Subgroups — C₄×C₈×D₄×C₆₁ #29523916

Order 15616.

1422 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₆₁	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₆₁	C₂	1	2	yes	maximal, complemented
3	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₈×C₄⋊C₄×C₆₁	C₂	1	2	yes	maximal, complemented
5	C₄×C₄⋊C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₂²⋊C₄×C₆₁	C₂	1	4	yes	maximal, complemented
7	C₄×C₂²⋊C₈×C₆₁	C₂	1	2	yes	maximal, complemented
8	C₄²×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₆₁	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₆₁	C₄	1	2	yes	—
11	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
13	C₈×D₄×C₆₁	C₄	1	16	yes	direct product factor
14	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₆₁	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₆₁	—	2	8	no	—
17	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₆₁	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₆₁	C₄	1	2	yes	—
24	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊C₄×C₆₁	C₄	1	4	yes	—
26	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
27	C₄³×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#336	C₂²	1	2	yes	—
29	C₆₁×#336	C₂²	1	4	yes	—
30	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₆₁	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
33	C₂²×C₈×C₆₁	—	2	8	no	—
34	C₂²×C₈×C₆₁	—	2	8	no	—
35	C₂²×C₈×C₆₁	C₂×C₄	1	16	yes	complemented
36	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
37	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
38	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
39	C₄×D₄×C₆₁	C₈	1	16	yes	direct product factor
40	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
41	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₆₁	—	2	4	no	—
46	C₂×C₄²×C₆₁	—	2	4	no	—
47	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₆₁	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
52	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₆₁	C₂×C₄	1	8	yes	complemented
55	C₂²⋊C₈×C₆₁	C₂×C₄	1	16	yes	complemented
56	C₄×C₈×C₆₁	—	2	8	no	—
57	C₄×C₈×C₆₁	—	2	4	no	—
58	C₄×C₈×C₆₁	—	2	4	no	—
59	C₄×C₈×C₆₁	—	2	2	no	—
60	C₄×C₈×C₆₁	C₂×C₄	1	8	yes	complemented
61	C₄×C₈×C₆₁	D₄	1	4	yes	direct product factor
62	#95×C₆₁	C₂×C₄	1	2	yes	—
63	#95×C₆₁	C₂×C₄	1	4	yes	—
64	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
65	C₂×D₄×C₆₁	C₄²	1	4	yes	—
66	C₂×D₄×C₆₁	C₂×C₈	1	8	yes	—
67	C₂²×C₄×C₆₁	—	2	8	no	—
68	C₂²×C₄×C₆₁	—	2	8	no	—
69	C₂²×C₄×C₆₁	—	2	2	no	—
70	C₂²×C₄×C₆₁	—	2	2	no	—
71	C₂²×C₄×C₆₁	—	2	4	no	—
72	C₂²×C₄×C₆₁	C₂×C₈	1	16	yes	complemented
73	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
76	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
78	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
81	C₂×C₈×C₆₁	—	2	4	no	—
82	C₂×C₈×C₆₁	—	2	2	no	—
83	C₂×C₈×C₆₁	—	2	2	no	—
84	C₂×C₈×C₆₁	—	2	4	no	—
85	C₂×C₈×C₆₁	—	2	32	no	—
86	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
87	C₂×C₈×C₆₁	C₂²×C₄	1	8	yes	—
88	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
89	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
90	C₂×C₈×C₆₁	#41	1	4	yes	—
91	C₄⋊C₄×C₆₁	C₄²	1	4	yes	—
92	C₄⋊C₄×C₆₁	C₂×C₈	1	8	yes	complemented
93	C₂²⋊C₄×C₆₁	C₄²	1	8	yes	—
94	C₂²⋊C₄×C₆₁	C₂×C₈	1	16	yes	complemented
95	C₄²×C₆₁	—	2	8	no	—
96	C₄²×C₆₁	—	2	4	no	—
97	C₄²×C₆₁	—	2	2	no	—
98	C₄²×C₆₁	—	2	2	no	—
99	C₄²×C₆₁	—	2	2	no	—
100	C₄²×C₆₁	C₂×C₈	1	8	yes	complemented
101	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
102	C₄²×C₆₁	C₂×D₄	1	2	yes	—
103	C₄²×C₆₁	#41	1	2	yes	—
104	C₂³×C₆₁	—	2	2	no	—
105	C₂³×C₆₁	—	2	2	no	—
106	C₂³×C₆₁	—	2	4	no	—
107	C₂³×C₆₁	C₂×C₄²	1	4	yes	—
108	C₂³×C₆₁	C₂²×C₈	1	8	yes	—
109	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
110	D₄×C₆₁	C₄×C₈	1	16	yes	direct product factor
111	C₂×C₄×C₆₁	—	2	4	no	—
112	C₂×C₄×C₆₁	—	2	2	no	—
113	C₂×C₄×C₆₁	—	2	2	no	—
114	C₂×C₄×C₆₁	—	2	2	no	—
115	C₂×C₄×C₆₁	—	2	2	no	—
116	C₂×C₄×C₆₁	—	2	2	no	—
117	C₂×C₄×C₆₁	—	2	4	no	—
118	C₂×C₄×C₆₁	—	2	8	no	—
119	C₂×C₄×C₆₁	—	2	8	no	—
120	C₂×C₄×C₆₁	—	2	32	no	—
121	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
122	C₂×C₄×C₆₁	C₂×C₄²	1	4	yes	—
123	C₂×C₄×C₆₁	C₂×C₄²	1	2	yes	—
124	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
125	C₂×C₄×C₆₁	C₂²×C₈	1	4	yes	—
126	C₂×C₄×C₆₁	C₂²×C₈	1	8	yes	—
127	C₂×C₄×C₆₁	C₂²×C₈	1	4	yes	—
128	C₂×C₄×C₆₁	C₂²×C₈	1	4	yes	—
129	C₂×C₄×C₆₁	#131	1	4	yes	—
130	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
131	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
133	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
134	C₈×C₆₁	—	2	8	no	—
135	C₈×C₆₁	—	2	4	no	—
136	C₈×C₆₁	C₄×D₄	1	8	yes	direct product factor
137	C₄×C₈×D₄	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂²×C₆₁	—	2	4	no	—
139	C₂²×C₆₁	—	2	8	no	—
140	C₂²×C₆₁	—	2	8	no	—
141	C₂²×C₆₁	—	2	4	no	—
142	C₂²×C₆₁	C₂×C₄×C₈	1	8	yes	complemented
143	C₂²×C₆₁	C₂²×C₄²	1	1	yes	characteristic
144	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
145	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
146	C₂²×C₆₁	C₂³×C₈	1	2	yes	—
147	C₂²×C₆₁	C₂×#131	1	2	yes	—
148	C₄×C₆₁	—	2	2	no	—
149	C₄×C₆₁	—	2	8	no	—
150	C₄×C₆₁	—	2	4	no	—
151	C₄×C₆₁	—	2	4	no	—
152	C₄×C₆₁	C₂×C₄×C₈	1	4	yes	complemented
153	C₄×C₆₁	C₈×D₄	1	8	yes	direct product factor
154	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
155	C₄×C₆₁	C₄×#41	1	2	yes	—
156	C₂×C₈×D₄	C₂×C₆₁	1	2	yes	—
157	C₂²×C₄×C₈	C₂×C₆₁	1	2	yes	complemented
158	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic
159	C₈×C₄⋊C₄	C₂×C₆₁	1	2	yes	complemented
160	C₄×C₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
161	C₈×C₂²⋊C₄	C₂×C₆₁	1	4	yes	complemented
162	C₄×C₂²⋊C₈	C₂×C₆₁	1	2	yes	complemented
163	C₄²×C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
164	C₂×C₆₁	—	2	8	no	—
165	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
166	C₂×C₆₁	C₂²×C₄×C₈	1	1	yes	characteristic
167	C₂×C₆₁	C₄×#131	1	1	yes	characteristic
168	C₂×C₆₁	C₂×C₈×D₄	1	2	yes	—
169	C₂×C₆₁	C₈×#41	1	2	yes	—
170	C₂³×C₈	C₂²×C₆₁	1	4	yes	—
171	C₂×C₄×D₄	C₄×C₆₁	1	2	yes	—
172	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
173	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
174	C₈×D₄	C₄×C₆₁	1	16	yes	direct product factor
175	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
176	C₂×C₂²⋊C₈	C₂²×C₆₁	1	4	yes	—
177	C₂×C₄×C₈	—	2	8	no	—
178	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₆₁	1	4	yes	—
180	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
181	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
182	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
183	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
184	C₄×C₄⋊C₄	C₄×C₆₁	1	2	yes	—
185	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
186	C₄×C₂²⋊C₄	C₄×C₆₁	1	4	yes	—
187	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
188	C₄³	C₂²×C₆₁	1	1	yes	characteristic
189	#336	C₂²×C₆₁	1	4	yes	—
190	#336	C₂²×C₆₁	1	2	yes	—
191	C₆₁	C₄×C₈×D₄	1	1	yes	characteristic, direct product factor, Sylow
192	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
193	C₂³×C₄	C₂×C₄×C₆₁	1	4	yes	—
194	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
195	C₂²×C₈	—	2	8	no	—
196	C₂²×C₈	—	2	8	no	—
197	C₂²×C₈	C₂×C₄×C₆₁	1	16	yes	complemented
198	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
199	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
200	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
201	C₄×D₄	C₈×C₆₁	1	16	yes	direct product factor
202	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
203	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
204	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
205	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
206	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
207	C₂×C₄²	—	2	4	no	—
208	C₂×C₄²	—	2	4	no	—
209	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
210	C₂×C₄²	C₂×C₄×C₆₁	1	4	yes	—
211	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
212	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
214	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
215	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
216	C₄⋊C₈	C₂×C₄×C₆₁	1	8	yes	complemented
217	C₂²⋊C₈	C₂×C₄×C₆₁	1	16	yes	complemented
218	C₄×C₈	—	2	8	no	—
219	C₄×C₈	—	2	4	no	—
220	C₄×C₈	—	2	4	no	—
221	C₄×C₈	—	2	2	no	—
222	C₄×C₈	C₂×C₄×C₆₁	1	8	yes	complemented
223	C₄×C₈	D₄×C₆₁	1	4	yes	direct product factor
224	#95	C₂×C₄×C₆₁	1	2	yes	—
225	#95	C₂×C₄×C₆₁	1	4	yes	—
226	C₂⁴	C₂²×C₄×C₆₁	1	2	yes	—
227	C₂×D₄	C₄²×C₆₁	1	4	yes	—
228	C₂×D₄	C₂×C₈×C₆₁	1	8	yes	—
229	C₂²×C₄	—	2	8	no	—
230	C₂²×C₄	—	2	8	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	C₂×C₈×C₆₁	1	16	yes	complemented
235	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
236	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
237	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
238	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
239	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
240	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
241	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
242	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
243	C₂×C₈	—	2	4	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	—	2	2	no	—
246	C₂×C₈	—	2	4	no	—
247	C₂×C₈	—	2	32	no	—
248	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
249	C₂×C₈	C₂²×C₄×C₆₁	1	8	yes	—
250	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
251	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
252	C₂×C₈	#41×C₆₁	1	4	yes	—
253	C₄⋊C₄	C₄²×C₆₁	1	4	yes	—
254	C₄⋊C₄	C₂×C₈×C₆₁	1	8	yes	complemented
255	C₂²⋊C₄	C₄²×C₆₁	1	8	yes	—
256	C₂²⋊C₄	C₂×C₈×C₆₁	1	16	yes	complemented
257	C₄²	—	2	8	no	—
258	C₄²	—	2	4	no	—
259	C₄²	—	2	2	no	—
260	C₄²	—	2	2	no	—
261	C₄²	—	2	2	no	—
262	C₄²	C₂×C₈×C₆₁	1	8	yes	complemented
263	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
264	C₄²	C₂×D₄×C₆₁	1	2	yes	—
265	C₄²	#41×C₆₁	1	2	yes	—
266	C₂³	—	2	4	no	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	2	no	—
269	C₂³	C₂×C₄²×C₆₁	1	4	yes	—
270	C₂³	C₂²×C₈×C₆₁	1	8	yes	—
271	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
272	D₄	C₄×C₈×C₆₁	1	16	yes	direct product factor
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	4	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	32	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
284	C₂×C₄	C₂×C₄²×C₆₁	1	4	yes	—
285	C₂×C₄	C₂×C₄²×C₆₁	1	2	yes	—
286	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
287	C₂×C₄	C₂²×C₈×C₆₁	1	4	yes	—
288	C₂×C₄	C₂²×C₈×C₆₁	1	8	yes	—
289	C₂×C₄	C₂²×C₈×C₆₁	1	4	yes	—
290	C₂×C₄	C₂²×C₈×C₆₁	1	4	yes	—
291	C₂×C₄	#131×C₆₁	1	4	yes	—
292	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
293	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
294	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
295	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
296	C₈	—	2	8	no	—
297	C₈	—	2	4	no	—
298	C₈	C₄×D₄×C₆₁	1	8	yes	direct product factor
299	C₂²	—	2	4	no	—
300	C₂²	—	2	4	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	2	8	no	—
303	C₂²	C₂×C₄×C₈×C₆₁	1	8	yes	complemented
304	C₂²	C₂²×C₄²×C₆₁	1	1	yes	characteristic
305	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
306	C₂²	C₄×#41×C₆₁	1	1	yes	characteristic
307	C₂²	C₂³×C₈×C₆₁	1	2	yes	—
308	C₂²	C₂×#131×C₆₁	1	2	yes	—
309	C₄	—	2	4	no	—
310	C₄	—	2	2	no	—
311	C₄	—	2	8	no	—
312	C₄	—	2	4	no	—
313	C₄	C₂×C₄×C₈×C₆₁	1	4	yes	complemented
314	C₄	C₈×D₄×C₆₁	1	8	yes	direct product factor
315	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
316	C₄	C₄×#41×C₆₁	1	2	yes	—
317	C₂	—	2	8	no	—
318	C₂	C₄²×D₄×C₆₁	1	1	yes	characteristic
319	C₂	C₂²×C₄×C₈×C₆₁	1	1	yes	characteristic
320	C₂	C₄×#131×C₆₁	1	1	yes	characteristic
321	C₂	C₂×C₈×D₄×C₆₁	1	2	yes	—
322	C₂	C₈×#41×C₆₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈×C₆₁	C₂²
commutator	C₂	C₂²×C₄×C₈×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂³×C₄
prime radical	C₂²×D₄×C₆₁	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₈×C₆₁	C₂	semidirect
4. C₈×C₄⋊C₄×C₆₁	C₂	semidirect
5. C₄×C₄⋊C₈×C₆₁	C₂	semidirect
6. C₈×C₂²⋊C₄×C₆₁	C₂	semidirect
7. C₄×C₂²⋊C₈×C₆₁	C₂	semidirect
8. C₄²×C₈×C₆₁	C₂	semidirect
13. C₈×D₄×C₆₁	C₄	direct (N × H)
35. C₂²×C₈×C₆₁	C₂×C₄	semidirect
39. C₄×D₄×C₆₁	C₈	direct (N × H)
54. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
55. C₂²⋊C₈×C₆₁	C₂×C₄	semidirect
60. C₄×C₈×C₆₁	C₂×C₄	semidirect
61. C₄×C₈×C₆₁	D₄	direct (N × H)
72. C₂²×C₄×C₆₁	C₂×C₈	semidirect
92. C₄⋊C₄×C₆₁	C₂×C₈	semidirect
94. C₂²⋊C₄×C₆₁	C₂×C₈	semidirect
100. C₄²×C₆₁	C₂×C₈	semidirect
110. D₄×C₆₁	C₄×C₈	direct (N × H)
136. C₈×C₆₁	C₄×D₄	direct (N × H)
137. C₄×C₈×D₄	C₆₁	direct (N × H)
142. C₂²×C₆₁	C₂×C₄×C₈	semidirect
152. C₄×C₆₁	C₂×C₄×C₈	semidirect
153. C₄×C₆₁	C₈×D₄	direct (N × H)
157. C₂²×C₄×C₈	C₂×C₆₁	semidirect
159. C₈×C₄⋊C₄	C₂×C₆₁	semidirect
160. C₄×C₄⋊C₈	C₂×C₆₁	semidirect
161. C₈×C₂²⋊C₄	C₂×C₆₁	semidirect
162. C₄×C₂²⋊C₈	C₂×C₆₁	semidirect
163. C₄²×C₈	C₂×C₆₁	semidirect
174. C₈×D₄	C₄×C₆₁	direct (N × H)
191. C₆₁	C₄×C₈×D₄	direct (N × H)
197. C₂²×C₈	C₂×C₄×C₆₁	semidirect
201. C₄×D₄	C₈×C₆₁	direct (N × H)
216. C₄⋊C₈	C₂×C₄×C₆₁	semidirect
217. C₂²⋊C₈	C₂×C₄×C₆₁	semidirect
222. C₄×C₈	C₂×C₄×C₆₁	semidirect
223. C₄×C₈	D₄×C₆₁	direct (N × H)
234. C₂²×C₄	C₂×C₈×C₆₁	semidirect
254. C₄⋊C₄	C₂×C₈×C₆₁	semidirect
256. C₂²⋊C₄	C₂×C₈×C₆₁	semidirect
262. C₄²	C₂×C₈×C₆₁	semidirect
272. D₄	C₄×C₈×C₆₁	direct (N × H)
298. C₈	C₄×D₄×C₆₁	direct (N × H)
303. C₂²	C₂×C₄×C₈×C₆₁	semidirect
313. C₄	C₂×C₄×C₈×C₆₁	semidirect
314. C₄	C₈×D₄×C₆₁	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×C₈×D₄×C₆₁	2
C₂²×C₄×C₈×C₆₁	2
C₄²×D₄×C₆₁	2
C₈×C₄⋊C₄×C₆₁	2
C₄×C₄⋊C₈×C₆₁	2
C₈×C₂²⋊C₄×C₆₁	2
C₄×C₂²⋊C₈×C₆₁	2
C₄²×C₈×C₆₁	2
C₄×C₈×D₄	61

Subgroups — C4×C8×D4×C61 #29523916

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₈×D₄×C₆₁ #29523916