Subgroups — #22580976

Order 8896.

126 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	Dic₁₃₉⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₃₉	C₄	1	2	yes	—
6	#14555769	—	2	2	no	—
7	C₂×C₁₃₉⋊C₈	C₂²	1	2	yes	—
8	C₄×Dic₁₃₉	C₄	1	1	yes	characteristic
9	C₄×Dic₁₃₉	C₄	1	1	yes	characteristic
10	C₄×Dic₁₃₉	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
12	M₁₆×C₁₃₉	—	2	2	no	—
13	C₂×C₈×C₁₃₉	C₂²	1	2	yes	—
14	C₂×Dic₁₃₉	—	2	4	no	—
15	C₂×Dic₁₃₉	C₂×C₄	1	2	yes	—
16	C₂×Dic₁₃₉	C₂×C₄	1	2	yes	—
17	C₁₃₉⋊C₈	—	2	2	no	—
18	C₂³×C₁₃₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₃₉	D₄	1	2	yes	—
21	C₂×C₄×C₁₃₉	Q₈	1	2	yes	—
22	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
23	C₈×C₁₃₉	—	2	2	no	—
24	C₂²×C₁₃₉	—	2	2	no	—
25	C₂²×C₁₃₉	C₄⋊C₄	1	2	yes	—
26	C₂²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₁₃₉	C₄⋊C₄	1	2	yes	—
28	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
29	C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
30	Dic₁₃₉	—	2	2	no	—
31	Dic₁₃₉	M₁₆	1	4	yes	complemented
32	C₂×C₁₃₉	—	2	2	no	—
33	C₂×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₁₃₉	C₂×M₁₆	1	2	yes	—
35	C₁₃₉	#423	1	1	yes	characteristic, complemented, Sylow
36	#423	—	139	1	no	maximal, Sylow
37	C₂×M₁₆	—	139	1	no	—
38	C₂×M₁₆	D₁₃₉	1	1	yes	characteristic
39	C₂×C₄²	—	139	1	no	—
40	C₄⋊C₈	—	139	4	no	—
41	C₂²×C₄	—	139	2	no	—
42	C₂²×C₄	C₂×D₁₃₉	1	1	yes	characteristic
43	M₁₆	—	2	2	no	—
44	M₁₆	—	278	2	no	—
45	C₂×C₈	—	139	2	no	—
46	C₂×C₈	C₂×D₁₃₉	1	2	yes	—
47	C₄²	—	139	1	no	—
48	C₄²	—	139	1	no	—
49	C₄²	—	139	2	no	—
50	C₂³	C₄×D₁₃₉	1	1	yes	characteristic
51	C₂×C₄	—	278	4	no	—
52	C₂×C₄	—	139	2	no	—
53	C₂×C₄	—	139	2	no	—
54	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
55	C₂×C₄	C₂²⋊D₁₃₉	1	2	yes	—
56	C₂×C₄	Dic₂₇₈	1	2	yes	—
57	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
58	C₈	—	2	2	no	—
59	C₈	—	278	2	no	—
60	C₂²	—	2	2	no	—
61	C₂²	Dic₁₃₉⋊C₄	1	2	yes	—
62	C₂²	C₂×C₄×D₁₃₉	1	1	yes	characteristic
63	C₄	—	278	2	no	—
64	C₄	—	139	4	no	—
65	C₄	Dic₁₃₉⋊C₄	1	2	yes	—
66	C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
67	C₄	C₂×Dic₂₇₈	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	C₂×Dic₁₃₉⋊C₄	1	1	yes	characteristic
70	C₂	M₁₆×D₁₃₉	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₃₉
commutator, socle	C₂²×C₁₃₉	C₂²×C₄
Fitting	C₂×M₁₆×C₁₃₉	C₂
hypercenter	C₂×M₁₆	D₁₃₉
hypocenter	C₁₃₉	#423
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. Dic₁₃₉⋊C₈	C₂	semidirect
31. Dic₁₃₉	M₁₆	semidirect
35. C₁₃₉	#423	semidirect