Subgroups — C₃₁×#22828 #21479587

Order 7936.

764 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	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1984	C₂	1	2	yes	maximal
3	C₃₁×#1916	C₂	1	4	yes	maximal
4	C₃₁×#1839	C₂	1	2	yes	maximal
5	C₃₁×#1831	C₂	1	1	yes	maximal, characteristic
6	C₈×C₄⋊C₄×C₃₁	C₂	1	2	yes	maximal
7	C₄×C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₃₁×#1744	C₂	1	2	yes	maximal
9	C₂×C₄×Q₈×C₃₁	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₃₁	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
16	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
18	C₄×C₄⋊C₄×C₃₁	C₄	1	2	yes	—
19	C₄×C₄⋊C₄×C₃₁	C₄	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
21	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
22	C₄³×C₃₁	C₂²	1	1	yes	characteristic
23	C₄³×C₃₁	C₂²	1	2	yes	—
24	C₃₁×#336	C₂²	1	2	yes	—
25	C₃₁×#336	C₂²	1	2	yes	—
26	C₃₁×#336	C₂²	1	1	yes	characteristic
27	C₃₁×#336	C₂²	1	4	yes	—
28	C₃₁×#336	C₂²	1	4	yes	—
29	C₃₁×#336	C₂²	1	4	yes	—
30	C₃₁×#336	C₂²	1	1	yes	characteristic
31	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
33	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
34	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
35	C₄×Q₈×C₃₁	—	2	4	no	—
36	C₄×Q₈×C₃₁	—	2	2	no	—
37	C₄×Q₈×C₃₁	—	2	2	no	—
38	C₄×Q₈×C₃₁	C₈	1	8	yes	complemented
39	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
54	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
56	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
58	C₃₁×C₄⋊C₈	—	2	4	no	—
59	C₃₁×C₄⋊C₈	—	2	4	no	—
60	C₄×C₈×C₃₁	—	2	8	no	—
61	C₄×C₈×C₃₁	—	2	4	no	—
62	C₃₁×#95	C₂×C₄	1	2	yes	—
63	C₃₁×#95	C₂×C₄	1	2	yes	—
64	C₃₁×#95	C₂×C₄	1	2	yes	—
65	C₂×Q₈×C₃₁	—	2	2	no	—
66	C₂×Q₈×C₃₁	—	2	2	no	—
67	C₂×Q₈×C₃₁	C₂×C₈	1	4	yes	—
68	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
69	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
72	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
75	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₃₁	—	2	2	no	—
80	C₂×C₈×C₃₁	—	2	2	no	—
81	C₂×C₈×C₃₁	—	2	2	no	—
82	C₂×C₈×C₃₁	—	2	4	no	—
83	C₂×C₈×C₃₁	—	2	2	no	—
84	C₂×C₈×C₃₁	—	2	4	no	—
85	C₂×C₈×C₃₁	—	2	2	no	—
86	C₂×C₈×C₃₁	—	2	4	no	—
87	C₂×C₈×C₃₁	#41	1	4	yes	—
88	C₄⋊C₄×C₃₁	—	2	4	no	—
89	C₄⋊C₄×C₃₁	—	2	2	no	—
90	C₄⋊C₄×C₃₁	—	2	4	no	—
91	C₄⋊C₄×C₃₁	C₂×C₈	1	8	yes	—
92	C₄⋊C₄×C₃₁	C₂×C₈	1	4	yes	—
93	C₄⋊C₄×C₃₁	M₁₆	1	4	yes	—
94	C₄²×C₃₁	—	2	4	no	—
95	C₄²×C₃₁	—	2	2	no	—
96	C₄²×C₃₁	—	2	2	no	—
97	C₄²×C₃₁	—	2	4	no	—
98	C₄²×C₃₁	—	2	4	no	—
99	C₄²×C₃₁	—	2	2	no	—
100	C₄²×C₃₁	—	2	2	no	—
101	C₄²×C₃₁	—	2	2	no	—
102	C₄²×C₃₁	—	2	2	no	—
103	C₄²×C₃₁	—	4	1	no	—
104	C₄²×C₃₁	—	4	2	no	—
105	C₄²×C₃₁	C₂×C₈	1	8	yes	—
106	C₄²×C₃₁	C₂×C₈	1	4	yes	—
107	C₄²×C₃₁	#41	1	2	yes	—
108	C₄²×C₃₁	#41	1	2	yes	—
109	#22828	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
111	Q₈×C₃₁	—	2	8	no	—
112	C₂×C₄×C₃₁	—	2	2	no	—
113	C₂×C₄×C₃₁	—	2	2	no	—
114	C₂×C₄×C₃₁	—	2	1	no	—
115	C₂×C₄×C₃₁	—	2	2	no	—
116	C₂×C₄×C₃₁	—	2	1	no	—
117	C₂×C₄×C₃₁	—	2	1	no	—
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	2	no	—
120	C₂×C₄×C₃₁	—	2	1	no	—
121	C₂×C₄×C₃₁	—	2	1	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	1	no	—
124	C₂×C₄×C₃₁	—	2	1	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	1	no	—
128	C₂×C₄×C₃₁	—	2	1	no	—
129	C₂×C₄×C₃₁	—	2	2	no	—
130	C₂×C₄×C₃₁	—	2	2	no	—
131	C₂×C₄×C₃₁	—	2	1	no	—
132	C₂×C₄×C₃₁	#117	1	2	yes	—
133	C₂×C₄×C₃₁	#117	1	2	yes	—
134	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
135	C₂×C₄×C₃₁	C₂²×C₈	1	4	yes	—
136	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
137	C₂×C₄×C₃₁	C₂²×C₈	1	4	yes	—
138	C₂×C₄×C₃₁	C₂²×C₈	1	2	yes	—
139	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
140	C₂×C₄×C₃₁	C₂×M₁₆	1	2	yes	—
141	C₂×C₄×C₃₁	#131	1	2	yes	—
142	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
144	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
145	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
146	C₈×C₃₁	—	2	4	no	—
147	C₈×C₃₁	—	4	2	no	—
148	C₈×C₃₁	—	4	4	no	—
149	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic
150	#1984	C₂×C₃₁	1	2	yes	—
151	#1916	C₂×C₃₁	1	4	yes	—
152	#1839	C₂×C₃₁	1	2	yes	—
153	#1831	C₂×C₃₁	1	1	yes	characteristic
154	C₈×C₄⋊C₄	C₂×C₃₁	1	2	yes	—
155	C₄×C₄⋊C₈	C₂×C₃₁	1	1	yes	characteristic
156	#1744	C₂×C₃₁	1	2	yes	—
157	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
158	C₂²×C₃₁	C₄×#41	1	1	yes	characteristic
159	C₂²×C₃₁	#519	1	1	yes	characteristic
160	C₂²×C₃₁	C₂³×C₈	1	1	yes	characteristic
161	C₂²×C₃₁	C₂²×M₁₆	1	1	yes	characteristic
162	C₂²×C₃₁	C₂×#131	1	1	yes	characteristic
163	C₂²×C₃₁	#568	1	1	yes	characteristic
164	C₄×C₃₁	—	2	4	no	—
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	2	4	no	—
167	C₄×C₃₁	—	2	2	no	—
168	C₄×C₃₁	—	2	4	no	—
169	C₄×C₃₁	—	2	2	no	—
170	C₄×C₃₁	—	2	2	no	—
171	C₄×C₃₁	—	4	2	no	—
172	C₄×C₃₁	—	4	1	no	—
173	C₄×C₃₁	#431	1	4	yes	—
174	C₄×C₃₁	#552	1	2	yes	—
175	C₄×C₃₁	#556	1	2	yes	—
176	C₂×C₄×Q₈	C₄×C₃₁	1	1	yes	characteristic
177	C₂×C₄×Q₈	C₄×C₃₁	1	1	yes	characteristic
178	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
179	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
180	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
182	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
183	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
184	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
185	C₄×C₄⋊C₄	C₄×C₃₁	1	2	yes	—
186	C₄×C₄⋊C₄	C₄×C₃₁	1	1	yes	characteristic
187	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
188	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
189	C₄³	C₂²×C₃₁	1	1	yes	characteristic
190	C₄³	C₂²×C₃₁	1	2	yes	—
191	#336	C₂²×C₃₁	1	2	yes	—
192	#336	C₂²×C₃₁	1	2	yes	—
193	#336	C₂²×C₃₁	1	1	yes	characteristic
194	#336	C₂²×C₃₁	1	4	yes	—
195	#336	C₂²×C₃₁	1	4	yes	—
196	#336	C₂²×C₃₁	1	4	yes	—
197	#336	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×C₃₁	#2356	1	1	yes	characteristic
199	C₂×C₃₁	C₂×#431	1	1	yes	characteristic
200	C₂×C₃₁	#2925	1	1	yes	characteristic
201	C₂×C₃₁	C₈×#41	1	1	yes	characteristic
202	C₂×C₃₁	#2970	1	1	yes	characteristic
203	C₂×C₃₁	#2982	1	1	yes	characteristic
204	C₂×C₃₁	#2984	1	1	yes	characteristic
205	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
206	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
207	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
208	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
209	C₄×Q₈	—	2	4	no	—
210	C₄×Q₈	—	2	2	no	—
211	C₄×Q₈	—	2	2	no	—
212	C₄×Q₈	C₈×C₃₁	1	8	yes	complemented
213	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
218	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
221	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
222	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
223	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
224	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
225	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
226	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
228	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
230	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
231	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
232	C₄⋊C₈	—	2	4	no	—
233	C₄⋊C₈	—	2	4	no	—
234	C₄×C₈	—	2	8	no	—
235	C₄×C₈	—	2	4	no	—
236	#95	C₂×C₄×C₃₁	1	2	yes	—
237	#95	C₂×C₄×C₃₁	1	2	yes	—
238	#95	C₂×C₄×C₃₁	1	2	yes	—
239	C₃₁	#22828	1	1	yes	characteristic, direct product factor, Sylow
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	—	2	2	no	—
242	C₂×Q₈	C₂×C₈×C₃₁	1	4	yes	—
243	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
244	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
245	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
246	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
247	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
250	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
253	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	4	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	4	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	4	no	—
262	C₂×C₈	#41×C₃₁	1	4	yes	—
263	C₄⋊C₄	—	2	4	no	—
264	C₄⋊C₄	—	2	2	no	—
265	C₄⋊C₄	—	2	4	no	—
266	C₄⋊C₄	C₂×C₈×C₃₁	1	8	yes	—
267	C₄⋊C₄	C₂×C₈×C₃₁	1	4	yes	—
268	C₄⋊C₄	M₁₆×C₃₁	1	4	yes	—
269	C₄²	—	2	4	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	—	2	4	no	—
273	C₄²	—	2	4	no	—
274	C₄²	—	2	2	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	2	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	4	1	no	—
279	C₄²	—	4	2	no	—
280	C₄²	C₂×C₈×C₃₁	1	8	yes	—
281	C₄²	C₂×C₈×C₃₁	1	4	yes	—
282	C₄²	#41×C₃₁	1	2	yes	—
283	C₄²	#41×C₃₁	1	2	yes	—
284	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
285	Q₈	—	2	8	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	1	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	C₃₁×#117	1	2	yes	—
307	C₂×C₄	C₃₁×#117	1	2	yes	—
308	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
309	C₂×C₄	C₂²×C₈×C₃₁	1	4	yes	—
310	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
311	C₂×C₄	C₂²×C₈×C₃₁	1	4	yes	—
312	C₂×C₄	C₂²×C₈×C₃₁	1	2	yes	—
313	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
314	C₂×C₄	C₂×M₁₆×C₃₁	1	2	yes	—
315	C₂×C₄	C₃₁×#131	1	2	yes	—
316	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
317	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
318	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
319	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
320	C₈	—	2	4	no	—
321	C₈	—	4	2	no	—
322	C₈	—	4	4	no	—
323	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
324	C₂²	C₄×#41×C₃₁	1	1	yes	characteristic
325	C₂²	C₃₁×#519	1	1	yes	characteristic
326	C₂²	C₂³×C₈×C₃₁	1	1	yes	characteristic
327	C₂²	C₂²×M₁₆×C₃₁	1	1	yes	characteristic
328	C₂²	C₂×C₃₁×#131	1	1	yes	characteristic
329	C₂²	C₃₁×#568	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	2	2	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	—	2	4	no	—
335	C₄	—	2	2	no	—
336	C₄	—	2	2	no	—
337	C₄	—	4	2	no	—
338	C₄	—	4	1	no	—
339	C₄	C₃₁×#431	1	4	yes	—
340	C₄	C₃₁×#552	1	2	yes	—
341	C₄	C₃₁×#556	1	2	yes	—
342	C₂	C₃₁×#2356	1	1	yes	characteristic
343	C₂	C₂×C₃₁×#431	1	1	yes	characteristic
344	C₂	C₃₁×#2925	1	1	yes	characteristic
345	C₂	C₈×#41×C₃₁	1	1	yes	characteristic
346	C₂	C₃₁×#2970	1	1	yes	characteristic
347	C₂	C₃₁×#2982	1	1	yes	characteristic
348	C₂	C₃₁×#2984	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle, prime radical	C₂³×C₃₁	C₂³×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
38. C₄×Q₈×C₃₁	C₈	semidirect
109. #22828	C₃₁	direct (N × H)
212. C₄×Q₈	C₈×C₃₁	semidirect
239. C₃₁	#22828	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×Q₈×C₃₁	2
C₃₁×#1984	2
C₃₁×#1916	2
C₃₁×#1839	2
C₃₁×#1831	2
C₈×C₄⋊C₄×C₃₁	2
C₄×C₃₁×C₄⋊C₈	2
C₃₁×#1744	2
#22828	31

Subgroups — C31×#22828 #21479587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#22828 #21479587