Subgroups — #22580694

Order 8896.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984834	C₂	1	1	yes	maximal, characteristic
2	#17984753	C₂	1	1	yes	maximal, characteristic
3	#97×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃₉⋊C₈	—	2	1	no	—
5	C₄⋊Dic₁₃₉	C₄	1	1	yes	characteristic
6	C₄⋊Dic₁₃₉	C₄	1	1	yes	characteristic
7	Dic₁₃₉⋊C₄	—	2	1	no	—
8	Dic₁₃₉⋊C₄	—	2	1	no	—
9	C₂×C₈×C₁₃₉	—	2	1	no	—
10	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₃₉	—	2	1	no	—
12	C₂×Dic₁₃₉	—	2	1	no	—
13	C₁₃₉⋊C₈	—	2	2	no	—
14	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
17	C₈×C₁₃₉	—	2	2	no	—
18	C₂²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₃₉	—	2	1	no	—
20	C₄×C₁₃₉	—	2	1	no	—
21	C₄×C₁₃₉	—	2	1	no	—
22	Dic₁₃₉	—	4	1	no	—
23	Dic₁₃₉	—	4	1	no	—
24	C₂×C₁₃₉	#101	1	1	yes	characteristic
25	C₂×C₁₃₉	#104	1	1	yes	characteristic
26	C₂×C₁₃₉	#104	1	1	yes	characteristic
27	C₁₃₉	#330	1	1	yes	characteristic, complemented, Sylow
28	#330	—	139	1	no	maximal, Sylow
29	#125	—	139	1	no	—
30	#97	—	139	1	no	—
31	#97	D₁₃₉	1	1	yes	characteristic
32	C₂×C₈	—	2	1	no	—
33	C₂×C₈	—	278	1	no	—
34	C₄⋊C₄	—	278	1	no	—
35	C₄⋊C₄	—	278	1	no	—
36	C₄⋊C₄	—	139	1	no	—
37	C₄⋊C₄	—	139	1	no	—
38	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
39	C₂×C₄	—	278	1	no	—
40	C₂×C₄	—	278	1	no	—
41	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
42	C₂×C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
43	C₂×C₄	D₅₅₆	1	1	yes	characteristic
44	C₈	—	2	2	no	—
45	C₈	—	278	2	no	—
46	C₂²	(C₂×D₁₃₉)⋊C₄	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	2	1	no	—
49	C₄	—	2	1	no	—
50	C₄	—	556	1	no	—
51	C₄	—	556	1	no	—
52	C₂	#17984760	1	1	yes	characteristic
53	C₂	#17984768	1	1	yes	characteristic
54	C₂	#17984770	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₁₃₉)⋊C₄
commutator	C₂×C₄×C₁₃₉	C₂×C₄
Frattini	C₄²	C₂×D₁₃₉
Fitting	#97×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²⋊C₄
hypercenter	#97	D₁₃₉
hypocenter	C₁₃₉	#330
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
27. C₁₃₉	#330	semidirect