Subgroups — C₂×C₃₁×#3189 #21517490

Order 7936.

2354 conjugacy classes of subgroups.

The subgroup lattice has 346 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	2	yes	maximal
2	C₃₁×#3189	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#484	C₂	1	4	yes	maximal, complemented
4	C₂×C₃₁×#467	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#451	C₂	1	4	yes	maximal, complemented
6	C₂²×C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
10	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
11	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
12	C₂×C₃₁×C₂²⋊Q₈	—	2	8	no	—
13	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
14	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
15	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	16	yes	—
16	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₃₁	—	2	2	no	—
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₃₁	—	2	2	no	—
20	C₃₁×#484	C₂²	1	32	yes	complemented
21	C₃₁×#467	C₂²	1	32	yes	complemented
22	C₃₁×#451	C₂²	1	32	yes	complemented
23	C₂×C₃₁×#107	C₂²	1	4	yes	complemented
24	C₂×C₃₁×#103	C₂²	1	8	yes	complemented
25	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
26	C₂×C₃₁×C₂²⋊C₈	C₂²	1	8	yes	—
27	C₂⁵×C₃₁	D₄	1	1	yes	characteristic
28	C₂²×Q₈×C₃₁	—	2	4	no	—
29	C₂²×Q₈×C₃₁	—	2	2	no	—
30	C₂²×Q₈×C₃₁	—	4	8	no	—
31	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
32	C₂²×Q₈×C₃₁	C₂³	1	8	yes	—
33	C₂³×C₄×C₃₁	—	2	2	no	—
34	C₂³×C₄×C₃₁	—	2	2	no	—
35	C₂³×C₄×C₃₁	—	4	4	no	—
36	C₂³×C₄×C₃₁	D₄	1	2	yes	—
37	C₂³×C₄×C₃₁	D₄	1	4	yes	—
38	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
40	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
42	C₂×Q₁₆×C₃₁	—	4	8	no	—
43	C₂×Q₁₆×C₃₁	C₂³	1	16	yes	complemented
44	C₂²×C₈×C₃₁	—	4	4	no	—
45	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
46	C₂²×C₈×C₃₁	C₂³	1	8	yes	—
47	C₃₁×C₂²⋊Q₈	—	2	8	no	—
48	C₃₁×C₂²⋊Q₈	—	2	8	no	—
49	C₃₁×C₂²⋊Q₈	—	2	16	no	—
50	C₃₁×C₂²⋊Q₈	—	2	16	no	—
51	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
52	C₃₁×C₂²⋊Q₈	C₂³	1	16	yes	—
53	C₂×C₄⋊C₄×C₃₁	—	2	16	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
55	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
56	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
57	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
58	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
61	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
63	C₃₁×#107	C₂³	1	16	yes	complemented
64	C₃₁×#103	C₂³	1	32	yes	complemented
65	C₃₁×C₂²⋊C₈	C₂³	1	16	yes	—
66	C₂⁴×C₃₁	—	4	2	no	—
67	C₂⁴×C₃₁	—	4	2	no	—
68	C₂⁴×C₃₁	Q₁₆	1	8	yes	complemented
69	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
70	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
71	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
72	C₂×Q₈×C₃₁	—	2	8	no	—
73	C₂×Q₈×C₃₁	—	2	4	no	—
74	C₂×Q₈×C₃₁	—	2	16	no	—
75	C₂×Q₈×C₃₁	—	4	16	no	—
76	C₂×Q₈×C₃₁	—	4	8	no	—
77	C₂×Q₈×C₃₁	—	4	16	no	—
78	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
79	C₂²×C₄×C₃₁	—	2	4	no	—
80	C₂²×C₄×C₃₁	—	2	8	no	—
81	C₂²×C₄×C₃₁	—	2	8	no	—
82	C₂²×C₄×C₃₁	—	2	8	no	—
83	C₂²×C₄×C₃₁	—	2	4	no	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	4	8	no	—
86	C₂²×C₄×C₃₁	—	4	8	no	—
87	C₂²×C₄×C₃₁	—	4	4	no	—
88	C₂²×C₄×C₃₁	—	4	2	no	—
89	C₂²×C₄×C₃₁	—	4	8	no	—
90	C₂²×C₄×C₃₁	—	4	8	no	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
98	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
100	Q₁₆×C₃₁	—	4	16	no	—
101	C₂×C₈×C₃₁	—	2	8	no	—
102	C₂×C₈×C₃₁	—	4	8	no	—
103	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
104	C₄⋊C₄×C₃₁	—	2	16	no	—
105	C₄⋊C₄×C₃₁	—	2	16	no	—
106	C₄⋊C₄×C₃₁	—	2	8	no	—
107	C₄⋊C₄×C₃₁	—	2	4	no	—
108	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
109	C₂²⋊C₄×C₃₁	—	2	16	no	—
110	C₂²⋊C₄×C₃₁	—	2	16	no	—
111	C₂×#3189	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₃₁	—	2	4	no	—
113	C₂³×C₃₁	—	2	2	no	—
114	C₂³×C₃₁	—	2	4	no	—
115	C₂³×C₃₁	—	2	2	no	—
116	C₂³×C₃₁	—	4	4	no	—
117	C₂³×C₃₁	—	4	16	no	—
118	C₂³×C₃₁	—	4	4	no	—
119	C₂³×C₃₁	C₂×Q₁₆	1	4	yes	—
120	C₂³×C₃₁	C₂×Q₁₆	1	8	yes	—
121	C₂³×C₃₁	C₂×Q₁₆	1	16	yes	complemented
122	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
123	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
124	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₃₁	—	2	16	no	—
126	Q₈×C₃₁	—	4	16	no	—
127	Q₈×C₃₁	—	4	8	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	4	no	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	—	2	8	no	—
132	C₂×C₄×C₃₁	—	2	4	no	—
133	C₂×C₄×C₃₁	—	2	8	no	—
134	C₂×C₄×C₃₁	—	2	8	no	—
135	C₂×C₄×C₃₁	—	2	8	no	—
136	C₂×C₄×C₃₁	—	4	8	no	—
137	C₂×C₄×C₃₁	—	4	4	no	—
138	C₂×C₄×C₃₁	—	4	16	no	—
139	C₂×C₄×C₃₁	—	4	16	no	—
140	C₂×C₄×C₃₁	—	4	8	no	—
141	C₂×C₄×C₃₁	—	4	8	no	—
142	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
144	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
145	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
146	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
147	C₈×C₃₁	—	2	8	no	—
148	C₂²×C₂²⋊Q₈	C₂×C₃₁	1	2	yes	—
149	#3189	C₂×C₃₁	1	16	yes	direct product factor
150	C₂×#484	C₂×C₃₁	1	4	yes	complemented
151	C₂×#467	C₂×C₃₁	1	4	yes	complemented
152	C₂×#451	C₂×C₃₁	1	4	yes	complemented
153	C₂²×C₂²⋊C₈	C₂×C₃₁	1	1	yes	characteristic
154	C₂²×C₃₁	—	2	16	no	—
155	C₂²×C₃₁	—	2	8	no	—
156	C₂²×C₃₁	—	2	4	no	—
157	C₂²×C₃₁	—	2	2	no	—
158	C₂²×C₃₁	—	2	4	no	—
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	4	16	no	—
161	C₂²×C₃₁	#534	1	2	yes	—
162	C₂²×C₃₁	C₂²×Q₁₆	1	4	yes	—
163	C₂²×C₃₁	C₂²×Q₁₆	1	8	yes	—
164	C₂²×C₃₁	C₂²×Q₁₆	1	2	yes	—
165	C₂²×C₃₁	#575	1	2	yes	—
166	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
167	C₄×C₃₁	—	2	2	no	—
168	C₄×C₃₁	—	2	4	no	—
169	C₄×C₃₁	—	4	8	no	—
170	C₄×C₃₁	—	4	8	no	—
171	C₄×C₃₁	#534	1	2	yes	—
172	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
173	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
174	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
175	C₂²×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
176	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
177	C₂×C₂²⋊Q₈	—	2	2	no	—
178	C₂×C₂²⋊Q₈	—	2	2	no	—
179	C₂×C₂²⋊Q₈	—	2	8	no	—
180	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
181	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	16	yes	—
182	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
183	C₂²×C₄⋊C₄	—	2	2	no	—
184	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
185	C₂²×C₂²⋊C₄	—	2	2	no	—
186	#484	C₂²×C₃₁	1	32	yes	complemented
187	#467	C₂²×C₃₁	1	32	yes	complemented
188	#451	C₂²×C₃₁	1	32	yes	complemented
189	C₂×#107	C₂²×C₃₁	1	4	yes	complemented
190	C₂×#103	C₂²×C₃₁	1	8	yes	complemented
191	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
192	C₂×C₂²⋊C₈	C₂²×C₃₁	1	8	yes	—
193	C₂×C₃₁	—	2	8	no	—
194	C₂×C₃₁	—	2	4	no	—
195	C₂×C₃₁	#3189	1	4	yes	direct product factor
196	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
197	C₂×C₃₁	C₂³×Q₁₆	1	1	yes	characteristic
198	C₂×C₃₁	C₂×#575	1	1	yes	characteristic
199	C₂⁵	D₄×C₃₁	1	1	yes	characteristic
200	C₂²×Q₈	—	2	2	no	—
201	C₂²×Q₈	—	2	4	no	—
202	C₂²×Q₈	—	4	8	no	—
203	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
204	C₂²×Q₈	C₂³×C₃₁	1	8	yes	—
205	C₂³×C₄	—	2	2	no	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	—	4	4	no	—
208	C₂³×C₄	D₄×C₃₁	1	2	yes	—
209	C₂³×C₄	D₄×C₃₁	1	4	yes	—
210	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
212	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
214	C₂×Q₁₆	—	4	8	no	—
215	C₂×Q₁₆	C₂³×C₃₁	1	16	yes	complemented
216	C₂²×C₈	—	4	4	no	—
217	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
218	C₂²×C₈	C₂³×C₃₁	1	8	yes	—
219	C₂²⋊Q₈	—	2	8	no	—
220	C₂²⋊Q₈	—	2	8	no	—
221	C₂²⋊Q₈	—	2	16	no	—
222	C₂²⋊Q₈	—	2	16	no	—
223	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
224	C₂²⋊Q₈	C₂³×C₃₁	1	16	yes	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	—	2	16	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
231	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
232	C₂×C₂²⋊C₄	—	2	4	no	—
233	C₂×C₂²⋊C₄	—	2	4	no	—
234	C₂×C₂²⋊C₄	—	2	16	no	—
235	#107	C₂³×C₃₁	1	16	yes	complemented
236	#103	C₂³×C₃₁	1	32	yes	complemented
237	C₂²⋊C₈	C₂³×C₃₁	1	16	yes	—
238	C₃₁	C₂×#3189	1	1	yes	characteristic, direct product factor, Sylow
239	C₂⁴	—	4	2	no	—
240	C₂⁴	—	4	2	no	—
241	C₂⁴	Q₁₆×C₃₁	1	8	yes	complemented
242	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
243	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
244	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
245	C₂×Q₈	—	2	8	no	—
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	2	16	no	—
248	C₂×Q₈	—	4	16	no	—
249	C₂×Q₈	—	4	8	no	—
250	C₂×Q₈	—	4	16	no	—
251	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	2	8	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	8	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	8	no	—
259	C₂²×C₄	—	4	8	no	—
260	C₂²×C₄	—	4	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	8	no	—
263	C₂²×C₄	—	4	8	no	—
264	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
266	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
267	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
269	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
270	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
271	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
273	Q₁₆	—	4	16	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	—	4	8	no	—
276	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	2	16	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
282	C₂²⋊C₄	—	2	16	no	—
283	C₂²⋊C₄	—	2	16	no	—
284	C₂³	—	2	4	no	—
285	C₂³	—	2	2	no	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	2	no	—
288	C₂³	—	4	4	no	—
289	C₂³	—	4	16	no	—
290	C₂³	—	4	4	no	—
291	C₂³	C₂×Q₁₆×C₃₁	1	4	yes	—
292	C₂³	C₂×Q₁₆×C₃₁	1	8	yes	—
293	C₂³	C₂×Q₁₆×C₃₁	1	16	yes	complemented
294	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
295	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
296	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
297	Q₈	—	2	16	no	—
298	Q₈	—	4	16	no	—
299	Q₈	—	4	8	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	4	4	no	—
309	C₂×C₄	—	4	8	no	—
310	C₂×C₄	—	4	16	no	—
311	C₂×C₄	—	4	16	no	—
312	C₂×C₄	—	4	8	no	—
313	C₂×C₄	—	4	8	no	—
314	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
315	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
316	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
317	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
318	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
319	C₈	—	2	8	no	—
320	C₂²	—	2	16	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	4	16	no	—
327	C₂²	C₃₁×#534	1	2	yes	—
328	C₂²	C₂²×Q₁₆×C₃₁	1	4	yes	—
329	C₂²	C₂²×Q₁₆×C₃₁	1	8	yes	—
330	C₂²	C₂²×Q₁₆×C₃₁	1	2	yes	—
331	C₂²	C₃₁×#575	1	2	yes	—
332	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
333	C₄	—	2	4	no	—
334	C₄	—	2	2	no	—
335	C₄	—	4	8	no	—
336	C₄	—	4	8	no	—
337	C₄	C₃₁×#534	1	2	yes	—
338	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
339	C₂	—	2	8	no	—
340	C₂	—	2	4	no	—
341	C₂	C₃₁×#3189	1	4	yes	direct product factor
342	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
343	C₂	C₂³×Q₁₆×C₃₁	1	1	yes	characteristic
344	C₂	C₂×C₃₁×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂⁵×C₃₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂⁴×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#3189	C₂	direct (N × H)
3. C₂×C₃₁×#484	C₂	semidirect
4. C₂×C₃₁×#467	C₂	semidirect
5. C₂×C₃₁×#451	C₂	semidirect
9. C₂²×Q₁₆×C₃₁	C₂²	semidirect
20. C₃₁×#484	C₂²	semidirect
21. C₃₁×#467	C₂²	semidirect
22. C₃₁×#451	C₂²	semidirect
23. C₂×C₃₁×#107	C₂²	semidirect
24. C₂×C₃₁×#103	C₂²	semidirect
43. C₂×Q₁₆×C₃₁	C₂³	semidirect
63. C₃₁×#107	C₂³	semidirect
64. C₃₁×#103	C₂³	semidirect
68. C₂⁴×C₃₁	Q₁₆	semidirect
111. C₂×#3189	C₃₁	direct (N × H)
121. C₂³×C₃₁	C₂×Q₁₆	semidirect
149. #3189	C₂×C₃₁	direct (N × H)
150. C₂×#484	C₂×C₃₁	semidirect
151. C₂×#467	C₂×C₃₁	semidirect
152. C₂×#451	C₂×C₃₁	semidirect
175. C₂²×Q₁₆	C₂²×C₃₁	semidirect
186. #484	C₂²×C₃₁	semidirect
187. #467	C₂²×C₃₁	semidirect
188. #451	C₂²×C₃₁	semidirect
189. C₂×#107	C₂²×C₃₁	semidirect
190. C₂×#103	C₂²×C₃₁	semidirect
195. C₂×C₃₁	#3189	direct (N × H)
215. C₂×Q₁₆	C₂³×C₃₁	semidirect
235. #107	C₂³×C₃₁	semidirect
236. #103	C₂³×C₃₁	semidirect
238. C₃₁	C₂×#3189	direct (N × H)
241. C₂⁴	Q₁₆×C₃₁	semidirect
293. C₂³	C₂×Q₁₆×C₃₁	semidirect
341. C₂	C₃₁×#3189	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
C₃₁×#3189	2
C₂×C₃₁×#484	2
C₂×C₃₁×#467	2
C₂×C₃₁×#451	2
C₂²×C₃₁×C₂²⋊C₈	2
C₂×#3189	31

Subgroups — C2×C31×#3189 #21517490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3189 #21517490