Group #19155458 — subgroups

Subgroups — C₂₃×#7832 #19155458

Order 5888.

322 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 94 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	C₂₃×#2810	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2100	C₂	1	3	yes	maximal
3	C₂₃×#1271	C₂	1	3	yes	maximal
4	C₂₃×#400	—	2	3	no	—
5	C₂₃×#389	C₂²	1	3	yes	—
6	C₂₃×#387	—	2	3	no	—
7	C₂₃×#384	C₂²	1	1	yes	characteristic
8	C₂₃×#340	—	2	3	no	—
9	C₂₃×#340	—	2	3	no	—
10	C₂₃×#336	C₂²	1	3	yes	—
11	C₂²×C₈×C₂₃	—	2	3	no	—
12	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
13	C₂×C₄⋊C₄×C₂₃	—	2	3	no	—
14	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
15	C₂×C₄⋊C₄×C₂₃	D₄	1	3	yes	—
16	C₂×C₄²×C₂₃	—	2	1	no	—
17	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
18	C₂₃×#95	—	2	3	no	—
19	C₂₃×#95	—	2	3	no	—
20	C₂₃×#95	—	2	1	no	—
21	C₂₃×#95	—	2	3	no	—
22	C₂²×C₄×C₂₃	—	2	3	no	—
23	C₂²×C₄×C₂₃	—	2	3	no	—
24	C₂²×C₄×C₂₃	—	4	1	no	—
25	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
26	C₂×C₈×C₂₃	—	4	3	no	—
27	C₂×C₈×C₂₃	—	4	3	no	—
28	C₂×C₈×C₂₃	—	4	3	no	—
29	C₄⋊C₄×C₂₃	—	2	3	no	—
30	C₄⋊C₄×C₂₃	—	2	3	no	—
31	C₄⋊C₄×C₂₃	—	4	3	no	—
32	C₄⋊C₄×C₂₃	—	4	6	no	—
33	C₄⋊C₄×C₂₃	—	4	3	no	—
34	C₄⋊C₄×C₂₃	—	4	3	no	—
35	C₄²×C₂₃	—	4	1	no	—
36	C₄²×C₂₃	—	8	1	no	—
37	#7832	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂³×C₂₃	#120	1	1	yes	characteristic
39	C₂×C₄×C₂₃	—	2	3	no	—
40	C₂×C₄×C₂₃	—	2	3	no	—
41	C₂×C₄×C₂₃	—	4	3	no	—
42	C₂×C₄×C₂₃	—	4	3	no	—
43	C₂×C₄×C₂₃	—	4	3	no	—
44	C₂×C₄×C₂₃	—	4	3	no	—
45	C₂×C₄×C₂₃	—	4	3	no	—
46	C₂×C₄×C₂₃	—	4	3	no	—
47	C₂×C₄×C₂₃	—	8	3	no	—
48	C₂×C₄×C₂₃	#135	1	3	yes	—
49	C₂×C₄×C₂₃	#137	1	3	yes	—
50	C₈×C₂₃	—	8	3	no	—
51	#2810	C₂×C₂₃	1	1	yes	characteristic
52	#2100	C₂×C₂₃	1	3	yes	—
53	#1271	C₂×C₂₃	1	3	yes	—
54	C₂²×C₂₃	#452	1	3	yes	—
55	C₂²×C₂₃	#454	1	3	yes	—
56	C₂²×C₂₃	#458	1	1	yes	characteristic
57	C₄×C₂₃	—	2	3	no	—
58	C₄×C₂₃	—	2	3	no	—
59	C₄×C₂₃	—	8	3	no	—
60	C₄×C₂₃	—	8	3	no	—
61	C₄×C₂₃	—	16	1	no	—
62	#400	—	2	3	no	—
63	#389	C₂²×C₂₃	1	3	yes	—
64	#387	—	2	3	no	—
65	#384	C₂²×C₂₃	1	1	yes	characteristic
66	#340	—	2	3	no	—
67	#340	—	2	3	no	—
68	#336	C₂²×C₂₃	1	3	yes	—
69	C₂×C₂₃	#1615	1	3	yes	—
70	C₂×C₂₃	#1638	1	3	yes	—
71	C₂×C₂₃	#1658	1	1	yes	characteristic
72	C₂²×C₈	—	2	3	no	—
73	C₂×C₄⋊C₄	—	2	3	no	—
74	C₂×C₄⋊C₄	—	2	3	no	—
75	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
76	C₂×C₄⋊C₄	D₄×C₂₃	1	3	yes	—
77	C₂×C₄²	—	2	1	no	—
78	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
79	#95	—	2	3	no	—
80	#95	—	2	3	no	—
81	#95	—	2	1	no	—
82	#95	—	2	3	no	—
83	C₂₃	#7832	1	1	yes	characteristic, direct product factor, Sylow
84	C₂²×C₄	—	2	3	no	—
85	C₂²×C₄	—	2	3	no	—
86	C₂²×C₄	—	4	1	no	—
87	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
88	C₂×C₈	—	4	3	no	—
89	C₂×C₈	—	4	3	no	—
90	C₂×C₈	—	4	3	no	—
91	C₄⋊C₄	—	2	3	no	—
92	C₄⋊C₄	—	2	3	no	—
93	C₄⋊C₄	—	4	3	no	—
94	C₄⋊C₄	—	4	6	no	—
95	C₄⋊C₄	—	4	3	no	—
96	C₄⋊C₄	—	4	3	no	—
97	C₄²	—	4	1	no	—
98	C₄²	—	8	1	no	—
99	C₂³	C₂₃×#120	1	1	yes	characteristic
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	4	3	no	—
103	C₂×C₄	—	4	3	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	—	4	3	no	—
106	C₂×C₄	—	4	3	no	—
107	C₂×C₄	—	4	3	no	—
108	C₂×C₄	—	8	3	no	—
109	C₂×C₄	C₂₃×#135	1	3	yes	—
110	C₂×C₄	C₂₃×#137	1	3	yes	—
111	C₈	—	8	3	no	—
112	C₂²	C₂₃×#452	1	3	yes	—
113	C₂²	C₂₃×#454	1	3	yes	—
114	C₂²	C₂₃×#458	1	1	yes	characteristic
115	C₄	—	2	3	no	—
116	C₄	—	2	3	no	—
117	C₄	—	8	3	no	—
118	C₄	—	8	3	no	—
119	C₄	—	16	1	no	—
120	C₂	C₂₃×#1615	1	3	yes	—
121	C₂	C₂₃×#1638	1	3	yes	—
122	C₂	C₂₃×#1658	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#2810

C₂

yes

maximal, characteristic

C₂₃×#2100

C₂

yes

maximal

C₂₃×#1271

C₂

yes

maximal

C₂₃×#400

—

C₂₃×#389

C₂²

yes

—

C₂₃×#387

—

C₂₃×#384

C₂²

yes

characteristic

C₂₃×#340

—

C₂₃×#340

—

C₂₃×#336

C₂²

yes

—

C₂²×C₈×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

—

C₂×C₄⋊C₄×C₂₃

D₄

yes

—

C₂×C₄²×C₂₃

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×#95

—

C₂₃×#95

—

C₂₃×#95

—

C₂₃×#95

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₂×D₄

yes

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

#7832

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

#120

yes

characteristic

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

#135

yes

—

C₂×C₄×C₂₃

#137

yes

—

C₈×C₂₃

—

#2810

C₂×C₂₃

yes

characteristic

#2100

C₂×C₂₃

yes

—

#1271

C₂×C₂₃

yes

—

C₂²×C₂₃

#452

yes

—

C₂²×C₂₃

#454

yes

—

C₂²×C₂₃

#458

yes

characteristic

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

—

#400

—

#389

C₂²×C₂₃

yes

—

#387

—

#384

C₂²×C₂₃

yes

—

—

C₂²×C₂₃

yes

—

C₂×C₂₃

#1615

yes

—

C₂×C₂₃

#1638

yes

—

C₂×C₂₃

#1658

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

D₄×C₂₃

yes

—

C₂×C₄⋊C₄

D₄×C₂₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂³×C₂₃

yes

—

—

—

—

C₂₃

#7832

yes

characteristic, direct product factor, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₂₃

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂³

C₂₃×#120

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₂₃×#135

yes

—

110

C₂×C₄

C₂₃×#137

yes

—

111

C₈

—

112

C₂²

C₂₃×#452

yes

—

113

C₂²

C₂₃×#454

yes

—

114

C₂²

C₂₃×#458

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

C₂₃×#1615

yes

—

121

C₂

C₂₃×#1638

yes

—

122

C₂

C₂₃×#1658

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₂₃

#120

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₂₃

LCS

G ▷ C₂×C₄² ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

N	H ≅ G/N	type
37. #7832	C₂₃	direct (N × H)
83. C₂₃	#7832	direct (N × H)

H ≅ G/N

type

37. #7832

C₂₃

direct (N × H)

83. C₂₃

#7832

direct (N × H)

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

subgroup	index
C₂₃×#2810	2
C₂₃×#2100	2
C₂₃×#1271	2
#7832	23

subgroup

index

C₂₃×#2810

C₂₃×#2100

C₂₃×#1271

#7832

Subgroups — C₂₃×#7832 #19155458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#7832 #19155458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#7832 #19155458