Subgroups — C₂×#11758415 #14521473

Order 1984.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₈×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₁₂₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#11758415	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄×C₃₁	—	2	1	no	—
6	C₂×Dic₆₂	—	2	1	no	—
7	D₈×C₃₁	—	2	1	no	—
8	D₈×C₃₁	C₂²	1	2	yes	—
9	C₂×C₈×C₃₁	C₂²	1	1	yes	characteristic
10	Dic₁₂₄	—	2	1	no	—
11	Dic₁₂₄	C₂²	1	2	yes	complemented
12	C₃₁⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂³×C₃₁	—	4	1	no	—
14	D₄×C₃₁	—	2	2	no	—
15	D₄×C₃₁	—	4	1	no	—
16	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
17	C₂×Dic₃₁	—	4	1	no	—
18	Dic₆₂	—	2	2	no	—
19	Dic₆₂	—	4	1	no	—
20	C₈×C₃₁	D₄	1	1	yes	characteristic
21	C₈×C₃₁	C₂³	1	1	yes	characteristic
22	C₂²×C₃₁	—	4	2	no	—
23	C₂²×C₃₁	—	8	2	no	—
24	C₂²×C₃₁	D₈	1	1	yes	characteristic
25	C₄×C₃₁	D₈	1	1	yes	characteristic
26	C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
27	Dic₃₁	—	4	2	no	—
28	C₂×SD₃₂	—	31	1	no	maximal, Sylow
29	C₂×C₃₁	—	8	2	no	—
30	C₂×C₃₁	SD₃₂	1	2	yes	complemented
31	C₂×C₃₁	C₂×D₈	1	1	yes	characteristic
32	C₂×Q₁₆	—	31	1	no	—
33	C₂×D₈	D₃₁	1	1	yes	characteristic
34	SD₃₂	—	31	4	no	—
35	C₂×C₁₆	—	31	1	no	—
36	C₃₁	C₂×SD₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₈	—	62	1	no	—
38	C₂×D₄	—	2	1	no	—
39	Q₁₆	—	31	2	no	—
40	Q₁₆	—	62	1	no	—
41	D₈	—	2	1	no	—
42	D₈	C₂×D₃₁	1	2	yes	—
43	C₂×C₈	C₂×D₃₁	1	1	yes	characteristic
44	C₁₆	—	31	2	no	—
45	C₂³	—	4	1	no	—
46	Q₈	—	62	2	no	—
47	Q₈	—	124	1	no	—
48	D₄	—	2	2	no	—
49	D₄	—	4	1	no	—
50	C₂×C₄	—	124	1	no	—
51	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
52	C₈	C₂²⋊D₃₁	1	1	yes	characteristic
53	C₈	C₂²×D₃₁	1	1	yes	characteristic
54	C₂²	—	4	2	no	—
55	C₂²	—	8	2	no	—
56	C₂²	#92479	1	1	yes	characteristic
57	C₄	—	124	2	no	—
58	C₄	#92479	1	1	yes	characteristic
59	C₄	C₂×C₂²⋊D₃₁	1	1	yes	characteristic
60	C₂	—	8	2	no	—
61	C₂	#11758415	1	2	yes	direct product factor
62	C₂	C₂×#92479	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#92479
commutator, cosocle	C₈×C₃₁	C₂³
Frattini	C₈	C₂²×D₃₁
Fitting, prime radical	C₂×D₈×C₃₁	C₂
socle	C₂²×C₃₁	D₈
hypercenter	C₂×D₈	D₃₁
hypocenter	C₃₁	C₂×SD₃₂
LCS	G ▷ C₈×C₃₁ ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₁₂₄	C₂	semidirect
3. #11758415	C₂	direct (N × H)
4. C₂×C₃₁⋊C₁₆	C₂	semidirect
11. Dic₁₂₄	C₂²	semidirect
12. C₃₁⋊C₁₆	C₂²	semidirect
30. C₂×C₃₁	SD₃₂	semidirect
36. C₃₁	C₂×SD₃₂	semidirect
61. C₂	#11758415	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₈×C₃₁	2
C₂×Dic₁₂₄	2
#11758415	2
C₂×C₃₁⋊C₁₆	2
C₂×SD₃₂	31

Subgroups — C2×#11758415 #14521473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11758415 #14521473