Subgroups — #22581012

Order 8896.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984799	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃₉⋊C₈	C₂	1	2	yes	maximal, complemented
3	(C₂×D₁₃₉)⋊C₈	C₂	1	2	yes	maximal
4	#17984753	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₃₉⋊C₈	C₂²	1	2	yes	—
8	Dic₁₃₉⋊C₄	C₄	1	2	yes	—
9	(C₂×D₁₃₉)⋊C₄	C₄	1	2	yes	—
10	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₃₉	C₂²	1	2	yes	—
12	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂²×D₁₃₉	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₃₉	C₂×C₄	1	2	yes	—
15	C₂×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
16	C₄×D₁₃₉	—	2	2	no	—
17	C₁₃₉⋊C₈	—	2	2	no	—
18	C₂×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
20	C₈×C₁₃₉	—	2	2	no	—
21	C₂²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
22	C₂×D₁₃₉	—	2	1	no	—
23	C₂×D₁₃₉	—	2	2	no	—
24	C₄×C₁₃₉	—	2	2	no	—
25	C₄×C₁₃₉	#41	1	2	yes	—
26	Dic₁₃₉	—	2	1	no	—
27	Dic₁₃₉	—	2	2	no	—
28	C₂×C₁₃₉	#117	1	1	yes	characteristic
29	C₂×C₁₃₉	#131	1	2	yes	—
30	D₁₃₉	—	4	1	no	—
31	C₁₃₉	#433	1	1	yes	characteristic, complemented, Sylow
32	#433	—	139	1	no	maximal, Sylow
33	#117	—	139	1	no	—
34	C₄⋊C₈	—	139	2	no	—
35	C₂²⋊C₈	—	139	2	no	—
36	#97	—	139	1	no	—
37	C₄×C₈	D₁₃₉	1	1	yes	characteristic, complemented
38	C₂²×C₄	—	139	1	no	—
39	C₂×C₈	—	139	2	no	—
40	C₂×C₈	C₂×D₁₃₉	1	2	yes	—
41	C₄⋊C₄	—	139	2	no	—
42	C₂²⋊C₄	—	139	2	no	—
43	C₄²	—	139	1	no	—
44	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
45	C₂³	—	139	1	no	—
46	C₂×C₄	—	278	2	no	—
47	C₂×C₄	—	139	2	no	—
48	C₂×C₄	—	139	1	no	—
49	C₂×C₄	C₄×D₁₃₉	1	2	yes	—
50	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
51	C₈	—	2	2	no	—
52	C₈	—	278	2	no	—
53	C₂²	—	278	1	no	—
54	C₂²	—	278	2	no	—
55	C₂²	C₂×C₄×D₁₃₉	1	1	yes	characteristic
56	C₄	—	2	2	no	—
57	C₄	—	278	1	no	—
58	C₄	—	278	2	no	—
59	C₄	#14555785	1	2	yes	—
60	C₂	—	556	1	no	—
61	C₂	#17984799	1	1	yes	characteristic
62	C₂	#17984848	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₃₉
commutator, socle	C₂²×C₁₃₉	C₂²×C₄
Fitting	C₄×C₈×C₁₃₉	C₂
hypercenter	C₄×C₈	D₁₃₉
hypocenter	C₁₃₉	#433
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
2. Dic₁₃₉⋊C₈	C₂	semidirect
4. #17984753	C₂	semidirect
5. C₄×C₈×C₁₃₉	C₂	semidirect
31. C₁₃₉	#433	semidirect
37. C₄×C₈	D₁₃₉	semidirect