Group #46837916 — subgroups

Subgroups — #46837916

Order 34688.

210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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	#31773925	C₂	1	2	yes	maximal, complemented
2	#31773913	C₂	1	2	yes	maximal
3	#31773865	C₂	1	1	yes	maximal, characteristic
4	#31773654	C₂	1	1	yes	maximal, characteristic, complemented
5	#430×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864654	C₂²	1	1	yes	characteristic
7	C₂²×C₂₇₁⋊C₈	C₂²	1	1	yes	characteristic
8	#22576119	C₂²	1	2	yes	—
9	Dic₂₇₁⋊C₈	—	2	4	no	—
10	#22576086	—	2	4	no	—
11	(C₂×D₂₇₁)⋊C₈	—	2	2	no	—
12	C₂×M₁₆×C₂₇₁	C₂²	1	2	yes	—
13	C₂×M₁₆×C₂₇₁	C₂²	1	1	yes	characteristic
14	#108×C₂₇₁	—	2	2	no	—
15	#16864654	—	2	2	no	—
16	#16864654	—	2	2	no	—
17	C₂×Dic₅₄₂	Q₈	1	1	yes	characteristic
18	C₂×D₁₀₈₄	Q₈	1	1	yes	characteristic
19	C₂×C₂²⋊D₂₇₁	—	2	1	no	—
20	C₂×C₄×D₂₇₁	—	2	1	no	—
21	C₂×C₂₇₁⋊C₈	—	2	1	no	—
22	C₂×C₂₇₁⋊C₈	—	2	2	no	—
23	C₄⋊Dic₂₇₁	—	2	2	no	—
24	C₂²⋊Dic₂₇₁	—	2	2	no	—
25	C₄×Dic₂₇₁	D₄	1	4	yes	—
26	C₂²×C₄×C₂₇₁	C₂³	1	1	yes	characteristic
27	M₁₆×C₂₇₁	—	2	2	no	—
28	M₁₆×C₂₇₁	—	2	2	no	—
29	M₁₆×C₂₇₁	—	2	2	no	—
30	C₂×C₈×C₂₇₁	—	2	2	no	—
31	C₂×C₈×C₂₇₁	D₄	1	2	yes	—
32	C₂²×D₂₇₁	—	2	1	no	—
33	Dic₅₄₂	—	2	2	no	—
34	D₁₀₈₄	—	2	2	no	—
35	C₂²⋊D₂₇₁	—	4	2	no	—
36	C₂×Dic₂₇₁	—	2	1	no	—
37	C₂×Dic₂₇₁	—	2	4	no	—
38	C₄×D₂₇₁	—	4	1	no	—
39	C₄×D₂₇₁	—	4	1	no	—
40	C₂₇₁⋊C₈	—	4	1	no	—
41	C₂³×C₂₇₁	#41	1	1	yes	characteristic
42	C₂×C₄×C₂₇₁	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₂₇₁	C₂×Q₈	1	1	yes	characteristic
45	C₂×C₄×C₂₇₁	#41	1	2	yes	—
46	C₈×C₂₇₁	—	2	2	no	—
47	C₈×C₂₇₁	—	4	2	no	—
48	C₂²×C₂₇₁	—	4	1	no	—
49	C₂²×C₂₇₁	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₂₇₁	#123	1	2	yes	—
51	C₂×D₂₇₁	—	4	2	no	—
52	C₂×D₂₇₁	—	4	1	no	—
53	C₄×C₂₇₁	C₂²⋊Q₈	1	2	yes	—
54	C₄×C₂₇₁	#123	1	1	yes	characteristic
55	C₄×C₂₇₁	#127	1	1	yes	characteristic
56	Dic₂₇₁	—	4	4	no	—
57	Dic₂₇₁	—	4	1	no	—
58	C₂×C₂₇₁	—	2	2	no	—
59	C₂×C₂₇₁	—	2	1	no	—
60	C₂×C₂₇₁	#399	1	1	yes	characteristic
61	D₂₇₁	—	8	1	no	—
62	C₂₇₁	#2098	1	1	yes	characteristic, complemented, Sylow
63	#2098	—	271	1	no	maximal, Sylow
64	#430	D₂₇₁	1	1	yes	characteristic, complemented
65	#424	—	271	2	no	—
66	#421	—	271	2	no	—
67	#408	—	271	1	no	—
68	H(3,ℤ/4)	—	271	1	no	—
69	C₂×#41	—	271	1	no	—
70	C₂×M₁₆	C₂×D₂₇₁	1	2	yes	—
71	C₂×M₁₆	C₂×D₂₇₁	1	1	yes	characteristic
72	C₂²×C₈	—	271	1	no	—
73	#117	—	271	2	no	—
74	#108	—	2	2	no	—
75	C₄⋊C₈	—	542	4	no	—
76	#104	—	542	4	no	—
77	C₂²⋊C₈	—	542	2	no	—
78	#41	—	542	2	no	—
79	#41	—	542	2	no	—
80	C₂×Q₈	—	271	1	no	—
81	C₂×D₄	—	271	1	no	—
82	C₂×D₄	—	542	1	no	—
83	C₂²×C₄	—	542	1	no	—
84	C₂²×C₄	C₂²×D₂₇₁	1	1	yes	characteristic
85	M₁₆	—	2	2	no	—
86	M₁₆	—	2	2	no	—
87	M₁₆	—	2	2	no	—
88	C₂×C₈	—	2	2	no	—
89	C₂×C₈	—	542	2	no	—
90	C₂×C₈	—	542	1	no	—
91	C₂×C₈	C₂²⋊D₂₇₁	1	2	yes	—
92	C₄⋊C₄	—	542	2	no	—
93	C₂²⋊C₄	—	542	2	no	—
94	C₄²	—	271	4	no	—
95	C₂³	—	542	1	no	—
96	C₂³	#16864655	1	1	yes	characteristic
97	Q₈	—	542	2	no	—
98	D₄	—	542	2	no	—
99	D₄	—	1084	2	no	—
100	C₂×C₄	—	542	1	no	—
101	C₂×C₄	—	542	4	no	—
102	C₂×C₄	—	1084	1	no	—
103	C₂×C₄	—	1084	1	no	—
104	C₂×C₄	D₄×D₂₇₁	1	2	yes	—
105	C₂×C₄	C₂×C₂²⋊D₂₇₁	1	1	yes	characteristic
106	C₂×C₄	Q₈×D₂₇₁	1	1	yes	characteristic
107	C₂×C₄	#16864654	1	2	yes	—
108	C₈	—	2	2	no	—
109	C₈	—	4	2	no	—
110	C₈	—	1084	1	no	—
111	C₂²	—	4	1	no	—
112	C₂²	—	1084	2	no	—
113	C₂²	—	1084	1	no	—
114	C₂²	#22576136	1	1	yes	characteristic
115	C₂²	#22576145	1	2	yes	—
116	C₄	—	1084	4	no	—
117	C₄	—	1084	1	no	—
118	C₄	#22576138	1	2	yes	—
119	C₄	#22576143	1	1	yes	characteristic
120	C₄	#22576156	1	1	yes	characteristic
121	C₂	—	2	2	no	—
122	C₂	—	2	1	no	—
123	C₂	—	2168	1	no	—
124	C₂	#31773832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31773925

C₂

yes

maximal, complemented

#31773913

C₂

yes

maximal

#31773865

C₂

yes

maximal, characteristic

#31773654

C₂

yes

maximal, characteristic, complemented

#430×C₂₇₁

C₂

yes

maximal, characteristic, complemented

C₂×#16864654

C₂²

yes

characteristic

C₂²×C₂₇₁⋊C₈

C₂²

yes

characteristic

#22576119

C₂²

yes

—

Dic₂₇₁⋊C₈

—

#22576086

—

(C₂×D₂₇₁)⋊C₈

—

C₂×M₁₆×C₂₇₁

C₂²

yes

—

C₂×M₁₆×C₂₇₁

C₂²

yes

characteristic

#108×C₂₇₁

—

#16864654

—

#16864654

—

C₂×Dic₅₄₂

Q₈

yes

characteristic

C₂×D₁₀₈₄

Q₈

yes

characteristic

C₂×C₂²⋊D₂₇₁

—

C₂×C₄×D₂₇₁

—

C₂×C₂₇₁⋊C₈

—

C₂×C₂₇₁⋊C₈

—

C₄⋊Dic₂₇₁

—

C₂²⋊Dic₂₇₁

—

C₄×Dic₂₇₁

D₄

yes

—

C₂²×C₄×C₂₇₁

C₂³

yes

characteristic

M₁₆×C₂₇₁

—

M₁₆×C₂₇₁

—

M₁₆×C₂₇₁

—

C₂×C₈×C₂₇₁

—

C₂×C₈×C₂₇₁

D₄

yes

—

C₂²×D₂₇₁

—

Dic₅₄₂

—

D₁₀₈₄

—

C₂²⋊D₂₇₁

—

C₂×Dic₂₇₁

—

C₂×Dic₂₇₁

—

C₄×D₂₇₁

—

C₄×D₂₇₁

—

C₂₇₁⋊C₈

—

C₂³×C₂₇₁

#41

yes

characteristic

C₂×C₄×C₂₇₁

C₂×D₄

yes

—

C₂×C₄×C₂₇₁

C₂×D₄

yes

characteristic

C₂×C₄×C₂₇₁

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₇₁

#41

yes

—

C₈×C₂₇₁

—

C₈×C₂₇₁

—

C₂²×C₂₇₁

—

C₂²×C₂₇₁

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₇₁

#123

yes

—

C₂×D₂₇₁

—

C₂×D₂₇₁

—

C₄×C₂₇₁

C₂²⋊Q₈

yes

—

C₄×C₂₇₁

yes

C₄×C₂₇₁

yes

Dic₂₇₁

—

Dic₂₇₁

—

C₂×C₂₇₁

—

C₂×C₂₇₁

—

C₂×C₂₇₁

#399

yes

characteristic

D₂₇₁

—

C₂₇₁

#2098

yes

characteristic, complemented, Sylow

#2098

—

271

maximal, Sylow

#430

D₂₇₁

yes

characteristic, complemented

#424

—

271

—

#421

—

271

—

#408

—

271

—

H(3,ℤ/4)

—

271

—

C₂×#41

—

271

—

C₂×M₁₆

C₂×D₂₇₁

yes

—

C₂×M₁₆

C₂×D₂₇₁

yes

characteristic

C₂²×C₈

—

271

—

#117

—

271

—

#108

—

C₄⋊C₈

—

542

—

#104

—

542

—

C₂²⋊C₈

—

542

—

#41

—

542

—

#41

—

542

—

C₂×Q₈

—

271

—

C₂×D₄

—

271

—

C₂×D₄

—

542

—

C₂²×C₄

—

542

—

C₂²×C₄

C₂²×D₂₇₁

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

542

—

C₂×C₈

—

542

—

C₂×C₈

C₂²⋊D₂₇₁

yes

—

C₄⋊C₄

—

542

—

C₂²⋊C₄

—

542

—

C₄²

—

271

—

C₂³

—

542

—

C₂³

#16864655

yes

characteristic

Q₈

—

542

—

D₄

—

542

—

D₄

—

1084

—

100

C₂×C₄

—

542

—

101

C₂×C₄

—

542

—

102

C₂×C₄

—

1084

—

103

C₂×C₄

—

1084

—

104

C₂×C₄

D₄×D₂₇₁

yes

—

105

C₂×C₄

C₂×C₂²⋊D₂₇₁

yes

characteristic

106

C₂×C₄

Q₈×D₂₇₁

yes

characteristic

107

C₂×C₄

#16864654

yes

—

108

C₈

—

109

C₈

—

110

C₈

—

1084

—

111

C₂²

—

112

C₂²

—

1084

—

113

C₂²

—

1084

—

114

C₂²

#22576136

yes

characteristic

115

C₂²

#22576145

yes

—

116

C₄

—

1084

—

117

C₄

—

1084

—

118

C₄

#22576138

yes

—

119

C₄

#22576143

yes

characteristic

120

C₄

#22576156

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

2168

—

124

C₂

#31773832

yes

characteristic

	subgroup	G/H
center	C₄	#22576156
commutator, cosocle	C₂²×C₄×C₂₇₁	C₂³
Frattini	C₂²×C₄	C₂²×D₂₇₁
Fitting	#430×C₂₇₁	C₂
socle	C₂×C₂₇₁	#399
prime radical	C₂×#16864654	C₂²
hypercenter	#430	D₂₇₁
hypocenter	C₂₇₁	#2098
LCS	G ▷ C₂²×C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

subgroup

G/H

center

C₄

#22576156

commutator, cosocle

C₂²×C₄×C₂₇₁

C₂³

Frattini

C₂²×C₄

C₂²×D₂₇₁

Fitting

#430×C₂₇₁

C₂

C₂×C₂₇₁

C₂²

D₂₇₁

C₂₇₁

G ▷ C₂²×C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #430

N	H ≅ G/N	type
1. #31773925	C₂	semidirect
4. #31773654	C₂	semidirect
5. #430×C₂₇₁	C₂	semidirect
62. C₂₇₁	#2098	semidirect
64. #430	D₂₇₁	semidirect

H ≅ G/N

type

1. #31773925

C₂

semidirect

4. #31773654

C₂

semidirect

5. #430×C₂₇₁

C₂

semidirect

62. C₂₇₁

#2098

semidirect

64. #430

D₂₇₁

semidirect

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

subgroup	index
#31773925	2
#31773913	2
#31773865	2
#31773654	2
#430×C₂₇₁	2
#2098	271

subgroup

index

#430×C₂₇₁

271

Subgroups — #46837916

Conjugacy classes of subgroups

Complements

Maximal subgroups