Group #20242874 — subgroups

Subgroups — #20242874

Order 6016.

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

normal subgroups only

This group has 166 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	#15689400	C₂	1	2	yes	maximal
2	#15689202	C₂	1	1	yes	maximal, characteristic
3	#15688874	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688869	C₂	1	2	yes	maximal, complemented
5	C₄₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625324	—	2	1	no	—
7	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
8	#13093957	—	2	2	no	—
9	C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
10	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	#13093944	—	2	2	no	—
12	(C₂×D₄₇)⋊C₈	—	2	1	no	—
13	C₂×Q₁₆×C₄₇	—	2	1	no	—
14	C₂×Q₁₆×C₄₇	—	2	1	no	—
15	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	—	2	2	no	—
18	C₂×D₁₈₈	D₄	1	1	yes	characteristic
19	C₂×C₄×D₄₇	—	2	1	no	—
20	Q₁₆×C₄₇	—	4	2	no	—
21	Q₁₆×C₄₇	—	4	2	no	—
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	2	no	—
25	C₄⋊C₄×C₄₇	—	2	2	no	—
26	C₄²×C₄₇	C₂³	1	1	yes	characteristic
27	(C₂×D₄₇)⋊C₄	—	2	1	no	—
28	C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
29	C₂×C₄₇⋊C₈	—	2	1	no	—
30	C₂×C₄₇⋊C₈	—	2	2	no	—
31	#10625324	—	4	2	no	—
32	C₂²×D₄₇	—	2	1	no	—
33	Q₈×C₄₇	—	4	2	no	—
34	Q₈×C₄₇	—	4	2	no	—
35	C₂×C₄×C₄₇	—	4	2	no	—
36	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
39	C₂×Dic₄₇	—	2	1	no	—
40	D₁₈₈	—	2	2	no	—
41	C₄×D₄₇	—	4	1	no	—
42	C₄×D₄₇	—	4	1	no	—
43	C₈×C₄₇	—	2	1	no	—
44	C₈×C₄₇	D₈	1	2	yes	—
45	C₄₇⋊C₈	—	4	1	no	—
46	C₄₇⋊C₈	—	4	2	no	—
47	C₂²×C₄₇	#121	1	1	yes	characteristic
48	C₂×D₄₇	—	4	1	no	—
49	C₂×D₄₇	—	4	1	no	—
50	C₂×D₄₇	—	4	1	no	—
51	C₄×C₄₇	—	2	1	no	—
52	C₄×C₄₇	—	8	2	no	—
53	C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
54	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
55	C₄×C₄₇	#137	1	2	yes	—
56	Dic₄₇	—	4	1	no	—
57	#1689	—	47	1	no	maximal, Sylow
58	C₂×C₄₇	#459	1	1	yes	characteristic
59	C₂×C₄₇	#470	1	1	yes	characteristic
60	C₂×C₄₇	#473	1	1	yes	characteristic
61	D₄₇	—	8	1	no	—
62	#494	D₄₇	1	1	yes	characteristic, complemented
63	#474	—	47	2	no	—
64	#436	—	47	1	no	—
65	#334	—	47	1	no	—
66	#332	—	47	2	no	—
67	C₄₇	#1689	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₁₆	—	2	1	no	—
69	C₂×Q₁₆	—	2	1	no	—
70	C₂×M₁₆	—	94	1	no	—
71	C₄⋊Q₈	C₂×D₄₇	1	2	yes	—
72	C₄×D₄	—	47	1	no	—
73	#107	—	94	2	no	—
74	C₄⋊C₈	—	47	1	no	—
75	C₄⋊C₈	—	47	2	no	—
76	#102	—	94	2	no	—
77	C₂²⋊C₈	—	94	1	no	—
78	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
79	C₂×Q₈	—	2	2	no	—
80	C₂×D₄	—	47	1	no	—
81	C₂²×C₄	—	94	1	no	—
82	Q₁₆	—	4	2	no	—
83	Q₁₆	—	4	2	no	—
84	M₁₆	—	188	2	no	—
85	C₂×C₈	—	94	2	no	—
86	C₂×C₈	—	94	1	no	—
87	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
88	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	2	2	no	—
91	C₄⋊C₄	—	47	1	no	—
92	C₂²⋊C₄	—	94	1	no	—
93	C₄²	C₂²×D₄₇	1	1	yes	characteristic
94	C₂³	—	94	1	no	—
95	Q₈	—	4	2	no	—
96	Q₈	—	4	2	no	—
97	D₄	—	94	2	no	—
98	C₂×C₄	—	4	2	no	—
99	C₂×C₄	—	94	1	no	—
100	C₂×C₄	—	188	1	no	—
101	C₂×C₄	—	188	1	no	—
102	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
103	C₂×C₄	#10625352	1	1	yes	characteristic
104	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
105	C₈	—	2	1	no	—
106	C₈	—	188	1	no	—
107	C₈	—	188	2	no	—
108	C₈	#10625334	1	2	yes	—
109	C₂²	—	188	1	no	—
110	C₂²	—	188	1	no	—
111	C₂²	—	188	1	no	—
112	C₂²	#13093995	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	8	2	no	—
115	C₄	—	188	1	no	—
116	C₄	C₂×#10625334	1	1	yes	characteristic
117	C₄	#13094050	1	1	yes	characteristic
118	C₄	#13094056	1	2	yes	—
119	C₂	—	376	1	no	—
120	C₂	#15689315	1	1	yes	characteristic
121	C₂	#15689378	1	1	yes	characteristic
122	C₂	#15689395	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689400

C₂

yes

maximal

#15689202

C₂

yes

maximal, characteristic

#15688874

C₂

yes

maximal, characteristic, complemented

#15688869

C₂

yes

maximal, complemented

C₄₇×#494

C₂

yes

maximal, characteristic, complemented

C₂×#10625324

—

C₄×D₁₈₈

C₂²

yes

characteristic

#13093957

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093944

—

(C₂×D₄₇)⋊C₈

—

C₂×Q₁₆×C₄₇

—

C₂×Q₁₆×C₄₇

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×D₁₈₈

D₄

yes

characteristic

C₂×C₄×D₄₇

—

Q₁₆×C₄₇

—

Q₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

D₄

yes

characteristic

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

#10625324

—

C₂²×D₄₇

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

D₈

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×D₈

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#494

D₄₇

yes

characteristic, complemented

—

—

—

—

C₄₇

#1689

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×M₁₆

—

C₄⋊Q₈

C₂×D₄₇

yes

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

Q₈

—

D₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

188

—

101

C₂×C₄

—

188

—

102

C₂×C₄

D₄×D₄₇

yes

characteristic

103

C₂×C₄

#10625352

yes

characteristic

104

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

105

C₈

—

106

C₈

—

188

—

107

C₈

—

188

—

108

C₈

#10625334

yes

—

109

C₂²

—

188

—

110

C₂²

—

188

—

111

C₂²

—

188

—

112

C₂²

#13093995

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

188

—

116

C₄

C₂×#10625334

yes

characteristic

117

C₄

#13094050

yes

characteristic

118

C₄

#13094056

yes

—

119

C₂

—

376

—

120

C₂

#15689315

yes

characteristic

121

C₂

#15689378

yes

characteristic

122

C₂

#15689395

yes

characteristic

	subgroup	G/H
center	C₂²	#13093995
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#494	C₂
socle	C₂²×C₄₇	#121
hypercenter	#494	D₄₇
hypocenter	C₄₇	#1689
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

subgroup

G/H

center

C₂²

#13093995

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#494

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #494

N	H ≅ G/N	type
3. #15688874	C₂	semidirect
4. #15688869	C₂	semidirect
5. C₄₇×#494	C₂	semidirect
62. #494	D₄₇	semidirect
67. C₄₇	#1689	semidirect

H ≅ G/N

type

3. #15688874

C₂

semidirect

4. #15688869

C₂

semidirect

5. C₄₇×#494

C₂

semidirect

62. #494

D₄₇

semidirect

67. C₄₇

#1689

semidirect

Subgroups — #20242874

Conjugacy classes of subgroups

Complements