Group #20241323 — subgroups

Subgroups — #20241323

Order 6016.

128 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 33 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	#15689086	C₂	1	1	yes	maximal, characteristic
2	#15688905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄₇	C₄	1	1	yes	characteristic
5	C₂×#10625329	C₄	1	1	yes	characteristic
6	#13093964	—	2	1	no	—
7	(C₂×D₄₇)⋊C₈	—	2	1	no	—
8	(C₂×D₄₇)⋊C₈	—	2	1	no	—
9	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
10	M₃₂×C₄₇	—	2	1	no	—
11	C₂³×D₄₇	C₈	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₄₇	C₈	1	1	yes	characteristic
14	C₂×C₄×D₄₇	—	2	1	no	—
15	C₂×C₄×D₄₇	—	2	1	no	—
16	C₂×C₄×D₄₇	—	4	1	no	—
17	C₂×C₄×D₄₇	—	4	1	no	—
18	M₁₆×C₄₇	—	4	1	no	—
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	#10625329	—	4	1	no	—
22	C₂×C₄₇⋊C₈	—	2	1	no	—
23	C₁₆×C₄₇	—	4	1	no	—
24	C₄₇⋊C₁₆	—	4	1	no	—
25	C₂³×C₄₇	C₂×C₈	1	1	yes	characteristic
26	C₂²×D₄₇	—	2	1	no	—
27	C₂²×D₄₇	—	4	2	no	—
28	C₂²×D₄₇	—	4	1	no	—
29	C₂×C₄×C₄₇	—	2	1	no	—
30	C₂×C₄×C₄₇	—	2	1	no	—
31	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
33	C₂×Dic₄₇	—	2	1	no	—
34	C₂×Dic₄₇	—	4	1	no	—
35	C₄×D₄₇	—	4	2	no	—
36	C₄×D₄₇	—	4	1	no	—
37	C₄×D₄₇	—	4	1	no	—
38	C₈×C₄₇	—	2	1	no	—
39	C₈×C₄₇	—	2	1	no	—
40	C₄₇⋊C₈	—	4	1	no	—
41	C₂²×C₄₇	—	2	1	no	—
42	C₂²×C₄₇	—	4	1	no	—
43	C₂²×C₄₇	C₂²⋊C₈	1	1	yes	characteristic
44	C₂×D₄₇	—	2	2	no	—
45	C₂×D₄₇	—	4	1	no	—
46	C₂×D₄₇	—	4	2	no	—
47	C₂×D₄₇	—	4	1	no	—
48	C₂×D₄₇	—	4	2	no	—
49	C₄×C₄₇	—	2	1	no	—
50	C₄×C₄₇	#99	1	1	yes	characteristic
51	C₄×C₄₇	#100	1	1	yes	characteristic
52	Dic₄₇	—	4	1	no	—
53	#1320	—	47	1	no	maximal, Sylow
54	C₂×C₄₇	—	2	1	no	—
55	C₂×C₄₇	—	4	1	no	—
56	C₂×C₄₇	#323	1	1	yes	characteristic
57	D₄₇	—	4	2	no	—
58	#407	—	47	1	no	—
59	#349	—	47	1	no	—
60	#349	D₄₇	1	1	yes	characteristic, complemented
61	C₄₇	#1320	1	1	yes	characteristic, complemented, Sylow
62	C₂³×C₄	—	47	1	no	—
63	C₂×M₁₆	—	47	1	no	—
64	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
65	M₃₂	—	2	1	no	—
66	M₃₂	—	94	1	no	—
67	C₂²⋊C₈	—	94	1	no	—
68	C₂²⋊C₈	—	94	1	no	—
69	C₂⁴	—	47	1	no	—
70	C₂²×C₄	—	47	1	no	—
71	C₂²×C₄	—	94	1	no	—
72	C₂²×C₄	—	94	1	no	—
73	C₂²×C₄	—	188	1	no	—
74	C₂²×C₄	—	188	1	no	—
75	C₂²×C₄	C₄×D₄₇	1	1	yes	characteristic
76	M₁₆	—	4	1	no	—
77	M₁₆	—	188	1	no	—
78	C₂×C₈	—	94	1	no	—
79	C₂×C₈	D₁₈₈	1	1	yes	characteristic
80	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
81	C₁₆	—	4	1	no	—
82	C₁₆	—	188	1	no	—
83	C₂³	—	94	1	no	—
84	C₂³	—	188	1	no	—
85	C₂³	—	188	2	no	—
86	C₂³	C₈×D₄₇	1	1	yes	characteristic
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	94	1	no	—
90	C₂×C₄	—	188	2	no	—
91	C₂×C₄	—	188	1	no	—
92	C₂×C₄	—	188	1	no	—
93	C₂×C₄	—	188	1	no	—
94	C₂×C₄	#10625324	1	1	yes	characteristic
95	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	2	1	no	—
98	C₈	—	188	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	4	1	no	—
101	C₂²	—	94	2	no	—
102	C₂²	—	188	1	no	—
103	C₂²	—	188	2	no	—
104	C₂²	—	188	2	no	—
105	C₂²	—	188	1	no	—
106	C₂²	(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	188	1	no	—
109	C₄	#13093938	1	1	yes	characteristic
110	C₄	#13093940	1	1	yes	characteristic
111	C₂	—	2	1	no	—
112	C₂	—	4	1	no	—
113	C₂	—	188	2	no	—
114	C₂	#15688846	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689086

C₂

yes

maximal, characteristic

#15688905

C₂

yes

maximal, characteristic, complemented

C₄₇×#349

C₂

yes

maximal, characteristic, complemented

C₂²×C₄×D₄₇

C₄

yes

characteristic

C₂×#10625329

C₄

yes

characteristic

#13093964

—

(C₂×D₄₇)⋊C₈

—

(C₂×D₄₇)⋊C₈

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

M₃₂×C₄₇

—

C₂³×D₄₇

C₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×Dic₄₇

C₈

yes

characteristic

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

C₂×C₄×D₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

#10625329

—

C₂×C₄₇⋊C₈

—

C₁₆×C₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

C₂×C₈

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₄×D₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²⋊C₈

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1320

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#323

yes

characteristic

D₄₇

—

#407

—

#349

—

#349

D₄₇

yes

characteristic, complemented

C₄₇

#1320

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

M₃₂

—

M₃₂

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

188

—

C₂²×C₄

—

188

—

C₂²×C₄

C₄×D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₁₆

—

C₁₆

—

188

—

C₂³

—

C₂³

—

188

—

C₂³

—

188

—

C₂³

C₈×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

#10625324

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

—

188

—

C₂²

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

188

—

103

C₂²

—

188

—

104

C₂²

—

188

—

105

C₂²

—

188

—

106

C₂²

(C₂×D₄₇)⋊C₈

yes

characteristic

107

C₄

—

108

C₄

—

188

—

109

C₄

#13093938

yes

characteristic

110

C₄

#13093940

yes

characteristic

111

C₂

—

112

C₂

—

113

C₂

—

188

—

114

C₂

#15688846

yes

characteristic

	subgroup	G/H
center	C₄	#13093938
commutator	C₂³×C₄₇	C₂×C₈
Frattini	C₂×M₁₆	C₂×D₄₇
Fitting	C₄₇×#349	C₂
socle	C₂×C₄₇	#323
hypercenter	#349	D₄₇
hypocenter	C₄₇	#1320
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₄

#13093938

commutator

C₂³×C₄₇

C₂×C₈

Frattini

C₂×M₁₆

C₂×D₄₇

Fitting

C₄₇×#349

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
2. #15688905	C₂	semidirect
3. C₄₇×#349	C₂	semidirect
60. #349	D₄₇	semidirect
61. C₄₇	#1320	semidirect

H ≅ G/N

type

2. #15688905

C₂

semidirect

3. C₄₇×#349

C₂

semidirect

60. #349

D₄₇

semidirect

61. C₄₇

#1320

semidirect

Subgroups — #20241323

Conjugacy classes of subgroups

Complements