Group #20266252 — subgroups

Subgroups — C₂×#15692342 #20266252

Order 6464.

266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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	#15692342	C₂	1	8	yes	maximal, direct product factor
2	C₂×#13108084	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13108083	C₂	1	2	yes	maximal, complemented
4	C₂×D₁₀₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#11717581	C₂	1	2	yes	maximal, complemented
6	C₂×#13108073	C₂	1	1	yes	maximal, characteristic
7	#13108084	C₂²	1	4	yes	complemented
8	#13108083	C₂²	1	8	yes	complemented
9	D₁₀₁⋊C₈	C₂²	1	4	yes	complemented
10	C₂×#11717581	C₂²	1	1	yes	characteristic
11	C₂×#11717581	C₂²	1	2	yes	—
12	C₂×#11717581	C₂²	1	1	yes	characteristic
13	C₂×#11717581	C₂²	1	8	yes	complemented
14	#13108073	C₄	1	4	yes	—
15	#13108073	C₂²	1	4	yes	—
16	C₂×Dic₂₀₂	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₁₀₁	C₄	1	2	yes	—
18	C₂²×Dic₁₀₁	C₂²	1	2	yes	—
19	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
20	C₂×D₄×C₁₀₁	C₄	1	1	yes	characteristic
21	C₂³×C₁₀₁	C₂×C₄	1	2	yes	—
22	C₂²×D₁₀₁	C₂×C₄	1	1	yes	characteristic
23	D₄×C₁₀₁	C₂×C₄	1	4	yes	—
24	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
25	C₂²⋊D₁₀₁	C₂×C₄	1	8	yes	—
26	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
27	C₂×Dic₁₀₁	C₂×C₄	1	4	yes	—
28	C₂×Dic₁₀₁	C₂³	1	1	yes	characteristic
29	C₂×Dic₁₀₁	C₂³	1	4	yes	—
30	C₄×D₁₀₁	C₂×C₄	1	2	yes	—
31	C₄×D₁₀₁	C₂³	1	2	yes	—
32	Dic₂₀₂	C₂×C₄	1	4	yes	—
33	#11717581	C₂³	1	2	yes	—
34	#11717581	C₂³	1	4	yes	—
35	#11717581	C₂³	1	2	yes	—
36	C₂²×C₁₀₁	—	2	4	no	—
37	C₂²×C₁₀₁	C₂²×C₄	1	4	yes	—
38	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×D₁₀₁	—	2	2	no	—
40	C₂×D₁₀₁	C₂²×C₄	1	2	yes	—
41	C₄×C₁₀₁	C₂²×C₄	1	2	yes	—
42	Dic₁₀₁	C₂²×C₄	1	4	yes	—
43	Dic₁₀₁	C₂²×C₄	1	1	yes	characteristic
44	Dic₁₀₁	C₂⁴	1	1	yes	characteristic
45	C₂×C₁₀₁	—	2	4	no	—
46	C₂×C₁₀₁	#131	1	2	yes	complemented
47	C₂×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
48	D₁₀₁	—	2	2	no	—
49	C₁₀₁	C₂×#131	1	1	yes	characteristic, complemented, Sylow
50	C₂×#131	—	101	1	no	maximal, Sylow
51	C₂×#41	—	101	1	no	—
52	#131	—	101	8	no	—
53	C₂×M₁₆	—	101	2	no	—
54	C₂×M₁₆	—	101	1	no	—
55	C₂²×C₈	—	101	2	no	—
56	C₂²×C₈	—	101	1	no	—
57	#41	—	101	4	no	—
58	#41	—	101	4	no	—
59	C₂×Q₈	—	101	1	no	—
60	C₂×D₄	—	101	2	no	—
61	C₂×D₄	#87938	1	1	yes	characteristic
62	C₂²×C₄	—	101	2	no	—
63	C₂²×C₄	—	101	1	no	—
64	M₁₆	—	101	8	no	—
65	M₁₆	—	101	4	no	—
66	C₂×C₈	—	101	1	no	—
67	C₂×C₈	—	101	2	no	—
68	C₂×C₈	—	101	1	no	—
69	C₂×C₈	—	101	8	no	—
70	C₂×C₈	—	101	4	no	—
71	C₂³	—	101	1	no	—
72	C₂³	C₂×#87938	1	2	yes	—
73	Q₈	—	101	4	no	—
74	D₄	—	101	8	no	—
75	D₄	C₂×#87938	1	4	yes	—
76	C₂×C₄	—	101	4	no	—
77	C₂×C₄	—	101	4	no	—
78	C₂×C₄	—	101	1	no	—
79	C₂×C₄	—	101	2	no	—
80	C₂×C₄	—	101	2	no	—
81	C₂×C₄	—	101	2	no	—
82	C₂×C₄	C₂×#87938	1	1	yes	characteristic
83	C₈	—	101	2	no	—
84	C₈	—	101	4	no	—
85	C₈	—	101	2	no	—
86	C₂²	—	2	4	no	—
87	C₂²	—	101	2	no	—
88	C₂²	—	202	2	no	—
89	C₂²	C₂²×#87938	1	4	yes	—
90	C₂²	C₂²×#87938	1	1	yes	characteristic
91	C₄	—	101	1	no	—
92	C₄	—	101	1	no	—
93	C₄	—	101	4	no	—
94	C₄	C₂²×#87938	1	2	yes	—
95	C₂	—	2	4	no	—
96	C₂	—	202	2	no	—
97	C₂	#15692342	1	2	yes	direct product factor
98	C₂	C₂³×#87938	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#15692342

C₂

yes

maximal, direct product factor

C₂×#13108084

C₂

yes

maximal, characteristic, complemented

C₂×#13108083

C₂

yes

maximal, complemented

C₂×D₁₀₁⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂²×#11717581

C₂

yes

maximal, complemented

C₂×#13108073

C₂

yes

maximal, characteristic

#13108084

C₂²

yes

complemented

#13108083

C₂²

yes

complemented

D₁₀₁⋊C₈

C₂²

yes

complemented

C₂×#11717581

C₂²

yes

characteristic

C₂×#11717581

C₂²

yes

—

C₂×#11717581

C₂²

yes

characteristic

C₂×#11717581

C₂²

yes

complemented

#13108073

C₄

yes

—

#13108073

C₂²

yes

—

C₂×Dic₂₀₂

C₄

yes

characteristic

C₂×C₂²⋊D₁₀₁

C₄

yes

—

C₂²×Dic₁₀₁

C₂²

yes

—

C₂×C₄×D₁₀₁

C₂²

yes

characteristic

C₂×D₄×C₁₀₁

C₄

yes

characteristic

C₂³×C₁₀₁

C₂×C₄

yes

—

C₂²×D₁₀₁

C₂×C₄

yes

characteristic

D₄×C₁₀₁

C₂×C₄

yes

—

C₂×C₄×C₁₀₁

C₂×C₄

yes

characteristic

C₂²⋊D₁₀₁

C₂×C₄

yes

—

C₂×Dic₁₀₁

C₂×C₄

yes

—

C₂×Dic₁₀₁

C₂×C₄

yes

—

C₂×Dic₁₀₁

C₂³

yes

characteristic

C₂×Dic₁₀₁

C₂³

yes

—

C₄×D₁₀₁

C₂×C₄

yes

—

C₄×D₁₀₁

C₂³

yes

—

Dic₂₀₂

C₂×C₄

yes

—

#11717581

C₂³

yes

—

#11717581

C₂³

yes

—

#11717581

C₂³

yes

—

C₂²×C₁₀₁

—

C₂²×C₁₀₁

C₂²×C₄

yes

—

C₂²×C₁₀₁

C₂²×C₄

yes

characteristic

C₂×D₁₀₁

—

C₂×D₁₀₁

C₂²×C₄

yes

—

C₄×C₁₀₁

C₂²×C₄

yes

—

Dic₁₀₁

C₂²×C₄

yes

—

Dic₁₀₁

C₂²×C₄

yes

characteristic

Dic₁₀₁

C₂⁴

yes

characteristic

C₂×C₁₀₁

—

C₂×C₁₀₁

#131

yes

complemented

C₂×C₁₀₁

C₂³×C₄

yes

characteristic

D₁₀₁

—

C₁₀₁

C₂×#131

yes

characteristic, complemented, Sylow

C₂×#131

—

101

maximal, Sylow

C₂×#41

—

101

—

#131

—

101

—

C₂×M₁₆

—

101

—

C₂×M₁₆

—

101

—

C₂²×C₈

—

101

—

C₂²×C₈

—

101

—

#41

—

101

—

#41

—

101

—

C₂×Q₈

—

101

—

C₂×D₄

—

101

—

C₂×D₄

#87938

yes

characteristic

C₂²×C₄

—

101

—

C₂²×C₄

—

101

—

M₁₆

—

101

—

M₁₆

—

101

—

C₂×C₈

—

101

—

C₂×C₈

—

101

—

C₂×C₈

—

101

—

C₂×C₈

—

101

—

C₂×C₈

—

101

—

C₂³

—

101

—

C₂³

C₂×#87938

yes

—

Q₈

—

101

—

D₄

—

101

—

D₄

C₂×#87938

yes

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

—

101

—

C₂×C₄

C₂×#87938

yes

characteristic

C₈

—

101

—

C₈

—

101

—

C₈

—

101

—

C₂²

—

C₂²

—

101

—

C₂²

—

202

—

C₂²

C₂²×#87938

yes

—

C₂²

C₂²×#87938

yes

characteristic

C₄

—

101

—

C₄

—

101

—

C₄

—

101

—

C₄

C₂²×#87938

yes

—

C₂

—

C₂

—

202

—

C₂

#15692342

yes

direct product factor

C₂

C₂³×#87938

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×#87938
commutator	C₂×C₁₀₁	C₂³×C₄
Frattini	C₂	C₂³×#87938
Fitting	C₂×D₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²×C₄
hypercenter	C₂×D₄	#87938
hypocenter	C₁₀₁	C₂×#131
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×D₄

subgroup

G/H

center

C₂²

C₂²×#87938

commutator

C₂×C₁₀₁

C₂³×C₄

Frattini

C₂

C₂³×#87938

Fitting

C₂×D₄×C₁₀₁

C₄

socle

C₂²×C₁₀₁

C₂²×C₄

C₂×D₄

C₁₀₁

G ▷ C₂×C₁₀₁ ▷ C₁₀₁

C₁ ◁ C₂² ◁ C₂×D₄

N	H ≅ G/N	type
1. #15692342	C₂	direct (N × H)
2. C₂×#13108084	C₂	semidirect
3. C₂×#13108083	C₂	semidirect
4. C₂×D₁₀₁⋊C₈	C₂	semidirect
5. C₂²×#11717581	C₂	semidirect
7. #13108084	C₂²	semidirect
8. #13108083	C₂²	semidirect
9. D₁₀₁⋊C₈	C₂²	semidirect
13. C₂×#11717581	C₂²	semidirect
46. C₂×C₁₀₁	#131	semidirect
49. C₁₀₁	C₂×#131	semidirect
97. C₂	#15692342	direct (N × H)

H ≅ G/N

type

1. #15692342

C₂

direct (N × H)

2. C₂×#13108084

C₂

semidirect

3. C₂×#13108083

C₂

semidirect

4. C₂×D₁₀₁⋊C₈

C₂

semidirect

5. C₂²×#11717581

C₂

semidirect

7. #13108084

C₂²

semidirect

8. #13108083

C₂²

semidirect

9. D₁₀₁⋊C₈

C₂²

semidirect

13. C₂×#11717581

C₂²

semidirect

46. C₂×C₁₀₁

#131

semidirect

49. C₁₀₁

C₂×#131

semidirect

97. C₂

#15692342

direct (N × H)

Subgroups — C₂×#15692342 #20266252

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15692342 #20266252

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15692342 #20266252