Group #22581298 — subgroups

Subgroups — #22581298

Order 8896.

118 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 41 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	#17984841	C₂	1	1	yes	maximal, characteristic, complemented
2	#17984838	C₂	1	1	yes	maximal, characteristic
3	#17984764	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984763	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984762	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×Dic₂₇₈	—	2	1	no	—
9	C₂×D₅₅₆	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
11	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
12	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
14	Dic₁₃₉⋊C₄	—	2	1	no	—
15	C₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×D₁₃₉	—	2	1	no	—
20	Dic₂₇₈	—	4	2	no	—
21	D₅₅₆	—	2	1	no	—
22	D₅₅₆	—	2	1	no	—
23	C₂²⋊D₁₃₉	—	4	2	no	—
24	C₂²⋊D₁₃₉	—	4	2	no	—
25	C₂×Dic₁₃₉	—	2	1	no	—
26	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
27	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
28	C₁₃₉⋊C₈	—	2	1	no	—
29	C₂³×C₁₃₉	—	2	1	no	—
30	D₄×C₁₃₉	—	2	1	no	—
31	D₄×C₁₃₉	—	2	1	no	—
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	—	4	1	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	—	4	1	no	—
40	C₂×D₁₃₉	—	4	1	no	—
41	C₂×D₁₃₉	—	4	1	no	—
42	C₄×C₁₃₉	—	4	1	no	—
43	C₄×C₁₃₉	#41	1	1	yes	characteristic
44	C₄×C₁₃₉	#41	1	1	yes	characteristic
45	Dic₁₃₉	—	4	1	no	—
46	Dic₁₃₉	D₈	1	2	yes	—
47	Dic₁₃₉	SD₁₆	1	2	yes	—
48	C₂×C₁₃₉	—	8	1	no	—
49	C₂×C₁₃₉	#124	1	1	yes	characteristic
50	C₂×C₁₃₉	C₂×D₈	1	1	yes	characteristic
51	C₂×C₁₃₉	C₂×SD₁₆	1	1	yes	characteristic
52	D₁₃₉	—	8	1	no	—
53	C₁₃₉	#486	1	1	yes	characteristic, complemented, Sylow
54	#486	—	139	1	no	maximal, Sylow
55	C₄⋊Q₈	—	139	1	no	—
56	#127	—	139	1	no	—
57	#102	—	139	1	no	—
58	#102	—	139	1	no	—
59	#102	—	139	1	no	—
60	#102	D₁₃₉	1	1	yes	characteristic, complemented
61	C₄×C₈	—	139	1	no	—
62	C₂×Q₈	—	278	1	no	—
63	C₂×D₄	—	278	1	no	—
64	C₂×D₄	—	278	1	no	—
65	C₂×D₄	—	139	1	no	—
66	C₂×D₄	C₂×D₁₃₉	1	1	yes	characteristic
67	C₂×C₈	—	139	1	no	—
68	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
69	C₄⋊C₄	—	278	1	no	—
70	C₄⋊C₄	—	139	1	no	—
71	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
72	C₄²	—	139	1	no	—
73	C₂³	—	2	1	no	—
74	C₂³	—	278	1	no	—
75	Q₈	—	556	2	no	—
76	D₄	—	2	1	no	—
77	D₄	—	2	1	no	—
78	D₄	—	278	1	no	—
79	D₄	—	278	1	no	—
80	D₄	—	556	2	no	—
81	D₄	—	556	2	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	278	1	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	—	278	1	no	—
89	C₂²	—	4	1	no	—
90	C₂²	—	4	1	no	—
91	C₂²	—	4	1	no	—
92	C₂²	—	556	1	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	—	556	1	no	—
98	C₄	—	139	2	no	—
99	C₄	—	139	2	no	—
100	C₄	#14555784	1	1	yes	characteristic
101	C₄	#14555785	1	1	yes	characteristic
102	C₂	—	8	1	no	—
103	C₂	—	1112	1	no	—
104	C₂	#17984828	1	1	yes	characteristic
105	C₂	D₈×D₁₃₉	1	1	yes	characteristic
106	C₂	SD₁₆×D₁₃₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17984841

C₂

yes

maximal, characteristic, complemented

#17984838

C₂

yes

maximal, characteristic

#17984764

C₂

yes

maximal, characteristic, complemented

#17984763

C₂

yes

maximal, characteristic, complemented

#17984762

C₂

yes

maximal, characteristic, complemented

C₈×Dic₁₃₉

C₂

yes

maximal, characteristic, complemented

#102×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₂₇₈

—

C₂×D₅₅₆

C₂²

yes

characteristic

C₂×C₂²⋊D₁₃₉

—

C₂×C₂²⋊D₁₃₉

—

C₂×C₁₃₉⋊C₈

C₂²

yes

characteristic

C₄⋊Dic₁₃₉

C₂²

yes

characteristic

Dic₁₃₉⋊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

—

Dic₂₇₈

—

D₅₅₆

—

D₅₅₆

—

C₂²⋊D₁₃₉

—

C₂²⋊D₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

D₄

yes

characteristic

C₂×Dic₁₃₉

D₄

yes

characteristic

C₁₃₉⋊C₈

—

C₂³×C₁₃₉

—

D₄×C₁₃₉

—

D₄×C₁₃₉

—

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

yes

C₄×C₁₃₉

yes

Dic₁₃₉

—

Dic₁₃₉

D₈

yes

—

Dic₁₃₉

SD₁₆

yes

—

C₂×C₁₃₉

—

C₂×C₁₃₉

#124

yes

characteristic

C₂×C₁₃₉

C₂×D₈

yes

characteristic

C₂×C₁₃₉

C₂×SD₁₆

yes

characteristic

D₁₃₉

—

C₁₃₉

#486

yes

characteristic, complemented, Sylow

#486

—

139

maximal, Sylow

C₄⋊Q₈

—

139

—

#127

—

139

—

#102

—

139

—

#102

—

139

—

#102

—

139

—

#102

D₁₃₉

yes

characteristic, complemented

C₄×C₈

—

139

—

C₂×Q₈

—

278

—

C₂×D₄

—

278

—

C₂×D₄

—

278

—

C₂×D₄

—

139

—

C₂×D₄

C₂×D₁₃₉

yes

characteristic

C₂×C₈

—

139

—

C₂×C₈

C₂×D₁₃₉

yes

characteristic

C₄⋊C₄

—

278

—

C₄⋊C₄

—

139

—

C₄⋊C₄

C₂×D₁₃₉

yes

characteristic

C₄²

—

139

—

C₂³

—

C₂³

—

278

—

Q₈

—

556

—

D₄

—

D₄

—

D₄

—

278

—

D₄

—

278

—

D₄

—

556

—

D₄

—

556

—

C₂×C₄

—

C₂×C₄

—

278

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

C₂²×D₁₃₉

yes

characteristic

C₈

—

C₈

—

278

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

556

—

C₂²

—

556

—

C₂²

—

556

—

C₂²

D₄×D₁₃₉

yes

characteristic

C₄

—

C₄

—

556

—

C₄

—

139

—

C₄

—

139

—

100

C₄

#14555784

yes

characteristic

101

C₄

#14555785

yes

characteristic

102

C₂

—

103

C₂

—

1112

—

104

C₂

#17984828

yes

characteristic

105

C₂

D₈×D₁₃₉

yes

characteristic

106

C₂

SD₁₆×D₁₃₉

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃₉
commutator	C₂×C₄×C₁₃₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#102×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#102	D₁₃₉
hypocenter	C₁₃₉	#486
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

subgroup

G/H

center

C₂²

D₄×D₁₃₉

commutator

C₂×C₄×C₁₃₉

C₂³

Frattini

C₂×C₄

C₂²×D₁₃₉

Fitting

#102×C₁₃₉

C₂

socle

C₂²×C₁₃₉

C₂×D₄

D₁₃₉

C₁₃₉

G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

N	H ≅ G/N	type
1. #17984841	C₂	semidirect
3. #17984764	C₂	semidirect
4. #17984763	C₂	semidirect
5. #17984762	C₂	semidirect
6. C₈×Dic₁₃₉	C₂	semidirect
7. #102×C₁₃₉	C₂	semidirect
53. C₁₃₉	#486	semidirect
60. #102	D₁₃₉	semidirect

H ≅ G/N

type

1. #17984841

C₂

semidirect

3. #17984764

C₂

semidirect

4. #17984763

C₂

semidirect

5. #17984762

C₂

semidirect

6. C₈×Dic₁₃₉

C₂

semidirect

7. #102×C₁₃₉

C₂

semidirect

53. C₁₃₉

#486

semidirect

60. #102

D₁₃₉

semidirect

Subgroups — #22581298

Conjugacy classes of subgroups

Complements