Group #20244899 — subgroups

Subgroups — #20244899

Order 6016.

176 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 67 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	#15689163	C₂	1	2	yes	maximal
2	#15689149	C₂	1	1	yes	maximal, characteristic
3	#15688892	C₂	1	2	yes	maximal
4	#15688888	C₂	1	1	yes	maximal, characteristic
5	C₂×#106×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	C₂²	1	1	yes	characteristic
7	C₂×#10625329	C₂²	1	2	yes	—
8	#13093983	C₂²	1	1	yes	characteristic
9	#13093957	—	2	2	no	—
10	#13093955	—	2	2	no	—
11	Dic₄₇⋊C₈	—	2	2	no	—
12	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	#106×C₄₇	—	2	2	no	—
15	C₂²×C₄×C₄₇	—	2	2	no	—
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	D₄	1	2	yes	—
19	C₄⋊C₄×C₄₇	—	2	2	no	—
20	C₄⋊C₄×C₄₇	—	2	2	no	—
21	C₂²⋊Dic₄₇	—	2	1	no	—
22	C₄⋊Dic₄₇	D₄	1	2	yes	—
23	C₄×Dic₄₇	—	2	1	no	—
24	#10625329	—	2	2	no	—
25	#10625329	—	2	2	no	—
26	#10625329	Q₈	1	4	yes	—
27	C₂×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄₇⋊C₈	—	2	1	no	—
29	C₂³×C₄₇	#41	1	1	yes	characteristic
30	C₂×C₄×C₄₇	—	4	2	no	—
31	C₂×C₄×C₄₇	—	8	2	no	—
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₄₇	#41	1	2	yes	—
36	C₂×Dic₄₇	—	2	2	no	—
37	C₈×C₄₇	—	2	2	no	—
38	C₄₇⋊C₈	—	2	4	no	—
39	C₄₇⋊C₈	—	4	1	no	—
40	C₂²×C₄₇	—	2	2	no	—
41	C₂²×C₄₇	#121	1	1	yes	characteristic
42	C₂²×C₄₇	#125	1	2	yes	—
43	C₄×C₄₇	—	8	2	no	—
44	C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
45	C₄×C₄₇	#123	1	1	yes	characteristic
46	C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
47	Dic₄₇	—	4	2	no	—
48	#2090	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	—	2	2	no	—
50	C₂×C₄₇	#398	1	1	yes	characteristic
51	C₂×C₄₇	#471	1	2	yes	—
52	#428	—	47	2	no	—
53	C₂×#106	D₄₇	1	1	yes	characteristic
54	#424	—	47	1	no	—
55	#343	—	47	2	no	—
56	#341	—	47	1	no	—
57	C₄₇	#2090	1	1	yes	characteristic, complemented, Sylow
58	C₂×M₁₆	—	47	2	no	—
59	C₂×M₁₆	—	47	1	no	—
60	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
61	#117	—	47	1	no	—
62	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
63	#107	—	94	2	no	—
64	#106	—	2	2	no	—
65	#106	—	94	2	no	—
66	C₄⋊C₈	—	94	2	no	—
67	C₂²×C₄	—	2	2	no	—
68	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
69	M₁₆	—	47	4	no	—
70	M₁₆	—	94	2	no	—
71	M₁₆	—	94	2	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	94	2	no	—
74	C₂×C₈	—	94	1	no	—
75	C₂×C₈	C₂²⋊D₄₇	1	2	yes	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄⋊C₄	—	47	2	no	—
79	C₂²⋊C₄	—	94	1	no	—
80	C₄²	—	94	1	no	—
81	C₂³	#10625352	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	8	2	no	—
84	C₂×C₄	—	94	2	no	—
85	C₂×C₄	#10625350	1	2	yes	—
86	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₄₇	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	94	4	no	—
91	C₈	—	188	1	no	—
92	C₂²	—	2	2	no	—
93	C₂²	#13093995	1	1	yes	characteristic
94	C₂²	#13094014	1	2	yes	—
95	C₄	—	8	2	no	—
96	C₄	—	188	2	no	—
97	C₄	#13094002	1	2	yes	—
98	C₄	#13094007	1	1	yes	characteristic
99	C₄	#13094022	1	1	yes	characteristic
100	C₂	—	2	2	no	—
101	C₂	#15689054	1	1	yes	characteristic
102	C₂	#15689383	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689163

C₂

yes

maximal

#15689149

C₂

yes

maximal, characteristic

#15688892

C₂

yes

maximal

#15688888

C₂

yes

maximal, characteristic

C₂×#106×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

C₂²

yes

characteristic

C₂×#10625329

C₂²

yes

—

#13093983

C₂²

yes

characteristic

#13093957

—

#13093955

—

Dic₄₇⋊C₈

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₇

C₂²

yes

—

#106×C₄₇

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

D₄

yes

—

C₄×Dic₄₇

—

#10625329

—

#10625329

—

#10625329

Q₈

yes

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

#41

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

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

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

#121

yes

characteristic

C₂²×C₄₇

#125

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂²⋊Q₈

yes

—

C₄×C₄₇

#123

yes

characteristic

C₄×C₄₇

C₄⋊Q₈

yes

characteristic

Dic₄₇

—

#2090

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

#398

yes

characteristic

C₂×C₄₇

#471

yes

—

#428

—

C₂×#106

D₄₇

yes

—

—

—

C₄₇

#2090

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

C₂×C₄⋊C₄

C₂×D₄₇

yes

—

#107

—

#106

—

#106

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#10625352

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#10625350

yes

—

C₂×C₄

D₄×D₄₇

yes

characteristic

C₂×C₄

Q₈×D₄₇

yes

—

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

C₂²

#13093995

yes

characteristic

C₂²

#13094014

yes

—

C₄

—

C₄

—

188

—

C₄

#13094002

yes

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#15689054

yes

characteristic

102

C₂

#15689383

yes

—

	subgroup	G/H
center	C₂²	#13093995
commutator	C₂²×C₄×C₄₇	C₂³
Frattini	C₂²×C₄	C₂²×D₄₇
Fitting	C₂×#106×C₄₇	C₂
socle	C₂²×C₄₇	#121
hypercenter	C₂×#106	D₄₇
hypocenter	C₄₇	#2090
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

subgroup

G/H

center

C₂²

#13093995

commutator

C₂²×C₄×C₄₇

C₂³

Frattini

C₂²×C₄

C₂²×D₄₇

Fitting

C₂×#106×C₄₇

C₂

C₂²×C₄₇

D₄₇

C₄₇

G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#106

N	H ≅ G/N	type
57. C₄₇	#2090	semidirect

H ≅ G/N

type

57. C₄₇

#2090

semidirect

Subgroups — #20244899

Conjugacy classes of subgroups

Complements