Group #19136756 — subgroups

Subgroups — #19136756

Order 5504.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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	C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
2	#14582726	C₂	1	1	yes	maximal, characteristic
3	#14582724	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₄₃⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
5	#14582702	C₂	1	1	yes	maximal, characteristic
6	#14582702	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#499	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
9	C₄×Dic₈₆	—	2	1	no	—
10	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
12	#13063259	C₂²	1	1	yes	characteristic
13	#13063250	—	2	1	no	—
14	#125×C₄₃	—	2	1	no	—
15	#107×C₄₃	C₂²	1	1	yes	characteristic
16	#107×C₄₃	C₂²	1	1	yes	characteristic
17	#106×C₄₃	—	2	1	no	—
18	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×Dic₈₆	—	2	1	no	—
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₄⋊C₄×C₄₃	—	2	1	no	—
24	C₄⋊C₄×C₄₃	—	4	1	no	—
25	C₄⋊C₄×C₄₃	—	4	1	no	—
26	C₄²×C₄₃	D₄	1	1	yes	characteristic
27	C₄⋊Dic₄₃	—	2	1	no	—
28	Dic₄₃⋊C₄	—	4	1	no	—
29	C₄×Dic₄₃	—	4	1	no	—
30	Dic₁₇₂	—	2	1	no	—
31	Dic₁₇₂	Q₈	1	2	yes	—
32	C₄₃⋊C₁₆	—	2	1	no	—
33	C₄₃⋊C₁₆	—	2	1	no	—
34	C₂×C₄×C₄₃	—	4	1	no	—
35	C₂×C₄×C₄₃	—	4	1	no	—
36	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
37	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₂×Dic₄₃	—	4	1	no	—
40	C₂×Dic₄₃	—	4	1	no	—
41	Dic₈₆	—	2	2	no	—
42	Dic₈₆	—	4	1	no	—
43	C₈×C₄₃	—	2	1	no	—
44	C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
45	C₈×C₄₃	#41	1	1	yes	characteristic
46	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	—	8	1	no	—
50	C₄×C₄₃	—	8	1	no	—
51	C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
52	C₄×C₄₃	#137	1	1	yes	characteristic
53	Dic₄₃	—	4	2	no	—
54	Dic₄₃	—	8	1	no	—
55	#2229	—	43	1	no	maximal, Sylow
56	C₂×C₄₃	#474	1	1	yes	characteristic
57	C₂×C₄₃	#508	1	1	yes	characteristic
58	C₂×C₄₃	#510	1	1	yes	characteristic
59	#499	D₄₃	1	1	yes	characteristic
60	C₄×Q₁₆	—	43	1	no	—
61	#367	—	43	1	no	—
62	#366	—	43	1	no	—
63	C₄⋊C₁₆	—	43	1	no	—
64	#358	—	43	1	no	—
65	#358	—	43	1	no	—
66	C₄₃	#2229	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₁₆	—	43	1	no	—
68	#125	—	2	1	no	—
69	C₄×Q₈	—	86	1	no	—
70	C₂×C₁₆	—	43	1	no	—
71	C₂×C₁₆	—	43	1	no	—
72	#107	—	43	1	no	—
73	#107	C₂×D₄₃	1	1	yes	characteristic
74	#107	C₂×D₄₃	1	1	yes	characteristic
75	#106	—	2	1	no	—
76	#103	—	86	1	no	—
77	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
78	C₂×Q₈	—	86	1	no	—
79	Q₁₆	—	43	2	no	—
80	Q₁₆	—	86	1	no	—
81	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
82	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	2	1	no	—
85	C₄⋊C₄	—	4	1	no	—
86	C₄⋊C₄	—	4	1	no	—
87	C₄⋊C₄	—	86	1	no	—
88	C₄⋊C₄	—	172	1	no	—
89	C₄²	—	172	1	no	—
90	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
91	C₁₆	—	86	1	no	—
92	C₁₆	—	86	1	no	—
93	Q₈	—	86	2	no	—
94	Q₈	—	172	1	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	172	1	no	—
98	C₂×C₄	—	172	1	no	—
99	C₂×C₄	#10621882	1	1	yes	characteristic
100	C₂×C₄	#10621882	1	1	yes	characteristic
101	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
102	C₈	—	2	1	no	—
103	C₈	Q₈×D₄₃	1	1	yes	characteristic
104	C₈	#10621902	1	1	yes	characteristic
105	C₂²	C₂×#10621882	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	8	1	no	—
109	C₄	—	8	1	no	—
110	C₄	—	344	1	no	—
111	C₄	—	172	2	no	—
112	C₄	#13063301	1	1	yes	characteristic
113	C₄	#13063356	1	1	yes	characteristic
114	C₂	#14583176	1	1	yes	characteristic
115	C₂	#14583329	1	1	yes	characteristic
116	C₂	#14583339	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×Dic₁₇₂

C₂

yes

maximal, characteristic

#14582726

C₂

yes

maximal, characteristic

#14582724

C₂

yes

maximal, characteristic

C₄⋊(C₄₃⋊C₁₆)

C₂

yes

maximal, characteristic

#14582702

C₂

yes

maximal, characteristic

#14582702

C₂

yes

maximal, characteristic

C₄₃×#499

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

characteristic

C₄×Dic₈₆

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063259

C₂²

yes

characteristic

#13063250

—

#125×C₄₃

—

#107×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

#106×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

Dic₁₇₂

—

Dic₁₇₂

Q₈

yes

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×Q₈

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₂²⋊Q₈

yes

characteristic

C₄×C₄₃

#137

yes

characteristic

Dic₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

characteristic

C₄×Q₁₆

—

#367

—

#366

—

C₄⋊C₁₆

—

#358

—

#358

—

C₄₃

#2229

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

#125

—

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₄₃

yes

characteristic

#107

C₂×D₄₃

yes

characteristic

#106

—

#103

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄²

—

172

—

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

Q₈

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#10621882

yes

characteristic

100

C₂×C₄

#10621882

yes

characteristic

101

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

102

C₈

—

103

C₈

Q₈×D₄₃

yes

characteristic

104

C₈

#10621902

yes

characteristic

105

C₂²

C₂×#10621882

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

344

—

111

C₄

—

172

—

112

C₄

#13063301

yes

characteristic

113

C₄

#13063356

yes

characteristic

114

C₂

#14583176

yes

characteristic

115

C₂

#14583329

yes

characteristic

116

C₂

#14583339

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#499	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#499	D₄₃
hypocenter	C₄₃	#2229
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#499

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

N	H ≅ G/N	type
66. C₄₃	#2229	semidirect

H ≅ G/N

type

66. C₄₃

#2229

semidirect

Subgroups — #19136756

Conjugacy classes of subgroups

Complements