Group #11928384 — subgroups

Subgroups — D₃×C₈×D₁₃ #11928384

Order 1248.

152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 64 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	C₄×D₃×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₈×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₃×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#10597591	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×#1055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃⋊C₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₁₃	—	3	1	no	maximal, Hall
9	C₂×D₃×D₁₃	C₄	1	1	yes	characteristic
10	C₄×D₃₉	C₂²	1	1	yes	characteristic
11	C₄×D₃×C₁₃	C₂²	1	1	yes	characteristic
12	C₃×C₄×D₁₃	C₂²	1	1	yes	characteristic
13	#64601	C₄	1	1	yes	characteristic
14	D₃×Dic₁₃	C₄	1	1	yes	characteristic
15	Dic₃×D₁₃	C₄	1	1	yes	characteristic
16	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₃⋊#1055	C₂²	1	1	yes	characteristic, complemented
18	C₃×#1055	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×C₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄×D₁₃	—	3	1	no	—
21	C₂×C₈×C₁₃	—	3	1	no	—
22	C₂×#1055	—	3	1	no	—
23	C₈×D₁₃	—	3	1	no	—
24	C₈×D₁₃	—	3	1	no	—
25	C₈×D₁₃	—	3	1	no	—
26	C₈×D₁₃	D₃	1	1	yes	characteristic, direct product factor
27	C₂×D₃₉	C₂×C₄	1	1	yes	characteristic
28	C₂×D₃×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₃×D₁₃	C₂×C₄	1	1	yes	characteristic
30	D₃×D₁₃	C₈	1	4	yes	direct product factor
31	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
32	Dic₃₉	C₂×C₄	1	1	yes	characteristic
33	C₃×Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	Dic₃×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₁₃	—	3	1	no	—
36	C₂×C₄×C₁₃	—	3	1	no	—
37	C₂×Dic₁₃	—	3	1	no	—
38	C₄×D₁₃	—	3	1	no	—
39	C₄×D₁₃	—	3	1	no	—
40	C₄×D₁₃	—	3	1	no	—
41	C₄×D₁₃	C₂×D₃	1	1	yes	characteristic
42	C₈×C₁₃	—	3	1	no	—
43	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
44	#1055	—	3	1	no	—
45	#1055	C₂×D₃	1	1	yes	characteristic, complemented
46	C₂×D₃×C₈	—	13	1	no	maximal, Hall
47	C₂×C₃×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	D₃₉	C₂×C₈	1	2	yes	complemented
49	C₃×D₁₃	C₂×C₈	1	2	yes	complemented
50	D₃×C₁₃	C₂×C₈	1	2	yes	complemented
51	C₂²×C₁₃	—	3	1	no	—
52	C₂×D₁₃	—	3	1	no	—
53	C₂×D₁₃	—	3	4	no	—
54	C₂×D₁₃	C₄×D₃	1	1	yes	characteristic
55	C₄×C₁₃	—	3	1	no	—
56	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
57	Dic₁₃	—	3	1	no	—
58	Dic₁₃	C₄×D₃	1	1	yes	characteristic
59	C₂×C₄×D₃	—	13	1	no	—
60	C₂×C₃×C₈	—	13	1	no	—
61	C₂×C₃⋊C₈	—	13	1	no	—
62	D₃×C₈	—	13	1	no	—
63	D₃×C₈	—	13	1	no	—
64	D₃×C₈	—	13	1	no	—
65	D₃×C₈	D₁₃	1	1	yes	characteristic, direct product factor
66	C₃×C₁₃	C₂²×C₈	1	1	yes	characteristic, complemented, Hall
67	C₂²×C₈	—	39	1	no	Sylow
68	C₂×C₁₃	—	3	2	no	—
69	C₂×C₁₃	C₂×C₄×D₃	1	1	yes	characteristic
70	D₁₃	—	3	2	no	—
71	D₁₃	D₃×C₈	1	2	yes	direct product factor
72	C₂²×D₃	—	13	1	no	—
73	C₂×C₃×C₄	—	13	1	no	—
74	C₂×Dic₃	—	13	1	no	—
75	C₄×D₃	—	13	1	no	—
76	C₄×D₃	—	13	1	no	—
77	C₄×D₃	—	13	1	no	—
78	C₄×D₃	C₂×D₁₃	1	1	yes	characteristic
79	C₃×C₈	—	13	1	no	—
80	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
81	C₃⋊C₈	—	13	1	no	—
82	C₃⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
83	C₂²×C₄	—	39	1	no	—
84	C₂×C₈	—	3	1	no	—
85	C₂×C₈	—	13	1	no	—
86	C₂×C₈	—	39	1	no	—
87	C₂×C₈	—	39	1	no	—
88	C₂×C₈	—	39	1	no	—
89	C₂×C₈	—	39	1	no	—
90	C₁₃	C₂×D₃×C₈	1	1	yes	characteristic, complemented, Sylow
91	C₂²×C₃	—	13	1	no	—
92	C₂×D₃	—	13	1	no	—
93	C₂×D₃	—	13	4	no	—
94	C₂×D₃	C₄×D₁₃	1	1	yes	characteristic
95	C₃×C₄	—	13	1	no	—
96	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
97	Dic₃	—	13	1	no	—
98	Dic₃	C₄×D₁₃	1	1	yes	characteristic
99	C₂³	—	39	1	no	—
100	C₂×C₄	—	3	1	no	—
101	C₂×C₄	—	13	1	no	—
102	C₂×C₄	—	39	1	no	—
103	C₂×C₄	—	39	1	no	—
104	C₂×C₄	—	39	1	no	—
105	C₂×C₄	—	39	1	no	—
106	C₈	—	3	1	no	—
107	C₈	—	13	1	no	—
108	C₈	—	39	1	no	—
109	C₈	D₃×D₁₃	1	1	yes	characteristic, direct product factor
110	C₂×C₃	—	13	2	no	—
111	C₂×C₃	C₂×C₄×D₁₃	1	1	yes	characteristic
112	D₃	—	13	2	no	—
113	D₃	C₈×D₁₃	1	2	yes	direct product factor
114	C₂²	—	3	1	no	—
115	C₂²	—	13	1	no	—
116	C₂²	—	39	4	no	—
117	C₂²	—	39	1	no	—
118	C₄	—	3	1	no	—
119	C₄	—	13	1	no	—
120	C₄	—	39	1	no	—
121	C₄	C₂×D₃×D₁₃	1	1	yes	characteristic
122	C₃	C₂×C₈×D₁₃	1	1	yes	characteristic, complemented, Sylow
123	C₂	—	3	2	no	—
124	C₂	—	13	2	no	—
125	C₂	—	39	2	no	—
126	C₂	C₄×D₃×D₁₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₃×D₁₃

C₂

yes

maximal, characteristic

C₈×D₃₉

C₂

yes

maximal, characteristic, complemented

D₃×C₈×C₁₃

C₂

yes

maximal, characteristic, complemented

C₃×C₈×D₁₃

C₂

yes

maximal, characteristic, complemented

#10597591

C₂

yes

maximal, characteristic, complemented

D₃×#1055

C₂

yes

maximal, characteristic, complemented

C₃⋊C₈×D₁₃

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₁₃

—

maximal, Hall

C₂×D₃×D₁₃

C₄

yes

characteristic

C₄×D₃₉

C₂²

yes

characteristic

C₄×D₃×C₁₃

C₂²

yes

characteristic

C₃×C₄×D₁₃

C₂²

yes

characteristic

#64601

C₄

yes

characteristic

D₃×Dic₁₃

C₄

yes

characteristic

Dic₃×D₁₃

C₄

yes

characteristic

C₃×C₈×C₁₃

C₂²

yes

characteristic, complemented

C₃⋊#1055

C₂²

yes

characteristic, complemented

C₃×#1055

C₂²

yes

characteristic, complemented

C₁₃×C₃⋊C₈

C₂²

yes

characteristic, complemented

C₂×C₄×D₁₃

—

C₂×C₈×C₁₃

—

C₂×#1055

—

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

D₃

yes

characteristic, direct product factor

C₂×D₃₉

C₂×C₄

yes

characteristic

C₂×D₃×C₁₃

C₂×C₄

yes

characteristic

C₂×C₃×D₁₃

C₂×C₄

yes

characteristic

D₃×D₁₃

C₈

yes

direct product factor

C₃×C₄×C₁₃

C₂³

yes

characteristic

Dic₃₉

C₂×C₄

yes

characteristic

C₃×Dic₁₃

C₂×C₄

yes

characteristic

Dic₃×C₁₃

C₂×C₄

yes

characteristic

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×Dic₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

C₂×D₃

yes

characteristic

C₈×C₁₃

—

C₈×C₁₃

C₂×D₃

yes

characteristic, complemented

#1055

—

#1055

C₂×D₃

yes

characteristic, complemented

C₂×D₃×C₈

—

maximal, Hall

C₂×C₃×C₁₃

C₂²×C₄

yes

characteristic

D₃₉

C₂×C₈

yes

complemented

C₃×D₁₃

C₂×C₈

yes

complemented

D₃×C₁₃

C₂×C₈

yes

complemented

C₂²×C₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

C₄×D₃

yes

characteristic

C₄×C₁₃

—

C₄×C₁₃

C₂²×D₃

yes

characteristic

Dic₁₃

—

Dic₁₃

C₄×D₃

yes

characteristic

C₂×C₄×D₃

—

C₂×C₃×C₈

—

C₂×C₃⋊C₈

—

D₃×C₈

—

D₃×C₈

—

D₃×C₈

—

D₃×C₈

D₁₃

yes

characteristic, direct product factor

C₃×C₁₃

C₂²×C₈

yes

characteristic, complemented, Hall

C₂²×C₈

—

Sylow

C₂×C₁₃

—

C₂×C₁₃

C₂×C₄×D₃

yes

characteristic

D₁₃

—

D₁₃

D₃×C₈

yes

direct product factor

C₂²×D₃

—

C₂×C₃×C₄

—

C₂×Dic₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

—

C₄×D₃

C₂×D₁₃

yes

characteristic

C₃×C₈

—

C₃×C₈

C₂×D₁₃

yes

characteristic, complemented

C₃⋊C₈

—

C₃⋊C₈

C₂×D₁₃

yes

characteristic, complemented

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₁₃

C₂×D₃×C₈

yes

characteristic, complemented, Sylow

C₂²×C₃

—

C₂×D₃

—

C₂×D₃

—

C₂×D₃

C₄×D₁₃

yes

characteristic

C₃×C₄

—

C₃×C₄

C₂²×D₁₃

yes

characteristic

Dic₃

—

Dic₃

C₄×D₁₃

yes

characteristic

C₂³

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₈

—

107

C₈

—

108

C₈

—

109

C₈

D₃×D₁₃

yes

characteristic, direct product factor

110

C₂×C₃

—

111

C₂×C₃

C₂×C₄×D₁₃

yes

characteristic

112

D₃

—

113

D₃

C₈×D₁₃

yes

direct product factor

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₂×D₃×D₁₃

yes

characteristic

122

C₃

C₂×C₈×D₁₃

yes

characteristic, complemented, Sylow

123

C₂

—

124

C₂

—

125

C₂

—

126

C₂

C₄×D₃×D₁₃

yes

characteristic

	subgroup	G/H
center, hypercenter	C₈	D₃×D₁₃
commutator, hypocenter	C₃×C₁₃	C₂²×C₈
Frattini	C₄	C₂×D₃×D₁₃
Fitting	C₃×C₈×C₁₃	C₂²
socle	C₂×C₃×C₁₃	C₂²×C₄
prime radical	C₂×D₃×D₁₃	C₄
cosocle	C₃×C₄×C₁₃	C₂³
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₈

subgroup

G/H

center, hypercenter

C₈

D₃×D₁₃

commutator, hypocenter

C₃×C₁₃

C₂²×C₈

Frattini

C₄

C₂×D₃×D₁₃

Fitting

C₃×C₈×C₁₃

C₂²

socle

C₂×C₃×C₁₃

C₂²×C₄

prime radical

C₂×D₃×D₁₃

C₄

cosocle

C₃×C₄×C₁₃

C₂³

LCS

G ▷ C₃×C₁₃

UCS

C₁ ◁ C₈

N	H ≅ G/N	type
2. C₈×D₃₉	C₂	semidirect
3. D₃×C₈×C₁₃	C₂	semidirect
4. C₃×C₈×D₁₃	C₂	semidirect
5. #10597591	C₂	semidirect
6. D₃×#1055	C₂	semidirect
7. C₃⋊C₈×D₁₃	C₂	semidirect
16. C₃×C₈×C₁₃	C₂²	semidirect
17. C₃⋊#1055	C₂²	semidirect
18. C₃×#1055	C₂²	semidirect
19. C₁₃×C₃⋊C₈	C₂²	semidirect
26. C₈×D₁₃	D₃	direct (N × H)
30. D₃×D₁₃	C₈	direct (N × H)
43. C₈×C₁₃	C₂×D₃	semidirect
45. #1055	C₂×D₃	semidirect
48. D₃₉	C₂×C₈	semidirect
49. C₃×D₁₃	C₂×C₈	semidirect
50. D₃×C₁₃	C₂×C₈	semidirect
65. D₃×C₈	D₁₃	direct (N × H)
66. C₃×C₁₃	C₂²×C₈	semidirect
71. D₁₃	D₃×C₈	direct (N × H)
80. C₃×C₈	C₂×D₁₃	semidirect
82. C₃⋊C₈	C₂×D₁₃	semidirect
90. C₁₃	C₂×D₃×C₈	semidirect
109. C₈	D₃×D₁₃	direct (N × H)
113. D₃	C₈×D₁₃	direct (N × H)
122. C₃	C₂×C₈×D₁₃	semidirect

H ≅ G/N

type

2. C₈×D₃₉

C₂

semidirect

3. D₃×C₈×C₁₃

C₂

semidirect

4. C₃×C₈×D₁₃

C₂

semidirect

5. #10597591

C₂

semidirect

6. D₃×#1055

C₂

semidirect

7. C₃⋊C₈×D₁₃

C₂

semidirect

16. C₃×C₈×C₁₃

C₂²

semidirect

17. C₃⋊#1055

C₂²

semidirect

18. C₃×#1055

C₂²

semidirect

19. C₁₃×C₃⋊C₈

C₂²

semidirect

26. C₈×D₁₃

D₃

direct (N × H)

30. D₃×D₁₃

C₈

direct (N × H)

43. C₈×C₁₃

C₂×D₃

semidirect

45. #1055

C₂×D₃

semidirect

48. D₃₉

C₂×C₈

semidirect

49. C₃×D₁₃

C₂×C₈

semidirect

50. D₃×C₁₃

C₂×C₈

semidirect

65. D₃×C₈

D₁₃

direct (N × H)

66. C₃×C₁₃

C₂²×C₈

semidirect

71. D₁₃

D₃×C₈

direct (N × H)

80. C₃×C₈

C₂×D₁₃

semidirect

82. C₃⋊C₈

C₂×D₁₃

semidirect

90. C₁₃

C₂×D₃×C₈

semidirect

109. C₈

D₃×D₁₃

direct (N × H)

113. D₃

C₈×D₁₃

direct (N × H)

122. C₃

C₂×C₈×D₁₃

semidirect

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

subgroup	index
C₄×D₃×D₁₃	2
C₈×D₃₉	2
D₃×C₈×C₁₃	2
C₃×C₈×D₁₃	2
#10597591	2
D₃×#1055	2
C₃⋊C₈×D₁₃	2
C₂×C₈×D₁₃	3
C₂×D₃×C₈	13

subgroup

index

C₄×D₃×D₁₃

C₈×D₃₉

D₃×C₈×C₁₃

C₃×C₈×D₁₃

#10597591

D₃×#1055

C₃⋊C₈×D₁₃

C₂×C₈×D₁₃

C₂×D₃×C₈

Subgroups — D₃×C₈×D₁₃ #11928384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D3×C8×D13 #11928384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₈×D₁₃ #11928384