Group #19143023 — subgroups

Subgroups — #19143023

Order 5504.

556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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×#13063332	C₂	1	2	yes	maximal
2	#14582855	C₂	1	6	yes	maximal, complemented
3	C₄×#10621877	C₂	1	3	yes	maximal, complemented
4	C₂×#13063236	C₂	1	3	yes	maximal, complemented
5	C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
6	#13063332	C₄	1	16	yes	complemented
7	C₂×#10621877	C₂²	1	6	yes	—
8	C₂²×C₄₃⋊C₈	C₂²	1	6	yes	—
9	#13063236	C₂²	1	1	yes	characteristic
10	#13063236	C₂²	1	3	yes	—
11	#13063236	C₂²	1	6	yes	—
12	C₄×C₄₃⋊C₈	C₂²	1	6	yes	—
13	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₄₃	C₄	1	2	yes	—
15	C₄×D₄×C₄₃	C₄	1	6	yes	—
16	#117×C₄₃	C₂²	1	3	yes	—
17	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
18	#41×C₄₃	C₂×C₄	1	8	yes	—
19	C₂×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×D₄×C₄₃	C₂×C₄	1	3	yes	—
21	C₂²×C₄×C₄₃	C₂×C₄	1	6	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
23	C₄⋊C₄×C₄₃	C₂×C₄	1	6	yes	—
24	C₂²⋊C₄×C₄₃	C₂×C₄	1	6	yes	—
25	C₄²×C₄₃	C₂×C₄	1	6	yes	—
26	C₄²×C₄₃	C₂³	1	1	yes	characteristic
27	C₄²×C₄₃	C₂³	1	3	yes	—
28	#10621877	C₂×C₄	1	24	yes	complemented
29	C₂×C₄₃⋊C₈	C₂×C₄	1	24	yes	complemented
30	C₂×C₄₃⋊C₈	C₂³	1	6	yes	—
31	C₂×C₄₃⋊C₈	C₂³	1	2	yes	—
32	C₂³×C₄₃	C₂²×C₄	1	3	yes	—
33	Q₈×C₄₃	C₄²	1	4	yes	—
34	D₄×C₄₃	C₄²	1	12	yes	—
35	C₂×C₄×C₄₃	—	4	6	no	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	12	yes	—
37	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
38	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
39	C₂×C₄×C₄₃	C₂²×C₄	1	3	yes	—
40	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
41	C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
42	C₄₃⋊C₈	C₂²×C₄	1	12	yes	—
43	C₂²×C₄₃	—	2	6	no	—
44	C₂²×C₄₃	C₂×C₄²	1	6	yes	—
45	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
46	C₄×C₄₃	—	2	2	no	—
47	C₄×C₄₃	—	2	6	no	—
48	C₄×C₄₃	C₂×C₄²	1	6	yes	—
49	C₄×C₄₃	C₂³×C₄	1	2	yes	—
50	#2875	—	43	1	no	maximal, Sylow
51	C₂×C₄₃	—	2	6	no	—
52	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
53	C₂×C₄₃	#568	1	2	yes	—
54	C₂×#131	—	43	2	no	—
55	C₄×#41	D₄₃	1	1	yes	characteristic
56	#405	—	43	6	no	—
57	C₄×M₁₆	—	43	3	no	—
58	C₂×#97	—	43	3	no	—
59	C₄₃	#2875	1	1	yes	characteristic, complemented, Sylow
60	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
61	#131	—	43	16	no	—
62	C₂×M₁₆	—	43	6	no	—
63	C₂²×C₈	—	43	6	no	—
64	C₄×Q₈	Dic₄₃	1	2	yes	—
65	C₄×D₄	Dic₄₃	1	6	yes	—
66	#117	C₂×D₄₃	1	3	yes	—
67	C₂×C₄²	C₂×D₄₃	1	3	yes	—
68	#97	—	43	1	no	—
69	#97	—	43	3	no	—
70	#97	—	43	6	no	—
71	C₄×C₈	—	43	6	no	—
72	#41	C₄×D₄₃	1	8	yes	—
73	C₂×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
74	C₂×D₄	C₂×Dic₄₃	1	3	yes	—
75	C₂²×C₄	C₂×Dic₄₃	1	6	yes	—
76	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
77	M₁₆	—	43	24	no	—
78	C₂×C₈	—	43	24	no	—
79	C₂×C₈	—	43	6	no	—
80	C₂×C₈	—	43	2	no	—
81	C₄⋊C₄	C₂×Dic₄₃	1	6	yes	—
82	C₂²⋊C₄	C₂×Dic₄₃	1	6	yes	—
83	C₄²	C₂×Dic₄₃	1	6	yes	—
84	C₄²	C₂²×D₄₃	1	3	yes	—
85	C₄²	C₂²×D₄₃	1	1	yes	characteristic
86	C₂³	C₂²×Dic₄₃	1	3	yes	—
87	Q₈	C₄×Dic₄₃	1	4	yes	—
88	D₄	C₄×Dic₄₃	1	12	yes	—
89	C₂×C₄	—	4	6	no	—
90	C₂×C₄	C₂×C₄×D₄₃	1	12	yes	—
91	C₂×C₄	C₂²×Dic₄₃	1	2	yes	—
92	C₂×C₄	C₂²×Dic₄₃	1	6	yes	—
93	C₂×C₄	C₂²×Dic₄₃	1	3	yes	—
94	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
95	C₈	—	43	4	no	—
96	C₈	—	43	12	no	—
97	C₂²	—	2	6	no	—
98	C₂²	C₂×C₄×Dic₄₃	1	6	yes	—
99	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
100	C₄	—	2	2	no	—
101	C₄	—	2	6	no	—
102	C₄	C₂×C₄×Dic₄₃	1	6	yes	—
103	C₄	C₂²×C₄×D₄₃	1	2	yes	—
104	C₂	—	2	6	no	—
105	C₂	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
106	C₂	#14583666	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063332

C₂

yes

maximal

#14582855

C₂

yes

maximal, complemented

C₄×#10621877

C₂

yes

maximal, complemented

C₂×#13063236

C₂

yes

maximal, complemented

C₄×#41×C₄₃

C₂

yes

maximal, characteristic

#13063332

C₄

yes

complemented

C₂×#10621877

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063236

C₂²

yes

characteristic

#13063236

C₂²

yes

—

#13063236

C₂²

yes

—

C₄×C₄₃⋊C₈

C₂²

yes

—

C₂×#41×C₄₃

C₂²

yes

characteristic

C₄×Q₈×C₄₃

C₄

yes

—

C₄×D₄×C₄₃

C₄

yes

—

#117×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

#41×C₄₃

C₂×C₄

yes

—

C₂×Q₈×C₄₃

C₂×C₄

yes

characteristic

C₂×D₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂×C₄

yes

—

C₂²⋊C₄×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

—

#10621877

C₂×C₄

yes

complemented

C₂×C₄₃⋊C₈

C₂×C₄

yes

complemented

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂²×C₄

yes

—

Q₈×C₄₃

C₄²

yes

—

D₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₄₃⋊C₈

C₂²×C₄

yes

—

C₄₃⋊C₈

C₂²×C₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×C₄²

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

—

C₄×C₄₃

C₂³×C₄

yes

—

#2875

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂²×C₄²

yes

characteristic

C₂×C₄₃

#568

yes

—

C₂×#131

—

C₄×#41

D₄₃

yes

characteristic

#405

—

C₄×M₁₆

—

C₂×#97

—

C₄₃

#2875

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₃

yes

characteristic

#131

—

C₂×M₁₆

—

C₂²×C₈

—

C₄×Q₈

Dic₄₃

yes

—

C₄×D₄

Dic₄₃

yes

—

#117

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

#97

—

#97

—

#97

—

C₄×C₈

—

#41

C₄×D₄₃

yes

—

C₂×Q₈

C₂×Dic₄₃

yes

characteristic

C₂×D₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

C₂×Dic₄₃

yes

—

C₂²⋊C₄

C₂×Dic₄₃

yes

—

C₄²

C₂×Dic₄₃

yes

—

C₄²

C₂²×D₄₃

yes

—

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

C₂²×Dic₄₃

yes

—

Q₈

C₄×Dic₄₃

yes

—

D₄

C₄×Dic₄₃

yes

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

C₂×C₄×Dic₄₃

yes

—

C₂²

C₂³×Dic₄₃

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

C₂×C₄×Dic₄₃

yes

—

103

C₄

C₂²×C₄×D₄₃

yes

—

104

C₂

—

105

C₂

C₂²×C₄×Dic₄₃

yes

characteristic

106

C₂

#14583666

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₄₃
commutator	C₂×C₄₃	C₂²×C₄²
Fitting	C₄×#41×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×C₄
hypercenter	C₄×#41	D₄₃
hypocenter	C₄₃	#2875
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

subgroup

G/H

center, Frattini

C₂×C₄

C₂³×D₄₃

commutator

C₂×C₄₃

C₂²×C₄²

Fitting

C₄×#41×C₄₃

C₂

socle

C₂²×C₄₃

C₂³×C₄

hypercenter

C₄×#41

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₄ ◁ C₄×#41

N	H ≅ G/N	type
2. #14582855	C₂	semidirect
3. C₄×#10621877	C₂	semidirect
4. C₂×#13063236	C₂	semidirect
6. #13063332	C₄	semidirect
28. #10621877	C₂×C₄	semidirect
29. C₂×C₄₃⋊C₈	C₂×C₄	semidirect
59. C₄₃	#2875	semidirect

H ≅ G/N

type

2. #14582855

C₂

semidirect

3. C₄×#10621877

C₂

semidirect

4. C₂×#13063236

C₂

semidirect

6. #13063332

C₄

semidirect

28. #10621877

C₂×C₄

semidirect

29. C₂×C₄₃⋊C₈

C₂×C₄

semidirect

59. C₄₃

#2875

semidirect

Subgroups — #19143023

Conjugacy classes of subgroups

Complements