Group #49093194 — subgroups

Subgroups — #49093194

Order 35968.

150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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	#31823487	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	—	2	1	no	—
5	C₂×#17985122	C₄	1	2	yes	—
6	C₄⋊#14555886	—	2	1	no	—
7	C₄⋊#14555886	—	2	1	no	—
8	#22582790	C₄	1	2	yes	—
9	C₄×#14555886	—	2	1	no	—
10	C₂×C₄²×C₂₈₁	C₂²	1	1	yes	characteristic
11	C₄⋊C₈×C₂₈₁	C₄	1	2	yes	—
12	C₂²⋊C₈×C₂₈₁	—	2	1	no	—
13	C₄×C₈×C₂₈₁	—	2	1	no	—
14	#17985122	—	2	4	no	—
15	#17985122	—	4	2	no	—
16	C₂×#14555886	—	2	2	no	—
17	C₂×#14555886	—	2	2	no	—
18	C₂²×C₄×C₂₈₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₂₈₁	D₄	1	1	yes	characteristic
20	C₂²×C₄×C₂₈₁	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₂₈₁	—	2	2	no	—
22	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₂₈₁	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
25	C₄²×C₂₈₁	D₄	1	1	yes	characteristic
26	#14555886	—	2	4	no	—
27	#14555886	—	4	2	no	—
28	C₂³×C₂₈₁	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₂₈₁	—	2	1	no	—
30	C₂×C₄×C₂₈₁	—	2	1	no	—
31	C₂×C₄×C₂₈₁	—	2	2	no	—
32	C₂×C₄×C₂₈₁	—	2	2	no	—
33	C₂×C₄×C₂₈₁	C₄²	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	C₂²⋊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	C₈×C₂₈₁	—	4	2	no	—
40	C₂²×C₂₈₁	—	2	1	no	—
41	C₂²×C₂₈₁	—	2	1	no	—
42	C₂²×C₂₈₁	—	2	1	no	—
43	C₂²×C₂₈₁	#95	1	1	yes	characteristic
44	C₄×C₂₈₁	—	2	1	no	—
45	C₄×C₂₈₁	—	2	1	no	—
46	C₄×C₂₈₁	—	2	1	no	—
47	C₄×C₂₈₁	#100	1	1	yes	characteristic
48	C₄×C₂₈₁	#101	1	1	yes	characteristic
49	C₄×C₂₈₁	#104	1	2	yes	—
50	C₄×C₂₈₁	#108	1	2	yes	—
51	C₂×C₂₈₁	—	4	1	no	—
52	C₂×C₂₈₁	#339	1	1	yes	characteristic
53	C₂×C₂₈₁	#341	1	1	yes	characteristic
54	C₂×C₂₈₁	#343	1	1	yes	characteristic
55	C₂₈₁	#1299	1	1	yes	characteristic, complemented, Sylow
56	#1299	—	281	1	no	maximal, Sylow
57	#431	D₂₈₁	1	1	yes	characteristic
58	#423	—	281	1	no	—
59	C₄×M₁₆	—	281	1	no	—
60	C₂×M₁₆	—	281	2	no	—
61	C₂×M₁₆	—	562	1	no	—
62	C₂×C₄²	C₂×D₂₈₁	1	1	yes	characteristic
63	C₄⋊C₈	—	562	1	no	—
64	C₄⋊C₈	—	562	1	no	—
65	C₄⋊C₈	Dic₂₈₁	1	2	yes	—
66	C₂²⋊C₈	—	2	1	no	—
67	#97	—	281	2	no	—
68	C₄×C₈	—	2	1	no	—
69	C₄×C₈	—	562	1	no	—
70	C₂²×C₄	C₄×D₂₈₁	1	1	yes	characteristic
71	C₂²×C₄	C₂²⋊D₂₈₁	1	1	yes	characteristic
72	C₂²×C₄	Dic₅₆₂	1	1	yes	characteristic
73	M₁₆	—	562	4	no	—
74	M₁₆	—	1124	2	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	562	2	no	—
77	C₂×C₈	—	562	2	no	—
78	C₄²	C₄×D₂₈₁	1	1	yes	characteristic
79	C₄²	C₂×Dic₂₈₁	1	1	yes	characteristic
80	C₄²	C₂²⋊D₂₈₁	1	1	yes	characteristic
81	C₄²	D₁₁₂₄	1	1	yes	characteristic
82	C₂³	#17985117	1	1	yes	characteristic
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	C₄×Dic₂₈₁	1	1	yes	characteristic
88	C₂×C₄	#17985115	1	1	yes	characteristic
89	C₂×C₄	#17985115	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₂₈₁	1	1	yes	characteristic
91	C₂×C₄	#17985117	1	1	yes	characteristic
92	C₂×C₄	C₄⋊Dic₂₈₁	1	1	yes	characteristic
93	C₈	—	4	2	no	—
94	C₈	—	562	4	no	—
95	C₈	—	1124	2	no	—
96	C₂²	—	2	1	no	—
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	#22582786	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	2	1	no	—
103	C₄	#22582795	1	1	yes	characteristic
104	C₄	#22582797	1	1	yes	characteristic
105	C₄	#22582806	1	2	yes	—
106	C₄	#22582815	1	2	yes	—
107	C₂	—	4	1	no	—
108	C₂	#31823222	1	1	yes	characteristic
109	C₂	#31823228	1	1	yes	characteristic
110	C₂	#31823231	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31823487

C₂

yes

maximal, characteristic

C₄×#17985122

C₂

yes

maximal, characteristic

#431×C₂₈₁

C₂

yes

maximal, characteristic

C₂×#17985122

—

C₂×#17985122

C₄

yes

—

C₄⋊#14555886

—

C₄⋊#14555886

—

#22582790

C₄

yes

—

C₄×#14555886

—

C₂×C₄²×C₂₈₁

C₂²

yes

characteristic

C₄⋊C₈×C₂₈₁

C₄

yes

—

C₂²⋊C₈×C₂₈₁

—

C₄×C₈×C₂₈₁

—

—

—

—

—

C₂²×C₄×C₂₈₁

C₂×C₄

yes

characteristic

C₂²×C₄×C₂₈₁

D₄

yes

characteristic

C₂²×C₄×C₂₈₁

Q₈

yes

characteristic

C₂×C₈×C₂₈₁

—

C₄²×C₂₈₁

C₂×C₄

yes

characteristic

C₄²×C₂₈₁

C₂×C₄

yes

characteristic

C₄²×C₂₈₁

D₄

yes

characteristic

C₄²×C₂₈₁

D₄

yes

characteristic

#14555886

—

#14555886

—

C₂³×C₂₈₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

—

C₂×C₄×C₂₈₁

C₄²

yes

characteristic

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

C₈×C₂₈₁

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

—

C₂²×C₂₈₁

#95

yes

characteristic

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

—

C₄×C₂₈₁

yes

C₄×C₂₈₁

yes

C₄×C₂₈₁

yes

—

C₄×C₂₈₁

#108

yes

—

C₂×C₂₈₁

—

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂×C₂₈₁

yes

C₂₈₁

yes

characteristic, complemented, Sylow

#1299

—

281

maximal, Sylow

#431

D₂₈₁

yes

characteristic

#423

—

281

—

C₄×M₁₆

—

281

—

C₂×M₁₆

—

281

—

C₂×M₁₆

—

562

—

C₂×C₄²

C₂×D₂₈₁

yes

characteristic

C₄⋊C₈

—

562

—

C₄⋊C₈

—

562

—

C₄⋊C₈

Dic₂₈₁

yes

—

C₂²⋊C₈

—

#97

—

281

—

C₄×C₈

—

C₄×C₈

—

562

—

C₂²×C₄

C₄×D₂₈₁

yes

characteristic

C₂²×C₄

C₂²⋊D₂₈₁

yes

characteristic

C₂²×C₄

Dic₅₆₂

yes

characteristic

M₁₆

—

562

—

M₁₆

—

1124

—

C₂×C₈

—

C₂×C₈

—

562

—

C₂×C₈

—

562

—

C₄²

C₄×D₂₈₁

yes

characteristic

C₄²

C₂×Dic₂₈₁

yes

characteristic

C₄²

C₂²⋊D₂₈₁

yes

characteristic

C₄²

D₁₁₂₄

yes

characteristic

C₂³

#17985117

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₂₈₁

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₂₈₁

yes

characteristic

C₂×C₄

#17985117

yes

characteristic

C₂×C₄

C₄⋊Dic₂₈₁

yes

characteristic

C₈

—

C₈

—

562

—

C₈

—

1124

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#22582786

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

#22582795

yes

characteristic

104

C₄

#22582797

yes

characteristic

105

C₄

#22582806

yes

—

106

C₄

#22582815

yes

—

107

C₂

—

108

C₂

#31823222

yes

characteristic

109

C₂

#31823228

yes

characteristic

110

C₂

#31823231

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#17985115
commutator	C₂×C₄×C₂₈₁	C₄²
Frattini	C₂×C₄²	C₂×D₂₈₁
Fitting	#431×C₂₈₁	C₂
socle	C₂²×C₂₈₁	#95
prime radical	C₂³×C₂₈₁	C₄⋊C₄
cosocle	C₂×C₄²×C₂₈₁	C₂²
hypercenter	#431	D₂₈₁
hypocenter	C₂₈₁	#1299
LCS	G ▷ C₂×C₄×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

#17985115

commutator

C₂×C₄×C₂₈₁

C₄²

Frattini

C₂×C₄²

C₂×D₂₈₁

Fitting

#431×C₂₈₁

C₂

socle

C₂²×C₂₈₁

#95

prime radical

C₂³×C₂₈₁

C₄⋊C₄

cosocle

C₂×C₄²×C₂₈₁

C₂²

D₂₈₁

C₂₈₁

G ▷ C₂×C₄×C₂₈₁ ▷ C₂²×C₂₈₁ ▷ C₂₈₁

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
55. C₂₈₁	#1299	semidirect

H ≅ G/N

type

55. C₂₈₁

#1299

semidirect

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

subgroup	index
#31823487	2
C₄×#17985122	2
#431×C₂₈₁	2
#1299	281

subgroup

index

#31823487

C₄×#17985122

#431×C₂₈₁

#1299

281

Subgroups — #49093194

Conjugacy classes of subgroups

Complements

Maximal subgroups