Group #19132488 — subgroups

Subgroups — #19132488

Order 5504.

172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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	#14582956	C₂	1	1	yes	maximal, characteristic
2	C₄×#10621877	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₂×#10621877	—	2	1	no	—
5	C₄⋊(C₄₃⋊C₈)	C₄	1	2	yes	complemented
6	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
7	#13063236	—	2	1	no	—
8	#13063236	C₄	1	2	yes	complemented
9	C₄×C₄₃⋊C₈	—	2	1	no	—
10	C₂×C₄²×C₄₃	—	2	1	no	—
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	#95×C₄₃	—	2	1	no	—
13	#95×C₄₃	C₄	1	2	yes	—
14	C₂²×C₄×C₄₃	—	2	2	no	—
15	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₄²×C₄₃	—	2	4	no	—
19	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₄²×C₄₃	D₄	1	1	yes	characteristic
22	C₄²×C₄₃	Q₈	1	1	yes	characteristic
23	#10621877	—	2	4	no	—
24	C₂×C₄₃⋊C₈	—	2	2	no	—
25	C₂×C₄₃⋊C₈	—	2	2	no	—
26	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₄₃	—	2	2	no	—
28	C₂×C₄×C₄₃	—	2	2	no	—
29	C₂×C₄×C₄₃	—	2	4	no	—
30	C₂×C₄×C₄₃	—	4	1	no	—
31	C₂×C₄×C₄₃	—	4	2	no	—
32	C₂×C₄×C₄₃	—	4	2	no	—
33	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
39	C₄₃⋊C₈	—	2	4	no	—
40	C₄₃⋊C₈	—	4	2	no	—
41	C₂²×C₄₃	—	2	1	no	—
42	C₂²×C₄₃	—	2	1	no	—
43	C₂²×C₄₃	#95	1	1	yes	characteristic
44	C₂²×C₄₃	#104	1	2	yes	—
45	C₄×C₄₃	—	2	1	no	—
46	C₄×C₄₃	—	2	1	no	—
47	C₄×C₄₃	—	2	1	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	—	2	1	no	—
50	C₄×C₄₃	—	4	4	no	—
51	C₄×C₄₃	#104	1	2	yes	—
52	#1300	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	—	2	2	no	—
54	C₂×C₄₃	#339	1	1	yes	characteristic
55	C₂×C₄₃	#339	1	1	yes	characteristic
56	C₂×C₄₃	#344	1	1	yes	characteristic
57	#432	—	43	1	no	—
58	C₄×M₁₆	—	43	1	no	—
59	#376	D₄₃	1	1	yes	characteristic
60	C₄₃	#1300	1	1	yes	characteristic, complemented, Sylow
61	C₂×M₁₆	—	86	1	no	—
62	C₂×C₄²	—	2	1	no	—
63	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
64	C₄⋊C₈	—	43	2	no	—
65	C₂²⋊C₈	—	86	1	no	—
66	#97	—	43	2	no	—
67	#97	—	86	1	no	—
68	C₄×C₈	—	86	1	no	—
69	#95	—	2	1	no	—
70	#95	Dic₄₃	1	2	yes	—
71	C₂²×C₄	—	2	2	no	—
72	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
73	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
74	C₂²×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
75	M₁₆	—	86	4	no	—
76	C₂×C₈	—	86	2	no	—
77	C₂×C₈	—	86	2	no	—
78	C₄²	—	2	4	no	—
79	C₄²	Dic₈₆	1	1	yes	characteristic
80	C₄²	C₄×D₄₃	1	1	yes	characteristic
81	C₄²	C₄×D₄₃	1	1	yes	characteristic
82	C₄²	D₁₇₂	1	1	yes	characteristic
83	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	4	2	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
91	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
92	C₂×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
93	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
94	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
95	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
96	C₈	—	86	4	no	—
97	C₈	—	172	2	no	—
98	C₂²	—	2	1	no	—
99	C₂²	—	2	1	no	—
100	C₂²	C₄₃⋊#95	1	1	yes	characteristic
101	C₂²	#13063252	1	2	yes	—
102	C₄	—	2	1	no	—
103	C₄	—	2	1	no	—
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	2	1	no	—
107	C₄	—	4	4	no	—
108	C₄	#13063253	1	2	yes	—
109	C₂	—	2	2	no	—
110	C₂	#14582658	1	1	yes	characteristic
111	C₂	#14582659	1	1	yes	characteristic
112	C₂	#14582669	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14582956

C₂

yes

maximal, characteristic

C₄×#10621877

C₂

yes

maximal, characteristic

C₄₃×#376

C₂

yes

maximal, characteristic

C₂×#10621877

—

C₄⋊(C₄₃⋊C₈)

C₄

yes

complemented

C₂²⋊(C₄₃⋊C₈)

—

#13063236

—

#13063236

C₄

yes

complemented

C₄×C₄₃⋊C₈

—

C₂×C₄²×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

—

#95×C₄₃

C₄

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

Q₈

yes

characteristic

#10621877

—

C₂×C₄₃⋊C₈

—

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

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

#95

yes

characteristic

C₂²×C₄₃

#104

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#104

yes

—

#1300

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₄×M₁₆

—

#376

D₄₃

yes

characteristic

C₄₃

#1300

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

C₄×C₈

—

#95

—

#95

Dic₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

Dic₈₆

yes

characteristic

C₄²

C₄×D₄₃

yes

characteristic

C₄²

C₄×D₄₃

yes

characteristic

C₄²

D₁₇₂

yes

characteristic

C₂³

C₂²⋊Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

characteristic

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

characteristic

C₈

—

C₈

—

172

—

C₂²

—

C₂²

—

100

C₂²

C₄₃⋊#95

yes

characteristic

101

C₂²

#13063252

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#13063253

yes

—

109

C₂

—

110

C₂

#14582658

yes

characteristic

111

C₂

#14582659

yes

characteristic

112

C₂

#14582669

yes

characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₄²
Frattini	C₂×C₄²	C₂×D₄₃
Fitting	C₄₃×#376	C₂
socle	C₂²×C₄₃	#95
hypercenter	#376	D₄₃
hypocenter	C₄₃	#1300
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

subgroup

G/H

center

C₂×C₄

(C₂×D₄₃)⋊C₄

commutator

C₂×C₄×C₄₃

C₄²

Frattini

C₂×C₄²

C₂×D₄₃

Fitting

C₄₃×#376

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #376

N	H ≅ G/N	type
5. C₄⋊(C₄₃⋊C₈)	C₄	semidirect
8. #13063236	C₄	semidirect
60. C₄₃	#1300	semidirect

H ≅ G/N

type

5. C₄⋊(C₄₃⋊C₈)

C₄

semidirect

8. #13063236

C₄

semidirect

60. C₄₃

#1300

semidirect

Subgroups — #19132488

Conjugacy classes of subgroups

Complements