Group #31814679 — subgroups

Subgroups — #31814679

Order 17792.

340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22580887	C₂	1	4	yes	maximal
2	#22580886	C₂	1	4	yes	maximal
3	#22580885	C₂	1	4	yes	maximal
4	#22580819	C₂	1	2	yes	maximal
5	#382×C₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₁₃₉	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₁₃₉	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₁₃₉	C₂²	1	4	yes	—
9	C₂×Dic₁₃₉⋊C₄	C₂²	1	4	yes	—
10	C₂×Dic₁₃₉⋊C₄	C₂²	1	4	yes	—
11	C₁₃₉⋊#95	C₂²	1	4	yes	—
12	C₁₃₉⋊#95	C₂²	1	4	yes	—
13	C₁₃₉⋊#95	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
16	#95×C₁₃₉	C₂²	1	4	yes	—
17	C₂²×Dic₁₃₉	C₂³	1	4	yes	—
18	C₂²×Dic₁₃₉	C₂³	1	4	yes	—
19	C₄⋊Dic₁₃₉	—	4	2	no	—
20	C₄⋊Dic₁₃₉	—	4	2	no	—
21	C₄⋊Dic₁₃₉	—	4	4	no	—
22	Dic₁₃₉⋊C₄	—	4	4	no	—
23	Dic₁₃₉⋊C₄	—	4	4	no	—
24	C₂²×C₄×C₁₃₉	C₂³	1	4	yes	—
25	C₂²×C₄×C₁₃₉	C₂³	1	2	yes	—
26	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
27	C₄⋊C₄×C₁₃₉	—	4	2	no	—
28	C₄²×C₁₃₉	Q₈	1	4	yes	—
29	C₂×Dic₁₃₉	—	2	4	no	—
30	C₂×Dic₁₃₉	—	2	4	no	—
31	C₂×Dic₁₃₉	—	2	4	no	—
32	C₂×Dic₁₃₉	—	2	4	no	—
33	C₂×Dic₁₃₉	—	2	4	no	—
34	C₂×Dic₁₃₉	—	2	4	no	—
35	C₂³×C₁₃₉	C₂⁴	1	1	yes	characteristic
36	C₂×C₄×C₁₃₉	—	2	1	no	—
37	C₂×C₄×C₁₃₉	—	2	2	no	—
38	C₂×C₄×C₁₃₉	—	2	2	no	—
39	C₂×C₄×C₁₃₉	—	2	1	no	—
40	C₂×C₄×C₁₃₉	—	2	4	no	—
41	C₂×C₄×C₁₃₉	—	2	4	no	—
42	C₂×C₄×C₁₃₉	—	2	4	no	—
43	C₂×C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
44	C₂×C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
45	C₂²×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
46	C₂²×C₁₃₉	H(5,𝔽₂)	1	1	yes	characteristic
47	C₂²×C₁₃₉	H(5,𝔽₂)	1	2	yes	—
48	C₂²×C₁₃₉	2₋¹⁺⁴	1	2	yes	—
49	C₂²×C₁₃₉	2₋¹⁺⁴	1	1	yes	characteristic
50	C₄×C₁₃₉	—	2	4	no	—
51	C₄×C₁₃₉	—	2	2	no	—
52	C₄×C₁₃₉	—	4	4	no	—
53	Dic₁₃₉	—	4	4	no	—
54	Dic₁₃₉	—	4	4	no	—
55	C₂×C₁₃₉	#544	1	2	yes	—
56	C₂×C₁₃₉	#544	1	1	yes	characteristic
57	C₂×C₁₃₉	#562	1	2	yes	—
58	C₂×C₁₃₉	#562	1	1	yes	characteristic
59	C₂×C₁₃₉	#564	1	1	yes	characteristic
60	C₁₃₉	#2845	1	1	yes	characteristic, complemented, Sylow
61	#2845	—	139	1	no	maximal, Sylow
62	#398	—	139	4	no	—
63	#398	—	139	4	no	—
64	#398	—	139	4	no	—
65	#382	—	139	2	no	—
66	#382	D₁₃₉	1	1	yes	characteristic
67	C₂×C₄⋊C₄	—	139	4	no	—
68	C₂×C₄⋊C₄	—	139	4	no	—
69	C₂×C₄⋊C₄	—	139	2	no	—
70	C₂×C₄⋊C₄	—	139	2	no	—
71	C₂×C₄⋊C₄	—	139	4	no	—
72	C₂×C₄⋊C₄	C₂×D₁₃₉	1	2	yes	—
73	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
74	#95	—	139	4	no	—
75	#95	—	139	4	no	—
76	#95	—	139	4	no	—
77	#95	C₂×D₁₃₉	1	4	yes	—
78	C₂²×C₄	—	139	4	no	—
79	C₂²×C₄	—	139	4	no	—
80	C₂²×C₄	C₂²×D₁₃₉	1	4	yes	—
81	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₁₃₉	1	2	yes	—
83	C₄⋊C₄	—	4	2	no	—
84	C₄⋊C₄	—	556	4	no	—
85	C₄⋊C₄	—	556	4	no	—
86	C₄⋊C₄	—	556	2	no	—
87	C₄⋊C₄	—	556	2	no	—
88	C₄⋊C₄	—	556	4	no	—
89	C₄²	Dic₂₇₈	1	4	yes	—
90	C₂³	C₂³×D₁₃₉	1	1	yes	characteristic
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	2	2	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	4	no	—
98	C₂×C₄	—	278	4	no	—
99	C₂×C₄	—	278	4	no	—
100	C₂×C₄	—	278	4	no	—
101	C₂×C₄	—	278	4	no	—
102	C₂×C₄	—	278	4	no	—
103	C₂×C₄	—	278	4	no	—
104	C₂×C₄	C₂×Dic₂₇₈	1	4	yes	—
105	C₂×C₄	C₂×Dic₂₇₈	1	2	yes	—
106	C₂²	C₂²×Dic₂₇₈	1	1	yes	characteristic
107	C₂²	#17984887	1	1	yes	characteristic
108	C₂²	#17984888	1	2	yes	—
109	C₂²	#17984889	1	2	yes	—
110	C₂²	#17984890	1	1	yes	characteristic
111	C₄	—	2	4	no	—
112	C₄	—	2	2	no	—
113	C₄	—	4	4	no	—
114	C₄	—	556	4	no	—
115	C₄	—	556	4	no	—
116	C₂	#22581581	1	2	yes	—
117	C₂	#22581584	1	1	yes	characteristic
118	C₂	#22581697	1	2	yes	—
119	C₂	#22581701	1	1	yes	characteristic
120	C₂	C₁₃₉⋊#564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22580887

C₂

yes

maximal

#22580886

C₂

yes

maximal

#22580885

C₂

yes

maximal

#22580819

C₂

yes

maximal

#382×C₁₃₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₁₃₉

C₂²

yes

—

C₂×C₄⋊Dic₁₃₉

C₂²

yes

—

C₂×C₄⋊Dic₁₃₉

C₂²

yes

—

C₂×Dic₁₃₉⋊C₄

C₂²

yes

—

C₂×Dic₁₃₉⋊C₄

C₂²

yes

—

C₁₃₉⋊#95

C₂²

yes

—

C₁₃₉⋊#95

C₂²

yes

—

C₁₃₉⋊#95

C₂²

yes

—

C₂×C₄⋊C₄×C₁₃₉

C₂²

yes

—

C₂×C₄²×C₁₃₉

C₂²

yes

characteristic

#95×C₁₃₉

C₂²

yes

—

C₂²×Dic₁₃₉

C₂³

yes

—

C₂²×Dic₁₃₉

C₂³

yes

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

Dic₁₃₉⋊C₄

—

Dic₁₃₉⋊C₄

—

C₂²×C₄×C₁₃₉

C₂³

yes

—

C₂²×C₄×C₁₃₉

C₂³

yes

—

C₂²×C₄×C₁₃₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

Q₈

yes

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂³×C₁₃₉

C₂⁴

yes

characteristic

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂×Q₈

yes

—

C₂×C₄×C₁₃₉

C₂×Q₈

yes

—

C₂²×C₁₃₉

C₂²×Q₈

yes

C₂²×C₁₃₉

yes

C₂²×C₁₃₉

yes

—

C₂²×C₁₃₉

2₋¹⁺⁴

yes

—

C₂²×C₁₃₉

2₋¹⁺⁴

yes

characteristic

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

C₂×C₁₃₉

#544

yes

—

C₂×C₁₃₉

#544

yes

characteristic

C₂×C₁₃₉

#562

yes

—

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

C₁₃₉

yes

characteristic, complemented, Sylow

#2845

—

139

maximal, Sylow

#398

—

139

—

#398

—

139

—

#398

—

139

—

#382

—

139

—

#382

D₁₃₉

yes

characteristic

C₂×C₄⋊C₄

—

139

—

C₂×C₄⋊C₄

—

139

—

C₂×C₄⋊C₄

—

139

—

C₂×C₄⋊C₄

—

139

—

C₂×C₄⋊C₄

—

139

—

C₂×C₄⋊C₄

C₂×D₁₃₉

yes

—

C₂×C₄²

C₂×D₁₃₉

yes

characteristic

#95

—

139

—

#95

—

139

—

#95

—

139

—

#95

C₂×D₁₃₉

yes

—

C₂²×C₄

—

139

—

C₂²×C₄

—

139

—

C₂²×C₄

C₂²×D₁₃₉

yes

—

C₂²×C₄

C₂²×D₁₃₉

yes

characteristic

C₂²×C₄

C₂²×D₁₃₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

556

—

C₄⋊C₄

—

556

—

C₄⋊C₄

—

556

—

C₄⋊C₄

—

556

—

C₄⋊C₄

—

556

—

C₄²

Dic₂₇₈

yes

—

C₂³

C₂³×D₁₃₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

100

C₂×C₄

—

278

—

101

C₂×C₄

—

278

—

102

C₂×C₄

—

278

—

103

C₂×C₄

—

278

—

104

C₂×C₄

C₂×Dic₂₇₈

yes

—

105

C₂×C₄

C₂×Dic₂₇₈

yes

—

106

C₂²

C₂²×Dic₂₇₈

yes

characteristic

107

C₂²

#17984887

yes

characteristic

108

C₂²

#17984888

yes

—

109

C₂²

#17984889

yes

—

110

C₂²

#17984890

yes

characteristic

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

556

—

115

C₄

—

556

—

116

C₂

#22581581

yes

—

117

C₂

#22581584

yes

characteristic

118

C₂

#22581697

yes

—

119

C₂

#22581701

yes

characteristic

120

C₂

C₁₃₉⋊#564

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₃₉
commutator, socle, prime radical, cosocle	C₂³×C₁₃₉	C₂⁴
Fitting	#382×C₁₃₉	C₂
hypercenter	#382	D₁₃₉
hypocenter	C₁₃₉	#2845
LCS	G ▷ C₂³×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ #382

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₃₉

commutator, socle, prime radical, cosocle

C₂³×C₁₃₉

C₂⁴

Fitting

#382×C₁₃₉

C₂

D₁₃₉

C₁₃₉

G ▷ C₂³×C₁₃₉ ▷ C₁₃₉

C₁ ◁ C₂³ ◁ #382

N	H ≅ G/N	type
60. C₁₃₉	#2845	semidirect

H ≅ G/N

type

60. C₁₃₉

#2845

semidirect

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

subgroup	index
#22580887	2
#22580886	2
#22580885	2
#22580819	2
#382×C₁₃₉	2
#2845	139

subgroup

index

#382×C₁₃₉

139

Subgroups — #31814679

Conjugacy classes of subgroups

Complements

Maximal subgroups