Subgroups — #31808631

Order 17792.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22581358	C₂	1	1	yes	maximal, characteristic
2	#22580757	C₂	1	4	yes	maximal
3	C₄×C₁₃₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#494×C₁₃₉	C₂	1	1	yes	maximal, characteristic
5	#17984842	—	2	1	no	—
6	C₂×C₁₃₉⋊C₁₆	C₂²	1	2	yes	—
7	#17984776	—	2	1	no	—
8	#17984776	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₁₃₉	—	2	1	no	—
10	C₂×Q₁₆×C₁₃₉	C₂²	1	2	yes	—
11	C₄⋊Q₈×C₁₃₉	—	2	1	no	—
12	C₄×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₂₇₈	—	4	1	no	—
14	C₄⋊Dic₁₃₉	—	2	2	no	—
15	C₄⋊Dic₁₃₉	—	4	1	no	—
16	C₁₃₉⋊C₁₆	—	2	2	no	—
17	C₂×Q₈×C₁₃₉	—	2	2	no	—
18	Q₁₆×C₁₃₉	—	2	4	no	—
19	Q₁₆×C₁₃₉	—	4	2	no	—
20	C₂×C₈×C₁₃₉	D₄	1	1	yes	characteristic
21	C₂×C₈×C₁₃₉	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₁₃₉	—	4	1	no	—
23	C₄⋊C₄×C₁₃₉	—	4	1	no	—
24	C₄²×C₁₃₉	D₄	1	1	yes	characteristic
25	Dic₂₇₈	—	8	2	no	—
26	C₂×Dic₁₃₉	—	4	2	no	—
27	Q₈×C₁₃₉	—	4	2	no	—
28	Q₈×C₁₃₉	—	4	2	no	—
29	C₂×C₄×C₁₃₉	—	4	2	no	—
30	C₂×C₄×C₁₃₉	D₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃₉	D₈	1	1	yes	characteristic
32	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
33	C₈×C₁₃₉	SD₁₆	1	2	yes	—
34	C₈×C₁₃₉	#41	1	2	yes	—
35	C₂²×C₁₃₉	C₂×D₈	1	1	yes	characteristic
36	C₄×C₁₃₉	—	8	2	no	—
37	C₄×C₁₃₉	SD₃₂	1	2	yes	—
38	C₄×C₁₃₉	Q₃₂	1	2	yes	—
39	C₄×C₁₃₉	#124	1	1	yes	characteristic
40	C₄×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
41	Dic₁₃₉	—	8	2	no	—
42	C₂×C₁₃₉	#486	1	1	yes	characteristic
43	C₂×C₁₃₉	C₂×SD₃₂	1	1	yes	characteristic
44	C₂×C₁₃₉	C₂×Q₃₂	1	1	yes	characteristic
45	C₁₃₉	#2241	1	1	yes	characteristic, complemented, Sylow
46	#2241	—	139	1	no	maximal, Sylow
47	#500	—	139	1	no	—
48	#494	D₁₃₉	1	1	yes	characteristic
49	#358	—	139	4	no	—
50	C₄×C₁₆	—	139	1	no	—
51	C₂×Q₁₆	—	2	1	no	—
52	C₂×Q₁₆	C₂×D₁₃₉	1	2	yes	—
53	C₄⋊Q₈	—	2	1	no	—
54	C₄⋊Q₈	—	278	1	no	—
55	C₂×C₁₆	—	139	2	no	—
56	#107	—	278	1	no	—
57	#107	—	139	2	no	—
58	C₄×C₈	C₂×D₁₃₉	1	1	yes	characteristic
59	C₂×Q₈	—	2	2	no	—
60	C₂×Q₈	—	556	1	no	—
61	Q₁₆	—	2	4	no	—
62	Q₁₆	—	4	2	no	—
63	C₂×C₈	C₂²⋊D₁₃₉	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₁₃₉	1	1	yes	characteristic
65	C₄⋊C₄	—	4	1	no	—
66	C₄⋊C₄	—	4	1	no	—
67	C₄⋊C₄	—	278	2	no	—
68	C₄⋊C₄	—	556	1	no	—
69	C₄²	C₂²⋊D₁₃₉	1	1	yes	characteristic
70	C₁₆	—	278	2	no	—
71	Q₈	—	4	2	no	—
72	Q₈	—	4	2	no	—
73	Q₈	—	1112	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	—	556	2	no	—
76	C₂×C₄	#14555770	1	1	yes	characteristic
77	C₂×C₄	#14555770	1	1	yes	characteristic
78	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
79	C₈	#14555773	1	2	yes	—
80	C₈	#14555784	1	2	yes	—
81	C₂²	C₂×#14555770	1	1	yes	characteristic
82	C₄	—	8	2	no	—
83	C₄	—	1112	2	no	—
84	C₄	#17984785	1	2	yes	—
85	C₄	#17984788	1	2	yes	—
86	C₄	#17984829	1	1	yes	characteristic
87	C₄	C₂×#14555773	1	1	yes	characteristic
88	C₂	#22581299	1	1	yes	characteristic
89	C₂	C₂×#17984785	1	1	yes	characteristic
90	C₂	C₂×#17984788	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14555770
commutator, cosocle	C₂×C₈×C₁₃₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₃₉
Fitting	#494×C₁₃₉	C₂
socle, prime radical	C₂²×C₁₃₉	C₂×D₈
hypercenter	#494	D₁₃₉
hypocenter	C₁₃₉	#2241
LCS	G ▷ C₂×C₈×C₁₃₉ ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
45. C₁₃₉	#2241	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22581358	2
#22580757	2
C₄×C₁₃₉⋊C₁₆	2
#494×C₁₃₉	2
#2241	139