Group #16809611 — subgroups

Subgroups — C₂³×D₁₃⋊C₁₆ #16809611

Order 3328.

2590 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.

normal subgroups only

This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1464 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	C₂²×D₁₃⋊C₁₆	C₂	1	28	yes	maximal, direct product factor
2	C₂³×#6092	C₂	1	2	yes	maximal, complemented
3	C₂³×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₄×D₁₃	C₄	1	1	yes	characteristic
5	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂³×#1055	C₂²	1	1	yes	characteristic
7	C₂²×C₈×D₁₃	C₄	1	14	yes	—
8	C₂²×C₈×D₁₃	C₂²	1	14	yes	—
9	C₂²×#6092	C₂²	1	28	yes	complemented
10	C₂×D₁₃⋊C₁₆	C₂²	1	112	yes	direct product factor
11	C₂⁴×D₁₃	C₈	1	1	yes	characteristic
12	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂³×Dic₁₃	C₈	1	1	yes	characteristic
14	C₂²×C₄×D₁₃	C₈	1	14	yes	—
15	C₂²×C₄×D₁₃	C₂×C₄	1	14	yes	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	14	yes	—
17	C₂²×#1055	C₂×C₄	1	7	yes	—
18	C₂²×#1055	C₂³	1	7	yes	—
19	C₂×C₈×D₁₃	C₂×C₄	1	84	yes	—
20	C₂×C₈×D₁₃	C₂³	1	28	yes	—
21	C₂×#6092	C₂³	1	56	yes	complemented
22	D₁₃⋊C₁₆	C₂³	1	64	yes	direct product factor
23	C₂⁴×C₁₆	—	13	1	no	maximal, Sylow
24	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂³×D₁₃	C₁₆	1	16	yes	complemented
26	C₂³×D₁₃	C₂×C₈	1	14	yes	—
27	C₂²×C₄×C₁₃	C₂×C₈	1	7	yes	—
28	C₂²×C₄×C₁₃	C₂²×C₄	1	7	yes	—
29	C₂²×Dic₁₃	C₂×C₈	1	14	yes	—
30	C₂×C₄×D₁₃	C₂×C₈	1	84	yes	—
31	C₂×C₄×D₁₃	C₂²×C₄	1	28	yes	—
32	C₂×C₈×C₁₃	C₂²×C₄	1	28	yes	—
33	C₂×#1055	C₂²×C₄	1	21	yes	—
34	C₂×#1055	C₂⁴	1	7	yes	—
35	C₈×D₁₃	C₂²×C₄	1	56	yes	—
36	C₈×D₁₃	C₂⁴	1	8	yes	—
37	#6092	C₂⁴	1	16	yes	complemented
38	C₂⁴×C₈	—	13	1	no	—
39	C₂³×C₁₆	—	13	2	no	—
40	C₂³×C₁₆	—	13	28	no	—
41	C₂³×C₁₃	C₂×C₁₆	1	8	yes	complemented
42	C₂³×C₁₃	C₂²×C₈	1	7	yes	—
43	C₂²×D₁₃	C₂×C₁₆	1	112	yes	complemented
44	C₂²×D₁₃	C₂²×C₈	1	28	yes	—
45	C₂×C₄×C₁₃	C₂²×C₈	1	21	yes	—
46	C₂×C₄×C₁₃	C₂³×C₄	1	7	yes	—
47	C₂×Dic₁₃	C₂²×C₈	1	28	yes	—
48	C₄×D₁₃	C₂²×C₈	1	56	yes	—
49	C₄×D₁₃	C₂³×C₄	1	8	yes	—
50	C₈×C₁₃	C₂³×C₄	1	8	yes	—
51	#1055	C₂³×C₄	1	7	yes	—
52	#1055	C₂⁵	1	1	yes	characteristic
53	C₂⁴×C₄	—	13	1	no	—
54	C₂³×C₈	—	13	1	no	—
55	C₂³×C₈	—	13	14	no	—
56	C₂³×C₈	—	13	14	no	—
57	C₂³×C₈	#261	1	1	yes	characteristic
58	C₂²×C₁₆	—	13	112	no	—
59	C₂²×C₁₆	—	13	28	no	—
60	C₂²×C₁₃	C₂²×C₁₆	1	28	yes	complemented
61	C₂²×C₁₃	C₂³×C₈	1	7	yes	—
62	C₂×D₁₃	C₂²×C₁₆	1	112	yes	complemented
63	C₂×D₁₃	C₂³×C₈	1	8	yes	—
64	C₄×C₁₃	C₂³×C₈	1	7	yes	—
65	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
66	Dic₁₃	C₂³×C₈	1	8	yes	—
67	C₂⁵	—	13	1	no	—
68	C₂³×C₄	—	13	1	no	—
69	C₂³×C₄	—	13	14	no	—
70	C₂³×C₄	—	13	14	no	—
71	C₂³×C₄	C₂×#261	1	1	yes	characteristic
72	C₂²×C₈	—	13	7	no	—
73	C₂²×C₈	—	13	7	no	—
74	C₂²×C₈	—	13	84	no	—
75	C₂²×C₈	—	13	28	no	—
76	C₂²×C₈	C₂×#261	1	14	yes	—
77	C₂×C₁₆	—	13	64	no	—
78	C₂×C₁₆	—	13	56	no	—
79	C₂×C₁₃	C₂³×C₁₆	1	14	yes	complemented
80	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
81	D₁₃	C₂³×C₁₆	1	16	yes	complemented
82	C₂⁴	—	13	16	no	—
83	C₂⁴	—	13	14	no	—
84	C₂⁴	D₁₃⋊C₈	1	1	yes	characteristic
85	C₂²×C₄	—	13	14	no	—
86	C₂²×C₄	—	13	84	no	—
87	C₂²×C₄	—	13	28	no	—
88	C₂²×C₄	D₁₃⋊C₈	1	7	yes	—
89	C₂²×C₄	C₂²×#261	1	7	yes	—
90	C₂×C₈	—	13	7	no	—
91	C₂×C₈	—	13	21	no	—
92	C₂×C₈	—	13	8	no	—
93	C₂×C₈	—	13	56	no	—
94	C₂×C₈	C₂²×#261	1	28	yes	—
95	C₁₆	—	13	16	no	—
96	C₁₃	C₂⁴×C₁₆	1	1	yes	characteristic, complemented, Sylow
97	C₂³	—	13	112	no	—
98	C₂³	—	13	28	no	—
99	C₂³	D₁₃⋊C₁₆	1	8	yes	direct product factor
100	C₂³	C₂×D₁₃⋊C₈	1	7	yes	—
101	C₂×C₄	—	13	28	no	—
102	C₂×C₄	—	13	56	no	—
103	C₂×C₄	—	13	8	no	—
104	C₂×C₄	C₂×D₁₃⋊C₈	1	21	yes	—
105	C₂×C₄	C₂³×#261	1	7	yes	—
106	C₈	—	13	1	no	—
107	C₈	—	13	7	no	—
108	C₈	C₂³×#261	1	8	yes	—
109	C₂²	—	13	112	no	—
110	C₂²	—	13	8	no	—
111	C₂²	C₂×D₁₃⋊C₁₆	1	28	yes	direct product factor
112	C₂²	C₂²×D₁₃⋊C₈	1	7	yes	—
113	C₄	—	13	8	no	—
114	C₄	C₂²×D₁₃⋊C₈	1	7	yes	—
115	C₄	C₂⁴×#261	1	1	yes	characteristic
116	C₂	—	13	16	no	—
117	C₂	C₂²×D₁₃⋊C₁₆	1	14	yes	direct product factor
118	C₂	C₂³×D₁₃⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₁₃⋊C₁₆

C₂

yes

maximal, direct product factor

C₂³×#6092

C₂

yes

maximal, complemented

C₂³×C₈×D₁₃

C₂

yes

maximal, characteristic

C₂³×C₄×D₁₃

C₄

yes

characteristic

C₂³×C₈×C₁₃

C₄

yes

characteristic

C₂³×#1055

C₂²

yes

characteristic

C₂²×C₈×D₁₃

C₄

yes

—

C₂²×C₈×D₁₃

C₂²

yes

—

C₂²×#6092

C₂²

yes

complemented

C₂×D₁₃⋊C₁₆

C₂²

112

yes

direct product factor

C₂⁴×D₁₃

C₈

yes

characteristic

C₂³×C₄×C₁₃

C₂×C₄

yes

characteristic

C₂³×Dic₁₃

C₈

yes

characteristic

C₂²×C₄×D₁₃

C₈

yes

—

C₂²×C₄×D₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×#1055

C₂×C₄

yes

—

C₂²×#1055

C₂³

yes

—

C₂×C₈×D₁₃

C₂×C₄

yes

—

C₂×C₈×D₁₃

C₂³

yes

—

C₂×#6092

C₂³

yes

complemented

D₁₃⋊C₁₆

C₂³

yes

direct product factor

C₂⁴×C₁₆

—

maximal, Sylow

C₂⁴×C₁₃

C₂×C₈

yes

characteristic

C₂³×D₁₃

C₁₆

yes

complemented

C₂³×D₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂×C₈

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

—

C₂²×Dic₁₃

C₂×C₈

yes

—

C₂×C₄×D₁₃

C₂×C₈

yes

—

C₂×C₄×D₁₃

C₂²×C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

—

C₂×#1055

C₂²×C₄

yes

—

C₂×#1055

C₂⁴

yes

—

C₈×D₁₃

C₂²×C₄

yes

—

C₈×D₁₃

C₂⁴

yes

—

#6092

C₂⁴

yes

complemented

C₂⁴×C₈

—

C₂³×C₁₆

—

C₂³×C₁₆

—

C₂³×C₁₃

C₂×C₁₆

yes

complemented

C₂³×C₁₃

C₂²×C₈

yes

—

C₂²×D₁₃

C₂×C₁₆

112

yes

complemented

C₂²×D₁₃

C₂²×C₈

yes

—

C₂×C₄×C₁₃

C₂²×C₈

yes

—

C₂×C₄×C₁₃

C₂³×C₄

yes

—

C₂×Dic₁₃

C₂²×C₈

yes

—

C₄×D₁₃

C₂²×C₈

yes

—

C₄×D₁₃

C₂³×C₄

yes

—

C₈×C₁₃

C₂³×C₄

yes

—

#1055

C₂³×C₄

yes

—

#1055

C₂⁵

yes

characteristic

C₂⁴×C₄

—

C₂³×C₈

—

C₂³×C₈

—

C₂³×C₈

—

C₂³×C₈

#261

yes

characteristic

C₂²×C₁₆

—

112

—

C₂²×C₁₆

—

C₂²×C₁₃

C₂²×C₁₆

yes

complemented

C₂²×C₁₃

C₂³×C₈

yes

—

C₂×D₁₃

C₂²×C₁₆

112

yes

complemented

C₂×D₁₃

C₂³×C₈

yes

—

C₄×C₁₃

C₂³×C₈

yes

—

C₄×C₁₃

C₂⁴×C₄

yes

characteristic

Dic₁₃

C₂³×C₈

yes

—

C₂⁵

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×#261

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×#261

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₃

C₂³×C₁₆

yes

complemented

C₂×C₁₃

C₂⁴×C₈

yes

characteristic

D₁₃

C₂³×C₁₆

yes

complemented

C₂⁴

—

C₂⁴

—

C₂⁴

D₁₃⋊C₈

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₁₃⋊C₈

yes

—

C₂²×C₄

C₂²×#261

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²×#261

yes

—

C₁₆

—

C₁₃

C₂⁴×C₁₆

yes

characteristic, complemented, Sylow

C₂³

—

112

—

C₂³

—

C₂³

D₁₃⋊C₁₆

yes

direct product factor

100

C₂³

C₂×D₁₃⋊C₈

yes

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂×D₁₃⋊C₈

yes

—

105

C₂×C₄

C₂³×#261

yes

—

106

C₈

—

107

C₈

—

108

C₈

C₂³×#261

yes

—

109

C₂²

—

112

—

110

C₂²

—

111

C₂²

C₂×D₁₃⋊C₁₆

yes

direct product factor

112

C₂²

C₂²×D₁₃⋊C₈

yes

—

113

C₄

—

114

C₄

C₂²×D₁₃⋊C₈

yes

—

115

C₄

C₂⁴×#261

yes

characteristic

116

C₂

—

117

C₂

C₂²×D₁₃⋊C₁₆

yes

direct product factor

118

C₂

C₂³×D₁₃⋊C₈

yes

characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₈	#261
commutator, hypocenter	C₁₃	C₂⁴×C₁₆
Frattini	C₄	C₂⁴×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle	C₂⁴×C₁₃	C₂×C₈
prime radical	C₂⁴×D₁₃	C₈
cosocle	#1055	C₂⁵
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂³×C₈

subgroup

G/H

center, hypercenter

C₂³×C₈

#261

commutator, hypocenter

C₁₃

C₂⁴×C₁₆

Frattini

C₄

C₂⁴×#261

Fitting

C₂³×C₈×C₁₃

C₄

socle

C₂⁴×C₁₃

C₂×C₈

prime radical

C₂⁴×D₁₃

C₈

C₂⁵

G ▷ C₁₃

C₁ ◁ C₂³×C₈

N	H ≅ G/N	type
1. C₂²×D₁₃⋊C₁₆	C₂	direct (N × H)
2. C₂³×#6092	C₂	semidirect
9. C₂²×#6092	C₂²	semidirect
10. C₂×D₁₃⋊C₁₆	C₂²	direct (N × H)
21. C₂×#6092	C₂³	semidirect
22. D₁₃⋊C₁₆	C₂³	direct (N × H)
25. C₂³×D₁₃	C₁₆	semidirect
37. #6092	C₂⁴	semidirect
41. C₂³×C₁₃	C₂×C₁₆	semidirect
43. C₂²×D₁₃	C₂×C₁₆	semidirect
60. C₂²×C₁₃	C₂²×C₁₆	semidirect
62. C₂×D₁₃	C₂²×C₁₆	semidirect
79. C₂×C₁₃	C₂³×C₁₆	semidirect
81. D₁₃	C₂³×C₁₆	semidirect
96. C₁₃	C₂⁴×C₁₆	semidirect
99. C₂³	D₁₃⋊C₁₆	direct (N × H)
111. C₂²	C₂×D₁₃⋊C₁₆	direct (N × H)
117. C₂	C₂²×D₁₃⋊C₁₆	direct (N × H)

H ≅ G/N

type

1. C₂²×D₁₃⋊C₁₆

C₂

direct (N × H)

2. C₂³×#6092

C₂

semidirect

9. C₂²×#6092

C₂²

semidirect

10. C₂×D₁₃⋊C₁₆

C₂²

direct (N × H)

21. C₂×#6092

C₂³

semidirect

22. D₁₃⋊C₁₆

C₂³

direct (N × H)

25. C₂³×D₁₃

C₁₆

semidirect

37. #6092

C₂⁴

semidirect

41. C₂³×C₁₃

C₂×C₁₆

semidirect

43. C₂²×D₁₃

C₂×C₁₆

semidirect

60. C₂²×C₁₃

C₂²×C₁₆

semidirect

62. C₂×D₁₃

C₂²×C₁₆

semidirect

79. C₂×C₁₃

C₂³×C₁₆

semidirect

81. D₁₃

C₂³×C₁₆

semidirect

96. C₁₃

C₂⁴×C₁₆

semidirect

99. C₂³

D₁₃⋊C₁₆

direct (N × H)

111. C₂²

C₂×D₁₃⋊C₁₆

direct (N × H)

117. C₂

C₂²×D₁₃⋊C₁₆

direct (N × H)

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

subgroup	index
C₂²×D₁₃⋊C₁₆	2
C₂³×#6092	2
C₂³×C₈×D₁₃	2
C₂⁴×C₁₆	13

subgroup

index

C₂²×D₁₃⋊C₁₆

C₂³×#6092

C₂³×C₈×D₁₃

C₂⁴×C₁₆

Subgroups — C₂³×D₁₃⋊C₁₆ #16809611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C23×D13⋊C16 #16809611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₁₃⋊C₁₆ #16809611