Subgroups — #22580675

Order 8896.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃₉⋊C₈	C₄	1	2	yes	—
5	C₂×C₁₃₉⋊C₈	C₄	1	2	yes	—
6	C₂×C₈×C₁₃₉	C₄	1	2	yes	—
7	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₁₃₉⋊C₈	—	2	2	no	—
9	C₁₃₉⋊C₈	C₈	1	4	yes	complemented
10	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
13	C₈×C₁₃₉	—	2	2	no	—
14	C₂²×C₁₃₉	C₄²	1	1	yes	characteristic
15	C₄×C₁₃₉	C₂×C₈	1	2	yes	—
16	C₄×C₁₃₉	M₁₆	1	2	yes	—
17	C₄×C₁₃₉	M₁₆	1	2	yes	—
18	C₂×C₁₃₉	C₄×C₈	1	1	yes	characteristic
19	C₂×C₁₃₉	#97	1	1	yes	characteristic
20	C₂×C₁₃₉	#97	1	1	yes	characteristic
21	C₁₃₉	#322	1	1	yes	characteristic, complemented, Sylow
22	#322	—	139	1	no	maximal, Sylow
23	C₄×C₈	—	139	1	no	—
24	C₄×C₈	—	139	1	no	—
25	C₄×C₈	D₁₃₉	1	1	yes	characteristic
26	C₂×C₈	—	139	2	no	—
27	C₂×C₈	—	139	2	no	—
28	C₂×C₈	Dic₁₃₉	1	2	yes	—
29	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
30	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
31	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
32	C₂×C₄	C₂×Dic₁₃₉	1	1	yes	characteristic
33	C₈	—	2	2	no	—
34	C₈	—	278	2	no	—
35	C₈	—	139	4	no	—
36	C₂²	C₄×Dic₁₃₉	1	1	yes	characteristic
37	C₄	C₈×D₁₃₉	1	2	yes	—
38	C₄	#14555768	1	2	yes	—
39	C₄	#14555769	1	2	yes	—
40	C₂	C₈×Dic₁₃₉	1	1	yes	characteristic
41	C₂	#17984752	1	1	yes	characteristic
42	C₂	#17984753	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂×D₁₃₉
commutator	C₂×C₁₃₉	C₄×C₈
Fitting	C₄×C₈×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₄²
hypercenter	C₄×C₈	D₁₃₉
hypocenter	C₁₃₉	#322
LCS	G ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
9. C₁₃₉⋊C₈	C₈	semidirect
21. C₁₃₉	#322	semidirect