Group #20241541 — subgroups

Subgroups — #20241541

Order 6016.

106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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	#15689305	C₂	1	1	yes	maximal, characteristic
2	#15688872	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#356	C₂	1	1	yes	maximal, characteristic, complemented
4	#13094072	C₄	1	1	yes	characteristic
5	#13094055	—	2	1	no	—
6	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
7	#13093952	—	2	1	no	—
8	#13093943	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	#101×C₄₇	—	2	1	no	—
11	C₂×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
13	#10625354	—	4	1	no	—
14	Q₈×D₄₇	—	4	1	no	—
15	#10625350	—	2	1	no	—
16	#10625350	—	4	1	no	—
17	M₁₆×C₄₇	—	4	1	no	—
18	C₄⋊C₄×C₄₇	—	4	1	no	—
19	C₄²×C₄₇	D₄	1	1	yes	characteristic
20	#10625337	—	4	1	no	—
21	#10625336	—	4	1	no	—
22	#10625329	—	2	1	no	—
23	C₂×C₄₇⋊C₈	—	4	1	no	—
24	Q₈×C₄₇	—	4	1	no	—
25	Q₈×C₄₇	—	4	1	no	—
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	—	2	1	no	—
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²⋊D₄₇	—	4	1	no	—
31	D₁₈₈	—	2	1	no	—
32	D₁₈₈	—	4	1	no	—
33	C₄×D₄₇	—	4	1	no	—
34	C₄×D₄₇	—	4	2	no	—
35	Dic₉₄	—	2	1	no	—
36	Dic₉₄	—	4	1	no	—
37	C₈×C₄₇	—	8	1	no	—
38	C₄₇⋊C₈	—	4	1	no	—
39	C₄₇⋊C₈	—	8	1	no	—
40	C₂²×C₄₇	#99	1	1	yes	characteristic
41	C₂×D₄₇	—	4	1	no	—
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	—	2	1	no	—
44	C₄×C₄₇	—	2	1	no	—
45	C₄×C₄₇	—	4	1	no	—
46	C₄×C₄₇	—	4	1	no	—
47	Dic₄₇	—	4	1	no	—
48	#1405	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	—	2	1	no	—
50	C₂×C₄₇	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
51	D₄₇	—	8	1	no	—
52	#456	—	47	1	no	—
53	#356	D₄₇	1	1	yes	characteristic, complemented
54	#333	—	47	1	no	—
55	C₄₇	#1405	1	1	yes	characteristic, complemented, Sylow
56	2₋¹⁺⁴	—	47	1	no	—
57	#137	—	94	1	no	—
58	C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
59	C₄⋊C₈	—	94	1	no	—
60	#104	—	94	1	no	—
61	#101	—	2	1	no	—
62	#101	—	47	1	no	—
63	#41	—	94	1	no	—
64	#41	—	188	1	no	—
65	#41	—	188	1	no	—
66	C₂×Q₈	—	188	1	no	—
67	C₂×Q₈	C₄×D₄₇	1	1	yes	characteristic
68	C₂×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
69	Q₁₆	—	188	1	no	—
70	SD₁₆	—	188	1	no	—
71	M₁₆	—	4	1	no	—
72	M₁₆	—	94	1	no	—
73	C₂×C₈	—	188	1	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄²	D₁₈₈	1	1	yes	characteristic
76	Q₈	—	4	1	no	—
77	Q₈	—	4	1	no	—
78	Q₈	—	94	1	no	—
79	Q₈	—	188	1	no	—
80	D₄	—	94	1	no	—
81	D₄	—	188	1	no	—
82	D₄	—	188	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	188	1	no	—
87	C₂×C₄	—	188	2	no	—
88	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
89	C₈	—	8	1	no	—
90	C₈	—	376	1	no	—
91	C₈	—	188	1	no	—
92	C₂²	—	188	1	no	—
93	C₂²	#13093938	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	4	1	no	—
98	C₄	—	4	1	no	—
99	C₄	—	188	1	no	—
100	C₂	—	2	1	no	—
101	C₂	—	376	1	no	—
102	C₂	#15688909	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689305

C₂

yes

maximal, characteristic

#15688872

C₂

yes

maximal, characteristic, complemented

C₄₇×#356

C₂

yes

maximal, characteristic, complemented

#13094072

C₄

yes

characteristic

#13094055

—

C₄⋊(C₄₇⋊C₈)

—

#13093952

—

#13093943

C₄

yes

characteristic

C₄⋊Q₈×C₄₇

C₂²

yes

characteristic

#101×C₄₇

—

C₂×Q₈×C₄₇

C₂×C₄

yes

characteristic

C₂×Q₈×C₄₇

D₄

yes

characteristic

#10625354

—

Q₈×D₄₇

—

#10625350

—

#10625350

—

M₁₆×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

—

—

—

C₂×C₄₇⋊C₈

—

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂²⋊D₄₇

—

D₁₈₈

—

D₁₈₈

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

#99

yes

characteristic

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

#1405

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

AΣL(1,𝔽₁₆)

yes

characteristic

D₄₇

—

#456

—

#356

D₄₇

yes

characteristic, complemented

#333

—

C₄₇

#1405

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

#137

—

C₄⋊Q₈

C₂×D₄₇

yes

characteristic

C₄⋊C₈

—

—

—

—

—

—

188

—

#41

—

188

—

C₂×Q₈

—

188

—

C₂×Q₈

C₄×D₄₇

yes

characteristic

C₂×Q₈

C₂²⋊D₄₇

yes

characteristic

Q₁₆

—

188

—

SD₁₆

—

188

—

M₁₆

—

M₁₆

—

C₂×C₈

—

188

—

C₄⋊C₄

—

C₄²

D₁₈₈

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

188

—

D₄

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

—

C₈

—

376

—

C₈

—

188

—

C₂²

—

188

—

C₂²

#13093938

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

188

—

100

C₂

—

101

C₂

—

376

—

102

C₂

#15688909

yes

characteristic

	subgroup	G/H
center	C₂	#15688909
commutator	C₂×Q₈×C₄₇	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₄₇
Fitting	C₄₇×#356	C₂
socle	C₂×C₄₇	AΣL(1,𝔽₁₆)
hypercenter	#356	D₄₇
hypocenter	C₄₇	#1405
LCS	G ▷ C₂×Q₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

subgroup

G/H

center

C₂

#15688909

commutator

C₂×Q₈×C₄₇

C₂×C₄

Frattini

C₄⋊Q₈

C₂×D₄₇

Fitting

C₄₇×#356

C₂

socle

C₂×C₄₇

AΣL(1,𝔽₁₆)

D₄₇

C₄₇

G ▷ C₂×Q₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

N	H ≅ G/N	type
2. #15688872	C₂	semidirect
3. C₄₇×#356	C₂	semidirect
53. #356	D₄₇	semidirect
55. C₄₇	#1405	semidirect

H ≅ G/N

type

2. #15688872

C₂

semidirect

3. C₄₇×#356

C₂

semidirect

53. #356

D₄₇

semidirect

55. C₄₇

#1405

semidirect

Subgroups — #20241541

Conjugacy classes of subgroups

Complements