Group #20241981 — subgroups

Subgroups — #20241981

Order 6016.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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	#15689679	C₂	1	1	yes	maximal, characteristic
2	#15689075	C₂	1	2	yes	maximal
3	#15688865	C₂	1	1	yes	maximal, characteristic, complemented
4	#15688864	C₂	1	2	yes	maximal, complemented
5	C₄₇×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10625324	—	2	2	no	—
7	#13094023	C₄	1	2	yes	—
8	#13094016	C₂²	1	1	yes	characteristic
9	#13094002	—	2	2	no	—
10	#13093989	—	2	2	no	—
11	#13093982	C₄	1	2	yes	—
12	C₄²×D₄₇	C₂²	1	1	yes	characteristic
13	#13093935	C₂²	1	2	yes	—
14	C₈×Dic₄₇	—	2	2	no	—
15	#125×C₄₇	C₂²	1	1	yes	characteristic
16	#97×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₄₇	D₄	1	2	yes	—
19	C₂×Dic₉₄	—	2	2	no	—
20	C₂×C₈×C₄₇	—	2	2	no	—
21	C₄⋊C₄×C₄₇	—	2	2	no	—
22	C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
23	C₄²×C₄₇	C₂³	1	1	yes	characteristic
24	(C₂×D₄₇)⋊C₄	—	2	2	no	—
25	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
26	Dic₄₇⋊C₄	—	2	2	no	—
27	Dic₄₇⋊C₄	—	2	2	no	—
28	C₄×Dic₄₇	—	2	2	no	—
29	C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₄₇	D₄	1	2	yes	—
31	C₂×C₄₇⋊C₈	—	2	2	no	—
32	#10625324	—	2	8	no	—
33	C₂²×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₄₇	—	2	2	no	—
35	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
37	C₂×Dic₄₇	—	2	2	no	—
38	C₂×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₄₇	C₂²⋊C₄	1	2	yes	—
40	C₄×D₄₇	—	2	2	no	—
41	C₄×D₄₇	—	2	4	no	—
42	Dic₉₄	—	4	4	no	—
43	C₈×C₄₇	—	2	4	no	—
44	C₄₇⋊C₈	—	2	4	no	—
45	C₂²×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×D₄₇	—	2	1	no	—
47	C₂×D₄₇	—	2	2	no	—
48	C₄×C₄₇	—	2	1	no	—
49	C₄×C₄₇	—	2	2	no	—
50	C₄×C₄₇	—	4	2	no	—
51	Dic₄₇	—	4	2	no	—
52	Dic₄₇	#101	1	2	yes	—
53	Dic₄₇	#104	1	4	yes	—
54	#1526	—	47	1	no	maximal, Sylow
55	C₂×C₄₇	C₂×#101	1	1	yes	characteristic
56	C₂×C₄₇	C₂×#104	1	2	yes	—
57	D₄₇	—	4	1	no	—
58	#533	—	47	1	no	—
59	C₄×M₁₆	—	47	2	no	—
60	#330	—	47	1	no	—
61	#330	—	47	2	no	—
62	#330	D₄₇	1	1	yes	characteristic, complemented
63	C₄₇	#1526	1	1	yes	characteristic, complemented, Sylow
64	C₂×M₁₆	—	94	2	no	—
65	C₄⋊Q₈	—	47	2	no	—
66	#125	—	47	1	no	—
67	#125	C₂×D₄₇	1	1	yes	characteristic
68	C₂²⋊Q₈	—	94	2	no	—
69	C₄×Q₈	—	94	2	no	—
70	#117	—	47	2	no	—
71	C₂×C₄²	—	47	1	no	—
72	#97	—	47	2	no	—
73	#97	C₂×D₄₇	1	2	yes	—
74	C₄×C₈	—	94	2	no	—
75	C₂×Q₈	—	94	2	no	—
76	C₂²×C₄	—	47	1	no	—
77	C₂²×C₄	—	47	2	no	—
78	M₁₆	—	94	8	no	—
79	C₂×C₈	—	2	2	no	—
80	C₂×C₈	—	94	2	no	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄⋊C₄	—	47	2	no	—
83	C₄⋊C₄	—	94	2	no	—
84	C₄⋊C₄	—	94	2	no	—
85	C₄⋊C₄	C₄×D₄₇	1	2	yes	—
86	C₂²⋊C₄	—	94	2	no	—
87	C₄²	—	47	1	no	—
88	C₄²	—	47	2	no	—
89	C₄²	—	94	2	no	—
90	C₄²	C₂²×D₄₇	1	1	yes	characteristic
91	C₂³	—	47	1	no	—
92	Q₈	—	188	4	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	—	47	1	no	—
95	C₂×C₄	—	47	2	no	—
96	C₂×C₄	—	94	4	no	—
97	C₂×C₄	—	94	2	no	—
98	C₂×C₄	—	94	2	no	—
99	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
100	C₂×C₄	D₄×D₄₇	1	2	yes	—
101	C₈	—	2	4	no	—
102	C₈	—	94	4	no	—
103	C₂²	—	94	1	no	—
104	C₂²	—	94	2	no	—
105	C₂²	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	2	no	—
108	C₄	—	4	2	no	—
109	C₄	—	47	2	no	—
110	C₄	—	47	4	no	—
111	C₄	—	188	2	no	—
112	C₂	—	188	1	no	—
113	C₂	#101×D₄₇	1	1	yes	characteristic
114	C₂	#104×D₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#15689679

C₂

yes

maximal, characteristic

#15689075

C₂

yes

maximal

#15688865

C₂

yes

maximal, characteristic, complemented

#15688864

C₂

yes

maximal, complemented

C₄₇×#330

C₂

yes

maximal, characteristic, complemented

C₂×#10625324

—

#13094023

C₄

yes

—

#13094016

C₂²

yes

—

—

C₄

yes

—

C₄²×D₄₇

C₂²

yes

characteristic

#13093935

C₂²

yes

—

C₈×Dic₄₇

—

#125×C₄₇

C₂²

yes

characteristic

#97×C₄₇

C₂²

yes

—

C₂×C₄×D₄₇

C₂×C₄

yes

characteristic

C₂×C₄×D₄₇

D₄

yes

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂×C₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

(C₂×D₄₇)⋊C₄

—

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₄×Dic₄₇

C₂×C₄

yes

characteristic

C₄×Dic₄₇

D₄

yes

—

C₂×C₄₇⋊C₈

—

#10625324

—

C₂²×D₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₇

C₂²⋊C₄

yes

—

C₄×D₄₇

—

C₄×D₄₇

—

Dic₉₄

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

Dic₄₇

—

Dic₄₇

#101

yes

—

Dic₄₇

#104

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

—

D₄₇

—

#533

—

C₄×M₁₆

—

#330

—

#330

—

#330

D₄₇

yes

characteristic, complemented

C₄₇

#1526

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₄₇

yes

characteristic

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

#97

—

#97

C₂×D₄₇

yes

—

C₄×C₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₄₇

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

C₂³

—

Q₈

—

188

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

100

C₂×C₄

D₄×D₄₇

yes

—

101

C₈

—

102

C₈

—

103

C₂²

—

104

C₂²

—

105

C₂²

C₂²⋊C₄×D₄₇

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

188

—

112

C₂

—

188

—

113

C₂

#101×D₄₇

yes

characteristic

114

C₂

#104×D₄₇

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#330	C₂
socle	C₂²×C₄₇	C₂×C₂²⋊C₄
hypercenter	#330	D₄₇
hypocenter	C₄₇	#1526
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₄₇

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#330

C₂

socle

C₂²×C₄₇

C₂×C₂²⋊C₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #15688865	C₂	semidirect
4. #15688864	C₂	semidirect
5. C₄₇×#330	C₂	semidirect
62. #330	D₄₇	semidirect
63. C₄₇	#1526	semidirect

H ≅ G/N

type

3. #15688865

C₂

semidirect

4. #15688864

C₂

semidirect

5. C₄₇×#330

C₂

semidirect

62. #330

D₄₇

semidirect

63. C₄₇

#1526

semidirect

Subgroups — #20241981

Conjugacy classes of subgroups

Complements