Group #19132611 — subgroups

Subgroups — #19132611

Order 5504.

114 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 35 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	#14583135	C₂	1	1	yes	maximal, characteristic
2	#14582664	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₄₄	C₄	1	1	yes	characteristic
5	C₂×#10621877	—	2	1	no	—
6	#13063299	—	2	1	no	—
7	#13063259	C₄	1	1	yes	characteristic
8	#13063247	—	2	1	no	—
9	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
12	C₂×C₂²⋊D₄₃	—	4	1	no	—
13	C₂×D₁₇₂	—	2	1	no	—
14	C₂×C₈×C₄₃	—	4	1	no	—
15	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
17	(C₂×D₄₃)⋊C₄	—	4	1	no	—
18	C₄⋊Dic₄₃	—	2	1	no	—
19	#10621877	—	2	2	no	—
20	#10621877	—	4	1	no	—
21	C₂×C₄₃⋊C₈	—	4	1	no	—
22	D₃₄₄	—	4	1	no	—
23	C₁₆×C₄₃	—	4	1	no	—
24	C₂³×C₄₃	SD₁₆	1	1	yes	characteristic
25	C₂²×D₄₃	—	4	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
30	C₂²⋊D₄₃	—	8	2	no	—
31	C₂×Dic₄₃	—	4	1	no	—
32	D₁₇₂	—	4	1	no	—
33	D₁₇₂	—	4	1	no	—
34	C₈×C₄₃	—	2	1	no	—
35	C₈×C₄₃	—	2	1	no	—
36	C₄₃⋊C₈	—	4	2	no	—
37	C₂²×C₄₃	—	2	1	no	—
38	C₂²×C₄₃	—	2	1	no	—
39	C₂²×C₄₃	—	2	1	no	—
40	C₂²×C₄₃	#102	1	1	yes	characteristic
41	C₂×D₄₃	—	8	1	no	—
42	C₂×D₄₃	—	8	1	no	—
43	C₂×D₄₃	—	8	1	no	—
44	C₄×C₄₃	—	2	1	no	—
45	C₄×C₄₃	#99	1	1	yes	characteristic
46	C₄×C₄₃	#104	1	1	yes	characteristic
47	Dic₄₃	—	8	1	no	—
48	#1349	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	4	1	no	—
50	C₂×C₄₃	#327	1	1	yes	characteristic
51	C₂×C₄₃	#359	1	1	yes	characteristic
52	C₂×C₄₃	#361	1	1	yes	characteristic
53	D₄₃	—	16	1	no	—
54	#466	—	43	1	no	—
55	C₂²⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
56	#341	—	43	1	no	—
57	C₄₃	#1349	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₈	—	43	1	no	—
59	C₂×M₁₆	—	86	1	no	—
60	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
61	#121	—	86	1	no	—
62	C₂×C₁₆	—	2	1	no	—
63	#107	—	43	1	no	—
64	#102	—	86	1	no	—
65	C₂×D₄	—	86	1	no	—
66	C₂×D₄	—	172	1	no	—
67	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
68	D₈	—	172	1	no	—
69	M₁₆	—	86	2	no	—
70	M₁₆	—	172	1	no	—
71	C₂×C₈	—	4	1	no	—
72	C₂×C₈	—	172	1	no	—
73	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
74	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
75	C₄⋊C₄	—	86	1	no	—
76	C₂²⋊C₄	—	172	1	no	—
77	C₁₆	—	4	1	no	—
78	C₂³	—	172	1	no	—
79	C₂³	#10621873	1	1	yes	characteristic
80	D₄	—	344	2	no	—
81	D₄	—	172	1	no	—
82	D₄	—	172	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	172	1	no	—
86	C₂×C₄	D₃₄₄	1	1	yes	characteristic
87	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	2	1	no	—
90	C₈	—	172	2	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	1	no	—
93	C₂²	—	2	1	no	—
94	C₂²	—	344	1	no	—
95	C₂²	—	344	1	no	—
96	C₂²	—	344	1	no	—
97	C₂²	#13063247	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	344	1	no	—
100	C₄	#13063239	1	1	yes	characteristic
101	C₄	#13063251	1	1	yes	characteristic
102	C₂	—	4	1	no	—
103	C₂	—	688	1	no	—
104	C₂	#14582634	1	1	yes	characteristic
105	C₂	#14582707	1	1	yes	characteristic
106	C₂	#14582713	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583135

C₂

yes

maximal, characteristic

#14582664

C₂

yes

maximal, characteristic, complemented

C₄₃×C₂²⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

C₄

yes

—

—

C₄

yes

characteristic

#13063247

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

D₃₄₄

—

C₁₆×C₄₃

—

C₂³×C₄₃

SD₁₆

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#102

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1349

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

—

#466

—

C₂²⋊C₁₆

D₄₃

yes

characteristic, complemented

#341

—

C₄₃

#1349

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#121

—

C₂×C₁₆

—

#107

—

#102

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂²×C₄

D₁₇₂

yes

characteristic

D₈

—

172

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₁₆

—

C₂³

—

172

—

C₂³

#10621873

yes

characteristic

D₄

—

344

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

D₃₄₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

#13063247

yes

characteristic

C₄

—

C₄

—

344

—

100

C₄

#13063239

yes

characteristic

101

C₄

#13063251

yes

characteristic

102

C₂

—

103

C₂

—

688

—

104

C₂

#14582634

yes

characteristic

105

C₂

#14582707

yes

characteristic

106

C₂

#14582713

yes

characteristic

	subgroup	G/H
center	C₂²	#13063247
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₄₃×C₂²⋊C₁₆	C₂
socle	C₂²×C₄₃	#102
hypercenter	C₂²⋊C₁₆	D₄₃
hypocenter	C₄₃	#1349
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂²

#13063247

commutator

C₂×C₈×C₄₃

C₂×C₄

Frattini

C₂²×C₈

C₂×D₄₃

Fitting

C₄₃×C₂²⋊C₁₆

C₂

socle

C₂²×C₄₃

#102

hypercenter

C₂²⋊C₁₆

D₄₃

hypocenter

C₄₃

#1349

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
2. #14582664	C₂	semidirect
3. C₄₃×C₂²⋊C₁₆	C₂	semidirect
55. C₂²⋊C₁₆	D₄₃	semidirect
57. C₄₃	#1349	semidirect

H ≅ G/N

type

2. #14582664

C₂

semidirect

3. C₄₃×C₂²⋊C₁₆

C₂

semidirect

55. C₂²⋊C₁₆

D₄₃

semidirect

57. C₄₃

#1349

semidirect

Subgroups — #19132611

Conjugacy classes of subgroups

Complements