Group #20245672 — subgroups

Subgroups — #20245672

Order 6016.

120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689527	C₂	1	1	yes	maximal, characteristic
2	#15689524	C₂	1	1	yes	maximal, characteristic
3	#15688951	C₂	1	1	yes	maximal, characteristic
4	#15688950	C₂	1	1	yes	maximal, characteristic
5	#15688948	C₂	1	1	yes	maximal, characteristic
6	#15688898	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#366	C₂	1	1	yes	maximal, characteristic
8	#13094023	—	2	1	no	—
9	#13094015	—	2	1	no	—
10	C₂×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
11	#13093958	C₂²	1	1	yes	characteristic
12	#13093958	C₂²	1	1	yes	characteristic
13	#13093957	—	2	1	no	—
14	#13093955	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	#107×C₄₇	C₂²	1	1	yes	characteristic
18	#107×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Dic₉₄	—	4	1	no	—
20	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
21	C₄⋊C₄×C₄₇	—	2	1	no	—
22	C₄⋊C₄×C₄₇	—	2	1	no	—
23	C₄⋊Dic₄₇	—	2	1	no	—
24	C₄⋊Dic₄₇	—	2	1	no	—
25	C₄⋊Dic₄₇	—	4	1	no	—
26	Dic₄₇⋊C₄	—	4	1	no	—
27	Dic₄₇⋊C₄	—	4	1	no	—
28	C₄×Dic₄₇	D₄	1	1	yes	characteristic
29	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
30	C₁₆×C₄₇	Q₈	1	2	yes	complemented
31	C₄₇⋊C₁₆	Q₈	1	2	yes	complemented
32	C₂×C₄×C₄₇	—	4	1	no	—
33	C₂×C₄×C₄₇	—	4	1	no	—
34	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
35	C₂×Dic₄₇	—	4	1	no	—
36	C₂×Dic₄₇	—	4	1	no	—
37	C₂×Dic₄₇	D₈	1	1	yes	characteristic
38	C₂×Dic₄₇	D₈	1	1	yes	characteristic
39	Dic₉₄	—	8	2	no	—
40	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
41	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
42	C₄₇⋊C₈	Q₁₆	1	2	yes	—
43	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
44	C₄×C₄₇	—	8	1	no	—
45	C₄×C₄₇	—	8	1	no	—
46	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
47	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
48	Dic₄₇	—	2	1	no	—
49	Dic₄₇	—	2	1	no	—
50	Dic₄₇	—	8	1	no	—
51	Dic₄₇	—	8	1	no	—
52	#2255	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	#500	1	1	yes	characteristic
54	C₂×C₄₇	#509	1	1	yes	characteristic
55	C₂×C₄₇	#510	1	1	yes	characteristic
56	#500	—	47	1	no	—
57	#499	—	47	1	no	—
58	#367	—	47	1	no	—
59	#367	—	47	1	no	—
60	#366	—	47	1	no	—
61	#366	D₄₇	1	1	yes	characteristic
62	#346	—	47	1	no	—
63	C₄₇	#2255	1	1	yes	characteristic, complemented, Sylow
64	C₄⋊Q₈	—	94	1	no	—
65	#125	—	94	1	no	—
66	C₂×C₁₆	—	47	1	no	—
67	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
68	#107	—	47	1	no	—
69	#107	—	47	1	no	—
70	#107	—	94	1	no	—
71	#107	C₂×D₄₇	1	1	yes	characteristic
72	#107	C₂×D₄₇	1	1	yes	characteristic
73	#106	—	94	1	no	—
74	C₄×C₈	—	47	1	no	—
75	C₂×Q₈	—	188	1	no	—
76	C₂×C₈	—	47	1	no	—
77	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
78	C₄⋊C₄	—	2	1	no	—
79	C₄⋊C₄	—	2	1	no	—
80	C₄⋊C₄	—	94	1	no	—
81	C₄⋊C₄	—	94	1	no	—
82	C₄⋊C₄	—	188	1	no	—
83	C₄⋊C₄	—	188	1	no	—
84	C₄⋊C₄	—	188	1	no	—
85	C₄²	—	47	1	no	—
86	C₁₆	—	47	2	no	—
87	C₁₆	Dic₉₄	1	2	yes	complemented
88	Q₈	—	376	2	no	—
89	C₂×C₄	—	4	1	no	—
90	C₂×C₄	—	4	1	no	—
91	C₂×C₄	—	47	1	no	—
92	C₂×C₄	—	47	1	no	—
93	C₂×C₄	—	188	1	no	—
94	C₂×C₄	—	188	1	no	—
95	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
96	C₈	—	47	2	no	—
97	C₈	C₂×Dic₉₄	1	1	yes	characteristic
98	C₈	Q₈×D₄₇	1	1	yes	characteristic
99	C₂²	D₈×D₄₇	1	1	yes	characteristic
100	C₄	—	8	1	no	—
101	C₄	—	8	1	no	—
102	C₄	—	94	1	no	—
103	C₄	—	94	1	no	—
104	C₄	—	376	1	no	—
105	C₄	—	376	1	no	—
106	C₄	#13094023	1	1	yes	characteristic
107	C₄	Q₁₆×D₄₇	1	1	yes	characteristic
108	C₂	#15689527	1	1	yes	characteristic
109	C₂	#15689557	1	1	yes	characteristic
110	C₂	#15689565	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689527

C₂

yes

maximal, characteristic

#15689524

C₂

yes

maximal, characteristic

#15688951

C₂

yes

maximal, characteristic

#15688950

C₂

yes

maximal, characteristic

#15688948

C₂

yes

maximal, characteristic

#15688898

C₂

yes

maximal, characteristic

C₄₇×#366

C₂

yes

maximal, characteristic

#13094023

—

#13094015

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093957

—

#13093955

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₁₆×C₄₇

Q₈

yes

complemented

C₄₇⋊C₁₆

Q₈

yes

complemented

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

D₈

yes

characteristic

C₂×Dic₄₇

D₈

yes

characteristic

Dic₉₄

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₄₇⋊C₈

Q₁₆

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

C₄×C₄₇

C₂×Q₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

—

D₄₇

yes

characteristic

#346

—

C₄₇

#2255

yes

characteristic, complemented, Sylow

C₄⋊Q₈

—

#125

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

—

—

C₂×D₄₇

yes

characteristic

#107

C₂×D₄₇

yes

characteristic

#106

—

C₄×C₈

—

C₂×Q₈

—

188

—

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

C₁₆

—

C₁₆

Dic₉₄

yes

complemented

Q₈

—

376

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₈

—

C₈

C₂×Dic₉₄

yes

characteristic

C₈

Q₈×D₄₇

yes

characteristic

C₂²

D₈×D₄₇

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

376

—

105

C₄

—

376

—

106

C₄

#13094023

yes

characteristic

107

C₄

Q₁₆×D₄₇

yes

characteristic

108

C₂

#15689527

yes

characteristic

109

C₂

#15689557

yes

characteristic

110

C₂

#15689565

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#366	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#366	D₄₇
hypocenter	C₄₇	#2255
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#366

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

N	H ≅ G/N	type
30. C₁₆×C₄₇	Q₈	semidirect
31. C₄₇⋊C₁₆	Q₈	semidirect
63. C₄₇	#2255	semidirect
87. C₁₆	Dic₉₄	semidirect

H ≅ G/N

type

30. C₁₆×C₄₇

Q₈

semidirect

31. C₄₇⋊C₁₆

Q₈

semidirect

63. C₄₇

#2255

semidirect

87. C₁₆

Dic₉₄

semidirect

Subgroups — #20245672

Conjugacy classes of subgroups

Complements