Group #22581055 — subgroups

Subgroups — #22581055

Order 8896.

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

normal subgroups only

This group has 120 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×#14555774	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₂₇₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₅₅₆	C₂	1	1	yes	maximal, characteristic
4	#17984776	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984767	C₂	1	1	yes	maximal, characteristic, complemented
6	#17984764	C₂	1	1	yes	maximal, characteristic
7	#97×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×C₄×D₁₃₉	—	2	1	no	—
11	#14555774	C₄	1	4	yes	complemented
12	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
14	Dic₁₃₉⋊C₄	—	2	1	no	—
15	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
16	C₄×Dic₁₃₉	—	2	1	no	—
17	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
20	C₂²×D₁₃₉	—	2	1	no	—
21	Dic₂₇₈	—	2	1	no	—
22	Dic₂₇₈	C₂×C₄	1	2	yes	complemented
23	D₅₅₆	—	2	1	no	—
24	D₅₅₆	C₂×C₄	1	2	yes	—
25	C₂×Dic₁₃₉	—	2	1	no	—
26	C₂×Dic₁₃₉	—	2	1	no	—
27	C₂×Dic₁₃₉	—	2	1	no	—
28	C₄×D₁₃₉	—	4	2	no	—
29	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
30	C₂×C₄×C₁₃₉	D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
32	C₈×C₁₃₉	—	2	1	no	—
33	C₈×C₁₃₉	C₂×C₄	1	2	yes	complemented
34	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
35	C₂×D₁₃₉	—	2	2	no	—
36	C₂×D₁₃₉	—	4	1	no	—
37	C₂×D₁₃₉	—	4	1	no	—
38	C₄×C₁₃₉	—	2	1	no	—
39	C₄×C₁₃₉	—	2	1	no	—
40	C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
41	C₄×C₁₃₉	#41	1	1	yes	characteristic
42	Dic₁₃₉	—	2	2	no	—
43	Dic₁₃₉	—	4	1	no	—
44	Dic₁₃₉	—	4	1	no	—
45	C₂×C₁₃₉	C₄×D₄	1	1	yes	characteristic
46	C₂×C₁₃₉	AGL(1,ℤ/8)	1	1	yes	characteristic
47	C₂×C₁₃₉	#137	1	1	yes	characteristic
48	D₁₃₉	—	4	2	no	—
49	C₁₃₉	#440	1	1	yes	characteristic, complemented, Sylow
50	#440	—	139	1	no	maximal, Sylow
51	C₂×SD₁₆	—	139	1	no	—
52	C₄×Q₈	—	139	1	no	—
53	C₄×D₄	—	139	1	no	—
54	#107	—	139	1	no	—
55	#103	—	139	1	no	—
56	#102	—	139	1	no	—
57	#97	D₁₃₉	1	1	yes	characteristic, complemented
58	C₂×Q₈	—	139	1	no	—
59	C₂×D₄	—	139	1	no	—
60	C₂²×C₄	—	278	1	no	—
61	SD₁₆	—	139	4	no	—
62	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
63	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
64	C₄⋊C₄	—	278	1	no	—
65	C₄⋊C₄	—	139	1	no	—
66	C₄⋊C₄	—	139	1	no	—
67	C₂²⋊C₄	—	278	1	no	—
68	C₄²	—	278	1	no	—
69	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
70	C₂³	—	278	1	no	—
71	Q₈	—	278	1	no	—
72	Q₈	—	139	2	no	—
73	D₄	—	278	1	no	—
74	D₄	—	139	2	no	—
75	C₂×C₄	—	278	1	no	—
76	C₂×C₄	—	278	1	no	—
77	C₂×C₄	—	278	1	no	—
78	C₂×C₄	—	556	2	no	—
79	C₂×C₄	D₅₅₆	1	1	yes	characteristic
80	C₂×C₄	D₅₅₆	1	1	yes	characteristic
81	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	C₄×D₁₃₉	1	2	yes	complemented
84	C₂²	—	278	2	no	—
85	C₂²	—	556	1	no	—
86	C₂²	—	556	1	no	—
87	C₂²	C₂×D₅₅₆	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	278	2	no	—
91	C₄	—	556	1	no	—
92	C₄	—	556	1	no	—
93	C₄	C₂×C₄×D₁₃₉	1	1	yes	characteristic
94	C₄	#14555785	1	1	yes	characteristic
95	C₂	—	556	2	no	—
96	C₂	C₄×D₅₅₆	1	1	yes	characteristic
97	C₂	#17984870	1	1	yes	characteristic
98	C₂	#17984875	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14555774

C₂

yes

maximal, characteristic

C₄×Dic₂₇₈

C₂

yes

maximal, characteristic, complemented

C₄×D₅₅₆

C₂

yes

maximal, characteristic

#17984776

C₂

yes

maximal, characteristic, complemented

#17984767

C₂

yes

maximal, characteristic, complemented

#17984764

C₂

yes

maximal, characteristic

#97×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₇₈

C₂²

yes

characteristic

C₂×D₅₅₆

C₂²

yes

characteristic

C₂×C₄×D₁₃₉

—

#14555774

C₄

yes

complemented

C₄⋊Dic₁₃₉

C₂²

yes

characteristic

C₄⋊Dic₁₃₉

C₂²

yes

characteristic

Dic₁₃₉⋊C₄

—

(C₂×D₁₃₉)⋊C₄

—

C₄×Dic₁₃₉

—

C₂×C₈×C₁₃₉

C₂²

yes

characteristic

C₂×C₈×C₁₃₉

C₂²

yes

characteristic

C₄²×C₁₃₉

C₂²

yes

characteristic

C₂²×D₁₃₉

—

Dic₂₇₈

—

Dic₂₇₈

C₂×C₄

yes

complemented

D₅₅₆

—

D₅₅₆

C₂×C₄

yes

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₄×D₁₃₉

—

C₂×C₄×C₁₃₉

D₄

yes

characteristic

C₂×C₄×C₁₃₉

D₄

yes

characteristic

C₂×C₄×C₁₃₉

C₂³

yes

characteristic

C₈×C₁₃₉

—

C₈×C₁₃₉

C₂×C₄

yes

complemented

C₂²×C₁₃₉

C₂×D₄

yes

characteristic

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

C₂²×C₄

yes

characteristic

C₄×C₁₃₉

#41

yes

characteristic

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

C₂×C₁₃₉

C₄×D₄

yes

C₂×C₁₃₉

yes

C₂×C₁₃₉

yes

D₁₃₉

—

C₁₃₉

#440

yes

characteristic, complemented, Sylow

#440

—

139

maximal, Sylow

C₂×SD₁₆

—

139

—

C₄×Q₈

—

139

—

C₄×D₄

—

139

—

#107

—

139

—

#103

—

139

—

#102

—

139

—

#97

D₁₃₉

yes

characteristic, complemented

C₂×Q₈

—

139

—

C₂×D₄

—

139

—

C₂²×C₄

—

278

—

SD₁₆

—

139

—

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₄⋊C₄

—

278

—

C₄⋊C₄

—

139

—

C₄⋊C₄

—

139

—

C₂²⋊C₄

—

278

—

C₄²

—

278

—

C₄²

C₂×D₁₃₉

yes

characteristic

C₂³

—

278

—

Q₈

—

278

—

Q₈

—

139

—

D₄

—

278

—

D₄

—

139

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

556

—

C₂×C₄

D₅₅₆

yes

characteristic

C₂×C₄

D₅₅₆

yes

characteristic

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

C₈

C₄×D₁₃₉

yes

complemented

C₂²

—

278

—

C₂²

—

556

—

C₂²

—

556

—

C₂²

C₂×D₅₅₆

yes

characteristic

C₄

—

C₄

—

C₄

—

278

—

C₄

—

556

—

C₄

—

556

—

C₄

C₂×C₄×D₁₃₉

yes

characteristic

C₄

#14555785

yes

characteristic

C₂

—

556

—

C₂

C₄×D₅₅₆

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	C₂×D₅₅₆
commutator	C₄×C₁₃₉	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#97×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#97	D₁₃₉
hypocenter	C₁₃₉	#440
LCS	G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×D₅₅₆

commutator

C₄×C₁₃₉

C₂²×C₄

Frattini

C₂×C₄

C₂²×D₁₃₉

Fitting

#97×C₁₃₉

C₂

socle

C₂²×C₁₃₉

C₂×D₄

D₁₃₉

C₁₃₉

G ▷ C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
2. C₄×Dic₂₇₈	C₂	semidirect
4. #17984776	C₂	semidirect
5. #17984767	C₂	semidirect
7. #97×C₁₃₉	C₂	semidirect
11. #14555774	C₄	semidirect
22. Dic₂₇₈	C₂×C₄	semidirect
33. C₈×C₁₃₉	C₂×C₄	semidirect
49. C₁₃₉	#440	semidirect
57. #97	D₁₃₉	semidirect
83. C₈	C₄×D₁₃₉	semidirect

H ≅ G/N

type

2. C₄×Dic₂₇₈

C₂

semidirect

4. #17984776

C₂

semidirect

5. #17984767

C₂

semidirect

7. #97×C₁₃₉

C₂

semidirect

11. #14555774

C₄

semidirect

22. Dic₂₇₈

C₂×C₄

semidirect

33. C₈×C₁₃₉

C₂×C₄

semidirect

49. C₁₃₉

#440

semidirect

57. #97

D₁₃₉

semidirect

83. C₈

C₄×D₁₃₉

semidirect

Subgroups — #22581055

Conjugacy classes of subgroups

Complements