Group #16809642 — subgroups

Subgroups — C₂⁴×D₁₃⋊C₈ #16809642

Order 3328.

15454 conjugacy classes of subgroups; only the 8408 normal subgroups are shown.

normal subgroups only

This group has 15454 conjugacy classes of subgroups — too many to draw. Only its 8408 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	C₂³×D₁₃⋊C₈	C₂	1	60	yes	maximal, direct product factor
2	C₂⁴×#1057	C₂	1	2	yes	maximal, complemented
3	C₂⁴×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂⁵×D₁₃	C₄	1	1	yes	characteristic
5	C₂⁴×C₄×C₁₃	C₄	1	1	yes	characteristic
6	C₂⁴×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂³×C₄×D₁₃	C₄	1	30	yes	—
8	C₂³×C₄×D₁₃	C₂²	1	30	yes	—
9	C₂³×#1057	C₂²	1	60	yes	complemented
10	C₂²×D₁₃⋊C₈	C₂²	1	560	yes	direct product factor
11	C₂⁵×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂⁴×D₁₃	C₈	1	32	yes	complemented
13	C₂⁴×D₁₃	C₂×C₄	1	30	yes	—
14	C₂³×C₄×C₁₃	C₂×C₄	1	30	yes	—
15	C₂³×Dic₁₃	C₂×C₄	1	15	yes	—
16	C₂³×Dic₁₃	C₂³	1	15	yes	—
17	C₂²×C₄×D₁₃	C₂×C₄	1	420	yes	—
18	C₂²×C₄×D₁₃	C₂³	1	140	yes	—
19	C₂²×#1057	C₂³	1	280	yes	complemented
20	C₂×D₁₃⋊C₈	C₂³	1	960	yes	direct product factor
21	C₂⁵×C₈	—	13	1	no	maximal, Sylow
22	C₂⁴×C₁₃	C₂×C₈	1	16	yes	complemented
23	C₂⁴×C₁₃	C₂²×C₄	1	15	yes	—
24	C₂³×D₁₃	C₂×C₈	1	480	yes	complemented
25	C₂³×D₁₃	C₂²×C₄	1	140	yes	—
26	C₂²×C₄×C₁₃	C₂²×C₄	1	140	yes	—
27	C₂²×Dic₁₃	C₂²×C₄	1	105	yes	—
28	C₂²×Dic₁₃	C₂⁴	1	35	yes	—
29	C₂×C₄×D₁₃	C₂²×C₄	1	840	yes	—
30	C₂×C₄×D₁₃	C₂⁴	1	120	yes	—
31	C₂×#1057	C₂⁴	1	240	yes	complemented
32	D₁₃⋊C₈	C₂⁴	1	256	yes	direct product factor
33	C₂⁵×C₄	—	13	1	no	—
34	C₂⁴×C₈	—	13	2	no	—
35	C₂⁴×C₈	—	13	60	no	—
36	C₂³×C₁₃	C₂²×C₈	1	120	yes	complemented
37	C₂³×C₁₃	C₂³×C₄	1	35	yes	—
38	C₂²×D₁₃	C₂²×C₈	1	1120	yes	complemented
39	C₂²×D₁₃	C₂³×C₄	1	120	yes	—
40	C₂×C₄×C₁₃	C₂³×C₄	1	120	yes	—
41	C₂×Dic₁₃	C₂³×C₄	1	105	yes	—
42	C₂×Dic₁₃	C₂⁵	1	15	yes	—
43	C₄×D₁₃	C₂³×C₄	1	240	yes	—
44	C₄×D₁₃	C₂⁵	1	16	yes	—
45	#1057	C₂⁵	1	32	yes	complemented
46	C₂⁶	—	13	1	no	—
47	C₂⁴×C₄	—	13	1	no	—
48	C₂⁴×C₄	—	13	30	no	—
49	C₂⁴×C₄	—	13	30	no	—
50	C₂⁴×C₄	#261	1	1	yes	characteristic
51	C₂³×C₈	—	13	560	no	—
52	C₂³×C₈	—	13	60	no	—
53	C₂²×C₁₃	C₂³×C₈	1	140	yes	complemented
54	C₂²×C₁₃	C₂⁴×C₄	1	15	yes	—
55	C₂×D₁₃	C₂³×C₈	1	480	yes	complemented
56	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
57	C₄×C₁₃	C₂⁴×C₄	1	16	yes	—
58	Dic₁₃	C₂⁴×C₄	1	15	yes	—
59	Dic₁₃	C₂⁶	1	1	yes	characteristic
60	C₂⁵	—	13	32	no	—
61	C₂⁵	—	13	30	no	—
62	C₂⁵	C₂×#261	1	1	yes	characteristic
63	C₂³×C₄	—	13	15	no	—
64	C₂³×C₄	—	13	15	no	—
65	C₂³×C₄	—	13	140	no	—
66	C₂³×C₄	—	13	420	no	—
67	C₂³×C₄	C₂×#261	1	30	yes	—
68	C₂²×C₈	—	13	960	no	—
69	C₂²×C₈	—	13	280	no	—
70	C₂×C₁₃	C₂⁴×C₈	1	30	yes	complemented
71	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
72	D₁₃	C₂⁴×C₈	1	32	yes	complemented
73	C₂⁴	—	13	480	no	—
74	C₂⁴	—	13	140	no	—
75	C₂⁴	D₁₃⋊C₈	1	16	yes	direct product factor
76	C₂⁴	C₂²×#261	1	15	yes	—
77	C₂²×C₄	—	13	35	no	—
78	C₂²×C₄	—	13	105	no	—
79	C₂²×C₄	—	13	120	no	—
80	C₂²×C₄	—	13	840	no	—
81	C₂²×C₄	C₂²×#261	1	140	yes	—
82	C₂×C₈	—	13	256	no	—
83	C₂×C₈	—	13	240	no	—
84	C₁₃	C₂⁵×C₈	1	1	yes	characteristic, complemented, Sylow
85	C₂³	—	13	1120	no	—
86	C₂³	—	13	120	no	—
87	C₂³	C₂×D₁₃⋊C₈	1	120	yes	direct product factor
88	C₂³	C₂³×#261	1	35	yes	—
89	C₂×C₄	—	13	15	no	—
90	C₂×C₄	—	13	105	no	—
91	C₂×C₄	—	13	16	no	—
92	C₂×C₄	—	13	240	no	—
93	C₂×C₄	C₂³×#261	1	120	yes	—
94	C₈	—	13	32	no	—
95	C₂²	—	13	480	no	—
96	C₂²	—	13	16	no	—
97	C₂²	C₂²×D₁₃⋊C₈	1	140	yes	direct product factor
98	C₂²	C₂⁴×#261	1	15	yes	—
99	C₄	—	13	15	no	—
100	C₄	—	13	1	no	—
101	C₄	C₂⁴×#261	1	16	yes	—
102	C₂	—	13	32	no	—
103	C₂	C₂³×D₁₃⋊C₈	1	30	yes	direct product factor
104	C₂	C₂⁵×#261	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂³×D₁₃⋊C₈

C₂

yes

maximal, direct product factor

C₂⁴×#1057

C₂

yes

maximal, complemented

C₂⁴×C₄×D₁₃

C₂

yes

maximal, characteristic

C₂⁵×D₁₃

C₄

yes

characteristic

C₂⁴×C₄×C₁₃

C₄

yes

characteristic

C₂⁴×Dic₁₃

C₂²

yes

characteristic

C₂³×C₄×D₁₃

C₄

yes

—

C₂³×C₄×D₁₃

C₂²

yes

—

C₂³×#1057

C₂²

yes

complemented

C₂²×D₁₃⋊C₈

C₂²

560

yes

direct product factor

C₂⁵×C₁₃

C₂×C₄

yes

characteristic

C₂⁴×D₁₃

C₈

yes

complemented

C₂⁴×D₁₃

C₂×C₄

yes

—

C₂³×C₄×C₁₃

C₂×C₄

yes

—

C₂³×Dic₁₃

C₂×C₄

yes

—

C₂³×Dic₁₃

C₂³

yes

—

C₂²×C₄×D₁₃

C₂×C₄

420

yes

—

C₂²×C₄×D₁₃

C₂³

140

yes

—

C₂²×#1057

C₂³

280

yes

complemented

C₂×D₁₃⋊C₈

C₂³

960

yes

direct product factor

C₂⁵×C₈

—

maximal, Sylow

C₂⁴×C₁₃

C₂×C₈

yes

complemented

C₂⁴×C₁₃

C₂²×C₄

yes

—

C₂³×D₁₃

C₂×C₈

480

yes

complemented

C₂³×D₁₃

C₂²×C₄

140

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

140

yes

—

C₂²×Dic₁₃

C₂²×C₄

105

yes

—

C₂²×Dic₁₃

C₂⁴

yes

—

C₂×C₄×D₁₃

C₂²×C₄

840

yes

—

C₂×C₄×D₁₃

C₂⁴

120

yes

—

C₂×#1057

C₂⁴

240

yes

complemented

D₁₃⋊C₈

C₂⁴

256

yes

direct product factor

C₂⁵×C₄

—

C₂⁴×C₈

—

C₂⁴×C₈

—

C₂³×C₁₃

C₂²×C₈

120

yes

complemented

C₂³×C₁₃

C₂³×C₄

yes

—

C₂²×D₁₃

C₂²×C₈

1120

yes

complemented

C₂²×D₁₃

C₂³×C₄

120

yes

—

C₂×C₄×C₁₃

C₂³×C₄

120

yes

—

C₂×Dic₁₃

C₂³×C₄

105

yes

—

C₂×Dic₁₃

C₂⁵

yes

—

C₄×D₁₃

C₂³×C₄

240

yes

—

C₄×D₁₃

C₂⁵

yes

—

#1057

C₂⁵

yes

complemented

C₂⁶

—

C₂⁴×C₄

—

C₂⁴×C₄

—

C₂⁴×C₄

—

C₂⁴×C₄

#261

yes

characteristic

C₂³×C₈

—

560

—

C₂³×C₈

—

C₂²×C₁₃

C₂³×C₈

140

yes

complemented

C₂²×C₁₃

C₂⁴×C₄

yes

—

C₂×D₁₃

C₂³×C₈

480

yes

complemented

C₂×D₁₃

C₂⁴×C₄

yes

—

C₄×C₁₃

C₂⁴×C₄

yes

—

Dic₁₃

C₂⁴×C₄

yes

—

Dic₁₃

C₂⁶

yes

characteristic

C₂⁵

—

C₂⁵

—

C₂⁵

C₂×#261

yes

characteristic

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

140

—

C₂³×C₄

—

420

—

C₂³×C₄

C₂×#261

yes

—

C₂²×C₈

—

960

—

C₂²×C₈

—

280

—

C₂×C₁₃

C₂⁴×C₈

yes

complemented

C₂×C₁₃

C₂⁵×C₄

yes

characteristic

D₁₃

C₂⁴×C₈

yes

complemented

C₂⁴

—

480

—

C₂⁴

—

140

—

C₂⁴

D₁₃⋊C₈

yes

direct product factor

C₂⁴

C₂²×#261

yes

—

C₂²×C₄

—

C₂²×C₄

—

105

—

C₂²×C₄

—

120

—

C₂²×C₄

—

840

—

C₂²×C₄

C₂²×#261

140

yes

—

C₂×C₈

—

256

—

C₂×C₈

—

240

—

C₁₃

C₂⁵×C₈

yes

characteristic, complemented, Sylow

C₂³

—

1120

—

C₂³

—

120

—

C₂³

C₂×D₁₃⋊C₈

120

yes

direct product factor

C₂³

C₂³×#261

yes

—

C₂×C₄

—

C₂×C₄

—

105

—

C₂×C₄

—

C₂×C₄

—

240

—

C₂×C₄

C₂³×#261

120

yes

—

C₈

—

C₂²

—

480

—

C₂²

—

C₂²

C₂²×D₁₃⋊C₈

140

yes

direct product factor

C₂²

C₂⁴×#261

yes

—

C₄

—

100

C₄

—

101

C₄

C₂⁴×#261

yes

—

102

C₂

—

103

C₂

C₂³×D₁₃⋊C₈

yes

direct product factor

104

C₂

C₂⁵×#261

yes

characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	#261
commutator, hypocenter	C₁₃	C₂⁵×C₈
Frattini	C₂	C₂⁵×#261
Fitting	C₂⁴×C₄×C₁₃	C₄
socle	C₂⁵×C₁₃	C₂×C₄
prime radical	C₂⁵×D₁₃	C₄
cosocle	Dic₁₃	C₂⁶
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂⁴×C₄

subgroup

G/H

center, hypercenter

C₂⁴×C₄

#261

commutator, hypocenter

C₁₃

C₂⁵×C₈

Frattini

C₂

C₂⁵×#261

Fitting

C₂⁴×C₄×C₁₃

C₄

socle

C₂⁵×C₁₃

C₂×C₄

prime radical

C₂⁵×D₁₃

C₄

cosocle

Dic₁₃

C₂⁶

LCS

G ▷ C₁₃

UCS

C₁ ◁ C₂⁴×C₄

N	H ≅ G/N	type
1. C₂³×D₁₃⋊C₈	C₂	direct (N × H)
2. C₂⁴×#1057	C₂	semidirect
9. C₂³×#1057	C₂²	semidirect
10. C₂²×D₁₃⋊C₈	C₂²	direct (N × H)
12. C₂⁴×D₁₃	C₈	semidirect
19. C₂²×#1057	C₂³	semidirect
20. C₂×D₁₃⋊C₈	C₂³	direct (N × H)
22. C₂⁴×C₁₃	C₂×C₈	semidirect
24. C₂³×D₁₃	C₂×C₈	semidirect
31. C₂×#1057	C₂⁴	semidirect
32. D₁₃⋊C₈	C₂⁴	direct (N × H)
36. C₂³×C₁₃	C₂²×C₈	semidirect
38. C₂²×D₁₃	C₂²×C₈	semidirect
45. #1057	C₂⁵	semidirect
53. C₂²×C₁₃	C₂³×C₈	semidirect
55. C₂×D₁₃	C₂³×C₈	semidirect
70. C₂×C₁₃	C₂⁴×C₈	semidirect
72. D₁₃	C₂⁴×C₈	semidirect
75. C₂⁴	D₁₃⋊C₈	direct (N × H)
84. C₁₃	C₂⁵×C₈	semidirect
87. C₂³	C₂×D₁₃⋊C₈	direct (N × H)
97. C₂²	C₂²×D₁₃⋊C₈	direct (N × H)
103. C₂	C₂³×D₁₃⋊C₈	direct (N × H)

H ≅ G/N

type

1. C₂³×D₁₃⋊C₈

C₂

direct (N × H)

2. C₂⁴×#1057

C₂

semidirect

9. C₂³×#1057

C₂²

semidirect

10. C₂²×D₁₃⋊C₈

C₂²

direct (N × H)

12. C₂⁴×D₁₃

C₈

semidirect

19. C₂²×#1057

C₂³

semidirect

20. C₂×D₁₃⋊C₈

C₂³

direct (N × H)

22. C₂⁴×C₁₃

C₂×C₈

semidirect

24. C₂³×D₁₃

C₂×C₈

semidirect

31. C₂×#1057

C₂⁴

semidirect

32. D₁₃⋊C₈

C₂⁴

direct (N × H)

36. C₂³×C₁₃

C₂²×C₈

semidirect

38. C₂²×D₁₃

C₂²×C₈

semidirect

45. #1057

C₂⁵

semidirect

53. C₂²×C₁₃

C₂³×C₈

semidirect

55. C₂×D₁₃

C₂³×C₈

semidirect

70. C₂×C₁₃

C₂⁴×C₈

semidirect

72. D₁₃

C₂⁴×C₈

semidirect

75. C₂⁴

D₁₃⋊C₈

direct (N × H)

84. C₁₃

C₂⁵×C₈

semidirect

87. C₂³

C₂×D₁₃⋊C₈

direct (N × H)

97. C₂²

C₂²×D₁₃⋊C₈

direct (N × H)

103. C₂

C₂³×D₁₃⋊C₈

direct (N × H)

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

subgroup	index
C₂³×D₁₃⋊C₈	2
C₂⁴×#1057	2
C₂⁴×C₄×D₁₃	2
C₂⁵×C₈	13

subgroup

index

C₂³×D₁₃⋊C₈

C₂⁴×#1057

C₂⁴×C₄×D₁₃

C₂⁵×C₈

Subgroups — C₂⁴×D₁₃⋊C₈ #16809642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C24×D13⋊C8 #16809642

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×D₁₃⋊C₈ #16809642