Group #22581072 — subgroups

Subgroups — #22581072

Order 8896.

104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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	#17984862	C₂	1	1	yes	maximal, characteristic
2	#17984850	C₂	1	1	yes	maximal, characteristic, complemented
3	#17984849	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984777	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984770	C₂	1	1	yes	maximal, characteristic, complemented
6	#17984753	C₂	1	1	yes	maximal, characteristic, complemented
7	#104×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#14555785	C₂²	1	1	yes	characteristic
9	#14555775	C₄	1	1	yes	characteristic, complemented
10	#14555773	C₄	1	1	yes	characteristic, complemented
11	#14555772	C₄	1	1	yes	characteristic, complemented
12	#14555770	C₄	1	1	yes	characteristic, complemented
13	#14555769	—	2	1	no	—
14	#14555769	C₂²	1	1	yes	characteristic
15	#14555768	—	2	1	no	—
16	C₂×C₁₃₉⋊C₈	—	2	1	no	—
17	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₈×D₁₃₉	—	2	1	no	—
20	#41×C₁₃₉	C₂²	1	1	yes	characteristic
21	M₁₆×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
23	Dic₂₇₈	C₂×C₄	1	1	yes	characteristic
24	D₅₅₆	C₂×C₄	1	1	yes	characteristic
25	C₂²⋊D₁₃₉	—	2	1	no	—
26	C₄×D₁₃₉	—	2	1	no	—
27	C₁₃₉⋊C₈	—	2	1	no	—
28	C₁₃₉⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₁₃₉⋊C₈	C₂×C₄	1	1	yes	characteristic
30	C₁₃₉⋊C₈	D₄	1	1	yes	characteristic
31	C₁₃₉⋊C₈	D₄	1	1	yes	characteristic
32	Q₈×C₁₃₉	C₂×C₄	1	1	yes	characteristic
33	D₄×C₁₃₉	—	2	1	no	—
34	D₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₃₉	—	2	1	no	—
36	C₂×C₄×C₁₃₉	—	2	1	no	—
37	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
38	C₈×C₁₃₉	—	2	1	no	—
39	C₂²×C₁₃₉	—	2	1	no	—
40	C₂²×C₁₃₉	#41	1	1	yes	characteristic
41	C₂×D₁₃₉	—	2	1	no	—
42	C₄×C₁₃₉	—	2	1	no	—
43	C₄×C₁₃₉	—	4	1	no	—
44	C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
45	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
46	Dic₁₃₉	—	2	1	no	—
47	C₂×C₁₃₉	—	2	1	no	—
48	C₂×C₁₃₉	—	4	1	no	—
49	C₂×C₁₃₉	C₄×D₄	1	1	yes	characteristic
50	D₁₃₉	—	4	1	no	—
51	C₁₃₉	#444	1	1	yes	characteristic, complemented, Sylow
52	#444	—	139	1	no	maximal, Sylow
53	#135	—	139	1	no	—
54	#131	—	139	1	no	—
55	#131	—	139	1	no	—
56	#108	—	139	1	no	—
57	#104	—	139	1	no	—
58	#104	D₁₃₉	1	1	yes	characteristic, complemented
59	#97	—	139	1	no	—
60	#41	—	139	1	no	—
61	#41	C₂×D₁₃₉	1	1	yes	characteristic
62	Q₁₆	—	139	1	no	—
63	SD₁₆	—	139	1	no	—
64	SD₁₆	—	139	1	no	—
65	D₈	—	139	1	no	—
66	M₁₆	—	278	1	no	—
67	M₁₆	—	278	1	no	—
68	M₁₆	—	139	1	no	—
69	M₁₆	C₂×D₁₃₉	1	1	yes	characteristic
70	C₂×C₈	—	278	1	no	—
71	C₂×C₈	—	278	1	no	—
72	C₂×C₈	—	139	1	no	—
73	C₂×C₈	—	139	1	no	—
74	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
75	Q₈	—	139	1	no	—
76	Q₈	C₄×D₁₃₉	1	1	yes	characteristic
77	D₄	—	2	1	no	—
78	D₄	—	278	1	no	—
79	D₄	—	139	1	no	—
80	D₄	C₄×D₁₃₉	1	1	yes	characteristic
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	278	1	no	—
84	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
85	C₈	—	2	1	no	—
86	C₈	—	278	1	no	—
87	C₈	—	139	1	no	—
88	C₈	—	139	1	no	—
89	C₈	—	139	1	no	—
90	C₈	—	139	1	no	—
91	C₂²	—	2	1	no	—
92	C₂²	—	278	1	no	—
93	C₂²	#14555784	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	4	1	no	—
96	C₄	—	278	1	no	—
97	C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
98	C₄	D₄×D₁₃₉	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	—	4	1	no	—
101	C₂	—	556	1	no	—
102	C₂	(C₂²⋊D₁₃₉)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17984862

C₂

yes

maximal, characteristic

#17984850

C₂

yes

maximal, characteristic, complemented

#17984849

C₂

yes

maximal, characteristic, complemented

#17984777

C₂

yes

maximal, characteristic, complemented

#17984770

C₂

yes

maximal, characteristic, complemented

#17984753

C₂

yes

maximal, characteristic, complemented

#104×C₁₃₉

C₂

yes

maximal, characteristic, complemented

#14555785

C₂²

yes

characteristic

#14555775

C₄

yes

characteristic, complemented

#14555773

C₄

yes

characteristic, complemented

#14555772

C₄

yes

characteristic, complemented

#14555770

C₄

yes

characteristic, complemented

#14555769

—

#14555769

C₂²

yes

characteristic

#14555768

—

C₂×C₁₃₉⋊C₈

—

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₈×D₁₃₉

—

#41×C₁₃₉

C₂²

yes

characteristic

M₁₆×C₁₃₉

C₂²

yes

characteristic

C₄²×C₁₃₉

C₂²

yes

characteristic

Dic₂₇₈

C₂×C₄

yes

characteristic

D₅₅₆

C₂×C₄

yes

characteristic

C₂²⋊D₁₃₉

—

C₄×D₁₃₉

—

C₁₃₉⋊C₈

—

C₁₃₉⋊C₈

C₂×C₄

yes

characteristic

C₁₃₉⋊C₈

C₂×C₄

yes

characteristic

C₁₃₉⋊C₈

D₄

yes

characteristic

C₁₃₉⋊C₈

D₄

yes

characteristic

Q₈×C₁₃₉

C₂×C₄

yes

characteristic

D₄×C₁₃₉

—

D₄×C₁₃₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₈×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

#41

yes

characteristic

C₂×D₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂²×C₄

yes

characteristic

C₄×C₁₃₉

C₂×D₄

yes

characteristic

Dic₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

C₄×D₄

yes

characteristic

D₁₃₉

—

C₁₃₉

#444

yes

characteristic, complemented, Sylow

#444

—

139

maximal, Sylow

#135

—

139

—

#131

—

139

—

#131

—

139

—

#108

—

139

—

#104

—

139

—

#104

D₁₃₉

yes

characteristic, complemented

#97

—

139

—

#41

—

139

—

#41

C₂×D₁₃₉

yes

characteristic

Q₁₆

—

139

—

SD₁₆

—

139

—

SD₁₆

—

139

—

D₈

—

139

—

M₁₆

—

278

—

M₁₆

—

278

—

M₁₆

—

139

—

M₁₆

C₂×D₁₃₉

yes

characteristic

C₂×C₈

—

278

—

C₂×C₈

—

278

—

C₂×C₈

—

139

—

C₂×C₈

—

139

—

C₄²

C₂×D₁₃₉

yes

characteristic

Q₈

—

139

—

Q₈

C₄×D₁₃₉

yes

characteristic

D₄

—

D₄

—

278

—

D₄

—

139

—

D₄

C₄×D₁₃₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

278

—

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

C₈

—

278

—

C₈

—

139

—

C₈

—

139

—

C₈

—

139

—

C₈

—

139

—

C₂²

—

C₂²

—

278

—

C₂²

#14555784

yes

characteristic

C₄

—

C₄

—

C₄

—

278

—

C₄

C₂×C₄×D₁₃₉

yes

characteristic

C₄

D₄×D₁₃₉

yes

characteristic

C₂

—

100

C₂

—

101

C₂

—

556

—

102

C₂

(C₂²⋊D₁₃₉)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	D₄×D₁₃₉
commutator	C₄×C₁₃₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#104×C₁₃₉	C₂
socle	C₂×C₁₃₉	C₄×D₄
hypercenter	#104	D₁₃₉
hypocenter	C₁₃₉	#444
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #104

subgroup

G/H

center

C₄

D₄×D₁₃₉

commutator

C₄×C₁₃₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×D₁₃₉

Fitting

#104×C₁₃₉

C₂

socle

C₂×C₁₃₉

C₄×D₄

D₁₃₉

C₁₃₉

G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #104

N	H ≅ G/N	type
2. #17984850	C₂	semidirect
3. #17984849	C₂	semidirect
4. #17984777	C₂	semidirect
5. #17984770	C₂	semidirect
6. #17984753	C₂	semidirect
7. #104×C₁₃₉	C₂	semidirect
9. #14555775	C₄	semidirect
10. #14555773	C₄	semidirect
11. #14555772	C₄	semidirect
12. #14555770	C₄	semidirect
51. C₁₃₉	#444	semidirect
58. #104	D₁₃₉	semidirect

H ≅ G/N

type

2. #17984850

C₂

semidirect

3. #17984849

C₂

semidirect

4. #17984777

C₂

semidirect

5. #17984770

C₂

semidirect

6. #17984753

C₂

semidirect

7. #104×C₁₃₉

C₂

semidirect

9. #14555775

C₄

semidirect

10. #14555773

C₄

semidirect

11. #14555772

C₄

semidirect

12. #14555770

C₄

semidirect

51. C₁₃₉

#444

semidirect

58. #104

D₁₃₉

semidirect

Subgroups — #22581072

Conjugacy classes of subgroups

Complements