Group #20241378 — subgroups

Subgroups — #20241378

Order 6016.

110 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 31 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	#15689376	C₂	1	1	yes	maximal, characteristic
2	#15688905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#338	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₇₆	C₄	1	1	yes	characteristic
5	#13093998	—	2	1	no	—
6	#13093964	—	2	1	no	—
7	#13093956	C₄	1	1	yes	characteristic
8	#13093946	—	2	1	no	—
9	C₂×M₁₆×C₄₇	—	2	1	no	—
10	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₇	—	4	1	no	—
13	C₂×D₁₈₈	—	2	1	no	—
14	M₁₆×C₄₇	—	4	1	no	—
15	M₁₆×C₄₇	—	4	1	no	—
16	M₁₆×C₄₇	—	4	1	no	—
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
20	(C₂×D₄₇)⋊C₄	—	4	1	no	—
21	C₄⋊Dic₄₇	—	2	1	no	—
22	D₃₇₆	—	4	1	no	—
23	C₄₇⋊C₁₆	—	4	1	no	—
24	C₂³×C₄₇	SD₁₆	1	1	yes	characteristic
25	C₂²×D₄₇	—	4	1	no	—
26	C₂×C₄×C₄₇	—	2	1	no	—
27	C₂×C₄×C₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
30	C₂²⋊D₄₇	—	8	2	no	—
31	C₂×Dic₄₇	—	4	1	no	—
32	D₁₈₈	—	4	1	no	—
33	D₁₈₈	—	4	1	no	—
34	C₈×C₄₇	—	2	1	no	—
35	C₈×C₄₇	—	2	1	no	—
36	C₈×C₄₇	—	4	2	no	—
37	C₂²×C₄₇	—	2	1	no	—
38	C₂²×C₄₇	—	4	1	no	—
39	C₂²×C₄₇	#102	1	1	yes	characteristic
40	C₂×D₄₇	—	8	1	no	—
41	C₂×D₄₇	—	8	1	no	—
42	C₂×D₄₇	—	8	1	no	—
43	C₄×C₄₇	—	2	1	no	—
44	C₄×C₄₇	#99	1	1	yes	characteristic
45	C₄×C₄₇	#104	1	1	yes	characteristic
46	Dic₄₇	—	8	1	no	—
47	#1341	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	—	2	1	no	—
49	C₂×C₄₇	—	4	1	no	—
50	C₂×C₄₇	#327	1	1	yes	characteristic
51	D₄₇	—	16	1	no	—
52	#469	—	47	1	no	—
53	#349	—	47	1	no	—
54	#338	D₄₇	1	1	yes	characteristic, complemented
55	C₄₇	#1341	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	47	1	no	—
57	C₂×M₁₆	—	2	1	no	—
58	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
59	#121	—	94	1	no	—
60	M₃₂	—	94	1	no	—
61	#106	—	47	1	no	—
62	#102	—	94	1	no	—
63	C₂×D₄	—	94	1	no	—
64	C₂×D₄	—	188	1	no	—
65	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
66	D₈	—	188	1	no	—
67	M₁₆	—	4	1	no	—
68	M₁₆	—	4	1	no	—
69	M₁₆	—	4	1	no	—
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
72	C₂×C₈	D₁₈₈	1	1	yes	characteristic
73	C₄⋊C₄	—	94	1	no	—
74	C₂²⋊C₄	—	188	1	no	—
75	C₁₆	—	188	1	no	—
76	C₂³	—	188	1	no	—
77	C₂³	#10625336	1	1	yes	characteristic
78	D₄	—	376	2	no	—
79	D₄	—	188	1	no	—
80	D₄	—	188	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	188	1	no	—
84	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
85	C₂×C₄	#10625334	1	1	yes	characteristic
86	C₈	—	2	1	no	—
87	C₈	—	2	1	no	—
88	C₈	—	4	2	no	—
89	C₂²	—	2	1	no	—
90	C₂²	—	4	1	no	—
91	C₂²	—	376	1	no	—
92	C₂²	—	376	1	no	—
93	C₂²	—	376	1	no	—
94	C₂²	#13093944	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	376	1	no	—
97	C₄	#13093938	1	1	yes	characteristic
98	C₄	#13093952	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	4	1	no	—
101	C₂	—	752	1	no	—
102	C₂	#15688856	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689376

C₂

yes

maximal, characteristic

#15688905

C₂

yes

maximal, characteristic, complemented

C₄₇×#338

C₂

yes

maximal, characteristic, complemented

C₂×D₃₇₆

C₄

yes

—

—

C₄

yes

characteristic

#13093946

—

C₂×M₁₆×C₄₇

—

C₂×M₁₆×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂×C₂²⋊D₄₇

—

C₂×D₁₈₈

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

—

D₃₇₆

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

SD₁₆

yes

characteristic

C₂²×D₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂²⋊D₄₇

—

C₂×Dic₄₇

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#102

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1341

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#327

yes

characteristic

D₄₇

—

#469

—

#349

—

#338

D₄₇

yes

characteristic, complemented

C₄₇

#1341

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₇

yes

characteristic

#121

—

M₃₂

—

#106

—

#102

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

D₈

—

188

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₁₆

—

188

—

C₂³

—

188

—

C₂³

#10625336

yes

characteristic

D₄

—

376

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

characteristic

C₂×C₄

#10625334

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

—

376

—

C₂²

#13093944

yes

characteristic

C₄

—

C₄

—

376

—

C₄

yes

C₄

yes

C₂

—

100

C₂

—

101

C₂

—

752

—

102

C₂

#15688856

yes

characteristic

	subgroup	G/H
center	C₂	#15688856
commutator	C₂×C₈×C₄₇	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₄₇
Fitting	C₄₇×#338	C₂
socle	C₂×C₄₇	#327
hypercenter	#338	D₄₇
hypocenter	C₄₇	#1341
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #338

subgroup

G/H

center

C₂

#15688856

commutator

C₂×C₈×C₄₇

C₂×C₄

Frattini

C₂×M₁₆

C₂×D₄₇

Fitting

C₄₇×#338

C₂

C₂×C₄₇

D₄₇

C₄₇

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #338

N	H ≅ G/N	type
2. #15688905	C₂	semidirect
3. C₄₇×#338	C₂	semidirect
54. #338	D₄₇	semidirect
55. C₄₇	#1341	semidirect

H ≅ G/N

type

2. #15688905

C₂

semidirect

3. C₄₇×#338

C₂

semidirect

54. #338

D₄₇

semidirect

55. C₄₇

#1341

semidirect

Subgroups — #20241378

Conjugacy classes of subgroups

Complements