Group #19133403 — subgroups

Subgroups — C₈×Dic₁₇₂ #19133403

Order 5504.

164 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 77 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	C₈×Dic₈₆	C₂	1	2	yes	maximal
2	C₄×Dic₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#14582652	C₂	1	1	yes	maximal, characteristic
4	#14582631	C₂	1	2	yes	maximal
5	C₈²×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₄	1	1	yes	characteristic
7	C₄×Dic₈₆	C₂²	1	2	yes	—
8	#13063259	C₄	1	1	yes	characteristic
9	C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
10	Dic₄₃⋊C₈	—	2	2	no	—
11	#13063250	C₄	1	2	yes	—
12	C₈×Dic₄₃	—	2	2	no	—
13	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×Dic₈₆	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₃	—	2	1	no	—
18	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
22	C₄²×C₄₃	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
24	Dic₄₃⋊C₄	—	2	2	no	—
25	C₄×Dic₄₃	—	2	2	no	—
26	C₂×C₄₃⋊C₈	—	2	2	no	—
27	Dic₁₇₂	C₈	1	4	yes	direct product factor
28	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	#41	1	1	yes	characteristic
31	C₂×Dic₄₃	—	2	2	no	—
32	C₂×Dic₄₃	—	2	2	no	—
33	Dic₈₆	—	2	2	no	—
34	Dic₈₆	C₂×C₈	1	4	yes	—
35	C₈×C₄₃	—	2	2	no	—
36	C₈×C₄₃	—	2	1	no	—
37	C₈×C₄₃	—	2	1	no	—
38	C₈×C₄₃	C₂×C₈	1	2	yes	—
39	C₈×C₄₃	Q₁₆	1	2	yes	complemented
40	C₄₃⋊C₈	—	4	2	no	—
41	C₂²×C₄₃	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₃	—	2	1	no	—
43	C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₄₃	#131	1	1	yes	characteristic
45	C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₄₃	#135	1	1	yes	characteristic
47	Dic₄₃	—	2	4	no	—
48	Dic₄₃	—	4	2	no	—
49	C₈×Q₁₆	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	C₈×D₄	1	1	yes	characteristic
51	C₂×C₄₃	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₄₃	#443	1	1	yes	characteristic
53	C₈×Q₈	—	43	2	no	—
54	C₄×Q₁₆	—	43	1	no	—
55	#335	—	43	1	no	—
56	Q₈⋊C₈	—	43	2	no	—
57	C₈²	D₄₃	1	1	yes	characteristic
58	C₄₃	C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	43	1	no	—
60	C₄×Q₈	—	43	2	no	—
61	#107	—	43	1	no	—
62	C₄⋊C₈	—	43	2	no	—
63	C₄⋊C₈	—	86	2	no	—
64	#103	—	43	2	no	—
65	C₄×C₈	—	86	2	no	—
66	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
67	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
68	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
69	C₂×Q₈	—	43	2	no	—
70	Q₁₆	—	43	4	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	86	2	no	—
73	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
74	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
75	C₂×C₈	D₁₇₂	1	1	yes	characteristic
76	C₂×C₈	D₁₇₂	1	1	yes	characteristic
77	C₄⋊C₄	—	43	2	no	—
78	C₄⋊C₄	—	86	2	no	—
79	C₄²	—	86	2	no	—
80	C₄²	C₂²×D₄₃	1	1	yes	characteristic
81	Q₈	—	43	4	no	—
82	Q₈	—	86	2	no	—
83	C₂×C₄	—	86	2	no	—
84	C₂×C₄	—	86	2	no	—
85	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
86	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
87	C₂×C₄	#10621898	1	1	yes	characteristic
88	C₈	—	2	2	no	—
89	C₈	—	2	1	no	—
90	C₈	—	2	1	no	—
91	C₈	—	172	2	no	—
92	C₈	C₈×D₄₃	1	2	yes	—
93	C₈	Dic₁₇₂	1	2	yes	direct product factor
94	C₂²	C₄×D₁₇₂	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	86	4	no	—
97	C₄	—	172	2	no	—
98	C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
99	C₄	#13063331	1	1	yes	characteristic
100	C₄	C₂×Dic₁₇₂	1	1	yes	characteristic
101	C₄	#13063347	1	1	yes	characteristic
102	C₂	C₈×D₁₇₂	1	1	yes	characteristic
103	C₂	C₄×Dic₁₇₂	1	1	yes	characteristic
104	C₂	#14583017	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₈₆

C₂

yes

maximal

C₄×Dic₁₇₂

C₂

yes

maximal, characteristic

#14582652

C₂

yes

maximal, characteristic

#14582631

C₂

yes

maximal

C₈²×C₄₃

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₄

yes

characteristic

C₄×Dic₈₆

C₂²

yes

—

#13063259

C₄

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₂²

yes

—

Dic₄₃⋊C₈

—

#13063250

C₄

yes

—

C₈×Dic₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×Dic₈₆

C₂×C₄

yes

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

D₄

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₄⋊Dic₄₃

C₂×C₄

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

C₈

yes

direct product factor

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

#41

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

C₂×C₈

yes

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×C₈

yes

—

C₈×C₄₃

Q₁₆

yes

complemented

C₄₃⋊C₈

—

C₂²×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂²×C₈

yes

characteristic

C₄×C₄₃

#131

yes

characteristic

C₄×C₄₃

C₂×Q₁₆

yes

characteristic

C₄×C₄₃

#135

yes

characteristic

Dic₄₃

—

Dic₄₃

—

C₈×Q₁₆

—

maximal, Sylow

C₂×C₄₃

C₈×D₄

yes

characteristic

C₂×C₄₃

C₄×Q₁₆

yes

characteristic

C₂×C₄₃

#443

yes

characteristic

C₈×Q₈

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

D₄₃

yes

characteristic

C₄₃

C₈×Q₁₆

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

D₁₇₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₃

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

#10621898

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

172

—

C₈

C₈×D₄₃

yes

—

C₈

Dic₁₇₂

yes

direct product factor

C₂²

C₄×D₁₇₂

yes

characteristic

C₄

—

C₄

—

C₄

—

172

—

C₄

C₂×C₈×D₄₃

yes

characteristic

C₄

#13063331

yes

characteristic

100

C₄

C₂×Dic₁₇₂

yes

characteristic

101

C₄

#13063347

yes

characteristic

102

C₂

C₈×D₁₇₂

yes

characteristic

103

C₂

C₄×Dic₁₇₂

yes

characteristic

104

C₂

#14583017

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₁₇₂
commutator	C₄×C₄₃	C₂²×C₈
Frattini	C₄²	C₂²×D₄₃
Fitting	C₈²×C₄₃	C₂
socle	C₂²×C₄₃	C₄×D₄
hypercenter	C₈²	D₄₃
hypocenter	C₄₃	C₈×Q₁₆
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₈

D₁₇₂

commutator

C₄×C₄₃

C₂²×C₈

Frattini

C₄²

C₂²×D₄₃

Fitting

C₈²×C₄₃

C₂

socle

C₂²×C₄₃

C₄×D₄

hypercenter

C₈²

D₄₃

hypocenter

C₄₃

C₈×Q₁₆

LCS

G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

N	H ≅ G/N	type
27. Dic₁₇₂	C₈	direct (N × H)
39. C₈×C₄₃	Q₁₆	semidirect
58. C₄₃	C₈×Q₁₆	semidirect
93. C₈	Dic₁₇₂	direct (N × H)

H ≅ G/N

type

27. Dic₁₇₂

C₈

direct (N × H)

39. C₈×C₄₃

Q₁₆

semidirect

58. C₄₃

C₈×Q₁₆

semidirect

93. C₈

Dic₁₇₂

direct (N × H)

Subgroups — C₈×Dic₁₇₂ #19133403

Conjugacy classes of subgroups

Complements

Subgroups — C8×Dic172 #19133403

Conjugacy classes of subgroups

Complements

Subgroups — C₈×Dic₁₇₂ #19133403