Group #19145103 — subgroups

Subgroups — C₂×#14583304 #19145103

Order 5504.

424 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 213 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×#13063325	C₂	1	2	yes	maximal
2	#14583304	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13063259	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₈₆	—	2	2	no	—
6	#13063325	—	2	4	no	—
7	#13063325	C₂²	1	8	yes	—
8	C₂×C₄⋊Dic₄₃	—	2	2	no	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
10	#13063259	C₂²	1	16	yes	—
11	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₃	C₂²	1	4	yes	—
14	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
17	C₂²×Dic₄₃	—	2	4	no	—
18	C₂×Dic₈₆	—	2	8	no	—
19	C₂×Dic₈₆	—	4	8	no	—
20	C₂×C₈×C₄₃	Q₈	1	8	yes	complemented
21	C₂×C₈×C₄₃	C₂³	1	4	yes	—
22	C₄²×C₄₃	D₄	1	2	yes	—
23	C₄²×C₄₃	C₂³	1	2	yes	—
24	C₄⋊Dic₄₃	—	2	8	no	—
25	C₄⋊Dic₄₃	—	2	4	no	—
26	C₄⋊Dic₄₃	C₂³	1	8	yes	—
27	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄×C₄₃	D₈	1	4	yes	—
29	C₂×C₄×C₄₃	Q₁₆	1	4	yes	—
30	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
33	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
35	C₂×Dic₄₃	—	2	8	no	—
36	C₂×Dic₄₃	—	4	8	no	—
37	Dic₈₆	—	4	16	no	—
38	C₈×C₄₃	C₂×Q₈	1	8	yes	complemented
39	C₂²×C₄₃	C₄⋊Q₈	1	2	yes	—
40	C₂²×C₄₃	C₂×D₈	1	2	yes	—
41	C₂²×C₄₃	C₂×Q₁₆	1	2	yes	—
42	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
43	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
44	C₄×C₄₃	C₂×D₈	1	4	yes	—
45	C₄×C₄₃	C₂×Q₁₆	1	4	yes	—
46	C₄×C₄₃	C₂²×Q₈	1	2	yes	—
47	Dic₄₃	—	4	8	no	—
48	C₂×#500	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	#500	1	4	yes	complemented
50	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₄₃	C₂²×D₈	1	1	yes	characteristic
52	C₂×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
53	C₂×C₄⋊Q₈	—	43	2	no	—
54	#500	—	43	8	no	—
55	C₂×#107	—	43	4	no	—
56	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
57	C₄₃	C₂×#500	1	1	yes	characteristic, complemented, Sylow
58	C₂²×Q₈	—	86	2	no	—
59	C₂²×C₈	C₂×D₄₃	1	2	yes	—
60	C₄⋊Q₈	—	43	8	no	—
61	C₄⋊Q₈	—	86	4	no	—
62	C₂×C₄⋊C₄	—	43	4	no	—
63	C₂×C₄⋊C₄	—	86	2	no	—
64	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
65	#107	—	43	16	no	—
66	C₄×C₈	C₂×D₄₃	1	4	yes	—
67	C₂×Q₈	—	86	8	no	—
68	C₂×Q₈	—	172	8	no	—
69	C₂²×C₄	—	86	4	no	—
70	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
71	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
73	C₂×C₈	Dic₈₆	1	8	yes	complemented
74	C₂×C₈	C₂²×D₄₃	1	4	yes	—
75	C₄⋊C₄	—	43	8	no	—
76	C₄⋊C₄	—	86	4	no	—
77	C₄⋊C₄	—	86	8	no	—
78	C₄²	D₁₇₂	1	2	yes	—
79	C₄²	C₂²×D₄₃	1	2	yes	—
80	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
81	Q₈	—	172	16	no	—
82	C₂×C₄	—	86	8	no	—
83	C₂×C₄	—	172	8	no	—
84	C₂×C₄	D₃₄₄	1	4	yes	—
85	C₂×C₄	Dic₁₇₂	1	4	yes	—
86	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
87	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
89	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
90	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
91	C₈	C₂×Dic₈₆	1	8	yes	complemented
92	C₂²	#13063325	1	2	yes	—
93	C₂²	C₂×D₃₄₄	1	2	yes	—
94	C₂²	C₂×Dic₁₇₂	1	2	yes	—
95	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
96	C₄	—	172	8	no	—
97	C₄	#13063325	1	2	yes	—
98	C₄	C₂×D₃₄₄	1	4	yes	—
99	C₄	C₂×Dic₁₇₂	1	4	yes	—
100	C₄	C₂²×Dic₈₆	1	2	yes	—
101	C₂	#14583304	1	4	yes	direct product factor
102	C₂	C₂×#13063325	1	1	yes	characteristic
103	C₂	C₂²×D₃₄₄	1	1	yes	characteristic
104	C₂	C₂²×Dic₁₇₂	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063325

C₂

yes

maximal

#14583304

C₂

yes

maximal, direct product factor

C₂×#13063259

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

—

#13063325

—

#13063325

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063259

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×C₈×C₄₃

Q₈

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

Q₁₆

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

C₂×Q₈

yes

complemented

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₂²×C₄₃

C₂×D₈

yes

—

C₂²×C₄₃

C₂×Q₁₆

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

C₂×D₈

yes

—

C₄×C₄₃

C₂×Q₁₆

yes

—

C₄×C₄₃

C₂²×Q₈

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

C₂²×D₈

yes

characteristic

C₂×C₄₃

C₂²×Q₁₆

yes

characteristic

C₂×C₄⋊Q₈

—

#500

—

C₂×#107

—

C₂×C₄×C₈

D₄₃

yes

characteristic

C₄₃

C₂×#500

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×C₈

C₂×D₄₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#107

—

C₄×C₈

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

172

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

Dic₈₆

yes

complemented

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₁₇₂

yes

—

C₄²

C₂²×D₄₃

yes

—

C₂³

C₂×D₁₇₂

yes

characteristic

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

D₃₄₄

yes

—

C₂×C₄

Dic₁₇₂

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

C₂×Dic₈₆

yes

complemented

C₂²

#13063325

yes

—

C₂²

C₂×D₃₄₄

yes

—

C₂²

C₂×Dic₁₇₂

yes

—

C₂²

C₂²×D₁₇₂

yes

characteristic

C₄

—

172

—

C₄

#13063325

yes

—

C₄

C₂×D₃₄₄

yes

—

C₄

C₂×Dic₁₇₂

yes

—

100

C₄

C₂²×Dic₈₆

yes

—

101

C₂

#14583304

yes

direct product factor

102

C₂

C₂×#13063325

yes

characteristic

103

C₂

C₂²×D₃₄₄

yes

characteristic

104

C₂

C₂²×Dic₁₇₂

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	C₂×#500
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

C₂×#500

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14583304	C₂	direct (N × H)
20. C₂×C₈×C₄₃	Q₈	semidirect
38. C₈×C₄₃	C₂×Q₈	semidirect
49. C₂×C₄₃	#500	semidirect
57. C₄₃	C₂×#500	semidirect
73. C₂×C₈	Dic₈₆	semidirect
91. C₈	C₂×Dic₈₆	semidirect
101. C₂	#14583304	direct (N × H)

H ≅ G/N

type

2. #14583304

C₂

direct (N × H)

20. C₂×C₈×C₄₃

Q₈

semidirect

38. C₈×C₄₃

C₂×Q₈

semidirect

49. C₂×C₄₃

#500

semidirect

57. C₄₃

C₂×#500

semidirect

73. C₂×C₈

Dic₈₆

semidirect

91. C₈

C₂×Dic₈₆

semidirect

101. C₂

#14583304

direct (N × H)

Subgroups — C₂×#14583304 #19145103

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583304 #19145103

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583304 #19145103