Group #18070000 — subgroups

Subgroups — #18070000

Order 4864.

120 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 47 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	#14565517	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#1373	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926976	C₄	1	1	yes	characteristic
5	#11926662	—	2	1	no	—
6	C₂×C₁₉⋊C₃₂	—	2	1	no	—
7	#11926374	C₄	1	1	yes	characteristic
8	#11926352	—	2	1	no	—
9	C₁₉×#364	—	2	1	no	—
10	C₄×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
11	#10597350	—	2	1	no	—
12	#10597347	—	4	1	no	—
13	C₁₉×M₃₂	—	4	1	no	—
14	C₂×C₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₁₉	D₄	1	1	yes	characteristic
16	C₄×C₈×C₁₉	D₄	1	1	yes	characteristic
17	#10597276	—	2	1	no	—
18	#10597262	—	4	1	no	—
19	Dic₁₅₂	C₈	1	1	yes	characteristic
20	#10597257	—	2	1	no	—
21	D₃₀₄	C₈	1	1	yes	characteristic
22	C₁₉⋊C₃₂	—	2	2	no	—
23	#64541	—	4	1	no	—
24	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₉	D₈	1	1	yes	characteristic
26	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
27	#64520	—	4	1	no	—
28	Dic₇₆	—	2	1	no	—
29	D₁₅₂	—	2	1	no	—
30	#64516	—	4	1	no	—
31	#64515	—	8	1	no	—
32	C₈×D₁₉	—	8	1	no	—
33	C₁₆×C₁₉	—	2	1	no	—
34	C₁₆×C₁₉	—	8	1	no	—
35	C₁₆×C₁₉	C₂×C₈	1	1	yes	characteristic
36	C₁₆×C₁₉	M₁₆	1	1	yes	characteristic
37	#7387	—	19	1	no	maximal, Sylow
38	C₂×C₄×C₁₉	—	2	1	no	—
39	C₂×C₄×C₁₉	#102	1	1	yes	characteristic
40	C₂²⋊D₁₉	—	8	1	no	—
41	D₇₆	—	4	1	no	—
42	C₄×D₁₉	—	8	1	no	—
43	Dic₃₈	—	4	1	no	—
44	C₈×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₈×C₁₉	#104	1	1	yes	characteristic
46	C₈×C₁₉	D₁₆	1	1	yes	characteristic
47	C₈×C₁₉	SD₃₂	1	1	yes	characteristic
48	C₁₉⋊C₈	—	8	1	no	—
49	#2178	—	19	1	no	—
50	C₄×C₃₂	—	19	1	no	—
51	#1373	D₁₉	1	1	yes	characteristic, complemented
52	C₂²×C₁₉	#359	1	1	yes	characteristic
53	C₂×D₁₉	—	8	1	no	—
54	C₄×C₁₉	—	2	2	no	—
55	C₄×C₁₉	D₄⋊C₈	1	1	yes	characteristic
56	C₄×C₁₉	#357	1	1	yes	characteristic
57	Dic₁₉	—	8	1	no	—
58	#508	—	19	1	no	—
59	#443	—	38	1	no	—
60	C₂×C₃₂	—	38	1	no	—
61	#368	—	19	1	no	—
62	#364	—	2	1	no	—
63	#359	—	38	1	no	—
64	C₄×C₁₆	C₂×D₁₉	1	1	yes	characteristic
65	C₂×C₁₉	—	2	1	no	—
66	C₂×C₁₉	#1331	1	1	yes	characteristic
67	D₁₉	—	16	1	no	—
68	#135	—	38	1	no	—
69	#131	—	76	1	no	—
70	Q₃₂	—	19	1	no	—
71	SD₃₂	—	38	1	no	—
72	D₁₆	—	19	1	no	—
73	M₃₂	—	4	1	no	—
74	C₂×C₁₆	C₄×D₁₉	1	1	yes	characteristic
75	C₂×C₁₆	D₇₆	1	1	yes	characteristic
76	#108	—	38	1	no	—
77	#104	—	76	1	no	—
78	C₄×C₈	C₂²⋊D₁₉	1	1	yes	characteristic
79	C₃₂	—	38	2	no	—
80	C₁₉	#7387	1	1	yes	characteristic, complemented, Sylow
81	#41	—	76	1	no	—
82	Q₁₆	—	38	1	no	—
83	SD₁₆	—	76	1	no	—
84	D₈	—	38	1	no	—
85	M₁₆	—	76	1	no	—
86	M₁₆	—	152	1	no	—
87	C₂×C₈	—	152	1	no	—
88	C₂×C₈	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
89	C₂×C₈	#64525	1	1	yes	characteristic
90	C₄²	#64527	1	1	yes	characteristic
91	C₁₆	—	2	1	no	—
92	C₁₆	—	8	1	no	—
93	C₁₆	C₈×D₁₉	1	1	yes	characteristic
94	C₁₆	#64515	1	1	yes	characteristic
95	Q₈	—	76	1	no	—
96	D₄	—	76	1	no	—
97	D₄	—	152	1	no	—
98	C₂×C₄	—	2	1	no	—
99	C₂×C₄	—	152	1	no	—
100	C₂×C₄	#10597266	1	1	yes	characteristic
101	C₈	—	152	1	no	—
102	C₈	(C₂×D₁₉)⋊C₈	1	1	yes	characteristic
103	C₈	#10597282	1	1	yes	characteristic
104	C₈	#10597283	1	1	yes	characteristic
105	C₈	#10597285	1	1	yes	characteristic
106	C₂²	—	152	1	no	—
107	C₂²	#11926350	1	1	yes	characteristic
108	C₄	—	2	2	no	—
109	C₄	—	152	1	no	—
110	C₄	#11926271	1	1	yes	characteristic
111	C₄	#11926344	1	1	yes	characteristic
112	C₂	—	2	1	no	—
113	C₂	—	304	1	no	—
114	C₂	#14561595	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565517

C₂

yes

maximal, characteristic

C₄×C₁₉⋊C₃₂

C₂

yes

maximal, characteristic, complemented

C₁₉×#1373

C₂

yes

maximal, characteristic, complemented

#11926976

C₄

yes

characteristic

#11926662

—

C₂×C₁₉⋊C₃₂

—

#11926374

C₄

yes

characteristic

#11926352

—

C₁₉×#364

—

C₄×C₁₆×C₁₉

C₂²

yes

characteristic

#10597350

—

#10597347

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

D₄

yes

characteristic

C₄×C₈×C₁₉

D₄

yes

characteristic

#10597276

—

#10597262

—

Dic₁₅₂

C₈

yes

characteristic

#10597257

—

D₃₀₄

C₈

yes

characteristic

C₁₉⋊C₃₂

—

#64541

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

SD₁₆

yes

characteristic

#64520

—

Dic₇₆

—

D₁₅₂

—

#64516

—

#64515

—

C₈×D₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

—

C₁₆×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

M₁₆

yes

characteristic

#7387

—

maximal, Sylow

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

characteristic

C₂²⋊D₁₉

—

D₇₆

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

C₂²⋊C₈

yes

characteristic

C₈×C₁₉

#104

yes

characteristic

C₈×C₁₉

D₁₆

yes

characteristic

C₈×C₁₉

SD₃₂

yes

characteristic

C₁₉⋊C₈

—

#2178

—

C₄×C₃₂

—

#1373

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

#359

yes

characteristic

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

D₄⋊C₈

yes

characteristic

C₄×C₁₉

#357

yes

characteristic

Dic₁₉

—

#508

—

#443

—

C₂×C₃₂

—

#368

—

#364

—

#359

—

C₄×C₁₆

C₂×D₁₉

yes

characteristic

C₂×C₁₉

—

C₂×C₁₉

#1331

yes

characteristic

D₁₉

—

#135

—

#131

—

Q₃₂

—

SD₃₂

—

D₁₆

—

M₃₂

—

C₂×C₁₆

C₄×D₁₉

yes

characteristic

C₂×C₁₆

D₇₆

yes

characteristic

#108

—

#104

—

C₄×C₈

C₂²⋊D₁₉

yes

characteristic

C₃₂

—

C₁₉

#7387

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

152

—

C₂×C₈

—

152

—

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

C₂×C₈

yes

C₄²

yes

C₁₆

—

C₁₆

—

C₁₆

C₈×D₁₉

yes

characteristic

C₁₆

#64515

yes

characteristic

Q₈

—

D₄

—

D₄

—

152

—

C₂×C₄

—

C₂×C₄

—

152

—

100

C₂×C₄

#10597266

yes

characteristic

101

C₈

—

152

—

102

C₈

(C₂×D₁₉)⋊C₈

yes

characteristic

103

C₈

#10597282

yes

characteristic

104

C₈

#10597283

yes

characteristic

105

C₈

#10597285

yes

characteristic

106

C₂²

—

152

—

107

C₂²

#11926350

yes

characteristic

108

C₄

—

109

C₄

—

152

—

110

C₄

#11926271

yes

characteristic

111

C₄

#11926344

yes

characteristic

112

C₂

—

113

C₂

—

304

—

114

C₂

#14561595

yes

characteristic

	subgroup	G/H
center	C₈	#10597283
commutator	C₁₆×C₁₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₁₉
Fitting	C₁₉×#1373	C₂
socle	C₂×C₁₉	#1331
prime radical	#11926976	C₄
cosocle	C₄×C₁₆×C₁₉	C₂²
hypercenter	#1373	D₁₉
hypocenter	C₁₉	#7387
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

subgroup

G/H

center

C₈

#10597283

commutator

C₁₆×C₁₉

C₂×C₈

Frattini

C₄×C₁₆

C₂×D₁₉

Fitting

C₁₉×#1373

C₂

C₂×C₁₉

C₄

C₄×C₁₆×C₁₉

C₂²

D₁₉

C₁₉

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

UCS

C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1373

N	H ≅ G/N	type
2. C₄×C₁₉⋊C₃₂	C₂	semidirect
3. C₁₉×#1373	C₂	semidirect
51. #1373	D₁₉	semidirect
80. C₁₉	#7387	semidirect

H ≅ G/N

type

2. C₄×C₁₉⋊C₃₂

C₂

semidirect

3. C₁₉×#1373

C₂

semidirect

51. #1373

D₁₉

semidirect

80. C₁₉

#7387

semidirect

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

subgroup	index
#14565517	2
C₄×C₁₉⋊C₃₂	2
C₁₉×#1373	2
#7387	19

subgroup

index

#14565517

C₄×C₁₉⋊C₃₂

C₁₉×#1373

#7387

Subgroups — #18070000

Conjugacy classes of subgroups

Complements

Maximal subgroups