Subgroups — C₂×C₃₁×#3444 #21519427

Order 7936.

8518 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3444	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#533	C₂	1	3	yes	maximal, complemented
3	C₂×C₃₁×#532	C₂	1	3	yes	maximal, complemented
4	C₂×C₃₁×#529	C₂	1	12	yes	maximal, complemented
5	C₂×C₃₁×#525	C₂	1	6	yes	maximal, complemented
6	C₂×C₄×#41×C₃₁	C₂	1	6	yes	maximal, complemented
7	C₂³×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₃₁	C₂²	1	6	yes	—
9	C₂⁴×C₄×C₃₁	C₂²	1	3	yes	—
10	C₃₁×#533	C₂²	1	48	yes	complemented
11	C₃₁×#532	C₂²	1	48	yes	complemented
12	C₂×C₃₁×C₄⋊Q₈	C₂²	1	3	yes	complemented
13	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
14	C₃₁×#529	C₂²	1	192	yes	complemented
15	C₂×C₃₁×#126	C₂²	1	8	yes	complemented
16	C₂×C₃₁×#125	C₂²	1	6	yes	complemented
17	C₂×C₃₁×#124	C₂²	1	6	yes	complemented
18	C₃₁×#525	C₂²	1	96	yes	complemented
19	C₂×C₃₁×#123	C₂²	1	12	yes	—
20	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	12	yes	—
21	C₂×C₃₁×#121	C₂²	1	12	yes	—
22	C₂×C₃₁×#120	C₂²	1	4	yes	—
23	C₄×#41×C₃₁	C₂²	1	96	yes	complemented
24	C₂×C₄×Q₈×C₃₁	C₂²	1	12	yes	complemented
25	C₂×C₄×D₄×C₃₁	C₂²	1	24	yes	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	12	yes	complemented
27	C₂×C₃₁×#117	C₂²	1	6	yes	—
28	C₂×C₃₁×#117	C₂²	1	12	yes	complemented
29	C₂²×C₄²×C₃₁	C₂²	1	6	yes	—
30	C₂²×C₄²×C₃₁	C₂²	1	3	yes	—
31	C₂²×C₄²×C₃₁	C₂²	1	3	yes	—
32	C₂²×C₄²×C₃₁	C₂²	1	16	yes	complemented
33	C₂²×C₄²×C₃₁	C₂²	1	4	yes	complemented
34	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
35	C₂×#41×C₃₁	—	2	48	no	—
36	C₂×#41×C₃₁	C₂³	1	48	yes	—
37	C₂²×Q₈×C₃₁	C₂³	1	6	yes	—
38	C₂²×D₄×C₃₁	C₂³	1	12	yes	—
39	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
40	C₂³×C₄×C₃₁	—	2	24	no	—
41	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
42	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
43	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
44	C₂³×C₄×C₃₁	C₂³	1	24	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	12	yes	—
46	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
47	C₃₁×C₄⋊Q₈	C₂³	1	24	yes	complemented
48	C₃₁×#127	C₂³	1	8	yes	complemented
49	C₃₁×#126	C₂³	1	64	yes	complemented
50	C₃₁×#125	C₂³	1	48	yes	complemented
51	C₃₁×#124	C₂³	1	48	yes	complemented
52	C₃₁×#123	C₂³	1	96	yes	—
53	C₃₁×C₂²⋊Q₈	C₂³	1	96	yes	—
54	C₃₁×#121	C₂³	1	96	yes	—
55	C₃₁×#120	C₂³	1	32	yes	—
56	C₄×Q₈×C₃₁	C₂³	1	96	yes	complemented
57	C₄×D₄×C₃₁	C₂³	1	192	yes	—
58	C₄×D₄×C₃₁	C₂³	1	96	yes	complemented
59	C₃₁×#117	C₂³	1	48	yes	—
60	C₃₁×#117	C₂³	1	96	yes	complemented
61	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
62	C₂×C₄⋊C₄×C₃₁	C₂³	1	24	yes	—
63	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
64	C₂×C₂²⋊C₄×C₃₁	C₂³	1	24	yes	—
65	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
66	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
67	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
68	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	C₂³	1	24	yes	—
71	C₂×C₄²×C₃₁	C₂³	1	48	yes	—
72	C₂×C₄²×C₃₁	C₂³	1	24	yes	—
73	C₂×C₄²×C₃₁	C₂³	1	12	yes	—
74	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₃₁	C₂³	1	32	yes	complemented
76	C₂⁴×C₃₁	—	2	12	no	—
77	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
78	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
79	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
80	#41×C₃₁	—	2	192	no	—
81	C₂×Q₈×C₃₁	—	2	24	no	—
82	C₂×Q₈×C₃₁	C₂⁴	1	24	yes	—
83	C₂×D₄×C₃₁	—	2	48	no	—
84	C₂×D₄×C₃₁	—	2	24	no	—
85	C₂×D₄×C₃₁	C₂⁴	1	48	yes	—
86	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
87	C₂²×C₄×C₃₁	—	2	12	no	—
88	C₂²×C₄×C₃₁	—	2	24	no	—
89	C₂²×C₄×C₃₁	—	2	24	no	—
90	C₂²×C₄×C₃₁	—	2	48	no	—
91	C₂²×C₄×C₃₁	—	2	96	no	—
92	C₂²×C₄×C₃₁	#41	1	24	yes	complemented
93	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
96	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
98	C₂²×C₄×C₃₁	C₂⁴	1	48	yes	—
99	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
100	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
101	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
102	C₄⋊C₄×C₃₁	C₂⁴	1	48	yes	—
103	C₄⋊C₄×C₃₁	C₂⁴	1	96	yes	—
104	C₂²⋊C₄×C₃₁	C₂⁴	1	48	yes	—
105	C₂²⋊C₄×C₃₁	C₂⁴	1	96	yes	—
106	C₄²×C₃₁	C₂⁴	1	12	yes	—
107	C₄²×C₃₁	C₂⁴	1	24	yes	—
108	C₄²×C₃₁	C₂⁴	1	12	yes	—
109	C₄²×C₃₁	C₂⁴	1	8	yes	—
110	C₄²×C₃₁	C₂⁴	1	4	yes	—
111	C₄²×C₃₁	C₂⁴	1	4	yes	—
112	C₄²×C₃₁	C₂⁴	1	48	yes	—
113	C₂×#3444	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₃₁	—	2	32	no	—
115	C₂³×C₃₁	—	2	24	no	—
116	C₂³×C₃₁	—	2	12	no	—
117	C₂³×C₃₁	—	2	24	no	—
118	C₂³×C₃₁	C₂×#41	1	12	yes	—
119	C₂³×C₃₁	C₂⁵	1	8	yes	—
120	C₂³×C₃₁	C₂⁵	1	6	yes	—
121	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
122	Q₈×C₃₁	—	2	48	no	—
123	D₄×C₃₁	—	2	96	no	—
124	D₄×C₃₁	—	2	48	no	—
125	C₂×C₄×C₃₁	—	2	24	no	—
126	C₂×C₄×C₃₁	—	2	12	no	—
127	C₂×C₄×C₃₁	—	2	24	no	—
128	C₂×C₄×C₃₁	—	2	48	no	—
129	C₂×C₄×C₃₁	—	2	48	no	—
130	C₂×C₄×C₃₁	—	2	96	no	—
131	C₂×C₄×C₃₁	C₂×#41	1	12	yes	—
132	C₂×C₄×C₃₁	C₂×#41	1	12	yes	—
133	C₂×C₄×C₃₁	C₂×#41	1	48	yes	complemented
134	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
135	C₂×C₄×C₃₁	C₂⁵	1	24	yes	—
136	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
137	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
138	#3444	C₂×C₃₁	1	32	yes	direct product factor
139	C₂×#533	C₂×C₃₁	1	3	yes	complemented
140	C₂×#532	C₂×C₃₁	1	3	yes	complemented
141	C₂×#529	C₂×C₃₁	1	12	yes	complemented
142	C₂×#525	C₂×C₃₁	1	6	yes	complemented
143	C₂×C₄×#41	C₂×C₃₁	1	6	yes	complemented
144	C₂³×C₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
145	C₂²×C₃₁	—	2	32	no	—
146	C₂²×C₃₁	—	2	12	no	—
147	C₂²×C₃₁	—	2	24	no	—
148	C₂²×C₃₁	—	2	24	no	—
149	C₂²×C₃₁	—	4	16	no	—
150	C₂²×C₃₁	C₂²×#41	1	12	yes	—
151	C₂²×C₃₁	C₂²×#41	1	6	yes	—
152	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
153	C₄×C₃₁	—	2	12	no	—
154	C₄×C₃₁	—	2	24	no	—
155	C₄×C₃₁	C₂²×#41	1	12	yes	—
156	C₄×C₃₁	C₂²×#41	1	12	yes	—
157	C₂²×#41	C₂²×C₃₁	1	6	yes	—
158	C₂⁴×C₄	C₂²×C₃₁	1	3	yes	—
159	#533	C₂²×C₃₁	1	48	yes	complemented
160	#532	C₂²×C₃₁	1	48	yes	complemented
161	C₂×C₄⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
162	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
163	#529	C₂²×C₃₁	1	192	yes	complemented
164	C₂×#126	C₂²×C₃₁	1	8	yes	complemented
165	C₂×#125	C₂²×C₃₁	1	6	yes	complemented
166	C₂×#124	C₂²×C₃₁	1	6	yes	complemented
167	#525	C₂²×C₃₁	1	96	yes	complemented
168	C₂×#123	C₂²×C₃₁	1	12	yes	—
169	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	12	yes	—
170	C₂×#121	C₂²×C₃₁	1	12	yes	—
171	C₂×#120	C₂²×C₃₁	1	4	yes	—
172	C₄×#41	C₂²×C₃₁	1	96	yes	complemented
173	C₂×C₄×Q₈	C₂²×C₃₁	1	12	yes	complemented
174	C₂×C₄×D₄	C₂²×C₃₁	1	24	yes	—
175	C₂×C₄×D₄	C₂²×C₃₁	1	12	yes	complemented
176	C₂×#117	C₂²×C₃₁	1	6	yes	—
177	C₂×#117	C₂²×C₃₁	1	12	yes	complemented
178	C₂²×C₄²	C₂²×C₃₁	1	3	yes	—
179	C₂²×C₄²	C₂²×C₃₁	1	6	yes	—
180	C₂²×C₄²	C₂²×C₃₁	1	3	yes	—
181	C₂²×C₄²	C₂²×C₃₁	1	16	yes	complemented
182	C₂²×C₄²	C₂²×C₃₁	1	4	yes	complemented
183	C₂×C₃₁	—	2	12	no	—
184	C₂×C₃₁	—	4	8	no	—
185	C₂×C₃₁	#3444	1	4	yes	direct product factor
186	C₂×C₃₁	C₂³×#41	1	3	yes	—
187	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
188	C₂×#41	—	2	48	no	—
189	C₂×#41	C₂³×C₃₁	1	48	yes	—
190	C₂²×Q₈	C₂³×C₃₁	1	6	yes	—
191	C₂²×D₄	C₂³×C₃₁	1	12	yes	—
192	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
193	C₂³×C₄	—	2	24	no	—
194	C₂³×C₄	C₂³×C₃₁	1	12	yes	—
195	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
196	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
197	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
198	C₂³×C₄	C₂³×C₃₁	1	24	yes	—
199	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
200	C₄⋊Q₈	C₂³×C₃₁	1	24	yes	complemented
201	#127	C₂³×C₃₁	1	8	yes	complemented
202	#126	C₂³×C₃₁	1	64	yes	complemented
203	#125	C₂³×C₃₁	1	48	yes	complemented
204	#124	C₂³×C₃₁	1	48	yes	complemented
205	#123	C₂³×C₃₁	1	96	yes	—
206	C₂²⋊Q₈	C₂³×C₃₁	1	96	yes	—
207	#121	C₂³×C₃₁	1	96	yes	—
208	#120	C₂³×C₃₁	1	32	yes	—
209	C₄×Q₈	C₂³×C₃₁	1	96	yes	complemented
210	C₄×D₄	C₂³×C₃₁	1	192	yes	—
211	C₄×D₄	C₂³×C₃₁	1	96	yes	complemented
212	#117	C₂³×C₃₁	1	48	yes	—
213	#117	C₂³×C₃₁	1	96	yes	complemented
214	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
215	C₂×C₄⋊C₄	C₂³×C₃₁	1	24	yes	—
216	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
217	C₂×C₂²⋊C₄	C₂³×C₃₁	1	24	yes	—
218	C₂×C₄²	C₂³×C₃₁	1	12	yes	—
219	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
220	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
221	C₂×C₄²	C₂³×C₃₁	1	24	yes	—
222	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
223	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
224	C₂×C₄²	C₂³×C₃₁	1	48	yes	—
225	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₃₁	1	24	yes	—
227	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₃₁	1	32	yes	complemented
229	C₃₁	C₂×#3444	1	1	yes	characteristic, direct product factor, Sylow
230	C₂⁴	—	2	12	no	—
231	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
232	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
233	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
234	#41	—	2	192	no	—
235	C₂×Q₈	—	2	24	no	—
236	C₂×Q₈	C₂⁴×C₃₁	1	24	yes	—
237	C₂×D₄	—	2	48	no	—
238	C₂×D₄	—	2	24	no	—
239	C₂×D₄	C₂⁴×C₃₁	1	48	yes	—
240	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
241	C₂²×C₄	—	2	12	no	—
242	C₂²×C₄	—	2	24	no	—
243	C₂²×C₄	—	2	24	no	—
244	C₂²×C₄	—	2	48	no	—
245	C₂²×C₄	—	2	96	no	—
246	C₂²×C₄	#41×C₃₁	1	24	yes	complemented
247	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
248	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
249	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
250	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
251	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
252	C₂²×C₄	C₂⁴×C₃₁	1	48	yes	—
253	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
254	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
255	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
256	C₄⋊C₄	C₂⁴×C₃₁	1	48	yes	—
257	C₄⋊C₄	C₂⁴×C₃₁	1	96	yes	—
258	C₂²⋊C₄	C₂⁴×C₃₁	1	48	yes	—
259	C₂²⋊C₄	C₂⁴×C₃₁	1	96	yes	—
260	C₄²	C₂⁴×C₃₁	1	4	yes	—
261	C₄²	C₂⁴×C₃₁	1	12	yes	—
262	C₄²	C₂⁴×C₃₁	1	24	yes	—
263	C₄²	C₂⁴×C₃₁	1	12	yes	—
264	C₄²	C₂⁴×C₃₁	1	8	yes	—
265	C₄²	C₂⁴×C₃₁	1	4	yes	—
266	C₄²	C₂⁴×C₃₁	1	48	yes	—
267	C₂³	—	2	32	no	—
268	C₂³	—	2	24	no	—
269	C₂³	—	2	12	no	—
270	C₂³	—	2	24	no	—
271	C₂³	C₂×#41×C₃₁	1	12	yes	—
272	C₂³	C₂⁵×C₃₁	1	8	yes	—
273	C₂³	C₂⁵×C₃₁	1	6	yes	—
274	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
275	Q₈	—	2	48	no	—
276	D₄	—	2	96	no	—
277	D₄	—	2	48	no	—
278	C₂×C₄	—	2	24	no	—
279	C₂×C₄	—	2	12	no	—
280	C₂×C₄	—	2	24	no	—
281	C₂×C₄	—	2	48	no	—
282	C₂×C₄	—	2	48	no	—
283	C₂×C₄	—	2	96	no	—
284	C₂×C₄	C₂×#41×C₃₁	1	12	yes	—
285	C₂×C₄	C₂×#41×C₃₁	1	12	yes	—
286	C₂×C₄	C₂×#41×C₃₁	1	48	yes	complemented
287	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
288	C₂×C₄	C₂⁵×C₃₁	1	24	yes	—
289	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
290	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
291	C₂²	—	2	32	no	—
292	C₂²	—	2	12	no	—
293	C₂²	—	2	24	no	—
294	C₂²	—	2	24	no	—
295	C₂²	—	4	16	no	—
296	C₂²	C₂²×#41×C₃₁	1	12	yes	—
297	C₂²	C₂²×#41×C₃₁	1	6	yes	—
298	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
299	C₄	—	2	12	no	—
300	C₄	—	2	24	no	—
301	C₄	C₂²×#41×C₃₁	1	12	yes	—
302	C₄	C₂²×#41×C₃₁	1	12	yes	—
303	C₂	—	2	12	no	—
304	C₂	—	4	8	no	—
305	C₂	C₃₁×#3444	1	4	yes	direct product factor
306	C₂	C₂³×#41×C₃₁	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²×C₃₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂³×C₃₁	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3444	C₂	direct (N × H)
2. C₂×C₃₁×#533	C₂	semidirect
3. C₂×C₃₁×#532	C₂	semidirect
4. C₂×C₃₁×#529	C₂	semidirect
5. C₂×C₃₁×#525	C₂	semidirect
6. C₂×C₄×#41×C₃₁	C₂	semidirect
7. C₂³×C₄²×C₃₁	C₂	semidirect
10. C₃₁×#533	C₂²	semidirect
11. C₃₁×#532	C₂²	semidirect
12. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
13. C₂×C₃₁×#127	C₂²	semidirect
14. C₃₁×#529	C₂²	semidirect
15. C₂×C₃₁×#126	C₂²	semidirect
16. C₂×C₃₁×#125	C₂²	semidirect
17. C₂×C₃₁×#124	C₂²	semidirect
18. C₃₁×#525	C₂²	semidirect
23. C₄×#41×C₃₁	C₂²	semidirect
24. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
26. C₂×C₄×D₄×C₃₁	C₂²	semidirect
28. C₂×C₃₁×#117	C₂²	semidirect
32. C₂²×C₄²×C₃₁	C₂²	semidirect
33. C₂²×C₄²×C₃₁	C₂²	semidirect
47. C₃₁×C₄⋊Q₈	C₂³	semidirect
48. C₃₁×#127	C₂³	semidirect
49. C₃₁×#126	C₂³	semidirect
50. C₃₁×#125	C₂³	semidirect
51. C₃₁×#124	C₂³	semidirect
56. C₄×Q₈×C₃₁	C₂³	semidirect
58. C₄×D₄×C₃₁	C₂³	semidirect
60. C₃₁×#117	C₂³	semidirect
75. C₂×C₄²×C₃₁	C₂³	semidirect
92. C₂²×C₄×C₃₁	#41	semidirect
113. C₂×#3444	C₃₁	direct (N × H)
133. C₂×C₄×C₃₁	C₂×#41	semidirect
138. #3444	C₂×C₃₁	direct (N × H)
139. C₂×#533	C₂×C₃₁	semidirect
140. C₂×#532	C₂×C₃₁	semidirect
141. C₂×#529	C₂×C₃₁	semidirect
142. C₂×#525	C₂×C₃₁	semidirect
143. C₂×C₄×#41	C₂×C₃₁	semidirect
144. C₂³×C₄²	C₂×C₃₁	semidirect
159. #533	C₂²×C₃₁	semidirect
160. #532	C₂²×C₃₁	semidirect
161. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
162. C₂×#127	C₂²×C₃₁	semidirect
163. #529	C₂²×C₃₁	semidirect
164. C₂×#126	C₂²×C₃₁	semidirect
165. C₂×#125	C₂²×C₃₁	semidirect
166. C₂×#124	C₂²×C₃₁	semidirect
167. #525	C₂²×C₃₁	semidirect
172. C₄×#41	C₂²×C₃₁	semidirect
173. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
175. C₂×C₄×D₄	C₂²×C₃₁	semidirect
177. C₂×#117	C₂²×C₃₁	semidirect
181. C₂²×C₄²	C₂²×C₃₁	semidirect
182. C₂²×C₄²	C₂²×C₃₁	semidirect
185. C₂×C₃₁	#3444	direct (N × H)
200. C₄⋊Q₈	C₂³×C₃₁	semidirect
201. #127	C₂³×C₃₁	semidirect
202. #126	C₂³×C₃₁	semidirect
203. #125	C₂³×C₃₁	semidirect
204. #124	C₂³×C₃₁	semidirect
209. C₄×Q₈	C₂³×C₃₁	semidirect
211. C₄×D₄	C₂³×C₃₁	semidirect
213. #117	C₂³×C₃₁	semidirect
228. C₂×C₄²	C₂³×C₃₁	semidirect
229. C₃₁	C₂×#3444	direct (N × H)
246. C₂²×C₄	#41×C₃₁	semidirect
286. C₂×C₄	C₂×#41×C₃₁	semidirect
305. C₂	C₃₁×#3444	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×#3444	2
C₂×C₃₁×#533	2
C₂×C₃₁×#532	2
C₂×C₃₁×#529	2
C₂×C₃₁×#525	2
C₂×C₄×#41×C₃₁	2
C₂³×C₄²×C₃₁	2
C₂×#3444	31

Subgroups — C2×C31×#3444 #21519427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3444 #21519427