Subgroups — #28380764

Order 14048.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20296330	C₂	1	1	yes	maximal, characteristic, complemented
2	#20296328	C₂	1	1	yes	maximal, characteristic, complemented
3	#20296319	C₂	1	1	yes	maximal, characteristic, complemented
4	#20296318	C₂	1	1	yes	maximal, characteristic, complemented
5	#20296314	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×D₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₈₇₈	C₂²	1	1	yes	characteristic
9	D₁₇₅₆	—	2	1	no	—
10	D₁₇₅₆	C₂²	1	1	yes	characteristic
11	C₂²⋊D₄₃₉	—	2	1	no	—
12	C₂×Dic₄₃₉	—	2	1	no	—
13	C₄×D₄₃₉	—	2	1	no	—
14	C₄×D₄₃₉	C₂²	1	1	yes	characteristic
15	C₄₃₉⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₄₃₉	C₂²	1	1	yes	characteristic
17	D₄×C₄₃₉	C₂²	1	1	yes	characteristic
18	C₈×C₄₃₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄₃₉	—	2	1	no	—
20	C₂×D₄₃₉	—	2	1	no	—
21	C₂×D₄₃₉	D₄	1	1	yes	characteristic
22	C₄×C₄₃₉	—	2	1	no	—
23	C₄×C₄₃₉	C₂³	1	1	yes	characteristic
24	Dic₄₃₉	—	2	1	no	—
25	Dic₄₃₉	D₄	1	1	yes	characteristic
26	C₂×C₄₃₉	—	4	1	no	—
27	C₂×C₄₃₉	C₂×D₄	1	1	yes	characteristic
28	D₄₃₉	—	2	1	no	—
29	D₄₃₉	—	4	1	no	—
30	C₄₃₉	#135	1	1	yes	characteristic, complemented, Sylow
31	#135	—	439	1	no	maximal, Sylow
32	#41	—	439	1	no	—
33	#41	—	439	1	no	—
34	Q₁₆	—	439	1	no	—
35	SD₁₆	—	439	1	no	—
36	SD₁₆	D₄₃₉	1	1	yes	characteristic, complemented
37	D₈	—	439	1	no	—
38	C₂×C₈	—	439	1	no	—
39	Q₈	—	439	1	no	—
40	Q₈	C₂×D₄₃₉	1	1	yes	characteristic
41	D₄	—	878	1	no	—
42	D₄	—	878	1	no	—
43	D₄	—	439	1	no	—
44	D₄	C₂×D₄₃₉	1	1	yes	characteristic
45	C₂×C₄	—	878	1	no	—
46	C₂×C₄	—	878	1	no	—
47	C₂×C₄	—	439	1	no	—
48	C₈	—	439	1	no	—
49	C₈	C₂×D₄₃₉	1	1	yes	characteristic
50	C₂²	—	2	1	no	—
51	C₂²	—	878	1	no	—
52	C₂²	—	439	1	no	—
53	C₄	—	2	1	no	—
54	C₄	—	878	1	no	—
55	C₄	—	439	1	no	—
56	C₄	C₂²×D₄₃₉	1	1	yes	characteristic
57	C₂	—	4	1	no	—
58	C₂	—	878	1	no	—
59	C₂	—	1756	1	no	—
60	C₂	D₄×D₄₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₄₃₉
commutator, cosocle	C₄×C₄₃₉	C₂³
Frattini	C₄	C₂²×D₄₃₉
Fitting	SD₁₆×C₄₃₉	C₂
socle	C₂×C₄₃₉	C₂×D₄
hypercenter	SD₁₆	D₄₃₉
hypocenter	C₄₃₉	#135
LCS	G ▷ C₄×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. #20296330	C₂	semidirect
2. #20296328	C₂	semidirect
3. #20296319	C₂	semidirect
4. #20296318	C₂	semidirect
5. #20296314	C₂	semidirect
6. C₈×D₄₃₉	C₂	semidirect
7. SD₁₆×C₄₃₉	C₂	semidirect
30. C₄₃₉	#135	semidirect
36. SD₁₆	D₄₃₉	semidirect

Maximal subgroups

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

subgroup	index
#20296330	2
#20296328	2
#20296319	2
#20296318	2
#20296314	2
C₈×D₄₃₉	2
SD₁₆×C₄₃₉	2
#135	439