Group #14577037 — subgroups

Subgroups — #14577037

Order 2432.

996 conjugacy classes of subgroups; only the 509 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 509 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	#11927173	C₂	1	12	yes	maximal, complemented
2	#11927170	C₂	1	3	yes	maximal
3	#11927096	C₂	1	12	yes	maximal, complemented
4	C₂×#10597323	C₂	1	3	yes	maximal
5	C₁₉×#543	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
7	C₁₉×C₂²⋊Q₈	C₂²	1	12	yes	—
8	C₂×C₂²⋊C₄×C₁₉	C₂²	1	3	yes	—
9	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	—
10	Q₈×Dic₁₉	C₂²	1	4	yes	complemented
11	#10597390	C₂²	1	12	yes	complemented
12	#10597370	C₂²	1	12	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	6	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	6	yes	—
15	#10597335	C₂²	1	24	yes	complemented
16	#10597334	C₂²	1	12	yes	complemented
17	#10597333	C₂²	1	12	yes	complemented
18	#10597324	C₂²	1	24	yes	—
19	#10597323	C₂²	1	12	yes	—
20	#10597323	C₂²	1	12	yes	—
21	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
22	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	6	yes	—
24	C₂²×Dic₁₉	Q₈	1	8	yes	complemented
25	C₂²×Dic₁₉	C₂³	1	6	yes	—
26	C₂²×Dic₁₉	C₂³	1	3	yes	—
27	C₂²×Dic₁₉	C₂³	1	3	yes	—
28	C₂×Dic₃₈	C₂³	1	12	yes	—
29	C₄⋊C₄×C₁₉	C₂³	1	12	yes	—
30	C₂²⋊C₄×C₁₉	C₂³	1	12	yes	—
31	C₂²⋊Dic₁₉	C₂³	1	12	yes	—
32	C₄⋊Dic₁₉	C₂³	1	12	yes	—
33	Dic₁₉⋊C₄	C₂³	1	24	yes	—
34	Dic₁₉⋊C₄	C₂³	1	24	yes	—
35	C₄×Dic₁₉	C₂³	1	12	yes	—
36	C₄×Dic₁₉	C₂³	1	12	yes	—
37	C₂³×C₁₉	—	4	2	no	—
38	C₂³×C₁₉	C₂×Q₈	1	4	yes	—
39	C₂³×C₁₉	C₂⁴	1	3	yes	—
40	Q₈×C₁₉	—	4	4	no	—
41	C₂×C₄×C₁₉	—	4	6	no	—
42	C₂×C₄×C₁₉	C₂⁴	1	12	yes	—
43	C₂×Dic₁₉	—	4	6	no	—
44	C₂×Dic₁₉	C₂×Q₈	1	12	yes	—
45	C₂×Dic₁₉	C₂×Q₈	1	12	yes	—
46	C₂×Dic₁₉	C₂⁴	1	12	yes	—
47	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₁₉	C₂⁴	1	3	yes	—
49	Dic₃₈	—	4	12	no	—
50	#3458	—	19	1	no	maximal, Sylow
51	C₂²×C₁₉	—	2	6	no	—
52	C₂²×C₁₉	—	4	4	no	—
53	C₂²×C₁₉	C₂²×Q₈	1	6	yes	—
54	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
55	C₄×C₁₉	—	2	12	no	—
56	Dic₁₉	—	2	12	no	—
57	Dic₁₉	C₂²×Q₈	1	2	yes	—
58	Dic₁₉	C₂²×Q₈	1	6	yes	—
59	#544	—	19	12	no	—
60	#543	—	19	3	no	—
61	#543	D₁₉	1	1	yes	characteristic
62	#533	—	19	12	no	—
63	C₂×#117	—	19	3	no	—
64	C₂×C₁₉	—	2	6	no	—
65	C₂×C₁₉	C₂³×Q₈	1	1	yes	characteristic
66	C₂×C₁₉	#585	1	2	yes	—
67	C₂³×C₄	—	19	1	no	—
68	C₄⋊Q₈	—	19	12	no	—
69	C₄⋊Q₈	—	19	12	no	—
70	#125	—	19	24	no	—
71	C₂²⋊Q₈	—	19	12	no	—
72	C₂²⋊Q₈	—	19	24	no	—
73	C₂²⋊Q₈	C₂×D₁₉	1	12	yes	—
74	C₄×Q₈	—	19	4	no	—
75	C₄×Q₈	—	19	12	no	—
76	#117	—	19	12	no	—
77	#117	—	19	12	no	—
78	C₂×C₄⋊C₄	—	19	6	no	—
79	C₂×C₂²⋊C₄	—	19	3	no	—
80	C₂×C₂²⋊C₄	C₂×D₁₉	1	3	yes	—
81	C₂×C₄²	—	19	6	no	—
82	C₁₉	#3458	1	1	yes	characteristic, complemented, Sylow
83	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
84	C₂×Q₈	—	19	12	no	—
85	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
86	C₂²×C₄	—	19	8	no	—
87	C₂²×C₄	—	19	3	no	—
88	C₂²×C₄	—	19	3	no	—
89	C₂²×C₄	—	19	6	no	—
90	C₂²×C₄	C₂²×D₁₉	1	6	yes	—
91	C₄⋊C₄	—	19	24	no	—
92	C₄⋊C₄	—	19	24	no	—
93	C₄⋊C₄	—	19	12	no	—
94	C₄⋊C₄	C₂²×D₁₉	1	12	yes	—
95	C₂²⋊C₄	—	19	12	no	—
96	C₂²⋊C₄	C₂²×D₁₉	1	12	yes	—
97	C₄²	—	19	12	no	—
98	C₄²	—	19	12	no	—
99	C₂³	—	4	2	no	—
100	C₂³	Q₈×D₁₉	1	4	yes	—
101	C₂³	C₂³×D₁₉	1	3	yes	—
102	Q₈	—	4	4	no	—
103	Q₈	—	76	12	no	—
104	C₂×C₄	—	4	6	no	—
105	C₂×C₄	—	19	12	no	—
106	C₂×C₄	—	19	12	no	—
107	C₂×C₄	—	19	1	no	—
108	C₂×C₄	—	19	3	no	—
109	C₂×C₄	—	19	12	no	—
110	C₂×C₄	—	76	6	no	—
111	C₂×C₄	C₂³×D₁₉	1	12	yes	—
112	C₂²	—	2	6	no	—
113	C₂²	—	4	4	no	—
114	C₂²	C₂×Q₈×D₁₉	1	6	yes	—
115	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
116	C₄	—	2	12	no	—
117	C₄	—	19	2	no	—
118	C₄	—	19	6	no	—
119	C₄	—	38	12	no	—
120	C₂	—	2	6	no	—
121	C₂	C₂²×Q₈×D₁₉	1	1	yes	characteristic
122	C₂	#11927379	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11927173

C₂

yes

maximal, complemented

#11927170

C₂

yes

maximal

#11927096

C₂

yes

maximal, complemented

C₂×#10597323

C₂

yes

maximal

C₁₉×#543

C₂

yes

maximal, characteristic

C₂³×Dic₁₉

C₂²

yes

characteristic

C₁₉×C₂²⋊Q₈

C₂²

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂²

yes

—

C₂×C₂²⋊Dic₁₉

C₂²

yes

—

Q₈×Dic₁₉

C₂²

yes

complemented

#10597390

C₂²

yes

complemented

#10597370

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597335

C₂²

yes

complemented

#10597334

C₂²

yes

complemented

#10597333

C₂²

yes

complemented

#10597324

C₂²

yes

—

#10597323

C₂²

yes

—

#10597323

C₂²

yes

—

C₂⁴×C₁₉

C₂³

yes

characteristic

C₂×Q₈×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

Q₈

yes

complemented

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

C₂³

yes

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊Dic₁₉

C₂³

yes

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

C₂³

yes

—

Dic₁₉⋊C₄

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₄×Dic₁₉

C₂³

yes

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×Q₈

yes

—

C₂³×C₁₉

C₂⁴

yes

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂⁴

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

C₂⁴

yes

—

C₂×Dic₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

C₂⁴

yes

—

Dic₃₈

—

#3458

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×Q₈

yes

—

C₂²×C₁₉

C₂⁵

yes

characteristic

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

C₂²×Q₈

yes

—

Dic₁₉

C₂²×Q₈

yes

—

#544

—

#543

—

#543

D₁₉

yes

characteristic

#533

—

C₂×#117

—

C₂×C₁₉

—

C₂×C₁₉

C₂³×Q₈

yes

characteristic

C₂×C₁₉

#585

yes

—

C₂³×C₄

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂²⋊Q₈

C₂×D₁₉

yes

—

C₄×Q₈

—

C₄×Q₈

—

#117

—

#117

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₁₉

#3458

yes

characteristic, complemented, Sylow

C₂⁴

C₂²×D₁₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

C₂²×D₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₁₉

yes

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂²×D₁₉

yes

—

C₄²

—

C₄²

—

C₂³

—

100

C₂³

Q₈×D₁₉

yes

—

101

C₂³

C₂³×D₁₉

yes

—

102

Q₈

—

103

Q₈

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂³×D₁₉

yes

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₂×Q₈×D₁₉

yes

—

115

C₂²

C₂⁴×D₁₉

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

—

121

C₂

C₂²×Q₈×D₁₉

yes

characteristic

122

C₂

#11927379

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#543	C₂
prime radical	C₂⁴×C₁₉	C₂³
hypercenter	#543	D₁₉
hypocenter	C₁₉	#3458
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #543

subgroup

G/H

center, Frattini

C₂²

C₂⁴×D₁₉

commutator, socle, cosocle

C₂²×C₁₉

C₂⁵

Fitting

C₁₉×#543

C₂

prime radical

C₂⁴×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₁₉ ▷ C₁₉

C₁ ◁ C₂² ◁ #543

N	H ≅ G/N	type
1. #11927173	C₂	semidirect
3. #11927096	C₂	semidirect
10. Q₈×Dic₁₉	C₂²	semidirect
11. #10597390	C₂²	semidirect
15. #10597335	C₂²	semidirect
16. #10597334	C₂²	semidirect
17. #10597333	C₂²	semidirect
24. C₂²×Dic₁₉	Q₈	semidirect
82. C₁₉	#3458	semidirect

H ≅ G/N

type

1. #11927173

C₂

semidirect

3. #11927096

C₂

semidirect

10. Q₈×Dic₁₉

C₂²

semidirect

11. #10597390

C₂²

semidirect

15. #10597335

C₂²

semidirect

16. #10597334

C₂²

semidirect

17. #10597333

C₂²

semidirect

24. C₂²×Dic₁₉

Q₈

semidirect

82. C₁₉

#3458

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#11927173	2
#11927170	2
#11927096	2
C₂×#10597323	2
C₁₉×#543	2
#3458	19

subgroup

index

C₁₉×#543

Subgroups — #14577037

Conjugacy classes of subgroups

Complements

Maximal subgroups