Group #22581341 — subgroups

Subgroups — #22581341

Order 8896.

144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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×#14555774	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14555773	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14555770	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984838	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984829	C₂	1	1	yes	maximal, characteristic, complemented
6	#17984752	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₇₈	C₂²	1	1	yes	characteristic
9	C₂×D₅₅₆	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊D₁₃₉	—	2	2	no	—
11	#14555774	—	2	2	no	—
12	#14555773	—	2	2	no	—
13	#14555770	—	2	2	no	—
14	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²⋊Dic₁₃₉	—	2	2	no	—
16	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	D₈×C₁₃₉	—	2	2	no	—
20	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
21	C₂²×D₁₃₉	—	2	1	no	—
22	Dic₂₇₈	—	2	1	no	—
23	Dic₂₇₈	—	2	1	no	—
24	D₅₅₆	—	2	1	no	—
25	D₅₅₆	—	2	1	no	—
26	C₂²⋊D₁₃₉	—	4	4	no	—
27	C₂×Dic₁₃₉	—	2	1	no	—
28	C₂×Dic₁₃₉	D₄	1	2	yes	—
29	C₁₃₉⋊C₈	D₄	1	2	yes	complemented
30	C₂³×C₁₃₉	—	2	1	no	—
31	C₂³×C₁₃₉	—	2	1	no	—
32	D₄×C₁₃₉	—	2	1	no	—
33	D₄×C₁₃₉	—	2	1	no	—
34	D₄×C₁₃₉	—	2	1	no	—
35	D₄×C₁₃₉	—	2	1	no	—
36	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
37	C₈×C₁₃₉	D₄	1	2	yes	complemented
38	C₂²×C₁₃₉	—	4	1	no	—
39	C₂²×C₁₃₉	—	4	1	no	—
40	C₂²×C₁₃₉	—	4	2	no	—
41	C₂²×C₁₃₉	—	4	2	no	—
42	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
43	C₂×D₁₃₉	—	4	1	no	—
44	C₂×D₁₃₉	—	4	2	no	—
45	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
46	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
47	Dic₁₃₉	—	2	2	no	—
48	Dic₁₃₉	—	4	1	no	—
49	C₂×C₁₃₉	—	8	1	no	—
50	C₂×C₁₃₉	—	8	1	no	—
51	C₂×C₁₃₉	#127	1	1	yes	characteristic
52	C₂×C₁₃₉	AGL(1,ℤ/8)	1	2	yes	—
53	D₁₃₉	—	8	1	no	—
54	C₁₃₉	#496	1	1	yes	characteristic, complemented, Sylow
55	#496	—	139	1	no	maximal, Sylow
56	C₂×SD₁₆	—	139	1	no	—
57	C₂×SD₁₆	—	139	1	no	—
58	C₂×D₈	—	139	1	no	—
59	C₂×D₈	D₁₃₉	1	1	yes	characteristic, complemented
60	#127	—	139	1	no	—
61	#124	—	139	1	no	—
62	#97	—	139	1	no	—
63	C₂×Q₈	—	139	1	no	—
64	C₂×D₄	—	278	2	no	—
65	C₂×D₄	—	139	1	no	—
66	C₂×D₄	C₂×D₁₃₉	1	1	yes	characteristic
67	C₂×D₄	C₂×D₁₃₉	1	1	yes	characteristic
68	SD₁₆	—	278	2	no	—
69	SD₁₆	—	278	2	no	—
70	D₈	—	2	2	no	—
71	D₈	—	278	2	no	—
72	C₂×C₈	—	139	1	no	—
73	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
74	C₂²⋊C₄	—	278	2	no	—
75	C₄²	—	139	1	no	—
76	C₂³	—	2	1	no	—
77	C₂³	—	2	1	no	—
78	C₂³	—	278	1	no	—
79	Q₈	—	278	1	no	—
80	Q₈	—	278	1	no	—
81	D₄	—	2	1	no	—
82	D₄	—	2	1	no	—
83	D₄	—	2	1	no	—
84	D₄	—	2	1	no	—
85	D₄	—	278	1	no	—
86	D₄	—	278	1	no	—
87	D₄	—	556	4	no	—
88	C₂×C₄	—	278	1	no	—
89	C₂×C₄	—	139	2	no	—
90	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
91	C₈	—	139	2	no	—
92	C₈	C₂²⋊D₁₃₉	1	2	yes	complemented
93	C₂²	—	4	1	no	—
94	C₂²	—	4	1	no	—
95	C₂²	—	4	2	no	—
96	C₂²	—	4	2	no	—
97	C₂²	—	556	1	no	—
98	C₂²	—	556	2	no	—
99	C₂²	D₄×D₁₃₉	1	1	yes	characteristic
100	C₄	—	278	2	no	—
101	C₄	—	556	1	no	—
102	C₄	D₄×D₁₃₉	1	1	yes	characteristic
103	C₄	C₂×C₂²⋊D₁₃₉	1	1	yes	characteristic
104	C₂	—	8	1	no	—
105	C₂	—	8	1	no	—
106	C₂	—	1112	1	no	—
107	C₂	#17984838	1	1	yes	characteristic
108	C₂	#17984866	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14555774

C₂

yes

maximal, characteristic, complemented

C₂×#14555773

C₂

yes

maximal, characteristic, complemented

C₂×#14555770

C₂

yes

maximal, characteristic, complemented

#17984838

C₂

yes

maximal, characteristic, complemented

#17984829

C₂

yes

maximal, characteristic, complemented

#17984752

C₂

yes

maximal, characteristic, complemented

C₂×D₈×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₇₈

C₂²

yes

characteristic

C₂×D₅₅₆

C₂²

yes

characteristic

C₂×C₂²⋊D₁₃₉

—

#14555774

—

#14555773

—

#14555770

—

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₂²⋊Dic₁₃₉

—

C₄×Dic₁₃₉

C₂²

yes

characteristic

C₂×D₄×C₁₃₉

C₂²

yes

characteristic

C₂×D₄×C₁₃₉

C₂²

yes

characteristic

D₈×C₁₃₉

—

C₂×C₈×C₁₃₉

C₂²

yes

characteristic

C₂²×D₁₃₉

—

Dic₂₇₈

—

Dic₂₇₈

—

D₅₅₆

—

D₅₅₆

—

C₂²⋊D₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

D₄

yes

—

C₁₃₉⋊C₈

D₄

yes

complemented

C₂³×C₁₃₉

—

C₂³×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₈×C₁₃₉

D₄

yes

complemented

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

C₂×D₄

yes

characteristic

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₄×C₁₃₉

C₂×D₄

yes

characteristic

C₄×C₁₃₉

C₂×D₄

yes

characteristic

Dic₁₃₉

—

Dic₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

#127

yes

characteristic

C₂×C₁₃₉

AGL(1,ℤ/8)

yes

—

D₁₃₉

—

C₁₃₉

#496

yes

characteristic, complemented, Sylow

#496

—

139

maximal, Sylow

C₂×SD₁₆

—

139

—

C₂×SD₁₆

—

139

—

C₂×D₈

—

139

—

C₂×D₈

D₁₃₉

yes

characteristic, complemented

#127

—

139

—

#124

—

139

—

#97

—

139

—

C₂×Q₈

—

139

—

C₂×D₄

—

278

—

C₂×D₄

—

139

—

C₂×D₄

C₂×D₁₃₉

yes

characteristic

C₂×D₄

C₂×D₁₃₉

yes

characteristic

SD₁₆

—

278

—

SD₁₆

—

278

—

D₈

—

D₈

—

278

—

C₂×C₈

—

139

—

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₂²⋊C₄

—

278

—

C₄²

—

139

—

C₂³

—

C₂³

—

C₂³

—

278

—

Q₈

—

278

—

Q₈

—

278

—

D₄

—

D₄

—

D₄

—

D₄

—

D₄

—

278

—

D₄

—

278

—

D₄

—

556

—

C₂×C₄

—

278

—

C₂×C₄

—

139

—

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

139

—

C₈

C₂²⋊D₁₃₉

yes

complemented

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

556

—

C₂²

—

556

—

C₂²

D₄×D₁₃₉

yes

characteristic

100

C₄

—

278

—

101

C₄

—

556

—

102

C₄

D₄×D₁₃₉

yes

characteristic

103

C₄

C₂×C₂²⋊D₁₃₉

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

—

1112

—

107

C₂

#17984838

yes

characteristic

108

C₂

#17984866

yes

—

	subgroup	G/H
center	C₂²	D₄×D₁₃₉
commutator	C₂×C₄×C₁₃₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	C₂×D₈×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	C₂×D₈	D₁₃₉
hypocenter	C₁₃₉	#496
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

subgroup

G/H

center

C₂²

D₄×D₁₃₉

commutator

C₂×C₄×C₁₃₉

C₂³

Frattini

C₂×C₄

C₂²×D₁₃₉

Fitting

C₂×D₈×C₁₃₉

C₂

socle

C₂²×C₁₃₉

C₂×D₄

hypercenter

C₂×D₈

D₁₃₉

hypocenter

C₁₃₉

#496

LCS

G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

N	H ≅ G/N	type
1. C₂×#14555774	C₂	semidirect
2. C₂×#14555773	C₂	semidirect
3. C₂×#14555770	C₂	semidirect
4. #17984838	C₂	semidirect
5. #17984829	C₂	semidirect
6. #17984752	C₂	semidirect
7. C₂×D₈×C₁₃₉	C₂	semidirect
29. C₁₃₉⋊C₈	D₄	semidirect
37. C₈×C₁₃₉	D₄	semidirect
54. C₁₃₉	#496	semidirect
59. C₂×D₈	D₁₃₉	semidirect
92. C₈	C₂²⋊D₁₃₉	semidirect

H ≅ G/N

type

1. C₂×#14555774

C₂

semidirect

2. C₂×#14555773

C₂

semidirect

3. C₂×#14555770

C₂

semidirect

4. #17984838

C₂

semidirect

5. #17984829

C₂

semidirect

6. #17984752

C₂

semidirect

7. C₂×D₈×C₁₃₉

C₂

semidirect

29. C₁₃₉⋊C₈

D₄

semidirect

37. C₈×C₁₃₉

D₄

semidirect

54. C₁₃₉

#496

semidirect

59. C₂×D₈

D₁₃₉

semidirect

92. C₈

C₂²⋊D₁₃₉

semidirect

Subgroups — #22581341

Conjugacy classes of subgroups

Complements