Group #20242298 — subgroups

Subgroups — #20242298

Order 6016.

148 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 65 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	#15689253	C₂	1	2	yes	maximal
2	C₄×Dic₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#15688874	C₂	1	1	yes	maximal, characteristic
4	#15688855	C₂	1	2	yes	maximal
5	C₄₇×#322	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	#13093934	—	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	2	yes	—
21	C₄²×C₄₇	C₂³	1	1	yes	characteristic
22	C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
23	Dic₄₇⋊C₄	—	2	2	no	—
24	C₄×Dic₄₇	—	2	2	no	—
25	C₂×C₄₇⋊C₈	—	2	2	no	—
26	Dic₁₈₈	—	2	2	no	—
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	—	2	2	no	—
34	C₈×C₄₇	—	2	1	no	—
35	C₈×C₄₇	—	2	2	no	—
36	C₈×C₄₇	—	4	1	no	—
37	C₈×C₄₇	M₁₆	1	2	yes	—
38	C₄₇⋊C₈	—	4	2	no	—
39	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
40	C₄×C₄₇	—	2	1	no	—
41	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₄₇	#131	1	1	yes	characteristic
43	C₄×C₄₇	#137	1	2	yes	—
44	Dic₄₇	—	4	2	no	—
45	Dic₄₇	—	4	2	no	—
46	#1593	—	47	1	no	maximal, Sylow
47	C₂×C₄₇	#436	1	1	yes	characteristic
48	C₂×C₄₇	#441	1	1	yes	characteristic
49	C₂×C₄₇	#444	1	1	yes	characteristic
50	#446	—	47	2	no	—
51	C₄×Q₁₆	—	47	1	no	—
52	#334	—	47	1	no	—
53	Q₈⋊C₈	—	47	2	no	—
54	#322	D₄₇	1	1	yes	characteristic
55	C₄₇	#1593	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	—	47	2	no	—
60	C₄⋊C₈	—	94	2	no	—
61	#103	—	47	2	no	—
62	#97	—	94	2	no	—
63	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
64	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
65	C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
66	C₂×Q₈	—	47	2	no	—
67	Q₁₆	—	94	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	94	2	no	—
70	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
71	C₂×C₈	C₄×D₄₇	1	1	yes	characteristic
72	C₂×C₈	D₁₈₈	1	2	yes	—
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	—	94	2	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	C₂×D₁₈₈	1	1	yes	characteristic
83	C₂×C₄	#10625350	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	2	2	no	—
86	C₈	—	4	1	no	—
87	C₈	—	188	2	no	—
88	C₈	#10625324	1	2	yes	—
89	C₂²	C₄×D₁₈₈	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	188	2	no	—
92	C₄	—	188	2	no	—
93	C₄	C₂×#10625324	1	1	yes	characteristic
94	C₄	#13094030	1	1	yes	characteristic
95	C₄	#13094057	1	2	yes	—
96	C₂	#15689202	1	1	yes	characteristic
97	C₂	#15689231	1	1	yes	characteristic
98	C₂	#15689246	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689253

C₂

yes

maximal

C₄×Dic₁₈₈

C₂

yes

maximal, characteristic

#15688874

C₂

yes

maximal, characteristic

#15688855

C₂

yes

maximal

C₄₇×#322

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

—

#13093934

—

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

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄⋊Dic₄₇

C₂×C₄

yes

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

C₂×C₄₇⋊C₈

—

Dic₁₈₈

—

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

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

—

C₈×C₄₇

M₁₆

yes

—

C₄₇⋊C₈

—

C₂²×C₄₇

C₄×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

C₂×M₁₆

yes

C₄×C₄₇

yes

C₄×C₄₇

yes

—

Dic₄₇

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₄×Q₁₆

—

#334

—

Q₈⋊C₈

—

#322

D₄₇

yes

characteristic

C₄₇

#1593

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

C₄⋊C₈

—

#103

—

#97

—

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

—

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

#10625324

yes

—

C₂²

C₄×D₁₈₈

yes

characteristic

C₄

—

C₄

—

188

—

C₄

—

188

—

C₄

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₄
Frattini	C₄²	C₂²×D₄₇
Fitting	C₄₇×#322	C₂
socle	C₂²×C₄₇	C₄×D₄
hypercenter	#322	D₄₇
hypocenter	C₄₇	#1593
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

subgroup

G/H

center

C₂×C₄

C₂×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂²×C₄

Frattini

C₄²

C₂²×D₄₇

Fitting

C₄₇×#322

C₂

socle

C₂²×C₄₇

C₄×D₄

D₄₇

C₄₇

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #322

N	H ≅ G/N	type
55. C₄₇	#1593	semidirect

H ≅ G/N

type

55. C₄₇

#1593

semidirect

Subgroups — #20242298

Conjugacy classes of subgroups

Complements