Group #19134114 — subgroups

Subgroups — #19134114

Order 5504.

152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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	#14583304	C₂	1	1	yes	maximal, characteristic
2	#14583110	C₂	1	2	yes	maximal
3	#14583029	C₂	1	1	yes	maximal, characteristic
4	#14582646	C₂	1	2	yes	maximal
5	C₄₃×#334	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	—	2	2	no	—
7	#13063325	C₂²	1	2	yes	—
8	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
9	#13063259	—	2	1	no	—
10	#13063259	—	2	1	no	—
11	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	Dic₄₃⋊C₈	—	2	1	no	—
13	#13063250	—	2	2	no	—
14	#13063235	—	2	1	no	—
15	C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×Dic₈₆	—	2	2	no	—
18	C₂×Dic₈₆	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	—	2	2	no	—
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₄²×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	2	2	no	—
25	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
26	Dic₄₃⋊C₄	—	2	1	no	—
27	C₄×Dic₄₃	—	2	1	no	—
28	C₂×C₄₃⋊C₈	—	2	1	no	—
29	Dic₁₇₂	—	4	4	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
33	C₂×Dic₄₃	—	2	1	no	—
34	C₂×Dic₄₃	—	2	1	no	—
35	C₂×Dic₄₃	—	4	2	no	—
36	Dic₈₆	—	2	2	no	—
37	Dic₈₆	—	4	2	no	—
38	Dic₈₆	—	4	2	no	—
39	C₈×C₄₃	—	2	1	no	—
40	C₈×C₄₃	—	4	2	no	—
41	C₈×C₄₃	Q₁₆	1	2	yes	complemented
42	C₄₃⋊C₈	—	4	1	no	—
43	C₂²×C₄₃	#121	1	1	yes	characteristic
44	C₄×C₄₃	—	2	1	no	—
45	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
47	C₄×C₄₃	#137	1	1	yes	characteristic
48	Dic₄₃	—	4	1	no	—
49	Dic₄₃	—	4	1	no	—
50	Dic₄₃	—	8	2	no	—
51	#1694	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	#462	1	1	yes	characteristic
53	C₂×C₄₃	#469	1	1	yes	characteristic
54	C₂×C₄₃	#473	1	1	yes	characteristic
55	#500	—	43	1	no	—
56	#462	—	43	2	no	—
57	#446	—	43	1	no	—
58	#334	D₄₃	1	1	yes	characteristic
59	#332	—	43	2	no	—
60	C₄₃	#1694	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₁₆	—	86	2	no	—
62	C₄⋊Q₈	—	43	2	no	—
63	C₄×Q₈	—	43	1	no	—
64	#107	—	86	1	no	—
65	#107	—	86	1	no	—
66	C₄⋊C₈	—	43	1	no	—
67	C₄⋊C₈	—	86	1	no	—
68	C₄⋊C₈	C₂×D₄₃	1	2	yes	—
69	#103	—	86	2	no	—
70	#97	—	86	1	no	—
71	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
72	C₂×Q₈	—	43	1	no	—
73	C₂×Q₈	—	86	2	no	—
74	Q₁₆	—	172	4	no	—
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	86	1	no	—
77	C₂×C₈	D₁₇₂	1	1	yes	characteristic
78	C₂×C₈	D₁₇₂	1	1	yes	characteristic
79	C₄⋊C₄	—	43	1	no	—
80	C₄⋊C₄	—	86	1	no	—
81	C₄⋊C₄	—	86	2	no	—
82	C₄⋊C₄	—	86	2	no	—
83	C₄²	—	86	1	no	—
84	C₄²	C₂²×D₄₃	1	1	yes	characteristic
85	Q₈	—	86	2	no	—
86	Q₈	—	172	2	no	—
87	Q₈	—	172	2	no	—
88	C₂×C₄	—	86	1	no	—
89	C₂×C₄	—	86	1	no	—
90	C₂×C₄	—	172	2	no	—
91	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
92	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
93	C₂×C₄	#10621902	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	4	2	no	—
96	C₈	—	172	1	no	—
97	C₈	Dic₁₇₂	1	2	yes	complemented
98	C₂²	#13063300	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	344	2	no	—
101	C₄	—	172	1	no	—
102	C₄	—	172	1	no	—
103	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
104	C₄	#13063352	1	2	yes	—
105	C₄	#13063358	1	1	yes	characteristic
106	C₂	#14583110	1	1	yes	characteristic
107	C₂	#14583153	1	1	yes	characteristic
108	C₂	#14583175	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583304

C₂

yes

maximal, characteristic

#14583110

C₂

yes

maximal

#14583029

C₂

yes

maximal, characteristic

#14582646

C₂

yes

maximal

C₄₃×#334

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

—

#13063325

C₂²

yes

—

C₄×Dic₈₆

C₂²

yes

characteristic

#13063259

—

#13063259

—

C₄⋊(C₄₃⋊C₈)

C₂²

yes

characteristic

Dic₄₃⋊C₈

—

#13063250

—

#13063235

—

C₄⋊C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

—

C₂×Dic₈₆

D₄

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

Q₁₆

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

#121

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

AGL(1,ℤ/8)

yes

—

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

D₄₃

yes

characteristic

#332

—

C₄₃

#1694

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

#107

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₃

yes

—

#103

—

#97

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621902

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₈

Dic₁₇₂

yes

complemented

C₂²

#13063300

yes

characteristic

C₄

—

100

C₄

—

344

—

101

C₄

—

172

—

102

C₄

—

172

—

103

C₄

C₂×Dic₁₇₂

yes

characteristic

104

C₄

#13063352

yes

—

105

C₄

#13063358

yes

characteristic

106

C₂

#14583110

yes

characteristic

107

C₂

#14583153

yes

characteristic

108

C₂

#14583175

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₄²×C₄₃	C₂³
Frattini	C₄²	C₂²×D₄₃
Fitting	C₄₃×#334	C₂
socle	C₂²×C₄₃	#121
hypercenter	#334	D₄₃
hypocenter	C₄₃	#1694
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #334

subgroup

G/H

center

C₂²

#13063300

commutator

C₄²×C₄₃

C₂³

Frattini

C₄²

C₂²×D₄₃

Fitting

C₄₃×#334

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #334

N	H ≅ G/N	type
41. C₈×C₄₃	Q₁₆	semidirect
60. C₄₃	#1694	semidirect
97. C₈	Dic₁₇₂	semidirect

H ≅ G/N

type

41. C₈×C₄₃

Q₁₆

semidirect

60. C₄₃

#1694

semidirect

97. C₈

Dic₁₇₂

semidirect

Subgroups — #19134114

Conjugacy classes of subgroups

Complements