Group #49121434 — subgroups

Subgroups — #49121434

Order 36224.

212 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 101 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×#22583546	C₂	1	1	yes	maximal, characteristic
2	C₂×#22583545	C₂	1	2	yes	maximal
3	#31826488	C₂	1	2	yes	maximal
4	C₂×#22583520	C₂	1	1	yes	maximal, characteristic
5	C₂×#108×C₂₈₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#17985376	C₂²	1	2	yes	—
7	C₂²×C₂₈₃⋊C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₂₈₃	C₂²	1	1	yes	characteristic
9	#22583546	—	2	2	no	—
10	#22583545	—	2	4	no	—
11	Dic₂₈₃⋊C₈	—	2	4	no	—
12	#22583520	C₄	1	4	yes	—
13	C₂×M₁₆×C₂₈₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₂₈₃	C₂²	1	1	yes	characteristic
15	#108×C₂₈₃	—	2	2	no	—
16	C₂²×Dic₂₈₃	Q₈	1	2	yes	—
17	#17985376	—	2	2	no	—
18	#17985376	—	2	2	no	—
19	C₂×C₂₈₃⋊C₈	—	2	2	no	—
20	C₂×C₂₈₃⋊C₈	C₂×C₄	1	2	yes	—
21	C₂×C₂₈₃⋊C₈	D₄	1	2	yes	—
22	C₂×C₂₈₃⋊C₈	Q₈	1	2	yes	—
23	C₄×Dic₂₈₃	C₂×C₄	1	2	yes	—
24	C₄×Dic₂₈₃	D₄	1	2	yes	—
25	C₂²×C₄×C₂₈₃	C₂³	1	1	yes	characteristic
26	M₁₆×C₂₈₃	—	2	2	no	—
27	M₁₆×C₂₈₃	—	2	2	no	—
28	C₂×C₈×C₂₈₃	—	2	2	no	—
29	C₂×C₈×C₂₈₃	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₂₈₃	D₄	1	2	yes	—
31	C₂×C₈×C₂₈₃	Q₈	1	2	yes	—
32	C₂×Dic₂₈₃	—	4	2	no	—
33	C₂×Dic₂₈₃	C₄⋊C₄	1	4	yes	—
34	C₂₈₃⋊C₈	—	4	2	no	—
35	C₂₈₃⋊C₈	C₄⋊C₄	1	4	yes	—
36	C₂³×C₂₈₃	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₂₈₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₂₈₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₂₈₃	C₂×Q₈	1	1	yes	characteristic
42	C₂×C₄×C₂₈₃	C₂×Q₈	1	1	yes	characteristic
43	C₈×C₂₈₃	—	4	2	no	—
44	C₈×C₂₈₃	C₄⋊C₄	1	4	yes	—
45	C₂²×C₂₈₃	—	2	2	no	—
46	C₂²×C₂₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₂²×C₂₈₃	C₄⋊Q₈	1	1	yes	characteristic
48	C₂²×C₂₈₃	C₄⋊Q₈	1	1	yes	characteristic
49	C₄×C₂₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₂₈₃	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₂₈₃	#127	1	1	yes	characteristic
52	C₄×C₂₈₃	C₄⋊Q₈	1	1	yes	characteristic
53	Dic₂₈₃	—	2	4	no	—
54	C₂×C₂₈₃	—	2	1	no	—
55	C₂×C₂₈₃	—	2	1	no	—
56	C₂×C₂₈₃	#384	1	1	yes	characteristic
57	C₂×C₂₈₃	#430	1	2	yes	—
58	C₂₈₃	#1849	1	1	yes	characteristic, complemented, Sylow
59	#1849	—	283	1	no	maximal, Sylow
60	C₂×#108	—	283	2	no	—
61	C₂×#108	—	283	1	no	—
62	C₂×#108	D₂₈₃	1	1	yes	characteristic
63	#423	—	283	2	no	—
64	C₂×#97	—	283	1	no	—
65	C₂×M₁₆	—	283	2	no	—
66	C₂×M₁₆	C₂×D₂₈₃	1	2	yes	—
67	C₂²×C₈	—	283	1	no	—
68	C₂²×C₈	C₂×D₂₈₃	1	1	yes	characteristic
69	C₂×C₄²	—	283	1	no	—
70	#108	—	2	2	no	—
71	#108	—	566	4	no	—
72	#108	—	566	2	no	—
73	C₄⋊C₈	—	566	4	no	—
74	#97	—	283	4	no	—
75	C₂²×C₄	—	283	2	no	—
76	C₂²×C₄	C₂²×D₂₈₃	1	1	yes	characteristic
77	M₁₆	—	2	2	no	—
78	M₁₆	—	2	2	no	—
79	M₁₆	—	566	2	no	—
80	M₁₆	—	566	2	no	—
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	283	2	no	—
83	C₂×C₈	—	283	2	no	—
84	C₂×C₈	—	283	2	no	—
85	C₂×C₈	—	566	2	no	—
86	C₂×C₈	C₄×D₂₈₃	1	2	yes	—
87	C₂×C₈	C₂²⋊D₂₈₃	1	2	yes	—
88	C₂×C₈	Dic₅₆₆	1	2	yes	—
89	C₄²	—	283	2	no	—
90	C₄²	—	283	2	no	—
91	C₂³	Q₈×D₂₈₃	1	1	yes	characteristic
92	C₂×C₄	—	283	4	no	—
93	C₂×C₄	—	1132	2	no	—
94	C₂×C₄	C₂×C₄×D₂₈₃	1	1	yes	characteristic
95	C₂×C₄	D₄×D₂₈₃	1	1	yes	characteristic
96	C₂×C₄	D₄×D₂₈₃	1	1	yes	characteristic
97	C₂×C₄	C₂×C₂²⋊D₂₈₃	1	1	yes	characteristic
98	C₂×C₄	Q₈×D₂₈₃	1	1	yes	characteristic
99	C₂×C₄	C₂×Dic₅₆₆	1	1	yes	characteristic
100	C₈	—	4	2	no	—
101	C₈	—	283	4	no	—
102	C₈	—	1132	2	no	—
103	C₈	Dic₂₈₃⋊C₄	1	4	yes	—
104	C₂²	—	2	2	no	—
105	C₂²	C₄⋊C₄×D₂₈₃	1	1	yes	characteristic
106	C₂²	#22583608	1	1	yes	characteristic
107	C₂²	#22583609	1	1	yes	characteristic
108	C₄	—	566	4	no	—
109	C₄	C₄⋊C₄×D₂₈₃	1	1	yes	characteristic
110	C₄	C₂×Dic₂₈₃⋊C₄	1	1	yes	characteristic
111	C₄	#22583606	1	1	yes	characteristic
112	C₄	#22583609	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	#31826334	1	1	yes	characteristic
116	C₂	#31826512	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22583546

C₂

yes

maximal, characteristic

C₂×#22583545

C₂

yes

maximal

#31826488

C₂

yes

maximal

C₂×#22583520

C₂

yes

maximal, characteristic

C₂×#108×C₂₈₃

C₂

yes

maximal, characteristic

C₂×#17985376

C₂²

yes

—

C₂²×C₂₈₃⋊C₈

C₂²

yes

characteristic

C₂×C₄×Dic₂₈₃

C₂²

yes

characteristic

#22583546

—

#22583545

—

Dic₂₈₃⋊C₈

—

#22583520

C₄

yes

—

C₂×M₁₆×C₂₈₃

C₂²

yes

—

C₂²×C₈×C₂₈₃

C₂²

yes

characteristic

#108×C₂₈₃

—

C₂²×Dic₂₈₃

Q₈

yes

—

#17985376

—

#17985376

—

C₂×C₂₈₃⋊C₈

—

C₂×C₂₈₃⋊C₈

C₂×C₄

yes

—

C₂×C₂₈₃⋊C₈

D₄

yes

—

C₂×C₂₈₃⋊C₈

Q₈

yes

—

C₄×Dic₂₈₃

C₂×C₄

yes

—

C₄×Dic₂₈₃

D₄

yes

—

C₂²×C₄×C₂₈₃

C₂³

yes

characteristic

M₁₆×C₂₈₃

—

M₁₆×C₂₈₃

—

C₂×C₈×C₂₈₃

—

C₂×C₈×C₂₈₃

C₂×C₄

yes

—

C₂×C₈×C₂₈₃

D₄

yes

—

C₂×C₈×C₂₈₃

Q₈

yes

—

C₂×Dic₂₈₃

—

C₂×Dic₂₈₃

C₄⋊C₄

yes

—

C₂₈₃⋊C₈

—

C₂₈₃⋊C₈

C₄⋊C₄

yes

—

C₂³×C₂₈₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₈₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₈₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₈₃

C₂×Q₈

yes

characteristic

C₈×C₂₈₃

—

C₈×C₂₈₃

C₄⋊C₄

yes

—

C₂²×C₂₈₃

—

C₂²×C₂₈₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₈₃

C₄⋊Q₈

yes

characteristic

C₂²×C₂₈₃

C₄⋊Q₈

yes

characteristic

C₄×C₂₈₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₈₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₈₃

#127

yes

characteristic

C₄×C₂₈₃

C₄⋊Q₈

yes

characteristic

Dic₂₈₃

—

C₂×C₂₈₃

—

C₂×C₂₈₃

—

C₂×C₂₈₃

#384

yes

characteristic

C₂×C₂₈₃

#430

yes

—

C₂₈₃

#1849

yes

characteristic, complemented, Sylow

#1849

—

283

maximal, Sylow

C₂×#108

—

283

—

C₂×#108

—

283

—

C₂×#108

D₂₈₃

yes

characteristic

#423

—

283

—

C₂×#97

—

283

—

C₂×M₁₆

—

283

—

C₂×M₁₆

C₂×D₂₈₃

yes

—

C₂²×C₈

—

283

—

C₂²×C₈

C₂×D₂₈₃

yes

characteristic

C₂×C₄²

—

283

—

#108

—

#108

—

566

—

#108

—

566

—

C₄⋊C₈

—

566

—

#97

—

283

—

C₂²×C₄

—

283

—

C₂²×C₄

C₂²×D₂₈₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

566

—

M₁₆

—

566

—

C₂×C₈

—

C₂×C₈

—

283

—

C₂×C₈

—

283

—

C₂×C₈

—

283

—

C₂×C₈

—

566

—

C₂×C₈

C₄×D₂₈₃

yes

—

C₂×C₈

C₂²⋊D₂₈₃

yes

—

C₂×C₈

Dic₅₆₆

yes

—

C₄²

—

283

—

C₄²

—

283

—

C₂³

Q₈×D₂₈₃

yes

characteristic

C₂×C₄

—

283

—

C₂×C₄

—

1132

—

C₂×C₄

C₂×C₄×D₂₈₃

yes

characteristic

C₂×C₄

D₄×D₂₈₃

yes

characteristic

C₂×C₄

D₄×D₂₈₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₂₈₃

yes

characteristic

C₂×C₄

Q₈×D₂₈₃

yes

characteristic

C₂×C₄

C₂×Dic₅₆₆

yes

characteristic

100

C₈

—

101

C₈

—

283

—

102

C₈

—

1132

—

103

C₈

Dic₂₈₃⋊C₄

yes

—

104

C₂²

—

105

C₂²

C₄⋊C₄×D₂₈₃

yes

characteristic

106

C₂²

#22583608

yes

characteristic

107

C₂²

#22583609

yes

characteristic

108

C₄

—

566

—

109

C₄

C₄⋊C₄×D₂₈₃

yes

characteristic

110

C₄

C₂×Dic₂₈₃⋊C₄

yes

characteristic

111

C₄

#22583606

yes

characteristic

112

C₄

#22583609

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

#31826334

yes

characteristic

116

C₂

#31826512

yes

—

	subgroup	G/H
center	C₂×C₄	D₄×D₂₈₃
commutator	C₂×C₄×C₂₈₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₈₃
Fitting	C₂×#108×C₂₈₃	C₂
socle	C₂²×C₂₈₃	C₂×C₄⋊C₄
prime radical	C₂³×C₂₈₃	C₂×Q₈
cosocle	C₂²×C₄×C₂₈₃	C₂³
hypercenter	C₂×#108	D₂₈₃
hypocenter	C₂₈₃	#1849
LCS	G ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

subgroup

G/H

center

C₂×C₄

D₄×D₂₈₃

commutator

C₂×C₄×C₂₈₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₂₈₃

Fitting

C₂×#108×C₂₈₃

C₂

socle

C₂²×C₂₈₃

C₂×C₄⋊C₄

prime radical

C₂³×C₂₈₃

C₂×Q₈

cosocle

C₂²×C₄×C₂₈₃

C₂³

D₂₈₃

C₂₈₃

G ▷ C₂×C₄×C₂₈₃ ▷ C₂×C₂₈₃ ▷ C₂₈₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

N	H ≅ G/N	type
58. C₂₈₃	#1849	semidirect

H ≅ G/N

type

58. C₂₈₃

#1849

semidirect

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

subgroup	index
C₂×#22583546	2
C₂×#22583545	2
#31826488	2
C₂×#22583520	2
C₂×#108×C₂₈₃	2
#1849	283

subgroup

index

C₂×#108×C₂₈₃

283

Subgroups — #49121434

Conjugacy classes of subgroups

Complements

Maximal subgroups