Group #22580913 — subgroups

Subgroups — C₂×(C₂×D₁₃₉)⋊C₈ #22580913

Order 8896.

202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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	C₂²×C₄×D₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₁₃₉)⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₃₉	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₃₉	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₃₉	—	2	2	no	—
8	C₂×C₄×D₁₃₉	—	2	2	no	—
9	C₂×C₄×D₁₃₉	C₄	1	2	yes	—
10	C₂×C₄×D₁₃₉	C₂²	1	2	yes	—
11	C₂×C₁₃₉⋊C₈	—	2	2	no	—
12	C₂×C₁₃₉⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₃₉	—	2	2	no	—
15	C₂×C₈×C₁₃₉	C₂²	1	2	yes	complemented
16	C₂²×D₁₃₉	—	2	2	no	—
17	C₂²×D₁₃₉	—	2	2	no	—
18	C₂²×D₁₃₉	C₈	1	4	yes	complemented
19	C₂²×D₁₃₉	C₂×C₄	1	2	yes	—
20	C₂×Dic₁₃₉	—	2	2	no	—
21	C₂×Dic₁₃₉	C₂×C₄	1	2	yes	—
22	C₄×D₁₃₉	—	2	4	no	—
23	C₄×D₁₃₉	—	2	2	no	—
24	C₄×D₁₃₉	—	2	2	no	—
25	C₁₃₉⋊C₈	—	2	2	no	—
26	C₂³×C₁₃₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₃₉	D₄	1	2	yes	—
29	C₂×C₄×C₁₃₉	D₄	1	2	yes	—
30	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
31	C₈×C₁₃₉	—	2	2	no	—
32	C₂²×C₁₃₉	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₁₃₉	C₂×C₈	1	2	yes	—
34	C₂²×C₁₃₉	M₁₆	1	2	yes	—
35	C₂²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₁₃₉	—	2	8	no	—
37	C₂×D₁₃₉	—	2	2	no	—
38	C₂×D₁₃₉	—	2	2	no	—
39	C₂×D₁₃₉	C₂×C₈	1	4	yes	complemented
40	C₄×C₁₃₉	C₂²⋊C₄	1	2	yes	—
41	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
42	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
43	Dic₁₃₉	—	2	2	no	—
44	C₂×C₁₃₉	C₂²⋊C₈	1	4	yes	complemented
45	C₂×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₁₃₉	C₂²×C₈	1	1	yes	characteristic
47	C₂×C₁₃₉	C₂×M₁₆	1	1	yes	characteristic
48	D₁₃₉	—	2	4	no	—
49	C₁₃₉	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₂²⋊C₈	—	139	1	no	maximal, Sylow
51	C₂³×C₄	—	139	1	no	—
52	C₂²×C₈	—	139	1	no	—
53	C₂²×C₈	D₁₃₉	1	1	yes	characteristic, complemented
54	C₂²⋊C₈	—	139	4	no	—
55	C₂⁴	—	139	1	no	—
56	C₂²×C₄	—	278	2	no	—
57	C₂²×C₄	—	278	2	no	—
58	C₂²×C₄	—	139	1	no	—
59	C₂²×C₄	—	139	2	no	—
60	C₂²×C₄	—	139	2	no	—
61	C₂²×C₄	C₂×D₁₃₉	1	1	yes	characteristic
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	278	2	no	—
64	C₂×C₈	—	139	2	no	—
65	C₂×C₈	C₂×D₁₃₉	1	2	yes	complemented
66	C₂³	—	278	2	no	—
67	C₂³	—	278	2	no	—
68	C₂³	—	139	4	no	—
69	C₂³	—	139	2	no	—
70	C₂³	C₄×D₁₃₉	1	1	yes	characteristic
71	C₂×C₄	—	278	2	no	—
72	C₂×C₄	—	278	4	no	—
73	C₂×C₄	—	278	2	no	—
74	C₂×C₄	—	278	2	no	—
75	C₂×C₄	—	139	2	no	—
76	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
77	C₂×C₄	C₂²⋊D₁₃₉	1	2	yes	—
78	C₂×C₄	D₅₅₆	1	2	yes	—
79	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
80	C₈	—	2	2	no	—
81	C₈	—	278	2	no	—
82	C₂²	—	278	2	no	—
83	C₂²	—	278	2	no	—
84	C₂²	—	278	8	no	—
85	C₂²	—	139	4	no	—
86	C₂²	(C₂×D₁₃₉)⋊C₄	1	2	yes	—
87	C₂²	C₈×D₁₃₉	1	2	yes	—
88	C₂²	#14555768	1	2	yes	—
89	C₂²	C₂×C₄×D₁₃₉	1	1	yes	characteristic
90	C₄	—	278	2	no	—
91	C₄	(C₂×D₁₃₉)⋊C₄	1	2	yes	—
92	C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
93	C₄	C₂×D₅₅₆	1	1	yes	characteristic
94	C₂	—	278	4	no	—
95	C₂	(C₂×D₁₃₉)⋊C₈	1	4	yes	direct product factor
96	C₂	C₂×(C₂×D₁₃₉)⋊C₄	1	1	yes	characteristic
97	C₂	C₂×C₈×D₁₃₉	1	1	yes	characteristic
98	C₂	C₂×#14555768	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×D₁₃₉

C₂

yes

maximal, characteristic

C₂²×C₁₃₉⋊C₈

C₂

yes

maximal, characteristic, complemented

(C₂×D₁₃₉)⋊C₈

C₂

yes

maximal, direct product factor

C₂²×C₈×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₃₉

C₄

yes

characteristic

C₂²×Dic₁₃₉

C₄

yes

characteristic

C₂×C₄×D₁₃₉

—

C₂×C₄×D₁₃₉

—

C₂×C₄×D₁₃₉

C₄

yes

—

C₂×C₄×D₁₃₉

C₂²

yes

—

C₂×C₁₃₉⋊C₈

—

C₂×C₁₃₉⋊C₈

C₂²

yes

complemented

C₂²×C₄×C₁₃₉

C₂²

yes

characteristic

C₂×C₈×C₁₃₉

—

C₂×C₈×C₁₃₉

C₂²

yes

complemented

C₂²×D₁₃₉

—

C₂²×D₁₃₉

—

C₂²×D₁₃₉

C₈

yes

complemented

C₂²×D₁₃₉

C₂×C₄

yes

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

C₂×C₄

yes

—

C₄×D₁₃₉

—

C₄×D₁₃₉

—

C₄×D₁₃₉

—

C₁₃₉⋊C₈

—

C₂³×C₁₃₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₃₉

D₄

yes

—

C₂×C₄×C₁₃₉

D₄

yes

—

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₈×C₁₃₉

—

C₂²×C₁₃₉

C₂²⋊C₄

yes

—

C₂²×C₁₃₉

C₂×C₈

yes

—

C₂²×C₁₃₉

M₁₆

yes

—

C₂²×C₁₃₉

C₂²×C₄

yes

characteristic

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₂×D₁₃₉

C₂×C₈

yes

complemented

C₄×C₁₃₉

C₂²⋊C₄

yes

—

C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₄×C₁₃₉

C₂×D₄

yes

characteristic

Dic₁₃₉

—

C₂×C₁₃₉

C₂²⋊C₈

yes

complemented

C₂×C₁₃₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₁₃₉

C₂²×C₈

yes

characteristic

C₂×C₁₃₉

C₂×M₁₆

yes

characteristic

D₁₃₉

—

C₁₃₉

C₂×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂×C₂²⋊C₈

—

139

maximal, Sylow

C₂³×C₄

—

139

—

C₂²×C₈

—

139

—

C₂²×C₈

D₁₃₉

yes

characteristic, complemented

C₂²⋊C₈

—

139

—

C₂⁴

—

139

—

C₂²×C₄

—

278

—

C₂²×C₄

—

278

—

C₂²×C₄

—

139

—

C₂²×C₄

—

139

—

C₂²×C₄

—

139

—

C₂²×C₄

C₂×D₁₃₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

278

—

C₂×C₈

—

139

—

C₂×C₈

C₂×D₁₃₉

yes

complemented

C₂³

—

278

—

C₂³

—

278

—

C₂³

—

139

—

C₂³

—

139

—

C₂³

C₄×D₁₃₉

yes

characteristic

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

139

—

C₂×C₄

C₄×D₁₃₉

yes

characteristic

C₂×C₄

C₂²⋊D₁₃₉

yes

—

C₂×C₄

D₅₅₆

yes

—

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

C₈

—

278

—

C₂²

—

278

—

C₂²

—

278

—

C₂²

—

278

—

C₂²

—

139

—

C₂²

(C₂×D₁₃₉)⋊C₄

yes

—

C₂²

C₈×D₁₃₉

yes

—

C₂²

#14555768

yes

—

C₂²

C₂×C₄×D₁₃₉

yes

characteristic

C₄

—

278

—

C₄

(C₂×D₁₃₉)⋊C₄

yes

—

C₄

C₂×C₂²⋊D₁₃₉

yes

characteristic

C₄

C₂×D₅₅₆

yes

characteristic

C₂

—

278

—

C₂

(C₂×D₁₃₉)⋊C₈

yes

direct product factor

C₂

C₂×(C₂×D₁₃₉)⋊C₄

yes

characteristic

C₂

C₂×C₈×D₁₃₉

yes

characteristic

C₂

C₂×#14555768

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₃₉
commutator	C₂×C₁₃₉	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	C₂²×C₈×C₁₃₉	C₂
socle	C₂³×C₁₃₉	C₂×C₄
hypercenter	C₂²×C₈	D₁₃₉
hypocenter	C₁₃₉	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²×C₄

C₂×D₁₃₉

commutator

C₂×C₁₃₉

C₂²×C₈

Frattini

C₂×C₄

C₂²×D₁₃₉

Fitting

C₂²×C₈×C₁₃₉

C₂

socle

C₂³×C₁₃₉

C₂×C₄

hypercenter

C₂²×C₈

D₁₃₉

hypocenter

C₁₃₉

C₂×C₂²⋊C₈

LCS

G ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. C₂²×C₁₃₉⋊C₈	C₂	semidirect
3. (C₂×D₁₃₉)⋊C₈	C₂	direct (N × H)
4. C₂²×C₈×C₁₃₉	C₂	semidirect
12. C₂×C₁₃₉⋊C₈	C₂²	semidirect
15. C₂×C₈×C₁₃₉	C₂²	semidirect
18. C₂²×D₁₃₉	C₈	semidirect
39. C₂×D₁₃₉	C₂×C₈	semidirect
44. C₂×C₁₃₉	C₂²⋊C₈	semidirect
49. C₁₃₉	C₂×C₂²⋊C₈	semidirect
53. C₂²×C₈	D₁₃₉	semidirect
65. C₂×C₈	C₂×D₁₃₉	semidirect
95. C₂	(C₂×D₁₃₉)⋊C₈	direct (N × H)

H ≅ G/N

type

2. C₂²×C₁₃₉⋊C₈

C₂

semidirect

3. (C₂×D₁₃₉)⋊C₈

C₂

direct (N × H)

4. C₂²×C₈×C₁₃₉

C₂

semidirect

12. C₂×C₁₃₉⋊C₈

C₂²

semidirect

15. C₂×C₈×C₁₃₉

C₂²

semidirect

18. C₂²×D₁₃₉

C₈

semidirect

39. C₂×D₁₃₉

C₂×C₈

semidirect

44. C₂×C₁₃₉

C₂²⋊C₈

semidirect

49. C₁₃₉

C₂×C₂²⋊C₈

semidirect

53. C₂²×C₈

D₁₃₉

semidirect

65. C₂×C₈

C₂×D₁₃₉

semidirect

95. C₂

(C₂×D₁₃₉)⋊C₈

direct (N × H)

Subgroups — C₂×(C₂×D₁₃₉)⋊C₈ #22580913

Conjugacy classes of subgroups

Complements

Subgroups — C2×(C2×D139)⋊C8 #22580913

Conjugacy classes of subgroups

Complements

Subgroups — C₂×(C₂×D₁₃₉)⋊C₈ #22580913