Subgroups — C₂×C₃₁×#3292 #21517862

Order 7936.

2766 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#576	C₂	1	4	yes	maximal, complemented
2	C₃₁×#3292	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃₁×#472	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#453	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#443	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	4	yes	complemented
8	C₃₁×#576	—	2	16	no	—
9	C₃₁×#576	C₂²	1	32	yes	complemented
10	C₂×C₃₁×AGL(1,ℤ/8)	—	2	8	no	—
11	C₂×C₃₁×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
12	C₂×C₃₁×#135	—	2	4	no	—
13	C₂×C₃₁×#135	C₂²	1	2	yes	—
14	C₂²×D₈×C₃₁	—	2	4	no	—
15	C₂²×D₈×C₃₁	C₂²	1	4	yes	complemented
16	C₂×C₃₁×#131	C₂²	1	4	yes	complemented
17	C₂×C₃₁×#127	C₂²	1	2	yes	complemented
18	C₃₁×#493	C₂²	1	8	yes	complemented
19	C₃₁×#472	C₂²	1	32	yes	complemented
20	C₃₁×#453	C₂²	1	32	yes	complemented
21	C₃₁×#443	C₂²	1	16	yes	complemented
22	C₂×C₃₁×#108	C₂²	1	2	yes	complemented
23	C₂×C₃₁×#104	C₂²	1	4	yes	complemented
24	C₂×C₃₁×#100	C₂²	1	4	yes	complemented
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₃₁×H(5,𝔽₂)	—	2	16	no	—
27	C₃₁×H(5,𝔽₂)	—	4	4	no	—
28	C₃₁×H(5,𝔽₂)	C₂³	1	16	yes	complemented
29	C₂×#41×C₃₁	—	2	8	no	—
30	C₂×#41×C₃₁	C₂³	1	4	yes	—
31	C₂²×D₄×C₃₁	—	2	8	no	—
32	C₂²×D₄×C₃₁	—	4	2	no	—
33	C₂²×D₄×C₃₁	—	4	4	no	—
34	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
35	C₃₁×AGL(1,ℤ/8)	—	2	16	no	—
36	C₃₁×AGL(1,ℤ/8)	—	2	64	no	—
37	C₃₁×AGL(1,ℤ/8)	C₂³	1	32	yes	complemented
38	C₃₁×#135	—	2	32	no	—
39	C₃₁×#135	D₄	1	8	yes	complemented
40	C₃₁×#135	C₂³	1	8	yes	—
41	C₂×Q₁₆×C₃₁	D₄	1	2	yes	complemented
42	C₂×SD₁₆×C₃₁	—	2	8	no	—
43	C₂×SD₁₆×C₃₁	D₄	1	4	yes	complemented
44	C₂×D₈×C₃₁	—	2	8	no	—
45	C₂×D₈×C₃₁	—	2	32	no	—
46	C₂×D₈×C₃₁	—	2	4	no	—
47	C₂×D₈×C₃₁	—	2	4	no	—
48	C₂×D₈×C₃₁	—	2	8	no	—
49	C₂×D₈×C₃₁	D₄	1	2	yes	complemented
50	C₂×D₈×C₃₁	C₂³	1	16	yes	complemented
51	C₃₁×#131	—	2	8	no	—
52	C₃₁×#131	C₂³	1	16	yes	complemented
53	C₂×M₁₆×C₃₁	—	2	4	no	—
54	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
55	C₂²×C₈×C₃₁	—	2	4	no	—
56	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
57	C₃₁×#127	—	4	2	no	—
58	C₃₁×#127	C₂³	1	8	yes	complemented
59	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
60	C₃₁×#108	C₂³	1	8	yes	complemented
61	C₃₁×#104	C₂³	1	16	yes	complemented
62	C₃₁×#100	C₂³	1	16	yes	complemented
63	C₄×C₈×C₃₁	C₂³	1	4	yes	complemented
64	C₂⁴×C₃₁	—	2	4	no	—
65	C₂⁴×C₃₁	—	4	4	no	—
66	#41×C₃₁	—	2	4	no	—
67	#41×C₃₁	—	2	4	no	—
68	#41×C₃₁	—	2	32	no	—
69	#41×C₃₁	—	4	16	no	—
70	#41×C₃₁	C₂×D₄	1	8	yes	—
71	#41×C₃₁	C₂⁴	1	8	yes	—
72	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
73	C₂×D₄×C₃₁	—	2	4	no	—
74	C₂×D₄×C₃₁	—	2	32	no	—
75	C₂×D₄×C₃₁	—	2	8	no	—
76	C₂×D₄×C₃₁	—	2	8	no	—
77	C₂×D₄×C₃₁	—	2	4	no	—
78	C₂×D₄×C₃₁	—	4	16	no	—
79	C₂×D₄×C₃₁	—	4	8	no	—
80	C₂×D₄×C₃₁	—	4	8	no	—
81	C₂×D₄×C₃₁	—	4	16	no	—
82	C₂×D₄×C₃₁	—	4	16	no	—
83	C₂×D₄×C₃₁	—	8	8	no	—
84	C₂×D₄×C₃₁	C₂×D₄	1	4	yes	—
85	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
86	C₂²×C₄×C₃₁	—	2	1	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	4	4	no	—
89	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
90	Q₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
91	SD₁₆×C₃₁	—	2	32	no	—
92	SD₁₆×C₃₁	C₂×D₄	1	16	yes	complemented
93	D₈×C₃₁	—	2	32	no	—
94	D₈×C₃₁	—	2	16	no	—
95	D₈×C₃₁	—	2	16	no	—
96	D₈×C₃₁	C₂×D₄	1	8	yes	complemented
97	M₁₆×C₃₁	—	2	4	no	—
98	M₁₆×C₃₁	—	2	16	no	—
99	M₁₆×C₃₁	C₂⁴	1	8	yes	—
100	C₂×C₈×C₃₁	—	2	4	no	—
101	C₂×C₈×C₃₁	—	2	16	no	—
102	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
106	C₄²×C₃₁	—	2	1	no	—
107	C₄²×C₃₁	C₂⁴	1	2	yes	—
108	C₂×#3292	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₃₁	—	2	4	no	—
110	C₂³×C₃₁	—	2	8	no	—
111	C₂³×C₃₁	—	4	16	no	—
112	C₂³×C₃₁	—	4	4	no	—
113	C₂³×C₃₁	—	4	4	no	—
114	C₂³×C₃₁	—	8	8	no	—
115	C₂³×C₃₁	—	16	8	no	—
116	C₂³×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
117	Q₈×C₃₁	—	2	4	no	—
118	Q₈×C₃₁	C₂²×D₄	1	8	yes	—
119	D₄×C₃₁	—	2	8	no	—
120	D₄×C₃₁	—	2	8	no	—
121	D₄×C₃₁	—	2	4	no	—
122	D₄×C₃₁	—	2	16	no	—
123	D₄×C₃₁	—	4	32	no	—
124	D₄×C₃₁	—	4	8	no	—
125	D₄×C₃₁	—	8	16	no	—
126	D₄×C₃₁	C₂²×D₄	1	8	yes	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	2	4	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	8	no	—
131	C₂×C₄×C₃₁	—	2	8	no	—
132	C₂×C₄×C₃₁	—	4	16	no	—
133	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
134	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
135	C₂×C₄×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
137	C₈×C₃₁	—	2	8	no	—
138	C₈×C₃₁	C₂²×D₄	1	4	yes	—
139	C₈×C₃₁	C₂²×D₄	1	4	yes	—
140	C₂×#576	C₂×C₃₁	1	4	yes	complemented
141	#3292	C₂×C₃₁	1	16	yes	direct product factor
142	C₂×#493	C₂×C₃₁	1	1	yes	characteristic, complemented
143	C₂×#472	C₂×C₃₁	1	4	yes	complemented
144	C₂×#453	C₂×C₃₁	1	4	yes	complemented
145	C₂×#443	C₂×C₃₁	1	2	yes	complemented
146	C₂²×C₃₁	—	2	2	no	—
147	C₂²×C₃₁	—	2	8	no	—
148	C₂²×C₃₁	—	4	8	no	—
149	C₂²×C₃₁	—	4	8	no	—
150	C₂²×C₃₁	—	8	8	no	—
151	C₂²×C₃₁	—	8	8	no	—
152	C₂²×C₃₁	—	16	4	no	—
153	C₂²×C₃₁	—	16	16	no	—
154	C₂²×C₃₁	D₄²	1	1	yes	characteristic
155	C₂²×C₃₁	D₄²	1	1	yes	characteristic
156	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
157	C₄×C₃₁	—	2	4	no	—
158	C₄×C₃₁	—	2	8	no	—
159	C₄×C₃₁	D₄²	1	2	yes	—
160	C₄×C₃₁	C₂³×D₄	1	2	yes	—
161	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	4	yes	complemented
162	#576	—	2	16	no	—
163	#576	C₂²×C₃₁	1	32	yes	complemented
164	C₂×AGL(1,ℤ/8)	—	2	8	no	—
165	C₂×AGL(1,ℤ/8)	C₂²×C₃₁	1	8	yes	complemented
166	C₂×#135	—	2	4	no	—
167	C₂×#135	C₂²×C₃₁	1	2	yes	—
168	C₂²×D₈	—	2	4	no	—
169	C₂²×D₈	C₂²×C₃₁	1	4	yes	complemented
170	C₂×#131	C₂²×C₃₁	1	4	yes	complemented
171	C₂×#127	C₂²×C₃₁	1	2	yes	complemented
172	#493	C₂²×C₃₁	1	8	yes	complemented
173	#472	C₂²×C₃₁	1	32	yes	complemented
174	#453	C₂²×C₃₁	1	32	yes	complemented
175	#443	C₂²×C₃₁	1	16	yes	complemented
176	C₂×#108	C₂²×C₃₁	1	2	yes	complemented
177	C₂×#104	C₂²×C₃₁	1	4	yes	complemented
178	C₂×#100	C₂²×C₃₁	1	4	yes	complemented
179	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
180	C₂×C₃₁	—	2	1	no	—
181	C₂×C₃₁	—	2	1	no	—
182	C₂×C₃₁	—	4	8	no	—
183	C₂×C₃₁	—	8	8	no	—
184	C₂×C₃₁	#3292	1	2	yes	direct product factor
185	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
186	H(5,𝔽₂)	—	2	16	no	—
187	H(5,𝔽₂)	—	4	4	no	—
188	H(5,𝔽₂)	C₂³×C₃₁	1	16	yes	complemented
189	C₂×#41	—	2	8	no	—
190	C₂×#41	C₂³×C₃₁	1	4	yes	—
191	C₂²×D₄	—	2	8	no	—
192	C₂²×D₄	—	4	2	no	—
193	C₂²×D₄	—	4	4	no	—
194	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
195	AGL(1,ℤ/8)	—	2	16	no	—
196	AGL(1,ℤ/8)	—	2	64	no	—
197	AGL(1,ℤ/8)	C₂³×C₃₁	1	32	yes	complemented
198	#135	—	2	32	no	—
199	#135	D₄×C₃₁	1	8	yes	complemented
200	#135	C₂³×C₃₁	1	8	yes	—
201	C₂×Q₁₆	D₄×C₃₁	1	2	yes	complemented
202	C₂×SD₁₆	—	2	8	no	—
203	C₂×SD₁₆	D₄×C₃₁	1	4	yes	complemented
204	C₂×D₈	—	2	8	no	—
205	C₂×D₈	—	2	32	no	—
206	C₂×D₈	—	2	4	no	—
207	C₂×D₈	—	2	4	no	—
208	C₂×D₈	—	2	8	no	—
209	C₂×D₈	D₄×C₃₁	1	2	yes	complemented
210	C₂×D₈	C₂³×C₃₁	1	16	yes	complemented
211	#131	—	2	8	no	—
212	#131	C₂³×C₃₁	1	16	yes	complemented
213	C₂×M₁₆	—	2	4	no	—
214	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
215	C₂²×C₈	—	2	4	no	—
216	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
217	#127	—	4	2	no	—
218	#127	C₂³×C₃₁	1	8	yes	complemented
219	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
220	#108	C₂³×C₃₁	1	8	yes	complemented
221	#104	C₂³×C₃₁	1	16	yes	complemented
222	#100	C₂³×C₃₁	1	16	yes	complemented
223	C₄×C₈	C₂³×C₃₁	1	4	yes	complemented
224	C₃₁	C₂×#3292	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁴	—	2	4	no	—
226	C₂⁴	—	4	4	no	—
227	#41	—	2	4	no	—
228	#41	—	2	4	no	—
229	#41	—	2	32	no	—
230	#41	—	4	16	no	—
231	#41	C₂×D₄×C₃₁	1	8	yes	—
232	#41	C₂⁴×C₃₁	1	8	yes	—
233	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
234	C₂×D₄	—	2	4	no	—
235	C₂×D₄	—	2	32	no	—
236	C₂×D₄	—	2	8	no	—
237	C₂×D₄	—	2	8	no	—
238	C₂×D₄	—	2	4	no	—
239	C₂×D₄	—	4	16	no	—
240	C₂×D₄	—	4	8	no	—
241	C₂×D₄	—	4	8	no	—
242	C₂×D₄	—	4	16	no	—
243	C₂×D₄	—	4	16	no	—
244	C₂×D₄	—	8	8	no	—
245	C₂×D₄	C₂×D₄×C₃₁	1	4	yes	—
246	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	4	no	—
250	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
251	Q₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
252	SD₁₆	—	2	32	no	—
253	SD₁₆	C₂×D₄×C₃₁	1	16	yes	complemented
254	D₈	—	2	32	no	—
255	D₈	—	2	16	no	—
256	D₈	—	2	16	no	—
257	D₈	C₂×D₄×C₃₁	1	8	yes	complemented
258	M₁₆	—	2	4	no	—
259	M₁₆	—	2	16	no	—
260	M₁₆	C₂⁴×C₃₁	1	8	yes	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	—	2	16	no	—
263	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
264	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
265	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
266	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
267	C₄²	—	2	1	no	—
268	C₄²	C₂⁴×C₃₁	1	2	yes	—
269	C₂³	—	2	4	no	—
270	C₂³	—	2	8	no	—
271	C₂³	—	4	16	no	—
272	C₂³	—	4	4	no	—
273	C₂³	—	4	4	no	—
274	C₂³	—	8	8	no	—
275	C₂³	—	16	8	no	—
276	C₂³	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
277	Q₈	—	2	4	no	—
278	Q₈	C₂²×D₄×C₃₁	1	8	yes	—
279	D₄	—	2	8	no	—
280	D₄	—	2	8	no	—
281	D₄	—	2	4	no	—
282	D₄	—	2	16	no	—
283	D₄	—	4	32	no	—
284	D₄	—	4	8	no	—
285	D₄	—	8	16	no	—
286	D₄	C₂²×D₄×C₃₁	1	8	yes	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	4	16	no	—
293	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
294	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
295	C₂×C₄	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
297	C₈	—	2	8	no	—
298	C₈	C₂²×D₄×C₃₁	1	4	yes	—
299	C₈	C₂²×D₄×C₃₁	1	4	yes	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	4	8	no	—
303	C₂²	—	4	8	no	—
304	C₂²	—	8	8	no	—
305	C₂²	—	8	8	no	—
306	C₂²	—	16	4	no	—
307	C₂²	—	16	16	no	—
308	C₂²	D₄²×C₃₁	1	1	yes	characteristic
309	C₂²	D₄²×C₃₁	1	1	yes	characteristic
310	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
311	C₄	—	2	4	no	—
312	C₄	—	2	8	no	—
313	C₄	D₄²×C₃₁	1	2	yes	—
314	C₄	C₂³×D₄×C₃₁	1	2	yes	—
315	C₂	—	2	1	no	—
316	C₂	—	2	1	no	—
317	C₂	—	4	8	no	—
318	C₂	—	8	8	no	—
319	C₂	C₃₁×#3292	1	2	yes	direct product factor
320	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#576	C₂	semidirect
2. C₃₁×#3292	C₂	direct (N × H)
3. C₂×C₃₁×#493	C₂	semidirect
4. C₂×C₃₁×#472	C₂	semidirect
5. C₂×C₃₁×#453	C₂	semidirect
6. C₂×C₃₁×#443	C₂	semidirect
7. C₂×C₃₁×H(5,𝔽₂)	C₂²	semidirect
9. C₃₁×#576	C₂²	semidirect
11. C₂×C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂²×D₈×C₃₁	C₂²	semidirect
16. C₂×C₃₁×#131	C₂²	semidirect
17. C₂×C₃₁×#127	C₂²	semidirect
18. C₃₁×#493	C₂²	semidirect
19. C₃₁×#472	C₂²	semidirect
20. C₃₁×#453	C₂²	semidirect
21. C₃₁×#443	C₂²	semidirect
22. C₂×C₃₁×#108	C₂²	semidirect
23. C₂×C₃₁×#104	C₂²	semidirect
24. C₂×C₃₁×#100	C₂²	semidirect
25. C₂×C₄×C₈×C₃₁	C₂²	semidirect
28. C₃₁×H(5,𝔽₂)	C₂³	semidirect
37. C₃₁×AGL(1,ℤ/8)	C₂³	semidirect
39. C₃₁×#135	D₄	semidirect
41. C₂×Q₁₆×C₃₁	D₄	semidirect
43. C₂×SD₁₆×C₃₁	D₄	semidirect
49. C₂×D₈×C₃₁	D₄	semidirect
50. C₂×D₈×C₃₁	C₂³	semidirect
52. C₃₁×#131	C₂³	semidirect
58. C₃₁×#127	C₂³	semidirect
60. C₃₁×#108	C₂³	semidirect
61. C₃₁×#104	C₂³	semidirect
62. C₃₁×#100	C₂³	semidirect
63. C₄×C₈×C₃₁	C₂³	semidirect
90. Q₁₆×C₃₁	C₂×D₄	semidirect
92. SD₁₆×C₃₁	C₂×D₄	semidirect
96. D₈×C₃₁	C₂×D₄	semidirect
108. C₂×#3292	C₃₁	direct (N × H)
140. C₂×#576	C₂×C₃₁	semidirect
141. #3292	C₂×C₃₁	direct (N × H)
142. C₂×#493	C₂×C₃₁	semidirect
143. C₂×#472	C₂×C₃₁	semidirect
144. C₂×#453	C₂×C₃₁	semidirect
145. C₂×#443	C₂×C₃₁	semidirect
161. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
163. #576	C₂²×C₃₁	semidirect
165. C₂×AGL(1,ℤ/8)	C₂²×C₃₁	semidirect
169. C₂²×D₈	C₂²×C₃₁	semidirect
170. C₂×#131	C₂²×C₃₁	semidirect
171. C₂×#127	C₂²×C₃₁	semidirect
172. #493	C₂²×C₃₁	semidirect
173. #472	C₂²×C₃₁	semidirect
174. #453	C₂²×C₃₁	semidirect
175. #443	C₂²×C₃₁	semidirect
176. C₂×#108	C₂²×C₃₁	semidirect
177. C₂×#104	C₂²×C₃₁	semidirect
178. C₂×#100	C₂²×C₃₁	semidirect
179. C₂×C₄×C₈	C₂²×C₃₁	semidirect
184. C₂×C₃₁	#3292	direct (N × H)
188. H(5,𝔽₂)	C₂³×C₃₁	semidirect
197. AGL(1,ℤ/8)	C₂³×C₃₁	semidirect
199. #135	D₄×C₃₁	semidirect
201. C₂×Q₁₆	D₄×C₃₁	semidirect
203. C₂×SD₁₆	D₄×C₃₁	semidirect
209. C₂×D₈	D₄×C₃₁	semidirect
210. C₂×D₈	C₂³×C₃₁	semidirect
212. #131	C₂³×C₃₁	semidirect
218. #127	C₂³×C₃₁	semidirect
220. #108	C₂³×C₃₁	semidirect
221. #104	C₂³×C₃₁	semidirect
222. #100	C₂³×C₃₁	semidirect
223. C₄×C₈	C₂³×C₃₁	semidirect
224. C₃₁	C₂×#3292	direct (N × H)
251. Q₁₆	C₂×D₄×C₃₁	semidirect
253. SD₁₆	C₂×D₄×C₃₁	semidirect
257. D₈	C₂×D₄×C₃₁	semidirect
319. C₂	C₃₁×#3292	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×#576	2
C₃₁×#3292	2
C₂×C₃₁×#493	2
C₂×C₃₁×#472	2
C₂×C₃₁×#453	2
C₂×C₃₁×#443	2
C₂×#3292	31

Subgroups — C2×C31×#3292 #21517862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3292 #21517862