Subgroups — C₂×C₃₁×#2168 #21490189

Order 7936.

754 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2168	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃₁×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₃₁	C₄	1	1	yes	characteristic
12	C₂×C₃₁×M₃₂	—	2	4	no	—
13	C₂×C₃₁×M₃₂	C₂²	1	4	yes	complemented
14	C₂²×C₁₆×C₃₁	—	2	4	no	—
15	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
16	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
18	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
19	C₂²×C₁₆×C₃₁	C₂²	1	4	yes	complemented
20	C₈×D₄×C₃₁	C₄	1	4	yes	—
21	C₈×D₄×C₃₁	C₂²	1	4	yes	—
22	C₂×C₃₁×C₄⋊C₈	C₄	1	1	yes	characteristic
23	C₂×C₃₁×C₂²⋊C₈	C₄	1	1	yes	characteristic
24	C₂×C₃₁×C₂²⋊C₈	C₄	1	1	yes	characteristic
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×C₄⋊C₁₆	C₂²	1	4	yes	complemented
27	C₃₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
28	C₃₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
29	C₃₁×#346	C₂²	1	4	yes	complemented
30	C₂²×D₄×C₃₁	C₈	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₃₁	—	2	2	no	—
34	C₂²×C₈×C₃₁	—	2	2	no	—
35	C₂²×C₈×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	1	yes	characteristic
39	C₂²×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₃₁	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₄×D₄×C₃₁	C₈	1	4	yes	—
46	C₄×D₄×C₃₁	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₃₁	C₈	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₃₁	C₈	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×C₃₁	C₈	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
51	C₃₁×M₃₂	—	2	8	no	—
52	C₂×C₁₆×C₃₁	—	2	2	no	—
53	C₂×C₁₆×C₃₁	—	2	2	no	—
54	C₂×C₁₆×C₃₁	—	2	2	no	—
55	C₂×C₁₆×C₃₁	—	2	8	no	—
56	C₂×C₁₆×C₃₁	D₄	1	4	yes	complemented
57	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
58	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
59	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
60	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
61	C₃₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
63	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
64	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
65	C₄×C₈×C₃₁	C₂³	1	2	yes	—
66	C₂⁴×C₃₁	C₂×C₈	1	1	yes	characteristic
67	C₂⁴×C₃₁	C₂×C₈	1	1	yes	characteristic
68	C₂×D₄×C₃₁	—	2	4	no	—
69	C₂×D₄×C₃₁	C₂×C₈	1	4	yes	—
70	C₂²×C₄×C₃₁	—	2	2	no	—
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	—	2	2	no	—
73	C₂²×C₄×C₃₁	—	2	2	no	—
74	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
75	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₃₁	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₈×C₃₁	—	2	2	no	—
84	C₂×C₈×C₃₁	—	2	2	no	—
85	C₂×C₈×C₃₁	—	2	2	no	—
86	C₂×C₈×C₃₁	—	2	4	no	—
87	C₂×C₈×C₃₁	—	2	4	no	—
88	C₂×C₈×C₃₁	—	2	2	no	—
89	C₂×C₈×C₃₁	—	2	2	no	—
90	C₂×C₈×C₃₁	—	2	2	no	—
91	C₂×C₈×C₃₁	—	2	2	no	—
92	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
97	C₂×C₈×C₃₁	#41	1	2	yes	—
98	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
99	C₄⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
100	C₂²⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
101	C₂²⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
102	C₄²×C₃₁	C₂×C₈	1	2	yes	—
103	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
104	C₁₆×C₃₁	—	2	2	no	—
105	C₁₆×C₃₁	—	2	2	no	—
106	C₁₆×C₃₁	—	2	2	no	—
107	C₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
108	C₂×#2168	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂³×C₃₁	—	2	2	no	—
110	C₂³×C₃₁	—	2	2	no	—
111	C₂³×C₃₁	—	2	2	no	—
112	C₂³×C₃₁	—	2	2	no	—
113	C₂³×C₃₁	—	2	2	no	—
114	C₂³×C₃₁	M₃₂	1	4	yes	complemented
115	C₂³×C₃₁	C₂²×C₈	1	2	yes	—
116	C₂³×C₃₁	C₂²×C₈	1	2	yes	—
117	C₂³×C₃₁	C₂²×C₈	1	1	yes	characteristic
118	D₄×C₃₁	—	2	8	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	2	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	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	2	4	no	—
129	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
131	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
132	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
133	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
134	C₂×C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
135	C₂×C₄×C₃₁	#131	1	2	yes	—
136	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
137	C₈×C₃₁	—	2	2	no	—
138	C₈×C₃₁	—	2	2	no	—
139	C₈×C₃₁	—	2	2	no	—
140	C₈×C₃₁	C₄×D₄	1	2	yes	—
141	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
142	C₈×C₃₁	C₂×#41	1	1	yes	characteristic
143	C₂²×M₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
144	C₂³×C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
145	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
146	#2168	C₂×C₃₁	1	8	yes	direct product factor
147	C₂×C₄⋊C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
148	C₂×C₂²⋊C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
149	C₂×C₂²⋊C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
150	C₂×#346	C₂×C₃₁	1	1	yes	characteristic, complemented
151	C₂²×C₃₁	—	2	2	no	—
152	C₂²×C₃₁	—	2	2	no	—
153	C₂²×C₃₁	—	2	8	no	—
154	C₂²×C₃₁	—	2	2	no	—
155	C₂²×C₃₁	—	2	2	no	—
156	C₂²×C₃₁	—	2	2	no	—
157	C₂²×C₃₁	—	4	4	no	—
158	C₂²×C₃₁	C₈×D₄	1	2	yes	—
159	C₂²×C₃₁	C₂×M₃₂	1	2	yes	—
160	C₂²×C₃₁	C₂×M₃₂	1	4	yes	complemented
161	C₂²×C₃₁	#504	1	2	yes	—
162	C₂²×C₃₁	C₂³×C₈	1	1	yes	characteristic
163	C₄×C₃₁	—	2	2	no	—
164	C₄×C₃₁	—	2	2	no	—
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	2	2	no	—
167	C₄×C₃₁	C₈×D₄	1	2	yes	—
168	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₃₁	C₂×#131	1	1	yes	characteristic
170	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
172	C₂×C₄×D₄	C₄×C₃₁	1	1	yes	characteristic
173	C₂×M₃₂	—	2	4	no	—
174	C₂×M₃₂	C₂²×C₃₁	1	4	yes	complemented
175	C₂²×C₁₆	—	2	4	no	—
176	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
177	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
178	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
179	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
180	C₂²×C₁₆	C₂²×C₃₁	1	4	yes	complemented
181	C₈×D₄	C₄×C₃₁	1	4	yes	—
182	C₈×D₄	C₂²×C₃₁	1	4	yes	—
183	C₂×C₄⋊C₈	C₄×C₃₁	1	1	yes	characteristic
184	C₂×C₂²⋊C₈	C₄×C₃₁	1	1	yes	characteristic
185	C₂×C₂²⋊C₈	C₄×C₃₁	1	1	yes	characteristic
186	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
187	C₄⋊C₁₆	C₂²×C₃₁	1	4	yes	complemented
188	C₂²⋊C₁₆	C₂²×C₃₁	1	4	yes	complemented
189	C₂²⋊C₁₆	C₂²×C₃₁	1	4	yes	complemented
190	#346	C₂²×C₃₁	1	4	yes	complemented
191	C₂×C₃₁	—	2	4	no	—
192	C₂×C₃₁	—	4	2	no	—
193	C₂×C₃₁	#2168	1	4	yes	direct product factor
194	C₂×C₃₁	C₂×C₈×D₄	1	1	yes	characteristic
195	C₂×C₃₁	C₂²×M₃₂	1	1	yes	characteristic
196	C₂×C₃₁	C₂×#504	1	1	yes	characteristic
197	C₂²×D₄	C₈×C₃₁	1	1	yes	characteristic
198	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
199	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
200	C₂²×C₈	—	2	2	no	—
201	C₂²×C₈	—	2	2	no	—
202	C₂²×C₈	—	2	2	no	—
203	C₂²×C₈	—	2	2	no	—
204	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
205	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
206	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
207	C₂²×C₈	C₂×C₄×C₃₁	1	2	yes	—
208	C₂²×C₈	C₂×C₄×C₃₁	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
210	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
211	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
212	C₄×D₄	C₈×C₃₁	1	4	yes	—
213	C₄×D₄	C₂×C₄×C₃₁	1	4	yes	—
214	C₂×C₄⋊C₄	C₈×C₃₁	1	1	yes	characteristic
215	C₂×C₂²⋊C₄	C₈×C₃₁	1	1	yes	characteristic
216	C₂×C₂²⋊C₄	C₈×C₃₁	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
218	M₃₂	—	2	8	no	—
219	C₂×C₁₆	—	2	2	no	—
220	C₂×C₁₆	—	2	2	no	—
221	C₂×C₁₆	—	2	2	no	—
222	C₂×C₁₆	—	2	8	no	—
223	C₂×C₁₆	D₄×C₃₁	1	4	yes	complemented
224	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
225	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
226	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
227	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
228	C₄⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
229	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
230	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
231	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
232	C₄×C₈	C₂³×C₃₁	1	2	yes	—
233	C₃₁	C₂×#2168	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	C₂×C₈×C₃₁	1	1	yes	characteristic
235	C₂⁴	C₂×C₈×C₃₁	1	1	yes	characteristic
236	C₂×D₄	—	2	4	no	—
237	C₂×D₄	C₂×C₈×C₃₁	1	4	yes	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	2	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
243	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
244	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
245	C₂²×C₄	C₂×C₈×C₃₁	1	1	yes	characteristic
246	C₂²×C₄	C₂×C₈×C₃₁	1	2	yes	—
247	C₂²×C₄	C₂×C₈×C₃₁	1	2	yes	—
248	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	4	no	—
255	C₂×C₈	—	2	4	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
261	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
262	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
263	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
264	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
265	C₂×C₈	#41×C₃₁	1	2	yes	—
266	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
267	C₄⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
268	C₂²⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
269	C₂²⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
270	C₄²	C₂×C₈×C₃₁	1	2	yes	—
271	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
272	C₁₆	—	2	2	no	—
273	C₁₆	—	2	2	no	—
274	C₁₆	—	2	2	no	—
275	C₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
276	C₂³	—	2	2	no	—
277	C₂³	—	2	2	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	2	no	—
280	C₂³	—	2	2	no	—
281	C₂³	C₃₁×M₃₂	1	4	yes	complemented
282	C₂³	C₂²×C₈×C₃₁	1	2	yes	—
283	C₂³	C₂²×C₈×C₃₁	1	2	yes	—
284	C₂³	C₂²×C₈×C₃₁	1	1	yes	characteristic
285	D₄	—	2	8	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
297	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
298	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
299	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
300	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
301	C₂×C₄	C₂²×C₈×C₃₁	1	1	yes	characteristic
302	C₂×C₄	C₃₁×#131	1	2	yes	—
303	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
304	C₈	—	2	2	no	—
305	C₈	—	2	2	no	—
306	C₈	—	2	2	no	—
307	C₈	C₄×D₄×C₃₁	1	2	yes	—
308	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
309	C₈	C₂×#41×C₃₁	1	1	yes	characteristic
310	C₂²	—	2	2	no	—
311	C₂²	—	2	2	no	—
312	C₂²	—	2	8	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	4	4	no	—
317	C₂²	C₈×D₄×C₃₁	1	2	yes	—
318	C₂²	C₂×C₃₁×M₃₂	1	2	yes	—
319	C₂²	C₂×C₃₁×M₃₂	1	4	yes	complemented
320	C₂²	C₃₁×#504	1	2	yes	—
321	C₂²	C₂³×C₈×C₃₁	1	1	yes	characteristic
322	C₄	—	2	2	no	—
323	C₄	—	2	2	no	—
324	C₄	—	2	2	no	—
325	C₄	—	2	2	no	—
326	C₄	C₈×D₄×C₃₁	1	2	yes	—
327	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
328	C₄	C₂×C₃₁×#131	1	1	yes	characteristic
329	C₂	—	2	4	no	—
330	C₂	—	4	2	no	—
331	C₂	C₃₁×#2168	1	4	yes	direct product factor
332	C₂	C₂×C₈×D₄×C₃₁	1	1	yes	characteristic
333	C₂	C₂²×C₃₁×M₃₂	1	1	yes	characteristic
334	C₂	C₂×C₃₁×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₃₁	C₂³
commutator	C₂²	C₂³×C₈×C₃₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
socle	C₂³×C₃₁	C₂²×C₈
prime radical	C₂²×D₄×C₃₁	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×M₃₂	C₂	semidirect
2. C₂³×C₁₆×C₃₁	C₂	semidirect
4. C₃₁×#2168	C₂	direct (N × H)
5. C₂×C₃₁×C₄⋊C₁₆	C₂	semidirect
6. C₂×C₃₁×C₂²⋊C₁₆	C₂	semidirect
7. C₂×C₃₁×C₂²⋊C₁₆	C₂	semidirect
8. C₂×C₃₁×#346	C₂	semidirect
13. C₂×C₃₁×M₃₂	C₂²	semidirect
19. C₂²×C₁₆×C₃₁	C₂²	semidirect
26. C₃₁×C₄⋊C₁₆	C₂²	semidirect
27. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
28. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
29. C₃₁×#346	C₂²	semidirect
56. C₂×C₁₆×C₃₁	D₄	semidirect
107. C₁₆×C₃₁	C₂×D₄	semidirect
108. C₂×#2168	C₃₁	direct (N × H)
114. C₂³×C₃₁	M₃₂	semidirect
143. C₂²×M₃₂	C₂×C₃₁	semidirect
144. C₂³×C₁₆	C₂×C₃₁	semidirect
146. #2168	C₂×C₃₁	direct (N × H)
147. C₂×C₄⋊C₁₆	C₂×C₃₁	semidirect
148. C₂×C₂²⋊C₁₆	C₂×C₃₁	semidirect
149. C₂×C₂²⋊C₁₆	C₂×C₃₁	semidirect
150. C₂×#346	C₂×C₃₁	semidirect
160. C₂²×C₃₁	C₂×M₃₂	semidirect
174. C₂×M₃₂	C₂²×C₃₁	semidirect
180. C₂²×C₁₆	C₂²×C₃₁	semidirect
187. C₄⋊C₁₆	C₂²×C₃₁	semidirect
188. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
189. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
190. #346	C₂²×C₃₁	semidirect
193. C₂×C₃₁	#2168	direct (N × H)
223. C₂×C₁₆	D₄×C₃₁	semidirect
233. C₃₁	C₂×#2168	direct (N × H)
275. C₁₆	C₂×D₄×C₃₁	semidirect
281. C₂³	C₃₁×M₃₂	semidirect
319. C₂²	C₂×C₃₁×M₃₂	semidirect
331. C₂	C₃₁×#2168	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×M₃₂	2
C₂³×C₁₆×C₃₁	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#2168	2
C₂×C₃₁×C₄⋊C₁₆	2
C₂×C₃₁×C₂²⋊C₁₆	2
C₂×C₃₁×#346	2
C₂×#2168	31

Subgroups — C2×C31×#2168 #21490189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2168 #21490189