Subgroups — C₂×#14520919 #16848112

Order 3968.

888 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₃₁	C₂	1	6	yes	maximal
2	#14520919	C₂	1	8	yes	maximal, direct product factor
3	C₂²×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×C₃₁	C₂²	1	3	yes	—
5	C₂³×Dic₃₁	C₂²	1	4	yes	—
6	C₂×C₄²×C₃₁	C₄	1	8	yes	complemented
7	C₂×C₄²×C₃₁	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₃₁	—	2	24	no	—
9	C₂×C₄⋊Dic₃₁	C₂²	1	24	yes	—
10	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
11	C₂²×C₄×C₃₁	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₃₁	D₄	1	12	yes	—
13	C₂²×C₄×C₃₁	Q₈	1	12	yes	—
14	C₂²×C₄×C₃₁	C₂³	1	6	yes	—
15	C₂²×Dic₃₁	—	2	24	no	—
16	C₂²×Dic₃₁	C₂³	1	8	yes	—
17	C₄²×C₃₁	C₂×C₄	1	16	yes	complemented
18	C₄⋊Dic₃₁	—	2	48	no	—
19	C₂³×C₃₁	C₂²×C₄	1	2	yes	—
20	C₂³×C₃₁	C₂×D₄	1	6	yes	—
21	C₂³×C₃₁	C₂×Q₈	1	6	yes	—
22	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
23	C₂×C₄×C₃₁	C₄⋊C₄	1	48	yes	complemented
24	C₂×C₄×C₃₁	C₂²×C₄	1	12	yes	—
25	C₂×C₄×C₃₁	C₂×D₄	1	12	yes	—
26	C₂×C₄×C₃₁	C₂×Q₈	1	12	yes	—
27	C₂×Dic₃₁	—	2	24	no	—
28	C₂×Dic₃₁	—	4	16	no	—
29	C₂×#384	—	31	1	no	maximal, Sylow
30	C₂²×C₃₁	C₂×C₄⋊C₄	1	12	yes	—
31	C₂²×C₃₁	#127	1	4	yes	—
32	C₂²×C₃₁	C₄⋊Q₈	1	12	yes	—
33	C₂²×C₃₁	C₂³×C₄	1	1	yes	characteristic
34	C₂²×C₃₁	C₂²×D₄	1	3	yes	—
35	C₂²×C₃₁	C₂²×Q₈	1	3	yes	—
36	C₄×C₃₁	C₂×C₄⋊C₄	1	24	yes	complemented
37	Dic₃₁	—	4	8	no	—
38	C₂²×C₄⋊C₄	—	31	6	no	—
39	C₂²×C₄²	D₃₁	1	1	yes	characteristic
40	#384	—	31	8	no	—
41	C₂×C₃₁	#384	1	8	yes	complemented
42	C₂×C₃₁	C₂²×C₄⋊C₄	1	3	yes	—
43	C₂×C₃₁	C₂×#127	1	1	yes	characteristic
44	C₂×C₃₁	C₂×C₄⋊Q₈	1	3	yes	—
45	C₂³×C₄	—	31	4	no	—
46	C₂³×C₄	C₂×D₃₁	1	3	yes	—
47	C₂×C₄⋊C₄	—	31	24	no	—
48	C₂×C₄⋊C₄	—	62	24	no	—
49	C₂×C₄²	Dic₃₁	1	8	yes	complemented
50	C₂×C₄²	C₂×D₃₁	1	4	yes	—
51	C₃₁	C₂×#384	1	1	yes	characteristic, complemented, Sylow
52	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
53	C₂²×C₄	—	31	8	no	—
54	C₂²×C₄	—	62	24	no	—
55	C₂²×C₄	Dic₆₂	1	12	yes	—
56	C₂²×C₄	D₁₂₄	1	12	yes	—
57	C₂²×C₄	C₂×Dic₃₁	1	12	yes	—
58	C₂²×C₄	C₂²×D₃₁	1	6	yes	—
59	C₄⋊C₄	—	62	48	no	—
60	C₄²	C₂×Dic₃₁	1	16	yes	complemented
61	C₂³	C₂×Dic₆₂	1	6	yes	—
62	C₂³	C₂×D₁₂₄	1	6	yes	—
63	C₂³	C₂²×Dic₃₁	1	2	yes	—
64	C₂³	C₂³×D₃₁	1	1	yes	characteristic
65	C₂×C₄	—	62	24	no	—
66	C₂×C₄	—	124	16	no	—
67	C₂×C₄	C₄⋊Dic₃₁	1	48	yes	complemented
68	C₂×C₄	C₂×Dic₆₂	1	12	yes	—
69	C₂×C₄	C₂×D₁₂₄	1	12	yes	—
70	C₂×C₄	C₂²×Dic₃₁	1	12	yes	—
71	C₂²	#11758446	1	12	yes	—
72	C₂²	#11758451	1	4	yes	—
73	C₂²	C₂×C₄⋊Dic₃₁	1	12	yes	—
74	C₂²	C₂²×Dic₆₂	1	3	yes	—
75	C₂²	C₂²×D₁₂₄	1	3	yes	—
76	C₂²	C₂³×Dic₃₁	1	1	yes	characteristic
77	C₄	—	124	8	no	—
78	C₄	C₂×C₄⋊Dic₃₁	1	24	yes	complemented
79	C₂	#14520919	1	8	yes	direct product factor
80	C₂	C₂²×C₄⋊Dic₃₁	1	3	yes	—
81	C₂	C₂×#11758451	1	1	yes	characteristic
82	C₂	C₂×#11758446	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₃₁
commutator	C₂²×C₃₁	C₂³×C₄
Frattini	C₂³	C₂³×D₃₁
Fitting	C₂²×C₄²×C₃₁	C₂
socle, prime radical	C₂⁴×C₃₁	C₂³
cosocle	C₂³×C₃₁	C₂⁴
hypercenter	C₂²×C₄²	D₃₁
hypocenter	C₃₁	C₂×#384
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
2. #14520919	C₂	direct (N × H)
6. C₂×C₄²×C₃₁	C₄	semidirect
17. C₄²×C₃₁	C₂×C₄	semidirect
23. C₂×C₄×C₃₁	C₄⋊C₄	semidirect
36. C₄×C₃₁	C₂×C₄⋊C₄	semidirect
41. C₂×C₃₁	#384	semidirect
49. C₂×C₄²	Dic₃₁	semidirect
51. C₃₁	C₂×#384	semidirect
60. C₄²	C₂×Dic₃₁	semidirect
67. C₂×C₄	C₄⋊Dic₃₁	semidirect
78. C₄	C₂×C₄⋊Dic₃₁	semidirect
79. C₂	#14520919	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×C₄⋊Dic₃₁	2
#14520919	2
C₂²×C₄²×C₃₁	2
C₂×#384	31

Subgroups — C2×#14520919 #16848112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14520919 #16848112