Group #14565850 — subgroups

Subgroups — #14565850

Order 2432.

134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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	#11926797	C₂	1	1	yes	maximal, characteristic
2	#11926593	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926367	C₂	1	2	yes	maximal, complemented
4	#11926358	C₂	1	2	yes	maximal, complemented
5	C₁₉×#349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
7	#10597376	—	2	1	no	—
8	C₂×#64520	—	2	1	no	—
9	C₂×D₁₅₂	C₂²	1	1	yes	characteristic
10	C₁₉×M₃₂	C₂²	1	2	yes	—
11	#10597278	—	2	1	no	—
12	#10597276	—	2	1	no	—
13	#10597276	C₂²	1	2	yes	—
14	#10597274	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂×C₂²⋊D₁₉	—	4	1	no	—
17	C₂×D₇₆	—	2	1	no	—
18	M₁₆×C₁₉	—	2	2	no	—
19	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	(C₂×D₁₉)⋊C₄	—	4	1	no	—
22	C₄⋊Dic₁₉	—	2	1	no	—
23	#64520	—	2	2	no	—
24	#64520	—	4	1	no	—
25	C₂×C₁₉⋊C₈	—	4	1	no	—
26	D₁₅₂	—	2	2	no	—
27	C₁₆×C₁₉	—	2	2	no	—
28	C₂³×C₁₉	SD₁₆	1	1	yes	characteristic
29	C₂²×D₁₉	—	4	1	no	—
30	C₂×C₄×C₁₉	—	2	1	no	—
31	C₂×C₄×C₁₉	—	2	1	no	—
32	C₂×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
33	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
34	C₂²⋊D₁₉	—	8	2	no	—
35	C₂×Dic₁₉	—	4	1	no	—
36	D₇₆	—	4	1	no	—
37	D₇₆	—	4	1	no	—
38	C₈×C₁₉	—	2	1	no	—
39	C₈×C₁₉	#41	1	2	yes	—
40	C₁₉⋊C₈	—	4	2	no	—
41	#2238	—	19	1	no	maximal, Sylow
42	C₂²×C₁₉	—	2	1	no	—
43	C₂²×C₁₉	—	4	1	no	—
44	C₂²×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
45	C₂×D₁₉	—	8	1	no	—
46	C₂×D₁₉	—	8	1	no	—
47	C₂×D₁₉	—	8	1	no	—
48	C₄×C₁₉	—	2	1	no	—
49	C₄×C₁₉	#123	1	1	yes	characteristic
50	C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
51	Dic₁₉	—	8	1	no	—
52	#469	—	19	1	no	—
53	#430	—	19	1	no	—
54	#365	—	19	2	no	—
55	#361	—	19	2	no	—
56	#349	D₁₉	1	1	yes	characteristic, complemented
57	C₂×C₁₉	—	2	1	no	—
58	C₂×C₁₉	—	4	1	no	—
59	C₂×C₁₉	#481	1	1	yes	characteristic
60	D₁₉	—	16	1	no	—
61	C₂×D₈	—	19	1	no	—
62	C₂×M₁₆	—	38	1	no	—
63	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
64	#121	—	38	1	no	—
65	M₃₂	C₂×D₁₉	1	2	yes	—
66	#108	—	19	2	no	—
67	#108	—	38	1	no	—
68	#106	—	19	1	no	—
69	#102	—	38	1	no	—
70	C₁₉	#2238	1	1	yes	characteristic, complemented, Sylow
71	C₂×D₄	—	38	1	no	—
72	C₂×D₄	—	76	1	no	—
73	C₂²×C₄	D₇₆	1	1	yes	characteristic
74	D₈	—	38	2	no	—
75	M₁₆	—	2	2	no	—
76	M₁₆	—	38	2	no	—
77	M₁₆	—	76	1	no	—
78	C₂×C₈	—	76	1	no	—
79	C₂×C₈	D₇₆	1	1	yes	characteristic
80	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
81	C₄⋊C₄	—	38	1	no	—
82	C₂²⋊C₄	—	76	1	no	—
83	C₁₆	—	2	2	no	—
84	C₂³	—	76	1	no	—
85	C₂³	#64516	1	1	yes	characteristic
86	D₄	—	76	1	no	—
87	D₄	—	76	1	no	—
88	D₄	—	152	2	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	76	1	no	—
92	C₂×C₄	#64516	1	1	yes	characteristic
93	C₂×C₄	C₂×D₇₆	1	1	yes	characteristic
94	C₈	—	2	1	no	—
95	C₈	—	76	2	no	—
96	C₈	#64543	1	2	yes	—
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	152	1	no	—
100	C₂²	—	152	1	no	—
101	C₂²	—	152	1	no	—
102	C₂²	C₂×#64516	1	1	yes	characteristic
103	C₄	—	2	1	no	—
104	C₄	—	152	1	no	—
105	C₄	#10597332	1	1	yes	characteristic
106	C₄	#10597354	1	1	yes	characteristic
107	C₂	—	2	1	no	—
108	C₂	—	4	1	no	—
109	C₂	—	304	1	no	—
110	C₂	#11926863	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11926797

C₂

yes

maximal, characteristic

#11926593

C₂

yes

maximal, characteristic, complemented

#11926367

C₂

yes

maximal, complemented

#11926358

C₂

yes

maximal, complemented

C₁₉×#349

C₂

yes

maximal, characteristic, complemented

C₂×M₁₆×C₁₉

C₂²

yes

characteristic

#10597376

—

C₂×#64520

—

C₂×D₁₅₂

C₂²

yes

characteristic

C₁₉×M₃₂

C₂²

yes

—

#10597278

—

#10597276

—

#10597276

C₂²

yes

—

#10597274

C₂²

yes

characteristic

C₂²×C₄×C₁₉

D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂×D₇₆

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

D₄

yes

characteristic

C₂×C₈×C₁₉

C₂³

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

D₁₅₂

—

C₁₆×C₁₉

—

C₂³×C₁₉

SD₁₆

yes

characteristic

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

SD₁₆

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₈×C₁₉

—

C₈×C₁₉

#41

yes

—

C₁₉⋊C₈

—

#2238

—

maximal, Sylow

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#481

yes

characteristic

D₁₉

—

C₂×D₈

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₁₉

yes

characteristic

#121

—

M₃₂

C₂×D₁₉

yes

—

—

—

—

—

C₁₉

#2238

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

D₇₆

yes

characteristic

D₈

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

D₇₆

yes

characteristic

C₂×C₈

C₂²×D₁₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

—

C₂³

#64516

yes

characteristic

D₄

—

D₄

—

D₄

—

152

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#64516

yes

characteristic

C₂×C₄

C₂×D₇₆

yes

characteristic

C₈

—

C₈

—

C₈

#64543

yes

—

C₂²

—

C₂²

—

C₂²

—

152

—

100

C₂²

—

152

—

101

C₂²

—

152

—

102

C₂²

C₂×#64516

yes

characteristic

103

C₄

—

104

C₄

—

152

—

105

C₄

#10597332

yes

characteristic

106

C₄

#10597354

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

—

304

—

110

C₂

#11926863

yes

characteristic

	subgroup	G/H
center	C₂	#11926863
commutator, cosocle	C₂×C₈×C₁₉	C₂³
Frattini	C₂×C₈	C₂²×D₁₉
Fitting	C₁₉×#349	C₂
socle	C₂×C₁₉	#481
prime radical	#11926797	C₂
hypercenter	#349	D₁₉
hypocenter	C₁₉	#2238
LCS	G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₂

#11926863

commutator, cosocle

C₂×C₈×C₁₉

C₂³

Frattini

C₂×C₈

C₂²×D₁₉

Fitting

C₁₉×#349

C₂

C₂×C₁₉

C₂

D₁₉

C₁₉

G ▷ C₂×C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
2. #11926593	C₂	semidirect
3. #11926367	C₂	semidirect
4. #11926358	C₂	semidirect
5. C₁₉×#349	C₂	semidirect
56. #349	D₁₉	semidirect
70. C₁₉	#2238	semidirect

H ≅ G/N

type

2. #11926593

C₂

semidirect

3. #11926367

C₂

semidirect

4. #11926358

C₂

semidirect

5. C₁₉×#349

C₂

semidirect

56. #349

D₁₉

semidirect

70. C₁₉

#2238

semidirect

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

subgroup	index
#11926797	2
#11926593	2
#11926367	2
#11926358	2
C₁₉×#349	2
#2238	19

subgroup

index

C₁₉×#349

Subgroups — #14565850

Conjugacy classes of subgroups

Complements

Maximal subgroups