Group #19133380 — subgroups

Subgroups — #19133380

Order 5504.

160 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14582956	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#14582652	C₂	1	2	yes	maximal, complemented
4	#14582650	C₂	1	2	yes	maximal, complemented
5	C₄₃×#431	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	—	2	1	no	—
7	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
8	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
9	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
12	#13063236	—	2	1	no	—
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₄₃	C₄	1	2	yes	—
15	C₂²⋊C₈×C₄₃	C₄	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂×C₄	1	4	yes	—
21	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₄₃	D₄	1	1	yes	characteristic
23	C₄²×C₄₃	Q₈	1	1	yes	characteristic
24	C₄²×C₄₃	C₂³	1	1	yes	characteristic
25	C₂×C₄₃⋊C₈	—	2	1	no	—
26	C₂×C₄₃⋊C₈	—	2	1	no	—
27	C₂×C₄₃⋊C₈	—	2	2	no	—
28	C₂×C₄₃⋊C₈	—	4	2	no	—
29	C₂³×C₄₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	2	no	—
31	C₂×C₄×C₄₃	—	2	2	no	—
32	C₂×C₄×C₄₃	—	2	1	no	—
33	C₂×C₄×C₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	C₈×C₄₃	—	2	4	no	—
41	C₄₃⋊C₈	—	4	1	no	—
42	C₄₃⋊C₈	—	4	2	no	—
43	C₄₃⋊C₈	—	4	1	no	—
44	C₂²×C₄₃	—	2	1	no	—
45	C₂²×C₄₃	—	2	1	no	—
46	C₂²×C₄₃	#108	1	2	yes	—
47	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	—	2	1	no	—
50	C₄×C₄₃	—	2	1	no	—
51	C₄×C₄₃	—	2	1	no	—
52	C₄×C₄₃	#131	1	2	yes	—
53	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
54	C₄×C₄₃	#137	1	1	yes	characteristic
55	#1573	—	43	1	no	maximal, Sylow
56	C₂×C₄₃	—	2	2	no	—
57	C₂×C₄₃	#424	1	1	yes	characteristic
58	C₂×C₄₃	#428	1	1	yes	characteristic
59	C₂×C₄₃	C₂×#108	1	1	yes	characteristic
60	#432	—	43	1	no	—
61	#431	D₄₃	1	1	yes	characteristic
62	C₂×C₄⋊C₈	—	43	1	no	—
63	#335	—	43	2	no	—
64	#334	—	43	2	no	—
65	C₄₃	#1573	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₈	—	86	1	no	—
67	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
68	C₄⋊C₈	—	43	1	no	—
69	C₄⋊C₈	—	43	2	no	—
70	C₄⋊C₈	—	43	1	no	—
71	C₄⋊C₈	—	86	1	no	—
72	C₄⋊C₈	Dic₄₃	1	2	yes	—
73	C₂²⋊C₈	—	86	1	no	—
74	C₂²⋊C₈	Dic₄₃	1	2	yes	—
75	#97	—	86	1	no	—
76	C₄×C₈	C₂×D₄₃	1	2	yes	—
77	C₂²×C₄	Dic₈₆	1	1	yes	characteristic
78	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
79	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
80	C₂×C₈	—	86	1	no	—
81	C₂×C₈	—	86	1	no	—
82	C₂×C₈	—	86	2	no	—
83	C₂×C₈	—	172	2	no	—
84	C₂×C₈	C₂×Dic₄₃	1	4	yes	—
85	C₄²	Dic₈₆	1	1	yes	characteristic
86	C₄²	D₁₇₂	1	1	yes	characteristic
87	C₄²	C₂×Dic₄₃	1	1	yes	characteristic
88	C₄²	C₂²×D₄₃	1	1	yes	characteristic
89	C₂³	C₄⋊Dic₄₃	1	1	yes	characteristic
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
95	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
96	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
97	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
98	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
99	C₂×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
100	C₈	—	2	4	no	—
101	C₈	—	172	2	no	—
102	C₈	—	172	1	no	—
103	C₈	—	172	1	no	—
104	C₂²	—	2	1	no	—
105	C₂²	—	2	1	no	—
106	C₂²	#13063261	1	2	yes	—
107	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	—	2	1	no	—
112	C₄	#13063332	1	2	yes	—
113	C₄	#13063353	1	1	yes	characteristic
114	C₄	#13063358	1	1	yes	characteristic
115	C₂	—	2	2	no	—
116	C₂	#14582926	1	1	yes	characteristic
117	C₂	#14582941	1	1	yes	characteristic
118	C₂	C₂×#13063261	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582956

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal, characteristic

#14582652

C₂

yes

maximal, complemented

#14582650

C₂

yes

maximal, complemented

C₄₃×#431

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

—

C₄⋊(C₄₃⋊C₈)

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

C₄

yes

—

C₂²⋊C₈×C₄₃

C₄

yes

—

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#108

yes

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#131

yes

—

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

C₂×C₄⋊C₈

—

#335

—

#334

—

C₄₃

#1573

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

Dic₄₃

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

Dic₄₃

yes

—

#97

—

C₄×C₈

C₂×D₄₃

yes

—

C₂²×C₄

Dic₈₆

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₂×Dic₄₃

yes

—

C₄²

Dic₈₆

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₄²

C₂×Dic₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

C₂×Dic₈₆

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

C₂²×Dic₄₃

yes

characteristic

100

C₈

—

101

C₈

—

172

—

102

C₈

—

172

—

103

C₈

—

172

—

104

C₂²

—

105

C₂²

—

106

C₂²

#13063261

yes

—

107

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

#13063332

yes

—

113

C₄

#13063353

yes

characteristic

114

C₄

#13063358

yes

characteristic

115

C₂

—

116

C₂

#14582926

yes

characteristic

117

C₂

#14582941

yes

characteristic

118

C₂

C₂×#13063261

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#431	C₂
socle	C₂²×C₄₃	C₂×C₄⋊C₄
hypercenter	#431	D₄₃
hypocenter	C₄₃	#1573
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

subgroup

G/H

center

C₂×C₄

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#431

C₂

socle

C₂²×C₄₃

C₂×C₄⋊C₄

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

N	H ≅ G/N	type
3. #14582652	C₂	semidirect
4. #14582650	C₂	semidirect
65. C₄₃	#1573	semidirect

H ≅ G/N

type

3. #14582652

C₂

semidirect

4. #14582650

C₂

semidirect

65. C₄₃

#1573

semidirect

Subgroups — #19133380

Conjugacy classes of subgroups

Complements