434	C₂²	C₆₁×#472	1	2	yes	—
435	C₂²	C₆₁×#473	1	2	yes	—
436	C₂²	C₂×#117×C₆₁	1	1	yes	characteristic
437	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
438	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	8	4	no	—
441	C₄	C₆₁×#380	1	2	yes	—
442	C₄	C₆₁×#380	1	2	yes	—
443	C₄	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
444	C₄	C₂²×C₄⋊C₄×C₆₁	1	1	yes	characteristic
445	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
446	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	4	4	no	—
451	C₂	C₆₁×#1816	1	4	yes	direct product factor
452	C₂	C₂×C₆₁×#380	1	1	yes	characteristic
453	C₂	C₂×C₆₁×#472	1	1	yes	characteristic
454	C₂	C₂×C₆₁×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	#121
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂³×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#108×C₆₁	C₂	semidirect
3. C₂²×#107×C₆₁	C₂	semidirect
5. C₆₁×#1816	C₂	direct (N × H)
6. C₂×C₆₁×#343	C₂	semidirect
10. C₂×#131×C₆₁	C₄	semidirect
19. C₂×#108×C₆₁	C₂²	semidirect
23. C₂×#107×C₆₁	C₂²	semidirect
28. C₆₁×#343	C₂²	semidirect
45. #131×C₆₁	C₂×C₄	semidirect
194. C₂×#1816	C₆₁	direct (N × H)
221. C₂²×#108	C₂×C₆₁	semidirect
222. C₂²×#107	C₂×C₆₁	semidirect
224. #1816	C₂×C₆₁	direct (N × H)
225. C₂×#343	C₂×C₆₁	semidirect
230. C₂×C₆₁	#1816	direct (N × H)
237. C₂×#131	C₄×C₆₁	semidirect
246. C₂×#108	C₂²×C₆₁	semidirect
250. C₂×#107	C₂²×C₆₁	semidirect
255. #343	C₂²×C₆₁	semidirect
256. C₆₁	C₂×#1816	direct (N × H)
273. #131	C₂×C₄×C₆₁	semidirect
451. C₂	C₆₁×#1816	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#131×C₆₁	2
C₂²×#108×C₆₁	2
C₂²×#107×C₆₁	2
C₂×C₆₁×#417	2
C₆₁×#1816	2
C₂×C₆₁×#343	2
C₂×#1816	61

Subgroups — C2×C61×#1816 #29524110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#1816 #29524110