Group #20245439 — subgroups

Subgroups — #20245439

Order 6016.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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×Dic₃₇₆	C₂	1	2	yes	maximal
2	#15689503	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
4	#15688928	C₂	1	2	yes	maximal
5	C₄₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	—	2	1	no	—
7	C₂×Dic₁₈₈	C₂²	1	2	yes	—
8	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
9	#13094024	—	2	1	no	—
10	C₄×Dic₉₄	—	2	1	no	—
11	Dic₃₇₆	—	2	4	no	—
12	#13093958	C₂²	1	1	yes	characteristic
13	#13093949	—	2	1	no	—
14	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₉₄	—	2	1	no	—
17	C₂×Dic₉₄	—	2	2	no	—
18	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
20	C₄²×C₄₇	D₄	1	1	yes	characteristic
21	C₄⋊Dic₄₇	—	2	1	no	—
22	C₄⋊Dic₄₇	—	4	1	no	—
23	C₄⋊Dic₄₇	—	4	1	no	—
24	Dic₄₇⋊C₄	—	4	1	no	—
25	C₄×Dic₄₇	—	4	1	no	—
26	Dic₁₈₈	—	2	2	no	—
27	Dic₁₈₈	—	2	1	no	—
28	Dic₁₈₈	—	2	2	no	—
29	Dic₁₈₈	—	4	2	no	—
30	Dic₁₈₈	D₄	1	2	yes	—
31	C₁₆×C₄₇	—	2	2	no	—
32	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
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	—	4	2	no	—
38	Dic₉₄	—	2	2	no	—
39	Dic₉₄	—	4	1	no	—
40	Dic₉₄	—	4	2	no	—
41	Dic₉₄	—	4	2	no	—
42	C₈×C₄₇	—	2	1	no	—
43	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
44	C₈×C₄₇	#41	1	1	yes	characteristic
45	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
46	C₄×C₄₇	—	2	1	no	—
47	C₄×C₄₇	Q₃₂	1	2	yes	complemented
48	C₄×C₄₇	#121	1	1	yes	characteristic
49	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
50	Dic₄₇	—	4	2	no	—
51	Dic₄₇	—	8	2	no	—
52	Dic₄₇	—	8	1	no	—
53	#2209	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	#459	1	1	yes	characteristic
55	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
56	C₂×C₄₇	#510	1	1	yes	characteristic
57	C₂×Q₃₂	—	47	2	no	—
58	#494	—	47	1	no	—
59	C₄×Q₁₆	—	47	1	no	—
60	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic
61	#358	—	47	2	no	—
62	C₄₇	#2209	1	1	yes	characteristic, complemented, Sylow
63	C₂×Q₁₆	—	47	1	no	—
64	C₂×Q₁₆	—	47	2	no	—
65	C₂×Q₁₆	—	94	1	no	—
66	C₄⋊Q₈	—	94	1	no	—
67	C₄×Q₈	—	94	1	no	—
68	Q₃₂	—	94	4	no	—
69	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
70	#107	—	47	1	no	—
71	#103	—	94	1	no	—
72	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
73	C₂×Q₈	—	94	1	no	—
74	C₂×Q₈	—	94	2	no	—
75	Q₁₆	—	47	2	no	—
76	Q₁₆	—	94	2	no	—
77	Q₁₆	—	94	1	no	—
78	Q₁₆	—	94	2	no	—
79	Q₁₆	—	188	2	no	—
80	C₂×C₈	D₁₈₈	1	1	yes	characteristic
81	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
82	C₄⋊C₄	—	94	1	no	—
83	C₄⋊C₄	—	188	1	no	—
84	C₄⋊C₄	—	188	1	no	—
85	C₄⋊C₄	—	188	1	no	—
86	C₄²	—	188	1	no	—
87	C₄²	D₁₈₈	1	1	yes	characteristic
88	C₁₆	—	2	2	no	—
89	Q₈	—	94	2	no	—
90	Q₈	—	188	2	no	—
91	Q₈	—	188	2	no	—
92	Q₈	—	188	1	no	—
93	C₂×C₄	—	188	1	no	—
94	C₂×C₄	—	188	2	no	—
95	C₂×C₄	—	188	1	no	—
96	C₂×C₄	D₃₇₆	1	1	yes	characteristic
97	C₂×C₄	D₃₇₆	1	1	yes	characteristic
98	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	D₄×D₄₇	1	1	yes	characteristic
101	C₈	#10625354	1	1	yes	characteristic
102	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	376	1	no	—
105	C₄	—	376	2	no	—
106	C₄	—	188	2	no	—
107	C₄	Dic₃₇₆	1	2	yes	complemented
108	C₄	#13093999	1	1	yes	characteristic
109	C₄	#13094052	1	1	yes	characteristic
110	C₂	#15689319	1	1	yes	characteristic
111	C₂	C₂×Dic₃₇₆	1	1	yes	characteristic
112	C₂	#15689566	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₃₇₆

C₂

yes

maximal

#15689503

C₂

yes

maximal, characteristic

C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal

C₄₇×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₂²

yes

—

C₂×Dic₁₈₈

C₂²

yes

characteristic

#13094024

—

C₄×Dic₉₄

—

Dic₃₇₆

—

#13093958

C₂²

yes

characteristic

#13093949

—

C₂×C₁₆×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

D₄

yes

—

C₁₆×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×D₄

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

Q₃₂

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×Q₃₂

yes

characteristic

C₂×C₄₇

#510

yes

characteristic

C₂×Q₃₂

—

#494

—

C₄×Q₁₆

—

C₄⋊C₁₆

D₄₇

yes

characteristic

#358

—

C₄₇

#2209

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

Q₃₂

—

C₂×C₁₆

C₂×D₄₇

yes

—

#107

—

#103

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

188

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

188

—

C₄²

D₁₈₈

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

188

—

Q₈

—

188

—

Q₈

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₈

—

100

C₈

D₄×D₄₇

yes

characteristic

101

C₈

#10625354

yes

characteristic

102

C₂²

C₂×D₃₇₆

yes

characteristic

103

C₄

—

104

C₄

—

376

—

105

C₄

—

376

—

106

C₄

—

188

—

107

C₄

Dic₃₇₆

yes

complemented

108

C₄

#13093999

yes

characteristic

109

C₄

#13094052

yes

characteristic

110

C₂

#15689319

yes

characteristic

111

C₂

C₂×Dic₃₇₆

yes

characteristic

112

C₂

#15689566

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×C₄⋊C₁₆	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#2209
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₃₇₆

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×C₄⋊C₁₆

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄⋊C₁₆

D₄₇

hypocenter

C₄₇

#2209

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
47. C₄×C₄₇	Q₃₂	semidirect
62. C₄₇	#2209	semidirect
107. C₄	Dic₃₇₆	semidirect

H ≅ G/N

type

47. C₄×C₄₇

Q₃₂

semidirect

62. C₄₇

#2209

semidirect

107. C₄

Dic₃₇₆

semidirect

Subgroups — #20245439

Conjugacy classes of subgroups

Complements