Group #20290933 — subgroups

Subgroups — C₂×#16811516 #20290933

Order 6784.

168 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 90 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×#13133291	C₂	1	2	yes	maximal
2	#16811516	C₂	1	4	yes	maximal, direct product factor
3	C₂×#13133127	C₂	1	1	yes	maximal, characteristic
4	#13133291	C₄	1	4	yes	complemented
5	#13133291	C₂²	1	4	yes	—
6	C₂×#11719910	C₄	1	4	yes	complemented
7	C₂²×#88322	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₅₃	C₄	1	1	yes	characteristic
9	#13133127	C₄	1	2	yes	—
10	#13133127	C₂²	1	2	yes	—
11	C₂²×C₈×C₅₃	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₅₃	—	2	1	no	—
14	C₂×C₈×C₅₃	—	2	1	no	—
15	C₂×C₈×C₅₃	—	2	1	no	—
16	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
17	C₄×Dic₅₃	—	2	1	no	—
18	C₄×Dic₅₃	C₂×C₄	1	2	yes	—
19	C₂×#88322	C₂×C₄	1	1	yes	characteristic
20	C₂×#88322	C₂×C₄	1	2	yes	—
21	C₂×#88322	C₂×C₄	1	2	yes	—
22	C₂×#88322	C₂³	1	1	yes	characteristic
23	#11719910	C₂×C₄	1	8	yes	complemented
24	C₂³×C₅₃	M₁₆	1	1	yes	characteristic
25	C₂×C₄×C₅₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₅₃	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₅₃	M₁₆	1	1	yes	characteristic
28	C₂×C₄×C₅₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₅₃	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₅₃	—	2	2	no	—
32	C₂×Dic₅₃	—	4	2	no	—
33	C₈×C₅₃	—	2	2	no	—
34	#88322	C₄²	1	2	yes	—
35	#88322	C₂²×C₄	1	2	yes	—
36	C₂²×C₅₃	—	2	2	no	—
37	C₂²×C₅₃	#97	1	1	yes	characteristic
38	C₂²×C₅₃	#97	1	1	yes	characteristic
39	C₂²×C₅₃	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₅₃	#97	1	1	yes	characteristic
41	C₄×C₅₃	#97	1	1	yes	characteristic
42	C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
43	C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
44	Dic₅₃	—	4	2	no	—
45	C₂×#347	—	53	1	no	maximal, Sylow
46	C₂×C₅₃	—	2	1	no	—
47	C₂×C₅₃	—	2	1	no	—
48	C₂×C₅₃	#347	1	2	yes	complemented
49	C₂×C₅₃	C₂×#97	1	1	yes	characteristic
50	C₂×M₃₂	—	53	2	no	—
51	C₂×#97	—	53	1	no	—
52	#347	—	53	4	no	—
53	C₅₃	C₂×#347	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	—	53	1	no	—
55	C₂²×C₈	#6157	1	1	yes	characteristic
56	C₂×C₄²	—	53	1	no	—
57	M₃₂	—	53	4	no	—
58	M₃₂	—	53	4	no	—
59	C₂×C₁₆	—	53	4	no	—
60	#97	—	53	2	no	—
61	#97	—	53	2	no	—
62	C₂²×C₄	—	106	1	no	—
63	C₂²×C₄	C₂×#6157	1	1	yes	characteristic
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	—	53	2	no	—
67	C₂×C₈	—	53	2	no	—
68	C₂×C₈	—	53	1	no	—
69	C₂×C₈	—	53	1	no	—
70	C₂×C₈	C₂×#6157	1	2	yes	—
71	C₄²	—	53	2	no	—
72	C₄²	—	106	1	no	—
73	C₁₆	—	53	8	no	—
74	C₂³	#11719936	1	1	yes	characteristic
75	C₂×C₄	—	106	2	no	—
76	C₂×C₄	—	212	2	no	—
77	C₂×C₄	#11719936	1	1	yes	characteristic
78	C₂×C₄	C₄×#6157	1	1	yes	characteristic
79	C₂×C₄	C₄×#6157	1	1	yes	characteristic
80	C₂×C₄	#11719940	1	1	yes	characteristic
81	C₂×C₄	#11719940	1	1	yes	characteristic
82	C₂×C₄	C₂²×#6157	1	1	yes	characteristic
83	C₈	—	2	2	no	—
84	C₈	—	53	2	no	—
85	C₈	—	53	2	no	—
86	C₂²	—	2	2	no	—
87	C₂²	#13133272	1	1	yes	characteristic
88	C₂²	#13133272	1	1	yes	characteristic
89	C₂²	C₂×#11719936	1	1	yes	characteristic
90	C₄	—	212	2	no	—
91	C₄	#13133272	1	1	yes	characteristic
92	C₄	#13133272	1	1	yes	characteristic
93	C₄	C₂×C₄×#6157	1	1	yes	characteristic
94	C₄	C₂×#11719940	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	—	2	1	no	—
97	C₂	#16811516	1	2	yes	direct product factor
98	C₂	C₂×#13133272	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13133291

C₂

yes

maximal

#16811516

C₂

yes

maximal, direct product factor

C₂×#13133127

C₂

yes

maximal, characteristic

#13133291

C₄

yes

complemented

#13133291

C₂²

yes

—

C₂×#11719910

C₄

yes

complemented

C₂²×#88322

C₂²

yes

characteristic

C₂×C₄×Dic₅₃

C₄

yes

characteristic

#13133127

C₄

yes

—

#13133127

C₂²

yes

—

C₂²×C₈×C₅₃

C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×C₄

yes

characteristic

C₂²×Dic₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂×C₄

yes

—

C₄×Dic₅₃

—

C₄×Dic₅₃

C₂×C₄

yes

—

C₂×#88322

C₂×C₄

yes

characteristic

C₂×#88322

C₂×C₄

yes

—

C₂×#88322

C₂×C₄

yes

—

C₂×#88322

C₂³

yes

characteristic

#11719910

C₂×C₄

yes

complemented

C₂³×C₅₃

M₁₆

yes

characteristic

C₂×C₄×C₅₃

C₄²

yes

characteristic

C₂×C₄×C₅₃

C₄²

yes

characteristic

C₂×C₄×C₅₃

M₁₆

yes

characteristic

C₂×C₄×C₅₃

M₁₆

yes

characteristic

C₂×C₄×C₅₃

M₁₆

yes

characteristic

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₈×C₅₃

—

#88322

C₄²

yes

—

#88322

C₂²×C₄

yes

—

C₂²×C₅₃

—

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

C₂×M₁₆

yes

C₄×C₅₃

yes

C₄×C₅₃

yes

C₄×C₅₃

C₂×C₄²

yes

characteristic

C₄×C₅₃

C₂×M₁₆

yes

characteristic

Dic₅₃

—

C₂×#347

—

maximal, Sylow

C₂×C₅₃

—

C₂×C₅₃

—

C₂×C₅₃

#347

yes

complemented

C₂×C₅₃

C₂×#97

yes

characteristic

C₂×M₃₂

—

C₂×#97

—

#347

—

C₅₃

C₂×#347

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

#6157

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#97

—

#97

—

C₂²×C₄

—

106

—

C₂²×C₄

C₂×#6157

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#6157

yes

—

C₄²

—

C₄²

—

106

—

C₁₆

—

C₂³

#11719936

yes

characteristic

C₂×C₄

—

106

—

C₂×C₄

—

212

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×#6157

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

212

—

C₄

yes

C₄

yes

C₄

C₂×C₄×#6157

yes

characteristic

C₄

C₂×#11719940

yes

characteristic

C₂

—

C₂

—

C₂

#16811516

yes

direct product factor

C₂

C₂×#13133272

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#6157
commutator	C₄×C₅₃	C₂×C₄²
Frattini	C₂×C₄	C₂²×#6157
Fitting	C₂²×C₈×C₅₃	C₄
socle	C₂²×C₅₃	#97
hypercenter	C₂²×C₈	#6157
hypocenter	C₅₃	C₂×#347
LCS	G ▷ C₄×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂×C₄

C₄×#6157

commutator

C₄×C₅₃

C₂×C₄²

Frattini

C₂×C₄

C₂²×#6157

Fitting

C₂²×C₈×C₅₃

C₄

C₂²×C₅₃

C₂²×C₈

C₅₃

G ▷ C₄×C₅₃ ▷ C₅₃

C₁ ◁ C₂×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #16811516	C₂	direct (N × H)
4. #13133291	C₄	semidirect
6. C₂×#11719910	C₄	semidirect
23. #11719910	C₂×C₄	semidirect
48. C₂×C₅₃	#347	semidirect
53. C₅₃	C₂×#347	semidirect
97. C₂	#16811516	direct (N × H)

H ≅ G/N

type

2. #16811516

C₂

direct (N × H)

4. #13133291

C₄

semidirect

6. C₂×#11719910

C₄

semidirect

23. #11719910

C₂×C₄

semidirect

48. C₂×C₅₃

#347

semidirect

53. C₅₃

C₂×#347

semidirect

97. C₂

#16811516

direct (N × H)

Subgroups — C₂×#16811516 #20290933

Conjugacy classes of subgroups

Complements

Subgroups — C2×#16811516 #20290933

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16811516 #20290933