Subgroups — C₃₁×#3481 #16843414

Order 3968.

1242 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	C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#554	C₂	1	2	yes	maximal, complemented
3	C₃₁×#553	C₂	1	4	yes	maximal, complemented
4	C₃₁×#551	C₂	1	4	yes	maximal, complemented
5	C₃₁×#546	C₂	1	4	yes	maximal, complemented
6	D₄²×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃₁×#529	C₂	1	4	yes	maximal, complemented
9	C₃₁×#525	C₂	1	4	yes	maximal, complemented
10	C₄×#41×C₃₁	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×D₄×C₃₁	C₂	1	4	yes	maximal, complemented
12	C₂×#41×C₃₁	C₂²	1	2	yes	—
13	C₂×#41×C₃₁	C₂²	1	2	yes	complemented
14	C₂²×D₄×C₃₁	C₂²	1	4	yes	—
15	C₂³×C₄×C₃₁	C₂²	1	4	yes	complemented
16	C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₃₁×#127	C₂²	1	1	yes	characteristic
18	C₃₁×#126	C₂²	1	8	yes	complemented
19	C₃₁×#125	C₂²	1	4	yes	complemented
20	C₃₁×#124	C₂²	1	4	yes	complemented
21	C₃₁×#124	C₂²	1	2	yes	complemented
22	C₃₁×#123	C₂²	1	4	yes	complemented
23	C₃₁×#123	C₂²	1	4	yes	complemented
24	C₃₁×#123	C₂²	1	8	yes	complemented
25	C₃₁×C₂²⋊Q₈	C₂²	1	8	yes	complemented
26	C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	complemented
27	C₃₁×#121	C₂²	1	4	yes	—
28	C₃₁×#121	C₂²	1	8	yes	complemented
29	C₃₁×#121	C₂²	1	4	yes	complemented
30	C₃₁×#120	C₂²	1	4	yes	—
31	C₃₁×#120	C₂²	1	4	yes	complemented
32	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
33	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
34	C₄×D₄×C₃₁	C₂²	1	2	yes	—
35	C₄×D₄×C₃₁	C₂²	1	4	yes	—
36	C₄×D₄×C₃₁	C₂²	1	2	yes	—
37	C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
38	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
39	C₄×D₄×C₃₁	C₂²	1	8	yes	complemented
40	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
41	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
42	C₄×D₄×C₃₁	C₂²	1	4	yes	complemented
43	C₃₁×#117	C₂²	1	4	yes	complemented
44	C₃₁×#117	C₂²	1	2	yes	complemented
45	C₃₁×#117	C₂²	1	4	yes	complemented
46	C₂×C₄⋊C₄×C₃₁	C₂²	1	4	yes	complemented
47	C₂×C₂²⋊C₄×C₃₁	C₂²	1	8	yes	complemented
48	C₂×C₄²×C₃₁	C₂²	1	4	yes	complemented
49	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
50	C₂⁴×C₃₁	C₂³	1	4	yes	—
51	#41×C₃₁	—	2	8	no	—
52	#41×C₃₁	—	4	4	no	—
53	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
54	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
55	C₂×D₄×C₃₁	—	2	16	no	—
56	C₂×D₄×C₃₁	C₂³	1	8	yes	—
57	C₂×D₄×C₃₁	C₂³	1	4	yes	—
58	C₂×D₄×C₃₁	C₂³	1	4	yes	—
59	C₂×D₄×C₃₁	C₂³	1	2	yes	—
60	C₂×D₄×C₃₁	C₂³	1	4	yes	—
61	C₂×D₄×C₃₁	C₂³	1	2	yes	—
62	C₂²×C₄×C₃₁	—	4	8	no	—
63	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
64	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
65	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
66	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
67	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
69	C₂²×C₄×C₃₁	C₂³	1	8	yes	—
70	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
71	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
72	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
73	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
74	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
75	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
76	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
77	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
78	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
79	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
80	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
81	C₂²⋊C₄×C₃₁	C₂³	1	8	yes	—
82	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
83	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
84	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
85	C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
86	C₄²×C₃₁	C₂³	1	1	yes	characteristic
87	C₄²×C₃₁	C₂³	1	4	yes	—
88	C₄²×C₃₁	C₂³	1	1	yes	characteristic
89	C₄²×C₃₁	C₂³	1	4	yes	—
90	C₄²×C₃₁	C₂³	1	2	yes	—
91	C₄²×C₃₁	C₂³	1	4	yes	—
92	C₂³×C₃₁	—	2	16	no	—
93	C₂³×C₃₁	—	4	4	no	—
94	C₂³×C₃₁	C₂⁴	1	4	yes	—
95	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
96	C₂³×C₃₁	C₂⁴	1	4	yes	—
97	Q₈×C₃₁	—	2	4	no	—
98	Q₈×C₃₁	—	4	2	no	—
99	D₄×C₃₁	—	2	16	no	—
100	D₄×C₃₁	—	2	8	no	—
101	D₄×C₃₁	—	2	8	no	—
102	D₄×C₃₁	—	4	4	no	—
103	D₄×C₃₁	—	4	2	no	—
104	D₄×C₃₁	#41	1	8	yes	complemented
105	C₂×C₄×C₃₁	—	2	8	no	—
106	C₂×C₄×C₃₁	—	2	8	no	—
107	C₂×C₄×C₃₁	—	2	4	no	—
108	C₂×C₄×C₃₁	—	2	8	no	—
109	C₂×C₄×C₃₁	—	2	8	no	—
110	C₂×C₄×C₃₁	—	2	2	no	—
111	C₂×C₄×C₃₁	—	4	4	no	—
112	C₂×C₄×C₃₁	—	4	8	no	—
113	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
114	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
115	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
116	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
117	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
118	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
119	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
120	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
121	#3481	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂²×C₃₁	—	2	4	no	—
123	C₂²×C₃₁	—	2	4	no	—
124	C₂²×C₃₁	—	2	2	no	—
125	C₂²×C₃₁	—	2	8	no	—
126	C₂²×C₃₁	—	2	4	no	—
127	C₂²×C₃₁	—	2	1	no	—
128	C₂²×C₃₁	—	4	16	no	—
129	C₂²×C₃₁	C₂×#41	1	8	yes	—
130	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
131	C₄×C₃₁	—	2	2	no	—
132	C₄×C₃₁	—	2	4	no	—
133	C₄×C₃₁	—	2	4	no	—
134	C₄×C₃₁	—	2	4	no	—
135	C₄×C₃₁	—	2	4	no	—
136	C₄×C₃₁	—	2	1	no	—
137	C₄×C₃₁	C₂×#41	1	4	yes	—
138	C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
139	#559	C₂×C₃₁	1	1	yes	characteristic, complemented
140	#554	C₂×C₃₁	1	2	yes	complemented
141	#553	C₂×C₃₁	1	4	yes	complemented
142	#551	C₂×C₃₁	1	4	yes	complemented
143	#546	C₂×C₃₁	1	4	yes	complemented
144	D₄²	C₂×C₃₁	1	1	yes	characteristic, complemented
145	#532	C₂×C₃₁	1	1	yes	characteristic, complemented
146	#529	C₂×C₃₁	1	4	yes	complemented
147	#525	C₂×C₃₁	1	4	yes	complemented
148	C₄×#41	C₂×C₃₁	1	2	yes	complemented
149	C₂×C₄×D₄	C₂×C₃₁	1	4	yes	complemented
150	C₂×C₃₁	—	2	8	no	—
151	C₂×C₃₁	—	4	1	no	—
152	C₂×C₃₁	—	4	4	no	—
153	C₂×C₃₁	C₂²×#41	1	2	yes	—
154	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×#41	C₂²×C₃₁	1	2	yes	—
156	C₂×#41	C₂²×C₃₁	1	2	yes	complemented
157	C₂²×D₄	C₂²×C₃₁	1	4	yes	—
158	C₂³×C₄	C₂²×C₃₁	1	4	yes	complemented
159	C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
160	#127	C₂²×C₃₁	1	1	yes	characteristic
161	#126	C₂²×C₃₁	1	8	yes	complemented
162	#125	C₂²×C₃₁	1	4	yes	complemented
163	#124	C₂²×C₃₁	1	4	yes	complemented
164	#124	C₂²×C₃₁	1	2	yes	complemented
165	#123	C₂²×C₃₁	1	4	yes	complemented
166	#123	C₂²×C₃₁	1	4	yes	complemented
167	#123	C₂²×C₃₁	1	8	yes	complemented
168	C₂²⋊Q₈	C₂²×C₃₁	1	8	yes	complemented
169	C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	complemented
170	#121	C₂²×C₃₁	1	4	yes	—
171	#121	C₂²×C₃₁	1	8	yes	complemented
172	#121	C₂²×C₃₁	1	4	yes	complemented
173	#120	C₂²×C₃₁	1	4	yes	—
174	#120	C₂²×C₃₁	1	4	yes	complemented
175	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
176	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
177	C₄×D₄	C₂²×C₃₁	1	2	yes	—
178	C₄×D₄	C₂²×C₃₁	1	4	yes	—
179	C₄×D₄	C₂²×C₃₁	1	2	yes	—
180	C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
181	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
182	C₄×D₄	C₂²×C₃₁	1	8	yes	complemented
183	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
184	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
185	C₄×D₄	C₂²×C₃₁	1	4	yes	complemented
186	#117	C₂²×C₃₁	1	4	yes	complemented
187	#117	C₂²×C₃₁	1	2	yes	complemented
188	#117	C₂²×C₃₁	1	4	yes	complemented
189	C₂×C₄⋊C₄	C₂²×C₃₁	1	4	yes	complemented
190	C₂×C₂²⋊C₄	C₂²×C₃₁	1	8	yes	complemented
191	C₂×C₄²	C₂²×C₃₁	1	4	yes	complemented
192	C₂×C₄²	C₂²×C₃₁	1	1	yes	characteristic, complemented
193	C₃₁	#3481	1	1	yes	characteristic, direct product factor, Sylow
194	C₂⁴	C₂³×C₃₁	1	4	yes	—
195	#41	—	2	8	no	—
196	#41	—	4	4	no	—
197	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
198	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
199	C₂×D₄	—	2	16	no	—
200	C₂×D₄	C₂³×C₃₁	1	8	yes	—
201	C₂×D₄	C₂³×C₃₁	1	4	yes	—
202	C₂×D₄	C₂³×C₃₁	1	4	yes	—
203	C₂×D₄	C₂³×C₃₁	1	2	yes	—
204	C₂×D₄	C₂³×C₃₁	1	4	yes	—
205	C₂×D₄	C₂³×C₃₁	1	2	yes	—
206	C₂²×C₄	—	4	8	no	—
207	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
208	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
209	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
210	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
211	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
213	C₂²×C₄	C₂³×C₃₁	1	8	yes	—
214	C₂²×C₄	C₂³×C₃₁	1	4	yes	—
215	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
216	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
217	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
218	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
219	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
220	C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
221	C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
222	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
223	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
224	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
225	C₂²⋊C₄	C₂³×C₃₁	1	8	yes	—
226	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
227	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
228	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
229	C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
230	C₄²	C₂³×C₃₁	1	2	yes	—
231	C₄²	C₂³×C₃₁	1	1	yes	characteristic
232	C₄²	C₂³×C₃₁	1	4	yes	—
233	C₄²	C₂³×C₃₁	1	4	yes	—
234	C₄²	C₂³×C₃₁	1	1	yes	characteristic
235	C₄²	C₂³×C₃₁	1	4	yes	—
236	C₂³	—	2	16	no	—
237	C₂³	—	4	4	no	—
238	C₂³	C₂⁴×C₃₁	1	4	yes	—
239	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
240	C₂³	C₂⁴×C₃₁	1	4	yes	—
241	Q₈	—	2	4	no	—
242	Q₈	—	4	2	no	—
243	D₄	—	2	16	no	—
244	D₄	—	2	8	no	—
245	D₄	—	2	8	no	—
246	D₄	—	4	4	no	—
247	D₄	—	4	2	no	—
248	D₄	#41×C₃₁	1	8	yes	complemented
249	C₂×C₄	—	2	8	no	—
250	C₂×C₄	—	2	8	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	8	no	—
253	C₂×C₄	—	2	8	no	—
254	C₂×C₄	—	2	2	no	—
255	C₂×C₄	—	4	4	no	—
256	C₂×C₄	—	4	8	no	—
257	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
258	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
259	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
260	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
261	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
262	C₂×C₄	C₂⁴×C₃₁	1	4	yes	—
263	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
264	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
265	C₂²	—	2	4	no	—
266	C₂²	—	2	4	no	—
267	C₂²	—	2	2	no	—
268	C₂²	—	2	8	no	—
269	C₂²	—	2	4	no	—
270	C₂²	—	2	1	no	—
271	C₂²	—	4	16	no	—
272	C₂²	C₂×#41×C₃₁	1	8	yes	—
273	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
274	C₄	—	2	2	no	—
275	C₄	—	2	4	no	—
276	C₄	—	2	4	no	—
277	C₄	—	2	4	no	—
278	C₄	—	2	4	no	—
279	C₄	—	2	1	no	—
280	C₄	C₂×#41×C₃₁	1	4	yes	—
281	C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
282	C₂	—	2	8	no	—
283	C₂	—	4	4	no	—
284	C₂	—	4	1	no	—
285	C₂	C₂²×#41×C₃₁	1	2	yes	—
286	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₃₁×#559	C₂	semidirect
2. C₃₁×#554	C₂	semidirect
3. C₃₁×#553	C₂	semidirect
4. C₃₁×#551	C₂	semidirect
5. C₃₁×#546	C₂	semidirect
6. D₄²×C₃₁	C₂	semidirect
7. C₃₁×#532	C₂	semidirect
8. C₃₁×#529	C₂	semidirect
9. C₃₁×#525	C₂	semidirect
10. C₄×#41×C₃₁	C₂	semidirect
11. C₂×C₄×D₄×C₃₁	C₂	semidirect
13. C₂×#41×C₃₁	C₂²	semidirect
15. C₂³×C₄×C₃₁	C₂²	semidirect
16. C₃₁×C₄⋊Q₈	C₂²	semidirect
18. C₃₁×#126	C₂²	semidirect
19. C₃₁×#125	C₂²	semidirect
20. C₃₁×#124	C₂²	semidirect
21. C₃₁×#124	C₂²	semidirect
22. C₃₁×#123	C₂²	semidirect
23. C₃₁×#123	C₂²	semidirect
24. C₃₁×#123	C₂²	semidirect
25. C₃₁×C₂²⋊Q₈	C₂²	semidirect
26. C₃₁×C₂²⋊Q₈	C₂²	semidirect
28. C₃₁×#121	C₂²	semidirect
29. C₃₁×#121	C₂²	semidirect
31. C₃₁×#120	C₂²	semidirect
32. C₄×Q₈×C₃₁	C₂²	semidirect
33. C₄×Q₈×C₃₁	C₂²	semidirect
37. C₄×D₄×C₃₁	C₂²	semidirect
38. C₄×D₄×C₃₁	C₂²	semidirect
39. C₄×D₄×C₃₁	C₂²	semidirect
40. C₄×D₄×C₃₁	C₂²	semidirect
41. C₄×D₄×C₃₁	C₂²	semidirect
42. C₄×D₄×C₃₁	C₂²	semidirect
43. C₃₁×#117	C₂²	semidirect
44. C₃₁×#117	C₂²	semidirect
45. C₃₁×#117	C₂²	semidirect
46. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
47. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
48. C₂×C₄²×C₃₁	C₂²	semidirect
49. C₂×C₄²×C₃₁	C₂²	semidirect
104. D₄×C₃₁	#41	semidirect
121. #3481	C₃₁	direct (N × H)
139. #559	C₂×C₃₁	semidirect
140. #554	C₂×C₃₁	semidirect
141. #553	C₂×C₃₁	semidirect
142. #551	C₂×C₃₁	semidirect
143. #546	C₂×C₃₁	semidirect
144. D₄²	C₂×C₃₁	semidirect
145. #532	C₂×C₃₁	semidirect
146. #529	C₂×C₃₁	semidirect
147. #525	C₂×C₃₁	semidirect
148. C₄×#41	C₂×C₃₁	semidirect
149. C₂×C₄×D₄	C₂×C₃₁	semidirect
156. C₂×#41	C₂²×C₃₁	semidirect
158. C₂³×C₄	C₂²×C₃₁	semidirect
159. C₄⋊Q₈	C₂²×C₃₁	semidirect
161. #126	C₂²×C₃₁	semidirect
162. #125	C₂²×C₃₁	semidirect
163. #124	C₂²×C₃₁	semidirect
164. #124	C₂²×C₃₁	semidirect
165. #123	C₂²×C₃₁	semidirect
166. #123	C₂²×C₃₁	semidirect
167. #123	C₂²×C₃₁	semidirect
168. C₂²⋊Q₈	C₂²×C₃₁	semidirect
169. C₂²⋊Q₈	C₂²×C₃₁	semidirect
171. #121	C₂²×C₃₁	semidirect
172. #121	C₂²×C₃₁	semidirect
174. #120	C₂²×C₃₁	semidirect
175. C₄×Q₈	C₂²×C₃₁	semidirect
176. C₄×Q₈	C₂²×C₃₁	semidirect
180. C₄×D₄	C₂²×C₃₁	semidirect
181. C₄×D₄	C₂²×C₃₁	semidirect
182. C₄×D₄	C₂²×C₃₁	semidirect
183. C₄×D₄	C₂²×C₃₁	semidirect
184. C₄×D₄	C₂²×C₃₁	semidirect
185. C₄×D₄	C₂²×C₃₁	semidirect
186. #117	C₂²×C₃₁	semidirect
187. #117	C₂²×C₃₁	semidirect
188. #117	C₂²×C₃₁	semidirect
189. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
190. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
191. C₂×C₄²	C₂²×C₃₁	semidirect
192. C₂×C₄²	C₂²×C₃₁	semidirect
193. C₃₁	#3481	direct (N × H)
248. D₄	#41×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₃₁×#559	2
C₃₁×#554	2
C₃₁×#553	2
C₃₁×#551	2
C₃₁×#546	2
D₄²×C₃₁	2
C₃₁×#532	2
C₃₁×#529	2
C₃₁×#525	2
C₄×#41×C₃₁	2
C₂×C₄×D₄×C₃₁	2
#3481	31

Subgroups — C31×#3481 #16843414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3481 #16843414