Subgroups — C₂²×C₃₁×#534 #21519428

Order 7936.

15230 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₃₁	C₂	1	2	yes	maximal, complemented
2	C₂×C₃₁×#534	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₃₁×#123	C₂	1	4	yes	maximal, complemented
4	C₂²×C₃₁×#121	C₂	1	4	yes	maximal, complemented
5	C₂²×C₃₁×#120	C₂	1	4	yes	maximal, complemented
6	C₂³×C₂²⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁶×C₃₁	C₂²	1	1	yes	characteristic
8	C₂⁶×C₃₁	C₂²	1	2	yes	complemented
9	C₂³×D₄×C₃₁	—	2	32	no	—
10	C₂³×D₄×C₃₁	C₂²	1	4	yes	—
11	C₂³×D₄×C₃₁	C₂²	1	4	yes	complemented
12	C₂³×D₄×C₃₁	C₂²	1	4	yes	complemented
13	C₂³×D₄×C₃₁	C₂²	1	48	yes	complemented
14	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	complemented
15	C₂⁴×C₄×C₃₁	C₂²	1	2	yes	complemented
16	C₃₁×#534	C₂²	1	256	yes	direct product factor
17	C₂×C₃₁×#123	C₂²	1	96	yes	complemented
18	C₂×C₃₁×#121	C₂²	1	96	yes	complemented
19	C₂×C₃₁×#120	C₂²	1	96	yes	complemented
20	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
21	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	4	yes	complemented
22	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
23	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	24	yes	complemented
24	C₂⁵×C₃₁	—	2	16	no	—
25	C₂⁵×C₃₁	—	4	8	no	—
26	C₂⁵×C₃₁	—	4	16	no	—
27	C₂⁵×C₃₁	D₄	1	16	yes	complemented
28	C₂⁵×C₃₁	C₂³	1	4	yes	—
29	C₂⁵×C₃₁	C₂³	1	2	yes	—
30	C₂⁵×C₃₁	C₂³	1	1	yes	characteristic
31	C₂⁵×C₃₁	C₂³	1	12	yes	—
32	C₂⁵×C₃₁	C₂³	1	24	yes	complemented
33	C₂²×D₄×C₃₁	—	2	32	no	—
34	C₂²×D₄×C₃₁	—	2	32	no	—
35	C₂²×D₄×C₃₁	—	2	384	no	—
36	C₂²×D₄×C₃₁	—	4	16	no	—
37	C₂²×D₄×C₃₁	C₂³	1	48	yes	—
38	C₂²×D₄×C₃₁	C₂³	1	48	yes	complemented
39	C₂²×D₄×C₃₁	C₂³	1	48	yes	complemented
40	C₂²×D₄×C₃₁	C₂³	1	128	yes	complemented
41	C₂³×C₄×C₃₁	—	2	16	no	—
42	C₂³×C₄×C₃₁	—	4	8	no	—
43	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
45	C₂³×C₄×C₃₁	C₂³	1	24	yes	complemented
46	C₂³×C₄×C₃₁	C₂³	1	24	yes	complemented
47	C₃₁×#123	C₂³	1	256	yes	complemented
48	C₃₁×#121	C₂³	1	256	yes	complemented
49	C₃₁×#120	C₂³	1	256	yes	complemented
50	C₂×C₄⋊C₄×C₃₁	C₂³	1	48	yes	complemented
51	C₂×C₂²⋊C₄×C₃₁	C₂³	1	48	yes	complemented
52	C₂×C₂²⋊C₄×C₃₁	C₂³	1	96	yes	complemented
53	C₂×C₂²⋊C₄×C₃₁	C₂³	1	64	yes	complemented
54	C₂⁴×C₃₁	—	2	8	no	—
55	C₂⁴×C₃₁	—	2	16	no	—
56	C₂⁴×C₃₁	—	2	16	no	—
57	C₂⁴×C₃₁	—	2	96	no	—
58	C₂⁴×C₃₁	—	2	32	no	—
59	C₂⁴×C₃₁	—	4	64	no	—
60	C₂⁴×C₃₁	—	4	48	no	—
61	C₂⁴×C₃₁	—	4	96	no	—
62	C₂⁴×C₃₁	—	4	128	no	—
63	C₂⁴×C₃₁	C₂×D₄	1	16	yes	—
64	C₂⁴×C₃₁	C₂×D₄	1	8	yes	—
65	C₂⁴×C₃₁	C₂×D₄	1	96	yes	complemented
66	C₂⁴×C₃₁	C₂⁴	1	24	yes	—
67	C₂⁴×C₃₁	C₂⁴	1	12	yes	—
68	C₂⁴×C₃₁	C₂⁴	1	6	yes	—
69	C₂⁴×C₃₁	C₂⁴	1	16	yes	—
70	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
71	C₂⁴×C₃₁	C₂⁴	1	32	yes	complemented
72	C₂×D₄×C₃₁	—	2	192	no	—
73	C₂×D₄×C₃₁	—	2	192	no	—
74	C₂×D₄×C₃₁	—	2	512	no	—
75	C₂×D₄×C₃₁	—	4	96	no	—
76	C₂×D₄×C₃₁	C₂⁴	1	64	yes	—
77	C₂×D₄×C₃₁	C₂⁴	1	64	yes	complemented
78	C₂×D₄×C₃₁	C₂⁴	1	64	yes	complemented
79	C₂²×C₄×C₃₁	—	2	16	no	—
80	C₂²×C₄×C₃₁	—	2	96	no	—
81	C₂²×C₄×C₃₁	—	2	16	no	—
82	C₂²×C₄×C₃₁	—	4	48	no	—
83	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
84	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
85	C₂²×C₄×C₃₁	C₂⁴	1	32	yes	complemented
86	C₂²×C₄×C₃₁	C₂⁴	1	32	yes	complemented
87	C₄⋊C₄×C₃₁	C₂⁴	1	64	yes	complemented
88	C₂²⋊C₄×C₃₁	C₂⁴	1	64	yes	complemented
89	C₂²⋊C₄×C₃₁	C₂⁴	1	128	yes	complemented
90	C₂²×#534	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂³×C₃₁	—	2	64	no	—
92	C₂³×C₃₁	—	2	32	no	—
93	C₂³×C₃₁	—	2	24	no	—
94	C₂³×C₃₁	—	2	48	no	—
95	C₂³×C₃₁	—	2	48	no	—
96	C₂³×C₃₁	—	2	64	no	—
97	C₂³×C₃₁	—	2	96	no	—
98	C₂³×C₃₁	—	4	192	no	—
99	C₂³×C₃₁	—	4	32	no	—
100	C₂³×C₃₁	—	4	64	no	—
101	C₂³×C₃₁	—	4	384	no	—
102	C₂³×C₃₁	—	4	64	no	—
103	C₂³×C₃₁	C₂²×D₄	1	48	yes	—
104	C₂³×C₃₁	C₂²×D₄	1	24	yes	—
105	C₂³×C₃₁	C₂²×D₄	1	4	yes	—
106	C₂³×C₃₁	C₂²×D₄	1	64	yes	complemented
107	C₂³×C₃₁	H(5,𝔽₂)	1	8	yes	—
108	C₂³×C₃₁	C₂⁵	1	16	yes	—
109	C₂³×C₃₁	C₂⁵	1	8	yes	—
110	C₂³×C₃₁	C₂⁵	1	4	yes	—
111	C₂³×C₃₁	C₂⁵	1	3	yes	—
112	D₄×C₃₁	—	2	128	no	—
113	D₄×C₃₁	—	2	128	no	—
114	D₄×C₃₁	—	4	64	no	—
115	C₂×C₄×C₃₁	—	2	48	no	—
116	C₂×C₄×C₃₁	—	2	64	no	—
117	C₂×C₄×C₃₁	—	2	48	no	—
118	C₂×C₄×C₃₁	—	4	32	no	—
119	C₂×C₄×C₃₁	C₂⁵	1	16	yes	—
120	C₂×C₄×C₃₁	C₂⁵	1	16	yes	—
121	C₂⁴×D₄	C₂×C₃₁	1	2	yes	complemented
122	C₂×#534	C₂×C₃₁	1	48	yes	direct product factor
123	C₂²×#123	C₂×C₃₁	1	4	yes	complemented
124	C₂²×#121	C₂×C₃₁	1	4	yes	complemented
125	C₂²×#120	C₂×C₃₁	1	4	yes	complemented
126	C₂³×C₂²⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
127	C₂²×C₃₁	—	2	8	no	—
128	C₂²×C₃₁	—	2	16	no	—
129	C₂²×C₃₁	—	2	96	no	—
130	C₂²×C₃₁	—	2	48	no	—
131	C₂²×C₃₁	—	2	16	no	—
132	C₂²×C₃₁	—	2	32	no	—
133	C₂²×C₃₁	—	4	64	no	—
134	C₂²×C₃₁	—	4	128	no	—
135	C₂²×C₃₁	—	4	96	no	—
136	C₂²×C₃₁	#534	1	16	yes	direct product factor
137	C₂²×C₃₁	C₂³×D₄	1	16	yes	—
138	C₂²×C₃₁	C₂³×D₄	1	8	yes	—
139	C₂²×C₃₁	C₂³×D₄	1	6	yes	—
140	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	12	yes	—
141	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
142	C₄×C₃₁	—	2	16	no	—
143	C₄×C₃₁	—	2	16	no	—
144	C₂⁶	C₂²×C₃₁	1	1	yes	characteristic
145	C₂⁶	C₂²×C₃₁	1	2	yes	complemented
146	C₂³×D₄	—	2	32	no	—
147	C₂³×D₄	C₂²×C₃₁	1	4	yes	—
148	C₂³×D₄	C₂²×C₃₁	1	4	yes	complemented
149	C₂³×D₄	C₂²×C₃₁	1	4	yes	complemented
150	C₂³×D₄	C₂²×C₃₁	1	48	yes	complemented
151	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	complemented
152	C₂⁴×C₄	C₂²×C₃₁	1	2	yes	complemented
153	#534	C₂²×C₃₁	1	256	yes	direct product factor
154	C₂×#123	C₂²×C₃₁	1	96	yes	complemented
155	C₂×#121	C₂²×C₃₁	1	96	yes	complemented
156	C₂×#120	C₂²×C₃₁	1	96	yes	complemented
157	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
158	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	4	yes	complemented
159	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
160	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	24	yes	complemented
161	C₂×C₃₁	—	2	16	no	—
162	C₂×C₃₁	—	2	8	no	—
163	C₂×C₃₁	—	4	16	no	—
164	C₂×C₃₁	C₂×#534	1	12	yes	direct product factor
165	C₂×C₃₁	C₂⁴×D₄	1	1	yes	characteristic
166	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	2	yes	—
167	C₂⁵	—	2	16	no	—
168	C₂⁵	—	4	8	no	—
169	C₂⁵	—	4	16	no	—
170	C₂⁵	D₄×C₃₁	1	16	yes	complemented
171	C₂⁵	C₂³×C₃₁	1	4	yes	—
172	C₂⁵	C₂³×C₃₁	1	2	yes	—
173	C₂⁵	C₂³×C₃₁	1	1	yes	characteristic
174	C₂⁵	C₂³×C₃₁	1	12	yes	—
175	C₂⁵	C₂³×C₃₁	1	24	yes	complemented
176	C₂²×D₄	—	2	32	no	—
177	C₂²×D₄	—	2	32	no	—
178	C₂²×D₄	—	2	384	no	—
179	C₂²×D₄	—	4	16	no	—
180	C₂²×D₄	C₂³×C₃₁	1	48	yes	—
181	C₂²×D₄	C₂³×C₃₁	1	48	yes	complemented
182	C₂²×D₄	C₂³×C₃₁	1	48	yes	complemented
183	C₂²×D₄	C₂³×C₃₁	1	128	yes	complemented
184	C₂³×C₄	—	2	16	no	—
185	C₂³×C₄	—	4	8	no	—
186	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
187	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
188	C₂³×C₄	C₂³×C₃₁	1	24	yes	complemented
189	C₂³×C₄	C₂³×C₃₁	1	24	yes	complemented
190	#123	C₂³×C₃₁	1	256	yes	complemented
191	#121	C₂³×C₃₁	1	256	yes	complemented
192	#120	C₂³×C₃₁	1	256	yes	complemented
193	C₂×C₄⋊C₄	C₂³×C₃₁	1	48	yes	complemented
194	C₂×C₂²⋊C₄	C₂³×C₃₁	1	48	yes	complemented
195	C₂×C₂²⋊C₄	C₂³×C₃₁	1	96	yes	complemented
196	C₂×C₂²⋊C₄	C₂³×C₃₁	1	64	yes	complemented
197	C₃₁	C₂²×#534	1	1	yes	characteristic, direct product factor, Sylow
198	C₂⁴	—	2	8	no	—
199	C₂⁴	—	2	16	no	—
200	C₂⁴	—	2	16	no	—
201	C₂⁴	—	2	96	no	—
202	C₂⁴	—	2	32	no	—
203	C₂⁴	—	4	64	no	—
204	C₂⁴	—	4	48	no	—
205	C₂⁴	—	4	96	no	—
206	C₂⁴	—	4	128	no	—
207	C₂⁴	C₂×D₄×C₃₁	1	16	yes	—
208	C₂⁴	C₂×D₄×C₃₁	1	8	yes	—
209	C₂⁴	C₂×D₄×C₃₁	1	96	yes	complemented
210	C₂⁴	C₂⁴×C₃₁	1	24	yes	—
211	C₂⁴	C₂⁴×C₃₁	1	12	yes	—
212	C₂⁴	C₂⁴×C₃₁	1	6	yes	—
213	C₂⁴	C₂⁴×C₃₁	1	16	yes	—
214	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
215	C₂⁴	C₂⁴×C₃₁	1	32	yes	complemented
216	C₂×D₄	—	2	192	no	—
217	C₂×D₄	—	2	192	no	—
218	C₂×D₄	—	2	512	no	—
219	C₂×D₄	—	4	96	no	—
220	C₂×D₄	C₂⁴×C₃₁	1	64	yes	—
221	C₂×D₄	C₂⁴×C₃₁	1	64	yes	complemented
222	C₂×D₄	C₂⁴×C₃₁	1	64	yes	complemented
223	C₂²×C₄	—	2	16	no	—
224	C₂²×C₄	—	2	96	no	—
225	C₂²×C₄	—	2	16	no	—
226	C₂²×C₄	—	4	48	no	—
227	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
228	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
229	C₂²×C₄	C₂⁴×C₃₁	1	32	yes	complemented
230	C₂²×C₄	C₂⁴×C₃₁	1	32	yes	complemented
231	C₄⋊C₄	C₂⁴×C₃₁	1	64	yes	complemented
232	C₂²⋊C₄	C₂⁴×C₃₁	1	64	yes	complemented
233	C₂²⋊C₄	C₂⁴×C₃₁	1	128	yes	complemented
234	C₂³	—	2	64	no	—
235	C₂³	—	2	32	no	—
236	C₂³	—	2	24	no	—
237	C₂³	—	2	48	no	—
238	C₂³	—	2	48	no	—
239	C₂³	—	2	64	no	—
240	C₂³	—	2	96	no	—
241	C₂³	—	4	192	no	—
242	C₂³	—	4	32	no	—
243	C₂³	—	4	64	no	—
244	C₂³	—	4	384	no	—
245	C₂³	—	4	64	no	—
246	C₂³	C₂²×D₄×C₃₁	1	48	yes	—
247	C₂³	C₂²×D₄×C₃₁	1	24	yes	—
248	C₂³	C₂²×D₄×C₃₁	1	4	yes	—
249	C₂³	C₂²×D₄×C₃₁	1	64	yes	complemented
250	C₂³	C₃₁×H(5,𝔽₂)	1	8	yes	—
251	C₂³	C₂⁵×C₃₁	1	16	yes	—
252	C₂³	C₂⁵×C₃₁	1	8	yes	—
253	C₂³	C₂⁵×C₃₁	1	4	yes	—
254	C₂³	C₂⁵×C₃₁	1	3	yes	—
255	D₄	—	2	128	no	—
256	D₄	—	2	128	no	—
257	D₄	—	4	64	no	—
258	C₂×C₄	—	2	48	no	—
259	C₂×C₄	—	2	64	no	—
260	C₂×C₄	—	2	48	no	—
261	C₂×C₄	—	4	32	no	—
262	C₂×C₄	C₂⁵×C₃₁	1	16	yes	—
263	C₂×C₄	C₂⁵×C₃₁	1	16	yes	—
264	C₂²	—	2	8	no	—
265	C₂²	—	2	16	no	—
266	C₂²	—	2	96	no	—
267	C₂²	—	2	48	no	—
268	C₂²	—	2	16	no	—
269	C₂²	—	2	32	no	—
270	C₂²	—	4	64	no	—
271	C₂²	—	4	128	no	—
272	C₂²	—	4	96	no	—
273	C₂²	C₃₁×#534	1	16	yes	direct product factor
274	C₂²	C₂³×D₄×C₃₁	1	16	yes	—
275	C₂²	C₂³×D₄×C₃₁	1	8	yes	—
276	C₂²	C₂³×D₄×C₃₁	1	6	yes	—
277	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	12	yes	—
278	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
279	C₄	—	2	16	no	—
280	C₄	—	2	16	no	—
281	C₂	—	2	16	no	—
282	C₂	—	2	8	no	—
283	C₂	—	4	16	no	—
284	C₂	C₂×C₃₁×#534	1	12	yes	direct product factor
285	C₂	C₂⁴×D₄×C₃₁	1	1	yes	characteristic
286	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₄×C₃₁	C₂	semidirect
2. C₂×C₃₁×#534	C₂	direct (N × H)
3. C₂²×C₃₁×#123	C₂	semidirect
4. C₂²×C₃₁×#121	C₂	semidirect
5. C₂²×C₃₁×#120	C₂	semidirect
6. C₂³×C₂²⋊C₄×C₃₁	C₂	semidirect
8. C₂⁶×C₃₁	C₂²	semidirect
11. C₂³×D₄×C₃₁	C₂²	semidirect
12. C₂³×D₄×C₃₁	C₂²	semidirect
13. C₂³×D₄×C₃₁	C₂²	semidirect
14. C₂⁴×C₄×C₃₁	C₂²	semidirect
15. C₂⁴×C₄×C₃₁	C₂²	semidirect
16. C₃₁×#534	C₂²	direct (N × H)
17. C₂×C₃₁×#123	C₂²	semidirect
18. C₂×C₃₁×#121	C₂²	semidirect
19. C₂×C₃₁×#120	C₂²	semidirect
20. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
21. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
27. C₂⁵×C₃₁	D₄	semidirect
32. C₂⁵×C₃₁	C₂³	semidirect
38. C₂²×D₄×C₃₁	C₂³	semidirect
39. C₂²×D₄×C₃₁	C₂³	semidirect
40. C₂²×D₄×C₃₁	C₂³	semidirect
45. C₂³×C₄×C₃₁	C₂³	semidirect
46. C₂³×C₄×C₃₁	C₂³	semidirect
47. C₃₁×#123	C₂³	semidirect
48. C₃₁×#121	C₂³	semidirect
49. C₃₁×#120	C₂³	semidirect
50. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
51. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
52. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
53. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
65. C₂⁴×C₃₁	C₂×D₄	semidirect
71. C₂⁴×C₃₁	C₂⁴	semidirect
77. C₂×D₄×C₃₁	C₂⁴	semidirect
78. C₂×D₄×C₃₁	C₂⁴	semidirect
85. C₂²×C₄×C₃₁	C₂⁴	semidirect
86. C₂²×C₄×C₃₁	C₂⁴	semidirect
87. C₄⋊C₄×C₃₁	C₂⁴	semidirect
88. C₂²⋊C₄×C₃₁	C₂⁴	semidirect
89. C₂²⋊C₄×C₃₁	C₂⁴	semidirect
90. C₂²×#534	C₃₁	direct (N × H)
106. C₂³×C₃₁	C₂²×D₄	semidirect
121. C₂⁴×D₄	C₂×C₃₁	semidirect
122. C₂×#534	C₂×C₃₁	direct (N × H)
123. C₂²×#123	C₂×C₃₁	semidirect
124. C₂²×#121	C₂×C₃₁	semidirect
125. C₂²×#120	C₂×C₃₁	semidirect
126. C₂³×C₂²⋊C₄	C₂×C₃₁	semidirect
136. C₂²×C₃₁	#534	direct (N × H)
145. C₂⁶	C₂²×C₃₁	semidirect
148. C₂³×D₄	C₂²×C₃₁	semidirect
149. C₂³×D₄	C₂²×C₃₁	semidirect
150. C₂³×D₄	C₂²×C₃₁	semidirect
151. C₂⁴×C₄	C₂²×C₃₁	semidirect
152. C₂⁴×C₄	C₂²×C₃₁	semidirect
153. #534	C₂²×C₃₁	direct (N × H)
154. C₂×#123	C₂²×C₃₁	semidirect
155. C₂×#121	C₂²×C₃₁	semidirect
156. C₂×#120	C₂²×C₃₁	semidirect
157. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
158. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
159. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
160. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
164. C₂×C₃₁	C₂×#534	direct (N × H)
170. C₂⁵	D₄×C₃₁	semidirect
175. C₂⁵	C₂³×C₃₁	semidirect
181. C₂²×D₄	C₂³×C₃₁	semidirect
182. C₂²×D₄	C₂³×C₃₁	semidirect
183. C₂²×D₄	C₂³×C₃₁	semidirect
188. C₂³×C₄	C₂³×C₃₁	semidirect
189. C₂³×C₄	C₂³×C₃₁	semidirect
190. #123	C₂³×C₃₁	semidirect
191. #121	C₂³×C₃₁	semidirect
192. #120	C₂³×C₃₁	semidirect
193. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
194. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
195. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
196. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
197. C₃₁	C₂²×#534	direct (N × H)
209. C₂⁴	C₂×D₄×C₃₁	semidirect
215. C₂⁴	C₂⁴×C₃₁	semidirect
221. C₂×D₄	C₂⁴×C₃₁	semidirect
222. C₂×D₄	C₂⁴×C₃₁	semidirect
229. C₂²×C₄	C₂⁴×C₃₁	semidirect
230. C₂²×C₄	C₂⁴×C₃₁	semidirect
231. C₄⋊C₄	C₂⁴×C₃₁	semidirect
232. C₂²⋊C₄	C₂⁴×C₃₁	semidirect
233. C₂²⋊C₄	C₂⁴×C₃₁	semidirect
249. C₂³	C₂²×D₄×C₃₁	semidirect
273. C₂²	C₃₁×#534	direct (N × H)
284. C₂	C₂×C₃₁×#534	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₃₁	2
C₂×C₃₁×#534	2
C₂²×C₃₁×#123	2
C₂²×C₃₁×#121	2
C₂²×C₃₁×#120	2
C₂³×C₂²⋊C₄×C₃₁	2
C₂²×#534	31

Subgroups — C22×C31×#534 #21519428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₁×#534 #21519428