Subgroups — C₂×C₃₁×#3192 #21517494

Order 7936.

3010 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#121	C₂	1	2	yes	maximal, complemented
2	C₃₁×#3192	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃₁×#481	C₂	1	4	yes	maximal, complemented
4	C₂×C₃₁×#469	C₂	1	4	yes	maximal, complemented
5	C₂×C₃₁×#447	C₂	1	4	yes	maximal, complemented
6	C₂×C₃₁×#407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₃₁	—	2	2	no	—
8	C₂³×D₄×C₃₁	C₂²	1	2	yes	complemented
9	C₂⁴×C₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₃₁	C₂²	1	4	yes	complemented
11	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
12	C₂×C₃₁×#121	—	2	2	no	—
13	C₂×C₃₁×#121	—	2	8	no	—
14	C₂×C₃₁×#121	—	2	2	no	—
15	C₂×C₃₁×#121	C₂²	1	4	yes	—
16	C₂×C₃₁×#121	C₂²	1	4	yes	complemented
17	C₂×C₃₁×#121	C₂²	1	16	yes	complemented
18	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊C₄×C₃₁	—	2	2	no	—
20	C₃₁×#481	C₂²	1	32	yes	complemented
21	C₃₁×#469	C₂²	1	32	yes	complemented
22	C₃₁×#447	C₂²	1	32	yes	complemented
23	C₂×C₃₁×#106	C₂²	1	4	yes	complemented
24	C₂×C₃₁×#102	C₂²	1	8	yes	complemented
25	C₃₁×#407	C₂²	1	8	yes	complemented
26	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	complemented
27	C₂⁵×C₃₁	—	2	2	no	—
28	C₂⁵×C₃₁	D₄	1	1	yes	characteristic
29	C₂²×D₄×C₃₁	—	2	4	no	—
30	C₂²×D₄×C₃₁	—	2	16	no	—
31	C₂²×D₄×C₃₁	—	2	4	no	—
32	C₂²×D₄×C₃₁	—	2	4	no	—
33	C₂²×D₄×C₃₁	—	2	2	no	—
34	C₂²×D₄×C₃₁	—	4	8	no	—
35	C₂²×D₄×C₃₁	—	4	16	no	—
36	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
37	C₂²×D₄×C₃₁	C₂³	1	8	yes	complemented
38	C₂³×C₄×C₃₁	—	2	2	no	—
39	C₂³×C₄×C₃₁	—	4	4	no	—
40	C₂³×C₄×C₃₁	D₄	1	2	yes	—
41	C₂³×C₄×C₃₁	D₄	1	4	yes	—
42	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
44	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
46	C₂×D₈×C₃₁	—	4	8	no	—
47	C₂×D₈×C₃₁	C₂³	1	16	yes	complemented
48	C₂×M₁₆×C₃₁	—	4	4	no	—
49	C₂×M₁₆×C₃₁	C₂³	1	8	yes	complemented
50	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
51	C₃₁×#121	—	2	8	no	—
52	C₃₁×#121	—	2	16	no	—
53	C₃₁×#121	—	2	8	no	—
54	C₃₁×#121	—	2	16	no	—
55	C₃₁×#121	C₂³	1	16	yes	—
56	C₃₁×#121	C₂³	1	16	yes	complemented
57	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
58	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	complemented
61	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	16	no	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	4	no	—
64	C₃₁×#106	C₂³	1	16	yes	complemented
65	C₃₁×#102	C₂³	1	32	yes	complemented
66	C₃₁×C₂²⋊C₈	C₂³	1	16	yes	complemented
67	C₂⁴×C₃₁	—	2	8	no	—
68	C₂⁴×C₃₁	—	2	8	no	—
69	C₂⁴×C₃₁	—	2	4	no	—
70	C₂⁴×C₃₁	—	4	2	no	—
71	C₂⁴×C₃₁	—	4	8	no	—
72	C₂⁴×C₃₁	—	4	8	no	—
73	C₂⁴×C₃₁	—	4	8	no	—
74	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×C₃₁	C₂×D₄	1	4	yes	—
76	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
77	C₂×D₄×C₃₁	—	2	16	no	—
78	C₂×D₄×C₃₁	—	2	16	no	—
79	C₂×D₄×C₃₁	—	2	4	no	—
80	C₂×D₄×C₃₁	—	2	8	no	—
81	C₂×D₄×C₃₁	—	2	16	no	—
82	C₂×D₄×C₃₁	—	4	16	no	—
83	C₂×D₄×C₃₁	—	4	8	no	—
84	C₂×D₄×C₃₁	—	4	16	no	—
85	C₂×D₄×C₃₁	—	4	64	no	—
86	C₂×D₄×C₃₁	—	4	16	no	—
87	C₂×D₄×C₃₁	—	4	16	no	—
88	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
89	C₂²×C₄×C₃₁	—	2	4	no	—
90	C₂²×C₄×C₃₁	—	2	8	no	—
91	C₂²×C₄×C₃₁	—	2	8	no	—
92	C₂²×C₄×C₃₁	—	2	4	no	—
93	C₂²×C₄×C₃₁	—	4	8	no	—
94	C₂²×C₄×C₃₁	—	4	8	no	—
95	C₂²×C₄×C₃₁	—	4	4	no	—
96	C₂²×C₄×C₃₁	—	4	2	no	—
97	C₂²×C₄×C₃₁	—	4	8	no	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	8	yes	—
103	C₂²×C₄×C₃₁	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
107	D₈×C₃₁	—	4	16	no	—
108	M₁₆×C₃₁	—	4	8	no	—
109	C₂×C₈×C₃₁	—	2	8	no	—
110	C₂×C₈×C₃₁	C₂⁴	1	8	yes	—
111	C₄⋊C₄×C₃₁	—	2	4	no	—
112	C₄⋊C₄×C₃₁	—	2	8	no	—
113	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
114	C₂²⋊C₄×C₃₁	—	2	16	no	—
115	C₂²⋊C₄×C₃₁	—	2	16	no	—
116	C₂×#3192	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂³×C₃₁	—	2	4	no	—
118	C₂³×C₃₁	—	2	4	no	—
119	C₂³×C₃₁	—	2	2	no	—
120	C₂³×C₃₁	—	2	16	no	—
121	C₂³×C₃₁	—	2	4	no	—
122	C₂³×C₃₁	—	2	8	no	—
123	C₂³×C₃₁	—	4	4	no	—
124	C₂³×C₃₁	—	4	16	no	—
125	C₂³×C₃₁	—	4	16	no	—
126	C₂³×C₃₁	—	4	16	no	—
127	C₂³×C₃₁	—	4	8	no	—
128	C₂³×C₃₁	—	4	8	no	—
129	C₂³×C₃₁	—	4	16	no	—
130	C₂³×C₃₁	—	4	8	no	—
131	C₂³×C₃₁	—	8	32	no	—
132	C₂³×C₃₁	AGL(1,ℤ/8)	1	8	yes	—
133	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
134	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
135	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₃₁	—	2	16	no	—
137	D₄×C₃₁	—	4	16	no	—
138	D₄×C₃₁	—	4	32	no	—
139	D₄×C₃₁	—	4	32	no	—
140	D₄×C₃₁	—	4	8	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	2	4	no	—
144	C₂×C₄×C₃₁	—	2	8	no	—
145	C₂×C₄×C₃₁	—	2	4	no	—
146	C₂×C₄×C₃₁	—	2	8	no	—
147	C₂×C₄×C₃₁	—	2	8	no	—
148	C₂×C₄×C₃₁	—	4	8	no	—
149	C₂×C₄×C₃₁	—	4	4	no	—
150	C₂×C₄×C₃₁	—	4	16	no	—
151	C₂×C₄×C₃₁	—	4	8	no	—
152	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
153	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₃₁	H(5,𝔽₂)	1	4	yes	—
156	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
157	C₈×C₃₁	—	2	8	no	—
158	C₂²×#121	C₂×C₃₁	1	2	yes	complemented
159	#3192	C₂×C₃₁	1	16	yes	direct product factor
160	C₂×#481	C₂×C₃₁	1	4	yes	complemented
161	C₂×#469	C₂×C₃₁	1	4	yes	complemented
162	C₂×#447	C₂×C₃₁	1	4	yes	complemented
163	C₂×#407	C₂×C₃₁	1	1	yes	characteristic, complemented
164	C₂²×C₃₁	—	2	4	no	—
165	C₂²×C₃₁	—	2	16	no	—
166	C₂²×C₃₁	—	2	4	no	—
167	C₂²×C₃₁	—	2	2	no	—
168	C₂²×C₃₁	—	2	4	no	—
169	C₂²×C₃₁	—	4	16	no	—
170	C₂²×C₃₁	—	4	4	no	—
171	C₂²×C₃₁	—	4	8	no	—
172	C₂²×C₃₁	—	4	8	no	—
173	C₂²×C₃₁	—	4	8	no	—
174	C₂²×C₃₁	—	8	32	no	—
175	C₂²×C₃₁	—	8	16	no	—
176	C₂²×C₃₁	#534	1	2	yes	—
177	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	8	yes	—
178	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
179	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
180	C₄×C₃₁	—	2	2	no	—
181	C₄×C₃₁	—	2	4	no	—
182	C₄×C₃₁	—	4	8	no	—
183	C₄×C₃₁	#534	1	2	yes	—
184	C₄×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
185	C₂³×D₄	—	2	2	no	—
186	C₂³×D₄	C₂²×C₃₁	1	2	yes	complemented
187	C₂⁴×C₄	C₂²×C₃₁	1	1	yes	characteristic
188	C₂²×D₈	C₂²×C₃₁	1	4	yes	complemented
189	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
190	C₂×#121	—	2	2	no	—
191	C₂×#121	—	2	8	no	—
192	C₂×#121	—	2	2	no	—
193	C₂×#121	C₂²×C₃₁	1	4	yes	—
194	C₂×#121	C₂²×C₃₁	1	4	yes	complemented
195	C₂×#121	C₂²×C₃₁	1	16	yes	complemented
196	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
197	C₂²×C₂²⋊C₄	—	2	2	no	—
198	#481	C₂²×C₃₁	1	32	yes	complemented
199	#469	C₂²×C₃₁	1	32	yes	complemented
200	#447	C₂²×C₃₁	1	32	yes	complemented
201	C₂×#106	C₂²×C₃₁	1	4	yes	complemented
202	C₂×#102	C₂²×C₃₁	1	8	yes	complemented
203	#407	C₂²×C₃₁	1	8	yes	complemented
204	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	complemented
205	C₂×C₃₁	—	2	8	no	—
206	C₂×C₃₁	—	4	2	no	—
207	C₂×C₃₁	—	8	8	no	—
208	C₂×C₃₁	#3192	1	4	yes	direct product factor
209	C₂×C₃₁	C₂×#534	1	1	yes	characteristic
210	C₂×C₃₁	C₂²×AGL(1,ℤ/8)	1	2	yes	—
211	C₂⁵	—	2	2	no	—
212	C₂⁵	D₄×C₃₁	1	1	yes	characteristic
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	2	4	no	—
215	C₂²×D₄	—	2	16	no	—
216	C₂²×D₄	—	2	2	no	—
217	C₂²×D₄	—	2	4	no	—
218	C₂²×D₄	—	4	8	no	—
219	C₂²×D₄	—	4	16	no	—
220	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
221	C₂²×D₄	C₂³×C₃₁	1	8	yes	complemented
222	C₂³×C₄	—	2	2	no	—
223	C₂³×C₄	—	4	4	no	—
224	C₂³×C₄	D₄×C₃₁	1	2	yes	—
225	C₂³×C₄	D₄×C₃₁	1	4	yes	—
226	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
227	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
228	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
230	C₂×D₈	—	4	8	no	—
231	C₂×D₈	C₂³×C₃₁	1	16	yes	complemented
232	C₂×M₁₆	—	4	4	no	—
233	C₂×M₁₆	C₂³×C₃₁	1	8	yes	complemented
234	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
235	#121	—	2	8	no	—
236	#121	—	2	16	no	—
237	#121	—	2	8	no	—
238	#121	—	2	16	no	—
239	#121	C₂³×C₃₁	1	16	yes	—
240	#121	C₂³×C₃₁	1	16	yes	complemented
241	C₂×C₄⋊C₄	—	2	4	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
244	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	complemented
245	C₂×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₂²⋊C₄	—	2	16	no	—
247	C₂×C₂²⋊C₄	—	2	4	no	—
248	#106	C₂³×C₃₁	1	16	yes	complemented
249	#102	C₂³×C₃₁	1	32	yes	complemented
250	C₂²⋊C₈	C₂³×C₃₁	1	16	yes	complemented
251	C₃₁	C₂×#3192	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁴	—	2	8	no	—
253	C₂⁴	—	2	4	no	—
254	C₂⁴	—	2	8	no	—
255	C₂⁴	—	4	2	no	—
256	C₂⁴	—	4	8	no	—
257	C₂⁴	—	4	8	no	—
258	C₂⁴	—	4	8	no	—
259	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
260	C₂⁴	C₂×D₄×C₃₁	1	4	yes	—
261	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
262	C₂×D₄	—	2	16	no	—
263	C₂×D₄	—	2	16	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	16	no	—
267	C₂×D₄	—	4	16	no	—
268	C₂×D₄	—	4	8	no	—
269	C₂×D₄	—	4	16	no	—
270	C₂×D₄	—	4	64	no	—
271	C₂×D₄	—	4	16	no	—
272	C₂×D₄	—	4	16	no	—
273	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	8	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	—	4	8	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	8	no	—
283	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
286	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₃₁	1	8	yes	—
288	C₂²×C₄	C₂×D₄×C₃₁	1	4	yes	—
289	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
290	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
291	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
292	D₈	—	4	16	no	—
293	M₁₆	—	4	8	no	—
294	C₂×C₈	—	2	8	no	—
295	C₂×C₈	C₂⁴×C₃₁	1	8	yes	—
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	8	no	—
298	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₂²⋊C₄	—	2	16	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	2	no	—
304	C₂³	—	2	16	no	—
305	C₂³	—	2	4	no	—
306	C₂³	—	2	8	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	4	16	no	—
309	C₂³	—	4	16	no	—
310	C₂³	—	4	16	no	—
311	C₂³	—	4	8	no	—
312	C₂³	—	4	8	no	—
313	C₂³	—	4	16	no	—
314	C₂³	—	4	8	no	—
315	C₂³	—	8	32	no	—
316	C₂³	C₃₁×AGL(1,ℤ/8)	1	8	yes	—
317	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
318	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
319	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
320	D₄	—	2	16	no	—
321	D₄	—	4	16	no	—
322	D₄	—	4	32	no	—
323	D₄	—	4	32	no	—
324	D₄	—	4	8	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	—	4	16	no	—
335	C₂×C₄	—	4	8	no	—
336	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₃₁×H(5,𝔽₂)	1	4	yes	—
340	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
341	C₈	—	2	8	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	16	no	—
344	C₂²	—	2	4	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	4	16	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	8	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	8	32	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₃₁×#534	1	2	yes	—
355	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	8	yes	—
356	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	4	yes	—
357	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	8	no	—
361	C₄	C₃₁×#534	1	2	yes	—
362	C₄	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
363	C₂	—	2	8	no	—
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₃₁×#3192	1	4	yes	direct product factor
367	C₂	C₂×C₃₁×#534	1	1	yes	characteristic
368	C₂	C₂²×C₃₁×AGL(1,ℤ/8)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂⁴×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#121	C₂	semidirect
2. C₃₁×#3192	C₂	direct (N × H)
3. C₂×C₃₁×#481	C₂	semidirect
4. C₂×C₃₁×#469	C₂	semidirect
5. C₂×C₃₁×#447	C₂	semidirect
6. C₂×C₃₁×#407	C₂	semidirect
8. C₂³×D₄×C₃₁	C₂²	semidirect
10. C₂²×D₈×C₃₁	C₂²	semidirect
11. C₂²×M₁₆×C₃₁	C₂²	semidirect
16. C₂×C₃₁×#121	C₂²	semidirect
17. C₂×C₃₁×#121	C₂²	semidirect
18. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
20. C₃₁×#481	C₂²	semidirect
21. C₃₁×#469	C₂²	semidirect
22. C₃₁×#447	C₂²	semidirect
23. C₂×C₃₁×#106	C₂²	semidirect
24. C₂×C₃₁×#102	C₂²	semidirect
25. C₃₁×#407	C₂²	semidirect
26. C₂×C₃₁×C₂²⋊C₈	C₂²	semidirect
37. C₂²×D₄×C₃₁	C₂³	semidirect
47. C₂×D₈×C₃₁	C₂³	semidirect
49. C₂×M₁₆×C₃₁	C₂³	semidirect
56. C₃₁×#121	C₂³	semidirect
60. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
64. C₃₁×#106	C₂³	semidirect
65. C₃₁×#102	C₂³	semidirect
66. C₃₁×C₂²⋊C₈	C₂³	semidirect
116. C₂×#3192	C₃₁	direct (N × H)
158. C₂²×#121	C₂×C₃₁	semidirect
159. #3192	C₂×C₃₁	direct (N × H)
160. C₂×#481	C₂×C₃₁	semidirect
161. C₂×#469	C₂×C₃₁	semidirect
162. C₂×#447	C₂×C₃₁	semidirect
163. C₂×#407	C₂×C₃₁	semidirect
186. C₂³×D₄	C₂²×C₃₁	semidirect
188. C₂²×D₈	C₂²×C₃₁	semidirect
189. C₂²×M₁₆	C₂²×C₃₁	semidirect
194. C₂×#121	C₂²×C₃₁	semidirect
195. C₂×#121	C₂²×C₃₁	semidirect
196. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
198. #481	C₂²×C₃₁	semidirect
199. #469	C₂²×C₃₁	semidirect
200. #447	C₂²×C₃₁	semidirect
201. C₂×#106	C₂²×C₃₁	semidirect
202. C₂×#102	C₂²×C₃₁	semidirect
203. #407	C₂²×C₃₁	semidirect
204. C₂×C₂²⋊C₈	C₂²×C₃₁	semidirect
208. C₂×C₃₁	#3192	direct (N × H)
221. C₂²×D₄	C₂³×C₃₁	semidirect
231. C₂×D₈	C₂³×C₃₁	semidirect
233. C₂×M₁₆	C₂³×C₃₁	semidirect
240. #121	C₂³×C₃₁	semidirect
244. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
248. #106	C₂³×C₃₁	semidirect
249. #102	C₂³×C₃₁	semidirect
250. C₂²⋊C₈	C₂³×C₃₁	semidirect
251. C₃₁	C₂×#3192	direct (N × H)
366. C₂	C₃₁×#3192	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#121	2
C₃₁×#3192	2
C₂×C₃₁×#481	2
C₂×C₃₁×#469	2
C₂×C₃₁×#447	2
C₂×C₃₁×#407	2
C₂×#3192	31

Subgroups — C2×C31×#3192 #21517494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3192 #21517494