Subgroups — C₂²×C₃₁×#472 #21517223

Order 7936.

2886 conjugacy classes of subgroups.

The subgroup lattice has 360 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	2	yes	maximal, complemented
2	C₂³×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#472	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₃₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃₁×#100	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
9	C₂×C₃₁×AGL(1,ℤ/8)	—	2	12	no	—
10	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
11	C₂²×SD₁₆×C₃₁	—	2	2	no	—
12	C₂²×D₈×C₃₁	—	2	2	no	—
13	C₂²×D₈×C₃₁	—	2	1	no	—
14	C₂²×D₈×C₃₁	—	2	1	no	—
15	C₂²×D₈×C₃₁	—	2	6	no	—
16	C₂²×D₈×C₃₁	C₂²	1	12	yes	complemented
17	C₂×C₃₁×#131	—	2	6	no	—
18	C₂×C₃₁×#131	C₂²	1	12	yes	complemented
19	C₂²×M₁₆×C₃₁	—	2	1	no	—
20	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
22	C₂³×C₈×C₃₁	—	2	1	no	—
23	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
24	C₃₁×#472	C₂²	1	64	yes	direct product factor
25	C₂×C₃₁×#108	C₂²	1	12	yes	complemented
26	C₂×C₃₁×#100	C₂²	1	24	yes	complemented
27	C₂⁵×C₃₁	—	2	2	no	—
28	C₂×#41×C₃₁	—	2	3	no	—
29	C₂×#41×C₃₁	—	2	3	no	—
30	C₂×#41×C₃₁	D₄	1	6	yes	—
31	C₂×#41×C₃₁	C₂³	1	6	yes	—
32	C₂²×Q₈×C₃₁	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₃₁	—	2	1	no	—
34	C₂²×D₄×C₃₁	—	2	6	no	—
35	C₂²×D₄×C₃₁	—	2	2	no	—
36	C₂²×D₄×C₃₁	—	2	2	no	—
37	C₂²×D₄×C₃₁	—	2	6	no	—
38	C₂²×D₄×C₃₁	—	2	6	no	—
39	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
40	C₂²×D₄×C₃₁	C₂³	1	12	yes	—
41	C₂³×C₄×C₃₁	—	2	1	no	—
42	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
43	C₃₁×AGL(1,ℤ/8)	—	2	48	no	—
44	C₃₁×AGL(1,ℤ/8)	C₂³	1	32	yes	complemented
45	C₂×SD₁₆×C₃₁	—	2	24	no	—
46	C₂×D₈×C₃₁	—	2	24	no	—
47	C₂×D₈×C₃₁	—	2	12	no	—
48	C₂×D₈×C₃₁	—	2	12	no	—
49	C₂×D₈×C₃₁	—	2	24	no	—
50	C₂×D₈×C₃₁	C₂³	1	16	yes	complemented
51	C₃₁×#131	—	2	24	no	—
52	C₃₁×#131	C₂³	1	16	yes	complemented
53	C₂×M₁₆×C₃₁	—	2	3	no	—
54	C₂×M₁₆×C₃₁	—	2	6	no	—
55	C₂×M₁₆×C₃₁	—	2	12	no	—
56	C₂×M₁₆×C₃₁	C₂³	1	6	yes	—
57	C₂×M₁₆×C₃₁	C₂³	1	12	yes	—
58	C₂²×C₈×C₃₁	—	2	1	no	—
59	C₂²×C₈×C₃₁	—	2	2	no	—
60	C₂²×C₈×C₃₁	—	2	12	no	—
61	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₃₁	D₄	1	6	yes	—
64	C₂²×C₈×C₃₁	C₂³	1	6	yes	—
65	C₃₁×#108	C₂³	1	16	yes	complemented
66	C₃₁×#100	C₂³	1	32	yes	complemented
67	C₂⁴×C₃₁	—	2	1	no	—
68	C₂⁴×C₃₁	—	2	12	no	—
69	C₂⁴×C₃₁	—	4	6	no	—
70	C₂⁴×C₃₁	—	4	2	no	—
71	C₂⁴×C₃₁	—	8	8	no	—
72	C₂⁴×C₃₁	#41	1	1	yes	characteristic
73	#41×C₃₁	—	2	12	no	—
74	#41×C₃₁	—	2	6	no	—
75	#41×C₃₁	—	2	6	no	—
76	#41×C₃₁	C₂×D₄	1	12	yes	—
77	#41×C₃₁	C₂⁴	1	4	yes	—
78	C₂×Q₈×C₃₁	—	2	3	no	—
79	C₂×Q₈×C₃₁	C₂×D₄	1	6	yes	—
80	C₂×D₄×C₃₁	—	2	6	no	—
81	C₂×D₄×C₃₁	—	2	6	no	—
82	C₂×D₄×C₃₁	—	2	3	no	—
83	C₂×D₄×C₃₁	—	2	12	no	—
84	C₂×D₄×C₃₁	—	2	12	no	—
85	C₂×D₄×C₃₁	—	2	12	no	—
86	C₂×D₄×C₃₁	—	2	12	no	—
87	C₂×D₄×C₃₁	—	2	12	no	—
88	C₂×D₄×C₃₁	—	4	6	no	—
89	C₂×D₄×C₃₁	—	4	6	no	—
90	C₂×D₄×C₃₁	—	4	12	no	—
91	C₂×D₄×C₃₁	C₂×D₄	1	6	yes	—
92	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
93	C₂²×C₄×C₃₁	—	2	1	no	—
94	C₂²×C₄×C₃₁	—	2	6	no	—
95	C₂²×C₄×C₃₁	—	2	6	no	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	#41	1	3	yes	—
101	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
102	SD₁₆×C₃₁	—	2	32	no	—
103	D₈×C₃₁	—	2	32	no	—
104	D₈×C₃₁	—	2	16	no	—
105	D₈×C₃₁	—	2	16	no	—
106	M₁₆×C₃₁	—	2	6	no	—
107	M₁₆×C₃₁	—	2	12	no	—
108	M₁₆×C₃₁	—	2	16	no	—
109	M₁₆×C₃₁	C₂⁴	1	4	yes	—
110	M₁₆×C₃₁	C₂⁴	1	8	yes	—
111	C₂×C₈×C₃₁	—	2	6	no	—
112	C₂×C₈×C₃₁	—	2	12	no	—
113	C₂×C₈×C₃₁	—	2	16	no	—
114	C₂×C₈×C₃₁	C₂×D₄	1	6	yes	—
115	C₂×C₈×C₃₁	C₂×D₄	1	6	yes	—
116	C₂×C₈×C₃₁	C₂×D₄	1	12	yes	—
117	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
118	C₂²×#472	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂³×C₃₁	—	2	4	no	—
120	C₂³×C₃₁	—	2	6	no	—
121	C₂³×C₃₁	—	2	8	no	—
122	C₂³×C₃₁	—	4	4	no	—
123	C₂³×C₃₁	—	4	12	no	—
124	C₂³×C₃₁	—	4	12	no	—
125	C₂³×C₃₁	—	8	24	no	—
126	C₂³×C₃₁	—	8	24	no	—
127	C₂³×C₃₁	—	8	8	no	—
128	C₂³×C₃₁	#121	1	3	yes	—
129	C₂³×C₃₁	#121	1	1	yes	characteristic
130	C₂³×C₃₁	C₂×#41	1	3	yes	—
131	Q₈×C₃₁	—	2	6	no	—
132	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
133	D₄×C₃₁	—	2	12	no	—
134	D₄×C₃₁	—	2	4	no	—
135	D₄×C₃₁	—	2	6	no	—
136	D₄×C₃₁	—	2	8	no	—
137	D₄×C₃₁	—	2	8	no	—
138	D₄×C₃₁	—	4	12	no	—
139	D₄×C₃₁	—	4	12	no	—
140	D₄×C₃₁	C₂²×D₄	1	4	yes	—
141	C₂×C₄×C₃₁	—	2	6	no	—
142	C₂×C₄×C₃₁	—	2	12	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	#121	1	3	yes	—
145	C₂×C₄×C₃₁	#121	1	3	yes	—
146	C₂×C₄×C₃₁	#121	1	6	yes	—
147	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
148	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
149	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
150	C₂×C₄×C₃₁	C₂²×D₄	1	3	yes	—
151	C₂×C₄×C₃₁	C₂×#41	1	3	yes	—
152	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
153	C₈×C₃₁	—	2	4	no	—
154	C₈×C₃₁	—	2	8	no	—
155	C₈×C₃₁	C₂²×D₄	1	4	yes	—
156	C₈×C₃₁	C₂²×D₄	1	4	yes	—
157	C₂²×AGL(1,ℤ/8)	C₂×C₃₁	1	2	yes	complemented
158	C₂³×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
159	C₂²×#131	C₂×C₃₁	1	1	yes	characteristic, complemented
160	C₂×#472	C₂×C₃₁	1	24	yes	direct product factor
161	C₂²×#108	C₂×C₃₁	1	1	yes	characteristic, complemented
162	C₂²×#100	C₂×C₃₁	1	2	yes	complemented
163	C₂²×C₃₁	—	2	6	no	—
164	C₂²×C₃₁	—	2	6	no	—
165	C₂²×C₃₁	—	2	4	no	—
166	C₂²×C₃₁	—	4	12	no	—
167	C₂²×C₃₁	—	4	8	no	—
168	C₂²×C₃₁	—	8	8	no	—
169	C₂²×C₃₁	—	8	24	no	—
170	C₂²×C₃₁	—	8	24	no	—
171	C₂²×C₃₁	#472	1	4	yes	direct product factor
172	C₂²×C₃₁	C₂×#121	1	3	yes	—
173	C₂²×C₃₁	C₂×#121	1	3	yes	—
174	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
175	C₄×C₃₁	—	2	4	no	—
176	C₄×C₃₁	C₂×#121	1	3	yes	—
177	C₄×C₃₁	C₂×#121	1	3	yes	—
178	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
179	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
180	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
181	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
182	C₂×AGL(1,ℤ/8)	—	2	12	no	—
183	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	24	yes	complemented
184	C₂²×SD₁₆	—	2	2	no	—
185	C₂²×D₈	—	2	2	no	—
186	C₂²×D₈	—	2	1	no	—
187	C₂²×D₈	—	2	1	no	—
188	C₂²×D₈	—	2	6	no	—
189	C₂²×D₈	C₂²×C₃₁	1	12	yes	complemented
190	C₂×#131	—	2	6	no	—
191	C₂×#131	C₂²×C₃₁	1	12	yes	complemented
192	C₂²×M₁₆	—	2	1	no	—
193	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
194	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
195	C₂³×C₈	—	2	1	no	—
196	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
197	#472	C₂²×C₃₁	1	64	yes	direct product factor
198	C₂×#108	C₂²×C₃₁	1	12	yes	complemented
199	C₂×#100	C₂²×C₃₁	1	24	yes	complemented
200	C₂×C₃₁	—	2	3	no	—
201	C₂×C₃₁	—	2	1	no	—
202	C₂×C₃₁	—	4	4	no	—
203	C₂×C₃₁	—	8	8	no	—
204	C₂×C₃₁	C₂×#472	1	6	yes	direct product factor
205	C₂×C₃₁	C₂²×#121	1	1	yes	characteristic
206	C₂⁵	—	2	2	no	—
207	C₂×#41	—	2	3	no	—
208	C₂×#41	—	2	3	no	—
209	C₂×#41	D₄×C₃₁	1	6	yes	—
210	C₂×#41	C₂³×C₃₁	1	6	yes	—
211	C₂²×Q₈	D₄×C₃₁	1	1	yes	characteristic
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	—	2	2	no	—
214	C₂²×D₄	—	2	6	no	—
215	C₂²×D₄	—	2	2	no	—
216	C₂²×D₄	—	2	6	no	—
217	C₂²×D₄	—	2	6	no	—
218	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
219	C₂²×D₄	C₂³×C₃₁	1	12	yes	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
222	AGL(1,ℤ/8)	—	2	48	no	—
223	AGL(1,ℤ/8)	C₂³×C₃₁	1	32	yes	complemented
224	C₂×SD₁₆	—	2	24	no	—
225	C₂×D₈	—	2	24	no	—
226	C₂×D₈	—	2	12	no	—
227	C₂×D₈	—	2	12	no	—
228	C₂×D₈	—	2	24	no	—
229	C₂×D₈	C₂³×C₃₁	1	16	yes	complemented
230	#131	—	2	24	no	—
231	#131	C₂³×C₃₁	1	16	yes	complemented
232	C₂×M₁₆	—	2	3	no	—
233	C₂×M₁₆	—	2	6	no	—
234	C₂×M₁₆	—	2	12	no	—
235	C₂×M₁₆	C₂³×C₃₁	1	6	yes	—
236	C₂×M₁₆	C₂³×C₃₁	1	12	yes	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	—	2	12	no	—
240	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
242	C₂²×C₈	D₄×C₃₁	1	6	yes	—
243	C₂²×C₈	C₂³×C₃₁	1	6	yes	—
244	#108	C₂³×C₃₁	1	16	yes	complemented
245	#100	C₂³×C₃₁	1	32	yes	complemented
246	C₃₁	C₂²×#472	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁴	—	2	1	no	—
248	C₂⁴	—	2	12	no	—
249	C₂⁴	—	4	6	no	—
250	C₂⁴	—	4	2	no	—
251	C₂⁴	—	8	8	no	—
252	C₂⁴	#41×C₃₁	1	1	yes	characteristic
253	#41	—	2	12	no	—
254	#41	—	2	6	no	—
255	#41	—	2	6	no	—
256	#41	C₂×D₄×C₃₁	1	12	yes	—
257	#41	C₂⁴×C₃₁	1	4	yes	—
258	C₂×Q₈	—	2	3	no	—
259	C₂×Q₈	C₂×D₄×C₃₁	1	6	yes	—
260	C₂×D₄	—	2	6	no	—
261	C₂×D₄	—	2	6	no	—
262	C₂×D₄	—	2	3	no	—
263	C₂×D₄	—	2	12	no	—
264	C₂×D₄	—	2	12	no	—
265	C₂×D₄	—	2	12	no	—
266	C₂×D₄	—	2	12	no	—
267	C₂×D₄	—	2	12	no	—
268	C₂×D₄	—	4	6	no	—
269	C₂×D₄	—	4	6	no	—
270	C₂×D₄	—	4	12	no	—
271	C₂×D₄	C₂×D₄×C₃₁	1	6	yes	—
272	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
273	C₂²×C₄	—	2	1	no	—
274	C₂²×C₄	—	2	6	no	—
275	C₂²×C₄	—	2	6	no	—
276	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
279	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
280	C₂²×C₄	#41×C₃₁	1	3	yes	—
281	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
282	SD₁₆	—	2	32	no	—
283	D₈	—	2	32	no	—
284	D₈	—	2	16	no	—
285	D₈	—	2	16	no	—
286	M₁₆	—	2	6	no	—
287	M₁₆	—	2	12	no	—
288	M₁₆	—	2	16	no	—
289	M₁₆	C₂⁴×C₃₁	1	4	yes	—
290	M₁₆	C₂⁴×C₃₁	1	8	yes	—
291	C₂×C₈	—	2	6	no	—
292	C₂×C₈	—	2	12	no	—
293	C₂×C₈	—	2	16	no	—
294	C₂×C₈	C₂×D₄×C₃₁	1	6	yes	—
295	C₂×C₈	C₂×D₄×C₃₁	1	6	yes	—
296	C₂×C₈	C₂×D₄×C₃₁	1	12	yes	—
297	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
298	C₂³	—	2	4	no	—
299	C₂³	—	2	6	no	—
300	C₂³	—	2	8	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	12	no	—
303	C₂³	—	4	12	no	—
304	C₂³	—	8	24	no	—
305	C₂³	—	8	24	no	—
306	C₂³	—	8	8	no	—
307	C₂³	C₃₁×#121	1	3	yes	—
308	C₂³	C₃₁×#121	1	1	yes	characteristic
309	C₂³	C₂×#41×C₃₁	1	3	yes	—
310	Q₈	—	2	6	no	—
311	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
312	D₄	—	2	12	no	—
313	D₄	—	2	4	no	—
314	D₄	—	2	6	no	—
315	D₄	—	2	8	no	—
316	D₄	—	2	8	no	—
317	D₄	—	4	12	no	—
318	D₄	—	4	12	no	—
319	D₄	C₂²×D₄×C₃₁	1	4	yes	—
320	C₂×C₄	—	2	6	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	C₃₁×#121	1	3	yes	—
324	C₂×C₄	C₃₁×#121	1	3	yes	—
325	C₂×C₄	C₃₁×#121	1	6	yes	—
326	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
327	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
328	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
329	C₂×C₄	C₂²×D₄×C₃₁	1	3	yes	—
330	C₂×C₄	C₂×#41×C₃₁	1	3	yes	—
331	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
332	C₈	—	2	4	no	—
333	C₈	—	2	8	no	—
334	C₈	C₂²×D₄×C₃₁	1	4	yes	—
335	C₈	C₂²×D₄×C₃₁	1	4	yes	—
336	C₂²	—	2	6	no	—
337	C₂²	—	2	6	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	4	12	no	—
340	C₂²	—	4	8	no	—
341	C₂²	—	8	8	no	—
342	C₂²	—	8	24	no	—
343	C₂²	—	8	24	no	—
344	C₂²	C₃₁×#472	1	4	yes	direct product factor
345	C₂²	C₂×C₃₁×#121	1	3	yes	—
346	C₂²	C₂×C₃₁×#121	1	3	yes	—
347	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
348	C₄	—	2	4	no	—
349	C₄	C₂×C₃₁×#121	1	3	yes	—
350	C₄	C₂×C₃₁×#121	1	3	yes	—
351	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
352	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
353	C₂	—	2	3	no	—
354	C₂	—	2	1	no	—
355	C₂	—	4	4	no	—
356	C₂	—	8	8	no	—
357	C₂	C₂×C₃₁×#472	1	6	yes	direct product factor
358	C₂	C₂²×C₃₁×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
2. C₂³×D₈×C₃₁	C₂	semidirect
3. C₂²×C₃₁×#131	C₂	semidirect
4. C₂×C₃₁×#472	C₂	direct (N × H)
5. C₂²×C₃₁×#108	C₂	semidirect
6. C₂²×C₃₁×#100	C₂	semidirect
10. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
16. C₂²×D₈×C₃₁	C₂²	semidirect
18. C₂×C₃₁×#131	C₂²	semidirect
24. C₃₁×#472	C₂²	direct (N × H)
25. C₂×C₃₁×#108	C₂²	semidirect
26. C₂×C₃₁×#100	C₂²	semidirect
44. C₃₁×AGL(1,ℤ/8)	C₂³	semidirect
50. C₂×D₈×C₃₁	C₂³	semidirect
52. C₃₁×#131	C₂³	semidirect
65. C₃₁×#108	C₂³	semidirect
66. C₃₁×#100	C₂³	semidirect
118. C₂²×#472	C₃₁	direct (N × H)
157. C₂²×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
158. C₂³×D₈	C₂×C₃₁	semidirect
159. C₂²×#131	C₂×C₃₁	semidirect
160. C₂×#472	C₂×C₃₁	direct (N × H)
161. C₂²×#108	C₂×C₃₁	semidirect
162. C₂²×#100	C₂×C₃₁	semidirect
171. C₂²×C₃₁	#472	direct (N × H)
183. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
189. C₂²×D₈	C₂²×C₃₁	semidirect
191. C₂×#131	C₂²×C₃₁	semidirect
197. #472	C₂²×C₃₁	direct (N × H)
198. C₂×#108	C₂²×C₃₁	semidirect
199. C₂×#100	C₂²×C₃₁	semidirect
204. C₂×C₃₁	C₂×#472	direct (N × H)
223. AGL(1,ℤ/8)	C₂³×C₃₁	semidirect
229. C₂×D₈	C₂³×C₃₁	semidirect
231. #131	C₂³×C₃₁	semidirect
244. #108	C₂³×C₃₁	semidirect
245. #100	C₂³×C₃₁	semidirect
246. C₃₁	C₂²×#472	direct (N × H)
344. C₂²	C₃₁×#472	direct (N × H)
357. C₂	C₂×C₃₁×#472	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
C₂³×D₈×C₃₁	2
C₂²×C₃₁×#131	2
C₂×C₃₁×#472	2
C₂²×C₃₁×#108	2
C₂²×C₃₁×#100	2
C₂²×#472	31

Subgroups — C22×C31×#472 #21517223

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#472 #21517223