Group #20245109 — subgroups

Subgroups — #20245109

Order 6016.

220 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 85 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	C₂²×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
2	#15689161	C₂	1	1	yes	maximal, characteristic
3	#15688928	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₉₄	—	2	1	no	—
6	C₂×Dic₁₈₈	—	2	1	no	—
7	C₂×Dic₁₈₈	—	2	2	no	—
8	C₂×Dic₁₈₈	C₄	1	4	yes	complemented
9	C₂×Dic₁₈₈	C₂²	1	2	yes	—
10	#13093983	—	2	1	no	—
11	#13093958	C₂²	1	2	yes	—
12	#13093956	—	2	1	no	—
13	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	M₃₂×C₄₇	—	2	2	no	—
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×Dic₉₄	—	2	4	no	—
19	C₂×Dic₉₄	—	2	2	no	—
20	C₂×Dic₉₄	—	4	1	no	—
21	C₂×Dic₉₄	—	4	2	no	—
22	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₇	D₄	1	2	yes	—
25	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
26	C₂²⋊Dic₄₇	—	4	1	no	—
27	C₄⋊Dic₄₇	—	2	2	no	—
28	C₄×Dic₄₇	—	4	1	no	—
29	Dic₁₈₈	—	2	4	no	—
30	Dic₁₈₈	—	2	2	no	—
31	Dic₁₈₈	C₂×C₄	1	4	yes	—
32	C₁₆×C₄₇	—	2	2	no	—
33	C₂³×C₄₇	D₈	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
36	C₂×C₄×C₄₇	SD₁₆	1	2	yes	—
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₄₇	—	4	4	no	—
39	C₂×Dic₄₇	—	4	2	no	—
40	C₂×Dic₄₇	—	4	2	no	—
41	Dic₉₄	—	2	4	no	—
42	Dic₉₄	—	4	4	no	—
43	Dic₉₄	—	4	2	no	—
44	C₈×C₄₇	C₂²⋊C₄	1	2	yes	—
45	C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄₇	—	2	2	no	—
48	C₂²×C₄₇	#102	1	2	yes	—
49	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
50	C₄×C₄₇	#102	1	2	yes	—
51	C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
53	Dic₄₇	—	4	4	no	—
54	Dic₄₇	—	8	2	no	—
55	#2141	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	—	2	2	no	—
57	C₂×C₄₇	C₂×#102	1	1	yes	characteristic
58	C₂×C₄₇	#510	1	2	yes	—
59	C₂²×Q₁₆	—	47	1	no	—
60	C₂×M₃₂	D₄₇	1	1	yes	characteristic
61	#427	—	47	1	no	—
62	#358	—	47	4	no	—
63	C₄₇	#2141	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₈	—	94	1	no	—
65	C₂×Q₁₆	—	47	4	no	—
66	C₂×Q₁₆	—	47	2	no	—
67	C₂×Q₁₆	—	94	1	no	—
68	C₂×Q₁₆	—	94	2	no	—
69	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
70	#117	—	94	1	no	—
71	M₃₂	—	2	2	no	—
72	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
73	#107	—	47	2	no	—
74	#106	—	94	1	no	—
75	C₂×Q₈	—	94	4	no	—
76	C₂×Q₈	—	94	2	no	—
77	C₂×Q₈	—	188	2	no	—
78	C₂×Q₈	—	188	1	no	—
79	C₂²×C₄	—	188	1	no	—
80	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
81	Q₁₆	—	47	4	no	—
82	Q₁₆	—	94	4	no	—
83	Q₁₆	—	94	2	no	—
84	C₂×C₈	C₄×D₄₇	1	2	yes	—
85	C₂×C₈	D₁₈₈	1	1	yes	characteristic
86	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
87	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
88	C₄⋊C₄	—	94	2	no	—
89	C₂²⋊C₄	—	188	1	no	—
90	C₄²	—	188	1	no	—
91	C₁₆	—	2	2	no	—
92	C₂³	D₃₇₆	1	1	yes	characteristic
93	Q₈	—	94	4	no	—
94	Q₈	—	188	4	no	—
95	Q₈	—	188	2	no	—
96	C₂×C₄	—	188	2	no	—
97	C₂×C₄	—	188	4	no	—
98	C₂×C₄	—	188	2	no	—
99	C₂×C₄	#10625325	1	2	yes	—
100	C₂×C₄	D₃₇₆	1	1	yes	characteristic
101	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
102	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
103	C₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
104	C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
105	C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
106	C₂²	—	2	2	no	—
107	C₂²	#13093946	1	2	yes	—
108	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
109	C₄	—	376	2	no	—
110	C₄	—	188	4	no	—
111	C₄	#13093946	1	2	yes	—
112	C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
113	C₄	C₂×#10625325	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	C₂×#13093946	1	1	yes	characteristic
116	C₂	#15689566	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₈₈

C₂

yes

maximal, characteristic

#15689161

C₂

yes

maximal, characteristic

#15688928

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₇

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

C₄

yes

complemented

C₂×Dic₁₈₈

C₂²

yes

—

#13093983

—

#13093958

C₂²

yes

—

#13093956

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

—

C₂×C₁₆×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

—

Dic₁₈₈

C₂×C₄

yes

—

C₁₆×C₄₇

—

C₂³×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

SD₁₆

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

C₂²⋊C₄

yes

—

C₈×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

#102

yes

—

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

#102

yes

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₄₇

C₂×SD₁₆

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2141

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂×#102

yes

characteristic

C₂×C₄₇

#510

yes

—

C₂²×Q₁₆

—

C₂×M₃₂

D₄₇

yes

characteristic

#427

—

#358

—

C₄₇

#2141

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

M₃₂

—

C₂×C₁₆

C₂×D₄₇

yes

—

#107

—

#106

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

188

—

C₂×Q₈

—

188

—

C₂²×C₄

—

188

—

C₂²×C₄

D₁₈₈

yes

characteristic

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

—

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₄²

—

188

—

C₁₆

—

C₂³

D₃₇₆

yes

characteristic

Q₈

—

Q₈

—

188

—

Q₈

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

#10625325

yes

—

100

C₂×C₄

D₃₇₆

yes

characteristic

101

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

102

C₂×C₄

C₂×D₁₈₈

yes

characteristic

103

C₈

(C₂×D₄₇)⋊C₄

yes

—

104

C₈

C₂×C₄×D₄₇

yes

characteristic

105

C₈

C₂×C₂²⋊D₄₇

yes

characteristic

106

C₂²

—

107

C₂²

#13093946

yes

—

108

C₂²

C₂×D₃₇₆

yes

characteristic

109

C₄

—

376

—

110

C₄

—

188

—

111

C₄

#13093946

yes

—

112

C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

113

C₄

C₂×#10625325

yes

characteristic

114

C₂

—

115

C₂

C₂×#13093946

yes

characteristic

116

C₂

#15689566

yes

—

	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	#2141
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

#2141

LCS

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #15688928	C₂	semidirect
8. C₂×Dic₁₈₈	C₄	semidirect
63. C₄₇	#2141	semidirect

H ≅ G/N

type

3. #15688928

C₂

semidirect

8. C₂×Dic₁₈₈

C₄

semidirect

63. C₄₇

#2141

semidirect

Subgroups — #20245109

Conjugacy classes of subgroups

Complements