Subgroups — C₂×#20301489 #28414132

Order 14752.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₉₂₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#20301489	C₂	1	4	yes	maximal, direct product factor
3	C₂×#16814779	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₄₆₁	C₂	1	1	yes	maximal, characteristic
5	Dic₉₂₂	—	2	1	no	—
6	Dic₉₂₂	C₂²	1	2	yes	complemented
7	C₂×Dic₄₆₁	—	2	1	no	—
8	#16814779	C₂²	1	2	yes	complemented
9	C₂³×C₄₆₁	—	2	1	no	—
10	D₄×C₄₆₁	—	2	1	no	—
11	D₄×C₄₆₁	C₂²	1	2	yes	—
12	C₂×C₄×C₄₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄₆₁	—	2	2	no	—
14	C₂²×C₄₆₁	—	4	2	no	—
15	C₂²×C₄₆₁	D₄	1	1	yes	characteristic
16	C₄×C₄₆₁	D₄	1	1	yes	characteristic
17	C₄×C₄₆₁	C₂³	1	1	yes	characteristic
18	Dic₄₆₁	—	2	2	no	—
19	C₂×C₄₆₁	—	4	2	no	—
20	C₂×C₄₆₁	SD₁₆	1	2	yes	complemented
21	C₂×C₄₆₁	C₂×D₄	1	1	yes	characteristic
22	C₄₆₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₂×SD₁₆	—	461	1	no	maximal, Sylow
24	C₂×Q₈	—	461	1	no	—
25	C₂×D₄	D₄₆₁	1	1	yes	characteristic
26	SD₁₆	—	461	4	no	—
27	C₂×C₈	—	461	1	no	—
28	C₂³	—	2	1	no	—
29	Q₈	—	922	1	no	—
30	Q₈	—	461	2	no	—
31	D₄	—	2	1	no	—
32	D₄	C₂×D₄₆₁	1	2	yes	—
33	C₂×C₄	—	922	1	no	—
34	C₂×C₄	C₂×D₄₆₁	1	1	yes	characteristic
35	C₈	—	461	2	no	—
36	C₂²	—	2	2	no	—
37	C₂²	—	4	2	no	—
38	C₂²	C₂²⋊D₄₆₁	1	1	yes	characteristic
39	C₄	—	922	2	no	—
40	C₄	C₂²⋊D₄₆₁	1	1	yes	characteristic
41	C₄	C₂²×D₄₆₁	1	1	yes	characteristic
42	C₂	—	4	2	no	—
43	C₂	#20301489	1	2	yes	direct product factor
44	C₂	C₂×C₂²⋊D₄₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₄₆₁
commutator, cosocle	C₄×C₄₆₁	C₂³
Frattini	C₄	C₂²×D₄₆₁
Fitting, prime radical	C₂×D₄×C₄₆₁	C₂
socle	C₂²×C₄₆₁	D₄
hypercenter	C₂×D₄	D₄₆₁
hypocenter	C₄₆₁	C₂×SD₁₆
LCS	G ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
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×Dic₉₂₂	C₂	semidirect
2. #20301489	C₂	direct (N × H)
3. C₂×#16814779	C₂	semidirect
6. Dic₉₂₂	C₂²	semidirect
8. #16814779	C₂²	semidirect
20. C₂×C₄₆₁	SD₁₆	semidirect
22. C₄₆₁	C₂×SD₁₆	semidirect
43. C₂	#20301489	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×Dic₉₂₂	2
#20301489	2
C₂×#16814779	2
C₂×D₄×C₄₆₁	2
C₂×SD₁₆	461

Subgroups — C2×#20301489 #28414132

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20301489 #28414132