Subgroups — #22580706

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	2	yes	maximal
2	C₄×C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃₉⋊C₈	—	2	2	no	—
4	C₂×C₈×C₁₃₉	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₃₉	C₄	1	1	yes	characteristic
6	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
7	C₁₃₉⋊C₈	—	4	2	no	—
8	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
10	C₂×C₄×C₁₃₉	Q₈	1	1	yes	characteristic
11	C₈×C₁₃₉	—	2	1	no	—
12	C₈×C₁₃₉	C₈	1	2	yes	complemented
13	C₂²×C₁₃₉	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₃₉	—	2	1	no	—
15	C₄×C₁₃₉	C₂×C₈	1	1	yes	characteristic
16	C₄×C₁₃₉	M₁₆	1	1	yes	characteristic
17	C₄×C₁₃₉	D₈	1	1	yes	characteristic
18	C₄×C₁₃₉	Q₁₆	1	1	yes	characteristic
19	C₂×C₁₃₉	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₃₉	#107	1	1	yes	characteristic
21	C₂×C₁₃₉	#108	1	1	yes	characteristic
22	C₁₃₉	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	139	1	no	maximal, Sylow
24	C₄⋊C₈	—	139	2	no	—
25	C₄×C₈	D₁₃₉	1	1	yes	characteristic
26	C₂×C₈	—	278	2	no	—
27	C₂×C₈	Dic₁₃₉	1	1	yes	characteristic
28	C₂×C₈	Dic₁₃₉	1	1	yes	characteristic
29	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
30	C₂×C₄	C₂×Dic₁₃₉	1	1	yes	characteristic
31	C₂×C₄	D₅₅₆	1	1	yes	characteristic
32	C₂×C₄	Dic₂₇₈	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	556	2	no	—
35	C₈	C₁₃₉⋊C₈	1	2	yes	complemented
36	C₂²	C₄⋊Dic₁₃₉	1	1	yes	characteristic
37	C₄	—	2	1	no	—
38	C₄	C₂×C₁₃₉⋊C₈	1	1	yes	characteristic
39	C₄	#14555769	1	1	yes	characteristic
40	C₄	D₁₁₁₂	1	1	yes	characteristic
41	C₄	Dic₅₅₆	1	1	yes	characteristic
42	C₂	C₄⋊(C₁₃₉⋊C₈)	1	1	yes	characteristic
43	C₂	#17984776	1	1	yes	characteristic
44	C₂	#17984778	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₅₅₆
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
12. C₈×C₁₃₉	C₈	semidirect
22. C₁₃₉	#335	semidirect
35. C₈	C₁₃₉⋊C₈	semidirect