Group #20241265 — subgroups

Subgroups — #20241265

Order 6016.

184 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 61 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	#15689087	C₂	1	2	yes	maximal
2	C₂×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10625329	—	2	2	no	—
4	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
5	C₂²⋊(C₄₇⋊C₈)	C₄	1	4	yes	—
6	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×C₈×C₄₇	C₄	1	2	yes	—
8	C₂²⋊C₈×C₄₇	—	2	2	no	—
9	C₂⁴×C₄₇	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₄₇	—	4	2	no	—
11	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₄₇	D₄	1	2	yes	—
14	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₄₇	—	2	2	no	—
16	C₂×C₈×C₄₇	—	4	2	no	—
17	#10625329	—	4	4	no	—
18	C₂×C₄₇⋊C₈	—	2	4	no	—
19	C₂³×C₄₇	—	2	2	no	—
20	C₂³×C₄₇	—	4	1	no	—
21	C₂³×C₄₇	—	4	1	no	—
22	C₂³×C₄₇	C₄⋊C₄	1	2	yes	—
23	C₂³×C₄₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₄₇	—	2	4	no	—
25	C₂×C₄×C₄₇	—	2	2	no	—
26	C₂×C₄×C₄₇	—	4	2	no	—
27	C₂×C₄×C₄₇	—	4	1	no	—
28	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
30	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
31	C₈×C₄₇	—	4	2	no	—
32	C₄₇⋊C₈	—	4	4	no	—
33	C₂²×C₄₇	—	2	1	no	—
34	C₂²×C₄₇	—	2	1	no	—
35	C₂²×C₄₇	—	2	2	no	—
36	C₂²×C₄₇	—	2	2	no	—
37	C₂²×C₄₇	—	2	2	no	—
38	C₂²×C₄₇	—	4	4	no	—
39	C₂²×C₄₇	#95	1	1	yes	characteristic
40	C₂²×C₄₇	#108	1	2	yes	—
41	C₄×C₄₇	—	2	2	no	—
42	C₄×C₄₇	—	2	1	no	—
43	C₄×C₄₇	#99	1	2	yes	—
44	#1293	—	47	1	no	maximal, Sylow
45	C₂×C₄₇	—	2	2	no	—
46	C₂×C₄₇	—	4	2	no	—
47	C₂×C₄₇	#338	1	1	yes	characteristic
48	C₂×C₄₇	#341	1	1	yes	characteristic
49	C₂×C₄₇	#342	1	1	yes	characteristic
50	#407	—	47	2	no	—
51	C₂×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
52	C₄₇	#1293	1	1	yes	characteristic, complemented, Sylow
53	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
54	C₂×M₁₆	—	94	2	no	—
55	C₂²×C₈	Dic₄₇	1	2	yes	—
56	C₂²⋊C₈	—	2	2	no	—
57	C₂²⋊C₈	—	47	4	no	—
58	C₂²⋊C₈	—	94	2	no	—
59	C₂⁴	Dic₉₄	1	1	yes	characteristic
60	C₂²×C₄	—	4	2	no	—
61	C₂²×C₄	C₄×D₄₇	1	2	yes	—
62	C₂²×C₄	D₁₈₈	1	1	yes	characteristic
63	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
64	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
65	M₁₆	—	188	4	no	—
66	C₂×C₈	—	2	2	no	—
67	C₂×C₈	—	4	2	no	—
68	C₂×C₈	—	94	4	no	—
69	C₂³	—	2	2	no	—
70	C₂³	—	4	1	no	—
71	C₂³	—	4	1	no	—
72	C₂³	Dic₄₇⋊C₄	1	2	yes	—
73	C₂³	C₄⋊Dic₄₇	1	1	yes	characteristic
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	—	4	1	no	—
78	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
79	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
80	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
81	C₈	—	4	2	no	—
82	C₈	—	188	4	no	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	2	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	—	2	2	no	—
88	C₂²	—	4	4	no	—
89	C₂²	C₄₇⋊#95	1	1	yes	characteristic
90	C₂²	#13093960	1	2	yes	—
91	C₄	—	2	2	no	—
92	C₄	—	2	1	no	—
93	C₄	#13093939	1	2	yes	—
94	C₂	—	2	2	no	—
95	C₂	—	4	2	no	—
96	C₂	C₄₇⋊#338	1	1	yes	characteristic
97	C₂	#15688888	1	1	yes	characteristic
98	C₂	#15688890	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689087

C₂

yes

maximal

C₂×C₂²⋊C₈×C₄₇

C₂

yes

maximal, characteristic

C₂×#10625329

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

C₄

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂²×C₈×C₄₇

C₄

yes

—

C₂²⋊C₈×C₄₇

—

C₂⁴×C₄₇

Q₈

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

D₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

—

C₂³×C₄₇

C₄⋊C₄

yes

—

C₂³×C₄₇

C₄⋊C₄

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#95

yes

characteristic

C₂²×C₄₇

#108

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#99

yes

—

#1293

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

yes

—

C₂×C₂²⋊C₈

D₄₇

yes

characteristic

C₄₇

#1293

yes

characteristic, complemented, Sylow

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

Dic₄₇

yes

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

C₂⁴

Dic₉₄

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

—

C₂²×C₄

D₁₈₈

yes

characteristic

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂³

—

C₂³

—

C₂³

—

C₂³

Dic₄₇⋊C₄

yes

—

C₂³

C₄⋊Dic₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₇

yes

characteristic

C₂×C₄

(C₂×D₄₇)⋊C₄

yes

—

C₂×C₄

C₂²⋊Dic₄₇

yes

characteristic

C₈

—

C₈

—

188

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄₇⋊#95

yes

characteristic

C₂²

#13093960

yes

—

C₄

—

C₄

—

C₄

#13093939

yes

—

C₂

—

C₂

—

C₂

C₄₇⋊#338

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	C₄₇⋊#95
commutator	C₂×C₄×C₄₇	C₄²
Frattini	C₂³×C₄	C₂×D₄₇
Fitting	C₂×C₂²⋊C₈×C₄₇	C₂
socle	C₂²×C₄₇	#95
hypercenter	C₂×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#1293
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center

C₂²

C₄₇⋊#95

commutator

C₂×C₄×C₄₇

C₄²

Frattini

C₂³×C₄

C₂×D₄₇

Fitting

C₂×C₂²⋊C₈×C₄₇

C₂

socle

C₂²×C₄₇

#95

hypercenter

C₂×C₂²⋊C₈

D₄₇

hypocenter

C₄₇

#1293

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
52. C₄₇	#1293	semidirect

H ≅ G/N

type

52. C₄₇

#1293

semidirect

Subgroups — #20241265

Conjugacy classes of subgroups

Complements