Group #49096056 — subgroups

Subgroups — #49096056

Order 35968.

200 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 93 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	#31823501	C₂	1	1	yes	maximal, characteristic
3	#31823489	C₂	1	2	yes	maximal
4	#31823223	C₂	1	2	yes	maximal
5	C₂×#97×C₂₈₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#17985122	C₂²	1	2	yes	—
7	#22582838	C₂²	1	2	yes	—
8	#22582815	—	2	2	no	—
9	#22582813	C₄	1	2	yes	complemented
10	#22582811	C₄	1	2	yes	complemented
11	#22582808	—	2	4	no	—
12	C₂²×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₂₈₁	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
15	#97×C₂₈₁	—	2	2	no	—
16	#17985122	—	2	2	no	—
17	#17985122	—	2	2	no	—
18	C₂×#14555886	—	2	2	no	—
19	C₄⋊Dic₂₈₁	C₂×C₄	1	4	yes	—
20	C₂²⋊Dic₂₈₁	—	2	2	no	—
21	C₄×Dic₂₈₁	—	2	2	no	—
22	C₂²×C₄×C₂₈₁	—	2	1	no	—
23	C₂²×C₄×C₂₈₁	C₂³	1	1	yes	characteristic
24	C₂×C₈×C₂₈₁	—	2	1	no	—
25	C₂×C₈×C₂₈₁	—	2	1	no	—
26	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×C₂₈₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₂₈₁	D₄	1	2	yes	—
29	C₂×C₈×C₂₈₁	D₄	1	2	yes	—
30	C₂×C₈×C₂₈₁	Q₈	1	2	yes	—
31	C₄²×C₂₈₁	—	2	1	no	—
32	C₄²×C₂₈₁	Q₈	1	2	yes	—
33	C₂×Dic₂₈₁	—	2	4	no	—
34	#14555886	—	4	2	no	—
35	C₂³×C₂₈₁	#41	1	1	yes	characteristic
36	C₂×C₄×C₂₈₁	—	2	2	no	—
37	C₂×C₄×C₂₈₁	—	4	2	no	—
38	C₂×C₄×C₂₈₁	C₂²×C₄	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	C₂×C₄×C₂₈₁	#41	1	1	yes	characteristic
44	C₈×C₂₈₁	—	2	2	no	—
45	C₈×C₂₈₁	C₄⋊C₄	1	2	yes	—
46	C₈×C₂₈₁	C₄⋊C₄	1	2	yes	—
47	C₂²×C₂₈₁	—	2	2	no	—
48	C₂²×C₂₈₁	C₄×D₄	1	1	yes	characteristic
49	C₂²×C₂₈₁	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₂₈₁	#125	1	1	yes	characteristic
51	C₄×C₂₈₁	—	4	2	no	—
52	C₄×C₂₈₁	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₂₈₁	C₄×Q₈	1	1	yes	characteristic
54	C₄×C₂₈₁	#121	1	1	yes	characteristic
55	C₄×C₂₈₁	C₄⋊Q₈	1	1	yes	characteristic
56	Dic₂₈₁	—	4	4	no	—
57	C₂×C₂₈₁	—	2	1	no	—
58	C₂×C₂₈₁	—	2	1	no	—
59	C₂×C₂₈₁	#389	1	1	yes	characteristic
60	C₂×C₂₈₁	#444	1	2	yes	—
61	C₂₈₁	#1946	1	1	yes	characteristic, complemented, Sylow
62	#1946	—	281	1	no	maximal, Sylow
63	C₂×#108	—	281	1	no	—
64	#427	—	281	1	no	—
65	#424	—	281	2	no	—
66	C₂×#97	D₂₈₁	1	1	yes	characteristic
67	#339	—	281	2	no	—
68	C₂×M₁₆	—	281	2	no	—
69	C₂²×C₈	C₂×D₂₈₁	1	1	yes	characteristic
70	C₂²×C₈	C₂×D₂₈₁	1	1	yes	characteristic
71	#117	—	281	2	no	—
72	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
73	#108	—	562	2	no	—
74	#107	—	281	2	no	—
75	#106	—	281	2	no	—
76	C₄⋊C₈	—	562	4	no	—
77	#97	—	2	2	no	—
78	C₂²×C₄	—	2	1	no	—
79	C₂²×C₄	C₂²×D₂₈₁	1	1	yes	characteristic
80	M₁₆	—	562	2	no	—
81	M₁₆	—	562	2	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	2	1	no	—
84	C₂×C₈	—	562	2	no	—
85	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
86	C₂×C₈	C₄×D₂₈₁	1	1	yes	characteristic
87	C₂×C₈	C₂²⋊D₂₈₁	1	2	yes	—
88	C₂×C₈	D₁₁₂₄	1	2	yes	—
89	C₂×C₈	Dic₅₆₂	1	2	yes	—
90	C₄⋊C₄	—	281	4	no	—
91	C₂²⋊C₄	—	562	2	no	—
92	C₄²	—	2	1	no	—
93	C₄²	—	562	2	no	—
94	C₄²	Dic₅₆₂	1	2	yes	—
95	C₂³	#17985138	1	1	yes	characteristic
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	562	4	no	—
99	C₂×C₄	C₂×C₄×D₂₈₁	1	1	yes	characteristic
100	C₂×C₄	C₂×C₂²⋊D₂₈₁	1	1	yes	characteristic
101	C₂×C₄	C₂×D₁₁₂₄	1	1	yes	characteristic
102	C₂×C₄	C₂×Dic₅₆₂	1	1	yes	characteristic
103	C₂×C₄	C₂×Dic₅₆₂	1	1	yes	characteristic
104	C₂×C₄	#17985138	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	1124	2	no	—
107	C₈	#17985117	1	2	yes	—
108	C₈	#17985117	1	2	yes	—
109	C₂²	—	2	2	no	—
110	C₂²	C₄×D₁₁₂₄	1	1	yes	characteristic
111	C₂²	#22582858	1	1	yes	characteristic
112	C₂²	#22582871	1	1	yes	characteristic
113	C₄	—	4	2	no	—
114	C₄	—	1124	4	no	—
115	C₄	C₂×#17985117	1	1	yes	characteristic
116	C₄	C₄×Dic₅₆₂	1	1	yes	characteristic
117	C₄	#22582853	1	1	yes	characteristic
118	C₄	#22582879	1	1	yes	characteristic
119	C₂	—	2	1	no	—
120	C₂	—	2	1	no	—
121	C₂	#31823361	1	1	yes	characteristic
122	C₂	#31823586	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22582815

C₂

yes

maximal, characteristic

#31823501

C₂

yes

maximal, characteristic

#31823489

C₂

yes

maximal

#31823223

C₂

yes

maximal

C₂×#97×C₂₈₁

C₂

yes

maximal, characteristic

C₂×#17985122

C₂²

yes

—

#22582838

C₂²

yes

—

#22582815

—

#22582813

C₄

yes

complemented

#22582811

C₄

yes

complemented

#22582808

—

C₂²×C₈×C₂₈₁

C₂²

yes

characteristic

C₂²×C₈×C₂₈₁

C₂²

yes

characteristic

C₂×C₄²×C₂₈₁

C₂²

yes

characteristic

#97×C₂₈₁

—

#17985122

—

#17985122

—

C₂×#14555886

—

C₄⋊Dic₂₈₁

C₂×C₄

yes

—

C₂²⋊Dic₂₈₁

—

C₄×Dic₂₈₁

—

C₂²×C₄×C₂₈₁

—

C₂²×C₄×C₂₈₁

C₂³

yes

characteristic

C₂×C₈×C₂₈₁

—

C₂×C₈×C₂₈₁

—

C₂×C₈×C₂₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₂₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₂₈₁

D₄

yes

—

C₂×C₈×C₂₈₁

D₄

yes

—

C₂×C₈×C₂₈₁

Q₈

yes

—

C₄²×C₂₈₁

—

C₄²×C₂₈₁

Q₈

yes

—

C₂×Dic₂₈₁

—

#14555886

—

C₂³×C₂₈₁

#41

yes

characteristic

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

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×Q₈

yes

characteristic

C₂×C₄×C₂₈₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₈₁

#41

yes

characteristic

C₈×C₂₈₁

—

C₈×C₂₈₁

C₄⋊C₄

yes

—

C₈×C₂₈₁

C₄⋊C₄

yes

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

C₄×D₄

yes

characteristic

C₂²×C₂₈₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₈₁

#125

yes

characteristic

C₄×C₂₈₁

—

C₄×C₂₈₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₈₁

C₄×Q₈

yes

characteristic

C₄×C₂₈₁

#121

yes

characteristic

C₄×C₂₈₁

C₄⋊Q₈

yes

characteristic

Dic₂₈₁

—

C₂×C₂₈₁

—

C₂×C₂₈₁

—

C₂×C₂₈₁

#389

yes

characteristic

C₂×C₂₈₁

#444

yes

—

C₂₈₁

#1946

yes

characteristic, complemented, Sylow

#1946

—

281

maximal, Sylow

C₂×#108

—

281

—

#427

—

281

—

#424

—

281

—

C₂×#97

D₂₈₁

yes

characteristic

#339

—

281

—

C₂×M₁₆

—

281

—

C₂²×C₈

C₂×D₂₈₁

yes

characteristic

C₂²×C₈

C₂×D₂₈₁

yes

characteristic

#117

—

281

—

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

#108

—

562

—

#107

—

281

—

#106

—

281

—

C₄⋊C₈

—

562

—

#97

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₂₈₁

yes

characteristic

M₁₆

—

562

—

M₁₆

—

562

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

562

—

C₂×C₈

C₄×D₂₈₁

yes

characteristic

C₂×C₈

C₄×D₂₈₁

yes

characteristic

C₂×C₈

C₂²⋊D₂₈₁

yes

—

C₂×C₈

D₁₁₂₄

yes

—

C₂×C₈

Dic₅₆₂

yes

—

C₄⋊C₄

—

281

—

C₂²⋊C₄

—

562

—

C₄²

—

C₄²

—

562

—

C₄²

Dic₅₆₂

yes

—

C₂³

#17985138

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

562

—

C₂×C₄

C₂×C₄×D₂₈₁

yes

characteristic

100

C₂×C₄

C₂×C₂²⋊D₂₈₁

yes

characteristic

101

C₂×C₄

C₂×D₁₁₂₄

yes

characteristic

102

C₂×C₄

C₂×Dic₅₆₂

yes

characteristic

103

C₂×C₄

C₂×Dic₅₆₂

yes

characteristic

104

C₂×C₄

#17985138

yes

characteristic

105

C₈

—

106

C₈

—

1124

—

107

C₈

#17985117

yes

—

108

C₈

#17985117

yes

—

109

C₂²

—

110

C₂²

C₄×D₁₁₂₄

yes

characteristic

111

C₂²

#22582858

yes

characteristic

112

C₂²

#22582871

yes

characteristic

113

C₄

—

114

C₄

—

1124

—

115

C₄

C₂×#17985117

yes

characteristic

116

C₄

C₄×Dic₅₆₂

yes

characteristic

117

C₄

#22582853

yes

characteristic

118

C₄

#22582879

yes

characteristic

119

C₂

—

120

C₂

—

121

C₂

#31823361

yes

characteristic

122

C₂

#31823586

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁₂₄
commutator	C₂×C₄×C₂₈₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₈₁
Fitting	C₂×#97×C₂₈₁	C₂
socle	C₂²×C₂₈₁	C₄×D₄
prime radical	C₂³×C₂₈₁	#41
cosocle	C₂²×C₄×C₂₈₁	C₂³
hypercenter	C₂×#97	D₂₈₁
hypocenter	C₂₈₁	#1946
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

C₂×D₁₁₂₄

commutator

C₂×C₄×C₂₈₁

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₈₁

Fitting

C₂×#97×C₂₈₁

C₂

socle

C₂²×C₂₈₁

C₄×D₄

prime radical

C₂³×C₂₈₁

#41

cosocle

C₂²×C₄×C₂₈₁

C₂³

hypercenter

C₂×#97

D₂₈₁

hypocenter

C₂₈₁

#1946

LCS

G ▷ C₂×C₄×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#97

N	H ≅ G/N	type
9. #22582813	C₄	semidirect
10. #22582811	C₄	semidirect
61. C₂₈₁	#1946	semidirect

H ≅ G/N

type

9. #22582813

C₄

semidirect

10. #22582811

C₄

semidirect

61. C₂₈₁

#1946

semidirect

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

subgroup	index
C₂×#22582815	2
#31823501	2
#31823489	2
#31823223	2
C₂×#97×C₂₈₁	2
#1946	281

subgroup

index

C₂×#97×C₂₈₁

281

Subgroups — #49096056

Conjugacy classes of subgroups

Complements

Maximal subgroups