Group #20243281 — subgroups

Subgroups — C₄×#13093958 #20243281

Order 6016.

280 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13093958	C₂	1	2	yes	maximal
2	C₄×C₄⋊Dic₄₇	C₂	1	2	yes	maximal
3	#15688886	C₂	1	2	yes	maximal
4	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
6	C₂×C₄×Dic₄₇	—	2	2	no	—
7	#13093958	C₄	1	8	yes	direct product factor
8	C₄₇⋊#95	—	2	2	no	—
9	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₄₇	C₄	1	4	yes	complemented
13	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₇	—	2	4	no	—
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₄₇	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
21	C₄²×C₄₇	C₂×C₄	1	2	yes	—
22	C₄²×C₄₇	Q₈	1	2	yes	—
23	C₄⋊Dic₄₇	—	2	4	no	—
24	C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
25	C₄×Dic₄₇	—	4	4	no	—
26	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	—	2	2	no	—
28	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₄₇	D₈	1	2	yes	—
31	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
32	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
33	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₄₇	#41	1	2	yes	—
36	C₂×Dic₄₇	—	2	8	no	—
37	C₂×Dic₄₇	—	4	4	no	—
38	C₂×Dic₄₇	—	4	4	no	—
39	C₈×C₄₇	—	2	2	no	—
40	C₈×C₄₇	C₄²	1	4	yes	complemented
41	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₄₇	C₄×D₄	1	2	yes	—
43	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
44	C₂²×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
45	C₂²×C₄₇	#135	1	2	yes	—
46	C₄×C₄₇	—	2	2	no	—
47	C₄×C₄₇	#107	1	4	yes	complemented
48	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
49	C₄×C₄₇	#117	1	1	yes	characteristic
50	C₄×C₄₇	C₄×Q₈	1	2	yes	—
51	Dic₄₇	—	4	8	no	—
52	C₄×#107	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₄₇	C₂×#107	1	1	yes	characteristic
55	C₂×C₄₇	#427	1	1	yes	characteristic
56	C₂×C₄₇	C₄×D₈	1	2	yes	—
57	C₂×C₄₇	C₄×Q₁₆	1	2	yes	—
58	C₂×#107	—	47	2	no	—
59	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic
60	C₄×C₄⋊C₄	—	47	2	no	—
61	#340	—	47	2	no	—
62	C₄₇	C₄×#107	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
64	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
65	C₂×C₄⋊C₄	—	47	4	no	—
66	C₂×C₄²	—	94	2	no	—
67	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
68	#107	—	47	8	no	—
69	C₄×C₈	Dic₄₇	1	4	yes	complemented
70	#95	—	94	2	no	—
71	C₂²×C₄	—	94	4	no	—
72	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
73	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
74	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	C₄×D₄₇	1	4	yes	—
77	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
78	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
79	C₄⋊C₄	—	47	8	no	—
80	C₄⋊C₄	—	94	4	no	—
81	C₄²	—	188	4	no	—
82	C₄²	Dic₉₄	1	2	yes	—
83	C₄²	C₂×Dic₄₇	1	2	yes	—
84	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	94	8	no	—
87	C₂×C₄	—	188	4	no	—
88	C₂×C₄	—	188	4	no	—
89	C₂×C₄	D₃₇₆	1	2	yes	—
90	C₂×C₄	Dic₁₈₈	1	2	yes	—
91	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
92	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
93	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
94	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
95	C₂×C₄	#10625350	1	2	yes	—
96	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
97	C₈	—	2	2	no	—
98	C₈	C₄×Dic₄₇	1	4	yes	complemented
99	C₂²	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
100	C₂²	C₄×D₁₈₈	1	2	yes	—
101	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
102	C₂²	C₂×Dic₁₈₈	1	1	yes	characteristic
103	C₂²	#13094046	1	2	yes	—
104	C₄	—	2	2	no	—
105	C₄	—	188	8	no	—
106	C₄	#13093958	1	4	yes	direct product factor
107	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
108	C₄	#13093983	1	1	yes	characteristic
109	C₄	C₄×Dic₉₄	1	2	yes	—
110	C₂	C₄×C₄⋊Dic₄₇	1	1	yes	characteristic
111	C₂	C₂×#13093958	1	1	yes	characteristic
112	C₂	#15689161	1	1	yes	characteristic
113	C₂	C₄×D₃₇₆	1	2	yes	—
114	C₂	C₄×Dic₁₈₈	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093958

C₂

yes

maximal

C₄×C₄⋊Dic₄₇

C₂

yes

maximal

#15688886

C₂

yes

maximal

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

—

#13093958

C₄

yes

direct product factor

C₄₇⋊#95

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

D₈

yes

—

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₄²

yes

complemented

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

C₄×D₄

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₂²×C₄₇

C₂×Q₁₆

yes

characteristic

C₂²×C₄₇

#135

yes

—

C₄×C₄₇

—

C₄×C₄₇

#107

yes

complemented

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

#117

yes

characteristic

C₄×C₄₇

C₄×Q₈

yes

—

Dic₄₇

—

C₄×#107

—

maximal, Sylow

C₂×C₄₇

C₄×C₄⋊C₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₄×D₈

yes

—

C₂×C₄₇

C₄×Q₁₆

yes

—

C₂×#107

—

C₂×C₄×C₈

D₄₇

yes

characteristic

C₄×C₄⋊C₄

—

#340

—

C₄₇

C₄×#107

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#107

—

C₄×C₈

Dic₄₇

yes

complemented

#95

—

C₂²×C₄

—

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

188

—

C₄²

Dic₉₄

yes

—

C₄²

C₂×Dic₄₇

yes

—

C₂³

C₂×D₁₈₈

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

—

C₂×C₄

Dic₁₈₈

yes

—

C₂×C₄

C₄⋊Dic₄₇

yes

—

C₂×C₄

C₄⋊Dic₄₇

yes

—

C₂×C₄

C₂×Dic₉₄

yes

characteristic

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

#10625350

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

C₄×Dic₄₇

yes

complemented

C₂²

C₂×C₄⋊Dic₄₇

yes

characteristic

100

C₂²

C₄×D₁₈₈

yes

—

101

C₂²

C₂×D₃₇₆

yes

characteristic

102

C₂²

C₂×Dic₁₈₈

yes

characteristic

103

C₂²

#13094046

yes

—

104

C₄

—

105

C₄

—

188

—

106

C₄

#13093958

yes

direct product factor

107

C₄

C₂×C₄×Dic₄₇

yes

characteristic

108

C₄

#13093983

yes

characteristic

109

C₄

C₄×Dic₉₄

yes

—

110

C₂

C₄×C₄⋊Dic₄₇

yes

characteristic

111

C₂

C₂×#13093958

yes

characteristic

112

C₂

#15689161

yes

characteristic

113

C₂

C₄×D₃₇₆

yes

—

114

C₂

C₄×Dic₁₈₈

yes

—

	subgroup	G/H
center	C₂²×C₄	D₁₈₈
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	C₄×#107
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂²×C₄

D₁₈₈

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×C₄×C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂×C₄×C₈

D₄₇

hypocenter

C₄₇

C₄×#107

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
7. #13093958	C₄	direct (N × H)
12. C₄×C₈×C₄₇	C₄	semidirect
40. C₈×C₄₇	C₄²	semidirect
47. C₄×C₄₇	#107	semidirect
62. C₄₇	C₄×#107	semidirect
69. C₄×C₈	Dic₄₇	semidirect
98. C₈	C₄×Dic₄₇	semidirect
106. C₄	#13093958	direct (N × H)

H ≅ G/N

type

7. #13093958

C₄

direct (N × H)

12. C₄×C₈×C₄₇

C₄

semidirect

40. C₈×C₄₇

C₄²

semidirect

47. C₄×C₄₇

#107

semidirect

62. C₄₇

C₄×#107

semidirect

69. C₄×C₈

Dic₄₇

semidirect

98. C₈

C₄×Dic₄₇

semidirect

106. C₄

#13093958

direct (N × H)

Subgroups — C₄×#13093958 #20243281

Conjugacy classes of subgroups

Complements

Subgroups — C4×#13093958 #20243281

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13093958 #20243281