Group #22581033 — subgroups

Subgroups — #22581033

Order 8896.

134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 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×#14555770	C₂	1	1	yes	maximal, characteristic
2	D₄×Dic₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#17984804	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984775	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984764	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₅₅₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₃₉	—	2	1	no	—
10	C₂×C₄×D₁₃₉	—	2	1	no	—
11	#14555770	C₄	1	4	yes	complemented
12	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
14	C₂²⋊Dic₁₃₉	—	2	1	no	—
15	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
16	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×D₁₃₉	—	2	1	no	—
21	D₅₅₆	—	2	1	no	—
22	D₅₅₆	C₂×C₄	1	2	yes	complemented
23	C₂×Dic₁₃₉	—	2	1	no	—
24	C₂×Dic₁₃₉	—	4	2	no	—
25	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
26	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
27	C₄×D₁₃₉	—	4	2	no	—
28	C₁₃₉⋊C₈	C₂×C₄	1	2	yes	complemented
29	C₂³×C₁₃₉	—	2	1	no	—
30	D₄×C₁₃₉	—	2	1	no	—
31	D₄×C₁₃₉	C₂×C₄	1	2	yes	complemented
32	C₂×C₄×C₁₃₉	—	2	1	no	—
33	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
34	C₈×C₁₃₉	—	2	1	no	—
35	C₂²×C₁₃₉	—	2	2	no	—
36	C₂²×C₁₃₉	—	4	1	no	—
37	C₂²×C₁₃₉	—	4	1	no	—
38	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
39	C₂×D₁₃₉	—	2	2	no	—
40	C₂×D₁₃₉	—	4	1	no	—
41	C₂×D₁₃₉	—	4	1	no	—
42	C₄×C₁₃₉	—	4	1	no	—
43	C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
44	C₄×C₁₃₉	#41	1	1	yes	characteristic
45	Dic₁₃₉	—	2	1	no	—
46	Dic₁₃₉	—	4	1	no	—
47	Dic₁₃₉	D₈	1	2	yes	complemented
48	C₂×C₁₃₉	—	4	2	no	—
49	C₂×C₁₃₉	C₄×D₄	1	1	yes	characteristic
50	C₂×C₁₃₉	C₂×D₈	1	1	yes	characteristic
51	C₂×C₁₃₉	#135	1	1	yes	characteristic
52	D₁₃₉	—	4	2	no	—
53	C₁₃₉	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
54	C₄×D₈	—	139	1	no	maximal, Sylow
55	C₂×D₈	—	139	1	no	—
56	C₄×D₄	—	139	1	no	—
57	C₄×D₄	—	139	1	no	—
58	#107	—	139	1	no	—
59	#102	—	139	1	no	—
60	#102	D₁₃₉	1	1	yes	characteristic, complemented
61	C₄×C₈	—	139	1	no	—
62	C₂×D₄	—	139	1	no	—
63	C₂×D₄	C₂×D₁₃₉	1	1	yes	characteristic
64	C₂²×C₄	—	278	1	no	—
65	C₂²×C₄	—	278	1	no	—
66	D₈	—	139	4	no	—
67	C₂×C₈	—	139	1	no	—
68	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
69	C₄⋊C₄	—	139	1	no	—
70	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
71	C₂²⋊C₄	—	278	1	no	—
72	C₂²⋊C₄	—	278	1	no	—
73	C₄²	—	139	1	no	—
74	C₂³	—	2	1	no	—
75	C₂³	—	278	1	no	—
76	D₄	—	2	1	no	—
77	D₄	—	278	1	no	—
78	D₄	—	139	2	no	—
79	D₄	C₄×D₁₃₉	1	2	yes	complemented
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	278	1	no	—
82	C₂×C₄	—	556	2	no	—
83	C₂×C₄	—	556	2	no	—
84	C₂×C₄	—	139	1	no	—
85	C₂×C₄	—	139	1	no	—
86	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
87	C₈	—	2	1	no	—
88	C₈	—	139	2	no	—
89	C₂²	—	2	2	no	—
90	C₂²	—	4	1	no	—
91	C₂²	—	4	1	no	—
92	C₂²	—	278	2	no	—
93	C₂²	—	556	1	no	—
94	C₂²	—	556	1	no	—
95	C₂²	D₄×D₁₃₉	1	1	yes	characteristic
96	C₄	—	4	1	no	—
97	C₄	—	278	1	no	—
98	C₄	—	556	1	no	—
99	C₄	—	139	2	no	—
100	C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
101	C₄	#14555784	1	1	yes	characteristic
102	C₂	—	4	2	no	—
103	C₂	—	556	2	no	—
104	C₂	(C₂²⋊D₁₃₉)⋊C₄	1	1	yes	characteristic
105	C₂	D₈×D₁₃₉	1	1	yes	characteristic
106	C₂	#17984863	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14555770

C₂

yes

maximal, characteristic

D₄×Dic₁₃₉

C₂

yes

maximal, characteristic, complemented

#17984804

C₂

yes

maximal, characteristic, complemented

#17984775

C₂

yes

maximal, characteristic, complemented

#17984764

C₂

yes

maximal, characteristic, complemented

C₈×Dic₁₃₉

C₂

yes

maximal, characteristic, complemented

#102×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×D₅₅₆

C₂²

yes

characteristic

C₂²×Dic₁₃₉

—

C₂×C₄×D₁₃₉

—

#14555770

C₄

yes

complemented

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₄⋊Dic₁₃₉

C₂²

yes

characteristic

C₂²⋊Dic₁₃₉

—

(C₂×D₁₃₉)⋊C₄

—

C₄×Dic₁₃₉

C₂²

yes

characteristic

C₂×D₄×C₁₃₉

C₂²

yes

characteristic

C₂×C₈×C₁₃₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₃₉

C₂²

yes

characteristic

C₂²×D₁₃₉

—

D₅₅₆

—

D₅₅₆

C₂×C₄

yes

complemented

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

D₄

yes

characteristic

C₂×Dic₁₃₉

D₄

yes

characteristic

C₄×D₁₃₉

—

C₁₃₉⋊C₈

C₂×C₄

yes

complemented

C₂³×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

C₂×C₄

yes

complemented

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₈×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

C₂×D₄

yes

characteristic

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂²×C₄

yes

characteristic

C₄×C₁₃₉

#41

yes

characteristic

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

D₈

yes

complemented

C₂×C₁₃₉

—

C₂×C₁₃₉

C₄×D₄

yes

characteristic

C₂×C₁₃₉

C₂×D₈

yes

characteristic

C₂×C₁₃₉

#135

yes

characteristic

D₁₃₉

—

C₁₃₉

C₄×D₈

yes

characteristic, complemented, Sylow

C₄×D₈

—

139

maximal, Sylow

C₂×D₈

—

139

—

C₄×D₄

—

139

—

C₄×D₄

—

139

—

#107

—

139

—

#102

—

139

—

#102

D₁₃₉

yes

characteristic, complemented

C₄×C₈

—

139

—

C₂×D₄

—

139

—

C₂×D₄

C₂×D₁₃₉

yes

characteristic

C₂²×C₄

—

278

—

C₂²×C₄

—

278

—

D₈

—

139

—

C₂×C₈

—

139

—

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₄⋊C₄

—

139

—

C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

C₂²⋊C₄

—

278

—

C₂²⋊C₄

—

278

—

C₄²

—

139

—

C₂³

—

C₂³

—

278

—

D₄

—

D₄

—

278

—

D₄

—

139

—

D₄

C₄×D₁₃₉

yes

complemented

C₂×C₄

—

C₂×C₄

—

278

—

C₂×C₄

—

556

—

C₂×C₄

—

556

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

C₈

—

139

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

278

—

C₂²

—

556

—

C₂²

—

556

—

C₂²

D₄×D₁₃₉

yes

characteristic

C₄

—

C₄

—

278

—

C₄

—

556

—

C₄

—

139

—

100

C₄

C₂×C₄×D₁₃₉

yes

characteristic

101

C₄

#14555784

yes

characteristic

102

C₂

—

103

C₂

—

556

—

104

C₂

(C₂²⋊D₁₃₉)⋊C₄

yes

characteristic

105

C₂

D₈×D₁₃₉

yes

characteristic

106

C₂

#17984863

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃₉
commutator	C₄×C₁₃₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#102×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#102	D₁₃₉
hypocenter	C₁₃₉	C₄×D₈
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

subgroup

G/H

center

C₂²

D₄×D₁₃₉

commutator

C₄×C₁₃₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×D₁₃₉

Fitting

#102×C₁₃₉

C₂

socle

C₂²×C₁₃₉

C₂×D₄

hypercenter

#102

D₁₃₉

hypocenter

C₁₃₉

C₄×D₈

LCS

G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

N	H ≅ G/N	type
2. D₄×Dic₁₃₉	C₂	semidirect
3. #17984804	C₂	semidirect
4. #17984775	C₂	semidirect
5. #17984764	C₂	semidirect
6. C₈×Dic₁₃₉	C₂	semidirect
7. #102×C₁₃₉	C₂	semidirect
11. #14555770	C₄	semidirect
22. D₅₅₆	C₂×C₄	semidirect
28. C₁₃₉⋊C₈	C₂×C₄	semidirect
31. D₄×C₁₃₉	C₂×C₄	semidirect
47. Dic₁₃₉	D₈	semidirect
53. C₁₃₉	C₄×D₈	semidirect
60. #102	D₁₃₉	semidirect
79. D₄	C₄×D₁₃₉	semidirect

H ≅ G/N

type

2. D₄×Dic₁₃₉

C₂

semidirect

3. #17984804

C₂

semidirect

4. #17984775

C₂

semidirect

5. #17984764

C₂

semidirect

6. C₈×Dic₁₃₉

C₂

semidirect

7. #102×C₁₃₉

C₂

semidirect

11. #14555770

C₄

semidirect

22. D₅₅₆

C₂×C₄

semidirect

28. C₁₃₉⋊C₈

C₂×C₄

semidirect

31. D₄×C₁₃₉

C₂×C₄

semidirect

47. Dic₁₃₉

D₈

semidirect

53. C₁₃₉

C₄×D₈

semidirect

60. #102

D₁₃₉

semidirect

79. D₄

C₄×D₁₃₉

semidirect

Subgroups — #22581033

Conjugacy classes of subgroups

Complements