Subgroups — C₂×C₄×C₃₁×AGL(1,ℤ/8) #21516915

Order 7936.

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×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₃₁×AGL(1,ℤ/8)	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₃₁×#442	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#440	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×D₈×C₃₁	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃₁×#418	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₃₁	—	2	1	no	—
16	C₂×C₃₁×AGL(1,ℤ/8)	C₄	1	16	yes	direct product factor
17	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	8	yes	—
18	C₂²×SD₁₆×C₃₁	C₂²	1	2	yes	—
19	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
22	C₄×#41×C₃₁	—	2	4	no	—
23	C₄×#41×C₃₁	C₂²	1	8	yes	complemented
24	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×D₄×C₃₁	—	2	1	no	—
27	C₂×C₄×D₄×C₃₁	—	2	1	no	—
28	C₂×C₄×D₄×C₃₁	—	2	1	no	—
29	C₂×C₄×D₄×C₃₁	—	2	4	no	—
30	C₂×C₄×D₄×C₃₁	—	2	1	no	—
31	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
34	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃₁×#117	—	2	1	no	—
37	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₃₁	—	2	1	no	—
40	C₂²×C₄²×C₃₁	—	2	1	no	—
41	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
42	C₃₁×#442	C₂²	1	16	yes	complemented
43	C₃₁×#440	C₂²	1	16	yes	complemented
44	C₄×SD₁₆×C₃₁	C₂²	1	16	yes	complemented
45	C₄×D₈×C₃₁	C₂²	1	16	yes	complemented
46	C₃₁×#428	C₂²	1	8	yes	complemented
47	C₂×C₃₁×#107	C₂²	1	2	yes	complemented
48	C₂×C₃₁×#106	C₂²	1	2	yes	complemented
49	C₃₁×#418	C₂²	1	8	yes	complemented
50	C₃₁×#417	C₂²	1	8	yes	complemented
51	C₂×C₃₁×#103	C₂²	1	2	yes	complemented
52	C₂×C₃₁×#102	C₂²	1	2	yes	—
53	C₂×C₃₁×#102	C₂²	1	2	yes	—
54	C₂×C₃₁×#102	C₂²	1	2	yes	complemented
55	C₄×M₁₆×C₃₁	C₂²	1	8	yes	complemented
56	C₂×C₃₁×#97	C₂²	1	2	yes	complemented
57	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	complemented
58	C₂⁵×C₃₁	—	2	1	no	—
59	C₂×#41×C₃₁	—	2	2	no	—
60	C₂×#41×C₃₁	—	2	4	no	—
61	C₂×#41×C₃₁	C₂×C₄	1	8	yes	complemented
62	C₂×#41×C₃₁	C₂³	1	4	yes	—
63	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₃₁	—	2	1	no	—
65	C₂²×D₄×C₃₁	—	2	1	no	—
66	C₂²×D₄×C₃₁	—	2	2	no	—
67	C₂²×D₄×C₃₁	—	2	4	no	—
68	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
69	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
70	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
72	C₂³×C₄×C₃₁	—	2	1	no	—
73	C₂³×C₄×C₃₁	—	2	1	no	—
74	C₂³×C₄×C₃₁	—	2	1	no	—
75	C₂³×C₄×C₃₁	—	2	2	no	—
76	C₂³×C₄×C₃₁	—	2	8	no	—
77	C₂³×C₄×C₃₁	—	2	1	no	—
78	C₂³×C₄×C₃₁	—	2	2	no	—
79	C₂³×C₄×C₃₁	—	4	8	no	—
80	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
83	C₃₁×AGL(1,ℤ/8)	C₂×C₄	1	64	yes	direct product factor
84	C₂×SD₁₆×C₃₁	C₂×C₄	1	16	yes	complemented
85	C₂×SD₁₆×C₃₁	C₂³	1	8	yes	—
86	C₂×D₈×C₃₁	C₂×C₄	1	16	yes	complemented
87	C₂×D₈×C₃₁	C₂³	1	8	yes	—
88	C₂×M₁₆×C₃₁	—	2	4	no	—
89	C₂×M₁₆×C₃₁	C₂×C₄	1	8	yes	complemented
90	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
91	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
92	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
93	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
94	C₄×Q₈×C₃₁	—	2	2	no	—
95	C₄×Q₈×C₃₁	—	2	2	no	—
96	C₄×Q₈×C₃₁	C₂³	1	4	yes	complemented
97	C₄×Q₈×C₃₁	C₂³	1	4	yes	complemented
98	C₄×D₄×C₃₁	—	2	8	no	—
99	C₄×D₄×C₃₁	—	2	8	no	—
100	C₄×D₄×C₃₁	—	2	4	no	—
101	C₄×D₄×C₃₁	—	2	4	no	—
102	C₄×D₄×C₃₁	—	2	8	no	—
103	C₄×D₄×C₃₁	—	2	8	no	—
104	C₄×D₄×C₃₁	—	2	2	no	—
105	C₄×D₄×C₃₁	—	2	2	no	—
106	C₄×D₄×C₃₁	C₂³	1	8	yes	—
107	C₄×D₄×C₃₁	C₂³	1	8	yes	—
108	C₄×D₄×C₃₁	C₂³	1	4	yes	complemented
109	C₄×D₄×C₃₁	C₂³	1	4	yes	complemented
110	C₃₁×#117	—	2	2	no	—
111	C₃₁×#117	—	2	8	no	—
112	C₃₁×#117	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
114	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
115	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
116	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
117	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
119	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
122	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
123	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
124	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
125	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
127	C₂×C₄²×C₃₁	—	2	1	no	—
128	C₂×C₄²×C₃₁	—	2	1	no	—
129	C₂×C₄²×C₃₁	—	2	1	no	—
130	C₂×C₄²×C₃₁	—	2	8	no	—
131	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₃₁	D₄	1	4	yes	—
133	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
134	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
136	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
137	C₃₁×#107	C₂³	1	8	yes	complemented
138	C₃₁×#106	C₂³	1	8	yes	complemented
139	C₃₁×#103	C₂³	1	8	yes	complemented
140	C₃₁×#102	C₂³	1	8	yes	—
141	C₃₁×#102	C₂³	1	8	yes	—
142	C₃₁×#102	C₂³	1	8	yes	complemented
143	C₃₁×#97	C₂³	1	8	yes	complemented
144	C₄×C₈×C₃₁	C₂³	1	8	yes	complemented
145	C₂⁴×C₃₁	—	2	8	no	—
146	C₂⁴×C₃₁	—	2	1	no	—
147	C₂⁴×C₃₁	—	2	2	no	—
148	C₂⁴×C₃₁	—	2	4	no	—
149	C₂⁴×C₃₁	—	4	4	no	—
150	C₂⁴×C₃₁	—	4	4	no	—
151	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
152	#41×C₃₁	—	2	16	no	—
153	#41×C₃₁	—	2	8	no	—
154	#41×C₃₁	C₂²×C₄	1	16	yes	complemented
155	C₂×Q₈×C₃₁	—	2	1	no	—
156	C₂×Q₈×C₃₁	—	2	2	no	—
157	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	complemented
158	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
159	C₂×D₄×C₃₁	—	2	8	no	—
160	C₂×D₄×C₃₁	—	2	4	no	—
161	C₂×D₄×C₃₁	—	2	8	no	—
162	C₂×D₄×C₃₁	—	2	16	no	—
163	C₂×D₄×C₃₁	—	2	4	no	—
164	C₂×D₄×C₃₁	—	2	2	no	—
165	C₂×D₄×C₃₁	—	2	1	no	—
166	C₂×D₄×C₃₁	—	2	4	no	—
167	C₂×D₄×C₃₁	—	2	8	no	—
168	C₂×D₄×C₃₁	—	2	2	no	—
169	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
170	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	complemented
171	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	complemented
172	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
173	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₃₁	—	2	1	no	—
175	C₂²×C₄×C₃₁	—	2	8	no	—
176	C₂²×C₄×C₃₁	—	2	4	no	—
177	C₂²×C₄×C₃₁	—	2	4	no	—
178	C₂²×C₄×C₃₁	—	2	1	no	—
179	C₂²×C₄×C₃₁	—	2	1	no	—
180	C₂²×C₄×C₃₁	—	2	4	no	—
181	C₂²×C₄×C₃₁	—	2	2	no	—
182	C₂²×C₄×C₃₁	—	2	4	no	—
183	C₂²×C₄×C₃₁	—	2	4	no	—
184	C₂²×C₄×C₃₁	—	2	8	no	—
185	C₂²×C₄×C₃₁	—	2	8	no	—
186	C₂²×C₄×C₃₁	—	4	2	no	—
187	C₂²×C₄×C₃₁	—	4	4	no	—
188	C₂²×C₄×C₃₁	—	4	8	no	—
189	C₂²×C₄×C₃₁	—	4	32	no	—
190	C₂²×C₄×C₃₁	—	4	4	no	—
191	C₂²×C₄×C₃₁	—	4	4	no	—
192	C₂²×C₄×C₃₁	—	4	8	no	—
193	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
194	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
198	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
199	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₃₁	#41	1	4	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
204	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
205	SD₁₆×C₃₁	C₂²×C₄	1	32	yes	complemented
206	D₈×C₃₁	C₂²×C₄	1	32	yes	complemented
207	M₁₆×C₃₁	—	2	8	no	—
208	M₁₆×C₃₁	C₂²×C₄	1	16	yes	complemented
209	C₂×C₈×C₃₁	—	2	4	no	—
210	C₂×C₈×C₃₁	C₂²×C₄	1	8	yes	complemented
211	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
212	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
213	C₄⋊C₄×C₃₁	—	2	4	no	—
214	C₄⋊C₄×C₃₁	—	2	2	no	—
215	C₄⋊C₄×C₃₁	—	2	4	no	—
216	C₄⋊C₄×C₃₁	—	2	4	no	—
217	C₄⋊C₄×C₃₁	—	2	1	no	—
218	C₄⋊C₄×C₃₁	—	2	1	no	—
219	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
220	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
221	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
222	C₂²⋊C₄×C₃₁	—	2	4	no	—
223	C₂²⋊C₄×C₃₁	—	2	8	no	—
224	C₂²⋊C₄×C₃₁	—	2	8	no	—
225	C₂²⋊C₄×C₃₁	—	2	4	no	—
226	C₂²⋊C₄×C₃₁	—	2	4	no	—
227	C₄²×C₃₁	—	2	4	no	—
228	C₄²×C₃₁	—	2	4	no	—
229	C₄²×C₃₁	—	2	4	no	—
230	C₄²×C₃₁	C₂×D₄	1	4	yes	—
231	C₄²×C₃₁	C₂×D₄	1	4	yes	—
232	C₄²×C₃₁	C₂×D₄	1	2	yes	—
233	C₄²×C₃₁	C₂×D₄	1	2	yes	—
234	C₄²×C₃₁	C₂⁴	1	2	yes	—
235	C₄²×C₃₁	C₂⁴	1	2	yes	—
236	C₂×C₄×AGL(1,ℤ/8)	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₃₁	—	2	2	no	—
238	C₂³×C₃₁	—	2	2	no	—
239	C₂³×C₃₁	—	2	4	no	—
240	C₂³×C₃₁	—	2	8	no	—
241	C₂³×C₃₁	—	2	16	no	—
242	C₂³×C₃₁	—	2	2	no	—
243	C₂³×C₃₁	—	2	4	no	—
244	C₂³×C₃₁	—	4	8	no	—
245	C₂³×C₃₁	—	4	32	no	—
246	C₂³×C₃₁	—	4	8	no	—
247	C₂³×C₃₁	—	4	4	no	—
248	C₂³×C₃₁	—	4	2	no	—
249	C₂³×C₃₁	—	4	2	no	—
250	C₂³×C₃₁	—	4	4	no	—
251	C₂³×C₃₁	C₄×D₄	1	4	yes	—
252	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
253	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₃₁	—	2	4	no	—
255	Q₈×C₃₁	—	2	2	no	—
256	Q₈×C₃₁	C₂³×C₄	1	4	yes	complemented
257	D₄×C₃₁	—	2	16	no	—
258	D₄×C₃₁	—	2	8	no	—
259	D₄×C₃₁	—	2	16	no	—
260	D₄×C₃₁	—	2	4	no	—
261	D₄×C₃₁	—	2	4	no	—
262	D₄×C₃₁	—	2	2	no	—
263	D₄×C₃₁	C₂³×C₄	1	8	yes	—
264	D₄×C₃₁	C₂³×C₄	1	4	yes	complemented
265	C₂×C₄×C₃₁	—	2	4	no	—
266	C₂×C₄×C₃₁	—	2	2	no	—
267	C₂×C₄×C₃₁	—	2	2	no	—
268	C₂×C₄×C₃₁	—	2	2	no	—
269	C₂×C₄×C₃₁	—	2	2	no	—
270	C₂×C₄×C₃₁	—	2	16	no	—
271	C₂×C₄×C₃₁	—	2	8	no	—
272	C₂×C₄×C₃₁	—	2	2	no	—
273	C₂×C₄×C₃₁	—	2	2	no	—
274	C₂×C₄×C₃₁	—	2	4	no	—
275	C₂×C₄×C₃₁	—	4	4	no	—
276	C₂×C₄×C₃₁	—	4	8	no	—
277	C₂×C₄×C₃₁	—	4	16	no	—
278	C₂×C₄×C₃₁	—	4	8	no	—
279	C₂×C₄×C₃₁	—	4	2	no	—
280	C₂×C₄×C₃₁	—	4	4	no	—
281	C₂×C₄×C₃₁	—	4	2	no	—
282	C₂×C₄×C₃₁	—	4	8	no	—
283	C₂×C₄×C₃₁	—	4	16	no	—
284	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
285	C₂×C₄×C₃₁	C₄×D₄	1	8	yes	—
286	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	4	yes	direct product factor
287	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
288	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
289	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
293	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
296	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
297	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
298	C₈×C₃₁	—	2	4	no	—
299	C₈×C₃₁	C₂³×C₄	1	8	yes	complemented
300	C₂²×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic
301	C₂×C₄×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
302	C₂²×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
303	C₄×AGL(1,ℤ/8)	C₂×C₃₁	1	16	yes	direct product factor
304	C₂×#442	C₂×C₃₁	1	2	yes	complemented
305	C₂×#440	C₂×C₃₁	1	2	yes	complemented
306	C₂×C₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
307	C₂×C₄×D₈	C₂×C₃₁	1	2	yes	complemented
308	C₂×#428	C₂×C₃₁	1	1	yes	characteristic, complemented
309	C₂×#417	C₂×C₃₁	1	1	yes	characteristic, complemented
310	C₂×#418	C₂×C₃₁	1	1	yes	characteristic, complemented
311	C₂×C₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
312	C₂²×C₃₁	—	2	8	no	—
313	C₂²×C₃₁	—	2	2	no	—
314	C₂²×C₃₁	—	2	2	no	—
315	C₂²×C₃₁	—	2	4	no	—
316	C₂²×C₃₁	—	2	8	no	—
317	C₂²×C₃₁	—	4	32	no	—
318	C₂²×C₃₁	—	4	8	no	—
319	C₂²×C₃₁	—	4	16	no	—
320	C₂²×C₃₁	—	4	4	no	—
321	C₂²×C₃₁	—	4	2	no	—
322	C₂²×C₃₁	—	4	2	no	—
323	C₂²×C₃₁	—	4	4	no	—
324	C₂²×C₃₁	C₂×C₄×D₄	1	4	yes	—
325	C₂²×C₃₁	C₂×C₄×D₄	1	2	yes	—
326	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
327	C₂²×C₃₁	#575	1	2	yes	—
328	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
329	C₄×C₃₁	—	2	4	no	—
330	C₄×C₃₁	—	2	2	no	—
331	C₄×C₃₁	—	2	2	no	—
332	C₄×C₃₁	—	2	2	no	—
333	C₄×C₃₁	—	4	2	no	—
334	C₄×C₃₁	—	4	4	no	—
335	C₄×C₃₁	—	4	2	no	—
336	C₄×C₃₁	C₂×C₄×D₄	1	4	yes	—
337	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
338	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	direct product factor
339	C₄×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
340	C₄×C₃₁	C₂²×#41	1	1	yes	characteristic
341	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
342	C₂³×D₄	C₂²×C₃₁	1	1	yes	characteristic
343	C₂⁴×C₄	—	2	1	no	—
344	C₂×AGL(1,ℤ/8)	C₄×C₃₁	1	16	yes	direct product factor
345	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	8	yes	—
346	C₂²×SD₁₆	C₂²×C₃₁	1	2	yes	—
347	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
348	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
349	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
350	C₄×#41	—	2	4	no	—
351	C₄×#41	C₂²×C₃₁	1	8	yes	complemented
352	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
353	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
354	C₂×C₄×D₄	—	2	1	no	—
355	C₂×C₄×D₄	—	2	1	no	—
356	C₂×C₄×D₄	—	2	1	no	—
357	C₂×C₄×D₄	—	2	4	no	—
358	C₂×C₄×D₄	—	2	1	no	—
359	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
360	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
362	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
363	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
364	C₂×#117	—	2	1	no	—
365	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
366	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	—	2	1	no	—
368	C₂²×C₄²	—	2	1	no	—
369	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
370	#442	C₂²×C₃₁	1	16	yes	complemented
371	#440	C₂²×C₃₁	1	16	yes	complemented
372	C₄×SD₁₆	C₂²×C₃₁	1	16	yes	complemented
373	C₄×D₈	C₂²×C₃₁	1	16	yes	complemented
374	#428	C₂²×C₃₁	1	8	yes	complemented
375	C₂×#107	C₂²×C₃₁	1	2	yes	complemented
376	C₂×#106	C₂²×C₃₁	1	2	yes	complemented
377	#418	C₂²×C₃₁	1	8	yes	complemented
378	#417	C₂²×C₃₁	1	8	yes	complemented
379	C₂×#103	C₂²×C₃₁	1	2	yes	complemented
380	C₂×#102	C₂²×C₃₁	1	2	yes	—
381	C₂×#102	C₂²×C₃₁	1	2	yes	—
382	C₂×#102	C₂²×C₃₁	1	2	yes	complemented
383	C₄×M₁₆	C₂²×C₃₁	1	8	yes	complemented
384	C₂×#97	C₂²×C₃₁	1	2	yes	complemented
385	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	complemented
386	C₂×C₃₁	—	2	4	no	—
387	C₂×C₃₁	—	4	4	no	—
388	C₂×C₃₁	—	4	8	no	—
389	C₂×C₃₁	C₄×AGL(1,ℤ/8)	1	4	yes	direct product factor
390	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
391	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
392	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
393	C₂⁵	—	2	1	no	—
394	C₂×#41	—	2	2	no	—
395	C₂×#41	—	2	4	no	—
396	C₂×#41	C₂×C₄×C₃₁	1	8	yes	complemented
397	C₂×#41	C₂³×C₃₁	1	4	yes	—
398	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
399	C₂²×D₄	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	—	2	2	no	—
402	C₂²×D₄	—	2	4	no	—
403	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
404	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
405	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
406	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
407	C₂³×C₄	—	2	1	no	—
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	—	2	2	no	—
410	C₂³×C₄	—	2	2	no	—
411	C₂³×C₄	—	2	8	no	—
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	—	2	1	no	—
414	C₂³×C₄	—	4	8	no	—
415	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
416	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
418	AGL(1,ℤ/8)	C₂×C₄×C₃₁	1	64	yes	direct product factor
419	C₂×SD₁₆	C₂×C₄×C₃₁	1	16	yes	complemented
420	C₂×SD₁₆	C₂³×C₃₁	1	8	yes	—
421	C₂×D₈	C₂×C₄×C₃₁	1	16	yes	complemented
422	C₂×D₈	C₂³×C₃₁	1	8	yes	—
423	C₂×M₁₆	—	2	4	no	—
424	C₂×M₁₆	C₂×C₄×C₃₁	1	8	yes	complemented
425	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
426	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
427	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
428	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
429	C₄×Q₈	—	2	2	no	—
430	C₄×Q₈	—	2	2	no	—
431	C₄×Q₈	C₂³×C₃₁	1	4	yes	complemented
432	C₄×Q₈	C₂³×C₃₁	1	4	yes	complemented
433	C₄×D₄	—	2	8	no	—
434	C₄×D₄	—	2	8	no	—
435	C₄×D₄	—	2	4	no	—
436	C₄×D₄	—	2	4	no	—
437	C₄×D₄	—	2	8	no	—
438	C₄×D₄	—	2	8	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	C₂³×C₃₁	1	8	yes	—
442	C₄×D₄	C₂³×C₃₁	1	8	yes	—
443	C₄×D₄	C₂³×C₃₁	1	4	yes	complemented
444	C₄×D₄	C₂³×C₃₁	1	4	yes	complemented
445	#117	—	2	2	no	—
446	#117	—	2	8	no	—
447	#117	C₂³×C₃₁	1	4	yes	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	2	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	2	no	—
458	C₂×C₂²⋊C₄	—	2	2	no	—
459	C₂×C₂²⋊C₄	—	2	8	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₄²	—	2	1	no	—
463	C₂×C₄²	—	2	1	no	—
464	C₂×C₄²	—	2	1	no	—
465	C₂×C₄²	—	2	8	no	—
466	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
467	C₂×C₄²	D₄×C₃₁	1	4	yes	—
468	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
472	#107	C₂³×C₃₁	1	8	yes	complemented
473	#106	C₂³×C₃₁	1	8	yes	complemented
474	#103	C₂³×C₃₁	1	8	yes	complemented
475	#102	C₂³×C₃₁	1	8	yes	—
476	#102	C₂³×C₃₁	1	8	yes	—
477	#102	C₂³×C₃₁	1	8	yes	complemented
478	#97	C₂³×C₃₁	1	8	yes	complemented
479	C₄×C₈	C₂³×C₃₁	1	8	yes	complemented
480	C₃₁	C₂×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, direct product factor, Sylow
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×C₃₁	1	1	yes	characteristic
488	#41	—	2	16	no	—
489	#41	—	2	8	no	—
490	#41	C₂²×C₄×C₃₁	1	16	yes	complemented
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	complemented
494	C₂×Q₈	C₂⁴×C₃₁	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×C₃₁	1	8	yes	—
506	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	complemented
507	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	complemented
508	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
509	C₂×D₄	C₂⁴×C₃₁	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	4	no	—
524	C₂²×C₄	—	4	8	no	—
525	C₂²×C₄	—	4	32	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	—	4	4	no	—
528	C₂²×C₄	—	4	8	no	—
529	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
530	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
533	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
534	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
535	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
537	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
538	C₂²×C₄	#41×C₃₁	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
540	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
541	SD₁₆	C₂²×C₄×C₃₁	1	32	yes	complemented
542	D₈	C₂²×C₄×C₃₁	1	32	yes	complemented
543	M₁₆	—	2	8	no	—
544	M₁₆	C₂²×C₄×C₃₁	1	16	yes	complemented
545	C₂×C₈	—	2	4	no	—
546	C₂×C₈	C₂²×C₄×C₃₁	1	8	yes	complemented
547	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
548	C₂×C₈	C₂⁴×C₃₁	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×C₃₁	1	2	yes	—
556	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
557	C₄⋊C₄	C₂⁴×C₃₁	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×C₃₁	1	4	yes	—
567	C₄²	C₂×D₄×C₃₁	1	4	yes	—
568	C₄²	C₂×D₄×C₃₁	1	2	yes	—
569	C₄²	C₂×D₄×C₃₁	1	2	yes	—
570	C₄²	C₂⁴×C₃₁	1	2	yes	—
571	C₄²	C₂⁴×C₃₁	1	2	yes	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	8	no	—
576	C₂³	—	2	16	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	4	no	—
579	C₂³	—	4	8	no	—
580	C₂³	—	4	32	no	—
581	C₂³	—	4	8	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×C₃₁	1	4	yes	—
587	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
588	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
589	Q₈	—	2	4	no	—
590	Q₈	—	2	2	no	—
591	Q₈	C₂³×C₄×C₃₁	1	4	yes	complemented
592	D₄	—	2	16	no	—
593	D₄	—	2	8	no	—
594	D₄	—	2	16	no	—
595	D₄	—	2	4	no	—
596	D₄	—	2	4	no	—
597	D₄	—	2	2	no	—
598	D₄	C₂³×C₄×C₃₁	1	8	yes	—
599	D₄	C₂³×C₄×C₃₁	1	4	yes	complemented
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	16	no	—
606	C₂×C₄	—	2	8	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×C₃₁	1	4	yes	—
620	C₂×C₄	C₄×D₄×C₃₁	1	8	yes	—
621	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	4	yes	direct product factor
622	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
623	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
624	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
625	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
628	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
630	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
631	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
632	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
633	C₈	—	2	4	no	—
634	C₈	C₂³×C₄×C₃₁	1	8	yes	complemented
635	C₂²	—	2	8	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	4	32	no	—
641	C₂²	—	4	16	no	—
642	C₂²	—	4	8	no	—
643	C₂²	—	4	4	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	4	no	—
647	C₂²	C₂×C₄×D₄×C₃₁	1	4	yes	—
648	C₂²	C₂×C₄×D₄×C₃₁	1	2	yes	—
649	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
650	C₂²	C₃₁×#575	1	2	yes	—
651	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
652	C₄	—	2	4	no	—
653	C₄	—	2	2	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	4	4	no	—
657	C₄	—	4	2	no	—
658	C₄	—	4	2	no	—
659	C₄	C₂×C₄×D₄×C₃₁	1	4	yes	—
660	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
661	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	direct product factor
662	C₄	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
663	C₄	C₂²×#41×C₃₁	1	1	yes	characteristic
664	C₂	—	2	4	no	—
665	C₂	—	4	8	no	—
666	C₂	—	4	4	no	—
667	C₂	C₄×C₃₁×AGL(1,ℤ/8)	1	4	yes	direct product factor
668	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
669	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
670	C₂	C₂×C₃₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂²×D₄
prime radical	C₂²×C₃₁×AGL(1,ℤ/8)	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₂²×C₄×D₄×C₃₁	C₂	semidirect
4. C₄×C₃₁×AGL(1,ℤ/8)	C₂	direct (N × H)
5. C₂×C₃₁×#442	C₂	semidirect
6. C₂×C₃₁×#440	C₂	semidirect
7. C₂×C₄×SD₁₆×C₃₁	C₂	semidirect
8. C₂×C₄×D₈×C₃₁	C₂	semidirect
9. C₂×C₃₁×#428	C₂	semidirect
10. C₂×C₃₁×#417	C₂	semidirect
11. C₂×C₃₁×#418	C₂	semidirect
12. C₂×C₄×M₁₆×C₃₁	C₂	semidirect
16. C₂×C₃₁×AGL(1,ℤ/8)	C₄	direct (N × H)
23. C₄×#41×C₃₁	C₂²	semidirect
24. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
25. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
33. C₂×C₄×D₄×C₃₁	C₂²	semidirect
34. C₂×C₄×D₄×C₃₁	C₂²	semidirect
35. C₂×C₄×D₄×C₃₁	C₂²	semidirect
42. C₃₁×#442	C₂²	semidirect
43. C₃₁×#440	C₂²	semidirect
44. C₄×SD₁₆×C₃₁	C₂²	semidirect
45. C₄×D₈×C₃₁	C₂²	semidirect
46. C₃₁×#428	C₂²	semidirect
47. C₂×C₃₁×#107	C₂²	semidirect
48. C₂×C₃₁×#106	C₂²	semidirect
49. C₃₁×#418	C₂²	semidirect
50. C₃₁×#417	C₂²	semidirect
51. C₂×C₃₁×#103	C₂²	semidirect
54. C₂×C₃₁×#102	C₂²	semidirect
55. C₄×M₁₆×C₃₁	C₂²	semidirect
56. C₂×C₃₁×#97	C₂²	semidirect
57. C₂×C₄×C₈×C₃₁	C₂²	semidirect
61. C₂×#41×C₃₁	C₂×C₄	semidirect
68. C₂²×D₄×C₃₁	C₂×C₄	semidirect
83. C₃₁×AGL(1,ℤ/8)	C₂×C₄	direct (N × H)
84. C₂×SD₁₆×C₃₁	C₂×C₄	semidirect
86. C₂×D₈×C₃₁	C₂×C₄	semidirect
89. C₂×M₁₆×C₃₁	C₂×C₄	semidirect
96. C₄×Q₈×C₃₁	C₂³	semidirect
97. C₄×Q₈×C₃₁	C₂³	semidirect
108. C₄×D₄×C₃₁	C₂³	semidirect
109. C₄×D₄×C₃₁	C₂³	semidirect
137. C₃₁×#107	C₂³	semidirect
138. C₃₁×#106	C₂³	semidirect
139. C₃₁×#103	C₂³	semidirect
142. C₃₁×#102	C₂³	semidirect
143. C₃₁×#97	C₂³	semidirect
144. C₄×C₈×C₃₁	C₂³	semidirect
154. #41×C₃₁	C₂²×C₄	semidirect
157. C₂×Q₈×C₃₁	C₂²×C₄	semidirect
170. C₂×D₄×C₃₁	C₂²×C₄	semidirect
171. C₂×D₄×C₃₁	C₂²×C₄	semidirect
205. SD₁₆×C₃₁	C₂²×C₄	semidirect
206. D₈×C₃₁	C₂²×C₄	semidirect
208. M₁₆×C₃₁	C₂²×C₄	semidirect
210. C₂×C₈×C₃₁	C₂²×C₄	semidirect
236. C₂×C₄×AGL(1,ℤ/8)	C₃₁	direct (N × H)
256. Q₈×C₃₁	C₂³×C₄	semidirect
264. D₄×C₃₁	C₂³×C₄	semidirect
286. C₂×C₄×C₃₁	AGL(1,ℤ/8)	direct (N × H)
299. C₈×C₃₁	C₂³×C₄	semidirect
301. C₂×C₄×#41	C₂×C₃₁	semidirect
302. C₂²×C₄×D₄	C₂×C₃₁	semidirect
303. C₄×AGL(1,ℤ/8)	C₂×C₃₁	direct (N × H)
304. C₂×#442	C₂×C₃₁	semidirect
305. C₂×#440	C₂×C₃₁	semidirect
306. C₂×C₄×SD₁₆	C₂×C₃₁	semidirect
307. C₂×C₄×D₈	C₂×C₃₁	semidirect
308. C₂×#428	C₂×C₃₁	semidirect
309. C₂×#417	C₂×C₃₁	semidirect
310. C₂×#418	C₂×C₃₁	semidirect
311. C₂×C₄×M₁₆	C₂×C₃₁	semidirect
338. C₄×C₃₁	C₂×AGL(1,ℤ/8)	direct (N × H)
344. C₂×AGL(1,ℤ/8)	C₄×C₃₁	direct (N × H)
351. C₄×#41	C₂²×C₃₁	semidirect
352. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
353. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
361. C₂×C₄×D₄	C₂²×C₃₁	semidirect
362. C₂×C₄×D₄	C₂²×C₃₁	semidirect
363. C₂×C₄×D₄	C₂²×C₃₁	semidirect
370. #442	C₂²×C₃₁	semidirect
371. #440	C₂²×C₃₁	semidirect
372. C₄×SD₁₆	C₂²×C₃₁	semidirect
373. C₄×D₈	C₂²×C₃₁	semidirect
374. #428	C₂²×C₃₁	semidirect
375. C₂×#107	C₂²×C₃₁	semidirect
376. C₂×#106	C₂²×C₃₁	semidirect
377. #418	C₂²×C₃₁	semidirect
378. #417	C₂²×C₃₁	semidirect
379. C₂×#103	C₂²×C₃₁	semidirect
382. C₂×#102	C₂²×C₃₁	semidirect
383. C₄×M₁₆	C₂²×C₃₁	semidirect
384. C₂×#97	C₂²×C₃₁	semidirect
385. C₂×C₄×C₈	C₂²×C₃₁	semidirect
389. C₂×C₃₁	C₄×AGL(1,ℤ/8)	direct (N × H)
396. C₂×#41	C₂×C₄×C₃₁	semidirect
403. C₂²×D₄	C₂×C₄×C₃₁	semidirect
418. AGL(1,ℤ/8)	C₂×C₄×C₃₁	direct (N × H)
419. C₂×SD₁₆	C₂×C₄×C₃₁	semidirect
421. C₂×D₈	C₂×C₄×C₃₁	semidirect
424. C₂×M₁₆	C₂×C₄×C₃₁	semidirect
431. C₄×Q₈	C₂³×C₃₁	semidirect
432. C₄×Q₈	C₂³×C₃₁	semidirect
443. C₄×D₄	C₂³×C₃₁	semidirect
444. C₄×D₄	C₂³×C₃₁	semidirect
472. #107	C₂³×C₃₁	semidirect
473. #106	C₂³×C₃₁	semidirect
474. #103	C₂³×C₃₁	semidirect
477. #102	C₂³×C₃₁	semidirect
478. #97	C₂³×C₃₁	semidirect
479. C₄×C₈	C₂³×C₃₁	semidirect
480. C₃₁	C₂×C₄×AGL(1,ℤ/8)	direct (N × H)
490. #41	C₂²×C₄×C₃₁	semidirect
493. C₂×Q₈	C₂²×C₄×C₃₁	semidirect
506. C₂×D₄	C₂²×C₄×C₃₁	semidirect
507. C₂×D₄	C₂²×C₄×C₃₁	semidirect
541. SD₁₆	C₂²×C₄×C₃₁	semidirect
542. D₈	C₂²×C₄×C₃₁	semidirect
544. M₁₆	C₂²×C₄×C₃₁	semidirect
546. C₂×C₈	C₂²×C₄×C₃₁	semidirect
591. Q₈	C₂³×C₄×C₃₁	semidirect
599. D₄	C₂³×C₄×C₃₁	semidirect
621. C₂×C₄	C₃₁×AGL(1,ℤ/8)	direct (N × H)
634. C₈	C₂³×C₄×C₃₁	semidirect
661. C₄	C₂×C₃₁×AGL(1,ℤ/8)	direct (N × H)
667. C₂	C₄×C₃₁×AGL(1,ℤ/8)	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×C₃₁×AGL(1,ℤ/8)	2
C₂×C₄×#41×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₄×C₃₁×AGL(1,ℤ/8)	2
C₂×C₃₁×#442	2
C₂×C₃₁×#440	2
C₂×C₄×SD₁₆×C₃₁	2
C₂×C₄×D₈×C₃₁	2
C₂×C₃₁×#428	2
C₂×C₃₁×#417	2
C₂×C₃₁×#418	2
C₂×C₄×M₁₆×C₃₁	2
C₂×C₄×AGL(1,ℤ/8)	31

Subgroups — C2×C4×C31×AGL(1,ℤ/8) #21516915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃₁×AGL(1,ℤ/8) #21516915