Group #18070164 — subgroups

Subgroups — #18070164

Order 4864.

136 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 37 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	#14565210	C₂	1	1	yes	maximal, characteristic
2	#14561546	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1327	C₂	1	1	yes	maximal, characteristic
4	#11926601	—	2	1	no	—
5	#11926593	C₄	1	1	yes	characteristic
6	#11926316	—	2	1	no	—
7	#11926304	—	2	1	no	—
8	#11926301	C₄	1	1	yes	characteristic
9	C₁₉×#423	C₂²	1	1	yes	characteristic
10	C₁₉×#349	—	2	1	no	—
11	C₂×M₁₆×C₁₉	C₂×C₄	1	1	yes	characteristic
12	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
14	#10597372	—	2	1	no	—
15	C₂×#64520	—	2	1	no	—
16	C₁₉×M₃₂	—	4	1	no	—
17	C₁₉×C₄⋊C₈	—	4	1	no	—
18	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
19	#10597276	—	4	1	no	—
20	C₄⋊(C₁₉⋊C₈)	—	4	1	no	—
21	#10597260	—	4	1	no	—
22	C₂²×C₄×C₁₉	—	2	1	no	—
23	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
24	M₁₆×C₁₉	—	4	1	no	—
25	M₁₆×C₁₉	—	4	1	no	—
26	C₂×C₈×C₁₉	—	2	1	no	—
27	C₂×C₈×C₁₉	—	2	1	no	—
28	C₄²×C₁₉	—	2	1	no	—
29	C₄²×C₁₉	SD₁₆	1	1	yes	characteristic
30	C₄²×C₁₉	Q₁₆	1	1	yes	characteristic
31	C₂²⋊Dic₁₉	—	4	1	no	—
32	C₄⋊Dic₁₉	—	4	1	no	—
33	C₄×Dic₁₉	—	4	1	no	—
34	#64520	—	4	1	no	—
35	#64520	—	4	1	no	—
36	C₂×C₁₉⋊C₈	—	4	2	no	—
37	C₂×C₁₉⋊C₈	—	4	1	no	—
38	C₁₆×C₁₉	—	8	1	no	—
39	#7441	—	19	1	no	maximal, Sylow
40	C₂³×C₁₉	#104	1	1	yes	characteristic
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	—	2	1	no	—
45	C₂×C₄×C₁₉	—	8	1	no	—
46	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
47	C₂×C₄×C₁₉	#103	1	1	yes	characteristic
48	C₂×Dic₁₉	—	8	1	no	—
49	C₈×C₁₉	—	4	1	no	—
50	C₈×C₁₉	—	4	1	no	—
51	C₁₉⋊C₈	—	8	2	no	—
52	C₁₉⋊C₈	—	8	1	no	—
53	#2102	—	19	1	no	—
54	#1327	D₁₉	1	1	yes	characteristic
55	#1307	—	19	1	no	—
56	C₂²×C₁₉	—	2	1	no	—
57	C₂²×C₁₉	—	4	1	no	—
58	C₂²×C₁₉	#328	1	1	yes	characteristic
59	C₄×C₁₉	—	2	1	no	—
60	C₄×C₁₉	—	4	1	no	—
61	C₄×C₁₉	—	4	1	no	—
62	C₄×C₁₉	#352	1	1	yes	characteristic
63	C₄×C₁₉	#355	1	1	yes	characteristic
64	Dic₁₉	—	16	1	no	—
65	#432	—	38	1	no	—
66	#430	—	19	1	no	—
67	#423	C₂×D₁₉	1	1	yes	characteristic
68	#349	—	2	1	no	—
69	#344	—	38	1	no	—
70	#339	—	38	1	no	—
71	H(3,ℤ/4)	—	19	1	no	—
72	C₂×C₁₉	—	2	1	no	—
73	C₂×C₁₉	—	4	1	no	—
74	C₂×C₁₉	#1353	1	1	yes	characteristic
75	C₂×M₁₆	—	38	1	no	—
76	C₂×M₁₆	C₄×D₁₉	1	1	yes	characteristic
77	C₂×M₁₆	C₂²⋊D₁₉	1	1	yes	characteristic
78	#117	—	38	1	no	—
79	C₂×C₄²	D₇₆	1	1	yes	characteristic
80	M₃₂	—	4	1	no	—
81	#108	—	76	1	no	—
82	C₄⋊C₈	—	4	1	no	—
83	C₄⋊C₈	—	76	1	no	—
84	C₂²⋊C₈	—	38	2	no	—
85	#97	—	76	1	no	—
86	C₁₉	#7441	1	1	yes	characteristic, complemented, Sylow
87	C₂²×C₄	—	2	1	no	—
88	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
89	M₁₆	—	4	1	no	—
90	M₁₆	—	4	1	no	—
91	M₁₆	—	76	1	no	—
92	M₁₆	—	76	1	no	—
93	C₂×C₈	—	2	1	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	76	2	no	—
96	C₂×C₈	—	76	1	no	—
97	C₄⋊C₄	—	76	1	no	—
98	C₂²⋊C₄	—	76	1	no	—
99	C₄²	—	2	1	no	—
100	C₄²	—	76	1	no	—
101	C₄²	#64516	1	1	yes	characteristic
102	C₄²	Dic₇₆	1	1	yes	characteristic
103	C₁₆	—	8	1	no	—
104	C₂³	#10597282	1	1	yes	characteristic
105	C₂×C₄	—	2	1	no	—
106	C₂×C₄	—	2	1	no	—
107	C₂×C₄	—	2	1	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	8	1	no	—
110	C₂×C₄	—	152	1	no	—
111	C₂×C₄	#10597263	1	1	yes	characteristic
112	C₂×C₄	#10597273	1	1	yes	characteristic
113	C₈	—	4	1	no	—
114	C₈	—	4	1	no	—
115	C₈	—	152	2	no	—
116	C₈	—	152	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	4	1	no	—
119	C₂²	#11926282	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	4	1	no	—
122	C₄	—	4	1	no	—
123	C₄	—	304	1	no	—
124	C₄	#11926333	1	1	yes	characteristic
125	C₄	#11926340	1	1	yes	characteristic
126	C₂	—	2	1	no	—
127	C₂	—	4	1	no	—
128	C₂	#14561663	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14565210

C₂

yes

maximal, characteristic

#14561546

C₂

yes

maximal, characteristic

C₁₉×#1327

C₂

yes

maximal, characteristic

#11926601

—

#11926593

C₄

yes

—

—

C₄

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#349

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

characteristic

C₂×M₁₆×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

characteristic

#10597372

—

C₂×#64520

—

C₁₉×M₃₂

—

C₁₉×C₄⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

#10597276

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

SD₁₆

yes

characteristic

C₄²×C₁₉

Q₁₆

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₁₆×C₁₉

—

—

C₂³×C₁₉

yes

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×Dic₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#2102

—

#1327

D₁₉

yes

characteristic

#1307

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#328

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

Dic₁₉

—

#432

—

#430

—

#423

C₂×D₁₉

yes

—

—

—

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1353

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

C₄×D₁₉

yes

characteristic

C₂×M₁₆

C₂²⋊D₁₉

yes

characteristic

#117

—

C₂×C₄²

D₇₆

yes

characteristic

M₃₂

—

#108

—

C₄⋊C₈

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₁₉

#7441

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

100

C₄²

—

101

C₄²

#64516

yes

characteristic

102

C₄²

Dic₇₆

yes

characteristic

103

C₁₆

—

104

C₂³

#10597282

yes

characteristic

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

152

—

111

C₂×C₄

#10597263

yes

characteristic

112

C₂×C₄

#10597273

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

—

152

—

116

C₈

—

152

—

117

C₂²

—

118

C₂²

—

119

C₂²

#11926282

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

304

—

124

C₄

#11926333

yes

characteristic

125

C₄

#11926340

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

#14561663

yes

characteristic

	subgroup	G/H
center	C₂	#14561663
commutator	C₂×M₁₆×C₁₉	C₂×C₄
Frattini	#423	C₂×D₁₉
Fitting	C₁₉×#1327	C₂
socle	C₂×C₁₉	#1353
prime radical	C₂³×C₁₉	#104
cosocle	C₁₉×#423	C₂²
hypercenter	#1327	D₁₉
hypocenter	C₁₉	#7441
LCS	G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

subgroup

G/H

center

C₂

#14561663

commutator

C₂×M₁₆×C₁₉

C₂×C₄

Frattini

#423

C₂×D₁₉

Fitting

C₁₉×#1327

C₂

C₂×C₁₉

C₂³×C₁₉

C₁₉×#423

C₂²

D₁₉

C₁₉

G ▷ C₂×M₁₆×C₁₉ ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #423 ◁ #1327

N	H ≅ G/N	type
86. C₁₉	#7441	semidirect

H ≅ G/N

type

86. C₁₉

#7441

semidirect

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

subgroup	index
#14565210	2
#14561546	2
C₁₉×#1327	2
#7441	19

subgroup

index

#14565210

#14561546

C₁₉×#1327

#7441

Subgroups — #18070164

Conjugacy classes of subgroups

Complements

Maximal subgroups