Group #20244990 — subgroups

Subgroups — C₂×#15688901 #20244990

Order 6016.

168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13093964	C₂	1	2	yes	maximal
2	#15688901	C₂	1	4	yes	maximal, direct product factor
3	C₂×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
4	#13093964	C₄	1	4	yes	complemented
5	#13093964	C₂²	1	4	yes	—
6	C₂×C₄₇⋊C₁₆	C₄	1	4	yes	complemented
7	C₂²×C₈×C₄₇	C₄	1	1	yes	characteristic
8	C₂²×C₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₄₇	C₄	1	1	yes	characteristic
10	#97×C₄₇	C₄	1	2	yes	—
11	#97×C₄₇	C₂²	1	2	yes	—
12	C₂²×C₄×C₄₇	—	2	1	no	—
13	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₄₇	—	2	1	no	—
15	C₂×C₈×C₄₇	—	2	1	no	—
16	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₄₇	C₂×C₄	1	2	yes	—
20	C₂×C₈×C₄₇	C₂³	1	1	yes	characteristic
21	C₄²×C₄₇	—	2	1	no	—
22	C₄²×C₄₇	C₂×C₄	1	2	yes	—
23	C₄₇⋊C₁₆	C₂×C₄	1	8	yes	complemented
24	C₂³×C₄₇	M₁₆	1	1	yes	characteristic
25	C₂×C₄×C₄₇	—	2	2	no	—
26	C₂×C₄×C₄₇	—	4	2	no	—
27	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₄₇	M₁₆	1	1	yes	characteristic
32	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₄₇	—	2	2	no	—
34	C₈×C₄₇	C₄²	1	2	yes	—
35	C₈×C₄₇	C₂²×C₄	1	2	yes	—
36	C₂²×C₄₇	—	2	2	no	—
37	C₂²×C₄₇	#97	1	1	yes	characteristic
38	C₂²×C₄₇	#97	1	1	yes	characteristic
39	C₂²×C₄₇	C₂×M₁₆	1	1	yes	characteristic
40	C₄×C₄₇	—	4	2	no	—
41	C₄×C₄₇	#97	1	1	yes	characteristic
42	C₄×C₄₇	#97	1	1	yes	characteristic
43	C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
44	C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
45	C₂×#347	—	47	1	no	maximal, Sylow
46	C₂×C₄₇	—	2	1	no	—
47	C₂×C₄₇	—	2	1	no	—
48	C₂×C₄₇	#347	1	2	yes	complemented
49	C₂×C₄₇	C₂×#97	1	1	yes	characteristic
50	C₂×M₃₂	—	47	2	no	—
51	C₂×#97	D₄₇	1	1	yes	characteristic
52	#347	—	47	4	no	—
53	C₄₇	C₂×#347	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₈	Dic₄₇	1	1	yes	characteristic
55	C₂²×C₈	C₂×D₄₇	1	1	yes	characteristic
56	C₂×C₄²	Dic₄₇	1	1	yes	characteristic
57	M₃₂	—	47	4	no	—
58	M₃₂	—	47	4	no	—
59	C₂×C₁₆	—	47	4	no	—
60	#97	Dic₄₇	1	2	yes	—
61	#97	C₂×D₄₇	1	2	yes	—
62	C₂²×C₄	—	2	1	no	—
63	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	C₄×D₄₇	1	2	yes	—
67	C₂×C₈	C₄×D₄₇	1	2	yes	—
68	C₂×C₈	C₂×Dic₄₇	1	2	yes	—
69	C₂×C₈	C₂×Dic₄₇	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₄₇	1	1	yes	characteristic
71	C₄²	—	2	1	no	—
72	C₄²	C₂×Dic₄₇	1	2	yes	—
73	C₁₆	—	47	8	no	—
74	C₂³	#10625329	1	1	yes	characteristic
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	4	2	no	—
77	C₂×C₄	#10625329	1	1	yes	characteristic
78	C₂×C₄	#10625329	1	1	yes	characteristic
79	C₂×C₄	#10625329	1	1	yes	characteristic
80	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
81	C₂×C₄	C₄×Dic₄₇	1	1	yes	characteristic
82	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
83	C₈	—	2	2	no	—
84	C₈	C₄×Dic₄₇	1	2	yes	—
85	C₈	C₂×C₄×D₄₇	1	2	yes	—
86	C₂²	—	2	2	no	—
87	C₂²	#13093935	1	1	yes	characteristic
88	C₂²	#13093935	1	1	yes	characteristic
89	C₂²	C₂×#10625329	1	1	yes	characteristic
90	C₄	—	4	2	no	—
91	C₄	#13093935	1	1	yes	characteristic
92	C₄	#13093935	1	1	yes	characteristic
93	C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
94	C₄	C₂×#10625329	1	1	yes	characteristic
95	C₂	—	2	1	no	—
96	C₂	—	2	1	no	—
97	C₂	#15688901	1	2	yes	direct product factor
98	C₂	C₂×#13093935	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13093964

C₂

yes

maximal

#15688901

C₂

yes

maximal, direct product factor

C₂×#97×C₄₇

C₂

yes

maximal, characteristic

#13093964

C₄

yes

complemented

#13093964

C₂²

yes

—

C₂×C₄₇⋊C₁₆

C₄

yes

complemented

C₂²×C₈×C₄₇

C₄

yes

characteristic

C₂²×C₈×C₄₇

C₂²

yes

characteristic

C₂×C₄²×C₄₇

C₄

yes

characteristic

#97×C₄₇

C₄

yes

—

#97×C₄₇

C₂²

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

characteristic

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂×C₄

yes

—

C₂×C₈×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

—

C₄²×C₄₇

C₂×C₄

yes

—

C₄₇⋊C₁₆

C₂×C₄

yes

complemented

C₂³×C₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

C₄²

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

M₁₆

yes

characteristic

C₂×C₄×C₄₇

C₂²×C₄

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

C₄²

yes

—

C₈×C₄₇

C₂²×C₄

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

yes

C₂²×C₄₇

yes

C₂²×C₄₇

C₂×M₁₆

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

yes

C₄×C₄₇

yes

C₄×C₄₇

C₂×C₄²

yes

characteristic

C₄×C₄₇

C₂×M₁₆

yes

characteristic

C₂×#347

—

maximal, Sylow

C₂×C₄₇

—

C₂×C₄₇

—

C₂×C₄₇

#347

yes

complemented

C₂×C₄₇

C₂×#97

yes

characteristic

C₂×M₃₂

—

C₂×#97

D₄₇

yes

characteristic

#347

—

C₄₇

C₂×#347

yes

characteristic, complemented, Sylow

C₂²×C₈

Dic₄₇

yes

characteristic

C₂²×C₈

C₂×D₄₇

yes

characteristic

C₂×C₄²

Dic₄₇

yes

characteristic

M₃₂

—

M₃₂

—

C₂×C₁₆

—

#97

Dic₄₇

yes

—

#97

C₂×D₄₇

yes

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₄×D₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

—

C₂×C₈

C₂×Dic₄₇

yes

characteristic

C₂×C₈

C₂²×D₄₇

yes

characteristic

C₄²

—

C₄²

C₂×Dic₄₇

yes

—

C₁₆

—

C₂³

#10625329

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₄×Dic₄₇

yes

characteristic

C₂×C₄

C₄×Dic₄₇

yes

characteristic

C₂×C₄

C₂²×Dic₄₇

yes

characteristic

C₈

—

C₈

C₄×Dic₄₇

yes

—

C₈

C₂×C₄×D₄₇

yes

—

C₂²

—

C₂²

yes

C₂²

yes

C₂²

yes

C₄

—

C₄

yes

C₄

yes

C₄

C₂×C₄×Dic₄₇

yes

characteristic

C₄

C₂×#10625329

yes

characteristic

C₂

—

C₂

—

C₂

#15688901

yes

direct product factor

C₂

C₂×#13093935

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄×Dic₄₇
commutator	C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₈	C₂²×D₄₇
Fitting	C₂×#97×C₄₇	C₂
socle	C₂²×C₄₇	#97
hypercenter	C₂×#97	D₄₇
hypocenter	C₄₇	C₂×#347
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

subgroup

G/H

center

C₂×C₄

C₄×Dic₄₇

commutator

C₄×C₄₇

C₂×C₄²

Frattini

C₂×C₈

C₂²×D₄₇

Fitting

C₂×#97×C₄₇

C₂

socle

C₂²×C₄₇

#97

hypercenter

C₂×#97

D₄₇

C₄₇

G ▷ C₄×C₄₇ ▷ C₄₇

C₁ ◁ C₂×C₄ ◁ C₂×#97

N	H ≅ G/N	type
2. #15688901	C₂	direct (N × H)
4. #13093964	C₄	semidirect
6. C₂×C₄₇⋊C₁₆	C₄	semidirect
23. C₄₇⋊C₁₆	C₂×C₄	semidirect
48. C₂×C₄₇	#347	semidirect
53. C₄₇	C₂×#347	semidirect
97. C₂	#15688901	direct (N × H)

H ≅ G/N

type

2. #15688901

C₂

direct (N × H)

4. #13093964

C₄

semidirect

6. C₂×C₄₇⋊C₁₆

C₄

semidirect

23. C₄₇⋊C₁₆

C₂×C₄

semidirect

48. C₂×C₄₇

#347

semidirect

53. C₄₇

C₂×#347

semidirect

97. C₂

#15688901

direct (N × H)

Subgroups — C₂×#15688901 #20244990

Conjugacy classes of subgroups

Complements

Subgroups — C2×#15688901 #20244990

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15688901 #20244990