Group #20242906 — subgroups

Subgroups — #20242906

Order 6016.

152 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 57 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	#15689528	C₂	1	1	yes	maximal, characteristic
2	#15689333	C₂	1	2	yes	maximal
3	#15688874	C₂	1	1	yes	maximal, characteristic
4	#15688868	C₂	1	2	yes	maximal
5	C₄₇×#446	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625337	—	2	2	no	—
7	#13094024	C₂²	1	2	yes	—
8	#13093958	—	2	1	no	—
9	#13093958	—	2	1	no	—
10	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	#13093947	—	2	2	no	—
12	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₄₇	—	2	1	no	—
14	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
15	#97×C₄₇	—	2	1	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
18	C₂×Dic₉₄	—	2	2	no	—
19	C₂×C₈×C₄₇	—	2	1	no	—
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₄₇	—	2	1	no	—
23	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
24	C₄²×C₄₇	—	2	1	no	—
25	C₄²×C₄₇	C₂³	1	1	yes	characteristic
26	#10625337	—	4	4	no	—
27	C₄⋊Dic₄₇	—	2	2	no	—
28	C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄₇⋊C₈	—	2	2	no	—
30	Q₈×C₄₇	—	2	2	no	—
31	C₂×C₄×C₄₇	—	2	1	no	—
32	C₂×C₄×C₄₇	—	2	1	no	—
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
36	C₂×Dic₄₇	—	4	2	no	—
37	Dic₉₄	—	4	2	no	—
38	Dic₉₄	—	4	2	no	—
39	C₈×C₄₇	—	2	1	no	—
40	C₈×C₄₇	—	4	1	no	—
41	C₈×C₄₇	Q₁₆	1	2	yes	complemented
42	C₄₇⋊C₈	—	4	2	no	—
43	C₂²×C₄₇	#121	1	1	yes	characteristic
44	C₄×C₄₇	—	2	1	no	—
45	C₄×C₄₇	—	4	1	no	—
46	C₄×C₄₇	—	4	1	no	—
47	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
48	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
49	C₄×C₄₇	#137	1	1	yes	characteristic
50	Dic₄₇	—	8	2	no	—
51	#1694	—	47	1	no	maximal, Sylow
52	C₂×C₄₇	#462	1	1	yes	characteristic
53	C₂×C₄₇	#469	1	1	yes	characteristic
54	C₂×C₄₇	#473	1	1	yes	characteristic
55	#500	—	47	1	no	—
56	#462	—	47	2	no	—
57	#446	D₄₇	1	1	yes	characteristic
58	#334	—	47	1	no	—
59	#332	—	47	2	no	—
60	C₄₇	#1694	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₁₆	—	94	2	no	—
62	C₄⋊Q₈	—	47	2	no	—
63	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
64	#107	—	94	1	no	—
65	#107	—	94	1	no	—
66	C₄⋊C₈	—	2	1	no	—
67	C₄⋊C₈	—	47	2	no	—
68	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
69	#103	—	94	2	no	—
70	#97	—	2	1	no	—
71	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
72	C₂×Q₈	—	94	2	no	—
73	C₂×Q₈	D₁₈₈	1	1	yes	characteristic
74	Q₁₆	—	188	4	no	—
75	C₂×C₈	—	2	1	no	—
76	C₂×C₈	—	94	2	no	—
77	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	94	2	no	—
81	C₄⋊C₄	—	94	2	no	—
82	C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
83	C₄²	—	2	1	no	—
84	C₄²	C₂²×D₄₇	1	1	yes	characteristic
85	Q₈	—	2	2	no	—
86	Q₈	—	188	2	no	—
87	Q₈	—	188	2	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	188	2	no	—
91	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
92	C₂×C₄	#10625350	1	1	yes	characteristic
93	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	1	no	—
96	C₈	—	188	2	no	—
97	C₈	#10625337	1	2	yes	complemented
98	C₂²	#13093998	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	—	376	2	no	—
103	C₄	C₂×#10625337	1	1	yes	characteristic
104	C₄	#13094052	1	2	yes	—
105	C₄	#13094054	1	1	yes	characteristic
106	C₂	#15689333	1	1	yes	characteristic
107	C₂	#15689376	1	1	yes	characteristic
108	C₂	#15689398	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic

#15689333

C₂

yes

maximal

#15688874

C₂

yes

maximal, characteristic

#15688868

C₂

yes

maximal

C₄₇×#446

C₂

yes

maximal, characteristic

C₂×#10625337

—

#13094024

C₂²

yes

—

#13093958

—

#13093958

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093947

—

C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂²

yes

characteristic

#97×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

D₄

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625337

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₂×C₄₇⋊C₈

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

Q₁₆

yes

complemented

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₄×C₄₇

AGL(1,ℤ/8)

yes

—

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

D₄₇

yes

characteristic

#334

—

#332

—

C₄₇

#1694

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₄₇

yes

characteristic

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

characteristic

#103

—

#97

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

D₁₈₈

yes

characteristic

Q₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₈₈

yes

characteristic

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

Q₈

—

Q₈

—

188

—

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₂×C₄

#10625350

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₈

yes

C₂²

yes

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

376

—

103

C₄

C₂×#10625337

yes

characteristic

104

C₄

#13094052

yes

—

105

C₄

#13094054

yes

characteristic

106

C₂

#15689333

yes

characteristic

107

C₂

#15689376

yes

characteristic

108

C₂

#15689398

yes

characteristic

	subgroup	G/H
center	C₂²	#13093998
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#446	C₂
socle	C₂²×C₄₇	#121
hypercenter	#446	D₄₇
hypocenter	C₄₇	#1694
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#13093998

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#446

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
41. C₈×C₄₇	Q₁₆	semidirect
60. C₄₇	#1694	semidirect
97. C₈	#10625337	semidirect

H ≅ G/N

type

41. C₈×C₄₇

Q₁₆

semidirect

60. C₄₇

#1694

semidirect

97. C₈

#10625337

semidirect

Subgroups — #20242906

Conjugacy classes of subgroups

Complements