Subgroups — D₆₁×#2171 #29833243

Order 15616.

654 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#504×D₆₁	C₂	1	2	yes	maximal, complemented
2	#443×D₆₁	C₂	1	1	yes	maximal, characteristic
3	#21447662	C₂	1	1	yes	maximal, characteristic, complemented
4	#21447661	C₂	1	1	yes	maximal, characteristic, complemented
5	#21447660	C₂	1	1	yes	maximal, characteristic, complemented
6	#21447659	C₂	1	2	yes	maximal, complemented
7	#21447658	C₂	1	2	yes	maximal, complemented
8	#364×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#350×D₆₁	C₂	1	2	yes	maximal, complemented
10	#346×D₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#2171	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₆₁	C₄	1	1	yes	characteristic
13	#131×D₆₁	C₂²	1	2	yes	—
14	#16840180	—	2	2	no	—
15	#16840180	C₂²	1	2	yes	complemented
16	#16840179	C₂²	1	2	yes	complemented
17	#16840178	—	2	2	no	—
18	#16840178	C₂²	1	2	yes	complemented
19	M₃₂×D₆₁	—	2	2	no	—
20	M₃₂×D₆₁	C₂²	1	2	yes	—
21	C₂×C₁₆×D₆₁	—	2	2	no	—
22	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₆₁	C₂²	1	1	yes	characteristic
24	#16839880	C₂²	1	1	yes	characteristic
25	#16839879	C₄	1	1	yes	characteristic
26	#16839878	C₄	1	1	yes	characteristic
27	#16839877	C₂²	1	2	yes	—
28	#16839876	C₄	1	2	yes	—
29	#108×D₆₁	C₄	1	1	yes	characteristic
30	#104×D₆₁	C₄	1	2	yes	—
31	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
32	#16839583	C₂²	1	1	yes	characteristic, complemented
33	#16839582	C₂²	1	2	yes	complemented
34	#16839547	C₂²	1	2	yes	complemented
35	#16839546	C₂²	1	2	yes	complemented
36	#16839545	C₂²	1	2	yes	complemented
37	#16839538	C₂²	1	1	yes	characteristic, complemented
38	#16839537	C₂²	1	1	yes	characteristic, complemented
39	#16839537	C₂²	1	1	yes	characteristic, complemented
40	C₆₁×#504	C₂²	1	2	yes	complemented
41	C₆₁×#443	C₂²	1	1	yes	characteristic
42	C₆₁×#364	C₂²	1	1	yes	characteristic, complemented
43	C₆₁×#350	C₂²	1	2	yes	complemented
44	C₆₁×#346	C₂²	1	1	yes	characteristic, complemented
45	#41×D₆₁	C₂×C₄	1	2	yes	—
46	#14519800	C₈	1	1	yes	characteristic
47	#14519799	C₂×C₄	1	1	yes	characteristic
48	#14519798	C₈	1	2	yes	—
49	#14519797	C₂×C₄	1	2	yes	—
50	#14519796	C₈	1	1	yes	characteristic
51	Q₁₆×D₆₁	C₈	1	1	yes	characteristic
52	SD₁₆×D₆₁	C₈	1	2	yes	—
53	D₈×D₆₁	C₈	1	1	yes	characteristic
54	#14519785	—	2	2	no	—
55	#14519785	C₂×C₄	1	2	yes	—
56	#14519784	C₂×C₄	1	2	yes	—
57	#14519783	—	2	2	no	—
58	#14519783	C₂³	1	2	yes	—
59	M₁₆×D₆₁	—	2	2	no	—
60	M₁₆×D₆₁	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₆₁	—	2	2	no	—
62	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
64	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
65	#14519717	—	2	2	no	—
66	#14519717	C₂³	1	2	yes	—
67	#14519716	—	2	2	no	—
68	#14519716	—	2	2	no	—
69	#14519716	—	2	2	no	—
70	C₂×#11758185	—	2	2	no	—
71	C₂×#11758185	C₂³	1	1	yes	characteristic
72	C₂×#11758185	C₂³	1	1	yes	characteristic
73	C₁₆×D₆₁	—	2	2	no	—
74	C₁₆×D₆₁	—	2	1	no	—
75	C₁₆×D₆₁	—	2	1	no	—
76	C₁₆×D₆₁	—	2	2	no	—
77	C₁₆×D₆₁	—	2	2	no	—
78	C₁₆×D₆₁	D₄	1	2	yes	—
79	C₁₆×D₆₁	D₄	1	2	yes	—
80	#14519713	C₂×C₄	1	1	yes	characteristic
81	#14519712	C₂×C₄	1	2	yes	—
82	#14519705	C₂×C₄	1	2	yes	—
83	#14519704	C₂×C₄	1	2	yes	—
84	#14519703	C₂×C₄	1	2	yes	—
85	C₄×#92418	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
88	#135×C₆₁	C₂×C₄	1	1	yes	characteristic
89	#131×C₆₁	C₂³	1	2	yes	—
90	M₃₂×C₆₁	—	2	2	no	—
91	M₃₂×C₆₁	C₂³	1	2	yes	—
92	C₂×C₁₆×C₆₁	—	2	2	no	—
93	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₆₁	C₂³	1	1	yes	characteristic
95	#108×C₆₁	C₂×C₄	1	1	yes	characteristic
96	#104×C₆₁	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
98	#41×C₆₁	C₂²×C₄	1	2	yes	—
99	#11758226	C₂×C₈	1	2	yes	—
100	Q₈×D₆₁	C₂×C₈	1	2	yes	—
101	#11758224	—	2	2	no	—
102	#11758224	C₂×C₈	1	2	yes	—
103	D₄×D₆₁	—	2	2	no	—
104	D₄×D₆₁	C₂×C₈	1	2	yes	—
105	#11758222	—	2	2	no	—
106	#11758222	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₆₁	—	2	2	no	—
108	C₂×C₄×D₆₁	—	2	1	no	—
109	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
110	Q₁₆×C₆₁	C₂×C₈	1	1	yes	characteristic
111	SD₁₆×C₆₁	C₂×C₈	1	2	yes	—
112	D₈×C₆₁	C₂×C₈	1	1	yes	characteristic
113	M₁₆×C₆₁	—	2	2	no	—
114	M₁₆×C₆₁	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₆₁	C₂⁴	1	1	yes	characteristic
118	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
119	#11758202	C₂×C₈	1	2	yes	—
120	#11758201	C₂×C₈	1	2	yes	—
121	#11758200	C₂×C₈	1	2	yes	—
122	#11758199	C₂×C₈	1	2	yes	—
123	C₄×Dic₆₁	—	2	1	no	—
124	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
125	#11758194	—	2	2	no	—
126	#11758194	C₂²×C₄	1	2	yes	—
127	C₂×#92418	—	2	2	no	—
128	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
129	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
130	Dic₂₄₄	C₂×C₈	1	1	yes	characteristic
131	D₄₈₈	C₂×C₈	1	1	yes	characteristic
132	#11758190	C₂×C₈	1	2	yes	—
133	#11758189	—	2	2	no	—
134	#11758189	—	2	2	no	—
135	#11758189	—	2	2	no	—
136	C₈×D₆₁	—	2	2	no	—
137	C₈×D₆₁	—	2	2	no	—
138	C₈×D₆₁	—	2	2	no	—
139	C₈×D₆₁	C₂×C₈	1	1	yes	characteristic
140	C₈×D₆₁	C₂×C₈	1	1	yes	characteristic
141	C₈×D₆₁	C₂×C₈	1	1	yes	characteristic
142	C₈×D₆₁	C₂×C₈	1	1	yes	characteristic
143	C₈×D₆₁	C₂×D₄	1	1	yes	characteristic
144	C₈×D₆₁	C₂×D₄	1	1	yes	characteristic
145	C₈×D₆₁	#41	1	1	yes	characteristic
146	C₈×D₆₁	#41	1	1	yes	characteristic
147	C₁₆×C₆₁	—	2	2	no	—
148	C₁₆×C₆₁	—	2	1	no	—
149	C₁₆×C₆₁	C₂×D₄	1	2	yes	—
150	#11758185	—	2	2	no	—
151	#11758185	—	2	1	no	—
152	#11758185	C₂×D₄	1	2	yes	—
153	C₂²×D₆₁	—	2	2	no	—
154	C₂²×D₆₁	#131	1	1	yes	characteristic
155	Q₈×C₆₁	C₂²×C₈	1	2	yes	—
156	D₄×C₆₁	—	2	2	no	—
157	D₄×C₆₁	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
161	C₂²⋊D₆₁	—	2	2	no	—
162	C₂²⋊D₆₁	—	2	2	no	—
163	C₂²⋊D₆₁	—	2	2	no	—
164	C₂×Dic₆₁	—	2	2	no	—
165	C₂×Dic₆₁	—	2	1	no	—
166	C₂×Dic₆₁	#131	1	1	yes	characteristic
167	D₂₄₄	—	2	2	no	—
168	D₂₄₄	C₂²×C₈	1	2	yes	—
169	C₄×D₆₁	—	2	2	no	—
170	C₄×D₆₁	—	2	2	no	—
171	C₄×D₆₁	—	2	2	no	—
172	C₄×D₆₁	—	4	2	no	—
173	C₄×D₆₁	C₄×D₄	1	1	yes	characteristic
174	C₄×D₆₁	C₄×D₄	1	1	yes	characteristic
175	C₄×D₆₁	C₂²×C₈	1	1	yes	characteristic
176	C₄×D₆₁	C₂²×C₈	1	1	yes	characteristic
177	Dic₁₂₂	—	2	2	no	—
178	Dic₁₂₂	C₂²×C₈	1	2	yes	—
179	C₈×C₆₁	—	2	2	no	—
180	C₈×C₆₁	C₂²×C₈	1	1	yes	characteristic
181	C₈×C₆₁	C₂²×C₈	1	1	yes	characteristic
182	C₈×C₆₁	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₆₁	C₂×#41	1	1	yes	characteristic
184	#92418	—	2	2	no	—
185	#92418	C₄×D₄	1	1	yes	characteristic
186	#92418	C₄×D₄	1	1	yes	characteristic
187	#92418	C₂²×C₈	1	1	yes	characteristic
188	#92418	C₂²×C₈	1	1	yes	characteristic
189	C₂×#2171	—	61	1	no	maximal, Sylow
190	C₂²×C₆₁	—	2	2	no	—
191	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
192	C₂×D₆₁	—	2	2	no	—
193	C₂×D₆₁	—	2	2	no	—
194	C₂×D₆₁	—	4	4	no	—
195	C₂×D₆₁	C₈×D₄	1	1	yes	characteristic
196	C₂×D₆₁	C₈×D₄	1	1	yes	characteristic
197	C₄×C₆₁	—	2	2	no	—
198	C₄×C₆₁	—	4	1	no	—
199	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
200	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
201	Dic₆₁	—	2	2	no	—
202	Dic₆₁	—	4	1	no	—
203	Dic₆₁	C₈×D₄	1	1	yes	characteristic
204	Dic₆₁	C₈×D₄	1	1	yes	characteristic
205	C₂×#504	—	61	2	no	—
206	C₂×#443	—	61	1	no	—
207	#2171	—	61	2	no	—
208	#2171	—	61	1	no	—
209	#2171	—	61	1	no	—
210	#2171	—	61	2	no	—
211	#2171	—	61	1	no	—
212	#2171	D₆₁	1	1	yes	characteristic, direct product factor
213	C₂×#364	—	61	1	no	—
214	C₂×#350	—	61	2	no	—
215	C₂×#346	—	61	1	no	—
216	C₂×C₆₁	—	2	1	no	—
217	C₂×C₆₁	—	4	2	no	—
218	C₂×C₆₁	C₂×C₈×D₄	1	1	yes	characteristic
219	D₆₁	—	2	1	no	—
220	D₆₁	—	4	2	no	—
221	D₆₁	#2171	1	2	yes	direct product factor
222	C₂×#135	—	61	1	no	—
223	C₂×#131	—	61	2	no	—
224	#504	—	61	2	no	—
225	#504	—	61	2	no	—
226	#504	—	61	2	no	—
227	#504	—	122	2	no	—
228	#504	—	122	2	no	—
229	#504	C₂×D₆₁	1	2	yes	complemented
230	C₂×M₃₂	—	61	2	no	—
231	C₂×M₃₂	—	122	2	no	—
232	C₂²×C₁₆	—	61	1	no	—
233	C₂²×C₁₆	—	61	1	no	—
234	C₂²×C₁₆	—	122	2	no	—
235	#443	—	61	1	no	—
236	#443	—	61	2	no	—
237	#443	—	61	1	no	—
238	#443	—	61	2	no	—
239	#443	—	61	1	no	—
240	#443	C₂×D₆₁	1	1	yes	characteristic
241	C₂×#108	—	61	1	no	—
242	C₂×#104	—	61	2	no	—
243	C₂×C₄×C₈	—	61	1	no	—
244	#364	—	61	2	no	—
245	#364	—	61	1	no	—
246	#364	C₂×D₆₁	1	1	yes	characteristic, complemented
247	#350	—	61	2	no	—
248	#350	—	61	2	no	—
249	#350	—	61	2	no	—
250	#350	C₂×D₆₁	1	2	yes	complemented
251	#346	—	61	1	no	—
252	#346	—	61	1	no	—
253	#346	—	61	1	no	—
254	#346	C₂×D₆₁	1	1	yes	characteristic, complemented
255	C₆₁	C₂×#2171	1	1	yes	characteristic, complemented, Sylow
256	C₂×#41	—	61	2	no	—
257	#135	—	61	2	no	—
258	#135	—	61	1	no	—
259	#135	—	61	2	no	—
260	#135	—	61	1	no	—
261	#135	—	61	1	no	—
262	#135	C₄×D₆₁	1	1	yes	characteristic
263	C₂×Q₁₆	—	61	1	no	—
264	C₂×SD₁₆	—	61	2	no	—
265	C₂×D₈	—	61	1	no	—
266	#131	—	61	2	no	—
267	#131	—	61	2	no	—
268	#131	—	61	2	no	—
269	#131	—	122	2	no	—
270	#131	—	122	2	no	—
271	#131	C₂²×D₆₁	1	2	yes	—
272	C₂×M₁₆	—	61	2	no	—
273	C₂×M₁₆	—	122	2	no	—
274	C₂²×C₈	—	61	1	no	—
275	C₂²×C₈	—	61	1	no	—
276	C₂²×C₈	—	122	2	no	—
277	C₂×C₄²	—	61	1	no	—
278	M₃₂	—	2	2	no	—
279	M₃₂	—	61	2	no	—
280	M₃₂	—	122	2	no	—
281	M₃₂	—	122	2	no	—
282	M₃₂	—	122	2	no	—
283	M₃₂	—	122	2	no	—
284	M₃₂	C₂²×D₆₁	1	2	yes	—
285	C₂×C₁₆	—	2	2	no	—
286	C₂×C₁₆	—	61	1	no	—
287	C₂×C₁₆	—	61	2	no	—
288	C₂×C₁₆	—	61	2	no	—
289	C₂×C₁₆	—	61	1	no	—
290	C₂×C₁₆	—	122	2	no	—
291	C₂×C₁₆	—	122	1	no	—
292	C₂×C₁₆	—	122	1	no	—
293	C₂×C₁₆	—	122	2	no	—
294	C₂×C₁₆	—	122	2	no	—
295	C₂×C₁₆	—	122	2	no	—
296	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₆₁	1	1	yes	characteristic
298	#108	—	61	2	no	—
299	#108	—	61	1	no	—
300	#108	C₄×D₆₁	1	1	yes	characteristic
301	#104	—	61	2	no	—
302	#104	—	61	2	no	—
303	#104	—	61	2	no	—
304	#104	C₄×D₆₁	1	2	yes	—
305	C₄×C₈	—	61	1	no	—
306	C₄×C₈	—	61	1	no	—
307	C₄×C₈	—	61	1	no	—
308	C₄×C₈	C₂²×D₆₁	1	1	yes	characteristic
309	#41	—	61	2	no	—
310	#41	—	61	2	no	—
311	#41	—	61	2	no	—
312	#41	—	122	2	no	—
313	#41	—	122	2	no	—
314	#41	C₂×C₄×D₆₁	1	2	yes	—
315	C₂×Q₈	—	61	2	no	—
316	C₂×D₄	—	61	2	no	—
317	C₂×D₄	—	122	2	no	—
318	C₂²×C₄	—	61	1	no	—
319	C₂²×C₄	—	122	2	no	—
320	C₂²×C₄	—	122	1	no	—
321	Q₁₆	—	61	2	no	—
322	Q₁₆	—	61	1	no	—
323	Q₁₆	C₈×D₆₁	1	1	yes	characteristic
324	SD₁₆	—	61	2	no	—
325	SD₁₆	—	61	2	no	—
326	SD₁₆	—	61	2	no	—
327	SD₁₆	C₈×D₆₁	1	2	yes	—
328	D₈	—	61	2	no	—
329	D₈	—	61	1	no	—
330	D₈	C₈×D₆₁	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	61	2	no	—
333	M₁₆	—	122	2	no	—
334	M₁₆	—	122	2	no	—
335	M₁₆	—	122	2	no	—
336	M₁₆	—	122	2	no	—
337	M₁₆	C₂×C₄×D₆₁	1	2	yes	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	61	1	no	—
340	C₂×C₈	—	61	1	no	—
341	C₂×C₈	—	61	1	no	—
342	C₂×C₈	—	61	1	no	—
343	C₂×C₈	—	61	1	no	—
344	C₂×C₈	—	61	1	no	—
345	C₂×C₈	—	61	1	no	—
346	C₂×C₈	—	61	1	no	—
347	C₂×C₈	—	61	1	no	—
348	C₂×C₈	—	61	1	no	—
349	C₂×C₈	—	122	2	no	—
350	C₂×C₈	—	122	2	no	—
351	C₂×C₈	—	122	2	no	—
352	C₂×C₈	—	122	2	no	—
353	C₂×C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₆₁	1	1	yes	characteristic
355	C₄²	—	61	1	no	—
356	C₄²	—	122	1	no	—
357	C₄²	C₂×C₄×D₆₁	1	1	yes	characteristic
358	C₁₆	—	2	2	no	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	61	2	no	—
361	C₁₆	—	122	2	no	—
362	C₁₆	—	122	1	no	—
363	C₁₆	D₄×D₆₁	1	2	yes	—
364	C₂³	—	61	1	no	—
365	C₂³	—	122	2	no	—
366	Q₈	—	61	2	no	—
367	Q₈	—	122	2	no	—
368	Q₈	C₂×C₈×D₆₁	1	2	yes	—
369	D₄	—	2	2	no	—
370	D₄	—	61	2	no	—
371	D₄	—	122	2	no	—
372	D₄	—	122	2	no	—
373	D₄	—	122	2	no	—
374	D₄	—	122	2	no	—
375	D₄	C₂×C₈×D₆₁	1	2	yes	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	61	1	no	—
379	C₂×C₄	—	61	1	no	—
380	C₂×C₄	—	61	1	no	—
381	C₂×C₄	—	61	1	no	—
382	C₂×C₄	—	61	1	no	—
383	C₂×C₄	—	122	2	no	—
384	C₂×C₄	—	122	2	no	—
385	C₂×C₄	—	122	2	no	—
386	C₂×C₄	—	122	2	no	—
387	C₂×C₄	—	122	1	no	—
388	C₂×C₄	—	244	2	no	—
389	C₂×C₄	C₂²×C₄×D₆₁	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	61	1	no	—
392	C₈	—	61	1	no	—
393	C₈	—	61	1	no	—
394	C₈	—	61	1	no	—
395	C₈	—	122	2	no	—
396	C₈	C₂×C₈×D₆₁	1	1	yes	characteristic
397	C₈	C₂×C₈×D₆₁	1	1	yes	characteristic
398	C₈	C₂×D₄×D₆₁	1	1	yes	characteristic
399	C₈	#41×D₆₁	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	61	1	no	—
402	C₂²	—	61	1	no	—
403	C₂²	—	122	2	no	—
404	C₂²	—	122	2	no	—
405	C₂²	—	244	4	no	—
406	C₂²	#131×D₆₁	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	61	1	no	—
410	C₄	—	61	1	no	—
411	C₄	—	122	2	no	—
412	C₄	—	244	1	no	—
413	C₄	C₄×D₄×D₆₁	1	1	yes	characteristic
414	C₄	C₂²×C₈×D₆₁	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	4	2	no	—
417	C₂	—	61	2	no	—
418	C₂	—	122	1	no	—
419	C₂	—	244	2	no	—
420	C₂	C₈×D₄×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₆₁
commutator	C₄×C₆₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₆₁
Fitting	C₆₁×#2171	C₂
socle	C₂×C₆₁	C₂×C₈×D₄
prime radical	#135×D₆₁	C₄
cosocle	C₂×C₈×C₆₁	C₂⁴
hypercenter	#2171	D₆₁
hypocenter	C₆₁	C₂×#2171
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2171

Complements

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

N	H ≅ G/N	type
1. #504×D₆₁	C₂	semidirect
3. #21447662	C₂	semidirect
4. #21447661	C₂	semidirect
5. #21447660	C₂	semidirect
6. #21447659	C₂	semidirect
7. #21447658	C₂	semidirect
8. #364×D₆₁	C₂	semidirect
9. #350×D₆₁	C₂	semidirect
10. #346×D₆₁	C₂	semidirect
11. C₆₁×#2171	C₂	semidirect
15. #16840180	C₂²	semidirect
16. #16840179	C₂²	semidirect
18. #16840178	C₂²	semidirect
32. #16839583	C₂²	semidirect
33. #16839582	C₂²	semidirect
34. #16839547	C₂²	semidirect
35. #16839546	C₂²	semidirect
36. #16839545	C₂²	semidirect
37. #16839538	C₂²	semidirect
38. #16839537	C₂²	semidirect
39. #16839537	C₂²	semidirect
40. C₆₁×#504	C₂²	semidirect
42. C₆₁×#364	C₂²	semidirect
43. C₆₁×#350	C₂²	semidirect
44. C₆₁×#346	C₂²	semidirect
212. #2171	D₆₁	direct (N × H)
221. D₆₁	#2171	direct (N × H)
229. #504	C₂×D₆₁	semidirect
246. #364	C₂×D₆₁	semidirect
250. #350	C₂×D₆₁	semidirect
254. #346	C₂×D₆₁	semidirect
255. C₆₁	C₂×#2171	semidirect

Maximal subgroups

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

subgroup	index
#504×D₆₁	2
#443×D₆₁	2
#21447662	2
#21447661	2
#21447660	2
#21447659	2
#21447658	2
#364×D₆₁	2
#350×D₆₁	2
#346×D₆₁	2
C₆₁×#2171	2
C₂×#2171	61

Subgroups — D61×#2171 #29833243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₁×#2171 #29833243