Subgroups — #22580751

Order 8896.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984840	C₂	1	1	yes	maximal, characteristic
2	#17984761	C₂	1	1	yes	maximal, characteristic
3	#101×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₇₈	C₄	1	1	yes	characteristic
5	#14555769	—	2	1	no	—
6	Dic₁₃₉⋊C₄	—	2	1	no	—
7	Dic₁₃₉⋊C₄	—	2	1	no	—
8	C₄×Dic₁₃₉	C₄	1	1	yes	characteristic
9	C₂×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
10	M₁₆×C₁₃₉	—	2	1	no	—
11	Dic₂₇₈	—	4	1	no	—
12	C₂×Dic₁₃₉	—	2	1	no	—
13	C₂×Dic₁₃₉	—	2	1	no	—
14	C₁₃₉⋊C₈	—	4	1	no	—
15	Q₈×C₁₃₉	—	4	1	no	—
16	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
19	C₈×C₁₃₉	—	4	1	no	—
20	C₂²×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₃₉	—	2	1	no	—
22	C₄×C₁₃₉	—	2	1	no	—
23	C₄×C₁₃₉	—	2	1	no	—
24	Dic₁₃₉	—	2	2	no	—
25	Dic₁₃₉	—	4	1	no	—
26	C₂×C₁₃₉	—	2	1	no	—
27	C₂×C₁₃₉	#99	1	1	yes	characteristic
28	C₁₃₉	#356	1	1	yes	characteristic, complemented, Sylow
29	#356	—	139	1	no	maximal, Sylow
30	C₄⋊Q₈	—	139	1	no	—
31	#101	—	139	1	no	—
32	#101	D₁₃₉	1	1	yes	characteristic
33	C₂×Q₈	—	139	1	no	—
34	C₂×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
35	M₁₆	—	2	1	no	—
36	M₁₆	—	278	1	no	—
37	C₄⋊C₄	—	278	1	no	—
38	C₄⋊C₄	—	278	1	no	—
39	C₄²	—	139	1	no	—
40	Q₈	—	4	1	no	—
41	Q₈	—	556	1	no	—
42	C₂×C₄	—	278	1	no	—
43	C₂×C₄	—	278	1	no	—
44	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
45	C₂×C₄	C₂²⋊D₁₃₉	1	1	yes	characteristic
46	C₂×C₄	D₅₅₆	1	1	yes	characteristic
47	C₈	—	4	1	no	—
48	C₈	—	556	1	no	—
49	C₂²	(C₂×D₁₃₉)⋊C₄	1	1	yes	characteristic
50	C₄	—	2	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	278	2	no	—
54	C₄	—	556	1	no	—
55	C₂	—	2	1	no	—
56	C₂	#17984756	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17984756
commutator	C₂×C₄×C₁₃₉	C₂×C₄
Frattini	C₂×Q₈	C₂×D₁₃₉
Fitting	#101×C₁₃₉	C₂
socle	C₂×C₁₃₉	#99
hypercenter	#101	D₁₃₉
hypocenter	C₁₃₉	#356
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂²×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #101

Complements

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

N	H ≅ G/N	type
28. C₁₃₉	#356	semidirect