Group #20260987 — subgroups

Subgroups — #20260987

Order 6208.

130 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 39 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×#13095496	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13095494	C₂	1	1	yes	maximal, characteristic, complemented
3	#15690785	C₂	1	1	yes	maximal, characteristic, complemented
4	#15690781	C₂	1	1	yes	maximal, characteristic, complemented
5	#15690741	C₂	1	1	yes	maximal, characteristic, complemented
6	#15690732	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₈₈	—	2	1	no	—
9	C₂×D₃₈₈	C₂²	1	1	yes	characteristic
10	C₂×C₂²⋊D₉₇	—	2	1	no	—
11	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
12	#13095496	—	2	2	no	—
13	#13095494	—	2	2	no	—
14	C₂×#11715895	C₂²	1	1	yes	characteristic
15	C₄⋊Dic₉₇	C₂²	1	1	yes	characteristic
16	C₂²⋊Dic₉₇	—	2	1	no	—
17	#13095488	—	2	1	no	—
18	C₂×D₄×C₉₇	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×C₉₇	C₂²	1	1	yes	characteristic
21	C₂³×C₉₇	—	2	1	no	—
22	C₂²×D₉₇	—	2	1	no	—
23	C₂²×D₉₇	D₄	1	1	yes	characteristic
24	D₄×C₉₇	—	2	1	no	—
25	D₄×C₉₇	—	2	1	no	—
26	C₂×C₄×C₉₇	—	2	1	no	—
27	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
28	C₂²⋊D₉₇	—	4	2	no	—
29	C₂×Dic₉₇	—	2	1	no	—
30	C₂×Dic₉₇	D₄	1	1	yes	characteristic
31	D₃₈₈	—	2	1	no	—
32	D₃₈₈	—	2	1	no	—
33	D₃₈₈	—	4	2	no	—
34	C₄×D₉₇	—	2	1	no	—
35	C₄×D₉₇	—	2	1	no	—
36	C₈×C₉₇	—	2	1	no	—
37	#11715895	D₄	1	2	yes	complemented
38	C₂²×C₉₇	—	4	1	no	—
39	C₂²×C₉₇	—	4	1	no	—
40	C₂²×C₉₇	—	4	1	no	—
41	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
42	C₂×D₉₇	—	2	1	no	—
43	C₂×D₉₇	—	2	1	no	—
44	C₂×D₉₇	—	2	1	no	—
45	C₂×D₉₇	—	4	1	no	—
46	C₂×D₉₇	—	4	1	no	—
47	C₂×D₉₇	—	4	1	no	—
48	C₄×C₉₇	—	4	1	no	—
49	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
50	C₄×C₉₇	#41	1	1	yes	characteristic
51	Dic₉₇	—	2	1	no	—
52	Dic₉₇	—	4	1	no	—
53	C₂×C₉₇	—	8	1	no	—
54	C₂×C₉₇	#121	1	1	yes	characteristic
55	C₂×C₉₇	AGL(1,ℤ/8)	1	1	yes	characteristic
56	C₂×C₉₇	AGL(1,ℤ/8)	1	1	yes	characteristic
57	D₉₇	—	4	1	no	—
58	D₉₇	—	8	1	no	—
59	C₉₇	#469	1	1	yes	characteristic, complemented, Sylow
60	#469	—	97	1	no	maximal, Sylow
61	C₂×D₈	—	97	1	no	—
62	C₂×M₁₆	—	97	1	no	—
63	#121	—	97	1	no	—
64	#121	—	97	1	no	—
65	#106	—	97	1	no	—
66	#102	—	97	1	no	—
67	#102	D₉₇	1	1	yes	characteristic, complemented
68	C₂×D₄	—	97	1	no	—
69	C₂×D₄	—	194	1	no	—
70	C₂×D₄	—	194	1	no	—
71	C₂×D₄	C₂×D₉₇	1	1	yes	characteristic
72	C₂²×C₄	—	97	1	no	—
73	D₈	—	194	2	no	—
74	M₁₆	—	194	2	no	—
75	C₂×C₈	—	97	1	no	—
76	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
77	C₄⋊C₄	—	97	1	no	—
78	C₄⋊C₄	C₂×D₉₇	1	1	yes	characteristic
79	C₂²⋊C₄	—	194	1	no	—
80	C₂²⋊C₄	—	194	1	no	—
81	C₂³	—	2	1	no	—
82	C₂³	—	97	1	no	—
83	C₂³	—	194	1	no	—
84	D₄	—	2	1	no	—
85	D₄	—	2	1	no	—
86	D₄	—	388	2	no	—
87	D₄	—	388	2	no	—
88	D₄	—	194	1	no	—
89	D₄	—	194	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	97	1	no	—
92	C₂×C₄	—	194	1	no	—
93	C₂×C₄	—	194	1	no	—
94	C₂×C₄	—	194	1	no	—
95	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
96	C₈	—	2	1	no	—
97	C₈	—	97	2	no	—
98	C₂²	—	4	1	no	—
99	C₂²	—	4	1	no	—
100	C₂²	—	4	1	no	—
101	C₂²	—	388	1	no	—
102	C₂²	—	388	1	no	—
103	C₂²	—	388	1	no	—
104	C₂²	—	194	1	no	—
105	C₂²	—	194	1	no	—
106	C₂²	—	194	1	no	—
107	C₂²	D₄×D₉₇	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	388	1	no	—
110	C₄	—	194	1	no	—
111	C₄	D₄×D₉₇	1	1	yes	characteristic
112	C₄	#13095511	1	1	yes	characteristic
113	C₂	—	8	1	no	—
114	C₂	—	776	1	no	—
115	C₂	—	388	1	no	—
116	C₂	#15690783	1	1	yes	characteristic
117	C₂	#15690834	1	1	yes	characteristic
118	C₂	#15690837	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13095496

C₂

yes

maximal, characteristic, complemented

C₂×#13095494

C₂

yes

maximal, characteristic, complemented

#15690785

C₂

yes

maximal, characteristic, complemented

#15690781

C₂

yes

maximal, characteristic, complemented

#15690741

C₂

yes

maximal, characteristic, complemented

#15690732

C₂

yes

maximal, characteristic, complemented

#102×C₉₇

C₂

yes

maximal, characteristic, complemented

C₂×D₃₈₈

—

C₂×D₃₈₈

C₂²

yes

characteristic

C₂×C₂²⋊D₉₇

—

C₂×C₄×D₉₇

C₂²

yes

—

—

C₂²

yes

characteristic

C₄⋊Dic₉₇

C₂²

yes

characteristic

C₂²⋊Dic₉₇

—

#13095488

—

C₂×D₄×C₉₇

C₂²

yes

characteristic

C₂×C₈×C₉₇

C₂²

yes

characteristic

C₄⋊C₄×C₉₇

C₂²

yes

characteristic

C₂³×C₉₇

—

C₂²×D₉₇

—

C₂²×D₉₇

D₄

yes

characteristic

D₄×C₉₇

—

D₄×C₉₇

—

C₂×C₄×C₉₇

—

C₂×C₄×C₉₇

C₂³

yes

characteristic

C₂²⋊D₉₇

—

C₂×Dic₉₇

—

C₂×Dic₉₇

D₄

yes

characteristic

D₃₈₈

—

D₃₈₈

—

D₃₈₈

—

C₄×D₉₇

—

C₄×D₉₇

—

C₈×C₉₇

—

#11715895

D₄

yes

complemented

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

—

C₂²×C₉₇

C₂×D₄

yes

characteristic

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

—

C₄×C₉₇

—

C₄×C₉₇

C₂×D₄

yes

characteristic

C₄×C₉₇

#41

yes

characteristic

Dic₉₇

—

Dic₉₇

—

C₂×C₉₇

—

C₂×C₉₇

yes

C₂×C₉₇

yes

C₂×C₉₇

yes

D₉₇

—

D₉₇

—

C₉₇

#469

yes

characteristic, complemented, Sylow

#469

—

maximal, Sylow

C₂×D₈

—

C₂×M₁₆

—

—

—

—

—

D₉₇

yes

characteristic, complemented

C₂×D₄

—

C₂×D₄

—

194

—

C₂×D₄

—

194

—

C₂×D₄

C₂×D₉₇

yes

characteristic

C₂²×C₄

—

D₈

—

194

—

M₁₆

—

194

—

C₂×C₈

—

C₂×C₈

C₂×D₉₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

C₂×D₉₇

yes

characteristic

C₂²⋊C₄

—

194

—

C₂²⋊C₄

—

194

—

C₂³

—

C₂³

—

C₂³

—

194

—

D₄

—

D₄

—

D₄

—

388

—

D₄

—

388

—

D₄

—

194

—

D₄

—

194

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

C₂²×D₉₇

yes

characteristic

C₈

—

C₈

—

C₂²

—

C₂²

—

100

C₂²

—

101

C₂²

—

388

—

102

C₂²

—

388

—

103

C₂²

—

388

—

104

C₂²

—

194

—

105

C₂²

—

194

—

106

C₂²

—

194

—

107

C₂²

D₄×D₉₇

yes

characteristic

108

C₄

—

109

C₄

—

388

—

110

C₄

—

194

—

111

C₄

D₄×D₉₇

yes

characteristic

112

C₄

#13095511

yes

characteristic

113

C₂

—

114

C₂

—

776

—

115

C₂

—

388

—

116

C₂

#15690783

yes

characteristic

117

C₂

#15690834

yes

characteristic

118

C₂

#15690837

yes

characteristic

	subgroup	G/H
center	C₂²	D₄×D₉₇
commutator	C₂×C₄×C₉₇	C₂³
Frattini	C₂×C₄	C₂²×D₉₇
Fitting	#102×C₉₇	C₂
socle	C₂²×C₉₇	C₂×D₄
hypercenter	#102	D₉₇
hypocenter	C₉₇	#469
LCS	G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

subgroup

G/H

center

C₂²

D₄×D₉₇

commutator

C₂×C₄×C₉₇

C₂³

Frattini

C₂×C₄

C₂²×D₉₇

Fitting

#102×C₉₇

C₂

socle

C₂²×C₉₇

C₂×D₄

D₉₇

C₉₇

G ▷ C₂×C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

N	H ≅ G/N	type
1. C₂×#13095496	C₂	semidirect
2. C₂×#13095494	C₂	semidirect
3. #15690785	C₂	semidirect
4. #15690781	C₂	semidirect
5. #15690741	C₂	semidirect
6. #15690732	C₂	semidirect
7. #102×C₉₇	C₂	semidirect
37. #11715895	D₄	semidirect
59. C₉₇	#469	semidirect
67. #102	D₉₇	semidirect

H ≅ G/N

type

1. C₂×#13095496

C₂

semidirect

2. C₂×#13095494

C₂

semidirect

3. #15690785

C₂

semidirect

4. #15690781

C₂

semidirect

5. #15690741

C₂

semidirect

6. #15690732

C₂

semidirect

7. #102×C₉₇

C₂

semidirect

37. #11715895

D₄

semidirect

59. C₉₇

#469

semidirect

67. #102

D₉₇

semidirect

Subgroups — #20260987

Conjugacy classes of subgroups

Complements