Group #18069999 — subgroups

Subgroups — #18069999

Order 4864.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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	C₄×Dic₁₅₂	C₂	1	1	yes	maximal, characteristic
2	#14561709	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1397	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₅₂	C₄	1	1	yes	characteristic
5	C₄×Dic₇₆	—	2	1	no	—
6	#11926370	C₄	1	1	yes	characteristic
7	#11926349	—	2	1	no	—
8	#11926297	—	2	1	no	—
9	C₂×C₁₉×C₃₂	—	2	1	no	—
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₇₆	—	2	1	no	—
12	C₄×Dic₃₈	—	4	1	no	—
13	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
15	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
16	#10597275	—	2	1	no	—
17	#10597273	—	4	1	no	—
18	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
19	Dic₁₅₂	—	2	1	no	—
20	Dic₁₅₂	C₈	1	2	yes	complemented
21	C₁₉×C₃₂	—	2	2	no	—
22	C₂×Dic₃₈	—	4	1	no	—
23	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉	SD₁₆	1	1	yes	characteristic
25	C₄²×C₁₉	D₈	1	1	yes	characteristic
26	C₄⋊Dic₁₉	—	4	1	no	—
27	Dic₁₉⋊C₄	—	8	1	no	—
28	C₄×Dic₁₉	—	8	1	no	—
29	C₂×C₁₉⋊C₈	—	8	1	no	—
30	Dic₇₆	—	2	2	no	—
31	Dic₇₆	—	4	1	no	—
32	C₁₆×C₁₉	—	2	1	no	—
33	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
34	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
35	#7386	—	19	1	no	maximal, Sylow
36	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
37	C₂×C₄×C₁₉	D₁₆	1	1	yes	characteristic
38	C₂×C₄×C₁₉	SD₃₂	1	1	yes	characteristic
39	C₂×Dic₁₉	—	8	1	no	—
40	C₂×Dic₁₉	—	8	1	no	—
41	Dic₃₈	—	4	2	no	—
42	Dic₃₈	—	8	1	no	—
43	C₈×C₁₉	—	2	1	no	—
44	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₈×C₁₉	#104	1	1	yes	characteristic
46	C₁₉⋊C₈	—	16	1	no	—
47	C₄×Q₃₂	—	19	1	no	—
48	#1397	D₁₉	1	1	yes	characteristic
49	#1372	—	19	1	no	—
50	C₂²×C₁₉	#357	1	1	yes	characteristic
51	C₄×C₁₉	—	2	1	no	—
52	C₄×C₁₉	—	2	1	no	—
53	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
54	C₄×C₁₉	#359	1	1	yes	characteristic
55	Dic₁₉	—	8	2	no	—
56	Dic₁₉	—	16	1	no	—
57	C₂×Q₃₂	—	19	1	no	—
58	C₄×Q₁₆	—	38	1	no	—
59	C₂×C₃₂	—	2	1	no	—
60	#366	—	19	1	no	—
61	#358	—	38	1	no	—
62	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
63	#335	—	38	1	no	—
64	C₂×C₁₉	#1331	1	1	yes	characteristic
65	C₂×C₁₉	#1418	1	1	yes	characteristic
66	C₂×C₁₉	#1420	1	1	yes	characteristic
67	C₂×Q₁₆	—	38	1	no	—
68	C₄×Q₈	—	76	1	no	—
69	Q₃₂	—	19	2	no	—
70	Q₃₂	—	38	1	no	—
71	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
72	C₂×C₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
73	#107	—	38	1	no	—
74	C₄⋊C₈	—	76	1	no	—
75	#103	—	76	1	no	—
76	C₄×C₈	D₇₆	1	1	yes	characteristic
77	C₃₂	—	2	2	no	—
78	C₁₉	#7386	1	1	yes	characteristic, complemented, Sylow
79	C₂×Q₈	—	76	1	no	—
80	Q₁₆	—	38	2	no	—
81	Q₁₆	—	76	1	no	—
82	C₂×C₈	—	152	1	no	—
83	C₂×C₈	#64516	1	1	yes	characteristic
84	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
85	C₄⋊C₄	—	76	1	no	—
86	C₄⋊C₄	—	152	1	no	—
87	C₄²	—	152	1	no	—
88	C₄²	D₁₅₂	1	1	yes	characteristic
89	C₁₆	—	2	1	no	—
90	C₁₆	C₈×D₁₉	1	1	yes	characteristic
91	C₁₆	#64515	1	1	yes	characteristic
92	Q₈	—	76	2	no	—
93	Q₈	—	152	1	no	—
94	C₂×C₄	—	152	1	no	—
95	C₂×C₄	—	152	1	no	—
96	C₂×C₄	D₃₀₄	1	1	yes	characteristic
97	C₂×C₄	#10597257	1	1	yes	characteristic
98	C₂×C₄	#10597278	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	304	1	no	—
101	C₈	#10597262	1	1	yes	characteristic
102	C₈	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
103	C₂²	#11926346	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	304	1	no	—
107	C₄	—	152	2	no	—
108	C₄	#11926273	1	1	yes	characteristic
109	C₄	#11926352	1	1	yes	characteristic
110	C₂	#14561597	1	1	yes	characteristic
111	C₂	#14561823	1	1	yes	characteristic
112	C₂	#14561829	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×Dic₁₅₂

C₂

yes

maximal, characteristic

#14561709

C₂

yes

maximal, characteristic

C₁₉×#1397

C₂

yes

maximal, characteristic

C₂×Dic₁₅₂

C₄

yes

characteristic

C₄×Dic₇₆

—

#11926370

C₄

yes

characteristic

#11926349

—

#11926297

—

C₂×C₁₉×C₃₂

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

C₂×Dic₇₆

—

C₄×Dic₃₈

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597275

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

Dic₁₅₂

—

Dic₁₅₂

C₈

yes

complemented

C₁₉×C₃₂

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

Dic₇₆

—

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

M₁₆

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

D₁₆

yes

characteristic

C₂×C₄×C₁₉

SD₃₂

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

#104

yes

characteristic

C₁₉⋊C₈

—

C₄×Q₃₂

—

#1397

D₁₉

yes

characteristic

#1372

—

C₂²×C₁₉

#357

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

#359

yes

characteristic

Dic₁₉

—

Dic₁₉

—

C₂×Q₃₂

—

C₄×Q₁₆

—

C₂×C₃₂

—

#366

—

#358

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

#335

—

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×C₁₉

yes

C₂×Q₁₆

—

C₄×Q₈

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₁₉

yes

characteristic

#107

—

C₄⋊C₈

—

#103

—

C₄×C₈

D₇₆

yes

characteristic

C₃₂

—

C₁₉

#7386

yes

characteristic, complemented, Sylow

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

152

—

C₂×C₈

#64516

yes

characteristic

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

152

—

C₄²

—

152

—

C₄²

D₁₅₂

yes

characteristic

C₁₆

—

C₁₆

C₈×D₁₉

yes

characteristic

C₁₆

#64515

yes

characteristic

Q₈

—

Q₈

—

152

—

C₂×C₄

—

152

—

C₂×C₄

—

152

—

C₂×C₄

D₃₀₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

100

C₈

—

304

—

101

C₈

#10597262

yes

characteristic

102

C₈

(C₂×D₁₉)⋊C₈

yes

characteristic

103

C₂²

#11926346

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

304

—

107

C₄

—

152

—

108

C₄

#11926273

yes

characteristic

109

C₄

#11926352

yes

characteristic

110

C₂

#14561597

yes

characteristic

111

C₂

#14561823

yes

characteristic

112

C₂

#14561829

yes

characteristic

	subgroup	G/H
center	C₂²	#11926346
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1397	C₂
socle, prime radical	C₂²×C₁₉	#357
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1397	D₁₉
hypocenter	C₁₉	#7386
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₂²

#11926346

commutator

C₁₆×C₁₉

C₂×C₈

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#1397

C₂

socle, prime radical

C₂²×C₁₉

#357

cosocle

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
20. Dic₁₅₂	C₈	semidirect
78. C₁₉	#7386	semidirect

H ≅ G/N

type

20. Dic₁₅₂

C₈

semidirect

78. C₁₉

#7386

semidirect

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

subgroup	index
C₄×Dic₁₅₂	2
#14561709	2
C₁₉×#1397	2
#7386	19

subgroup

index

C₄×Dic₁₅₂

#14561709

C₁₉×#1397

#7386

Subgroups — #18069999

Conjugacy classes of subgroups

Complements

Maximal subgroups