Subgroups — C₂×C₃₁×#2502 #21491524

Order 7936.

3094 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#2502	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#398	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#391	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#385	C₂	1	4	yes	maximal
7	C₂×C₃₁×#384	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁×C₂²⋊Q₈	—	2	8	no	—
13	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	—
14	C₂²×C₄⋊C₄×C₃₁	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₃₁	C₂²	1	8	yes	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₃₁	C₂²	1	8	yes	—
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
23	C₂²×C₄²×C₃₁	C₂²	1	2	yes	—
24	C₃₁×#398	C₂²	1	32	yes	complemented
25	C₃₁×#391	C₂²	1	16	yes	complemented
26	C₃₁×#385	C₂²	1	32	yes	—
27	C₃₁×#384	C₂²	1	16	yes	complemented
28	C₄×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	—
29	C₂×C₃₁×#95	C₂²	1	2	yes	—
30	C₂×C₃₁×#95	C₂²	1	8	yes	—
31	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
32	C₂²×Q₈×C₃₁	—	2	4	no	—
33	C₂²×Q₈×C₃₁	—	2	8	no	—
34	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
35	C₂³×C₄×C₃₁	—	2	8	no	—
36	C₂³×C₄×C₃₁	—	2	8	no	—
37	C₂³×C₄×C₃₁	—	4	8	no	—
38	C₂³×C₄×C₃₁	D₄	1	8	yes	—
39	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
41	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
42	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
43	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	8	yes	—
46	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
47	C₃₁×C₂²⋊Q₈	—	2	32	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	32	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
52	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
53	C₂×C₄⋊C₄×C₃₁	—	4	16	no	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	32	yes	—
59	C₂×C₂²⋊C₄×C₃₁	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₃₁	Q₈	1	16	yes	complemented
61	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
62	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
63	C₂×C₄²×C₃₁	—	2	8	no	—
64	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
65	C₃₁×#95	C₂³	1	8	yes	—
66	C₃₁×#95	C₂³	1	32	yes	—
67	C₂⁴×C₃₁	—	2	4	no	—
68	C₂⁴×C₃₁	—	2	4	no	—
69	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
70	C₂⁴×C₃₁	C₂×Q₈	1	8	yes	—
71	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
72	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₃₁	—	2	8	no	—
74	C₂×Q₈×C₃₁	—	2	16	no	—
75	C₂×Q₈×C₃₁	—	4	16	no	—
76	C₂²×C₄×C₃₁	—	2	8	no	—
77	C₂²×C₄×C₃₁	—	2	4	no	—
78	C₂²×C₄×C₃₁	—	2	8	no	—
79	C₂²×C₄×C₃₁	—	2	32	no	—
80	C₂²×C₄×C₃₁	—	2	16	no	—
81	C₂²×C₄×C₃₁	—	2	4	no	—
82	C₂²×C₄×C₃₁	—	2	4	no	—
83	C₂²×C₄×C₃₁	—	2	16	no	—
84	C₂²×C₄×C₃₁	—	2	8	no	—
85	C₂²×C₄×C₃₁	—	2	8	no	—
86	C₂²×C₄×C₃₁	—	2	8	no	—
87	C₂²×C₄×C₃₁	—	2	16	no	—
88	C₂²×C₄×C₃₁	—	4	16	no	—
89	C₂²×C₄×C₃₁	—	4	32	no	—
90	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	16	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₃₁	C₂×Q₈	1	16	yes	—
94	C₂²×C₄×C₃₁	#41	1	8	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
98	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
100	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
101	C₄⋊C₄×C₃₁	—	2	16	no	—
102	C₄⋊C₄×C₃₁	—	2	16	no	—
103	C₄⋊C₄×C₃₁	—	2	8	no	—
104	C₄⋊C₄×C₃₁	—	2	16	no	—
105	C₄⋊C₄×C₃₁	—	4	32	no	—
106	C₂²⋊C₄×C₃₁	—	2	16	no	—
107	C₂²⋊C₄×C₃₁	C₂×Q₈	1	32	yes	complemented
108	C₄²×C₃₁	—	2	16	no	—
109	C₂×#2502	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₃₁	—	2	8	no	—
111	C₂³×C₃₁	—	2	8	no	—
112	C₂³×C₃₁	—	2	32	no	—
113	C₂³×C₃₁	—	2	4	no	—
114	C₂³×C₃₁	—	2	4	no	—
115	C₂³×C₃₁	C₄⋊Q₈	1	16	yes	—
116	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
117	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
118	C₂³×C₃₁	C₂²×Q₈	1	8	yes	—
119	C₂³×C₃₁	C₂²×Q₈	1	4	yes	—
120	C₂³×C₃₁	C₂×#41	1	4	yes	—
121	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
122	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
123	Q₈×C₃₁	—	4	16	no	—
124	C₂×C₄×C₃₁	—	2	8	no	—
125	C₂×C₄×C₃₁	—	2	32	no	—
126	C₂×C₄×C₃₁	—	2	8	no	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	2	8	no	—
129	C₂×C₄×C₃₁	—	2	32	no	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	—	2	4	no	—
132	C₂×C₄×C₃₁	—	2	8	no	—
133	C₂×C₄×C₃₁	—	2	8	no	—
134	C₂×C₄×C₃₁	—	2	8	no	—
135	C₂×C₄×C₃₁	—	2	16	no	—
136	C₂×C₄×C₃₁	—	4	32	no	—
137	C₂×C₄×C₃₁	—	4	8	no	—
138	C₂×C₄×C₃₁	—	4	8	no	—
139	C₂×C₄×C₃₁	—	4	16	no	—
140	C₂×C₄×C₃₁	#123	1	16	yes	—
141	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
142	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
143	C₂×C₄×C₃₁	C₂²×Q₈	1	16	yes	—
144	C₂×C₄×C₃₁	C₂×#41	1	8	yes	—
145	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
146	C₂³×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic
147	#2502	C₂×C₃₁	1	16	yes	direct product factor
148	C₂×#398	C₂×C₃₁	1	4	yes	complemented
149	C₂×#391	C₂×C₃₁	1	2	yes	complemented
150	C₂×#385	C₂×C₃₁	1	4	yes	—
151	C₂×#384	C₂×C₃₁	1	2	yes	complemented
152	C₂×C₄×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic
153	C₂²×C₃₁	—	2	4	no	—
154	C₂²×C₃₁	—	2	4	no	—
155	C₂²×C₃₁	—	2	16	no	—
156	C₂²×C₃₁	—	2	32	no	—
157	C₂²×C₃₁	C₂×#123	1	4	yes	—
158	C₂²×C₃₁	C₂×C₄⋊Q₈	1	8	yes	—
159	C₂²×C₃₁	C₂×C₄⋊Q₈	1	4	yes	—
160	C₂²×C₃₁	#535	1	4	yes	—
161	C₂²×C₃₁	#554	1	16	yes	—
162	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
163	C₂²×C₃₁	C₂³×Q₈	1	2	yes	—
164	C₂²×C₃₁	C₂²×#41	1	2	yes	—
165	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
166	C₄×C₃₁	—	2	4	no	—
167	C₄×C₃₁	—	2	16	no	—
168	C₄×C₃₁	—	4	4	no	—
169	C₄×C₃₁	—	4	4	no	—
170	C₄×C₃₁	—	4	8	no	—
171	C₄×C₃₁	C₂×#123	1	8	yes	—
172	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
173	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
174	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	—
175	C₂×C₂²⋊Q₈	—	2	8	no	—
176	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	8	yes	—
177	C₂²×C₄⋊C₄	—	2	8	no	—
178	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
179	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
180	C₂²×C₄⋊C₄	C₂²×C₃₁	1	8	yes	—
181	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
182	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
183	C₂²×C₄⋊C₄	C₂²×C₃₁	1	8	yes	—
184	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
185	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
186	C₂²×C₄²	C₂²×C₃₁	1	2	yes	—
187	#398	C₂²×C₃₁	1	32	yes	complemented
188	#391	C₂²×C₃₁	1	16	yes	complemented
189	#385	C₂²×C₃₁	1	32	yes	—
190	#384	C₂²×C₃₁	1	16	yes	complemented
191	C₄×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	—
192	C₂×#95	C₂²×C₃₁	1	2	yes	—
193	C₂×#95	C₂²×C₃₁	1	8	yes	—
194	C₂×C₃₁	—	2	8	no	—
195	C₂×C₃₁	#2502	1	8	yes	direct product factor
196	C₂×C₃₁	C₂²×#123	1	1	yes	characteristic
197	C₂×C₃₁	C₂²×C₄⋊Q₈	1	1	yes	characteristic
198	C₂×C₃₁	C₂×#535	1	1	yes	characteristic
199	C₂×C₃₁	C₂×#554	1	4	yes	—
200	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	—	2	8	no	—
203	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
204	C₂³×C₄	—	2	8	no	—
205	C₂³×C₄	—	2	8	no	—
206	C₂³×C₄	—	4	8	no	—
207	C₂³×C₄	D₄×C₃₁	1	8	yes	—
208	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
209	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
210	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
211	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
213	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
214	C₂³×C₄	C₂³×C₃₁	1	8	yes	—
215	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
216	C₂²⋊Q₈	—	2	32	no	—
217	C₂×C₄⋊C₄	—	2	8	no	—
218	C₂×C₄⋊C₄	—	2	32	no	—
219	C₂×C₄⋊C₄	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	2	8	no	—
222	C₂×C₄⋊C₄	—	4	16	no	—
223	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
224	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
225	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
226	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
227	C₂×C₄⋊C₄	C₂³×C₃₁	1	32	yes	—
228	C₂×C₂²⋊C₄	—	2	8	no	—
229	C₂×C₂²⋊C₄	Q₈×C₃₁	1	16	yes	complemented
230	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
231	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
232	C₂×C₄²	—	2	8	no	—
233	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
234	#95	C₂³×C₃₁	1	8	yes	—
235	#95	C₂³×C₃₁	1	32	yes	—
236	C₃₁	C₂×#2502	1	1	yes	characteristic, direct product factor, Sylow
237	C₂⁴	—	2	4	no	—
238	C₂⁴	—	2	4	no	—
239	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
240	C₂⁴	C₂×Q₈×C₃₁	1	8	yes	—
241	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
242	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
243	C₂×Q₈	—	2	8	no	—
244	C₂×Q₈	—	2	16	no	—
245	C₂×Q₈	—	4	16	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	32	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	16	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	8	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	16	no	—
258	C₂²×C₄	—	4	16	no	—
259	C₂²×C₄	—	4	32	no	—
260	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
261	C₂²×C₄	C₂×D₄×C₃₁	1	16	yes	—
262	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
263	C₂²×C₄	C₂×Q₈×C₃₁	1	16	yes	—
264	C₂²×C₄	#41×C₃₁	1	8	yes	—
265	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
266	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
267	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
268	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
271	C₄⋊C₄	—	2	16	no	—
272	C₄⋊C₄	—	2	16	no	—
273	C₄⋊C₄	—	2	8	no	—
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	4	32	no	—
276	C₂²⋊C₄	—	2	16	no	—
277	C₂²⋊C₄	C₂×Q₈×C₃₁	1	32	yes	complemented
278	C₄²	—	2	16	no	—
279	C₂³	—	2	8	no	—
280	C₂³	—	2	8	no	—
281	C₂³	—	2	32	no	—
282	C₂³	—	2	4	no	—
283	C₂³	—	2	4	no	—
284	C₂³	C₃₁×C₄⋊Q₈	1	16	yes	—
285	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
286	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
287	C₂³	C₂²×Q₈×C₃₁	1	8	yes	—
288	C₂³	C₂²×Q₈×C₃₁	1	4	yes	—
289	C₂³	C₂×#41×C₃₁	1	4	yes	—
290	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
291	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
292	Q₈	—	4	16	no	—
293	C₂×C₄	—	2	8	no	—
294	C₂×C₄	—	2	32	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	8	no	—
298	C₂×C₄	—	2	32	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	8	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	16	no	—
305	C₂×C₄	—	4	32	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	—	4	8	no	—
308	C₂×C₄	—	4	16	no	—
309	C₂×C₄	C₃₁×#123	1	16	yes	—
310	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
311	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
312	C₂×C₄	C₂²×Q₈×C₃₁	1	16	yes	—
313	C₂×C₄	C₂×#41×C₃₁	1	8	yes	—
314	C₂²	—	2	4	no	—
315	C₂²	—	2	4	no	—
316	C₂²	—	2	16	no	—
317	C₂²	—	2	32	no	—
318	C₂²	C₂×C₃₁×#123	1	4	yes	—
319	C₂²	C₂×C₃₁×C₄⋊Q₈	1	8	yes	—
320	C₂²	C₂×C₃₁×C₄⋊Q₈	1	4	yes	—
321	C₂²	C₃₁×#535	1	4	yes	—
322	C₂²	C₃₁×#554	1	16	yes	—
323	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
324	C₂²	C₂³×Q₈×C₃₁	1	2	yes	—
325	C₂²	C₂²×#41×C₃₁	1	2	yes	—
326	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
327	C₄	—	2	4	no	—
328	C₄	—	2	16	no	—
329	C₄	—	4	4	no	—
330	C₄	—	4	8	no	—
331	C₄	—	4	4	no	—
332	C₄	C₂×C₃₁×#123	1	8	yes	—
333	C₂	—	2	8	no	—
334	C₂	C₃₁×#2502	1	8	yes	direct product factor
335	C₂	C₂²×C₃₁×#123	1	1	yes	characteristic
336	C₂	C₂²×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
337	C₂	C₂×C₃₁×#535	1	1	yes	characteristic
338	C₂	C₂×C₃₁×#554	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#2502	C₂	direct (N × H)
4. C₂×C₃₁×#398	C₂	semidirect
5. C₂×C₃₁×#391	C₂	semidirect
7. C₂×C₃₁×#384	C₂	semidirect
24. C₃₁×#398	C₂²	semidirect
25. C₃₁×#391	C₂²	semidirect
27. C₃₁×#384	C₂²	semidirect
60. C₂×C₂²⋊C₄×C₃₁	Q₈	semidirect
107. C₂²⋊C₄×C₃₁	C₂×Q₈	semidirect
109. C₂×#2502	C₃₁	direct (N × H)
147. #2502	C₂×C₃₁	direct (N × H)
148. C₂×#398	C₂×C₃₁	semidirect
149. C₂×#391	C₂×C₃₁	semidirect
151. C₂×#384	C₂×C₃₁	semidirect
187. #398	C₂²×C₃₁	semidirect
188. #391	C₂²×C₃₁	semidirect
190. #384	C₂²×C₃₁	semidirect
195. C₂×C₃₁	#2502	direct (N × H)
229. C₂×C₂²⋊C₄	Q₈×C₃₁	semidirect
236. C₃₁	C₂×#2502	direct (N × H)
277. C₂²⋊C₄	C₂×Q₈×C₃₁	semidirect
334. C₂	C₃₁×#2502	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×C₂²⋊Q₈	2
C₂³×C₄⋊C₄×C₃₁	2
C₃₁×#2502	2
C₂×C₃₁×#398	2
C₂×C₃₁×#391	2
C₂×C₃₁×#385	2
C₂×C₃₁×#384	2
C₂×C₄×C₂²⋊C₄×C₃₁	2
C₂×#2502	31

Subgroups — C2×C31×#2502 #21491524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2502 #21491524