Group #20245176 — subgroups

Subgroups — #20245176

Order 6016.

156 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 93 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	#15689161	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093958	C₂	1	1	yes	maximal, characteristic
3	#15688951	C₂	1	2	yes	maximal, complemented
4	#15688949	C₂	1	2	yes	maximal, complemented
5	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#13093983	—	2	1	no	—
7	C₂×C₄⋊Dic₄₇	—	2	1	no	—
8	#13093958	—	2	1	no	—
9	#13093958	C₂²	1	2	yes	—
10	#13093958	C₂²	1	1	yes	characteristic
11	#13093958	C₂²	1	1	yes	characteristic
12	#13093956	—	2	1	no	—
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	M₃₂×C₄₇	C₄	1	4	yes	complemented
15	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	4	1	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	Q₈	1	2	yes	—
21	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
22	C₂²⋊Dic₄₇	—	4	1	no	—
23	C₄⋊Dic₄₇	—	2	1	no	—
24	C₄⋊Dic₄₇	—	2	1	no	—
25	C₄⋊Dic₄₇	—	2	2	no	—
26	C₄⋊Dic₄₇	—	4	1	no	—
27	C₄×Dic₄₇	—	4	1	no	—
28	C₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
29	C₂³×C₄₇	D₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
31	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
32	C₂×C₄×C₄₇	Q₁₆	1	2	yes	—
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂×Dic₄₇	—	4	1	no	—
35	C₂×Dic₄₇	—	4	1	no	—
36	C₂×Dic₄₇	—	4	2	no	—
37	C₂×Dic₄₇	—	8	2	no	—
38	C₈×C₄₇	C₄⋊C₄	1	2	yes	—
39	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
41	C₂²×C₄₇	—	2	1	no	—
42	C₂²×C₄₇	—	2	1	no	—
43	C₂²×C₄₇	#107	1	2	yes	—
44	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
45	C₄×C₄₇	#107	1	2	yes	—
46	C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
47	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
48	Dic₄₇	—	8	1	no	—
49	Dic₄₇	—	8	2	no	—
50	Dic₄₇	—	8	1	no	—
51	#2159	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	—	2	2	no	—
53	C₂×C₄₇	C₂×#107	1	1	yes	characteristic
54	C₂×C₄₇	#509	1	1	yes	characteristic
55	C₂×C₄₇	#510	1	1	yes	characteristic
56	C₂×M₃₂	D₄₇	1	1	yes	characteristic
57	#427	—	47	1	no	—
58	C₂×#107	—	47	1	no	—
59	#367	—	47	2	no	—
60	#366	—	47	2	no	—
61	C₄₇	#2159	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
63	#117	—	94	1	no	—
64	C₂×C₄⋊C₄	—	94	1	no	—
65	M₃₂	Dic₄₇	1	4	yes	complemented
66	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
67	#107	—	47	1	no	—
68	#107	—	47	2	no	—
69	#107	—	47	1	no	—
70	#107	—	94	1	no	—
71	#106	—	94	1	no	—
72	C₂²×C₄	—	188	1	no	—
73	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
74	C₂×C₈	Dic₉₄	1	2	yes	—
75	C₂×C₈	D₁₈₈	1	1	yes	characteristic
76	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
77	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
78	C₄⋊C₄	—	94	1	no	—
79	C₄⋊C₄	—	94	1	no	—
80	C₄⋊C₄	—	94	2	no	—
81	C₄⋊C₄	—	188	1	no	—
82	C₂²⋊C₄	—	188	1	no	—
83	C₄²	—	188	1	no	—
84	C₁₆	C₂×Dic₄₇	1	4	yes	complemented
85	C₂³	D₃₇₆	1	1	yes	characteristic
86	C₂×C₄	—	376	2	no	—
87	C₂×C₄	—	188	1	no	—
88	C₂×C₄	—	188	1	no	—
89	C₂×C₄	—	188	2	no	—
90	C₂×C₄	D₃₇₆	1	1	yes	characteristic
91	C₂×C₄	Dic₁₈₈	1	2	yes	—
92	C₂×C₄	C₄⋊Dic₄₇	1	2	yes	—
93	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
94	C₈	C₄⋊Dic₄₇	1	2	yes	—
95	C₈	C₂×Dic₉₄	1	1	yes	characteristic
96	C₈	C₂²×Dic₄₇	1	1	yes	characteristic
97	C₂²	—	2	1	no	—
98	C₂²	—	2	1	no	—
99	C₂²	#13093958	1	2	yes	—
100	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
101	C₄	—	376	2	no	—
102	C₄	—	376	1	no	—
103	C₄	—	376	1	no	—
104	C₄	#13093958	1	2	yes	—
105	C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
106	C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
107	C₂	—	2	2	no	—
108	C₂	C₂×#13093958	1	1	yes	characteristic
109	C₂	#15689561	1	1	yes	characteristic
110	C₂	#15689566	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689161

C₂

yes

maximal, characteristic

C₂×#13093958

C₂

yes

maximal, characteristic

#15688951

C₂

yes

maximal, complemented

#15688949

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₇

C₂

yes

maximal, characteristic

#13093983

—

C₂×C₄⋊Dic₄₇

—

#13093958

—

#13093958

C₂²

yes

—

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093956

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

C₄

yes

complemented

C₂×C₁₆×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₁₆×C₄₇

C₂×C₄

yes

complemented

C₂³×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

Q₁₆

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#107

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

#107

yes

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₇

C₂×Q₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2159

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×M₃₂

D₄₇

yes

—

—

—

—

C₄₇

#2159

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

M₃₂

Dic₄₇

yes

complemented

C₂×C₁₆

C₂×D₄₇

yes

—

—

—

—

—

—

C₂²×C₄

—

188

—

C₂²×C₄

D₁₈₈

yes

characteristic

C₂×C₈

Dic₉₄

yes

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₄²

—

188

—

C₁₆

C₂×Dic₄₇

yes

complemented

C₂³

D₃₇₆

yes

characteristic

C₂×C₄

—

376

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

Dic₁₈₈

yes

—

C₂×C₄

C₄⋊Dic₄₇

yes

—

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₈

C₄⋊Dic₄₇

yes

—

C₈

C₂×Dic₉₄

yes

characteristic

C₈

C₂²×Dic₄₇

yes

characteristic

C₂²

—

C₂²

—

C₂²

#13093958

yes

—

100

C₂²

C₂×D₃₇₆

yes

characteristic

101

C₄

—

376

—

102

C₄

—

376

—

103

C₄

—

376

—

104

C₄

#13093958

yes

—

105

C₄

C₂×C₄⋊Dic₄₇

yes

characteristic

106

C₄

C₂×Dic₁₈₈

yes

characteristic

107

C₂

—

108

C₂

C₂×#13093958

yes

characteristic

109

C₂

#15689561

yes

characteristic

110

C₂

#15689566

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₈×C₄₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×M₃₂×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₂×M₃₂	D₄₇
hypocenter	C₄₇	#2159
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₃₇₆

commutator

C₈×C₄₇

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×M₃₂×C₄₇

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₂×M₃₂

D₄₇

hypocenter

C₄₇

#2159

LCS

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #15688951	C₂	semidirect
4. #15688949	C₂	semidirect
14. M₃₂×C₄₇	C₄	semidirect
28. C₁₆×C₄₇	C₂×C₄	semidirect
61. C₄₇	#2159	semidirect
65. M₃₂	Dic₄₇	semidirect
84. C₁₆	C₂×Dic₄₇	semidirect

H ≅ G/N

type

3. #15688951

C₂

semidirect

4. #15688949

C₂

semidirect

14. M₃₂×C₄₇

C₄

semidirect

28. C₁₆×C₄₇

C₂×C₄

semidirect

61. C₄₇

#2159

semidirect

65. M₃₂

Dic₄₇

semidirect

84. C₁₆

C₂×Dic₄₇

semidirect

Subgroups — #20245176

Conjugacy classes of subgroups

Complements