Group #25005569 — subgroups

Subgroups — C₂×C₈×C₄₃⋊C₁₆ #25005569

Order 11008.

398 conjugacy classes of subgroups; only the 339 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 339 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×C₄×C₄₃⋊C₁₆	C₂	1	2	yes	maximal
2	C₈×C₄₃⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄₃⋊C₁₆	C₄	1	4	yes	—
5	C₄×C₄₃⋊C₁₆	C₄	1	4	yes	—
6	C₄×C₄₃⋊C₁₆	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₄₃	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
9	C₈²×C₄₃	C₄	1	2	yes	—
10	C₈²×C₄₃	C₂²	1	2	yes	—
11	C₂×C₄₃⋊C₁₆	C₈	1	16	yes	direct product factor
12	C₂×C₄₃⋊C₁₆	C₂×C₄	1	8	yes	—
13	C₂²×C₈×C₄₃	C₈	1	4	yes	—
14	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₈×C₄₃	C₈	1	4	yes	—
17	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
21	C₂²×C₄×C₄₃	C₄²	1	1	yes	characteristic
22	C₂²×C₄×C₄₃	C₂×C₈	1	2	yes	—
23	C₂×C₈×C₄₃	C₁₆	1	16	yes	complemented
24	C₂×C₈×C₄₃	C₄²	1	2	yes	—
25	C₂×C₈×C₄₃	C₂×C₈	1	8	yes	—
26	C₂×C₈×C₄₃	C₂×C₈	1	8	yes	—
27	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
28	C₄²×C₄₃	C₄²	1	1	yes	characteristic
29	C₄²×C₄₃	C₂×C₈	1	2	yes	—
30	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
31	C₄₃⋊C₁₆	C₂×C₈	1	16	yes	direct product factor
32	C₂³×C₄₃	C₄×C₈	1	1	yes	characteristic
33	C₂×C₄×C₄₃	C₄×C₈	1	4	yes	—
34	C₂×C₄×C₄₃	C₄×C₈	1	1	yes	characteristic
35	C₂×C₄×C₄₃	C₄×C₈	1	2	yes	—
36	C₂×C₄×C₄₃	C₂×C₁₆	1	8	yes	—
37	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
39	C₈×C₄₃	C₄×C₈	1	4	yes	—
40	C₈×C₄₃	C₂×C₁₆	1	16	yes	complemented
41	C₈×C₄₃	C₂²×C₈	1	4	yes	—
42	C₂×C₈×C₁₆	—	43	1	no	maximal, Sylow
43	C₂²×C₄₃	C₈²	1	2	yes	—
44	C₂²×C₄₃	C₄×C₁₆	1	4	yes	—
45	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
46	C₄×C₄₃	C₈²	1	2	yes	—
47	C₄×C₄₃	C₄×C₁₆	1	4	yes	—
48	C₄×C₄₃	C₂×C₄×C₈	1	2	yes	—
49	C₄×C₄₃	C₂²×C₁₆	1	4	yes	—
50	C₂×C₄×C₁₆	—	43	2	no	—
51	C₂×C₈²	D₄₃	1	1	yes	characteristic
52	C₈×C₁₆	—	43	4	no	—
53	C₂×C₄₃	C₈×C₁₆	1	4	yes	complemented
54	C₂×C₄₃	C₂×C₈²	1	1	yes	characteristic
55	C₂×C₄₃	C₂×C₄×C₁₆	1	2	yes	—
56	C₂²×C₁₆	—	43	4	no	—
57	C₂×C₄×C₈	Dic₄₃	1	2	yes	—
58	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
59	C₄×C₁₆	—	43	4	no	—
60	C₄×C₁₆	—	43	4	no	—
61	C₈²	Dic₄₃	1	2	yes	—
62	C₈²	C₂×D₄₃	1	2	yes	—
63	C₄₃	C₂×C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	C₄₃⋊C₈	1	4	yes	—
65	C₂²×C₈	C₄×D₄₃	1	2	yes	—
66	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
67	C₂×C₁₆	—	43	16	no	—
68	C₂×C₁₆	—	43	8	no	—
69	C₄×C₈	C₄₃⋊C₈	1	4	yes	—
70	C₄×C₈	C₄×D₄₃	1	2	yes	—
71	C₄×C₈	C₂×Dic₄₃	1	4	yes	—
72	C₄×C₈	C₂×Dic₄₃	1	1	yes	characteristic
73	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
74	C₂²×C₄	C₂×C₄₃⋊C₈	1	2	yes	—
75	C₂²×C₄	C₄×Dic₄₃	1	1	yes	characteristic
76	C₂×C₈	C₄₃⋊C₁₆	1	16	yes	direct product factor
77	C₂×C₈	C₈×D₄₃	1	8	yes	—
78	C₂×C₈	C₂×C₄₃⋊C₈	1	8	yes	—
79	C₂×C₈	C₄×Dic₄₃	1	2	yes	—
80	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
81	C₄²	C₂×C₄₃⋊C₈	1	2	yes	—
82	C₄²	C₄×Dic₄₃	1	1	yes	characteristic
83	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
84	C₁₆	—	43	16	no	—
85	C₂³	C₄×C₄₃⋊C₈	1	1	yes	characteristic
86	C₂×C₄	C₈×Dic₄₃	1	4	yes	—
87	C₂×C₄	C₄×C₄₃⋊C₈	1	1	yes	characteristic
88	C₂×C₄	C₄×C₄₃⋊C₈	1	2	yes	—
89	C₂×C₄	C₂×C₄₃⋊C₁₆	1	8	yes	—
90	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
91	C₂×C₄	C₂²×C₄₃⋊C₈	1	2	yes	—
92	C₈	C₈×Dic₄₃	1	4	yes	—
93	C₈	C₂×C₄₃⋊C₁₆	1	16	yes	direct product factor
94	C₈	C₂×C₈×D₄₃	1	4	yes	—
95	C₂²	C₈×C₄₃⋊C₈	1	2	yes	—
96	C₂²	C₄×C₄₃⋊C₁₆	1	4	yes	—
97	C₂²	C₂×C₄×C₄₃⋊C₈	1	1	yes	characteristic
98	C₄	C₈×C₄₃⋊C₈	1	2	yes	—
99	C₄	C₄×C₄₃⋊C₁₆	1	4	yes	—
100	C₄	C₂×C₈×Dic₄₃	1	2	yes	—
101	C₄	C₂²×C₄₃⋊C₁₆	1	4	yes	—
102	C₂	C₈×C₄₃⋊C₁₆	1	4	yes	direct product factor
103	C₂	C₂×C₈×C₄₃⋊C₈	1	1	yes	characteristic
104	C₂	C₂×C₄×C₄₃⋊C₁₆	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₄₃⋊C₁₆

C₂

yes

maximal

C₈×C₄₃⋊C₁₆

C₂

yes

maximal, direct product factor

C₂×C₈²×C₄₃

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₁₆

C₄

yes

—

C₄×C₄₃⋊C₁₆

C₄

yes

—

C₄×C₄₃⋊C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₄₃

C₄

yes

—

C₂×C₄×C₈×C₄₃

C₂²

yes

characteristic

C₈²×C₄₃

C₄

yes

—

C₈²×C₄₃

C₂²

yes

—

C₂×C₄₃⋊C₁₆

C₈

yes

direct product factor

C₂×C₄₃⋊C₁₆

C₂×C₄

yes

—

C₂²×C₈×C₄₃

C₈

yes

—

C₂²×C₈×C₄₃

C₂×C₄

yes

—

C₂×C₄²×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₈

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂×C₄

yes

characteristic

C₄×C₈×C₄₃

C₂×C₄

yes

—

C₄×C₈×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₄²

yes

characteristic

C₂²×C₄×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₁₆

yes

complemented

C₂×C₈×C₄₃

C₄²

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂×C₈

yes

—

C₂×C₈×C₄₃

C₂²×C₄

yes

—

C₄²×C₄₃

C₄²

yes

characteristic

C₄²×C₄₃

C₂×C₈

yes

—

C₄²×C₄₃

C₂²×C₄

yes

characteristic

C₄₃⋊C₁₆

C₂×C₈

yes

direct product factor

C₂³×C₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

C₄×C₈

yes

—

C₂×C₄×C₄₃

C₄×C₈

yes

characteristic

C₂×C₄×C₄₃

C₄×C₈

yes

—

C₂×C₄×C₄₃

C₂×C₁₆

yes

—

C₂×C₄×C₄₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₈

yes

—

C₈×C₄₃

C₄×C₈

yes

—

C₈×C₄₃

C₂×C₁₆

yes

complemented

C₈×C₄₃

C₂²×C₈

yes

—

C₂×C₈×C₁₆

—

maximal, Sylow

C₂²×C₄₃

C₈²

yes

—

C₂²×C₄₃

C₄×C₁₆

yes

—

C₂²×C₄₃

C₂×C₄×C₈

yes

characteristic

C₄×C₄₃

C₈²

yes

—

C₄×C₄₃

C₄×C₁₆

yes

—

C₄×C₄₃

C₂×C₄×C₈

yes

—

C₄×C₄₃

C₂²×C₁₆

yes

—

C₂×C₄×C₁₆

—

C₂×C₈²

D₄₃

yes

characteristic

C₈×C₁₆

—

C₂×C₄₃

C₈×C₁₆

yes

complemented

C₂×C₄₃

C₂×C₈²

yes

characteristic

C₂×C₄₃

C₂×C₄×C₁₆

yes

—

C₂²×C₁₆

—

C₂×C₄×C₈

Dic₄₃

yes

—

C₂×C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₁₆

—

C₄×C₁₆

—

C₈²

Dic₄₃

yes

—

C₈²

C₂×D₄₃

yes

—

C₄₃

C₂×C₈×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₈

C₄₃⋊C₈

yes

—

C₂²×C₈

C₄×D₄₃

yes

—

C₂×C₄²

C₂×Dic₄₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

C₄₃⋊C₈

yes

—

C₄×C₈

C₄×D₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

—

C₄×C₈

C₂×Dic₄₃

yes

characteristic

C₄×C₈

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂×C₄₃⋊C₈

yes

—

C₂²×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₈

C₄₃⋊C₁₆

yes

direct product factor

C₂×C₈

C₈×D₄₃

yes

—

C₂×C₈

C₂×C₄₃⋊C₈

yes

—

C₂×C₈

C₄×Dic₄₃

yes

—

C₂×C₈

C₂×C₄×D₄₃

yes

—

C₄²

C₂×C₄₃⋊C₈

yes

—

C₄²

C₄×Dic₄₃

yes

characteristic

C₄²

C₂²×Dic₄₃

yes

characteristic

C₁₆

—

C₂³

C₄×C₄₃⋊C₈

yes

characteristic

C₂×C₄

C₈×Dic₄₃

yes

—

C₂×C₄

C₄×C₄₃⋊C₈

yes

characteristic

C₂×C₄

C₄×C₄₃⋊C₈

yes

—

C₂×C₄

C₂×C₄₃⋊C₁₆

yes

—

C₂×C₄

C₂×C₄×Dic₄₃

yes

characteristic

C₂×C₄

C₂²×C₄₃⋊C₈

yes

—

C₈

C₈×Dic₄₃

yes

—

C₈

C₂×C₄₃⋊C₁₆

yes

direct product factor

C₈

C₂×C₈×D₄₃

yes

—

C₂²

C₈×C₄₃⋊C₈

yes

—

C₂²

C₄×C₄₃⋊C₁₆

yes

—

C₂²

C₂×C₄×C₄₃⋊C₈

yes

characteristic

C₄

C₈×C₄₃⋊C₈

yes

—

C₄

C₄×C₄₃⋊C₁₆

yes

—

100

C₄

C₂×C₈×Dic₄₃

yes

—

101

C₄

C₂²×C₄₃⋊C₁₆

yes

—

102

C₂

C₈×C₄₃⋊C₁₆

yes

direct product factor

103

C₂

C₂×C₈×C₄₃⋊C₈

yes

characteristic

104

C₂

C₂×C₄×C₄₃⋊C₁₆

yes

—

	subgroup	G/H
center, hypercenter	C₂×C₈²	D₄₃
commutator, hypocenter	C₄₃	C₂×C₈×C₁₆
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₂×C₈²×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₄×C₈
cosocle	C₄×C₈×C₄₃	C₂³
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂×C₈²

subgroup

G/H

center, hypercenter

C₂×C₈²

D₄₃

commutator, hypocenter

C₄₃

C₂×C₈×C₁₆

Frattini

C₄×C₈

C₂²×D₄₃

Fitting

C₂×C₈²×C₄₃

C₂

socle, prime radical

C₂³×C₄₃

C₄×C₈

cosocle

C₄×C₈×C₄₃

C₂³

LCS

G ▷ C₄₃

UCS

C₁ ◁ C₂×C₈²

N	H ≅ G/N	type
2. C₈×C₄₃⋊C₁₆	C₂	direct (N × H)
11. C₂×C₄₃⋊C₁₆	C₈	direct (N × H)
23. C₂×C₈×C₄₃	C₁₆	semidirect
31. C₄₃⋊C₁₆	C₂×C₈	direct (N × H)
40. C₈×C₄₃	C₂×C₁₆	semidirect
53. C₂×C₄₃	C₈×C₁₆	semidirect
63. C₄₃	C₂×C₈×C₁₆	semidirect
76. C₂×C₈	C₄₃⋊C₁₆	direct (N × H)
93. C₈	C₂×C₄₃⋊C₁₆	direct (N × H)
102. C₂	C₈×C₄₃⋊C₁₆	direct (N × H)

H ≅ G/N

type

2. C₈×C₄₃⋊C₁₆

C₂

direct (N × H)

11. C₂×C₄₃⋊C₁₆

C₈

direct (N × H)

23. C₂×C₈×C₄₃

C₁₆

semidirect

31. C₄₃⋊C₁₆

C₂×C₈

direct (N × H)

40. C₈×C₄₃

C₂×C₁₆

semidirect

53. C₂×C₄₃

C₈×C₁₆

semidirect

63. C₄₃

C₂×C₈×C₁₆

semidirect

76. C₂×C₈

C₄₃⋊C₁₆

direct (N × H)

93. C₈

C₂×C₄₃⋊C₁₆

direct (N × H)

102. C₂

C₈×C₄₃⋊C₁₆

direct (N × H)

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

subgroup	index
C₂×C₄×C₄₃⋊C₁₆	2
C₈×C₄₃⋊C₁₆	2
C₂×C₈²×C₄₃	2
C₂×C₈×C₁₆	43

subgroup

index

C₂×C₄×C₄₃⋊C₁₆

C₈×C₄₃⋊C₁₆

C₂×C₈²×C₄₃

C₂×C₈×C₁₆

Subgroups — C₂×C₈×C₄₃⋊C₁₆ #25005569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C8×C43⋊C16 #25005569

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₄₃⋊C₁₆ #25005569