Subgroups — #43248146

Order 28352.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28381905	C₂	1	2	yes	maximal, complemented
2	Dic₃₅₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#28381830	C₂	1	2	yes	maximal, complemented
4	C₁₆×D₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₆×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#20296786	—	2	2	no	—
7	Dic₁₇₇₂	C₂²	1	2	yes	—
8	#20296775	—	2	2	no	—
9	C₈×D₄₄₃	C₂²	1	1	yes	characteristic
10	C₄₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	D₈×C₄₄₃	C₂²	1	2	yes	—
12	C₁₆×C₄₄₃	C₂²	1	1	yes	characteristic
13	Dic₈₈₆	—	2	2	no	—
14	C₂²⋊D₄₄₃	—	4	2	no	—
15	C₂×Dic₄₄₃	—	4	2	no	—
16	C₄×D₄₄₃	D₄	1	1	yes	characteristic
17	C₄₄₃⋊C₈	D₄	1	1	yes	characteristic
18	D₄×C₄₄₃	—	2	2	no	—
19	C₈×C₄₄₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄₄₃	—	4	2	no	—
21	C₂×D₄₄₃	D₈	1	1	yes	characteristic
22	C₄×C₄₄₃	C₂×D₄	1	1	yes	characteristic
23	Dic₄₄₃	—	4	2	no	—
24	Dic₄₄₃	D₈	1	1	yes	characteristic
25	C₂×C₄₄₃	—	8	2	no	—
26	C₂×C₄₄₃	C₂×D₈	1	1	yes	characteristic
27	D₄₄₃	—	2	1	no	—
28	C₄₄₃	#508	1	1	yes	characteristic, complemented, Sylow
29	#508	—	443	1	no	maximal, Sylow
30	#135	—	443	2	no	—
31	Q₃₂	—	443	1	no	—
32	SD₃₂	—	443	2	no	—
33	D₁₆	D₄₄₃	1	1	yes	characteristic, complemented
34	C₂×C₁₆	—	443	1	no	—
35	#41	—	886	2	no	—
36	Q₁₆	—	443	2	no	—
37	SD₁₆	—	886	2	no	—
38	D₈	C₂×D₄₄₃	1	2	yes	—
39	C₂×C₈	—	443	1	no	—
40	C₁₆	—	443	1	no	—
41	C₁₆	C₂×D₄₄₃	1	1	yes	characteristic
42	Q₈	—	886	2	no	—
43	D₄	—	2	2	no	—
44	D₄	—	1772	2	no	—
45	C₂×C₄	—	443	1	no	—
46	C₂×C₄	—	1772	2	no	—
47	C₈	—	443	1	no	—
48	C₈	C₂²×D₄₄₃	1	1	yes	characteristic
49	C₂²	—	4	2	no	—
50	C₂²	—	443	1	no	—
51	C₄	—	443	1	no	—
52	C₄	—	1772	2	no	—
53	C₄	D₄×D₄₄₃	1	1	yes	characteristic
54	C₂	—	8	2	no	—
55	C₂	—	886	1	no	—
56	C₂	D₈×D₄₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×D₄₄₃
commutator, cosocle	C₈×C₄₄₃	C₂³
Frattini	C₈	C₂²×D₄₄₃
Fitting	D₁₆×C₄₄₃	C₂
socle	C₂×C₄₄₃	C₂×D₈
hypercenter	D₁₆	D₄₄₃
hypocenter	C₄₄₃	#508
LCS	G ▷ C₈×C₄₄₃ ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #28381905	C₂	semidirect
2. Dic₃₅₄₄	C₂	semidirect
3. #28381830	C₂	semidirect
4. C₁₆×D₄₄₃	C₂	semidirect
5. D₁₆×C₄₄₃	C₂	semidirect
28. C₄₄₃	#508	semidirect
33. D₁₆	D₄₄₃	semidirect

Maximal subgroups

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

subgroup	index
#28381905	2
Dic₃₅₄₄	2
#28381830	2
C₁₆×D₄₄₃	2
D₁₆×C₄₄₃	2
#508	443