Subgroups — C₂×#30681223 #46777696

Order 33632.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₁₀₂	C₂	1	1	yes	maximal, characteristic
2	#30681223	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₀₅₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₁₀₅₁	C₂	1	1	yes	maximal, characteristic
5	Dic₂₁₀₂	—	2	1	no	—
6	Dic₂₁₀₂	C₂²	1	2	yes	—
7	C₂×Dic₁₀₅₁	—	2	1	no	—
8	C₁₀₅₁⋊C₈	C₂²	1	2	yes	—
9	Q₈×C₁₀₅₁	—	2	1	no	—
10	Q₈×C₁₀₅₁	C₂²	1	2	yes	—
11	C₂×C₄×C₁₀₅₁	—	2	1	no	—
12	C₂×C₄×C₁₀₅₁	C₂²	1	1	yes	characteristic
13	C₂²×C₁₀₅₁	D₄	1	1	yes	characteristic
14	C₄×C₁₀₅₁	—	2	2	no	—
15	C₄×C₁₀₅₁	D₄	1	1	yes	characteristic
16	C₄×C₁₀₅₁	C₂³	1	1	yes	characteristic
17	Dic₁₀₅₁	—	2	2	no	—
18	C₂×C₁₀₅₁	Q₁₆	1	2	yes	complemented
19	C₂×C₁₀₅₁	C₂×D₄	1	1	yes	characteristic
20	C₁₀₅₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	1051	1	no	maximal, Sylow
22	C₂×Q₈	—	1051	1	no	—
23	C₂×Q₈	D₁₀₅₁	1	1	yes	characteristic
24	Q₁₆	—	1051	4	no	—
25	C₂×C₈	—	1051	1	no	—
26	Q₈	—	2	1	no	—
27	Q₈	—	1051	2	no	—
28	Q₈	—	2102	1	no	—
29	Q₈	C₂×D₁₀₅₁	1	2	yes	—
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	—	2102	1	no	—
32	C₂×C₄	C₂×D₁₀₅₁	1	1	yes	characteristic
33	C₈	—	1051	2	no	—
34	C₂²	C₂²⋊D₁₀₅₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	2102	2	no	—
37	C₄	C₂²⋊D₁₀₅₁	1	1	yes	characteristic
38	C₄	C₂²×D₁₀₅₁	1	1	yes	characteristic
39	C₂	#30681223	1	2	yes	direct product factor
40	C₂	C₂×C₂²⋊D₁₀₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₁₀₅₁
commutator, cosocle	C₄×C₁₀₅₁	C₂³
Frattini	C₄	C₂²×D₁₀₅₁
Fitting	C₂×Q₈×C₁₀₅₁	C₂
socle, prime radical	C₂²×C₁₀₅₁	D₄
hypercenter	C₂×Q₈	D₁₀₅₁
hypocenter	C₁₀₅₁	C₂×Q₁₆
LCS	G ▷ C₄×C₁₀₅₁ ▷ C₂×C₁₀₅₁ ▷ C₁₀₅₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #30681223	C₂	direct (N × H)
18. C₂×C₁₀₅₁	Q₁₆	semidirect
20. C₁₀₅₁	C₂×Q₁₆	semidirect
39. C₂	#30681223	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×Dic₂₁₀₂	2
#30681223	2
C₂×C₁₀₅₁⋊C₈	2
C₂×Q₈×C₁₀₅₁	2
C₂×Q₁₆	1051

Subgroups — C2×#30681223 #46777696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#30681223 #46777696