Subgroups — C₃₁×#34257 #21491016

Order 7936.

5050 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2341	C₂	1	8	yes	maximal, complemented
5	Q₈×C₂²⋊C₄×C₃₁	C₂	1	8	yes	maximal, complemented
6	C₃₁×#2311	C₂	1	6	yes	maximal, complemented
7	C₃₁×#2297	C₂	1	6	yes	maximal, complemented
8	C₂×C₃₁×2₋¹⁺⁴	—	2	8	no	—
9	C₂×C₃₁×2₋¹⁺⁴	—	2	8	no	—
10	C₂×C₃₁×2₋¹⁺⁴	C₄	1	16	yes	complemented
11	C₂²×#41×C₃₁	C₂²	1	6	yes	—
12	C₂²×#41×C₃₁	C₂²	1	4	yes	—
13	C₂³×Q₈×C₃₁	C₂²	1	4	yes	—
14	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic
15	C₃₁×#519	—	2	8	no	—
16	C₂×C₄×Q₈×C₃₁	—	2	8	no	—
17	C₂×C₄×Q₈×C₃₁	C₂²	1	8	yes	—
18	C₂×C₄×Q₈×C₃₁	C₂²	1	8	yes	—
19	C₂×C₃₁×#117	C₂²	1	6	yes	—
20	C₂²×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
21	C₂²×C₄²×C₃₁	C₂²	1	3	yes	—
22	C₃₁×#391	C₂²	1	12	yes	—
23	C₃₁×#391	C₂²	1	12	yes	—
24	C₃₁×#390	C₂²	1	12	yes	—
25	C₃₁×#390	C₂²	1	12	yes	—
26	C₃₁×#386	C₂²	1	12	yes	—
27	C₃₁×#386	C₂²	1	4	yes	—
28	C₃₁×#380	C₂²	1	24	yes	—
29	C₄×C₂²⋊C₄×C₃₁	C₂²	1	24	yes	—
30	C₃₁×2₋¹⁺⁴	—	2	128	no	—
31	C₂×#41×C₃₁	—	2	16	no	—
32	C₂×#41×C₃₁	—	2	16	no	—
33	C₂×#41×C₃₁	—	2	24	no	—
34	C₂×#41×C₃₁	—	2	24	no	—
35	C₂×#41×C₃₁	C₂×C₄	1	48	yes	—
36	C₂×#41×C₃₁	C₂×C₄	1	32	yes	complemented
37	C₂²×Q₈×C₃₁	—	2	16	no	—
38	C₂²×Q₈×C₃₁	—	2	16	no	—
39	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	—
40	C₂²×Q₈×C₃₁	C₂×C₄	1	32	yes	complemented
41	C₂²×Q₈×C₃₁	D₄	1	8	yes	—
42	C₂²×Q₈×C₃₁	D₄	1	8	yes	—
43	C₂²×Q₈×C₃₁	C₂³	1	6	yes	—
44	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
45	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
46	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
47	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₃₁	C₂³	1	12	yes	—
49	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
50	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
51	C₄×Q₈×C₃₁	—	2	32	no	—
52	C₄×Q₈×C₃₁	—	2	32	no	—
53	C₃₁×#117	—	2	24	no	—
54	C₂×C₄⋊C₄×C₃₁	—	2	12	no	—
55	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
56	C₂×C₄⋊C₄×C₃₁	C₂³	1	12	yes	—
57	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
59	C₂×C₂²⋊C₄×C₃₁	C₂³	1	24	yes	—
60	C₂×C₄²×C₃₁	—	2	12	no	—
61	C₂×C₄²×C₃₁	C₂³	1	12	yes	—
62	C₂×C₄²×C₃₁	C₂³	1	12	yes	—
63	C₃₁×#95	C₂³	1	8	yes	—
64	C₃₁×#95	C₂³	1	24	yes	—
65	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
66	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
67	#41×C₃₁	—	2	128	no	—
68	#41×C₃₁	—	2	192	no	—
69	C₂×Q₈×C₃₁	—	2	128	no	—
70	C₂×Q₈×C₃₁	—	2	12	no	—
71	C₂×Q₈×C₃₁	—	2	12	no	—
72	C₂×Q₈×C₃₁	C₂²⋊C₄	1	64	yes	complemented
73	C₂×Q₈×C₃₁	C₂²×C₄	1	24	yes	—
74	C₂×Q₈×C₃₁	C₂²×C₄	1	16	yes	—
75	C₂×Q₈×C₃₁	C₂×D₄	1	16	yes	—
76	C₂×Q₈×C₃₁	C₂×D₄	1	16	yes	—
77	C₂×D₄×C₃₁	—	2	8	no	—
78	C₂×D₄×C₃₁	—	2	8	no	—
79	C₂×D₄×C₃₁	—	2	12	no	—
80	C₂×D₄×C₃₁	—	2	12	no	—
81	C₂×D₄×C₃₁	C₂²×C₄	1	16	yes	—
82	C₂×D₄×C₃₁	C₂²×C₄	1	24	yes	—
83	C₂²×C₄×C₃₁	—	2	2	no	—
84	C₂²×C₄×C₃₁	—	2	24	no	—
85	C₂²×C₄×C₃₁	—	2	24	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	6	no	—
88	C₂²×C₄×C₃₁	—	4	6	no	—
89	C₂²×C₄×C₃₁	C₂²×C₄	1	48	yes	—
90	C₂²×C₄×C₃₁	C₂²×C₄	1	12	yes	—
91	C₂²×C₄×C₃₁	C₂×D₄	1	12	yes	—
92	C₂²×C₄×C₃₁	C₂×D₄	1	12	yes	—
93	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
94	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
96	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
98	C₄⋊C₄×C₃₁	—	2	24	no	—
99	C₄⋊C₄×C₃₁	—	2	24	no	—
100	C₂²⋊C₄×C₃₁	—	2	8	no	—
101	C₂²⋊C₄×C₃₁	—	2	16	no	—
102	C₂²⋊C₄×C₃₁	—	4	24	no	—
103	C₄²×C₃₁	—	2	24	no	—
104	C₄²×C₃₁	—	2	24	no	—
105	#34257	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₃₁	—	2	2	no	—
107	C₂³×C₃₁	—	2	2	no	—
108	C₂³×C₃₁	—	2	4	no	—
109	C₂³×C₃₁	—	2	4	no	—
110	C₂³×C₃₁	—	2	8	no	—
111	C₂³×C₃₁	—	2	8	no	—
112	C₂³×C₃₁	C₂³×C₄	1	8	yes	—
113	C₂³×C₃₁	C₂³×C₄	1	2	yes	—
114	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
115	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
116	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
117	Q₈×C₃₁	—	2	48	no	—
118	Q₈×C₃₁	C₂×C₂²⋊C₄	1	64	yes	—
119	D₄×C₃₁	—	2	32	no	—
120	D₄×C₃₁	—	2	48	no	—
121	C₂×C₄×C₃₁	—	2	8	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	4	no	—
124	C₂×C₄×C₃₁	—	2	4	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	96	no	—
127	C₂×C₄×C₃₁	—	2	8	no	—
128	C₂×C₄×C₃₁	—	2	6	no	—
129	C₂×C₄×C₃₁	—	2	8	no	—
130	C₂×C₄×C₃₁	—	2	8	no	—
131	C₂×C₄×C₃₁	—	2	12	no	—
132	C₂×C₄×C₃₁	—	4	12	no	—
133	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	48	yes	—
134	C₂×C₄×C₃₁	C₂³×C₄	1	8	yes	—
135	C₂×C₄×C₃₁	C₂³×C₄	1	12	yes	—
136	C₂×C₄×C₃₁	C₂²×D₄	1	12	yes	—
137	C₂×C₄×C₃₁	C₂²×D₄	1	12	yes	—
138	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	complemented
139	C₂²×2₋¹⁺⁴	C₂×C₃₁	1	1	yes	characteristic
140	C₂×#519	C₂×C₃₁	1	1	yes	characteristic, complemented
141	C₂²×C₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
142	#2341	C₂×C₃₁	1	8	yes	complemented
143	Q₈×C₂²⋊C₄	C₂×C₃₁	1	8	yes	complemented
144	#2311	C₂×C₃₁	1	6	yes	complemented
145	#2297	C₂×C₃₁	1	6	yes	complemented
146	C₂²×C₃₁	—	2	4	no	—
147	C₂²×C₃₁	—	2	2	no	—
148	C₂²×C₃₁	—	2	2	no	—
149	C₂²×C₃₁	—	2	4	no	—
150	C₂²×C₃₁	—	2	8	no	—
151	C₂²×C₃₁	—	2	16	no	—
152	C₂²×C₃₁	—	4	4	no	—
153	C₂²×C₃₁	—	4	4	no	—
154	C₂²×C₃₁	—	4	8	no	—
155	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	4	yes	—
156	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
157	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
158	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
159	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
160	C₂²×C₃₁	#585	1	2	yes	—
161	C₄×C₃₁	—	2	8	no	—
162	C₄×C₃₁	—	2	4	no	—
163	C₄×C₃₁	—	4	6	no	—
164	C₄×C₃₁	—	4	8	no	—
165	C₄×C₃₁	C₂²×C₂²⋊C₄	1	24	yes	—
166	C₂×2₋¹⁺⁴	—	2	8	no	—
167	C₂×2₋¹⁺⁴	—	2	8	no	—
168	C₂×2₋¹⁺⁴	C₄×C₃₁	1	16	yes	complemented
169	C₂²×#41	C₂²×C₃₁	1	6	yes	—
170	C₂²×#41	C₂²×C₃₁	1	4	yes	—
171	C₂³×Q₈	C₂²×C₃₁	1	4	yes	—
172	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic
173	#519	—	2	8	no	—
174	C₂×C₄×Q₈	—	2	8	no	—
175	C₂×C₄×Q₈	C₂²×C₃₁	1	8	yes	—
176	C₂×C₄×Q₈	C₂²×C₃₁	1	8	yes	—
177	C₂×#117	C₂²×C₃₁	1	6	yes	—
178	C₂²×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
179	C₂²×C₄²	C₂²×C₃₁	1	3	yes	—
180	#391	C₂²×C₃₁	1	12	yes	—
181	#391	C₂²×C₃₁	1	12	yes	—
182	#390	C₂²×C₃₁	1	12	yes	—
183	#390	C₂²×C₃₁	1	12	yes	—
184	#386	C₂²×C₃₁	1	12	yes	—
185	#386	C₂²×C₃₁	1	4	yes	—
186	#380	C₂²×C₃₁	1	24	yes	—
187	C₄×C₂²⋊C₄	C₂²×C₃₁	1	24	yes	—
188	C₂×C₃₁	—	2	4	no	—
189	C₂×C₃₁	—	4	8	no	—
190	C₂×C₃₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₃₁	C₄×2₋¹⁺⁴	1	2	yes	—
192	C₂×C₃₁	#3486	1	1	yes	characteristic
193	C₂×C₃₁	#3487	1	1	yes	characteristic
194	C₂×C₃₁	#3497	1	2	yes	—
195	2₋¹⁺⁴	—	2	128	no	—
196	C₂×#41	—	2	16	no	—
197	C₂×#41	—	2	16	no	—
198	C₂×#41	—	2	24	no	—
199	C₂×#41	—	2	24	no	—
200	C₂×#41	C₂×C₄×C₃₁	1	48	yes	—
201	C₂×#41	C₂×C₄×C₃₁	1	32	yes	complemented
202	C₂²×Q₈	—	2	16	no	—
203	C₂²×Q₈	—	2	16	no	—
204	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	—
205	C₂²×Q₈	C₂×C₄×C₃₁	1	32	yes	complemented
206	C₂²×Q₈	D₄×C₃₁	1	8	yes	—
207	C₂²×Q₈	D₄×C₃₁	1	8	yes	—
208	C₂²×Q₈	C₂³×C₃₁	1	6	yes	—
209	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
210	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
211	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
212	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₃₁	1	12	yes	—
214	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
215	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
216	C₄×Q₈	—	2	32	no	—
217	C₄×Q₈	—	2	32	no	—
218	#117	—	2	24	no	—
219	C₂×C₄⋊C₄	—	2	12	no	—
220	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
221	C₂×C₄⋊C₄	C₂³×C₃₁	1	12	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
224	C₂×C₂²⋊C₄	C₂³×C₃₁	1	24	yes	—
225	C₂×C₄²	—	2	12	no	—
226	C₂×C₄²	C₂³×C₃₁	1	12	yes	—
227	C₂×C₄²	C₂³×C₃₁	1	12	yes	—
228	#95	C₂³×C₃₁	1	8	yes	—
229	#95	C₂³×C₃₁	1	24	yes	—
230	C₃₁	#34257	1	1	yes	characteristic, direct product factor, Sylow
231	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
232	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
233	#41	—	2	128	no	—
234	#41	—	2	192	no	—
235	C₂×Q₈	—	2	128	no	—
236	C₂×Q₈	—	2	12	no	—
237	C₂×Q₈	—	2	12	no	—
238	C₂×Q₈	C₂²⋊C₄×C₃₁	1	64	yes	complemented
239	C₂×Q₈	C₂²×C₄×C₃₁	1	24	yes	—
240	C₂×Q₈	C₂²×C₄×C₃₁	1	16	yes	—
241	C₂×Q₈	C₂×D₄×C₃₁	1	16	yes	—
242	C₂×Q₈	C₂×D₄×C₃₁	1	16	yes	—
243	C₂×D₄	—	2	8	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	2	12	no	—
246	C₂×D₄	—	2	12	no	—
247	C₂×D₄	C₂²×C₄×C₃₁	1	16	yes	—
248	C₂×D₄	C₂²×C₄×C₃₁	1	24	yes	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	24	no	—
251	C₂²×C₄	—	2	24	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	6	no	—
254	C₂²×C₄	—	4	6	no	—
255	C₂²×C₄	C₂²×C₄×C₃₁	1	48	yes	—
256	C₂²×C₄	C₂²×C₄×C₃₁	1	12	yes	—
257	C₂²×C₄	C₂×D₄×C₃₁	1	12	yes	—
258	C₂²×C₄	C₂×D₄×C₃₁	1	12	yes	—
259	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
260	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
261	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
262	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
263	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
264	C₄⋊C₄	—	2	24	no	—
265	C₄⋊C₄	—	2	24	no	—
266	C₂²⋊C₄	—	2	8	no	—
267	C₂²⋊C₄	—	2	16	no	—
268	C₂²⋊C₄	—	4	24	no	—
269	C₄²	—	2	24	no	—
270	C₄²	—	2	24	no	—
271	C₂³	—	2	2	no	—
272	C₂³	—	2	2	no	—
273	C₂³	—	2	4	no	—
274	C₂³	—	2	4	no	—
275	C₂³	—	2	8	no	—
276	C₂³	—	2	8	no	—
277	C₂³	C₂³×C₄×C₃₁	1	8	yes	—
278	C₂³	C₂³×C₄×C₃₁	1	2	yes	—
279	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
280	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
281	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
282	Q₈	—	2	48	no	—
283	Q₈	C₂×C₂²⋊C₄×C₃₁	1	64	yes	—
284	D₄	—	2	32	no	—
285	D₄	—	2	48	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	4	no	—
290	C₂×C₄	—	2	2	no	—
291	C₂×C₄	—	2	96	no	—
292	C₂×C₄	—	2	8	no	—
293	C₂×C₄	—	2	6	no	—
294	C₂×C₄	—	2	8	no	—
295	C₂×C₄	—	2	8	no	—
296	C₂×C₄	—	2	12	no	—
297	C₂×C₄	—	4	12	no	—
298	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	48	yes	—
299	C₂×C₄	C₂³×C₄×C₃₁	1	8	yes	—
300	C₂×C₄	C₂³×C₄×C₃₁	1	12	yes	—
301	C₂×C₄	C₂²×D₄×C₃₁	1	12	yes	—
302	C₂×C₄	C₂²×D₄×C₃₁	1	12	yes	—
303	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	complemented
304	C₂²	—	2	4	no	—
305	C₂²	—	2	2	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	4	no	—
308	C₂²	—	2	8	no	—
309	C₂²	—	2	16	no	—
310	C₂²	—	4	4	no	—
311	C₂²	—	4	4	no	—
312	C₂²	—	4	8	no	—
313	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	4	yes	—
314	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
315	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
316	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
317	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
318	C₂²	C₃₁×#585	1	2	yes	—
319	C₄	—	2	8	no	—
320	C₄	—	2	4	no	—
321	C₄	—	4	6	no	—
322	C₄	—	4	8	no	—
323	C₄	C₂²×C₂²⋊C₄×C₃₁	1	24	yes	—
324	C₂	—	2	4	no	—
325	C₂	—	4	8	no	—
326	C₂	C₂³×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
327	C₂	C₄×C₃₁×2₋¹⁺⁴	1	2	yes	—
328	C₂	C₃₁×#3486	1	1	yes	characteristic
329	C₂	C₃₁×#3487	1	1	yes	characteristic
330	C₂	C₃₁×#3497	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
prime radical	C₂²×C₃₁×2₋¹⁺⁴	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#519	C₂	semidirect
3. C₂²×C₄×Q₈×C₃₁	C₂	semidirect
4. C₃₁×#2341	C₂	semidirect
5. Q₈×C₂²⋊C₄×C₃₁	C₂	semidirect
6. C₃₁×#2311	C₂	semidirect
7. C₃₁×#2297	C₂	semidirect
10. C₂×C₃₁×2₋¹⁺⁴	C₄	semidirect
36. C₂×#41×C₃₁	C₂×C₄	semidirect
40. C₂²×Q₈×C₃₁	C₂×C₄	semidirect
72. C₂×Q₈×C₃₁	C₂²⋊C₄	semidirect
105. #34257	C₃₁	direct (N × H)
138. C₂×C₄×C₃₁	2₋¹⁺⁴	semidirect
140. C₂×#519	C₂×C₃₁	semidirect
141. C₂²×C₄×Q₈	C₂×C₃₁	semidirect
142. #2341	C₂×C₃₁	semidirect
143. Q₈×C₂²⋊C₄	C₂×C₃₁	semidirect
144. #2311	C₂×C₃₁	semidirect
145. #2297	C₂×C₃₁	semidirect
168. C₂×2₋¹⁺⁴	C₄×C₃₁	semidirect
201. C₂×#41	C₂×C₄×C₃₁	semidirect
205. C₂²×Q₈	C₂×C₄×C₃₁	semidirect
230. C₃₁	#34257	direct (N × H)
238. C₂×Q₈	C₂²⋊C₄×C₃₁	semidirect
303. C₂×C₄	C₃₁×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×2₋¹⁺⁴	2
C₂×C₃₁×#519	2
C₂²×C₄×Q₈×C₃₁	2
C₃₁×#2341	2
Q₈×C₂²⋊C₄×C₃₁	2
C₃₁×#2311	2
C₃₁×#2297	2
#34257	31

Subgroups — C31×#34257 #21491016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#34257 #21491016