Group #20253727 — subgroups

Subgroups — C₂×#15689491 #20253727

Order 6016.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13094016	C₂	1	1	yes	maximal, characteristic
2	#15689491	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13093948	C₂	1	4	yes	maximal
4	C₂×#13093935	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
7	#13094016	—	2	2	no	—
8	#13094016	C₂²	1	4	yes	—
9	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
10	C₂×Dic₄₇⋊C₄	—	2	2	no	—
11	#13093948	C₂²	1	16	yes	—
12	#13093935	C₂²	1	4	yes	—
13	C₂²×Q₈×C₄₇	C₂²	1	2	yes	—
14	C₄⋊Q₈×C₄₇	—	2	2	no	—
15	C₄⋊Q₈×C₄₇	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
17	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×Q₈×C₄₇	—	2	2	no	—
19	C₂×Q₈×C₄₇	—	2	8	no	—
20	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
21	C₂²×C₄×C₄₇	—	2	2	no	—
22	C₂²×C₄×C₄₇	D₄	1	2	yes	—
23	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂²×Dic₄₇	—	2	2	no	—
25	C₄⋊C₄×C₄₇	—	2	8	no	—
26	C₄²×C₄₇	D₄	1	2	yes	—
27	C₄²×C₄₇	C₂³	1	2	yes	—
28	C₄⋊Dic₄₇	—	2	2	no	—
29	C₄⋊Dic₄₇	C₂³	1	4	yes	—
30	Dic₄₇⋊C₄	—	2	8	no	—
31	C₂×C₄₇⋊C₈	—	2	4	no	—
32	C₂×C₄₇⋊C₈	C₂³	1	4	yes	—
33	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
34	Q₈×C₄₇	—	2	8	no	—
35	Q₈×C₄₇	—	4	4	no	—
36	C₂×C₄×C₄₇	—	2	4	no	—
37	C₂×C₄×C₄₇	—	2	4	no	—
38	C₂×C₄×C₄₇	—	4	4	no	—
39	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
40	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₄₇	#41	1	4	yes	—
42	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
43	C₂×Dic₄₇	—	2	4	no	—
44	C₂×Dic₄₇	—	4	4	no	—
45	C₄₇⋊C₈	—	2	4	no	—
46	C₂²×C₄₇	#124	1	2	yes	—
47	C₂²×C₄₇	#137	1	4	yes	—
48	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
49	C₄×C₄₇	—	2	4	no	—
50	C₄×C₄₇	—	4	4	no	—
51	C₄×C₄₇	#124	1	2	yes	—
52	C₄×C₄₇	C₂×#41	1	2	yes	—
53	Dic₄₇	—	4	4	no	—
54	C₂×#491	—	47	1	no	maximal, Sylow
55	C₂×C₄₇	#491	1	4	yes	complemented
56	C₂×C₄₇	C₂×#124	1	1	yes	characteristic
57	C₂×C₄₇	C₂×#137	1	2	yes	—
58	C₂×C₄⋊Q₈	D₄₇	1	1	yes	characteristic
59	C₂×#125	—	47	1	no	—
60	#491	—	47	8	no	—
61	C₂×#103	—	47	4	no	—
62	C₂×#97	—	47	1	no	—
63	C₄₇	C₂×#491	1	1	yes	characteristic, complemented, Sylow
64	C₂²×Q₈	C₂×D₄₇	1	2	yes	—
65	C₂²×C₈	—	47	2	no	—
66	C₄⋊Q₈	—	2	2	no	—
67	C₄⋊Q₈	C₂×D₄₇	1	4	yes	—
68	#125	—	47	4	no	—
69	#125	—	94	2	no	—
70	C₂×C₄⋊C₄	—	2	2	no	—
71	C₂×C₄⋊C₄	—	47	2	no	—
72	C₂×C₄⋊C₄	—	94	2	no	—
73	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
74	#103	—	47	16	no	—
75	#97	—	47	4	no	—
76	C₂×Q₈	—	2	2	no	—
77	C₂×Q₈	—	2	8	no	—
78	C₂×Q₈	C₂²×D₄₇	1	4	yes	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	94	2	no	—
81	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
82	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
83	C₂×C₈	—	47	4	no	—
84	C₂×C₈	—	94	4	no	—
85	C₄⋊C₄	—	2	8	no	—
86	C₄⋊C₄	—	47	4	no	—
87	C₄⋊C₄	—	94	8	no	—
88	C₄⋊C₄	—	94	2	no	—
89	C₄²	C₂²⋊D₄₇	1	2	yes	—
90	C₄²	C₂²×D₄₇	1	2	yes	—
91	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
92	Q₈	—	2	8	no	—
93	Q₈	—	4	4	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	4	4	no	—
97	C₂×C₄	—	94	4	no	—
98	C₂×C₄	—	188	4	no	—
99	C₂×C₄	#10625352	1	4	yes	—
100	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
101	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
102	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
103	C₈	—	94	4	no	—
104	C₂²	#13094011	1	2	yes	—
105	C₂²	#13094055	1	4	yes	—
106	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
107	C₄	—	2	4	no	—
108	C₄	—	4	4	no	—
109	C₄	—	188	4	no	—
110	C₄	#13094011	1	2	yes	—
111	C₄	C₂×#10625352	1	2	yes	—
112	C₂	#15689491	1	4	yes	direct product factor
113	C₂	C₂×#13094011	1	1	yes	characteristic
114	C₂	C₂×#13094055	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094016

C₂

yes

maximal, characteristic

#15689491

C₂

yes

maximal, direct product factor

C₂×#13093948

C₂

yes

maximal

C₂×#13093935

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₄₇

C₂

yes

maximal, characteristic

C₂²×C₄₇⋊C₈

C₂²

yes

—

#13094016

—

#13094016

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

—

#13093948

C₂²

yes

—

#13093935

C₂²

yes

—

C₂²×Q₈×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

C₂×C₄⋊C₄×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×Dic₄₇

—

C₄⋊C₄×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

C₂³

yes

—

Dic₄₇⋊C₄

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

C₂³

yes

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

#124

yes

—

C₂²×C₄₇

#137

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#124

yes

—

C₄×C₄₇

C₂×#41

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₄⋊Q₈

D₄₇

yes

—

—

—

C₂×#97

—

C₄₇

C₂×#491

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₇

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₇

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

#103

—

#97

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₄₇

yes

—

C₄²

C₂²×D₄₇

yes

—

C₂³

C₂×C₂²⋊D₄₇

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

188

—

C₂×C₄

#10625352

yes

—

100

C₂×C₄

C₂×C₂²⋊D₄₇

yes

—

101

C₂×C₄

C₂×C₂²⋊D₄₇

yes

characteristic

102

C₂×C₄

C₂³×D₄₇

yes

characteristic

103

C₈

—

104

C₂²

#13094011

yes

—

105

C₂²

#13094055

yes

—

106

C₂²

C₂²×C₂²⋊D₄₇

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

188

—

110

C₄

#13094011

yes

—

111

C₄

C₂×#10625352

yes

—

112

C₂

#15689491

yes

direct product factor

113

C₂

C₂×#13094011

yes

characteristic

114

C₂

C₂×#13094055

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×C₄⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×#491
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₇

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂×C₄⋊Q₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₄₇

hypocenter

C₄₇

C₂×#491

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
2. #15689491	C₂	direct (N × H)
55. C₂×C₄₇	#491	semidirect
63. C₄₇	C₂×#491	semidirect
112. C₂	#15689491	direct (N × H)

H ≅ G/N

type

2. #15689491

C₂

direct (N × H)

55. C₂×C₄₇

#491

semidirect

63. C₄₇

C₂×#491

semidirect

112. C₂

#15689491

direct (N × H)

Subgroups — C₂×#15689491 #20253727

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689491 #20253727

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689491 #20253727