Subgroups — #22580705

Order 8896.

54 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	—	2	1	no	—
5	C₂×C₁₃₉⋊C₈	C₄	1	1	yes	characteristic
6	C₂×C₁₃₉⋊C₈	C₄	1	1	yes	characteristic
7	C₂×C₈×C₁₃₉	—	2	1	no	—
8	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₁₃₉⋊C₈	—	2	1	no	—
10	C₁₃₉⋊C₈	—	4	1	no	—
11	C₁₃₉⋊C₈	C₈	1	2	yes	complemented
12	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
14	C₂×C₄×C₁₃₉	Q₈	1	1	yes	characteristic
15	C₈×C₁₃₉	—	4	1	no	—
16	C₂²×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
17	C₄×C₁₃₉	—	2	1	no	—
18	C₄×C₁₃₉	C₂×C₈	1	1	yes	characteristic
19	C₄×C₁₃₉	M₁₆	1	1	yes	characteristic
20	C₄×C₁₃₉	D₈	1	1	yes	characteristic
21	C₄×C₁₃₉	Q₁₆	1	1	yes	characteristic
22	C₂×C₁₃₉	C₄⋊C₈	1	1	yes	characteristic
23	C₂×C₁₃₉	#107	1	1	yes	characteristic
24	C₂×C₁₃₉	#108	1	1	yes	characteristic
25	C₁₃₉	#335	1	1	yes	characteristic, complemented, Sylow
26	#335	—	139	1	no	maximal, Sylow
27	C₄⋊C₈	—	139	1	no	—
28	C₄⋊C₈	D₁₃₉	1	1	yes	characteristic
29	C₄×C₈	—	139	1	no	—
30	C₂×C₈	—	2	1	no	—
31	C₂×C₈	—	278	1	no	—
32	C₂×C₈	—	139	1	no	—
33	C₂×C₈	—	139	1	no	—
34	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
35	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
36	C₂×C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
37	C₂×C₄	Dic₂₇₈	1	1	yes	characteristic
38	C₈	—	4	1	no	—
39	C₈	—	278	1	no	—
40	C₈	—	556	1	no	—
41	C₈	—	139	2	no	—
42	C₂²	Dic₁₃₉⋊C₄	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	C₈×D₁₃₉	1	1	yes	characteristic
45	C₄	#14555768	1	1	yes	characteristic
46	C₄	#14555770	1	1	yes	characteristic
47	C₄	#14555775	1	1	yes	characteristic
48	C₂	Dic₁₃₉⋊C₈	1	1	yes	characteristic
49	C₂	#17984775	1	1	yes	characteristic
50	C₂	#17984777	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₃₉
commutator	C₄×C₁₃₉	C₂×C₈
Frattini	C₄²	C₂×D₁₃₉
Fitting	C₄⋊C₈×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₄⋊C₄
hypercenter	C₄⋊C₈	D₁₃₉
hypocenter	C₁₃₉	#335
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
11. C₁₃₉⋊C₈	C₈	semidirect
25. C₁₃₉	#335	semidirect