Group #20245553 — subgroups

Subgroups — #20245553

Order 6016.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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	#15689525	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#15688951	C₂	1	1	yes	maximal, characteristic
4	#15688949	C₂	1	1	yes	maximal, characteristic
5	#15688928	C₂	1	1	yes	maximal, characteristic
6	#15688928	C₂	1	1	yes	maximal, characteristic
7	C₄₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	#13094016	—	2	1	no	—
10	C₄×Dic₉₄	—	2	1	no	—
11	#13093958	C₂²	1	1	yes	characteristic
12	#13093958	C₂²	1	1	yes	characteristic
13	#13093958	C₂²	1	1	yes	characteristic
14	#13093956	—	2	1	no	—
15	#13093949	—	2	1	no	—
16	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Dic₉₄	—	2	1	no	—
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₄²×C₄₇	D₄	1	1	yes	characteristic
23	C₄⋊Dic₄₇	—	2	1	no	—
24	C₄⋊Dic₄₇	—	2	1	no	—
25	C₄⋊Dic₄₇	—	2	1	no	—
26	Dic₄₇⋊C₄	—	4	1	no	—
27	Dic₄₇⋊C₄	—	4	1	no	—
28	Dic₄₇⋊C₄	—	4	1	no	—
29	C₄×Dic₄₇	—	4	1	no	—
30	Dic₁₈₈	—	2	1	no	—
31	Dic₁₈₈	Q₈	1	2	yes	—
32	C₁₆×C₄₇	—	2	1	no	—
33	C₁₆×C₄₇	—	2	1	no	—
34	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
35	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₄₇	—	4	1	no	—
38	C₂×Dic₄₇	—	4	1	no	—
39	C₂×Dic₄₇	—	4	1	no	—
40	C₂×Dic₄₇	—	4	1	no	—
41	Dic₉₄	—	2	2	no	—
42	Dic₉₄	—	4	1	no	—
43	C₈×C₄₇	—	2	1	no	—
44	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₄₇	#41	1	1	yes	characteristic
46	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
47	C₄×C₄₇	—	2	1	no	—
48	C₄×C₄₇	—	2	1	no	—
49	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
50	C₄×C₄₇	#137	1	1	yes	characteristic
51	Dic₄₇	—	4	2	no	—
52	Dic₄₇	—	8	1	no	—
53	Dic₄₇	—	8	1	no	—
54	Dic₄₇	—	8	1	no	—
55	#2229	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	#474	1	1	yes	characteristic
57	C₂×C₄₇	#508	1	1	yes	characteristic
58	C₂×C₄₇	#510	1	1	yes	characteristic
59	#499	—	47	1	no	—
60	C₄×Q₁₆	—	47	1	no	—
61	#367	—	47	1	no	—
62	#366	—	47	1	no	—
63	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic
64	#358	—	47	1	no	—
65	#358	—	47	1	no	—
66	C₄₇	#2229	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₁₆	—	47	1	no	—
68	#125	—	94	1	no	—
69	C₄×Q₈	—	94	1	no	—
70	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
71	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
72	#107	—	47	1	no	—
73	#107	—	47	1	no	—
74	#107	—	47	1	no	—
75	#106	—	94	1	no	—
76	#103	—	94	1	no	—
77	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
78	C₂×Q₈	—	94	1	no	—
79	Q₁₆	—	47	2	no	—
80	Q₁₆	—	94	1	no	—
81	C₂×C₈	D₁₈₈	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
83	C₄⋊C₄	—	94	1	no	—
84	C₄⋊C₄	—	94	1	no	—
85	C₄⋊C₄	—	94	1	no	—
86	C₄⋊C₄	—	188	1	no	—
87	C₄⋊C₄	—	188	1	no	—
88	C₄⋊C₄	—	188	1	no	—
89	C₄²	—	188	1	no	—
90	C₄²	D₁₈₈	1	1	yes	characteristic
91	C₁₆	—	2	1	no	—
92	C₁₆	—	2	1	no	—
93	Q₈	—	94	2	no	—
94	Q₈	—	188	1	no	—
95	C₂×C₄	—	188	1	no	—
96	C₂×C₄	—	188	1	no	—
97	C₂×C₄	—	188	1	no	—
98	C₂×C₄	—	188	1	no	—
99	C₂×C₄	D₃₇₆	1	1	yes	characteristic
100	C₂×C₄	D₃₇₆	1	1	yes	characteristic
101	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	#10625352	1	1	yes	characteristic
104	C₈	Q₈×D₄₇	1	1	yes	characteristic
105	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	376	1	no	—
109	C₄	—	376	1	no	—
110	C₄	—	376	1	no	—
111	C₄	—	188	2	no	—
112	C₄	#13094004	1	1	yes	characteristic
113	C₄	#13094057	1	1	yes	characteristic
114	C₂	#15689404	1	1	yes	characteristic
115	C₂	#15689555	1	1	yes	characteristic
116	C₂	#15689566	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689525

C₂

yes

maximal, characteristic

C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#15688951

C₂

yes

maximal, characteristic

#15688949

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, characteristic

C₄₇×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

characteristic

#13094016

—

C₄×Dic₉₄

—

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093956

—

#13093949

—

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

Q₈

yes

—

C₁₆×C₄₇

—

C₁₆×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₄×Q₁₆

—

#367

—

#366

—

C₄⋊C₁₆

D₄₇

yes

characteristic

#358

—

#358

—

C₄₇

#2229

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

#125

—

C₄×Q₈

—

C₂×C₁₆

C₂×D₄₇

yes

characteristic

C₂×C₁₆

C₂×D₄₇

yes

—

—

—

—

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

188

—

C₄²

D₁₈₈

yes

characteristic

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

characteristic

100

C₂×C₄

D₃₇₆

yes

characteristic

101

C₂×C₄

C₂×D₁₈₈

yes

characteristic

102

C₈

—

103

C₈

#10625352

yes

characteristic

104

C₈

Q₈×D₄₇

yes

characteristic

105

C₂²

C₂×D₃₇₆

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

376

—

109

C₄

—

376

—

110

C₄

—

376

—

111

C₄

—

188

—

112

C₄

#13094004

yes

characteristic

113

C₄

#13094057

yes

characteristic

114

C₂

#15689404

yes

characteristic

115

C₂

#15689555

yes

characteristic

116

C₂

#15689566

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×C₄⋊C₁₆	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#2229
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₃₇₆

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×C₄⋊C₁₆

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄⋊C₁₆

D₄₇

hypocenter

C₄₇

#2229

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
66. C₄₇	#2229	semidirect

H ≅ G/N

type

66. C₄₇

#2229

semidirect

Subgroups — #20245553

Conjugacy classes of subgroups

Complements