Group #18070398 — subgroups

Subgroups — #18070398

Order 4864.

152 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 25 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	#14563240	C₂	1	1	yes	maximal, characteristic
2	#14561798	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1408	C₂	1	1	yes	maximal, characteristic
4	#11926924	C₄	1	1	yes	characteristic, complemented
5	#11926890	—	2	1	no	—
6	#11926890	—	2	1	no	—
7	#11926337	—	2	1	no	—
8	C₈×C₁₉⋊C₈	C₄	1	1	yes	characteristic, complemented
9	C₁₉×#493	C₂²	1	1	yes	characteristic
10	C₁₉×#353	—	2	1	no	—
11	C₂×D₈×C₁₉	—	4	1	no	—
12	C₁₉×#127	D₄	1	1	yes	characteristic
13	C₁₉×#127	D₄	1	1	yes	characteristic
14	C₂×Dic₇₆	—	4	1	no	—
15	#10597315	—	2	1	no	—
16	C₁₉×#99	—	4	1	no	—
17	C₄×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
18	#10597291	—	4	1	no	—
19	#10597289	—	4	2	no	—
20	#10597289	—	4	2	no	—
21	C₄×C₁₉⋊C₈	—	2	1	no	—
22	C₂×D₄×C₁₉	—	2	1	no	—
23	C₂×D₄×C₁₉	—	2	1	no	—
24	C₂×D₄×C₁₉	—	4	1	no	—
25	C₂×D₄×C₁₉	—	4	1	no	—
26	C₂×Dic₃₈	—	4	1	no	—
27	D₈×C₁₉	—	8	2	no	—
28	C₂×C₈×C₁₉	—	2	1	no	—
29	C₂²⋊C₄×C₁₉	—	8	1	no	—
30	C₄²×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²⋊Dic₁₉	—	8	1	no	—
32	C₄⋊Dic₁₉	—	4	1	no	—
33	C₄⋊Dic₁₉	—	4	1	no	—
34	C₂×C₁₉⋊C₈	—	2	2	no	—
35	Dic₇₆	—	8	2	no	—
36	#7530	—	19	1	no	maximal, Sylow
37	C₂³×C₁₉	—	4	1	no	—
38	C₂³×C₁₉	—	4	1	no	—
39	D₄×C₁₉	—	8	1	no	—
40	D₄×C₁₉	—	8	1	no	—
41	D₄×C₁₉	—	8	2	no	—
42	D₄×C₁₉	—	8	2	no	—
43	C₂×C₄×C₁₉	—	2	1	no	—
44	C₂×C₄×C₁₉	—	16	1	no	—
45	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
46	C₂×Dic₁₉	—	8	1	no	—
47	C₂×Dic₁₉	—	16	1	no	—
48	Dic₃₈	—	8	2	no	—
49	C₈×C₁₉	—	2	2	no	—
50	C₁₉⋊C₈	—	4	2	no	—
51	#1709	—	19	1	no	—
52	#1408	—	19	1	no	—
53	#1408	D₁₉	1	1	yes	characteristic
54	C₂²×C₁₉	—	8	1	no	—
55	C₂²×C₁₉	—	8	1	no	—
56	C₂²×C₁₉	—	16	1	no	—
57	C₂²×C₁₉	—	16	1	no	—
58	C₂²×C₁₉	#353	1	1	yes	characteristic
59	C₄×C₁₉	—	2	2	no	—
60	C₄×C₁₉	—	2	1	no	—
61	C₄×C₁₉	—	32	1	no	—
62	Dic₁₉	—	16	1	no	—
63	Dic₁₉	—	32	1	no	—
64	#494	—	19	1	no	—
65	#493	C₂×D₁₉	1	1	yes	characteristic
66	#486	—	38	1	no	—
67	#486	—	38	1	no	—
68	#353	—	2	1	no	—
69	#353	—	38	1	no	—
70	C₈²	—	19	1	no	—
71	C₂×C₁₉	—	2	1	no	—
72	C₂×C₁₉	—	16	1	no	—
73	C₂×C₁₉	—	16	1	no	—
74	C₂×C₁₉	#1408	1	1	yes	characteristic
75	C₂×Q₁₆	—	76	1	no	—
76	C₂×D₈	—	4	1	no	—
77	C₄⋊Q₈	—	38	1	no	—
78	#127	D₇₆	1	1	yes	characteristic
79	#127	C₂²⋊D₁₉	1	1	yes	characteristic
80	#102	—	76	2	no	—
81	#102	—	76	2	no	—
82	#99	—	4	1	no	—
83	#99	—	76	1	no	—
84	C₄×C₈	—	38	1	no	—
85	C₄×C₈	C₄×D₁₉	1	1	yes	characteristic
86	C₁₉	#7530	1	1	yes	characteristic, complemented, Sylow
87	C₂×Q₈	—	76	1	no	—
88	C₂×D₄	—	2	1	no	—
89	C₂×D₄	—	2	1	no	—
90	C₂×D₄	—	4	1	no	—
91	C₂×D₄	—	4	1	no	—
92	Q₁₆	—	152	2	no	—
93	D₈	—	8	2	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	38	2	no	—
96	C₄⋊C₄	—	76	1	no	—
97	C₄⋊C₄	—	76	1	no	—
98	C₂²⋊C₄	—	8	1	no	—
99	C₂²⋊C₄	—	152	1	no	—
100	C₄²	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
101	C₂³	—	4	1	no	—
102	C₂³	—	4	1	no	—
103	Q₈	—	152	2	no	—
104	D₄	—	8	1	no	—
105	D₄	—	8	1	no	—
106	D₄	—	8	2	no	—
107	D₄	—	8	2	no	—
108	C₂×C₄	—	2	1	no	—
109	C₂×C₄	—	16	1	no	—
110	C₂×C₄	—	304	1	no	—
111	C₂×C₄	—	152	1	no	—
112	C₂×C₄	#10597263	1	1	yes	characteristic
113	C₈	—	2	2	no	—
114	C₈	—	76	2	no	—
115	C₂²	—	8	1	no	—
116	C₂²	—	8	1	no	—
117	C₂²	—	16	1	no	—
118	C₂²	—	16	1	no	—
119	C₂²	#11926336	1	1	yes	characteristic
120	C₄	—	2	2	no	—
121	C₄	—	2	1	no	—
122	C₄	—	32	1	no	—
123	C₄	—	304	1	no	—
124	C₄	—	608	1	no	—
125	C₂	—	2	1	no	—
126	C₂	—	16	1	no	—
127	C₂	—	16	1	no	—
128	C₂	#14561797	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563240

C₂

yes

maximal, characteristic

#14561798

C₂

yes

maximal, characteristic

C₁₉×#1408

C₂

yes

maximal, characteristic

#11926924

C₄

yes

characteristic, complemented

#11926890

—

#11926890

—

#11926337

—

C₈×C₁₉⋊C₈

C₄

yes

characteristic, complemented

C₁₉×#493

C₂²

yes

characteristic

C₁₉×#353

—

C₂×D₈×C₁₉

—

C₁₉×#127

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₂×Dic₇₆

—

#10597315

—

C₁₉×#99

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

—

—

C₄×C₁₉⋊C₈

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×Dic₃₈

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₂×C₁₉⋊C₈

—

Dic₇₆

—

#7530

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

characteristic

C₂×Dic₁₉

—

C₂×Dic₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₁₉⋊C₈

—

#1709

—

#1408

—

#1408

D₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#353

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

Dic₁₉

—

Dic₁₉

—

#494

—

#493

C₂×D₁₉

yes

—

—

—

—

C₈²

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

—

C₂×C₁₉

#1408

yes

characteristic

C₂×Q₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

D₇₆

yes

characteristic

#127

C₂²⋊D₁₉

yes

—

—

—

—

C₄×C₈

—

C₄×C₈

C₄×D₁₉

yes

characteristic

C₁₉

#7530

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

152

—

D₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

152

—

100

C₄²

(C₂×D₁₉)⋊C₄

yes

characteristic

101

C₂³

—

102

C₂³

—

103

Q₈

—

152

—

104

D₄

—

105

D₄

—

106

D₄

—

107

D₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂×C₄

—

304

—

111

C₂×C₄

—

152

—

112

C₂×C₄

#10597263

yes

characteristic

113

C₈

—

114

C₈

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

119

C₂²

#11926336

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

304

—

124

C₄

—

608

—

125

C₂

—

126

C₂

—

127

C₂

—

128

C₂

#14561797

yes

characteristic

	subgroup	G/H
center	C₂	#14561797
commutator	C₄×C₈×C₁₉	C₂×C₄
Frattini	#493	C₂×D₁₉
Fitting	C₁₉×#1408	C₂
socle	C₂×C₁₉	#1408
prime radical, cosocle	C₁₉×#493	C₂²
hypercenter	#1408	D₁₉
hypocenter	C₁₉	#7530
LCS	G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1408

subgroup

G/H

center

C₂

#14561797

commutator

C₄×C₈×C₁₉

C₂×C₄

Frattini

#493

C₂×D₁₉

Fitting

C₁₉×#1408

C₂

socle

C₂×C₁₉

#1408

prime radical, cosocle

C₁₉×#493

C₂²

D₁₉

C₁₉

G ▷ C₄×C₈×C₁₉ ▷ C₄²×C₁₉ ▷ C₂×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #493 ◁ #1408

N	H ≅ G/N	type
4. #11926924	C₄	semidirect
8. C₈×C₁₉⋊C₈	C₄	semidirect
86. C₁₉	#7530	semidirect

H ≅ G/N

type

4. #11926924

C₄

semidirect

8. C₈×C₁₉⋊C₈

C₄

semidirect

86. C₁₉

#7530

semidirect

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

subgroup	index
#14563240	2
#14561798	2
C₁₉×#1408	2
#7530	19

subgroup

index

#14563240

#14561798

C₁₉×#1408

#7530

Subgroups — #18070398

Conjugacy classes of subgroups

Complements

Maximal subgroups