Group #35313376 — subgroups

Subgroups — C₂×C₈×C₈₃⋊C₁₆ #35313376

Order 21248.

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×C₈₃⋊C₁₆	C₂	1	2	yes	maximal
2	C₈×C₈₃⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈²×C₈₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈₃⋊C₁₆	C₄	1	4	yes	—
5	C₄×C₈₃⋊C₁₆	C₄	1	4	yes	—
6	C₄×C₈₃⋊C₁₆	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₈₃	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₈₃	C₂²	1	1	yes	characteristic
9	C₈²×C₈₃	C₄	1	2	yes	—
10	C₈²×C₈₃	C₂²	1	2	yes	—
11	C₂×C₈₃⋊C₁₆	C₈	1	16	yes	direct product factor
12	C₂×C₈₃⋊C₁₆	C₂×C₄	1	8	yes	—
13	C₂²×C₈×C₈₃	C₈	1	4	yes	—
14	C₂²×C₈×C₈₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₈×C₈₃	C₈	1	4	yes	—
17	C₄×C₈×C₈₃	C₂×C₄	1	2	yes	—
18	C₄×C₈×C₈₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₈₃	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₈₃	C₂³	1	1	yes	characteristic
21	C₈₃⋊C₁₆	C₂×C₈	1	16	yes	direct product factor
22	C₂²×C₄×C₈₃	C₄²	1	1	yes	characteristic
23	C₂²×C₄×C₈₃	C₂×C₈	1	2	yes	—
24	C₂×C₈×C₈₃	C₁₆	1	16	yes	complemented
25	C₂×C₈×C₈₃	C₄²	1	2	yes	—
26	C₂×C₈×C₈₃	C₂×C₈	1	8	yes	—
27	C₂×C₈×C₈₃	C₂×C₈	1	8	yes	—
28	C₂×C₈×C₈₃	C₂²×C₄	1	2	yes	—
29	C₄²×C₈₃	C₄²	1	1	yes	characteristic
30	C₄²×C₈₃	C₂×C₈	1	2	yes	—
31	C₄²×C₈₃	C₂²×C₄	1	1	yes	characteristic
32	C₂³×C₈₃	C₄×C₈	1	1	yes	characteristic
33	C₂×C₄×C₈₃	C₄×C₈	1	4	yes	—
34	C₂×C₄×C₈₃	C₄×C₈	1	1	yes	characteristic
35	C₂×C₄×C₈₃	C₄×C₈	1	2	yes	—
36	C₂×C₄×C₈₃	C₂×C₁₆	1	8	yes	—
37	C₂×C₄×C₈₃	C₂×C₄²	1	1	yes	characteristic
38	C₂×C₄×C₈₃	C₂²×C₈	1	2	yes	—
39	C₈×C₈₃	C₄×C₈	1	4	yes	—
40	C₈×C₈₃	C₂×C₁₆	1	16	yes	complemented
41	C₈×C₈₃	C₂²×C₈	1	4	yes	—
42	C₂²×C₈₃	C₈²	1	2	yes	—
43	C₂²×C₈₃	C₄×C₁₆	1	4	yes	—
44	C₂²×C₈₃	C₂×C₄×C₈	1	1	yes	characteristic
45	C₄×C₈₃	C₈²	1	2	yes	—
46	C₄×C₈₃	C₄×C₁₆	1	4	yes	—
47	C₄×C₈₃	C₂×C₄×C₈	1	2	yes	—
48	C₄×C₈₃	C₂²×C₁₆	1	4	yes	—
49	C₂×C₈×C₁₆	—	83	1	no	maximal, Sylow
50	C₂×C₈₃	C₈×C₁₆	1	4	yes	complemented
51	C₂×C₈₃	C₂×C₈²	1	1	yes	characteristic
52	C₂×C₈₃	C₂×C₄×C₁₆	1	2	yes	—
53	C₂×C₄×C₁₆	—	83	2	no	—
54	C₂×C₈²	D₈₃	1	1	yes	characteristic
55	C₈×C₁₆	—	83	4	no	—
56	C₈₃	C₂×C₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₁₆	—	83	4	no	—
58	C₂×C₄×C₈	Dic₈₃	1	2	yes	—
59	C₂×C₄×C₈	C₂×D₈₃	1	1	yes	characteristic
60	C₄×C₁₆	—	83	4	no	—
61	C₄×C₁₆	—	83	4	no	—
62	C₈²	Dic₈₃	1	2	yes	—
63	C₈²	C₂×D₈₃	1	2	yes	—
64	C₂²×C₈	C₈₃⋊C₈	1	4	yes	—
65	C₂²×C₈	C₄×D₈₃	1	2	yes	—
66	C₂×C₄²	C₂×Dic₈₃	1	1	yes	characteristic
67	C₂×C₁₆	—	83	16	no	—
68	C₂×C₁₆	—	83	8	no	—
69	C₄×C₈	C₈₃⋊C₈	1	4	yes	—
70	C₄×C₈	C₄×D₈₃	1	2	yes	—
71	C₄×C₈	C₂×Dic₈₃	1	1	yes	characteristic
72	C₄×C₈	C₂×Dic₈₃	1	4	yes	—
73	C₄×C₈	C₂²×D₈₃	1	1	yes	characteristic
74	C₂²×C₄	C₄×Dic₈₃	1	1	yes	characteristic
75	C₂²×C₄	C₂×C₈₃⋊C₈	1	2	yes	—
76	C₂×C₈	C₈₃⋊C₁₆	1	16	yes	direct product factor
77	C₂×C₈	C₄×Dic₈₃	1	2	yes	—
78	C₂×C₈	C₈×D₈₃	1	8	yes	—
79	C₂×C₈	C₂×C₈₃⋊C₈	1	8	yes	—
80	C₂×C₈	C₂×C₄×D₈₃	1	2	yes	—
81	C₄²	C₄×Dic₈₃	1	1	yes	characteristic
82	C₄²	C₂×C₈₃⋊C₈	1	2	yes	—
83	C₄²	C₂²×Dic₈₃	1	1	yes	characteristic
84	C₁₆	—	83	16	no	—
85	C₂³	C₄×C₈₃⋊C₈	1	1	yes	characteristic
86	C₂×C₄	C₈×Dic₈₃	1	4	yes	—
87	C₂×C₄	C₄×C₈₃⋊C₈	1	1	yes	characteristic
88	C₂×C₄	C₄×C₈₃⋊C₈	1	2	yes	—
89	C₂×C₄	C₂×C₈₃⋊C₁₆	1	8	yes	—
90	C₂×C₄	C₂×C₄×Dic₈₃	1	1	yes	characteristic
91	C₂×C₄	C₂²×C₈₃⋊C₈	1	2	yes	—
92	C₈	C₈×Dic₈₃	1	4	yes	—
93	C₈	C₂×C₈₃⋊C₁₆	1	16	yes	direct product factor
94	C₈	C₂×C₈×D₈₃	1	4	yes	—
95	C₂²	C₈×C₈₃⋊C₈	1	2	yes	—
96	C₂²	C₄×C₈₃⋊C₁₆	1	4	yes	—
97	C₂²	C₂×C₄×C₈₃⋊C₈	1	1	yes	characteristic
98	C₄	C₈×C₈₃⋊C₈	1	2	yes	—
99	C₄	C₄×C₈₃⋊C₁₆	1	4	yes	—
100	C₄	C₂×C₈×Dic₈₃	1	2	yes	—
101	C₄	C₂²×C₈₃⋊C₁₆	1	4	yes	—
102	C₂	C₈×C₈₃⋊C₁₆	1	4	yes	direct product factor
103	C₂	C₂×C₈×C₈₃⋊C₈	1	1	yes	characteristic
104	C₂	C₂×C₄×C₈₃⋊C₁₆	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₈₃⋊C₁₆

C₂

yes

maximal

C₈×C₈₃⋊C₁₆

C₂

yes

maximal, direct product factor

C₂×C₈²×C₈₃

C₂

yes

maximal, characteristic

C₂²×C₈₃⋊C₁₆

C₄

yes

—

C₄×C₈₃⋊C₁₆

C₄

yes

—

C₄×C₈₃⋊C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₈₃

C₄

yes

—

C₂×C₄×C₈×C₈₃

C₂²

yes

characteristic

C₈²×C₈₃

C₄

yes

—

C₈²×C₈₃

C₂²

yes

—

C₂×C₈₃⋊C₁₆

C₈

yes

direct product factor

C₂×C₈₃⋊C₁₆

C₂×C₄

yes

—

C₂²×C₈×C₈₃

C₈

yes

—

C₂²×C₈×C₈₃

C₂×C₄

yes

—

C₂×C₄²×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₈

yes

—

C₄×C₈×C₈₃

C₂×C₄

yes

—

C₄×C₈×C₈₃

C₂×C₄

yes

characteristic

C₄×C₈×C₈₃

C₂×C₄

yes

—

C₄×C₈×C₈₃

C₂³

yes

characteristic

C₈₃⋊C₁₆

C₂×C₈

yes

direct product factor

C₂²×C₄×C₈₃

C₄²

yes

characteristic

C₂²×C₄×C₈₃

C₂×C₈

yes

—

C₂×C₈×C₈₃

C₁₆

yes

complemented

C₂×C₈×C₈₃

C₄²

yes

—

C₂×C₈×C₈₃

C₂×C₈

yes

—

C₂×C₈×C₈₃

C₂×C₈

yes

—

C₂×C₈×C₈₃

C₂²×C₄

yes

—

C₄²×C₈₃

C₄²

yes

characteristic

C₄²×C₈₃

C₂×C₈

yes

—

C₄²×C₈₃

C₂²×C₄

yes

characteristic

C₂³×C₈₃

C₄×C₈

yes

characteristic

C₂×C₄×C₈₃

C₄×C₈

yes

—

C₂×C₄×C₈₃

C₄×C₈

yes

characteristic

C₂×C₄×C₈₃

C₄×C₈

yes

—

C₂×C₄×C₈₃

C₂×C₁₆

yes

—

C₂×C₄×C₈₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₈

yes

—

C₈×C₈₃

C₄×C₈

yes

—

C₈×C₈₃

C₂×C₁₆

yes

complemented

C₈×C₈₃

C₂²×C₈

yes

—

C₂²×C₈₃

C₈²

yes

—

C₂²×C₈₃

C₄×C₁₆

yes

—

C₂²×C₈₃

C₂×C₄×C₈

yes

characteristic

C₄×C₈₃

C₈²

yes

—

C₄×C₈₃

C₄×C₁₆

yes

—

C₄×C₈₃

C₂×C₄×C₈

yes

—

C₄×C₈₃

C₂²×C₁₆

yes

—

C₂×C₈×C₁₆

—

maximal, Sylow

C₂×C₈₃

C₈×C₁₆

yes

complemented

C₂×C₈₃

C₂×C₈²

yes

characteristic

C₂×C₈₃

C₂×C₄×C₁₆

yes

—

C₂×C₄×C₁₆

—

C₂×C₈²

D₈₃

yes

characteristic

C₈×C₁₆

—

C₈₃

C₂×C₈×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂×C₄×C₈

Dic₈₃

yes

—

C₂×C₄×C₈

C₂×D₈₃

yes

characteristic

C₄×C₁₆

—

C₄×C₁₆

—

C₈²

Dic₈₃

yes

—

C₈²

C₂×D₈₃

yes

—

C₂²×C₈

C₈₃⋊C₈

yes

—

C₂²×C₈

C₄×D₈₃

yes

—

C₂×C₄²

C₂×Dic₈₃

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

C₈₃⋊C₈

yes

—

C₄×C₈

C₄×D₈₃

yes

—

C₄×C₈

C₂×Dic₈₃

yes

characteristic

C₄×C₈

C₂×Dic₈₃

yes

—

C₄×C₈

C₂²×D₈₃

yes

characteristic

C₂²×C₄

C₄×Dic₈₃

yes

characteristic

C₂²×C₄

C₂×C₈₃⋊C₈

yes

—

C₂×C₈

C₈₃⋊C₁₆

yes

direct product factor

C₂×C₈

C₄×Dic₈₃

yes

—

C₂×C₈

C₈×D₈₃

yes

—

C₂×C₈

C₂×C₈₃⋊C₈

yes

—

C₂×C₈

C₂×C₄×D₈₃

yes

—

C₄²

C₄×Dic₈₃

yes

characteristic

C₄²

C₂×C₈₃⋊C₈

yes

—

C₄²

C₂²×Dic₈₃

yes

characteristic

C₁₆

—

C₂³

C₄×C₈₃⋊C₈

yes

characteristic

C₂×C₄

C₈×Dic₈₃

yes

—

C₂×C₄

C₄×C₈₃⋊C₈

yes

characteristic

C₂×C₄

C₄×C₈₃⋊C₈

yes

—

C₂×C₄

C₂×C₈₃⋊C₁₆

yes

—

C₂×C₄

C₂×C₄×Dic₈₃

yes

characteristic

C₂×C₄

C₂²×C₈₃⋊C₈

yes

—

C₈

C₈×Dic₈₃

yes

—

C₈

C₂×C₈₃⋊C₁₆

yes

direct product factor

C₈

C₂×C₈×D₈₃

yes

—

C₂²

C₈×C₈₃⋊C₈

yes

—

C₂²

C₄×C₈₃⋊C₁₆

yes

—

C₂²

C₂×C₄×C₈₃⋊C₈

yes

characteristic

C₄

C₈×C₈₃⋊C₈

yes

—

C₄

C₄×C₈₃⋊C₁₆

yes

—

100

C₄

C₂×C₈×Dic₈₃

yes

—

101

C₄

C₂²×C₈₃⋊C₁₆

yes

—

102

C₂

C₈×C₈₃⋊C₁₆

yes

direct product factor

103

C₂

C₂×C₈×C₈₃⋊C₈

yes

characteristic

104

C₂

C₂×C₄×C₈₃⋊C₁₆

yes

—

	subgroup	G/H
center, hypercenter	C₂×C₈²	D₈₃
commutator, hypocenter	C₈₃	C₂×C₈×C₁₆
Frattini	C₄×C₈	C₂²×D₈₃
Fitting	C₂×C₈²×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	C₄×C₈
cosocle	C₄×C₈×C₈₃	C₂³
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₂×C₈²

subgroup

G/H

center, hypercenter

C₂×C₈²

D₈₃

commutator, hypocenter

C₈₃

C₂×C₈×C₁₆

Frattini

C₄×C₈

C₂²×D₈₃

Fitting

C₂×C₈²×C₈₃

C₂

socle, prime radical

C₂³×C₈₃

C₄×C₈

cosocle

C₄×C₈×C₈₃

C₂³

LCS

G ▷ C₈₃

UCS

C₁ ◁ C₂×C₈²

N	H ≅ G/N	type
2. C₈×C₈₃⋊C₁₆	C₂	direct (N × H)
11. C₂×C₈₃⋊C₁₆	C₈	direct (N × H)
21. C₈₃⋊C₁₆	C₂×C₈	direct (N × H)
24. C₂×C₈×C₈₃	C₁₆	semidirect
40. C₈×C₈₃	C₂×C₁₆	semidirect
50. C₂×C₈₃	C₈×C₁₆	semidirect
56. C₈₃	C₂×C₈×C₁₆	semidirect
76. C₂×C₈	C₈₃⋊C₁₆	direct (N × H)
93. C₈	C₂×C₈₃⋊C₁₆	direct (N × H)
102. C₂	C₈×C₈₃⋊C₁₆	direct (N × H)

H ≅ G/N

type

2. C₈×C₈₃⋊C₁₆

C₂

direct (N × H)

11. C₂×C₈₃⋊C₁₆

C₈

direct (N × H)

21. C₈₃⋊C₁₆

C₂×C₈

direct (N × H)

24. C₂×C₈×C₈₃

C₁₆

semidirect

40. C₈×C₈₃

C₂×C₁₆

semidirect

50. C₂×C₈₃

C₈×C₁₆

semidirect

56. C₈₃

C₂×C₈×C₁₆

semidirect

76. C₂×C₈

C₈₃⋊C₁₆

direct (N × H)

93. C₈

C₂×C₈₃⋊C₁₆

direct (N × H)

102. C₂

C₈×C₈₃⋊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×C₈₃⋊C₁₆	2
C₈×C₈₃⋊C₁₆	2
C₂×C₈²×C₈₃	2
C₂×C₈×C₁₆	83

subgroup

index

C₂×C₄×C₈₃⋊C₁₆

C₈×C₈₃⋊C₁₆

C₂×C₈²×C₈₃

C₂×C₈×C₁₆

Subgroups — C₂×C₈×C₈₃⋊C₁₆ #35313376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C8×C83⋊C16 #35313376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₈₃⋊C₁₆ #35313376