Group #20245775 — subgroups

Subgroups — C₂×#15688989 #20245775

Order 6016.

712 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 389 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	C₂²×C₄⋊Dic₄₇	C₂	1	2	yes	maximal
2	#15688989	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄₇⋊#95	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₇	C₂²	1	4	yes	—
6	C₂×C₄⋊Dic₄₇	—	2	8	no	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	8	yes	—
8	C₄₇⋊#95	C₂²	1	16	yes	—
9	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
10	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₇	C₄	1	8	yes	complemented
12	C₂×C₄²×C₄₇	C₂²	1	4	yes	—
13	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	—	2	8	no	—
15	C₂²×C₄×C₄₇	C₂×C₄	1	8	yes	—
16	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₄₇	D₄	1	4	yes	—
18	C₂²×C₄×C₄₇	Q₈	1	4	yes	—
19	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
21	C₂²×Dic₄₇	—	2	8	no	—
22	C₂²×Dic₄₇	—	2	16	no	—
23	C₂²×Dic₄₇	C₂³	1	8	yes	—
24	C₄²×C₄₇	C₂×C₄	1	16	yes	complemented
25	C₄⋊Dic₄₇	—	2	16	no	—
26	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
27	C₂³×C₄₇	C₂×D₄	1	2	yes	—
28	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
29	C₂³×C₄₇	#41	1	8	yes	—
30	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₄₇	—	2	16	no	—
32	C₂×C₄×C₄₇	—	2	8	no	—
33	C₂×C₄×C₄₇	C₄⋊C₄	1	16	yes	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	8	yes	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
36	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
37	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
38	C₂×Dic₄₇	—	2	8	no	—
39	C₂×Dic₄₇	—	2	16	no	—
40	C₂×Dic₄₇	—	4	16	no	—
41	C₂²×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
42	C₂²×C₄₇	#117	1	8	yes	—
43	C₂²×C₄₇	#124	1	8	yes	—
44	C₂²×C₄₇	#125	1	8	yes	—
45	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
46	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
47	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
48	C₂²×C₄₇	C₂×#41	1	4	yes	—
49	C₄×C₄₇	—	2	8	no	—
50	C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
51	Dic₄₇	—	4	8	no	—
52	C₂×#382	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	#382	1	8	yes	complemented
54	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄₇	C₂×#117	1	2	yes	—
56	C₂×C₄₇	C₂×#124	1	2	yes	—
57	C₂×C₄₇	C₂×#125	1	2	yes	—
58	C₂²×C₄⋊C₄	—	47	2	no	—
59	C₂²×C₄²	D₄₇	1	1	yes	characteristic
60	#382	—	47	8	no	—
61	C₂×#95	—	47	4	no	—
62	C₄₇	C₂×#382	1	1	yes	characteristic, complemented, Sylow
63	C₂³×C₄	—	47	4	no	—
64	C₂³×C₄	C₂×D₄₇	1	2	yes	—
65	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
66	C₂×C₄⋊C₄	—	47	8	no	—
67	C₂×C₄⋊C₄	—	94	8	no	—
68	C₂×C₄²	Dic₄₇	1	8	yes	complemented
69	C₂×C₄²	C₂×D₄₇	1	4	yes	—
70	#95	—	47	16	no	—
71	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
72	C₂²×C₄	—	2	8	no	—
73	C₂²×C₄	—	47	8	no	—
74	C₂²×C₄	—	94	8	no	—
75	C₂²×C₄	—	94	16	no	—
76	C₂²×C₄	Dic₉₄	1	4	yes	—
77	C₂²×C₄	D₁₈₈	1	4	yes	—
78	C₂²×C₄	C₂×Dic₄₇	1	8	yes	—
79	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
80	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
81	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
82	C₄⋊C₄	—	94	16	no	—
83	C₄²	C₂×Dic₄₇	1	16	yes	complemented
84	C₂³	C₂×Dic₉₄	1	2	yes	—
85	C₂³	C₂×D₁₈₈	1	2	yes	—
86	C₂³	#10625350	1	8	yes	—
87	C₂³	C₂²×Dic₄₇	1	2	yes	—
88	C₂³	C₂³×D₄₇	1	1	yes	characteristic
89	C₂×C₄	—	2	16	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	94	8	no	—
92	C₂×C₄	—	94	16	no	—
93	C₂×C₄	—	188	16	no	—
94	C₂×C₄	C₄⋊Dic₄₇	1	16	yes	—
95	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
96	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
97	C₂×C₄	C₂²×Dic₄₇	1	8	yes	—
98	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
99	C₂²	C₂×C₄⋊Dic₄₇	1	4	yes	—
100	C₂²	#13093983	1	8	yes	—
101	C₂²	#13094012	1	8	yes	—
102	C₂²	#13094016	1	8	yes	—
103	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
104	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
105	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
106	C₂²	C₂×#10625350	1	4	yes	—
107	C₄	—	2	8	no	—
108	C₄	—	188	8	no	—
109	C₄	C₂×C₄⋊Dic₄₇	1	8	yes	—
110	C₂	#15688989	1	8	yes	direct product factor
111	C₂	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
112	C₂	C₂×#13093983	1	2	yes	—
113	C₂	C₂×#13094012	1	2	yes	—
114	C₂	C₂×#13094016	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₇

C₂

yes

maximal

#15688989

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂²×C₄²×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₄

yes

complemented

C₂×C₄²×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂³

yes

—

C₄²×C₄₇

C₂×C₄

yes

complemented

C₄⋊Dic₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂×Q₈

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

#125

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₄₇

C₂×#117

yes

—

C₂×C₄₇

C₂×#124

yes

—

C₂×C₄₇

C₂×#125

yes

—

C₂²×C₄⋊C₄

—

C₂²×C₄²

D₄₇

yes

characteristic

#382

—

C₂×#95

—

C₄₇

C₂×#382

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

Dic₄₇

yes

complemented

C₂×C₄²

C₂×D₄₇

yes

—

#95

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₉₄

yes

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄²

C₂×Dic₄₇

yes

complemented

C₂³

C₂×Dic₉₄

yes

—

C₂³

C₂×D₁₈₈

yes

—

C₂³

#10625350

yes

—

C₂³

C₂²×Dic₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₄⋊Dic₄₇

yes

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂²

C₂×C₄⋊Dic₄₇

yes

—

100

C₂²

#13093983

yes

—

101

C₂²

#13094012

yes

—

102

C₂²

#13094016

yes

—

103

C₂²

C₂³×Dic₄₇

yes

characteristic

104

C₂²

C₂²×D₁₈₈

yes

characteristic

105

C₂²

C₂²×Dic₉₄

yes

characteristic

106

C₂²

C₂×#10625350

yes

—

107

C₄

—

108

C₄

—

188

—

109

C₄

C₂×C₄⋊Dic₄₇

yes

—

110

C₂

#15688989

yes

direct product factor

111

C₂

C₂²×C₄⋊Dic₄₇

yes

characteristic

112

C₂

C₂×#13093983

yes

—

113

C₂

C₂×#13094012

yes

—

114

C₂

C₂×#13094016

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂²×C₄²×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂²×C₄²	D₄₇
hypocenter	C₄₇	C₂×#382
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

subgroup

G/H

center

C₂⁴

C₂²×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂²×C₄²×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂²×C₄²

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂⁴ ◁ C₂²×C₄²

N	H ≅ G/N	type
2. #15688989	C₂	direct (N × H)
11. C₂×C₄²×C₄₇	C₄	semidirect
24. C₄²×C₄₇	C₂×C₄	semidirect
53. C₂×C₄₇	#382	semidirect
62. C₄₇	C₂×#382	semidirect
68. C₂×C₄²	Dic₄₇	semidirect
83. C₄²	C₂×Dic₄₇	semidirect
110. C₂	#15688989	direct (N × H)

H ≅ G/N

type

2. #15688989

C₂

direct (N × H)

11. C₂×C₄²×C₄₇

C₄

semidirect

24. C₄²×C₄₇

C₂×C₄

semidirect

53. C₂×C₄₇

#382

semidirect

62. C₄₇

C₂×#382

semidirect

68. C₂×C₄²

Dic₄₇

semidirect

83. C₄²

C₂×Dic₄₇

semidirect

110. C₂

#15688989

direct (N × H)

Subgroups — C₂×#15688989 #20245775

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15688989 #20245775

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688989 #20245775