Group #19136945 — subgroups

Subgroups — C₄²×Dic₈₆ #19136945

Order 5504.

684 conjugacy classes of subgroups; only the 381 normal subgroups are shown.

normal subgroups only

This group has 684 conjugacy classes of subgroups — too many to draw. Only its 381 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×Dic₈₆	C₂	1	3	yes	maximal
2	C₄×Dic₄₃⋊C₄	C₂	1	6	yes	maximal
3	C₄×C₄⋊Dic₄₃	C₂	1	3	yes	maximal
4	C₄²×Dic₄₃	C₂	1	2	yes	maximal
5	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
7	C₄×Dic₈₆	C₄	1	24	yes	direct product factor
8	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
9	C₂×Dic₄₃⋊C₄	C₂²	1	6	yes	—
10	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
11	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
12	C₄₃⋊#95	C₂²	1	6	yes	—
13	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
19	C₂²×Dic₄₃	C₂³	1	6	yes	—
20	C₂²×Dic₄₃	C₂³	1	2	yes	—
21	C₂×Dic₈₆	C₂×C₄	1	12	yes	—
22	C₄²×C₄₃	—	2	6	no	—
23	C₄²×C₄₃	C₂×C₄	1	12	yes	—
24	C₄²×C₄₃	Q₈	1	4	yes	complemented
25	C₄⋊Dic₄₃	C₂×C₄	1	12	yes	—
26	Dic₄₃⋊C₄	C₂×C₄	1	24	yes	—
27	C₄×Dic₄₃	—	2	12	no	—
28	C₄×Dic₄₃	C₂×C₄	1	24	yes	—
29	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	6	no	—
31	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
32	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
33	C₂×C₄×C₄₃	C₂²×C₄	1	6	yes	—
34	C₂×C₄×C₄₃	C₂×Q₈	1	6	yes	—
35	C₂×C₄×C₄₃	#41	1	6	yes	—
36	C₂×Dic₄₃	—	2	12	no	—
37	C₂×Dic₄₃	C₂²×C₄	1	12	yes	—
38	C₂×Dic₄₃	C₂²×C₄	1	12	yes	—
39	Dic₈₆	C₄²	1	16	yes	direct product factor
40	C₂²×C₄₃	C₂³×C₄	1	3	yes	—
41	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₄₃	C₂×#41	1	3	yes	—
43	C₄×C₄₃	—	2	6	no	—
44	C₄×C₄₃	C₂×C₄²	1	4	yes	—
45	C₄×C₄₃	C₄×Q₈	1	12	yes	complemented
46	Dic₄₃	—	2	12	no	—
47	Dic₄₃	C₂×C₄²	1	8	yes	—
48	C₄²×Q₈	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	C₂²×C₄²	1	1	yes	characteristic
50	C₂×C₄₃	C₂×C₄×Q₈	1	3	yes	—
51	C₂×C₄₃	C₄×#41	1	3	yes	—
52	C₂×C₄×Q₈	—	43	3	no	—
53	C₄×C₄⋊C₄	—	43	3	no	—
54	C₄×C₄⋊C₄	—	43	6	no	—
55	C₄³	—	43	2	no	—
56	C₄³	D₄₃	1	1	yes	characteristic
57	C₄₃	C₄²×Q₈	1	1	yes	characteristic, complemented, Sylow
58	C₂²×Q₈	—	43	1	no	—
59	C₄×Q₈	—	43	24	no	—
60	C₂×C₄⋊C₄	—	43	6	no	—
61	C₂×C₄⋊C₄	—	43	3	no	—
62	C₂×C₄²	—	43	6	no	—
63	C₂×C₄²	—	43	6	no	—
64	C₂×C₄²	C₂×D₄₃	1	3	yes	—
65	C₂×C₄²	C₂×D₄₃	1	3	yes	—
66	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
67	#95	—	43	6	no	—
68	C₂×Q₈	—	43	12	no	—
69	C₂²×C₄	—	43	2	no	—
70	C₂²×C₄	—	43	6	no	—
71	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
72	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
73	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
74	C₄⋊C₄	—	43	24	no	—
75	C₄⋊C₄	—	43	12	no	—
76	C₄²	—	2	6	no	—
77	C₄²	—	43	24	no	—
78	C₄²	—	86	12	no	—
79	C₄²	Dic₈₆	1	4	yes	direct product factor
80	C₄²	C₄×D₄₃	1	12	yes	—
81	C₂³	C₂³×D₄₃	1	1	yes	characteristic
82	Q₈	—	43	16	no	—
83	C₂×C₄	—	2	6	no	—
84	C₂×C₄	—	43	12	no	—
85	C₂×C₄	—	43	12	no	—
86	C₂×C₄	—	86	12	no	—
87	C₂×C₄	C₂×Dic₈₆	1	6	yes	—
88	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
89	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
90	C₂×C₄	C₂×C₄×D₄₃	1	6	yes	—
91	C₂×C₄	#10621898	1	6	yes	—
92	C₂²	C₂²×C₄×D₄₃	1	3	yes	—
93	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
94	C₂²	C₂×#10621898	1	3	yes	—
95	C₄	—	2	6	no	—
96	C₄	—	43	8	no	—
97	C₄	—	86	12	no	—
98	C₄	C₄²×D₄₃	1	4	yes	—
99	C₄	C₄×Dic₈₆	1	12	yes	direct product factor
100	C₂	C₂×C₄²×D₄₃	1	1	yes	characteristic
101	C₂	C₂×C₄×Dic₈₆	1	3	yes	—
102	C₂	C₄×#10621898	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₈₆

C₂

yes

maximal

C₄×Dic₄₃⋊C₄

C₂

yes

maximal

C₄×C₄⋊Dic₄₃

C₂

yes

maximal

C₄²×Dic₄₃

C₂

yes

maximal

C₄³×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

characteristic

C₄×Dic₈₆

C₄

yes

direct product factor

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

C₂×C₄

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

Q₈

yes

complemented

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

C₂×C₄

yes

—

C₄×Dic₄₃

—

C₄×Dic₄₃

C₂×C₄

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂²×C₄

yes

—

C₂×Dic₄₃

C₂²×C₄

yes

—

Dic₈₆

C₄²

yes

direct product factor

C₂²×C₄₃

C₂³×C₄

yes

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄²

yes

—

C₄×C₄₃

C₄×Q₈

yes

complemented

Dic₄₃

—

Dic₄₃

C₂×C₄²

yes

—

C₄²×Q₈

—

maximal, Sylow

C₂×C₄₃

C₂²×C₄²

yes

characteristic

C₂×C₄₃

C₂×C₄×Q₈

yes

—

C₂×C₄₃

C₄×#41

yes

—

C₂×C₄×Q₈

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

C₄³

—

C₄³

D₄₃

yes

characteristic

C₄₃

C₄²×Q₈

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

Dic₈₆

yes

direct product factor

C₄²

C₄×D₄₃

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

#10621898

yes

—

C₂²

C₂²×C₄×D₄₃

yes

—

C₂²

C₂²×Dic₈₆

yes

characteristic

C₂²

C₂×#10621898

yes

—

C₄

—

C₄

—

C₄

—

C₄

C₄²×D₄₃

yes

—

C₄

C₄×Dic₈₆

yes

direct product factor

100

C₂

C₂×C₄²×D₄₃

yes

characteristic

101

C₂

C₂×C₄×Dic₈₆

yes

—

102

C₂

C₄×#10621898

yes

—

	subgroup	G/H
center	C₂×C₄²	C₂×D₄₃
commutator	C₂×C₄₃	C₂²×C₄²
Frattini	C₂³	C₂³×D₄₃
Fitting	C₄³×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₄³	D₄₃
hypocenter	C₄₃	C₄²×Q₈
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄³

subgroup

G/H

center

C₂×C₄²

C₂×D₄₃

commutator

C₂×C₄₃

C₂²×C₄²

Frattini

C₂³

C₂³×D₄₃

Fitting

C₄³×C₄₃

C₂

socle

C₂³×C₄₃

C₂⁴

hypercenter

C₄³

D₄₃

hypocenter

C₄₃

C₄²×Q₈

LCS

G ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄² ◁ C₄³

N	H ≅ G/N	type
7. C₄×Dic₈₆	C₄	direct (N × H)
24. C₄²×C₄₃	Q₈	semidirect
39. Dic₈₆	C₄²	direct (N × H)
45. C₄×C₄₃	C₄×Q₈	semidirect
57. C₄₃	C₄²×Q₈	semidirect
79. C₄²	Dic₈₆	direct (N × H)
99. C₄	C₄×Dic₈₆	direct (N × H)

H ≅ G/N

type

7. C₄×Dic₈₆

C₄

direct (N × H)

24. C₄²×C₄₃

Q₈

semidirect

39. Dic₈₆

C₄²

direct (N × H)

45. C₄×C₄₃

C₄×Q₈

semidirect

57. C₄₃

C₄²×Q₈

semidirect

79. C₄²

Dic₈₆

direct (N × H)

99. C₄

C₄×Dic₈₆

direct (N × H)

Subgroups — C₄²×Dic₈₆ #19136945

Conjugacy classes of subgroups

Complements

Subgroups — C42×Dic86 #19136945

Conjugacy classes of subgroups

Complements

Subgroups — C₄²×Dic₈₆ #19136945