Group #14563264 — subgroups

Subgroups — #14563264

Order 2432.

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

normal subgroups only

This group has 220 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
2	#11926918	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×#498	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₂×#64527	—	2	4	no	—
8	C₂×D₁₅₂	—	2	2	no	—
9	#10597320	C₂²	1	1	yes	characteristic
10	#10597320	C₂²	1	1	yes	characteristic
11	C₁₉×#106	—	2	2	no	—
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	2	no	—
16	C₂×D₇₆	—	2	2	no	—
17	C₂×D₇₆	—	2	2	no	—
18	C₂×D₇₆	—	2	1	no	—
19	C₂×D₇₆	—	2	1	no	—
20	C₂×C₈×C₁₉	D₄	1	2	yes	—
21	C₄⋊C₄×C₁₉	—	2	2	no	—
22	C₄⋊C₄×C₁₉	—	2	2	no	—
23	C₄²×C₁₉	C₂³	1	1	yes	characteristic
24	#64527	—	4	8	no	—
25	C₂×C₁₉⋊C₈	D₄	1	4	yes	—
26	D₁₅₂	—	4	4	no	—
27	C₂²×D₁₉	—	4	1	no	—
28	C₂²×D₁₉	—	4	1	no	—
29	Q₈×C₁₉	—	4	4	no	—
30	C₂×C₄×C₁₉	—	4	2	no	—
31	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
33	D₇₆	—	4	2	no	—
34	D₇₆	—	4	2	no	—
35	D₇₆	—	4	4	no	—
36	D₇₆	—	4	4	no	—
37	C₈×C₁₉	SD₁₆	1	4	yes	complemented
38	C₁₉⋊C₈	—	2	4	no	—
39	#1715	—	19	1	no	maximal, Sylow
40	C₂²×C₁₉	#127	1	1	yes	characteristic
41	C₂×D₁₉	—	8	1	no	—
42	C₂×D₁₉	—	8	1	no	—
43	C₂×D₁₉	—	8	2	no	—
44	C₂×D₁₉	—	8	2	no	—
45	C₄×C₁₉	—	8	2	no	—
46	C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
47	C₄×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
48	#498	D₁₉	1	1	yes	characteristic, complemented
49	#493	—	19	1	no	—
50	#492	—	19	2	no	—
51	#486	—	19	2	no	—
52	#322	—	19	1	no	—
53	C₂×C₁₉	#492	1	1	yes	characteristic
54	C₂×C₁₉	#496	1	2	yes	—
55	D₁₉	—	16	1	no	—
56	D₁₉	—	16	1	no	—
57	C₂×SD₁₆	—	38	4	no	—
58	C₂×D₈	—	38	2	no	—
59	C₄⋊Q₈	C₂×D₁₉	1	2	yes	—
60	#127	—	19	1	no	—
61	#127	—	19	1	no	—
62	#106	—	2	2	no	—
63	#102	—	38	4	no	—
64	C₄×C₈	—	19	2	no	—
65	C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
66	C₁₉	#1715	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	2	2	no	—
68	C₂×D₄	—	38	2	no	—
69	C₂×D₄	—	38	2	no	—
70	C₂×D₄	—	38	1	no	—
71	C₂×D₄	—	38	1	no	—
72	SD₁₆	—	76	8	no	—
73	D₈	—	76	4	no	—
74	C₂×C₈	—	19	4	no	—
75	C₂×C₈	C₂²⋊D₁₉	1	2	yes	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	2	2	no	—
78	C₄²	C₂²×D₁₉	1	1	yes	characteristic
79	C₂³	—	76	1	no	—
80	C₂³	—	76	1	no	—
81	Q₈	—	4	4	no	—
82	D₄	—	76	2	no	—
83	D₄	—	76	2	no	—
84	D₄	—	76	4	no	—
85	D₄	—	76	4	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	D₄×D₁₉	1	2	yes	—
88	C₂×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
89	C₈	—	38	4	no	—
90	C₈	#64527	1	4	yes	complemented
91	C₂²	—	152	1	no	—
92	C₂²	—	152	1	no	—
93	C₂²	—	152	2	no	—
94	C₂²	—	152	2	no	—
95	C₂²	#10597386	1	1	yes	characteristic
96	C₄	—	8	2	no	—
97	C₄	#10597360	1	4	yes	—
98	C₄	C₂×#64527	1	2	yes	—
99	C₂	—	304	1	no	—
100	C₂	—	304	1	no	—
101	C₂	#11926918	1	1	yes	characteristic
102	C₂	#11926930	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11926921

C₂

yes

maximal, characteristic

#11926918

C₂

yes

maximal, complemented

#11926892

C₂

yes

maximal, complemented

#11926265

C₂

yes

maximal, characteristic, complemented

C₁₉×#498

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

—

C₂×#64527

—

C₂×D₁₅₂

—

#10597320

C₂²

yes

characteristic

#10597320

C₂²

yes

characteristic

C₁₉×#106

—

C₄×C₈×C₁₉

C₂²

yes

characteristic

#10597266

—

C₄×C₁₉⋊C₈

C₂²

yes

—

C₂×Q₈×C₁₉

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₈×C₁₉

D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

#64527

—

C₂×C₁₉⋊C₈

D₄

yes

—

D₁₅₂

—

C₂²×D₁₉

—

C₂²×D₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

D₇₆

—

D₇₆

—

D₇₆

—

D₇₆

—

C₈×C₁₉

SD₁₆

yes

complemented

C₁₉⋊C₈

—

—

C₂²×C₁₉

yes

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

C₂×SD₁₆

yes

—

C₄×C₁₉

AGL(1,ℤ/8)

yes

—

#498

D₁₉

yes

characteristic, complemented

—

—

—

—

C₂×C₁₉

#492

yes

characteristic

C₂×C₁₉

#496

yes

—

D₁₉

—

D₁₉

—

C₂×SD₁₆

—

C₂×D₈

—

C₄⋊Q₈

C₂×D₁₉

yes

—

—

—

—

—

C₄×C₈

—

C₄×C₈

C₂×D₁₉

yes

characteristic

C₁₉

#1715

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

SD₁₆

—

D₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₁₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²×D₁₉

yes

characteristic

C₂³

—

C₂³

—

Q₈

—

D₄

—

D₄

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

D₄×D₁₉

yes

—

C₂×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

C₈

—

C₈

#64527

yes

complemented

C₂²

—

152

—

C₂²

—

152

—

C₂²

—

152

—

C₂²

—

152

—

C₂²

#10597386

yes

characteristic

C₄

—

C₄

#10597360

yes

—

C₄

C₂×#64527

yes

—

C₂

—

304

—

100

C₂

—

304

—

101

C₂

#11926918

yes

characteristic

102

C₂

#11926930

yes

—

	subgroup	G/H
center	C₂²	#10597386
commutator, cosocle	C₄²×C₁₉	C₂³
Frattini	C₄²	C₂²×D₁₉
Fitting	C₁₉×#498	C₂
socle	C₂²×C₁₉	#127
prime radical	#11926921	C₂
hypercenter	#498	D₁₉
hypocenter	C₁₉	#1715
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

#10597386

commutator, cosocle

C₄²×C₁₉

C₂³

Frattini

C₄²

C₂²×D₁₉

Fitting

C₁₉×#498

C₂

C₂²×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #11926918	C₂	semidirect
3. #11926892	C₂	semidirect
4. #11926265	C₂	semidirect
5. C₁₉×#498	C₂	semidirect
37. C₈×C₁₉	SD₁₆	semidirect
48. #498	D₁₉	semidirect
66. C₁₉	#1715	semidirect
90. C₈	#64527	semidirect

H ≅ G/N

type

2. #11926918

C₂

semidirect

3. #11926892

C₂

semidirect

4. #11926265

C₂

semidirect

5. C₁₉×#498

C₂

semidirect

37. C₈×C₁₉

SD₁₆

semidirect

48. #498

D₁₉

semidirect

66. C₁₉

#1715

semidirect

90. C₈

#64527

semidirect

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

subgroup	index
#11926921	2
#11926918	2
#11926892	2
#11926265	2
C₁₉×#498	2
#1715	19

subgroup

index

C₁₉×#498

Subgroups — #14563264

Conjugacy classes of subgroups

Complements

Maximal subgroups