Group #20251751 — subgroups

Subgroups — #20251751

Order 6016.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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	C₂×#13094016	C₂	1	2	yes	maximal
2	#15689021	C₂	1	8	yes	maximal
3	#15688993	C₂	1	2	yes	maximal
4	#15688989	C₂	1	2	yes	maximal
5	C₄³×C₄₇	C₂	1	1	yes	maximal, characteristic
6	#13094016	—	2	8	no	—
7	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₄₇	C₂²	1	8	yes	—
9	C₂×Dic₄₇⋊C₄	C₂²	1	8	yes	—
10	C₄₇⋊#95	C₂²	1	8	yes	—
11	C₂×C₄²×C₄₇	C₂²	1	4	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
17	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
19	C₂²×Dic₄₇	C₂³	1	8	yes	—
20	C₄²×C₄₇	—	2	8	no	—
21	C₄²×C₄₇	D₄	1	4	yes	—
22	C₄²×C₄₇	Q₈	1	4	yes	—
23	C₄²×C₄₇	Q₈	1	4	yes	—
24	C₄⋊Dic₄₇	—	2	8	no	—
25	C₄⋊Dic₄₇	—	2	16	no	—
26	Dic₄₇⋊C₄	—	2	16	no	—
27	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₄₇	—	2	4	no	—
29	C₂×C₄×C₄₇	—	2	4	no	—
30	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₄₇	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₄₇	#41	1	8	yes	—
37	C₂×Dic₄₇	—	2	8	no	—
38	C₂×Dic₄₇	—	2	16	no	—
39	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
40	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
41	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₄₇	C₂×#41	1	4	yes	—
43	C₄×C₄₇	—	2	4	no	—
44	C₄×C₄₇	—	2	4	no	—
45	C₄×C₄₇	#125	1	8	yes	complemented
46	C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
47	Dic₄₇	—	4	8	no	—
48	#2859	—	47	1	no	maximal, Sylow
49	C₂×C₄₇	C₂×#125	1	2	yes	—
50	C₂×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₄₇	#532	1	2	yes	—
52	C₂×C₄₇	#533	1	2	yes	—
53	C₂×#125	—	47	2	no	—
54	#389	—	47	8	no	—
55	#384	—	47	2	no	—
56	#382	—	47	2	no	—
57	C₄³	D₄₇	1	1	yes	characteristic
58	C₄₇	#2859	1	1	yes	characteristic, complemented, Sylow
59	#125	—	94	8	no	—
60	C₂×C₄⋊C₄	—	47	8	no	—
61	C₂×C₄⋊C₄	—	47	4	no	—
62	C₂×C₄⋊C₄	—	47	8	no	—
63	C₂×C₄²	C₂×D₄₇	1	4	yes	—
64	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
67	#95	—	47	8	no	—
68	C₂²×C₄	—	47	8	no	—
69	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
70	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
71	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
73	C₄⋊C₄	—	94	16	no	—
74	C₄⋊C₄	—	94	8	no	—
75	C₄⋊C₄	—	94	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₉₄	1	4	yes	—
78	C₄²	Dic₉₄	1	4	yes	—
79	C₄²	D₁₈₈	1	4	yes	—
80	C₂³	C₂³×D₄₇	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	94	8	no	—
84	C₂×C₄	—	94	16	no	—
85	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
86	C₂×C₄	C₂×Dic₉₄	1	4	yes	—
87	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
88	C₂×C₄	C₂×Dic₉₄	1	2	yes	—
89	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
90	C₂×C₄	C₂×D₁₈₈	1	2	yes	—
91	C₂×C₄	#10625350	1	8	yes	—
92	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
93	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
94	C₂²	C₂²×Dic₉₄	1	1	yes	characteristic
95	C₂²	C₂×#10625350	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	188	8	no	—
99	C₄	#13094016	1	8	yes	complemented
100	C₄	#13094024	1	4	yes	—
101	C₂	C₂×#13094016	1	2	yes	—
102	C₂	C₂×#13094024	1	1	yes	characteristic
103	C₂	#15689673	1	2	yes	—
104	C₂	#15689680	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13094016

C₂

yes

maximal

#15689021

C₂

yes

maximal

#15688993

C₂

yes

maximal

#15688989

C₂

yes

maximal

C₄³×C₄₇

C₂

yes

maximal, characteristic

#13094016

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×C₄⋊Dic₄₇

C₂²

yes

—

C₂×Dic₄₇⋊C₄

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄²×C₄₇

Q₈

yes

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

C₂×Q₈

yes

—

C₂×C₄×C₄₇

#41

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂²×Q₈

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#125

yes

complemented

C₄×C₄₇

C₄⋊Q₈

yes

—

Dic₄₇

—

#2859

—

maximal, Sylow

C₂×C₄₇

C₂×#125

yes

—

C₂×C₄₇

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₇

#532

yes

—

C₂×C₄₇

#533

yes

—

—

—

—

—

C₄³

D₄₇

yes

characteristic

C₄₇

#2859

yes

characteristic, complemented, Sylow

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₇

yes

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₂×C₄²

C₂×D₄₇

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

C₂²×C₄

C₂²×D₄₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₉₄

yes

—

C₄²

Dic₉₄

yes

—

C₄²

D₁₈₈

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×Dic₉₄

yes

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂×C₄

#10625350

yes

—

C₂²

C₂²×D₁₈₈

yes

characteristic

C₂²

C₂²×Dic₉₄

yes

characteristic

C₂²

C₂²×Dic₉₄

yes

characteristic

C₂²

C₂×#10625350

yes

—

C₄

—

C₄

—

C₄

—

188

—

C₄

#13094016

yes

complemented

100

C₄

#13094024

yes

—

101

C₂

C₂×#13094016

yes

—

102

C₂

C₂×#13094024

yes

characteristic

103

C₂

#15689673

yes

—

104

C₂

#15689680

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂⁴
Fitting	C₄³×C₄₇	C₂
hypercenter	C₄³	D₄₇
hypocenter	C₄₇	#2859
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₇

commutator, socle

C₂³×C₄₇

C₂⁴

Fitting

C₄³×C₄₇

C₂

hypercenter

C₄³

D₄₇

C₄₇

G ▷ C₂³×C₄₇ ▷ C₄₇

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
45. C₄×C₄₇	#125	semidirect
58. C₄₇	#2859	semidirect
99. C₄	#13094016	semidirect

H ≅ G/N

type

45. C₄×C₄₇

#125

semidirect

58. C₄₇

#2859

semidirect

99. C₄

#13094016

semidirect

Subgroups — #20251751

Conjugacy classes of subgroups

Complements