Subgroups — #22580996

Order 8896.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555769	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#17984775	C₂	1	2	yes	maximal, complemented
4	#17984773	C₂	1	2	yes	maximal, complemented
5	#117×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₃₉	—	2	1	no	—
7	#14555769	C₄	1	4	yes	complemented
8	C₂×C₁₃₉⋊C₈	C₂²	1	2	yes	—
9	C₄⋊Dic₁₃₉	—	2	1	no	—
10	C₄⋊Dic₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
15	C₄²×C₁₃₉	—	2	1	no	—
16	C₂×Dic₁₃₉	—	2	2	no	—
17	C₂×Dic₁₃₉	—	4	2	no	—
18	C₁₃₉⋊C₈	C₂×C₄	1	4	yes	complemented
19	C₂³×C₁₃₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₃₉	—	2	1	no	—
21	C₂×C₄×C₁₃₉	—	2	1	no	—
22	C₂×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
23	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₃₉	Q₈	1	2	yes	—
25	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
26	C₂²×C₁₃₉	—	2	1	no	—
27	C₂²×C₁₃₉	—	2	1	no	—
28	C₂²×C₁₃₉	C₄⋊C₄	1	2	yes	—
29	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
30	C₄×C₁₃₉	—	4	1	no	—
31	C₄×C₁₃₉	—	4	1	no	—
32	C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
33	C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
34	C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
35	Dic₁₃₉	—	4	2	no	—
36	C₂×C₁₃₉	—	2	2	no	—
37	C₂×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
39	C₂×C₁₃₉	#137	1	1	yes	characteristic
40	C₁₃₉	#428	1	1	yes	characteristic, complemented, Sylow
41	#428	—	139	1	no	maximal, Sylow
42	C₂×M₁₆	—	139	1	no	—
43	#117	D₁₃₉	1	1	yes	characteristic
44	C₂×C₄⋊C₄	—	139	1	no	—
45	#107	—	139	2	no	—
46	#106	—	139	2	no	—
47	C₂²×C₄	—	278	1	no	—
48	C₂²×C₄	C₂×D₁₃₉	1	1	yes	characteristic
49	M₁₆	—	139	4	no	—
50	C₂×C₈	—	139	2	no	—
51	C₄⋊C₄	—	278	1	no	—
52	C₄⋊C₄	—	139	2	no	—
53	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
54	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
55	C₂²⋊C₄	—	2	1	no	—
56	C₄²	—	2	1	no	—
57	C₂³	C₂²⋊D₁₃₉	1	1	yes	characteristic
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	278	2	no	—
61	C₂×C₄	—	556	2	no	—
62	C₂×C₄	C₄×D₁₃₉	1	2	yes	—
63	C₂×C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
64	C₂×C₄	Dic₂₇₈	1	2	yes	—
65	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
66	C₈	—	139	4	no	—
67	C₂²	—	2	1	no	—
68	C₂²	—	2	1	no	—
69	C₂²	Dic₁₃₉⋊C₄	1	2	yes	—
70	C₂²	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	556	2	no	—
74	C₄	Dic₁₃₉⋊C₄	1	2	yes	—
75	C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
76	C₄	C₂×Dic₂₇₈	1	1	yes	characteristic
77	C₂	—	2	2	no	—
78	C₂	C₂×Dic₁₃₉⋊C₄	1	1	yes	characteristic
79	C₂	#17984867	1	1	yes	characteristic
80	C₂	#17984872	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₃₉
commutator	C₄×C₁₃₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#117×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#117	D₁₃₉
hypocenter	C₁₃₉	#428
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #17984775	C₂	semidirect
4. #17984773	C₂	semidirect
7. #14555769	C₄	semidirect
18. C₁₃₉⋊C₈	C₂×C₄	semidirect
40. C₁₃₉	#428	semidirect