Subgroups — C₂×C₄×AGL(1,ℤ/8)×C₆₁ #29563589

Order 15616.

3242 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₆₁×#442	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#440	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×SD₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×D₈×C₆₁	C₂	1	2	yes	maximal, complemented
9	C₂×C₆₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₆₁	—	2	1	no	—
16	C₂×AGL(1,ℤ/8)×C₆₁	C₄	1	16	yes	direct product factor
17	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	8	yes	—
18	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
19	C₂²×D₈×C₆₁	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
22	C₄×#41×C₆₁	—	2	4	no	—
23	C₄×#41×C₆₁	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₄×C₆₁	—	2	1	no	—
27	C₂×C₄×D₄×C₆₁	—	2	1	no	—
28	C₂×C₄×D₄×C₆₁	—	2	1	no	—
29	C₂×C₄×D₄×C₆₁	—	2	4	no	—
30	C₂×C₄×D₄×C₆₁	—	2	1	no	—
31	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₁	C₂²	1	8	yes	complemented
34	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×#117×C₆₁	—	2	1	no	—
37	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
40	C₂²×C₄²×C₆₁	—	2	1	no	—
41	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#442	C₂²	1	16	yes	complemented
43	C₆₁×#440	C₂²	1	16	yes	complemented
44	C₄×SD₁₆×C₆₁	C₂²	1	16	yes	complemented
45	C₄×D₈×C₆₁	C₂²	1	16	yes	complemented
46	C₆₁×#428	C₂²	1	8	yes	complemented
47	C₂×#107×C₆₁	C₂²	1	2	yes	complemented
48	C₂×#106×C₆₁	C₂²	1	2	yes	complemented
49	C₆₁×#418	C₂²	1	8	yes	complemented
50	C₆₁×#417	C₂²	1	8	yes	complemented
51	C₂×#103×C₆₁	C₂²	1	2	yes	complemented
52	C₂×#102×C₆₁	C₂²	1	2	yes	—
53	C₂×#102×C₆₁	C₂²	1	2	yes	—
54	C₂×#102×C₆₁	C₂²	1	2	yes	complemented
55	C₄×M₁₆×C₆₁	C₂²	1	8	yes	complemented
56	C₂×#97×C₆₁	C₂²	1	2	yes	complemented
57	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	complemented
58	C₂⁵×C₆₁	—	2	1	no	—
59	C₂×#41×C₆₁	—	2	2	no	—
60	C₂×#41×C₆₁	—	2	4	no	—
61	C₂×#41×C₆₁	C₂×C₄	1	8	yes	complemented
62	C₂×#41×C₆₁	C₂³	1	4	yes	—
63	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₆₁	—	2	1	no	—
65	C₂²×D₄×C₆₁	—	2	1	no	—
66	C₂²×D₄×C₆₁	—	2	2	no	—
67	C₂²×D₄×C₆₁	—	2	4	no	—
68	C₂²×D₄×C₆₁	C₂×C₄	1	8	yes	complemented
69	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
70	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
72	C₂³×C₄×C₆₁	—	2	1	no	—
73	C₂³×C₄×C₆₁	—	2	1	no	—
74	C₂³×C₄×C₆₁	—	2	2	no	—
75	C₂³×C₄×C₆₁	—	2	8	no	—
76	C₂³×C₄×C₆₁	—	2	1	no	—
77	C₂³×C₄×C₆₁	—	2	2	no	—
78	C₂³×C₄×C₆₁	—	2	1	no	—
79	C₂³×C₄×C₆₁	—	4	8	no	—
80	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
83	AGL(1,ℤ/8)×C₆₁	C₂×C₄	1	64	yes	direct product factor
84	C₂×SD₁₆×C₆₁	C₂×C₄	1	16	yes	complemented
85	C₂×SD₁₆×C₆₁	C₂³	1	8	yes	—
86	C₂×D₈×C₆₁	C₂×C₄	1	16	yes	complemented
87	C₂×D₈×C₆₁	C₂³	1	8	yes	—
88	C₂×M₁₆×C₆₁	—	2	4	no	—
89	C₂×M₁₆×C₆₁	C₂×C₄	1	8	yes	complemented
90	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
91	C₂×M₁₆×C₆₁	C₂³	1	4	yes	—
92	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
93	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
94	C₄×Q₈×C₆₁	—	2	2	no	—
95	C₄×Q₈×C₆₁	—	2	2	no	—
96	C₄×Q₈×C₆₁	C₂³	1	4	yes	complemented
97	C₄×Q₈×C₆₁	C₂³	1	4	yes	complemented
98	C₄×D₄×C₆₁	—	2	8	no	—
99	C₄×D₄×C₆₁	—	2	8	no	—
100	C₄×D₄×C₆₁	—	2	4	no	—
101	C₄×D₄×C₆₁	—	2	4	no	—
102	C₄×D₄×C₆₁	—	2	8	no	—
103	C₄×D₄×C₆₁	—	2	8	no	—
104	C₄×D₄×C₆₁	—	2	2	no	—
105	C₄×D₄×C₆₁	—	2	2	no	—
106	C₄×D₄×C₆₁	C₂³	1	8	yes	—
107	C₄×D₄×C₆₁	C₂³	1	8	yes	—
108	C₄×D₄×C₆₁	C₂³	1	4	yes	complemented
109	C₄×D₄×C₆₁	C₂³	1	4	yes	complemented
110	#117×C₆₁	—	2	2	no	—
111	#117×C₆₁	—	2	8	no	—
112	#117×C₆₁	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
114	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
115	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
116	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
117	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
124	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
125	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
127	C₂×C₄²×C₆₁	—	2	1	no	—
128	C₂×C₄²×C₆₁	—	2	1	no	—
129	C₂×C₄²×C₆₁	—	2	1	no	—
130	C₂×C₄²×C₆₁	—	2	8	no	—
131	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₆₁	D₄	1	4	yes	—
133	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
137	#107×C₆₁	C₂³	1	8	yes	complemented
138	#106×C₆₁	C₂³	1	8	yes	complemented
139	#103×C₆₁	C₂³	1	8	yes	complemented
140	#102×C₆₁	C₂³	1	8	yes	—
141	#102×C₆₁	C₂³	1	8	yes	—
142	#102×C₆₁	C₂³	1	8	yes	complemented
143	#97×C₆₁	C₂³	1	8	yes	complemented
144	C₄×C₈×C₆₁	C₂³	1	8	yes	complemented
145	C₂⁴×C₆₁	—	2	8	no	—
146	C₂⁴×C₆₁	—	2	1	no	—
147	C₂⁴×C₆₁	—	2	2	no	—
148	C₂⁴×C₆₁	—	2	4	no	—
149	C₂⁴×C₆₁	—	4	4	no	—
150	C₂⁴×C₆₁	—	4	4	no	—
151	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
152	#41×C₆₁	—	2	16	no	—
153	#41×C₆₁	—	2	8	no	—
154	#41×C₆₁	C₂²×C₄	1	16	yes	complemented
155	C₂×Q₈×C₆₁	—	2	1	no	—
156	C₂×Q₈×C₆₁	—	2	2	no	—
157	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	complemented
158	C₂×Q₈×C₆₁	C₂⁴	1	2	yes	—
159	C₂×D₄×C₆₁	—	2	8	no	—
160	C₂×D₄×C₆₁	—	2	4	no	—
161	C₂×D₄×C₆₁	—	2	8	no	—
162	C₂×D₄×C₆₁	—	2	16	no	—
163	C₂×D₄×C₆₁	—	2	4	no	—
164	C₂×D₄×C₆₁	—	2	2	no	—
165	C₂×D₄×C₆₁	—	2	1	no	—
166	C₂×D₄×C₆₁	—	2	4	no	—
167	C₂×D₄×C₆₁	—	2	8	no	—
168	C₂×D₄×C₆₁	—	2	2	no	—
169	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₆₁	C₂²×C₄	1	16	yes	complemented
171	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	complemented
172	C₂×D₄×C₆₁	C₂⁴	1	4	yes	—
173	C₂×D₄×C₆₁	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₆₁	—	2	1	no	—
175	C₂²×C₄×C₆₁	—	2	8	no	—
176	C₂²×C₄×C₆₁	—	2	4	no	—
177	C₂²×C₄×C₆₁	—	2	4	no	—
178	C₂²×C₄×C₆₁	—	2	1	no	—
179	C₂²×C₄×C₆₁	—	2	1	no	—
180	C₂²×C₄×C₆₁	—	2	4	no	—
181	C₂²×C₄×C₆₁	—	2	2	no	—
182	C₂²×C₄×C₆₁	—	2	4	no	—
183	C₂²×C₄×C₆₁	—	2	4	no	—
184	C₂²×C₄×C₆₁	—	2	8	no	—
185	C₂²×C₄×C₆₁	—	2	8	no	—
186	C₂²×C₄×C₆₁	—	4	2	no	—
187	C₂²×C₄×C₆₁	—	4	4	no	—
188	C₂²×C₄×C₆₁	—	4	8	no	—
189	C₂²×C₄×C₆₁	—	4	32	no	—
190	C₂²×C₄×C₆₁	—	4	4	no	—
191	C₂²×C₄×C₆₁	—	4	4	no	—
192	C₂²×C₄×C₆₁	—	4	8	no	—
193	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₆₁	#41	1	4	yes	—
203	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
205	SD₁₆×C₆₁	C₂²×C₄	1	32	yes	complemented
206	D₈×C₆₁	C₂²×C₄	1	32	yes	complemented
207	M₁₆×C₆₁	—	2	8	no	—
208	M₁₆×C₆₁	C₂²×C₄	1	16	yes	complemented
209	C₂×C₈×C₆₁	—	2	4	no	—
210	C₂×C₈×C₆₁	C₂²×C₄	1	8	yes	complemented
211	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
212	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
213	C₄⋊C₄×C₆₁	—	2	4	no	—
214	C₄⋊C₄×C₆₁	—	2	2	no	—
215	C₄⋊C₄×C₆₁	—	2	4	no	—
216	C₄⋊C₄×C₆₁	—	2	4	no	—
217	C₄⋊C₄×C₆₁	—	2	1	no	—
218	C₄⋊C₄×C₆₁	—	2	1	no	—
219	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
220	C₄⋊C₄×C₆₁	C₂⁴	1	2	yes	—
221	C₄⋊C₄×C₆₁	C₂⁴	1	4	yes	—
222	C₂²⋊C₄×C₆₁	—	2	4	no	—
223	C₂²⋊C₄×C₆₁	—	2	8	no	—
224	C₂²⋊C₄×C₆₁	—	2	8	no	—
225	C₂²⋊C₄×C₆₁	—	2	4	no	—
226	C₂²⋊C₄×C₆₁	—	2	4	no	—
227	C₄²×C₆₁	—	2	4	no	—
228	C₄²×C₆₁	—	2	4	no	—
229	C₄²×C₆₁	—	2	4	no	—
230	C₄²×C₆₁	C₂×D₄	1	4	yes	—
231	C₄²×C₆₁	C₂×D₄	1	4	yes	—
232	C₄²×C₆₁	C₂×D₄	1	2	yes	—
233	C₄²×C₆₁	C₂×D₄	1	2	yes	—
234	C₄²×C₆₁	C₂⁴	1	2	yes	—
235	C₄²×C₆₁	C₂⁴	1	2	yes	—
236	C₂³×C₆₁	—	2	2	no	—
237	C₂³×C₆₁	—	2	2	no	—
238	C₂³×C₆₁	—	2	4	no	—
239	C₂³×C₆₁	—	2	8	no	—
240	C₂³×C₆₁	—	2	16	no	—
241	C₂³×C₆₁	—	2	2	no	—
242	C₂³×C₆₁	—	2	4	no	—
243	C₂³×C₆₁	—	4	8	no	—
244	C₂³×C₆₁	—	4	32	no	—
245	C₂³×C₆₁	—	4	8	no	—
246	C₂³×C₆₁	—	4	4	no	—
247	C₂³×C₆₁	—	4	2	no	—
248	C₂³×C₆₁	—	4	2	no	—
249	C₂³×C₆₁	—	4	4	no	—
250	C₂³×C₆₁	C₄×D₄	1	4	yes	—
251	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
252	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
253	Q₈×C₆₁	—	2	4	no	—
254	Q₈×C₆₁	—	2	2	no	—
255	Q₈×C₆₁	C₂³×C₄	1	4	yes	complemented
256	D₄×C₆₁	—	2	16	no	—
257	D₄×C₆₁	—	2	8	no	—
258	D₄×C₆₁	—	2	16	no	—
259	D₄×C₆₁	—	2	4	no	—
260	D₄×C₆₁	—	2	4	no	—
261	D₄×C₆₁	—	2	2	no	—
262	D₄×C₆₁	C₂³×C₄	1	8	yes	—
263	D₄×C₆₁	C₂³×C₄	1	4	yes	complemented
264	C₂×C₄×C₆₁	—	2	4	no	—
265	C₂×C₄×C₆₁	—	2	2	no	—
266	C₂×C₄×C₆₁	—	2	2	no	—
267	C₂×C₄×C₆₁	—	2	2	no	—
268	C₂×C₄×C₆₁	—	2	2	no	—
269	C₂×C₄×C₆₁	—	2	16	no	—
270	C₂×C₄×C₆₁	—	2	8	no	—
271	C₂×C₄×C₆₁	—	2	2	no	—
272	C₂×C₄×C₆₁	—	2	2	no	—
273	C₂×C₄×C₆₁	—	2	4	no	—
274	C₂×C₄×C₆₁	—	4	4	no	—
275	C₂×C₄×C₆₁	—	4	8	no	—
276	C₂×C₄×C₆₁	—	4	16	no	—
277	C₂×C₄×C₆₁	—	4	8	no	—
278	C₂×C₄×C₆₁	—	4	2	no	—
279	C₂×C₄×C₆₁	—	4	4	no	—
280	C₂×C₄×C₆₁	—	4	2	no	—
281	C₂×C₄×C₆₁	—	4	8	no	—
282	C₂×C₄×C₆₁	—	4	16	no	—
283	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
284	C₂×C₄×C₆₁	C₄×D₄	1	8	yes	—
285	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	4	yes	direct product factor
286	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
288	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
295	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
296	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
297	C₈×C₆₁	—	2	4	no	—
298	C₈×C₆₁	C₂³×C₄	1	8	yes	complemented
299	C₂×C₄×AGL(1,ℤ/8)	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂²×C₆₁	—	2	8	no	—
301	C₂²×C₆₁	—	2	2	no	—
302	C₂²×C₆₁	—	2	2	no	—
303	C₂²×C₆₁	—	2	4	no	—
304	C₂²×C₆₁	—	2	8	no	—
305	C₂²×C₆₁	—	4	32	no	—
306	C₂²×C₆₁	—	4	8	no	—
307	C₂²×C₆₁	—	4	16	no	—
308	C₂²×C₆₁	—	4	4	no	—
309	C₂²×C₆₁	—	4	2	no	—
310	C₂²×C₆₁	—	4	2	no	—
311	C₂²×C₆₁	—	4	4	no	—
312	C₂²×C₆₁	C₂×C₄×D₄	1	4	yes	—
313	C₂²×C₆₁	C₂×C₄×D₄	1	2	yes	—
314	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
315	C₂²×C₆₁	#575	1	2	yes	—
316	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
317	C₄×C₆₁	—	2	4	no	—
318	C₄×C₆₁	—	2	2	no	—
319	C₄×C₆₁	—	2	2	no	—
320	C₄×C₆₁	—	2	2	no	—
321	C₄×C₆₁	—	4	2	no	—
322	C₄×C₆₁	—	4	4	no	—
323	C₄×C₆₁	—	4	2	no	—
324	C₄×C₆₁	C₂×C₄×D₄	1	4	yes	—
325	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
326	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	4	yes	direct product factor
327	C₄×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
328	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
329	C₂²×AGL(1,ℤ/8)	C₂×C₆₁	1	1	yes	characteristic
330	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic, complemented
331	C₂²×C₄×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
332	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	16	yes	direct product factor
333	C₂×#442	C₂×C₆₁	1	2	yes	complemented
334	C₂×#440	C₂×C₆₁	1	2	yes	complemented
335	C₂×C₄×SD₁₆	C₂×C₆₁	1	2	yes	complemented
336	C₂×C₄×D₈	C₂×C₆₁	1	2	yes	complemented
337	C₂×#428	C₂×C₆₁	1	1	yes	characteristic, complemented
338	C₂×#417	C₂×C₆₁	1	1	yes	characteristic, complemented
339	C₂×#418	C₂×C₆₁	1	1	yes	characteristic, complemented
340	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
341	C₂×C₆₁	—	2	4	no	—
342	C₂×C₆₁	—	4	4	no	—
343	C₂×C₆₁	—	4	8	no	—
344	C₂×C₆₁	C₄×AGL(1,ℤ/8)	1	4	yes	direct product factor
345	C₂×C₆₁	C₂²×C₄×D₄	1	1	yes	characteristic
346	C₂×C₆₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
347	C₂×C₆₁	C₂×#575	1	1	yes	characteristic
348	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
349	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
350	C₂⁴×C₄	—	2	1	no	—
351	C₂×AGL(1,ℤ/8)	C₄×C₆₁	1	16	yes	direct product factor
352	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	8	yes	—
353	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
354	C₂²×D₈	C₂²×C₆₁	1	2	yes	—
355	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
356	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
357	C₄×#41	—	2	4	no	—
358	C₄×#41	C₂²×C₆₁	1	8	yes	complemented
359	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
360	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic, complemented
361	C₂×C₄×D₄	—	2	1	no	—
362	C₂×C₄×D₄	—	2	1	no	—
363	C₂×C₄×D₄	—	2	1	no	—
364	C₂×C₄×D₄	—	2	4	no	—
365	C₂×C₄×D₄	—	2	1	no	—
366	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
367	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
368	C₂×C₄×D₄	C₂²×C₆₁	1	8	yes	complemented
369	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
370	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic, complemented
371	C₂×#117	—	2	1	no	—
372	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
373	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
374	C₂²×C₂²⋊C₄	—	2	1	no	—
375	C₂²×C₄²	—	2	1	no	—
376	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
377	#442	C₂²×C₆₁	1	16	yes	complemented
378	#440	C₂²×C₆₁	1	16	yes	complemented
379	C₄×SD₁₆	C₂²×C₆₁	1	16	yes	complemented
380	C₄×D₈	C₂²×C₆₁	1	16	yes	complemented
381	#428	C₂²×C₆₁	1	8	yes	complemented
382	C₂×#107	C₂²×C₆₁	1	2	yes	complemented
383	C₂×#106	C₂²×C₆₁	1	2	yes	complemented
384	#418	C₂²×C₆₁	1	8	yes	complemented
385	#417	C₂²×C₆₁	1	8	yes	complemented
386	C₂×#103	C₂²×C₆₁	1	2	yes	complemented
387	C₂×#102	C₂²×C₆₁	1	2	yes	—
388	C₂×#102	C₂²×C₆₁	1	2	yes	—
389	C₂×#102	C₂²×C₆₁	1	2	yes	complemented
390	C₄×M₁₆	C₂²×C₆₁	1	8	yes	complemented
391	C₂×#97	C₂²×C₆₁	1	2	yes	complemented
392	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	complemented
393	C₆₁	C₂×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
394	C₂⁵	—	2	1	no	—
395	C₂×#41	—	2	2	no	—
396	C₂×#41	—	2	4	no	—
397	C₂×#41	C₂×C₄×C₆₁	1	8	yes	complemented
398	C₂×#41	C₂³×C₆₁	1	4	yes	—
399	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	2	1	no	—
402	C₂²×D₄	—	2	2	no	—
403	C₂²×D₄	—	2	4	no	—
404	C₂²×D₄	C₂×C₄×C₆₁	1	8	yes	complemented
405	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
406	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	—	2	1	no	—
410	C₂³×C₄	—	2	2	no	—
411	C₂³×C₄	—	2	2	no	—
412	C₂³×C₄	—	2	8	no	—
413	C₂³×C₄	—	2	1	no	—
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	4	8	no	—
416	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
417	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
419	AGL(1,ℤ/8)	C₂×C₄×C₆₁	1	64	yes	direct product factor
420	C₂×SD₁₆	C₂×C₄×C₆₁	1	16	yes	complemented
421	C₂×SD₁₆	C₂³×C₆₁	1	8	yes	—
422	C₂×D₈	C₂×C₄×C₆₁	1	16	yes	complemented
423	C₂×D₈	C₂³×C₆₁	1	8	yes	—
424	C₂×M₁₆	—	2	4	no	—
425	C₂×M₁₆	C₂×C₄×C₆₁	1	8	yes	complemented
426	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
427	C₂×M₁₆	C₂³×C₆₁	1	4	yes	—
428	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
429	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	—	2	2	no	—
432	C₄×Q₈	C₂³×C₆₁	1	4	yes	complemented
433	C₄×Q₈	C₂³×C₆₁	1	4	yes	complemented
434	C₄×D₄	—	2	8	no	—
435	C₄×D₄	—	2	8	no	—
436	C₄×D₄	—	2	4	no	—
437	C₄×D₄	—	2	4	no	—
438	C₄×D₄	—	2	8	no	—
439	C₄×D₄	—	2	8	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	C₂³×C₆₁	1	8	yes	—
443	C₄×D₄	C₂³×C₆₁	1	8	yes	—
444	C₄×D₄	C₂³×C₆₁	1	4	yes	complemented
445	C₄×D₄	C₂³×C₆₁	1	4	yes	complemented
446	#117	—	2	2	no	—
447	#117	—	2	8	no	—
448	#117	C₂³×C₆₁	1	4	yes	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	2	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
454	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	2	no	—
459	C₂×C₂²⋊C₄	—	2	2	no	—
460	C₂×C₂²⋊C₄	—	2	8	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	2	8	no	—
467	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
468	C₂×C₄²	D₄×C₆₁	1	4	yes	—
469	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
472	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
473	#107	C₂³×C₆₁	1	8	yes	complemented
474	#106	C₂³×C₆₁	1	8	yes	complemented
475	#103	C₂³×C₆₁	1	8	yes	complemented
476	#102	C₂³×C₆₁	1	8	yes	—
477	#102	C₂³×C₆₁	1	8	yes	—
478	#102	C₂³×C₆₁	1	8	yes	complemented
479	#97	C₂³×C₆₁	1	8	yes	complemented
480	C₄×C₈	C₂³×C₆₁	1	8	yes	complemented
481	C₂⁴	—	2	8	no	—
482	C₂⁴	—	2	1	no	—
483	C₂⁴	—	2	2	no	—
484	C₂⁴	—	2	4	no	—
485	C₂⁴	—	4	4	no	—
486	C₂⁴	—	4	4	no	—
487	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
488	#41	—	2	16	no	—
489	#41	—	2	8	no	—
490	#41	C₂²×C₄×C₆₁	1	16	yes	complemented
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	complemented
494	C₂×Q₈	C₂⁴×C₆₁	1	2	yes	—
495	C₂×D₄	—	2	8	no	—
496	C₂×D₄	—	2	4	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	16	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	1	no	—
502	C₂×D₄	—	2	4	no	—
503	C₂×D₄	—	2	8	no	—
504	C₂×D₄	—	2	2	no	—
505	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
506	C₂×D₄	C₂²×C₄×C₆₁	1	16	yes	complemented
507	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	complemented
508	C₂×D₄	C₂⁴×C₆₁	1	4	yes	—
509	C₂×D₄	C₂⁴×C₆₁	1	2	yes	—
510	C₂²×C₄	—	2	1	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	1	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	8	no	—
521	C₂²×C₄	—	2	8	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	8	no	—
524	C₂²×C₄	—	4	32	no	—
525	C₂²×C₄	—	4	4	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	—	4	8	no	—
528	C₂²×C₄	—	4	4	no	—
529	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
530	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
534	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
535	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
537	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
538	C₂²×C₄	#41×C₆₁	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
541	SD₁₆	C₂²×C₄×C₆₁	1	32	yes	complemented
542	D₈	C₂²×C₄×C₆₁	1	32	yes	complemented
543	M₁₆	—	2	8	no	—
544	M₁₆	C₂²×C₄×C₆₁	1	16	yes	complemented
545	C₂×C₈	—	2	4	no	—
546	C₂×C₈	C₂²×C₄×C₆₁	1	8	yes	complemented
547	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
548	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
549	C₄⋊C₄	—	2	4	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	4	no	—
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
556	C₄⋊C₄	C₂⁴×C₆₁	1	2	yes	—
557	C₄⋊C₄	C₂⁴×C₆₁	1	4	yes	—
558	C₂²⋊C₄	—	2	4	no	—
559	C₂²⋊C₄	—	2	8	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	4	no	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	4	no	—
566	C₄²	C₂×D₄×C₆₁	1	4	yes	—
567	C₄²	C₂×D₄×C₆₁	1	4	yes	—
568	C₄²	C₂×D₄×C₆₁	1	2	yes	—
569	C₄²	C₂×D₄×C₆₁	1	2	yes	—
570	C₄²	C₂⁴×C₆₁	1	2	yes	—
571	C₄²	C₂⁴×C₆₁	1	2	yes	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	4	no	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	8	no	—
578	C₂³	—	2	16	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	8	no	—
581	C₂³	—	4	32	no	—
582	C₂³	—	4	4	no	—
583	C₂³	—	4	2	no	—
584	C₂³	—	4	2	no	—
585	C₂³	—	4	4	no	—
586	C₂³	C₄×D₄×C₆₁	1	4	yes	—
587	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
588	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
589	Q₈	—	2	2	no	—
590	Q₈	—	2	4	no	—
591	Q₈	C₂³×C₄×C₆₁	1	4	yes	complemented
592	D₄	—	2	16	no	—
593	D₄	—	2	4	no	—
594	D₄	—	2	2	no	—
595	D₄	—	2	8	no	—
596	D₄	—	2	16	no	—
597	D₄	—	2	4	no	—
598	D₄	C₂³×C₄×C₆₁	1	8	yes	—
599	D₄	C₂³×C₄×C₆₁	1	4	yes	complemented
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	16	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	4	no	—
610	C₂×C₄	—	4	4	no	—
611	C₂×C₄	—	4	8	no	—
612	C₂×C₄	—	4	16	no	—
613	C₂×C₄	—	4	8	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	16	no	—
619	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
620	C₂×C₄	C₄×D₄×C₆₁	1	8	yes	—
621	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	4	yes	direct product factor
622	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
624	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
625	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
628	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
631	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
632	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
633	C₈	—	2	4	no	—
634	C₈	C₂³×C₄×C₆₁	1	8	yes	complemented
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	8	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	4	32	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	8	no	—
646	C₂²	—	4	16	no	—
647	C₂²	C₂×C₄×D₄×C₆₁	1	4	yes	—
648	C₂²	C₂×C₄×D₄×C₆₁	1	2	yes	—
649	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
650	C₂²	C₆₁×#575	1	2	yes	—
651	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
652	C₄	—	2	2	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	4	no	—
656	C₄	—	4	2	no	—
657	C₄	—	4	4	no	—
658	C₄	—	4	2	no	—
659	C₄	C₂×C₄×D₄×C₆₁	1	4	yes	—
660	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
661	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	4	yes	direct product factor
662	C₄	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
663	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
664	C₂	—	2	4	no	—
665	C₂	—	4	8	no	—
666	C₂	—	4	4	no	—
667	C₂	C₄×AGL(1,ℤ/8)×C₆₁	1	4	yes	direct product factor
668	C₂	C₂²×C₄×D₄×C₆₁	1	1	yes	characteristic
669	C₂	C₂²×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
670	C₂	C₂×C₆₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
prime radical	C₂²×AGL(1,ℤ/8)×C₆₁	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₆₁	C₂	semidirect
3. C₂²×C₄×D₄×C₆₁	C₂	semidirect
4. C₄×AGL(1,ℤ/8)×C₆₁	C₂	direct (N × H)
5. C₂×C₆₁×#442	C₂	semidirect
6. C₂×C₆₁×#440	C₂	semidirect
7. C₂×C₄×SD₁₆×C₆₁	C₂	semidirect
8. C₂×C₄×D₈×C₆₁	C₂	semidirect
9. C₂×C₆₁×#428	C₂	semidirect
10. C₂×C₆₁×#417	C₂	semidirect
11. C₂×C₆₁×#418	C₂	semidirect
12. C₂×C₄×M₁₆×C₆₁	C₂	semidirect
16. C₂×AGL(1,ℤ/8)×C₆₁	C₄	direct (N × H)
23. C₄×#41×C₆₁	C₂²	semidirect
24. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
25. C₂×C₄×Q₈×C₆₁	C₂²	semidirect
33. C₂×C₄×D₄×C₆₁	C₂²	semidirect
34. C₂×C₄×D₄×C₆₁	C₂²	semidirect
35. C₂×C₄×D₄×C₆₁	C₂²	semidirect
42. C₆₁×#442	C₂²	semidirect
43. C₆₁×#440	C₂²	semidirect
44. C₄×SD₁₆×C₆₁	C₂²	semidirect
45. C₄×D₈×C₆₁	C₂²	semidirect
46. C₆₁×#428	C₂²	semidirect
47. C₂×#107×C₆₁	C₂²	semidirect
48. C₂×#106×C₆₁	C₂²	semidirect
49. C₆₁×#418	C₂²	semidirect
50. C₆₁×#417	C₂²	semidirect
51. C₂×#103×C₆₁	C₂²	semidirect
54. C₂×#102×C₆₁	C₂²	semidirect
55. C₄×M₁₆×C₆₁	C₂²	semidirect
56. C₂×#97×C₆₁	C₂²	semidirect
57. C₂×C₄×C₈×C₆₁	C₂²	semidirect
61. C₂×#41×C₆₁	C₂×C₄	semidirect
68. C₂²×D₄×C₆₁	C₂×C₄	semidirect
83. AGL(1,ℤ/8)×C₆₁	C₂×C₄	direct (N × H)
84. C₂×SD₁₆×C₆₁	C₂×C₄	semidirect
86. C₂×D₈×C₆₁	C₂×C₄	semidirect
89. C₂×M₁₆×C₆₁	C₂×C₄	semidirect
96. C₄×Q₈×C₆₁	C₂³	semidirect
97. C₄×Q₈×C₆₁	C₂³	semidirect
108. C₄×D₄×C₆₁	C₂³	semidirect
109. C₄×D₄×C₆₁	C₂³	semidirect
137. #107×C₆₁	C₂³	semidirect
138. #106×C₆₁	C₂³	semidirect
139. #103×C₆₁	C₂³	semidirect
142. #102×C₆₁	C₂³	semidirect
143. #97×C₆₁	C₂³	semidirect
144. C₄×C₈×C₆₁	C₂³	semidirect
154. #41×C₆₁	C₂²×C₄	semidirect
157. C₂×Q₈×C₆₁	C₂²×C₄	semidirect
170. C₂×D₄×C₆₁	C₂²×C₄	semidirect
171. C₂×D₄×C₆₁	C₂²×C₄	semidirect
205. SD₁₆×C₆₁	C₂²×C₄	semidirect
206. D₈×C₆₁	C₂²×C₄	semidirect
208. M₁₆×C₆₁	C₂²×C₄	semidirect
210. C₂×C₈×C₆₁	C₂²×C₄	semidirect
255. Q₈×C₆₁	C₂³×C₄	semidirect
263. D₄×C₆₁	C₂³×C₄	semidirect
285. C₂×C₄×C₆₁	AGL(1,ℤ/8)	direct (N × H)
298. C₈×C₆₁	C₂³×C₄	semidirect
299. C₂×C₄×AGL(1,ℤ/8)	C₆₁	direct (N × H)
326. C₄×C₆₁	C₂×AGL(1,ℤ/8)	direct (N × H)
330. C₂×C₄×#41	C₂×C₆₁	semidirect
331. C₂²×C₄×D₄	C₂×C₆₁	semidirect
332. C₄×AGL(1,ℤ/8)	C₂×C₆₁	direct (N × H)
333. C₂×#442	C₂×C₆₁	semidirect
334. C₂×#440	C₂×C₆₁	semidirect
335. C₂×C₄×SD₁₆	C₂×C₆₁	semidirect
336. C₂×C₄×D₈	C₂×C₆₁	semidirect
337. C₂×#428	C₂×C₆₁	semidirect
338. C₂×#417	C₂×C₆₁	semidirect
339. C₂×#418	C₂×C₆₁	semidirect
340. C₂×C₄×M₁₆	C₂×C₆₁	semidirect
344. C₂×C₆₁	C₄×AGL(1,ℤ/8)	direct (N × H)
351. C₂×AGL(1,ℤ/8)	C₄×C₆₁	direct (N × H)
358. C₄×#41	C₂²×C₆₁	semidirect
359. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
360. C₂×C₄×Q₈	C₂²×C₆₁	semidirect
368. C₂×C₄×D₄	C₂²×C₆₁	semidirect
369. C₂×C₄×D₄	C₂²×C₆₁	semidirect
370. C₂×C₄×D₄	C₂²×C₆₁	semidirect
377. #442	C₂²×C₆₁	semidirect
378. #440	C₂²×C₆₁	semidirect
379. C₄×SD₁₆	C₂²×C₆₁	semidirect
380. C₄×D₈	C₂²×C₆₁	semidirect
381. #428	C₂²×C₆₁	semidirect
382. C₂×#107	C₂²×C₆₁	semidirect
383. C₂×#106	C₂²×C₆₁	semidirect
384. #418	C₂²×C₆₁	semidirect
385. #417	C₂²×C₆₁	semidirect
386. C₂×#103	C₂²×C₆₁	semidirect
389. C₂×#102	C₂²×C₆₁	semidirect
390. C₄×M₁₆	C₂²×C₆₁	semidirect
391. C₂×#97	C₂²×C₆₁	semidirect
392. C₂×C₄×C₈	C₂²×C₆₁	semidirect
393. C₆₁	C₂×C₄×AGL(1,ℤ/8)	direct (N × H)
397. C₂×#41	C₂×C₄×C₆₁	semidirect
404. C₂²×D₄	C₂×C₄×C₆₁	semidirect
419. AGL(1,ℤ/8)	C₂×C₄×C₆₁	direct (N × H)
420. C₂×SD₁₆	C₂×C₄×C₆₁	semidirect
422. C₂×D₈	C₂×C₄×C₆₁	semidirect
425. C₂×M₁₆	C₂×C₄×C₆₁	semidirect
432. C₄×Q₈	C₂³×C₆₁	semidirect
433. C₄×Q₈	C₂³×C₆₁	semidirect
444. C₄×D₄	C₂³×C₆₁	semidirect
445. C₄×D₄	C₂³×C₆₁	semidirect
473. #107	C₂³×C₆₁	semidirect
474. #106	C₂³×C₆₁	semidirect
475. #103	C₂³×C₆₁	semidirect
478. #102	C₂³×C₆₁	semidirect
479. #97	C₂³×C₆₁	semidirect
480. C₄×C₈	C₂³×C₆₁	semidirect
490. #41	C₂²×C₄×C₆₁	semidirect
493. C₂×Q₈	C₂²×C₄×C₆₁	semidirect
506. C₂×D₄	C₂²×C₄×C₆₁	semidirect
507. C₂×D₄	C₂²×C₄×C₆₁	semidirect
541. SD₁₆	C₂²×C₄×C₆₁	semidirect
542. D₈	C₂²×C₄×C₆₁	semidirect
544. M₁₆	C₂²×C₄×C₆₁	semidirect
546. C₂×C₈	C₂²×C₄×C₆₁	semidirect
591. Q₈	C₂³×C₄×C₆₁	semidirect
599. D₄	C₂³×C₄×C₆₁	semidirect
621. C₂×C₄	AGL(1,ℤ/8)×C₆₁	direct (N × H)
634. C₈	C₂³×C₄×C₆₁	semidirect
661. C₄	C₂×AGL(1,ℤ/8)×C₆₁	direct (N × H)
667. C₂	C₄×AGL(1,ℤ/8)×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
C₂²×AGL(1,ℤ/8)×C₆₁	2
C₂×C₄×#41×C₆₁	2
C₂²×C₄×D₄×C₆₁	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₂×C₆₁×#442	2
C₂×C₆₁×#440	2
C₂×C₄×SD₁₆×C₆₁	2
C₂×C₄×D₈×C₆₁	2
C₂×C₆₁×#428	2
C₂×C₆₁×#417	2
C₂×C₆₁×#418	2
C₂×C₄×M₁₆×C₆₁	2
C₂×C₄×AGL(1,ℤ/8)	61

Subgroups — C2×C4×AGL(1,ℤ/8)×C61 #29563589

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×AGL(1,ℤ/8)×C₆₁ #29563589