Group #19132759 — subgroups

Subgroups — #19132759

Order 5504.

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

normal subgroups only

This group has 110 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	#14583271	C₂	1	1	yes	maximal, characteristic
2	#14582692	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#353	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621883	—	2	1	no	—
5	C₂×#10621883	—	2	1	no	—
6	#13063325	C₄	1	1	yes	characteristic, complemented
7	#13063240	—	2	1	no	—
8	C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic, complemented
9	#127×C₄₃	C₂²	1	1	yes	characteristic
10	#99×C₄₃	—	2	1	no	—
11	C₂×D₄×C₄₃	—	4	1	no	—
12	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
13	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
14	C₂×Dic₈₆	—	2	1	no	—
15	C₂²⋊C₄×C₄₃	—	4	1	no	—
16	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂²⋊Dic₄₃	—	4	1	no	—
18	#10621883	—	4	2	no	—
19	#10621883	—	4	2	no	—
20	C₄⋊Dic₄₃	—	4	1	no	—
21	C₂×C₄₃⋊C₈	—	2	1	no	—
22	C₂³×C₄₃	—	2	1	no	—
23	C₂³×C₄₃	—	2	1	no	—
24	D₄×C₄₃	—	4	1	no	—
25	D₄×C₄₃	—	4	1	no	—
26	D₄×C₄₃	—	8	2	no	—
27	C₂×C₄×C₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃	—	8	1	no	—
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₄₃	—	4	1	no	—
31	C₂×Dic₄₃	—	8	1	no	—
32	Dic₈₆	—	4	1	no	—
33	Dic₈₆	—	4	1	no	—
34	C₄₃⋊C₈	—	2	2	no	—
35	C₂²×C₄₃	—	4	1	no	—
36	C₂²×C₄₃	—	4	1	no	—
37	C₂²×C₄₃	—	8	1	no	—
38	C₂²×C₄₃	—	8	1	no	—
39	C₂²×C₄₃	#99	1	1	yes	characteristic
40	C₄×C₄₃	—	2	2	no	—
41	C₄×C₄₃	—	2	1	no	—
42	C₄×C₄₃	—	16	1	no	—
43	Dic₄₃	—	8	1	no	—
44	Dic₄₃	—	16	1	no	—
45	#1409	—	43	1	no	maximal, Sylow
46	C₂×C₄₃	—	2	1	no	—
47	C₂×C₄₃	—	8	1	no	—
48	C₂×C₄₃	—	8	1	no	—
49	C₂×C₄₃	#353	1	1	yes	characteristic
50	#492	—	43	1	no	—
51	#353	—	43	1	no	—
52	#353	D₄₃	1	1	yes	characteristic
53	C₄₃	#1409	1	1	yes	characteristic, complemented, Sylow
54	C₂×SD₁₆	—	86	1	no	—
55	C₂×SD₁₆	—	86	1	no	—
56	C₄⋊Q₈	—	43	1	no	—
57	#127	C₂×D₄₃	1	1	yes	characteristic
58	#99	—	2	1	no	—
59	#99	—	86	1	no	—
60	C₄×C₈	—	43	1	no	—
61	C₂×Q₈	—	86	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×D₄	D₁₇₂	1	1	yes	characteristic
64	C₂×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
65	SD₁₆	—	172	2	no	—
66	SD₁₆	—	172	2	no	—
67	C₂×C₈	—	86	1	no	—
68	C₄⋊C₄	—	172	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₂²⋊C₄	—	172	1	no	—
71	C₄²	C₄×D₄₃	1	1	yes	characteristic
72	C₂³	—	2	1	no	—
73	C₂³	—	2	1	no	—
74	Q₈	—	172	1	no	—
75	Q₈	—	172	1	no	—
76	D₄	—	4	1	no	—
77	D₄	—	4	1	no	—
78	D₄	—	8	2	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	—	344	1	no	—
82	C₂×C₄	—	172	1	no	—
83	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
84	C₈	—	86	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	—	8	1	no	—
88	C₂²	—	8	1	no	—
89	C₂²	#13063239	1	1	yes	characteristic
90	C₄	—	2	2	no	—
91	C₄	—	2	1	no	—
92	C₄	—	16	1	no	—
93	C₄	—	344	1	no	—
94	C₄	—	688	1	no	—
95	C₂	—	2	1	no	—
96	C₂	—	8	1	no	—
97	C₂	—	8	1	no	—
98	C₂	#14582691	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583271

C₂

yes

maximal, characteristic

#14582692

C₂

yes

maximal, characteristic

C₄₃×#353

C₂

yes

maximal, characteristic

C₂×#10621883

—

C₂×#10621883

—

#13063325

C₄

yes

characteristic, complemented

#13063240

—

C₄×C₄₃⋊C₈

C₄

yes

characteristic, complemented

#127×C₄₃

C₂²

yes

characteristic

#99×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

D₄

yes

characteristic

C₂×D₄×C₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₂²⋊Dic₄₃

—

#10621883

—

#10621883

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

—

C₂³×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#99

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#1409

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

C₄₃

#1409

yes

characteristic, complemented, Sylow

C₂×SD₁₆

—

C₂×SD₁₆

—

C₄⋊Q₈

—

#127

C₂×D₄₃

yes

characteristic

#99

—

#99

—

C₄×C₈

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

D₁₇₂

yes

characteristic

C₂×D₄

C₂²⋊D₄₃

yes

characteristic

SD₁₆

—

172

—

SD₁₆

—

172

—

C₂×C₈

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

C₄×D₄₃

yes

characteristic

C₂³

—

C₂³

—

Q₈

—

172

—

Q₈

—

172

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

—

172

—

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#13063239

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

344

—

C₄

—

688

—

C₂

—

C₂

—

C₂

—

C₂

#14582691

yes

characteristic

	subgroup	G/H
center	C₂	#14582691
commutator	C₄²×C₄₃	C₂×C₄
Frattini	#127	C₂×D₄₃
Fitting	C₄₃×#353	C₂
socle	C₂×C₄₃	#353
hypercenter	#353	D₄₃
hypocenter	C₄₃	#1409
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #353

subgroup

G/H

center

C₂

#14582691

commutator

C₄²×C₄₃

C₂×C₄

Frattini

#127

C₂×D₄₃

Fitting

C₄₃×#353

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #127 ◁ #353

N	H ≅ G/N	type
6. #13063325	C₄	semidirect
8. C₄×C₄₃⋊C₈	C₄	semidirect
53. C₄₃	#1409	semidirect

H ≅ G/N

type

6. #13063325

C₄

semidirect

8. C₄×C₄₃⋊C₈

C₄

semidirect

53. C₄₃

#1409

semidirect

Subgroups — #19132759

Conjugacy classes of subgroups

Complements