Subgroups — C₂×C₃₁×#1982 #21478014

Order 7936.

2374 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#127	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃₁×#102	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#1982	C₂	1	8	yes	maximal, direct product factor
6	C₂³×D₄×C₃₁	—	2	1	no	—
7	C₂³×D₄×C₃₁	—	2	1	no	—
8	C₂³×D₄×C₃₁	C₂²	1	2	yes	—
9	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
10	C₂×C₃₁×#127	—	2	2	no	—
11	C₂×C₃₁×#127	—	2	4	no	—
12	C₂×C₃₁×#127	C₄	1	8	yes	complemented
13	C₂×C₃₁×#127	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
15	C₂²×C₄²×C₃₁	—	2	1	no	—
16	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×C₄⋊C₈	—	2	4	no	—
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	complemented
19	C₂×C₃₁×#102	—	2	16	no	—
20	C₂×C₃₁×#102	C₂²	1	16	yes	complemented
21	C₄×C₄⋊C₄×C₃₁	—	2	2	no	—
22	C₄×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
23	C₂×C₃₁×#95	—	2	1	no	—
24	C₂⁵×C₃₁	—	2	2	no	—
25	C₂²×D₄×C₃₁	—	2	8	no	—
26	C₂²×D₄×C₃₁	—	2	8	no	—
27	C₂²×D₄×C₃₁	—	2	8	no	—
28	C₂²×D₄×C₃₁	—	2	2	no	—
29	C₂²×D₄×C₃₁	—	2	4	no	—
30	C₂²×D₄×C₃₁	—	2	4	no	—
31	C₂²×D₄×C₃₁	—	2	4	no	—
32	C₂²×D₄×C₃₁	—	2	8	no	—
33	C₂²×D₄×C₃₁	—	4	8	no	—
34	C₂²×D₄×C₃₁	—	4	4	no	—
35	C₂²×D₄×C₃₁	—	4	4	no	—
36	C₂²×D₄×C₃₁	C₂×C₄	1	8	yes	—
37	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
38	C₂³×C₄×C₃₁	—	2	2	no	—
39	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	—	2	8	no	—
43	C₂²×C₈×C₃₁	—	2	4	no	—
44	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
45	C₃₁×#127	—	2	16	no	—
46	C₃₁×#127	—	2	8	no	—
47	C₃₁×#127	C₂×C₄	1	16	yes	complemented
48	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	complemented
51	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
52	C₂×C₄²×C₃₁	—	2	4	no	—
53	C₂×C₄²×C₃₁	—	4	4	no	—
54	C₂×C₄²×C₃₁	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₃₁	D₄	1	2	yes	—
56	C₂×C₄²×C₃₁	D₄	1	4	yes	—
57	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
58	C₃₁×C₄⋊C₈	—	2	8	no	—
59	C₃₁×#102	—	2	32	no	—
60	C₃₁×#95	—	2	4	no	—
61	C₂⁴×C₃₁	—	2	8	no	—
62	C₂⁴×C₃₁	—	2	4	no	—
63	C₂⁴×C₃₁	—	4	8	no	—
64	C₂⁴×C₃₁	—	4	4	no	—
65	C₂⁴×C₃₁	—	4	4	no	—
66	C₂⁴×C₃₁	—	4	8	no	—
67	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
68	C₂×D₄×C₃₁	—	2	8	no	—
69	C₂×D₄×C₃₁	—	2	16	no	—
70	C₂×D₄×C₃₁	—	2	16	no	—
71	C₂×D₄×C₃₁	—	2	32	no	—
72	C₂×D₄×C₃₁	—	2	8	no	—
73	C₂×D₄×C₃₁	—	2	4	no	—
74	C₂×D₄×C₃₁	—	2	8	no	—
75	C₂×D₄×C₃₁	—	4	16	no	—
76	C₂×D₄×C₃₁	—	4	32	no	—
77	C₂×D₄×C₃₁	—	4	32	no	—
78	C₂×D₄×C₃₁	—	4	8	no	—
79	C₂×D₄×C₃₁	—	4	8	no	—
80	C₂×D₄×C₃₁	—	4	8	no	—
81	C₂×D₄×C₃₁	—	4	8	no	—
82	C₂×D₄×C₃₁	—	4	8	no	—
83	C₂×D₄×C₃₁	C₂²×C₄	1	8	yes	—
84	C₂²×C₄×C₃₁	—	2	4	no	—
85	C₂²×C₄×C₃₁	—	2	8	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	4	4	no	—
88	C₂²×C₄×C₃₁	—	4	4	no	—
89	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₃₁	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₃₁	D₈	1	4	yes	—
92	C₂²×C₄×C₃₁	SD₁₆	1	4	yes	—
93	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₃₁	#41	1	4	yes	—
100	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₃₁	—	2	8	no	—
102	C₂×C₈×C₃₁	—	2	4	no	—
103	C₂×C₈×C₃₁	—	4	8	no	—
104	C₄⋊C₄×C₃₁	—	2	8	no	—
105	C₄⋊C₄×C₃₁	—	2	4	no	—
106	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	complemented
107	C₄²×C₃₁	—	4	8	no	—
108	C₄²×C₃₁	C₂²⋊C₄	1	8	yes	—
109	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
110	C₄²×C₃₁	C₂×D₄	1	4	yes	—
111	C₂×#1982	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂³×C₃₁	—	2	8	no	—
113	C₂³×C₃₁	—	4	8	no	—
114	C₂³×C₃₁	—	4	4	no	—
115	C₂³×C₃₁	—	4	4	no	—
116	C₂³×C₃₁	—	4	8	no	—
117	C₂³×C₃₁	—	4	16	no	—
118	C₂³×C₃₁	—	4	16	no	—
119	C₂³×C₃₁	—	4	16	no	—
120	C₂³×C₃₁	—	8	16	no	—
121	C₂³×C₃₁	—	8	16	no	—
122	C₂³×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
123	C₂³×C₃₁	#121	1	4	yes	—
124	C₂³×C₃₁	C₂×D₈	1	2	yes	—
125	C₂³×C₃₁	C₂×SD₁₆	1	2	yes	—
126	C₂³×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
127	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
128	D₄×C₃₁	—	2	16	no	—
129	D₄×C₃₁	—	4	32	no	—
130	D₄×C₃₁	—	4	4	no	—
131	D₄×C₃₁	—	4	4	no	—
132	D₄×C₃₁	—	4	16	no	—
133	D₄×C₃₁	—	4	32	no	—
134	C₂×C₄×C₃₁	—	2	4	no	—
135	C₂×C₄×C₃₁	—	2	8	no	—
136	C₂×C₄×C₃₁	—	2	8	no	—
137	C₂×C₄×C₃₁	—	4	4	no	—
138	C₂×C₄×C₃₁	—	4	4	no	—
139	C₂×C₄×C₃₁	—	4	16	no	—
140	C₂×C₄×C₃₁	#102	1	16	yes	complemented
141	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
142	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
144	C₂×C₄×C₃₁	C₄×D₄	1	8	yes	—
145	C₂×C₄×C₃₁	#121	1	4	yes	—
146	C₂×C₄×C₃₁	#124	1	4	yes	—
147	C₂×C₄×C₃₁	#127	1	4	yes	—
148	C₂×C₄×C₃₁	C₂×D₈	1	4	yes	—
149	C₂×C₄×C₃₁	C₂×SD₁₆	1	4	yes	—
150	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
152	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
154	C₈×C₃₁	—	4	4	no	—
155	C₂²×#127	C₂×C₃₁	1	1	yes	characteristic
156	C₂²×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
157	C₂²×#102	C₂×C₃₁	1	4	yes	complemented
158	C₂×C₄×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
159	#1982	C₂×C₃₁	1	8	yes	direct product factor
160	C₂²×C₃₁	—	4	8	no	—
161	C₂²×C₃₁	—	4	8	no	—
162	C₂²×C₃₁	—	4	8	no	—
163	C₂²×C₃₁	—	8	32	no	—
164	C₂²×C₃₁	—	8	8	no	—
165	C₂²×C₃₁	—	8	8	no	—
166	C₂²×C₃₁	#390	1	4	yes	—
167	C₂²×C₃₁	C₂×#102	1	4	yes	—
168	C₂²×C₃₁	#418	1	4	yes	—
169	C₂²×C₃₁	#459	1	8	yes	—
170	C₂²×C₃₁	#460	1	8	yes	—
171	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₃₁	C₂×#121	1	2	yes	—
173	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
174	C₂²×C₃₁	C₂²×SD₁₆	1	1	yes	characteristic
175	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
176	C₄×C₃₁	—	2	4	no	—
177	C₄×C₃₁	—	4	8	no	—
178	C₄×C₃₁	#390	1	4	yes	—
179	C₄×C₃₁	C₂×#102	1	8	yes	complemented
180	C₄×C₃₁	C₂×C₄×D₄	1	2	yes	—
181	C₄×C₃₁	C₂×#124	1	1	yes	characteristic
182	C₄×C₃₁	C₂×#127	1	1	yes	characteristic
183	C₂³×D₄	—	2	1	no	—
184	C₂³×D₄	—	2	1	no	—
185	C₂³×D₄	C₂²×C₃₁	1	2	yes	—
186	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
187	C₂×#127	—	2	2	no	—
188	C₂×#127	—	2	4	no	—
189	C₂×#127	C₄×C₃₁	1	8	yes	complemented
190	C₂×#127	C₂²×C₃₁	1	4	yes	—
191	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
192	C₂²×C₄²	—	2	1	no	—
193	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×C₄⋊C₈	—	2	4	no	—
195	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	complemented
196	C₂×#102	—	2	16	no	—
197	C₂×#102	C₂²×C₃₁	1	16	yes	complemented
198	C₄×C₄⋊C₄	—	2	2	no	—
199	C₄×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
200	C₂×#95	—	2	1	no	—
201	C₂×C₃₁	—	8	8	no	—
202	C₂×C₃₁	#1982	1	8	yes	direct product factor
203	C₂×C₃₁	C₂×#390	1	1	yes	characteristic
204	C₂×C₃₁	C₂²×#102	1	1	yes	characteristic
205	C₂×C₃₁	C₂×#418	1	1	yes	characteristic
206	C₂×C₃₁	C₂×#459	1	2	yes	—
207	C₂×C₃₁	C₂×#460	1	2	yes	—
208	C₂⁵	—	2	2	no	—
209	C₂²×D₄	—	2	8	no	—
210	C₂²×D₄	—	2	8	no	—
211	C₂²×D₄	—	2	8	no	—
212	C₂²×D₄	—	2	2	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	4	no	—
215	C₂²×D₄	—	2	4	no	—
216	C₂²×D₄	—	2	8	no	—
217	C₂²×D₄	—	4	8	no	—
218	C₂²×D₄	—	4	4	no	—
219	C₂²×D₄	—	4	4	no	—
220	C₂²×D₄	C₂×C₄×C₃₁	1	8	yes	—
221	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
225	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
226	C₂²×C₈	—	2	8	no	—
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
229	#127	—	2	16	no	—
230	#127	—	2	8	no	—
231	#127	C₂×C₄×C₃₁	1	16	yes	complemented
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	4	no	—
234	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	complemented
235	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
236	C₂×C₄²	—	2	4	no	—
237	C₂×C₄²	—	4	4	no	—
238	C₂×C₄²	C₂×C₄×C₃₁	1	4	yes	—
239	C₂×C₄²	D₄×C₃₁	1	2	yes	—
240	C₂×C₄²	D₄×C₃₁	1	4	yes	—
241	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
242	C₄⋊C₈	—	2	8	no	—
243	#102	—	2	32	no	—
244	#95	—	2	4	no	—
245	C₃₁	C₂×#1982	1	1	yes	characteristic, direct product factor, Sylow
246	C₂⁴	—	2	8	no	—
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	4	8	no	—
249	C₂⁴	—	4	4	no	—
250	C₂⁴	—	4	4	no	—
251	C₂⁴	—	4	8	no	—
252	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	2	16	no	—
255	C₂×D₄	—	2	16	no	—
256	C₂×D₄	—	2	32	no	—
257	C₂×D₄	—	2	8	no	—
258	C₂×D₄	—	2	4	no	—
259	C₂×D₄	—	2	8	no	—
260	C₂×D₄	—	4	32	no	—
261	C₂×D₄	—	4	16	no	—
262	C₂×D₄	—	4	32	no	—
263	C₂×D₄	—	4	8	no	—
264	C₂×D₄	—	4	8	no	—
265	C₂×D₄	—	4	8	no	—
266	C₂×D₄	—	4	8	no	—
267	C₂×D₄	—	4	8	no	—
268	C₂×D₄	C₂²×C₄×C₃₁	1	8	yes	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
275	C₂²×C₄	C₂²⋊C₄×C₃₁	1	4	yes	—
276	C₂²×C₄	D₈×C₃₁	1	4	yes	—
277	C₂²×C₄	SD₁₆×C₃₁	1	4	yes	—
278	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
281	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
284	C₂²×C₄	#41×C₃₁	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
286	C₂×C₈	—	2	8	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	4	8	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	complemented
292	C₄²	—	4	8	no	—
293	C₄²	C₂²⋊C₄×C₃₁	1	8	yes	—
294	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
295	C₄²	C₂×D₄×C₃₁	1	4	yes	—
296	C₂³	—	2	8	no	—
297	C₂³	—	4	16	no	—
298	C₂³	—	4	16	no	—
299	C₂³	—	4	8	no	—
300	C₂³	—	4	4	no	—
301	C₂³	—	4	4	no	—
302	C₂³	—	4	8	no	—
303	C₂³	—	4	16	no	—
304	C₂³	—	8	16	no	—
305	C₂³	—	8	16	no	—
306	C₂³	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
307	C₂³	C₃₁×#121	1	4	yes	—
308	C₂³	C₂×D₈×C₃₁	1	2	yes	—
309	C₂³	C₂×SD₁₆×C₃₁	1	2	yes	—
310	C₂³	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
311	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
312	D₄	—	2	16	no	—
313	D₄	—	4	32	no	—
314	D₄	—	4	32	no	—
315	D₄	—	4	4	no	—
316	D₄	—	4	4	no	—
317	D₄	—	4	16	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	4	16	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	C₃₁×#102	1	16	yes	complemented
325	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
328	C₂×C₄	C₄×D₄×C₃₁	1	8	yes	—
329	C₂×C₄	C₃₁×#121	1	4	yes	—
330	C₂×C₄	C₃₁×#124	1	4	yes	—
331	C₂×C₄	C₃₁×#127	1	4	yes	—
332	C₂×C₄	C₂×D₈×C₃₁	1	4	yes	—
333	C₂×C₄	C₂×SD₁₆×C₃₁	1	4	yes	—
334	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
336	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
338	C₈	—	4	4	no	—
339	C₂²	—	4	8	no	—
340	C₂²	—	4	8	no	—
341	C₂²	—	4	8	no	—
342	C₂²	—	8	32	no	—
343	C₂²	—	8	8	no	—
344	C₂²	—	8	8	no	—
345	C₂²	C₃₁×#390	1	4	yes	—
346	C₂²	C₂×C₃₁×#102	1	4	yes	—
347	C₂²	C₃₁×#418	1	4	yes	—
348	C₂²	C₃₁×#459	1	8	yes	—
349	C₂²	C₃₁×#460	1	8	yes	—
350	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
351	C₂²	C₂×C₃₁×#121	1	2	yes	—
352	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
353	C₂²	C₂²×SD₁₆×C₃₁	1	1	yes	characteristic
354	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
355	C₄	—	2	4	no	—
356	C₄	—	4	8	no	—
357	C₄	C₃₁×#390	1	4	yes	—
358	C₄	C₂×C₃₁×#102	1	8	yes	complemented
359	C₄	C₂×C₄×D₄×C₃₁	1	2	yes	—
360	C₄	C₂×C₃₁×#124	1	1	yes	characteristic
361	C₄	C₂×C₃₁×#127	1	1	yes	characteristic
362	C₂	—	8	8	no	—
363	C₂	C₃₁×#1982	1	8	yes	direct product factor
364	C₂	C₂×C₃₁×#390	1	1	yes	characteristic
365	C₂	C₂²×C₃₁×#102	1	1	yes	characteristic
366	C₂	C₂×C₃₁×#418	1	1	yes	characteristic
367	C₂	C₂×C₃₁×#459	1	2	yes	—
368	C₂	C₂×C₃₁×#460	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂²×C₃₁×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃₁×C₄⋊C₈	C₂	semidirect
3. C₂²×C₃₁×#102	C₂	semidirect
4. C₂×C₄×C₄⋊C₄×C₃₁	C₂	semidirect
5. C₃₁×#1982	C₂	direct (N × H)
12. C₂×C₃₁×#127	C₄	semidirect
18. C₂×C₃₁×C₄⋊C₈	C₂²	semidirect
20. C₂×C₃₁×#102	C₂²	semidirect
22. C₄×C₄⋊C₄×C₃₁	C₂²	semidirect
47. C₃₁×#127	C₂×C₄	semidirect
50. C₂×C₄⋊C₄×C₃₁	D₄	semidirect
106. C₄⋊C₄×C₃₁	C₂×D₄	semidirect
111. C₂×#1982	C₃₁	direct (N × H)
140. C₂×C₄×C₃₁	#102	semidirect
156. C₂²×C₄⋊C₈	C₂×C₃₁	semidirect
157. C₂²×#102	C₂×C₃₁	semidirect
158. C₂×C₄×C₄⋊C₄	C₂×C₃₁	semidirect
159. #1982	C₂×C₃₁	direct (N × H)
179. C₄×C₃₁	C₂×#102	semidirect
189. C₂×#127	C₄×C₃₁	semidirect
195. C₂×C₄⋊C₈	C₂²×C₃₁	semidirect
197. C₂×#102	C₂²×C₃₁	semidirect
199. C₄×C₄⋊C₄	C₂²×C₃₁	semidirect
202. C₂×C₃₁	#1982	direct (N × H)
231. #127	C₂×C₄×C₃₁	semidirect
234. C₂×C₄⋊C₄	D₄×C₃₁	semidirect
245. C₃₁	C₂×#1982	direct (N × H)
291. C₄⋊C₄	C₂×D₄×C₃₁	semidirect
324. C₂×C₄	C₃₁×#102	semidirect
358. C₄	C₂×C₃₁×#102	semidirect
363. C₂	C₃₁×#1982	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×#127	2
C₂²×C₃₁×C₄⋊C₈	2
C₂²×C₃₁×#102	2
C₂×C₄×C₄⋊C₄×C₃₁	2
C₃₁×#1982	2
C₂×#1982	31

Subgroups — C2×C31×#1982 #21478014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1982 #21478014