Subgroups — C₂×C₃₁×#3414 #21519390

Order 7936.

2098 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#135	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3414	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#510	C₂	1	4	yes	maximal, complemented
4	C₂×C₃₁×#509	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#508	C₂	1	4	yes	maximal, complemented
6	C₂²×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₃₁	—	2	2	no	—
8	C₂×C₃₁×#135	—	2	2	no	—
9	C₂×C₃₁×#135	—	2	2	no	—
10	C₂×C₃₁×#135	—	2	8	no	—
11	C₂×C₃₁×#135	C₂²	1	4	yes	—
12	C₂×C₃₁×#135	C₂²	1	4	yes	complemented
13	C₂×C₃₁×#135	C₂²	1	16	yes	complemented
14	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
15	C₂²×SD₁₆×C₃₁	—	2	2	no	—
16	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
17	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₃₁×#510	C₂²	1	32	yes	complemented
19	C₃₁×#509	C₂²	1	32	yes	complemented
20	C₃₁×#508	C₂²	1	32	yes	complemented
21	C₂×C₃₁×Q₃₂	C₂²	1	4	yes	complemented
22	C₂×C₃₁×SD₃₂	C₂²	1	8	yes	complemented
23	C₂×C₃₁×D₁₆	C₂²	1	4	yes	complemented
24	C₂×C₃₁×M₃₂	C₂²	1	4	yes	complemented
25	C₂×C₃₁×M₃₂	C₂²	1	8	yes	complemented
26	C₂²×C₁₆×C₃₁	C₂²	1	2	yes	complemented
27	C₂×#41×C₃₁	—	2	4	no	—
28	C₂×#41×C₃₁	—	2	16	no	—
29	C₂×#41×C₃₁	—	2	4	no	—
30	C₂×#41×C₃₁	—	4	2	no	—
31	C₂×#41×C₃₁	—	4	8	no	—
32	C₂×#41×C₃₁	—	4	2	no	—
33	C₂²×Q₈×C₃₁	—	2	2	no	—
34	C₂²×D₄×C₃₁	—	2	2	no	—
35	C₂²×D₄×C₃₁	—	4	2	no	—
36	C₂³×C₄×C₃₁	—	4	2	no	—
37	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
38	C₃₁×#135	—	2	8	no	—
39	C₃₁×#135	—	2	16	no	—
40	C₃₁×#135	—	2	8	no	—
41	C₃₁×#135	—	2	16	no	—
42	C₃₁×#135	C₂³	1	16	yes	—
43	C₃₁×#135	C₂³	1	16	yes	complemented
44	C₂×Q₁₆×C₃₁	—	2	2	no	—
45	C₂×Q₁₆×C₃₁	—	2	4	no	—
46	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
47	C₂×Q₁₆×C₃₁	C₂³	1	8	yes	complemented
48	C₂×SD₁₆×C₃₁	—	2	4	no	—
49	C₂×SD₁₆×C₃₁	—	2	4	no	—
50	C₂×SD₁₆×C₃₁	—	2	16	no	—
51	C₂×D₈×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	—	2	4	no	—
53	C₂×D₈×C₃₁	C₂³	1	4	yes	—
54	C₂×D₈×C₃₁	C₂³	1	8	yes	complemented
55	C₂²×C₈×C₃₁	D₄	1	2	yes	—
56	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₃₁	D₄	1	4	yes	—
58	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
61	C₃₁×Q₃₂	C₂³	1	16	yes	complemented
62	C₃₁×SD₃₂	C₂³	1	32	yes	complemented
63	C₃₁×D₁₆	C₂³	1	16	yes	complemented
64	C₃₁×M₃₂	C₂³	1	16	yes	complemented
65	C₂×C₁₆×C₃₁	C₂³	1	4	yes	—
66	C₂×C₁₆×C₃₁	C₂³	1	8	yes	complemented
67	C₂⁴×C₃₁	—	4	2	no	—
68	C₂⁴×C₃₁	D₈	1	1	yes	characteristic
69	#41×C₃₁	—	2	16	no	—
70	#41×C₃₁	—	2	16	no	—
71	#41×C₃₁	—	4	16	no	—
72	#41×C₃₁	—	4	8	no	—
73	#41×C₃₁	—	4	8	no	—
74	#41×C₃₁	—	4	16	no	—
75	C₂×Q₈×C₃₁	—	2	4	no	—
76	C₂×Q₈×C₃₁	—	2	8	no	—
77	C₂×Q₈×C₃₁	—	4	2	no	—
78	C₂×Q₈×C₃₁	—	4	4	no	—
79	C₂×D₄×C₃₁	—	2	4	no	—
80	C₂×D₄×C₃₁	—	2	8	no	—
81	C₂×D₄×C₃₁	—	4	4	no	—
82	C₂×D₄×C₃₁	—	4	4	no	—
83	C₂×D₄×C₃₁	—	4	16	no	—
84	C₂×D₄×C₃₁	—	4	2	no	—
85	C₂×D₄×C₃₁	—	4	4	no	—
86	C₂²×C₄×C₃₁	—	4	2	no	—
87	C₂²×C₄×C₃₁	—	4	4	no	—
88	C₂²×C₄×C₃₁	—	4	16	no	—
89	C₂²×C₄×C₃₁	—	4	4	no	—
90	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
91	C₂²×C₄×C₃₁	D₈	1	4	yes	—
92	C₂²×C₄×C₃₁	D₈	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	Q₁₆×C₃₁	—	2	4	no	—
97	Q₁₆×C₃₁	—	2	8	no	—
98	Q₁₆×C₃₁	C₂⁴	1	8	yes	—
99	SD₁₆×C₃₁	—	2	16	no	—
100	SD₁₆×C₃₁	—	2	16	no	—
101	D₈×C₃₁	—	2	4	no	—
102	D₈×C₃₁	—	2	8	no	—
103	D₈×C₃₁	C₂⁴	1	8	yes	—
104	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
106	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₃₁	C₂×D₄	1	8	yes	—
108	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
112	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
113	C₁₆×C₃₁	C₂⁴	1	8	yes	—
114	C₂×#3414	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₃₁	—	4	2	no	—
116	C₂³×C₃₁	—	4	8	no	—
117	C₂³×C₃₁	—	4	4	no	—
118	C₂³×C₃₁	—	8	8	no	—
119	C₂³×C₃₁	C₂×D₈	1	2	yes	—
120	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
121	C₂³×C₃₁	C₂×D₈	1	4	yes	—
122	Q₈×C₃₁	—	2	8	no	—
123	Q₈×C₃₁	—	4	8	no	—
124	Q₈×C₃₁	—	4	4	no	—
125	D₄×C₃₁	—	2	8	no	—
126	D₄×C₃₁	—	4	16	no	—
127	D₄×C₃₁	—	4	16	no	—
128	D₄×C₃₁	—	4	8	no	—
129	D₄×C₃₁	—	4	4	no	—
130	C₂×C₄×C₃₁	—	4	8	no	—
131	C₂×C₄×C₃₁	—	4	4	no	—
132	C₂×C₄×C₃₁	—	4	16	no	—
133	C₂×C₄×C₃₁	—	4	16	no	—
134	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
135	C₂×C₄×C₃₁	C₂×D₈	1	8	yes	—
136	C₂×C₄×C₃₁	C₂×D₈	1	4	yes	—
137	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
138	C₂×C₄×C₃₁	C₂×D₈	1	4	yes	—
139	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
142	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
143	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
144	C₈×C₃₁	C₂²×D₄	1	4	yes	—
145	C₈×C₃₁	C₂²×D₄	1	2	yes	—
146	C₈×C₃₁	C₂⁵	1	1	yes	characteristic
147	C₂²×#135	C₂×C₃₁	1	2	yes	complemented
148	#3414	C₂×C₃₁	1	16	yes	direct product factor
149	C₂×#510	C₂×C₃₁	1	4	yes	complemented
150	C₂×#509	C₂×C₃₁	1	4	yes	complemented
151	C₂×#508	C₂×C₃₁	1	4	yes	complemented
152	C₂²×M₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
153	C₂²×C₃₁	—	2	4	no	—
154	C₂²×C₃₁	—	2	2	no	—
155	C₂²×C₃₁	—	4	4	no	—
156	C₂²×C₃₁	—	4	8	no	—
157	C₂²×C₃₁	—	8	16	no	—
158	C₂²×C₃₁	—	8	8	no	—
159	C₂²×C₃₁	C₂²×D₈	1	4	yes	—
160	C₂²×C₃₁	C₂²×D₈	1	2	yes	—
161	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
162	C₄×C₃₁	—	4	8	no	—
163	C₄×C₃₁	C₂²×D₈	1	2	yes	—
164	C₄×C₃₁	C₂²×D₈	1	4	yes	—
165	C₄×C₃₁	C₂²×D₈	1	1	yes	characteristic
166	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
167	C₂²×#41	—	2	2	no	—
168	C₂×#135	—	2	2	no	—
169	C₂×#135	—	2	2	no	—
170	C₂×#135	—	2	8	no	—
171	C₂×#135	C₂²×C₃₁	1	4	yes	—
172	C₂×#135	C₂²×C₃₁	1	4	yes	complemented
173	C₂×#135	C₂²×C₃₁	1	16	yes	complemented
174	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
175	C₂²×SD₁₆	—	2	2	no	—
176	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
177	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
178	#510	C₂²×C₃₁	1	32	yes	complemented
179	#509	C₂²×C₃₁	1	32	yes	complemented
180	#508	C₂²×C₃₁	1	32	yes	complemented
181	C₂×Q₃₂	C₂²×C₃₁	1	4	yes	complemented
182	C₂×SD₃₂	C₂²×C₃₁	1	8	yes	complemented
183	C₂×D₁₆	C₂²×C₃₁	1	4	yes	complemented
184	C₂×M₃₂	C₂²×C₃₁	1	4	yes	complemented
185	C₂×M₃₂	C₂²×C₃₁	1	8	yes	complemented
186	C₂²×C₁₆	C₂²×C₃₁	1	2	yes	complemented
187	C₂×C₃₁	—	2	4	no	—
188	C₂×C₃₁	—	2	2	no	—
189	C₂×C₃₁	—	8	8	no	—
190	C₂×C₃₁	#3414	1	2	yes	direct product factor
191	C₂×C₃₁	C₂³×D₈	1	1	yes	characteristic
192	C₂×#41	—	2	4	no	—
193	C₂×#41	—	2	4	no	—
194	C₂×#41	—	2	16	no	—
195	C₂×#41	—	4	2	no	—
196	C₂×#41	—	4	2	no	—
197	C₂×#41	—	4	8	no	—
198	C₂²×Q₈	—	2	2	no	—
199	C₂²×D₄	—	2	2	no	—
200	C₂²×D₄	—	4	2	no	—
201	C₂³×C₄	—	4	2	no	—
202	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
203	#135	—	2	8	no	—
204	#135	—	2	16	no	—
205	#135	—	2	8	no	—
206	#135	—	2	16	no	—
207	#135	C₂³×C₃₁	1	16	yes	—
208	#135	C₂³×C₃₁	1	16	yes	complemented
209	C₂×Q₁₆	—	2	2	no	—
210	C₂×Q₁₆	—	2	4	no	—
211	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
212	C₂×Q₁₆	C₂³×C₃₁	1	8	yes	complemented
213	C₂×SD₁₆	—	2	4	no	—
214	C₂×SD₁₆	—	2	4	no	—
215	C₂×SD₁₆	—	2	16	no	—
216	C₂×D₈	—	2	2	no	—
217	C₂×D₈	—	2	4	no	—
218	C₂×D₈	C₂³×C₃₁	1	4	yes	—
219	C₂×D₈	C₂³×C₃₁	1	8	yes	complemented
220	C₂²×C₈	D₄×C₃₁	1	2	yes	—
221	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
222	C₂²×C₈	D₄×C₃₁	1	4	yes	—
223	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
224	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
226	Q₃₂	C₂³×C₃₁	1	16	yes	complemented
227	SD₃₂	C₂³×C₃₁	1	32	yes	complemented
228	D₁₆	C₂³×C₃₁	1	16	yes	complemented
229	M₃₂	C₂³×C₃₁	1	16	yes	complemented
230	C₂×C₁₆	C₂³×C₃₁	1	4	yes	—
231	C₂×C₁₆	C₂³×C₃₁	1	8	yes	complemented
232	C₃₁	C₂×#3414	1	1	yes	characteristic, direct product factor, Sylow
233	C₂⁴	—	4	2	no	—
234	C₂⁴	D₈×C₃₁	1	1	yes	characteristic
235	#41	—	2	16	no	—
236	#41	—	2	16	no	—
237	#41	—	4	16	no	—
238	#41	—	4	8	no	—
239	#41	—	4	8	no	—
240	#41	—	4	16	no	—
241	C₂×Q₈	—	2	4	no	—
242	C₂×Q₈	—	2	8	no	—
243	C₂×Q₈	—	4	2	no	—
244	C₂×Q₈	—	4	4	no	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	—	2	8	no	—
247	C₂×D₄	—	4	4	no	—
248	C₂×D₄	—	4	4	no	—
249	C₂×D₄	—	4	16	no	—
250	C₂×D₄	—	4	2	no	—
251	C₂×D₄	—	4	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	4	no	—
254	C₂²×C₄	—	4	16	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	D₈×C₃₁	1	2	yes	—
257	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
258	C₂²×C₄	D₈×C₃₁	1	4	yes	—
259	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
260	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
262	Q₁₆	—	2	4	no	—
263	Q₁₆	—	2	8	no	—
264	Q₁₆	C₂⁴×C₃₁	1	8	yes	—
265	SD₁₆	—	2	16	no	—
266	SD₁₆	—	2	16	no	—
267	D₈	—	2	4	no	—
268	D₈	—	2	8	no	—
269	D₈	C₂⁴×C₃₁	1	8	yes	—
270	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
271	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
272	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
273	C₂×C₈	C₂×D₄×C₃₁	1	8	yes	—
274	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
275	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
276	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
277	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
278	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
279	C₁₆	C₂⁴×C₃₁	1	8	yes	—
280	C₂³	—	4	2	no	—
281	C₂³	—	4	8	no	—
282	C₂³	—	4	4	no	—
283	C₂³	—	8	8	no	—
284	C₂³	C₂×D₈×C₃₁	1	2	yes	—
285	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
286	C₂³	C₂×D₈×C₃₁	1	4	yes	—
287	Q₈	—	2	8	no	—
288	Q₈	—	4	8	no	—
289	Q₈	—	4	4	no	—
290	D₄	—	2	8	no	—
291	D₄	—	4	16	no	—
292	D₄	—	4	16	no	—
293	D₄	—	4	8	no	—
294	D₄	—	4	4	no	—
295	C₂×C₄	—	4	8	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	16	no	—
298	C₂×C₄	—	4	16	no	—
299	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
300	C₂×C₄	C₂×D₈×C₃₁	1	8	yes	—
301	C₂×C₄	C₂×D₈×C₃₁	1	4	yes	—
302	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
303	C₂×C₄	C₂×D₈×C₃₁	1	4	yes	—
304	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
305	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
306	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
307	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
308	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
309	C₈	C₂²×D₄×C₃₁	1	4	yes	—
310	C₈	C₂²×D₄×C₃₁	1	2	yes	—
311	C₈	C₂⁵×C₃₁	1	1	yes	characteristic
312	C₂²	—	2	4	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	8	no	—
316	C₂²	—	8	16	no	—
317	C₂²	—	8	8	no	—
318	C₂²	C₂²×D₈×C₃₁	1	4	yes	—
319	C₂²	C₂²×D₈×C₃₁	1	2	yes	—
320	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
321	C₄	—	4	8	no	—
322	C₄	C₂²×D₈×C₃₁	1	2	yes	—
323	C₄	C₂²×D₈×C₃₁	1	4	yes	—
324	C₄	C₂²×D₈×C₃₁	1	1	yes	characteristic
325	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
326	C₂	—	2	4	no	—
327	C₂	—	2	2	no	—
328	C₂	—	8	8	no	—
329	C₂	C₃₁×#3414	1	2	yes	direct product factor
330	C₂	C₂³×D₈×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₃₁
socle	C₂²×C₃₁	C₂²×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#135	C₂	semidirect
2. C₃₁×#3414	C₂	direct (N × H)
3. C₂×C₃₁×#510	C₂	semidirect
4. C₂×C₃₁×#509	C₂	semidirect
5. C₂×C₃₁×#508	C₂	semidirect
6. C₂²×C₃₁×M₃₂	C₂	semidirect
12. C₂×C₃₁×#135	C₂²	semidirect
13. C₂×C₃₁×#135	C₂²	semidirect
14. C₂²×Q₁₆×C₃₁	C₂²	semidirect
16. C₂²×D₈×C₃₁	C₂²	semidirect
18. C₃₁×#510	C₂²	semidirect
19. C₃₁×#509	C₂²	semidirect
20. C₃₁×#508	C₂²	semidirect
21. C₂×C₃₁×Q₃₂	C₂²	semidirect
22. C₂×C₃₁×SD₃₂	C₂²	semidirect
23. C₂×C₃₁×D₁₆	C₂²	semidirect
24. C₂×C₃₁×M₃₂	C₂²	semidirect
25. C₂×C₃₁×M₃₂	C₂²	semidirect
26. C₂²×C₁₆×C₃₁	C₂²	semidirect
43. C₃₁×#135	C₂³	semidirect
47. C₂×Q₁₆×C₃₁	C₂³	semidirect
54. C₂×D₈×C₃₁	C₂³	semidirect
61. C₃₁×Q₃₂	C₂³	semidirect
62. C₃₁×SD₃₂	C₂³	semidirect
63. C₃₁×D₁₆	C₂³	semidirect
64. C₃₁×M₃₂	C₂³	semidirect
66. C₂×C₁₆×C₃₁	C₂³	semidirect
114. C₂×#3414	C₃₁	direct (N × H)
147. C₂²×#135	C₂×C₃₁	semidirect
148. #3414	C₂×C₃₁	direct (N × H)
149. C₂×#510	C₂×C₃₁	semidirect
150. C₂×#509	C₂×C₃₁	semidirect
151. C₂×#508	C₂×C₃₁	semidirect
152. C₂²×M₃₂	C₂×C₃₁	semidirect
172. C₂×#135	C₂²×C₃₁	semidirect
173. C₂×#135	C₂²×C₃₁	semidirect
174. C₂²×Q₁₆	C₂²×C₃₁	semidirect
176. C₂²×D₈	C₂²×C₃₁	semidirect
178. #510	C₂²×C₃₁	semidirect
179. #509	C₂²×C₃₁	semidirect
180. #508	C₂²×C₃₁	semidirect
181. C₂×Q₃₂	C₂²×C₃₁	semidirect
182. C₂×SD₃₂	C₂²×C₃₁	semidirect
183. C₂×D₁₆	C₂²×C₃₁	semidirect
184. C₂×M₃₂	C₂²×C₃₁	semidirect
185. C₂×M₃₂	C₂²×C₃₁	semidirect
186. C₂²×C₁₆	C₂²×C₃₁	semidirect
190. C₂×C₃₁	#3414	direct (N × H)
208. #135	C₂³×C₃₁	semidirect
212. C₂×Q₁₆	C₂³×C₃₁	semidirect
219. C₂×D₈	C₂³×C₃₁	semidirect
226. Q₃₂	C₂³×C₃₁	semidirect
227. SD₃₂	C₂³×C₃₁	semidirect
228. D₁₆	C₂³×C₃₁	semidirect
229. M₃₂	C₂³×C₃₁	semidirect
231. C₂×C₁₆	C₂³×C₃₁	semidirect
232. C₃₁	C₂×#3414	direct (N × H)
329. C₂	C₃₁×#3414	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×#135	2
C₃₁×#3414	2
C₂×C₃₁×#510	2
C₂×C₃₁×#509	2
C₂×C₃₁×#508	2
C₂²×C₃₁×M₃₂	2
C₂×#3414	31

Subgroups — C2×C31×#3414 #21519390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3414 #21519390