Group #19135385 — subgroups

Subgroups — #19135385

Order 5504.

184 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 89 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	#14582947	C₂	1	2	yes	maximal
2	C₂×#13063261	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063261	C₂	1	1	yes	maximal, characteristic
4	#14582669	C₂	1	2	yes	maximal
5	C₄₃×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	2	yes	—
7	C₂×#10621877	C₂²	1	2	yes	—
8	#13063261	—	2	1	no	—
9	#13063261	—	2	1	no	—
10	#13063261	C₄	1	4	yes	complemented
11	#13063260	—	2	4	no	—
12	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	#117×C₄₃	C₂²	1	1	yes	characteristic
15	#97×C₄₃	—	2	1	no	—
16	C₄×C₈×C₄₃	—	2	1	no	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	M₁₆×C₄₃	—	2	1	no	—
19	M₁₆×C₄₃	D₄	1	2	yes	—
20	C₂×C₈×C₄₃	—	2	1	no	—
21	C₂×C₈×C₄₃	C₂×C₄	1	2	yes	—
22	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₈×C₄₃	Q₈	1	2	yes	—
25	C₄⋊C₄×C₄₃	—	2	1	no	—
26	C₂²⋊C₄×C₄₃	Q₈	1	2	yes	—
27	C₄²×C₄₃	—	2	1	no	—
28	#10621877	—	2	2	no	—
29	#10621877	—	2	2	no	—
30	#10621877	—	2	2	no	—
31	#10621877	C₂×C₄	1	4	yes	—
32	C₂×C₄₃⋊C₈	—	2	2	no	—
33	C₂×C₄₃⋊C₈	—	2	2	no	—
34	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₄₃	—	2	2	no	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
40	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
41	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
42	C₈×C₄₃	—	2	2	no	—
43	C₈×C₄₃	C₄⋊C₄	1	2	yes	—
44	C₈×C₄₃	C₄⋊C₄	1	2	yes	—
45	C₄₃⋊C₈	—	2	4	no	—
46	C₄₃⋊C₈	—	4	2	no	—
47	C₂²×C₄₃	—	4	1	no	—
48	C₂²×C₄₃	C₄×Q₈	1	1	yes	characteristic
49	C₂²×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₂²×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
51	C₄×C₄₃	—	4	2	no	—
52	C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
54	C₄×C₄₃	#121	1	1	yes	characteristic
55	C₄×C₄₃	#125	1	1	yes	characteristic
56	#1953	—	43	1	no	maximal, Sylow
57	C₂×C₄₃	—	2	1	no	—
58	C₂×C₄₃	—	2	1	no	—
59	C₂×C₄₃	—	2	1	no	—
60	C₂×C₄₃	#389	1	1	yes	characteristic
61	#430	—	43	2	no	—
62	C₂×#108	—	43	1	no	—
63	C₂×#108	—	43	1	no	—
64	#405	D₄₃	1	1	yes	characteristic
65	#344	—	43	2	no	—
66	C₄₃	#1953	1	1	yes	characteristic, complemented, Sylow
67	C₂×M₁₆	—	43	2	no	—
68	C₂×M₁₆	—	43	2	no	—
69	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
70	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
71	#117	C₂×D₄₃	1	1	yes	characteristic
72	#108	—	43	4	no	—
73	#108	—	86	4	no	—
74	#108	—	86	1	no	—
75	#108	—	86	1	no	—
76	#97	—	2	1	no	—
77	C₄×C₈	—	2	1	no	—
78	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
79	M₁₆	—	2	1	no	—
80	M₁₆	—	43	4	no	—
81	M₁₆	—	86	2	no	—
82	M₁₆	—	86	2	no	—
83	M₁₆	—	86	2	no	—
84	M₁₆	D₁₇₂	1	2	yes	—
85	C₂×C₈	—	2	1	no	—
86	C₂×C₈	—	86	2	no	—
87	C₂×C₈	—	86	2	no	—
88	C₂×C₈	Dic₈₆	1	2	yes	—
89	C₂×C₈	C₄×D₄₃	1	2	yes	—
90	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
91	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
92	C₄⋊C₄	—	2	1	no	—
93	C₂²⋊C₄	Dic₈₆	1	2	yes	—
94	C₄²	—	2	1	no	—
95	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
96	C₂×C₄	—	2	2	no	—
97	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
98	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
99	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
100	C₂×C₄	#10621898	1	1	yes	characteristic
101	C₂×C₄	#10621898	1	1	yes	characteristic
102	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
103	C₈	—	2	2	no	—
104	C₈	—	86	4	no	—
105	C₈	—	172	2	no	—
106	C₈	Dic₄₃⋊C₄	1	2	yes	—
107	C₈	Dic₄₃⋊C₄	1	2	yes	—
108	C₂²	—	4	1	no	—
109	C₂²	C₄×Dic₈₆	1	1	yes	characteristic
110	C₂²	#13063304	1	1	yes	characteristic
111	C₂²	#13063325	1	1	yes	characteristic
112	C₄	—	4	2	no	—
113	C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
114	C₄	C₄×D₁₇₂	1	1	yes	characteristic
115	C₄	#13063299	1	1	yes	characteristic
116	C₄	#13063317	1	1	yes	characteristic
117	C₂	—	2	1	no	—
118	C₂	—	2	1	no	—
119	C₂	—	2	1	no	—
120	C₂	#14582797	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582947

C₂

yes

maximal

C₂×#13063261

C₂

yes

maximal, characteristic

C₂×#13063261

C₂

yes

maximal, characteristic

#14582669

C₂

yes

maximal

C₄₃×#405

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

—

C₂×#10621877

C₂²

yes

—

#13063261

—

#13063261

—

#13063261

C₄

yes

complemented

#13063260

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₈×C₄₃

C₂²

yes

characteristic

#117×C₄₃

C₂²

yes

characteristic

#97×C₄₃

—

C₄×C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

M₁₆×C₄₃

—

M₁₆×C₄₃

D₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

Q₈

yes

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

Q₈

yes

—

C₄²×C₄₃

—

—

—

—

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

C₂×C₄×C₄₃

yes

C₂×C₄×C₄₃

yes

C₈×C₄₃

—

C₈×C₄₃

C₄⋊C₄

yes

—

C₈×C₄₃

C₄⋊C₄

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄×Q₈

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

characteristic

C₂²×C₄₃

C₄⋊Q₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₄₃

C₄×D₄

yes

C₄×C₄₃

yes

C₄×C₄₃

yes

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

D₄₃

yes

characteristic

#344

—

C₄₃

#1953

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²×C₈

C₂×D₄₃

yes

characteristic

#117

C₂×D₄₃

yes

—

—

—

—

—

C₄×C₈

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

D₁₇₂

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

Dic₈₆

yes

—

C₂×C₈

C₄×D₄₃

yes

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

Dic₈₆

yes

—

C₄²

—

C₂³

C₂×Dic₈₆

yes

characteristic

C₂×C₄

—

C₂×C₄

C₂×Dic₈₆

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

100

C₂×C₄

#10621898

yes

characteristic

101

C₂×C₄

#10621898

yes

characteristic

102

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

103

C₈

—

104

C₈

—

105

C₈

—

172

—

106

C₈

Dic₄₃⋊C₄

yes

—

107

C₈

Dic₄₃⋊C₄

yes

—

108

C₂²

—

109

C₂²

C₄×Dic₈₆

yes

characteristic

110

C₂²

#13063304

yes

characteristic

111

C₂²

#13063325

yes

characteristic

112

C₄

—

113

C₄

C₂×Dic₄₃⋊C₄

yes

characteristic

114

C₄

C₄×D₁₇₂

yes

characteristic

115

C₄

#13063299

yes

characteristic

116

C₄

#13063317

yes

characteristic

117

C₂

—

118

C₂

—

119

C₂

—

120

C₂

#14582797

yes

characteristic

	subgroup	G/H
center	C₄	#13063299
commutator	C₂×C₄×C₄₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#405	C₂
socle	C₂×C₄₃	#389
hypercenter	#405	D₄₃
hypocenter	C₄₃	#1953
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #405

subgroup

G/H

center

C₄

#13063299

commutator

C₂×C₄×C₄₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#405

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #405

N	H ≅ G/N	type
10. #13063261	C₄	semidirect
66. C₄₃	#1953	semidirect

H ≅ G/N

type

10. #13063261

C₄

semidirect

66. C₄₃

#1953

semidirect

Subgroups — #19135385

Conjugacy classes of subgroups

Complements