Group #14573974 — subgroups

Subgroups — C₂×#11926912 #14573974

Order 2432.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂×#10597316	C₂	1	1	yes	maximal, characteristic
2	#11926912	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10597292	C₂	1	4	yes	maximal
4	C₂×#10597260	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₉	C₂²	1	2	yes	—
7	C₁₉×C₄⋊Q₈	—	2	2	no	—
8	C₁₉×C₄⋊Q₈	C₂²	1	4	yes	—
9	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₁₉	C₂²	1	2	yes	—
12	C₂×Dic₁₉⋊C₄	—	2	2	no	—
13	C₂²×C₁₉⋊C₈	C₂²	1	2	yes	—
14	#10597316	—	2	2	no	—
15	#10597316	C₂²	1	4	yes	—
16	#10597292	C₂²	1	16	yes	—
17	#10597260	C₂²	1	4	yes	—
18	C₂×Q₈×C₁₉	—	2	2	no	—
19	C₂×Q₈×C₁₉	—	2	8	no	—
20	C₂×Q₈×C₁₉	C₂³	1	4	yes	—
21	C₂²×C₄×C₁₉	—	2	2	no	—
22	C₂²×C₄×C₁₉	D₄	1	2	yes	—
23	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
24	C₂²×Dic₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	—	2	8	no	—
26	C₄²×C₁₉	D₄	1	2	yes	—
27	C₄²×C₁₉	C₂³	1	2	yes	—
28	C₄⋊Dic₁₉	—	2	2	no	—
29	C₄⋊Dic₁₉	C₂³	1	4	yes	—
30	Dic₁₉⋊C₄	—	2	8	no	—
31	C₂×C₁₉⋊C₈	—	2	4	no	—
32	C₂×C₁₉⋊C₈	C₂³	1	4	yes	—
33	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
34	Q₈×C₁₉	—	2	8	no	—
35	Q₈×C₁₉	—	4	4	no	—
36	C₂×C₄×C₁₉	—	2	4	no	—
37	C₂×C₄×C₁₉	—	2	4	no	—
38	C₂×C₄×C₁₉	—	4	4	no	—
39	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
40	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₁₉	#41	1	4	yes	—
42	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
43	C₂×Dic₁₉	—	2	4	no	—
44	C₂×Dic₁₉	—	4	4	no	—
45	C₁₉⋊C₈	—	2	4	no	—
46	C₂×#491	—	19	1	no	maximal, Sylow
47	C₂²×C₁₉	#124	1	2	yes	—
48	C₂²×C₁₉	#137	1	4	yes	—
49	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
50	C₄×C₁₉	—	2	4	no	—
51	C₄×C₁₉	—	4	4	no	—
52	C₄×C₁₉	#124	1	2	yes	—
53	C₄×C₁₉	C₂×#41	1	2	yes	—
54	Dic₁₉	—	4	4	no	—
55	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
56	C₂×#125	—	19	1	no	—
57	#491	—	19	8	no	—
58	C₂×#103	—	19	4	no	—
59	C₂×#97	—	19	1	no	—
60	C₂×C₁₉	#491	1	4	yes	complemented
61	C₂×C₁₉	C₂×#124	1	1	yes	characteristic
62	C₂×C₁₉	C₂×#137	1	2	yes	—
63	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
64	C₂²×C₈	—	19	2	no	—
65	C₄⋊Q₈	—	2	2	no	—
66	C₄⋊Q₈	C₂×D₁₉	1	4	yes	—
67	#125	—	19	4	no	—
68	#125	—	38	2	no	—
69	C₂×C₄⋊C₄	—	2	2	no	—
70	C₂×C₄⋊C₄	—	19	2	no	—
71	C₂×C₄⋊C₄	—	38	2	no	—
72	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
73	#103	—	19	16	no	—
74	#97	—	19	4	no	—
75	C₁₉	C₂×#491	1	1	yes	characteristic, complemented, Sylow
76	C₂×Q₈	—	2	2	no	—
77	C₂×Q₈	—	2	8	no	—
78	C₂×Q₈	C₂²×D₁₉	1	4	yes	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	38	2	no	—
81	C₂²×C₄	C₂²⋊D₁₉	1	2	yes	—
82	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
83	C₂×C₈	—	19	4	no	—
84	C₂×C₈	—	38	4	no	—
85	C₄⋊C₄	—	2	8	no	—
86	C₄⋊C₄	—	19	4	no	—
87	C₄⋊C₄	—	38	8	no	—
88	C₄⋊C₄	—	38	2	no	—
89	C₄²	C₂²⋊D₁₉	1	2	yes	—
90	C₄²	C₂²×D₁₉	1	2	yes	—
91	C₂³	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
92	Q₈	—	2	8	no	—
93	Q₈	—	4	4	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	4	4	no	—
97	C₂×C₄	—	38	4	no	—
98	C₂×C₄	—	76	4	no	—
99	C₂×C₄	#64543	1	4	yes	—
100	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
101	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
102	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
103	C₈	—	38	4	no	—
104	C₂²	#10597382	1	2	yes	—
105	C₂²	#10597388	1	4	yes	—
106	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
107	C₄	—	2	4	no	—
108	C₄	—	4	4	no	—
109	C₄	—	76	4	no	—
110	C₄	#10597382	1	2	yes	—
111	C₄	C₂×#64543	1	2	yes	—
112	C₂	#11926912	1	4	yes	direct product factor
113	C₂	C₂×#10597382	1	1	yes	characteristic
114	C₂	C₂×#10597388	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597316

C₂

yes

maximal, characteristic

#11926912

C₂

yes

maximal, direct product factor

C₂×#10597292

C₂

yes

maximal

C₂×#10597260

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

—

C₂²×C₁₉⋊C₈

C₂²

yes

—

#10597316

—

#10597316

C₂²

yes

—

#10597292

C₂²

yes

—

#10597260

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

D₄

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄²×C₁₉

C₂³

yes

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

#41

yes

—

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₁₉⋊C₈

—

C₂×#491

—

maximal, Sylow

C₂²×C₁₉

#124

yes

—

C₂²×C₁₉

#137

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#124

yes

—

C₄×C₁₉

C₂×#41

yes

—

Dic₁₉

—

C₂×C₄⋊Q₈

D₁₉

yes

—

—

—

C₂×#97

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₁₉

yes

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

#103

—

#97

—

C₁₉

C₂×#491

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₁₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₁₉

yes

—

C₄²

C₂²×D₁₉

yes

—

C₂³

C₂×C₂²⋊D₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64543

yes

—

100

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

101

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

102

C₂×C₄

C₂³×D₁₉

yes

characteristic

103

C₈

—

104

C₂²

#10597382

yes

—

105

C₂²

#10597388

yes

—

106

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

#10597382

yes

—

111

C₄

C₂×#64543

yes

—

112

C₂

#11926912

yes

direct product factor

113

C₂

C₂×#10597382

yes

characteristic

114

C₂

C₂×#10597388

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	C₂×#491
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

socle, prime radical

C₂³×C₁₉

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₁₉

hypocenter

C₁₉

C₂×#491

LCS

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
2. #11926912	C₂	direct (N × H)
60. C₂×C₁₉	#491	semidirect
75. C₁₉	C₂×#491	semidirect
112. C₂	#11926912	direct (N × H)

H ≅ G/N

type

2. #11926912

C₂

direct (N × H)

60. C₂×C₁₉

#491

semidirect

75. C₁₉

C₂×#491

semidirect

112. C₂

#11926912

direct (N × H)

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

subgroup	index
C₂×#10597316	2
#11926912	2
C₂×#10597292	2
C₂×#10597260	2
C₂×C₁₉×C₄⋊Q₈	2
C₂×#491	19

subgroup

index

C₂×C₁₉×C₄⋊Q₈

Subgroups — C₂×#11926912 #14573974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11926912 #14573974

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11926912 #14573974