Group #11928975 — subgroups

Subgroups — SD₁₆×D₃₉ #11928975

Order 1248.

136 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 43 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	Q₈×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₃₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#10597669	C₂	1	1	yes	maximal, characteristic, complemented
5	#10597668	C₂	1	1	yes	maximal, characteristic, complemented
6	#10597658	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆×D₁₃	—	3	1	no	maximal, Hall
9	C₂²×D₃₉	—	2	1	no	—
10	C₃×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
11	C₃×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	#64625	—	2	1	no	—
13	D₁₅₆	C₂²	1	1	yes	characteristic
14	C₄×D₃₉	—	2	1	no	—
15	C₄×D₃₉	C₂²	1	1	yes	characteristic
16	Dic₇₈	—	2	1	no	—
17	Dic₇₈	C₂²	1	1	yes	characteristic, complemented
18	C₃×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
19	C₃⋊#1055	C₂²	1	1	yes	characteristic, complemented
20	Q₈×D₁₃	—	3	1	no	—
21	D₄×D₁₃	—	3	1	no	—
22	C₁₃×SD₁₆	D₃	1	1	yes	characteristic, complemented
23	#6106	—	3	1	no	—
24	#6105	—	3	1	no	—
25	#6095	—	3	1	no	—
26	C₈×D₁₃	—	3	1	no	—
27	C₂²×C₃×C₁₃	—	2	1	no	—
28	C₂×D₃₉	—	2	1	no	—
29	C₂×D₃₉	—	4	2	no	—
30	C₂×D₃₉	D₄	1	1	yes	characteristic
31	C₃×C₄×C₁₃	—	2	1	no	—
32	C₃×C₄×C₁₃	C₂³	1	1	yes	characteristic
33	Dic₃₉	—	2	1	no	—
34	Dic₃₉	D₄	1	1	yes	characteristic
35	C₂²×D₁₃	—	6	1	no	—
36	Q₈×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
37	D₄×C₁₃	C₂×D₃	1	1	yes	characteristic
38	C₂²⋊D₁₃	—	6	1	no	—
39	D₅₂	—	3	1	no	—
40	C₄×D₁₃	—	3	1	no	—
41	C₄×D₁₃	—	6	1	no	—
42	Dic₂₆	—	3	1	no	—
43	Dic₂₆	—	6	1	no	—
44	C₈×C₁₃	C₂×D₃	1	1	yes	characteristic, complemented
45	#1055	—	3	1	no	—
46	D₃×SD₁₆	—	13	1	no	maximal, Hall
47	C₂×C₃×C₁₃	—	4	1	no	—
48	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
49	D₃₉	—	4	1	no	—
50	D₃₉	SD₁₆	1	2	yes	direct product factor
51	C₂²×C₁₃	—	2	1	no	—
52	C₂×D₁₃	—	3	1	no	—
53	C₂×D₁₃	—	6	1	no	—
54	C₂×D₁₃	—	12	2	no	—
55	C₄×C₁₃	—	2	1	no	—
56	C₄×C₁₃	C₂²×D₃	1	1	yes	characteristic
57	Dic₁₃	—	3	1	no	—
58	Dic₁₃	—	6	1	no	—
59	D₃×Q₈	—	13	1	no	—
60	D₃×D₄	—	13	1	no	—
61	C₃×SD₁₆	D₁₃	1	1	yes	characteristic, complemented
62	#215	—	13	1	no	—
63	#214	—	13	1	no	—
64	#204	—	13	1	no	—
65	D₃×C₈	—	13	1	no	—
66	C₃×C₁₃	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
67	C₂×SD₁₆	—	39	1	no	Sylow
68	C₂×C₁₃	—	4	1	no	—
69	C₂×C₁₃	D₃×D₄	1	1	yes	characteristic
70	D₁₃	—	3	2	no	—
71	D₁₃	—	12	1	no	—
72	C₂²×D₃	—	26	1	no	—
73	C₃×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
74	C₃×D₄	C₂×D₁₃	1	1	yes	characteristic
75	#67	—	26	1	no	—
76	D₁₂	—	13	1	no	—
77	C₄×D₃	—	13	1	no	—
78	C₄×D₃	—	26	1	no	—
79	Dic₆	—	13	1	no	—
80	Dic₆	—	26	1	no	—
81	C₃×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
82	C₃⋊C₈	—	13	1	no	—
83	C₂×Q₈	—	39	1	no	—
84	C₂×D₄	—	39	1	no	—
85	SD₁₆	—	39	1	no	—
86	SD₁₆	—	39	1	no	—
87	SD₁₆	—	39	1	no	—
88	SD₁₆	D₃₉	1	1	yes	characteristic, direct product factor
89	C₂×C₈	—	39	1	no	—
90	C₁₃	D₃×SD₁₆	1	1	yes	characteristic, complemented, Sylow
91	C₂²×C₃	—	2	1	no	—
92	C₂×D₃	—	13	1	no	—
93	C₂×D₃	—	26	1	no	—
94	C₂×D₃	—	52	2	no	—
95	C₃×C₄	—	2	1	no	—
96	C₃×C₄	C₂²×D₁₃	1	1	yes	characteristic
97	Dic₃	—	13	1	no	—
98	Dic₃	—	26	1	no	—
99	C₂³	—	78	1	no	—
100	Q₈	—	39	1	no	—
101	Q₈	—	78	1	no	—
102	Q₈	C₂×D₃₉	1	1	yes	characteristic, complemented
103	D₄	—	39	1	no	—
104	D₄	—	78	1	no	—
105	D₄	C₂×D₃₉	1	1	yes	characteristic
106	C₂×C₄	—	39	1	no	—
107	C₂×C₄	—	78	1	no	—
108	C₈	—	39	1	no	—
109	C₈	C₂×D₃₉	1	1	yes	characteristic, complemented
110	C₂×C₃	—	4	1	no	—
111	C₂×C₃	D₄×D₁₃	1	1	yes	characteristic
112	D₃	—	13	2	no	—
113	D₃	—	52	1	no	—
114	C₂²	—	2	1	no	—
115	C₂²	—	39	1	no	—
116	C₂²	—	78	1	no	—
117	C₂²	—	156	2	no	—
118	C₄	—	2	1	no	—
119	C₄	—	39	1	no	—
120	C₄	—	78	1	no	—
121	C₄	C₂²×D₃₉	1	1	yes	characteristic
122	C₃	SD₁₆×D₁₃	1	1	yes	characteristic, complemented, Sylow
123	C₂	—	4	1	no	—
124	C₂	—	39	2	no	—
125	C₂	—	156	1	no	—
126	C₂	D₄×D₃₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×D₃₉

C₂

yes

maximal, characteristic, complemented

D₄×D₃₉

C₂

yes

maximal, characteristic

C₃×C₁₃×SD₁₆

C₂

yes

maximal, characteristic, complemented

#10597669

C₂

yes

maximal, characteristic, complemented

#10597668

C₂

yes

maximal, characteristic, complemented

#10597658

C₂

yes

maximal, characteristic, complemented

C₈×D₃₉

C₂

yes

maximal, characteristic, complemented

SD₁₆×D₁₃

—

maximal, Hall

C₂²×D₃₉

—

C₃×Q₈×C₁₃

C₂²

yes

characteristic, complemented

C₃×D₄×C₁₃

C₂²

yes

characteristic

#64625

—

D₁₅₆

C₂²

yes

characteristic

C₄×D₃₉

—

C₄×D₃₉

C₂²

yes

characteristic

Dic₇₈

—

Dic₇₈

C₂²

yes

characteristic, complemented

C₃×C₈×C₁₃

C₂²

yes

characteristic, complemented

C₃⋊#1055

C₂²

yes

characteristic, complemented

Q₈×D₁₃

—

D₄×D₁₃

—

C₁₃×SD₁₆

D₃

yes

characteristic, complemented

#6106

—

#6105

—

#6095

—

C₈×D₁₃

—

C₂²×C₃×C₁₃

—

C₂×D₃₉

—

C₂×D₃₉

—

C₂×D₃₉

D₄

yes

characteristic

C₃×C₄×C₁₃

—

C₃×C₄×C₁₃

C₂³

yes

characteristic

Dic₃₉

—

Dic₃₉

D₄

yes

characteristic

C₂²×D₁₃

—

Q₈×C₁₃

C₂×D₃

yes

characteristic, complemented

D₄×C₁₃

C₂×D₃

yes

characteristic

C₂²⋊D₁₃

—

D₅₂

—

C₄×D₁₃

—

C₄×D₁₃

—

Dic₂₆

—

Dic₂₆

—

C₈×C₁₃

C₂×D₃

yes

characteristic, complemented

#1055

—

D₃×SD₁₆

—

maximal, Hall

C₂×C₃×C₁₃

—

C₂×C₃×C₁₃

C₂×D₄

yes

characteristic

D₃₉

—

D₃₉

SD₁₆

yes

direct product factor

C₂²×C₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₂×D₁₃

—

C₄×C₁₃

—

C₄×C₁₃

C₂²×D₃

yes

characteristic

Dic₁₃

—

Dic₁₃

—

D₃×Q₈

—

D₃×D₄

—

C₃×SD₁₆

D₁₃

yes

characteristic, complemented

#215

—

#214

—

#204

—

D₃×C₈

—

C₃×C₁₃

C₂×SD₁₆

yes

characteristic, complemented, Hall

C₂×SD₁₆

—

Sylow

C₂×C₁₃

—

C₂×C₁₃

D₃×D₄

yes

characteristic

D₁₃

—

D₁₃

—

C₂²×D₃

—

C₃×Q₈

C₂×D₁₃

yes

characteristic, complemented

C₃×D₄

C₂×D₁₃

yes

characteristic

#67

—

D₁₂

—

C₄×D₃

—

C₄×D₃

—

Dic₆

—

Dic₆

—

C₃×C₈

C₂×D₁₃

yes

characteristic, complemented

C₃⋊C₈

—

C₂×Q₈

—

C₂×D₄

—

SD₁₆

—

SD₁₆

—

SD₁₆

—

SD₁₆

D₃₉

yes

characteristic, direct product factor

C₂×C₈

—

C₁₃

D₃×SD₁₆

yes

characteristic, complemented, Sylow

C₂²×C₃

—

C₂×D₃

—

C₂×D₃

—

C₂×D₃

—

C₃×C₄

—

C₃×C₄

C₂²×D₁₃

yes

characteristic

Dic₃

—

Dic₃

—

C₂³

—

100

Q₈

—

101

Q₈

—

102

Q₈

C₂×D₃₉

yes

characteristic, complemented

103

D₄

—

104

D₄

—

105

D₄

C₂×D₃₉

yes

characteristic

106

C₂×C₄

—

107

C₂×C₄

—

108

C₈

—

109

C₈

C₂×D₃₉

yes

characteristic, complemented

110

C₂×C₃

—

111

C₂×C₃

D₄×D₁₃

yes

characteristic

112

D₃

—

113

D₃

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

—

156

—

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

C₂²×D₃₉

yes

characteristic

122

C₃

SD₁₆×D₁₃

yes

characteristic, complemented, Sylow

123

C₂

—

124

C₂

—

125

C₂

—

156

—

126

C₂

D₄×D₃₉

yes

characteristic

	subgroup	G/H
center	C₂	D₄×D₃₉
commutator, cosocle	C₃×C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₃₉
Fitting	C₃×C₁₃×SD₁₆	C₂
socle	C₂×C₃×C₁₃	C₂×D₄
prime radical	D₄×D₃₉	C₂
hypercenter	SD₁₆	D₃₉
hypocenter	C₃×C₁₃	C₂×SD₁₆
LCS	G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

subgroup

G/H

center

C₂

D₄×D₃₉

commutator, cosocle

C₃×C₄×C₁₃

C₂³

Frattini

C₄

C₂²×D₃₉

Fitting

C₃×C₁₃×SD₁₆

C₂

socle

C₂×C₃×C₁₃

C₂×D₄

prime radical

D₄×D₃₉

C₂

hypercenter

SD₁₆

D₃₉

hypocenter

C₃×C₁₃

C₂×SD₁₆

LCS

G ▷ C₃×C₄×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃

UCS

C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

N	H ≅ G/N	type
1. Q₈×D₃₉	C₂	semidirect
3. C₃×C₁₃×SD₁₆	C₂	semidirect
4. #10597669	C₂	semidirect
5. #10597668	C₂	semidirect
6. #10597658	C₂	semidirect
7. C₈×D₃₉	C₂	semidirect
10. C₃×Q₈×C₁₃	C₂²	semidirect
17. Dic₇₈	C₂²	semidirect
18. C₃×C₈×C₁₃	C₂²	semidirect
19. C₃⋊#1055	C₂²	semidirect
22. C₁₃×SD₁₆	D₃	semidirect
36. Q₈×C₁₃	C₂×D₃	semidirect
44. C₈×C₁₃	C₂×D₃	semidirect
50. D₃₉	SD₁₆	direct (N × H)
61. C₃×SD₁₆	D₁₃	semidirect
66. C₃×C₁₃	C₂×SD₁₆	semidirect
73. C₃×Q₈	C₂×D₁₃	semidirect
81. C₃×C₈	C₂×D₁₃	semidirect
88. SD₁₆	D₃₉	direct (N × H)
90. C₁₃	D₃×SD₁₆	semidirect
102. Q₈	C₂×D₃₉	semidirect
109. C₈	C₂×D₃₉	semidirect
122. C₃	SD₁₆×D₁₃	semidirect

H ≅ G/N

type

1. Q₈×D₃₉

C₂

semidirect

3. C₃×C₁₃×SD₁₆

C₂

semidirect

4. #10597669

C₂

semidirect

5. #10597668

C₂

semidirect

6. #10597658

C₂

semidirect

7. C₈×D₃₉

C₂

semidirect

10. C₃×Q₈×C₁₃

C₂²

semidirect

17. Dic₇₈

C₂²

semidirect

18. C₃×C₈×C₁₃

C₂²

semidirect

19. C₃⋊#1055

C₂²

semidirect

22. C₁₃×SD₁₆

D₃

semidirect

36. Q₈×C₁₃

C₂×D₃

semidirect

44. C₈×C₁₃

C₂×D₃

semidirect

50. D₃₉

SD₁₆

direct (N × H)

61. C₃×SD₁₆

D₁₃

semidirect

66. C₃×C₁₃

C₂×SD₁₆

semidirect

73. C₃×Q₈

C₂×D₁₃

semidirect

81. C₃×C₈

C₂×D₁₃

semidirect

88. SD₁₆

D₃₉

direct (N × H)

90. C₁₃

D₃×SD₁₆

semidirect

102. Q₈

C₂×D₃₉

semidirect

109. C₈

C₂×D₃₉

semidirect

122. C₃

SD₁₆×D₁₃

semidirect

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

subgroup	index
Q₈×D₃₉	2
D₄×D₃₉	2
C₃×C₁₃×SD₁₆	2
#10597669	2
#10597668	2
#10597658	2
C₈×D₃₉	2
SD₁₆×D₁₃	3
D₃×SD₁₆	13

subgroup

index

Q₈×D₃₉

D₄×D₃₉

C₃×C₁₃×SD₁₆

#10597669

#10597668

#10597658

C₈×D₃₉

SD₁₆×D₁₃

D₃×SD₁₆

Subgroups — SD₁₆×D₃₉ #11928975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD16×D39 #11928975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₃₉ #11928975