Subgroups — C₄×D₆₁⋊M₃₂ #30623812

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₁⋊M₃₂	C₂	1	2	yes	maximal
2	#21462026	C₂	1	2	yes	maximal, complemented
3	#21462025	C₂	1	2	yes	maximal, complemented
4	C₄×#14519852	C₂	1	2	yes	maximal, complemented
5	C₄×#14519851	C₂	1	2	yes	maximal, complemented
6	#21462020	C₂	1	2	yes	maximal, complemented
7	C₄×D₆₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
9	C₂×#14519852	C₂²	1	4	yes	—
10	D₆₁⋊M₃₂	C₄	1	16	yes	direct product factor
11	C₂×#14519851	C₂²	1	4	yes	—
12	C₂×D₆₁⋊C₁₆	C₂²	1	4	yes	—
13	#16840651	C₂²	1	4	yes	complemented
14	#16840650	C₂²	1	4	yes	complemented
15	#16840648	C₂²	1	4	yes	complemented
16	C₄×#11758187	C₂²	1	4	yes	complemented
17	C₂²×C₈×D₆₁	C₄	1	1	yes	characteristic
18	C₂²×C₈×D₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄²×D₆₁	C₄	1	1	yes	characteristic
20	C₂×C₄×#92418	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₆₁	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₆₁	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₆₁	C₄	1	1	yes	characteristic
24	C₄×C₈×D₆₁	C₄	1	1	yes	characteristic
25	C₄×C₈×D₆₁	C₄	1	1	yes	characteristic
26	C₄×C₈×D₆₁	C₄	1	1	yes	characteristic
27	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
32	#14519852	C₂×C₄	1	16	yes	complemented
33	#14519851	C₂×C₄	1	16	yes	complemented
34	D₆₁⋊C₁₆	C₂×C₄	1	16	yes	complemented
35	C₂×#11758187	C₂³	1	8	yes	—
36	C₂²×C₄×D₆₁	C₈	1	2	yes	—
37	C₂²×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×#92418	C₂×C₄	1	1	yes	characteristic
39	C₂²×#92418	C₂³	1	1	yes	characteristic
40	C₂×C₈×D₆₁	C₈	1	8	yes	—
41	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₆₁	C₂×C₄	1	8	yes	—
44	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
49	C₂×C₈×D₆₁	C₂³	1	1	yes	characteristic
50	C₂×C₄×Dic₆₁	C₈	1	2	yes	—
51	C₂×C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₆₁	C₈	1	2	yes	—
53	C₄²×D₆₁	C₈	1	2	yes	—
54	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₆₁	C₂×C₄	1	1	yes	characteristic
58	C₄×#92418	C₂×C₄	1	1	yes	characteristic
59	C₄×#92418	C₂×C₄	1	1	yes	characteristic
60	C₄×#92418	C₂³	1	1	yes	characteristic
61	C₄×#92418	C₂³	1	1	yes	characteristic
62	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
63	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
64	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
65	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
66	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
67	C₈×Dic₆₁	C₂×C₄	1	1	yes	characteristic
68	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
69	C₈×Dic₆₁	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
73	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
77	C₂³×D₆₁	C₂×C₈	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
80	C₂²×Dic₆₁	C₂×C₈	1	2	yes	—
81	C₂²×Dic₆₁	C₂×C₈	1	1	yes	characteristic
82	C₂×C₄×D₆₁	—	2	8	no	—
83	C₂×C₄×D₆₁	C₄²	1	4	yes	—
84	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
85	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
86	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
87	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
88	C₂×C₄×D₆₁	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₆₁	C₂×C₈	1	4	yes	—
90	C₂×C₄×D₆₁	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₆₁	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₆₁	C₄²	1	4	yes	—
94	C₂×C₈×C₆₁	C₂×C₈	1	4	yes	—
95	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₆₁	C₂×C₈	1	2	yes	—
100	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
102	C₄×Dic₆₁	C₂×C₈	1	2	yes	—
103	C₄×Dic₆₁	C₂×C₈	1	2	yes	—
104	C₄×Dic₆₁	C₂×C₈	1	2	yes	—
105	C₄×Dic₆₁	C₂×C₈	1	2	yes	—
106	C₄×Dic₆₁	C₂×C₈	1	2	yes	—
107	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
108	C₄×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
109	C₂×#92418	C₂×C₈	1	4	yes	—
110	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
111	C₂×#92418	C₂²×C₄	1	4	yes	—
112	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
113	C₂×#92418	C₂²×C₄	1	1	yes	characteristic
114	C₂×#92418	C₂⁴	1	1	yes	characteristic
115	C₈×D₆₁	C₄²	1	4	yes	—
116	C₈×D₆₁	C₄²	1	4	yes	—
117	C₈×D₆₁	C₂×C₈	1	4	yes	—
118	C₈×D₆₁	C₂×C₈	1	4	yes	—
119	C₈×D₆₁	C₂×C₈	1	4	yes	—
120	C₈×D₆₁	C₂×C₈	1	4	yes	—
121	C₈×D₆₁	C₂²×C₄	1	4	yes	—
122	C₈×D₆₁	C₂²×C₄	1	4	yes	—
123	#11758187	C₂²×C₄	1	16	yes	complemented
124	C₂³×C₆₁	C₂²×C₈	1	1	yes	characteristic
125	C₂²×D₆₁	—	2	4	no	—
126	C₂²×D₆₁	C₄×C₈	1	4	yes	—
127	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
128	C₂²×D₆₁	C₂²×C₈	1	1	yes	characteristic
129	C₂×C₄×C₆₁	—	2	4	no	—
130	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₆₁	C₂²×C₈	1	1	yes	characteristic
134	C₂×C₄×C₆₁	C₂²×C₈	1	2	yes	—
135	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
136	C₂×Dic₆₁	—	2	4	no	—
137	C₂×Dic₆₁	C₄×C₈	1	4	yes	—
138	C₂×Dic₆₁	C₂²×C₈	1	2	yes	—
139	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
140	C₂×Dic₆₁	C₂²×C₈	1	1	yes	characteristic
141	C₂×Dic₆₁	C₂²×C₈	1	2	yes	—
142	C₄×D₆₁	—	2	4	no	—
143	C₄×D₆₁	—	2	4	no	—
144	C₄×D₆₁	—	2	4	no	—
145	C₄×D₆₁	C₄×C₈	1	4	yes	—
146	C₄×D₆₁	C₄×C₈	1	4	yes	—
147	C₄×D₆₁	M₃₂	1	8	yes	complemented
148	C₄×D₆₁	C₂×C₄²	1	2	yes	—
149	C₄×D₆₁	C₂×C₄²	1	2	yes	—
150	C₄×D₆₁	C₂²×C₈	1	2	yes	—
151	C₄×D₆₁	C₂²×C₈	1	2	yes	—
152	C₈×C₆₁	C₂×C₄²	1	2	yes	—
153	C₈×C₆₁	C₂×C₄²	1	2	yes	—
154	C₈×C₆₁	C₂²×C₈	1	2	yes	—
155	C₈×C₆₁	C₂²×C₈	1	2	yes	—
156	#92418	C₂×C₄²	1	2	yes	—
157	#92418	C₂²×C₈	1	2	yes	—
158	#92418	C₂²×C₈	1	2	yes	—
159	#92418	C₂³×C₄	1	2	yes	—
160	C₂×C₄×M₃₂	—	61	1	no	maximal, Sylow
161	C₂²×C₆₁	—	2	2	no	—
162	C₂²×C₆₁	C₂×C₄×C₈	1	2	yes	—
163	C₂²×C₆₁	C₂³×C₈	1	1	yes	characteristic
164	C₂×D₆₁	—	2	2	no	—
165	C₂×D₆₁	—	2	8	no	—
166	C₂×D₆₁	C₂×C₄×C₈	1	2	yes	—
167	C₂×D₆₁	C₂×C₄×C₈	1	2	yes	—
168	C₂×D₆₁	C₂×M₃₂	1	4	yes	—
169	C₄×C₆₁	—	2	2	no	—
170	C₄×C₆₁	C₂×C₄×C₈	1	2	yes	—
171	C₄×C₆₁	C₂×M₃₂	1	4	yes	complemented
172	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
173	C₄×C₆₁	C₂³×C₈	1	1	yes	characteristic
174	Dic₆₁	—	2	2	no	—
175	Dic₆₁	C₂×C₄×C₈	1	2	yes	—
176	Dic₆₁	C₂×C₄×C₈	1	2	yes	—
177	Dic₆₁	C₂×M₃₂	1	4	yes	complemented
178	C₂²×M₃₂	—	61	2	no	—
179	C₂²×C₄×C₈	—	61	1	no	—
180	C₄×M₃₂	—	61	2	no	—
181	C₄×M₃₂	—	61	2	no	—
182	C₄×M₃₂	—	61	2	no	—
183	C₄×M₃₂	—	61	2	no	—
184	C₂×#346	—	61	2	no	—
185	C₂×C₄×C₁₆	—	61	2	no	—
186	C₂×C₆₁	—	2	2	no	—
187	C₂×C₆₁	C₂²×C₄×C₈	1	1	yes	characteristic
188	C₂×C₆₁	C₂²×M₃₂	1	2	yes	—
189	D₆₁	—	2	2	no	—
190	D₆₁	C₄×M₃₂	1	4	yes	complemented
191	C₂³×C₈	—	61	1	no	—
192	C₂³×C₈	—	61	1	no	—
193	C₂²×C₄²	—	61	1	no	—
194	C₂×M₃₂	—	61	4	no	—
195	C₂×M₃₂	—	61	4	no	—
196	C₂×M₃₂	—	61	16	no	—
197	C₂²×C₁₆	—	61	4	no	—
198	C₂×C₄×C₈	—	61	1	no	—
199	C₂×C₄×C₈	—	61	1	no	—
200	C₂×C₄×C₈	—	61	1	no	—
201	C₂×C₄×C₈	—	61	1	no	—
202	C₂×C₄×C₈	—	61	1	no	—
203	C₂×C₄×C₈	—	61	1	no	—
204	C₂×C₄×C₈	—	61	1	no	—
205	C₂×C₄×C₈	—	61	1	no	—
206	C₂×C₄×C₈	—	61	1	no	—
207	C₂×C₄×C₈	—	61	1	no	—
208	C₂×C₄×C₈	—	61	1	no	—
209	C₂×C₄×C₈	#6923	1	1	yes	characteristic
210	#346	—	61	4	no	—
211	#346	—	61	4	no	—
212	C₄×C₁₆	—	61	4	no	—
213	C₄×C₁₆	—	61	4	no	—
214	C₆₁	C₂×C₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
215	C₂³×C₄	—	61	1	no	—
216	C₂³×C₄	—	61	2	no	—
217	C₂²×C₈	—	61	1	no	—
218	C₂²×C₈	—	61	1	no	—
219	C₂²×C₈	—	61	8	no	—
220	C₂²×C₈	—	61	8	no	—
221	C₂²×C₈	—	61	1	no	—
222	C₂²×C₈	—	61	1	no	—
223	C₂²×C₈	—	61	1	no	—
224	C₂²×C₈	—	61	1	no	—
225	C₂²×C₈	—	61	1	no	—
226	C₂²×C₈	—	61	1	no	—
227	C₂²×C₈	—	61	1	no	—
228	C₂²×C₈	—	61	1	no	—
229	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
230	C₂²×C₈	C₂×#6923	1	1	yes	characteristic
231	C₂×C₄²	—	61	2	no	—
232	C₂×C₄²	—	61	1	no	—
233	C₂×C₄²	—	61	2	no	—
234	C₂×C₄²	—	61	2	no	—
235	C₂×C₄²	—	61	1	no	—
236	C₂×C₄²	—	61	1	no	—
237	C₂×C₄²	—	61	1	no	—
238	C₂×C₄²	—	61	1	no	—
239	C₂×C₄²	C₂×#6923	1	1	yes	characteristic
240	M₃₂	—	61	16	no	—
241	M₃₂	—	61	16	no	—
242	C₂×C₁₆	—	61	8	no	—
243	C₂×C₁₆	—	61	16	no	—
244	C₄×C₈	—	61	1	no	—
245	C₄×C₈	—	61	1	no	—
246	C₄×C₈	—	61	1	no	—
247	C₄×C₈	—	61	1	no	—
248	C₄×C₈	—	61	1	no	—
249	C₄×C₈	—	61	1	no	—
250	C₄×C₈	—	61	1	no	—
251	C₄×C₈	—	61	1	no	—
252	C₄×C₈	—	61	1	no	—
253	C₄×C₈	—	61	1	no	—
254	C₄×C₈	—	61	1	no	—
255	C₄×C₈	—	61	1	no	—
256	C₄×C₈	C₂×#6923	1	1	yes	characteristic
257	C₄×C₈	C₂×#6923	1	1	yes	characteristic
258	C₄×C₈	C₂×#6923	1	1	yes	characteristic
259	C₄×C₈	C₂×#6923	1	1	yes	characteristic
260	C₂⁴	—	61	1	no	—
261	C₂²×C₄	—	61	1	no	—
262	C₂²×C₄	—	61	4	no	—
263	C₂²×C₄	—	61	1	no	—
264	C₂²×C₄	—	61	1	no	—
265	C₂²×C₄	—	61	2	no	—
266	C₂²×C₄	—	61	4	no	—
267	C₂²×C₄	—	61	1	no	—
268	C₂²×C₄	—	61	1	no	—
269	C₂²×C₄	—	61	2	no	—
270	C₂²×C₄	—	61	2	no	—
271	C₂²×C₄	—	61	2	no	—
272	C₂²×C₄	—	61	2	no	—
273	C₂²×C₄	—	122	8	no	—
274	C₂²×C₄	D₆₁⋊C₈	1	2	yes	—
275	C₂²×C₄	C₂²×#6923	1	1	yes	characteristic
276	C₂×C₈	—	61	4	no	—
277	C₂×C₈	—	61	4	no	—
278	C₂×C₈	—	61	1	no	—
279	C₂×C₈	—	61	1	no	—
280	C₂×C₈	—	61	1	no	—
281	C₂×C₈	—	61	1	no	—
282	C₂×C₈	—	61	4	no	—
283	C₂×C₈	—	61	4	no	—
284	C₂×C₈	—	61	4	no	—
285	C₂×C₈	—	61	4	no	—
286	C₂×C₈	—	61	4	no	—
287	C₂×C₈	—	61	4	no	—
288	C₂×C₈	—	61	4	no	—
289	C₂×C₈	—	61	4	no	—
290	C₂×C₈	D₆₁⋊C₈	1	4	yes	—
291	C₂×C₈	C₄×#6923	1	4	yes	—
292	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
293	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
294	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
295	C₂×C₈	C₂²×#6923	1	1	yes	characteristic
296	C₄²	—	61	2	no	—
297	C₄²	—	61	2	no	—
298	C₄²	—	61	2	no	—
299	C₄²	—	61	2	no	—
300	C₄²	—	61	2	no	—
301	C₄²	—	61	1	no	—
302	C₄²	—	61	1	no	—
303	C₄²	D₆₁⋊C₈	1	2	yes	—
304	C₄²	C₂²×#6923	1	1	yes	characteristic
305	C₄²	C₂²×#6923	1	1	yes	characteristic
306	C₁₆	—	61	16	no	—
307	C₂³	—	61	1	no	—
308	C₂³	—	61	4	no	—
309	C₂³	—	61	1	no	—
310	C₂³	—	122	4	no	—
311	C₂³	C₂×D₆₁⋊C₈	1	1	yes	characteristic
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	61	4	no	—
314	C₂×C₄	—	61	1	no	—
315	C₂×C₄	—	61	1	no	—
316	C₂×C₄	—	61	2	no	—
317	C₂×C₄	—	61	4	no	—
318	C₂×C₄	—	61	4	no	—
319	C₂×C₄	—	61	8	no	—
320	C₂×C₄	—	61	2	no	—
321	C₂×C₄	—	61	2	no	—
322	C₂×C₄	—	61	2	no	—
323	C₂×C₄	—	61	2	no	—
324	C₂×C₄	—	61	2	no	—
325	C₂×C₄	—	122	4	no	—
326	C₂×C₄	—	122	4	no	—
327	C₂×C₄	—	122	4	no	—
328	C₂×C₄	—	122	4	no	—
329	C₂×C₄	C₂×C₄×#6923	1	2	yes	—
330	C₂×C₄	C₂×D₆₁⋊C₈	1	2	yes	—
331	C₂×C₄	C₂×D₆₁⋊C₈	1	1	yes	characteristic
332	C₂×C₄	C₂×D₆₁⋊C₈	1	2	yes	—
333	C₂×C₄	C₂×D₆₁⋊C₈	1	2	yes	—
334	C₂×C₄	C₂³×#6923	1	1	yes	characteristic
335	C₈	—	61	2	no	—
336	C₈	—	61	2	no	—
337	C₈	—	61	2	no	—
338	C₈	—	61	2	no	—
339	C₈	C₂×C₄×#6923	1	2	yes	—
340	C₈	C₂×C₄×#6923	1	2	yes	—
341	C₈	C₂×D₆₁⋊C₈	1	2	yes	—
342	C₈	C₂×D₆₁⋊C₈	1	2	yes	—
343	C₂²	—	2	2	no	—
344	C₂²	—	61	2	no	—
345	C₂²	—	61	4	no	—
346	C₂²	—	61	2	no	—
347	C₂²	—	122	8	no	—
348	C₂²	—	122	2	no	—
349	C₂²	C₄×D₆₁⋊C₈	1	2	yes	—
350	C₂²	C₂²×D₆₁⋊C₈	1	1	yes	characteristic
351	C₄	—	2	2	no	—
352	C₄	—	61	2	no	—
353	C₄	—	61	2	no	—
354	C₄	—	61	4	no	—
355	C₄	—	122	2	no	—
356	C₄	C₄×D₆₁⋊C₈	1	2	yes	—
357	C₄	D₆₁⋊M₃₂	1	4	yes	direct product factor
358	C₄	C₂²×C₄×#6923	1	1	yes	characteristic
359	C₄	C₂²×D₆₁⋊C₈	1	1	yes	characteristic
360	C₂	—	2	2	no	—
361	C₂	—	61	4	no	—
362	C₂	—	122	2	no	—
363	C₂	C₂×C₄×D₆₁⋊C₈	1	1	yes	characteristic
364	C₂	C₂×D₆₁⋊M₃₂	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#6923
commutator	C₂×C₆₁	C₂²×C₄×C₈
Frattini	C₂×C₄	C₂³×#6923
Fitting	C₂×C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂³×C₈
prime radical	C₂³×D₆₁	C₂×C₈
cosocle	C₂×#92418	C₂⁴
hypercenter	C₂×C₄×C₈	#6923
hypocenter	C₆₁	C₂×C₄×M₃₂
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #21462026	C₂	semidirect
3. #21462025	C₂	semidirect
4. C₄×#14519852	C₂	semidirect
5. C₄×#14519851	C₂	semidirect
6. #21462020	C₂	semidirect
7. C₄×D₆₁⋊C₁₆	C₂	semidirect
10. D₆₁⋊M₃₂	C₄	direct (N × H)
13. #16840651	C₂²	semidirect
14. #16840650	C₂²	semidirect
15. #16840648	C₂²	semidirect
16. C₄×#11758187	C₂²	semidirect
32. #14519852	C₂×C₄	semidirect
33. #14519851	C₂×C₄	semidirect
34. D₆₁⋊C₁₆	C₂×C₄	semidirect
123. #11758187	C₂²×C₄	semidirect
147. C₄×D₆₁	M₃₂	semidirect
171. C₄×C₆₁	C₂×M₃₂	semidirect
177. Dic₆₁	C₂×M₃₂	semidirect
190. D₆₁	C₄×M₃₂	semidirect
214. C₆₁	C₂×C₄×M₃₂	semidirect
357. C₄	D₆₁⋊M₃₂	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×D₆₁⋊M₃₂	2
#21462026	2
#21462025	2
C₄×#14519852	2
C₄×#14519851	2
#21462020	2
C₄×D₆₁⋊C₁₆	2
C₂×C₄×C₈×D₆₁	2
C₂×C₄×M₃₂	61

Subgroups — C4×D61⋊M32 #30623812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₆₁⋊M₃₂ #30623812