Group #19157929 — subgroups

Subgroups — C₂₃×#10303 #19157929

Order 5888.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3255	C₂	1	3	yes	maximal
2	C₂₃×#1994	C₂	1	3	yes	maximal
3	C₂₃×#1309	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#533	C₂²	1	3	yes	—
5	C₂₃×#475	—	2	6	no	—
6	C₂₃×#470	—	2	6	no	—
7	C₂₃×#462	—	2	6	no	—
8	C₂₃×#423	C₂²	1	3	yes	—
9	C₄³×C₂₃	C₂²	1	1	yes	characteristic
10	C₂₃×#339	—	2	6	no	—
11	C₂×Q₁₆×C₂₃	—	2	6	no	—
12	C₂×M₁₆×C₂₃	D₄	1	6	yes	—
13	C₂₃×C₄⋊Q₈	D₄	1	6	yes	—
14	C₂₃×#125	—	2	3	no	—
15	C₂₃×C₂²⋊Q₈	—	2	6	no	—
16	C₄×Q₈×C₂₃	—	2	6	no	—
17	C₂₃×#117	—	2	3	no	—
18	C₂×C₄²×C₂₃	—	2	3	no	—
19	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
20	C₂₃×#106	—	2	6	no	—
21	C₂₃×C₄⋊C₈	—	2	6	no	—
22	C₂₃×#103	—	2	12	no	—
23	C₂×Q₈×C₂₃	—	2	6	no	—
24	C₂²×C₄×C₂₃	—	4	1	no	—
25	C₂²×C₄×C₂₃	C₂×D₄	1	3	yes	—
26	Q₁₆×C₂₃	—	8	6	no	—
27	M₁₆×C₂₃	—	4	6	no	—
28	C₂×C₈×C₂₃	—	2	6	no	—
29	C₄⋊C₄×C₂₃	—	2	6	no	—
30	C₄⋊C₄×C₂₃	—	2	6	no	—
31	C₄⋊C₄×C₂₃	—	4	6	no	—
32	C₂²⋊C₄×C₂₃	—	4	3	no	—
33	C₄²×C₂₃	—	2	6	no	—
34	C₄²×C₂₃	—	4	3	no	—
35	C₄²×C₂₃	—	4	3	no	—
36	C₄²×C₂₃	C₂×D₄	1	3	yes	—
37	C₄²×C₂₃	#41	1	1	yes	characteristic
38	#10303	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂³×C₂₃	#127	1	1	yes	characteristic
40	Q₈×C₂₃	—	4	6	no	—
41	Q₈×C₂₃	—	4	6	no	—
42	C₂×C₄×C₂₃	—	2	3	no	—
43	C₂×C₄×C₂₃	—	2	3	no	—
44	C₂×C₄×C₂₃	—	4	6	no	—
45	C₂×C₄×C₂₃	—	4	6	no	—
46	C₂×C₄×C₂₃	#120	1	3	yes	—
47	C₂×C₄×C₂₃	#121	1	3	yes	—
48	C₈×C₂₃	—	4	6	no	—
49	#3255	C₂×C₂₃	1	3	yes	—
50	#1994	C₂×C₂₃	1	3	yes	—
51	#1309	C₂×C₂₃	1	1	yes	characteristic
52	C₂²×C₂₃	—	2	3	no	—
53	C₂²×C₂₃	#392	1	1	yes	characteristic
54	C₄×C₂₃	—	2	3	no	—
55	C₄×C₂₃	—	4	4	no	—
56	C₄×C₂₃	—	8	6	no	—
57	C₄×C₂₃	#455	1	3	yes	—
58	C₄×C₂₃	#456	1	3	yes	—
59	#533	C₂²×C₂₃	1	3	yes	—
60	#475	—	2	6	no	—
61	#470	—	2	6	no	—
62	#462	—	2	6	no	—
63	#423	C₂²×C₂₃	1	3	yes	—
64	C₄³	C₂²×C₂₃	1	1	yes	characteristic
65	#339	—	2	6	no	—
66	C₂×C₂₃	—	4	1	no	—
67	C₂×C₂₃	#2007	1	3	yes	—
68	C₂×Q₁₆	—	2	6	no	—
69	C₂×M₁₆	D₄×C₂₃	1	6	yes	—
70	C₄⋊Q₈	D₄×C₂₃	1	6	yes	—
71	#125	—	2	3	no	—
72	C₂²⋊Q₈	—	2	6	no	—
73	C₄×Q₈	—	2	6	no	—
74	#117	—	2	3	no	—
75	C₂×C₄²	—	2	3	no	—
76	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
77	#106	—	2	6	no	—
78	C₄⋊C₈	—	2	6	no	—
79	#103	—	2	12	no	—
80	C₂₃	#10303	1	1	yes	characteristic, direct product factor, Sylow
81	C₂×Q₈	—	2	6	no	—
82	C₂²×C₄	—	4	1	no	—
83	C₂²×C₄	C₂×D₄×C₂₃	1	3	yes	—
84	Q₁₆	—	8	6	no	—
85	M₁₆	—	4	6	no	—
86	C₂×C₈	—	2	6	no	—
87	C₄⋊C₄	—	2	6	no	—
88	C₄⋊C₄	—	2	6	no	—
89	C₄⋊C₄	—	4	6	no	—
90	C₂²⋊C₄	—	4	3	no	—
91	C₄²	—	2	6	no	—
92	C₄²	—	4	3	no	—
93	C₄²	—	4	3	no	—
94	C₄²	C₂×D₄×C₂₃	1	3	yes	—
95	C₄²	#41×C₂₃	1	1	yes	characteristic
96	C₂³	C₂₃×#127	1	1	yes	characteristic
97	Q₈	—	4	6	no	—
98	Q₈	—	4	6	no	—
99	C₂×C₄	—	2	3	no	—
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	4	6	no	—
102	C₂×C₄	—	4	6	no	—
103	C₂×C₄	C₂₃×#120	1	3	yes	—
104	C₂×C₄	C₂₃×#121	1	3	yes	—
105	C₈	—	4	6	no	—
106	C₂²	—	2	3	no	—
107	C₂²	C₂₃×#392	1	1	yes	characteristic
108	C₄	—	2	3	no	—
109	C₄	—	4	4	no	—
110	C₄	—	8	6	no	—
111	C₄	C₂₃×#455	1	3	yes	—
112	C₄	C₂₃×#456	1	3	yes	—
113	C₂	—	4	1	no	—
114	C₂	C₂₃×#2007	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂₃×#3255

C₂

yes

maximal

C₂₃×#1994

C₂

yes

maximal

C₂₃×#1309

C₂

yes

maximal, characteristic

C₂₃×#533

C₂²

yes

—

C₂₃×#475

—

C₂₃×#470

—

C₂₃×#462

—

C₂₃×#423

C₂²

yes

—

C₄³×C₂₃

C₂²

yes

characteristic

C₂₃×#339

—

C₂×Q₁₆×C₂₃

—

C₂×M₁₆×C₂₃

D₄

yes

—

C₂₃×C₄⋊Q₈

D₄

yes

—

C₂₃×#125

—

C₂₃×C₂²⋊Q₈

—

C₄×Q₈×C₂₃

—

C₂₃×#117

—

C₂×C₄²×C₂₃

—

C₂×C₄²×C₂₃

C₂³

yes

characteristic

C₂₃×#106

—

C₂₃×C₄⋊C₈

—

C₂₃×#103

—

C₂×Q₈×C₂₃

—

C₂²×C₄×C₂₃

—

C₂²×C₄×C₂₃

C₂×D₄

yes

—

Q₁₆×C₂₃

—

M₁₆×C₂₃

—

C₂×C₈×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

—

C₂²⋊C₄×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

—

C₄²×C₂₃

C₂×D₄

yes

—

C₄²×C₂₃

#41

yes

characteristic

#10303

C₂₃

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₂₃

#127

yes

characteristic

Q₈×C₂₃

—

Q₈×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

#120

yes

—

C₂×C₄×C₂₃

#121

yes

—

C₈×C₂₃

—

#3255

C₂×C₂₃

yes

—

#1994

C₂×C₂₃

yes

—

#1309

C₂×C₂₃

yes

characteristic

C₂²×C₂₃

—

C₂²×C₂₃

#392

yes

characteristic

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

#455

yes

—

C₄×C₂₃

#456

yes

—

#533

C₂²×C₂₃

yes

—

—

—

—

C₂²×C₂₃

yes

—

C₄³

C₂²×C₂₃

yes

characteristic

#339

—

C₂×C₂₃

—

C₂×C₂₃

#2007

yes

—

C₂×Q₁₆

—

C₂×M₁₆

D₄×C₂₃

yes

—

C₄⋊Q₈

D₄×C₂₃

yes

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂³×C₂₃

yes

characteristic

#106

—

C₄⋊C₈

—

#103

—

C₂₃

#10303

yes

characteristic, direct product factor, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₂₃

yes

—

Q₁₆

—

M₁₆

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×D₄×C₂₃

yes

—

C₄²

#41×C₂₃

yes

characteristic

C₂³

C₂₃×#127

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₂₃×#120

yes

—

104

C₂×C₄

C₂₃×#121

yes

—

105

C₈

—

106

C₂²

—

107

C₂²

C₂₃×#392

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

C₂₃×#455

yes

—

112

C₄

C₂₃×#456

yes

—

113

C₂

—

114

C₂

C₂₃×#2007

yes

—

	subgroup	G/H
center, socle	C₂²×C₂₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₂₃
prime radical	C₂³×C₂₃	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₂₃

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₂₃

prime radical

C₂³×C₂₃

#127

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

N	H ≅ G/N	type
38. #10303	C₂₃	direct (N × H)
80. C₂₃	#10303	direct (N × H)

H ≅ G/N

type

38. #10303

C₂₃

direct (N × H)

80. C₂₃

#10303

direct (N × H)

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

subgroup	index
C₂₃×#3255	2
C₂₃×#1994	2
C₂₃×#1309	2
#10303	23

subgroup

index

C₂₃×#3255

C₂₃×#1994

C₂₃×#1309

#10303

Subgroups — C₂₃×#10303 #19157929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×#10303 #19157929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#10303 #19157929