Subgroups — C₆₁×#21209 #29524642

Order 15616.

1618 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#421	C₂	1	4	yes	maximal, complemented
4	C₄×#117×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1963	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1962	C₂	1	4	yes	maximal, complemented
7	C₂²×#41×C₆₁	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
9	C₆₁×#532	—	2	2	no	—
10	C₆₁×#532	—	2	2	no	—
11	C₆₁×#532	C₄	1	2	yes	complemented
12	C₆₁×#532	C₄	1	2	yes	complemented
13	C₆₁×#532	C₂²	1	2	yes	—
14	C₆₁×#532	C₂²	1	2	yes	—
15	C₂×C₄⋊Q₈×C₆₁	C₄	1	1	yes	characteristic, complemented
16	C₂×#127×C₆₁	C₄	1	1	yes	characteristic, complemented
17	C₂×#124×C₆₁	C₄	1	2	yes	complemented
18	C₂×#121×C₆₁	—	2	2	no	—
19	C₂×C₄×D₄×C₆₁	—	2	2	no	—
20	C₂×#117×C₆₁	C₂²	1	2	yes	—
21	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#423	—	2	2	no	—
23	C₆₁×#423	C₂²	1	2	yes	complemented
24	C₆₁×#423	C₂²	1	2	yes	complemented
25	C₂×C₄⋊C₈×C₆₁	—	2	2	no	—
26	C₆₁×#421	—	2	16	no	—
27	C₂×#104×C₆₁	C₂²	1	16	yes	complemented
28	C₄×C₄⋊C₄×C₆₁	—	2	2	no	—
29	C₄×C₂²⋊C₄×C₆₁	—	2	2	no	—
30	C₆₁×#376	C₂²	1	2	yes	complemented
31	C₄³×C₆₁	C₂²	1	2	yes	complemented
32	C₂×#41×C₆₁	—	2	2	no	—
33	C₂×#41×C₆₁	—	2	2	no	—
34	C₂×#41×C₆₁	—	2	8	no	—
35	C₂×#41×C₆₁	—	2	8	no	—
36	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
37	C₂×#41×C₆₁	C₂³	1	4	yes	—
38	C₂²×Q₈×C₆₁	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₆₁	—	2	2	no	—
40	C₂²×D₄×C₆₁	—	2	2	no	—
41	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₆₁	—	2	2	no	—
43	C₂³×C₄×C₆₁	D₄	1	2	yes	—
44	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₆₁	—	2	2	no	—
46	C₂×M₁₆×C₆₁	—	2	8	no	—
47	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
48	C₂²×C₈×C₆₁	—	2	2	no	—
49	C₄⋊Q₈×C₆₁	—	2	2	no	—
50	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
51	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
52	#127×C₆₁	—	2	2	no	—
53	#127×C₆₁	C₂×C₄	1	2	yes	—
54	#127×C₆₁	C₂×C₄	1	2	yes	—
55	#124×C₆₁	—	2	4	no	—
56	#124×C₆₁	C₂×C₄	1	4	yes	—
57	#124×C₆₁	C₂×C₄	1	4	yes	—
58	#121×C₆₁	—	2	4	no	—
59	#121×C₆₁	—	2	4	no	—
60	#121×C₆₁	—	2	4	no	—
61	#121×C₆₁	—	2	4	no	—
62	C₄×D₄×C₆₁	—	2	4	no	—
63	C₄×D₄×C₆₁	—	2	4	no	—
64	C₄×D₄×C₆₁	—	2	4	no	—
65	C₄×D₄×C₆₁	—	2	4	no	—
66	#117×C₆₁	—	2	4	no	—
67	#117×C₆₁	D₄	1	8	yes	complemented
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
72	C₂×C₄²×C₆₁	—	2	4	no	—
73	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	D₄	1	2	yes	—
78	C₂×C₄²×C₆₁	D₄	1	2	yes	—
79	C₂×C₄²×C₆₁	D₄	1	2	yes	—
80	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₆₁	—	2	4	no	—
84	C₄⋊C₈×C₆₁	—	2	4	no	—
85	#104×C₆₁	—	2	32	no	—
86	#95×C₆₁	—	2	4	no	—
87	C₂⁴×C₆₁	—	2	2	no	—
88	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
89	#41×C₆₁	—	2	16	no	—
90	#41×C₆₁	—	2	8	no	—
91	#41×C₆₁	—	2	8	no	—
92	#41×C₆₁	—	4	8	no	—
93	#41×C₆₁	—	4	4	no	—
94	#41×C₆₁	—	4	4	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	8	no	—
97	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
98	C₂×D₄×C₆₁	—	2	4	no	—
99	C₂×D₄×C₆₁	—	2	4	no	—
100	C₂×D₄×C₆₁	—	2	4	no	—
101	C₂×D₄×C₆₁	—	2	4	no	—
102	C₂×D₄×C₆₁	—	2	2	no	—
103	C₂×D₄×C₆₁	—	2	8	no	—
104	C₂×D₄×C₆₁	—	4	8	no	—
105	C₂×D₄×C₆₁	—	4	8	no	—
106	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	4	no	—
109	C₂²×C₄×C₆₁	—	2	4	no	—
110	C₂²×C₄×C₆₁	—	2	4	no	—
111	C₂²×C₄×C₆₁	—	4	4	no	—
112	C₂²×C₄×C₆₁	—	4	4	no	—
113	C₂²×C₄×C₆₁	—	4	4	no	—
114	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
115	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
117	C₂²×C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
126	C₂²×C₄×C₆₁	#41	1	4	yes	—
127	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₆₁	—	2	8	no	—
129	M₁₆×C₆₁	—	4	4	no	—
130	C₂×C₈×C₆₁	—	2	4	no	—
131	C₂×C₈×C₆₁	—	4	4	no	—
132	C₄⋊C₄×C₆₁	—	2	4	no	—
133	C₄⋊C₄×C₆₁	—	2	4	no	—
134	C₄⋊C₄×C₆₁	—	2	8	no	—
135	C₂²⋊C₄×C₆₁	—	2	8	no	—
136	C₂²⋊C₄×C₆₁	—	2	8	no	—
137	C₂²⋊C₄×C₆₁	—	2	8	no	—
138	C₄²×C₆₁	—	2	4	no	—
139	C₄²×C₆₁	—	4	8	no	—
140	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
141	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
142	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
143	C₄²×C₆₁	C₂²⋊C₄	1	2	yes	—
144	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₆₁	C₂×D₄	1	2	yes	—
149	C₄²×C₆₁	C₂×D₄	1	2	yes	—
150	C₄²×C₆₁	C₂×D₄	1	8	yes	complemented
151	C₂³×C₆₁	—	2	4	no	—
152	C₂³×C₆₁	—	4	2	no	—
153	C₂³×C₆₁	—	4	8	no	—
154	C₂³×C₆₁	—	4	4	no	—
155	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂³×C₆₁	#121	1	4	yes	—
158	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₆₁	—	2	8	no	—
160	Q₈×C₆₁	—	4	4	no	—
161	D₄×C₆₁	—	2	8	no	—
162	D₄×C₆₁	—	4	8	no	—
163	D₄×C₆₁	—	4	8	no	—
164	D₄×C₆₁	—	4	8	no	—
165	D₄×C₆₁	—	4	4	no	—
166	D₄×C₆₁	—	4	8	no	—
167	C₂×C₄×C₆₁	—	2	4	no	—
168	C₂×C₄×C₆₁	—	2	4	no	—
169	C₂×C₄×C₆₁	—	2	4	no	—
170	C₂×C₄×C₆₁	—	2	4	no	—
171	C₂×C₄×C₆₁	—	2	8	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	8	no	—
176	C₂×C₄×C₆₁	—	4	4	no	—
177	C₂×C₄×C₆₁	—	4	4	no	—
178	C₂×C₄×C₆₁	—	4	4	no	—
179	C₂×C₄×C₆₁	—	4	8	no	—
180	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
187	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
188	C₂×C₄×C₆₁	#121	1	4	yes	—
189	C₂×C₄×C₆₁	#124	1	2	yes	—
190	C₂×C₄×C₆₁	#124	1	2	yes	—
191	C₂×C₄×C₆₁	#127	1	2	yes	—
192	C₂×C₄×C₆₁	#127	1	2	yes	—
193	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
197	C₈×C₆₁	—	4	4	no	—
198	#21209	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	2	2	no	—
201	C₂²×C₆₁	—	2	2	no	—
202	C₂²×C₆₁	—	4	4	no	—
203	C₂²×C₆₁	—	4	8	no	—
204	C₂²×C₆₁	—	4	4	no	—
205	C₂²×C₆₁	—	8	8	no	—
206	C₂²×C₆₁	#390	1	2	yes	—
207	C₂²×C₆₁	#390	1	2	yes	—
208	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
209	C₂²×C₆₁	C₂×#121	1	2	yes	—
210	C₄×C₆₁	—	2	2	no	—
211	C₄×C₆₁	—	2	2	no	—
212	C₄×C₆₁	—	2	2	no	—
213	C₄×C₆₁	—	4	8	no	—
214	C₄×C₆₁	—	4	4	no	—
215	C₄×C₆₁	#390	1	2	yes	—
216	C₄×C₆₁	#390	1	2	yes	—
217	C₄×C₆₁	#421	1	4	yes	complemented
218	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
219	C₄×C₆₁	C₂×#124	1	1	yes	characteristic
220	C₄×C₆₁	C₂×#127	1	1	yes	characteristic
221	C₂×#532	C₂×C₆₁	1	1	yes	characteristic
222	C₂×#423	C₂×C₆₁	1	1	yes	characteristic, complemented
223	C₂×#421	C₂×C₆₁	1	4	yes	complemented
224	C₄×#117	C₂×C₆₁	1	1	yes	characteristic, complemented
225	#1963	C₂×C₆₁	1	4	yes	complemented
226	#1962	C₂×C₆₁	1	4	yes	complemented
227	C₂×C₆₁	—	2	2	no	—
228	C₂×C₆₁	—	2	2	no	—
229	C₂×C₆₁	—	2	2	no	—
230	C₂×C₆₁	—	8	4	no	—
231	C₂×C₆₁	C₂×#390	1	1	yes	characteristic
232	C₂×C₆₁	C₂×#421	1	2	yes	—
233	C₂²×#41	C₂²×C₆₁	1	2	yes	—
234	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
235	#532	—	2	2	no	—
236	#532	—	2	2	no	—
237	#532	C₄×C₆₁	1	2	yes	complemented
238	#532	C₄×C₆₁	1	2	yes	complemented
239	#532	C₂²×C₆₁	1	2	yes	—
240	#532	C₂²×C₆₁	1	2	yes	—
241	C₂×C₄⋊Q₈	C₄×C₆₁	1	1	yes	characteristic, complemented
242	C₂×#127	C₄×C₆₁	1	1	yes	characteristic, complemented
243	C₂×#124	C₄×C₆₁	1	2	yes	complemented
244	C₂×#121	—	2	2	no	—
245	C₂×C₄×D₄	—	2	2	no	—
246	C₂×#117	C₂²×C₆₁	1	2	yes	—
247	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
248	#423	—	2	2	no	—
249	#423	C₂²×C₆₁	1	2	yes	complemented
250	#423	C₂²×C₆₁	1	2	yes	complemented
251	C₂×C₄⋊C₈	—	2	2	no	—
252	#421	—	2	16	no	—
253	C₂×#104	C₂²×C₆₁	1	16	yes	complemented
254	C₄×C₄⋊C₄	—	2	2	no	—
255	C₄×C₂²⋊C₄	—	2	2	no	—
256	#376	C₂²×C₆₁	1	2	yes	complemented
257	C₄³	C₂²×C₆₁	1	2	yes	complemented
258	C₆₁	#21209	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	8	no	—
262	C₂×#41	—	2	8	no	—
263	C₂×#41	C₂×C₄×C₆₁	1	4	yes	—
264	C₂×#41	C₂³×C₆₁	1	4	yes	—
265	C₂²×Q₈	C₂×C₄×C₆₁	1	2	yes	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂³×C₄	D₄×C₆₁	1	2	yes	—
271	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	8	no	—
274	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
275	C₂²×C₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	C₄⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
278	C₄⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
279	#127	—	2	2	no	—
280	#127	C₂×C₄×C₆₁	1	2	yes	—
281	#127	C₂×C₄×C₆₁	1	2	yes	—
282	#124	—	2	4	no	—
283	#124	C₂×C₄×C₆₁	1	4	yes	—
284	#124	C₂×C₄×C₆₁	1	4	yes	—
285	#121	—	2	4	no	—
286	#121	—	2	4	no	—
287	#121	—	2	4	no	—
288	#121	—	2	4	no	—
289	C₄×D₄	—	2	4	no	—
290	C₄×D₄	—	2	4	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	4	no	—
293	#117	—	2	4	no	—
294	#117	D₄×C₆₁	1	8	yes	complemented
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₄²	—	2	4	no	—
300	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
301	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
302	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
303	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
304	C₂×C₄²	D₄×C₆₁	1	2	yes	—
305	C₂×C₄²	D₄×C₆₁	1	2	yes	—
306	C₂×C₄²	D₄×C₆₁	1	2	yes	—
307	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
308	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
310	C₄⋊C₈	—	2	4	no	—
311	C₄⋊C₈	—	2	4	no	—
312	#104	—	2	32	no	—
313	#95	—	2	4	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
316	#41	—	2	16	no	—
317	#41	—	2	8	no	—
318	#41	—	2	8	no	—
319	#41	—	4	8	no	—
320	#41	—	4	4	no	—
321	#41	—	4	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	8	no	—
324	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	4	8	no	—
332	C₂×D₄	—	4	8	no	—
333	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
342	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
343	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
344	C₂²×C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
345	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
353	C₂²×C₄	#41×C₆₁	1	4	yes	—
354	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
355	M₁₆	—	2	8	no	—
356	M₁₆	—	4	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	4	4	no	—
359	C₄⋊C₄	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	8	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	4	8	no	—
367	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
368	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
369	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
370	C₄²	C₂²⋊C₄×C₆₁	1	2	yes	—
371	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
372	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
373	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
374	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
375	C₄²	C₂×D₄×C₆₁	1	2	yes	—
376	C₄²	C₂×D₄×C₆₁	1	2	yes	—
377	C₄²	C₂×D₄×C₆₁	1	8	yes	complemented
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	8	no	—
381	C₂³	—	4	4	no	—
382	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
383	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
384	C₂³	#121×C₆₁	1	4	yes	—
385	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
386	Q₈	—	2	8	no	—
387	Q₈	—	4	4	no	—
388	D₄	—	2	8	no	—
389	D₄	—	4	8	no	—
390	D₄	—	4	8	no	—
391	D₄	—	4	8	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	8	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	—	4	4	no	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
410	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
411	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
412	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
413	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
414	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
415	C₂×C₄	#121×C₆₁	1	4	yes	—
416	C₂×C₄	#124×C₆₁	1	2	yes	—
417	C₂×C₄	#124×C₆₁	1	2	yes	—
418	C₂×C₄	#127×C₆₁	1	2	yes	—
419	C₂×C₄	#127×C₆₁	1	2	yes	—
420	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
424	C₈	—	4	4	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	8	no	—
431	C₂²	—	8	8	no	—
432	C₂²	C₆₁×#390	1	2	yes	—
433	C₂²	C₆₁×#390	1	2	yes	—
434	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
435	C₂²	C₂×#121×C₆₁	1	2	yes	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	8	no	—
440	C₄	—	4	4	no	—
441	C₄	C₆₁×#390	1	2	yes	—
442	C₄	C₆₁×#390	1	2	yes	—
443	C₄	C₆₁×#421	1	4	yes	complemented
444	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
445	C₄	C₂×#124×C₆₁	1	1	yes	characteristic
446	C₄	C₂×#127×C₆₁	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	—	8	4	no	—
451	C₂	C₂×C₆₁×#390	1	1	yes	characteristic
452	C₂	C₂×C₆₁×#421	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
prime radical	C₂×C₆₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#423	C₂	semidirect
3. C₂×C₆₁×#421	C₂	semidirect
4. C₄×#117×C₆₁	C₂	semidirect
5. C₆₁×#1963	C₂	semidirect
6. C₆₁×#1962	C₂	semidirect
11. C₆₁×#532	C₄	semidirect
12. C₆₁×#532	C₄	semidirect
15. C₂×C₄⋊Q₈×C₆₁	C₄	semidirect
16. C₂×#127×C₆₁	C₄	semidirect
17. C₂×#124×C₆₁	C₄	semidirect
23. C₆₁×#423	C₂²	semidirect
24. C₆₁×#423	C₂²	semidirect
27. C₂×#104×C₆₁	C₂²	semidirect
30. C₆₁×#376	C₂²	semidirect
31. C₄³×C₆₁	C₂²	semidirect
67. #117×C₆₁	D₄	semidirect
150. C₄²×C₆₁	C₂×D₄	semidirect
198. #21209	C₆₁	direct (N × H)
217. C₄×C₆₁	#421	semidirect
222. C₂×#423	C₂×C₆₁	semidirect
223. C₂×#421	C₂×C₆₁	semidirect
224. C₄×#117	C₂×C₆₁	semidirect
225. #1963	C₂×C₆₁	semidirect
226. #1962	C₂×C₆₁	semidirect
237. #532	C₄×C₆₁	semidirect
238. #532	C₄×C₆₁	semidirect
241. C₂×C₄⋊Q₈	C₄×C₆₁	semidirect
242. C₂×#127	C₄×C₆₁	semidirect
243. C₂×#124	C₄×C₆₁	semidirect
249. #423	C₂²×C₆₁	semidirect
250. #423	C₂²×C₆₁	semidirect
253. C₂×#104	C₂²×C₆₁	semidirect
256. #376	C₂²×C₆₁	semidirect
257. C₄³	C₂²×C₆₁	semidirect
258. C₆₁	#21209	direct (N × H)
294. #117	D₄×C₆₁	semidirect
377. C₄²	C₂×D₄×C₆₁	semidirect
443. C₄	C₆₁×#421	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#532	2
C₂×C₆₁×#423	2
C₂×C₆₁×#421	2
C₄×#117×C₆₁	2
C₆₁×#1963	2
C₆₁×#1962	2
#21209	61

Subgroups — C61×#21209 #29524642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21209 #29524642