Subgroups — C₃₁×#22717 #21479476

Order 7936.

822 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×M₁₆×C₃₁	C₂	1	2	yes	maximal
2	C₂×C₈×D₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1950	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1855	C₂	1	4	yes	maximal, complemented
5	C₃₁×#1837	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1810	C₂	1	2	yes	maximal, complemented
7	C₄×C₃₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃₁×#341	C₂	1	2	yes	maximal, complemented
9	C₂²×M₁₆×C₃₁	C₂²	1	4	yes	—
10	C₂³×C₈×C₃₁	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
12	C₃₁×#436	—	2	2	no	—
13	C₃₁×#435	—	2	4	no	—
14	C₈×D₄×C₃₁	—	2	2	no	—
15	C₈×D₄×C₃₁	C₄	1	4	yes	—
16	C₈×D₄×C₃₁	C₄	1	2	yes	—
17	C₈×D₄×C₃₁	C₄	1	2	yes	—
18	C₂×C₃₁×#108	C₂²	1	2	yes	—
19	C₂×C₃₁×#108	C₂²	1	4	yes	—
20	C₃₁×#423	C₂²	1	2	yes	—
21	C₂×C₃₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₃₁×#407	C₂²	1	4	yes	—
23	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#341	C₂²	1	1	yes	characteristic
27	C₃₁×#341	C₂²	1	2	yes	—
28	C₃₁×#341	C₂²	1	2	yes	—
29	C₃₁×#341	C₂²	1	4	yes	—
30	C₃₁×#341	C₂²	1	1	yes	characteristic
31	C₂²×D₄×C₃₁	Q₈	1	1	yes	characteristic
32	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
33	C₂×M₁₆×C₃₁	—	2	4	no	—
34	C₂×M₁₆×C₃₁	—	2	8	no	—
35	C₂×M₁₆×C₃₁	—	4	4	no	—
36	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
37	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
38	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
39	C₂²×C₈×C₃₁	—	2	4	no	—
40	C₂²×C₈×C₃₁	—	4	4	no	—
41	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
46	C₄×D₄×C₃₁	C₂×C₄	1	2	yes	—
47	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₄×D₄×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
50	C₄×D₄×C₃₁	D₄	1	2	yes	—
51	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₃₁	Q₈	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×C₃₁	Q₈	1	2	yes	—
54	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
55	C₃₁×#108	—	2	4	no	—
56	C₃₁×#108	—	4	4	no	—
57	C₃₁×C₄⋊C₈	—	2	2	no	—
58	C₃₁×C₄⋊C₈	—	2	2	no	—
59	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
60	C₃₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₃₁×C₂²⋊C₈	—	2	4	no	—
62	C₃₁×C₂²⋊C₈	—	2	4	no	—
63	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
64	C₃₁×C₂²⋊C₈	C₂×C₄	1	4	yes	—
65	C₃₁×#97	—	2	2	no	—
66	C₄×C₈×C₃₁	—	2	2	no	—
67	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₃₁	C₂×C₄	1	2	yes	—
69	C₂⁴×C₃₁	C₂×Q₈	1	2	yes	—
70	C₂×D₄×C₃₁	—	2	4	no	—
71	C₂×D₄×C₃₁	C₄⋊C₄	1	2	yes	—
72	C₂×D₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
73	C₂×D₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	—	2	4	no	—
75	C₂²×C₄×C₃₁	—	2	4	no	—
76	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
83	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
84	M₁₆×C₃₁	—	2	2	no	—
85	M₁₆×C₃₁	—	2	2	no	—
86	M₁₆×C₃₁	—	2	4	no	—
87	M₁₆×C₃₁	—	2	2	no	—
88	M₁₆×C₃₁	—	2	4	no	—
89	M₁₆×C₃₁	—	4	8	no	—
90	M₁₆×C₃₁	#41	1	4	yes	—
91	C₂×C₈×C₃₁	—	2	2	no	—
92	C₂×C₈×C₃₁	—	2	2	no	—
93	C₂×C₈×C₃₁	—	2	4	no	—
94	C₂×C₈×C₃₁	—	2	2	no	—
95	C₂×C₈×C₃₁	—	2	2	no	—
96	C₂×C₈×C₃₁	—	2	4	no	—
97	C₂×C₈×C₃₁	—	4	4	no	—
98	C₂×C₈×C₃₁	—	4	4	no	—
99	C₂×C₈×C₃₁	—	4	8	no	—
100	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
101	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
103	C₄⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
104	C₄⋊C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄⋊C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
106	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
107	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
108	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
109	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	2	yes	—
110	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
114	#22717	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂³×C₃₁	—	2	4	no	—
116	C₂³×C₃₁	—	2	4	no	—
117	C₂³×C₃₁	—	4	2	no	—
118	C₂³×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
119	C₂³×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
120	C₂³×C₃₁	C₂²×Q₈	1	1	yes	characteristic
121	D₄×C₃₁	—	2	4	no	—
122	D₄×C₃₁	—	2	2	no	—
123	D₄×C₃₁	#108	1	4	yes	complemented
124	C₂×C₄×C₃₁	—	2	4	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	2	no	—
128	C₂×C₄×C₃₁	—	2	2	no	—
129	C₂×C₄×C₃₁	—	2	4	no	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	4	1	no	—
133	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
142	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
143	C₈×C₃₁	—	2	2	no	—
144	C₈×C₃₁	—	2	2	no	—
145	C₈×C₃₁	—	2	4	no	—
146	C₈×C₃₁	—	2	4	no	—
147	C₈×C₃₁	—	4	4	no	—
148	C₈×C₃₁	—	4	2	no	—
149	D₄×M₁₆	C₂×C₃₁	1	2	yes	—
150	C₂×C₈×D₄	C₂×C₃₁	1	1	yes	characteristic
151	#1950	C₂×C₃₁	1	2	yes	complemented
152	#1855	C₂×C₃₁	1	4	yes	complemented
153	#1837	C₂×C₃₁	1	1	yes	characteristic, complemented
154	#1810	C₂×C₃₁	1	2	yes	complemented
155	C₄×#108	C₂×C₃₁	1	1	yes	characteristic, complemented
156	C₂×#341	C₂×C₃₁	1	2	yes	complemented
157	C₂²×C₃₁	—	2	2	no	—
158	C₂²×C₃₁	—	2	1	no	—
159	C₂²×C₃₁	—	2	1	no	—
160	C₂²×C₃₁	—	2	2	no	—
161	C₂²×C₃₁	—	2	2	no	—
162	C₂²×C₃₁	—	2	2	no	—
163	C₂²×C₃₁	—	2	2	no	—
164	C₂²×C₃₁	—	4	8	no	—
165	C₂²×C₃₁	C₂×#108	1	4	yes	—
166	C₂²×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×C₃₁	#554	1	2	yes	—
168	C₄×C₃₁	—	2	2	no	—
169	C₄×C₃₁	—	2	2	no	—
170	C₄×C₃₁	—	2	1	no	—
171	C₄×C₃₁	—	2	1	no	—
172	C₄×C₃₁	—	2	1	no	—
173	C₄×C₃₁	C₂×#108	1	2	yes	—
174	C₄×C₃₁	C₄×#41	1	1	yes	characteristic
175	C₄×C₃₁	#518	1	1	yes	characteristic
176	C₄×C₃₁	#546	1	2	yes	—
177	C₂²×M₁₆	C₂²×C₃₁	1	4	yes	—
178	C₂³×C₈	C₂²×C₃₁	1	2	yes	—
179	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
180	#436	—	2	2	no	—
181	#435	—	2	4	no	—
182	C₈×D₄	—	2	2	no	—
183	C₈×D₄	C₄×C₃₁	1	4	yes	—
184	C₈×D₄	C₄×C₃₁	1	2	yes	—
185	C₈×D₄	C₄×C₃₁	1	2	yes	—
186	C₂×#108	C₂²×C₃₁	1	2	yes	—
187	C₂×#108	C₂²×C₃₁	1	4	yes	—
188	#423	C₂²×C₃₁	1	2	yes	—
189	C₂×C₄⋊C₈	C₂²×C₃₁	1	1	yes	characteristic
190	#407	C₂²×C₃₁	1	4	yes	—
191	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
192	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
193	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
194	#341	C₂²×C₃₁	1	1	yes	characteristic
195	#341	C₂²×C₃₁	1	2	yes	—
196	#341	C₂²×C₃₁	1	2	yes	—
197	#341	C₂²×C₃₁	1	4	yes	—
198	#341	C₂²×C₃₁	1	1	yes	characteristic
199	C₂×C₃₁	—	2	2	no	—
200	C₂×C₃₁	—	2	4	no	—
201	C₂×C₃₁	—	4	2	no	—
202	C₂×C₃₁	#2349	1	1	yes	characteristic
203	C₂×C₃₁	C₂²×#108	1	1	yes	characteristic
204	C₂×C₃₁	#2916	1	1	yes	characteristic
205	C₂²×D₄	Q₈×C₃₁	1	1	yes	characteristic
206	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
207	C₂×M₁₆	—	2	4	no	—
208	C₂×M₁₆	—	2	8	no	—
209	C₂×M₁₆	—	4	4	no	—
210	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
211	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
212	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	—	4	4	no	—
215	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
216	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
217	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
219	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
220	C₄×D₄	C₂×C₄×C₃₁	1	2	yes	—
221	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
222	C₄×D₄	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
224	C₄×D₄	D₄×C₃₁	1	2	yes	—
225	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
226	C₂×C₄⋊C₄	Q₈×C₃₁	1	1	yes	characteristic
227	C₂×C₂²⋊C₄	Q₈×C₃₁	1	2	yes	—
228	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
229	#108	—	2	4	no	—
230	#108	—	4	4	no	—
231	C₄⋊C₈	—	2	2	no	—
232	C₄⋊C₈	—	2	2	no	—
233	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
234	C₄⋊C₈	C₂×C₄×C₃₁	1	2	yes	—
235	C₂²⋊C₈	—	2	4	no	—
236	C₂²⋊C₈	—	2	4	no	—
237	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
238	C₂²⋊C₈	C₂×C₄×C₃₁	1	4	yes	—
239	#97	—	2	2	no	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
242	C₄×C₈	C₂×C₄×C₃₁	1	2	yes	—
243	C₃₁	#22717	1	1	yes	characteristic, direct product factor, Sylow
244	C₂⁴	C₂×Q₈×C₃₁	1	2	yes	—
245	C₂×D₄	—	2	4	no	—
246	C₂×D₄	C₄⋊C₄×C₃₁	1	2	yes	—
247	C₂×D₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
248	C₂×D₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
254	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
255	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
256	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
257	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
258	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
259	M₁₆	—	2	2	no	—
260	M₁₆	—	2	2	no	—
261	M₁₆	—	2	4	no	—
262	M₁₆	—	2	2	no	—
263	M₁₆	—	2	4	no	—
264	M₁₆	—	4	8	no	—
265	M₁₆	#41×C₃₁	1	4	yes	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	4	4	no	—
273	C₂×C₈	—	4	4	no	—
274	C₂×C₈	—	4	8	no	—
275	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
276	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
277	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
278	C₄⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
279	C₄⋊C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
280	C₄⋊C₄	C₄⋊C₄×C₃₁	1	1	yes	characteristic
281	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
282	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
283	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
284	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	2	yes	—
285	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
286	C₄²	C₂²×C₄×C₃₁	1	1	yes	characteristic
287	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
289	C₂³	—	2	4	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	4	2	no	—
292	C₂³	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
293	C₂³	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
294	C₂³	C₂²×Q₈×C₃₁	1	1	yes	characteristic
295	D₄	—	2	4	no	—
296	D₄	—	2	2	no	—
297	D₄	C₃₁×#108	1	4	yes	complemented
298	C₂×C₄	—	2	4	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	4	1	no	—
307	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
308	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
309	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
310	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
311	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
312	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	1	yes	characteristic
313	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
315	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
316	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
317	C₈	—	2	2	no	—
318	C₈	—	2	2	no	—
319	C₈	—	2	4	no	—
320	C₈	—	2	4	no	—
321	C₈	—	4	4	no	—
322	C₈	—	4	2	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	4	8	no	—
331	C₂²	C₂×C₃₁×#108	1	4	yes	—
332	C₂²	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
333	C₂²	C₃₁×#554	1	2	yes	—
334	C₄	—	2	2	no	—
335	C₄	—	2	2	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	C₂×C₃₁×#108	1	2	yes	—
340	C₄	C₄×#41×C₃₁	1	1	yes	characteristic
341	C₄	C₃₁×#518	1	1	yes	characteristic
342	C₄	C₃₁×#546	1	2	yes	—
343	C₂	—	2	2	no	—
344	C₂	—	2	4	no	—
345	C₂	—	4	2	no	—
346	C₂	C₃₁×#2349	1	1	yes	characteristic
347	C₂	C₂²×C₃₁×#108	1	1	yes	characteristic
348	C₂	C₃₁×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₃₁	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#1950	C₂	semidirect
4. C₃₁×#1855	C₂	semidirect
5. C₃₁×#1837	C₂	semidirect
6. C₃₁×#1810	C₂	semidirect
7. C₄×C₃₁×#108	C₂	semidirect
8. C₂×C₃₁×#341	C₂	semidirect
114. #22717	C₃₁	direct (N × H)
123. D₄×C₃₁	#108	semidirect
151. #1950	C₂×C₃₁	semidirect
152. #1855	C₂×C₃₁	semidirect
153. #1837	C₂×C₃₁	semidirect
154. #1810	C₂×C₃₁	semidirect
155. C₄×#108	C₂×C₃₁	semidirect
156. C₂×#341	C₂×C₃₁	semidirect
243. C₃₁	#22717	direct (N × H)
297. D₄	C₃₁×#108	semidirect

Maximal subgroups

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

subgroup	index
D₄×M₁₆×C₃₁	2
C₂×C₈×D₄×C₃₁	2
C₃₁×#1950	2
C₃₁×#1855	2
C₃₁×#1837	2
C₃₁×#1810	2
C₄×C₃₁×#108	2
C₂×C₃₁×#341	2
#22717	31

Subgroups — C31×#22717 #21479476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22717 #21479476