Group #19136358 — subgroups

Subgroups — C₂×#14582720 #19136358

Order 5504.

168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13063265	C₂	1	2	yes	maximal
2	#14582720	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
4	#13063265	—	2	2	no	—
5	#13063265	C₂²	1	4	yes	—
6	C₂×C₄₃⋊C₁₆	—	2	2	no	—
7	C₂²×C₈×C₄₃	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₄₃	C₄	1	1	yes	characteristic
10	C₄×C₈×C₄₃	C₄	1	2	yes	—
11	C₄×C₈×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄×C₄₃	—	2	1	no	—
13	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₃	C₈	1	2	yes	—
15	C₂×C₈×C₄₃	C₈	1	2	yes	—
16	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
22	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
23	C₄²×C₄₃	—	2	1	no	—
24	C₄²×C₄₃	C₂×C₄	1	2	yes	—
25	C₄₃⋊C₁₆	—	2	4	no	—
26	C₂³×C₄₃	M₁₆	1	1	yes	characteristic
27	C₂×C₄×C₄₃	—	2	4	no	—
28	C₂×C₄×C₄₃	—	2	2	no	—
29	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
36	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
37	C₈×C₄₃	C₂×C₈	1	4	yes	—
38	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	C₂²×C₄₃	—	2	2	no	—
41	C₂²×C₄₃	C₄⋊C₈	1	1	yes	characteristic
42	C₂²×C₄₃	C₄⋊C₈	1	1	yes	characteristic
43	C₂²×C₄₃	C₂×M₁₆	1	1	yes	characteristic
44	C₄×C₄₃	—	2	4	no	—
45	C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
46	C₄×C₄₃	C₄⋊C₈	1	1	yes	characteristic
47	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
49	C₂×#364	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	—	2	1	no	—
52	C₂×C₄₃	#364	1	2	yes	complemented
53	C₂×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
54	C₂×M₃₂	—	43	2	no	—
55	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
56	#364	—	43	4	no	—
57	C₄₃	C₂×#364	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₈	Dic₄₃	1	1	yes	characteristic
59	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
60	C₂×C₄²	Dic₄₃	1	1	yes	characteristic
61	M₃₂	—	43	4	no	—
62	M₃₂	—	86	2	no	—
63	C₂×C₁₆	—	86	2	no	—
64	C₄×C₈	Dic₄₃	1	2	yes	—
65	C₄×C₈	C₂×D₄₃	1	2	yes	—
66	C₂²×C₄	—	2	1	no	—
67	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
68	C₂×C₈	C₄₃⋊C₈	1	2	yes	—
69	C₂×C₈	C₄₃⋊C₈	1	2	yes	—
70	C₂×C₈	Dic₈₆	1	1	yes	characteristic
71	C₂×C₈	Dic₈₆	1	1	yes	characteristic
72	C₂×C₈	D₁₇₂	1	1	yes	characteristic
73	C₂×C₈	D₁₇₂	1	1	yes	characteristic
74	C₂×C₈	C₂×Dic₄₃	1	2	yes	—
75	C₂×C₈	C₂×Dic₄₃	1	1	yes	characteristic
76	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
77	C₄²	—	2	1	no	—
78	C₄²	C₂×Dic₄₃	1	2	yes	—
79	C₁₆	—	86	4	no	—
80	C₂³	#10621877	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
84	C₂×C₄	C₂×C₄₃⋊C₈	1	1	yes	characteristic
85	C₂×C₄	#10621877	1	1	yes	characteristic
86	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
87	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
88	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
89	C₈	C₂×C₄₃⋊C₈	1	4	yes	—
90	C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
91	C₈	C₄⋊Dic₄₃	1	1	yes	characteristic
92	C₈	C₂×Dic₈₆	1	1	yes	characteristic
93	C₈	C₂×D₁₇₂	1	1	yes	characteristic
94	C₂²	—	2	2	no	—
95	C₂²	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
96	C₂²	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
97	C₂²	C₂×#10621877	1	1	yes	characteristic
98	C₄	—	2	4	no	—
99	C₄	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
100	C₄	C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic
101	C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
102	C₄	C₂²×C₄₃⋊C₈	1	1	yes	characteristic
103	C₂	—	2	1	no	—
104	C₂	—	2	1	no	—
105	C₂	#14582720	1	2	yes	direct product factor
106	C₂	C₂×C₄⋊(C₄₃⋊C₈)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063265

C₂

yes

maximal

#14582720

C₂

yes

maximal, direct product factor

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

#13063265

—

#13063265

C₂²

yes

—

C₂×C₄₃⋊C₁₆

—

C₂²×C₈×C₄₃

C₄

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₄

yes

characteristic

C₄×C₈×C₄₃

C₄

yes

—

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₈

yes

—

C₂×C₈×C₄₃

C₈

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₈×C₄₃

C₂×C₈

yes

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

C₄⋊C₈

yes

characteristic

C₂²×C₄₃

C₄⋊C₈

yes

characteristic

C₂²×C₄₃

C₂×M₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄⋊C₈

yes

characteristic

C₄×C₄₃

C₄⋊C₈

yes

characteristic

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₂²×C₈

yes

characteristic

C₂×#364

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#364

yes

complemented

C₂×C₄₃

C₂×C₄⋊C₈

yes

characteristic

C₂×M₃₂

—

C₂×C₄×C₈

D₄₃

yes

characteristic

#364

—

C₄₃

C₂×#364

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄²

Dic₄₃

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

Dic₄₃

yes

—

C₄×C₈

C₂×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₄₃⋊C₈

yes

—

C₂×C₈

C₄₃⋊C₈

yes

—

C₂×C₈

Dic₈₆

yes

characteristic

C₂×C₈

Dic₈₆

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂×Dic₄₃

yes

—

C₂×C₈

C₂×Dic₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

—

C₄²

C₂×Dic₄₃

yes

—

C₁₆

—

C₂³

#10621877

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄₃⋊C₈

yes

characteristic

C₂×C₄

C₂×C₄₃⋊C₈

yes

characteristic

C₂×C₄

#10621877

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

C₈

C₂×C₄₃⋊C₈

yes

—

C₈

C₄⋊Dic₄₃

yes

characteristic

C₈

C₄⋊Dic₄₃

yes

characteristic

C₈

C₂×Dic₈₆

yes

characteristic

C₈

C₂×D₁₇₂

yes

characteristic

C₂²

—

C₂²

C₄⋊(C₄₃⋊C₈)

yes

characteristic

C₂²

C₄⋊(C₄₃⋊C₈)

yes

characteristic

C₂²

C₂×#10621877

yes

characteristic

C₄

—

C₄

C₄⋊(C₄₃⋊C₈)

yes

characteristic

100

C₄

C₄⋊(C₄₃⋊C₈)

yes

characteristic

101

C₄

C₂×C₄⋊Dic₄₃

yes

characteristic

102

C₄

C₂²×C₄₃⋊C₈

yes

characteristic

103

C₂

—

104

C₂

—

105

C₂

#14582720

yes

direct product factor

106

C₂

C₂×C₄⋊(C₄₃⋊C₈)

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₁₇₂
commutator	C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₄⋊C₈
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	C₂×#364
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₈

D₁₇₂

commutator

C₄×C₄₃

C₂²×C₈

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂²×C₄₃

C₄⋊C₈

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

C₂×#364

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14582720	C₂	direct (N × H)
52. C₂×C₄₃	#364	semidirect
57. C₄₃	C₂×#364	semidirect
105. C₂	#14582720	direct (N × H)

H ≅ G/N

type

2. #14582720

C₂

direct (N × H)

52. C₂×C₄₃

#364

semidirect

57. C₄₃

C₂×#364

semidirect

105. C₂

#14582720

direct (N × H)

Subgroups — C₂×#14582720 #19136358

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14582720 #19136358

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582720 #19136358