Group #20241432 — subgroups

Subgroups — #20241432

Order 6016.

102 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 39 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	#15689507	C₂	1	1	yes	maximal, characteristic
2	#15688874	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Dic₁₈₈	C₄	1	1	yes	characteristic
5	C₂×#10625325	—	2	1	no	—
6	C₂×D₃₇₆	C₄	1	1	yes	characteristic
7	#13094012	—	2	1	no	—
8	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
9	C₂×C₁₆×C₄₇	—	2	1	no	—
10	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×D₁₈₈	—	2	1	no	—
12	C₂×Dic₉₄	—	2	1	no	—
13	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
15	C₄²×C₄₇	D₄	1	1	yes	characteristic
16	(C₂×D₄₇)⋊C₄	—	4	1	no	—
17	(C₂×D₄₇)⋊C₄	—	4	1	no	—
18	C₂×C₄₇⋊C₈	—	4	1	no	—
19	Dic₁₈₈	—	4	1	no	—
20	D₃₇₆	—	4	1	no	—
21	#10625325	—	4	1	no	—
22	#10625325	—	4	1	no	—
23	C₁₆×C₄₇	—	4	1	no	—
24	C₂²×D₄₇	—	4	1	no	—
25	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
27	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
28	C₂×Dic₄₇	—	4	1	no	—
29	D₁₈₈	—	4	1	no	—
30	D₁₈₈	—	4	1	no	—
31	Dic₉₄	—	4	1	no	—
32	Dic₉₄	—	4	1	no	—
33	C₈×C₄₇	—	2	1	no	—
34	C₈×C₄₇	D₈	1	1	yes	characteristic
35	C₈×C₄₇	SD₁₆	1	1	yes	characteristic
36	C₄₇⋊C₈	—	8	1	no	—
37	C₂²×C₄₇	#102	1	1	yes	characteristic
38	C₂×D₄₇	—	8	1	no	—
39	C₂×D₄₇	—	8	1	no	—
40	C₂×D₄₇	—	8	1	no	—
41	C₄×C₄₇	—	2	1	no	—
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	#100	1	1	yes	characteristic
44	C₄×C₄₇	#102	1	1	yes	characteristic
45	Dic₄₇	—	8	1	no	—
46	#1360	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	#331	1	1	yes	characteristic
48	C₂×C₄₇	#359	1	1	yes	characteristic
49	C₂×C₄₇	#360	1	1	yes	characteristic
50	D₄₇	—	16	1	no	—
51	#495	—	47	1	no	—
52	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic, complemented
53	#334	—	47	1	no	—
54	C₄₇	#1360	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₁₆	—	47	1	no	—
56	C₂×SD₁₆	—	94	1	no	—
57	C₂×D₈	—	47	1	no	—
58	#124	—	94	1	no	—
59	C₂×C₁₆	—	2	1	no	—
60	C₄⋊C₈	—	94	1	no	—
61	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
62	C₂×Q₈	—	94	1	no	—
63	C₂×D₄	—	94	1	no	—
64	Q₁₆	—	188	1	no	—
65	SD₁₆	—	188	1	no	—
66	SD₁₆	—	188	1	no	—
67	D₈	—	188	1	no	—
68	C₂×C₈	—	188	1	no	—
69	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
71	C₂²⋊C₄	—	188	1	no	—
72	C₂²⋊C₄	—	188	1	no	—
73	C₄²	D₁₈₈	1	1	yes	characteristic
74	C₁₆	—	4	1	no	—
75	C₂³	—	188	1	no	—
76	Q₈	—	188	1	no	—
77	Q₈	—	188	1	no	—
78	D₄	—	188	1	no	—
79	D₄	—	188	1	no	—
80	C₂×C₄	—	188	1	no	—
81	C₂×C₄	#10625325	1	1	yes	characteristic
82	C₂×C₄	D₃₇₆	1	1	yes	characteristic
83	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	376	1	no	—
86	C₈	#10625334	1	1	yes	characteristic
87	C₈	#10625336	1	1	yes	characteristic
88	C₂²	—	376	1	no	—
89	C₂²	—	376	1	no	—
90	C₂²	—	376	1	no	—
91	C₂²	#13093946	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	2	1	no	—
94	C₄	—	376	1	no	—
95	C₄	#13093940	1	1	yes	characteristic
96	C₄	#13093944	1	1	yes	characteristic
97	C₂	—	752	1	no	—
98	C₂	#15688866	1	1	yes	characteristic
99	C₂	#15688931	1	1	yes	characteristic
100	C₂	#15688934	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689507

C₂

yes

maximal, characteristic

#15688874

C₂

yes

maximal, characteristic, complemented

C₄₇×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₈₈

C₄

yes

characteristic

C₂×#10625325

—

C₂×D₃₇₆

C₄

yes

characteristic

#13094012

—

C₄⋊(C₄₇⋊C₈)

—

C₂×C₁₆×C₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×D₁₈₈

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

(C₂×D₄₇)⋊C₄

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

D₃₇₆

—

#10625325

—

#10625325

—

C₁₆×C₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

SD₁₆

yes

characteristic

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

D₈

yes

characteristic

C₈×C₄₇

SD₁₆

yes

characteristic

C₄₇⋊C₈

—

C₂²×C₄₇

#102

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

D₄₇

—

#495

—

C₄⋊C₁₆

D₄₇

yes

characteristic, complemented

#334

—

C₄₇

#1360

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#124

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

188

—

SD₁₆

—

188

—

SD₁₆

—

188

—

D₈

—

188

—

C₂×C₈

—

188

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₂²⋊C₄

—

188

—

C₂²⋊C₄

—

188

—

C₄²

D₁₈₈

yes

characteristic

C₁₆

—

C₂³

—

188

—

Q₈

—

188

—

Q₈

—

188

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

#10625325

yes

characteristic

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₈

—

C₈

—

376

—

C₈

yes

C₈

yes

C₂²

—

376

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

#13093946

yes

characteristic

C₄

—

C₄

—

C₄

—

376

—

C₄

yes

C₄

yes

C₂

—

752

—

C₂

yes

C₂

yes

100

C₂

#15688934

yes

characteristic

	subgroup	G/H
center	C₂²	#13093946
commutator	C₂×C₈×C₄₇	C₂×C₄
Frattini	C₄×C₈	C₂×D₄₇
Fitting	C₄₇×C₄⋊C₁₆	C₂
socle	C₂²×C₄₇	#102
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#1360
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

#13093946

commutator

C₂×C₈×C₄₇

C₂×C₄

Frattini

C₄×C₈

C₂×D₄₇

Fitting

C₄₇×C₄⋊C₁₆

C₂

socle

C₂²×C₄₇

#102

hypercenter

C₄⋊C₁₆

D₄₇

hypocenter

C₄₇

#1360

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
2. #15688874	C₂	semidirect
3. C₄₇×C₄⋊C₁₆	C₂	semidirect
52. C₄⋊C₁₆	D₄₇	semidirect
54. C₄₇	#1360	semidirect

H ≅ G/N

type

2. #15688874

C₂

semidirect

3. C₄₇×C₄⋊C₁₆

C₂

semidirect

52. C₄⋊C₁₆

D₄₇

semidirect

54. C₄₇

#1360

semidirect

Subgroups — #20241432

Conjugacy classes of subgroups

Complements