Group #19132744 — subgroups

Subgroups — #19132744

Order 5504.

112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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	#14583076	C₂	1	1	yes	maximal, characteristic
2	#14582696	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#329	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063370	C₄	1	1	yes	characteristic
5	#13063356	—	2	1	no	—
6	#13063253	—	2	1	no	—
7	#13063244	—	2	1	no	—
8	#13063242	C₄	1	1	yes	characteristic
9	#124×C₄₃	C₂²	1	1	yes	characteristic
10	#97×C₄₃	—	2	1	no	—
11	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
12	C₂×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₂²⋊D₄₃	—	4	1	no	—
14	#10621900	—	4	1	no	—
15	D₄×D₄₃	—	4	1	no	—
16	#10621898	—	2	1	no	—
17	C₂×C₈×C₄₃	—	4	1	no	—
18	C₂²⋊C₄×C₄₃	—	4	1	no	—
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	#10621885	—	4	1	no	—
21	#10621884	—	4	1	no	—
22	#10621877	—	2	1	no	—
23	#10621877	—	4	1	no	—
24	C₂³×C₄₃	—	2	1	no	—
25	C₂²×D₄₃	—	4	1	no	—
26	Q₈×C₄₃	—	4	1	no	—
27	D₄×C₄₃	—	4	1	no	—
28	C₂×C₄×C₄₃	—	2	1	no	—
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²⋊D₄₃	—	4	2	no	—
32	C₂²⋊D₄₃	—	4	1	no	—
33	C₂×Dic₄₃	—	4	1	no	—
34	D₁₇₂	—	2	1	no	—
35	C₄×D₄₃	—	4	1	no	—
36	Dic₈₆	—	2	1	no	—
37	C₈×C₄₃	—	4	2	no	—
38	C₄₃⋊C₈	—	4	1	no	—
39	C₄₃⋊C₈	—	8	1	no	—
40	C₂²×C₄₃	—	4	1	no	—
41	C₂²×C₄₃	—	8	1	no	—
42	C₂²×C₄₃	#99	1	1	yes	characteristic
43	C₂×D₄₃	—	4	1	no	—
44	C₂×D₄₃	—	16	1	no	—
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	—	4	1	no	—
47	C₄×C₄₃	—	4	1	no	—
48	Dic₄₃	—	4	1	no	—
49	#1403	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	—	8	1	no	—
52	C₂×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
53	D₄₃	—	8	1	no	—
54	#455	—	43	1	no	—
55	#355	—	43	1	no	—
56	#329	D₄₃	1	1	yes	characteristic, complemented
57	C₄₃	#1403	1	1	yes	characteristic, complemented, Sylow
58	H(5,𝔽₂)	—	43	1	no	—
59	#137	—	86	1	no	—
60	#124	C₂×D₄₃	1	1	yes	characteristic
61	#104	—	86	1	no	—
62	#101	—	86	1	no	—
63	#100	—	43	1	no	—
64	#97	—	2	1	no	—
65	#41	—	86	1	no	—
66	#41	—	172	1	no	—
67	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
68	C₂×D₄	—	172	1	no	—
69	C₂×D₄	—	172	1	no	—
70	C₂×D₄	C₄×D₄₃	1	1	yes	characteristic
71	Q₁₆	—	172	1	no	—
72	SD₁₆	—	172	1	no	—
73	M₁₆	—	86	1	no	—
74	M₁₆	—	172	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂²⋊C₄	—	4	1	no	—
77	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
78	C₂³	—	2	1	no	—
79	C₂³	—	172	1	no	—
80	Q₈	—	4	1	no	—
81	Q₈	—	86	1	no	—
82	D₄	—	4	1	no	—
83	D₄	—	86	1	no	—
84	D₄	—	172	2	no	—
85	D₄	—	172	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	172	1	no	—
89	C₂×C₄	—	172	1	no	—
90	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	344	1	no	—
93	C₈	—	172	1	no	—
94	C₂²	—	4	1	no	—
95	C₂²	—	8	1	no	—
96	C₂²	—	172	1	no	—
97	C₂²	—	688	1	no	—
98	C₂²	#13063239	1	1	yes	characteristic
99	C₄	—	2	1	no	—
100	C₄	—	4	1	no	—
101	C₄	—	4	1	no	—
102	C₄	—	172	1	no	—
103	C₂	—	2	1	no	—
104	C₂	—	8	1	no	—
105	C₂	—	344	1	no	—
106	C₂	#14582687	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583076

C₂

yes

maximal, characteristic

#14582696

C₂

yes

maximal, characteristic, complemented

C₄₃×#329

C₂

yes

maximal, characteristic, complemented

#13063370

C₄

yes

—

—

—

C₄

yes

characteristic

#124×C₄₃

C₂²

yes

characteristic

#97×C₄₃

—

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

#10621900

—

D₄×D₄₃

—

#10621898

—

C₂×C₈×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

—

—

—

—

C₂³×C₄₃

—

C₂²×D₄₃

—

Q₈×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

C₄×D₄₃

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#99

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1403

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

AΣL(1,𝔽₁₆)

yes

characteristic

D₄₃

—

#455

—

#355

—

#329

D₄₃

yes

characteristic, complemented

C₄₃

#1403

yes

characteristic, complemented, Sylow

H(5,𝔽₂)

—

#137

—

#124

C₂×D₄₃

yes

—

—

—

—

—

—

172

—

C₂×Q₈

D₁₇₂

yes

characteristic

C₂×D₄

—

172

—

C₂×D₄

—

172

—

C₂×D₄

C₄×D₄₃

yes

characteristic

Q₁₆

—

172

—

SD₁₆

—

172

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

C₂²⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₂³

—

C₂³

—

172

—

Q₈

—

Q₈

—

D₄

—

D₄

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

344

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

—

172

—

C₂²

—

688

—

C₂²

#13063239

yes

characteristic

C₄

—

100

C₄

—

101

C₄

—

102

C₄

—

172

—

103

C₂

—

104

C₂

—

105

C₂

—

344

—

106

C₂

#14582687

yes

characteristic

	subgroup	G/H
center	C₂	#14582687
commutator	C₂×D₄×C₄₃	C₂×C₄
Frattini	#124	C₂×D₄₃
Fitting	C₄₃×#329	C₂
socle	C₂×C₄₃	AΣL(1,𝔽₁₆)
hypercenter	#329	D₄₃
hypocenter	C₄₃	#1403
LCS	G ▷ C₂×D₄×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #329

subgroup

G/H

center

C₂

#14582687

commutator

C₂×D₄×C₄₃

C₂×C₄

Frattini

#124

C₂×D₄₃

Fitting

C₄₃×#329

C₂

socle

C₂×C₄₃

AΣL(1,𝔽₁₆)

D₄₃

C₄₃

G ▷ C₂×D₄×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #329

N	H ≅ G/N	type
2. #14582696	C₂	semidirect
3. C₄₃×#329	C₂	semidirect
56. #329	D₄₃	semidirect
57. C₄₃	#1403	semidirect

H ≅ G/N

type

2. #14582696

C₂

semidirect

3. C₄₃×#329

C₂

semidirect

56. #329

D₄₃

semidirect

57. C₄₃

#1403

semidirect

Subgroups — #19132744

Conjugacy classes of subgroups

Complements