Group #19136922 — subgroups

Subgroups — C₂×#14582745 #19136922

Order 5504.

840 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 469 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	C₂²×C₄×Dic₄₃	C₂	1	2	yes	maximal
2	#14582745	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄₃⋊#95	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₃	C₂²	1	4	yes	—
6	C₂×C₄×Dic₄₃	C₄	1	16	yes	complemented
7	C₂×C₄×Dic₄₃	C₂²	1	8	yes	—
8	C₄₃⋊#95	C₂²	1	16	yes	—
9	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
10	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₃	C₄	1	8	yes	complemented
12	C₂×C₄²×C₄₃	C₂²	1	4	yes	—
13	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	—	2	8	no	—
15	C₂²×C₄×C₄₃	C₂×C₄	1	8	yes	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	8	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
20	C₂²×Dic₄₃	—	2	16	no	—
21	C₂²×Dic₄₃	C₂×C₄	1	16	yes	—
22	C₂²×Dic₄₃	C₂³	1	8	yes	—
23	C₄²×C₄₃	C₂×C₄	1	16	yes	complemented
24	C₄×Dic₄₃	C₂×C₄	1	32	yes	complemented
25	C₂³×C₄₃	C₂²×C₄	1	4	yes	—
26	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
27	C₂³×C₄₃	#41	1	8	yes	—
28	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	16	no	—
30	C₂×C₄×C₄₃	—	2	8	no	—
31	C₂×C₄×C₄₃	C₄²	1	16	yes	—
32	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
33	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
34	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
35	C₂×Dic₄₃	—	2	32	no	—
36	C₂×Dic₄₃	—	2	16	no	—
37	C₂×Dic₄₃	C₂²×C₄	1	16	yes	—
38	C₂²×C₄₃	C₂×C₄²	1	4	yes	—
39	C₂²×C₄₃	#117	1	16	yes	—
40	C₂²×C₄₃	#117	1	8	yes	—
41	C₂²×C₄₃	C₂³×C₄	1	2	yes	—
42	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
43	C₂²×C₄₃	C₂×#41	1	4	yes	—
44	C₄×C₄₃	—	2	8	no	—
45	C₄×C₄₃	C₂×C₄²	1	8	yes	—
46	Dic₄₃	—	2	16	no	—
47	C₂×#376	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	#376	1	8	yes	complemented
49	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
50	C₂×C₄₃	C₂×#117	1	4	yes	—
51	C₂×C₄₃	C₂×#117	1	2	yes	—
52	C₂²×C₄²	—	43	2	no	—
53	C₂²×C₄²	D₄₃	1	1	yes	characteristic
54	#376	—	43	8	no	—
55	C₂×#95	—	43	4	no	—
56	C₄₃	C₂×#376	1	1	yes	characteristic, complemented, Sylow
57	C₂³×C₄	—	43	4	no	—
58	C₂³×C₄	C₂×D₄₃	1	2	yes	—
59	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
60	C₂×C₄²	—	43	8	no	—
61	C₂×C₄²	—	43	16	no	—
62	C₂×C₄²	Dic₄₃	1	8	yes	complemented
63	C₂×C₄²	C₂×D₄₃	1	4	yes	—
64	#95	—	43	16	no	—
65	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
66	C₂²×C₄	—	2	8	no	—
67	C₂²×C₄	—	43	16	no	—
68	C₂²×C₄	—	43	8	no	—
69	C₂²×C₄	—	86	16	no	—
70	C₂²×C₄	C₄×D₄₃	1	8	yes	—
71	C₂²×C₄	C₂×Dic₄₃	1	8	yes	—
72	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
73	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
74	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
75	C₄²	—	43	32	no	—
76	C₄²	C₂×Dic₄₃	1	16	yes	complemented
77	C₂³	C₂×C₄×D₄₃	1	4	yes	—
78	C₂³	#10621898	1	8	yes	—
79	C₂³	C₂²×Dic₄₃	1	2	yes	—
80	C₂³	C₂³×D₄₃	1	1	yes	characteristic
81	C₂×C₄	—	2	16	no	—
82	C₂×C₄	—	2	8	no	—
83	C₂×C₄	—	43	16	no	—
84	C₂×C₄	—	86	32	no	—
85	C₂×C₄	—	86	16	no	—
86	C₂×C₄	C₄×Dic₄₃	1	16	yes	—
87	C₂×C₄	C₂×C₄×D₄₃	1	8	yes	—
88	C₂×C₄	C₂²×Dic₄₃	1	8	yes	—
89	C₂×C₄	C₂²×Dic₄₃	1	4	yes	—
90	C₂²	C₂×C₄×Dic₄₃	1	4	yes	—
91	C₂²	#13063282	1	16	yes	—
92	C₂²	#13063284	1	8	yes	—
93	C₂²	C₂²×C₄×D₄₃	1	2	yes	—
94	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
95	C₂²	C₂×#10621898	1	4	yes	—
96	C₄	—	2	8	no	—
97	C₄	—	86	16	no	—
98	C₄	C₂×C₄×Dic₄₃	1	8	yes	—
99	C₂	#14582745	1	8	yes	direct product factor
100	C₂	C₂²×C₄×Dic₄₃	1	1	yes	characteristic
101	C₂	C₂×#13063282	1	4	yes	—
102	C₂	C₂×#13063284	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×Dic₄₃

C₂

yes

maximal

#14582745

C₂

yes

maximal, direct product factor

C₂×C₄₃⋊#95

C₂

yes

maximal

C₂²×C₄²×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₄

yes

complemented

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₄

yes

complemented

C₂×C₄²×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂×C₄

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄²×C₄₃

C₂×C₄

yes

complemented

C₄×Dic₄₃

C₂×C₄

yes

complemented

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂²×C₄₃

C₂×C₄²

yes

—

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

C₂³×C₄

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂²×C₄²

yes

characteristic

C₂×C₄₃

C₂×#117

yes

—

C₂×C₄₃

C₂×#117

yes

—

C₂²×C₄²

—

C₂²×C₄²

D₄₃

yes

characteristic

#376

—

C₂×#95

—

C₄₃

C₂×#376

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

Dic₄₃

yes

complemented

C₂×C₄²

C₂×D₄₃

yes

—

#95

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄²

—

C₄²

C₂×Dic₄₃

yes

complemented

C₂³

C₂×C₄×D₄₃

yes

—

C₂³

#10621898

yes

—

C₂³

C₂²×Dic₄₃

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂²

C₂×C₄×Dic₄₃

yes

—

C₂²

#13063282

yes

—

C₂²

#13063284

yes

—

C₂²

C₂²×C₄×D₄₃

yes

—

C₂²

C₂³×Dic₄₃

yes

characteristic

C₂²

C₂×#10621898

yes

—

C₄

—

C₄

—

C₄

C₂×C₄×Dic₄₃

yes

—

C₂

#14582745

yes

direct product factor

100

C₂

C₂²×C₄×Dic₄₃

yes

characteristic

101

C₂

C₂×#13063282

yes

—

102

C₂

C₂×#13063284

yes

—

	subgroup	G/H
center	C₂³×C₄	C₂×D₄₃
commutator	C₂×C₄₃	C₂²×C₄²
Frattini	C₂³	C₂³×D₄₃
Fitting	C₂²×C₄²×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂³
hypercenter	C₂²×C₄²	D₄₃
hypocenter	C₄₃	C₂×#376
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

subgroup

G/H

center

C₂³×C₄

C₂×D₄₃

commutator

C₂×C₄₃

C₂²×C₄²

Frattini

C₂³

C₂³×D₄₃

Fitting

C₂²×C₄²×C₄₃

C₂

socle

C₂⁴×C₄₃

C₂³

hypercenter

C₂²×C₄²

D₄₃

C₄₃

G ▷ C₂×C₄₃ ▷ C₄₃

C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

N	H ≅ G/N	type
2. #14582745	C₂	direct (N × H)
6. C₂×C₄×Dic₄₃	C₄	semidirect
11. C₂×C₄²×C₄₃	C₄	semidirect
23. C₄²×C₄₃	C₂×C₄	semidirect
24. C₄×Dic₄₃	C₂×C₄	semidirect
48. C₂×C₄₃	#376	semidirect
56. C₄₃	C₂×#376	semidirect
62. C₂×C₄²	Dic₄₃	semidirect
76. C₄²	C₂×Dic₄₃	semidirect
99. C₂	#14582745	direct (N × H)

H ≅ G/N

type

2. #14582745

C₂

direct (N × H)

6. C₂×C₄×Dic₄₃

C₄

semidirect

11. C₂×C₄²×C₄₃

C₄

semidirect

23. C₄²×C₄₃

C₂×C₄

semidirect

24. C₄×Dic₄₃

C₂×C₄

semidirect

48. C₂×C₄₃

#376

semidirect

56. C₄₃

C₂×#376

semidirect

62. C₂×C₄²

Dic₄₃

semidirect

76. C₄²

C₂×Dic₄₃

semidirect

99. C₂

#14582745

direct (N × H)

Subgroups — C₂×#14582745 #19136922

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14582745 #19136922

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582745 #19136922