Group #14563299 — subgroups

Subgroups — #14563299

Order 2432.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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	#11926921	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926920	C₂	1	2	yes	maximal, complemented
3	#11926892	C₂	1	2	yes	maximal, complemented
4	#11926265	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×SD₁₆×C₁₉	—	2	2	no	—
7	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₉×#127	C₂²	1	1	yes	characteristic
9	C₂×#64525	—	2	4	no	—
10	C₂×D₁₅₂	—	2	2	no	—
11	#10597320	C₂²	1	2	yes	—
12	C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
13	#10597266	—	2	4	no	—
14	C₄×C₁₉⋊C₈	C₂²	1	2	yes	—
15	C₂×Q₈×C₁₉	—	2	1	no	—
16	C₂×D₄×C₁₉	—	2	2	no	—
17	C₂×D₄×C₁₉	—	2	1	no	—
18	C₂×D₇₆	—	2	2	no	—
19	C₂×D₇₆	—	2	2	no	—
20	C₂×D₇₆	—	2	2	no	—
21	SD₁₆×C₁₉	—	4	4	no	—
22	C₂×C₈×C₁₉	D₄	1	2	yes	—
23	C₄⋊C₄×C₁₉	—	2	2	no	—
24	C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	#64525	—	4	8	no	—
26	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
27	D₁₅₂	—	4	4	no	—
28	C₂³×C₁₉	—	4	1	no	—
29	C₂²×D₁₉	—	4	2	no	—
30	Q₈×C₁₉	—	4	2	no	—
31	D₄×C₁₉	—	4	2	no	—
32	D₄×C₁₉	—	4	4	no	—
33	C₂×C₄×C₁₉	—	4	1	no	—
34	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
36	D₇₆	—	4	4	no	—
37	D₇₆	—	4	4	no	—
38	D₇₆	—	4	4	no	—
39	C₈×C₁₉	D₈	1	4	yes	complemented
40	C₁₉⋊C₈	—	2	4	no	—
41	#1721	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	8	1	no	—
43	C₂²×C₁₉	—	8	2	no	—
44	C₂²×C₁₉	#127	1	1	yes	characteristic
45	C₂×D₁₉	—	8	2	no	—
46	C₂×D₁₉	—	8	2	no	—
47	C₂×D₁₉	—	8	2	no	—
48	C₄×C₁₉	—	8	1	no	—
49	C₄×C₁₉	C₂×D₈	1	2	yes	—
50	C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
51	#493	—	19	2	no	—
52	#493	—	19	1	no	—
53	#492	D₁₉	1	1	yes	characteristic, complemented
54	#486	—	19	2	no	—
55	#322	—	19	1	no	—
56	C₂×C₁₉	—	16	1	no	—
57	C₂×C₁₉	#493	1	1	yes	characteristic
58	C₂×C₁₉	#496	1	2	yes	—
59	D₁₉	—	16	2	no	—
60	C₂×SD₁₆	—	2	2	no	—
61	C₂×D₈	—	38	4	no	—
62	C₂×D₈	—	38	2	no	—
63	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
64	#127	—	19	2	no	—
65	#127	C₂×D₁₉	1	1	yes	characteristic
66	#102	—	38	4	no	—
67	C₄×C₈	—	19	2	no	—
68	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
69	C₁₉	#1721	1	1	yes	characteristic, complemented, Sylow
70	C₂×Q₈	—	2	1	no	—
71	C₂×D₄	—	2	2	no	—
72	C₂×D₄	—	2	1	no	—
73	C₂×D₄	—	38	2	no	—
74	C₂×D₄	—	38	2	no	—
75	C₂×D₄	—	38	2	no	—
76	SD₁₆	—	4	4	no	—
77	D₈	—	76	8	no	—
78	D₈	—	76	4	no	—
79	C₂×C₈	—	19	4	no	—
80	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
81	C₄⋊C₄	—	2	2	no	—
82	C₄²	C₂²×D₁₉	1	1	yes	characteristic
83	C₂³	—	4	1	no	—
84	C₂³	—	76	2	no	—
85	Q₈	—	4	2	no	—
86	D₄	—	4	2	no	—
87	D₄	—	4	4	no	—
88	D₄	—	76	4	no	—
89	D₄	—	76	4	no	—
90	D₄	—	76	4	no	—
91	C₂×C₄	—	4	1	no	—
92	C₂×C₄	D₄×D₁₉	1	2	yes	—
93	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
94	C₈	—	38	4	no	—
95	C₈	#64525	1	4	yes	complemented
96	C₂²	—	8	1	no	—
97	C₂²	—	8	2	no	—
98	C₂²	—	152	2	no	—
99	C₂²	—	152	2	no	—
100	C₂²	—	152	2	no	—
101	C₂²	#10597386	1	1	yes	characteristic
102	C₄	—	8	1	no	—
103	C₄	#10597360	1	4	yes	—
104	C₄	C₂×#64525	1	2	yes	—
105	C₂	—	16	1	no	—
106	C₂	—	304	2	no	—
107	C₂	#11926920	1	1	yes	characteristic
108	C₂	#11926930	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926921

C₂

yes

maximal, characteristic, complemented

#11926920

C₂

yes

maximal, complemented

#11926892

C₂

yes

maximal, complemented

#11926265

C₂

yes

maximal, characteristic, complemented

C₁₉×#492

C₂

yes

maximal, characteristic, complemented

C₂×SD₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#127

C₂²

yes

characteristic

C₂×#64525

—

C₂×D₁₅₂

—

#10597320

C₂²

yes

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597266

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

SD₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64525

—

C₂×C₁₉⋊C₈

D₄

yes

—

D₁₅₂

—

C₂³×C₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

D₈

yes

complemented

C₁₉⋊C₈

—

#1721

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#127

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×D₈

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

#493

—

#493

—

#492

D₁₉

yes

characteristic, complemented

#486

—

#322

—

C₂×C₁₉

—

C₂×C₁₉

#493

yes

characteristic

C₂×C₁₉

#496

yes

—

D₁₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

#127

—

#127

C₂×D₁₉

yes

characteristic

#102

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1721

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

D₈

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

—

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

#64525

yes

complemented

C₂²

—

C₂²

—

C₂²

—

152

—

C₂²

—

152

—

100

C₂²

—

152

—

101

C₂²

#10597386

yes

characteristic

102

C₄

—

103

C₄

#10597360

yes

—

104

C₄

C₂×#64525

yes

—

105

C₂

—

106

C₂

—

304

—

107

C₂

#11926920

yes

characteristic

108

C₂

#11926930

yes

—

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#492	C₂
socle	C₂²×C₁₉	#127
hypercenter	#492	D₁₉
hypocenter	C₁₉	#1721
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

subgroup

G/H

center

C₂²

#10597386

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#492

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #492

N	H ≅ G/N	type
1. #11926921	C₂	semidirect
2. #11926920	C₂	semidirect
3. #11926892	C₂	semidirect
4. #11926265	C₂	semidirect
5. C₁₉×#492	C₂	semidirect
39. C₈×C₁₉	D₈	semidirect
53. #492	D₁₉	semidirect
69. C₁₉	#1721	semidirect
95. C₈	#64525	semidirect

H ≅ G/N

type

1. #11926921

C₂

semidirect

2. #11926920

C₂

semidirect

3. #11926892

C₂

semidirect

4. #11926265

C₂

semidirect

5. C₁₉×#492

C₂

semidirect

39. C₈×C₁₉

D₈

semidirect

53. #492

D₁₉

semidirect

69. C₁₉

#1721

semidirect

95. C₈

#64525

semidirect

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

subgroup	index
#11926921	2
#11926920	2
#11926892	2
#11926265	2
C₁₉×#492	2
#1721	19

subgroup

index

C₁₉×#492

Subgroups — #14563299

Conjugacy classes of subgroups

Complements

Maximal subgroups