Group #20245541 — subgroups

Subgroups — #20245541

Order 6016.

130 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 55 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	#15689528	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#15688949	C₂	1	2	yes	maximal
4	#15688928	C₂	1	2	yes	maximal
5	C₄₇×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₈₈	C₂²	1	1	yes	characteristic
7	#13094024	—	2	1	no	—
8	C₄×Dic₉₄	—	2	1	no	—
9	#13093958	—	2	1	no	—
10	#13093958	C₂²	1	1	yes	characteristic
11	#13093958	C₂²	1	2	yes	—
12	#13093949	—	2	1	no	—
13	C₂×C₁₆×C₄₇	C₂²	1	2	yes	—
14	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×Dic₉₄	—	2	1	no	—
16	C₂×Dic₉₄	—	4	1	no	—
17	C₂×C₈×C₄₇	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
19	C₄²×C₄₇	D₄	1	1	yes	characteristic
20	C₄⋊Dic₄₇	—	2	1	no	—
21	C₄⋊Dic₄₇	—	2	2	no	—
22	C₄⋊Dic₄₇	—	4	1	no	—
23	Dic₄₇⋊C₄	—	4	1	no	—
24	C₄×Dic₄₇	—	4	1	no	—
25	Dic₁₈₈	—	2	1	no	—
26	Dic₁₈₈	Q₈	1	2	yes	complemented
27	C₁₆×C₄₇	—	2	2	no	—
28	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₇	D₈	1	1	yes	characteristic
30	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
31	C₂×Dic₄₇	—	4	1	no	—
32	C₂×Dic₄₇	—	4	1	no	—
33	C₂×Dic₄₇	—	4	2	no	—
34	Dic₉₄	—	2	2	no	—
35	Dic₉₄	—	4	1	no	—
36	Dic₉₄	—	8	2	no	—
37	C₈×C₄₇	—	2	1	no	—
38	C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
39	C₈×C₄₇	#41	1	1	yes	characteristic
40	C₂²×C₄₇	C₂×D₈	1	1	yes	characteristic
41	C₄×C₄₇	—	2	1	no	—
42	C₄×C₄₇	Q₃₂	1	2	yes	—
43	C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
44	C₄×C₄₇	#137	1	1	yes	characteristic
45	Dic₄₇	—	4	2	no	—
46	Dic₄₇	—	8	2	no	—
47	Dic₄₇	—	8	1	no	—
48	#2227	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	#474	1	1	yes	characteristic
50	C₂×C₄₇	C₂×Q₃₂	1	1	yes	characteristic
51	C₂×C₄₇	#509	1	1	yes	characteristic
52	#500	—	47	1	no	—
53	C₄×Q₁₆	—	47	1	no	—
54	#366	—	47	2	no	—
55	C₄⋊C₁₆	D₄₇	1	1	yes	characteristic
56	#358	—	47	2	no	—
57	C₄₇	#2227	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	—	47	1	no	—
59	C₄⋊Q₈	—	94	1	no	—
60	C₄×Q₈	—	94	1	no	—
61	C₂×C₁₆	C₂×D₄₇	1	2	yes	—
62	#107	—	47	2	no	—
63	#107	—	47	1	no	—
64	#107	—	94	1	no	—
65	#103	—	94	1	no	—
66	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
67	C₂×Q₈	—	94	1	no	—
68	C₂×Q₈	—	188	1	no	—
69	Q₁₆	—	47	2	no	—
70	Q₁₆	—	94	1	no	—
71	C₂×C₈	D₁₈₈	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
73	C₄⋊C₄	—	94	1	no	—
74	C₄⋊C₄	—	94	2	no	—
75	C₄⋊C₄	—	188	1	no	—
76	C₄⋊C₄	—	188	1	no	—
77	C₄²	—	188	1	no	—
78	C₄²	D₁₈₈	1	1	yes	characteristic
79	C₁₆	—	2	2	no	—
80	Q₈	—	94	2	no	—
81	Q₈	—	376	2	no	—
82	Q₈	—	188	1	no	—
83	C₂×C₄	—	188	1	no	—
84	C₂×C₄	—	188	2	no	—
85	C₂×C₄	—	188	1	no	—
86	C₂×C₄	D₃₇₆	1	1	yes	characteristic
87	C₂×C₄	D₃₇₆	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	#10625352	1	1	yes	characteristic
91	C₈	Q₈×D₄₇	1	1	yes	characteristic
92	C₂²	C₂×D₃₇₆	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	376	2	no	—
95	C₄	—	376	1	no	—
96	C₄	—	188	2	no	—
97	C₄	Dic₃₇₆	1	2	yes	—
98	C₄	#13094004	1	1	yes	characteristic
99	C₄	#13094057	1	1	yes	characteristic
100	C₂	#15689404	1	1	yes	characteristic
101	C₂	C₂×Dic₃₇₆	1	1	yes	characteristic
102	C₂	#15689561	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689528

C₂

yes

maximal, characteristic

C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#15688949

C₂

yes

maximal

#15688928

C₂

yes

maximal

C₄₇×C₄⋊C₁₆

C₂

yes

maximal, characteristic

C₂×Dic₁₈₈

C₂²

yes

characteristic

#13094024

—

C₄×Dic₉₄

—

#13093958

—

#13093958

C₂²

yes

characteristic

#13093958

C₂²

yes

—

#13093949

—

C₂×C₁₆×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Dic₉₄

—

C₂×Dic₉₄

—

C₂×C₈×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

D₄

yes

characteristic

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

Dic₁₈₈

—

Dic₁₈₈

Q₈

yes

complemented

C₁₆×C₄₇

—

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

D₈

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

C₈×C₄₇

C₂×Q₈

yes

characteristic

C₈×C₄₇

#41

yes

characteristic

C₂²×C₄₇

C₂×D₈

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

Q₃₂

yes

—

C₄×C₄₇

C₂²⋊Q₈

yes

characteristic

C₄×C₄₇

#137

yes

characteristic

Dic₄₇

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂×Q₃₂

yes

C₂×C₄₇

yes

—

C₄×Q₁₆

—

#366

—

C₄⋊C₁₆

D₄₇

yes

characteristic

#358

—

C₄₇

#2227

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄×Q₈

—

C₂×C₁₆

C₂×D₄₇

yes

—

—

—

—

—

C₄×C₈

C₂×D₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

188

—

Q₁₆

—

Q₁₆

—

C₂×C₈

D₁₈₈

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

188

—

C₄⋊C₄

—

188

—

C₄²

—

188

—

C₄²

D₁₈₈

yes

characteristic

C₁₆

—

Q₈

—

Q₈

—

376

—

Q₈

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

—

188

—

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

D₃₇₆

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₈

—

C₈

#10625352

yes

characteristic

C₈

Q₈×D₄₇

yes

characteristic

C₂²

C₂×D₃₇₆

yes

characteristic

C₄

—

C₄

—

376

—

C₄

—

376

—

C₄

—

188

—

C₄

Dic₃₇₆

yes

—

C₄

yes

C₄

yes

100

C₂

#15689404

yes

characteristic

101

C₂

C₂×Dic₃₇₆

yes

characteristic

102

C₂

#15689561

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₃₇₆
commutator	C₂×C₈×C₄₇	C₂³
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₄₇×C₄⋊C₁₆	C₂
socle	C₂²×C₄₇	C₂×D₈
hypercenter	C₄⋊C₁₆	D₄₇
hypocenter	C₄₇	#2227
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center

C₂²

C₂×D₃₇₆

commutator

C₂×C₈×C₄₇

C₂³

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₄₇×C₄⋊C₁₆

C₂

socle

C₂²×C₄₇

C₂×D₈

hypercenter

C₄⋊C₁₆

D₄₇

hypocenter

C₄₇

#2227

LCS

G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
26. Dic₁₈₈	Q₈	semidirect
57. C₄₇	#2227	semidirect

H ≅ G/N

type

26. Dic₁₈₈

Q₈

semidirect

57. C₄₇

#2227

semidirect

Subgroups — #20245541

Conjugacy classes of subgroups

Complements