Subgroups — #22581138

Order 8896.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984890	C₂	1	1	yes	maximal, characteristic
2	#17984875	C₂	1	2	yes	maximal, complemented
3	#17984840	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984768	C₂	1	2	yes	maximal, complemented
5	#101×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14555786	—	2	2	no	—
7	#14555785	—	2	2	no	—
8	#14555785	C₂²	1	2	yes	—
9	C₂×Dic₂₇₈	C₂²	1	1	yes	characteristic
10	Q₈×D₁₃₉	—	2	2	no	—
11	Dic₅₅₆	—	2	2	no	—
12	#14555774	—	2	2	no	—
13	Dic₁₃₉⋊C₄	—	2	2	no	—
14	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
15	C₂×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
16	M₁₆×C₁₃₉	C₂²	1	2	yes	—
17	Dic₂₇₈	—	2	2	no	—
18	Dic₂₇₈	—	2	2	no	—
19	Dic₂₇₈	D₄	1	2	yes	—
20	D₅₅₆	—	2	2	no	—
21	D₅₅₆	D₄	1	2	yes	—
22	C₂²⋊D₁₃₉	—	2	2	no	—
23	C₂×Dic₁₃₉	—	2	1	no	—
24	C₂×Dic₁₃₉	—	2	1	no	—
25	C₄×D₁₃₉	—	2	4	no	—
26	C₄×D₁₃₉	—	2	2	no	—
27	Q₈×C₁₃₉	—	2	2	no	—
28	C₂×C₄×C₁₃₉	D₄	1	2	yes	—
29	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
30	C₈×C₁₃₉	—	2	2	no	—
31	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₃₉	—	2	2	no	—
33	C₄×C₁₃₉	—	2	2	no	—
34	C₄×C₁₃₉	C₂×D₄	1	2	yes	—
35	Dic₁₃₉	—	2	2	no	—
36	Dic₁₃₉	—	2	2	no	—
37	Dic₁₃₉	—	4	1	no	—
38	C₂×C₁₃₉	—	2	1	no	—
39	C₂×C₁₃₉	#120	1	1	yes	characteristic
40	D₁₃₉	—	4	2	no	—
41	C₁₃₉	#456	1	1	yes	characteristic, complemented, Sylow
42	#456	—	139	1	no	maximal, Sylow
43	2₋¹⁺⁴	—	139	1	no	—
44	#137	—	139	2	no	—
45	C₄⋊Q₈	—	139	1	no	—
46	#104	—	139	2	no	—
47	#101	D₁₃₉	1	1	yes	characteristic, complemented
48	#41	—	278	2	no	—
49	#41	—	278	2	no	—
50	#41	—	139	2	no	—
51	C₂×Q₈	—	278	2	no	—
52	C₂×Q₈	—	139	1	no	—
53	C₂×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
54	Q₁₆	—	278	2	no	—
55	SD₁₆	—	278	2	no	—
56	M₁₆	C₂×D₁₃₉	1	2	yes	—
57	C₄⋊C₄	—	278	2	no	—
58	C₄²	—	139	1	no	—
59	Q₈	—	2	2	no	—
60	Q₈	—	278	2	no	—
61	Q₈	—	278	2	no	—
62	Q₈	—	139	2	no	—
63	D₄	—	278	2	no	—
64	D₄	—	278	2	no	—
65	D₄	—	139	2	no	—
66	C₂×C₄	—	278	4	no	—
67	C₂×C₄	—	278	1	no	—
68	C₂×C₄	—	278	2	no	—
69	C₂×C₄	—	278	1	no	—
70	C₂×C₄	D₅₅₆	1	2	yes	—
71	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂²	—	278	2	no	—
74	C₂²	C₂×D₅₅₆	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	278	2	no	—
77	C₄	—	278	2	no	—
78	C₄	—	556	1	no	—
79	C₄	D₄×D₁₃₉	1	2	yes	—
80	C₂	—	2	1	no	—
81	C₂	—	556	2	no	—
82	C₂	#17984812	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17984812
commutator	C₂×C₄×C₁₃₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#101×C₁₃₉	C₂
socle	C₂×C₁₃₉	#120
hypercenter	#101	D₁₃₉
hypocenter	C₁₃₉	#456
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #101

Complements

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

N	H ≅ G/N	type
2. #17984875	C₂	semidirect
3. #17984840	C₂	semidirect
4. #17984768	C₂	semidirect
5. #101×C₁₃₉	C₂	semidirect
41. C₁₃₉	#456	semidirect
47. #101	D₁₃₉	semidirect