Group #19132534 — subgroups

Subgroups — #19132534

Order 5504.

108 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 108 conjugacy classes of subgroups — too many to draw. Only its 43 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	C₂×Dic₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₄₃×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₈	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₄₃	C₄	1	1	yes	characteristic
6	C₂×C₄₃⋊C₁₆	—	2	1	no	—
7	Dic₄₃⋊C₈	—	2	1	no	—
8	Dic₄₃⋊C₈	—	2	1	no	—
9	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₄₃	C₈	1	1	yes	characteristic
13	C₂²×Dic₄₃	C₈	1	1	yes	characteristic
14	C₂×C₈×C₄₃	—	4	1	no	—
15	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
17	C₄×Dic₄₃	—	2	1	no	—
18	C₄×Dic₄₃	—	2	1	no	—
19	C₂×C₄₃⋊C₈	—	2	1	no	—
20	C₂×C₄₃⋊C₈	—	4	1	no	—
21	C₁₆×C₄₃	—	4	1	no	—
22	C₄₃⋊C₁₆	—	4	1	no	—
23	C₂³×C₄₃	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₄₃	—	2	1	no	—
25	C₂×C₄×C₄₃	—	2	1	no	—
26	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
28	C₂×Dic₄₃	—	2	1	no	—
29	C₂×Dic₄₃	—	2	1	no	—
30	C₂×Dic₄₃	—	2	1	no	—
31	C₂×Dic₄₃	—	4	1	no	—
32	C₂×Dic₄₃	C₁₆	1	2	yes	complemented
33	C₈×C₄₃	—	2	1	no	—
34	C₈×C₄₃	—	2	1	no	—
35	C₄₃⋊C₈	—	4	1	no	—
36	C₂²×C₄₃	—	2	1	no	—
37	C₂²×C₄₃	—	2	1	no	—
38	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₂²×C₄₃	C₂×C₁₆	1	1	yes	characteristic
40	C₂²×C₄₃	M₃₂	1	1	yes	characteristic
41	C₄×C₄₃	—	2	1	no	—
42	C₄×C₄₃	#99	1	1	yes	characteristic
43	C₄×C₄₃	#101	1	1	yes	characteristic
44	Dic₄₃	—	2	2	no	—
45	Dic₄₃	—	4	1	no	—
46	#1322	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	—	2	1	no	—
48	C₂×C₄₃	—	2	1	no	—
49	C₂×C₄₃	#324	1	1	yes	characteristic
50	C₂×C₄₃	C₂²⋊C₁₆	1	1	yes	characteristic
51	C₂×C₄₃	#349	1	1	yes	characteristic
52	C₂×C₄⋊C₈	—	43	1	no	—
53	C₂²⋊C₁₆	—	43	1	no	—
54	C₂²⋊C₁₆	D₄₃	1	1	yes	characteristic
55	C₄₃	#1322	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₈	—	43	1	no	—
57	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
58	C₂×C₄²	—	43	1	no	—
59	C₂×C₁₆	—	2	1	no	—
60	C₂×C₁₆	—	86	1	no	—
61	C₄⋊C₈	—	86	1	no	—
62	C₄⋊C₈	—	86	1	no	—
63	C₂²×C₄	—	43	1	no	—
64	C₂²×C₄	—	43	1	no	—
65	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
66	C₂×C₈	—	4	1	no	—
67	C₂×C₈	—	86	1	no	—
68	C₂×C₈	—	172	1	no	—
69	C₂×C₈	D₁₇₂	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
71	C₄²	—	86	1	no	—
72	C₄²	—	86	1	no	—
73	C₁₆	—	4	1	no	—
74	C₁₆	—	172	1	no	—
75	C₂³	C₈×D₄₃	1	1	yes	characteristic
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	43	2	no	—
79	C₂×C₄	—	86	1	no	—
80	C₂×C₄	—	86	1	no	—
81	C₂×C₄	—	86	1	no	—
82	C₂×C₄	—	172	1	no	—
83	C₂×C₄	#10621872	1	1	yes	characteristic
84	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
85	C₈	—	2	1	no	—
86	C₈	—	2	1	no	—
87	C₈	—	172	1	no	—
88	C₂²	—	2	1	no	—
89	C₂²	—	2	1	no	—
90	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
91	C₂²	C₁₆×D₄₃	1	1	yes	characteristic
92	C₂²	#13063264	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	86	2	no	—
95	C₄	—	172	1	no	—
96	C₄	#13063239	1	1	yes	characteristic
97	C₄	#13063243	1	1	yes	characteristic
98	C₂	—	2	1	no	—
99	C₂	—	2	1	no	—
100	C₂	#14582624	1	1	yes	characteristic
101	C₂	(C₂×D₄₃)⋊C₁₆	1	1	yes	characteristic
102	C₂	#14582680	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₄₃⋊C₈

C₂

yes

maximal, characteristic

C₂²⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic

C₄₃×C₂²⋊C₁₆

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₄

yes

characteristic

C₂×C₄×Dic₄₃

C₄

yes

characteristic

C₂×C₄₃⋊C₁₆

—

Dic₄₃⋊C₈

—

Dic₄₃⋊C₈

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×Dic₄₃

C₈

yes

characteristic

C₂²×Dic₄₃

C₈

yes

characteristic

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄×Dic₄₃

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₁₆

yes

complemented

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₈

yes

characteristic

C₂²×C₄₃

C₂×C₁₆

yes

characteristic

C₂²×C₄₃

M₃₂

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#1322

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

#324

yes

characteristic

C₂×C₄₃

C₂²⋊C₁₆

yes

characteristic

C₂×C₄₃

#349

yes

characteristic

C₂×C₄⋊C₈

—

C₂²⋊C₁₆

—

C₂²⋊C₁₆

D₄₃

yes

characteristic

C₄₃

#1322

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

172

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄²

—

C₄²

—

C₁₆

—

C₁₆

—

172

—

C₂³

C₈×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

#10621872

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

C₂²

—

C₂²

(C₂×D₄₃)⋊C₈

yes

characteristic

C₂²

C₁₆×D₄₃

yes

characteristic

C₂²

#13063264

yes

characteristic

C₄

—

C₄

—

C₄

—

172

—

C₄

yes

C₄

yes

C₂

—

C₂

—

100

C₂

#14582624

yes

characteristic

101

C₂

(C₂×D₄₃)⋊C₁₆

yes

characteristic

102

C₂

#14582680

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₃)⋊C₄
commutator	C₂²×C₄₃	C₂×C₁₆
Frattini	C₂²×C₈	C₂×D₄₃
Fitting	C₄₃×C₂²⋊C₁₆	C₂
socle	C₂²×C₄₃	C₂²⋊C₈
hypercenter	C₂²⋊C₁₆	D₄₃
hypocenter	C₄₃	#1322
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂×C₄

(C₂×D₄₃)⋊C₄

commutator

C₂²×C₄₃

C₂×C₁₆

Frattini

C₂²×C₈

C₂×D₄₃

Fitting

C₄₃×C₂²⋊C₁₆

C₂

socle

C₂²×C₄₃

C₂²⋊C₈

hypercenter

C₂²⋊C₁₆

D₄₃

hypocenter

C₄₃

#1322

LCS

G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
32. C₂×Dic₄₃	C₁₆	semidirect
55. C₄₃	#1322	semidirect

H ≅ G/N

type

32. C₂×Dic₄₃

C₁₆

semidirect

55. C₄₃

#1322

semidirect

Subgroups — #19132534

Conjugacy classes of subgroups

Complements