Group #49093152 — subgroups

Subgroups — #49093152

Order 35968.

160 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 81 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×C₄⋊#14555886	C₂	1	1	yes	maximal, characteristic
2	C₄×#17985122	C₂	1	1	yes	maximal, characteristic
3	#431×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985122	C₄	1	2	yes	—
5	C₂²×#14555886	C₄	1	2	yes	—
6	C₄⋊#14555886	—	2	1	no	—
7	C₄⋊#14555886	—	2	1	no	—
8	#22582790	—	2	1	no	—
9	C₄×#14555886	—	2	1	no	—
10	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₂₈₁	—	2	1	no	—
12	C₂²⋊C₈×C₂₈₁	C₄	1	2	yes	—
13	C₄×C₈×C₂₈₁	—	2	1	no	—
14	#17985122	—	2	2	no	—
15	#17985122	C₈	1	4	yes	complemented
16	C₂×#14555886	—	2	2	no	—
17	C₂×#14555886	—	2	2	no	—
18	C₂×#14555886	—	4	2	no	—
19	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₂₈₁	—	2	2	no	—
23	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
24	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
25	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
26	C₄²×C₂₈₁	Q₈	1	1	yes	characteristic
27	#14555886	—	2	4	no	—
28	#14555886	—	4	2	no	—
29	C₂³×C₂₈₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₂₈₁	—	2	1	no	—
31	C₂×C₄×C₂₈₁	—	2	1	no	—
32	C₂×C₄×C₂₈₁	—	4	1	no	—
33	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₈₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×C₂₈₁	C₂×C₈	1	2	yes	—
40	C₂×C₄×C₂₈₁	M₁₆	1	2	yes	—
41	C₈×C₂₈₁	—	4	2	no	—
42	C₂²×C₂₈₁	—	2	1	no	—
43	C₂²×C₂₈₁	—	2	1	no	—
44	C₂²×C₂₈₁	#95	1	1	yes	characteristic
45	C₂²×C₂₈₁	C₄×C₈	1	1	yes	characteristic
46	C₂²×C₂₈₁	#97	1	1	yes	characteristic
47	C₄×C₂₈₁	—	2	1	no	—
48	C₄×C₂₈₁	—	2	1	no	—
49	C₄×C₂₈₁	—	2	1	no	—
50	C₄×C₂₈₁	C₂²⋊C₈	1	2	yes	—
51	C₄×C₂₈₁	#100	1	1	yes	characteristic
52	C₄×C₂₈₁	#101	1	1	yes	characteristic
53	C₄×C₂₈₁	C₄⋊C₈	1	2	yes	—
54	C₂×C₂₈₁	—	2	1	no	—
55	C₂×C₂₈₁	—	2	1	no	—
56	C₂×C₂₈₁	#336	1	1	yes	characteristic
57	C₂×C₂₈₁	#343	1	1	yes	characteristic
58	C₂×C₂₈₁	#344	1	1	yes	characteristic
59	C₂₈₁	#1283	1	1	yes	characteristic, complemented, Sylow
60	#1283	—	281	1	no	maximal, Sylow
61	#431	D₂₈₁	1	1	yes	characteristic
62	C₂×C₄⋊C₈	—	281	1	no	—
63	C₄×M₁₆	—	281	1	no	—
64	C₂×M₁₆	—	281	2	no	—
65	C₂²×C₈	—	281	2	no	—
66	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
67	C₄⋊C₈	—	2	1	no	—
68	C₄⋊C₈	—	562	1	no	—
69	C₄⋊C₈	—	562	1	no	—
70	C₂²⋊C₈	Dic₂₈₁	1	2	yes	—
71	#97	—	562	1	no	—
72	C₄×C₈	—	2	1	no	—
73	C₄×C₈	—	562	1	no	—
74	C₂²×C₄	C₄×D₂₈₁	1	1	yes	characteristic
75	C₂²×C₄	C₄×D₂₈₁	1	1	yes	characteristic
76	C₂²×C₄	C₂×Dic₂₈₁	1	1	yes	characteristic
77	M₁₆	—	281	4	no	—
78	M₁₆	—	562	2	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	562	2	no	—
81	C₂×C₈	—	562	2	no	—
82	C₂×C₈	—	1124	2	no	—
83	C₄²	C₂²⋊D₂₈₁	1	1	yes	characteristic
84	C₄²	C₂²⋊D₂₈₁	1	1	yes	characteristic
85	C₄²	D₁₁₂₄	1	1	yes	characteristic
86	C₄²	Dic₅₆₂	1	1	yes	characteristic
87	C₂³	C₄×Dic₂₈₁	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	#17985115	1	1	yes	characteristic
92	C₂×C₄	#17985115	1	1	yes	characteristic
93	C₂×C₄	C₂²⋊Dic₂₈₁	1	1	yes	characteristic
94	C₂×C₄	#17985117	1	1	yes	characteristic
95	C₂×C₄	#17985117	1	1	yes	characteristic
96	C₂×C₄	C₄⋊Dic₂₈₁	1	1	yes	characteristic
97	C₂×C₄	C₈×D₂₈₁	1	2	yes	—
98	C₂×C₄	#17985121	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	562	4	no	—
101	C₈	—	1124	2	no	—
102	C₂²	—	2	1	no	—
103	C₂²	—	2	1	no	—
104	C₂²	#22582786	1	1	yes	characteristic
105	C₂²	C₈×Dic₂₈₁	1	1	yes	characteristic
106	C₂²	#22582789	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	#22582791	1	2	yes	—
111	C₄	#22582795	1	1	yes	characteristic
112	C₄	#22582797	1	1	yes	characteristic
113	C₄	#22582808	1	2	yes	—
114	C₂	—	2	1	no	—
115	C₂	—	2	1	no	—
116	C₂	#31823217	1	1	yes	characteristic
117	C₂	#31823231	1	1	yes	characteristic
118	C₂	#31823233	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#14555886

C₂

yes

maximal, characteristic

C₄×#17985122

C₂

yes

maximal, characteristic

#431×C₂₈₁

C₂

yes

maximal, characteristic

C₂×#17985122

C₄

yes

—

C₂²×#14555886

C₄

yes

—

—

—

—

—

C₂×C₄²×C₂₈₁

C₂²

yes

characteristic

C₄⋊C₈×C₂₈₁

—

C₂²⋊C₈×C₂₈₁

C₄

yes

—

C₄×C₈×C₂₈₁

—

#17985122

—

#17985122

C₈

yes

—

—

—

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂×C₈×C₂₈₁

—

C₄²×C₂₈₁

D₄

yes

characteristic

C₄²×C₂₈₁

D₄

yes

characteristic

C₄²×C₂₈₁

D₄

yes

characteristic

C₄²×C₂₈₁

Q₈

yes

characteristic

#14555886

—

#14555886

—

C₂³×C₂₈₁

C₄²

yes

characteristic

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₈₁

C₂×C₈

yes

—

C₂×C₄×C₂₈₁

M₁₆

yes

—

C₈×C₂₈₁

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

#95

yes

characteristic

C₂²×C₂₈₁

C₄×C₈

yes

characteristic

C₂²×C₂₈₁

#97

yes

characteristic

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

C₂²⋊C₈

yes

—

C₄×C₂₈₁

yes

C₄×C₂₈₁

yes

C₄×C₂₈₁

C₄⋊C₈

yes

—

C₂×C₂₈₁

—

C₂×C₂₈₁

—

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂₈₁

yes

characteristic, complemented, Sylow

#1283

—

281

maximal, Sylow

#431

D₂₈₁

yes

characteristic

C₂×C₄⋊C₈

—

281

—

C₄×M₁₆

—

281

—

C₂×M₁₆

—

281

—

C₂²×C₈

—

281

—

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

562

—

C₄⋊C₈

—

562

—

C₂²⋊C₈

Dic₂₈₁

yes

—

#97

—

562

—

C₄×C₈

—

C₄×C₈

—

562

—

C₂²×C₄

C₄×D₂₈₁

yes

characteristic

C₂²×C₄

C₄×D₂₈₁

yes

characteristic

C₂²×C₄

C₂×Dic₂₈₁

yes

characteristic

M₁₆

—

281

—

M₁₆

—

562

—

C₂×C₈

—

C₂×C₈

—

562

—

C₂×C₈

—

562

—

C₂×C₈

—

1124

—

C₄²

C₂²⋊D₂₈₁

yes

characteristic

C₄²

C₂²⋊D₂₈₁

yes

characteristic

C₄²

D₁₁₂₄

yes

characteristic

C₄²

Dic₅₆₂

yes

characteristic

C₂³

C₄×Dic₂₈₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₂₈₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₄⋊Dic₂₈₁

yes

characteristic

C₂×C₄

C₈×D₂₈₁

yes

—

C₂×C₄

#17985121

yes

—

C₈

—

100

C₈

—

562

—

101

C₈

—

1124

—

102

C₂²

—

103

C₂²

—

104

C₂²

#22582786

yes

characteristic

105

C₂²

C₈×Dic₂₈₁

yes

characteristic

106

C₂²

#22582789

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

#22582791

yes

—

111

C₄

#22582795

yes

characteristic

112

C₄

#22582797

yes

characteristic

113

C₄

#22582808

yes

—

114

C₂

—

115

C₂

—

116

C₂

#31823217

yes

characteristic

117

C₂

#31823231

yes

characteristic

118

C₂

#31823233

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#17985115
commutator	C₂²×C₂₈₁	C₄×C₈
Frattini	C₂×C₄²	C₂×D₂₈₁
Fitting	#431×C₂₈₁	C₂
socle	C₂²×C₂₈₁	#95
prime radical	C₂³×C₂₈₁	C₄²
cosocle	C₂×C₄²×C₂₈₁	C₂²
hypercenter	#431	D₂₈₁
hypocenter	C₂₈₁	#1283
LCS	G ▷ C₂²×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

#17985115

commutator

C₂²×C₂₈₁

C₄×C₈

Frattini

C₂×C₄²

C₂×D₂₈₁

Fitting

#431×C₂₈₁

C₂

socle

C₂²×C₂₈₁

#95

prime radical

C₂³×C₂₈₁

C₄²

cosocle

C₂×C₄²×C₂₈₁

C₂²

D₂₈₁

C₂₈₁

G ▷ C₂²×C₂₈₁ ▷ C₂×C₂₈₁ ▷ C₂₈₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
15. #17985122	C₈	semidirect
59. C₂₈₁	#1283	semidirect

H ≅ G/N

type

15. #17985122

C₈

semidirect

59. C₂₈₁

#1283

semidirect

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

subgroup	index
C₂×C₄⋊#14555886	2
C₄×#17985122	2
#431×C₂₈₁	2
#1283	281

subgroup

index

C₂×C₄⋊#14555886

C₄×#17985122

#431×C₂₈₁

#1283

281

Subgroups — #49093152

Conjugacy classes of subgroups

Complements

Maximal subgroups