Subgroups — C₃₁×#17829 #21474588

Order 7936.

610 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#41×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2925	C₂	1	2	yes	maximal
3	C₃₁×#1572	C₂	1	4	yes	maximal, complemented
4	C₃₁×#1570	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1568	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1564	C₂	1	2	yes	maximal, complemented
8	C₂×C₃₁×#335	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
10	C₈×Q₈×C₃₁	C₄	1	1	yes	characteristic
11	C₈×Q₈×C₃₁	C₄	1	1	yes	characteristic
12	C₈×D₄×C₃₁	C₄	1	1	yes	characteristic
13	C₈×D₄×C₃₁	C₄	1	2	yes	—
14	C₈×D₄×C₃₁	C₄	1	1	yes	characteristic
15	C₈×D₄×C₃₁	C₄	1	2	yes	—
16	C₃₁×#433	—	2	4	no	—
17	C₃₁×#432	C₂²	1	4	yes	—
18	C₃₁×#431	C₂²	1	4	yes	—
19	C₃₁×#431	C₂²	1	1	yes	characteristic
20	C₃₁×#431	C₂²	1	2	yes	—
21	C₃₁×#423	C₂²	1	2	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
23	C₃₁×#408	—	2	2	no	—
24	C₃₁×#405	—	2	2	no	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
27	C₃₁×#335	C₂²	1	1	yes	characteristic
28	C₃₁×#335	C₂²	1	1	yes	characteristic
29	C₃₁×#335	C₂²	1	2	yes	—
30	C₃₁×#335	C₂²	1	2	yes	—
31	C₃₁×#335	C₂²	1	2	yes	—
32	C₃₁×#334	C₂²	1	4	yes	—
33	C₃₁×#334	C₂²	1	4	yes	—
34	C₂×#41×C₃₁	D₄	1	1	yes	characteristic
35	C₂×M₁₆×C₃₁	—	2	2	no	—
36	C₂²×C₈×C₃₁	—	2	2	no	—
37	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
39	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
41	C₄×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
42	C₄×Q₈×C₃₁	Q₈	1	1	yes	characteristic
43	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
44	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₄×D₄×C₃₁	Q₈	1	2	yes	—
46	C₄×D₄×C₃₁	Q₈	1	1	yes	characteristic
47	C₃₁×#117	D₄	1	1	yes	characteristic
48	C₃₁×#117	D₄	1	2	yes	—
49	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
51	C₃₁×C₄⋊C₈	—	2	2	no	—
52	C₃₁×C₄⋊C₈	—	2	2	no	—
53	C₃₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₃₁×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
56	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
57	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
58	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
59	C₃₁×C₄⋊C₈	C₂³	1	4	yes	—
60	C₃₁×C₂²⋊C₈	—	2	4	no	—
61	C₃₁×C₂²⋊C₈	—	2	4	no	—
62	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
63	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
64	C₃₁×C₂²⋊C₈	C₂×C₄	1	2	yes	—
65	C₃₁×#97	—	2	4	no	—
66	C₄×C₈×C₃₁	—	2	4	no	—
67	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
68	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
70	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
72	C₄×C₈×C₃₁	C₂³	1	2	yes	—
73	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
74	#41×C₃₁	—	2	2	no	—
75	#41×C₃₁	—	2	2	no	—
76	C₂×Q₈×C₃₁	C₄⋊C₄	1	1	yes	characteristic
77	C₂×D₄×C₃₁	C₄⋊C₄	1	2	yes	—
78	C₂×D₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
85	M₁₆×C₃₁	—	4	4	no	—
86	C₂×C₈×C₃₁	—	2	2	no	—
87	C₂×C₈×C₃₁	—	2	4	no	—
88	C₂×C₈×C₃₁	—	2	2	no	—
89	C₂×C₈×C₃₁	—	2	4	no	—
90	C₂×C₈×C₃₁	—	2	2	no	—
91	C₂×C₈×C₃₁	—	4	1	no	—
92	C₂×C₈×C₃₁	—	4	2	no	—
93	C₂×C₈×C₃₁	—	4	4	no	—
94	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
100	C₄⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
101	C₄⋊C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
103	C₄⋊C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
104	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
105	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
106	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
107	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
108	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₃₁	C₂×D₄	1	2	yes	—
110	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₂×Q₈	1	2	yes	—
112	C₄²×C₃₁	C₂×Q₈	1	1	yes	characteristic
113	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
114	#17829	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
116	C₂³×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
117	Q₈×C₃₁	—	2	2	no	—
118	D₄×C₃₁	—	2	4	no	—
119	D₄×C₃₁	—	2	2	no	—
120	C₂×C₄×C₃₁	—	2	1	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	1	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	4	1	no	—
127	C₂×C₄×C₃₁	—	4	2	no	—
128	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₃₁	#135	1	2	yes	—
135	C₂×C₄×C₃₁	#135	1	2	yes	—
136	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
139	C₈×C₃₁	—	2	2	no	—
140	C₈×C₃₁	—	2	1	no	—
141	C₈×C₃₁	—	2	1	no	—
142	C₈×C₃₁	—	2	2	no	—
143	C₈×C₃₁	—	2	1	no	—
144	C₈×C₃₁	—	4	2	no	—
145	C₈×C₃₁	—	4	2	no	—
146	C₈×C₃₁	—	4	4	no	—
147	C₈×C₃₁	#131	1	2	yes	—
148	C₈×#41	C₂×C₃₁	1	1	yes	characteristic
149	#2925	C₂×C₃₁	1	2	yes	—
150	#1572	C₂×C₃₁	1	4	yes	complemented
151	#1570	C₂×C₃₁	1	2	yes	complemented
152	#1568	C₂×C₃₁	1	2	yes	complemented
153	#1567	C₂×C₃₁	1	1	yes	characteristic, complemented
154	#1564	C₂×C₃₁	1	2	yes	complemented
155	C₂×#335	C₂×C₃₁	1	1	yes	characteristic, complemented
156	C₂²×C₃₁	—	2	1	no	—
157	C₂²×C₃₁	—	2	1	no	—
158	C₂²×C₃₁	—	2	2	no	—
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	2	2	no	—
161	C₂²×C₃₁	#427	1	2	yes	—
162	C₂²×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
163	C₄×C₃₁	—	2	1	no	—
164	C₄×C₃₁	—	2	2	no	—
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	2	1	no	—
167	C₄×C₃₁	—	2	1	no	—
168	C₄×C₃₁	—	2	2	no	—
169	C₄×C₃₁	#427	1	2	yes	—
170	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
171	C₄×C₃₁	#568	1	1	yes	characteristic
172	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
173	C₄×C₃₁	C₂×#135	1	1	yes	characteristic
174	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
175	C₈×Q₈	C₄×C₃₁	1	1	yes	characteristic
176	C₈×Q₈	C₄×C₃₁	1	1	yes	characteristic
177	C₈×D₄	C₄×C₃₁	1	1	yes	characteristic
178	C₈×D₄	C₄×C₃₁	1	2	yes	—
179	C₈×D₄	C₄×C₃₁	1	1	yes	characteristic
180	C₈×D₄	C₄×C₃₁	1	2	yes	—
181	#433	—	2	4	no	—
182	#432	C₂²×C₃₁	1	4	yes	—
183	#431	C₂²×C₃₁	1	4	yes	—
184	#431	C₂²×C₃₁	1	1	yes	characteristic
185	#431	C₂²×C₃₁	1	2	yes	—
186	#423	C₂²×C₃₁	1	2	yes	—
187	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
188	#408	—	2	2	no	—
189	#405	—	2	2	no	—
190	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
192	#335	C₂²×C₃₁	1	1	yes	characteristic
193	#335	C₂²×C₃₁	1	1	yes	characteristic
194	#335	C₂²×C₃₁	1	2	yes	—
195	#335	C₂²×C₃₁	1	2	yes	—
196	#335	C₂²×C₃₁	1	2	yes	—
197	#334	C₂²×C₃₁	1	4	yes	—
198	#334	C₂²×C₃₁	1	4	yes	—
199	C₂×C₃₁	—	2	2	no	—
200	C₂×C₃₁	—	4	2	no	—
201	C₂×C₃₁	#2906	1	1	yes	characteristic
202	C₂×C₃₁	C₂×#427	1	1	yes	characteristic
203	C₂×C₃₁	#2916	1	1	yes	characteristic
204	C₂×#41	D₄×C₃₁	1	1	yes	characteristic
205	C₂×M₁₆	—	2	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
208	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
209	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
210	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
211	C₄×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
212	C₄×Q₈	Q₈×C₃₁	1	1	yes	characteristic
213	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
214	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₄×D₄	Q₈×C₃₁	1	2	yes	—
216	C₄×D₄	Q₈×C₃₁	1	1	yes	characteristic
217	#117	D₄×C₃₁	1	1	yes	characteristic
218	#117	D₄×C₃₁	1	2	yes	—
219	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
220	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
221	C₄⋊C₈	—	2	2	no	—
222	C₄⋊C₈	—	2	2	no	—
223	C₄⋊C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₄⋊C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
225	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
226	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
227	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
228	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
229	C₄⋊C₈	C₂³×C₃₁	1	4	yes	—
230	C₂²⋊C₈	—	2	4	no	—
231	C₂²⋊C₈	—	2	4	no	—
232	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
233	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
234	C₂²⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
235	#97	—	2	4	no	—
236	C₄×C₈	—	2	4	no	—
237	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
238	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
239	C₄×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
240	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
241	C₄×C₈	C₂³×C₃₁	1	2	yes	—
242	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
243	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
244	C₃₁	#17829	1	1	yes	characteristic, direct product factor, Sylow
245	#41	—	2	2	no	—
246	#41	—	2	2	no	—
247	C₂×Q₈	C₄⋊C₄×C₃₁	1	1	yes	characteristic
248	C₂×D₄	C₄⋊C₄×C₃₁	1	2	yes	—
249	C₂×D₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
252	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
254	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
255	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
256	M₁₆	—	4	4	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	4	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	4	1	no	—
263	C₂×C₈	—	4	2	no	—
264	C₂×C₈	—	4	4	no	—
265	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
266	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
267	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
268	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
270	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
271	C₄⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
272	C₄⋊C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
273	C₄⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
274	C₄⋊C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
275	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
276	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
277	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
278	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
279	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
280	C₄²	C₂×D₄×C₃₁	1	2	yes	—
281	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
282	C₄²	C₂×Q₈×C₃₁	1	2	yes	—
283	C₄²	C₂×Q₈×C₃₁	1	1	yes	characteristic
284	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
285	C₂³	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
286	C₂³	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
287	Q₈	—	2	2	no	—
288	D₄	—	2	4	no	—
289	D₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	4	1	no	—
297	C₂×C₄	—	4	2	no	—
298	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
299	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
300	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
301	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
302	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
303	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
304	C₂×C₄	C₃₁×#135	1	2	yes	—
305	C₂×C₄	C₃₁×#135	1	2	yes	—
306	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
308	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
309	C₈	—	2	2	no	—
310	C₈	—	2	1	no	—
311	C₈	—	2	1	no	—
312	C₈	—	2	2	no	—
313	C₈	—	2	1	no	—
314	C₈	—	4	2	no	—
315	C₈	—	4	2	no	—
316	C₈	—	4	4	no	—
317	C₈	C₃₁×#131	1	2	yes	—
318	C₂²	—	2	1	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	C₃₁×#427	1	2	yes	—
324	C₂²	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
325	C₄	—	2	1	no	—
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	2	no	—
331	C₄	C₃₁×#427	1	2	yes	—
332	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
333	C₄	C₃₁×#568	1	1	yes	characteristic
334	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
335	C₄	C₂×C₃₁×#135	1	1	yes	characteristic
336	C₂	—	2	2	no	—
337	C₂	—	4	2	no	—
338	C₂	C₃₁×#2906	1	1	yes	characteristic
339	C₂	C₂×C₃₁×#427	1	1	yes	characteristic
340	C₂	C₃₁×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₄²	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₃₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₄×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#1572	C₂	semidirect
4. C₃₁×#1570	C₂	semidirect
5. C₃₁×#1568	C₂	semidirect
6. C₃₁×#1567	C₂	semidirect
7. C₃₁×#1564	C₂	semidirect
8. C₂×C₃₁×#335	C₂	semidirect
114. #17829	C₃₁	direct (N × H)
150. #1572	C₂×C₃₁	semidirect
151. #1570	C₂×C₃₁	semidirect
152. #1568	C₂×C₃₁	semidirect
153. #1567	C₂×C₃₁	semidirect
154. #1564	C₂×C₃₁	semidirect
155. C₂×#335	C₂×C₃₁	semidirect
244. C₃₁	#17829	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#41×C₃₁	2
C₃₁×#2925	2
C₃₁×#1572	2
C₃₁×#1570	2
C₃₁×#1568	2
C₃₁×#1567	2
C₃₁×#1564	2
C₂×C₃₁×#335	2
#17829	31

Subgroups — C31×#17829 #21474588

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#17829 #21474588