Group #19136367 — subgroups

Subgroups — #19136367

Order 5504.

144 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 81 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×#13063265	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063261	C₂	1	1	yes	maximal, characteristic
3	#14582721	C₂	1	4	yes	maximal, complemented
4	C₄₃×#427	C₂	1	1	yes	maximal, characteristic
5	C₂×#10621877	—	2	1	no	—
6	#13063265	C₄	1	2	yes	complemented
7	#13063265	C₂²	1	2	yes	—
8	C₂×C₄₃⋊C₁₆	C₄	1	2	yes	complemented
9	#13063261	—	2	1	no	—
10	#13063261	C₂²	1	2	yes	—
11	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	#117×C₄₃	—	2	1	no	—
13	#107×C₄₃	—	2	1	no	—
14	#106×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
20	C₂×C₈×C₄₃	Q₈	1	1	yes	characteristic
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₄₃	—	2	2	no	—
23	C₂²⋊C₄×C₄₃	—	4	1	no	—
24	C₄²×C₄₃	—	4	1	no	—
25	#10621877	—	2	2	no	—
26	#10621877	—	4	1	no	—
27	C₂×C₄₃⋊C₈	—	4	1	no	—
28	C₄₃⋊C₁₆	C₂×C₄	1	4	yes	—
29	C₂³×C₄₃	SD₁₆	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	4	2	no	—
31	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
35	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
37	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
38	C₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
40	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
41	C₄₃⋊C₈	—	4	2	no	—
42	C₂²×C₄₃	—	4	1	no	—
43	C₂²×C₄₃	#106	1	1	yes	characteristic
44	C₂²×C₄₃	#106	1	1	yes	characteristic
45	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
46	C₄×C₄₃	—	8	2	no	—
47	C₄×C₄₃	#106	1	1	yes	characteristic
48	C₄×C₄₃	#106	1	1	yes	characteristic
49	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
51	#2155	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	—	2	1	no	—
53	C₂×C₄₃	—	2	1	no	—
54	C₂×C₄₃	—	2	1	no	—
55	C₂×C₄₃	C₂×#106	1	1	yes	characteristic
56	C₂×M₃₂	—	43	1	no	—
57	C₂×#108	—	43	1	no	—
58	#427	D₄₃	1	1	yes	characteristic
59	#365	—	43	4	no	—
60	C₄₃	#2155	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	86	1	no	—
62	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
63	#117	—	2	1	no	—
64	M₃₂	—	43	2	no	—
65	M₃₂	—	43	2	no	—
66	C₂×C₁₆	—	43	2	no	—
67	#108	—	43	2	no	—
68	#108	—	86	1	no	—
69	#107	—	2	1	no	—
70	#106	C₂×D₄₃	1	2	yes	—
71	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
72	M₁₆	—	86	2	no	—
73	M₁₆	—	172	1	no	—
74	C₂×C₈	—	172	1	no	—
75	C₂×C₈	Dic₈₆	1	1	yes	characteristic
76	C₂×C₈	Dic₈₆	1	1	yes	characteristic
77	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
78	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
79	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
80	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
81	C₄⋊C₄	—	2	2	no	—
82	C₂²⋊C₄	—	4	1	no	—
83	C₄²	—	4	1	no	—
84	C₁₆	—	43	4	no	—
85	C₂³	#10621883	1	1	yes	characteristic
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
88	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
89	C₂×C₄	#10621883	1	1	yes	characteristic
90	C₂×C₄	#10621884	1	1	yes	characteristic
91	C₂×C₄	#10621884	1	1	yes	characteristic
92	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
93	C₈	—	172	2	no	—
94	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
95	C₈	Dic₄₃⋊C₄	1	1	yes	characteristic
96	C₈	C₂×Dic₈₆	1	1	yes	characteristic
97	C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
98	C₂²	—	4	1	no	—
99	C₂²	#13063256	1	1	yes	characteristic
100	C₂²	#13063256	1	1	yes	characteristic
101	C₂²	C₂×#10621883	1	1	yes	characteristic
102	C₄	—	8	2	no	—
103	C₄	#13063256	1	1	yes	characteristic
104	C₄	#13063256	1	1	yes	characteristic
105	C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
106	C₄	C₂×#10621884	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	2	1	no	—
109	C₂	—	2	1	no	—
110	C₂	C₂×#13063256	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063265

C₂

yes

maximal, characteristic

C₂×#13063261

C₂

yes

maximal, characteristic

#14582721

C₂

yes

maximal, complemented

C₄₃×#427

C₂

yes

maximal, characteristic

C₂×#10621877

—

#13063265

C₄

yes

complemented

#13063265

C₂²

yes

—

C₂×C₄₃⋊C₁₆

C₄

yes

complemented

#13063261

—

#13063261

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#117×C₄₃

—

#107×C₄₃

—

#106×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₄²×C₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₄₃⋊C₁₆

C₂×C₄

yes

—

C₂³×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₈×C₄₃

C₄⋊C₄

yes

characteristic

C₈×C₄₃

C₂²×C₄

yes

characteristic

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₂×SD₁₆

yes

characteristic

#2155

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

C₂×#106

yes

characteristic

C₂×M₃₂

—

C₂×#108

—

#427

D₄₃

yes

characteristic

#365

—

C₄₃

#2155

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#117

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

—

—

—

C₂×D₄₃

yes

—

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

Dic₈₆

yes

characteristic

C₂×C₈

Dic₈₆

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₁₆

—

C₂³

#10621883

yes

characteristic

C₂×C₄

—

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

—

172

—

C₈

Dic₄₃⋊C₄

yes

characteristic

C₈

Dic₄₃⋊C₄

yes

characteristic

C₈

C₂×Dic₈₆

yes

characteristic

C₈

C₂×C₄×D₄₃

yes

characteristic

C₂²

—

C₂²

#13063256

yes

characteristic

100

C₂²

#13063256

yes

characteristic

101

C₂²

C₂×#10621883

yes

characteristic

102

C₄

—

103

C₄

#13063256

yes

characteristic

104

C₄

#13063256

yes

characteristic

105

C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

106

C₄

C₂×#10621884

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

110

C₂

C₂×#13063256

yes

characteristic

	subgroup	G/H
center	C₄	#13063256
commutator	C₈×C₄₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#427	C₂
socle	C₂×C₄₃	C₂×#106
hypercenter	#427	D₄₃
hypocenter	C₄₃	#2155
LCS	G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

subgroup

G/H

center

C₄

#13063256

commutator

C₈×C₄₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#427

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

N	H ≅ G/N	type
3. #14582721	C₂	semidirect
6. #13063265	C₄	semidirect
8. C₂×C₄₃⋊C₁₆	C₄	semidirect
60. C₄₃	#2155	semidirect

H ≅ G/N

type

3. #14582721

C₂

semidirect

6. #13063265

C₄

semidirect

8. C₂×C₄₃⋊C₁₆

C₄

semidirect

60. C₄₃

#2155

semidirect

Subgroups — #19136367

Conjugacy classes of subgroups

Complements