Group #20245552 — subgroups

Subgroups — #20245552

Order 6016.

124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15688950	C₂	1	1	yes	maximal, characteristic
3	#15688948	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
5	#15688927	C₂	1	1	yes	maximal, characteristic
6	#15688927	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
8	#13094016	—	2	1	no	—
9	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	#13093958	C₂²	1	1	yes	characteristic
12	#13093958	C₂²	1	1	yes	characteristic
13	#13093956	—	2	1	no	—
14	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
15	C₄×Q₈×C₄₇	—	2	1	no	—
16	#107×C₄₇	C₂²	1	1	yes	characteristic
17	#103×C₄₇	—	2	1	no	—
18	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₇	—	2	1	no	—
20	Q₁₆×C₄₇	—	2	1	no	—
21	Q₁₆×C₄₇	Q₈	1	2	yes	—
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	1	no	—
25	C₄⋊C₄×C₄₇	—	4	1	no	—
26	C₄²×C₄₇	—	4	1	no	—
27	C₄²×C₄₇	D₄	1	1	yes	characteristic
28	C₄⋊Dic₄₇	—	2	1	no	—
29	C₄⋊Dic₄₇	—	2	1	no	—
30	Dic₄₇⋊C₄	—	4	1	no	—
31	Dic₄₇⋊C₄	—	4	1	no	—
32	C₄₇⋊C₁₆	—	2	1	no	—
33	C₄₇⋊C₁₆	—	2	1	no	—
34	Q₈×C₄₇	—	2	2	no	—
35	Q₈×C₄₇	—	4	1	no	—
36	C₂×C₄×C₄₇	—	4	1	no	—
37	C₂×C₄×C₄₇	—	4	1	no	—
38	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
39	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
40	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₄₇	—	4	1	no	—
42	C₂×Dic₄₇	—	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	—	4	2	no	—
50	C₄×C₄₇	—	8	1	no	—
51	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
52	C₄×C₄₇	#137	1	1	yes	characteristic
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	D₄₇	1	1	yes	characteristic
61	#367	—	47	1	no	—
62	#366	—	47	1	no	—
63	C₄⋊C₁₆	—	47	1	no	—
64	#358	—	47	1	no	—
65	#358	—	47	1	no	—
66	C₄₇	#2229	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
68	#125	—	94	1	no	—
69	C₄×Q₈	—	2	1	no	—
70	C₂×C₁₆	—	47	1	no	—
71	C₂×C₁₆	—	47	1	no	—
72	#107	—	47	1	no	—
73	#107	—	47	1	no	—
74	#107	C₂×D₄₇	1	1	yes	characteristic
75	#106	—	94	1	no	—
76	#103	—	2	1	no	—
77	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
78	C₂×Q₈	—	2	1	no	—
79	Q₁₆	—	2	1	no	—
80	Q₁₆	Dic₉₄	1	2	yes	—
81	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	4	1	no	—
85	C₄⋊C₄	—	94	1	no	—
86	C₄⋊C₄	—	94	1	no	—
87	C₄⋊C₄	—	188	1	no	—
88	C₄⋊C₄	—	188	1	no	—
89	C₄²	—	4	1	no	—
90	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
91	C₁₆	—	94	1	no	—
92	C₁₆	—	94	1	no	—
93	Q₈	—	2	2	no	—
94	Q₈	—	4	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	188	1	no	—
98	C₂×C₄	—	188	1	no	—
99	C₂×C₄	#10625334	1	1	yes	characteristic
100	C₂×C₄	#10625334	1	1	yes	characteristic
101	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	C₂×Dic₉₄	1	1	yes	characteristic
104	C₈	#10625350	1	1	yes	characteristic
105	C₂²	C₂×#10625334	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	4	2	no	—
109	C₄	—	8	1	no	—
110	C₄	—	376	1	no	—
111	C₄	—	376	1	no	—
112	C₄	#13094003	1	1	yes	characteristic
113	C₄	#13094054	1	1	yes	characteristic
114	C₂	#15689403	1	1	yes	characteristic
115	C₂	#15689553	1	1	yes	characteristic
116	C₂	#15689564	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689525

C₂

yes

maximal, characteristic

#15688950

C₂

yes

maximal, characteristic

#15688948

C₂

yes

maximal, characteristic

C₄⋊(C₄₇⋊C₁₆)

C₂

yes

maximal, characteristic

#15688927

C₂

yes

maximal, characteristic

#15688927

C₂

yes

maximal, characteristic

C₄×Q₁₆×C₄₇

C₂

yes

maximal, characteristic

#13094016

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093956

—

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

—

#107×C₄₇

C₂²

yes

characteristic

#103×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

Q₈

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄₇⋊C₁₆

—

C₄₇⋊C₁₆

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

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

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₄×Q₁₆

D₄₇

yes

characteristic

#367

—

#366

—

C₄⋊C₁₆

—

#358

—

#358

—

C₄₇

#2229

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

#125

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

—

#107

C₂×D₄₇

yes

characteristic

#106

—

#103

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

Q₁₆

—

Q₁₆

Dic₉₄

yes

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

C₄²

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

#10625334

yes

characteristic

100

C₂×C₄

#10625334

yes

characteristic

101

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

102

C₈

—

103

C₈

C₂×Dic₉₄

yes

characteristic

104

C₈

#10625350

yes

characteristic

105

C₂²

C₂×#10625334

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

376

—

111

C₄

—

376

—

112

C₄

#13094003

yes

characteristic

113

C₄

#13094054

yes

characteristic

114

C₂

#15689403

yes

characteristic

115

C₂

#15689553

yes

characteristic

116

C₂

#15689564

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10625334
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄×Q₁₆	D₄₇
hypocenter	C₄₇	#2229
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

subgroup

G/H

center

C₂²

C₂×#10625334

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄×Q₁₆×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄×Q₁₆

D₄₇

hypocenter

C₄₇

#2229

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×Q₁₆

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

H ≅ G/N

type

66. C₄₇

#2229

semidirect

Subgroups — #20245552

Conjugacy classes of subgroups

Complements