Subgroups — C₃₁×#25909 #21482668

Order 7936.

1092 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#489	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2850	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#2026	C₂	1	2	yes	maximal, complemented
5	C₃₁×#2025	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1993	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1875	C₂	1	2	yes	maximal
8	C₃₁×#1873	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1749	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃₁×#533	—	2	8	no	—
11	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
12	C₂×C₃₁×#125	C₂²	1	2	yes	—
13	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
14	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
15	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₃₁	—	2	2	no	—
18	C₂×C₃₁×#117	C₂²	1	2	yes	—
19	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
20	C₃₁×#489	—	2	8	no	—
21	C₂×C₃₁×#103	C₂²	1	4	yes	—
22	C₂×C₃₁×#102	C₂²	1	4	yes	—
23	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
24	C₂×C₃₁×#97	C₂²	1	2	yes	—
25	C₃₁×#391	C₂²	1	1	yes	characteristic
26	C₃₁×#390	C₂²	1	1	yes	characteristic
27	C₃₁×#388	—	2	2	no	—
28	C₃₁×#386	—	2	2	no	—
29	C₃₁×#382	C₂²	1	1	yes	characteristic
30	C₃₁×#340	C₂²	1	4	yes	—
31	C₃₁×#340	C₂²	1	4	yes	—
32	C₃₁×#336	C₂²	1	2	yes	—
33	C₂²×Q₈×C₃₁	—	2	2	no	—
34	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
35	C₂²×D₄×C₃₁	—	2	1	no	—
36	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₃₁	D₄	1	2	yes	—
38	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
40	C₃₁×C₄⋊Q₈	—	2	4	no	—
41	C₃₁×C₄⋊Q₈	D₄	1	8	yes	complemented
42	C₃₁×#125	—	2	8	no	—
43	C₃₁×#124	—	2	4	no	—
44	C₃₁×C₂²⋊Q₈	—	2	16	no	—
45	C₃₁×C₂²⋊Q₈	—	2	4	no	—
46	C₃₁×#121	—	2	4	no	—
47	C₄×Q₈×C₃₁	—	2	16	no	—
48	C₃₁×#117	—	2	8	no	—
49	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₄²×C₃₁	—	2	2	no	—
61	C₂×C₄²×C₃₁	—	2	4	no	—
62	C₂×C₄²×C₃₁	D₄	1	2	yes	—
63	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
65	C₃₁×#103	—	2	8	no	—
66	C₃₁×#102	—	2	8	no	—
67	C₃₁×C₂²⋊C₈	—	2	4	no	—
68	C₃₁×#97	—	2	4	no	—
69	C₃₁×#95	—	2	2	no	—
70	C₃₁×#95	—	2	2	no	—
71	C₂⁴×C₃₁	—	2	1	no	—
72	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₃₁	—	2	8	no	—
74	C₂×Q₈×C₃₁	—	2	2	no	—
75	C₂×Q₈×C₃₁	—	2	2	no	—
76	C₂×Q₈×C₃₁	—	2	2	no	—
77	C₂×Q₈×C₃₁	—	4	4	no	—
78	C₂×Q₈×C₃₁	—	4	4	no	—
79	C₂×D₄×C₃₁	—	2	2	no	—
80	C₂×D₄×C₃₁	—	2	2	no	—
81	C₂×D₄×C₃₁	—	2	2	no	—
82	C₂×D₄×C₃₁	—	4	4	no	—
83	C₂×D₄×C₃₁	—	4	2	no	—
84	C₂²×C₄×C₃₁	—	2	2	no	—
85	C₂²×C₄×C₃₁	—	2	2	no	—
86	C₂²×C₄×C₃₁	—	2	4	no	—
87	C₂²×C₄×C₃₁	—	2	4	no	—
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	—	2	1	no	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	—	4	2	no	—
92	C₂²×C₄×C₃₁	—	4	2	no	—
93	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₃₁	#41	1	4	yes	—
97	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₃₁	—	2	4	no	—
99	C₂×C₈×C₃₁	—	2	4	no	—
100	C₂×C₈×C₃₁	—	2	4	no	—
101	C₄⋊C₄×C₃₁	—	2	16	no	—
102	C₄⋊C₄×C₃₁	—	2	8	no	—
103	C₄⋊C₄×C₃₁	—	2	4	no	—
104	C₄⋊C₄×C₃₁	—	2	2	no	—
105	C₄⋊C₄×C₃₁	—	2	2	no	—
106	C₄⋊C₄×C₃₁	—	4	2	no	—
107	C₄⋊C₄×C₃₁	C₂×D₄	1	8	yes	—
108	C₂²⋊C₄×C₃₁	—	2	8	no	—
109	C₂²⋊C₄×C₃₁	—	4	4	no	—
110	C₂²⋊C₄×C₃₁	—	4	2	no	—
111	C₂²⋊C₄×C₃₁	—	4	4	no	—
112	C₂²⋊C₄×C₃₁	—	4	2	no	—
113	C₄²×C₃₁	—	2	8	no	—
114	C₄²×C₃₁	—	2	4	no	—
115	C₄²×C₃₁	—	2	2	no	—
116	C₄²×C₃₁	C₂×D₄	1	4	yes	—
117	#25909	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₃₁	—	2	1	no	—
119	C₂³×C₃₁	—	2	1	no	—
120	C₂³×C₃₁	—	2	2	no	—
121	C₂³×C₃₁	—	2	2	no	—
122	C₂³×C₃₁	—	4	1	no	—
123	C₂³×C₃₁	—	4	1	no	—
124	C₂³×C₃₁	—	4	1	no	—
125	C₂³×C₃₁	—	4	2	no	—
126	C₂³×C₃₁	—	4	2	no	—
127	C₂³×C₃₁	#124	1	2	yes	—
128	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₃₁	—	4	16	no	—
130	Q₈×C₃₁	—	4	4	no	—
131	D₄×C₃₁	—	4	4	no	—
132	D₄×C₃₁	—	8	4	no	—
133	C₂×C₄×C₃₁	—	2	1	no	—
134	C₂×C₄×C₃₁	—	2	1	no	—
135	C₂×C₄×C₃₁	—	2	2	no	—
136	C₂×C₄×C₃₁	—	2	2	no	—
137	C₂×C₄×C₃₁	—	2	8	no	—
138	C₂×C₄×C₃₁	—	2	2	no	—
139	C₂×C₄×C₃₁	—	2	8	no	—
140	C₂×C₄×C₃₁	—	2	2	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	4	8	no	—
143	C₂×C₄×C₃₁	—	4	4	no	—
144	C₂×C₄×C₃₁	—	4	4	no	—
145	C₂×C₄×C₃₁	—	4	1	no	—
146	C₂×C₄×C₃₁	—	4	1	no	—
147	C₂×C₄×C₃₁	—	4	1	no	—
148	C₂×C₄×C₃₁	—	4	1	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	2	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	#120	1	4	yes	—
153	C₂×C₄×C₃₁	#124	1	2	yes	—
154	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
155	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
156	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
157	C₈×C₃₁	—	4	4	no	—
158	C₂×#533	C₂×C₃₁	1	1	yes	characteristic, complemented
159	C₂×#489	C₂×C₃₁	1	2	yes	complemented
160	#2850	C₂×C₃₁	1	1	yes	characteristic
161	#2026	C₂×C₃₁	1	2	yes	complemented
162	#2025	C₂×C₃₁	1	2	yes	complemented
163	#1993	C₂×C₃₁	1	2	yes	complemented
164	#1875	C₂×C₃₁	1	2	yes	—
165	#1873	C₂×C₃₁	1	2	yes	complemented
166	#1749	C₂×C₃₁	1	1	yes	characteristic, complemented
167	C₂²×C₃₁	—	2	2	no	—
168	C₂²×C₃₁	—	2	2	no	—
169	C₂²×C₃₁	—	2	2	no	—
170	C₂²×C₃₁	—	4	2	no	—
171	C₂²×C₃₁	—	4	2	no	—
172	C₂²×C₃₁	—	8	1	no	—
173	C₂²×C₃₁	—	8	1	no	—
174	C₂²×C₃₁	—	8	1	no	—
175	C₂²×C₃₁	—	8	2	no	—
176	C₂²×C₃₁	—	8	2	no	—
177	C₂²×C₃₁	C₂×#120	1	1	yes	characteristic
178	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
179	C₂²×C₃₁	#536	1	1	yes	characteristic
180	C₂²×C₃₁	#575	1	2	yes	—
181	C₂²×C₃₁	#575	1	2	yes	—
182	C₄×C₃₁	—	2	2	no	—
183	C₄×C₃₁	—	2	4	no	—
184	C₄×C₃₁	—	4	2	no	—
185	C₄×C₃₁	—	4	8	no	—
186	C₄×C₃₁	—	8	1	no	—
187	C₄×C₃₁	—	8	1	no	—
188	C₄×C₃₁	—	8	1	no	—
189	C₄×C₃₁	#548	1	4	yes	—
190	#533	—	2	8	no	—
191	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
192	C₂×#125	C₂²×C₃₁	1	2	yes	—
193	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
194	C₂×C₂²⋊Q₈	—	2	2	no	—
195	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
196	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
197	C₂×C₄×Q₈	—	2	2	no	—
198	C₂×#117	C₂²×C₃₁	1	2	yes	—
199	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
200	#489	—	2	8	no	—
201	C₂×#103	C₂²×C₃₁	1	4	yes	—
202	C₂×#102	C₂²×C₃₁	1	4	yes	—
203	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
204	C₂×#97	C₂²×C₃₁	1	2	yes	—
205	#391	C₂²×C₃₁	1	1	yes	characteristic
206	#390	C₂²×C₃₁	1	1	yes	characteristic
207	#388	—	2	2	no	—
208	#386	—	2	2	no	—
209	#382	C₂²×C₃₁	1	1	yes	characteristic
210	#340	C₂²×C₃₁	1	4	yes	—
211	#340	C₂²×C₃₁	1	4	yes	—
212	#336	C₂²×C₃₁	1	2	yes	—
213	C₂×C₃₁	—	4	2	no	—
214	C₂×C₃₁	—	16	1	no	—
215	C₂×C₃₁	#2436	1	1	yes	characteristic
216	C₂×C₃₁	#3005	1	2	yes	—
217	C₂×C₃₁	#3135	1	1	yes	characteristic
218	C₂×C₃₁	#3140	1	1	yes	characteristic
219	C₂×C₃₁	#3240	1	2	yes	—
220	C₂²×Q₈	—	2	2	no	—
221	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
224	C₂³×C₄	D₄×C₃₁	1	2	yes	—
225	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
227	C₄⋊Q₈	—	2	4	no	—
228	C₄⋊Q₈	D₄×C₃₁	1	8	yes	complemented
229	#125	—	2	8	no	—
230	#124	—	2	4	no	—
231	C₂²⋊Q₈	—	2	16	no	—
232	C₂²⋊Q₈	—	2	4	no	—
233	#121	—	2	4	no	—
234	C₄×Q₈	—	2	16	no	—
235	#117	—	2	8	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
240	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	1	no	—
244	C₂×C₂²⋊C₄	—	2	1	no	—
245	C₂×C₂²⋊C₄	—	2	2	no	—
246	C₂×C₂²⋊C₄	—	2	2	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	—	2	4	no	—
249	C₂×C₄²	D₄×C₃₁	1	2	yes	—
250	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
252	#103	—	2	8	no	—
253	#102	—	2	8	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	#97	—	2	4	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	C₃₁	#25909	1	1	yes	characteristic, direct product factor, Sylow
259	C₂⁴	—	2	1	no	—
260	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	4	4	no	—
266	C₂×Q₈	—	4	4	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	4	4	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	#41×C₃₁	1	4	yes	—
285	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	2	4	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	4	2	no	—
295	C₄⋊C₄	C₂×D₄×C₃₁	1	8	yes	—
296	C₂²⋊C₄	—	2	8	no	—
297	C₂²⋊C₄	—	4	4	no	—
298	C₂²⋊C₄	—	4	2	no	—
299	C₂²⋊C₄	—	4	4	no	—
300	C₂²⋊C₄	—	4	2	no	—
301	C₄²	—	2	8	no	—
302	C₄²	—	2	4	no	—
303	C₄²	—	2	2	no	—
304	C₄²	C₂×D₄×C₃₁	1	4	yes	—
305	C₂³	—	2	1	no	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	4	1	no	—
312	C₂³	—	4	2	no	—
313	C₂³	—	4	2	no	—
314	C₂³	C₃₁×#124	1	2	yes	—
315	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
316	Q₈	—	4	16	no	—
317	Q₈	—	4	4	no	—
318	D₄	—	4	4	no	—
319	D₄	—	8	4	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	8	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	C₃₁×#120	1	4	yes	—
340	C₂×C₄	C₃₁×#124	1	2	yes	—
341	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
342	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
343	C₂×C₄	C₃₁×2₋¹⁺⁴	1	2	yes	—
344	C₈	—	4	4	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	1	no	—
351	C₂²	—	8	1	no	—
352	C₂²	—	8	1	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	C₂×C₃₁×#120	1	1	yes	characteristic
356	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
357	C₂²	C₃₁×#536	1	1	yes	characteristic
358	C₂²	C₃₁×#575	1	2	yes	—
359	C₂²	C₃₁×#575	1	2	yes	—
360	C₄	—	2	2	no	—
361	C₄	—	2	4	no	—
362	C₄	—	4	2	no	—
363	C₄	—	4	8	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	—	8	1	no	—
367	C₄	C₃₁×#548	1	4	yes	—
368	C₂	—	4	2	no	—
369	C₂	—	16	1	no	—
370	C₂	C₃₁×#2436	1	1	yes	characteristic
371	C₂	C₃₁×#3005	1	2	yes	—
372	C₂	C₃₁×#3135	1	1	yes	characteristic
373	C₂	C₃₁×#3140	1	1	yes	characteristic
374	C₂	C₃₁×#3240	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#121	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#533	C₂	semidirect
2. C₂×C₃₁×#489	C₂	semidirect
4. C₃₁×#2026	C₂	semidirect
5. C₃₁×#2025	C₂	semidirect
6. C₃₁×#1993	C₂	semidirect
8. C₃₁×#1873	C₂	semidirect
9. C₃₁×#1749	C₂	semidirect
41. C₃₁×C₄⋊Q₈	D₄	semidirect
117. #25909	C₃₁	direct (N × H)
158. C₂×#533	C₂×C₃₁	semidirect
159. C₂×#489	C₂×C₃₁	semidirect
161. #2026	C₂×C₃₁	semidirect
162. #2025	C₂×C₃₁	semidirect
163. #1993	C₂×C₃₁	semidirect
165. #1873	C₂×C₃₁	semidirect
166. #1749	C₂×C₃₁	semidirect
228. C₄⋊Q₈	D₄×C₃₁	semidirect
258. C₃₁	#25909	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×#533	2
C₂×C₃₁×#489	2
C₃₁×#2850	2
C₃₁×#2026	2
C₃₁×#2025	2
C₃₁×#1993	2
C₃₁×#1875	2
C₃₁×#1873	2
C₃₁×#1749	2
#25909	31

Subgroups — C31×#25909 #21482668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#25909 #21482668