Subgroups — C₂×C₃₁×#542 #16843387

Order 3968.

1132 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#542	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#126	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#124	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃₁×#124	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#123	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃₁×#121	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₃₁	C₂²	1	2	yes	—
15	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
16	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
17	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₃₁	C₂²	1	2	yes	—
19	C₃₁×C₄⋊Q₈	C₂²	1	8	yes	complemented
20	C₃₁×#126	C₂²	1	16	yes	complemented
21	C₃₁×#124	C₂²	1	8	yes	complemented
22	C₃₁×#124	C₂²	1	16	yes	complemented
23	C₃₁×#123	C₂²	1	16	yes	complemented
24	C₃₁×C₂²⋊Q₈	C₂²	1	16	yes	complemented
25	C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	complemented
26	C₃₁×#121	C₂²	1	8	yes	—
27	C₄×Q₈×C₃₁	C₂²	1	8	yes	complemented
28	C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
29	C₃₁×#117	C₂²	1	8	yes	complemented
30	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
35	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
36	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
37	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
41	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
42	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
43	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
44	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
47	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
48	C₂⁴×C₃₁	C₂³	1	2	yes	—
49	C₂×Q₈×C₃₁	—	2	4	no	—
50	C₂×Q₈×C₃₁	—	4	4	no	—
51	C₂×Q₈×C₃₁	C₂³	1	4	yes	—
52	C₂×Q₈×C₃₁	C₂³	1	8	yes	—
53	C₂×D₄×C₃₁	—	2	4	no	—
54	C₂×D₄×C₃₁	—	4	4	no	—
55	C₂×D₄×C₃₁	C₂³	1	4	yes	—
56	C₂×D₄×C₃₁	C₂³	1	8	yes	—
57	C₂²×C₄×C₃₁	—	2	4	no	—
58	C₂²×C₄×C₃₁	—	4	4	no	—
59	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
60	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
61	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
63	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
66	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
68	C₂²×C₄×C₃₁	C₂³	1	8	yes	—
69	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
70	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
71	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
72	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
73	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
74	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
75	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
76	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
77	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
78	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
79	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
80	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
81	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
82	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
83	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
84	C₄²×C₃₁	C₂³	1	4	yes	—
85	C₄²×C₃₁	C₂³	1	4	yes	—
86	C₄²×C₃₁	C₂³	1	8	yes	—
87	C₂³×C₃₁	—	2	2	no	—
88	C₂³×C₃₁	—	2	4	no	—
89	C₂³×C₃₁	—	2	4	no	—
90	C₂³×C₃₁	—	2	2	no	—
91	C₂³×C₃₁	—	2	2	no	—
92	C₂³×C₃₁	—	2	4	no	—
93	C₂³×C₃₁	C₂⁴	1	2	yes	—
94	C₂³×C₃₁	C₂⁴	1	4	yes	—
95	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
96	Q₈×C₃₁	—	2	8	no	—
97	Q₈×C₃₁	—	4	8	no	—
98	D₄×C₃₁	—	2	8	no	—
99	D₄×C₃₁	—	4	8	no	—
100	C₂×C₄×C₃₁	—	2	2	no	—
101	C₂×C₄×C₃₁	—	2	4	no	—
102	C₂×C₄×C₃₁	—	2	2	no	—
103	C₂×C₄×C₃₁	—	2	4	no	—
104	C₂×C₄×C₃₁	—	2	4	no	—
105	C₂×C₄×C₃₁	—	2	2	no	—
106	C₂×C₄×C₃₁	—	2	2	no	—
107	C₂×C₄×C₃₁	—	2	2	no	—
108	C₂×C₄×C₃₁	—	2	8	no	—
109	C₂×C₄×C₃₁	—	4	8	no	—
110	C₂×C₄×C₃₁	#41	1	4	yes	—
111	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
112	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
113	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
114	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
115	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
116	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
117	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
118	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
119	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
120	C₂×#542	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
121	C₂²×C₃₁	—	2	2	no	—
122	C₂²×C₃₁	—	2	4	no	—
123	C₂²×C₃₁	—	2	4	no	—
124	C₂²×C₃₁	—	2	2	no	—
125	C₂²×C₃₁	—	2	2	no	—
126	C₂²×C₃₁	—	2	4	no	—
127	C₂²×C₃₁	—	4	4	no	—
128	C₂²×C₃₁	—	4	8	no	—
129	C₂²×C₃₁	C₂×#41	1	2	yes	—
130	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
131	C₂²×C₃₁	2₋¹⁺⁴	1	2	yes	—
132	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
133	C₄×C₃₁	—	2	2	no	—
134	C₄×C₃₁	—	2	4	no	—
135	C₄×C₃₁	—	2	2	no	—
136	C₄×C₃₁	—	2	4	no	—
137	C₄×C₃₁	—	2	4	no	—
138	C₄×C₃₁	—	2	2	no	—
139	C₄×C₃₁	—	2	2	no	—
140	C₄×C₃₁	—	2	2	no	—
141	C₄×C₃₁	C₂×#41	1	4	yes	—
142	#542	C₂×C₃₁	1	16	yes	direct product factor
143	C₂×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
144	C₂×#126	C₂×C₃₁	1	2	yes	complemented
145	C₂×#124	C₂×C₃₁	1	1	yes	characteristic, complemented
146	C₂×#124	C₂×C₃₁	1	2	yes	complemented
147	C₂×#123	C₂×C₃₁	1	2	yes	complemented
148	C₂×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	complemented
149	C₂×C₂²⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
150	C₂×#121	C₂×C₃₁	1	1	yes	characteristic
151	C₂×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
152	C₂×C₄×D₄	C₂×C₃₁	1	1	yes	characteristic, complemented
153	C₂×#117	C₂×C₃₁	1	1	yes	characteristic, complemented
154	C₂×C₃₁	—	4	2	no	—
155	C₂×C₃₁	—	4	4	no	—
156	C₂×C₃₁	#542	1	4	yes	direct product factor
157	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
158	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
160	C₂²×Q₈	C₂²×C₃₁	1	1	yes	characteristic
161	C₂²×Q₈	C₂²×C₃₁	1	2	yes	—
162	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
163	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
164	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic
165	C₂³×C₄	C₂²×C₃₁	1	2	yes	—
166	C₄⋊Q₈	C₂²×C₃₁	1	8	yes	complemented
167	#126	C₂²×C₃₁	1	16	yes	complemented
168	#124	C₂²×C₃₁	1	8	yes	complemented
169	#124	C₂²×C₃₁	1	16	yes	complemented
170	#123	C₂²×C₃₁	1	16	yes	complemented
171	C₂²⋊Q₈	C₂²×C₃₁	1	16	yes	complemented
172	C₂²⋊Q₈	C₂²×C₃₁	1	8	yes	complemented
173	#121	C₂²×C₃₁	1	8	yes	—
174	C₄×Q₈	C₂²×C₃₁	1	8	yes	complemented
175	C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
176	#117	C₂²×C₃₁	1	8	yes	complemented
177	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
178	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
179	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
180	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
181	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
182	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
183	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
184	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
185	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
186	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
187	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
188	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
189	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
190	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
191	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
192	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic
193	C₂×C₄²	C₂²×C₃₁	1	2	yes	—
194	C₃₁	C₂×#542	1	1	yes	characteristic, direct product factor, Sylow
195	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
196	C₂⁴	C₂³×C₃₁	1	2	yes	—
197	C₂×Q₈	—	2	4	no	—
198	C₂×Q₈	—	4	4	no	—
199	C₂×Q₈	C₂³×C₃₁	1	4	yes	—
200	C₂×Q₈	C₂³×C₃₁	1	8	yes	—
201	C₂×D₄	—	2	4	no	—
202	C₂×D₄	—	4	4	no	—
203	C₂×D₄	C₂³×C₃₁	1	4	yes	—
204	C₂×D₄	C₂³×C₃₁	1	8	yes	—
205	C₂²×C₄	—	2	4	no	—
206	C₂²×C₄	—	4	4	no	—
207	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
208	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
209	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
210	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
211	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
213	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
214	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
215	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
216	C₂²×C₄	C₂³×C₃₁	1	8	yes	—
217	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
218	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
219	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
220	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
221	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
222	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
223	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
224	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
225	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
226	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
227	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
228	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
229	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
230	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
231	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
232	C₄²	C₂³×C₃₁	1	4	yes	—
233	C₄²	C₂³×C₃₁	1	4	yes	—
234	C₄²	C₂³×C₃₁	1	8	yes	—
235	C₂³	—	2	2	no	—
236	C₂³	—	2	4	no	—
237	C₂³	—	2	4	no	—
238	C₂³	—	2	2	no	—
239	C₂³	—	2	2	no	—
240	C₂³	—	2	4	no	—
241	C₂³	C₂⁴×C₃₁	1	2	yes	—
242	C₂³	C₂⁴×C₃₁	1	4	yes	—
243	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
244	Q₈	—	2	8	no	—
245	Q₈	—	4	8	no	—
246	D₄	—	2	8	no	—
247	D₄	—	4	8	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	4	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	4	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	2	2	no	—
256	C₂×C₄	—	2	8	no	—
257	C₂×C₄	—	4	8	no	—
258	C₂×C₄	#41×C₃₁	1	4	yes	—
259	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
260	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
261	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
262	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
263	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
264	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
265	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
266	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
267	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
268	C₂²	—	2	2	no	—
269	C₂²	—	2	4	no	—
270	C₂²	—	2	4	no	—
271	C₂²	—	2	2	no	—
272	C₂²	—	2	2	no	—
273	C₂²	—	2	4	no	—
274	C₂²	—	4	4	no	—
275	C₂²	—	4	8	no	—
276	C₂²	C₂×#41×C₃₁	1	2	yes	—
277	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
278	C₂²	C₃₁×2₋¹⁺⁴	1	2	yes	—
279	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
280	C₄	—	2	2	no	—
281	C₄	—	2	4	no	—
282	C₄	—	2	2	no	—
283	C₄	—	2	4	no	—
284	C₄	—	2	4	no	—
285	C₄	—	2	2	no	—
286	C₄	—	2	2	no	—
287	C₄	—	2	2	no	—
288	C₄	C₂×#41×C₃₁	1	4	yes	—
289	C₂	—	4	2	no	—
290	C₂	—	4	4	no	—
291	C₂	C₃₁×#542	1	4	yes	direct product factor
292	C₂	C₂²×#41×C₃₁	1	1	yes	characteristic
293	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
294	C₂	C₂×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
prime radical	C₂×C₃₁×#121	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#542	C₂	direct (N × H)
2. C₂×C₃₁×C₄⋊Q₈	C₂	semidirect
3. C₂×C₃₁×#126	C₂	semidirect
4. C₂×C₃₁×#124	C₂	semidirect
5. C₂×C₃₁×#124	C₂	semidirect
6. C₂×C₃₁×#123	C₂	semidirect
7. C₂×C₃₁×C₂²⋊Q₈	C₂	semidirect
8. C₂×C₃₁×C₂²⋊Q₈	C₂	semidirect
10. C₂×C₄×Q₈×C₃₁	C₂	semidirect
11. C₂×C₄×D₄×C₃₁	C₂	semidirect
12. C₂×C₃₁×#117	C₂	semidirect
19. C₃₁×C₄⋊Q₈	C₂²	semidirect
20. C₃₁×#126	C₂²	semidirect
21. C₃₁×#124	C₂²	semidirect
22. C₃₁×#124	C₂²	semidirect
23. C₃₁×#123	C₂²	semidirect
24. C₃₁×C₂²⋊Q₈	C₂²	semidirect
25. C₃₁×C₂²⋊Q₈	C₂²	semidirect
27. C₄×Q₈×C₃₁	C₂²	semidirect
28. C₄×D₄×C₃₁	C₂²	semidirect
29. C₃₁×#117	C₂²	semidirect
120. C₂×#542	C₃₁	direct (N × H)
142. #542	C₂×C₃₁	direct (N × H)
143. C₂×C₄⋊Q₈	C₂×C₃₁	semidirect
144. C₂×#126	C₂×C₃₁	semidirect
145. C₂×#124	C₂×C₃₁	semidirect
146. C₂×#124	C₂×C₃₁	semidirect
147. C₂×#123	C₂×C₃₁	semidirect
148. C₂×C₂²⋊Q₈	C₂×C₃₁	semidirect
149. C₂×C₂²⋊Q₈	C₂×C₃₁	semidirect
151. C₂×C₄×Q₈	C₂×C₃₁	semidirect
152. C₂×C₄×D₄	C₂×C₃₁	semidirect
153. C₂×#117	C₂×C₃₁	semidirect
156. C₂×C₃₁	#542	direct (N × H)
166. C₄⋊Q₈	C₂²×C₃₁	semidirect
167. #126	C₂²×C₃₁	semidirect
168. #124	C₂²×C₃₁	semidirect
169. #124	C₂²×C₃₁	semidirect
170. #123	C₂²×C₃₁	semidirect
171. C₂²⋊Q₈	C₂²×C₃₁	semidirect
172. C₂²⋊Q₈	C₂²×C₃₁	semidirect
174. C₄×Q₈	C₂²×C₃₁	semidirect
175. C₄×D₄	C₂²×C₃₁	semidirect
176. #117	C₂²×C₃₁	semidirect
194. C₃₁	C₂×#542	direct (N × H)
291. C₂	C₃₁×#542	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁×#542	2
C₂×C₃₁×C₄⋊Q₈	2
C₂×C₃₁×#126	2
C₂×C₃₁×#124	2
C₂×C₃₁×#123	2
C₂×C₃₁×C₂²⋊Q₈	2
C₂×C₃₁×#121	2
C₂×C₄×Q₈×C₃₁	2
C₂×C₄×D₄×C₃₁	2
C₂×C₃₁×#117	2
C₂×#542	31

Subgroups — C2×C31×#542 #16843387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#542 #16843387