Group #20245715 — subgroups

Subgroups — C₂×#15688969 #20245715

Order 6016.

840 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 840 conjugacy classes of subgroups — too many to draw. Only its 469 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	C₂²×C₄×Dic₄₇	C₂	1	2	yes	maximal
2	#15688969	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄₇⋊#95	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₇	C₂²	1	4	yes	—
6	C₂×C₄×Dic₄₇	C₄	1	16	yes	complemented
7	C₂×C₄×Dic₄₇	C₂²	1	8	yes	—
8	C₄₇⋊#95	C₂²	1	16	yes	—
9	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
10	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₇	C₄	1	8	yes	complemented
12	C₂×C₄²×C₄₇	C₂²	1	4	yes	—
13	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₄₇	—	2	8	no	—
15	C₂²×C₄×C₄₇	C₂×C₄	1	8	yes	—
16	C₂²×C₄×C₄₇	C₂×C₄	1	8	yes	—
17	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
19	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
20	C₂²×Dic₄₇	—	2	16	no	—
21	C₂²×Dic₄₇	C₂×C₄	1	16	yes	—
22	C₂²×Dic₄₇	C₂³	1	8	yes	—
23	C₄²×C₄₇	C₂×C₄	1	16	yes	complemented
24	C₄×Dic₄₇	C₂×C₄	1	32	yes	complemented
25	C₂³×C₄₇	C₂²×C₄	1	4	yes	—
26	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
27	C₂³×C₄₇	#41	1	8	yes	—
28	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₄₇	—	2	16	no	—
30	C₂×C₄×C₄₇	—	2	8	no	—
31	C₂×C₄×C₄₇	C₄²	1	16	yes	—
32	C₂×C₄×C₄₇	C₂²×C₄	1	8	yes	—
33	C₂×C₄×C₄₇	C₂²×C₄	1	8	yes	—
34	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
35	C₂×Dic₄₇	—	2	32	no	—
36	C₂×Dic₄₇	—	2	16	no	—
37	C₂×Dic₄₇	C₂²×C₄	1	16	yes	—
38	C₂²×C₄₇	C₂×C₄²	1	4	yes	—
39	C₂²×C₄₇	#117	1	16	yes	—
40	C₂²×C₄₇	#117	1	8	yes	—
41	C₂²×C₄₇	C₂³×C₄	1	2	yes	—
42	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
43	C₂²×C₄₇	C₂×#41	1	4	yes	—
44	C₄×C₄₇	—	2	8	no	—
45	C₄×C₄₇	C₂×C₄²	1	8	yes	—
46	Dic₄₇	—	2	16	no	—
47	C₂×#376	—	47	1	no	maximal, Sylow
48	C₂×C₄₇	#376	1	8	yes	complemented
49	C₂×C₄₇	C₂²×C₄²	1	1	yes	characteristic
50	C₂×C₄₇	C₂×#117	1	4	yes	—
51	C₂×C₄₇	C₂×#117	1	2	yes	—
52	C₂²×C₄²	—	47	2	no	—
53	C₂²×C₄²	D₄₇	1	1	yes	characteristic
54	#376	—	47	8	no	—
55	C₂×#95	—	47	4	no	—
56	C₄₇	C₂×#376	1	1	yes	characteristic, complemented, Sylow
57	C₂³×C₄	—	47	4	no	—
58	C₂³×C₄	C₂×D₄₇	1	2	yes	—
59	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
60	C₂×C₄²	—	47	16	no	—
61	C₂×C₄²	—	47	8	no	—
62	C₂×C₄²	Dic₄₇	1	8	yes	complemented
63	C₂×C₄²	C₂×D₄₇	1	4	yes	—
64	#95	—	47	16	no	—
65	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
66	C₂²×C₄	—	2	8	no	—
67	C₂²×C₄	—	47	16	no	—
68	C₂²×C₄	—	47	8	no	—
69	C₂²×C₄	—	94	16	no	—
70	C₂²×C₄	C₄×D₄₇	1	8	yes	—
71	C₂²×C₄	C₂×Dic₄₇	1	8	yes	—
72	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
73	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
74	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
75	C₄²	—	47	32	no	—
76	C₄²	C₂×Dic₄₇	1	16	yes	complemented
77	C₂³	C₂×C₄×D₄₇	1	4	yes	—
78	C₂³	#10625350	1	8	yes	—
79	C₂³	C₂²×Dic₄₇	1	2	yes	—
80	C₂³	C₂³×D₄₇	1	1	yes	characteristic
81	C₂×C₄	—	2	16	no	—
82	C₂×C₄	—	2	8	no	—
83	C₂×C₄	—	47	16	no	—
84	C₂×C₄	—	94	32	no	—
85	C₂×C₄	—	94	16	no	—
86	C₂×C₄	C₄×Dic₄₇	1	16	yes	—
87	C₂×C₄	C₂×C₄×D₄₇	1	8	yes	—
88	C₂×C₄	C₂²×Dic₄₇	1	8	yes	—
89	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
90	C₂²	C₂×C₄×Dic₄₇	1	4	yes	—
91	C₂²	#13093981	1	16	yes	—
92	C₂²	#13093983	1	8	yes	—
93	C₂²	C₂²×C₄×D₄₇	1	2	yes	—
94	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
95	C₂²	C₂×#10625350	1	4	yes	—
96	C₄	—	2	8	no	—
97	C₄	—	94	16	no	—
98	C₄	C₂×C₄×Dic₄₇	1	8	yes	—
99	C₂	#15688969	1	8	yes	direct product factor
100	C₂	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
101	C₂	C₂×#13093981	1	4	yes	—
102	C₂	C₂×#13093983	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×Dic₄₇

C₂

yes

maximal

#15688969

C₂

yes

maximal, direct product factor

C₂×C₄₇⋊#95

C₂

yes

maximal

C₂²×C₄²×C₄₇

C₂

yes

maximal, characteristic

C₂³×Dic₄₇

C₂²

yes

—

C₂×C₄×Dic₄₇

C₄

yes

complemented

C₂×C₄×Dic₄₇

C₂²

yes

—

C₄₇⋊#95

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

—

C₂³×C₄×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₄

yes

complemented

C₂×C₄²×C₄₇

C₂²

yes

—

C₂⁴×C₄₇

C₂³

yes

characteristic

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂×C₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

C₂³

yes

—

C₂²×Dic₄₇

—

C₂²×Dic₄₇

C₂×C₄

yes

—

C₂²×Dic₄₇

C₂³

yes

—

C₄²×C₄₇

C₂×C₄

yes

complemented

C₄×Dic₄₇

C₂×C₄

yes

complemented

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

C₂²×C₄

yes

—

C₂³×C₄₇

#41

yes

—

C₂³×C₄₇

C₂⁴

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×C₄×C₄₇

C₂²×C₄

yes

—

C₂×Dic₄₇

—

C₂×Dic₄₇

—

C₂×Dic₄₇

C₂²×C₄

yes

—

C₂²×C₄₇

C₂×C₄²

yes

—

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

#117

yes

—

C₂²×C₄₇

C₂³×C₄

yes

—

C₂²×C₄₇

C₂³×C₄

yes

characteristic

C₂²×C₄₇

C₂×#41

yes

—

C₄×C₄₇

—

C₄×C₄₇

C₂×C₄²

yes

—

Dic₄₇

—

—

C₂×C₄₇

yes

C₂×C₄₇

C₂²×C₄²

yes

characteristic

C₂×C₄₇

C₂×#117

yes

—

C₂×C₄₇

C₂×#117

yes

—

C₂²×C₄²

—

C₂²×C₄²

D₄₇

yes

characteristic

#376

—

C₂×#95

—

C₄₇

C₂×#376

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

C₂×D₄₇

yes

—

C₂³×C₄

C₂×D₄₇

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

Dic₄₇

yes

complemented

C₂×C₄²

C₂×D₄₇

yes

—

#95

—

C₂⁴

C₂²×D₄₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂×Dic₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₂²×C₄

C₂²×D₄₇

yes

—

C₄²

—

C₄²

C₂×Dic₄₇

yes

complemented

C₂³

C₂×C₄×D₄₇

yes

—

C₂³

#10625350

yes

—

C₂³

C₂²×Dic₄₇

yes

—

C₂³

C₂³×D₄₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₇

yes

—

C₂×C₄

C₂×C₄×D₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂×C₄

C₂²×Dic₄₇

yes

—

C₂²

C₂×C₄×Dic₄₇

yes

—

C₂²

#13093981

yes

—

C₂²

#13093983

yes

—

C₂²

C₂²×C₄×D₄₇

yes

—

C₂²

C₂³×Dic₄₇

yes

characteristic

C₂²

C₂×#10625350

yes

—

C₄

—

C₄

—

C₄

C₂×C₄×Dic₄₇

yes

—

C₂

#15688969

yes

direct product factor

100

C₂

C₂²×C₄×Dic₄₇

yes

characteristic

101

C₂

C₂×#13093981

yes

—

102

C₂

C₂×#13093983

yes

—

	subgroup	G/H
center	C₂³×C₄	C₂×D₄₇
commutator	C₂×C₄₇	C₂²×C₄²
Frattini	C₂³	C₂³×D₄₇
Fitting	C₂²×C₄²×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂²×C₄²	D₄₇
hypocenter	C₄₇	C₂×#376
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

subgroup

G/H

center

C₂³×C₄

C₂×D₄₇

commutator

C₂×C₄₇

C₂²×C₄²

Frattini

C₂³

C₂³×D₄₇

Fitting

C₂²×C₄²×C₄₇

C₂

socle

C₂⁴×C₄₇

C₂³

hypercenter

C₂²×C₄²

D₄₇

C₄₇

G ▷ C₂×C₄₇ ▷ C₄₇

C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

N	H ≅ G/N	type
2. #15688969	C₂	direct (N × H)
6. C₂×C₄×Dic₄₇	C₄	semidirect
11. C₂×C₄²×C₄₇	C₄	semidirect
23. C₄²×C₄₇	C₂×C₄	semidirect
24. C₄×Dic₄₇	C₂×C₄	semidirect
48. C₂×C₄₇	#376	semidirect
56. C₄₇	C₂×#376	semidirect
62. C₂×C₄²	Dic₄₇	semidirect
76. C₄²	C₂×Dic₄₇	semidirect
99. C₂	#15688969	direct (N × H)

H ≅ G/N

type

2. #15688969

C₂

direct (N × H)

6. C₂×C₄×Dic₄₇

C₄

semidirect

11. C₂×C₄²×C₄₇

C₄

semidirect

23. C₄²×C₄₇

C₂×C₄

semidirect

24. C₄×Dic₄₇

C₂×C₄

semidirect

48. C₂×C₄₇

#376

semidirect

56. C₄₇

C₂×#376

semidirect

62. C₂×C₄²

Dic₄₇

semidirect

76. C₄²

C₂×Dic₄₇

semidirect

99. C₂

#15688969

direct (N × H)

Subgroups — C₂×#15688969 #20245715

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15688969 #20245715

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688969 #20245715