Subgroups — C₂×C₃₁×#2057 #21480307

Order 7936.

1454 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#107	C₂	1	2	yes	maximal
3	C₂×C₃₁×#389	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2057	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#340	C₂	1	2	yes	maximal
6	C₂×C₃₁×#336	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₃₁	—	2	1	no	—
8	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
9	C₂×C₃₁×C₄⋊Q₈	—	2	8	no	—
10	C₂×C₃₁×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	—
12	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₃₁	—	2	1	no	—
14	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#107	—	2	8	no	—
19	C₂×C₃₁×#107	C₂²	1	8	yes	—
20	C₃₁×#389	—	2	2	no	—
21	C₃₁×#389	C₂²	1	4	yes	—
22	C₂×C₃₁×#95	—	2	1	no	—
23	C₃₁×#340	C₂²	1	8	yes	—
24	C₃₁×#336	C₂²	1	4	yes	—
25	C₂²×Q₈×C₃₁	—	2	8	no	—
26	C₂²×Q₈×C₃₁	—	2	4	no	—
27	C₂²×Q₈×C₃₁	—	4	4	no	—
28	C₂²×Q₈×C₃₁	—	4	4	no	—
29	C₂³×C₄×C₃₁	—	2	2	no	—
30	C₂³×C₄×C₃₁	—	2	1	no	—
31	C₂³×C₄×C₃₁	—	2	1	no	—
32	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
35	C₂²×C₈×C₃₁	—	2	4	no	—
36	C₂²×C₈×C₃₁	—	2	4	no	—
37	C₂²×C₈×C₃₁	Q₈	1	8	yes	complemented
38	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
39	C₃₁×C₄⋊Q₈	—	2	16	no	—
40	C₃₁×C₄⋊Q₈	—	2	16	no	—
41	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
42	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
43	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
45	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
46	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
48	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₃₁	—	4	4	no	—
51	C₂×C₄⋊C₄×C₃₁	D₄	1	8	yes	—
52	C₂×C₄⋊C₄×C₃₁	Q₈	1	4	yes	complemented
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
56	C₂×C₄²×C₃₁	—	2	4	no	—
57	C₂×C₄²×C₃₁	D₄	1	2	yes	—
58	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
59	C₃₁×#107	—	2	16	no	—
60	C₃₁×#95	—	2	4	no	—
61	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
62	C₂×Q₈×C₃₁	—	2	16	no	—
63	C₂×Q₈×C₃₁	—	4	8	no	—
64	C₂×Q₈×C₃₁	—	4	32	no	—
65	C₂×Q₈×C₃₁	—	4	8	no	—
66	C₂²×C₄×C₃₁	—	2	2	no	—
67	C₂²×C₄×C₃₁	—	2	2	no	—
68	C₂²×C₄×C₃₁	—	2	2	no	—
69	C₂²×C₄×C₃₁	—	2	2	no	—
70	C₂²×C₄×C₃₁	—	2	8	no	—
71	C₂²×C₄×C₃₁	—	2	4	no	—
72	C₂²×C₄×C₃₁	—	2	2	no	—
73	C₂²×C₄×C₃₁	—	2	4	no	—
74	C₂²×C₄×C₃₁	—	2	2	no	—
75	C₂²×C₄×C₃₁	—	4	2	no	—
76	C₂²×C₄×C₃₁	—	4	4	no	—
77	C₂²×C₄×C₃₁	—	4	4	no	—
78	C₂²×C₄×C₃₁	—	4	2	no	—
79	C₂²×C₄×C₃₁	—	4	2	no	—
80	C₂²×C₄×C₃₁	—	4	2	no	—
81	C₂²×C₄×C₃₁	—	4	2	no	—
82	C₂²×C₄×C₃₁	D₈	1	4	yes	—
83	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
84	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
88	C₂²×C₄×C₃₁	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
90	C₂²×C₄×C₃₁	#41	1	2	yes	—
91	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₃₁	—	2	16	no	—
93	C₂×C₈×C₃₁	—	2	4	no	—
94	C₂×C₈×C₃₁	—	2	4	no	—
95	C₂×C₈×C₃₁	C₂×Q₈	1	8	yes	complemented
96	C₄⋊C₄×C₃₁	—	2	16	no	—
97	C₄⋊C₄×C₃₁	—	2	8	no	—
98	C₄⋊C₄×C₃₁	—	2	4	no	—
99	C₄⋊C₄×C₃₁	—	2	4	no	—
100	C₄⋊C₄×C₃₁	—	2	2	no	—
101	C₄⋊C₄×C₃₁	—	2	4	no	—
102	C₄⋊C₄×C₃₁	—	4	2	no	—
103	C₄⋊C₄×C₃₁	—	4	8	no	—
104	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
105	C₄⋊C₄×C₃₁	C₂×Q₈	1	4	yes	complemented
106	C₄²×C₃₁	—	2	4	no	—
107	C₄²×C₃₁	—	2	4	no	—
108	C₂×#2057	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₃₁	#120	1	2	yes	—
110	C₂³×C₃₁	C₂²⋊Q₈	1	2	yes	—
111	C₂³×C₃₁	C₄⋊Q₈	1	2	yes	—
112	C₂³×C₃₁	C₂×D₈	1	2	yes	—
113	C₂³×C₃₁	C₂×Q₁₆	1	2	yes	—
114	C₂³×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
115	C₂³×C₃₁	#137	1	2	yes	—
116	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
117	Q₈×C₃₁	—	4	32	no	—
118	C₂×C₄×C₃₁	—	2	2	no	—
119	C₂×C₄×C₃₁	—	2	2	no	—
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	8	no	—
123	C₂×C₄×C₃₁	—	2	8	no	—
124	C₂×C₄×C₃₁	—	2	8	no	—
125	C₂×C₄×C₃₁	—	2	4	no	—
126	C₂×C₄×C₃₁	—	4	2	no	—
127	C₂×C₄×C₃₁	—	4	4	no	—
128	C₂×C₄×C₃₁	—	4	4	no	—
129	C₂×C₄×C₃₁	—	4	2	no	—
130	C₂×C₄×C₃₁	—	4	16	no	—
131	C₂×C₄×C₃₁	—	4	8	no	—
132	C₂×C₄×C₃₁	—	4	2	no	—
133	C₂×C₄×C₃₁	—	4	2	no	—
134	C₂×C₄×C₃₁	—	4	2	no	—
135	C₂×C₄×C₃₁	—	8	4	no	—
136	C₂×C₄×C₃₁	#120	1	2	yes	—
137	C₂×C₄×C₃₁	C₂²⋊Q₈	1	8	yes	—
138	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₃₁	C₄⋊Q₈	1	8	yes	—
140	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₃₁	C₂×D₈	1	4	yes	—
142	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
143	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₃₁	C₂²×Q₈	1	2	yes	—
145	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
147	C₈×C₃₁	—	2	8	no	—
148	C₂²×C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic
149	C₂²×#107	C₂×C₃₁	1	2	yes	—
150	C₂×#389	C₂×C₃₁	1	1	yes	characteristic
151	#2057	C₂×C₃₁	1	8	yes	direct product factor
152	C₂×#340	C₂×C₃₁	1	2	yes	—
153	C₂×#336	C₂×C₃₁	1	1	yes	characteristic
154	C₂²×C₃₁	#395	1	4	yes	—
155	C₂²×C₃₁	#447	1	4	yes	—
156	C₂²×C₃₁	#451	1	4	yes	—
157	C₂²×C₃₁	#474	1	4	yes	—
158	C₂²×C₃₁	#477	1	4	yes	—
159	C₂²×C₃₁	#500	1	4	yes	—
160	C₂²×C₃₁	#501	1	4	yes	—
161	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
162	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
163	C₂²×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
164	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
165	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
166	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂²×C₃₁	C₂×#137	1	1	yes	characteristic
168	C₄×C₃₁	—	2	4	no	—
169	C₄×C₃₁	—	2	4	no	—
170	C₄×C₃₁	—	4	8	no	—
171	C₄×C₃₁	—	4	4	no	—
172	C₄×C₃₁	—	8	2	no	—
173	C₄×C₃₁	#395	1	4	yes	—
174	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
175	C₄×C₃₁	C₂×C₄⋊Q₈	1	2	yes	—
176	C₂³×Q₈	—	2	1	no	—
177	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
178	C₂×C₄⋊Q₈	—	2	8	no	—
179	C₂×C₄⋊Q₈	—	2	2	no	—
180	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
181	C₂²×C₄⋊C₄	—	2	1	no	—
182	C₂²×C₄⋊C₄	—	2	1	no	—
183	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
184	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
185	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
186	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
187	C₂×#107	—	2	8	no	—
188	C₂×#107	C₂²×C₃₁	1	8	yes	—
189	#389	—	2	2	no	—
190	#389	C₂²×C₃₁	1	4	yes	—
191	C₂×#95	—	2	1	no	—
192	#340	C₂²×C₃₁	1	8	yes	—
193	#336	C₂²×C₃₁	1	4	yes	—
194	C₂×C₃₁	#2057	1	8	yes	direct product factor
195	C₂×C₃₁	C₂×#395	1	1	yes	characteristic
196	C₂×C₃₁	C₂×#447	1	1	yes	characteristic
197	C₂×C₃₁	C₂×#451	1	1	yes	characteristic
198	C₂×C₃₁	C₂×#474	1	1	yes	characteristic
199	C₂×C₃₁	C₂×#477	1	1	yes	characteristic
200	C₂×C₃₁	C₂×#500	1	1	yes	characteristic
201	C₂×C₃₁	C₂×#501	1	1	yes	characteristic
202	C₂²×Q₈	—	2	8	no	—
203	C₂²×Q₈	—	2	4	no	—
204	C₂²×Q₈	—	4	4	no	—
205	C₂²×Q₈	—	4	4	no	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	—	2	1	no	—
208	C₂³×C₄	—	2	1	no	—
209	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
210	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
211	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂²×C₈	—	2	4	no	—
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	Q₈×C₃₁	1	8	yes	complemented
215	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
216	C₄⋊Q₈	—	2	16	no	—
217	C₄⋊Q₈	—	2	16	no	—
218	C₂×C₄⋊C₄	—	2	8	no	—
219	C₂×C₄⋊C₄	—	2	4	no	—
220	C₂×C₄⋊C₄	—	2	2	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	4	4	no	—
228	C₂×C₄⋊C₄	D₄×C₃₁	1	8	yes	—
229	C₂×C₄⋊C₄	Q₈×C₃₁	1	4	yes	complemented
230	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
231	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
232	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
233	C₂×C₄²	—	2	4	no	—
234	C₂×C₄²	D₄×C₃₁	1	2	yes	—
235	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
236	#107	—	2	16	no	—
237	#95	—	2	4	no	—
238	C₃₁	C₂×#2057	1	1	yes	characteristic, direct product factor, Sylow
239	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
240	C₂×Q₈	—	2	16	no	—
241	C₂×Q₈	—	4	32	no	—
242	C₂×Q₈	—	4	8	no	—
243	C₂×Q₈	—	4	8	no	—
244	C₂²×C₄	—	2	2	no	—
245	C₂²×C₄	—	2	2	no	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	8	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	—	4	4	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	—	4	2	no	—
257	C₂²×C₄	—	4	2	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	D₈×C₃₁	1	4	yes	—
261	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
262	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
263	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
264	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
266	C₂²×C₄	C₂×Q₈×C₃₁	1	4	yes	—
267	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
268	C₂²×C₄	#41×C₃₁	1	2	yes	—
269	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
270	C₂×C₈	—	2	16	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	C₂×Q₈×C₃₁	1	8	yes	complemented
274	C₄⋊C₄	—	2	16	no	—
275	C₄⋊C₄	—	2	8	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	2	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	4	2	no	—
281	C₄⋊C₄	—	4	8	no	—
282	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
283	C₄⋊C₄	C₂×Q₈×C₃₁	1	4	yes	complemented
284	C₄²	—	2	4	no	—
285	C₄²	—	2	4	no	—
286	C₂³	C₃₁×#120	1	2	yes	—
287	C₂³	C₃₁×C₂²⋊Q₈	1	2	yes	—
288	C₂³	C₃₁×C₄⋊Q₈	1	2	yes	—
289	C₂³	C₂×D₈×C₃₁	1	2	yes	—
290	C₂³	C₂×Q₁₆×C₃₁	1	2	yes	—
291	C₂³	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
292	C₂³	C₃₁×#137	1	2	yes	—
293	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
294	Q₈	—	4	32	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	8	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	16	no	—
304	C₂×C₄	—	4	8	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	4	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	C₃₁×#120	1	2	yes	—
314	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
315	C₂×C₄	C₃₁×C₂²⋊Q₈	1	8	yes	—
316	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
317	C₂×C₄	C₃₁×C₄⋊Q₈	1	8	yes	—
318	C₂×C₄	C₂×D₈×C₃₁	1	4	yes	—
319	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
320	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
321	C₂×C₄	C₂²×Q₈×C₃₁	1	2	yes	—
322	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
323	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
324	C₈	—	2	8	no	—
325	C₂²	C₃₁×#395	1	4	yes	—
326	C₂²	C₃₁×#447	1	4	yes	—
327	C₂²	C₃₁×#451	1	4	yes	—
328	C₂²	C₃₁×#474	1	4	yes	—
329	C₂²	C₃₁×#477	1	4	yes	—
330	C₂²	C₃₁×#500	1	4	yes	—
331	C₂²	C₃₁×#501	1	4	yes	—
332	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
333	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
334	C₂²	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
335	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
336	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
337	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
338	C₂²	C₂×C₃₁×#137	1	1	yes	characteristic
339	C₄	—	2	4	no	—
340	C₄	—	2	4	no	—
341	C₄	—	4	8	no	—
342	C₄	—	4	4	no	—
343	C₄	—	8	2	no	—
344	C₄	C₃₁×#395	1	4	yes	—
345	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
346	C₄	C₂×C₃₁×C₄⋊Q₈	1	2	yes	—
347	C₂	C₃₁×#2057	1	8	yes	direct product factor
348	C₂	C₂×C₃₁×#395	1	1	yes	characteristic
349	C₂	C₂×C₃₁×#447	1	1	yes	characteristic
350	C₂	C₂×C₃₁×#451	1	1	yes	characteristic
351	C₂	C₂×C₃₁×#474	1	1	yes	characteristic
352	C₂	C₂×C₃₁×#477	1	1	yes	characteristic
353	C₂	C₂×C₃₁×#500	1	1	yes	characteristic
354	C₂	C₂×C₃₁×#501	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
LCS	G ▷ C₂²×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
4. C₃₁×#2057	C₂	direct (N × H)
37. C₂²×C₈×C₃₁	Q₈	semidirect
52. C₂×C₄⋊C₄×C₃₁	Q₈	semidirect
95. C₂×C₈×C₃₁	C₂×Q₈	semidirect
105. C₄⋊C₄×C₃₁	C₂×Q₈	semidirect
108. C₂×#2057	C₃₁	direct (N × H)
151. #2057	C₂×C₃₁	direct (N × H)
194. C₂×C₃₁	#2057	direct (N × H)
214. C₂²×C₈	Q₈×C₃₁	semidirect
229. C₂×C₄⋊C₄	Q₈×C₃₁	semidirect
238. C₃₁	C₂×#2057	direct (N × H)
273. C₂×C₈	C₂×Q₈×C₃₁	semidirect
283. C₄⋊C₄	C₂×Q₈×C₃₁	semidirect
347. C₂	C₃₁×#2057	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×C₄⋊Q₈	2
C₂²×C₃₁×#107	2
C₂×C₃₁×#389	2
C₃₁×#2057	2
C₂×C₃₁×#340	2
C₂×C₃₁×#336	2
C₂×#2057	31

Subgroups — C2×C31×#2057 #21480307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2057 #21480307