Subgroups — C₂×C₃₁×#3416 #21519392

Order 7936.

2074 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#578	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#576	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3416	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#510	C₂	1	3	yes	maximal, complemented
5	C₂×C₃₁×#509	C₂	1	3	yes	maximal, complemented
6	C₂×C₃₁×#508	C₂	1	3	yes	maximal, complemented
7	C₂²×C₃₁×SD₃₂	C₂	1	3	yes	maximal, complemented
8	C₂×C₃₁×#504	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×2₋¹⁺⁴	—	2	1	no	—
10	C₂×C₃₁×H(5,𝔽₂)	—	2	1	no	—
11	C₃₁×#578	—	2	4	no	—
12	C₃₁×#578	C₂²	1	8	yes	complemented
13	C₃₁×#576	—	2	4	no	—
14	C₃₁×#576	C₂²	1	8	yes	complemented
15	C₂×C₃₁×#137	—	2	3	no	—
16	C₂×C₃₁×AGL(1,ℤ/8)	—	2	3	no	—
17	C₂×C₃₁×#135	C₂²	1	3	yes	—
18	C₂×C₃₁×#135	C₂²	1	3	yes	complemented
19	C₂²×Q₁₆×C₃₁	C₂²	1	3	yes	complemented
20	C₂²×D₈×C₃₁	C₂²	1	3	yes	—
21	C₂×C₃₁×#131	C₂²	1	1	yes	characteristic
22	C₃₁×#510	C₂²	1	24	yes	complemented
23	C₃₁×#509	C₂²	1	24	yes	complemented
24	C₃₁×#508	C₂²	1	24	yes	complemented
25	C₂×C₃₁×Q₃₂	C₂²	1	3	yes	complemented
26	C₂×C₃₁×SD₃₂	C₂²	1	3	yes	complemented
27	C₂×C₃₁×SD₃₂	C₂²	1	6	yes	complemented
28	C₂×C₃₁×SD₃₂	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃₁×SD₃₂	C₂²	1	24	yes	complemented
30	C₂×C₃₁×D₁₆	C₂²	1	3	yes	complemented
31	C₃₁×#504	C₂²	1	8	yes	complemented
32	C₂×C₃₁×M₃₂	C₂²	1	3	yes	complemented
33	C₂²×C₁₆×C₃₁	C₂²	1	3	yes	complemented
34	C₃₁×2₋¹⁺⁴	—	2	8	no	—
35	C₃₁×2₋¹⁺⁴	—	4	4	no	—
36	C₃₁×H(5,𝔽₂)	—	2	8	no	—
37	C₃₁×H(5,𝔽₂)	—	4	4	no	—
38	C₂×#41×C₃₁	—	2	3	no	—
39	C₂×#41×C₃₁	—	2	3	no	—
40	C₂×#41×C₃₁	—	4	1	no	—
41	C₂×#41×C₃₁	—	4	3	no	—
42	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
43	C₂²×Q₈×C₃₁	—	2	3	no	—
44	C₂²×Q₈×C₃₁	—	4	1	no	—
45	C₂²×D₄×C₃₁	—	2	3	no	—
46	C₂²×D₄×C₃₁	—	4	3	no	—
47	C₃₁×#137	—	2	24	no	—
48	C₃₁×AGL(1,ℤ/8)	—	2	24	no	—
49	C₃₁×#135	—	2	6	no	—
50	C₃₁×#135	—	2	6	no	—
51	C₃₁×#135	C₂³	1	12	yes	—
52	C₃₁×#135	C₂³	1	12	yes	complemented
53	C₂×Q₁₆×C₃₁	—	2	3	no	—
54	C₂×Q₁₆×C₃₁	—	2	6	no	—
55	C₂×Q₁₆×C₃₁	C₂³	1	3	yes	—
56	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
57	C₂×Q₁₆×C₃₁	C₂³	1	12	yes	complemented
58	C₂×SD₁₆×C₃₁	—	2	3	no	—
59	C₂×SD₁₆×C₃₁	—	2	3	no	—
60	C₂×D₈×C₃₁	—	2	3	no	—
61	C₂×D₈×C₃₁	—	2	6	no	—
62	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic
63	C₂×D₈×C₃₁	C₂³	1	3	yes	—
64	C₂×D₈×C₃₁	C₂³	1	12	yes	—
65	C₃₁×#131	D₄	1	4	yes	—
66	C₃₁×#131	C₂³	1	4	yes	—
67	C₂×M₁₆×C₃₁	D₄	1	3	yes	—
68	C₂²×C₈×C₃₁	C₂³	1	3	yes	—
69	C₃₁×Q₃₂	C₂³	1	12	yes	complemented
70	C₃₁×SD₃₂	C₂³	1	12	yes	complemented
71	C₃₁×SD₃₂	C₂³	1	24	yes	complemented
72	C₃₁×SD₃₂	C₂³	1	4	yes	complemented
73	C₃₁×D₁₆	C₂³	1	12	yes	complemented
74	C₃₁×M₃₂	C₂³	1	12	yes	complemented
75	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₁₆×C₃₁	C₂³	1	3	yes	—
77	C₂×C₁₆×C₃₁	C₂³	1	12	yes	complemented
78	C₂⁴×C₃₁	—	4	3	no	—
79	#41×C₃₁	—	2	12	no	—
80	#41×C₃₁	—	2	12	no	—
81	#41×C₃₁	—	4	8	no	—
82	#41×C₃₁	—	4	24	no	—
83	#41×C₃₁	—	4	6	no	—
84	#41×C₃₁	—	4	6	no	—
85	#41×C₃₁	D₈	1	4	yes	—
86	#41×C₃₁	C₂×D₄	1	4	yes	—
87	C₂×Q₈×C₃₁	—	2	1	no	—
88	C₂×Q₈×C₃₁	—	2	3	no	—
89	C₂×Q₈×C₃₁	—	2	12	no	—
90	C₂×Q₈×C₃₁	—	4	8	no	—
91	C₂×Q₈×C₃₁	—	4	3	no	—
92	C₂×Q₈×C₃₁	—	4	6	no	—
93	C₂×Q₈×C₃₁	D₈	1	1	yes	characteristic
94	C₂×D₄×C₃₁	—	2	3	no	—
95	C₂×D₄×C₃₁	—	2	12	no	—
96	C₂×D₄×C₃₁	—	2	1	no	—
97	C₂×D₄×C₃₁	—	4	3	no	—
98	C₂×D₄×C₃₁	—	4	3	no	—
99	C₂×D₄×C₃₁	—	4	24	no	—
100	C₂×D₄×C₃₁	—	4	3	no	—
101	C₂×D₄×C₃₁	—	4	6	no	—
102	C₂×D₄×C₃₁	D₈	1	3	yes	—
103	C₂²×C₄×C₃₁	—	4	3	no	—
104	C₂²×C₄×C₃₁	—	4	3	no	—
105	C₂²×C₄×C₃₁	—	4	3	no	—
106	C₂²×C₄×C₃₁	C₂×D₄	1	3	yes	—
107	Q₁₆×C₃₁	—	2	3	no	—
108	Q₁₆×C₃₁	—	2	12	no	—
109	Q₁₆×C₃₁	—	2	1	no	—
110	Q₁₆×C₃₁	C₂⁴	1	6	yes	—
111	Q₁₆×C₃₁	C₂⁴	1	2	yes	—
112	SD₁₆×C₃₁	—	2	12	no	—
113	SD₁₆×C₃₁	—	2	12	no	—
114	D₈×C₃₁	—	2	3	no	—
115	D₈×C₃₁	—	2	12	no	—
116	D₈×C₃₁	—	2	1	no	—
117	D₈×C₃₁	C₂⁴	1	2	yes	—
118	D₈×C₃₁	C₂⁴	1	6	yes	—
119	M₁₆×C₃₁	C₂×D₄	1	12	yes	—
120	C₂×C₈×C₃₁	C₂×D₄	1	3	yes	—
121	C₂×C₈×C₃₁	C₂×D₄	1	6	yes	—
122	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₃₁	C₂⁴	1	6	yes	—
124	C₁₆×C₃₁	C₂⁴	1	2	yes	—
125	C₁₆×C₃₁	C₂⁴	1	6	yes	—
126	C₂×#3416	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
127	C₂³×C₃₁	—	4	1	no	—
128	C₂³×C₃₁	—	4	3	no	—
129	C₂³×C₃₁	—	4	12	no	—
130	C₂³×C₃₁	—	16	6	no	—
131	C₂³×C₃₁	C₂×D₈	1	3	yes	—
132	Q₈×C₃₁	—	2	2	no	—
133	Q₈×C₃₁	—	2	6	no	—
134	Q₈×C₃₁	—	4	12	no	—
135	Q₈×C₃₁	—	4	3	no	—
136	Q₈×C₃₁	—	4	1	no	—
137	Q₈×C₃₁	C₂×D₈	1	4	yes	—
138	D₄×C₃₁	—	2	6	no	—
139	D₄×C₃₁	—	2	2	no	—
140	D₄×C₃₁	—	4	12	no	—
141	D₄×C₃₁	—	4	12	no	—
142	D₄×C₃₁	—	4	12	no	—
143	D₄×C₃₁	—	4	3	no	—
144	D₄×C₃₁	—	4	1	no	—
145	D₄×C₃₁	C₂×D₈	1	12	yes	—
146	C₂×C₄×C₃₁	—	4	12	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	3	no	—
149	C₂×C₄×C₃₁	—	4	12	no	—
150	C₂×C₄×C₃₁	—	4	12	no	—
151	C₂×C₄×C₃₁	C₂×D₈	1	6	yes	—
152	C₂×C₄×C₃₁	C₂×D₈	1	3	yes	—
153	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
156	C₈×C₃₁	C₂²×D₄	1	6	yes	—
157	C₈×C₃₁	C₂⁵	1	1	yes	characteristic
158	C₂×#578	C₂×C₃₁	1	1	yes	characteristic, complemented
159	C₂×#576	C₂×C₃₁	1	1	yes	characteristic, complemented
160	#3416	C₂×C₃₁	1	16	yes	direct product factor
161	C₂×#510	C₂×C₃₁	1	3	yes	complemented
162	C₂×#509	C₂×C₃₁	1	3	yes	complemented
163	C₂×#508	C₂×C₃₁	1	3	yes	complemented
164	C₂²×SD₃₂	C₂×C₃₁	1	3	yes	complemented
165	C₂×#504	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂²×C₃₁	—	2	6	no	—
167	C₂²×C₃₁	—	4	2	no	—
168	C₂²×C₃₁	—	4	6	no	—
169	C₂²×C₃₁	—	8	2	no	—
170	C₂²×C₃₁	—	8	6	no	—
171	C₂²×C₃₁	—	16	12	no	—
172	C₂²×C₃₁	C₂²×D₈	1	6	yes	—
173	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
174	C₄×C₃₁	—	4	2	no	—
175	C₄×C₃₁	—	4	6	no	—
176	C₄×C₃₁	C₂²×D₈	1	6	yes	—
177	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
178	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
179	C₂×2₋¹⁺⁴	—	2	1	no	—
180	C₂×H(5,𝔽₂)	—	2	1	no	—
181	#578	—	2	4	no	—
182	#578	C₂²×C₃₁	1	8	yes	complemented
183	#576	—	2	4	no	—
184	#576	C₂²×C₃₁	1	8	yes	complemented
185	C₂×#137	—	2	3	no	—
186	C₂×AGL(1,ℤ/8)	—	2	3	no	—
187	C₂×#135	C₂²×C₃₁	1	3	yes	—
188	C₂×#135	C₂²×C₃₁	1	3	yes	complemented
189	C₂²×Q₁₆	C₂²×C₃₁	1	3	yes	complemented
190	C₂²×D₈	C₂²×C₃₁	1	3	yes	—
191	C₂×#131	C₂²×C₃₁	1	1	yes	characteristic
192	#510	C₂²×C₃₁	1	24	yes	complemented
193	#509	C₂²×C₃₁	1	24	yes	complemented
194	#508	C₂²×C₃₁	1	24	yes	complemented
195	C₂×Q₃₂	C₂²×C₃₁	1	3	yes	complemented
196	C₂×SD₃₂	C₂²×C₃₁	1	3	yes	complemented
197	C₂×SD₃₂	C₂²×C₃₁	1	6	yes	complemented
198	C₂×SD₃₂	C₂²×C₃₁	1	1	yes	characteristic, complemented
199	C₂×SD₃₂	C₂²×C₃₁	1	24	yes	complemented
200	C₂×D₁₆	C₂²×C₃₁	1	3	yes	complemented
201	#504	C₂²×C₃₁	1	8	yes	complemented
202	C₂×M₃₂	C₂²×C₃₁	1	3	yes	complemented
203	C₂²×C₁₆	C₂²×C₃₁	1	3	yes	complemented
204	C₂×C₃₁	—	2	6	no	—
205	C₂×C₃₁	—	8	2	no	—
206	C₂×C₃₁	—	8	6	no	—
207	C₂×C₃₁	#3416	1	2	yes	direct product factor
208	C₂×C₃₁	C₂³×D₈	1	1	yes	characteristic
209	2₋¹⁺⁴	—	2	8	no	—
210	2₋¹⁺⁴	—	4	4	no	—
211	H(5,𝔽₂)	—	2	8	no	—
212	H(5,𝔽₂)	—	4	4	no	—
213	C₂×#41	—	2	3	no	—
214	C₂×#41	—	2	3	no	—
215	C₂×#41	—	4	1	no	—
216	C₂×#41	—	4	3	no	—
217	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
218	C₂²×Q₈	—	2	3	no	—
219	C₂²×Q₈	—	4	1	no	—
220	C₂²×D₄	—	2	3	no	—
221	C₂²×D₄	—	4	3	no	—
222	#137	—	2	24	no	—
223	AGL(1,ℤ/8)	—	2	24	no	—
224	#135	—	2	6	no	—
225	#135	—	2	6	no	—
226	#135	C₂³×C₃₁	1	12	yes	—
227	#135	C₂³×C₃₁	1	12	yes	complemented
228	C₂×Q₁₆	—	2	3	no	—
229	C₂×Q₁₆	—	2	6	no	—
230	C₂×Q₁₆	C₂³×C₃₁	1	3	yes	—
231	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
232	C₂×Q₁₆	C₂³×C₃₁	1	12	yes	complemented
233	C₂×SD₁₆	—	2	3	no	—
234	C₂×SD₁₆	—	2	3	no	—
235	C₂×D₈	—	2	3	no	—
236	C₂×D₈	—	2	6	no	—
237	C₂×D₈	C₂³×C₃₁	1	3	yes	—
238	C₂×D₈	C₂³×C₃₁	1	12	yes	—
239	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic
240	#131	D₄×C₃₁	1	4	yes	—
241	#131	C₂³×C₃₁	1	4	yes	—
242	C₂×M₁₆	D₄×C₃₁	1	3	yes	—
243	C₂²×C₈	C₂³×C₃₁	1	3	yes	—
244	Q₃₂	C₂³×C₃₁	1	12	yes	complemented
245	SD₃₂	C₂³×C₃₁	1	12	yes	complemented
246	SD₃₂	C₂³×C₃₁	1	24	yes	complemented
247	SD₃₂	C₂³×C₃₁	1	4	yes	complemented
248	D₁₆	C₂³×C₃₁	1	12	yes	complemented
249	M₃₂	C₂³×C₃₁	1	12	yes	complemented
250	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×C₁₆	C₂³×C₃₁	1	3	yes	—
252	C₂×C₁₆	C₂³×C₃₁	1	12	yes	complemented
253	C₃₁	C₂×#3416	1	1	yes	characteristic, direct product factor, Sylow
254	C₂⁴	—	4	3	no	—
255	#41	—	2	12	no	—
256	#41	—	2	12	no	—
257	#41	—	4	8	no	—
258	#41	—	4	24	no	—
259	#41	—	4	6	no	—
260	#41	—	4	6	no	—
261	#41	D₈×C₃₁	1	4	yes	—
262	#41	C₂×D₄×C₃₁	1	4	yes	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×Q₈	—	2	3	no	—
265	C₂×Q₈	—	2	12	no	—
266	C₂×Q₈	—	4	8	no	—
267	C₂×Q₈	—	4	3	no	—
268	C₂×Q₈	—	4	6	no	—
269	C₂×Q₈	D₈×C₃₁	1	1	yes	characteristic
270	C₂×D₄	—	2	3	no	—
271	C₂×D₄	—	2	12	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	4	3	no	—
274	C₂×D₄	—	4	3	no	—
275	C₂×D₄	—	4	24	no	—
276	C₂×D₄	—	4	3	no	—
277	C₂×D₄	—	4	6	no	—
278	C₂×D₄	D₈×C₃₁	1	3	yes	—
279	C₂²×C₄	—	4	3	no	—
280	C₂²×C₄	—	4	3	no	—
281	C₂²×C₄	—	4	3	no	—
282	C₂²×C₄	C₂×D₄×C₃₁	1	3	yes	—
283	Q₁₆	—	2	3	no	—
284	Q₁₆	—	2	12	no	—
285	Q₁₆	—	2	1	no	—
286	Q₁₆	C₂⁴×C₃₁	1	6	yes	—
287	Q₁₆	C₂⁴×C₃₁	1	2	yes	—
288	SD₁₆	—	2	12	no	—
289	SD₁₆	—	2	12	no	—
290	D₈	—	2	3	no	—
291	D₈	—	2	12	no	—
292	D₈	—	2	1	no	—
293	D₈	C₂⁴×C₃₁	1	2	yes	—
294	D₈	C₂⁴×C₃₁	1	6	yes	—
295	M₁₆	C₂×D₄×C₃₁	1	12	yes	—
296	C₂×C₈	C₂×D₄×C₃₁	1	3	yes	—
297	C₂×C₈	C₂×D₄×C₃₁	1	6	yes	—
298	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
299	C₂×C₈	C₂⁴×C₃₁	1	6	yes	—
300	C₁₆	C₂⁴×C₃₁	1	2	yes	—
301	C₁₆	C₂⁴×C₃₁	1	6	yes	—
302	C₂³	—	4	1	no	—
303	C₂³	—	4	3	no	—
304	C₂³	—	4	12	no	—
305	C₂³	—	16	6	no	—
306	C₂³	C₂×D₈×C₃₁	1	3	yes	—
307	Q₈	—	2	2	no	—
308	Q₈	—	2	6	no	—
309	Q₈	—	4	12	no	—
310	Q₈	—	4	3	no	—
311	Q₈	—	4	1	no	—
312	Q₈	C₂×D₈×C₃₁	1	4	yes	—
313	D₄	—	2	6	no	—
314	D₄	—	2	2	no	—
315	D₄	—	4	12	no	—
316	D₄	—	4	12	no	—
317	D₄	—	4	12	no	—
318	D₄	—	4	3	no	—
319	D₄	—	4	1	no	—
320	D₄	C₂×D₈×C₃₁	1	12	yes	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	3	no	—
323	C₂×C₄	—	4	12	no	—
324	C₂×C₄	—	4	12	no	—
325	C₂×C₄	—	4	12	no	—
326	C₂×C₄	C₂×D₈×C₃₁	1	3	yes	—
327	C₂×C₄	C₂×D₈×C₃₁	1	6	yes	—
328	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
330	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
331	C₈	C₂²×D₄×C₃₁	1	6	yes	—
332	C₈	C₂⁵×C₃₁	1	1	yes	characteristic
333	C₂²	—	2	6	no	—
334	C₂²	—	4	2	no	—
335	C₂²	—	4	6	no	—
336	C₂²	—	8	6	no	—
337	C₂²	—	8	2	no	—
338	C₂²	—	16	12	no	—
339	C₂²	C₂²×D₈×C₃₁	1	6	yes	—
340	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
341	C₄	—	4	2	no	—
342	C₄	—	4	6	no	—
343	C₄	C₂²×D₈×C₃₁	1	6	yes	—
344	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
345	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
346	C₂	—	2	6	no	—
347	C₂	—	8	6	no	—
348	C₂	—	8	2	no	—
349	C₂	C₃₁×#3416	1	2	yes	direct product factor
350	C₂	C₂³×D₈×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₃₁
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×#41×C₃₁ ◁ C₂×C₃₁×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#578	C₂	semidirect
2. C₂×C₃₁×#576	C₂	semidirect
3. C₃₁×#3416	C₂	direct (N × H)
4. C₂×C₃₁×#510	C₂	semidirect
5. C₂×C₃₁×#509	C₂	semidirect
6. C₂×C₃₁×#508	C₂	semidirect
7. C₂²×C₃₁×SD₃₂	C₂	semidirect
8. C₂×C₃₁×#504	C₂	semidirect
12. C₃₁×#578	C₂²	semidirect
14. C₃₁×#576	C₂²	semidirect
18. C₂×C₃₁×#135	C₂²	semidirect
19. C₂²×Q₁₆×C₃₁	C₂²	semidirect
22. C₃₁×#510	C₂²	semidirect
23. C₃₁×#509	C₂²	semidirect
24. C₃₁×#508	C₂²	semidirect
25. C₂×C₃₁×Q₃₂	C₂²	semidirect
26. C₂×C₃₁×SD₃₂	C₂²	semidirect
27. C₂×C₃₁×SD₃₂	C₂²	semidirect
28. C₂×C₃₁×SD₃₂	C₂²	semidirect
29. C₂×C₃₁×SD₃₂	C₂²	semidirect
30. C₂×C₃₁×D₁₆	C₂²	semidirect
31. C₃₁×#504	C₂²	semidirect
32. C₂×C₃₁×M₃₂	C₂²	semidirect
33. C₂²×C₁₆×C₃₁	C₂²	semidirect
52. C₃₁×#135	C₂³	semidirect
57. C₂×Q₁₆×C₃₁	C₂³	semidirect
69. C₃₁×Q₃₂	C₂³	semidirect
70. C₃₁×SD₃₂	C₂³	semidirect
71. C₃₁×SD₃₂	C₂³	semidirect
72. C₃₁×SD₃₂	C₂³	semidirect
73. C₃₁×D₁₆	C₂³	semidirect
74. C₃₁×M₃₂	C₂³	semidirect
77. C₂×C₁₆×C₃₁	C₂³	semidirect
126. C₂×#3416	C₃₁	direct (N × H)
158. C₂×#578	C₂×C₃₁	semidirect
159. C₂×#576	C₂×C₃₁	semidirect
160. #3416	C₂×C₃₁	direct (N × H)
161. C₂×#510	C₂×C₃₁	semidirect
162. C₂×#509	C₂×C₃₁	semidirect
163. C₂×#508	C₂×C₃₁	semidirect
164. C₂²×SD₃₂	C₂×C₃₁	semidirect
165. C₂×#504	C₂×C₃₁	semidirect
182. #578	C₂²×C₃₁	semidirect
184. #576	C₂²×C₃₁	semidirect
188. C₂×#135	C₂²×C₃₁	semidirect
189. C₂²×Q₁₆	C₂²×C₃₁	semidirect
192. #510	C₂²×C₃₁	semidirect
193. #509	C₂²×C₃₁	semidirect
194. #508	C₂²×C₃₁	semidirect
195. C₂×Q₃₂	C₂²×C₃₁	semidirect
196. C₂×SD₃₂	C₂²×C₃₁	semidirect
197. C₂×SD₃₂	C₂²×C₃₁	semidirect
198. C₂×SD₃₂	C₂²×C₃₁	semidirect
199. C₂×SD₃₂	C₂²×C₃₁	semidirect
200. C₂×D₁₆	C₂²×C₃₁	semidirect
201. #504	C₂²×C₃₁	semidirect
202. C₂×M₃₂	C₂²×C₃₁	semidirect
203. C₂²×C₁₆	C₂²×C₃₁	semidirect
207. C₂×C₃₁	#3416	direct (N × H)
227. #135	C₂³×C₃₁	semidirect
232. C₂×Q₁₆	C₂³×C₃₁	semidirect
244. Q₃₂	C₂³×C₃₁	semidirect
245. SD₃₂	C₂³×C₃₁	semidirect
246. SD₃₂	C₂³×C₃₁	semidirect
247. SD₃₂	C₂³×C₃₁	semidirect
248. D₁₆	C₂³×C₃₁	semidirect
249. M₃₂	C₂³×C₃₁	semidirect
252. C₂×C₁₆	C₂³×C₃₁	semidirect
253. C₃₁	C₂×#3416	direct (N × H)
349. C₂	C₃₁×#3416	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×C₃₁×#578	2
C₂×C₃₁×#576	2
C₃₁×#3416	2
C₂×C₃₁×#510	2
C₂×C₃₁×#509	2
C₂×C₃₁×#508	2
C₂²×C₃₁×SD₃₂	2
C₂×C₃₁×#504	2
C₂×#3416	31

Subgroups — C2×C31×#3416 #21519392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3416 #21519392