Subgroups — C₃₁×#33851 #21490610

Order 7936.

674 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃₁×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3285	C₂	1	2	yes	maximal, complemented
4	C₃₁×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#2215	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2211	C₂	1	2	yes	maximal, complemented
8	C₃₁×#2189	C₂	1	2	yes	maximal, complemented
9	C₃₁×#2185	C₂	1	2	yes	maximal, complemented
10	C₄×C₃₁×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#135	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#548	—	2	2	no	—
15	C₃₁×#508	—	2	4	no	—
16	C₂×C₃₁×Q₃₂	—	2	4	no	—
17	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₃₁×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×Q₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₃₁×D₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
25	C₃₁×#495	C₂²	1	2	yes	—
26	C₃₁×#467	C₂²	1	2	yes	—
27	C₃₁×#466	C₂²	1	2	yes	—
28	C₃₁×#464	—	2	2	no	—
29	C₃₁×#452	—	2	2	no	—
30	C₃₁×#448	—	2	2	no	—
31	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	—
32	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
33	C₃₁×#366	C₂²	1	1	yes	characteristic
34	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₃₁×#358	C₂²	1	2	yes	—
36	C₃₁×#358	C₂²	1	2	yes	—
37	C₃₁×#357	C₂²	1	2	yes	—
38	C₃₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₃₁×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
41	C₂×#41×C₃₁	—	2	2	no	—
42	C₂²×Q₈×C₃₁	—	2	2	no	—
43	C₃₁×#135	—	2	4	no	—
44	C₃₁×#135	—	4	2	no	—
45	C₂×Q₁₆×C₃₁	—	2	4	no	—
46	C₂×Q₁₆×C₃₁	—	2	2	no	—
47	C₂×Q₁₆×C₃₁	—	4	2	no	—
48	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
50	C₂×SD₁₆×C₃₁	—	2	2	no	—
51	C₂×SD₁₆×C₃₁	—	2	2	no	—
52	C₂×D₈×C₃₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
55	C₃₁×#124	—	2	2	no	—
56	C₃₁×#124	—	4	2	no	—
57	C₃₁×C₂²⋊Q₈	—	2	2	no	—
58	C₃₁×C₂²⋊Q₈	—	4	2	no	—
59	C₃₁×#121	—	2	2	no	—
60	C₃₁×#121	—	4	2	no	—
61	C₄×Q₈×C₃₁	—	2	2	no	—
62	C₄×D₄×C₃₁	—	4	2	no	—
63	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
64	C₃₁×Q₃₂	—	2	4	no	—
65	C₃₁×Q₃₂	—	2	2	no	—
66	C₃₁×Q₃₂	D₄	1	4	yes	complemented
67	C₃₁×SD₃₂	—	2	4	no	—
68	C₃₁×SD₃₂	—	4	2	no	—
69	C₃₁×D₁₆	—	2	2	no	—
70	C₂×C₁₆×C₃₁	—	2	2	no	—
71	C₂×C₁₆×C₃₁	—	2	2	no	—
72	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
73	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
75	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
76	C₃₁×#107	C₂³	1	2	yes	—
77	C₃₁×C₄⋊C₈	D₄	1	1	yes	characteristic
78	C₃₁×#103	—	2	2	no	—
79	C₃₁×#103	—	2	2	no	—
80	C₃₁×#102	—	2	2	no	—
81	C₃₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
82	C₃₁×C₂²⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
84	#41×C₃₁	—	4	4	no	—
85	#41×C₃₁	—	8	2	no	—
86	C₂×Q₈×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	—	2	2	no	—
88	C₂×Q₈×C₃₁	—	4	4	no	—
89	C₂×Q₈×C₃₁	—	4	2	no	—
90	C₂×Q₈×C₃₁	—	8	2	no	—
91	C₂×D₄×C₃₁	—	2	2	no	—
92	C₂×D₄×C₃₁	—	4	2	no	—
93	C₂×D₄×C₃₁	—	4	2	no	—
94	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₃₁	—	4	2	no	—
96	C₂²×C₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	Q₁₆×C₃₁	—	2	2	no	—
100	Q₁₆×C₃₁	—	2	2	no	—
101	Q₁₆×C₃₁	—	2	2	no	—
102	Q₁₆×C₃₁	—	4	4	no	—
103	Q₁₆×C₃₁	C₂×D₄	1	4	yes	—
104	SD₁₆×C₃₁	—	4	4	no	—
105	SD₁₆×C₃₁	—	8	2	no	—
106	D₈×C₃₁	—	2	2	no	—
107	D₈×C₃₁	—	2	2	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	1	no	—
110	C₂×C₈×C₃₁	—	2	1	no	—
111	C₂×C₈×C₃₁	—	2	1	no	—
112	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₃₁	—	2	2	no	—
117	C₄⋊C₄×C₃₁	—	4	2	no	—
118	C₄⋊C₄×C₃₁	—	4	2	no	—
119	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
120	C₂²⋊C₄×C₃₁	—	4	2	no	—
121	C₂²⋊C₄×C₃₁	—	4	2	no	—
122	C₂²⋊C₄×C₃₁	—	4	2	no	—
123	C₂²⋊C₄×C₃₁	—	4	2	no	—
124	C₂²⋊C₄×C₃₁	D₈	1	1	yes	characteristic
125	C₂²⋊C₄×C₃₁	D₈	1	1	yes	characteristic
126	C₄²×C₃₁	—	4	2	no	—
127	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
128	C₁₆×C₃₁	—	2	1	no	—
129	C₁₆×C₃₁	—	2	1	no	—
130	C₁₆×C₃₁	—	2	1	no	—
131	C₁₆×C₃₁	C₂×D₄	1	2	yes	—
132	#33851	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂³×C₃₁	—	4	2	no	—
134	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
135	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
136	Q₈×C₃₁	—	2	4	no	—
137	Q₈×C₃₁	—	4	2	no	—
138	Q₈×C₃₁	—	4	2	no	—
139	Q₈×C₃₁	—	4	2	no	—
140	Q₈×C₃₁	—	8	4	no	—
141	D₄×C₃₁	—	2	2	no	—
142	D₄×C₃₁	—	4	2	no	—
143	D₄×C₃₁	—	4	2	no	—
144	D₄×C₃₁	—	8	4	no	—
145	D₄×C₃₁	—	8	4	no	—
146	C₂×C₄×C₃₁	—	2	1	no	—
147	C₂×C₄×C₃₁	—	2	1	no	—
148	C₂×C₄×C₃₁	—	2	1	no	—
149	C₂×C₄×C₃₁	—	2	1	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	8	4	no	—
154	C₂×C₄×C₃₁	—	8	4	no	—
155	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₃₁	—	2	1	no	—
161	C₈×C₃₁	—	2	1	no	—
162	C₈×C₃₁	—	2	1	no	—
163	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×#508	C₂×C₃₁	1	1	yes	characteristic, complemented
166	C₂²×Q₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
167	#3285	C₂×C₃₁	1	2	yes	complemented
168	#2249	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#2216	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#2215	C₂×C₃₁	1	1	yes	characteristic, complemented
171	#2211	C₂×C₃₁	1	2	yes	complemented
172	#2189	C₂×C₃₁	1	2	yes	complemented
173	#2185	C₂×C₃₁	1	2	yes	complemented
174	C₄×Q₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
175	D₄×C₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
176	C₂²×C₃₁	—	2	1	no	—
177	C₂²×C₃₁	—	2	1	no	—
178	C₂²×C₃₁	—	2	1	no	—
179	C₂²×C₃₁	—	2	1	no	—
180	C₂²×C₃₁	—	2	1	no	—
181	C₂²×C₃₁	—	8	2	no	—
182	C₂²×C₃₁	—	8	2	no	—
183	C₂²×C₃₁	—	8	2	no	—
184	C₂²×C₃₁	#508	1	2	yes	complemented
185	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
186	C₄×C₃₁	—	2	1	no	—
187	C₄×C₃₁	—	2	1	no	—
188	C₄×C₃₁	—	2	1	no	—
189	C₄×C₃₁	—	2	1	no	—
190	C₄×C₃₁	—	4	4	no	—
191	C₄×C₃₁	—	8	2	no	—
192	C₄×C₃₁	—	8	2	no	—
193	C₄×C₃₁	D₄²	1	1	yes	characteristic
194	C₄×C₃₁	#576	1	1	yes	characteristic
195	C₂×#135	C₂²×C₃₁	1	2	yes	—
196	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
197	#548	—	2	2	no	—
198	#508	—	2	4	no	—
199	C₂×Q₃₂	—	2	4	no	—
200	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
201	C₂×Q₃₂	C₂²×C₃₁	1	1	yes	characteristic
202	C₂×Q₃₂	C₂²×C₃₁	1	1	yes	characteristic
203	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
204	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
205	C₂×D₁₆	C₂²×C₃₁	1	1	yes	characteristic
206	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
207	C₂²×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
208	#495	C₂²×C₃₁	1	2	yes	—
209	#467	C₂²×C₃₁	1	2	yes	—
210	#466	C₂²×C₃₁	1	2	yes	—
211	#464	—	2	2	no	—
212	#452	—	2	2	no	—
213	#448	—	2	2	no	—
214	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	—
215	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
216	#366	C₂²×C₃₁	1	1	yes	characteristic
217	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
218	#358	C₂²×C₃₁	1	2	yes	—
219	#358	C₂²×C₃₁	1	2	yes	—
220	#357	C₂²×C₃₁	1	2	yes	—
221	C₂²⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
222	C₂²⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
223	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
224	C₂×C₃₁	—	2	2	no	—
225	C₂×C₃₁	—	4	1	no	—
226	C₂×C₃₁	—	16	2	no	—
227	C₂×C₃₁	D₄×D₈	1	1	yes	characteristic
228	C₂×C₃₁	C₂×#508	1	1	yes	characteristic
229	C₂×C₃₁	#3417	1	1	yes	characteristic
230	C₂×#41	—	2	2	no	—
231	C₂²×Q₈	—	2	2	no	—
232	#135	—	2	4	no	—
233	#135	—	4	2	no	—
234	C₂×Q₁₆	—	2	4	no	—
235	C₂×Q₁₆	—	2	2	no	—
236	C₂×Q₁₆	—	4	2	no	—
237	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
238	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
239	C₂×SD₁₆	—	2	2	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×D₈	C₂³×C₃₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
244	#124	—	2	2	no	—
245	#124	—	4	2	no	—
246	C₂²⋊Q₈	—	2	2	no	—
247	C₂²⋊Q₈	—	4	2	no	—
248	#121	—	2	2	no	—
249	#121	—	4	2	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×D₄	—	4	2	no	—
252	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
253	Q₃₂	—	2	4	no	—
254	Q₃₂	—	2	2	no	—
255	Q₃₂	D₄×C₃₁	1	4	yes	complemented
256	SD₃₂	—	2	4	no	—
257	SD₃₂	—	4	2	no	—
258	D₁₆	—	2	2	no	—
259	C₂×C₁₆	—	2	2	no	—
260	C₂×C₁₆	—	2	2	no	—
261	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
262	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
263	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
264	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
265	#107	C₂³×C₃₁	1	2	yes	—
266	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
267	#103	—	2	2	no	—
268	#103	—	2	2	no	—
269	#102	—	2	2	no	—
270	C₂²⋊C₈	D₄×C₃₁	1	1	yes	characteristic
271	C₂²⋊C₈	D₄×C₃₁	1	1	yes	characteristic
272	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
273	C₃₁	#33851	1	1	yes	characteristic, direct product factor, Sylow
274	#41	—	4	4	no	—
275	#41	—	8	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	4	4	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	8	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	2	no	—
284	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
289	Q₁₆	—	2	2	no	—
290	Q₁₆	—	2	2	no	—
291	Q₁₆	—	2	2	no	—
292	Q₁₆	—	4	4	no	—
293	Q₁₆	C₂×D₄×C₃₁	1	4	yes	—
294	SD₁₆	—	4	4	no	—
295	SD₁₆	—	8	2	no	—
296	D₈	—	2	2	no	—
297	D₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	2	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	D₈×C₃₁	1	1	yes	characteristic
315	C₂²⋊C₄	D₈×C₃₁	1	1	yes	characteristic
316	C₄²	—	4	2	no	—
317	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₁₆	—	2	1	no	—
319	C₁₆	—	2	1	no	—
320	C₁₆	—	2	1	no	—
321	C₁₆	C₂×D₄×C₃₁	1	2	yes	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
324	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
325	Q₈	—	2	4	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	4	2	no	—
329	Q₈	—	8	4	no	—
330	D₄	—	2	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	4	2	no	—
333	D₄	—	8	4	no	—
334	D₄	—	8	4	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	8	4	no	—
343	C₂×C₄	—	8	4	no	—
344	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
346	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
347	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
348	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	2	1	no	—
352	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
353	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	C₃₁×#508	1	2	yes	complemented
363	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	4	4	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	D₄²×C₃₁	1	1	yes	characteristic
372	C₄	C₃₁×#576	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	16	2	no	—
376	C₂	D₄×D₈×C₃₁	1	1	yes	characteristic
377	C₂	C₂×C₃₁×#508	1	1	yes	characteristic
378	C₂	C₃₁×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄×D₄×C₃₁ ◁ C₈×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#508	C₂	semidirect
2. C₂²×C₃₁×Q₃₂	C₂	semidirect
3. C₃₁×#3285	C₂	semidirect
4. C₃₁×#2249	C₂	semidirect
5. C₃₁×#2216	C₂	semidirect
6. C₃₁×#2215	C₂	semidirect
7. C₃₁×#2211	C₂	semidirect
8. C₃₁×#2189	C₂	semidirect
9. C₃₁×#2185	C₂	semidirect
10. C₄×C₃₁×Q₃₂	C₂	semidirect
11. D₄×C₁₆×C₃₁	C₂	semidirect
66. C₃₁×Q₃₂	D₄	semidirect
132. #33851	C₃₁	direct (N × H)
165. C₂×#508	C₂×C₃₁	semidirect
166. C₂²×Q₃₂	C₂×C₃₁	semidirect
167. #3285	C₂×C₃₁	semidirect
168. #2249	C₂×C₃₁	semidirect
169. #2216	C₂×C₃₁	semidirect
170. #2215	C₂×C₃₁	semidirect
171. #2211	C₂×C₃₁	semidirect
172. #2189	C₂×C₃₁	semidirect
173. #2185	C₂×C₃₁	semidirect
174. C₄×Q₃₂	C₂×C₃₁	semidirect
175. D₄×C₁₆	C₂×C₃₁	semidirect
184. C₂²×C₃₁	#508	semidirect
255. Q₃₂	D₄×C₃₁	semidirect
273. C₃₁	#33851	direct (N × H)
362. C₂²	C₃₁×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#508	2
C₂²×C₃₁×Q₃₂	2
C₃₁×#3285	2
C₃₁×#2249	2
C₃₁×#2216	2
C₃₁×#2215	2
C₃₁×#2211	2
C₃₁×#2189	2
C₃₁×#2185	2
C₄×C₃₁×Q₃₂	2
D₄×C₁₆×C₃₁	2
#33851	31

Subgroups — C31×#33851 #21490610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33851 #21490610