Group #15683737 — subgroups

Subgroups — C₂×#13092786 #15683737

Order 2944.

384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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	C₂×#10625040	C₂	1	1	yes	maximal, characteristic
2	C₂×#10625041	C₂	1	1	yes	maximal, characteristic
3	#13092786	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10624998	C₂	1	4	yes	maximal
5	C₂×C₂₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₆	C₂²	1	2	yes	—
7	C₂²×C₈×C₂₃	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₂₃	—	2	2	no	—
10	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	—
11	C₂×Dic₂₃⋊C₄	—	2	2	no	—
12	#10625041	—	2	2	no	—
13	#10625041	C₂²	1	4	yes	—
14	#10625040	—	2	2	no	—
15	#10625040	C₂²	1	4	yes	—
16	C₂₃×#97	C₂²	1	4	yes	—
17	#10624998	C₂²	1	16	yes	—
18	C₂²×C₄×C₂₃	D₄	1	2	yes	—
19	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₂₃	—	2	2	no	—
21	C₂²×Dic₂₃	—	2	2	no	—
22	C₂×Dic₄₆	—	2	8	no	—
23	C₂×Dic₄₆	—	2	2	no	—
24	C₂×Dic₄₆	C₂³	1	4	yes	—
25	C₂×C₈×C₂₃	—	2	4	no	—
26	C₂×C₈×C₂₃	C₂³	1	4	yes	—
27	C₄²×C₂₃	D₄	1	2	yes	—
28	C₄²×C₂₃	C₂³	1	2	yes	—
29	C₄⋊Dic₂₃	—	2	8	no	—
30	C₄⋊Dic₂₃	—	2	2	no	—
31	C₄⋊Dic₂₃	C₂³	1	4	yes	—
32	Dic₂₃⋊C₄	—	2	8	no	—
33	C₂³×C₂₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₂₃	—	2	4	no	—
35	C₂×C₄×C₂₃	C₂×D₄	1	4	yes	—
36	C₂×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₃	#41	1	4	yes	—
38	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
39	C₂×Dic₂₃	—	2	4	no	—
40	C₂×Dic₂₃	—	2	4	no	—
41	C₂×Dic₂₃	—	4	4	no	—
42	C₂×Dic₂₃	—	4	4	no	—
43	Dic₄₆	—	2	8	no	—
44	Dic₄₆	—	4	4	no	—
45	C₈×C₂₃	—	2	4	no	—
46	C₂×#491	—	23	1	no	maximal, Sylow
47	C₂²×C₂₃	#124	1	2	yes	—
48	C₂²×C₂₃	#137	1	4	yes	—
49	C₂²×C₂₃	C₂²×D₄	1	1	yes	characteristic
50	C₄×C₂₃	—	2	4	no	—
51	C₄×C₂₃	#124	1	2	yes	—
52	C₄×C₂₃	C₂×#41	1	2	yes	—
53	Dic₂₃	—	4	4	no	—
54	Dic₂₃	—	4	4	no	—
55	C₂×C₄⋊Q₈	—	23	1	no	—
56	C₂×#125	—	23	1	no	—
57	#491	—	23	8	no	—
58	C₂×#103	—	23	4	no	—
59	C₂×#97	D₂₃	1	1	yes	characteristic
60	C₂×C₂₃	#491	1	4	yes	complemented
61	C₂×C₂₃	C₂×#124	1	1	yes	characteristic
62	C₂×C₂₃	C₂×#137	1	2	yes	—
63	C₂²×Q₈	—	23	2	no	—
64	C₂²×C₈	C₂×D₂₃	1	2	yes	—
65	C₄⋊Q₈	—	23	4	no	—
66	C₄⋊Q₈	—	46	2	no	—
67	#125	—	23	4	no	—
68	#125	—	46	2	no	—
69	C₂×C₄⋊C₄	—	23	2	no	—
70	C₂×C₄⋊C₄	—	46	2	no	—
71	C₂×C₄⋊C₄	—	46	2	no	—
72	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
73	#103	—	23	16	no	—
74	#97	C₂×D₂₃	1	4	yes	—
75	C₂₃	C₂×#491	1	1	yes	characteristic, complemented, Sylow
76	C₂×Q₈	—	23	4	no	—
77	C₂×Q₈	—	46	2	no	—
78	C₂×Q₈	—	46	8	no	—
79	C₂²×C₄	—	46	2	no	—
80	C₂²×C₄	—	46	2	no	—
81	C₂²×C₄	D₉₂	1	2	yes	—
82	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
83	C₂×C₈	—	2	4	no	—
84	C₂×C₈	C₂²×D₂₃	1	4	yes	—
85	C₄⋊C₄	—	23	4	no	—
86	C₄⋊C₄	—	46	2	no	—
87	C₄⋊C₄	—	46	8	no	—
88	C₄⋊C₄	—	46	8	no	—
89	C₄²	D₉₂	1	2	yes	—
90	C₄²	C₂²×D₂₃	1	2	yes	—
91	C₂³	C₂×D₉₂	1	1	yes	characteristic
92	Q₈	—	46	8	no	—
93	Q₈	—	92	4	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	46	4	no	—
96	C₂×C₄	—	46	4	no	—
97	C₂×C₄	—	92	4	no	—
98	C₂×C₄	—	92	4	no	—
99	C₂×C₄	C₂×D₉₂	1	4	yes	—
100	C₂×C₄	C₂×D₉₂	1	1	yes	characteristic
101	C₂×C₄	#67288	1	4	yes	—
102	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
103	C₈	—	2	4	no	—
104	C₂²	#10625046	1	2	yes	—
105	C₂²	#10625080	1	4	yes	—
106	C₂²	C₂²×D₉₂	1	1	yes	characteristic
107	C₄	—	2	4	no	—
108	C₄	—	92	4	no	—
109	C₄	—	92	4	no	—
110	C₄	#10625046	1	2	yes	—
111	C₄	C₂×#67288	1	2	yes	—
112	C₂	#13092786	1	4	yes	direct product factor
113	C₂	C₂×#10625046	1	1	yes	characteristic
114	C₂	C₂×#10625080	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10625040

C₂

yes

maximal, characteristic

C₂×#10625041

C₂

yes

maximal, characteristic

#13092786

C₂

yes

maximal, direct product factor

C₂×#10624998

C₂

yes

maximal

C₂×C₂₃×#97

C₂

yes

maximal, characteristic

C₂²×Dic₄₆

C₂²

yes

—

C₂²×C₈×C₂₃

C₂²

yes

—

C₂×C₄²×C₂₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₂₃

—

C₂×C₄⋊Dic₂₃

C₂²

yes

—

C₂×Dic₂₃⋊C₄

—

#10625041

—

#10625041

C₂²

yes

—

#10625040

—

#10625040

C₂²

yes

—

C₂₃×#97

C₂²

yes

—

#10624998

C₂²

yes

—

C₂²×C₄×C₂₃

D₄

yes

—

C₂²×C₄×C₂₃

C₂³

yes

characteristic

C₂²×Dic₂₃

—

C₂²×Dic₂₃

—

C₂×Dic₄₆

—

C₂×Dic₄₆

—

C₂×Dic₄₆

C₂³

yes

—

C₂×C₈×C₂₃

—

C₂×C₈×C₂₃

C₂³

yes

—

C₄²×C₂₃

D₄

yes

—

C₄²×C₂₃

C₂³

yes

—

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

—

C₄⋊Dic₂₃

C₂³

yes

—

Dic₂₃⋊C₄

—

C₂³×C₂₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₃

—

C₂×C₄×C₂₃

C₂×D₄

yes

—

C₂×C₄×C₂₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₃

#41

yes

—

C₂×C₄×C₂₃

C₂⁴

yes

characteristic

C₂×Dic₂₃

—

C₂×Dic₂₃

—

C₂×Dic₂₃

—

C₂×Dic₂₃

—

Dic₄₆

—

Dic₄₆

—

C₈×C₂₃

—

C₂×#491

—

maximal, Sylow

C₂²×C₂₃

#124

yes

—

C₂²×C₂₃

#137

yes

—

C₂²×C₂₃

C₂²×D₄

yes

characteristic

C₄×C₂₃

—

C₄×C₂₃

#124

yes

—

C₄×C₂₃

C₂×#41

yes

—

Dic₂₃

—

Dic₂₃

—

C₂×C₄⋊Q₈

—

C₂×#125

—

#491

—

C₂×#103

—

C₂×#97

D₂₃

yes

C₂×C₂₃

yes

C₂×C₂₃

yes

C₂×C₂₃

yes

—

C₂²×Q₈

—

C₂²×C₈

C₂×D₂₃

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₂₃

yes

characteristic

#103

—

#97

C₂×D₂₃

yes

—

C₂₃

C₂×#491

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₉₂

yes

—

C₂²×C₄

C₂²×D₂₃

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂²×D₂₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

D₉₂

yes

—

C₄²

C₂²×D₂₃

yes

—

C₂³

C₂×D₉₂

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₉₂

yes

—

100

C₂×C₄

C₂×D₉₂

yes

characteristic

101

C₂×C₄

#67288

yes

—

102

C₂×C₄

C₂³×D₂₃

yes

characteristic

103

C₈

—

104

C₂²

#10625046

yes

—

105

C₂²

#10625080

yes

—

106

C₂²

C₂²×D₉₂

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

#10625046

yes

—

111

C₄

C₂×#67288

yes

—

112

C₂

#13092786

yes

direct product factor

113

C₂

C₂×#10625046

yes

characteristic

114

C₂

C₂×#10625080

yes

—

	subgroup	G/H
center	C₂³	C₂×D₉₂
commutator, cosocle	C₂×C₄×C₂₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂×C₂₃×#97	C₂
socle, prime radical	C₂³×C₂₃	C₂×D₄
hypercenter	C₂×#97	D₂₃
hypocenter	C₂₃	C₂×#491
LCS	G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₉₂

commutator, cosocle

C₂×C₄×C₂₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₂₃

Fitting

C₂×C₂₃×#97

C₂

socle, prime radical

C₂³×C₂₃

C₂×D₄

hypercenter

C₂×#97

D₂₃

hypocenter

C₂₃

C₂×#491

LCS

G ▷ C₂×C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
3. #13092786	C₂	direct (N × H)
60. C₂×C₂₃	#491	semidirect
75. C₂₃	C₂×#491	semidirect
112. C₂	#13092786	direct (N × H)

H ≅ G/N

type

3. #13092786

C₂

direct (N × H)

60. C₂×C₂₃

#491

semidirect

75. C₂₃

C₂×#491

semidirect

112. C₂

#13092786

direct (N × H)

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

subgroup	index
C₂×#10625040	2
C₂×#10625041	2
#13092786	2
C₂×#10624998	2
C₂×C₂₃×#97	2
C₂×#491	23

subgroup

index

C₂×C₂₃×#97

Subgroups — C₂×#13092786 #15683737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#13092786 #15683737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092786 #15683737