Subgroups — #28381919

Order 14176.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20296787	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₈₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₁₇₇₂	C₂	1	2	yes	maximal, complemented
4	#20296776	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₈₈₆	—	2	1	no	—
7	Dic₈₈₆	C₂²	1	2	yes	—
8	Dic₈₈₆	C₂²	1	1	yes	characteristic
9	D₁₇₇₂	C₂²	1	1	yes	characteristic
10	C₂²⋊D₄₄₃	—	2	1	no	—
11	C₂×Dic₄₄₃	—	2	1	no	—
12	C₄×D₄₄₃	—	2	1	no	—
13	C₂×C₄×C₄₄₃	C₂²	1	1	yes	characteristic
14	C₈×C₄₄₃	C₂²	1	2	yes	—
15	C₂²×C₄₄₃	D₄	1	1	yes	characteristic
16	C₂×D₄₄₃	—	2	1	no	—
17	C₄×C₄₄₃	D₄	1	1	yes	characteristic
18	C₄×C₄₄₃	C₂³	1	1	yes	characteristic
19	Dic₄₄₃	—	2	1	no	—
20	Dic₄₄₃	—	2	2	no	—
21	C₂×C₄₄₃	—	2	1	no	—
22	C₂×C₄₄₃	C₂×D₄	1	1	yes	characteristic
23	D₄₄₃	—	4	1	no	—
24	C₄₄₃	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	443	1	no	maximal, Sylow
26	#41	—	443	1	no	—
27	C₂×Q₈	—	443	1	no	—
28	Q₁₆	—	443	2	no	—
29	SD₁₆	—	443	2	no	—
30	M₁₆	D₄₄₃	1	1	yes	characteristic, complemented
31	Q₈	—	886	1	no	—
32	Q₈	—	443	2	no	—
33	Q₈	—	443	1	no	—
34	D₄	—	886	1	no	—
35	D₄	—	443	1	no	—
36	C₂×C₄	—	886	1	no	—
37	C₂×C₄	—	886	1	no	—
38	C₂×C₄	C₂×D₄₄₃	1	1	yes	characteristic
39	C₈	C₂×D₄₄₃	1	2	yes	—
40	C₂²	—	886	1	no	—
41	C₂²	D₁₇₇₂	1	1	yes	characteristic
42	C₄	—	886	1	no	—
43	C₄	—	886	2	no	—
44	C₄	D₁₇₇₂	1	1	yes	characteristic
45	C₄	C₂²×D₄₄₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	1772	1	no	—
48	C₂	C₂×D₁₇₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₁₇₇₂
commutator, cosocle	C₄×C₄₄₃	C₂³
Frattini	C₄	C₂²×D₄₄₃
Fitting	M₁₆×C₄₄₃	C₂
socle	C₂×C₄₄₃	C₂×D₄
prime radical	#20296787	C₂
hypercenter	M₁₆	D₄₄₃
hypocenter	C₄₄₃	#137
LCS	G ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₈₈₆	C₂	semidirect
3. Dic₁₇₇₂	C₂	semidirect
4. #20296776	C₂	semidirect
5. M₁₆×C₄₄₃	C₂	semidirect
24. C₄₄₃	#137	semidirect
30. M₁₆	D₄₄₃	semidirect

Maximal subgroups

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

subgroup	index
#20296787	2
C₂×Dic₈₈₆	2
Dic₁₇₇₂	2
#20296776	2
M₁₆×C₄₄₃	2
#137	443