Group #20243541 — subgroups

Subgroups — #20243541

Order 6016.

256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₄₇⋊C₈	C₂	1	4	yes	maximal
3	#15688969	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
7	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
8	Dic₄₇⋊C₈	—	2	8	no	—
9	C₄₇⋊#95	C₄	1	2	yes	—
10	C₄₇⋊#95	C₄	1	2	yes	—
11	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₄₇	—	2	2	no	—
14	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₄₇	—	2	2	no	—
19	C₂×C₈×C₄₇	—	2	4	no	—
20	C₄²×C₄₇	D₄	1	2	yes	—
21	C₄²×C₄₇	Q₈	1	2	yes	—
22	C₄×Dic₄₇	D₄	1	4	yes	—
23	C₄×Dic₄₇	Q₈	1	4	yes	—
24	C₂×C₄₇⋊C₈	—	2	4	no	—
25	C₂×C₄₇⋊C₈	—	2	2	no	—
26	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₇	—	2	2	no	—
28	C₂×C₄×C₄₇	—	2	2	no	—
29	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
31	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
35	C₂×Dic₄₇	—	2	4	no	—
36	C₂×Dic₄₇	—	2	4	no	—
37	C₂×Dic₄₇	C₄⋊C₄	1	8	yes	—
38	C₈×C₄₇	—	4	2	no	—
39	C₄₇⋊C₈	—	4	2	no	—
40	C₂²×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
41	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₂²×C₄₇	#131	1	2	yes	—
43	C₂²×C₄₇	#131	1	2	yes	—
44	C₄×C₄₇	—	2	2	no	—
45	C₄×C₄₇	—	2	2	no	—
46	C₄×C₄₇	#127	1	1	yes	characteristic
47	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
48	C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
49	Dic₄₇	—	2	8	no	—
50	#1843	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	#384	1	1	yes	characteristic
52	C₂×C₄₇	#424	1	4	yes	—
53	C₂×C₄₇	#424	1	1	yes	characteristic
54	C₂×C₄₇	#424	1	1	yes	characteristic
55	C₂×C₄⋊C₈	—	47	4	no	—
56	C₂×C₄⋊C₈	—	47	1	no	—
57	C₂×C₄⋊C₈	D₄₇	1	1	yes	characteristic
58	#376	—	47	1	no	—
59	C₄₇	#1843	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	47	2	no	—
61	C₂²×C₈	C₂×D₄₇	1	2	yes	—
62	C₂×C₄²	—	47	2	no	—
63	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
64	C₄⋊C₈	—	2	2	no	—
65	C₄⋊C₈	—	94	8	no	—
66	C₄⋊C₈	—	94	2	no	—
67	#95	—	47	2	no	—
68	#95	—	47	2	no	—
69	C₂²×C₄	—	47	4	no	—
70	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
71	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
73	C₂×C₈	—	2	4	no	—
74	C₂×C₈	—	2	2	no	—
75	C₂×C₈	—	94	4	no	—
76	C₂×C₈	—	94	2	no	—
77	C₄²	—	47	4	no	—
78	C₄²	—	47	4	no	—
79	C₄²	Dic₉₄	1	2	yes	—
80	C₄²	C₂²⋊D₄₇	1	2	yes	—
81	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	47	8	no	—
85	C₂×C₄	—	94	4	no	—
86	C₂×C₄	—	94	4	no	—
87	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
88	C₂×C₄	Dic₄₇⋊C₄	1	2	yes	—
89	C₂×C₄	C₂×Dic₉₄	1	1	yes	characteristic
90	C₂×C₄	D₄×D₄₇	1	2	yes	—
91	C₂×C₄	Q₈×D₄₇	1	2	yes	—
92	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
93	C₈	—	4	2	no	—
94	C₈	—	188	2	no	—
95	C₂²	C₄⋊C₄×D₄₇	1	2	yes	—
96	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
97	C₂²	#13094030	1	2	yes	—
98	C₂²	#13094032	1	2	yes	—
99	C₄	—	2	2	no	—
100	C₄	—	2	2	no	—
101	C₄	—	94	8	no	—
102	C₄	#13094020	1	1	yes	characteristic
103	C₄	#13094022	1	1	yes	characteristic
104	C₄	#13094023	1	2	yes	—
105	C₂	#15688992	1	1	yes	characteristic
106	C₂	#15689148	1	4	yes	—
107	C₂	#15689149	1	1	yes	characteristic
108	C₂	#15689151	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₄₇⋊C₈)

C₂

yes

maximal, characteristic

C₂×Dic₄₇⋊C₈

C₂

yes

maximal

#15688969

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄⋊(C₄₇⋊C₈)

—

Dic₄₇⋊C₈

—

C₄₇⋊#95

C₄

yes

—

C₄₇⋊#95

C₄

yes

—

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄⋊C₈×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄×Dic₄₇

D₄

yes

—

C₄×Dic₄₇

Q₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₄⋊C₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₄⋊C₄

yes

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

—

C₂²×C₄₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₄₇

#131

yes

—

C₂²×C₄₇

#131

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#127

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₄₇

yes

characteristic

#376

—

C₄₇

#1843

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₄×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

Dic₉₄

yes

—

C₄²

C₂²⋊D₄₇

yes

—

C₂³

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

Dic₄₇⋊C₄

yes

—

C₂×C₄

Dic₄₇⋊C₄

yes

—

C₂×C₄

C₂×Dic₉₄

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

—

C₂×C₄

Q₈×D₄₇

yes

—

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

C₈

—

C₈

—

188

—

C₂²

C₄⋊C₄×D₄₇

yes

—

C₂²

C₂×Dic₄₇⋊C₄

yes

characteristic

C₂²

#13094030

yes

—

C₂²

#13094032

yes

—

C₄

—

100

C₄

—

101

C₄

—

102

C₄

#13094020

yes

characteristic

103

C₄

#13094022

yes

characteristic

104

C₄

#13094023

yes

—

105

C₂

#15688992

yes

characteristic

106

C₂

#15689148

yes

—

107

C₂

#15689149

yes

characteristic

108

C₂

#15689151

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₇
commutator, socle	C₂³×C₄₇	C₂²×C₄
Fitting	C₂×C₄⋊C₈×C₄₇	C₂
hypercenter	C₂×C₄⋊C₈	D₄₇
hypocenter	C₄₇	#1843
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₇

commutator, socle

C₂³×C₄₇

C₂²×C₄

Fitting

C₂×C₄⋊C₈×C₄₇

C₂

hypercenter

C₂×C₄⋊C₈

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
59. C₄₇	#1843	semidirect

H ≅ G/N

type

59. C₄₇

#1843

semidirect

Subgroups — #20243541

Conjugacy classes of subgroups

Complements