Subgroups — C₃₁×#33839 #21490598

Order 7936.

712 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#509	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3280	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2249	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2220	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2210	C₂	1	2	yes	maximal, complemented
6	C₃₁×#2189	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2184	C₂	1	2	yes	maximal, complemented
8	C₄×C₃₁×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#2169	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#135	C₂²	1	2	yes	—
11	C₂²×D₈×C₃₁	C₂²	1	2	yes	complemented
12	C₃₁×#546	—	2	2	no	—
13	C₃₁×#509	—	2	8	no	—
14	C₂×C₃₁×Q₃₂	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
16	C₂×C₃₁×SD₃₂	C₂²	1	2	yes	complemented
17	C₂×C₃₁×D₁₆	C₂²	1	2	yes	—
18	C₂×C₃₁×D₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃₁×D₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×M₃₂	C₂²	1	2	yes	complemented
21	C₃₁×#495	C₂²	1	2	yes	complemented
22	C₃₁×#467	C₂²	1	2	yes	complemented
23	C₃₁×#466	C₂²	1	2	yes	—
24	C₃₁×#463	—	2	2	no	—
25	C₃₁×#450	—	2	2	no	—
26	C₃₁×#449	—	2	2	no	—
27	C₄×D₈×C₃₁	C₂²	1	2	yes	complemented
28	C₈×D₄×C₃₁	C₂²	1	1	yes	characteristic
29	C₃₁×#366	C₂²	1	1	yes	characteristic, complemented
30	C₃₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₃₁×#358	C₂²	1	2	yes	complemented
32	C₃₁×#357	C₂²	1	2	yes	complemented
33	C₃₁×#357	C₂²	1	2	yes	complemented
34	C₃₁×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
35	C₄×C₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
36	C₂×#41×C₃₁	—	2	2	no	—
37	C₂²×D₄×C₃₁	—	2	2	no	—
38	C₃₁×#135	—	2	4	no	—
39	C₃₁×#135	—	4	2	no	—
40	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
41	C₂×SD₁₆×C₃₁	—	2	2	no	—
42	C₂×SD₁₆×C₃₁	—	2	2	no	—
43	C₂×D₈×C₃₁	—	2	4	no	—
44	C₂×D₈×C₃₁	—	2	2	no	—
45	C₂×D₈×C₃₁	—	4	2	no	—
46	C₂×D₈×C₃₁	C₂³	1	2	yes	—
47	C₂×D₈×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
49	C₃₁×#124	—	2	2	no	—
50	C₃₁×#123	—	4	2	no	—
51	C₃₁×C₂²⋊Q₈	—	2	2	no	—
52	C₃₁×#121	—	2	2	no	—
53	C₃₁×#121	—	4	2	no	—
54	C₃₁×#120	—	4	2	no	—
55	C₄×D₄×C₃₁	—	2	2	no	—
56	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₃₁	—	4	2	no	—
58	C₃₁×Q₃₂	—	4	1	no	—
59	C₃₁×SD₃₂	—	2	4	no	—
60	C₃₁×SD₃₂	—	2	4	no	—
61	C₃₁×D₁₆	—	2	4	no	—
62	C₃₁×D₁₆	—	4	1	no	—
63	C₃₁×D₁₆	D₄	1	4	yes	complemented
64	C₃₁×M₃₂	—	2	4	no	—
65	C₂×C₁₆×C₃₁	C₂³	1	2	yes	—
66	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₁₆×C₃₁	C₂³	1	1	yes	characteristic
68	C₃₁×#107	C₂³	1	2	yes	—
69	C₃₁×C₄⋊C₈	D₄	1	1	yes	characteristic
70	C₃₁×#103	—	2	2	no	—
71	C₃₁×#102	—	2	2	no	—
72	C₃₁×#102	—	2	2	no	—
73	C₃₁×C₂²⋊C₈	D₄	1	2	yes	—
74	C₄×C₈×C₃₁	C₂³	1	1	yes	characteristic
75	C₂⁴×C₃₁	—	4	2	no	—
76	#41×C₃₁	—	4	4	no	—
77	#41×C₃₁	—	8	2	no	—
78	C₂×Q₈×C₃₁	—	2	2	no	—
79	C₂×D₄×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	2	2	no	—
81	C₂×D₄×C₃₁	—	4	4	no	—
82	C₂×D₄×C₃₁	—	4	2	no	—
83	C₂×D₄×C₃₁	—	4	2	no	—
84	C₂×D₄×C₃₁	—	4	2	no	—
85	C₂×D₄×C₃₁	—	8	2	no	—
86	C₂×D₄×C₃₁	D₈	1	1	yes	characteristic
87	C₂²×C₄×C₃₁	—	4	2	no	—
88	C₂²×C₄×C₃₁	—	4	2	no	—
89	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
90	Q₁₆×C₃₁	—	2	2	no	—
91	Q₁₆×C₃₁	—	2	2	no	—
92	SD₁₆×C₃₁	—	4	4	no	—
93	SD₁₆×C₃₁	—	8	2	no	—
94	D₈×C₃₁	—	2	2	no	—
95	D₈×C₃₁	—	2	2	no	—
96	D₈×C₃₁	—	2	2	no	—
97	D₈×C₃₁	—	4	4	no	—
98	D₈×C₃₁	C₂×D₄	1	4	yes	—
99	C₂×C₈×C₃₁	—	2	2	no	—
100	C₂×C₈×C₃₁	—	2	2	no	—
101	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
102	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
104	C₄⋊C₄×C₃₁	—	2	2	no	—
105	C₄⋊C₄×C₃₁	—	4	2	no	—
106	C₄⋊C₄×C₃₁	D₈	1	1	yes	characteristic
107	C₂²⋊C₄×C₃₁	—	4	2	no	—
108	C₂²⋊C₄×C₃₁	—	4	2	no	—
109	C₂²⋊C₄×C₃₁	—	4	2	no	—
110	C₂²⋊C₄×C₃₁	—	4	2	no	—
111	C₂²⋊C₄×C₃₁	—	4	2	no	—
112	C₂²⋊C₄×C₃₁	D₈	1	2	yes	—
113	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
114	C₁₆×C₃₁	—	2	2	no	—
115	C₁₆×C₃₁	—	2	1	no	—
116	C₁₆×C₃₁	C₂×D₄	1	2	yes	—
117	#33839	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₃₁	—	4	2	no	—
119	C₂³×C₃₁	—	4	2	no	—
120	C₂³×C₃₁	—	8	4	no	—
121	C₂³×C₃₁	—	8	4	no	—
122	C₂³×C₃₁	—	16	2	no	—
123	C₂³×C₃₁	C₂×D₈	1	2	yes	—
124	Q₈×C₃₁	—	4	2	no	—
125	Q₈×C₃₁	—	4	2	no	—
126	D₄×C₃₁	—	2	4	no	—
127	D₄×C₃₁	—	4	1	no	—
128	D₄×C₃₁	—	4	2	no	—
129	D₄×C₃₁	—	4	2	no	—
130	D₄×C₃₁	—	4	2	no	—
131	D₄×C₃₁	—	8	4	no	—
132	D₄×C₃₁	—	8	4	no	—
133	D₄×C₃₁	—	16	2	no	—
134	C₂×C₄×C₃₁	—	2	2	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	4	2	no	—
137	C₂×C₄×C₃₁	—	4	2	no	—
138	C₂×C₄×C₃₁	—	8	4	no	—
139	C₂×C₄×C₃₁	—	16	2	no	—
140	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
141	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
142	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
143	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
144	C₈×C₃₁	—	2	2	no	—
145	C₈×C₃₁	—	2	1	no	—
146	C₈×C₃₁	C₂²×D₄	1	1	yes	characteristic
147	C₈×C₃₁	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂×#509	C₂×C₃₁	1	2	yes	complemented
149	#3280	C₂×C₃₁	1	2	yes	complemented
150	#2249	C₂×C₃₁	1	1	yes	characteristic, complemented
151	#2220	C₂×C₃₁	1	2	yes	complemented
152	#2210	C₂×C₃₁	1	2	yes	complemented
153	#2189	C₂×C₃₁	1	2	yes	complemented
154	#2184	C₂×C₃₁	1	2	yes	complemented
155	C₄×D₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
156	#2169	C₂×C₃₁	1	1	yes	characteristic, complemented
157	C₂²×C₃₁	—	2	2	no	—
158	C₂²×C₃₁	—	2	2	no	—
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	4	4	no	—
161	C₂²×C₃₁	—	8	2	no	—
162	C₂²×C₃₁	—	8	2	no	—
163	C₂²×C₃₁	—	8	2	no	—
164	C₂²×C₃₁	—	8	2	no	—
165	C₂²×C₃₁	—	8	2	no	—
166	C₂²×C₃₁	—	16	8	no	—
167	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
168	C₄×C₃₁	—	2	1	no	—
169	C₄×C₃₁	—	2	1	no	—
170	C₄×C₃₁	—	2	2	no	—
171	C₄×C₃₁	—	8	2	no	—
172	C₄×C₃₁	—	8	2	no	—
173	C₄×C₃₁	D₄²	1	1	yes	characteristic
174	C₄×C₃₁	#576	1	1	yes	characteristic
175	C₂×#135	C₂²×C₃₁	1	2	yes	—
176	C₂²×D₈	C₂²×C₃₁	1	2	yes	complemented
177	#546	—	2	2	no	—
178	#509	—	2	8	no	—
179	C₂×Q₃₂	C₂²×C₃₁	1	1	yes	characteristic, complemented
180	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
181	C₂×SD₃₂	C₂²×C₃₁	1	2	yes	complemented
182	C₂×D₁₆	C₂²×C₃₁	1	2	yes	—
183	C₂×D₁₆	C₂²×C₃₁	1	1	yes	characteristic
184	C₂×D₁₆	C₂²×C₃₁	1	1	yes	characteristic
185	C₂×M₃₂	C₂²×C₃₁	1	2	yes	complemented
186	#495	C₂²×C₃₁	1	2	yes	complemented
187	#467	C₂²×C₃₁	1	2	yes	complemented
188	#466	C₂²×C₃₁	1	2	yes	—
189	#463	—	2	2	no	—
190	#450	—	2	2	no	—
191	#449	—	2	2	no	—
192	C₄×D₈	C₂²×C₃₁	1	2	yes	complemented
193	C₈×D₄	C₂²×C₃₁	1	1	yes	characteristic
194	#366	C₂²×C₃₁	1	1	yes	characteristic, complemented
195	C₄⋊C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
196	#358	C₂²×C₃₁	1	2	yes	complemented
197	#357	C₂²×C₃₁	1	2	yes	complemented
198	#357	C₂²×C₃₁	1	2	yes	complemented
199	C₂²⋊C₁₆	C₂²×C₃₁	1	2	yes	complemented
200	C₄×C₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
201	C₂×C₃₁	—	4	2	no	—
202	C₂×C₃₁	—	8	4	no	—
203	C₂×C₃₁	—	16	2	no	—
204	C₂×C₃₁	D₄×D₈	1	1	yes	characteristic
205	C₂×C₃₁	#3414	1	1	yes	characteristic
206	C₂×C₃₁	#3415	1	1	yes	characteristic
207	C₂×#41	—	2	2	no	—
208	C₂²×D₄	—	2	2	no	—
209	#135	—	2	4	no	—
210	#135	—	4	2	no	—
211	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
212	C₂×SD₁₆	—	2	2	no	—
213	C₂×SD₁₆	—	2	2	no	—
214	C₂×D₈	—	2	4	no	—
215	C₂×D₈	—	2	2	no	—
216	C₂×D₈	—	4	2	no	—
217	C₂×D₈	C₂³×C₃₁	1	2	yes	—
218	C₂×D₈	C₂³×C₃₁	1	2	yes	—
219	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
220	#124	—	2	2	no	—
221	#123	—	4	2	no	—
222	C₂²⋊Q₈	—	2	2	no	—
223	#121	—	2	2	no	—
224	#121	—	4	2	no	—
225	#120	—	4	2	no	—
226	C₄×D₄	—	2	2	no	—
227	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	—	4	2	no	—
229	Q₃₂	—	4	1	no	—
230	SD₃₂	—	2	4	no	—
231	SD₃₂	—	2	4	no	—
232	D₁₆	—	2	4	no	—
233	D₁₆	—	4	1	no	—
234	D₁₆	D₄×C₃₁	1	4	yes	complemented
235	M₃₂	—	2	4	no	—
236	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
237	C₂×C₁₆	C₂³×C₃₁	1	2	yes	—
238	C₂×C₁₆	C₂³×C₃₁	1	1	yes	characteristic
239	#107	C₂³×C₃₁	1	2	yes	—
240	C₄⋊C₈	D₄×C₃₁	1	1	yes	characteristic
241	#103	—	2	2	no	—
242	#102	—	2	2	no	—
243	#102	—	2	2	no	—
244	C₂²⋊C₈	D₄×C₃₁	1	2	yes	—
245	C₄×C₈	C₂³×C₃₁	1	1	yes	characteristic
246	C₃₁	#33839	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁴	—	4	2	no	—
248	#41	—	4	4	no	—
249	#41	—	8	2	no	—
250	C₂×Q₈	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	4	4	no	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	—	8	2	no	—
258	C₂×D₄	D₈×C₃₁	1	1	yes	characteristic
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
262	Q₁₆	—	2	2	no	—
263	Q₁₆	—	2	2	no	—
264	SD₁₆	—	4	4	no	—
265	SD₁₆	—	8	2	no	—
266	D₈	—	2	2	no	—
267	D₈	—	2	2	no	—
268	D₈	—	2	2	no	—
269	D₈	—	4	4	no	—
270	D₈	C₂×D₄×C₃₁	1	4	yes	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
274	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
275	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	4	2	no	—
278	C₄⋊C₄	D₈×C₃₁	1	1	yes	characteristic
279	C₂²⋊C₄	—	4	2	no	—
280	C₂²⋊C₄	—	4	2	no	—
281	C₂²⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	4	2	no	—
283	C₂²⋊C₄	—	4	2	no	—
284	C₂²⋊C₄	D₈×C₃₁	1	2	yes	—
285	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
286	C₁₆	—	2	2	no	—
287	C₁₆	—	2	1	no	—
288	C₁₆	C₂×D₄×C₃₁	1	2	yes	—
289	C₂³	—	4	2	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	8	4	no	—
292	C₂³	—	8	4	no	—
293	C₂³	—	16	2	no	—
294	C₂³	C₂×D₈×C₃₁	1	2	yes	—
295	Q₈	—	4	2	no	—
296	Q₈	—	4	2	no	—
297	D₄	—	2	4	no	—
298	D₄	—	4	1	no	—
299	D₄	—	4	2	no	—
300	D₄	—	4	2	no	—
301	D₄	—	4	2	no	—
302	D₄	—	8	4	no	—
303	D₄	—	8	4	no	—
304	D₄	—	16	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	8	4	no	—
310	C₂×C₄	—	16	2	no	—
311	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
312	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
313	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
315	C₈	—	2	2	no	—
316	C₈	—	2	1	no	—
317	C₈	C₂²×D₄×C₃₁	1	1	yes	characteristic
318	C₈	C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂²	—	2	2	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	8	2	no	—
324	C₂²	—	8	2	no	—
325	C₂²	—	8	2	no	—
326	C₂²	—	8	2	no	—
327	C₂²	—	8	2	no	—
328	C₂²	—	16	8	no	—
329	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
330	C₄	—	2	1	no	—
331	C₄	—	2	1	no	—
332	C₄	—	2	2	no	—
333	C₄	—	8	2	no	—
334	C₄	—	8	2	no	—
335	C₄	D₄²×C₃₁	1	1	yes	characteristic
336	C₄	C₃₁×#576	1	1	yes	characteristic
337	C₂	—	4	2	no	—
338	C₂	—	8	4	no	—
339	C₂	—	16	2	no	—
340	C₂	D₄×D₈×C₃₁	1	1	yes	characteristic
341	C₂	C₃₁×#3414	1	1	yes	characteristic
342	C₂	C₃₁×#3415	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×#509	C₂	semidirect
2. C₃₁×#3280	C₂	semidirect
3. C₃₁×#2249	C₂	semidirect
4. C₃₁×#2220	C₂	semidirect
5. C₃₁×#2210	C₂	semidirect
6. C₃₁×#2189	C₂	semidirect
7. C₃₁×#2184	C₂	semidirect
8. C₄×C₃₁×D₁₆	C₂	semidirect
9. C₃₁×#2169	C₂	semidirect
11. C₂²×D₈×C₃₁	C₂²	semidirect
14. C₂×C₃₁×Q₃₂	C₂²	semidirect
15. C₂×C₃₁×SD₃₂	C₂²	semidirect
16. C₂×C₃₁×SD₃₂	C₂²	semidirect
20. C₂×C₃₁×M₃₂	C₂²	semidirect
21. C₃₁×#495	C₂²	semidirect
22. C₃₁×#467	C₂²	semidirect
27. C₄×D₈×C₃₁	C₂²	semidirect
29. C₃₁×#366	C₂²	semidirect
30. C₃₁×C₄⋊C₁₆	C₂²	semidirect
31. C₃₁×#358	C₂²	semidirect
32. C₃₁×#357	C₂²	semidirect
33. C₃₁×#357	C₂²	semidirect
34. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
35. C₄×C₁₆×C₃₁	C₂²	semidirect
63. C₃₁×D₁₆	D₄	semidirect
117. #33839	C₃₁	direct (N × H)
148. C₂×#509	C₂×C₃₁	semidirect
149. #3280	C₂×C₃₁	semidirect
150. #2249	C₂×C₃₁	semidirect
151. #2220	C₂×C₃₁	semidirect
152. #2210	C₂×C₃₁	semidirect
153. #2189	C₂×C₃₁	semidirect
154. #2184	C₂×C₃₁	semidirect
155. C₄×D₁₆	C₂×C₃₁	semidirect
156. #2169	C₂×C₃₁	semidirect
176. C₂²×D₈	C₂²×C₃₁	semidirect
179. C₂×Q₃₂	C₂²×C₃₁	semidirect
180. C₂×SD₃₂	C₂²×C₃₁	semidirect
181. C₂×SD₃₂	C₂²×C₃₁	semidirect
185. C₂×M₃₂	C₂²×C₃₁	semidirect
186. #495	C₂²×C₃₁	semidirect
187. #467	C₂²×C₃₁	semidirect
192. C₄×D₈	C₂²×C₃₁	semidirect
194. #366	C₂²×C₃₁	semidirect
195. C₄⋊C₁₆	C₂²×C₃₁	semidirect
196. #358	C₂²×C₃₁	semidirect
197. #357	C₂²×C₃₁	semidirect
198. #357	C₂²×C₃₁	semidirect
199. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
200. C₄×C₁₆	C₂²×C₃₁	semidirect
234. D₁₆	D₄×C₃₁	semidirect
246. C₃₁	#33839	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#509	2
C₃₁×#3280	2
C₃₁×#2249	2
C₃₁×#2220	2
C₃₁×#2210	2
C₃₁×#2189	2
C₃₁×#2184	2
C₄×C₃₁×D₁₆	2
C₃₁×#2169	2
#33839	31

Subgroups — C31×#33839 #21490598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33839 #21490598