Group #20241502 — subgroups

Subgroups — #20241502

Order 6016.

128 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 69 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	C₂×#13093964	C₂	1	1	yes	maximal, characteristic
2	#15689161	C₂	1	1	yes	maximal, characteristic
3	C₂×#108×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093983	—	2	1	no	—
5	#13093964	—	2	1	no	—
6	#13093964	C₄	1	2	yes	complemented
7	C₂×C₄₇⋊C₁₆	—	2	1	no	—
8	#13093958	—	2	1	no	—
9	#13093956	C₄	1	2	yes	—
10	C₂×M₁₆×C₄₇	—	2	1	no	—
11	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
12	#108×C₄₇	—	2	1	no	—
13	#108×C₄₇	C₄	1	2	yes	complemented
14	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
15	M₁₆×C₄₇	—	2	2	no	—
16	M₁₆×C₄₇	—	4	1	no	—
17	C₂×C₈×C₄₇	—	4	1	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
22	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₇	Q₈	1	1	yes	characteristic
24	C₂²⋊Dic₄₇	—	4	1	no	—
25	C₄⋊Dic₄₇	—	2	2	no	—
26	C₄×Dic₄₇	—	4	1	no	—
27	C₄₇⋊C₁₆	—	2	2	no	—
28	C₂³×C₄₇	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
33	C₂×C₄×C₄₇	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₄₇	Q₁₆	1	1	yes	characteristic
35	C₂×Dic₄₇	—	4	2	no	—
36	C₈×C₄₇	—	4	2	no	—
37	C₈×C₄₇	C₄²	1	1	yes	characteristic
38	C₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
39	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
40	C₈×C₄₇	C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₄₇	—	4	1	no	—
42	C₂²×C₄₇	#102	1	1	yes	characteristic
43	C₂²×C₄₇	#103	1	1	yes	characteristic
44	C₂²×C₄₇	#106	1	1	yes	characteristic
45	C₄×C₄₇	#95	1	1	yes	characteristic
46	C₄×C₄₇	#102	1	1	yes	characteristic
47	C₄×C₄₇	#103	1	1	yes	characteristic
48	C₄×C₄₇	#107	1	1	yes	characteristic
49	Dic₄₇	—	8	2	no	—
50	#1389	—	47	1	no	maximal, Sylow
51	C₂×C₄₇	—	2	1	no	—
52	C₂×C₄₇	—	2	1	no	—
53	C₂×C₄₇	—	2	1	no	—
54	C₂×C₄₇	#340	1	1	yes	characteristic
55	C₂×M₃₂	—	47	1	no	—
56	C₂×#108	D₄₇	1	1	yes	characteristic
57	#427	—	47	1	no	—
58	C₄₇	#1389	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	2	1	no	—
60	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
61	#117	—	94	1	no	—
62	M₃₂	—	47	2	no	—
63	M₃₂	—	94	1	no	—
64	C₂×C₁₆	—	94	1	no	—
65	#108	—	2	1	no	—
66	#108	Dic₄₇	1	2	yes	complemented
67	#107	—	94	1	no	—
68	#106	—	47	2	no	—
69	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
70	M₁₆	—	2	2	no	—
71	M₁₆	—	4	1	no	—
72	C₂×C₈	—	4	1	no	—
73	C₂×C₈	Dic₉₄	1	1	yes	characteristic
74	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
75	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
76	C₂×C₈	D₁₈₈	1	1	yes	characteristic
77	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
78	C₂×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
79	C₄⋊C₄	—	94	2	no	—
80	C₂²⋊C₄	—	188	1	no	—
81	C₄²	—	188	1	no	—
82	C₁₆	—	94	2	no	—
83	C₂³	#10625336	1	1	yes	characteristic
84	C₂×C₄	—	188	2	no	—
85	C₂×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
86	C₂×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
87	C₂×C₄	#10625334	1	1	yes	characteristic
88	C₂×C₄	#10625335	1	1	yes	characteristic
89	C₂×C₄	#10625337	1	1	yes	characteristic
90	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	C₄×Dic₄₇	1	1	yes	characteristic
93	C₈	Dic₄₇⋊C₄	1	1	yes	characteristic
94	C₈	C₄⋊Dic₄₇	1	1	yes	characteristic
95	C₈	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
96	C₂²	—	4	1	no	—
97	C₂²	#13093944	1	1	yes	characteristic
98	C₂²	#13093948	1	1	yes	characteristic
99	C₂²	#13093955	1	1	yes	characteristic
100	C₄	—	376	2	no	—
101	C₄	C₄₇⋊#95	1	1	yes	characteristic
102	C₄	#13093945	1	1	yes	characteristic
103	C₄	#13093947	1	1	yes	characteristic
104	C₄	#13093957	1	1	yes	characteristic
105	C₂	—	2	1	no	—
106	C₂	—	2	1	no	—
107	C₂	—	2	1	no	—
108	C₂	#15688885	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093964

C₂

yes

maximal, characteristic

#15689161

C₂

yes

maximal, characteristic

C₂×#108×C₄₇

C₂

yes

maximal, characteristic

#13093983

—

#13093964

—

#13093964

C₄

yes

complemented

C₂×C₄₇⋊C₁₆

—

#13093958

—

#13093956

C₄

yes

—

C₂×M₁₆×C₄₇

—

C₂²×C₈×C₄₇

C₂²

yes

characteristic

#108×C₄₇

—

#108×C₄₇

C₄

yes

complemented

C₂²×C₄×C₄₇

D₄

yes

characteristic

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

Q₈

yes

characteristic

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄×Dic₄₇

—

C₄₇⋊C₁₆

—

C₂³×C₄₇

SD₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

SD₁₆

yes

characteristic

C₂×C₄×C₄₇

Q₁₆

yes

characteristic

C₂×Dic₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₄²

yes

characteristic

C₈×C₄₇

C₂²⋊C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₈×C₄₇

C₄⋊C₄

yes

characteristic

C₂²×C₄₇

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

Dic₄₇

—

#1389

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#340

yes

characteristic

C₂×M₃₂

—

C₂×#108

D₄₇

yes

characteristic

#427

—

C₄₇

#1389

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₇

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#108

—

#108

Dic₄₇

yes

complemented

#107

—

#106

—

C₂²×C₄

C₂²⋊D₄₇

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

Dic₉₄

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²⋊D₄₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

188

—

C₄²

—

188

—

C₁₆

—

C₂³

#10625336

yes

characteristic

C₂×C₄

—

188

—

C₂×C₄

Dic₄₇⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

C₈

—

C₈

C₄×Dic₄₇

yes

characteristic

C₈

Dic₄₇⋊C₄

yes

characteristic

C₈

C₄⋊Dic₄₇

yes

characteristic

C₈

(C₂×D₄₇)⋊C₄

yes

characteristic

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

100

C₄

—

376

—

101

C₄

C₄₇⋊#95

yes

characteristic

102

C₄

#13093945

yes

characteristic

103

C₄

#13093947

yes

characteristic

104

C₄

#13093957

yes

characteristic

105

C₂

—

106

C₂

—

107

C₂

—

108

C₂

#15688885

yes

characteristic

	subgroup	G/H
center	C₄	#13093945
commutator	C₈×C₄₇	C₄²
Frattini	C₂²×C₈	C₂×D₄₇
Fitting	C₂×#108×C₄₇	C₂
socle	C₂×C₄₇	#340
hypercenter	C₂×#108	D₄₇
hypocenter	C₄₇	#1389
LCS	G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

subgroup

G/H

center

C₄

#13093945

commutator

C₈×C₄₇

C₄²

Frattini

C₂²×C₈

C₂×D₄₇

Fitting

C₂×#108×C₄₇

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

N	H ≅ G/N	type
6. #13093964	C₄	semidirect
13. #108×C₄₇	C₄	semidirect
58. C₄₇	#1389	semidirect
66. #108	Dic₄₇	semidirect

H ≅ G/N

type

6. #13093964

C₄

semidirect

13. #108×C₄₇

C₄

semidirect

58. C₄₇

#1389

semidirect

66. #108

Dic₄₇

semidirect

Subgroups — #20241502

Conjugacy classes of subgroups

Complements