Group #46835443 — subgroups

Subgroups — #46835443

Order 34688.

228 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 57 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	#31774627	C₂	1	1	yes	maximal, characteristic, complemented
2	#31774271	C₂	1	1	yes	maximal, characteristic
3	#31774098	C₂	1	2	yes	maximal
4	#31773627	C₂	1	2	yes	maximal, complemented
5	#333×C₂₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16864643	—	2	2	no	—
7	C₂×#16864641	—	2	2	no	—
8	#22576159	—	2	2	no	—
9	#22576158	—	2	2	no	—
10	#22576157	C₂²	1	1	yes	characteristic
11	C₄×Dic₅₄₂	C₂²	1	2	yes	—
12	#22576125	—	2	2	no	—
13	#22576082	—	2	2	no	—
14	C₄×C₂₇₁⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×C₂₇₁	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₂₇₁	C₂²	1	2	yes	—
17	C₂×Dic₅₄₂	—	2	2	no	—
18	C₂×Dic₅₄₂	D₄	1	2	yes	—
19	C₂×D₁₀₈₄	—	2	1	no	—
20	C₂×D₁₀₈₄	—	2	2	no	—
21	#16864643	—	4	4	no	—
22	#16864641	—	4	4	no	—
23	C₂×C₂₇₁⋊C₈	—	2	1	no	—
24	C₄⋊Dic₂₇₁	D₄	1	2	yes	—
25	Dic₂₇₁⋊C₄	—	2	4	no	—
26	Dic₂₇₁⋊C₄	—	2	2	no	—
27	C₄×Dic₂₇₁	—	2	2	no	—
28	C₄×Dic₂₇₁	—	2	2	no	—
29	C₂×Q₈×C₂₇₁	D₄	1	2	yes	—
30	C₂×C₈×C₂₇₁	—	2	2	no	—
31	C₄⋊C₄×C₂₇₁	—	2	2	no	—
32	C₄²×C₂₇₁	C₂³	1	1	yes	characteristic
33	C₂²×D₂₇₁	—	4	1	no	—
34	Dic₅₄₂	—	2	2	no	—
35	Dic₅₄₂	—	8	2	no	—
36	Dic₅₄₂	SD₁₆	1	4	yes	complemented
37	D₁₀₈₄	—	4	2	no	—
38	D₁₀₈₄	—	4	2	no	—
39	D₁₀₈₄	—	4	2	no	—
40	C₂×Dic₂₇₁	—	2	2	no	—
41	C₂×Dic₂₇₁	—	2	2	no	—
42	C₂₇₁⋊C₈	—	2	2	no	—
43	Q₈×C₂₇₁	—	4	2	no	—
44	C₂×C₄×C₂₇₁	—	2	2	no	—
45	C₂×C₄×C₂₇₁	C₂×D₄	1	2	yes	—
46	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
47	C₈×C₂₇₁	—	4	2	no	—
48	C₂²×C₂₇₁	#120	1	1	yes	characteristic
49	C₂×D₂₇₁	—	8	2	no	—
50	C₂×D₂₇₁	—	8	1	no	—
51	C₄×C₂₇₁	—	2	1	no	—
52	C₄×C₂₇₁	—	4	2	no	—
53	C₄×C₂₇₁	C₂×SD₁₆	1	2	yes	—
54	C₄×C₂₇₁	#137	1	2	yes	—
55	Dic₂₇₁	—	2	4	no	—
56	Dic₂₇₁	—	4	2	no	—
57	C₂×C₂₇₁	#448	1	2	yes	—
58	C₂×C₂₇₁	#453	1	1	yes	characteristic
59	D₂₇₁	—	16	1	no	—
60	C₂₇₁	#1623	1	1	yes	characteristic, complemented, Sylow
61	#1623	—	271	1	no	maximal, Sylow
62	Q₈²	—	271	1	no	—
63	#492	—	271	1	no	—
64	#460	—	271	2	no	—
65	#333	D₂₇₁	1	1	yes	characteristic, complemented
66	Q₈⋊C₈	—	271	2	no	—
67	C₂×SD₁₆	—	542	2	no	—
68	C₂×SD₁₆	—	542	2	no	—
69	C₄⋊Q₈	—	542	2	no	—
70	C₄⋊Q₈	—	542	2	no	—
71	C₄⋊Q₈	C₂×D₂₇₁	1	1	yes	characteristic
72	#127	—	271	1	no	—
73	C₄×Q₈	—	271	2	no	—
74	C₄×Q₈	—	542	2	no	—
75	C₄⋊C₈	C₂×D₂₇₁	1	2	yes	—
76	#102	—	542	2	no	—
77	C₄×C₈	—	271	1	no	—
78	C₂×Q₈	—	271	2	no	—
79	C₂×Q₈	—	542	2	no	—
80	C₂×Q₈	D₁₀₈₄	1	2	yes	—
81	C₂×D₄	—	542	2	no	—
82	C₂×D₄	—	542	1	no	—
83	SD₁₆	—	1084	4	no	—
84	SD₁₆	—	1084	4	no	—
85	C₂×C₈	—	2	2	no	—
86	C₂×C₈	—	542	1	no	—
87	C₄⋊C₄	—	2	2	no	—
88	C₄⋊C₄	—	271	2	no	—
89	C₄⋊C₄	—	542	4	no	—
90	C₄⋊C₄	—	542	2	no	—
91	C₄²	—	542	2	no	—
92	C₄²	—	542	2	no	—
93	C₄²	C₂²×D₂₇₁	1	1	yes	characteristic
94	C₂³	—	1084	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	271	4	no	—
97	Q₈	—	542	2	no	—
98	Q₈	—	2168	2	no	—
99	D₄	—	1084	2	no	—
100	D₄	—	1084	2	no	—
101	D₄	—	1084	2	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	542	2	no	—
104	C₂×C₄	—	542	2	no	—
105	C₂×C₄	D₄×D₂₇₁	1	2	yes	—
106	C₂×C₄	C₂×D₁₀₈₄	1	1	yes	characteristic
107	C₈	—	4	2	no	—
108	C₈	—	542	2	no	—
109	C₂²	—	2168	2	no	—
110	C₂²	—	2168	1	no	—
111	C₂²	#22576130	1	1	yes	characteristic
112	C₄	—	2	1	no	—
113	C₄	—	4	2	no	—
114	C₄	—	542	4	no	—
115	C₄	—	1084	2	no	—
116	C₄	SD₁₆×D₂₇₁	1	2	yes	—
117	C₄	#22576192	1	2	yes	—
118	C₂	—	4336	1	no	—
119	C₂	#31774037	1	2	yes	—
120	C₂	#31774067	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31774627

C₂

yes

maximal, characteristic, complemented

#31774271

C₂

yes

maximal, characteristic

#31774098

C₂

yes

maximal

#31773627

C₂

yes

maximal, complemented

#333×C₂₇₁

C₂

yes

maximal, characteristic, complemented

—

—

—

—

C₂²

yes

characteristic

C₄×Dic₅₄₂

C₂²

yes

—

#22576125

—

#22576082

—

C₄×C₂₇₁⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₂₇₁

C₂²

yes

characteristic

C₄⋊C₈×C₂₇₁

C₂²

yes

—

C₂×Dic₅₄₂

—

C₂×Dic₅₄₂

D₄

yes

—

C₂×D₁₀₈₄

—

C₂×D₁₀₈₄

—

#16864643

—

#16864641

—

C₂×C₂₇₁⋊C₈

—

C₄⋊Dic₂₇₁

D₄

yes

—

Dic₂₇₁⋊C₄

—

Dic₂₇₁⋊C₄

—

C₄×Dic₂₇₁

—

C₄×Dic₂₇₁

—

C₂×Q₈×C₂₇₁

D₄

yes

—

C₂×C₈×C₂₇₁

—

C₄⋊C₄×C₂₇₁

—

C₄²×C₂₇₁

C₂³

yes

characteristic

C₂²×D₂₇₁

—

Dic₅₄₂

—

Dic₅₄₂

—

Dic₅₄₂

SD₁₆

yes

complemented

D₁₀₈₄

—

D₁₀₈₄

—

D₁₀₈₄

—

C₂×Dic₂₇₁

—

C₂×Dic₂₇₁

—

C₂₇₁⋊C₈

—

Q₈×C₂₇₁

—

C₂×C₄×C₂₇₁

—

C₂×C₄×C₂₇₁

C₂×D₄

yes

—

C₂×C₄×C₂₇₁

C₂×D₄

yes

characteristic

C₈×C₂₇₁

—

C₂²×C₂₇₁

#120

yes

characteristic

C₂×D₂₇₁

—

C₂×D₂₇₁

—

C₄×C₂₇₁

—

C₄×C₂₇₁

—

C₄×C₂₇₁

C₂×SD₁₆

yes

—

C₄×C₂₇₁

#137

yes

—

Dic₂₇₁

—

Dic₂₇₁

—

C₂×C₂₇₁

#448

yes

—

C₂×C₂₇₁

#453

yes

characteristic

D₂₇₁

—

C₂₇₁

#1623

yes

characteristic, complemented, Sylow

#1623

—

271

maximal, Sylow

Q₈²

—

271

—

#492

—

271

—

#460

—

271

—

#333

D₂₇₁

yes

characteristic, complemented

Q₈⋊C₈

—

271

—

C₂×SD₁₆

—

542

—

C₂×SD₁₆

—

542

—

C₄⋊Q₈

—

542

—

C₄⋊Q₈

—

542

—

C₄⋊Q₈

C₂×D₂₇₁

yes

characteristic

#127

—

271

—

C₄×Q₈

—

271

—

C₄×Q₈

—

542

—

C₄⋊C₈

C₂×D₂₇₁

yes

—

#102

—

542

—

C₄×C₈

—

271

—

C₂×Q₈

—

271

—

C₂×Q₈

—

542

—

C₂×Q₈

D₁₀₈₄

yes

—

C₂×D₄

—

542

—

C₂×D₄

—

542

—

SD₁₆

—

1084

—

SD₁₆

—

1084

—

C₂×C₈

—

C₂×C₈

—

542

—

C₄⋊C₄

—

C₄⋊C₄

—

271

—

C₄⋊C₄

—

542

—

C₄⋊C₄

—

542

—

C₄²

—

542

—

C₄²

—

542

—

C₄²

C₂²×D₂₇₁

yes

characteristic

C₂³

—

1084

—

Q₈

—

Q₈

—

271

—

Q₈

—

542

—

Q₈

—

2168

—

D₄

—

1084

—

100

D₄

—

1084

—

101

D₄

—

1084

—

102

C₂×C₄

—

103

C₂×C₄

—

542

—

104

C₂×C₄

—

542

—

105

C₂×C₄

D₄×D₂₇₁

yes

—

106

C₂×C₄

C₂×D₁₀₈₄

yes

characteristic

107

C₈

—

108

C₈

—

542

—

109

C₂²

—

2168

—

110

C₂²

—

2168

—

111

C₂²

#22576130

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

542

—

115

C₄

—

1084

—

116

C₄

SD₁₆×D₂₇₁

yes

—

117

C₄

#22576192

yes

—

118

C₂

—

4336

—

119

C₂

#31774037

yes

—

120

C₂

#31774067

yes

characteristic

	subgroup	G/H
center	C₂²	#22576130
commutator, cosocle	C₄²×C₂₇₁	C₂³
Frattini	C₄²	C₂²×D₂₇₁
Fitting	#333×C₂₇₁	C₂
socle	C₂²×C₂₇₁	#120
prime radical	#22576157	C₂²
hypercenter	#333	D₂₇₁
hypocenter	C₂₇₁	#1623
LCS	G ▷ C₄²×C₂₇₁ ▷ C₂²×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

#22576130

commutator, cosocle

C₄²×C₂₇₁

C₂³

Frattini

C₄²

C₂²×D₂₇₁

Fitting

#333×C₂₇₁

C₂

C₂²×C₂₇₁

C₂²

D₂₇₁

C₂₇₁

G ▷ C₄²×C₂₇₁ ▷ C₂²×C₂₇₁ ▷ C₂₇₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
1. #31774627	C₂	semidirect
4. #31773627	C₂	semidirect
5. #333×C₂₇₁	C₂	semidirect
36. Dic₅₄₂	SD₁₆	semidirect
60. C₂₇₁	#1623	semidirect
65. #333	D₂₇₁	semidirect

H ≅ G/N

type

1. #31774627

C₂

semidirect

4. #31773627

C₂

semidirect

5. #333×C₂₇₁

C₂

semidirect

36. Dic₅₄₂

SD₁₆

semidirect

60. C₂₇₁

#1623

semidirect

65. #333

D₂₇₁

semidirect

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

subgroup	index
#31774627	2
#31774271	2
#31774098	2
#31773627	2
#333×C₂₇₁	2
#1623	271

subgroup

index

#333×C₂₇₁

271

Subgroups — #46835443

Conjugacy classes of subgroups

Complements

Maximal subgroups