Group #19135947 — subgroups

Subgroups — #19135947

Order 5504.

314 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 75 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	#14582771	C₂	1	3	yes	maximal
2	#14582666	C₂	1	3	yes	maximal
3	C₄₃×#543	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₄₃	C₂²	1	1	yes	characteristic
5	C₂×Dic₄₃⋊C₄	—	2	3	no	—
6	C₂×C₂²⋊Dic₄₃	C₂²	1	3	yes	—
7	C₄₃⋊#95	—	2	3	no	—
8	C₂²⋊Q₈×C₄₃	—	2	3	no	—
9	C₂²⋊Q₈×C₄₃	—	2	3	no	—
10	C₂×C₂²⋊C₄×C₄₃	C₂²	1	3	yes	—
11	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
12	C₂×Q₈×C₄₃	—	2	1	no	—
13	C₂×Q₈×C₄₃	—	2	1	no	—
14	C₂²×C₄×C₄₃	D₄	1	3	yes	—
15	C₂²×C₄×C₄₃	D₄	1	3	yes	—
16	C₂²×Dic₄₃	—	2	3	no	—
17	C₂²×Dic₄₃	—	2	3	no	—
18	C₂²×Dic₄₃	—	4	2	no	—
19	C₄⋊C₄×C₄₃	—	2	3	no	—
20	C₄⋊C₄×C₄₃	—	2	3	no	—
21	C₂²⋊C₄×C₄₃	—	2	6	no	—
22	C₂²⋊Dic₄₃	—	2	3	no	—
23	C₂²⋊Dic₄₃	Q₈	1	6	yes	complemented
24	Dic₄₃⋊C₄	—	4	6	no	—
25	C₂³×C₄₃	—	4	1	no	—
26	C₂³×C₄₃	—	4	1	no	—
27	C₂³×C₄₃	C₂×D₄	1	3	yes	—
28	C₂³×C₄₃	C₂×Q₈	1	3	yes	—
29	C₂³×C₄₃	#41	1	1	yes	characteristic
30	Q₈×C₄₃	—	8	1	no	—
31	Q₈×C₄₃	—	8	1	no	—
32	C₂×C₄×C₄₃	—	2	3	no	—
33	C₂×C₄×C₄₃	—	2	3	no	—
34	C₂×C₄×C₄₃	—	4	3	no	—
35	C₂×C₄×C₄₃	—	4	3	no	—
36	C₂×Dic₄₃	—	2	6	no	—
37	C₂×Dic₄₃	—	2	6	no	—
38	C₂×Dic₄₃	—	4	3	no	—
39	C₂×Dic₄₃	—	4	3	no	—
40	C₂×Dic₄₃	—	4	3	no	—
41	C₂×Dic₄₃	—	4	1	no	—
42	C₂²×C₄₃	—	2	3	no	—
43	C₂²×C₄₃	—	2	3	no	—
44	C₂²×C₄₃	—	4	3	no	—
45	C₂²×C₄₃	—	4	1	no	—
46	C₂²×C₄₃	#120	1	1	yes	characteristic
47	C₂²×C₄₃	C₂²⋊Q₈	1	3	yes	—
48	C₂²×C₄₃	C₄⋊Q₈	1	3	yes	—
49	C₄×C₄₃	—	4	3	no	—
50	C₄×C₄₃	—	4	3	no	—
51	Dic₄₃	—	4	6	no	—
52	Dic₄₃	—	4	2	no	—
53	#2062	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	—	2	3	no	—
55	C₂×C₄₃	—	2	3	no	—
56	C₂×C₄₃	#395	1	1	yes	characteristic
57	C₂×C₄₃	B(4,𝔽₂)	1	1	yes	characteristic
58	C₂×C₄₃	#458	1	1	yes	characteristic
59	#543	D₄₃	1	1	yes	characteristic
60	#385	—	43	3	no	—
61	#342	—	43	3	no	—
62	C₄₃	#2062	1	1	yes	characteristic, complemented, Sylow
63	C₂³×C₄	—	43	1	no	—
64	C₂²⋊Q₈	—	2	3	no	—
65	C₂²⋊Q₈	—	2	3	no	—
66	C₂×C₄⋊C₄	—	86	3	no	—
67	C₂×C₂²⋊C₄	—	43	3	no	—
68	C₂×C₂²⋊C₄	C₂×D₄₃	1	3	yes	—
69	#95	—	86	3	no	—
70	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
71	C₂×Q₈	—	2	1	no	—
72	C₂×Q₈	—	2	1	no	—
73	C₂²×C₄	—	86	3	no	—
74	C₂²×C₄	—	86	3	no	—
75	C₂²×C₄	—	172	2	no	—
76	C₂²×C₄	C₂²⋊D₄₃	1	3	yes	—
77	C₂²×C₄	C₂²⋊D₄₃	1	3	yes	—
78	C₄⋊C₄	—	2	3	no	—
79	C₄⋊C₄	—	2	3	no	—
80	C₄⋊C₄	—	172	6	no	—
81	C₂²⋊C₄	—	2	6	no	—
82	C₂²⋊C₄	—	43	6	no	—
83	C₂²⋊C₄	—	86	3	no	—
84	C₂³	—	4	1	no	—
85	C₂³	—	4	1	no	—
86	C₂³	Q₈×D₄₃	1	3	yes	—
87	C₂³	#10621902	1	1	yes	characteristic
88	C₂³	C₂×C₂²⋊D₄₃	1	3	yes	—
89	Q₈	—	8	1	no	—
90	Q₈	—	8	1	no	—
91	C₂×C₄	—	2	3	no	—
92	C₂×C₄	—	2	3	no	—
93	C₂×C₄	—	4	3	no	—
94	C₂×C₄	—	4	3	no	—
95	C₂×C₄	—	86	6	no	—
96	C₂×C₄	—	86	6	no	—
97	C₂×C₄	—	172	3	no	—
98	C₂×C₄	—	172	3	no	—
99	C₂×C₄	—	172	3	no	—
100	C₂×C₄	—	172	1	no	—
101	C₂²	—	2	3	no	—
102	C₂²	—	2	3	no	—
103	C₂²	—	4	3	no	—
104	C₂²	—	4	1	no	—
105	C₂²	#13063294	1	1	yes	characteristic
106	C₂²	#13063301	1	3	yes	—
107	C₂²	#13063323	1	3	yes	—
108	C₄	—	4	3	no	—
109	C₄	—	4	3	no	—
110	C₄	—	172	6	no	—
111	C₄	—	172	2	no	—
112	C₂	—	2	3	no	—
113	C₂	—	2	3	no	—
114	C₂	#14582818	1	1	yes	characteristic
115	C₂	#14583086	1	1	yes	characteristic
116	C₂	#14583089	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582771

C₂

yes

maximal

#14582666

C₂

yes

maximal

C₄₃×#543

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

characteristic

C₂×Dic₄₃⋊C₄

—

C₂×C₂²⋊Dic₄₃

C₂²

yes

—

C₄₃⋊#95

—

C₂²⋊Q₈×C₄₃

—

C₂²⋊Q₈×C₄₃

—

C₂×C₂²⋊C₄×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₄⋊C₄×C₄₃

—

C₄⋊C₄×C₄₃

—

C₂²⋊C₄×C₄₃

—

C₂²⋊Dic₄₃

—

C₂²⋊Dic₄₃

Q₈

yes

complemented

Dic₄₃⋊C₄

—

C₂³×C₄₃

—

C₂³×C₄₃

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

#41

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#120

yes

characteristic

C₂²×C₄₃

C₂²⋊Q₈

yes

—

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

Dic₄₃

—

#2062

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

D₄₃

yes

characteristic

#385

—

#342

—

C₄₃

#2062

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₄₃

yes

—

#95

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

172

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

Q₈×D₄₃

yes

—

C₂³

#10621902

yes

characteristic

C₂³

C₂×C₂²⋊D₄₃

yes

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

100

C₂×C₄

—

172

—

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

#13063294

yes

characteristic

106

C₂²

#13063301

yes

—

107

C₂²

#13063323

yes

—

108

C₄

—

109

C₄

—

110

C₄

—

172

—

111

C₄

—

172

—

112

C₂

—

113

C₂

—

114

C₂

#14582818

yes

characteristic

115

C₂

#14583086

yes

characteristic

116

C₂

#14583089

yes

characteristic

	subgroup	G/H
center	C₂²	#13063294
commutator	C₂⁴×C₄₃	C₂³
Frattini	C₂⁴	C₂²×D₄₃
Fitting	C₄₃×#543	C₂
socle	C₂²×C₄₃	#120
hypercenter	#543	D₄₃
hypocenter	C₄₃	#2062
LCS	G ▷ C₂⁴×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

subgroup

G/H

center

C₂²

#13063294

commutator

C₂⁴×C₄₃

C₂³

Frattini

C₂⁴

C₂²×D₄₃

Fitting

C₄₃×#543

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂⁴×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂⁴ ◁ #543

N	H ≅ G/N	type
23. C₂²⋊Dic₄₃	Q₈	semidirect
62. C₄₃	#2062	semidirect

H ≅ G/N

type

23. C₂²⋊Dic₄₃

Q₈

semidirect

62. C₄₃

#2062

semidirect

Subgroups — #19135947

Conjugacy classes of subgroups

Complements