Group #14572031 — subgroups

Subgroups — #14572031

Order 2432.

648 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 245 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×#10597315	C₂	1	1	yes	maximal, characteristic
2	C₂×#10597390	C₂	1	4	yes	maximal
3	#11926413	C₂	1	8	yes	maximal
4	C₄²×Dic₁₉	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	C₂²×Dic₃₈	C₂²	1	2	yes	—
8	C₁₉×C₄⋊Q₈	—	2	4	no	—
9	C₂×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
10	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
11	#10597390	—	2	16	no	—
12	C₂×C₄⋊Dic₁₉	C₂²	1	4	yes	—
13	C₂×Dic₁₉⋊C₄	C₂²	1	16	yes	—
14	C₂×C₄×Dic₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Dic₁₉	C₂²	1	4	yes	—
16	#10597315	—	2	4	no	—
17	C₂×Q₈×C₁₉	—	2	8	no	—
18	C₂×Q₈×C₁₉	—	2	4	no	—
19	C₂²×C₄×C₁₉	C₂³	1	4	yes	—
20	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
21	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
22	C₂²×Dic₁₉	C₂³	1	4	yes	—
23	C₂²×Dic₁₉	C₂³	1	4	yes	—
24	C₂×Dic₃₈	—	2	8	no	—
25	C₂×Dic₃₈	—	2	4	no	—
26	C₄⋊C₄×C₁₉	—	2	8	no	—
27	C₄²×C₁₉	D₄	1	4	yes	—
28	C₄⋊Dic₁₉	—	2	8	no	—
29	Dic₁₉⋊C₄	—	2	32	no	—
30	C₄×Dic₁₉	D₄	1	8	yes	—
31	C₄×Dic₁₉	Q₈	1	16	yes	complemented
32	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
33	Q₈×C₁₉	—	4	8	no	—
34	C₂×C₄×C₁₉	—	2	8	no	—
35	C₂×C₄×C₁₉	—	2	4	no	—
36	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
37	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
38	C₂×C₄×C₁₉	C₂×D₄	1	4	yes	—
39	C₂×C₄×C₁₉	C₂×Q₈	1	8	yes	—
40	C₂×Dic₁₉	—	2	8	no	—
41	C₂×Dic₁₉	—	2	4	no	—
42	C₂×Dic₁₉	C₂×D₄	1	8	yes	—
43	C₂×Dic₁₉	C₂×Q₈	1	16	yes	—
44	Dic₃₈	—	4	8	no	—
45	#2868	—	19	1	no	maximal, Sylow
46	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
47	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
48	C₂²×C₁₉	C₂²×Q₈	1	4	yes	—
49	C₄×C₁₉	—	4	4	no	—
50	C₄×C₁₉	#127	1	4	yes	—
51	C₄×C₁₉	C₄⋊Q₈	1	8	yes	complemented
52	Dic₁₉	—	4	4	no	—
53	Dic₁₉	C₄⋊Q₈	1	16	yes	complemented
54	C₂×C₄⋊Q₈	—	19	4	no	—
55	C₂×C₄⋊Q₈	—	19	1	no	—
56	C₂×C₄⋊Q₈	D₁₉	1	1	yes	characteristic
57	#384	—	19	8	no	—
58	C₄³	—	19	1	no	—
59	C₂×C₁₉	C₂×#127	1	1	yes	characteristic
60	C₂×C₁₉	C₂×C₄⋊Q₈	1	4	yes	—
61	C₂×C₁₉	C₂×C₄⋊Q₈	1	2	yes	—
62	C₂²×Q₈	—	19	2	no	—
63	C₂²×Q₈	C₂×D₁₉	1	2	yes	—
64	C₄⋊Q₈	—	2	4	no	—
65	C₄⋊Q₈	—	38	16	no	—
66	C₄⋊Q₈	—	38	4	no	—
67	C₂×C₄⋊C₄	—	19	16	no	—
68	C₂×C₄⋊C₄	—	19	4	no	—
69	C₂×C₄⋊C₄	C₂×D₁₉	1	4	yes	—
70	C₂×C₄²	—	19	2	no	—
71	C₂×C₄²	—	19	4	no	—
72	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
73	C₁₉	#2868	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	2	8	no	—
75	C₂×Q₈	—	2	4	no	—
76	C₂×Q₈	—	38	8	no	—
77	C₂×Q₈	—	38	4	no	—
78	C₂²×C₄	—	19	4	no	—
79	C₂²×C₄	—	19	4	no	—
80	C₂²×C₄	C₂²×D₁₉	1	4	yes	—
81	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
82	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
83	C₄⋊C₄	—	2	8	no	—
84	C₄⋊C₄	—	38	32	no	—
85	C₄⋊C₄	—	38	8	no	—
86	C₄²	—	19	8	no	—
87	C₄²	—	19	16	no	—
88	C₄²	C₂²⋊D₁₉	1	4	yes	—
89	C₂³	C₂³×D₁₉	1	1	yes	characteristic
90	Q₈	—	4	8	no	—
91	Q₈	—	76	8	no	—
92	C₂×C₄	—	2	8	no	—
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	19	8	no	—
95	C₂×C₄	—	19	16	no	—
96	C₂×C₄	—	38	8	no	—
97	C₂×C₄	—	38	4	no	—
98	C₂×C₄	D₄×D₁₉	1	4	yes	—
99	C₂×C₄	Q₈×D₁₉	1	8	yes	—
100	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
101	C₂×C₄	C₂×C₂²⋊D₁₉	1	4	yes	—
102	C₂²	C₂×D₄×D₁₉	1	2	yes	—
103	C₂²	C₂×Q₈×D₁₉	1	4	yes	—
104	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
105	C₄	—	4	4	no	—
106	C₄	—	19	16	no	—
107	C₄	—	76	4	no	—
108	C₄	#10597386	1	4	yes	—
109	C₄	#10597390	1	8	yes	complemented
110	C₂	C₂×#10597386	1	1	yes	characteristic
111	C₂	C₄⋊Q₈×D₁₉	1	4	yes	—
112	C₂	C₂×#10597390	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10597315

C₂

yes

maximal, characteristic

C₂×#10597390

C₂

yes

maximal

#11926413

C₂

yes

maximal

C₄²×Dic₁₉

C₂

yes

maximal, characteristic

C₂×C₁₉×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₉

C₂²

yes

—

C₂²×Dic₃₈

C₂²

yes

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

C₂²

yes

—

C₂×C₄²×C₁₉

C₂²

yes

characteristic

#10597390

—

C₂×C₄⋊Dic₁₉

C₂²

yes

—

C₂×Dic₁₉⋊C₄

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

C₂×C₄×Dic₁₉

C₂²

yes

—

#10597315

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×C₄×C₁₉

C₂³

yes

characteristic

C₂²×C₄×C₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂²×Dic₁₉

C₂³

yes

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

D₄

yes

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

D₄

yes

—

C₄×Dic₁₉

Q₈

yes

complemented

C₂³×C₁₉

C₂⁴

yes

characteristic

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×Q₈

yes

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

—

C₂×Dic₁₉

C₂×Q₈

yes

—

Dic₃₈

—

#2868

—

maximal, Sylow

C₂²×C₁₉

C₂²×D₄

yes

—

C₂²×C₁₉

C₂²×D₄

yes

characteristic

C₂²×C₁₉

C₂²×Q₈

yes

—

C₄×C₁₉

—

C₄×C₁₉

#127

yes

—

C₄×C₁₉

C₄⋊Q₈

yes

complemented

Dic₁₉

—

Dic₁₉

C₄⋊Q₈

yes

complemented

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

D₁₉

yes

characteristic

#384

—

C₄³

—

C₂×C₁₉

C₂×#127

yes

characteristic

C₂×C₁₉

C₂×C₄⋊Q₈

yes

—

C₂×C₁₉

C₂×C₄⋊Q₈

yes

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₁₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₉

yes

characteristic

C₁₉

#2868

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₉

yes

—

C₂²×C₄

C₂²×D₁₉

yes

characteristic

C₂²×C₄

C₂²×D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

C₂²⋊D₁₉

yes

—

C₂³

C₂³×D₁₉

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

—

C₂×C₄

Q₈×D₁₉

yes

—

100

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

101

C₂×C₄

C₂×C₂²⋊D₁₉

yes

—

102

C₂²

C₂×D₄×D₁₉

yes

—

103

C₂²

C₂×Q₈×D₁₉

yes

—

104

C₂²

C₂²×C₂²⋊D₁₉

yes

characteristic

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

#10597386

yes

—

109

C₄

#10597390

yes

complemented

110

C₂

C₂×#10597386

yes

characteristic

111

C₂

C₄⋊Q₈×D₁₉

yes

—

112

C₂

C₂×#10597390

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, prime radical, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₁₉×C₄⋊Q₈	C₂
hypercenter	C₂×C₄⋊Q₈	D₁₉
hypocenter	C₁₉	#2868
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₉

commutator, socle, prime radical, cosocle

C₂³×C₁₉

C₂⁴

Fitting

C₂×C₁₉×C₄⋊Q₈

C₂

hypercenter

C₂×C₄⋊Q₈

D₁₉

C₁₉

G ▷ C₂³×C₁₉ ▷ C₁₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
31. C₄×Dic₁₉	Q₈	semidirect
51. C₄×C₁₉	C₄⋊Q₈	semidirect
53. Dic₁₉	C₄⋊Q₈	semidirect
73. C₁₉	#2868	semidirect
109. C₄	#10597390	semidirect

H ≅ G/N

type

31. C₄×Dic₁₉

Q₈

semidirect

51. C₄×C₁₉

C₄⋊Q₈

semidirect

53. Dic₁₉

C₄⋊Q₈

semidirect

73. C₁₉

#2868

semidirect

109. C₄

#10597390

semidirect

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

subgroup	index
C₂×#10597315	2
C₂×#10597390	2
#11926413	2
C₄²×Dic₁₉	2
C₂×C₁₉×C₄⋊Q₈	2
#2868	19

subgroup

index

C₂×#10597315

C₂×#10597390

#11926413

C₄²×Dic₁₉

C₂×C₁₉×C₄⋊Q₈

#2868

Subgroups — #14572031

Conjugacy classes of subgroups

Complements

Maximal subgroups