Group #19145099 — subgroups

Subgroups — C₂×#14583301 #19145099

Order 5504.

360 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13063317	C₂	1	2	yes	maximal
2	#14583301	C₂	1	8	yes	maximal, direct product factor
3	C₂×#13063259	C₂	1	2	yes	maximal
4	C₂×#13063257	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	#13063317	—	2	4	no	—
7	#13063317	C₂²	1	8	yes	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
9	C₂×Dic₄₃⋊C₄	—	2	4	no	—
10	#13063259	C₂²	1	8	yes	—
11	#13063257	C₂²	1	8	yes	—
12	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂²	1	4	yes	—
16	C₂²×C₄×C₄₃	D₄	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×Dic₄₃	—	2	4	no	—
19	C₂×C₈×C₄₃	Q₈	1	4	yes	—
20	C₂×C₈×C₄₃	Q₈	1	4	yes	—
21	C₂×C₈×C₄₃	C₂³	1	2	yes	—
22	C₂×C₈×C₄₃	C₂³	1	2	yes	—
23	C₄²×C₄₃	D₄	1	2	yes	—
24	C₄²×C₄₃	C₂³	1	2	yes	—
25	C₄⋊Dic₄₃	—	2	4	no	—
26	C₄⋊Dic₄₃	C₂³	1	8	yes	—
27	Dic₄₃⋊C₄	—	2	16	no	—
28	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	4	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
33	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
35	C₂×Dic₄₃	—	2	8	no	—
36	C₂×Dic₄₃	—	4	8	no	—
37	C₈×C₄₃	C₂×Q₈	1	4	yes	—
38	C₈×C₄₃	C₂×Q₈	1	4	yes	—
39	C₂²×C₄₃	C₄⋊Q₈	1	2	yes	—
40	C₂²×C₄₃	#135	1	4	yes	—
41	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
42	C₄×C₄₃	—	2	4	no	—
43	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
44	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
45	C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
46	Dic₄₃	—	4	8	no	—
47	C₂×#499	—	43	1	no	maximal, Sylow
48	C₂×C₄₃	#499	1	4	yes	complemented
49	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₄₃	C₂×#135	1	2	yes	—
51	C₂×#125	—	43	2	no	—
52	#499	—	43	8	no	—
53	C₂×#107	—	43	2	no	—
54	C₂×#106	—	43	2	no	—
55	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
56	C₄₃	C₂×#499	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
58	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
59	#125	—	43	8	no	—
60	#125	—	86	4	no	—
61	C₂×C₄⋊C₄	—	43	4	no	—
62	C₂×C₄⋊C₄	—	86	4	no	—
63	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
64	#107	—	43	8	no	—
65	#106	—	43	8	no	—
66	C₄×C₈	C₂×D₄₃	1	4	yes	—
67	C₂²×C₄	—	86	4	no	—
68	C₂²×C₄	D₁₇₂	1	2	yes	—
69	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
70	C₂×C₈	Dic₈₆	1	4	yes	—
71	C₂×C₈	Dic₈₆	1	4	yes	—
72	C₂×C₈	C₂²×D₄₃	1	2	yes	—
73	C₂×C₈	C₂²×D₄₃	1	2	yes	—
74	C₄⋊C₄	—	43	8	no	—
75	C₄⋊C₄	—	86	4	no	—
76	C₄⋊C₄	—	86	16	no	—
77	C₄²	D₁₇₂	1	2	yes	—
78	C₄²	C₂²×D₄₃	1	2	yes	—
79	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
80	C₂×C₄	—	2	4	no	—
81	C₂×C₄	—	86	8	no	—
82	C₂×C₄	—	172	8	no	—
83	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
84	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
85	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
86	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
87	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
88	C₈	C₂×Dic₈₆	1	4	yes	—
89	C₈	C₂×Dic₈₆	1	4	yes	—
90	C₂²	#13063325	1	2	yes	—
91	C₂²	#13063347	1	4	yes	—
92	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
93	C₄	—	2	4	no	—
94	C₄	—	172	8	no	—
95	C₄	#13063325	1	2	yes	—
96	C₄	C₂²×Dic₈₆	1	1	yes	characteristic
97	C₄	C₂²×Dic₈₆	1	1	yes	characteristic
98	C₂	#14583301	1	4	yes	direct product factor
99	C₂	C₂×#13063325	1	1	yes	characteristic
100	C₂	C₂×#13063347	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063317

C₂

yes

maximal

#14583301

C₂

yes

maximal, direct product factor

C₂×#13063259

C₂

yes

maximal

C₂×#13063257

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

#13063317

—

#13063317

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

#13063259

C₂²

yes

—

#13063257

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

Q₈

yes

—

C₂×C₈×C₄₃

Q₈

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

C₂×Q₈

yes

—

C₈×C₄₃

C₂×Q₈

yes

—

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₂²×C₄₃

#135

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

C₂²×Q₈

yes

characteristic

C₄×C₄₃

C₂²×Q₈

yes

characteristic

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

C₂×#135

yes

—

—

—

—

—

C₂×C₄×C₈

D₄₃

yes

characteristic

C₄₃

C₂×#499

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#107

—

#106

—

C₄×C₈

C₂×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

C₂²×D₄₃

yes

—

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₁₇₂

yes

—

C₄²

C₂²×D₄₃

yes

—

C₂³

C₂×D₁₇₂

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

C₂×Dic₈₆

yes

—

C₈

C₂×Dic₈₆

yes

—

C₂²

#13063325

yes

—

C₂²

#13063347

yes

—

C₂²

C₂²×D₁₇₂

yes

characteristic

C₄

—

C₄

—

172

—

C₄

#13063325

yes

—

C₄

C₂²×Dic₈₆

yes

characteristic

C₄

C₂²×Dic₈₆

yes

characteristic

C₂

#14583301

yes

direct product factor

C₂

C₂×#13063325

yes

characteristic

100

C₂

C₂×#13063347

yes

—

	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×#499
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×#499

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14583301	C₂	direct (N × H)
48. C₂×C₄₃	#499	semidirect
56. C₄₃	C₂×#499	semidirect
98. C₂	#14583301	direct (N × H)

H ≅ G/N

type

2. #14583301

C₂

direct (N × H)

48. C₂×C₄₃

#499

semidirect

56. C₄₃

C₂×#499

semidirect

98. C₂

#14583301

direct (N × H)

Subgroups — C₂×#14583301 #19145099

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583301 #19145099

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583301 #19145099