Group #49095476 — subgroups

Subgroups — #49095476

Order 35968.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂×#22582815	C₂	1	1	yes	maximal, characteristic
2	C₂×#22582814	C₂	1	2	yes	maximal
3	#31823486	C₂	1	2	yes	maximal
4	C₂×#22582789	C₂	1	1	yes	maximal, characteristic
5	C₂×#108×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#17985122	C₂²	1	2	yes	—
7	C₂²×#14555886	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₈₁	C₂²	1	1	yes	characteristic
9	#22582815	—	2	2	no	—
10	#22582814	—	2	4	no	—
11	#22582808	—	2	4	no	—
12	#22582789	C₄	1	4	yes	—
13	C₂×M₁₆×C₂₈₁	C₂²	1	2	yes	—
14	C₂²×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
15	#108×C₂₈₁	—	2	2	no	—
16	C₂²×Dic₂₈₁	Q₈	1	2	yes	—
17	#17985122	—	2	2	no	—
18	#17985122	—	2	2	no	—
19	C₂×#14555886	—	2	2	no	—
20	C₂×#14555886	C₂×C₄	1	2	yes	—
21	C₂×#14555886	D₄	1	2	yes	—
22	C₂×#14555886	Q₈	1	2	yes	—
23	C₄×Dic₂₈₁	C₂×C₄	1	2	yes	—
24	C₄×Dic₂₈₁	D₄	1	2	yes	—
25	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
26	M₁₆×C₂₈₁	—	2	2	no	—
27	M₁₆×C₂₈₁	—	2	2	no	—
28	C₂×C₈×C₂₈₁	—	2	2	no	—
29	C₂×C₈×C₂₈₁	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₂₈₁	D₄	1	2	yes	—
31	C₂×C₈×C₂₈₁	Q₈	1	2	yes	—
32	C₂×Dic₂₈₁	—	4	2	no	—
33	C₂×Dic₂₈₁	C₄⋊C₄	1	4	yes	—
34	#14555886	—	4	2	no	—
35	#14555886	C₄⋊C₄	1	4	yes	—
36	C₂³×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₈₁	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
43	C₈×C₂₈₁	—	4	2	no	—
44	C₈×C₂₈₁	C₄⋊C₄	1	4	yes	—
45	C₂²×C₂₈₁	—	2	2	no	—
46	C₂²×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
48	C₂²×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
49	C₄×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₂₈₁	#127	1	1	yes	characteristic
52	C₄×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
53	Dic₂₈₁	—	2	4	no	—
54	C₂×C₂₈₁	—	2	1	no	—
55	C₂×C₂₈₁	—	2	1	no	—
56	C₂×C₂₈₁	#384	1	1	yes	characteristic
57	C₂×C₂₈₁	#430	1	2	yes	—
58	C₂₈₁	#1849	1	1	yes	characteristic, complemented, Sylow
59	#1849	—	281	1	no	maximal, Sylow
60	C₂×#108	—	281	2	no	—
61	C₂×#108	—	281	1	no	—
62	C₂×#108	D₂₈₁	1	1	yes	characteristic
63	#423	—	281	2	no	—
64	C₂×#97	—	281	1	no	—
65	C₂×M₁₆	—	281	2	no	—
66	C₂×M₁₆	C₂×D₂₈₁	1	2	yes	—
67	C₂²×C₈	—	281	1	no	—
68	C₂²×C₈	C₂×D₂₈₁	1	1	yes	characteristic
69	C₂×C₄²	—	281	1	no	—
70	#108	—	2	2	no	—
71	#108	—	562	4	no	—
72	#108	—	562	2	no	—
73	C₄⋊C₈	—	562	4	no	—
74	#97	—	281	4	no	—
75	C₂²×C₄	—	281	2	no	—
76	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	562	2	no	—
80	M₁₆	—	562	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	281	2	no	—
83	C₂×C₈	—	281	2	no	—
84	C₂×C₈	—	281	2	no	—
85	C₂×C₈	—	562	2	no	—
86	C₂×C₈	C₄×D₂₈₁	1	2	yes	—
87	C₂×C₈	C₂²⋊D₂₈₁	1	2	yes	—
88	C₂×C₈	Dic₅₆₂	1	2	yes	—
89	C₄²	—	281	2	no	—
90	C₄²	—	281	2	no	—
91	C₂³	Q₈×D₂₈₁	1	1	yes	characteristic
92	C₂×C₄	—	281	4	no	—
93	C₂×C₄	—	1124	2	no	—
94	C₂×C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
95	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
96	C₂×C₄	D₄×D₂₈₁	1	1	yes	characteristic
97	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₂₈₁	1	1	yes	characteristic
99	C₂×C₄	C₂×Dic₅₆₂	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	281	4	no	—
102	C₈	—	1124	2	no	—
103	C₈	#17985117	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	C₄⋊C₄×D₂₈₁	1	1	yes	characteristic
106	C₂²	#22582877	1	1	yes	characteristic
107	C₂²	#22582878	1	1	yes	characteristic
108	C₄	—	562	4	no	—
109	C₄	C₄⋊C₄×D₂₈₁	1	1	yes	characteristic
110	C₄	C₂×#17985117	1	1	yes	characteristic
111	C₄	#22582875	1	1	yes	characteristic
112	C₄	#22582878	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#31823332	1	1	yes	characteristic
116	C₂	#31823510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22582815

C₂

yes

maximal, characteristic

C₂×#22582814

C₂

yes

maximal

#31823486

C₂

yes

maximal

C₂×#22582789

C₂

yes

maximal, characteristic

C₂×#108×C₂₈₁

C₂

yes

maximal, characteristic

C₂×#17985122

C₂²

yes

—

C₂²×#14555886

C₂²

yes

characteristic

C₂×C₄×Dic₂₈₁

C₂²

yes

—

—

—

C₄

yes

—

C₂×M₁₆×C₂₈₁

C₂²

yes

—

C₂²×C₈×C₂₈₁

C₂²

yes

characteristic

#108×C₂₈₁

—

C₂²×Dic₂₈₁

Q₈

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#14555886

D₄

yes

—

C₂×#14555886

Q₈

yes

—

C₄×Dic₂₈₁

C₂×C₄

yes

—

C₄×Dic₂₈₁

D₄

yes

—

C₂²×C₄×C₂₈₁

C₂³

yes

characteristic

M₁₆×C₂₈₁

—

M₁₆×C₂₈₁

—

C₂×C₈×C₂₈₁

—

C₂×C₈×C₂₈₁

C₂×C₄

yes

—

C₂×C₈×C₂₈₁

D₄

yes

—

C₂×C₈×C₂₈₁

Q₈

yes

—

C₂×Dic₂₈₁

—

C₂×Dic₂₈₁

C₄⋊C₄

yes

—

#14555886

—

#14555886

C₄⋊C₄

yes

—

C₂³×C₂₈₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₈₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₈₁

C₂×Q₈

yes

characteristic

C₈×C₂₈₁

—

C₈×C₂₈₁

C₄⋊C₄

yes

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₈₁

C₄⋊Q₈

yes

characteristic

C₂²×C₂₈₁

C₄⋊Q₈

yes

characteristic

C₄×C₂₈₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₈₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₈₁

#127

yes

characteristic

C₄×C₂₈₁

C₄⋊Q₈

yes

characteristic

Dic₂₈₁

—

C₂×C₂₈₁

—

C₂×C₂₈₁

—

C₂×C₂₈₁

#384

yes

characteristic

C₂×C₂₈₁

#430

yes

—

C₂₈₁

#1849

yes

characteristic, complemented, Sylow

#1849

—

281

maximal, Sylow

C₂×#108

—

281

—

C₂×#108

—

281

—

C₂×#108

D₂₈₁

yes

characteristic

#423

—

281

—

C₂×#97

—

281

—

C₂×M₁₆

—

281

—

C₂×M₁₆

C₂×D₂₈₁

yes

—

C₂²×C₈

—

281

—

C₂²×C₈

C₂×D₂₈₁

yes

characteristic

C₂×C₄²

—

281

—

#108

—

#108

—

562

—

#108

—

562

—

C₄⋊C₈

—

562

—

#97

—

281

—

C₂²×C₄

—

281

—

C₂²×C₄

C₂²×D₂₈₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

562

—

M₁₆

—

562

—

C₂×C₈

—

C₂×C₈

—

281

—

C₂×C₈

—

281

—

C₂×C₈

—

281

—

C₂×C₈

—

562

—

C₂×C₈

C₄×D₂₈₁

yes

—

C₂×C₈

C₂²⋊D₂₈₁

yes

—

C₂×C₈

Dic₅₆₂

yes

—

C₄²

—

281

—

C₄²

—

281

—

C₂³

Q₈×D₂₈₁

yes

characteristic

C₂×C₄

—

281

—

C₂×C₄

—

1124

—

C₂×C₄

C₂×C₄×D₂₈₁

yes

characteristic

C₂×C₄

D₄×D₂₈₁

yes

characteristic

C₂×C₄

D₄×D₂₈₁

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₈₁

yes

characteristic

C₂×C₄

Q₈×D₂₈₁

yes

characteristic

C₂×C₄

C₂×Dic₅₆₂

yes

characteristic

100

C₈

—

101

C₈

—

281

—

102

C₈

—

1124

—

103

C₈

#17985117

yes

—

104

C₂²

—

105

C₂²

C₄⋊C₄×D₂₈₁

yes

characteristic

106

C₂²

#22582877

yes

characteristic

107

C₂²

#22582878

yes

characteristic

108

C₄

—

562

—

109

C₄

C₄⋊C₄×D₂₈₁

yes

characteristic

110

C₄

C₂×#17985117

yes

characteristic

111

C₄

#22582875

yes

characteristic

112

C₄

#22582878

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#31823332

yes

characteristic

116

C₂

#31823510

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₈₁
commutator	C₂×C₄×C₂₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₈₁
Fitting	C₂×#108×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₂×C₄⋊C₄
prime radical	C₂³×C₂₈₁	C₂×Q₈
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	C₂×#108	D₂₈₁
hypocenter	C₂₈₁	#1849
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₂₈₁

commutator

C₂×C₄×C₂₈₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₈₁

Fitting

C₂×#108×C₂₈₁

C₂

socle

C₂²×C₂₈₁

C₂×C₄⋊C₄

prime radical

C₂³×C₂₈₁

C₂×Q₈

cosocle

C₂²×C₄×C₂₈₁

C₂³

D₂₈₁

C₂₈₁

G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
58. C₂₈₁	#1849	semidirect

H ≅ G/N

type

58. C₂₈₁

#1849

semidirect

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

subgroup	index
C₂×#22582815	2
C₂×#22582814	2
#31823486	2
C₂×#22582789	2
C₂×#108×C₂₈₁	2
#1849	281

subgroup

index

C₂×#108×C₂₈₁

281

Subgroups — #49095476

Conjugacy classes of subgroups

Complements

Maximal subgroups