Group #22580925 — subgroups

Subgroups — #22580925

Order 8896.

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

normal subgroups only

This group has 158 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×#14555784	C₂	1	1	yes	maximal, characteristic
2	#17984798	C₂	1	2	yes	maximal, complemented
3	#17984757	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984756	C₂	1	2	yes	maximal, complemented
5	#99×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14555784	—	2	2	no	—
7	#14555784	—	2	2	no	—
8	C₂×Dic₂₇₈	C₄	1	1	yes	characteristic, complemented
9	C₂×C₂²⋊D₁₃₉	C₄	1	1	yes	characteristic, complemented
10	C₂×C₂²⋊D₁₃₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₃₉	C₄	1	1	yes	characteristic, complemented
12	C₂²×Dic₁₃₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₃₉	C₄	1	1	yes	characteristic, complemented
14	Dic₁₃₉⋊C₄	—	2	2	no	—
15	C₂²⋊Dic₁₃₉	C₂²	1	2	yes	—
16	C₄×Dic₁₃₉	—	2	2	no	—
17	C₂×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₂²⋊C₄×C₁₃₉	C₂²	1	2	yes	—
19	C₂²×D₁₃₉	C₂×C₄	1	1	yes	characteristic
20	Dic₂₇₈	—	2	2	no	—
21	C₂²⋊D₁₃₉	—	2	2	no	—
22	C₂²⋊D₁₃₉	—	2	2	no	—
23	C₂×Dic₁₃₉	—	2	1	no	—
24	C₂×Dic₁₃₉	—	2	1	no	—
25	C₂×Dic₁₃₉	—	2	2	no	—
26	C₂×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
27	C₂×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
28	C₂×Dic₁₃₉	C₂×C₄	1	1	yes	characteristic
29	C₂×Dic₁₃₉	D₄	1	2	yes	—
30	C₂×Dic₁₃₉	D₄	1	2	yes	—
31	C₄×D₁₃₉	—	2	1	no	—
32	C₄×D₁₃₉	—	2	1	no	—
33	C₂³×C₁₃₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₁₃₉	C₂³	1	1	yes	characteristic
35	D₄×C₁₃₉	—	2	2	no	—
36	C₂×C₄×C₁₃₉	—	2	2	no	—
37	C₂×C₄×C₁₃₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₁₃₉	—	2	1	no	—
39	C₂²×C₁₃₉	—	4	1	no	—
40	C₂²×C₁₃₉	—	4	1	no	—
41	C₂²×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₁₃₉	C₂×D₄	1	2	yes	—
43	C₂×D₁₃₉	—	2	1	no	—
44	C₂×D₁₃₉	—	4	1	no	—
45	C₄×C₁₃₉	—	2	1	no	—
46	C₄×C₁₃₉	—	4	2	no	—
47	Dic₁₃₉	—	2	1	no	—
48	Dic₁₃₉	—	4	2	no	—
49	Dic₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
50	Dic₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
51	Dic₁₃₉	C₂²⋊C₄	1	2	yes	—
52	C₂×C₁₃₉	—	2	2	no	—
53	C₂×C₁₃₉	—	2	1	no	—
54	C₂×C₁₃₉	—	4	1	no	—
55	C₂×C₁₃₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	D₁₃₉	—	4	1	no	—
57	C₁₃₉	#410	1	1	yes	characteristic, complemented, Sylow
58	#410	—	139	1	no	maximal, Sylow
59	C₂×#41	—	139	1	no	—
60	#117	—	139	2	no	—
61	#99	—	139	1	no	—
62	#99	—	139	2	no	—
63	#99	D₁₃₉	1	1	yes	characteristic, complemented
64	#41	—	278	2	no	—
65	#41	—	278	2	no	—
66	C₂×Q₈	—	139	1	no	—
67	C₂×D₄	—	139	1	no	—
68	C₂×D₄	—	139	1	no	—
69	C₂×D₄	C₂×D₁₃₉	1	1	yes	characteristic
70	C₂²×C₄	—	139	1	no	—
71	C₂²×C₄	—	139	1	no	—
72	C₂²×C₄	—	139	1	no	—
73	C₄⋊C₄	—	278	2	no	—
74	C₂²⋊C₄	—	139	2	no	—
75	C₂²⋊C₄	C₂×D₁₃₉	1	2	yes	—
76	C₄²	—	278	2	no	—
77	C₂³	—	139	1	no	—
78	C₂³	C₄×D₁₃₉	1	1	yes	characteristic
79	C₂³	C₂²×D₁₃₉	1	1	yes	characteristic
80	Q₈	—	278	2	no	—
81	D₄	—	2	2	no	—
82	D₄	—	278	2	no	—
83	D₄	—	278	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	278	1	no	—
86	C₂×C₄	—	278	1	no	—
87	C₂×C₄	—	278	1	no	—
88	C₂×C₄	—	278	1	no	—
89	C₂×C₄	—	278	2	no	—
90	C₂×C₄	—	139	1	no	—
91	C₂×C₄	—	139	1	no	—
92	C₂×C₄	—	139	1	no	—
93	C₂×C₄	—	139	2	no	—
94	C₂×C₄	—	139	2	no	—
95	C₂×C₄	C₄×D₁₃₉	1	1	yes	characteristic
96	C₂²	—	2	1	no	—
97	C₂²	—	4	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	278	1	no	—
100	C₂²	—	556	1	no	—
101	C₂²	C₂×C₄×D₁₃₉	1	1	yes	characteristic
102	C₂²	D₄×D₁₃₉	1	2	yes	—
103	C₄	—	2	1	no	—
104	C₄	—	4	2	no	—
105	C₄	—	278	1	no	—
106	C₄	—	556	2	no	—
107	C₄	—	139	1	no	—
108	C₄	—	139	1	no	—
109	C₄	—	139	2	no	—
110	C₂	—	2	2	no	—
111	C₂	—	2	1	no	—
112	C₂	—	4	1	no	—
113	C₂	—	556	1	no	—
114	C₂	C₂²⋊C₄×D₁₃₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14555784

C₂

yes

maximal, characteristic

#17984798

C₂

yes

maximal, complemented

#17984757

C₂

yes

maximal, characteristic, complemented

#17984756

C₂

yes

maximal, complemented

#99×C₁₃₉

C₂

yes

maximal, characteristic, complemented

#14555784

—

#14555784

—

C₂×Dic₂₇₈

C₄

yes

characteristic, complemented

C₂×C₂²⋊D₁₃₉

C₄

yes

characteristic, complemented

C₂×C₂²⋊D₁₃₉

C₂²

yes

characteristic

C₂²×Dic₁₃₉

C₄

yes

characteristic, complemented

C₂²×Dic₁₃₉

C₂²

yes

characteristic

C₂×C₄×D₁₃₉

C₄

yes

characteristic, complemented

Dic₁₃₉⋊C₄

—

C₂²⋊Dic₁₃₉

C₂²

yes

—

C₄×Dic₁₃₉

—

C₂×D₄×C₁₃₉

C₂²

yes

characteristic

C₂²⋊C₄×C₁₃₉

C₂²

yes

—

C₂²×D₁₃₉

C₂×C₄

yes

characteristic

Dic₂₇₈

—

C₂²⋊D₁₃₉

—

C₂²⋊D₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

C₂×C₄

yes

characteristic

C₂×Dic₁₃₉

C₂×C₄

yes

characteristic

C₂×Dic₁₃₉

C₂×C₄

yes

characteristic

C₂×Dic₁₃₉

D₄

yes

—

C₂×Dic₁₃₉

D₄

yes

—

C₄×D₁₃₉

—

C₄×D₁₃₉

—

C₂³×C₁₃₉

C₂×C₄

yes

characteristic

C₂³×C₁₃₉

C₂³

yes

characteristic

D₄×C₁₃₉

—

C₂×C₄×C₁₃₉

—

C₂×C₄×C₁₃₉

C₂×C₄

yes

characteristic

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

—

C₂²×C₁₃₉

C₂²×C₄

yes

characteristic

C₂²×C₁₃₉

C₂×D₄

yes

—

C₂×D₁₃₉

—

C₂×D₁₃₉

—

C₄×C₁₃₉

—

C₄×C₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

—

Dic₁₃₉

C₂²⋊C₄

yes

characteristic

Dic₁₃₉

C₂²⋊C₄

yes

characteristic

Dic₁₃₉

C₂²⋊C₄

yes

—

C₂×C₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

—

C₂×C₁₃₉

C₂×C₂²⋊C₄

yes

characteristic

D₁₃₉

—

C₁₃₉

#410

yes

characteristic, complemented, Sylow

#410

—

139

maximal, Sylow

C₂×#41

—

139

—

#117

—

139

—

#99

—

139

—

#99

—

139

—

#99

D₁₃₉

yes

characteristic, complemented

#41

—

278

—

#41

—

278

—

C₂×Q₈

—

139

—

C₂×D₄

—

139

—

C₂×D₄

—

139

—

C₂×D₄

C₂×D₁₃₉

yes

characteristic

C₂²×C₄

—

139

—

C₂²×C₄

—

139

—

C₂²×C₄

—

139

—

C₄⋊C₄

—

278

—

C₂²⋊C₄

—

139

—

C₂²⋊C₄

C₂×D₁₃₉

yes

—

C₄²

—

278

—

C₂³

—

139

—

C₂³

C₄×D₁₃₉

yes

characteristic

C₂³

C₂²×D₁₃₉

yes

characteristic

Q₈

—

278

—

D₄

—

D₄

—

278

—

D₄

—

278

—

C₂×C₄

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

278

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

—

139

—

C₂×C₄

C₄×D₁₃₉

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

—

278

—

100

C₂²

—

556

—

101

C₂²

C₂×C₄×D₁₃₉

yes

characteristic

102

C₂²

D₄×D₁₃₉

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

278

—

106

C₄

—

556

—

107

C₄

—

139

—

108

C₄

—

139

—

109

C₄

—

139

—

110

C₂

—

111

C₂

—

112

C₂

—

113

C₂

—

556

—

114

C₂

C₂²⋊C₄×D₁₃₉

yes

characteristic

	subgroup	G/H
center	C₂	C₂²⋊C₄×D₁₃₉
commutator	C₂²×C₁₃₉	C₂²×C₄
Frattini	C₂³	C₂²×D₁₃₉
Fitting	#99×C₁₃₉	C₂
socle	C₂×C₁₃₉	C₂×C₂²⋊C₄
hypercenter	#99	D₁₃₉
hypocenter	C₁₃₉	#410
LCS	G ▷ C₂²×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ #99

subgroup

G/H

center

C₂

C₂²⋊C₄×D₁₃₉

commutator

C₂²×C₁₃₉

C₂²×C₄

Frattini

C₂³

C₂²×D₁₃₉

Fitting

#99×C₁₃₉

C₂

socle

C₂×C₁₃₉

C₂×C₂²⋊C₄

D₁₃₉

C₁₃₉

G ▷ C₂²×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂ ◁ C₂³ ◁ #99

N	H ≅ G/N	type
2. #17984798	C₂	semidirect
3. #17984757	C₂	semidirect
4. #17984756	C₂	semidirect
5. #99×C₁₃₉	C₂	semidirect
8. C₂×Dic₂₇₈	C₄	semidirect
9. C₂×C₂²⋊D₁₃₉	C₄	semidirect
11. C₂²×Dic₁₃₉	C₄	semidirect
13. C₂×C₄×D₁₃₉	C₄	semidirect
57. C₁₃₉	#410	semidirect
63. #99	D₁₃₉	semidirect

H ≅ G/N

type

2. #17984798

C₂

semidirect

3. #17984757

C₂

semidirect

4. #17984756

C₂

semidirect

5. #99×C₁₃₉

C₂

semidirect

8. C₂×Dic₂₇₈

C₄

semidirect

9. C₂×C₂²⋊D₁₃₉

C₄

semidirect

11. C₂²×Dic₁₃₉

C₄

semidirect

13. C₂×C₄×D₁₃₉

C₄

semidirect

57. C₁₃₉

#410

semidirect

63. #99

D₁₃₉

semidirect

Subgroups — #22580925

Conjugacy classes of subgroups

Complements