Subgroups — C₂×#11758465 #14521592

Order 1984.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₆₂	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊Dic₃₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₁⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₃₁	C₂	1	1	yes	maximal, characteristic
6	#11758465	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×C₃₁	C₂²	1	2	yes	—
8	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
9	C₂²×Dic₃₁	C₂²	1	2	yes	—
10	C₂²×Dic₃₁	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃₁	C₂²	1	1	yes	characteristic
12	C₂×Dic₆₂	—	2	8	no	—
13	C₂×Dic₆₂	C₂²	1	8	yes	—
14	C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
15	C₄⋊Dic₃₁	C₂²	1	4	yes	—
16	Dic₃₁⋊C₄	C₂²	1	8	yes	—
17	C₄×Dic₃₁	C₂²	1	4	yes	—
18	C₂³×C₃₁	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₃₁	—	2	4	no	—
20	C₂×C₄×C₃₁	Q₈	1	4	yes	complemented
21	C₂×C₄×C₃₁	C₂³	1	4	yes	—
22	C₂×C₄×C₃₁	C₂³	1	2	yes	—
23	C₂×Dic₃₁	—	2	4	no	—
24	C₂×Dic₃₁	D₄	1	4	yes	—
25	C₂×Dic₃₁	Q₈	1	4	yes	complemented
26	C₂×Dic₃₁	C₂³	1	4	yes	—
27	C₂×Dic₃₁	C₂³	1	2	yes	—
28	C₂×Dic₃₁	C₂³	1	2	yes	—
29	Dic₆₂	—	2	16	no	—
30	C₂²×C₃₁	C₂×D₄	1	2	yes	—
31	C₂²×C₃₁	C₂×Q₈	1	2	yes	—
32	C₂²×C₃₁	C₂×Q₈	1	2	yes	—
33	C₂²×C₃₁	C₂⁴	1	1	yes	characteristic
34	C₄×C₃₁	—	2	4	no	—
35	C₄×C₃₁	C₂×Q₈	1	4	yes	complemented
36	Dic₃₁	—	2	4	no	—
37	Dic₃₁	C₂×D₄	1	4	yes	—
38	Dic₃₁	C₂×Q₈	1	4	yes	complemented
39	C₂×C₄⋊Q₈	—	31	1	no	maximal, Sylow
40	C₂×C₃₁	C₄⋊Q₈	1	4	yes	complemented
41	C₂×C₃₁	C₂²×D₄	1	1	yes	characteristic
42	C₂×C₃₁	C₂²×Q₈	1	1	yes	characteristic
43	C₂×C₃₁	C₂²×Q₈	1	1	yes	characteristic
44	C₂²×Q₈	—	31	2	no	—
45	C₄⋊Q₈	—	31	8	no	—
46	C₂×C₄⋊C₄	—	31	2	no	—
47	C₂×C₄⋊C₄	—	31	1	no	—
48	C₂×C₄⋊C₄	D₃₁	1	1	yes	characteristic
49	C₂×C₄²	—	31	1	no	—
50	C₃₁	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₈	—	31	8	no	—
52	C₂×Q₈	—	62	8	no	—
53	C₂²×C₄	—	31	1	no	—
54	C₂²×C₄	—	31	1	no	—
55	C₂²×C₄	—	31	2	no	—
56	C₂²×C₄	C₂×D₃₁	1	2	yes	—
57	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
58	C₄⋊C₄	—	31	8	no	—
59	C₄⋊C₄	—	31	4	no	—
60	C₄⋊C₄	C₂×D₃₁	1	4	yes	—
61	C₄²	—	31	4	no	—
62	C₂³	C₂²×D₃₁	1	1	yes	characteristic
63	Q₈	—	62	16	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	31	4	no	—
66	C₂×C₄	—	31	4	no	—
67	C₂×C₄	—	31	2	no	—
68	C₂×C₄	—	31	2	no	—
69	C₂×C₄	—	31	4	no	—
70	C₂×C₄	—	62	4	no	—
71	C₂×C₄	Dic₆₂	1	4	yes	complemented
72	C₂×C₄	C₂²×D₃₁	1	4	yes	—
73	C₂×C₄	C₂²×D₃₁	1	2	yes	—
74	C₂²	C₂×Dic₆₂	1	2	yes	—
75	C₂²	D₄×D₃₁	1	2	yes	—
76	C₂²	Q₈×D₃₁	1	2	yes	—
77	C₂²	C₂³×D₃₁	1	1	yes	characteristic
78	C₄	—	2	4	no	—
79	C₄	—	31	4	no	—
80	C₄	—	31	4	no	—
81	C₄	—	62	4	no	—
82	C₄	C₂×Dic₆₂	1	4	yes	complemented
83	C₂	#11758465	1	4	yes	direct product factor
84	C₂	C₂²×Dic₆₂	1	1	yes	characteristic
85	C₂	C₂×D₄×D₃₁	1	1	yes	characteristic
86	C₂	C₂×Q₈×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃₁
commutator, cosocle	C₂²×C₃₁	C₂⁴
Frattini	C₂²	C₂³×D₃₁
Fitting	C₂×C₄⋊C₄×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂³
hypercenter	C₂×C₄⋊C₄	D₃₁
hypocenter	C₃₁	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #11758465	C₂	direct (N × H)
20. C₂×C₄×C₃₁	Q₈	semidirect
25. C₂×Dic₃₁	Q₈	semidirect
35. C₄×C₃₁	C₂×Q₈	semidirect
38. Dic₃₁	C₂×Q₈	semidirect
40. C₂×C₃₁	C₄⋊Q₈	semidirect
50. C₃₁	C₂×C₄⋊Q₈	semidirect
71. C₂×C₄	Dic₆₂	semidirect
82. C₄	C₂×Dic₆₂	semidirect
83. C₂	#11758465	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×Dic₆₂	2
C₂×C₄⋊C₄×C₃₁	2
C₂×C₄⋊Dic₃₁	2
C₂×Dic₃₁⋊C₄	2
C₂×C₄×Dic₃₁	2
#11758465	2
C₂×C₄⋊Q₈	31

Subgroups — C2×#11758465 #14521592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758465 #14521592