Group #19132748 — subgroups

Subgroups — #19132748

Order 5504.

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

normal subgroups only

This group has 106 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	#14583081	C₂	1	1	yes	maximal, characteristic
2	#14582648	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#356	C₂	1	1	yes	maximal, characteristic, complemented
4	#13063373	C₄	1	1	yes	characteristic
5	#13063356	—	2	1	no	—
6	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
7	#13063253	—	2	1	no	—
8	#13063244	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	#101×C₄₃	—	2	1	no	—
11	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
13	#10621902	—	4	1	no	—
14	Q₈×D₄₃	—	4	1	no	—
15	#10621898	—	2	1	no	—
16	#10621898	—	4	1	no	—
17	M₁₆×C₄₃	—	4	1	no	—
18	C₄⋊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	C₂×C₄₃⋊C₈	—	4	1	no	—
24	Q₈×C₄₃	—	4	1	no	—
25	Q₈×C₄₃	—	4	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃	—	2	1	no	—
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²⋊D₄₃	—	4	1	no	—
31	D₁₇₂	—	2	1	no	—
32	D₁₇₂	—	4	1	no	—
33	C₄×D₄₃	—	4	1	no	—
34	C₄×D₄₃	—	4	2	no	—
35	Dic₈₆	—	2	1	no	—
36	Dic₈₆	—	4	1	no	—
37	C₈×C₄₃	—	8	1	no	—
38	C₄₃⋊C₈	—	4	1	no	—
39	C₄₃⋊C₈	—	8	1	no	—
40	C₂²×C₄₃	#99	1	1	yes	characteristic
41	C₂×D₄₃	—	4	1	no	—
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	—	2	1	no	—
45	C₄×C₄₃	—	4	1	no	—
46	C₄×C₄₃	—	4	1	no	—
47	Dic₄₃	—	4	1	no	—
48	#1405	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	2	1	no	—
50	C₂×C₄₃	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
51	D₄₃	—	8	1	no	—
52	#456	—	43	1	no	—
53	#356	D₄₃	1	1	yes	characteristic, complemented
54	#333	—	43	1	no	—
55	C₄₃	#1405	1	1	yes	characteristic, complemented, Sylow
56	2₋¹⁺⁴	—	43	1	no	—
57	#137	—	86	1	no	—
58	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
59	C₄⋊C₈	—	86	1	no	—
60	#104	—	86	1	no	—
61	#101	—	2	1	no	—
62	#101	—	43	1	no	—
63	#41	—	86	1	no	—
64	#41	—	172	1	no	—
65	#41	—	172	1	no	—
66	C₂×Q₈	—	172	1	no	—
67	C₂×Q₈	C₄×D₄₃	1	1	yes	characteristic
68	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
69	Q₁₆	—	172	1	no	—
70	SD₁₆	—	172	1	no	—
71	M₁₆	—	4	1	no	—
72	M₁₆	—	86	1	no	—
73	C₂×C₈	—	172	1	no	—
74	C₄⋊C₄	—	4	1	no	—
75	C₄²	D₁₇₂	1	1	yes	characteristic
76	Q₈	—	4	1	no	—
77	Q₈	—	4	1	no	—
78	Q₈	—	86	1	no	—
79	Q₈	—	172	1	no	—
80	D₄	—	86	1	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	—	2	1	no	—
86	C₂×C₄	—	172	1	no	—
87	C₂×C₄	—	172	2	no	—
88	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
89	C₈	—	8	1	no	—
90	C₈	—	344	1	no	—
91	C₈	—	172	1	no	—
92	C₂²	—	172	1	no	—
93	C₂²	#13063239	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	2	1	no	—
96	C₄	—	2	1	no	—
97	C₄	—	4	1	no	—
98	C₄	—	4	1	no	—
99	C₄	—	172	1	no	—
100	C₂	—	2	1	no	—
101	C₂	—	344	1	no	—
102	C₂	#14582685	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583081

C₂

yes

maximal, characteristic

#14582648

C₂

yes

maximal, characteristic, complemented

C₄₃×#356

C₂

yes

maximal, characteristic, complemented

#13063373

C₄

yes

characteristic

#13063356

—

C₄⋊(C₄₃⋊C₈)

—

#13063253

—

#13063244

C₄

yes

characteristic

C₄⋊Q₈×C₄₃

C₂²

yes

characteristic

#101×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×Q₈×C₄₃

D₄

yes

characteristic

#10621902

—

Q₈×D₄₃

—

#10621898

—

#10621898

—

M₁₆×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

—

—

—

C₂×C₄₃⋊C₈

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂²⋊D₄₃

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

#99

yes

characteristic

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#1405

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

AΣL(1,𝔽₁₆)

yes

characteristic

D₄₃

—

#456

—

#356

D₄₃

yes

characteristic, complemented

#333

—

C₄₃

#1405

yes

characteristic, complemented, Sylow

2₋¹⁺⁴

—

#137

—

C₄⋊Q₈

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

—

—

—

—

—

172

—

#41

—

172

—

C₂×Q₈

—

172

—

C₂×Q₈

C₄×D₄₃

yes

characteristic

C₂×Q₈

C₂²⋊D₄₃

yes

characteristic

Q₁₆

—

172

—

SD₁₆

—

172

—

M₁₆

—

M₁₆

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄²

D₁₇₂

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

Q₈

—

172

—

D₄

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

344

—

C₈

—

172

—

C₂²

—

172

—

C₂²

#13063239

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

172

—

100

C₂

—

101

C₂

—

344

—

102

C₂

#14582685

yes

characteristic

	subgroup	G/H
center	C₂	#14582685
commutator	C₂×Q₈×C₄₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₄₃
Fitting	C₄₃×#356	C₂
socle	C₂×C₄₃	AΣL(1,𝔽₁₆)
hypercenter	#356	D₄₃
hypocenter	C₄₃	#1405
LCS	G ▷ C₂×Q₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

subgroup

G/H

center

C₂

#14582685

commutator

C₂×Q₈×C₄₃

C₂×C₄

Frattini

C₄⋊Q₈

C₂×D₄₃

Fitting

C₄₃×#356

C₂

socle

C₂×C₄₃

AΣL(1,𝔽₁₆)

D₄₃

C₄₃

G ▷ C₂×Q₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

N	H ≅ G/N	type
2. #14582648	C₂	semidirect
3. C₄₃×#356	C₂	semidirect
53. #356	D₄₃	semidirect
55. C₄₃	#1405	semidirect

H ≅ G/N

type

2. #14582648

C₂

semidirect

3. C₄₃×#356

C₂

semidirect

53. #356

D₄₃

semidirect

55. C₄₃

#1405

semidirect

Subgroups — #19132748

Conjugacy classes of subgroups

Complements