Group #20245469 — subgroups

Subgroups — #20245469

Order 6016.

150 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 49 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	#15689563	C₂	1	2	yes	maximal
2	#15689503	C₂	1	1	yes	maximal, characteristic, complemented
3	#15688944	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688938	C₂	1	2	yes	maximal, complemented
5	C₄₇×#443	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	—	2	1	no	—
7	C₂×Dic₁₈₈	C₂²	1	2	yes	—
8	#13094024	—	2	1	no	—
9	#13093970	—	2	2	no	—
10	#13093968	—	2	2	no	—
11	#13093964	C₂²	1	2	yes	—
12	#135×C₄₇	C₂²	1	1	yes	characteristic
13	#131×C₄₇	—	2	1	no	—
14	#108×C₄₇	C₂²	1	1	yes	characteristic
15	#104×C₄₇	—	2	1	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	#41×C₄₇	—	2	1	no	—
18	C₂×Dic₉₄	—	2	2	no	—
19	Q₁₆×C₄₇	D₄	1	1	yes	characteristic
20	SD₁₆×C₄₇	—	2	1	no	—
21	D₈×C₄₇	D₄	1	1	yes	characteristic
22	M₁₆×C₄₇	—	2	1	no	—
23	M₁₆×C₄₇	—	4	1	no	—
24	C₂×C₈×C₄₇	—	4	1	no	—
25	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
26	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
27	C₄²×C₄₇	D₄	1	1	yes	characteristic
28	C₄⋊Dic₄₇	—	4	2	no	—
29	Dic₁₈₈	—	2	2	no	—
30	Dic₁₈₈	—	2	2	no	—
31	Dic₁₈₈	—	4	1	no	—
32	Dic₁₈₈	—	4	1	no	—
33	C₄₇⋊C₁₆	—	2	2	no	—
34	Q₈×C₄₇	—	2	1	no	—
35	D₄×C₄₇	—	2	1	no	—
36	D₄×C₄₇	—	4	1	no	—
37	C₂×C₄×C₄₇	—	2	1	no	—
38	C₂×C₄×C₄₇	—	4	1	no	—
39	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
40	C₂×Dic₄₇	—	4	2	no	—
41	Dic₉₄	—	4	2	no	—
42	Dic₉₄	—	4	2	no	—
43	C₈×C₄₇	—	4	1	no	—
44	C₈×C₄₇	D₈	1	1	yes	characteristic
45	C₈×C₄₇	D₈	1	1	yes	characteristic
46	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
47	C₈×C₄₇	#41	1	1	yes	characteristic
48	C₂²×C₄₇	—	4	1	no	—
49	C₂²×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
50	C₄×C₄₇	—	2	2	no	—
51	C₄×C₄₇	—	4	1	no	—
52	C₄×C₄₇	#121	1	1	yes	characteristic
53	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
54	Dic₄₇	—	8	2	no	—
55	#2214	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	—	2	1	no	—
57	C₂×C₄₇	—	8	1	no	—
58	C₂×C₄₇	#459	1	1	yes	characteristic
59	#510	—	47	2	no	—
60	#494	—	47	1	no	—
61	#443	D₄₇	1	1	yes	characteristic
62	#364	—	47	1	no	—
63	#362	—	47	2	no	—
64	C₄₇	#2214	1	1	yes	characteristic, complemented, Sylow
65	#135	C₂×D₄₇	1	1	yes	characteristic
66	C₂×Q₁₆	—	47	2	no	—
67	C₂×Q₁₆	—	94	1	no	—
68	#131	—	2	1	no	—
69	C₄⋊Q₈	—	94	1	no	—
70	Q₃₂	—	94	2	no	—
71	SD₃₂	—	94	2	no	—
72	M₃₂	—	47	2	no	—
73	#108	C₂×D₄₇	1	1	yes	characteristic
74	#104	—	2	1	no	—
75	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
76	#41	—	2	1	no	—
77	C₂×Q₈	—	94	2	no	—
78	Q₁₆	—	94	2	no	—
79	Q₁₆	—	94	2	no	—
80	Q₁₆	—	188	1	no	—
81	Q₁₆	—	188	1	no	—
82	Q₁₆	D₁₈₈	1	1	yes	characteristic
83	SD₁₆	—	2	1	no	—
84	D₈	D₁₈₈	1	1	yes	characteristic
85	M₁₆	—	2	1	no	—
86	M₁₆	—	4	1	no	—
87	C₂×C₈	—	4	1	no	—
88	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
89	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
90	C₄⋊C₄	—	188	2	no	—
91	C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
92	C₁₆	—	94	2	no	—
93	Q₈	—	2	1	no	—
94	Q₈	—	188	2	no	—
95	Q₈	—	188	2	no	—
96	D₄	—	2	1	no	—
97	D₄	—	4	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	4	1	no	—
100	C₂×C₄	—	188	2	no	—
101	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
102	C₈	—	4	1	no	—
103	C₈	#10625334	1	1	yes	characteristic
104	C₈	#10625334	1	1	yes	characteristic
105	C₈	C₂×D₁₈₈	1	1	yes	characteristic
106	C₈	#10625350	1	1	yes	characteristic
107	C₂²	—	4	1	no	—
108	C₂²	#13094049	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	4	1	no	—
111	C₄	—	376	2	no	—
112	C₄	#13093998	1	1	yes	characteristic
113	C₄	C₂×#10625334	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	8	1	no	—
116	C₂	#15689318	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689563

C₂

yes

maximal

#15689503

C₂

yes

maximal, characteristic, complemented

#15688944

C₂

yes

maximal, characteristic, complemented

#15688938

C₂

yes

maximal, complemented

C₄₇×#443

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂²

yes

—

—

—

—

C₂²

yes

—

#135×C₄₇

C₂²

yes

characteristic

#131×C₄₇

—

#108×C₄₇

C₂²

yes

characteristic

#104×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

#41×C₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

D₄

yes

characteristic

SD₁₆×C₄₇

—

D₈×C₄₇

D₄

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

C₄₇⋊C₁₆

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

D₈

yes

characteristic

C₈×C₄₇

D₈

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

AGL(1,ℤ/8)

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#121

yes

characteristic

C₄×C₄₇

C₂×D₈

yes

characteristic

Dic₄₇

—

#2214

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#364

—

#362

—

C₄₇

#2214

yes

characteristic, complemented, Sylow

#135

C₂×D₄₇

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

#131

—

C₄⋊Q₈

—

Q₃₂

—

SD₃₂

—

M₃₂

—

#108

C₂×D₄₇

yes

characteristic

#104

—

C₄×C₈

C₂×D₄₇

yes

characteristic

#41

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

188

—

Q₁₆

—

188

—

Q₁₆

D₁₈₈

yes

characteristic

SD₁₆

—

D₈

D₁₈₈

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

188

—

C₄²

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

188

—

Q₈

—

188

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

188

—

101

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

102

C₈

—

103

C₈

#10625334

yes

characteristic

104

C₈

#10625334

yes

characteristic

105

C₈

C₂×D₁₈₈

yes

characteristic

106

C₈

#10625350

yes

characteristic

107

C₂²

—

108

C₂²

#13094049

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

376

—

112

C₄

#13093998

yes

characteristic

113

C₄

C₂×#10625334

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

#15689318

yes

characteristic

	subgroup	G/H
center	C₂	#15689318
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#443	C₂
socle	C₂×C₄₇	#459
hypercenter	#443	D₄₇
hypocenter	C₄₇	#2214
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

subgroup

G/H

center

C₂

#15689318

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#443

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #443

N	H ≅ G/N	type
2. #15689503	C₂	semidirect
3. #15688944	C₂	semidirect
4. #15688938	C₂	semidirect
64. C₄₇	#2214	semidirect

H ≅ G/N

type

2. #15689503

C₂

semidirect

3. #15688944

C₂

semidirect

4. #15688938

C₂

semidirect

64. C₄₇

#2214

semidirect

Subgroups — #20245469

Conjugacy classes of subgroups

Complements