Group #20242196 — subgroups

Subgroups — C₈×Dic₁₈₈ #20242196

Order 6016.

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×Dic₉₄	C₂	1	2	yes	maximal
2	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#15688876	C₂	1	1	yes	maximal, characteristic
4	#15688855	C₂	1	2	yes	maximal
5	C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	C₄	1	1	yes	characteristic
7	C₄×Dic₉₄	C₂²	1	2	yes	—
8	#13093958	C₄	1	1	yes	characteristic
9	C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
10	Dic₄₇⋊C₈	—	2	2	no	—
11	#13093949	C₄	1	2	yes	—
12	C₈×Dic₄₇	—	2	2	no	—
13	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	—	2	1	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
22	C₄²×C₄₇	C₂³	1	1	yes	characteristic
23	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
24	Dic₄₇⋊C₄	—	2	2	no	—
25	C₄×Dic₄₇	—	2	2	no	—
26	C₂×C₄₇⋊C₈	—	2	2	no	—
27	Dic₁₈₈	C₈	1	4	yes	direct product factor
28	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
31	C₂×Dic₄₇	—	2	2	no	—
32	C₂×Dic₄₇	—	2	2	no	—
33	Dic₉₄	—	2	2	no	—
34	Dic₉₄	C₂×C₈	1	4	yes	—
35	C₈×C₄₇	—	2	2	no	—
36	C₈×C₄₇	—	2	1	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	C₂×C₈	1	2	yes	—
39	C₈×C₄₇	Q₁₆	1	2	yes	complemented
40	C₄₇⋊C₈	—	4	2	no	—
41	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
44	C₄×C₄₇	#131	1	1	yes	characteristic
45	C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
46	C₄×C₄₇	#135	1	1	yes	characteristic
47	Dic₄₇	—	2	4	no	—
48	Dic₄₇	—	4	2	no	—
49	C₈×Q₁₆	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	C₈×D₄	1	1	yes	characteristic
51	C₂×C₄₇	C₄×Q₁₆	1	1	yes	characteristic
52	C₂×C₄₇	#443	1	1	yes	characteristic
53	C₈×Q₈	—	47	2	no	—
54	C₄×Q₁₆	—	47	1	no	—
55	#335	—	47	1	no	—
56	Q₈⋊C₈	—	47	2	no	—
57	C₈²	D₄₇	1	1	yes	characteristic
58	C₄₇	C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	47	1	no	—
60	C₄×Q₈	—	47	2	no	—
61	#107	—	47	1	no	—
62	C₄⋊C₈	—	47	2	no	—
63	C₄⋊C₈	—	94	2	no	—
64	#103	—	47	2	no	—
65	C₄×C₈	—	94	2	no	—
66	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
67	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
68	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
69	C₂×Q₈	—	47	2	no	—
70	Q₁₆	—	47	4	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	94	2	no	—
73	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
74	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
75	C₂×C₈	D₁₈₈	1	1	yes	characteristic
76	C₂×C₈	D₁₈₈	1	1	yes	characteristic
77	C₄⋊C₄	—	47	2	no	—
78	C₄⋊C₄	—	94	2	no	—
79	C₄²	—	94	2	no	—
80	C₄²	C₂²×D₄₇	1	1	yes	characteristic
81	Q₈	—	47	4	no	—
82	Q₈	—	94	2	no	—
83	C₂×C₄	—	94	2	no	—
84	C₂×C₄	—	94	2	no	—
85	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
86	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
87	C₂×C₄	#10625350	1	1	yes	characteristic
88	C₈	—	2	2	no	—
89	C₈	—	2	1	no	—
90	C₈	—	2	1	no	—
91	C₈	—	188	2	no	—
92	C₈	C₈×D₄₇	1	2	yes	—
93	C₈	Dic₁₈₈	1	2	yes	direct product factor
94	C₂²	C₄×D₁₈₈	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	94	4	no	—
97	C₄	—	188	2	no	—
98	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
99	C₄	#13094030	1	1	yes	characteristic
100	C₄	C₂×Dic₁₈₈	1	1	yes	characteristic
101	C₄	#13094046	1	1	yes	characteristic
102	C₂	C₈×D₁₈₈	1	1	yes	characteristic
103	C₂	C₄×Dic₁₈₈	1	1	yes	characteristic
104	C₂	#15689241	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×Dic₉₄

C₂

yes

maximal

C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#15688876

C₂

yes

maximal, characteristic

#15688855

C₂

yes

maximal

C₈²×C₄₇

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₄

yes

characteristic

C₄×Dic₉₄

C₂²

yes

—

#13093958

C₄

yes

characteristic

C₄⋊(C₄₇⋊C₈)

C₂²

yes

—

Dic₄₇⋊C₈

—

#13093949

C₄

yes

—

C₈×Dic₄₇

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

C₂×C₄

yes

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

D₄

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

C₈

yes

direct product factor

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

#41

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

C₂×C₈

yes

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

C₂×C₈

yes

—

C₈×C₄₇

Q₁₆

yes

complemented

C₄₇⋊C₈

—

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂²×C₈

yes

characteristic

C₄×C₄₇

#131

yes

characteristic

C₄×C₄₇

C₂×Q₁₆

yes

characteristic

C₄×C₄₇

#135

yes

characteristic

Dic₄₇

—

Dic₄₇

—

C₈×Q₁₆

—

maximal, Sylow

C₂×C₄₇

C₈×D₄

yes

characteristic

C₂×C₄₇

C₄×Q₁₆

yes

characteristic

C₂×C₄₇

#443

yes

characteristic

C₈×Q₈

—

C₄×Q₁₆

—

#335

—

Q₈⋊C₈

—

C₈²

D₄₇

yes

characteristic

C₄₇

C₈×Q₁₆

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

D₁₈₈

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²×D₄₇

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄×D₄₇

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₂×C₄

#10625350

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

188

—

C₈

C₈×D₄₇

yes

—

C₈

Dic₁₈₈

yes

direct product factor

C₂²

C₄×D₁₈₈

yes

characteristic

C₄

—

C₄

—

C₄

—

188

—

C₄

C₂×C₈×D₄₇

yes

characteristic

C₄

#13094030

yes

characteristic

100

C₄

C₂×Dic₁₈₈

yes

characteristic

101

C₄

#13094046

yes

characteristic

102

C₂

C₈×D₁₈₈

yes

characteristic

103

C₂

C₄×Dic₁₈₈

yes

characteristic

104

C₂

#15689241

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₁₈₈
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₄²	C₂²×D₄₇
Fitting	C₈²×C₄₇	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	C₈²	D₄₇
hypocenter	C₄₇	C₈×Q₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

subgroup

G/H

center

C₂×C₈

D₁₈₈

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₄²

C₂²×D₄₇

Fitting

C₈²×C₄₇

C₂

socle

C₂²×C₄₇

C₄×D₄

hypercenter

C₈²

D₄₇

hypocenter

C₄₇

C₈×Q₁₆

LCS

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

N	H ≅ G/N	type
27. Dic₁₈₈	C₈	direct (N × H)
39. C₈×C₄₇	Q₁₆	semidirect
58. C₄₇	C₈×Q₁₆	semidirect
93. C₈	Dic₁₈₈	direct (N × H)

H ≅ G/N

type

27. Dic₁₈₈

C₈

direct (N × H)

39. C₈×C₄₇

Q₁₆

semidirect

58. C₄₇

C₈×Q₁₆

semidirect

93. C₈

Dic₁₈₈

direct (N × H)

Subgroups — C₈×Dic₁₈₈ #20242196

Conjugacy classes of subgroups

Complements

Subgroups — C8×Dic188 #20242196

Conjugacy classes of subgroups

Complements

Subgroups — C₈×Dic₁₈₈ #20242196