Group #20245974 — subgroups

Subgroups — #20245974

Order 6016.

784 conjugacy classes of subgroups; only the 309 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 309 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×#13093983	C₂	1	2	yes	maximal
2	#15689030	C₂	1	8	yes	maximal, complemented
3	#15688986	C₂	1	4	yes	maximal
4	C₂³×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	#13093983	—	2	8	no	—
6	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
7	C₂×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
8	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
9	C₄₇⋊#95	C₂²	1	16	yes	—
10	C₂²×Q₈×C₄₇	—	2	8	no	—
11	C₂²×Q₈×C₄₇	C₄	1	8	yes	complemented
12	C₂²×Q₈×C₄₇	C₂²	1	4	yes	—
13	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
14	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
16	C₂×Q₈×C₄₇	—	2	32	no	—
17	C₂×Q₈×C₄₇	—	2	8	no	—
18	C₂×Q₈×C₄₇	—	2	8	no	—
19	C₂×Q₈×C₄₇	C₂×C₄	1	16	yes	—
20	C₂²×C₄×C₄₇	—	2	8	no	—
21	C₂²×C₄×C₄₇	C₂×C₄	1	8	yes	—
22	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
23	C₂²×C₄×C₄₇	D₄	1	8	yes	—
24	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
25	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
26	C₂²×Dic₄₇	C₂³	1	8	yes	—
27	C₂²⋊Dic₄₇	—	2	8	no	—
28	C₄⋊Dic₄₇	—	2	8	no	—
29	C₄×Dic₄₇	—	2	8	no	—
30	C₂³×C₄₇	—	2	4	no	—
31	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
32	C₂³×C₄₇	C₂×D₄	1	4	yes	—
33	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
34	Q₈×C₄₇	—	2	32	no	—
35	C₂×C₄×C₄₇	—	2	16	no	—
36	C₂×C₄×C₄₇	—	2	8	no	—
37	C₂×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
38	C₂×C₄×C₄₇	C₂²×C₄	1	8	yes	—
39	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
40	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
41	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
42	C₂×Dic₄₇	—	2	8	no	—
43	C₂×Dic₄₇	—	2	16	no	—
44	C₂²×C₄₇	—	2	4	no	—
45	C₂²×C₄₇	—	2	8	no	—
46	C₂²×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
47	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
48	C₂²×C₄₇	C₂²×D₄	1	2	yes	—
49	C₂²×C₄₇	2₋¹⁺⁴	1	4	yes	—
50	C₄×C₄₇	—	2	8	no	—
51	C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
52	Dic₄₇	—	4	8	no	—
53	#2310	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	—	2	4	no	—
55	C₂×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄₇	#519	1	2	yes	—
57	C₂×C₄₇	#536	1	4	yes	—
58	C₂³×Q₈	D₄₇	1	1	yes	characteristic
59	C₂×#117	—	47	2	no	—
60	#391	—	47	8	no	—
61	#381	—	47	4	no	—
62	C₄₇	#2310	1	1	yes	characteristic, complemented, Sylow
63	C₂²×Q₈	—	2	8	no	—
64	C₂²×Q₈	Dic₄₇	1	8	yes	complemented
65	C₂²×Q₈	C₂×D₄₇	1	4	yes	—
66	C₂³×C₄	C₂×D₄₇	1	2	yes	—
67	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
68	#117	—	94	8	no	—
69	C₂×C₄⋊C₄	—	47	4	no	—
70	C₂×C₂²⋊C₄	—	47	4	no	—
71	C₂×C₄²	—	47	4	no	—
72	#95	—	47	16	no	—
73	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
74	C₂×Q₈	—	2	32	no	—
75	C₂×Q₈	—	2	8	no	—
76	C₂×Q₈	—	2	8	no	—
77	C₂×Q₈	C₂×Dic₄₇	1	16	yes	—
78	C₂²×C₄	—	2	8	no	—
79	C₂²×C₄	—	47	8	no	—
80	C₂²×C₄	C₂×Dic₄₇	1	8	yes	—
81	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
82	C₂²×C₄	C₂²⋊D₄₇	1	8	yes	—
83	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
84	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
85	C₄⋊C₄	—	94	8	no	—
86	C₂²⋊C₄	—	94	8	no	—
87	C₄²	—	94	8	no	—
88	C₂³	—	2	4	no	—
89	C₂³	C₂²×Dic₄₇	1	2	yes	—
90	C₂³	C₂×C₂²⋊D₄₇	1	4	yes	—
91	C₂³	C₂³×D₄₇	1	1	yes	characteristic
92	Q₈	—	2	32	no	—
93	C₂×C₄	—	2	16	no	—
94	C₂×C₄	—	2	8	no	—
95	C₂×C₄	—	94	8	no	—
96	C₂×C₄	—	94	16	no	—
97	C₂×C₄	C₂²⋊Dic₄₇	1	16	yes	—
98	C₂×C₄	C₂²×Dic₄₇	1	8	yes	—
99	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
100	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
101	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
102	C₂²	—	2	4	no	—
103	C₂²	—	2	8	no	—
104	C₂²	C₂×C₂²⋊Dic₄₇	1	4	yes	—
105	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
106	C₂²	C₂²×C₂²⋊D₄₇	1	2	yes	—
107	C₂²	#13094072	1	4	yes	—
108	C₄	—	2	8	no	—
109	C₄	—	188	8	no	—
110	C₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
111	C₂	—	2	4	no	—
112	C₂	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
113	C₂	#15689601	1	2	yes	—
114	C₂	#15689697	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093983

C₂

yes

maximal

#15689030

C₂

yes

maximal, complemented

#15688986

C₂

yes

maximal

C₂³×Q₈×C₄₇

C₂

yes

maximal, characteristic

#13093983

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₂²⋊Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂²×Q₈×C₄₇

—

C₂²×Q₈×C₄₇

C₄

yes

complemented

C₂²×Q₈×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂×D₄

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

Q₈×C₄₇

—

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×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂²×D₄

yes

—

C₂²×C₄₇

2₋¹⁺⁴

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₂²⋊C₄

yes

—

Dic₄₇

—

#2310

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

C₂²×C₂²⋊C₄

yes

characteristic

C₂×C₄₇

#519

yes

—

C₂×C₄₇

#536

yes

—

C₂³×Q₈

D₄₇

yes

—

—

—

C₄₇

#2310

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

Dic₄₇

yes

complemented

C₂²×Q₈

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

—

#95

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×Dic₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

C₂³

C₂²×Dic₄₇

yes

—

C₂³

C₂×C₂²⋊D₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊Dic₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

100

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

101

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

102

C₂²

—

103

C₂²

—

104

C₂²

C₂×C₂²⋊Dic₄₇

yes

—

105

C₂²

C₂³×Dic₄₇

yes

characteristic

106

C₂²

C₂²×C₂²⋊D₄₇

yes

—

107

C₂²

#13094072

yes

—

108

C₄

—

109

C₄

—

188

—

110

C₄

C₂×C₂²⋊Dic₄₇

yes

—

111

C₂

—

112

C₂

C₂²×C₂²⋊Dic₄₇

yes

characteristic

113

C₂

#15689601

yes

—

114

C₂

#15689697

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₂³×Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂³×Q₈	D₄₇
hypocenter	C₄₇	#2310
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator

C₂²×C₄₇

C₂³×C₄

Fitting

C₂³×Q₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂⁴

hypercenter

C₂³×Q₈

D₄₇

C₄₇

G ▷ C₂²×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₂³×Q₈

N	H ≅ G/N	type
2. #15689030	C₂	semidirect
11. C₂²×Q₈×C₄₇	C₄	semidirect
62. C₄₇	#2310	semidirect
64. C₂²×Q₈	Dic₄₇	semidirect

H ≅ G/N

type

2. #15689030

C₂

semidirect

11. C₂²×Q₈×C₄₇

C₄

semidirect

62. C₄₇

#2310

semidirect

64. C₂²×Q₈

Dic₄₇

semidirect

Subgroups — #20245974

Conjugacy classes of subgroups

Complements