Group #22580960 — subgroups

Subgroups — #22580960

Order 8896.

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

normal subgroups only

This group has 150 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×Q₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#14555768	C₂	1	1	yes	maximal, characteristic
3	#17984800	C₂	1	1	yes	maximal, characteristic
4	#17984767	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984766	C₂	1	1	yes	maximal, characteristic, complemented
6	#17984765	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₇₈	—	2	1	no	—
9	C₂×Dic₂₇₈	C₂²	1	1	yes	characteristic
10	Q₈×D₁₃₉	—	2	2	no	—
11	Q₈×D₁₃₉	C₄	1	4	yes	complemented
12	C₂×C₄×D₁₃₉	—	2	1	no	—
13	C₂×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
14	#14555768	—	2	2	no	—
15	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
17	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
18	C₄×Dic₁₃₉	—	2	1	no	—
19	C₂×Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
22	C₂²×D₁₃₉	D₄	1	1	yes	characteristic
23	Dic₂₇₈	—	2	1	no	—
24	Dic₂₇₈	—	2	4	no	—
25	Dic₂₇₈	C₂×C₄	1	2	yes	—
26	C₂×Dic₁₃₉	—	2	1	no	—
27	C₂×Dic₁₃₉	—	2	1	no	—
28	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
29	C₄×D₁₃₉	—	2	4	no	—
30	C₄×D₁₃₉	C₂×C₄	1	2	yes	—
31	C₄×D₁₃₉	D₄	1	2	yes	—
32	C₁₃₉⋊C₈	—	2	1	no	—
33	Q₈×C₁₃₉	—	2	1	no	—
34	Q₈×C₁₃₉	C₂×C₄	1	2	yes	—
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	C₂×D₄	1	1	yes	characteristic
40	C₂×D₁₃₉	—	2	1	no	—
41	C₂×D₁₃₉	—	2	1	no	—
42	C₂×D₁₃₉	C₂²⋊C₄	1	2	yes	—
43	C₄×C₁₃₉	—	2	2	no	—
44	C₄×C₁₃₉	—	4	1	no	—
45	C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
46	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
47	Dic₁₃₉	—	2	2	no	—
48	Dic₁₃₉	—	4	1	no	—
49	Dic₁₃₉	C₂²⋊C₄	1	2	yes	—
50	C₂×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₁₃₉	#137	1	1	yes	characteristic
52	C₂×C₁₃₉	#137	1	1	yes	characteristic
53	D₁₃₉	—	2	2	no	—
54	C₁₃₉	#419	1	1	yes	characteristic, complemented, Sylow
55	#419	—	139	1	no	maximal, Sylow
56	C₂²×Q₈	—	139	1	no	—
57	C₂×M₁₆	—	139	1	no	—
58	#117	—	139	1	no	—
59	#103	—	139	1	no	—
60	#103	—	139	1	no	—
61	#103	—	139	1	no	—
62	#103	D₁₃₉	1	1	yes	characteristic, complemented
63	C₂×Q₈	—	278	1	no	—
64	C₂×Q₈	—	278	2	no	—
65	C₂×Q₈	—	139	4	no	—
66	C₂×Q₈	—	139	1	no	—
67	C₂×Q₈	C₂×D₁₃₉	1	1	yes	characteristic
68	C₂²×C₄	—	278	1	no	—
69	C₂²×C₄	—	139	1	no	—
70	M₁₆	—	278	2	no	—
71	C₂×C₈	—	139	1	no	—
72	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
73	C₄⋊C₄	—	139	1	no	—
74	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
75	C₂²⋊C₄	—	278	1	no	—
76	C₄²	—	278	1	no	—
77	C₂³	—	139	1	no	—
78	Q₈	—	2	1	no	—
79	Q₈	—	278	4	no	—
80	Q₈	—	278	1	no	—
81	Q₈	—	139	2	no	—
82	Q₈	C₄×D₁₃₉	1	2	yes	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	278	4	no	—
86	C₂×C₄	—	278	1	no	—
87	C₂×C₄	—	278	1	no	—
88	C₂×C₄	—	139	1	no	—
89	C₂×C₄	—	139	2	no	—
90	C₂×C₄	—	139	2	no	—
91	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
92	C₈	—	2	1	no	—
93	C₈	—	278	1	no	—
94	C₂²	—	278	1	no	—
95	C₂²	—	278	1	no	—
96	C₂²	—	139	2	no	—
97	C₂²	D₄×D₁₃₉	1	1	yes	characteristic
98	C₄	—	2	2	no	—
99	C₄	—	4	1	no	—
100	C₄	—	278	2	no	—
101	C₄	—	556	1	no	—
102	C₄	—	139	2	no	—
103	C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
104	C₄	D₄×D₁₃₉	1	1	yes	characteristic
105	C₂	—	278	2	no	—
106	C₂	C₂²⋊C₄×D₁₃₉	1	1	yes	characteristic
107	C₂	#17984871	1	1	yes	characteristic
108	C₂	#17984874	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Q₈×D₁₃₉

C₂

yes

maximal, characteristic

C₂×#14555768

C₂

yes

maximal, characteristic

#17984800

C₂

yes

maximal, characteristic

#17984767

C₂

yes

maximal, characteristic, complemented

#17984766

C₂

yes

maximal, characteristic, complemented

#17984765

C₂

yes

maximal, characteristic, complemented

#103×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₇₈

—

C₂×Dic₂₇₈

C₂²

yes

characteristic

Q₈×D₁₃₉

—

Q₈×D₁₃₉

C₄

yes

complemented

C₂×C₄×D₁₃₉

—

C₂×C₄×D₁₃₉

C₂²

yes

characteristic

#14555768

—

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₄⋊Dic₁₃₉

C₂²

yes

characteristic

(C₂×D₁₃₉)⋊C₄

—

C₄×Dic₁₃₉

—

C₂×Q₈×C₁₃₉

C₂²

yes

characteristic

C₂×C₈×C₁₃₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₂²×D₁₃₉

D₄

yes

characteristic

Dic₂₇₈

—

Dic₂₇₈

—

Dic₂₇₈

C₂×C₄

yes

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

D₄

yes

characteristic

C₄×D₁₃₉

—

C₄×D₁₃₉

C₂×C₄

yes

—

C₄×D₁₃₉

D₄

yes

—

C₁₃₉⋊C₈

—

Q₈×C₁₃₉

—

Q₈×C₁₃₉

C₂×C₄

yes

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₈×C₁₃₉

—

C₂²×C₁₃₉

C₂×D₄

yes

characteristic

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₂×D₁₃₉

C₂²⋊C₄

yes

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂²×C₄

yes

characteristic

C₄×C₁₃₉

C₂×D₄

yes

characteristic

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

C₂²⋊C₄

yes

—

C₂×C₁₃₉

C₂×C₂²⋊C₄

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

D₁₃₉

—

C₁₃₉

#419

yes

characteristic, complemented, Sylow

#419

—

139

maximal, Sylow

C₂²×Q₈

—

139

—

C₂×M₁₆

—

139

—

#117

—

139

—

#103

—

139

—

#103

—

139

—

#103

—

139

—

#103

D₁₃₉

yes

characteristic, complemented

C₂×Q₈

—

278

—

C₂×Q₈

—

278

—

C₂×Q₈

—

139

—

C₂×Q₈

—

139

—

C₂×Q₈

C₂×D₁₃₉

yes

characteristic

C₂²×C₄

—

278

—

C₂²×C₄

—

139

—

M₁₆

—

278

—

C₂×C₈

—

139

—

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₄⋊C₄

—

139

—

C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

C₂²⋊C₄

—

278

—

C₄²

—

278

—

C₂³

—

139

—

Q₈

—

Q₈

—

278

—

Q₈

—

278

—

Q₈

—

139

—

Q₈

C₄×D₁₃₉

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

C₈

—

278

—

C₂²

—

278

—

C₂²

—

278

—

C₂²

—

139

—

C₂²

D₄×D₁₃₉

yes

characteristic

C₄

—

C₄

—

100

C₄

—

278

—

101

C₄

—

556

—

102

C₄

—

139

—

103

C₄

C₂×C₄×D₁₃₉

yes

characteristic

104

C₄

D₄×D₁₃₉

yes

characteristic

105

C₂

—

278

—

106

C₂

C₂²⋊C₄×D₁₃₉

yes

characteristic

107

C₂

#17984871

yes

characteristic

108

C₂

#17984874

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃₉
commutator	C₄×C₁₃₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#103×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#103	D₁₃₉
hypocenter	C₁₃₉	#419
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

subgroup

G/H

center

C₂²

D₄×D₁₃₉

commutator

C₄×C₁₃₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×D₁₃₉

Fitting

#103×C₁₃₉

C₂

socle

C₂²×C₁₃₉

C₂×D₄

D₁₃₉

C₁₃₉

G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

N	H ≅ G/N	type
4. #17984767	C₂	semidirect
5. #17984766	C₂	semidirect
6. #17984765	C₂	semidirect
7. #103×C₁₃₉	C₂	semidirect
11. Q₈×D₁₃₉	C₄	semidirect
54. C₁₃₉	#419	semidirect
62. #103	D₁₃₉	semidirect

H ≅ G/N

type

4. #17984767

C₂

semidirect

5. #17984766

C₂

semidirect

6. #17984765

C₂

semidirect

7. #103×C₁₃₉

C₂

semidirect

11. Q₈×D₁₃₉

C₄

semidirect

54. C₁₃₉

#419

semidirect

62. #103

D₁₃₉

semidirect

Subgroups — #22580960

Conjugacy classes of subgroups

Complements