Group #20246309 — subgroups

Subgroups — #20246309

Order 6016.

552 conjugacy classes of subgroups; only the 313 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 313 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×Q₈×Dic₄₇	C₂	1	2	yes	maximal
2	#15689022	C₂	1	6	yes	maximal
3	#15688989	C₂	1	3	yes	maximal
4	C₄×C₄⋊Dic₄₇	C₂	1	3	yes	maximal
5	C₂×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	Q₈×Dic₄₇	—	2	8	no	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	6	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	6	yes	—
9	C₂×C₄×Dic₄₇	C₂²	1	6	yes	—
10	C₄₇⋊#95	C₂²	1	1	yes	characteristic
11	C₄₇⋊#95	C₂²	1	3	yes	—
12	C₄₇⋊#95	C₂²	1	6	yes	—
13	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₄₇	C₄	1	8	yes	complemented
15	C₂×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
16	C₂×C₄²×C₄₇	C₂²	1	3	yes	—
17	C₂×Q₈×C₄₇	C₂×C₄	1	4	yes	—
18	C₂×Q₈×C₄₇	D₄	1	4	yes	—
19	C₂×Q₈×C₄₇	Q₈	1	4	yes	—
20	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
22	C₂²×C₄×C₄₇	C₂³	1	3	yes	—
23	C₂²×Dic₄₇	C₂³	1	6	yes	—
24	C₂²×Dic₄₇	C₂³	1	2	yes	—
25	C₄⋊C₄×C₄₇	C₂×C₄	1	12	yes	—
26	C₄²×C₄₇	C₂×C₄	1	12	yes	—
27	C₄⋊Dic₄₇	—	2	12	no	—
28	C₄⋊Dic₄₇	—	2	12	no	—
29	C₄×Dic₄₇	—	2	12	no	—
30	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
31	Q₈×C₄₇	C₄⋊C₄	1	16	yes	complemented
32	C₂×C₄×C₄₇	—	2	6	no	—
33	C₂×C₄×C₄₇	—	2	2	no	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	6	yes	—
36	C₂×C₄×C₄₇	C₂²×C₄	1	6	yes	—
37	C₂×C₄×C₄₇	C₂×D₄	1	6	yes	—
38	C₂×C₄×C₄₇	C₂×Q₈	1	6	yes	—
39	C₂×Dic₄₇	—	2	2	no	—
40	C₂×Dic₄₇	—	2	2	no	—
41	C₂×Dic₄₇	—	2	6	no	—
42	C₂×Dic₄₇	—	2	6	no	—
43	C₂×Dic₄₇	—	2	6	no	—
44	C₂×Dic₄₇	#41	1	4	yes	—
45	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
46	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
47	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
48	C₂²×C₄₇	C₂×#41	1	2	yes	—
49	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
50	C₄×C₄₇	—	2	6	no	—
51	C₄×C₄₇	—	2	2	no	—
52	C₄×C₄₇	C₂×C₄⋊C₄	1	12	yes	—
53	Dic₄₇	—	2	4	no	—
54	Dic₄₇	—	4	6	no	—
55	#2351	—	47	1	no	maximal, Sylow
56	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₄₇	C₄×#41	1	1	yes	characteristic
58	C₂×C₄₇	#519	1	1	yes	characteristic
59	C₂×C₄₇	#548	1	2	yes	—
60	C₂×C₄₇	#557	1	2	yes	—
61	C₂×C₄×Q₈	—	47	2	no	—
62	C₂×C₄×Q₈	D₄₇	1	1	yes	characteristic
63	#389	—	47	6	no	—
64	#382	—	47	3	no	—
65	C₄×C₄⋊C₄	—	47	3	no	—
66	C₄₇	#2351	1	1	yes	characteristic, complemented, Sylow
67	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
68	C₄×Q₈	—	94	8	no	—
69	C₄×Q₈	Dic₄₇	1	8	yes	complemented
70	C₂×C₄⋊C₄	—	47	6	no	—
71	C₂×C₄⋊C₄	—	47	6	no	—
72	C₂×C₄⋊C₄	C₂×D₄₇	1	3	yes	—
73	C₂×C₄²	—	47	6	no	—
74	C₂×C₄²	C₂×D₄₇	1	3	yes	—
75	#95	—	47	1	no	—
76	#95	—	47	3	no	—
77	#95	—	47	6	no	—
78	C₂×Q₈	Dic₉₄	1	4	yes	—
79	C₂×Q₈	D₁₈₈	1	4	yes	—
80	C₂×Q₈	C₂×Dic₄₇	1	4	yes	—
81	C₂²×C₄	—	47	2	no	—
82	C₂²×C₄	—	47	6	no	—
83	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
84	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
85	C₂²×C₄	C₂²×D₄₇	1	3	yes	—
86	C₄⋊C₄	—	94	12	no	—
87	C₄⋊C₄	—	94	12	no	—
88	C₄⋊C₄	C₂×Dic₄₇	1	12	yes	—
89	C₄²	—	94	12	no	—
90	C₄²	C₂×Dic₄₇	1	12	yes	—
91	C₂³	C₂³×D₄₇	1	1	yes	characteristic
92	Q₈	C₄⋊Dic₄₇	1	16	yes	complemented
93	C₂×C₄	—	2	6	no	—
94	C₂×C₄	—	2	2	no	—
95	C₂×C₄	—	47	4	no	—
96	C₂×C₄	—	94	2	no	—
97	C₂×C₄	—	94	2	no	—
98	C₂×C₄	—	94	6	no	—
99	C₂×C₄	—	94	6	no	—
100	C₂×C₄	—	94	6	no	—
101	C₂×C₄	C₂×Dic₉₄	1	6	yes	—
102	C₂×C₄	C₂×D₁₈₈	1	6	yes	—
103	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
104	C₂×C₄	C₂²×Dic₄₇	1	6	yes	—
105	C₂×C₄	C₂²×Dic₄₇	1	6	yes	—
106	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
107	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
108	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
109	C₂²	#41×D₄₇	1	2	yes	—
110	C₂²	#13094072	1	2	yes	—
111	C₄	—	2	6	no	—
112	C₄	—	2	2	no	—
113	C₄	—	94	4	no	—
114	C₄	—	188	6	no	—
115	C₄	C₂×C₄⋊Dic₄₇	1	12	yes	—
116	C₂	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
117	C₂	#41×Dic₄₇	1	1	yes	characteristic
118	C₂	#15689601	1	1	yes	characteristic
119	C₂	#15689785	1	2	yes	—
120	C₂	#15689849	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×Dic₄₇

C₂

yes

maximal

#15689022

C₂

yes

maximal

#15688989

C₂

yes

maximal

C₄×C₄⋊Dic₄₇

C₂

yes

maximal

C₂×C₄×Q₈×C₄₇

C₂

yes

maximal, characteristic

Q₈×Dic₄₇

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

characteristic

C₄₇⋊#95

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

characteristic

C₄×Q₈×C₄₇

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂×Q₈×C₄₇

D₄

yes

—

C₂×Q₈×C₄₇

Q₈

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

C₂⁴

yes

characteristic

Q₈×C₄₇

C₄⋊C₄

yes

complemented

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

#41

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄⋊C₄

yes

—

Dic₄₇

—

Dic₄₇

—

#2351

—

maximal, Sylow

C₂×C₄₇

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₄₇

C₄×#41

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

#557

yes

—

C₂×C₄×Q₈

—

C₂×C₄×Q₈

D₄₇

yes

characteristic

#389

—

#382

—

C₄×C₄⋊C₄

—

C₄₇

#2351

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

characteristic

C₄×Q₈

—

C₄×Q₈

Dic₄₇

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

—

#95

—

#95

—

#95

—

C₂×Q₈

Dic₉₄

yes

—

C₂×Q₈

D₁₈₈

yes

—

C₂×Q₈

C₂×Dic₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₄₇

yes

—

C₄²

—

C₄²

C₂×Dic₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

C₄⋊Dic₄₇

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

C₂×Dic₉₄

yes

—

102

C₂×C₄

C₂×D₁₈₈

yes

—

103

C₂×C₄

C₂²×Dic₄₇

yes

—

104

C₂×C₄

C₂²×Dic₄₇

yes

—

105

C₂×C₄

C₂²×Dic₄₇

yes

—

106

C₂²

C₂³×Dic₄₇

yes

characteristic

107

C₂²

C₂²×D₁₈₈

yes

characteristic

108

C₂²

C₂²×Dic₉₄

yes

characteristic

109

C₂²

#41×D₄₇

yes

—

110

C₂²

#13094072

yes

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

188

—

115

C₄

C₂×C₄⋊Dic₄₇

yes

—

116

C₂

C₂²×C₄⋊Dic₄₇

yes

characteristic

117

C₂

#41×Dic₄₇

yes

characteristic

118

C₂

#15689601

yes

characteristic

119

C₂

#15689785

yes

—

120

C₂

#15689849

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₂×C₄×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂×C₄×Q₈	D₄₇
hypocenter	C₄₇	#2351
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Fitting

C₂×C₄×Q₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

hypercenter

C₂×C₄×Q₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

N	H ≅ G/N	type
14. C₄×Q₈×C₄₇	C₄	semidirect
31. Q₈×C₄₇	C₄⋊C₄	semidirect
66. C₄₇	#2351	semidirect
69. C₄×Q₈	Dic₄₇	semidirect
92. Q₈	C₄⋊Dic₄₇	semidirect

H ≅ G/N

type

14. C₄×Q₈×C₄₇

C₄

semidirect

31. Q₈×C₄₇

C₄⋊C₄

semidirect

66. C₄₇

#2351

semidirect

69. C₄×Q₈

Dic₄₇

semidirect

92. Q₈

C₄⋊Dic₄₇

semidirect

Subgroups — #20246309

Conjugacy classes of subgroups

Complements