Subgroups — #22580708

Order 8896.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃₉⋊C₈	C₂	1	2	yes	maximal
2	C₂×C₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃₉⋊C₈	—	2	2	no	—
4	C₂×C₁₃₉⋊C₈	—	2	2	no	—
5	C₂×C₁₃₉⋊C₈	C₄	1	4	yes	complemented
6	C₂²×C₄×C₁₃₉	C₄	1	2	yes	—
7	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₄²×C₁₃₉	—	2	2	no	—
9	C₁₃₉⋊C₈	—	2	4	no	—
10	C₂³×C₁₃₉	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₃₉	—	2	2	no	—
12	C₂×C₄×C₁₃₉	—	2	2	no	—
13	C₂×C₄×C₁₃₉	C₈	1	4	yes	complemented
14	C₂×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
15	C₂×C₄×C₁₃₉	D₄	1	2	yes	—
16	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₃₉	Q₈	1	1	yes	characteristic
18	C₂²×C₁₃₉	C₄²	1	1	yes	characteristic
19	C₂²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
20	C₂²×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂²×C₁₃₉	C₂×C₈	1	2	yes	—
22	C₂²×C₁₃₉	M₁₆	1	2	yes	—
23	C₄×C₁₃₉	—	2	4	no	—
24	C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
25	C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
26	C₂×C₁₃₉	#95	1	1	yes	characteristic
27	C₂×C₁₃₉	C₄×C₈	1	1	yes	characteristic
28	C₂×C₁₃₉	#97	1	1	yes	characteristic
29	C₂×C₁₃₉	C₂²⋊C₈	1	2	yes	—
30	C₂×C₁₃₉	C₄⋊C₈	1	2	yes	—
31	C₁₃₉	#336	1	1	yes	characteristic, complemented, Sylow
32	#336	—	139	1	no	maximal, Sylow
33	C₂²×C₈	—	139	2	no	—
34	C₂×C₄²	D₁₃₉	1	1	yes	characteristic
35	C₂²×C₄	Dic₁₃₉	1	2	yes	—
36	C₂²×C₄	C₂×D₁₃₉	1	1	yes	characteristic
37	C₂×C₈	—	278	2	no	—
38	C₂×C₈	—	278	2	no	—
39	C₂×C₈	—	139	4	no	—
40	C₄²	—	2	2	no	—
41	C₂³	C₂×Dic₁₃₉	1	1	yes	characteristic
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	C₁₃₉⋊C₈	1	4	yes	complemented
45	C₂×C₄	C₄×D₁₃₉	1	2	yes	—
46	C₂×C₄	C₂²⋊D₁₃₉	1	2	yes	—
47	C₂×C₄	D₅₅₆	1	1	yes	characteristic
48	C₂×C₄	Dic₂₇₈	1	1	yes	characteristic
49	C₈	—	278	4	no	—
50	C₂²	C₄×Dic₁₃₉	1	1	yes	characteristic
51	C₂²	C₂²⋊Dic₁₃₉	1	1	yes	characteristic
52	C₂²	C₄⋊Dic₁₃₉	1	1	yes	characteristic
53	C₂²	C₂×C₁₃₉⋊C₈	1	2	yes	—
54	C₂²	#14555769	1	2	yes	—
55	C₄	—	2	4	no	—
56	C₄	(C₂×D₁₃₉)⋊C₄	1	2	yes	—
57	C₄	Dic₁₃₉⋊C₄	1	2	yes	—
58	C₂	C₁₃₉⋊#95	1	1	yes	characteristic
59	C₂	C₄×C₁₃₉⋊C₈	1	1	yes	characteristic
60	C₂	#17984753	1	1	yes	characteristic
61	C₂	C₂²⋊(C₁₃₉⋊C₈)	1	2	yes	—
62	C₂	C₄⋊(C₁₃₉⋊C₈)	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₁₃₉
commutator	C₂×C₁₃₉	C₄×C₈
Fitting	C₂×C₄²×C₁₃₉	C₂
socle	C₂³×C₁₃₉	C₂×C₄
hypercenter	C₂×C₄²	D₁₃₉
hypocenter	C₁₃₉	#336
LCS	G ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
5. C₂×C₁₃₉⋊C₈	C₄	semidirect
13. C₂×C₄×C₁₃₉	C₈	semidirect
31. C₁₃₉	#336	semidirect
44. C₂×C₄	C₁₃₉⋊C₈	semidirect