Group #20242872 — subgroups

Subgroups — #20242872

Order 6016.

184 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 57 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	#15689500	C₂	1	1	yes	maximal, characteristic
2	#15689323	C₂	1	2	yes	maximal, complemented
3	#15688874	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688866	C₂	1	2	yes	maximal, complemented
5	C₄₇×#446	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625336	—	2	2	no	—
7	C₂×D₃₇₆	—	2	1	no	—
8	C₂×D₃₇₆	—	2	1	no	—
9	#13094021	C₂²	1	2	yes	—
10	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	#13093944	—	2	2	no	—
12	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₄₇	—	2	1	no	—
14	C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
15	#97×C₄₇	—	2	1	no	—
16	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
18	C₂×D₁₈₈	—	2	2	no	—
19	C₂×D₁₈₈	—	2	2	no	—
20	C₂×D₁₈₈	—	2	2	no	—
21	C₂×C₈×C₄₇	—	2	1	no	—
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
24	C₄⋊C₄×C₄₇	—	2	1	no	—
25	C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
26	C₄²×C₄₇	—	2	1	no	—
27	C₄²×C₄₇	C₂³	1	1	yes	characteristic
28	#10625336	—	4	4	no	—
29	C₂×C₄₇⋊C₈	—	2	2	no	—
30	D₃₇₆	—	4	2	no	—
31	D₃₇₆	—	4	2	no	—
32	C₂²×D₄₇	—	4	2	no	—
33	Q₈×C₄₇	—	2	2	no	—
34	C₂×C₄×C₄₇	—	2	1	no	—
35	C₂×C₄×C₄₇	—	2	1	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	D₁₈₈	—	4	2	no	—
40	D₁₈₈	—	4	2	no	—
41	D₁₈₈	—	4	2	no	—
42	D₁₈₈	—	4	2	no	—
43	D₁₈₈	—	8	2	no	—
44	C₈×C₄₇	—	2	1	no	—
45	C₈×C₄₇	—	4	1	no	—
46	C₈×C₄₇	SD₁₆	1	2	yes	complemented
47	C₄₇⋊C₈	—	4	2	no	—
48	C₂²×C₄₇	#121	1	1	yes	characteristic
49	C₂×D₄₇	—	8	2	no	—
50	C₂×D₄₇	—	8	2	no	—
51	C₂×D₄₇	—	8	2	no	—
52	C₄×C₄₇	—	2	1	no	—
53	C₄×C₄₇	—	4	1	no	—
54	C₄×C₄₇	—	4	1	no	—
55	C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
56	C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
57	C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
58	#1688	—	47	1	no	maximal, Sylow
59	C₂×C₄₇	#460	1	1	yes	characteristic
60	C₂×C₄₇	#469	1	1	yes	characteristic
61	C₂×C₄₇	#472	1	1	yes	characteristic
62	D₄₇	—	16	2	no	—
63	#493	—	47	1	no	—
64	#460	—	47	2	no	—
65	#446	D₄₇	1	1	yes	characteristic, complemented
66	#334	—	47	1	no	—
67	#331	—	47	2	no	—
68	C₄₇	#1688	1	1	yes	characteristic, complemented, Sylow
69	C₂×SD₁₆	—	94	2	no	—
70	C₂×D₈	—	94	1	no	—
71	C₂×D₈	—	94	1	no	—
72	#127	—	47	2	no	—
73	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
74	C₄⋊C₈	—	2	1	no	—
75	C₄⋊C₈	—	47	2	no	—
76	C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
77	#102	—	94	2	no	—
78	#97	—	2	1	no	—
79	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
80	C₂×Q₈	D₁₈₈	1	1	yes	characteristic
81	C₂×D₄	—	94	2	no	—
82	C₂×D₄	—	94	2	no	—
83	C₂×D₄	—	94	2	no	—
84	SD₁₆	—	188	4	no	—
85	D₈	—	188	2	no	—
86	D₈	—	188	2	no	—
87	C₂×C₈	—	2	1	no	—
88	C₂×C₈	—	94	2	no	—
89	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
90	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
91	C₄⋊C₄	—	2	1	no	—
92	C₄⋊C₄	D₁₈₈	1	1	yes	characteristic
93	C₄²	—	2	1	no	—
94	C₄²	C₂²×D₄₇	1	1	yes	characteristic
95	C₂³	—	188	2	no	—
96	Q₈	—	2	2	no	—
97	D₄	—	376	2	no	—
98	D₄	—	188	2	no	—
99	D₄	—	188	2	no	—
100	D₄	—	188	2	no	—
101	D₄	—	188	2	no	—
102	C₂×C₄	—	2	1	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
105	C₂×C₄	#10625350	1	1	yes	characteristic
106	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
107	C₈	—	2	1	no	—
108	C₈	—	4	1	no	—
109	C₈	—	188	2	no	—
110	C₈	#10625336	1	2	yes	complemented
111	C₂²	—	376	2	no	—
112	C₂²	—	376	2	no	—
113	C₂²	—	376	2	no	—
114	C₂²	#13093998	1	1	yes	characteristic
115	C₄	—	2	1	no	—
116	C₄	—	4	1	no	—
117	C₄	—	4	1	no	—
118	C₄	C₂×#10625336	1	1	yes	characteristic
119	C₄	#13094049	1	1	yes	characteristic
120	C₄	#13094052	1	2	yes	—
121	C₂	—	752	2	no	—
122	C₂	#15689323	1	1	yes	characteristic
123	C₂	#15689376	1	1	yes	characteristic
124	C₂	#15689393	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689500

C₂

yes

maximal, characteristic

#15689323

C₂

yes

maximal, complemented

#15688874

C₂

yes

maximal, characteristic, complemented

#15688866

C₂

yes

maximal, complemented

C₄₇×#446

C₂

yes

maximal, characteristic, complemented

C₂×#10625336

—

C₂×D₃₇₆

—

C₂×D₃₇₆

—

#13094021

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

#13093944

—

C₄×Q₈×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

—

C₄⋊C₈×C₄₇

C₂²

yes

characteristic

#97×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

D₄

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

C₂³

yes

characteristic

#10625336

—

C₂×C₄₇⋊C₈

—

D₃₇₆

—

D₃₇₆

—

C₂²×D₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

SD₁₆

yes

complemented

C₄₇⋊C₈

—

C₂²×C₄₇

#121

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×SD₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#493

—

#460

—

#446

D₄₇

yes

characteristic, complemented

#334

—

#331

—

C₄₇

#1688

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

#127

—

C₄×Q₈

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

characteristic

#102

—

#97

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

D₁₈₈

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

188

—

D₈

—

188

—

D₈

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

D₁₈₈

yes

characteristic

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

188

—

Q₈

—

D₄

—

376

—

D₄

—

188

—

D₄

—

188

—

100

D₄

—

188

—

101

D₄

—

188

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×D₁₈₈

yes

characteristic

105

C₂×C₄

#10625350

yes

characteristic

106

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

188

—

110

C₈

#10625336

yes

complemented

111

C₂²

—

376

—

112

C₂²

—

376

—

113

C₂²

—

376

—

114

C₂²

#13093998

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

C₂×#10625336

yes

characteristic

119

C₄

#13094049

yes

characteristic

120

C₄

#13094052

yes

—

121

C₂

—

752

—

122

C₂

#15689323

yes

characteristic

123

C₂

#15689376

yes

characteristic

124

C₂

#15689393

yes

characteristic

	subgroup	G/H
center	C₂²	#13093998
commutator	C₄²×C₄₇	C₂³
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#446	C₂
socle	C₂²×C₄₇	#121
hypercenter	#446	D₄₇
hypocenter	C₄₇	#1688
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #446

subgroup

G/H

center

C₂²

#13093998

commutator

C₄²×C₄₇

C₂³

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#446

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #446

N	H ≅ G/N	type
2. #15689323	C₂	semidirect
3. #15688874	C₂	semidirect
4. #15688866	C₂	semidirect
5. C₄₇×#446	C₂	semidirect
46. C₈×C₄₇	SD₁₆	semidirect
65. #446	D₄₇	semidirect
68. C₄₇	#1688	semidirect
110. C₈	#10625336	semidirect

H ≅ G/N

type

2. #15689323

C₂

semidirect

3. #15688874

C₂

semidirect

4. #15688866

C₂

semidirect

5. C₄₇×#446

C₂

semidirect

46. C₈×C₄₇

SD₁₆

semidirect

65. #446

D₄₇

semidirect

68. C₄₇

#1688

semidirect

110. C₈

#10625336

semidirect

Subgroups — #20242872

Conjugacy classes of subgroups

Complements