Subgroups — C₂×C₁₆×Dic₃₁ #16847297

Order 3968.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₃₁	C₂	1	1	yes	maximal, characteristic
3	C₁₆×Dic₃₁	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×Dic₃₁	C₄	1	1	yes	characteristic
7	C₂²×C₃₁⋊C₈	C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₃₁	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₃₁	C₂²	1	2	yes	—
10	C₈×Dic₃₁	C₄	1	2	yes	—
11	C₈×Dic₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁⋊C₁₆	C₄	1	4	yes	complemented
13	C₂×C₃₁⋊C₁₆	C₂²	1	2	yes	—
14	C₂²×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×Dic₃₁	C₈	1	2	yes	—
16	C₂×C₈×C₃₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₃₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
20	C₄×Dic₃₁	C₈	1	2	yes	—
21	C₄×Dic₃₁	C₂×C₄	1	2	yes	—
22	C₂×C₃₁⋊C₈	C₈	1	4	yes	—
23	C₂×C₃₁⋊C₈	C₂×C₄	1	2	yes	—
24	C₁₆×C₃₁	C₂×C₄	1	4	yes	complemented
25	C₃₁⋊C₁₆	C₂×C₄	1	4	yes	complemented
26	C₂³×C₃₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₃₁	C₄²	1	2	yes	—
28	C₂×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₃₁	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₃₁	C₁₆	1	8	yes	direct product factor
32	C₂×Dic₃₁	C₂×C₈	1	4	yes	—
33	C₈×C₃₁	C₄²	1	2	yes	—
34	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
36	C₃₁⋊C₈	C₂×C₈	1	4	yes	—
37	C₂×C₄×C₁₆	—	31	1	no	maximal, Sylow
38	C₂²×C₃₁	C₄×C₈	1	2	yes	—
39	C₂²×C₃₁	C₂×C₁₆	1	4	yes	—
40	C₂²×C₃₁	C₂²×C₈	1	1	yes	characteristic
41	C₄×C₃₁	C₄×C₈	1	2	yes	—
42	C₄×C₃₁	C₂×C₄²	1	1	yes	characteristic
43	C₄×C₃₁	C₂²×C₈	1	1	yes	characteristic
44	Dic₃₁	C₂×C₁₆	1	8	yes	direct product factor
45	C₂²×C₁₆	—	31	1	no	—
46	C₂²×C₁₆	D₃₁	1	1	yes	characteristic
47	C₂×C₄×C₈	—	31	1	no	—
48	C₄×C₁₆	—	31	4	no	—
49	C₂×C₃₁	C₄×C₁₆	1	4	yes	complemented
50	C₂×C₃₁	C₂×C₄×C₈	1	1	yes	characteristic
51	C₂×C₃₁	C₂²×C₁₆	1	2	yes	—
52	C₂²×C₈	—	31	1	no	—
53	C₂²×C₈	C₂×D₃₁	1	1	yes	characteristic
54	C₂×C₄²	—	31	1	no	—
55	C₂×C₁₆	—	31	4	no	—
56	C₂×C₁₆	—	31	2	no	—
57	C₂×C₁₆	Dic₃₁	1	4	yes	direct product factor
58	C₂×C₁₆	C₂×D₃₁	1	2	yes	—
59	C₄×C₈	—	31	2	no	—
60	C₄×C₈	—	31	2	no	—
61	C₃₁	C₂×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	—	31	2	no	—
63	C₂²×C₄	C₄×D₃₁	1	1	yes	characteristic
64	C₂×C₈	—	31	4	no	—
65	C₂×C₈	—	31	2	no	—
66	C₂×C₈	C₄×D₃₁	1	1	yes	characteristic
67	C₂×C₈	C₄×D₃₁	1	2	yes	—
68	C₂×C₈	C₂×Dic₃₁	1	2	yes	—
69	C₂×C₈	C₂²×D₃₁	1	1	yes	characteristic
70	C₄²	—	31	2	no	—
71	C₄²	—	31	2	no	—
72	C₁₆	—	31	4	no	—
73	C₁₆	C₂×Dic₃₁	1	4	yes	direct product factor
74	C₂³	C₈×D₃₁	1	1	yes	characteristic
75	C₂×C₄	—	31	8	no	—
76	C₂×C₄	—	31	4	no	—
77	C₂×C₄	C₈×D₃₁	1	1	yes	characteristic
78	C₂×C₄	C₈×D₃₁	1	2	yes	—
79	C₂×C₄	C₄×Dic₃₁	1	2	yes	—
80	C₂×C₄	C₂×C₄×D₃₁	1	1	yes	characteristic
81	C₈	—	31	4	no	—
82	C₈	C₄×Dic₃₁	1	2	yes	—
83	C₈	C₂×C₄×D₃₁	1	1	yes	characteristic
84	C₈	C₂²×Dic₃₁	1	1	yes	characteristic
85	C₂²	C₁₆×D₃₁	1	4	yes	—
86	C₂²	C₈×Dic₃₁	1	2	yes	—
87	C₂²	C₂×C₈×D₃₁	1	1	yes	characteristic
88	C₄	—	31	8	no	—
89	C₄	C₈×Dic₃₁	1	2	yes	—
90	C₄	C₂×C₈×D₃₁	1	1	yes	characteristic
91	C₄	C₂×C₄×Dic₃₁	1	1	yes	characteristic
92	C₂	C₁₆×Dic₃₁	1	4	yes	direct product factor
93	C₂	C₂×C₈×Dic₃₁	1	1	yes	characteristic
94	C₂	C₂×C₁₆×D₃₁	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₂²×C₁₆	D₃₁
commutator, hypocenter	C₃₁	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×D₃₁
Fitting	C₂²×C₁₆×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂×C₈
cosocle	C₂×C₈×C₃₁	C₂³
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₁₆×Dic₃₁	C₂	direct (N × H)
8. C₂×C₁₆×C₃₁	C₄	semidirect
12. C₂×C₃₁⋊C₁₆	C₄	semidirect
24. C₁₆×C₃₁	C₂×C₄	semidirect
25. C₃₁⋊C₁₆	C₂×C₄	semidirect
31. C₂×Dic₃₁	C₁₆	direct (N × H)
44. Dic₃₁	C₂×C₁₆	direct (N × H)
49. C₂×C₃₁	C₄×C₁₆	semidirect
57. C₂×C₁₆	Dic₃₁	direct (N × H)
61. C₃₁	C₂×C₄×C₁₆	semidirect
73. C₁₆	C₂×Dic₃₁	direct (N × H)
92. C₂	C₁₆×Dic₃₁	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⋊C₁₆	2
C₂×C₈×Dic₃₁	2
C₁₆×Dic₃₁	2
C₂²×C₁₆×C₃₁	2
C₂×C₄×C₁₆	31

Subgroups — C2×C16×Dic31 #16847297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×Dic₃₁ #16847297