Subgroups — C₆₁×#19953 #29523386

Order 15616.

638 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3354	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3341	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1691	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1675	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1646	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1635	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₆₁	—	2	1	no	—
13	C₆₁×#555	C₂²	1	2	yes	—
14	C₆₁×#547	C₂²	1	2	yes	—
15	C₆₁×#500	C₂²	1	1	yes	characteristic
16	C₆₁×#498	C₂²	1	2	yes	—
17	C₆₁×#494	C₂²	1	1	yes	characteristic
18	C₆₁×#487	C₂²	1	2	yes	—
19	C₆₁×#482	—	2	2	no	—
20	C₆₁×#482	—	2	2	no	—
21	C₆₁×#481	—	2	2	no	—
22	C₆₁×#476	C₂²	1	2	yes	—
23	C₆₁×#476	C₂²	1	2	yes	—
24	C₆₁×#474	C₂²	1	2	yes	—
25	C₆₁×#469	—	2	2	no	—
26	C₆₁×#467	—	2	1	no	—
27	C₆₁×#466	—	2	1	no	—
28	C₆₁×#461	C₂²	1	2	yes	—
29	C₆₁×#452	—	2	2	no	—
30	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#436	C₂²	1	2	yes	—
33	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#428	—	2	2	no	—
36	C₆₁×#427	—	2	1	no	—
37	C₆₁×#335	C₂²	1	1	yes	characteristic
38	C₆₁×#335	C₂²	1	1	yes	characteristic
39	C₆₁×#333	C₂²	1	2	yes	—
40	C₆₁×#332	C₂²	1	2	yes	—
41	C₆₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₆₁×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₆₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₆₁	—	2	2	no	—
46	#135×C₆₁	—	4	4	no	—
47	C₂×Q₁₆×C₆₁	—	2	1	no	—
48	C₂×Q₁₆×C₆₁	—	2	1	no	—
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
51	C₂×D₈×C₆₁	D₄	1	1	yes	characteristic
52	C₂×M₁₆×C₆₁	—	2	2	no	—
53	C₂²×C₈×C₆₁	—	2	1	no	—
54	C₂²×C₈×C₆₁	—	2	1	no	—
55	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
57	#124×C₆₁	—	4	2	no	—
58	#123×C₆₁	—	4	2	no	—
59	C₂²⋊Q₈×C₆₁	—	2	2	no	—
60	#121×C₆₁	—	2	2	no	—
61	#121×C₆₁	—	2	2	no	—
62	#121×C₆₁	—	2	2	no	—
63	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₆₁	C₂³	1	2	yes	—
65	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
66	#117×C₆₁	—	2	2	no	—
67	#117×C₆₁	—	2	2	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	#107×C₆₁	—	2	1	no	—
70	#107×C₆₁	—	2	1	no	—
71	#107×C₆₁	—	2	2	no	—
72	#107×C₆₁	D₄	1	1	yes	characteristic
73	#107×C₆₁	D₄	1	1	yes	characteristic
74	#106×C₆₁	—	2	2	no	—
75	#106×C₆₁	—	2	2	no	—
76	#106×C₆₁	—	2	2	no	—
77	#106×C₆₁	—	2	2	no	—
78	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
80	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
81	#103×C₆₁	—	2	2	no	—
82	#103×C₆₁	—	4	2	no	—
83	#102×C₆₁	—	2	2	no	—
84	#102×C₆₁	—	2	2	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	D₄	1	2	yes	—
87	#102×C₆₁	D₄	1	1	yes	characteristic
88	#102×C₆₁	D₄	1	1	yes	characteristic
89	C₂²⋊C₈×C₆₁	—	2	1	no	—
90	C₂²⋊C₈×C₆₁	—	2	1	no	—
91	C₂²⋊C₈×C₆₁	—	2	2	no	—
92	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
95	#41×C₆₁	—	4	4	no	—
96	#41×C₆₁	—	8	2	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	4	2	no	—
100	C₂×D₄×C₆₁	—	4	2	no	—
101	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	4	2	no	—
108	Q₁₆×C₆₁	—	4	2	no	—
109	Q₁₆×C₆₁	—	8	1	no	—
110	SD₁₆×C₆₁	—	4	4	no	—
111	D₈×C₆₁	—	2	2	no	—
112	D₈×C₆₁	—	2	2	no	—
113	M₁₆×C₆₁	—	4	4	no	—
114	C₂×C₈×C₆₁	—	2	1	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	1	no	—
118	C₂×C₈×C₆₁	—	4	2	no	—
119	C₂×C₈×C₆₁	—	4	2	no	—
120	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	4	2	no	—
129	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₆₁	—	2	1	no	—
133	C₂²⋊C₄×C₆₁	—	2	2	no	—
134	C₂²⋊C₄×C₆₁	—	2	1	no	—
135	C₂²⋊C₄×C₆₁	—	4	2	no	—
136	C₂²⋊C₄×C₆₁	—	4	2	no	—
137	C₂²⋊C₄×C₆₁	—	4	2	no	—
138	C₄²×C₆₁	—	4	2	no	—
139	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
140	C₂³×C₆₁	—	2	1	no	—
141	C₂³×C₆₁	—	2	1	no	—
142	C₂³×C₆₁	—	2	2	no	—
143	Q₈×C₆₁	—	4	2	no	—
144	Q₈×C₆₁	—	4	2	no	—
145	Q₈×C₆₁	—	8	2	no	—
146	D₄×C₆₁	—	2	1	no	—
147	D₄×C₆₁	—	2	1	no	—
148	D₄×C₆₁	—	2	2	no	—
149	D₄×C₆₁	—	2	2	no	—
150	D₄×C₆₁	—	2	1	no	—
151	D₄×C₆₁	—	2	1	no	—
152	D₄×C₆₁	—	8	4	no	—
153	D₄×C₆₁	—	16	2	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	4	2	no	—
158	C₂×C₄×C₆₁	—	4	1	no	—
159	C₂×C₄×C₆₁	—	4	1	no	—
160	C₂×C₄×C₆₁	—	4	1	no	—
161	C₂×C₄×C₆₁	—	4	1	no	—
162	C₂×C₄×C₆₁	—	4	2	no	—
163	C₂×C₄×C₆₁	—	4	2	no	—
164	C₂×C₄×C₆₁	—	4	2	no	—
165	C₂×C₄×C₆₁	—	8	4	no	—
166	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
169	C₈×C₆₁	—	2	1	no	—
170	C₈×C₆₁	—	2	1	no	—
171	C₈×C₆₁	—	4	1	no	—
172	C₈×C₆₁	—	4	2	no	—
173	C₈×C₆₁	—	4	1	no	—
174	C₈×C₆₁	—	4	1	no	—
175	C₈×C₆₁	#135	1	2	yes	complemented
176	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
177	#19953	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₆₁	—	4	1	no	—
179	C₂²×C₆₁	—	4	1	no	—
180	C₂²×C₆₁	—	4	2	no	—
181	C₂²×C₆₁	—	4	2	no	—
182	C₂²×C₆₁	—	4	1	no	—
183	C₂²×C₆₁	—	4	1	no	—
184	C₂²×C₆₁	—	4	1	no	—
185	C₂²×C₆₁	—	4	2	no	—
186	C₂²×C₆₁	—	4	1	no	—
187	C₂²×C₆₁	D₄²	1	1	yes	characteristic
188	C₄×C₆₁	—	2	1	no	—
189	C₄×C₆₁	—	4	1	no	—
190	C₄×C₆₁	—	4	1	no	—
191	C₄×C₆₁	—	4	2	no	—
192	C₄×C₆₁	—	8	2	no	—
193	C₄×C₆₁	—	8	2	no	—
194	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
195	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₄×C₆₁	#577	1	1	yes	characteristic
197	C₄×C₆₁	#578	1	1	yes	characteristic
198	#3354	C₂×C₆₁	1	2	yes	complemented
199	#3341	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#3283	C₂×C₆₁	1	1	yes	characteristic, complemented
201	#1707	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#1691	C₂×C₆₁	1	2	yes	complemented
203	#1675	C₂×C₆₁	1	1	yes	characteristic, complemented
204	#1669	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#1646	C₂×C₆₁	1	2	yes	complemented
206	#1635	C₂×C₆₁	1	2	yes	complemented
207	#1589	C₂×C₆₁	1	1	yes	characteristic, complemented
208	C₈×D₈	C₂×C₆₁	1	1	yes	characteristic, complemented
209	C₂×C₆₁	—	8	1	no	—
210	C₂×C₆₁	—	8	1	no	—
211	C₂×C₆₁	—	8	2	no	—
212	C₂×C₆₁	#3272	1	1	yes	characteristic
213	C₂×C₆₁	#3283	1	1	yes	characteristic
214	C₂×C₆₁	#3290	1	1	yes	characteristic
215	C₂×#135	—	2	1	no	—
216	#555	C₂²×C₆₁	1	2	yes	—
217	#547	C₂²×C₆₁	1	2	yes	—
218	#500	C₂²×C₆₁	1	1	yes	characteristic
219	#498	C₂²×C₆₁	1	2	yes	—
220	#494	C₂²×C₆₁	1	1	yes	characteristic
221	#487	C₂²×C₆₁	1	2	yes	—
222	#482	—	2	2	no	—
223	#482	—	2	2	no	—
224	#481	—	2	2	no	—
225	#476	C₂²×C₆₁	1	2	yes	—
226	#476	C₂²×C₆₁	1	2	yes	—
227	#474	C₂²×C₆₁	1	2	yes	—
228	#469	—	2	2	no	—
229	#467	—	2	1	no	—
230	#466	—	2	1	no	—
231	#461	C₂²×C₆₁	1	2	yes	—
232	#452	—	2	2	no	—
233	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
234	C₄×D₈	C₂²×C₆₁	1	1	yes	characteristic
235	#436	C₂²×C₆₁	1	2	yes	—
236	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
237	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
238	#428	—	2	2	no	—
239	#427	—	2	1	no	—
240	#335	C₂²×C₆₁	1	1	yes	characteristic
241	#335	C₂²×C₆₁	1	1	yes	characteristic
242	#333	C₂²×C₆₁	1	2	yes	—
243	#332	C₂²×C₆₁	1	2	yes	—
244	D₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
245	D₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
246	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
247	C₈²	C₂²×C₆₁	1	1	yes	characteristic
248	C₆₁	#19953	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#41	—	2	2	no	—
250	#135	—	4	4	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
255	C₂×D₈	D₄×C₆₁	1	1	yes	characteristic
256	C₂×M₁₆	—	2	2	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
260	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
261	#124	—	4	2	no	—
262	#123	—	4	2	no	—
263	C₂²⋊Q₈	—	2	2	no	—
264	#121	—	2	2	no	—
265	#121	—	2	2	no	—
266	#121	—	2	2	no	—
267	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
268	C₄×D₄	C₂³×C₆₁	1	2	yes	—
269	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
270	#117	—	2	2	no	—
271	#117	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	2	no	—
273	#107	—	2	1	no	—
274	#107	—	2	1	no	—
275	#107	—	2	2	no	—
276	#107	D₄×C₆₁	1	1	yes	characteristic
277	#107	D₄×C₆₁	1	1	yes	characteristic
278	#106	—	2	2	no	—
279	#106	—	2	2	no	—
280	#106	—	2	2	no	—
281	#106	—	2	2	no	—
282	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
283	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
284	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
285	#103	—	2	2	no	—
286	#103	—	4	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	#102	D₄×C₆₁	1	2	yes	—
291	#102	D₄×C₆₁	1	1	yes	characteristic
292	#102	D₄×C₆₁	1	1	yes	characteristic
293	C₂²⋊C₈	—	2	1	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
299	#41	—	4	4	no	—
300	#41	—	8	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	2	no	—
305	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
306	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
307	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	4	2	no	—
312	Q₁₆	—	4	2	no	—
313	Q₁₆	—	8	1	no	—
314	SD₁₆	—	4	4	no	—
315	D₈	—	2	2	no	—
316	D₈	—	2	2	no	—
317	M₁₆	—	4	4	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
334	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
335	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
336	C₂²⋊C₄	—	2	1	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	2	1	no	—
339	C₂²⋊C₄	—	4	2	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₄²	—	4	2	no	—
343	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	2	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	2	no	—
349	Q₈	—	8	2	no	—
350	D₄	—	2	1	no	—
351	D₄	—	2	1	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	8	4	no	—
357	D₄	—	16	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	8	4	no	—
370	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
372	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	4	1	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	#135×C₆₁	1	2	yes	complemented
380	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	D₄²×C₆₁	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
398	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
399	C₄	C₆₁×#577	1	1	yes	characteristic
400	C₄	C₆₁×#578	1	1	yes	characteristic
401	C₂	—	8	1	no	—
402	C₂	—	8	2	no	—
403	C₂	—	8	1	no	—
404	C₂	C₆₁×#3272	1	1	yes	characteristic
405	C₂	C₆₁×#3283	1	1	yes	characteristic
406	C₂	C₆₁×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3354	C₂	semidirect
2. C₆₁×#3341	C₂	semidirect
3. C₆₁×#3283	C₂	semidirect
4. C₆₁×#1707	C₂	semidirect
5. C₆₁×#1691	C₂	semidirect
6. C₆₁×#1675	C₂	semidirect
7. C₆₁×#1669	C₂	semidirect
8. C₆₁×#1646	C₂	semidirect
9. C₆₁×#1635	C₂	semidirect
10. C₆₁×#1589	C₂	semidirect
11. C₈×D₈×C₆₁	C₂	semidirect
175. C₈×C₆₁	#135	semidirect
177. #19953	C₆₁	direct (N × H)
198. #3354	C₂×C₆₁	semidirect
199. #3341	C₂×C₆₁	semidirect
200. #3283	C₂×C₆₁	semidirect
201. #1707	C₂×C₆₁	semidirect
202. #1691	C₂×C₆₁	semidirect
203. #1675	C₂×C₆₁	semidirect
204. #1669	C₂×C₆₁	semidirect
205. #1646	C₂×C₆₁	semidirect
206. #1635	C₂×C₆₁	semidirect
207. #1589	C₂×C₆₁	semidirect
208. C₈×D₈	C₂×C₆₁	semidirect
248. C₆₁	#19953	direct (N × H)
379. C₈	#135×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3354	2
C₆₁×#3341	2
C₆₁×#3283	2
C₆₁×#1707	2
C₆₁×#1691	2
C₆₁×#1675	2
C₆₁×#1669	2
C₆₁×#1646	2
C₆₁×#1635	2
C₆₁×#1589	2
C₈×D₈×C₆₁	2
#19953	61

Subgroups — C61×#19953 #29523386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19953 #29523386