Group #19133965 — subgroups

Subgroups — #19133965

Order 5504.

156 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14583279	C₂	1	1	yes	maximal, characteristic
2	#14583184	C₂	1	2	yes	maximal
3	#14582652	C₂	1	1	yes	maximal, characteristic
4	#14582646	C₂	1	2	yes	maximal
5	C₈×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	—	2	1	no	—
7	C₂×Dic₁₇₂	—	2	1	no	—
8	#13063325	C₂²	1	2	yes	—
9	#13063256	—	2	2	no	—
10	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
11	#13063249	—	2	2	no	—
12	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₈×C₄₃	—	2	1	no	—
14	C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	—	2	1	no	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×Dic₈₆	—	2	2	no	—
19	C₂×C₈×C₄₃	—	2	1	no	—
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
24	C₄²×C₄₃	—	2	1	no	—
25	C₄²×C₄₃	C₂³	1	1	yes	characteristic
26	C₄⋊Dic₄₃	—	2	2	no	—
27	C₄⋊Dic₄₃	—	2	2	no	—
28	C₂×C₄₃⋊C₈	—	2	2	no	—
29	Dic₁₇₂	—	4	2	no	—
30	Dic₁₇₂	—	4	2	no	—
31	Q₈×C₄₃	—	2	1	no	—
32	Q₈×C₄₃	Q₁₆	1	2	yes	complemented
33	C₂×C₄×C₄₃	—	2	1	no	—
34	C₂×C₄×C₄₃	—	2	1	no	—
35	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
38	C₂×Dic₄₃	—	4	2	no	—
39	Dic₈₆	—	4	2	no	—
40	Dic₈₆	—	4	2	no	—
41	C₈×C₄₃	—	2	1	no	—
42	C₈×C₄₃	—	4	1	no	—
43	C₈×C₄₃	SD₁₆	1	2	yes	—
44	C₄₃⋊C₈	—	4	2	no	—
45	C₂²×C₄₃	#121	1	1	yes	characteristic
46	C₄×C₄₃	—	2	2	no	—
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	4	1	no	—
49	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
50	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
51	C₄×C₄₃	#135	1	1	yes	characteristic
52	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
53	Dic₄₃	—	8	2	no	—
54	#1670	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	#460	1	1	yes	characteristic
56	C₂×C₄₃	#467	1	1	yes	characteristic
57	C₂×C₄₃	#473	1	1	yes	characteristic
58	#494	—	43	1	no	—
59	#475	—	43	2	no	—
60	C₈×Q₈	D₄₃	1	1	yes	characteristic
61	#335	—	43	1	no	—
62	#332	—	43	2	no	—
63	C₄₃	#1670	1	1	yes	characteristic, complemented, Sylow
64	C₂×Q₁₆	—	86	1	no	—
65	C₂×Q₁₆	—	86	1	no	—
66	C₄⋊Q₈	—	43	2	no	—
67	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
68	#106	—	86	2	no	—
69	C₄⋊C₈	—	2	1	no	—
70	C₄⋊C₈	—	43	2	no	—
71	C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
72	#103	—	86	2	no	—
73	C₄×C₈	—	2	1	no	—
74	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
75	C₂×Q₈	—	86	2	no	—
76	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
77	Q₁₆	—	172	2	no	—
78	Q₁₆	—	172	2	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	86	2	no	—
81	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
82	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	86	2	no	—
85	C₄⋊C₄	—	86	2	no	—
86	C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
87	C₄²	—	2	1	no	—
88	C₄²	C₂²×D₄₃	1	1	yes	characteristic
89	Q₈	—	2	1	no	—
90	Q₈	—	172	2	no	—
91	Q₈	—	172	2	no	—
92	Q₈	Dic₁₇₂	1	2	yes	complemented
93	C₂×C₄	—	2	1	no	—
94	C₂×C₄	—	2	1	no	—
95	C₂×C₄	—	172	2	no	—
96	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
97	C₂×C₄	#10621898	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	4	1	no	—
101	C₈	—	172	2	no	—
102	C₈	#10621884	1	2	yes	—
103	C₂²	#13063299	1	1	yes	characteristic
104	C₄	—	2	2	no	—
105	C₄	—	2	1	no	—
106	C₄	—	4	1	no	—
107	C₄	—	344	2	no	—
108	C₄	C₂×#10621884	1	1	yes	characteristic
109	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
110	C₄	#13063347	1	1	yes	characteristic
111	C₄	#13063350	1	1	yes	characteristic
112	C₂	#14583099	1	1	yes	characteristic
113	C₂	#14583140	1	1	yes	characteristic
114	C₂	#14583174	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583279

C₂

yes

maximal, characteristic

#14583184

C₂

yes

maximal

#14582652

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal

C₈×Q₈×C₄₃

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

—

C₂×Dic₁₇₂

—

#13063325

C₂²

yes

—

#13063256

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

#13063249

—

C₄×Q₈×C₄₃

C₂²

yes

characteristic

C₄⋊C₈×C₄₃

—

C₄⋊C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

Dic₁₇₂

—

Q₈×C₄₃

—

Q₈×C₄₃

Q₁₆

yes

complemented

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

SD₁₆

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

C₈×Q₈

D₄₃

yes

characteristic

#335

—

#332

—

C₄₃

#1670

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

C₂×D₄₃

yes

characteristic

#106

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

characteristic

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

D₁₇₂

yes

characteristic

Q₁₆

—

172

—

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

D₁₇₂

yes

characteristic

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

172

—

Q₈

—

172

—

Q₈

Dic₁₇₂

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

#10621898

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

172

—

102

C₈

#10621884

yes

—

103

C₂²

#13063299

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

344

—

108

C₄

C₂×#10621884

yes

characteristic

109

C₄

C₂×Dic₁₇₂

yes

characteristic

110

C₄

#13063347

yes

characteristic

111

C₄

#13063350

yes

characteristic

112

C₂

#14583099

yes

characteristic

113

C₂

#14583140

yes

characteristic

114

C₂

#14583174

yes

characteristic

	subgroup	G/H
center	C₂²	#13063299
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈×Q₈×C₄₃	C₂
socle	C₂²×C₄₃	#121
hypercenter	C₈×Q₈	D₄₃
hypocenter	C₄₃	#1670
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

subgroup

G/H

center

C₂²

#13063299

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₈×Q₈×C₄₃

C₂

socle

C₂²×C₄₃

#121

hypercenter

C₈×Q₈

D₄₃

hypocenter

C₄₃

#1670

LCS

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈×Q₈

N	H ≅ G/N	type
32. Q₈×C₄₃	Q₁₆	semidirect
63. C₄₃	#1670	semidirect
92. Q₈	Dic₁₇₂	semidirect

H ≅ G/N

type

32. Q₈×C₄₃

Q₁₆

semidirect

63. C₄₃

#1670

semidirect

92. Q₈

Dic₁₇₂

semidirect

Subgroups — #19133965

Conjugacy classes of subgroups

Complements