Subgroups — #22581353

Order 8896.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984833	C₂	1	2	yes	maximal
2	#17984775	C₂	1	2	yes	maximal
3	#17984774	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#106×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₃₉	—	2	2	no	—
8	C₄⋊Dic₁₃₉	C₂²	1	2	yes	—
9	Dic₁₃₉⋊C₄	—	2	2	no	—
10	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
11	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
13	C₂×Dic₁₃₉	—	2	2	no	—
14	C₂×Dic₁₃₉	D₄	1	2	yes	—
15	C₁₃₉⋊C₈	Q₈	1	2	yes	—
16	C₂×C₄×C₁₃₉	—	2	2	no	—
17	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
18	C₈×C₁₃₉	Q₈	1	2	yes	—
19	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
20	C₄×C₁₃₉	—	4	2	no	—
21	C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
22	C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
23	Dic₁₃₉	—	2	2	no	—
24	Dic₁₃₉	—	4	2	no	—
25	C₂×C₁₃₉	C₄⋊Q₈	1	1	yes	characteristic
26	C₂×C₁₃₉	#135	1	2	yes	—
27	C₁₃₉	#499	1	1	yes	characteristic, complemented, Sylow
28	#499	—	139	1	no	maximal, Sylow
29	#125	—	139	2	no	—
30	#107	—	139	2	no	—
31	#106	—	139	1	no	—
32	#106	D₁₃₉	1	1	yes	characteristic
33	C₄×C₈	—	139	1	no	—
34	C₂×C₈	—	139	1	no	—
35	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
36	C₄⋊C₄	—	278	2	no	—
37	C₄⋊C₄	—	278	2	no	—
38	C₄⋊C₄	—	139	2	no	—
39	C₄⋊C₄	C₂×D₁₃₉	1	2	yes	—
40	C₄²	—	139	1	no	—
41	C₂×C₄	—	2	2	no	—
42	C₂×C₄	—	278	2	no	—
43	C₂×C₄	—	139	2	no	—
44	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
45	C₈	—	139	2	no	—
46	C₈	Dic₂₇₈	1	2	yes	—
47	C₂²	D₄×D₁₃₉	1	1	yes	characteristic
48	C₄	—	4	2	no	—
49	C₄	—	278	2	no	—
50	C₄	—	556	2	no	—
51	C₄	Q₈×D₁₃₉	1	1	yes	characteristic
52	C₄	C₂×Dic₂₇₈	1	1	yes	characteristic
53	C₂	#17984841	1	1	yes	characteristic
54	C₂	#17984863	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₃₉
commutator	C₂×C₄×C₁₃₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#106×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#106	D₁₃₉
hypocenter	C₁₃₉	#499
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
27. C₁₃₉	#499	semidirect