Group #19132540 — subgroups

Subgroups — #19132540

Order 5504.

134 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 37 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	#14582768	C₂	1	1	yes	maximal, characteristic
2	#14582625	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#324	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
5	C₂×Dic₄₃⋊C₄	—	2	1	no	—
6	C₂×Dic₄₃⋊C₄	—	2	1	no	—
7	C₂×C₄×Dic₄₃	C₄	1	1	yes	characteristic
8	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
9	C₂×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²⋊C₈×C₄₃	—	2	1	no	—
11	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
13	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
14	C₂²×Dic₄₃	—	2	1	no	—
15	C₂²×Dic₄₃	—	2	1	no	—
16	C₂×C₈×C₄₃	—	4	1	no	—
17	C₄⋊C₄×C₄₃	—	4	1	no	—
18	C₄⋊Dic₄₃	—	4	1	no	—
19	Dic₄₃⋊C₄	—	4	2	no	—
20	Dic₄₃⋊C₄	—	4	2	no	—
21	C₄×Dic₄₃	—	2	1	no	—
22	C₄×Dic₄₃	C₈	1	2	yes	complemented
23	C₂×C₄₃⋊C₈	—	4	1	no	—
24	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₃	—	2	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃	—	2	1	no	—
29	C₂×C₄×C₄₃	—	4	1	no	—
30	C₂×C₄×C₄₃	—	4	1	no	—
31	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₄₃	M₁₆	1	1	yes	characteristic
33	C₂×Dic₄₃	—	2	2	no	—
34	C₂×Dic₄₃	—	2	2	no	—
35	C₂×Dic₄₃	—	2	2	no	—
36	C₂×Dic₄₃	—	4	1	no	—
37	C₂×Dic₄₃	—	4	1	no	—
38	C₂×Dic₄₃	—	4	1	no	—
39	C₈×C₄₃	—	8	1	no	—
40	C₄₃⋊C₈	—	8	1	no	—
41	C₂²×C₄₃	—	2	1	no	—
42	C₂²×C₄₃	—	2	1	no	—
43	C₂²×C₄₃	C₂²⋊C₈	1	1	yes	characteristic
44	C₂²×C₄₃	#99	1	1	yes	characteristic
45	C₂²×C₄₃	#101	1	1	yes	characteristic
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	4	1	no	—
49	C₄×C₄₃	—	4	1	no	—
50	Dic₄₃	—	2	4	no	—
51	Dic₄₃	—	8	1	no	—
52	#1325	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	—	2	1	no	—
54	C₂×C₄₃	—	2	1	no	—
55	C₂×C₄₃	#324	1	1	yes	characteristic
56	C₂×C₄₃	#353	1	1	yes	characteristic
57	C₂×C₄₃	#356	1	1	yes	characteristic
58	#384	—	43	1	no	—
59	#324	—	43	1	no	—
60	#324	D₄₃	1	1	yes	characteristic
61	C₄₃	#1325	1	1	yes	characteristic, complemented, Sylow
62	C₂×C₄⋊C₄	—	43	1	no	—
63	C₂×C₄⋊C₄	—	86	1	no	—
64	C₂×C₄⋊C₄	—	86	1	no	—
65	C₂×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
66	C₂×C₄²	—	43	1	no	—
67	C₂²⋊C₈	—	2	1	no	—
68	C₂²⋊C₈	—	86	1	no	—
69	C₂²×C₄	—	86	1	no	—
70	C₂²×C₄	—	86	1	no	—
71	C₂²×C₄	C₄×D₄₃	1	1	yes	characteristic
72	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
73	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
74	C₂×C₈	—	4	1	no	—
75	C₂×C₈	—	172	1	no	—
76	C₄⋊C₄	—	4	1	no	—
77	C₄⋊C₄	—	172	1	no	—
78	C₄⋊C₄	—	172	2	no	—
79	C₄⋊C₄	—	172	2	no	—
80	C₄²	—	43	2	no	—
81	C₄²	—	86	1	no	—
82	C₂³	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	4	1	no	—
89	C₂×C₄	—	86	2	no	—
90	C₂×C₄	—	86	2	no	—
91	C₂×C₄	—	86	2	no	—
92	C₂×C₄	—	172	1	no	—
93	C₂×C₄	—	172	1	no	—
94	C₂×C₄	—	172	1	no	—
95	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
96	C₂×C₄	#10621872	1	1	yes	characteristic
97	C₈	—	8	1	no	—
98	C₈	—	344	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	(C₂×D₄₃)⋊C₈	1	1	yes	characteristic
102	C₂²	#13063239	1	1	yes	characteristic
103	C₂²	#13063243	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	4	1	no	—
107	C₄	—	4	1	no	—
108	C₄	—	86	4	no	—
109	C₄	—	344	1	no	—
110	C₂	—	2	1	no	—
111	C₂	—	2	1	no	—
112	C₂	#14582624	1	1	yes	characteristic
113	C₂	#14582691	1	1	yes	characteristic
114	C₂	#14582697	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582768

C₂

yes

maximal, characteristic

#14582625

C₂

yes

maximal, characteristic

C₄₃×#324

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₄₃

C₄

yes

characteristic

C₂×Dic₄₃⋊C₄

—

C₂×Dic₄₃⋊C₄

—

C₂×C₄×Dic₄₃

C₄

yes

characteristic

C₂²⋊(C₄₃⋊C₈)

—

C₂×C₄⋊C₄×C₄₃

C₂²

yes

characteristic

C₂²⋊C₈×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂×C₈×C₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₈

yes

complemented

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

M₁₆

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₈×C₄₃

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂²⋊C₈

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#1325

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

—

D₄₃

yes

characteristic

C₄₃

#1325

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

characteristic

C₂×C₄²

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₃

yes

characteristic

C₂²×C₄

D₁₇₂

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄⋊C₄

—

172

—

C₄²

—

C₄²

—

C₂³

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

C₈×D₄₃

yes

characteristic

C₂×C₄

#10621872

yes

characteristic

C₈

—

C₈

—

344

—

C₂²

—

100

C₂²

—

101

C₂²

(C₂×D₄₃)⋊C₈

yes

characteristic

102

C₂²

#13063239

yes

characteristic

103

C₂²

#13063243

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

344

—

110

C₂

—

111

C₂

—

112

C₂

#14582624

yes

characteristic

113

C₂

#14582691

yes

characteristic

114

C₂

#14582697

yes

characteristic

	subgroup	G/H
center	C₂²	#13063239
commutator	C₂×C₄×C₄₃	C₂×C₈
Frattini	C₂×C₄⋊C₄	C₂×D₄₃
Fitting	C₄₃×#324	C₂
socle	C₂²×C₄₃	#99
hypercenter	#324	D₄₃
hypocenter	C₄₃	#1325
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #324

subgroup

G/H

center

C₂²

#13063239

commutator

C₂×C₄×C₄₃

C₂×C₈

Frattini

C₂×C₄⋊C₄

C₂×D₄₃

Fitting

C₄₃×#324

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂×C₄⋊C₄ ◁ #324

N	H ≅ G/N	type
22. C₄×Dic₄₃	C₈	semidirect
61. C₄₃	#1325	semidirect

H ≅ G/N

type

22. C₄×Dic₄₃

C₈

semidirect

61. C₄₃

#1325

semidirect

Subgroups — #19132540

Conjugacy classes of subgroups

Complements