Group #15672033 — subgroups

Subgroups — #15672033

Order 2944.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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	#13092973	C₂	1	1	yes	maximal, characteristic
2	#13092472	C₂	1	2	yes	maximal
3	#13092159	C₂	1	1	yes	maximal, characteristic, complemented
4	#13092158	C₂	1	2	yes	maximal, complemented
5	C₂₃×#330	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#125	C₂²	1	1	yes	characteristic
7	#10625067	—	2	2	no	—
8	#10625063	C₄	1	2	yes	—
9	#10625059	C₄	1	2	yes	—
10	#10625058	—	2	2	no	—
11	C₄²×D₂₃	C₂²	1	1	yes	characteristic
12	#10625041	C₂²	1	1	yes	characteristic
13	C₂₃×#97	C₂²	1	2	yes	—
14	(C₂×D₂₃)⋊C₈	—	2	2	no	—
15	Dic₂₃⋊C₈	—	2	2	no	—
16	#10624985	C₂²	1	2	yes	—
17	C₂×C₄×D₂₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₂₃	D₄	1	2	yes	—
19	C₂×Dic₄₆	—	2	2	no	—
20	C₂×C₈×C₂₃	—	2	2	no	—
21	C₄⋊C₄×C₂₃	—	2	2	no	—
22	C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
23	C₄²×C₂₃	C₂³	1	1	yes	characteristic
24	(C₂×D₂₃)⋊C₄	—	2	2	no	—
25	C₄⋊Dic₂₃	C₂×C₄	1	2	yes	—
26	Dic₂₃⋊C₄	—	2	2	no	—
27	Dic₂₃⋊C₄	—	2	2	no	—
28	C₄×Dic₂₃	—	2	2	no	—
29	C₄×Dic₂₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₂₃	D₄	1	2	yes	—
31	C₂×C₂₃⋊C₈	—	2	2	no	—
32	C₂²×D₂₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₃	—	2	2	no	—
34	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₂₃	C₂×D₄	1	2	yes	—
36	C₂×Dic₂₃	—	2	2	no	—
37	C₂×Dic₂₃	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₂₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₂₃	—	2	2	no	—
40	C₄×D₂₃	—	4	2	no	—
41	Dic₄₆	—	4	4	no	—
42	C₈×C₂₃	—	4	2	no	—
43	C₂₃⋊C₈	—	4	2	no	—
44	#1537	—	23	1	no	maximal, Sylow
45	C₂²×C₂₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×D₂₃	—	2	1	no	—
47	C₂×D₂₃	—	2	2	no	—
48	C₄×C₂₃	—	2	1	no	—
49	C₄×C₂₃	—	2	2	no	—
50	C₄×C₂₃	—	4	2	no	—
51	Dic₂₃	—	2	2	no	—
52	Dic₂₃	—	4	2	no	—
53	Dic₂₃	#101	1	2	yes	—
54	#533	—	23	1	no	—
55	#432	—	23	2	no	—
56	#330	—	23	1	no	—
57	#330	—	23	2	no	—
58	#330	D₂₃	1	1	yes	characteristic, complemented
59	C₂×C₂₃	C₂×#101	1	1	yes	characteristic
60	C₂×C₂₃	#421	1	2	yes	—
61	D₂₃	—	4	1	no	—
62	C₄⋊Q₈	—	23	2	no	—
63	#125	—	23	1	no	—
64	#125	C₂×D₂₃	1	1	yes	characteristic
65	C₂²⋊Q₈	—	46	2	no	—
66	C₄×Q₈	—	46	2	no	—
67	#117	—	23	2	no	—
68	C₂×C₄²	—	23	1	no	—
69	C₄⋊C₈	—	46	2	no	—
70	C₂²⋊C₈	—	46	2	no	—
71	#97	—	23	2	no	—
72	#97	C₂×D₂₃	1	2	yes	—
73	C₂₃	#1537	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	46	2	no	—
75	C₂²×C₄	—	23	1	no	—
76	C₂²×C₄	—	23	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	46	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	23	2	no	—
81	C₄⋊C₄	—	46	2	no	—
82	C₄⋊C₄	—	46	2	no	—
83	C₄⋊C₄	C₄×D₂₃	1	2	yes	—
84	C₂²⋊C₄	—	46	2	no	—
85	C₄²	—	23	1	no	—
86	C₄²	—	23	2	no	—
87	C₄²	—	46	2	no	—
88	C₄²	C₂²×D₂₃	1	1	yes	characteristic
89	C₂³	—	23	1	no	—
90	Q₈	—	92	4	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	23	1	no	—
93	C₂×C₄	—	23	2	no	—
94	C₂×C₄	—	46	2	no	—
95	C₂×C₄	—	46	2	no	—
96	C₂×C₄	—	92	2	no	—
97	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
98	C₂×C₄	D₄×D₂₃	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	92	2	no	—
101	C₂²	—	46	1	no	—
102	C₂²	—	46	2	no	—
103	C₂²	C₂²⋊C₄×D₂₃	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	23	2	no	—
108	C₄	—	46	2	no	—
109	C₄	—	92	2	no	—
110	C₂	—	92	1	no	—
111	C₂	#101×D₂₃	1	1	yes	characteristic
112	C₂	#13092432	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#13092973

C₂

yes

maximal, characteristic

#13092472

C₂

yes

maximal

#13092159

C₂

yes

maximal, characteristic, complemented

#13092158

C₂

yes

maximal, complemented

C₂₃×#330

C₂

yes

maximal, characteristic, complemented

C₂₃×#125

C₂²

yes

characteristic

#10625067

—

#10625063

C₄

yes

—

#10625059

C₄

yes

—

#10625058

—

C₄²×D₂₃

C₂²

yes

characteristic

#10625041

C₂²

yes

characteristic

C₂₃×#97

C₂²

yes

—

(C₂×D₂₃)⋊C₈

—

Dic₂₃⋊C₈

—

#10624985

C₂²

yes

—

C₂×C₄×D₂₃

C₂×C₄

yes

characteristic

C₂×C₄×D₂₃

D₄

yes

—

C₂×Dic₄₆

—

C₂×C₈×C₂₃

—

C₄⋊C₄×C₂₃

—

C₄⋊C₄×C₂₃

C₂×C₄

yes

—

C₄²×C₂₃

C₂³

yes

characteristic

(C₂×D₂₃)⋊C₄

—

C₄⋊Dic₂₃

C₂×C₄

yes

—

Dic₂₃⋊C₄

—

Dic₂₃⋊C₄

—

C₄×Dic₂₃

—

C₄×Dic₂₃

C₂×C₄

yes

characteristic

C₄×Dic₂₃

D₄

yes

—

C₂×C₂₃⋊C₈

—

C₂²×D₂₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₂₃

C₂×D₄

yes

—

C₂×Dic₂₃

—

C₂×Dic₂₃

C₂²⋊C₄

yes

—

C₂×Dic₂₃

C₂²⋊C₄

yes

characteristic

C₄×D₂₃

—

C₄×D₂₃

—

Dic₄₆

—

C₈×C₂₃

—

C₂₃⋊C₈

—

#1537

—

maximal, Sylow

C₂²×C₂₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₂₃

—

C₂×D₂₃

—

C₄×C₂₃

—

C₄×C₂₃

—

C₄×C₂₃

—

Dic₂₃

—

Dic₂₃

—

Dic₂₃

#101

yes

—

—

—

—

—

D₂₃

yes

characteristic, complemented

C₂×C₂₃

C₂×#101

yes

characteristic

C₂×C₂₃

#421

yes

—

D₂₃

—

C₄⋊Q₈

—

#125

—

#125

C₂×D₂₃

yes

characteristic

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

C₂×D₂₃

yes

—

C₂₃

#1537

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₄×D₂₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂²×D₂₃

yes

characteristic

C₂³

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₂₃

yes

characteristic

C₂×C₄

D₄×D₂₃

yes

—

C₈

—

100

C₈

—

101

C₂²

—

102

C₂²

—

103

C₂²

C₂²⋊C₄×D₂₃

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₂

—

111

C₂

#101×D₂₃

yes

characteristic

112

C₂

#13092432

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₂₃
commutator	C₂×C₄×C₂₃	C₂²×C₄
Frattini	C₄²	C₂²×D₂₃
Fitting	C₂₃×#330	C₂
socle	C₂²×C₂₃	C₂×C₂²⋊C₄
prime radical	C₂²×D₂₃	C₂²⋊C₄
cosocle	C₄²×C₂₃	C₂³
hypercenter	#330	D₂₃
hypocenter	C₂₃	#1537
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₂₃

commutator

C₂×C₄×C₂₃

C₂²×C₄

Frattini

C₄²

C₂²×D₂₃

Fitting

C₂₃×#330

C₂

socle

C₂²×C₂₃

C₂×C₂²⋊C₄

prime radical

C₂²×D₂₃

C₂²⋊C₄

cosocle

C₄²×C₂₃

C₂³

D₂₃

C₂₃

G ▷ C₂×C₄×C₂₃ ▷ C₂²×C₂₃ ▷ C₂₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #13092159	C₂	semidirect
4. #13092158	C₂	semidirect
5. C₂₃×#330	C₂	semidirect
58. #330	D₂₃	semidirect
73. C₂₃	#1537	semidirect

H ≅ G/N

type

3. #13092159

C₂

semidirect

4. #13092158

C₂

semidirect

5. C₂₃×#330

C₂

semidirect

58. #330

D₂₃

semidirect

73. C₂₃

#1537

semidirect

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

subgroup	index
#13092973	2
#13092472	2
#13092159	2
#13092158	2
C₂₃×#330	2
#1537	23

subgroup

index

C₂₃×#330

Subgroups — #15672033

Conjugacy classes of subgroups

Complements

Maximal subgroups