Subgroups — C₂×C₄×C₃₁⋊C₁₆ #16847298

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

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

Complements

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

N	H ≅ G/N	type
2. C₄×C₃₁⋊C₁₆	C₂	direct (N × H)
9. C₂×C₃₁⋊C₁₆	C₄	direct (N × H)
20. C₃₁⋊C₁₆	C₂×C₄	direct (N × H)
22. C₂×C₄×C₃₁	C₁₆	semidirect
36. C₄×C₃₁	C₂×C₁₆	semidirect
42. C₂×C₃₁	C₄×C₁₆	semidirect
52. C₃₁	C₂×C₄×C₁₆	semidirect
64. C₂×C₄	C₃₁⋊C₁₆	direct (N × H)
77. C₄	C₂×C₃₁⋊C₁₆	direct (N × H)
80. C₂	C₄×C₃₁⋊C₁₆	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
C₄×C₃₁⋊C₁₆	2
C₂×C₄×C₈×C₃₁	2
C₂×C₄×C₁₆	31

Subgroups — C2×C4×C31⋊C16 #16847298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₃₁⋊C₁₆ #16847298