Group #20245151 — subgroups

Subgroups — C₂×#15688944 #20245151

Order 6016.

168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13093964	C₂	1	2	yes	maximal
2	#15688944	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093964	—	2	2	no	—
5	#13093964	C₂²	1	4	yes	—
6	C₂×C₄₇⋊C₁₆	—	2	2	no	—
7	C₂²×C₈×C₄₇	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₄₇	C₄	1	1	yes	characteristic
10	C₄×C₈×C₄₇	C₄	1	2	yes	—
11	C₄×C₈×C₄₇	C₂²	1	2	yes	—
12	C₂²×C₄×C₄₇	—	2	1	no	—
13	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	C₈	1	2	yes	—
15	C₂×C₈×C₄₇	C₈	1	2	yes	—
16	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
22	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
23	C₄²×C₄₇	—	2	1	no	—
24	C₄²×C₄₇	C₂×C₄	1	2	yes	—
25	C₄₇⋊C₁₆	—	2	4	no	—
26	C₂³×C₄₇	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₄₇	—	2	4	no	—
28	C₂×C₄×C₄₇	—	2	2	no	—
29	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
36	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
37	C₈×C₄₇	C₂×C₈	1	4	yes	—
38	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₄₇	—	2	2	no	—
41	C₂²×C₄₇	C₄⋊C₈	1	1	yes	characteristic
42	C₂²×C₄₇	C₄⋊C₈	1	1	yes	characteristic
43	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₄₇	—	2	4	no	—
45	C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
46	C₄×C₄₇	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
49	C₂×#364	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	—	2	1	no	—
51	C₂×C₄₇	—	2	1	no	—
52	C₂×C₄₇	#364	1	2	yes	complemented
53	C₂×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂×M₃₂	—	47	2	no	—
55	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
56	#364	—	47	4	no	—
57	C₄₇	C₂×#364	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	Dic₄₇	1	1	yes	characteristic
59	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
60	C₂×C₄²	Dic₄₇	1	1	yes	characteristic
61	M₃₂	—	47	4	no	—
62	M₃₂	—	94	2	no	—
63	C₂×C₁₆	—	94	2	no	—
64	C₄×C₈	Dic₄₇	1	2	yes	—
65	C₄×C₈	C₂×D₄₇	1	2	yes	—
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
68	C₂×C₈	C₄₇⋊C₈	1	2	yes	—
69	C₂×C₈	C₄₇⋊C₈	1	2	yes	—
70	C₂×C₈	Dic₉₄	1	1	yes	characteristic
71	C₂×C₈	Dic₉₄	1	1	yes	characteristic
72	C₂×C₈	D₁₈₈	1	1	yes	characteristic
73	C₂×C₈	D₁₈₈	1	1	yes	characteristic
74	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
75	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
77	C₄²	—	2	1	no	—
78	C₄²	C₂×Dic₄₇	1	2	yes	—
79	C₁₆	—	94	4	no	—
80	C₂³	#10625329	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
84	C₂×C₄	C₂×C₄₇⋊C₈	1	1	yes	characteristic
85	C₂×C₄	#10625329	1	1	yes	characteristic
86	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
87	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
88	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
89	C₈	C₂×C₄₇⋊C₈	1	4	yes	—
90	C₈	C₄⋊Dic₄₇	1	1	yes	characteristic
91	C₈	C₄⋊Dic₄₇	1	1	yes	characteristic
92	C₈	C₂×Dic₉₄	1	1	yes	characteristic
93	C₈	C₂×D₁₈₈	1	1	yes	characteristic
94	C₂²	—	2	2	no	—
95	C₂²	C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
96	C₂²	C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
97	C₂²	C₂×#10625329	1	1	yes	characteristic
98	C₄	—	2	4	no	—
99	C₄	C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
100	C₄	C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic
101	C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
102	C₄	C₂²×C₄₇⋊C₈	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	#15688944	1	2	yes	direct product factor
106	C₂	C₂×C₄⋊(C₄₇⋊C₈)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093964

C₂

yes

maximal

#15688944

C₂

yes

maximal, direct product factor

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic

#13093964

—

#13093964

C₂²

yes

—

C₂×C₄₇⋊C₁₆

—

C₂²×C₈×C₄₇

C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₄

yes

characteristic

C₄×C₈×C₄₇

C₄

yes

—

C₄×C₈×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₈

yes

—

C₂×C₈×C₄₇

C₈

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

C₂×C₈

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₈×C₄₇

C₂×C₈

yes

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

C₄⋊C₈

yes

characteristic

C₂²×C₄₇

C₄⋊C₈

yes

characteristic

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₄⋊C₈

yes

characteristic

C₄×C₄₇

C₄⋊C₈

yes

characteristic

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₂²×C₈

yes

characteristic

C₂×#364

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#364

yes

complemented

C₂×C₄₇

C₂×C₄⋊C₈

yes

characteristic

C₂×M₃₂

—

C₂×C₄×C₈

D₄₇

yes

characteristic

#364

—

C₄₇

C₂×#364

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

Dic₄₇

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

Dic₄₇

yes

—

C₄×C₈

C₂×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₄₇⋊C₈

yes

—

C₂×C₈

C₄₇⋊C₈

yes

—

C₂×C₈

Dic₉₄

yes

characteristic

C₂×C₈

Dic₉₄

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

—

C₄²

C₂×Dic₄₇

yes

—

C₁₆

—

C₂³

#10625329

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄₇⋊C₈

yes

characteristic

C₂×C₄

C₂×C₄₇⋊C₈

yes

characteristic

C₂×C₄

#10625329

yes

characteristic

C₂×C₄

C₄⋊Dic₄₇

yes

characteristic

C₂×C₄

C₄⋊Dic₄₇

yes

characteristic

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

C₂×C₄₇⋊C₈

yes

—

C₈

C₄⋊Dic₄₇

yes

characteristic

C₈

C₄⋊Dic₄₇

yes

characteristic

C₈

C₂×Dic₉₄

yes

characteristic

C₈

C₂×D₁₈₈

yes

characteristic

C₂²

—

C₂²

C₄⋊(C₄₇⋊C₈)

yes

characteristic

C₂²

C₄⋊(C₄₇⋊C₈)

yes

characteristic

C₂²

C₂×#10625329

yes

characteristic

C₄

—

C₄

C₄⋊(C₄₇⋊C₈)

yes

characteristic

100

C₄

C₄⋊(C₄₇⋊C₈)

yes

characteristic

101

C₄

C₂×C₄⋊Dic₄₇

yes

characteristic

102

C₄

C₂²×C₄₇⋊C₈

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

#15688944

yes

direct product factor

106

C₂

C₂×C₄⋊(C₄₇⋊C₈)

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₁₈₈
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂²×C₄₇	C₄⋊C₈
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	C₂×#364
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₈

D₁₈₈

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×C₄×C₈×C₄₇

C₂

socle

C₂²×C₄₇

C₄⋊C₈

hypercenter

C₂×C₄×C₈

D₄₇

hypocenter

C₄₇

C₂×#364

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #15688944	C₂	direct (N × H)
52. C₂×C₄₇	#364	semidirect
57. C₄₇	C₂×#364	semidirect
105. C₂	#15688944	direct (N × H)

H ≅ G/N

type

2. #15688944

C₂

direct (N × H)

52. C₂×C₄₇

#364

semidirect

57. C₄₇

C₂×#364

semidirect

105. C₂

#15688944

direct (N × H)

Subgroups — C₂×#15688944 #20245151

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15688944 #20245151

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688944 #20245151