Group #20245538 — subgroups

Subgroups — #20245538

Order 6016.

130 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 51 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	Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#15688949	C₂	1	1	yes	maximal, characteristic
4	#15688948	C₂	1	1	yes	maximal, characteristic
5	Dic₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	#15688927	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#358	C₂	1	1	yes	maximal, characteristic
8	#13094023	—	2	1	no	—
9	Q₈×Dic₄₇	—	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	#13093948	—	2	1	no	—
15	C₈×Dic₄₇	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	#107×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₇	—	2	1	no	—
20	C₂×Dic₉₄	—	4	1	no	—
21	Q₁₆×C₄₇	—	2	1	no	—
22	Q₁₆×C₄₇	Q₈	1	2	yes	complemented
23	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	1	no	—
25	C₄⋊Dic₄₇	—	2	1	no	—
26	C₄⋊Dic₄₇	—	2	1	no	—
27	C₄⋊Dic₄₇	—	4	1	no	—
28	Dic₄₇⋊C₄	—	4	1	no	—
29	C₄×Dic₄₇	—	4	1	no	—
30	C₄×Dic₄₇	D₄	1	1	yes	characteristic
31	C₂×C₄₇⋊C₈	D₄	1	1	yes	characteristic
32	C₁₆×C₄₇	—	2	1	no	—
33	C₄₇⋊C₁₆	—	2	1	no	—
34	Q₈×C₄₇	—	2	2	no	—
35	Q₈×C₄₇	—	4	1	no	—
36	C₂×C₄×C₄₇	—	4	1	no	—
37	C₂×C₄×C₄₇	—	4	1	no	—
38	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₄₇	—	4	1	no	—
40	C₂×Dic₄₇	—	4	1	no	—
41	C₂×Dic₄₇	D₈	1	1	yes	characteristic
42	C₂×Dic₄₇	D₈	1	1	yes	characteristic
43	Dic₉₄	—	8	2	no	—
44	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₄₇	#41	1	1	yes	characteristic
46	C₄₇⋊C₈	—	2	1	no	—
47	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
48	C₄×C₄₇	—	4	2	no	—
49	C₄×C₄₇	—	8	1	no	—
50	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
51	C₄×C₄₇	#137	1	1	yes	characteristic
52	Dic₄₇	—	2	1	no	—
53	Dic₄₇	—	8	1	no	—
54	Dic₄₇	—	8	1	no	—
55	Dic₄₇	Q₃₂	1	2	yes	—
56	#2227	—	47	1	no	maximal, Sylow
57	C₂×C₄₇	#474	1	1	yes	characteristic
58	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
59	C₂×C₄₇	#509	1	1	yes	characteristic
60	#500	—	47	1	no	—
61	C₄×Q₁₆	—	47	1	no	—
62	#366	—	47	1	no	—
63	#366	—	47	1	no	—
64	C₄⋊C₁₆	—	47	1	no	—
65	#358	—	47	1	no	—
66	#358	D₄₇	1	1	yes	characteristic
67	C₄₇	#2227	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
69	C₄⋊Q₈	—	94	1	no	—
70	C₄×Q₈	—	94	1	no	—
71	C₂×C₁₆	—	47	1	no	—
72	C₂×C₁₆	C₂×D₄₇	1	1	yes	characteristic
73	#107	—	47	1	no	—
74	#107	—	47	1	no	—
75	#107	—	94	1	no	—
76	#107	C₂×D₄₇	1	1	yes	characteristic
77	#103	—	94	1	no	—
78	C₄×C₈	—	47	1	no	—
79	C₂×Q₈	—	2	1	no	—
80	C₂×Q₈	—	188	1	no	—
81	Q₁₆	—	2	1	no	—
82	Q₁₆	Dic₉₄	1	2	yes	complemented
83	C₂×C₈	—	47	1	no	—
84	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
85	C₄⋊C₄	—	2	1	no	—
86	C₄⋊C₄	—	94	1	no	—
87	C₄⋊C₄	—	94	1	no	—
88	C₄⋊C₄	—	188	1	no	—
89	C₄⋊C₄	—	188	1	no	—
90	C₄²	—	47	1	no	—
91	C₄²	—	188	1	no	—
92	C₁₆	—	2	1	no	—
93	C₁₆	—	94	1	no	—
94	Q₈	—	2	2	no	—
95	Q₈	—	4	1	no	—
96	Q₈	—	376	2	no	—
97	C₂×C₄	—	4	1	no	—
98	C₂×C₄	—	4	1	no	—
99	C₂×C₄	—	47	1	no	—
100	C₂×C₄	—	47	1	no	—
101	C₂×C₄	—	188	1	no	—
102	C₂×C₄	—	188	1	no	—
103	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
104	C₈	—	94	1	no	—
105	C₈	C₂×Dic₉₄	1	1	yes	characteristic
106	C₈	#10625352	1	1	yes	characteristic
107	C₂²	D₈×D₄₇	1	1	yes	characteristic
108	C₄	—	4	2	no	—
109	C₄	—	8	1	no	—
110	C₄	—	47	2	no	—
111	C₄	—	94	1	no	—
112	C₄	—	376	1	no	—
113	C₄	—	376	1	no	—
114	C₄	#13094001	1	1	yes	characteristic
115	C₄	#13094053	1	1	yes	characteristic
116	C₂	#15689401	1	1	yes	characteristic
117	C₂	Q₃₂×D₄₇	1	1	yes	characteristic
118	C₂	#15689560	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689527

C₂

yes

maximal, characteristic

Q₁₆×Dic₄₇

C₂

yes

maximal, characteristic

#15688949

C₂

yes

maximal, characteristic

#15688948

C₂

yes

maximal, characteristic

Dic₄₇⋊C₁₆

C₂

yes

maximal, characteristic

#15688927

C₂

yes

maximal, characteristic

C₄₇×#358

C₂

yes

maximal, characteristic

#13094023

—

Q₈×Dic₄₇

—

C₂×C₄₇⋊C₁₆

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

characteristic

#13093957

—

#13093948

—

C₈×Dic₄₇

C₂²

yes

characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

characteristic

C₂×C₁₆×C₄₇

C₂²

yes

characteristic

#107×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Dic₉₄

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

Q₈

yes

complemented

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

D₄

yes

characteristic

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

Q₈×C₄₇

—

Q₈×C₄₇

—

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

#41

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

Dic₄₇

Q₃₂

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×Q₃₂

yes

C₂×C₄₇

yes

—

C₄×Q₁₆

—

#366

—

#366

—

C₄⋊C₁₆

—

#358

—

#358

D₄₇

yes

characteristic

C₄₇

#2227

yes

characteristic, complemented, Sylow

C₂×Q₁₆

C₂×D₄₇

yes

characteristic

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₇

yes

—

—

—

C₂×D₄₇

yes

characteristic

#103

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

188

—

Q₁₆

—

Q₁₆

Dic₉₄

yes

complemented

C₂×C₈

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

C₄²

—

188

—

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

Q₈

—

376

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

188

—

102

C₂×C₄

—

188

—

103

C₂×C₄

D₄×D₄₇

yes

characteristic

104

C₈

—

105

C₈

C₂×Dic₉₄

yes

characteristic

106

C₈

#10625352

yes

characteristic

107

C₂²

D₈×D₄₇

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

376

—

113

C₄

—

376

—

114

C₄

#13094001

yes

characteristic

115

C₄

#13094053

yes

characteristic

116

C₂

#15689401

yes

characteristic

117

C₂

Q₃₂×D₄₇

yes

characteristic

118

C₂

#15689560

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₇
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×#358	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	#358	D₄₇
hypocenter	C₄₇	#2227
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₄₇

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×#358

C₂

socle

C₂²×C₄₇

C₂×D₈

D₄₇

C₄₇

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
22. Q₁₆×C₄₇	Q₈	semidirect
67. C₄₇	#2227	semidirect
82. Q₁₆	Dic₉₄	semidirect

H ≅ G/N

type

22. Q₁₆×C₄₇

Q₈

semidirect

67. C₄₇

#2227

semidirect

82. Q₁₆

Dic₉₄

semidirect

Subgroups — #20245538

Conjugacy classes of subgroups

Complements