Group #20244657 — subgroups

Subgroups — #20244657

Order 6016.

256 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 67 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	#15689149	C₂	1	1	yes	maximal, characteristic
3	#15689133	C₂	1	2	yes	maximal
4	C₂×#13093942	C₂	1	2	yes	maximal
5	C₄₇×#341	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₉₄	C₂²	1	2	yes	—
7	C₂×Dic₁₈₈	—	2	4	no	—
8	C₂×Dic₁₈₈	—	2	2	no	—
9	C₂×#10625329	C₂²	1	1	yes	characteristic
10	#13093983	C₂²	1	1	yes	characteristic
11	Dic₄₇⋊C₈	—	2	2	no	—
12	#13093949	—	2	4	no	—
13	#13093942	—	2	4	no	—
14	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₇	—	2	2	no	—
18	C₂×Dic₉₄	—	2	2	no	—
19	C₂×Dic₉₄	—	2	2	no	—
20	C₂×Dic₉₄	—	2	2	no	—
21	C₂×Dic₉₄	—	2	2	no	—
22	C₂×Dic₉₄	—	2	2	no	—
23	C₂×Dic₉₄	D₄	1	4	yes	—
24	M₁₆×C₄₇	—	2	2	no	—
25	M₁₆×C₄₇	—	2	2	no	—
26	C₂×C₈×C₄₇	—	2	2	no	—
27	C₂×C₈×C₄₇	—	2	2	no	—
28	C₂×C₈×C₄₇	D₄	1	2	yes	—
29	C₂²⋊Dic₄₇	—	2	1	no	—
30	C₄⋊Dic₄₇	D₄	1	2	yes	—
31	C₄×Dic₄₇	—	2	1	no	—
32	#10625329	—	2	2	no	—
33	C₂×C₄₇⋊C₈	—	2	1	no	—
34	Dic₁₈₈	—	2	8	no	—
35	C₂³×C₄₇	#41	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₇	#41	1	2	yes	—
40	C₂×Dic₄₇	—	2	2	no	—
41	C₂×Dic₄₇	—	2	4	no	—
42	C₂×Dic₄₇	—	4	2	no	—
43	C₂×Dic₄₇	—	4	2	no	—
44	Dic₉₄	—	2	4	no	—
45	Dic₉₄	—	2	4	no	—
46	Dic₉₄	—	4	2	no	—
47	Dic₉₄	—	4	2	no	—
48	C₈×C₄₇	—	2	2	no	—
49	C₈×C₄₇	—	4	2	no	—
50	C₄₇⋊C₈	—	4	1	no	—
51	C₂²×C₄₇	—	2	2	no	—
52	C₂²×C₄₇	#121	1	1	yes	characteristic
53	C₂²×C₄₇	#123	1	2	yes	—
54	C₄×C₄₇	#120	1	1	yes	characteristic
55	C₄×C₄₇	#121	1	2	yes	—
56	C₄×C₄₇	#124	1	1	yes	characteristic
57	Dic₄₇	—	4	4	no	—
58	Dic₄₇	—	4	2	no	—
59	#2047	—	47	1	no	maximal, Sylow
60	C₂×C₄₇	—	2	2	no	—
61	C₂×C₄₇	#394	1	1	yes	characteristic
62	C₂×C₄₇	#473	1	2	yes	—
63	C₂²×Q₁₆	—	47	1	no	—
64	#424	—	47	1	no	—
65	#419	—	47	2	no	—
66	C₂×#101	—	47	2	no	—
67	#341	D₄₇	1	1	yes	characteristic
68	C₄₇	#2047	1	1	yes	characteristic, complemented, Sylow
69	C₂²×Q₈	—	47	2	no	—
70	C₂×Q₁₆	—	94	4	no	—
71	C₂×Q₁₆	—	94	2	no	—
72	C₂×M₁₆	—	47	1	no	—
73	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
74	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
75	#117	—	47	1	no	—
76	C₄⋊C₈	—	94	2	no	—
77	#103	—	94	4	no	—
78	#101	—	94	4	no	—
79	C₂×Q₈	—	47	4	no	—
80	C₂×Q₈	—	94	2	no	—
81	C₂×Q₈	—	94	2	no	—
82	C₂×Q₈	—	94	2	no	—
83	C₂×Q₈	—	94	2	no	—
84	C₂×Q₈	—	94	2	no	—
85	C₂²×C₄	—	94	2	no	—
86	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
87	Q₁₆	—	94	8	no	—
88	M₁₆	—	2	2	no	—
89	M₁₆	—	2	2	no	—
90	M₁₆	—	94	2	no	—
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	94	1	no	—
94	C₂×C₈	D₁₈₈	1	2	yes	—
95	C₄⋊C₄	—	47	2	no	—
96	C₂²⋊C₄	—	94	1	no	—
97	C₄²	—	94	1	no	—
98	C₂³	#10625354	1	1	yes	characteristic
99	Q₈	—	94	4	no	—
100	Q₈	—	94	4	no	—
101	Q₈	—	188	2	no	—
102	Q₈	—	188	2	no	—
103	C₂×C₄	—	94	2	no	—
104	C₂×C₄	—	94	4	no	—
105	C₂×C₄	—	188	2	no	—
106	C₂×C₄	—	188	2	no	—
107	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
108	C₂×C₄	#10625350	1	2	yes	—
109	C₂×C₄	D₄×D₄₇	1	2	yes	—
110	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	4	2	no	—
113	C₈	—	188	1	no	—
114	C₂²	—	2	2	no	—
115	C₂²	#13093999	1	1	yes	characteristic
116	C₂²	#13094009	1	2	yes	—
117	C₄	—	188	4	no	—
118	C₄	—	188	2	no	—
119	C₄	#13093994	1	1	yes	characteristic
120	C₄	#13093997	1	2	yes	—
121	C₄	#13094012	1	1	yes	characteristic
122	C₂	—	2	2	no	—
123	C₂	#15689041	1	1	yes	characteristic
124	C₂	#15689399	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₈₈

C₂

yes

maximal, characteristic

#15689149

C₂

yes

maximal, characteristic

#15689133

C₂

yes

maximal

C₂×#13093942

C₂

yes

maximal

C₄₇×#341

C₂

yes

maximal, characteristic

C₂²×Dic₉₄

C₂²

yes

—

C₂×Dic₁₈₈

—

C₂×Dic₁₈₈

—

C₂×#10625329

C₂²

yes

characteristic

#13093983

C₂²

yes

characteristic

Dic₄₇⋊C₈

—

#13093949

—

#13093942

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×Dic₉₄

D₄

yes

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₂²×C₄₇

#123

yes

—

C₄×C₄₇

#120

yes

characteristic

C₄×C₄₇

#121

yes

—

C₄×C₄₇

#124

yes

characteristic

Dic₄₇

—

Dic₄₇

—

#2047

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#394

yes

characteristic

C₂×C₄₇

#473

yes

—

C₂²×Q₁₆

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2047

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

C₄⋊C₈

—

#103

—

#101

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#10625354

yes

characteristic

Q₈

—

100

Q₈

—

101

Q₈

—

188

—

102

Q₈

—

188

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

188

—

106

C₂×C₄

—

188

—

107

C₂×C₄

C₂×D₁₈₈

yes

characteristic

108

C₂×C₄

#10625350

yes

—

109

C₂×C₄

D₄×D₄₇

yes

—

110

C₂×C₄

D₄×D₄₇

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

188

—

114

C₂²

—

115

C₂²

#13093999

yes

characteristic

116

C₂²

#13094009

yes

—

117

C₄

—

188

—

118

C₄

—

188

—

119

C₄

#13093994

yes

characteristic

120

C₄

#13093997

yes

—

121

C₄

#13094012

yes

characteristic

122

C₂

—

123

C₂

#15689041

yes

characteristic

124

C₂

#15689399

yes

—

	subgroup	G/H
center	C₂²	#13093999
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#341	C₂
socle	C₂²×C₄₇	#121
hypercenter	#341	D₄₇
hypocenter	C₄₇	#2047
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#13093999

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#341

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
68. C₄₇	#2047	semidirect

H ≅ G/N

type

68. C₄₇

#2047

semidirect

Subgroups — #20244657

Conjugacy classes of subgroups

Complements