Group #22580978 — subgroups

Subgroups — #22580978

Order 8896.

114 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 55 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×#14555768	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic
3	#17984799	C₂	1	1	yes	maximal, characteristic
4	C₄⋊(C₁₃₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₁₃₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
9	#14555768	—	2	2	no	—
10	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
12	C₈×D₁₃₉	—	2	2	no	—
13	Dic₁₃₉⋊C₄	C₄	1	1	yes	characteristic
14	Dic₁₃₉⋊C₄	C₄	1	1	yes	characteristic
15	(C₂×D₁₃₉)⋊C₄	C₄	1	1	yes	characteristic
16	(C₂×D₁₃₉)⋊C₄	C₄	1	1	yes	characteristic
17	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×D₁₃₉	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
25	C₄×D₁₃₉	D₄	1	2	yes	—
26	C₄×D₁₃₉	Q₈	1	2	yes	—
27	C₁₃₉⋊C₈	—	2	1	no	—
28	C₁₃₉⋊C₈	—	2	1	no	—
29	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
32	C₈×C₁₃₉	—	2	1	no	—
33	C₈×C₁₃₉	—	2	1	no	—
34	C₂²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
35	C₂×D₁₃₉	—	2	1	no	—
36	C₂×D₁₃₉	—	2	1	no	—
37	C₂×D₁₃₉	C₄⋊C₄	1	2	yes	—
38	C₄×C₁₃₉	—	2	1	no	—
39	C₄×C₁₃₉	—	2	1	no	—
40	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
41	C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
42	Dic₁₃₉	—	2	1	no	—
43	Dic₁₃₉	—	2	1	no	—
44	Dic₁₃₉	C₄⋊C₄	1	2	yes	—
45	C₂×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₁₃₉	#131	1	1	yes	characteristic
47	C₂×C₁₃₉	#131	1	1	yes	characteristic
48	D₁₃₉	—	2	2	no	—
49	C₁₃₉	#424	1	1	yes	characteristic, complemented, Sylow
50	#424	—	139	1	no	maximal, Sylow
51	C₂×M₁₆	—	139	1	no	—
52	C₂²×C₈	—	139	1	no	—
53	#117	—	139	1	no	—
54	C₄⋊C₈	—	139	1	no	—
55	C₄⋊C₈	—	139	1	no	—
56	C₄⋊C₈	—	139	1	no	—
57	C₄⋊C₈	D₁₃₉	1	1	yes	characteristic, complemented
58	C₂²×C₄	—	139	1	no	—
59	M₁₆	—	278	2	no	—
60	C₂×C₈	—	278	2	no	—
61	C₂×C₈	—	139	1	no	—
62	C₂×C₈	—	139	1	no	—
63	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
64	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
65	C₄⋊C₄	—	139	1	no	—
66	C₄⋊C₄	—	139	1	no	—
67	C₂²⋊C₄	—	139	1	no	—
68	C₂²⋊C₄	—	139	1	no	—
69	C₄²	—	139	1	no	—
70	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
71	C₂³	—	139	1	no	—
72	C₂×C₄	—	139	1	no	—
73	C₂×C₄	—	139	1	no	—
74	C₂×C₄	—	139	1	no	—
75	C₂×C₄	—	139	2	no	—
76	C₂×C₄	—	139	2	no	—
77	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
78	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
79	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	2	1	no	—
82	C₈	—	278	1	no	—
83	C₈	—	278	1	no	—
84	C₂²	—	278	1	no	—
85	C₂²	—	278	1	no	—
86	C₂²	—	139	2	no	—
87	C₂²	C₂×C₄×D₁₃₉	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	278	1	no	—
91	C₄	—	278	1	no	—
92	C₄	—	139	2	no	—
93	C₄	D₄×D₁₃₉	1	1	yes	characteristic
94	C₄	Q₈×D₁₃₉	1	1	yes	characteristic
95	C₂	—	278	2	no	—
96	C₂	C₄⋊C₄×D₁₃₉	1	1	yes	characteristic
97	C₂	#17984848	1	1	yes	characteristic
98	C₂	#17984850	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14555768

C₂

yes

maximal, characteristic

C₂×C₈×D₁₃₉

C₂

yes

maximal, characteristic

#17984799

C₂

yes

maximal, characteristic

C₄⋊(C₁₃₉⋊C₈)

C₂

yes

maximal, characteristic, complemented

Dic₁₃₉⋊C₈

C₂

yes

maximal, characteristic, complemented

Dic₁₃₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₄⋊C₈×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×C₄×D₁₃₉

C₂²

yes

characteristic

#14555768

—

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₈×D₁₃₉

—

Dic₁₃₉⋊C₄

C₄

yes

characteristic

Dic₁₃₉⋊C₄

C₄

yes

characteristic

(C₂×D₁₃₉)⋊C₄

C₄

yes

characteristic

(C₂×D₁₃₉)⋊C₄

C₄

yes

characteristic

C₄×Dic₁₃₉

C₂²

yes

characteristic

C₂×C₈×C₁₃₉

C₂²

yes

characteristic

C₂×C₈×C₁₃₉

C₂²

yes

characteristic

C₄²×C₁₃₉

C₂²

yes

characteristic

C₂²×D₁₃₉

C₂×C₄

yes

characteristic

C₂×Dic₁₃₉

C₂×C₄

yes

characteristic

C₂×Dic₁₃₉

C₂×C₄

yes

characteristic

C₂×Dic₁₃₉

C₂×C₄

yes

characteristic

C₄×D₁₃₉

D₄

yes

—

C₄×D₁₃₉

Q₈

yes

—

C₁₃₉⋊C₈

—

C₁₃₉⋊C₈

—

C₂×C₄×C₁₃₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₈×C₁₃₉

—

C₈×C₁₃₉

—

C₂²×C₁₃₉

C₂²×C₄

yes

characteristic

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₂×D₁₃₉

C₄⋊C₄

yes

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₄×C₁₃₉

C₂×Q₈

yes

characteristic

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

C₄⋊C₄

yes

—

C₂×C₁₃₉

C₂×C₄⋊C₄

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

D₁₃₉

—

C₁₃₉

#424

yes

characteristic, complemented, Sylow

#424

—

139

maximal, Sylow

C₂×M₁₆

—

139

—

C₂²×C₈

—

139

—

#117

—

139

—

C₄⋊C₈

—

139

—

C₄⋊C₈

—

139

—

C₄⋊C₈

—

139

—

C₄⋊C₈

D₁₃₉

yes

characteristic, complemented

C₂²×C₄

—

139

—

M₁₆

—

278

—

C₂×C₈

—

278

—

C₂×C₈

—

139

—

C₂×C₈

—

139

—

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₄⋊C₄

—

139

—

C₄⋊C₄

—

139

—

C₂²⋊C₄

—

139

—

C₂²⋊C₄

—

139

—

C₄²

—

139

—

C₄²

C₂×D₁₃₉

yes

characteristic

C₂³

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

C₄×D₁₃₉

yes

characteristic

C₂×C₄

C₄×D₁₃₉

yes

characteristic

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

C₈

—

C₈

—

278

—

C₈

—

278

—

C₂²

—

278

—

C₂²

—

278

—

C₂²

—

139

—

C₂²

C₂×C₄×D₁₃₉

yes

characteristic

C₄

—

C₄

—

C₄

—

278

—

C₄

—

278

—

C₄

—

139

—

C₄

D₄×D₁₃₉

yes

characteristic

C₄

Q₈×D₁₃₉

yes

characteristic

C₂

—

278

—

C₂

C₄⋊C₄×D₁₃₉

yes

C₂

yes

C₂

yes

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₃₉
commutator, socle	C₂²×C₁₃₉	C₂²×C₄
Fitting	C₄⋊C₈×C₁₃₉	C₂
hypercenter	C₄⋊C₈	D₁₃₉
hypocenter	C₁₃₉	#424
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×D₁₃₉

commutator, socle

C₂²×C₁₃₉

C₂²×C₄

Fitting

C₄⋊C₈×C₁₃₉

C₂

hypercenter

C₄⋊C₈

D₁₃₉

C₁₃₉

G ▷ C₂²×C₁₃₉ ▷ C₁₃₉

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
4. C₄⋊(C₁₃₉⋊C₈)	C₂	semidirect
5. Dic₁₃₉⋊C₈	C₂	semidirect
6. Dic₁₃₉⋊C₈	C₂	semidirect
7. C₄⋊C₈×C₁₃₉	C₂	semidirect
49. C₁₃₉	#424	semidirect
57. C₄⋊C₈	D₁₃₉	semidirect

H ≅ G/N

type

4. C₄⋊(C₁₃₉⋊C₈)

C₂

semidirect

5. Dic₁₃₉⋊C₈

C₂

semidirect

6. Dic₁₃₉⋊C₈

C₂

semidirect

7. C₄⋊C₈×C₁₃₉

C₂

semidirect

49. C₁₃₉

#424

semidirect

57. C₄⋊C₈

D₁₃₉

semidirect

Subgroups — #22580978

Conjugacy classes of subgroups

Complements