Subgroups — C₄×C₃₁×#432 #21477225

Order 7936.

1206 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×#432	C₂	1	2	yes	maximal
2	C₂×C₄³×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₃₁×#1767	C₂	1	2	yes	maximal, complemented
4	C₄×C₃₁×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1749	C₂	1	2	yes	maximal
6	C₄×C₃₁×C₂²⋊C₈	C₂	1	2	yes	maximal
7	C₃₁×#1745	C₂	1	2	yes	maximal, complemented
8	C₄×C₃₁×#97	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄²×C₃₁	C₄	1	2	yes	—
10	C₂²×C₄²×C₃₁	C₄	1	2	yes	—
11	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
14	C₃₁×#432	C₄	1	16	yes	direct product factor
15	C₂×C₃₁×C₄⋊C₈	C₂²	1	4	yes	—
16	C₂×C₃₁×C₂²⋊C₈	C₂²	1	4	yes	—
17	C₂×C₃₁×#97	C₂²	1	4	yes	—
18	C₂×C₃₁×#97	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₃₁	C₂²	1	4	yes	—
20	C₄³×C₃₁	C₄	1	2	yes	—
21	C₄³×C₃₁	C₄	1	2	yes	—
22	C₄³×C₃₁	C₂²	1	1	yes	characteristic
23	C₄³×C₃₁	C₂²	1	1	yes	characteristic
24	C₄³×C₃₁	C₂²	1	1	yes	characteristic
25	C₄³×C₃₁	C₂²	1	1	yes	characteristic
26	C₃₁×#336	C₂²	1	4	yes	—
27	C₃₁×#336	C₂²	1	4	yes	—
28	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
30	C₂³×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₃₁	C₂×C₄	1	2	yes	—
32	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
33	C₂²×C₈×C₃₁	C₂³	1	8	yes	—
34	C₂×C₄²×C₃₁	—	2	8	no	—
35	C₂×C₄²×C₃₁	—	2	8	no	—
36	C₂×C₄²×C₃₁	—	2	4	no	—
37	C₂×C₄²×C₃₁	—	2	4	no	—
38	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
41	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
42	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
44	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
46	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₃₁	C₂×C₄	1	8	yes	—
50	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
55	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
57	C₃₁×C₄⋊C₈	C₂×C₄	1	16	yes	complemented
58	C₃₁×C₂²⋊C₈	C₂×C₄	1	16	yes	—
59	C₃₁×#97	—	2	8	no	—
60	C₃₁×#97	C₂×C₄	1	16	yes	complemented
61	C₄×C₈×C₃₁	—	2	8	no	—
62	C₂⁴×C₃₁	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₃₁	—	2	4	no	—
64	C₂²×C₄×C₃₁	—	2	4	no	—
65	C₂²×C₄×C₃₁	—	2	4	no	—
66	C₂²×C₄×C₃₁	—	2	4	no	—
67	C₂²×C₄×C₃₁	—	2	4	no	—
68	C₂²×C₄×C₃₁	—	2	4	no	—
69	C₂²×C₄×C₃₁	—	2	4	no	—
70	C₂²×C₄×C₃₁	—	2	2	no	—
71	C₂²×C₄×C₃₁	—	2	2	no	—
72	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
73	C₂²×C₄×C₃₁	C₄²	1	4	yes	—
74	C₂²×C₄×C₃₁	M₁₆	1	8	yes	—
75	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₃₁	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₃₁	—	2	8	no	—
87	C₂×C₈×C₃₁	—	2	8	no	—
88	C₂×C₈×C₃₁	C₂²×C₄	1	16	yes	—
89	C₄²×C₃₁	—	2	4	no	—
90	C₄²×C₃₁	—	2	4	no	—
91	C₄²×C₃₁	—	2	4	no	—
92	C₄²×C₃₁	—	2	4	no	—
93	C₄²×C₃₁	—	2	4	no	—
94	C₄²×C₃₁	—	2	4	no	—
95	C₄²×C₃₁	—	2	4	no	—
96	C₄²×C₃₁	—	2	4	no	—
97	C₄²×C₃₁	—	2	4	no	—
98	C₄²×C₃₁	—	2	2	no	—
99	C₄²×C₃₁	—	2	2	no	—
100	C₄²×C₃₁	C₄²	1	4	yes	—
101	C₄²×C₃₁	C₄²	1	4	yes	—
102	C₄²×C₃₁	M₁₆	1	8	yes	—
103	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
104	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
105	C₄²×C₃₁	#41	1	4	yes	—
106	C₄²×C₃₁	#41	1	4	yes	—
107	C₄×#432	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂³×C₃₁	—	2	1	no	—
109	C₂³×C₃₁	—	2	1	no	—
110	C₂³×C₃₁	—	2	2	no	—
111	C₂³×C₃₁	C₂×C₄²	1	2	yes	—
112	C₂³×C₃₁	C₂×M₁₆	1	4	yes	—
113	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
114	C₂×C₄×C₃₁	—	2	16	no	—
115	C₂×C₄×C₃₁	—	2	2	no	—
116	C₂×C₄×C₃₁	—	2	2	no	—
117	C₂×C₄×C₃₁	—	2	1	no	—
118	C₂×C₄×C₃₁	—	2	1	no	—
119	C₂×C₄×C₃₁	—	2	2	no	—
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	8	no	—
127	C₂×C₄×C₃₁	—	2	8	no	—
128	C₂×C₄×C₃₁	—	2	8	no	—
129	C₂×C₄×C₃₁	—	2	16	no	—
130	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
131	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₃₁	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₃₁	#117	1	4	yes	—
136	C₂×C₄×C₃₁	#117	1	4	yes	—
137	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
138	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
139	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
140	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
141	C₂×C₄×C₃₁	C₂×M₁₆	1	4	yes	—
142	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
143	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
144	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
145	C₈×C₃₁	—	2	16	no	—
146	C₂×#432	C₂×C₃₁	1	2	yes	—
147	C₂×C₄³	C₂×C₃₁	1	1	yes	characteristic
148	#1767	C₂×C₃₁	1	2	yes	complemented
149	C₄×C₄⋊C₈	C₂×C₃₁	1	2	yes	complemented
150	#1749	C₂×C₃₁	1	2	yes	—
151	C₄×C₂²⋊C₈	C₂×C₃₁	1	2	yes	—
152	#1745	C₂×C₃₁	1	2	yes	complemented
153	C₄×#97	C₂×C₃₁	1	2	yes	complemented
154	C₂²×C₃₁	—	2	2	no	—
155	C₂²×C₃₁	—	2	4	no	—
156	C₂²×C₃₁	—	2	4	no	—
157	C₂²×C₃₁	—	2	2	no	—
158	C₂²×C₃₁	C₄×M₁₆	1	4	yes	—
159	C₂²×C₃₁	C₂²×C₄²	1	1	yes	characteristic
160	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
161	C₂²×C₃₁	C₂×#117	1	1	yes	characteristic
162	C₂²×C₃₁	C₂²×M₁₆	1	2	yes	—
163	C₂²×C₃₁	C₂²×M₁₆	1	2	yes	—
164	C₄×C₃₁	—	2	2	no	—
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	2	2	no	—
167	C₄×C₃₁	—	2	4	no	—
168	C₄×C₃₁	—	2	4	no	—
169	C₄×C₃₁	—	2	4	no	—
170	C₄×C₃₁	—	2	2	no	—
171	C₄×C₃₁	C₄×M₁₆	1	4	yes	—
172	C₄×C₃₁	#432	1	8	yes	direct product factor
173	C₄×C₃₁	C₄×#41	1	4	yes	—
174	C₂²×C₄²	C₄×C₃₁	1	2	yes	—
175	C₂²×C₄²	C₄×C₃₁	1	2	yes	—
176	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
177	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
178	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
179	#432	C₄×C₃₁	1	16	yes	direct product factor
180	C₂×C₄⋊C₈	C₂²×C₃₁	1	4	yes	—
181	C₂×C₂²⋊C₈	C₂²×C₃₁	1	4	yes	—
182	C₂×#97	C₂²×C₃₁	1	4	yes	—
183	C₂×#97	C₂²×C₃₁	1	4	yes	—
184	C₂×C₄×C₈	C₂²×C₃₁	1	4	yes	—
185	C₄³	C₄×C₃₁	1	2	yes	—
186	C₄³	C₄×C₃₁	1	2	yes	—
187	C₄³	C₂²×C₃₁	1	1	yes	characteristic
188	C₄³	C₂²×C₃₁	1	1	yes	characteristic
189	C₄³	C₂²×C₃₁	1	1	yes	characteristic
190	C₄³	C₂²×C₃₁	1	1	yes	characteristic
191	#336	C₂²×C₃₁	1	4	yes	—
192	#336	C₂²×C₃₁	1	4	yes	—
193	C₂×C₃₁	—	2	4	no	—
194	C₂×C₃₁	C₄×#117	1	1	yes	characteristic
195	C₂×C₃₁	C₂×C₄×M₁₆	1	1	yes	characteristic
196	C₂×C₃₁	C₂×C₄×M₁₆	1	1	yes	characteristic
197	C₂×C₃₁	C₂×#432	1	2	yes	—
198	C₂×C₃₁	#2920	1	2	yes	—
199	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
200	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
201	C₂³×C₄	C₂×C₄×C₃₁	1	1	yes	characteristic
202	C₂³×C₄	C₂×C₄×C₃₁	1	2	yes	—
203	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
204	C₂²×C₈	C₂³×C₃₁	1	8	yes	—
205	C₂×C₄²	—	2	8	no	—
206	C₂×C₄²	—	2	8	no	—
207	C₂×C₄²	—	2	4	no	—
208	C₂×C₄²	—	2	4	no	—
209	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
210	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
211	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
212	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
213	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
214	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
215	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
216	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
217	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
218	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₃₁	1	8	yes	—
221	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
222	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
226	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
228	C₄⋊C₈	C₂×C₄×C₃₁	1	16	yes	complemented
229	C₂²⋊C₈	C₂×C₄×C₃₁	1	16	yes	—
230	#97	—	2	8	no	—
231	#97	C₂×C₄×C₃₁	1	16	yes	complemented
232	C₄×C₈	—	2	8	no	—
233	C₃₁	C₄×#432	1	1	yes	characteristic, direct product factor, Sylow
234	C₂⁴	C₂²×C₄×C₃₁	1	1	yes	characteristic
235	C₂²×C₄	—	2	4	no	—
236	C₂²×C₄	—	2	4	no	—
237	C₂²×C₄	—	2	4	no	—
238	C₂²×C₄	—	2	4	no	—
239	C₂²×C₄	—	2	4	no	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	4	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	2	2	no	—
244	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
245	C₂²×C₄	C₄²×C₃₁	1	4	yes	—
246	C₂²×C₄	M₁₆×C₃₁	1	8	yes	—
247	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₃₁	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
257	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
258	C₂×C₈	—	2	8	no	—
259	C₂×C₈	—	2	8	no	—
260	C₂×C₈	C₂²×C₄×C₃₁	1	16	yes	—
261	C₄²	—	2	4	no	—
262	C₄²	—	2	4	no	—
263	C₄²	—	2	4	no	—
264	C₄²	—	2	4	no	—
265	C₄²	—	2	4	no	—
266	C₄²	—	2	4	no	—
267	C₄²	—	2	4	no	—
268	C₄²	—	2	4	no	—
269	C₄²	—	2	4	no	—
270	C₄²	—	2	2	no	—
271	C₄²	—	2	2	no	—
272	C₄²	C₄²×C₃₁	1	4	yes	—
273	C₄²	C₄²×C₃₁	1	4	yes	—
274	C₄²	M₁₆×C₃₁	1	8	yes	—
275	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
276	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
277	C₄²	#41×C₃₁	1	4	yes	—
278	C₄²	#41×C₃₁	1	4	yes	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	1	no	—
281	C₂³	—	2	2	no	—
282	C₂³	C₂×C₄²×C₃₁	1	2	yes	—
283	C₂³	C₂×M₁₆×C₃₁	1	4	yes	—
284	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
285	C₂×C₄	—	2	16	no	—
286	C₂×C₄	—	2	8	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	1	no	—
290	C₂×C₄	—	2	1	no	—
291	C₂×C₄	—	2	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	16	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
302	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
303	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
304	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
305	C₂×C₄	C₂×C₄²×C₃₁	1	2	yes	—
306	C₂×C₄	C₃₁×#117	1	4	yes	—
307	C₂×C₄	C₃₁×#117	1	4	yes	—
308	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
309	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
310	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
311	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
312	C₂×C₄	C₂×M₁₆×C₃₁	1	4	yes	—
313	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
314	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
315	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
316	C₈	—	2	16	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	4	no	—
319	C₂²	—	2	4	no	—
320	C₂²	—	2	2	no	—
321	C₂²	C₄×M₁₆×C₃₁	1	4	yes	—
322	C₂²	C₂²×C₄²×C₃₁	1	1	yes	characteristic
323	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
324	C₂²	C₂×C₃₁×#117	1	1	yes	characteristic
325	C₂²	C₂²×M₁₆×C₃₁	1	2	yes	—
326	C₂²	C₂²×M₁₆×C₃₁	1	2	yes	—
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	4	no	—
331	C₄	—	2	4	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	2	no	—
334	C₄	C₄×M₁₆×C₃₁	1	4	yes	—
335	C₄	C₃₁×#432	1	8	yes	direct product factor
336	C₄	C₄×#41×C₃₁	1	4	yes	—
337	C₂	—	2	4	no	—
338	C₂	C₄×C₃₁×#117	1	1	yes	characteristic
339	C₂	C₂×C₄×M₁₆×C₃₁	1	1	yes	characteristic
340	C₂	C₂×C₄×M₁₆×C₃₁	1	1	yes	characteristic
341	C₂	C₂×C₃₁×#432	1	2	yes	—
342	C₂	C₃₁×#2920	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₃₁×#1767	C₂	semidirect
4. C₄×C₃₁×C₄⋊C₈	C₂	semidirect
7. C₃₁×#1745	C₂	semidirect
8. C₄×C₃₁×#97	C₂	semidirect
14. C₃₁×#432	C₄	direct (N × H)
57. C₃₁×C₄⋊C₈	C₂×C₄	semidirect
60. C₃₁×#97	C₂×C₄	semidirect
107. C₄×#432	C₃₁	direct (N × H)
148. #1767	C₂×C₃₁	semidirect
149. C₄×C₄⋊C₈	C₂×C₃₁	semidirect
152. #1745	C₂×C₃₁	semidirect
153. C₄×#97	C₂×C₃₁	semidirect
172. C₄×C₃₁	#432	direct (N × H)
179. #432	C₄×C₃₁	direct (N × H)
228. C₄⋊C₈	C₂×C₄×C₃₁	semidirect
231. #97	C₂×C₄×C₃₁	semidirect
233. C₃₁	C₄×#432	direct (N × H)
335. C₄	C₃₁×#432	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×#432	2
C₂×C₄³×C₃₁	2
C₃₁×#1767	2
C₄×C₃₁×C₄⋊C₈	2
C₃₁×#1749	2
C₄×C₃₁×C₂²⋊C₈	2
C₃₁×#1745	2
C₄×C₃₁×#97	2
C₄×#432	31

Subgroups — C4×C31×#432 #21477225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₁×#432 #21477225