Subgroups — C₂×C₃₁×#1942 #21477909

Order 7936.

1182 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#107	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃₁×#389	C₂	1	2	yes	maximal
5	C₃₁×#1942	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×#340	C₂	1	2	yes	maximal
7	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
8	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₃₁	—	2	2	no	—
10	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
12	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#107	—	2	4	no	—
14	C₂×C₃₁×#107	C₄	1	8	yes	complemented
15	C₂×C₃₁×#107	C₂²	1	4	yes	—
16	C₂×C₃₁×#107	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₃₁	—	2	4	no	—
18	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
19	C₃₁×#389	—	2	4	no	—
20	C₃₁×#389	C₂²	1	8	yes	—
21	C₂×C₃₁×#95	—	2	2	no	—
22	C₃₁×#340	C₂²	1	8	yes	—
23	C₂³×C₄×C₃₁	—	2	2	no	—
24	C₂³×C₄×C₃₁	—	2	2	no	—
25	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
28	C₂²×C₈×C₃₁	—	2	2	no	—
29	C₂²×C₈×C₃₁	—	2	2	no	—
30	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₃₁	D₄	1	4	yes	—
32	C₂²×C₈×C₃₁	Q₈	1	4	yes	—
33	C₂²×C₈×C₃₁	Q₈	1	4	yes	—
34	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
35	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
36	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
37	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
38	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
39	C₂×C₄⋊C₄×C₃₁	—	2	4	no	—
40	C₂×C₄⋊C₄×C₃₁	—	2	8	no	—
41	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
42	C₂×C₄⋊C₄×C₃₁	—	4	8	no	—
43	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
45	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
46	C₂×C₄²×C₃₁	—	2	2	no	—
47	C₂×C₄²×C₃₁	—	2	2	no	—
48	C₂×C₄²×C₃₁	D₄	1	2	yes	—
49	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
50	C₃₁×#107	—	2	8	no	—
51	C₃₁×#107	C₂×C₄	1	16	yes	complemented
52	C₄×C₈×C₃₁	—	2	8	no	—
53	C₃₁×#95	—	2	8	no	—
54	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₃₁	—	2	2	no	—
56	C₂²×C₄×C₃₁	—	2	2	no	—
57	C₂²×C₄×C₃₁	—	2	2	no	—
58	C₂²×C₄×C₃₁	—	2	2	no	—
59	C₂²×C₄×C₃₁	—	2	8	no	—
60	C₂²×C₄×C₃₁	—	2	4	no	—
61	C₂²×C₄×C₃₁	—	2	4	no	—
62	C₂²×C₄×C₃₁	—	4	4	no	—
63	C₂²×C₄×C₃₁	—	4	4	no	—
64	C₂²×C₄×C₃₁	—	4	4	no	—
65	C₂²×C₄×C₃₁	—	4	4	no	—
66	C₂²×C₄×C₃₁	—	4	4	no	—
67	C₂²×C₄×C₃₁	D₈	1	4	yes	—
68	C₂²×C₄×C₃₁	Q₁₆	1	4	yes	—
69	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
70	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
71	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
72	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
73	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
75	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
76	C₂²×C₄×C₃₁	#41	1	2	yes	—
77	C₂²×C₄×C₃₁	#41	1	2	yes	—
78	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
79	C₂×C₈×C₃₁	—	2	8	no	—
80	C₂×C₈×C₃₁	—	2	2	no	—
81	C₂×C₈×C₃₁	—	2	2	no	—
82	C₂×C₈×C₃₁	C₄⋊C₄	1	16	yes	complemented
83	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
84	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
85	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	—
86	C₂×C₈×C₃₁	C₂×Q₈	1	4	yes	—
87	C₄⋊C₄×C₃₁	—	2	8	no	—
88	C₄⋊C₄×C₃₁	—	2	4	no	—
89	C₄⋊C₄×C₃₁	—	2	4	no	—
90	C₄⋊C₄×C₃₁	—	2	4	no	—
91	C₄⋊C₄×C₃₁	—	4	4	no	—
92	C₄⋊C₄×C₃₁	—	4	16	no	—
93	C₄⋊C₄×C₃₁	C₂²×C₄	1	8	yes	—
94	C₄²×C₃₁	—	2	4	no	—
95	C₄²×C₃₁	—	2	2	no	—
96	C₄²×C₃₁	—	2	2	no	—
97	C₂×#1942	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂³×C₃₁	C₄×D₄	1	2	yes	—
99	C₂³×C₃₁	#121	1	2	yes	—
100	C₂³×C₃₁	C₄⋊Q₈	1	2	yes	—
101	C₂³×C₃₁	C₂×D₈	1	2	yes	—
102	C₂³×C₃₁	C₂×Q₁₆	1	2	yes	—
103	C₂³×C₃₁	#135	1	2	yes	—
104	C₂³×C₃₁	#135	1	2	yes	—
105	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
106	C₂×C₄×C₃₁	—	2	2	no	—
107	C₂×C₄×C₃₁	—	2	2	no	—
108	C₂×C₄×C₃₁	—	2	2	no	—
109	C₂×C₄×C₃₁	—	2	2	no	—
110	C₂×C₄×C₃₁	—	2	8	no	—
111	C₂×C₄×C₃₁	—	2	8	no	—
112	C₂×C₄×C₃₁	—	2	8	no	—
113	C₂×C₄×C₃₁	—	4	4	no	—
114	C₂×C₄×C₃₁	—	4	4	no	—
115	C₂×C₄×C₃₁	—	4	16	no	—
116	C₂×C₄×C₃₁	—	4	4	no	—
117	C₂×C₄×C₃₁	—	4	4	no	—
118	C₂×C₄×C₃₁	—	4	4	no	—
119	C₂×C₄×C₃₁	—	8	8	no	—
120	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
121	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
122	C₂×C₄×C₃₁	C₄×Q₈	1	4	yes	—
123	C₂×C₄×C₃₁	#121	1	2	yes	—
124	C₂×C₄×C₃₁	C₂²⋊Q₈	1	4	yes	—
125	C₂×C₄×C₃₁	#125	1	4	yes	—
126	C₂×C₄×C₃₁	C₄⋊Q₈	1	2	yes	—
127	C₂×C₄×C₃₁	C₂×D₈	1	4	yes	—
128	C₂×C₄×C₃₁	C₂×Q₁₆	1	4	yes	—
129	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
132	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
134	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
135	C₈×C₃₁	—	2	4	no	—
136	C₈×C₃₁	C₂×C₄⋊C₄	1	8	yes	complemented
137	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic
138	C₂²×#107	C₂×C₃₁	1	1	yes	characteristic
139	C₂²×C₄×C₈	C₂×C₃₁	1	1	yes	characteristic
140	C₂×#389	C₂×C₃₁	1	2	yes	—
141	#1942	C₂×C₃₁	1	8	yes	direct product factor
142	C₂×#340	C₂×C₃₁	1	2	yes	—
143	C₂²×C₃₁	#389	1	4	yes	—
144	C₂²×C₃₁	C₄×D₈	1	4	yes	—
145	C₂²×C₃₁	C₄×Q₁₆	1	4	yes	—
146	C₂²×C₃₁	#466	1	4	yes	—
147	C₂²×C₃₁	#467	1	4	yes	—
148	C₂²×C₃₁	#499	1	4	yes	—
149	C₂²×C₃₁	#500	1	4	yes	—
150	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
151	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
152	C₂²×C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
153	C₂²×C₃₁	C₂²×D₈	1	1	yes	characteristic
154	C₂²×C₃₁	C₂²×Q₁₆	1	1	yes	characteristic
155	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
156	C₂²×C₃₁	C₂×#135	1	1	yes	characteristic
157	C₄×C₃₁	—	2	4	no	—
158	C₄×C₃₁	—	2	4	no	—
159	C₄×C₃₁	—	4	8	no	—
160	C₄×C₃₁	—	8	4	no	—
161	C₄×C₃₁	#389	1	4	yes	—
162	C₄×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
163	C₄×C₃₁	C₂×C₄×Q₈	1	1	yes	characteristic
164	C₄×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
165	C₄×C₃₁	C₂×#125	1	1	yes	characteristic
166	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
167	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
168	C₂²×C₄⋊C₄	—	2	2	no	—
169	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
170	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
171	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
172	C₂×#107	—	2	4	no	—
173	C₂×#107	C₄×C₃₁	1	8	yes	complemented
174	C₂×#107	C₂²×C₃₁	1	4	yes	—
175	C₂×#107	C₂²×C₃₁	1	4	yes	—
176	C₂×C₄×C₈	—	2	4	no	—
177	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
178	#389	—	2	4	no	—
179	#389	C₂²×C₃₁	1	8	yes	—
180	C₂×#95	—	2	2	no	—
181	#340	C₂²×C₃₁	1	8	yes	—
182	C₂×C₃₁	#1942	1	8	yes	direct product factor
183	C₂×C₃₁	C₂×#389	1	1	yes	characteristic
184	C₂×C₃₁	C₂×C₄×D₈	1	1	yes	characteristic
185	C₂×C₃₁	C₂×C₄×Q₁₆	1	1	yes	characteristic
186	C₂×C₃₁	C₂×#466	1	1	yes	characteristic
187	C₂×C₃₁	C₂×#467	1	1	yes	characteristic
188	C₂×C₃₁	C₂×#499	1	1	yes	characteristic
189	C₂×C₃₁	C₂×#500	1	1	yes	characteristic
190	C₂³×C₄	—	2	2	no	—
191	C₂³×C₄	—	2	2	no	—
192	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
193	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
194	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
195	C₂²×C₈	—	2	2	no	—
196	C₂²×C₈	—	2	2	no	—
197	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
198	C₂²×C₈	D₄×C₃₁	1	4	yes	—
199	C₂²×C₈	Q₈×C₃₁	1	4	yes	—
200	C₂²×C₈	Q₈×C₃₁	1	4	yes	—
201	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
202	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
203	C₂×C₄⋊C₄	—	2	2	no	—
204	C₂×C₄⋊C₄	—	2	4	no	—
205	C₂×C₄⋊C₄	—	2	4	no	—
206	C₂×C₄⋊C₄	—	2	4	no	—
207	C₂×C₄⋊C₄	—	2	8	no	—
208	C₂×C₄⋊C₄	—	2	2	no	—
209	C₂×C₄⋊C₄	—	4	8	no	—
210	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	8	yes	—
211	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
212	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
213	C₂×C₄²	—	2	2	no	—
214	C₂×C₄²	—	2	2	no	—
215	C₂×C₄²	D₄×C₃₁	1	2	yes	—
216	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
217	#107	—	2	8	no	—
218	#107	C₂×C₄×C₃₁	1	16	yes	complemented
219	C₄×C₈	—	2	8	no	—
220	#95	—	2	8	no	—
221	C₃₁	C₂×#1942	1	1	yes	characteristic, direct product factor, Sylow
222	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	2	2	no	—
225	C₂²×C₄	—	2	2	no	—
226	C₂²×C₄	—	2	2	no	—
227	C₂²×C₄	—	2	8	no	—
228	C₂²×C₄	—	2	4	no	—
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	4	4	no	—
231	C₂²×C₄	—	4	4	no	—
232	C₂²×C₄	—	4	4	no	—
233	C₂²×C₄	—	4	4	no	—
234	C₂²×C₄	—	4	4	no	—
235	C₂²×C₄	D₈×C₃₁	1	4	yes	—
236	C₂²×C₄	Q₁₆×C₃₁	1	4	yes	—
237	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
238	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
239	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
240	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
241	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
242	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
243	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
244	C₂²×C₄	#41×C₃₁	1	2	yes	—
245	C₂²×C₄	#41×C₃₁	1	2	yes	—
246	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
247	C₂×C₈	—	2	8	no	—
248	C₂×C₈	—	2	2	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	C₄⋊C₄×C₃₁	1	16	yes	complemented
251	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
252	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
253	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	—
254	C₂×C₈	C₂×Q₈×C₃₁	1	4	yes	—
255	C₄⋊C₄	—	2	8	no	—
256	C₄⋊C₄	—	2	4	no	—
257	C₄⋊C₄	—	2	4	no	—
258	C₄⋊C₄	—	2	4	no	—
259	C₄⋊C₄	—	4	4	no	—
260	C₄⋊C₄	—	4	16	no	—
261	C₄⋊C₄	C₂²×C₄×C₃₁	1	8	yes	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	2	no	—
264	C₄²	—	2	2	no	—
265	C₂³	C₄×D₄×C₃₁	1	2	yes	—
266	C₂³	C₃₁×#121	1	2	yes	—
267	C₂³	C₃₁×C₄⋊Q₈	1	2	yes	—
268	C₂³	C₂×D₈×C₃₁	1	2	yes	—
269	C₂³	C₂×Q₁₆×C₃₁	1	2	yes	—
270	C₂³	C₃₁×#135	1	2	yes	—
271	C₂³	C₃₁×#135	1	2	yes	—
272	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
273	C₂×C₄	—	2	8	no	—
274	C₂×C₄	—	2	8	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	8	no	—
280	C₂×C₄	—	4	16	no	—
281	C₂×C₄	—	4	4	no	—
282	C₂×C₄	—	4	4	no	—
283	C₂×C₄	—	4	4	no	—
284	C₂×C₄	—	4	4	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	—	8	8	no	—
287	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
288	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
289	C₂×C₄	C₄×Q₈×C₃₁	1	4	yes	—
290	C₂×C₄	C₃₁×#121	1	2	yes	—
291	C₂×C₄	C₃₁×C₂²⋊Q₈	1	4	yes	—
292	C₂×C₄	C₃₁×#125	1	4	yes	—
293	C₂×C₄	C₃₁×C₄⋊Q₈	1	2	yes	—
294	C₂×C₄	C₂×D₈×C₃₁	1	4	yes	—
295	C₂×C₄	C₂×Q₁₆×C₃₁	1	4	yes	—
296	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
297	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
298	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
299	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
300	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
301	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
302	C₈	—	2	4	no	—
303	C₈	C₂×C₄⋊C₄×C₃₁	1	8	yes	complemented
304	C₂²	C₃₁×#389	1	4	yes	—
305	C₂²	C₄×D₈×C₃₁	1	4	yes	—
306	C₂²	C₄×Q₁₆×C₃₁	1	4	yes	—
307	C₂²	C₃₁×#466	1	4	yes	—
308	C₂²	C₃₁×#467	1	4	yes	—
309	C₂²	C₃₁×#499	1	4	yes	—
310	C₂²	C₃₁×#500	1	4	yes	—
311	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
312	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
313	C₂²	C₂×C₃₁×C₄⋊Q₈	1	1	yes	characteristic
314	C₂²	C₂²×D₈×C₃₁	1	1	yes	characteristic
315	C₂²	C₂²×Q₁₆×C₃₁	1	1	yes	characteristic
316	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
317	C₂²	C₂×C₃₁×#135	1	1	yes	characteristic
318	C₄	—	2	4	no	—
319	C₄	—	2	4	no	—
320	C₄	—	4	8	no	—
321	C₄	—	8	4	no	—
322	C₄	C₃₁×#389	1	4	yes	—
323	C₄	C₂²×C₄⋊C₄×C₃₁	1	1	yes	characteristic
324	C₄	C₂×C₄×Q₈×C₃₁	1	1	yes	characteristic
325	C₄	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
326	C₄	C₂×C₃₁×#125	1	1	yes	characteristic
327	C₂	C₃₁×#1942	1	8	yes	direct product factor
328	C₂	C₂×C₃₁×#389	1	1	yes	characteristic
329	C₂	C₂×C₄×D₈×C₃₁	1	1	yes	characteristic
330	C₂	C₂×C₄×Q₁₆×C₃₁	1	1	yes	characteristic
331	C₂	C₂×C₃₁×#466	1	1	yes	characteristic
332	C₂	C₂×C₃₁×#467	1	1	yes	characteristic
333	C₂	C₂×C₃₁×#499	1	1	yes	characteristic
334	C₂	C₂×C₃₁×#500	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
5. C₃₁×#1942	C₂	direct (N × H)
14. C₂×C₃₁×#107	C₄	semidirect
51. C₃₁×#107	C₂×C₄	semidirect
82. C₂×C₈×C₃₁	C₄⋊C₄	semidirect
97. C₂×#1942	C₃₁	direct (N × H)
136. C₈×C₃₁	C₂×C₄⋊C₄	semidirect
141. #1942	C₂×C₃₁	direct (N × H)
173. C₂×#107	C₄×C₃₁	semidirect
182. C₂×C₃₁	#1942	direct (N × H)
218. #107	C₂×C₄×C₃₁	semidirect
221. C₃₁	C₂×#1942	direct (N × H)
250. C₂×C₈	C₄⋊C₄×C₃₁	semidirect
303. C₈	C₂×C₄⋊C₄×C₃₁	semidirect
327. C₂	C₃₁×#1942	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×#107	2
C₂²×C₄×C₈×C₃₁	2
C₂×C₃₁×#389	2
C₃₁×#1942	2
C₂×C₃₁×#340	2
C₂×#1942	31

Subgroups — C2×C31×#1942 #21477909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1942 #21477909