Subgroups — C₂×#22552352 #30659722

Order 16672.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₀₄₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#22552352	C₂	1	4	yes	maximal, direct product factor
3	C₂×#16861960	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₅₂₁	C₂	1	1	yes	maximal, characteristic
5	Dic₁₀₄₂	—	2	1	no	—
6	Dic₁₀₄₂	C₂²	1	2	yes	complemented
7	C₂×Dic₅₂₁	—	2	1	no	—
8	#16861960	C₂²	1	2	yes	complemented
9	C₂³×C₅₂₁	—	2	1	no	—
10	D₄×C₅₂₁	—	2	1	no	—
11	D₄×C₅₂₁	C₂²	1	2	yes	—
12	C₂×C₄×C₅₂₁	C₂²	1	1	yes	characteristic
13	C₂²×C₅₂₁	—	2	2	no	—
14	C₂²×C₅₂₁	—	4	2	no	—
15	C₂²×C₅₂₁	D₄	1	1	yes	characteristic
16	C₄×C₅₂₁	D₄	1	1	yes	characteristic
17	C₄×C₅₂₁	C₂³	1	1	yes	characteristic
18	Dic₅₂₁	—	2	2	no	—
19	C₂×C₅₂₁	—	4	2	no	—
20	C₂×C₅₂₁	SD₁₆	1	2	yes	complemented
21	C₂×C₅₂₁	C₂×D₄	1	1	yes	characteristic
22	C₅₂₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	521	1	no	maximal, Sylow
24	C₂×Q₈	—	521	1	no	—
25	C₂×D₄	D₅₂₁	1	1	yes	characteristic
26	SD₁₆	—	521	4	no	—
27	C₂×C₈	—	521	1	no	—
28	C₂³	—	2	1	no	—
29	Q₈	—	521	2	no	—
30	Q₈	—	1042	1	no	—
31	D₄	—	2	1	no	—
32	D₄	C₂×D₅₂₁	1	2	yes	—
33	C₂×C₄	—	1042	1	no	—
34	C₂×C₄	C₂×D₅₂₁	1	1	yes	characteristic
35	C₈	—	521	2	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂²⋊D₅₂₁	1	1	yes	characteristic
39	C₄	—	1042	2	no	—
40	C₄	C₂²⋊D₅₂₁	1	1	yes	characteristic
41	C₄	C₂²×D₅₂₁	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	#22552352	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₅₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₅₂₁
commutator, cosocle	C₄×C₅₂₁	C₂³
Frattini	C₄	C₂²×D₅₂₁
Fitting, prime radical	C₂×D₄×C₅₂₁	C₂
socle	C₂²×C₅₂₁	D₄
hypercenter	C₂×D₄	D₅₂₁
hypocenter	C₅₂₁	C₂×SD₁₆
LCS	G ▷ C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₁₀₄₂	C₂	semidirect
2. #22552352	C₂	direct (N × H)
3. C₂×#16861960	C₂	semidirect
6. Dic₁₀₄₂	C₂²	semidirect
8. #16861960	C₂²	semidirect
20. C₂×C₅₂₁	SD₁₆	semidirect
22. C₅₂₁	C₂×SD₁₆	semidirect
43. C₂	#22552352	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×Dic₁₀₄₂	2
#22552352	2
C₂×#16861960	2
C₂×D₄×C₅₂₁	2
C₂×SD₁₆	521

Subgroups — C2×#22552352 #30659722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22552352 #30659722