Subgroups — #28380774

Order 14048.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20296329	C₂	1	1	yes	maximal, characteristic
2	#20296319	C₂	1	2	yes	maximal, complemented
3	#20296316	C₂	1	2	yes	maximal, complemented
4	#20296313	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₄₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₈₇₈	C₂²	1	1	yes	characteristic
7	D₁₇₅₆	C₂²	1	1	yes	characteristic
8	C₂²⋊D₄₃₉	—	2	1	no	—
9	C₄×D₄₃₉	—	2	1	no	—
10	C₄₃₉⋊C₈	C₂²	1	2	yes	—
11	Q₈×C₄₃₉	—	2	1	no	—
12	Q₈×C₄₃₉	C₂²	1	2	yes	—
13	C₂×C₄×C₄₃₉	—	2	1	no	—
14	C₂×C₄×C₄₃₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄₃₉	D₄	1	1	yes	characteristic
16	C₂×D₄₃₉	—	2	1	no	—
17	C₄×C₄₃₉	—	2	2	no	—
18	C₄×C₄₃₉	D₄	1	1	yes	characteristic
19	C₄×C₄₃₉	C₂³	1	1	yes	characteristic
20	Dic₄₃₉	—	2	1	no	—
21	C₂×C₄₃₉	—	2	1	no	—
22	C₂×C₄₃₉	C₂×D₄	1	1	yes	characteristic
23	D₄₃₉	—	4	1	no	—
24	C₄₃₉	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	439	1	no	maximal, Sylow
26	#41	—	439	1	no	—
27	C₂×Q₈	D₄₃₉	1	1	yes	characteristic, complemented
28	Q₁₆	—	439	2	no	—
29	SD₁₆	—	439	2	no	—
30	M₁₆	—	439	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	439	1	no	—
33	Q₈	C₂×D₄₃₉	1	2	yes	—
34	D₄	—	878	1	no	—
35	D₄	—	439	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	878	1	no	—
38	C₂×C₄	C₂×D₄₃₉	1	1	yes	characteristic
39	C₈	—	439	2	no	—
40	C₂²	—	878	1	no	—
41	C₂²	C₂²⋊D₄₃₉	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	878	1	no	—
44	C₄	C₂²⋊D₄₃₉	1	1	yes	characteristic
45	C₄	C₂²×D₄₃₉	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	1756	1	no	—
48	C₂	C₂×C₂²⋊D₄₃₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₄₃₉
commutator, cosocle	C₄×C₄₃₉	C₂³
Frattini	C₄	C₂²×D₄₃₉
Fitting	C₂×Q₈×C₄₃₉	C₂
socle	C₂×C₄₃₉	C₂×D₄
prime radical	#20296329	C₂
hypercenter	C₂×Q₈	D₄₃₉
hypocenter	C₄₃₉	#137
LCS	G ▷ C₄×C₄₃₉ ▷ C₂×C₄₃₉ ▷ C₄₃₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #20296319	C₂	semidirect
3. #20296316	C₂	semidirect
4. #20296313	C₂	semidirect
5. C₂×Q₈×C₄₃₉	C₂	semidirect
24. C₄₃₉	#137	semidirect
27. C₂×Q₈	D₄₃₉	semidirect

Maximal subgroups

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

subgroup	index
#20296329	2
#20296319	2
#20296316	2
#20296313	2
C₂×Q₈×C₄₃₉	2
#137	439