Group #19132579 — subgroups

Subgroups — #19132579

Order 5504.

114 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 31 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	#14583152	C₂	1	1	yes	maximal, characteristic
2	#14582681	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₄₄	C₄	1	1	yes	characteristic, complemented
5	#13063299	—	2	1	no	—
6	#13063265	—	2	1	no	—
7	#13063257	C₄	1	1	yes	characteristic, complemented
8	#13063247	—	2	1	no	—
9	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	#117×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	M₁₆×C₄₃	—	4	1	no	—
15	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₄⋊C₄×C₄₃	—	4	1	no	—
18	C₂²⋊C₄×C₄₃	—	4	1	no	—
19	C₄²×C₄₃	—	2	2	no	—
20	(C₂×D₄₃)⋊C₄	—	4	1	no	—
21	C₄⋊Dic₄₃	—	2	1	no	—
22	D₃₄₄	—	4	1	no	—
23	C₄₃⋊C₁₆	—	4	1	no	—
24	C₂³×C₄₃	D₈	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	—	4	2	no	—
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
31	C₂²⋊D₄₃	—	8	2	no	—
32	C₂×Dic₄₃	—	4	1	no	—
33	D₁₇₂	—	4	1	no	—
34	D₁₇₂	—	4	1	no	—
35	C₈×C₄₃	—	2	1	no	—
36	C₈×C₄₃	—	2	1	no	—
37	C₂²×C₄₃	—	2	1	no	—
38	C₂²×C₄₃	—	4	1	no	—
39	C₂²×C₄₃	#102	1	1	yes	characteristic
40	C₂×D₄₃	—	8	1	no	—
41	C₂×D₄₃	—	8	1	no	—
42	C₂×D₄₃	—	8	1	no	—
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	—	8	2	no	—
45	C₄×C₄₃	#99	1	1	yes	characteristic
46	C₄×C₄₃	#104	1	1	yes	characteristic
47	Dic₄₃	—	8	1	no	—
48	#1339	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	2	1	no	—
50	C₂×C₄₃	—	4	1	no	—
51	C₂×C₄₃	#327	1	1	yes	characteristic
52	D₄₃	—	16	1	no	—
53	#469	—	43	1	no	—
54	#349	—	43	1	no	—
55	H(3,ℤ/4)	D₄₃	1	1	yes	characteristic, complemented
56	C₄₃	#1339	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₈	—	43	1	no	—
58	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
59	#121	—	86	1	no	—
60	#117	—	2	1	no	—
61	M₃₂	—	86	1	no	—
62	#106	—	43	1	no	—
63	#102	—	86	1	no	—
64	C₂×D₄	—	86	1	no	—
65	C₂×D₄	—	172	1	no	—
66	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
67	D₈	—	172	1	no	—
68	M₁₆	—	4	1	no	—
69	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
70	C₂×C₈	D₁₇₂	1	1	yes	characteristic
71	C₄⋊C₄	—	4	1	no	—
72	C₄⋊C₄	—	86	1	no	—
73	C₂²⋊C₄	—	4	1	no	—
74	C₂²⋊C₄	—	172	1	no	—
75	C₄²	—	2	2	no	—
76	C₁₆	—	172	1	no	—
77	C₂³	—	172	1	no	—
78	C₂³	#10621882	1	1	yes	characteristic
79	D₄	—	344	2	no	—
80	D₄	—	172	1	no	—
81	D₄	—	172	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	4	2	no	—
85	C₂×C₄	—	172	1	no	—
86	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
87	C₂×C₄	#10621884	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	2	1	no	—
90	C₂²	—	2	1	no	—
91	C₂²	—	4	1	no	—
92	C₂²	—	344	1	no	—
93	C₂²	—	344	1	no	—
94	C₂²	—	344	1	no	—
95	C₂²	#13063245	1	1	yes	characteristic
96	C₄	—	2	1	no	—
97	C₄	—	8	2	no	—
98	C₄	—	344	1	no	—
99	C₄	#13063239	1	1	yes	characteristic
100	C₄	#13063253	1	1	yes	characteristic
101	C₂	—	2	1	no	—
102	C₂	—	4	1	no	—
103	C₂	—	688	1	no	—
104	C₂	#14582632	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583152

C₂

yes

maximal, characteristic

#14582681

C₂

yes

maximal, characteristic, complemented

C₄₃×H(3,ℤ/4)

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

C₄

yes

characteristic, complemented

#13063299

—

#13063265

—

#13063257

C₄

yes

characteristic, complemented

#13063247

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

#117×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

D₃₄₄

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

D₈

yes

characteristic

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂²⋊D₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

—

C₈×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#102

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

#1339

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#327

yes

characteristic

D₄₃

—

#469

—

#349

—

H(3,ℤ/4)

D₄₃

yes

characteristic, complemented

C₄₃

#1339

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

#121

—

#117

—

M₃₂

—

#106

—

#102

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

D₈

—

172

—

M₁₆

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

—

C₁₆

—

172

—

C₂³

—

172

—

C₂³

#10621882

yes

characteristic

D₄

—

344

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

#10621884

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

#13063245

yes

characteristic

C₄

—

C₄

—

C₄

—

344

—

C₄

#13063239

yes

characteristic

100

C₄

#13063253

yes

characteristic

101

C₂

—

102

C₂

—

103

C₂

—

688

—

104

C₂

#14582632

yes

characteristic

	subgroup	G/H
center	C₂	#14582632
commutator	C₂×C₈×C₄₃	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₄₃
Fitting	C₄₃×H(3,ℤ/4)	C₂
socle	C₂×C₄₃	#327
hypercenter	H(3,ℤ/4)	D₄₃
hypocenter	C₄₃	#1339
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₂

#14582632

commutator

C₂×C₈×C₄₃

C₂×C₄

Frattini

C₂×M₁₆

C₂×D₄₃

Fitting

C₄₃×H(3,ℤ/4)

C₂

C₂×C₄₃

D₄₃

C₄₃

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
2. #14582681	C₂	semidirect
3. C₄₃×H(3,ℤ/4)	C₂	semidirect
4. C₂×D₃₄₄	C₄	semidirect
7. #13063257	C₄	semidirect
55. H(3,ℤ/4)	D₄₃	semidirect
56. C₄₃	#1339	semidirect

H ≅ G/N

type

2. #14582681

C₂

semidirect

3. C₄₃×H(3,ℤ/4)

C₂

semidirect

4. C₂×D₃₄₄

C₄

semidirect

7. #13063257

C₄

semidirect

55. H(3,ℤ/4)

D₄₃

semidirect

56. C₄₃

#1339

semidirect

Subgroups — #19132579

Conjugacy classes of subgroups

Complements