Group #20253800 — subgroups

Subgroups — C₂×#15689500 #20253800

Order 6016.

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

normal subgroups only

This group has 760 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	C₂²×D₃₇₆	C₂	1	4	yes	maximal, complemented
2	C₂×#13094021	C₂	1	2	yes	maximal, complemented
3	#15689500	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₈₈	—	2	4	no	—
6	C₂²×D₁₈₈	C₂²	1	4	yes	—
7	C₂×D₃₇₆	—	2	16	no	—
8	C₂×D₃₇₆	C₂²	1	16	yes	complemented
9	#13094021	—	2	4	no	—
10	#13094021	C₂²	1	8	yes	complemented
11	C₂²×C₈×C₄₇	C₂²	1	2	yes	—
12	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₄₇	C₂²	1	4	yes	complemented
14	C₂³×D₄₇	—	2	4	no	—
15	C₂²×C₄×C₄₇	D₄	1	2	yes	—
16	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
17	C₂×D₁₈₈	—	2	16	no	—
18	C₂×D₁₈₈	—	2	4	no	—
19	C₂×D₁₈₈	—	2	16	no	—
20	C₂×D₁₈₈	—	4	16	no	—
21	C₂×D₁₈₈	C₂³	1	8	yes	—
22	C₂×C₈×C₄₇	D₄	1	8	yes	complemented
23	C₂×C₈×C₄₇	C₂³	1	4	yes	—
24	C₄²×C₄₇	D₄	1	2	yes	—
25	C₄²×C₄₇	C₂³	1	2	yes	—
26	D₃₇₆	—	2	32	no	—
27	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₂²×D₄₇	—	2	8	no	—
29	C₂²×D₄₇	—	4	8	no	—
30	C₂²×D₄₇	—	4	16	no	—
31	C₂×C₄×C₄₇	D₈	1	8	yes	complemented
32	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
35	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
36	D₁₈₈	—	2	16	no	—
37	D₁₈₈	—	4	8	no	—
38	D₁₈₈	—	4	32	no	—
39	C₈×C₄₇	C₂×D₄	1	8	yes	complemented
40	C₂²×C₄₇	#127	1	2	yes	—
41	C₂²×C₄₇	C₂×D₈	1	4	yes	—
42	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
43	C₂×D₄₇	—	4	8	no	—
44	C₂×D₄₇	—	4	16	no	—
45	C₂×D₄₇	—	8	16	no	—
46	C₄×C₄₇	#127	1	2	yes	—
47	C₄×C₄₇	C₂×D₈	1	8	yes	complemented
48	C₄×C₄₇	C₂²×D₄	1	2	yes	—
49	C₂×#493	—	47	1	no	maximal, Sylow
50	C₂×C₄₇	#493	1	4	yes	complemented
51	C₂×C₄₇	C₂×#127	1	1	yes	characteristic
52	C₂×C₄₇	C₂²×D₈	1	2	yes	—
53	D₄₇	—	8	8	no	—
54	C₂²×D₈	—	47	4	no	—
55	C₂×#127	—	47	2	no	—
56	#493	—	47	8	no	—
57	C₂×C₄×C₈	D₄₇	1	1	yes	characteristic, complemented
58	C₄₇	C₂×#493	1	1	yes	characteristic, complemented, Sylow
59	C₂²×D₄	—	47	4	no	—
60	C₂²×D₄	—	94	4	no	—
61	C₂×D₈	—	47	16	no	—
62	C₂×D₈	—	94	16	no	—
63	C₂²×C₈	C₂×D₄₇	1	2	yes	—
64	#127	—	47	8	no	—
65	#127	—	94	4	no	—
66	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
67	C₄×C₈	C₂×D₄₇	1	4	yes	complemented
68	C₂⁴	—	94	4	no	—
69	C₂×D₄	—	47	8	no	—
70	C₂×D₄	—	94	16	no	—
71	C₂×D₄	—	94	16	no	—
72	C₂×D₄	—	94	4	no	—
73	C₂×D₄	—	188	16	no	—
74	C₂²×C₄	D₁₈₈	1	2	yes	—
75	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
76	D₈	—	94	32	no	—
77	C₂×C₈	D₁₈₈	1	8	yes	complemented
78	C₂×C₈	C₂²×D₄₇	1	4	yes	—
79	C₄²	D₁₈₈	1	2	yes	—
80	C₄²	C₂²×D₄₇	1	2	yes	—
81	C₂³	—	94	8	no	—
82	C₂³	—	188	8	no	—
83	C₂³	—	188	16	no	—
84	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
85	D₄	—	94	16	no	—
86	D₄	—	188	8	no	—
87	D₄	—	188	32	no	—
88	C₂×C₄	D₃₇₆	1	8	yes	complemented
89	C₂×C₄	C₂×D₁₈₈	1	1	yes	characteristic
90	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
91	C₂×C₄	C₂×D₁₈₈	1	4	yes	—
92	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
93	C₈	C₂×D₁₈₈	1	8	yes	complemented
94	C₂²	—	376	16	no	—
95	C₂²	—	188	16	no	—
96	C₂²	—	188	8	no	—
97	C₂²	#13094021	1	2	yes	—
98	C₂²	C₂×D₃₇₆	1	4	yes	—
99	C₂²	C₂²×D₁₈₈	1	1	yes	characteristic
100	C₄	#13094021	1	2	yes	—
101	C₄	C₂×D₃₇₆	1	8	yes	complemented
102	C₄	C₂²×D₁₈₈	1	2	yes	—
103	C₂	—	376	8	no	—
104	C₂	#15689500	1	4	yes	direct product factor
105	C₂	C₂×#13094021	1	1	yes	characteristic
106	C₂	C₂²×D₃₇₆	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₃₇₆

C₂

yes

maximal, complemented

C₂×#13094021

C₂

yes

maximal, complemented

#15689500

C₂

yes

maximal, direct product factor

C₂×C₄×C₈×C₄₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₈₈

—

C₂²×D₁₈₈

C₂²

yes

—

C₂×D₃₇₆

—

C₂×D₃₇₆

C₂²

yes

complemented

#13094021

—

#13094021

C₂²

yes

complemented

C₂²×C₈×C₄₇

C₂²

yes

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

complemented

C₂³×D₄₇

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

—

C₂×D₁₈₈

C₂³

yes

—

C₂×C₈×C₄₇

D₄

yes

complemented

C₂×C₈×C₄₇

C₂³

yes

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

—

D₃₇₆

—

C₂³×C₄₇

C₂×D₄

yes

characteristic

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂²×D₄₇

—

C₂×C₄×C₄₇

D₈

yes

complemented

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

D₁₈₈

—

D₁₈₈

—

D₁₈₈

—

C₈×C₄₇

C₂×D₄

yes

complemented

C₂²×C₄₇

#127

yes

—

C₂²×C₄₇

C₂×D₈

yes

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₂×D₄₇

—

C₂×D₄₇

—

C₂×D₄₇

—

C₄×C₄₇

#127

yes

—

C₄×C₄₇

C₂×D₈

yes

complemented

C₄×C₄₇

C₂²×D₄

yes

—

—

C₂×C₄₇

yes

C₂×C₄₇

yes

C₂×C₄₇

C₂²×D₈

yes

—

D₄₇

—

C₂²×D₈

—

C₂×#127

—

#493

—

C₂×C₄×C₈

D₄₇

yes

characteristic, complemented

C₄₇

C₂×#493

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

C₂×D₈

—

C₂×D₈

—

C₂²×C₈

C₂×D₄₇

yes

—

#127

—

#127

—

C₂×C₄²

C₂×D₄₇

yes

characteristic

C₄×C₈

C₂×D₄₇

yes

complemented

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

188

—

C₂²×C₄

D₁₈₈

yes

—

C₂²×C₄

C₂²×D₄₇

yes

characteristic

D₈

—

C₂×C₈

D₁₈₈

yes

complemented

C₂×C₈

C₂²×D₄₇

yes

—

C₄²

D₁₈₈

yes

—

C₄²

C₂²×D₄₇

yes

—

C₂³

—

C₂³

—

188

—

C₂³

—

188

—

C₂³

C₂×D₁₈₈

yes

characteristic

D₄

—

D₄

—

188

—

D₄

—

188

—

C₂×C₄

D₃₇₆

yes

complemented

C₂×C₄

C₂×D₁₈₈

yes

characteristic

C₂×C₄

C₂×D₁₈₈

yes

—

C₂×C₄

C₂×D₁₈₈

yes

—

C₂×C₄

C₂³×D₄₇

yes

characteristic

C₈

C₂×D₁₈₈

yes

complemented

C₂²

—

376

—

C₂²

—

188

—

C₂²

—

188

—

C₂²

#13094021

yes

—

C₂²

C₂×D₃₇₆

yes

—

C₂²

C₂²×D₁₈₈

yes

characteristic

100

C₄

#13094021

yes

—

101

C₄

C₂×D₃₇₆

yes

complemented

102

C₄

C₂²×D₁₈₈

yes

—

103

C₂

—

376

—

104

C₂

#15689500

yes

direct product factor

105

C₂

C₂×#13094021

yes

characteristic

106

C₂

C₂²×D₃₇₆

yes

—

	subgroup	G/H
center	C₂³	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂×C₄×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂×C₄×C₈	D₄₇
hypocenter	C₄₇	C₂×#493
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂³

C₂×D₁₈₈

commutator

C₂×C₄×C₄₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₇

Fitting

C₂×C₄×C₈×C₄₇

C₂

socle

C₂³×C₄₇

C₂×D₄

hypercenter

C₂×C₄×C₈

D₄₇

hypocenter

C₄₇

C₂×#493

LCS

G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
1. C₂²×D₃₇₆	C₂	semidirect
2. C₂×#13094021	C₂	semidirect
3. #15689500	C₂	direct (N × H)
4. C₂×C₄×C₈×C₄₇	C₂	semidirect
8. C₂×D₃₇₆	C₂²	semidirect
10. #13094021	C₂²	semidirect
13. C₄×C₈×C₄₇	C₂²	semidirect
22. C₂×C₈×C₄₇	D₄	semidirect
31. C₂×C₄×C₄₇	D₈	semidirect
39. C₈×C₄₇	C₂×D₄	semidirect
47. C₄×C₄₇	C₂×D₈	semidirect
50. C₂×C₄₇	#493	semidirect
57. C₂×C₄×C₈	D₄₇	semidirect
58. C₄₇	C₂×#493	semidirect
67. C₄×C₈	C₂×D₄₇	semidirect
77. C₂×C₈	D₁₈₈	semidirect
88. C₂×C₄	D₃₇₆	semidirect
93. C₈	C₂×D₁₈₈	semidirect
101. C₄	C₂×D₃₇₆	semidirect
104. C₂	#15689500	direct (N × H)

H ≅ G/N

type

1. C₂²×D₃₇₆

C₂

semidirect

2. C₂×#13094021

C₂

semidirect

3. #15689500

C₂

direct (N × H)

4. C₂×C₄×C₈×C₄₇

C₂

semidirect

8. C₂×D₃₇₆

C₂²

semidirect

10. #13094021

C₂²

semidirect

13. C₄×C₈×C₄₇

C₂²

semidirect

22. C₂×C₈×C₄₇

D₄

semidirect

31. C₂×C₄×C₄₇

D₈

semidirect

39. C₈×C₄₇

C₂×D₄

semidirect

47. C₄×C₄₇

C₂×D₈

semidirect

50. C₂×C₄₇

#493

semidirect

57. C₂×C₄×C₈

D₄₇

semidirect

58. C₄₇

C₂×#493

semidirect

67. C₄×C₈

C₂×D₄₇

semidirect

77. C₂×C₈

D₁₈₈

semidirect

88. C₂×C₄

D₃₇₆

semidirect

93. C₈

C₂×D₁₈₈

semidirect

101. C₄

C₂×D₃₇₆

semidirect

104. C₂

#15689500

direct (N × H)

Subgroups — C₂×#15689500 #20253800

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15689500 #20253800

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689500 #20253800