Subgroups — C₃₁×#33517 #21490276

Order 7936.

1380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#509	C₂	1	2	yes	maximal, complemented
3	C₃₁×#3050	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#2187	C₂	1	4	yes	maximal, complemented
5	C₃₁×#2184	C₂	1	4	yes	maximal, complemented
6	C₃₁×#2140	C₂	1	2	yes	maximal, complemented
7	C₃₁×#2112	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₃₁	—	2	1	no	—
9	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic, complemented
10	C₂²×D₈×C₃₁	—	2	8	no	—
11	C₂²×D₈×C₃₁	—	2	1	no	—
12	C₂²×D₈×C₃₁	—	2	2	no	—
13	C₂²×D₈×C₃₁	C₂²	1	4	yes	—
14	C₂²×D₈×C₃₁	C₂²	1	2	yes	—
15	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#525	—	2	1	no	—
17	C₃₁×#509	—	2	8	no	—
18	C₂×C₃₁×SD₃₂	C₂²	1	4	yes	complemented
19	C₂×C₃₁×D₁₆	C₂²	1	4	yes	complemented
20	C₂×C₃₁×M₃₂	C₂²	1	2	yes	complemented
21	C₃₁×#467	C₂²	1	2	yes	complemented
22	C₃₁×#466	C₂²	1	2	yes	complemented
23	C₃₁×#465	—	2	2	no	—
24	C₃₁×#427	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×#416	—	2	1	no	—
26	C₃₁×#357	C₂²	1	8	yes	complemented
27	C₃₁×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
28	C₂⁵×C₃₁	—	4	1	no	—
29	C₂×#41×C₃₁	—	2	1	no	—
30	C₂²×D₄×C₃₁	—	2	8	no	—
31	C₂²×D₄×C₃₁	—	2	4	no	—
32	C₂²×D₄×C₃₁	—	2	2	no	—
33	C₂²×D₄×C₃₁	—	4	4	no	—
34	C₂²×D₄×C₃₁	—	4	2	no	—
35	C₂²×D₄×C₃₁	—	4	1	no	—
36	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
37	C₃₁×#135	—	2	4	no	—
38	C₂×Q₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
39	C₂×SD₁₆×C₃₁	—	2	1	no	—
40	C₂×D₈×C₃₁	—	2	8	no	—
41	C₂×D₈×C₃₁	—	2	16	no	—
42	C₂×D₈×C₃₁	—	2	16	no	—
43	C₂×D₈×C₃₁	—	2	4	no	—
44	C₂×D₈×C₃₁	—	2	2	no	—
45	C₂×D₈×C₃₁	—	2	4	no	—
46	C₂×D₈×C₃₁	D₄	1	8	yes	complemented
47	C₂×D₈×C₃₁	C₂³	1	4	yes	—
48	C₂×D₈×C₃₁	C₂³	1	1	yes	characteristic, complemented
49	C₂²×C₈×C₃₁	—	2	4	no	—
50	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	D₄	1	2	yes	—
52	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
53	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
54	C₃₁×#123	—	4	1	no	—
55	C₃₁×C₂²⋊Q₈	—	2	2	no	—
56	C₃₁×#121	—	2	2	no	—
57	C₃₁×#120	—	4	1	no	—
58	C₄×D₄×C₃₁	—	4	2	no	—
59	C₃₁×#117	—	2	1	no	—
60	C₃₁×SD₃₂	—	2	8	no	—
61	C₃₁×D₁₆	—	2	8	no	—
62	C₃₁×M₃₂	—	2	4	no	—
63	C₂×C₁₆×C₃₁	C₂³	1	4	yes	complemented
64	C₃₁×#107	C₂³	1	2	yes	complemented
65	C₃₁×#106	—	2	1	no	—
66	C₃₁×#103	—	2	2	no	—
67	C₃₁×#102	—	2	2	no	—
68	C₂⁴×C₃₁	—	4	8	no	—
69	C₂⁴×C₃₁	—	4	4	no	—
70	C₂⁴×C₃₁	—	4	2	no	—
71	C₂⁴×C₃₁	—	8	8	no	—
72	C₂⁴×C₃₁	D₈	1	1	yes	characteristic
73	#41×C₃₁	—	4	2	no	—
74	#41×C₃₁	—	4	2	no	—
75	C₂×Q₈×C₃₁	—	2	1	no	—
76	C₂×D₄×C₃₁	—	2	16	no	—
77	C₂×D₄×C₃₁	—	2	8	no	—
78	C₂×D₄×C₃₁	—	2	4	no	—
79	C₂×D₄×C₃₁	—	2	1	no	—
80	C₂×D₄×C₃₁	—	4	8	no	—
81	C₂×D₄×C₃₁	—	4	8	no	—
82	C₂×D₄×C₃₁	—	4	16	no	—
83	C₂×D₄×C₃₁	—	4	2	no	—
84	C₂×D₄×C₃₁	—	4	1	no	—
85	C₂×D₄×C₃₁	—	4	4	no	—
86	C₂×D₄×C₃₁	—	4	2	no	—
87	C₂×D₄×C₃₁	—	4	4	no	—
88	C₂²×C₄×C₃₁	—	2	2	no	—
89	C₂²×C₄×C₃₁	—	2	2	no	—
90	C₂²×C₄×C₃₁	—	4	1	no	—
91	C₂²×C₄×C₃₁	D₈	1	2	yes	—
92	C₂²×C₄×C₃₁	D₈	1	1	yes	characteristic
93	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
95	Q₁₆×C₃₁	—	2	2	no	—
96	SD₁₆×C₃₁	—	4	2	no	—
97	D₈×C₃₁	—	2	16	no	—
98	D₈×C₃₁	—	2	8	no	—
99	D₈×C₃₁	—	2	4	no	—
100	D₈×C₃₁	—	2	2	no	—
101	D₈×C₃₁	C₂×D₄	1	8	yes	—
102	C₂×C₈×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	4	no	—
104	C₂×C₈×C₃₁	—	2	4	no	—
105	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
106	C₂×C₈×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
108	C₂×C₈×C₃₁	C₂⁴	1	1	yes	characteristic
109	C₄⋊C₄×C₃₁	—	2	2	no	—
110	C₄⋊C₄×C₃₁	—	4	2	no	—
111	C₂²⋊C₄×C₃₁	—	4	1	no	—
112	C₂²⋊C₄×C₃₁	—	4	2	no	—
113	C₂²⋊C₄×C₃₁	—	4	2	no	—
114	C₄²×C₃₁	—	4	1	no	—
115	C₁₆×C₃₁	—	2	4	no	—
116	#33517	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	2	2	no	—
118	C₂³×C₃₁	—	2	4	no	—
119	C₂³×C₃₁	—	4	16	no	—
120	C₂³×C₃₁	—	4	4	no	—
121	C₂³×C₃₁	—	4	8	no	—
122	C₂³×C₃₁	—	4	1	no	—
123	C₂³×C₃₁	—	8	32	no	—
124	C₂³×C₃₁	—	8	8	no	—
125	C₂³×C₃₁	—	8	8	no	—
126	C₂³×C₃₁	—	8	8	no	—
127	C₂³×C₃₁	C₂×D₈	1	1	yes	characteristic
128	C₂³×C₃₁	C₂×D₈	1	2	yes	—
129	Q₈×C₃₁	—	4	1	no	—
130	Q₈×C₃₁	—	4	1	no	—
131	D₄×C₃₁	—	2	8	no	—
132	D₄×C₃₁	—	4	16	no	—
133	D₄×C₃₁	—	4	1	no	—
134	D₄×C₃₁	—	4	4	no	—
135	D₄×C₃₁	—	4	1	no	—
136	D₄×C₃₁	—	4	8	no	—
137	D₄×C₃₁	—	8	2	no	—
138	D₄×C₃₁	—	8	4	no	—
139	C₂×C₄×C₃₁	—	2	2	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	4	2	no	—
144	C₂×C₄×C₃₁	—	4	1	no	—
145	C₂×C₄×C₃₁	—	8	2	no	—
146	C₂×C₄×C₃₁	#120	1	2	yes	—
147	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
148	C₂×C₄×C₃₁	C₂×D₈	1	1	yes	characteristic
149	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
151	C₈×C₃₁	—	2	2	no	—
152	C₈×C₃₁	#120	1	2	yes	—
153	C₈×C₃₁	C₂²×D₄	1	2	yes	—
154	C₂³×D₈	C₂×C₃₁	1	1	yes	characteristic, complemented
155	C₂×#509	C₂×C₃₁	1	2	yes	complemented
156	#3050	C₂×C₃₁	1	1	yes	characteristic, complemented
157	#2187	C₂×C₃₁	1	4	yes	complemented
158	#2184	C₂×C₃₁	1	4	yes	complemented
159	#2140	C₂×C₃₁	1	2	yes	complemented
160	#2112	C₂×C₃₁	1	1	yes	characteristic, complemented
161	C₂²×C₃₁	—	2	8	no	—
162	C₂²×C₃₁	—	2	2	no	—
163	C₂²×C₃₁	—	2	2	no	—
164	C₂²×C₃₁	—	2	2	no	—
165	C₂²×C₃₁	—	4	8	no	—
166	C₂²×C₃₁	—	8	16	no	—
167	C₂²×C₃₁	—	8	32	no	—
168	C₂²×C₃₁	—	8	8	no	—
169	C₂²×C₃₁	—	8	2	no	—
170	C₂²×C₃₁	—	8	1	no	—
171	C₂²×C₃₁	#447	1	2	yes	—
172	C₂²×C₃₁	#509	1	4	yes	complemented
173	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
174	C₄×C₃₁	—	2	2	no	—
175	C₄×C₃₁	—	8	2	no	—
176	C₄×C₃₁	—	8	1	no	—
177	C₄×C₃₁	#447	1	2	yes	—
178	C₄×C₃₁	C₂×#120	1	1	yes	characteristic
179	C₄×C₃₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂³×D₄	—	2	1	no	—
181	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic, complemented
182	C₂²×D₈	—	2	8	no	—
183	C₂²×D₈	—	2	1	no	—
184	C₂²×D₈	—	2	2	no	—
185	C₂²×D₈	C₂²×C₃₁	1	4	yes	—
186	C₂²×D₈	C₂²×C₃₁	1	2	yes	—
187	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
188	#525	—	2	1	no	—
189	#509	—	2	8	no	—
190	C₂×SD₃₂	C₂²×C₃₁	1	4	yes	complemented
191	C₂×D₁₆	C₂²×C₃₁	1	4	yes	complemented
192	C₂×M₃₂	C₂²×C₃₁	1	2	yes	complemented
193	#467	C₂²×C₃₁	1	2	yes	complemented
194	#466	C₂²×C₃₁	1	2	yes	complemented
195	#465	—	2	2	no	—
196	#427	C₂²×C₃₁	1	1	yes	characteristic, complemented
197	#416	—	2	1	no	—
198	#357	C₂²×C₃₁	1	8	yes	complemented
199	C₂²⋊C₁₆	C₂²×C₃₁	1	4	yes	complemented
200	C₂×C₃₁	—	2	2	no	—
201	C₂×C₃₁	—	2	4	no	—
202	C₂×C₃₁	—	8	8	no	—
203	C₂×C₃₁	—	16	1	no	—
204	C₂×C₃₁	C₂×#447	1	1	yes	characteristic
205	C₂×C₃₁	C₂×#509	1	2	yes	—
206	C₂⁵	—	4	1	no	—
207	C₂×#41	—	2	1	no	—
208	C₂²×D₄	—	2	8	no	—
209	C₂²×D₄	—	2	4	no	—
210	C₂²×D₄	—	2	2	no	—
211	C₂²×D₄	—	4	4	no	—
212	C₂²×D₄	—	4	2	no	—
213	C₂²×D₄	—	4	1	no	—
214	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
215	#135	—	2	4	no	—
216	C₂×Q₁₆	C₂³×C₃₁	1	1	yes	characteristic, complemented
217	C₂×SD₁₆	—	2	1	no	—
218	C₂×D₈	—	2	8	no	—
219	C₂×D₈	—	2	16	no	—
220	C₂×D₈	—	2	16	no	—
221	C₂×D₈	—	2	4	no	—
222	C₂×D₈	—	2	2	no	—
223	C₂×D₈	—	2	4	no	—
224	C₂×D₈	D₄×C₃₁	1	8	yes	complemented
225	C₂×D₈	C₂³×C₃₁	1	4	yes	—
226	C₂×D₈	C₂³×C₃₁	1	1	yes	characteristic, complemented
227	C₂²×C₈	—	2	4	no	—
228	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
229	C₂²×C₈	D₄×C₃₁	1	2	yes	—
230	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
232	#123	—	4	1	no	—
233	C₂²⋊Q₈	—	2	2	no	—
234	#121	—	2	2	no	—
235	#120	—	4	1	no	—
236	C₄×D₄	—	4	2	no	—
237	#117	—	2	1	no	—
238	SD₃₂	—	2	8	no	—
239	D₁₆	—	2	8	no	—
240	M₃₂	—	2	4	no	—
241	C₂×C₁₆	C₂³×C₃₁	1	4	yes	complemented
242	#107	C₂³×C₃₁	1	2	yes	complemented
243	#106	—	2	1	no	—
244	#103	—	2	2	no	—
245	#102	—	2	2	no	—
246	C₃₁	#33517	1	1	yes	characteristic, direct product factor, Sylow
247	C₂⁴	—	4	8	no	—
248	C₂⁴	—	4	4	no	—
249	C₂⁴	—	4	2	no	—
250	C₂⁴	—	8	8	no	—
251	C₂⁴	D₈×C₃₁	1	1	yes	characteristic
252	#41	—	4	2	no	—
253	#41	—	4	2	no	—
254	C₂×Q₈	—	2	1	no	—
255	C₂×D₄	—	2	16	no	—
256	C₂×D₄	—	2	8	no	—
257	C₂×D₄	—	2	4	no	—
258	C₂×D₄	—	2	1	no	—
259	C₂×D₄	—	4	8	no	—
260	C₂×D₄	—	4	16	no	—
261	C₂×D₄	—	4	8	no	—
262	C₂×D₄	—	4	2	no	—
263	C₂×D₄	—	4	1	no	—
264	C₂×D₄	—	4	4	no	—
265	C₂×D₄	—	4	2	no	—
266	C₂×D₄	—	4	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	D₈×C₃₁	1	2	yes	—
271	C₂²×C₄	D₈×C₃₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
273	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
274	Q₁₆	—	2	2	no	—
275	SD₁₆	—	4	2	no	—
276	D₈	—	2	16	no	—
277	D₈	—	2	8	no	—
278	D₈	—	2	4	no	—
279	D₈	—	2	2	no	—
280	D₈	C₂×D₄×C₃₁	1	8	yes	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
285	C₂×C₈	C₂×D₄×C₃₁	1	1	yes	characteristic
286	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
287	C₂×C₈	C₂⁴×C₃₁	1	1	yes	characteristic
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	4	2	no	—
290	C₂²⋊C₄	—	4	1	no	—
291	C₂²⋊C₄	—	4	2	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₄²	—	4	1	no	—
294	C₁₆	—	2	4	no	—
295	C₂³	—	2	2	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	4	16	no	—
298	C₂³	—	4	8	no	—
299	C₂³	—	4	4	no	—
300	C₂³	—	4	1	no	—
301	C₂³	—	8	32	no	—
302	C₂³	—	8	8	no	—
303	C₂³	—	8	8	no	—
304	C₂³	—	8	8	no	—
305	C₂³	C₂×D₈×C₃₁	1	1	yes	characteristic
306	C₂³	C₂×D₈×C₃₁	1	2	yes	—
307	Q₈	—	4	1	no	—
308	Q₈	—	4	1	no	—
309	D₄	—	2	8	no	—
310	D₄	—	4	16	no	—
311	D₄	—	4	8	no	—
312	D₄	—	4	1	no	—
313	D₄	—	4	4	no	—
314	D₄	—	4	1	no	—
315	D₄	—	8	2	no	—
316	D₄	—	8	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	8	2	no	—
324	C₂×C₄	C₃₁×#120	1	2	yes	—
325	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
326	C₂×C₄	C₂×D₈×C₃₁	1	1	yes	characteristic
327	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
328	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
329	C₈	—	2	2	no	—
330	C₈	C₃₁×#120	1	2	yes	—
331	C₈	C₂²×D₄×C₃₁	1	2	yes	—
332	C₂²	—	2	8	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	8	16	no	—
338	C₂²	—	8	32	no	—
339	C₂²	—	8	8	no	—
340	C₂²	—	8	2	no	—
341	C₂²	—	8	1	no	—
342	C₂²	C₃₁×#447	1	2	yes	—
343	C₂²	C₃₁×#509	1	4	yes	complemented
344	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
345	C₄	—	2	2	no	—
346	C₄	—	8	2	no	—
347	C₄	—	8	1	no	—
348	C₄	C₃₁×#447	1	2	yes	—
349	C₄	C₂×C₃₁×#120	1	1	yes	characteristic
350	C₄	C₂×C₃₁×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₂	—	2	2	no	—
352	C₂	—	2	4	no	—
353	C₂	—	8	8	no	—
354	C₂	—	16	1	no	—
355	C₂	C₂×C₃₁×#447	1	1	yes	characteristic
356	C₂	C₂×C₃₁×#509	1	2	yes	—

	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 ◁ C₂³×C₄×C₃₁ ◁ C₂³×C₈×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×D₈×C₃₁	C₂	semidirect
2. C₂×C₃₁×#509	C₂	semidirect
3. C₃₁×#3050	C₂	semidirect
4. C₃₁×#2187	C₂	semidirect
5. C₃₁×#2184	C₂	semidirect
6. C₃₁×#2140	C₂	semidirect
7. C₃₁×#2112	C₂	semidirect
9. C₂×C₃₁×#135	C₂²	semidirect
18. C₂×C₃₁×SD₃₂	C₂²	semidirect
19. C₂×C₃₁×D₁₆	C₂²	semidirect
20. C₂×C₃₁×M₃₂	C₂²	semidirect
21. C₃₁×#467	C₂²	semidirect
22. C₃₁×#466	C₂²	semidirect
24. C₃₁×#427	C₂²	semidirect
26. C₃₁×#357	C₂²	semidirect
27. C₃₁×C₂²⋊C₁₆	C₂²	semidirect
38. C₂×Q₁₆×C₃₁	C₂³	semidirect
46. C₂×D₈×C₃₁	D₄	semidirect
48. C₂×D₈×C₃₁	C₂³	semidirect
63. C₂×C₁₆×C₃₁	C₂³	semidirect
64. C₃₁×#107	C₂³	semidirect
116. #33517	C₃₁	direct (N × H)
154. C₂³×D₈	C₂×C₃₁	semidirect
155. C₂×#509	C₂×C₃₁	semidirect
156. #3050	C₂×C₃₁	semidirect
157. #2187	C₂×C₃₁	semidirect
158. #2184	C₂×C₃₁	semidirect
159. #2140	C₂×C₃₁	semidirect
160. #2112	C₂×C₃₁	semidirect
172. C₂²×C₃₁	#509	semidirect
181. C₂×#135	C₂²×C₃₁	semidirect
190. C₂×SD₃₂	C₂²×C₃₁	semidirect
191. C₂×D₁₆	C₂²×C₃₁	semidirect
192. C₂×M₃₂	C₂²×C₃₁	semidirect
193. #467	C₂²×C₃₁	semidirect
194. #466	C₂²×C₃₁	semidirect
196. #427	C₂²×C₃₁	semidirect
198. #357	C₂²×C₃₁	semidirect
199. C₂²⋊C₁₆	C₂²×C₃₁	semidirect
216. C₂×Q₁₆	C₂³×C₃₁	semidirect
224. C₂×D₈	D₄×C₃₁	semidirect
226. C₂×D₈	C₂³×C₃₁	semidirect
241. C₂×C₁₆	C₂³×C₃₁	semidirect
242. #107	C₂³×C₃₁	semidirect
246. C₃₁	#33517	direct (N × H)
343. C₂²	C₃₁×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₃₁	2
C₂×C₃₁×#509	2
C₃₁×#3050	2
C₃₁×#2187	2
C₃₁×#2184	2
C₃₁×#2140	2
C₃₁×#2112	2
#33517	31

Subgroups — C31×#33517 #21490276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#33517 #21490276