Group #20276563 — subgroups

Subgroups — C₄×D₈₄₈ #20276563

Order 6784.

174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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×D₈₄₈	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄₂₄	C₂	1	2	yes	maximal, complemented
3	#16810449	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810425	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₂₄	C₂²	1	2	yes	—
7	C₄×D₂₁₂	—	2	2	no	—
8	D₈₄₈	C₄	1	4	yes	direct product factor
9	#13133151	C₂²	1	2	yes	—
10	#13133139	—	2	2	no	—
11	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₅₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
14	C₂×D₂₁₂	—	2	2	no	—
15	C₂×C₄×D₅₃	—	4	2	no	—
16	C₂×C₈×C₅₃	D₄	1	1	yes	characteristic
17	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
18	C₄²×C₅₃	D₄	1	1	yes	characteristic
19	#11719921	—	4	2	no	—
20	C₄⋊Dic₅₃	—	2	2	no	—
21	D₄₂₄	—	2	2	no	—
22	D₄₂₄	C₂×C₄	1	4	yes	complemented
23	C₁₆×C₅₃	—	2	1	no	—
24	C₁₆×C₅₃	C₂×C₄	1	2	yes	complemented
25	C₂²×D₅₃	—	4	2	no	—
26	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₅₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₅₃	—	4	2	no	—
30	D₂₁₂	—	2	4	no	—
31	D₂₁₂	—	4	2	no	—
32	C₄×D₅₃	—	8	4	no	—
33	C₈×C₅₃	—	2	1	no	—
34	C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₅₃	#41	1	1	yes	characteristic
36	C₂²×C₅₃	C₂×D₈	1	1	yes	characteristic
37	C₂×D₅₃	—	4	4	no	—
38	C₂×D₅₃	—	8	2	no	—
39	C₂×D₅₃	—	8	2	no	—
40	C₄×C₅₃	—	2	1	no	—
41	C₄×C₅₃	D₁₆	1	2	yes	complemented
42	C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
43	C₄×C₅₃	#135	1	1	yes	characteristic
44	Dic₅₃	—	8	2	no	—
45	C₄×D₁₆	—	53	1	no	maximal, Sylow
46	C₂×C₅₃	C₄×D₈	1	1	yes	characteristic
47	C₂×C₅₃	C₂×D₁₆	1	1	yes	characteristic
48	C₂×C₅₃	#508	1	1	yes	characteristic
49	D₅₃	—	8	4	no	—
50	C₂×D₁₆	—	53	1	no	—
51	C₄×D₈	—	53	2	no	—
52	#366	—	53	1	no	—
53	#357	—	53	2	no	—
54	C₄×C₁₆	D₅₃	1	1	yes	characteristic, complemented
55	C₅₃	C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	53	2	no	—
57	C₄×D₄	—	106	2	no	—
58	D₁₆	—	53	4	no	—
59	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
60	C₂×C₁₆	C₂×D₅₃	1	1	yes	characteristic
61	#107	—	53	2	no	—
62	#102	—	106	2	no	—
63	C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
64	C₂×D₄	—	106	2	no	—
65	C₂²×C₄	—	212	2	no	—
66	D₈	—	53	4	no	—
67	D₈	—	106	2	no	—
68	C₂×C₈	D₂₁₂	1	1	yes	characteristic
69	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
70	C₄⋊C₄	—	106	2	no	—
71	C₂²⋊C₄	—	212	2	no	—
72	C₄²	D₂₁₂	1	1	yes	characteristic
73	C₁₆	—	2	1	no	—
74	C₁₆	C₄×D₅₃	1	2	yes	complemented
75	C₂³	—	212	2	no	—
76	D₄	—	106	4	no	—
77	D₄	—	212	2	no	—
78	C₂×C₄	—	424	4	no	—
79	C₂×C₄	—	212	2	no	—
80	C₂×C₄	D₄₂₄	1	1	yes	characteristic
81	C₂×C₄	D₄₂₄	1	1	yes	characteristic
82	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
85	C₈	#11719945	1	1	yes	characteristic
86	C₂²	—	424	2	no	—
87	C₂²	—	424	2	no	—
88	C₂²	—	212	4	no	—
89	C₂²	C₂×D₄₂₄	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	424	2	no	—
92	C₄	D₈₄₈	1	2	yes	direct product factor
93	C₄	C₄×D₂₁₂	1	1	yes	characteristic
94	C₄	#13133239	1	1	yes	characteristic
95	C₂	—	424	4	no	—
96	C₂	C₄×D₄₂₄	1	1	yes	characteristic
97	C₂	C₂×D₈₄₈	1	1	yes	characteristic
98	C₂	#16811055	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₈₄₈

C₂

yes

maximal, characteristic

C₄×D₄₂₄

C₂

yes

maximal, complemented

#16810449

C₂

yes

maximal, characteristic, complemented

#16810425

C₂

yes

maximal, complemented

C₄×C₁₆×C₅₃

C₂

yes

maximal, characteristic, complemented

C₂×D₄₂₄

C₂²

yes

—

C₄×D₂₁₂

—

D₈₄₈

C₄

yes

direct product factor

#13133151

C₂²

yes

—

#13133139

—

C₂×C₁₆×C₅₃

C₂²

yes

characteristic

C₂×C₁₆×C₅₃

C₂²

yes

characteristic

C₄×C₈×C₅₃

C₂²

yes

characteristic

C₂×D₂₁₂

—

C₂×C₄×D₅₃

—

C₂×C₈×C₅₃

D₄

yes

characteristic

C₂×C₈×C₅₃

C₂³

yes

characteristic

C₄²×C₅₃

D₄

yes

characteristic

#11719921

—

C₄⋊Dic₅₃

—

D₄₂₄

—

D₄₂₄

C₂×C₄

yes

complemented

C₁₆×C₅₃

—

C₁₆×C₅₃

C₂×C₄

yes

complemented

C₂²×D₅₃

—

C₂×C₄×C₅₃

D₈

yes

characteristic

C₂×C₄×C₅₃

D₈

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×Dic₅₃

—

D₂₁₂

—

D₂₁₂

—

C₄×D₅₃

—

C₈×C₅₃

—

C₈×C₅₃

C₂²×C₄

yes

characteristic

C₈×C₅₃

#41

yes

characteristic

C₂²×C₅₃

C₂×D₈

yes

characteristic

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₄×C₅₃

—

C₄×C₅₃

D₁₆

yes

complemented

C₄×C₅₃

C₄×D₄

yes

characteristic

C₄×C₅₃

#135

yes

characteristic

Dic₅₃

—

C₄×D₁₆

—

maximal, Sylow

C₂×C₅₃

C₄×D₈

yes

characteristic

C₂×C₅₃

C₂×D₁₆

yes

characteristic

C₂×C₅₃

#508

yes

characteristic

D₅₃

—

C₂×D₁₆

—

C₄×D₈

—

#366

—

#357

—

C₄×C₁₆

D₅₃

yes

characteristic, complemented

C₅₃

C₄×D₁₆

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₄×D₄

—

106

—

D₁₆

—

C₂×C₁₆

C₂×D₅₃

yes

characteristic

C₂×C₁₆

C₂×D₅₃

yes

characteristic

#107

—

#102

—

106

—

C₄×C₈

C₂×D₅₃

yes

characteristic

C₂×D₄

—

106

—

C₂²×C₄

—

212

—

D₈

—

D₈

—

106

—

C₂×C₈

D₂₁₂

yes

characteristic

C₂×C₈

C₂²×D₅₃

yes

characteristic

C₄⋊C₄

—

106

—

C₂²⋊C₄

—

212

—

C₄²

D₂₁₂

yes

characteristic

C₁₆

—

C₁₆

C₄×D₅₃

yes

complemented

C₂³

—

212

—

D₄

—

106

—

D₄

—

212

—

C₂×C₄

—

424

—

C₂×C₄

—

212

—

C₂×C₄

D₄₂₄

yes

characteristic

C₂×C₄

D₄₂₄

yes

characteristic

C₂×C₄

C₂×D₂₁₂

yes

characteristic

C₈

—

C₈

C₂×C₄×D₅₃

yes

characteristic

C₈

#11719945

yes

characteristic

C₂²

—

424

—

C₂²

—

424

—

C₂²

—

212

—

C₂²

C₂×D₄₂₄

yes

characteristic

C₄

—

C₄

—

424

—

C₄

D₈₄₈

yes

direct product factor

C₄

C₄×D₂₁₂

yes

characteristic

C₄

#13133239

yes

characteristic

C₂

—

424

—

C₂

C₄×D₄₂₄

yes

characteristic

C₂

C₂×D₈₄₈

yes

characteristic

C₂

#16811055

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₄₂₄
commutator	C₈×C₅₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₅₃
Fitting	C₄×C₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂×D₈
hypercenter	C₄×C₁₆	D₅₃
hypocenter	C₅₃	C₄×D₁₆
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

subgroup

G/H

center

C₂×C₄

D₄₂₄

commutator

C₈×C₅₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₅₃

Fitting

C₄×C₁₆×C₅₃

C₂

socle

C₂²×C₅₃

C₂×D₈

hypercenter

C₄×C₁₆

D₅₃

hypocenter

C₅₃

C₄×D₁₆

LCS

G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

N	H ≅ G/N	type
2. C₄×D₄₂₄	C₂	semidirect
3. #16810449	C₂	semidirect
4. #16810425	C₂	semidirect
5. C₄×C₁₆×C₅₃	C₂	semidirect
8. D₈₄₈	C₄	direct (N × H)
22. D₄₂₄	C₂×C₄	semidirect
24. C₁₆×C₅₃	C₂×C₄	semidirect
41. C₄×C₅₃	D₁₆	semidirect
54. C₄×C₁₆	D₅₃	semidirect
55. C₅₃	C₄×D₁₆	semidirect
74. C₁₆	C₄×D₅₃	semidirect
92. C₄	D₈₄₈	direct (N × H)

H ≅ G/N

type

2. C₄×D₄₂₄

C₂

semidirect

3. #16810449

C₂

semidirect

4. #16810425

C₂

semidirect

5. C₄×C₁₆×C₅₃

C₂

semidirect

8. D₈₄₈

C₄

direct (N × H)

22. D₄₂₄

C₂×C₄

semidirect

24. C₁₆×C₅₃

C₂×C₄

semidirect

41. C₄×C₅₃

D₁₆

semidirect

54. C₄×C₁₆

D₅₃

semidirect

55. C₅₃

C₄×D₁₆

semidirect

74. C₁₆

C₄×D₅₃

semidirect

92. C₄

D₈₄₈

direct (N × H)

Subgroups — C₄×D₈₄₈ #20276563

Conjugacy classes of subgroups

Complements

Subgroups — C4×D848 #20276563

Conjugacy classes of subgroups

Complements

Subgroups — C₄×D₈₄₈ #20276563