Group #20244895 — subgroups

Subgroups — #20244895

Order 6016.

176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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	#15689165	C₂	1	2	yes	maximal
2	C₂×#13093958	C₂	1	1	yes	maximal, characteristic
3	#15689149	C₂	1	1	yes	maximal, characteristic
4	#15688891	C₂	1	2	yes	maximal
5	C₄₇×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	1	yes	characteristic
7	#13093983	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	#13093958	—	2	2	no	—
10	#13093958	—	2	2	no	—
11	#13093956	—	2	2	no	—
12	Dic₄₇⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₇	—	2	2	no	—
17	M₁₆×C₄₇	—	2	2	no	—
18	M₁₆×C₄₇	Q₈	1	4	yes	—
19	C₂×C₈×C₄₇	—	2	2	no	—
20	C₂×C₈×C₄₇	—	2	2	no	—
21	C₂×C₈×C₄₇	D₄	1	2	yes	—
22	C₂²⋊Dic₄₇	—	2	1	no	—
23	C₄⋊Dic₄₇	—	2	2	no	—
24	C₄⋊Dic₄₇	—	2	2	no	—
25	C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
26	C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
27	C₄×Dic₄₇	—	2	1	no	—
28	#10625329	—	2	2	no	—
29	C₂×C₄₇⋊C₈	—	2	1	no	—
30	C₂³×C₄₇	#41	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₄₇	#41	1	2	yes	—
35	C₂×Dic₄₇	—	2	1	no	—
36	C₂×Dic₄₇	—	2	1	no	—
37	C₂×Dic₄₇	—	4	2	no	—
38	C₂×Dic₄₇	—	8	2	no	—
39	C₈×C₄₇	—	2	4	no	—
40	C₈×C₄₇	—	2	2	no	—
41	C₄₇⋊C₈	—	4	1	no	—
42	C₂²×C₄₇	—	2	1	no	—
43	C₂²×C₄₇	—	2	1	no	—
44	C₂²×C₄₇	#121	1	1	yes	characteristic
45	C₂²×C₄₇	#125	1	2	yes	—
46	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₄₇	#123	1	1	yes	characteristic
48	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
49	Dic₄₇	—	4	1	no	—
50	Dic₄₇	—	4	1	no	—
51	Dic₄₇	—	8	2	no	—
52	#2089	—	47	1	no	maximal, Sylow
53	C₂×C₄₇	—	2	2	no	—
54	C₂×C₄₇	#398	1	1	yes	characteristic
55	C₂×C₄₇	#472	1	1	yes	characteristic
56	C₂×C₄₇	#473	1	1	yes	characteristic
57	#428	—	47	2	no	—
58	C₂×#107	—	47	1	no	—
59	#424	—	47	1	no	—
60	#343	—	47	2	no	—
61	#341	D₄₇	1	1	yes	characteristic
62	C₄₇	#2089	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₁₆	—	47	1	no	—
64	C₂×M₁₆	C₂×D₄₇	1	2	yes	—
65	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
66	#117	—	47	1	no	—
67	C₂×C₄⋊C₄	—	47	2	no	—
68	#107	—	94	2	no	—
69	#107	—	94	2	no	—
70	#106	—	94	2	no	—
71	C₄⋊C₈	—	94	2	no	—
72	C₂²×C₄	—	94	2	no	—
73	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	94	2	no	—
76	M₁₆	Dic₉₄	1	4	yes	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	94	1	no	—
80	C₂×C₈	D₁₈₈	1	2	yes	—
81	C₄⋊C₄	—	47	1	no	—
82	C₄⋊C₄	—	47	1	no	—
83	C₄⋊C₄	—	94	2	no	—
84	C₄⋊C₄	—	94	2	no	—
85	C₂²⋊C₄	—	94	1	no	—
86	C₄²	—	94	1	no	—
87	C₂³	#10625354	1	1	yes	characteristic
88	C₂×C₄	—	94	1	no	—
89	C₂×C₄	—	94	1	no	—
90	C₂×C₄	—	376	2	no	—
91	C₂×C₄	—	188	2	no	—
92	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
93	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
94	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
95	C₂×C₄	#10625352	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	2	no	—
98	C₈	—	188	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#13093999	1	1	yes	characteristic
102	C₂²	#13094015	1	2	yes	—
103	C₄	—	376	2	no	—
104	C₄	—	188	1	no	—
105	C₄	—	188	1	no	—
106	C₄	#13094001	1	2	yes	—
107	C₄	#13094008	1	1	yes	characteristic
108	C₄	#13094024	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#15689055	1	1	yes	characteristic
111	C₂	#15689394	1	1	yes	characteristic
112	C₂	#15689399	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689165

C₂

yes

maximal

C₂×#13093958

C₂

yes

maximal, characteristic

#15689149

C₂

yes

maximal, characteristic

#15688891

C₂

yes

maximal

C₄₇×#341

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

characteristic

#13093983

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₇

C₂²

yes

—

#13093958

—

#13093958

—

#13093956

—

Dic₄₇⋊C₈

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

Q₈

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

D₄

yes

characteristic

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₂²×C₄₇

#125

yes

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

C₄×C₄₇

#123

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

#2089

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

—

—

—

D₄₇

yes

characteristic

C₄₇

#2089

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Dic₉₄

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#10625354

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

376

—

C₂×C₄

—

188

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625352

yes

—

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

100

C₂²

—

101

C₂²

#13093999

yes

characteristic

102

C₂²

#13094015

yes

—

103

C₄

—

376

—

104

C₄

—

188

—

105

C₄

—

188

—

106

C₄

#13094001

yes

—

107

C₄

#13094008

yes

characteristic

108

C₄

#13094024

yes

characteristic

109

C₂

—

110

C₂

#15689055

yes

characteristic

111

C₂

#15689394

yes

characteristic

112

C₂

#15689399

yes

characteristic

	subgroup	G/H
center	C₂²	#13093999
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₄₇×#341	C₂
socle	C₂²×C₄₇	#121
hypercenter	#341	D₄₇
hypocenter	C₄₇	#2089
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#13093999

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₄₇×#341

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
62. C₄₇	#2089	semidirect

H ≅ G/N

type

62. C₄₇

#2089

semidirect

Subgroups — #20244895

Conjugacy classes of subgroups

Complements