Subgroups — C₃₁×#33844 #21490603

Order 7936.

674 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#510	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3287	C₂	1	1	yes	maximal, characteristic
3	D₄×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#2220	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2207	C₂	1	1	yes	maximal, characteristic, 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	C₃₁×#2169	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×#550	—	2	1	no	—
15	D₄×Q₈×C₃₁	—	2	1	no	—
16	C₃₁×#510	—	2	8	no	—
17	C₂×C₃₁×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₃₁×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₃₁×M₃₂	C₂²	1	2	yes	—
23	C₃₁×#494	C₂²	1	1	yes	characteristic
24	C₃₁×#493	C₂²	1	1	yes	characteristic
25	C₃₁×#467	C₂²	1	2	yes	—
26	C₃₁×#466	C₂²	1	2	yes	—
27	C₃₁×#462	—	2	1	no	—
28	C₃₁×#460	—	2	1	no	—
29	C₃₁×#451	—	2	2	no	—
30	C₃₁×#449	—	2	2	no	—
31	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
32	C₄×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
34	C₃₁×#366	C₂²	1	1	yes	characteristic
35	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₃₁×#358	C₂²	1	1	yes	characteristic
37	C₃₁×#358	C₂²	1	1	yes	characteristic
38	C₃₁×#358	C₂²	1	2	yes	—
39	C₃₁×#357	C₂²	1	2	yes	—
40	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic
42	C₂×#41×C₃₁	—	2	2	no	—
43	C₂²×Q₈×C₃₁	—	2	2	no	—
44	C₃₁×#135	—	2	4	no	—
45	C₃₁×#135	—	4	2	no	—
46	C₂×Q₁₆×C₃₁	—	2	4	no	—
47	C₂×Q₁₆×C₃₁	—	2	2	no	—
48	C₂×Q₁₆×C₃₁	—	2	1	no	—
49	C₂×Q₁₆×C₃₁	—	4	2	no	—
50	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
51	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×SD₁₆×C₃₁	—	2	2	no	—
54	C₂×D₈×C₃₁	—	2	1	no	—
55	C₂×D₈×C₃₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
57	C₃₁×C₄⋊Q₈	—	2	1	no	—
58	C₃₁×C₄⋊Q₈	—	4	1	no	—
59	C₃₁×#127	—	2	1	no	—
60	C₃₁×#127	—	4	1	no	—
61	C₃₁×C₂²⋊Q₈	—	2	2	no	—
62	C₃₁×C₂²⋊Q₈	—	4	2	no	—
63	C₃₁×#121	—	2	2	no	—
64	C₃₁×#121	—	4	2	no	—
65	C₄×Q₈×C₃₁	—	2	1	no	—
66	C₄×Q₈×C₃₁	—	2	1	no	—
67	C₄×D₄×C₃₁	—	4	1	no	—
68	C₄×D₄×C₃₁	—	4	1	no	—
69	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
70	C₃₁×Q₃₂	—	2	4	no	—
71	C₃₁×Q₃₂	D₄	1	4	yes	complemented
72	C₃₁×SD₃₂	—	2	4	no	—
73	C₃₁×SD₃₂	—	2	4	no	—
74	C₃₁×SD₃₂	—	4	2	no	—
75	C₃₁×M₃₂	—	2	4	no	—
76	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
77	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
78	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
79	C₃₁×#107	C₂³	1	1	yes	characteristic
80	C₃₁×#107	C₂³	1	1	yes	characteristic
81	C₃₁×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₃₁×#103	—	2	1	no	—
83	C₃₁×#103	—	2	1	no	—
84	C₃₁×#103	—	2	2	no	—
85	C₃₁×#102	—	2	2	no	—
86	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
87	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
88	#41×C₃₁	—	4	4	no	—
89	#41×C₃₁	—	8	2	no	—
90	C₂×Q₈×C₃₁	—	2	1	no	—
91	C₂×Q₈×C₃₁	—	2	1	no	—
92	C₂×Q₈×C₃₁	—	2	2	no	—
93	C₂×Q₈×C₃₁	—	4	4	no	—
94	C₂×Q₈×C₃₁	—	4	2	no	—
95	C₂×Q₈×C₃₁	—	8	2	no	—
96	C₂×D₄×C₃₁	—	2	2	no	—
97	C₂×D₄×C₃₁	—	4	2	no	—
98	C₂×D₄×C₃₁	—	4	2	no	—
99	C₂×D₄×C₃₁	—	4	1	no	—
100	C₂×D₄×C₃₁	—	4	1	no	—
101	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	—	4	2	no	—
103	C₂²×C₄×C₃₁	—	4	2	no	—
104	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
105	Q₁₆×C₃₁	—	2	2	no	—
106	Q₁₆×C₃₁	—	2	1	no	—
107	Q₁₆×C₃₁	—	2	1	no	—
108	Q₁₆×C₃₁	—	2	2	no	—
109	Q₁₆×C₃₁	—	4	4	no	—
110	Q₁₆×C₃₁	—	8	1	no	—
111	Q₁₆×C₃₁	C₂×D₄	1	2	yes	—
112	Q₁₆×C₃₁	C₂×D₄	1	2	yes	—
113	SD₁₆×C₃₁	—	4	4	no	—
114	D₈×C₃₁	—	2	2	no	—
115	D₈×C₃₁	—	2	2	no	—
116	D₈×C₃₁	—	8	1	no	—
117	C₂×C₈×C₃₁	—	2	2	no	—
118	C₂×C₈×C₃₁	—	2	2	no	—
119	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
121	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
122	C₄⋊C₄×C₃₁	—	2	1	no	—
123	C₄⋊C₄×C₃₁	—	2	1	no	—
124	C₄⋊C₄×C₃₁	—	4	1	no	—
125	C₄⋊C₄×C₃₁	—	4	1	no	—
126	C₄⋊C₄×C₃₁	—	4	1	no	—
127	C₄⋊C₄×C₃₁	—	4	2	no	—
128	C₄⋊C₄×C₃₁	—	4	1	no	—
129	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
130	C₂²⋊C₄×C₃₁	—	4	2	no	—
131	C₂²⋊C₄×C₃₁	—	4	2	no	—
132	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
133	C₄²×C₃₁	—	4	1	no	—
134	C₄²×C₃₁	—	4	1	no	—
135	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
136	C₁₆×C₃₁	—	2	2	no	—
137	C₁₆×C₃₁	—	2	1	no	—
138	C₁₆×C₃₁	C₂×D₄	1	2	yes	—
139	#33844	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₃₁	—	4	2	no	—
141	C₂³×C₃₁	C₂×D₈	1	2	yes	—
142	Q₈×C₃₁	—	2	2	no	—
143	Q₈×C₃₁	—	2	2	no	—
144	Q₈×C₃₁	—	4	1	no	—
145	Q₈×C₃₁	—	4	1	no	—
146	Q₈×C₃₁	—	4	2	no	—
147	Q₈×C₃₁	—	4	2	no	—
148	Q₈×C₃₁	—	8	4	no	—
149	D₄×C₃₁	—	2	2	no	—
150	D₄×C₃₁	—	4	2	no	—
151	D₄×C₃₁	—	4	2	no	—
152	D₄×C₃₁	—	8	4	no	—
153	D₄×C₃₁	—	8	2	no	—
154	D₄×C₃₁	—	16	1	no	—
155	D₄×C₃₁	—	16	2	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	4	1	no	—
159	C₂×C₄×C₃₁	—	4	1	no	—
160	C₂×C₄×C₃₁	—	4	1	no	—
161	C₂×C₄×C₃₁	—	4	1	no	—
162	C₂×C₄×C₃₁	—	4	2	no	—
163	C₂×C₄×C₃₁	—	8	4	no	—
164	C₂×C₄×C₃₁	—	8	4	no	—
165	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
167	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₈×C₃₁	—	2	2	no	—
170	C₈×C₃₁	—	2	1	no	—
171	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×#510	C₂×C₃₁	1	2	yes	complemented
174	#3287	C₂×C₃₁	1	1	yes	characteristic
175	D₄×Q₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
176	#2248	C₂×C₃₁	1	1	yes	characteristic, complemented
177	#2220	C₂×C₃₁	1	2	yes	complemented
178	#2209	C₂×C₃₁	1	1	yes	characteristic, complemented
179	#2207	C₂×C₃₁	1	1	yes	characteristic, complemented
180	#2189	C₂×C₃₁	1	2	yes	complemented
181	#2185	C₂×C₃₁	1	2	yes	complemented
182	C₄×Q₃₂	C₂×C₃₁	1	1	yes	characteristic, complemented
183	#2169	C₂×C₃₁	1	1	yes	characteristic, complemented
184	C₂²×C₃₁	—	2	2	no	—
185	C₂²×C₃₁	—	2	2	no	—
186	C₂²×C₃₁	—	2	2	no	—
187	C₂²×C₃₁	—	8	2	no	—
188	C₂²×C₃₁	—	8	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
191	C₄×C₃₁	—	2	1	no	—
192	C₄×C₃₁	—	2	2	no	—
193	C₄×C₃₁	—	4	2	no	—
194	C₄×C₃₁	—	4	2	no	—
195	C₄×C₃₁	—	8	1	no	—
196	C₄×C₃₁	—	8	1	no	—
197	C₄×C₃₁	—	8	2	no	—
198	C₄×C₃₁	#510	1	2	yes	complemented
199	C₄×C₃₁	D₄²	1	1	yes	characteristic
200	C₄×C₃₁	#576	1	1	yes	characteristic
201	C₂×#135	C₂²×C₃₁	1	2	yes	—
202	C₂²×Q₁₆	C₂²×C₃₁	1	2	yes	—
203	#550	—	2	1	no	—
204	D₄×Q₈	—	2	1	no	—
205	#510	—	2	8	no	—
206	C₂×Q₃₂	C₂²×C₃₁	1	2	yes	—
207	C₂×Q₃₂	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
209	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
210	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	—
211	C₂×M₃₂	C₂²×C₃₁	1	2	yes	—
212	#494	C₂²×C₃₁	1	1	yes	characteristic
213	#493	C₂²×C₃₁	1	1	yes	characteristic
214	#467	C₂²×C₃₁	1	2	yes	—
215	#466	C₂²×C₃₁	1	2	yes	—
216	#462	—	2	1	no	—
217	#460	—	2	1	no	—
218	#451	—	2	2	no	—
219	#449	—	2	2	no	—
220	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
221	C₄×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic
222	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
223	#366	C₂²×C₃₁	1	1	yes	characteristic
224	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic
225	#358	C₂²×C₃₁	1	1	yes	characteristic
226	#358	C₂²×C₃₁	1	1	yes	characteristic
227	#358	C₂²×C₃₁	1	2	yes	—
228	#357	C₂²×C₃₁	1	2	yes	—
229	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	—
230	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic
231	C₂×C₃₁	—	4	2	no	—
232	C₂×C₃₁	—	16	2	no	—
233	C₂×C₃₁	D₄×D₈	1	1	yes	characteristic
234	C₂×C₃₁	C₂×#510	1	1	yes	characteristic
235	C₂×C₃₁	#3416	1	1	yes	characteristic
236	C₂×#41	—	2	2	no	—
237	C₂²×Q₈	—	2	2	no	—
238	#135	—	2	4	no	—
239	#135	—	4	2	no	—
240	C₂×Q₁₆	—	2	4	no	—
241	C₂×Q₁₆	—	2	2	no	—
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×Q₁₆	—	4	2	no	—
244	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
245	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
246	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	C₂³×C₃₁	1	2	yes	—
250	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	4	1	no	—
253	#127	—	2	1	no	—
254	#127	—	4	1	no	—
255	C₂²⋊Q₈	—	2	2	no	—
256	C₂²⋊Q₈	—	4	2	no	—
257	#121	—	2	2	no	—
258	#121	—	4	2	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×D₄	—	4	1	no	—
262	C₄×D₄	—	4	1	no	—
263	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
264	Q₃₂	—	2	4	no	—
265	Q₃₂	D₄×C₃₁	1	4	yes	complemented
266	SD₃₂	—	2	4	no	—
267	SD₃₂	—	2	4	no	—
268	SD₃₂	—	4	2	no	—
269	M₃₂	—	2	4	no	—
270	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
271	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
272	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
273	#107	C₂³×C₃₁	1	1	yes	characteristic
274	#107	C₂³×C₃₁	1	1	yes	characteristic
275	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
276	#103	—	2	1	no	—
277	#103	—	2	1	no	—
278	#103	—	2	2	no	—
279	#102	—	2	2	no	—
280	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
281	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
282	C₃₁	#33844	1	1	yes	characteristic, direct product factor, Sylow
283	#41	—	4	4	no	—
284	#41	—	8	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	4	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	8	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	2	1	no	—
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	2	2	no	—
304	Q₁₆	—	4	4	no	—
305	Q₁₆	—	8	1	no	—
306	Q₁₆	C₂×D₄×C₃₁	1	2	yes	—
307	Q₁₆	C₂×D₄×C₃₁	1	2	yes	—
308	SD₁₆	—	4	4	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	2	no	—
311	D₈	—	8	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
315	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
316	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
331	C₁₆	—	2	2	no	—
332	C₁₆	—	2	1	no	—
333	C₁₆	C₂×D₄×C₃₁	1	2	yes	—
334	C₂³	—	4	2	no	—
335	C₂³	C₂×D₈×C₃₁	1	2	yes	—
336	Q₈	—	2	2	no	—
337	Q₈	—	2	2	no	—
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	8	4	no	—
343	D₄	—	2	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	D₄	—	8	4	no	—
347	D₄	—	8	2	no	—
348	D₄	—	16	1	no	—
349	D₄	—	16	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	8	4	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
360	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
361	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	1	no	—
365	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
366	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	2	no	—
381	C₄	C₃₁×#510	1	2	yes	complemented
382	C₄	D₄²×C₃₁	1	1	yes	characteristic
383	C₄	C₃₁×#576	1	1	yes	characteristic
384	C₂	—	4	2	no	—
385	C₂	—	16	2	no	—
386	C₂	D₄×D₈×C₃₁	1	1	yes	characteristic
387	C₂	C₂×C₃₁×#510	1	1	yes	characteristic
388	C₂	C₃₁×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃₁
prime radical	C₃₁×#3287	C₂
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×#510	C₂	semidirect
3. D₄×Q₁₆×C₃₁	C₂	semidirect
4. C₃₁×#2248	C₂	semidirect
5. C₃₁×#2220	C₂	semidirect
6. C₃₁×#2209	C₂	semidirect
7. C₃₁×#2207	C₂	semidirect
8. C₃₁×#2189	C₂	semidirect
9. C₃₁×#2185	C₂	semidirect
10. C₄×C₃₁×Q₃₂	C₂	semidirect
11. C₃₁×#2169	C₂	semidirect
71. C₃₁×Q₃₂	D₄	semidirect
139. #33844	C₃₁	direct (N × H)
173. C₂×#510	C₂×C₃₁	semidirect
175. D₄×Q₁₆	C₂×C₃₁	semidirect
176. #2248	C₂×C₃₁	semidirect
177. #2220	C₂×C₃₁	semidirect
178. #2209	C₂×C₃₁	semidirect
179. #2207	C₂×C₃₁	semidirect
180. #2189	C₂×C₃₁	semidirect
181. #2185	C₂×C₃₁	semidirect
182. C₄×Q₃₂	C₂×C₃₁	semidirect
183. #2169	C₂×C₃₁	semidirect
198. C₄×C₃₁	#510	semidirect
265. Q₃₂	D₄×C₃₁	semidirect
282. C₃₁	#33844	direct (N × H)
381. C₄	C₃₁×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#510	2
C₃₁×#3287	2
D₄×Q₁₆×C₃₁	2
C₃₁×#2248	2
C₃₁×#2220	2
C₃₁×#2209	2
C₃₁×#2207	2
C₃₁×#2189	2
C₃₁×#2185	2
C₄×C₃₁×Q₃₂	2
C₃₁×#2169	2
#33844	31

Subgroups — C31×#33844 #21490603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33844 #21490603