Group #18069936 — subgroups

Subgroups — #18069936

Order 4864.

184 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 43 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	#14561586	C₂	1	2	yes	maximal
2	C₁₉×#1994	C₂	1	1	yes	maximal, characteristic
3	#11926326	—	2	2	no	—
4	C₁₉×#533	C₄	1	1	yes	characteristic
5	C₁₉×#423	C₂²	1	1	yes	characteristic
6	C₄³×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#339	—	2	2	no	—
8	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
9	C₁₉×C₄⋊Q₈	—	2	1	no	—
10	C₁₉×#125	C₈	1	2	yes	—
11	C₁₉×C₂²⋊Q₈	—	4	1	no	—
12	C₄×Q₈×C₁₉	—	4	1	no	—
13	C₁₉×#117	—	2	1	no	—
14	C₂×C₄²×C₁₉	—	2	1	no	—
15	C₂×C₄²×C₁₉	—	4	1	no	—
16	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	#10597269	—	4	2	no	—
19	C₂×Q₈×C₁₉	—	4	1	no	—
20	C₂²×C₄×C₁₉	—	2	1	no	—
21	C₂²×C₄×C₁₉	—	4	1	no	—
22	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
23	M₁₆×C₁₉	—	4	2	no	—
24	C₂×C₈×C₁₉	—	2	2	no	—
25	C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₄⋊C₄×C₁₉	—	4	2	no	—
27	C₄⋊C₄×C₁₉	—	4	1	no	—
28	C₂²⋊C₄×C₁₉	—	4	1	no	—
29	C₄²×C₁₉	—	2	1	no	—
30	C₄²×C₁₉	—	2	2	no	—
31	C₄²×C₁₉	—	4	1	no	—
32	C₄²×C₁₉	—	4	4	no	—
33	C₄²×C₁₉	—	4	1	no	—
34	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
35	C₄²×C₁₉	M₁₆	1	1	yes	characteristic
36	C₁₉⋊C₁₆	—	8	2	no	—
37	#7361	—	19	1	no	maximal, Sylow
38	C₂³×C₁₉	#100	1	1	yes	characteristic
39	Q₈×C₁₉	—	8	2	no	—
40	C₂×C₄×C₁₉	—	2	1	no	—
41	C₂×C₄×C₁₉	—	2	1	no	—
42	C₂×C₄×C₁₉	—	2	1	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	4	2	no	—
45	C₂×C₄×C₁₉	—	4	2	no	—
46	C₂×C₄×C₁₉	—	4	4	no	—
47	C₂×C₄×C₁₉	—	4	2	no	—
48	C₂×C₄×C₁₉	C₂²⋊C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
50	C₈×C₁₉	—	4	2	no	—
51	#1994	D₁₉	1	1	yes	characteristic
52	#1327	—	19	2	no	—
53	C₂²×C₁₉	—	2	1	no	—
54	C₂²×C₁₉	—	4	1	no	—
55	C₂²×C₁₉	#323	1	1	yes	characteristic
56	C₄×C₁₉	—	2	2	no	—
57	C₄×C₁₉	—	2	1	no	—
58	C₄×C₁₉	—	4	1	no	—
59	C₄×C₁₉	—	4	4	no	—
60	C₄×C₁₉	—	8	2	no	—
61	C₄×C₁₉	#354	1	1	yes	characteristic
62	C₄×C₁₉	#356	1	1	yes	characteristic
63	#533	Dic₁₉	1	1	yes	characteristic
64	#423	C₂×D₁₉	1	1	yes	characteristic
65	C₄³	Dic₁₉	1	1	yes	characteristic
66	#349	—	38	2	no	—
67	#339	—	2	2	no	—
68	C₂×C₁₉	—	2	1	no	—
69	C₂×C₁₉	—	4	1	no	—
70	C₂×C₁₉	#1319	1	1	yes	characteristic
71	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
72	C₄⋊Q₈	—	2	1	no	—
73	#125	C₁₉⋊C₈	1	2	yes	—
74	C₂²⋊Q₈	—	4	1	no	—
75	C₄×Q₈	—	4	1	no	—
76	#117	—	2	1	no	—
77	C₂×C₄²	—	2	1	no	—
78	C₂×C₄²	—	4	1	no	—
79	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
80	M₃₂	—	76	2	no	—
81	C₄⋊C₈	—	4	1	no	—
82	C₁₉	#7361	1	1	yes	characteristic, complemented, Sylow
83	C₂×Q₈	—	4	1	no	—
84	C₂²×C₄	—	2	1	no	—
85	C₂²×C₄	—	4	1	no	—
86	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
87	M₁₆	—	4	2	no	—
88	C₂×C₈	—	2	2	no	—
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	4	2	no	—
91	C₄⋊C₄	—	4	1	no	—
92	C₂²⋊C₄	—	4	1	no	—
93	C₄²	—	2	1	no	—
94	C₄²	—	2	2	no	—
95	C₄²	—	4	1	no	—
96	C₄²	—	4	4	no	—
97	C₄²	—	4	1	no	—
98	C₄²	C₂×C₁₉⋊C₈	1	1	yes	characteristic
99	C₄²	#64520	1	1	yes	characteristic
100	C₁₆	—	152	2	no	—
101	C₂³	#10597290	1	1	yes	characteristic
102	Q₈	—	8	2	no	—
103	C₂×C₄	—	2	1	no	—
104	C₂×C₄	—	2	1	no	—
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	4	2	no	—
108	C₂×C₄	—	4	2	no	—
109	C₂×C₄	—	4	4	no	—
110	C₂×C₄	—	4	2	no	—
111	C₂×C₄	C₂²⋊(C₁₉⋊C₈)	1	1	yes	characteristic
112	C₂×C₄	#10597291	1	1	yes	characteristic
113	C₈	—	4	2	no	—
114	C₂²	—	2	1	no	—
115	C₂²	—	4	1	no	—
116	C₂²	#11926268	1	1	yes	characteristic
117	C₄	—	2	2	no	—
118	C₄	—	2	1	no	—
119	C₄	—	4	1	no	—
120	C₄	—	4	4	no	—
121	C₄	—	8	2	no	—
122	C₄	#11926339	1	1	yes	characteristic
123	C₄	#11926343	1	1	yes	characteristic
124	C₂	—	2	1	no	—
125	C₂	—	4	1	no	—
126	C₂	#14561569	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14561586

C₂

yes

maximal

C₁₉×#1994

C₂

yes

maximal, characteristic

#11926326

—

C₁₉×#533

C₄

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄³×C₁₉

C₄

yes

characteristic

C₁₉×#339

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

—

C₁₉×#125

C₈

yes

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

#10597269

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

M₁₆

yes

characteristic

C₁₉⋊C₁₆

—

—

C₂³×C₁₉

yes

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₉

#99

yes

characteristic

C₈×C₁₉

—

#1994

D₁₉

yes

characteristic

#1327

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#323

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

yes

characteristic

#423

C₂×D₁₉

yes

characteristic

C₄³

Dic₁₉

yes

characteristic

#349

—

#339

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1319

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

—

C₄⋊Q₈

—

#125

C₁₉⋊C₈

yes

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

M₃₂

—

C₄⋊C₈

—

C₁₉

#7361

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×C₁₉⋊C₈

yes

characteristic

C₄²

#64520

yes

characteristic

100

C₁₆

—

152

—

101

C₂³

#10597290

yes

characteristic

102

Q₈

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

C₂²⋊(C₁₉⋊C₈)

yes

characteristic

112

C₂×C₄

#10597291

yes

characteristic

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

#11926268

yes

characteristic

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

#11926339

yes

characteristic

123

C₄

#11926343

yes

characteristic

124

C₂

—

125

C₂

—

126

C₂

#14561569

yes

characteristic

	subgroup	G/H
center	C₄	#11926339
commutator	C₄²×C₁₉	C₂×C₈
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1994	C₂
socle	C₂×C₁₉	#1319
prime radical	C₂³×C₁₉	#100
cosocle	C₁₉×#423	C₂²
hypercenter	#1994	D₁₉
hypocenter	C₁₉	#7361
LCS	G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1994

subgroup

G/H

center

C₄

#11926339

commutator

C₄²×C₁₉

C₂×C₈

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1994

C₂

C₂×C₁₉

C₂³×C₁₉

C₁₉×#423

C₂²

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1994

N	H ≅ G/N	type
82. C₁₉	#7361	semidirect

H ≅ G/N

type

82. C₁₉

#7361

semidirect

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

subgroup	index
#14561586	2
C₁₉×#1994	2
#7361	19

subgroup

index

#14561586

C₁₉×#1994

#7361

Subgroups — #18069936

Conjugacy classes of subgroups

Complements

Maximal subgroups