Subgroups — #22580770

Order 8896.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₅₅₆	C₂	1	1	yes	maximal, characteristic
2	#17984778	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₇₈	—	2	1	no	—
5	Dic₅₅₆	—	2	1	no	—
6	Dic₅₅₆	C₄	1	2	yes	—
7	#14555769	—	2	1	no	—
8	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₁₆×C₁₃₉	—	2	1	no	—
10	Dic₂₇₈	—	2	2	no	—
11	Dic₂₇₈	—	4	1	no	—
12	C₂×Dic₁₃₉	—	4	1	no	—
13	C₁₃₉⋊C₈	—	4	1	no	—
14	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
15	C₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
16	C₈×C₁₃₉	D₄	1	1	yes	characteristic
17	C₂²×C₁₃₉	SD₁₆	1	1	yes	characteristic
18	C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₃₉	D₈	1	1	yes	characteristic
20	Dic₁₃₉	—	4	2	no	—
21	C₂×C₁₃₉	—	2	1	no	—
22	C₂×C₁₃₉	#102	1	1	yes	characteristic
23	C₁₃₉	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	139	1	no	maximal, Sylow
25	C₂×Q₁₆	—	139	1	no	—
26	M₃₂	D₁₃₉	1	1	yes	characteristic
27	#108	—	139	1	no	—
28	C₂×Q₈	—	278	1	no	—
29	Q₁₆	—	278	1	no	—
30	Q₁₆	—	139	2	no	—
31	M₁₆	—	278	1	no	—
32	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
33	C₁₆	—	2	1	no	—
34	Q₈	—	278	2	no	—
35	Q₈	—	556	1	no	—
36	C₂×C₄	—	556	1	no	—
37	C₂×C₄	D₅₅₆	1	1	yes	characteristic
38	C₈	—	556	1	no	—
39	C₈	C₄×D₁₃₉	1	1	yes	characteristic
40	C₈	C₂²⋊D₁₃₉	1	1	yes	characteristic
41	C₂²	#14555774	1	1	yes	characteristic
42	C₄	—	556	2	no	—
43	C₄	(C₂×D₁₃₉)⋊C₄	1	1	yes	characteristic
44	C₄	D₁₁₁₂	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#17984764	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17984764
commutator	C₈×C₁₃₉	C₂×C₄
Frattini	C₂×C₈	C₂×D₁₃₉
Fitting	M₃₂×C₁₃₉	C₂
socle	C₂×C₁₃₉	#102
hypercenter	M₃₂	D₁₃₉
hypocenter	C₁₃₉	#362
LCS	G ▷ C₈×C₁₃₉ ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
23. C₁₃₉	#362	semidirect