Group #20242206 — subgroups

Subgroups — #20242206

Order 6016.

160 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 71 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	#15689247	C₂	1	2	yes	maximal
2	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#15688853	C₂	1	2	yes	maximal
4	#15688844	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#334	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	Dic₄₇⋊C₈	—	2	2	no	—
10	#13093949	C₄	1	2	yes	—
11	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₈×Dic₄₇	—	2	2	no	—
14	C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
15	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×Dic₉₄	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	—	2	2	no	—
18	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₄₇	C₂³	1	1	yes	characteristic
21	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
22	Dic₄₇⋊C₄	—	2	2	no	—
23	C₄×Dic₄₇	—	2	2	no	—
24	C₂×C₄₇⋊C₈	—	2	1	no	—
25	C₂×C₄₇⋊C₈	D₄	1	2	yes	—
26	Dic₁₈₈	C₈	1	4	yes	complemented
27	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₄₇	#41	1	1	yes	characteristic
30	C₂×Dic₄₇	—	2	2	no	—
31	C₂×Dic₄₇	—	2	2	no	—
32	Dic₉₄	—	2	2	no	—
33	Dic₉₄	C₂×C₈	1	4	yes	—
34	C₈×C₄₇	—	2	1	no	—
35	C₈×C₄₇	—	4	2	no	—
36	C₈×C₄₇	C₂×C₈	1	2	yes	—
37	C₄₇⋊C₈	—	2	2	no	—
38	C₄₇⋊C₈	—	4	1	no	—
39	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
40	C₄×C₄₇	—	2	1	no	—
41	C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₄₇	#131	1	1	yes	characteristic
43	C₄×C₄₇	#137	1	2	yes	—
44	Dic₄₇	—	2	4	no	—
45	Dic₄₇	—	4	2	no	—
46	#1579	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	C₈×D₄	1	1	yes	characteristic
48	C₂×C₄₇	#441	1	1	yes	characteristic
49	C₂×C₄₇	#444	1	1	yes	characteristic
50	C₈×Q₈	—	47	2	no	—
51	C₄×Q₁₆	—	47	1	no	—
52	#334	D₄₇	1	1	yes	characteristic
53	Q₈⋊C₈	—	47	2	no	—
54	#322	—	47	1	no	—
55	C₄₇	#1579	1	1	yes	characteristic, complemented, Sylow
56	C₂×Q₁₆	—	47	1	no	—
57	C₄×Q₈	—	47	2	no	—
58	#107	—	47	1	no	—
59	C₄⋊C₈	—	94	2	no	—
60	C₄⋊C₈	C₂×D₄₇	1	2	yes	—
61	#103	—	47	2	no	—
62	C₄×C₈	—	47	1	no	—
63	C₄×C₈	—	47	1	no	—
64	C₄×C₈	—	94	2	no	—
65	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
66	C₂×Q₈	—	47	2	no	—
67	Q₁₆	—	47	4	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	47	2	no	—
70	C₂×C₈	—	94	1	no	—
71	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
72	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
73	C₄⋊C₄	—	47	2	no	—
74	C₄⋊C₄	—	94	2	no	—
75	C₄²	—	94	2	no	—
76	C₄²	C₂²×D₄₇	1	1	yes	characteristic
77	Q₈	—	47	4	no	—
78	Q₈	—	94	2	no	—
79	C₂×C₄	—	94	2	no	—
80	C₂×C₄	—	94	2	no	—
81	C₂×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
82	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
83	C₂×C₄	#10625354	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	4	2	no	—
86	C₈	—	94	2	no	—
87	C₈	—	188	1	no	—
88	C₈	C₈×D₄₇	1	2	yes	—
89	C₂²	#13093986	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	94	4	no	—
92	C₄	—	188	2	no	—
93	C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
94	C₄	#13094032	1	1	yes	characteristic
95	C₄	#13094053	1	2	yes	—
96	C₂	#15689188	1	1	yes	characteristic
97	C₂	#15689229	1	1	yes	characteristic
98	C₂	#15689244	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689247

C₂

yes

maximal

C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#15688853

C₂

yes

maximal

#15688844

C₂

yes

maximal, characteristic

C₄₇×#334

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₄

yes

characteristic

C₄×Dic₉₄

C₂²

yes

—

#13093958

C₄

yes

characteristic

Dic₄₇⋊C₈

—

#13093949

C₄

yes

—

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₄×C₄₇⋊C₈

C₂²

yes

characteristic

C₈×Dic₄₇

—

C₄⋊C₈×C₄₇

C₂²

yes

—

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

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

D₄

yes

—

Dic₁₈₈

C₈

yes

complemented

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

C₂×C₈

yes

—

C₄₇⋊C₈

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂²×C₈

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

Dic₄₇

—

#1579

—

maximal, Sylow

C₂×C₄₇

C₈×D₄

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

C₈×Q₈

—

C₄×Q₁₆

—

#334

D₄₇

yes

characteristic

Q₈⋊C₈

—

#322

—

C₄₇

#1579

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

C₂×D₄₇

yes

—

#103

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

characteristic

C₂×C₈

C₄×D₄₇

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

D₄×D₄₇

yes

characteristic

C₂×C₄

#10625354

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

188

—

C₈

C₈×D₄₇

yes

—

C₂²

#13093986

yes

characteristic

C₄

—

C₄

—

C₄

—

188

—

C₄

C₂×C₈×D₄₇

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₈
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#334	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	#334	D₄₇
hypocenter	C₄₇	#1579
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₄₇

commutator

C₄×C₄₇

C₂²×C₈

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#334

C₂

socle

C₂²×C₄₇

C₄×D₄

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
26. Dic₁₈₈	C₈	semidirect
55. C₄₇	#1579	semidirect

H ≅ G/N

type

26. Dic₁₈₈

C₈

semidirect

55. C₄₇

#1579

semidirect

Subgroups — #20242206

Conjugacy classes of subgroups

Complements