Subgroups — #31807983

Order 17792.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22580981	C₂	1	1	yes	maximal, characteristic
2	#22580724	C₂	1	2	yes	maximal
3	#22580717	C₂	1	2	yes	maximal
4	C₁₃₉⋊#338	C₂	1	1	yes	maximal, characteristic
5	#430×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#14555769	C₂²	1	2	yes	—
7	C₂²×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
8	#17984801	C₂²	1	1	yes	characteristic
9	Dic₁₃₉⋊C₈	—	2	2	no	—
10	C₂×M₁₆×C₁₃₉	C₂²	1	2	yes	—
11	C₂×M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
12	#108×C₁₃₉	—	2	2	no	—
13	#14555769	—	2	2	no	—
14	#14555769	—	2	2	no	—
15	C₂×C₁₃₉⋊C₈	—	2	1	no	—
16	C₂×C₁₃₉⋊C₈	—	2	2	no	—
17	C₂×C₁₃₉⋊C₈	—	2	2	no	—
18	C₄⋊Dic₁₃₉	—	2	1	no	—
19	C₂²⋊Dic₁₃₉	Q₈	1	2	yes	—
20	C₄×Dic₁₃₉	—	2	1	no	—
21	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₁₃₉	—	2	2	no	—
23	M₁₆×C₁₃₉	—	2	2	no	—
24	M₁₆×C₁₃₉	—	2	2	no	—
25	C₂×C₈×C₁₃₉	—	2	2	no	—
26	C₂×C₈×C₁₃₉	D₄	1	2	yes	—
27	C₂×Dic₁₃₉	—	2	2	no	—
28	C₁₃₉⋊C₈	—	4	1	no	—
29	C₁₃₉⋊C₈	—	4	2	no	—
30	C₂³×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₁₃₉	#41	1	2	yes	—
33	C₂×C₄×C₁₃₉	#41	1	2	yes	—
34	C₂×C₄×C₁₃₉	#41	1	1	yes	characteristic
35	C₈×C₁₃₉	—	2	2	no	—
36	C₈×C₁₃₉	—	4	2	no	—
37	C₂²×C₁₃₉	—	4	1	no	—
38	C₂²×C₁₃₉	C₂²⋊Q₈	1	1	yes	characteristic
39	C₂²×C₁₃₉	#125	1	2	yes	—
40	C₄×C₁₃₉	#123	1	1	yes	characteristic
41	C₄×C₁₃₉	#124	1	1	yes	characteristic
42	C₄×C₁₃₉	#126	1	2	yes	—
43	Dic₁₃₉	—	4	2	no	—
44	C₂×C₁₃₉	—	2	1	no	—
45	C₂×C₁₃₉	—	2	2	no	—
46	C₂×C₁₃₉	#400	1	1	yes	characteristic
47	C₁₃₉	#2103	1	1	yes	characteristic, complemented, Sylow
48	#2103	—	139	1	no	maximal, Sylow
49	#430	D₁₃₉	1	1	yes	characteristic
50	#424	—	139	1	no	—
51	#344	—	139	2	no	—
52	#341	—	139	2	no	—
53	#338	—	139	1	no	—
54	C₂×M₁₆	—	139	2	no	—
55	C₂×M₁₆	C₂×D₁₃₉	1	2	yes	—
56	C₂×M₁₆	C₂×D₁₃₉	1	1	yes	characteristic
57	C₂²×C₈	—	139	1	no	—
58	#117	—	139	1	no	—
59	#108	—	2	2	no	—
60	C₄⋊C₈	—	278	2	no	—
61	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	278	2	no	—
66	M₁₆	—	278	2	no	—
67	C₂×C₈	—	2	2	no	—
68	C₂×C₈	—	278	1	no	—
69	C₂×C₈	—	278	2	no	—
70	C₂×C₈	—	278	2	no	—
71	C₂×C₈	C₂²⋊D₁₃₉	1	2	yes	—
72	C₄⋊C₄	—	278	1	no	—
73	C₂²⋊C₄	—	139	2	no	—
74	C₄²	—	278	1	no	—
75	C₂³	Q₈×D₁₃₉	1	1	yes	characteristic
76	C₂×C₄	—	278	2	no	—
77	C₂×C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
78	C₂×C₄	#14555784	1	2	yes	—
79	C₂×C₄	#14555785	1	2	yes	—
80	C₂×C₄	#14555786	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	2	no	—
83	C₈	—	556	1	no	—
84	C₈	—	556	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	#17984818	1	1	yes	characteristic
87	C₂²	#17984832	1	2	yes	—
88	C₄	—	556	2	no	—
89	C₄	#17984825	1	1	yes	characteristic
90	C₄	#17984829	1	1	yes	characteristic
91	C₄	#17984837	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#22580891	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17984829
commutator, cosocle	C₂²×C₄×C₁₃₉	C₂³
Frattini	C₂²×C₄	C₂²×D₁₃₉
Fitting	#430×C₁₃₉	C₂
socle	C₂×C₁₃₉	#400
prime radical	C₂³×C₁₃₉	C₂×Q₈
hypercenter	#430	D₁₃₉
hypocenter	C₁₃₉	#2103
LCS	G ▷ C₂²×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

Complements

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

N	H ≅ G/N	type
47. C₁₃₉	#2103	semidirect

Maximal subgroups

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

subgroup	index
#22580981	2
#22580724	2
#22580717	2
C₁₃₉⋊#338	2
#430×C₁₃₉	2
#2103	139