Group #19136102 — subgroups

Subgroups — #19136102

Order 5504.

176 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 71 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	#14582941	C₂	1	2	yes	maximal
2	C₂×#13063259	C₂	1	1	yes	maximal, characteristic
3	#14582925	C₂	1	1	yes	maximal, characteristic
4	#14582667	C₂	1	2	yes	maximal
5	C₄₃×#341	C₂	1	1	yes	maximal, characteristic
6	C₂×#10621877	C₂²	1	1	yes	characteristic
7	#13063284	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
9	#13063259	—	2	2	no	—
10	#13063259	—	2	2	no	—
11	#13063257	—	2	2	no	—
12	Dic₄₃⋊C₈	—	2	2	no	—
13	C₂×M₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
16	C₂²×Dic₄₃	—	2	2	no	—
17	M₁₆×C₄₃	—	2	2	no	—
18	M₁₆×C₄₃	Q₈	1	4	yes	—
19	C₂×C₈×C₄₃	—	2	2	no	—
20	C₂×C₈×C₄₃	—	2	2	no	—
21	C₂×C₈×C₄₃	D₄	1	2	yes	—
22	C₂²⋊Dic₄₃	—	2	1	no	—
23	C₄⋊Dic₄₃	—	2	2	no	—
24	C₄⋊Dic₄₃	—	2	2	no	—
25	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
26	C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
27	C₄×Dic₄₃	—	2	1	no	—
28	#10621877	—	2	2	no	—
29	C₂×C₄₃⋊C₈	—	2	1	no	—
30	C₂³×C₄₃	#41	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
34	C₂×C₄×C₄₃	#41	1	2	yes	—
35	C₂×Dic₄₃	—	2	1	no	—
36	C₂×Dic₄₃	—	2	1	no	—
37	C₂×Dic₄₃	—	4	2	no	—
38	C₂×Dic₄₃	—	8	2	no	—
39	C₈×C₄₃	—	2	4	no	—
40	C₈×C₄₃	—	2	2	no	—
41	C₄₃⋊C₈	—	4	1	no	—
42	C₂²×C₄₃	—	2	1	no	—
43	C₂²×C₄₃	—	2	1	no	—
44	C₂²×C₄₃	#121	1	1	yes	characteristic
45	C₂²×C₄₃	#125	1	2	yes	—
46	C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₄₃	#123	1	1	yes	characteristic
48	C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
49	Dic₄₃	—	4	1	no	—
50	Dic₄₃	—	4	1	no	—
51	Dic₄₃	—	8	2	no	—
52	#2089	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	—	2	2	no	—
54	C₂×C₄₃	#398	1	1	yes	characteristic
55	C₂×C₄₃	#472	1	1	yes	characteristic
56	C₂×C₄₃	#473	1	1	yes	characteristic
57	#428	—	43	2	no	—
58	C₂×#107	—	43	1	no	—
59	#424	—	43	1	no	—
60	#343	—	43	2	no	—
61	#341	D₄₃	1	1	yes	characteristic
62	C₄₃	#2089	1	1	yes	characteristic, complemented, Sylow
63	C₂×M₁₆	—	43	1	no	—
64	C₂×M₁₆	C₂×D₄₃	1	2	yes	—
65	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
66	#117	—	43	1	no	—
67	C₂×C₄⋊C₄	—	43	2	no	—
68	#107	—	86	2	no	—
69	#107	—	86	2	no	—
70	#106	—	86	2	no	—
71	C₄⋊C₈	—	86	2	no	—
72	C₂²×C₄	—	86	2	no	—
73	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	86	2	no	—
76	M₁₆	Dic₈₆	1	4	yes	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	2	no	—
79	C₂×C₈	—	86	1	no	—
80	C₂×C₈	D₁₇₂	1	2	yes	—
81	C₄⋊C₄	—	43	1	no	—
82	C₄⋊C₄	—	43	1	no	—
83	C₄⋊C₄	—	86	2	no	—
84	C₄⋊C₄	—	86	2	no	—
85	C₂²⋊C₄	—	86	1	no	—
86	C₄²	—	86	1	no	—
87	C₂³	#10621902	1	1	yes	characteristic
88	C₂×C₄	—	86	1	no	—
89	C₂×C₄	—	86	1	no	—
90	C₂×C₄	—	344	2	no	—
91	C₂×C₄	—	172	2	no	—
92	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
93	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
94	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
95	C₂×C₄	#10621900	1	2	yes	—
96	C₈	—	2	4	no	—
97	C₈	—	2	2	no	—
98	C₈	—	172	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#13063300	1	1	yes	characteristic
102	C₂²	#13063316	1	2	yes	—
103	C₄	—	344	2	no	—
104	C₄	—	172	1	no	—
105	C₄	—	172	1	no	—
106	C₄	#13063302	1	2	yes	—
107	C₄	#13063309	1	1	yes	characteristic
108	C₄	#13063325	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#14582831	1	1	yes	characteristic
111	C₂	#14583170	1	1	yes	characteristic
112	C₂	#14583175	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582941

C₂

yes

maximal

C₂×#13063259

C₂

yes

maximal, characteristic

#14582925

C₂

yes

maximal, characteristic

#14582667

C₂

yes

maximal

C₄₃×#341

C₂

yes

maximal, characteristic

C₂×#10621877

C₂²

yes

characteristic

#13063284

C₂²

yes

characteristic

C₂×C₄⋊Dic₄₃

C₂²

yes

—

#13063259

—

#13063259

—

#13063257

—

Dic₄₃⋊C₈

—

C₂×M₁₆×C₄₃

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

M₁₆×C₄₃

—

M₁₆×C₄₃

Q₈

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

—

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

D₄

yes

characteristic

C₄⋊Dic₄₃

D₄

yes

characteristic

C₄×Dic₄₃

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

#41

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

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#121

yes

characteristic

C₂²×C₄₃

#125

yes

—

C₄×C₄₃

C₂²⋊Q₈

yes

—

C₄×C₄₃

#123

yes

characteristic

C₄×C₄₃

C₄⋊Q₈

yes

characteristic

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

#2089

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2089

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

#117

—

C₂×C₄⋊C₄

—

#107

—

#107

—

#106

—

C₄⋊C₈

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

Dic₈₆

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

#10621902

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

344

—

C₂×C₄

—

172

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

D₄×D₄₃

yes

characteristic

C₂×C₄

#10621900

yes

—

C₈

—

C₈

—

C₈

—

172

—

C₂²

—

100

C₂²

—

101

C₂²

#13063300

yes

characteristic

102

C₂²

#13063316

yes

—

103

C₄

—

344

—

104

C₄

—

172

—

105

C₄

—

172

—

106

C₄

#13063302

yes

—

107

C₄

#13063309

yes

characteristic

108

C₄

#13063325

yes

characteristic

109

C₂

—

110

C₂

#14582831

yes

characteristic

111

C₂

#14583170

yes

characteristic

112

C₂

#14583175

yes

characteristic

	subgroup	G/H
center	C₂²	#13063300
commutator	C₂²×C₄×C₄₃	C₂³
Frattini	C₂²×C₄	C₂²×D₄₃
Fitting	C₄₃×#341	C₂
socle	C₂²×C₄₃	#121
hypercenter	#341	D₄₃
hypocenter	C₄₃	#2089
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

subgroup

G/H

center

C₂²

#13063300

commutator

C₂²×C₄×C₄₃

C₂³

Frattini

C₂²×C₄

C₂²×D₄₃

Fitting

C₄₃×#341

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #341

N	H ≅ G/N	type
62. C₄₃	#2089	semidirect

H ≅ G/N

type

62. C₄₃

#2089

semidirect

Subgroups — #19136102

Conjugacy classes of subgroups

Complements