Group #20241511 — subgroups

Subgroups — #20241511

Order 6016.

158 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 53 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	#15689107	C₂	1	2	yes	maximal
2	C₄₇×#408	C₂	1	1	yes	maximal, characteristic
3	C₂×#10625329	—	2	2	no	—
4	#13093943	—	2	2	no	—
5	#13093941	C₄	1	4	yes	—
6	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×M₁₆×C₄₇	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₄₇	C₄	1	1	yes	characteristic
9	C₂²⋊C₈×C₄₇	—	2	2	no	—
10	#41×C₄₇	—	4	1	no	—
11	#41×C₄₇	—	4	1	no	—
12	C₂×Q₈×C₄₇	D₄	1	1	yes	characteristic
13	C₂×D₄×C₄₇	C₂×C₄	1	2	yes	—
14	C₂×D₄×C₄₇	Q₈	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₄×C₄₇	D₄	1	2	yes	—
17	M₁₆×C₄₇	—	4	1	no	—
18	C₂×C₈×C₄₇	—	2	1	no	—
19	C₂×C₈×C₄₇	—	2	1	no	—
20	C₂×C₈×C₄₇	—	4	1	no	—
21	#10625329	—	2	4	no	—
22	#10625329	—	4	2	no	—
23	C₂×C₄₇⋊C₈	—	4	2	no	—
24	C₂³×C₄₇	C₄²	1	1	yes	characteristic
25	C₂³×C₄₇	C₄⋊C₄	1	2	yes	—
26	Q₈×C₄₇	—	4	1	no	—
27	D₄×C₄₇	—	4	2	no	—
28	D₄×C₄₇	—	4	1	no	—
29	C₂×C₄×C₄₇	—	2	2	no	—
30	C₂×C₄×C₄₇	—	2	2	no	—
31	C₂×C₄×C₄₇	—	2	1	no	—
32	C₂×C₄×C₄₇	—	2	1	no	—
33	C₂×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
34	C₂×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
36	C₈×C₄₇	—	4	1	no	—
37	C₈×C₄₇	—	4	1	no	—
38	C₄₇⋊C₈	—	4	4	no	—
39	C₂²×C₄₇	—	2	1	no	—
40	C₂²×C₄₇	—	2	2	no	—
41	C₂²×C₄₇	—	4	1	no	—
42	C₂²×C₄₇	—	4	2	no	—
43	C₂²×C₄₇	#95	1	1	yes	characteristic
44	C₄×C₄₇	—	2	2	no	—
45	C₄×C₄₇	—	2	1	no	—
46	C₄×C₄₇	#99	1	1	yes	characteristic
47	C₄×C₄₇	#99	1	1	yes	characteristic
48	#1392	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	—	2	1	no	—
50	C₂×C₄₇	—	4	1	no	—
51	C₂×C₄₇	—	4	2	no	—
52	C₂×C₄₇	#342	1	1	yes	characteristic
53	#413	—	47	2	no	—
54	#408	D₄₇	1	1	yes	characteristic
55	C₄₇	#1392	1	1	yes	characteristic, complemented, Sylow
56	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
57	C₂×M₁₆	—	94	2	no	—
58	C₂×M₁₆	Dic₄₇	1	1	yes	characteristic
59	C₂²×C₈	Dic₄₇	1	1	yes	characteristic
60	#101	—	94	2	no	—
61	#100	—	47	4	no	—
62	C₂²⋊C₈	—	2	2	no	—
63	#41	—	4	1	no	—
64	#41	—	4	1	no	—
65	C₂×Q₈	D₁₈₈	1	1	yes	characteristic
66	C₂×D₄	Dic₉₄	1	1	yes	characteristic
67	C₂×D₄	C₄×D₄₇	1	2	yes	—
68	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
69	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
70	M₁₆	—	4	1	no	—
71	M₁₆	—	94	4	no	—
72	M₁₆	—	188	2	no	—
73	C₂×C₈	—	2	1	no	—
74	C₂×C₈	—	2	1	no	—
75	C₂×C₈	—	4	1	no	—
76	C₂×C₈	—	188	2	no	—
77	C₂³	C₄×Dic₄₇	1	1	yes	characteristic
78	C₂³	Dic₄₇⋊C₄	1	2	yes	—
79	Q₈	—	4	1	no	—
80	D₄	—	4	1	no	—
81	D₄	—	4	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	2	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
87	C₂×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
88	C₂×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
89	C₈	—	4	1	no	—
90	C₈	—	4	1	no	—
91	C₈	—	188	4	no	—
92	C₂²	—	2	1	no	—
93	C₂²	—	2	2	no	—
94	C₂²	—	4	1	no	—
95	C₂²	—	4	2	no	—
96	C₂²	C₄₇⋊#95	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	2	1	no	—
99	C₄	#13093939	1	1	yes	characteristic
100	C₄	#13093939	1	1	yes	characteristic
101	C₂	—	2	1	no	—
102	C₂	—	4	1	no	—
103	C₂	—	4	2	no	—
104	C₂	#15688890	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15689107

C₂

yes

maximal

C₄₇×#408

C₂

yes

maximal, characteristic

C₂×#10625329

—

#13093943

—

#13093941

C₄

yes

—

C₂×#41×C₄₇

C₂²

yes

characteristic

C₂×M₁₆×C₄₇

C₄

yes

characteristic

C₂²×C₈×C₄₇

C₄

yes

characteristic

C₂²⋊C₈×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

D₄

yes

characteristic

C₂×D₄×C₄₇

C₂×C₄

yes

—

C₂×D₄×C₄₇

Q₈

yes

characteristic

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₇

D₄

yes

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

#10625329

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

C₄²

yes

characteristic

C₂³×C₄₇

C₄⋊C₄

yes

—

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

—

C₂×C₄×C₄₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄⋊C₄

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

—

C₄₇⋊C₈

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

#95

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

yes

—

D₄₇

yes

characteristic

C₄₇

#1392

yes

characteristic, complemented, Sylow

C₂×#41

C₂×D₄₇

yes

characteristic

C₂×M₁₆

—

C₂×M₁₆

Dic₄₇

yes

characteristic

C₂²×C₈

Dic₄₇

yes

characteristic

#101

—

#100

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

D₁₈₈

yes

characteristic

C₂×D₄

Dic₉₄

yes

characteristic

C₂×D₄

C₄×D₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂²×C₄

C₂²⋊D₄₇

yes

—

M₁₆

—

M₁₆

—

M₁₆

—

188

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

188

—

C₂³

C₄×Dic₄₇

yes

characteristic

C₂³

Dic₄₇⋊C₄

yes

—

Q₈

—

D₄

—

D₄

—

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

—

C₈

—

188

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₄₇⋊#95

yes

characteristic

C₄

—

C₄

—

C₄

#13093939

yes

characteristic

100

C₄

#13093939

yes

characteristic

101

C₂

—

102

C₂

—

103

C₂

—

104

C₂

#15688890

yes

characteristic

	subgroup	G/H
center	C₄	#13093939
commutator	C₂³×C₄₇	C₄²
Frattini	C₂×#41	C₂×D₄₇
Fitting	C₄₇×#408	C₂
socle	C₂×C₄₇	#342
hypercenter	#408	D₄₇
hypocenter	C₄₇	#1392
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×#41 ◁ #408

subgroup

G/H

center

C₄

#13093939

commutator

C₂³×C₄₇

C₄²

Frattini

C₂×#41

C₂×D₄₇

Fitting

C₄₇×#408

C₂

C₂×C₄₇

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×#41 ◁ #408

N	H ≅ G/N	type
55. C₄₇	#1392	semidirect

H ≅ G/N

type

55. C₄₇

#1392

semidirect

Subgroups — #20241511

Conjugacy classes of subgroups

Complements