Group #18085616 — subgroups

Subgroups — #18085616

Order 4864.

476 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14564458	C₂	1	3	yes	maximal
2	#14561516	C₂	1	3	yes	maximal, complemented
3	C₁₉×#2845	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597320	C₂²	1	1	yes	characteristic
5	C₂×#10597266	—	2	6	no	—
6	C₂×#10597260	C₂²	1	3	yes	—
7	C₁₉×#398	—	2	6	no	—
8	C₁₉×#382	C₂²	1	3	yes	—
9	C₂²×D₇₆	—	2	3	no	—
10	C₂×C₄⋊C₄×C₁₉	—	2	6	no	—
11	C₂×C₄⋊C₄×C₁₉	D₄	1	6	yes	—
12	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
13	C₂²×C₁₉⋊C₈	—	2	3	no	—
14	#10597320	—	2	3	no	—
15	#10597320	Q₈	1	2	yes	—
16	C₁₉×#95	—	2	2	no	—
17	C₁₉×#95	—	2	6	no	—
18	#10597266	—	4	12	no	—
19	#10597260	—	2	6	no	—
20	C₂³×D₁₉	—	4	1	no	—
21	C₂²×C₄×C₁₉	—	2	6	no	—
22	C₂²×C₄×C₁₉	C₂×D₄	1	3	yes	—
23	C₂×D₇₆	—	2	6	no	—
24	C₂×D₇₆	—	4	6	no	—
25	C₂×D₇₆	—	4	6	no	—
26	C₂×D₇₆	—	4	3	no	—
27	C₄⋊C₄×C₁₉	—	4	6	no	—
28	C₄⋊C₄×C₁₉	—	8	6	no	—
29	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
30	C₄²×C₁₉	#41	1	3	yes	—
31	C₂×C₁₉⋊C₈	—	2	6	no	—
32	C₂×C₁₉⋊C₈	—	4	3	no	—
33	C₂×C₁₉⋊C₈	—	4	3	no	—
34	#10360	—	19	1	no	maximal, Sylow
35	C₂³×C₁₉	#120	1	1	yes	characteristic
36	C₂²×D₁₉	—	4	2	no	—
37	C₂²×D₁₉	—	8	3	no	—
38	C₂²×D₁₉	—	8	3	no	—
39	C₂×C₄×C₁₉	—	2	3	no	—
40	C₂×C₄×C₁₉	—	2	3	no	—
41	C₂×C₄×C₁₉	—	4	6	no	—
42	C₂×C₄×C₁₉	—	4	6	no	—
43	C₂×C₄×C₁₉	—	4	6	no	—
44	C₂×C₄×C₁₉	C₂²⋊Q₈	1	3	yes	—
45	C₂×C₄×C₁₉	#124	1	3	yes	—
46	D₇₆	—	4	12	no	—
47	D₇₆	—	8	6	no	—
48	C₁₉⋊C₈	—	4	6	no	—
49	#2845	D₁₉	1	1	yes	characteristic, complemented
50	#1961	—	19	3	no	—
51	#1295	—	19	3	no	—
52	C₂²×C₁₉	#393	1	1	yes	characteristic
53	C₂²×C₁₉	#453	1	3	yes	—
54	C₂²×C₁₉	#454	1	3	yes	—
55	C₂×D₁₉	—	8	6	no	—
56	C₂×D₁₉	—	16	3	no	—
57	C₂×D₁₉	—	16	1	no	—
58	C₄×C₁₉	—	2	3	no	—
59	C₄×C₁₉	—	2	3	no	—
60	C₄×C₁₉	—	8	6	no	—
61	C₂×#127	—	19	1	no	—
62	C₂×#102	—	38	6	no	—
63	C₂×#97	—	19	3	no	—
64	#398	—	2	6	no	—
65	#382	C₂×D₁₉	1	3	yes	—
66	C₂×C₁₉	#1656	1	3	yes	—
67	C₂×C₁₉	#1658	1	1	yes	characteristic
68	C₂×C₁₉	#2027	1	3	yes	—
69	D₁₉	—	16	2	no	—
70	C₂²×D₄	—	38	3	no	—
71	C₂²×C₈	—	38	3	no	—
72	#127	—	19	2	no	—
73	#127	—	38	3	no	—
74	C₂×C₄⋊C₄	—	2	6	no	—
75	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	6	yes	—
76	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
77	#102	—	76	12	no	—
78	#97	—	38	6	no	—
79	#95	—	2	2	no	—
80	#95	—	2	6	no	—
81	C₁₉	#10360	1	1	yes	characteristic, complemented, Sylow
82	C₂⁴	—	76	1	no	—
83	C₂×D₄	—	38	6	no	—
84	C₂×D₄	—	76	6	no	—
85	C₂×D₄	—	76	6	no	—
86	C₂×D₄	—	76	3	no	—
87	C₂²×C₄	—	2	6	no	—
88	C₂²×C₄	C₂×C₂²⋊D₁₉	1	3	yes	—
89	C₂×C₈	—	38	6	no	—
90	C₂×C₈	—	76	3	no	—
91	C₂×C₈	—	76	3	no	—
92	C₄⋊C₄	—	4	6	no	—
93	C₄⋊C₄	—	8	6	no	—
94	C₄²	Q₈×D₁₉	1	1	yes	characteristic
95	C₄²	#64545	1	3	yes	—
96	C₂³	—	76	2	no	—
97	C₂³	—	152	3	no	—
98	C₂³	—	152	3	no	—
99	C₂³	#10597399	1	1	yes	characteristic
100	D₄	—	76	12	no	—
101	D₄	—	152	6	no	—
102	C₂×C₄	—	2	3	no	—
103	C₂×C₄	—	2	3	no	—
104	C₂×C₄	—	4	6	no	—
105	C₂×C₄	—	4	6	no	—
106	C₂×C₄	—	4	6	no	—
107	C₂×C₄	#10597392	1	3	yes	—
108	C₂×C₄	#10597393	1	3	yes	—
109	C₈	—	76	6	no	—
110	C₂²	—	304	3	no	—
111	C₂²	—	304	1	no	—
112	C₂²	—	152	6	no	—
113	C₂²	#11926455	1	1	yes	characteristic
114	C₂²	#11926712	1	3	yes	—
115	C₂²	#11926717	1	3	yes	—
116	C₄	—	2	3	no	—
117	C₄	—	2	3	no	—
118	C₄	—	8	6	no	—
119	C₂	—	304	2	no	—
120	C₂	#14562928	1	3	yes	—
121	C₂	#14562937	1	1	yes	characteristic
122	C₂	#14564788	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564458

C₂

yes

maximal

#14561516

C₂

yes

maximal, complemented

C₁₉×#2845

C₂

yes

maximal, characteristic, complemented

C₂×#10597320

C₂²

yes

characteristic

C₂×#10597266

—

C₂×#10597260

C₂²

yes

—

C₁₉×#398

—

C₁₉×#382

C₂²

yes

—

C₂²×D₇₆

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

#10597320

—

#10597320

Q₈

yes

—

C₁₉×#95

—

C₁₉×#95

—

#10597266

—

#10597260

—

C₂³×D₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×D₇₆

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×Q₈

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₉

#124

yes

—

D₇₆

—

D₇₆

—

C₁₉⋊C₈

—

#2845

D₁₉

yes

characteristic, complemented

#1961

—

#1295

—

C₂²×C₁₉

#393

yes

characteristic

C₂²×C₁₉

#453

yes

—

C₂²×C₁₉

#454

yes

—

C₂×D₁₉

—

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂×#127

—

C₂×#102

—

C₂×#97

—

#398

—

#382

C₂×D₁₉

yes

—

C₂×C₁₉

#1656

yes

—

C₂×C₁₉

#1658

yes

characteristic

C₂×C₁₉

#2027

yes

—

D₁₉

—

C₂²×D₄

—

C₂²×C₈

—

#127

—

#127

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₉

yes

—

C₂×C₄²

C₂²×D₁₉

yes

—

—

—

—

C₁₉

#10360

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Q₈×D₁₉

yes

characteristic

C₄²

#64545

yes

—

C₂³

—

C₂³

—

152

—

C₂³

—

152

—

C₂³

#10597399

yes

characteristic

100

D₄

—

101

D₄

—

152

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

#10597392

yes

—

108

C₂×C₄

#10597393

yes

—

109

C₈

—

110

C₂²

—

304

—

111

C₂²

—

304

—

112

C₂²

—

152

—

113

C₂²

#11926455

yes

characteristic

114

C₂²

#11926712

yes

—

115

C₂²

#11926717

yes

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₂

—

304

—

120

C₂

#14562928

yes

—

121

C₂

#14562937

yes

characteristic

122

C₂

#14564788

yes

—

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2845	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	#2845	D₁₉
hypocenter	C₁₉	#10360
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#10597399

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2845

C₂

C₂³×C₁₉

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
2. #14561516	C₂	semidirect
3. C₁₉×#2845	C₂	semidirect
49. #2845	D₁₉	semidirect
81. C₁₉	#10360	semidirect

H ≅ G/N

type

2. #14561516

C₂

semidirect

3. C₁₉×#2845

C₂

semidirect

49. #2845

D₁₉

semidirect

81. C₁₉

#10360

semidirect

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

subgroup	index
#14564458	2
#14561516	2
C₁₉×#2845	2
#10360	19

subgroup

index

#14564458

#14561516

C₁₉×#2845

#10360

Subgroups — #18085616

Conjugacy classes of subgroups

Complements

Maximal subgroups